Analysis of the Influences on Soil Moisture Trends in the Scott Valley (California, USA) and Spatiotemporal Analysis of Field Soil Moisture for Validating Satellite Estimates

Master Thesis of Fabio Francesco Vinci, Matr.-Nr.: 2016610

Institut für Angewandte Geowissenschaften

Darmstadt, March 2015

II

Declaration of Authorship

Hereby I certify, Fabio Francesco Vinci (Matrikel No. 2016610) that the complete work of this master

thesis

“Analysis of the Influences on Soil Moisture Trends in the Scott Valley (California, USA) and

Spatiotemporal Analysis of Field Soil Moisture for Validating Satellite Estimates”

was done by myself and only by using the referenced literature and the described methods. This

thesis was not submitted in identical or similar form to another examination authority and it was not

published before.

…Darmstadt, 09/03/2015….. ………………………………

Place, date Signature

First supervisor: Prof. Dr. Christoph Schüth

Second supervisor: Dr. Laura Foglia

III

Abstract

Soil moisture is a useful tool for better understanding the climatic conditions of a certain area and

how they change in time. It is strictly connected with several hydrological, geological, climatic and

environmental parameters influencing each other (Mohanty and Skaggs, 2001)[45]. It can thus be

very useful to understand the overall conditions of an area. Nowadays a global network of soil

moisture recording stations is not available yet. The few existing sites cover just small areas with

confined climatic and environmental conditions, and the time span of their database is usually

short, a season or a couple of years. They are a good supply for detailed analyses on specific

climatic events or environments, but it is almost impossible to distribute such a close-up network

worldwide. On the other hand, satellite-soil moisture data cover larger areas, up to global scale,

and with a spatial resolution of 25-50 km2 ca., their time span sets back to 1930s, and they are a

cheap source of information that is immediately available.

This work focuses on soil moisture trends in the Scott Valley watershed, California (USA), from

2006 to 2014, particularly on summer and winter season for two areas located N and S in the

valley. The AOI extension is 200 km2 ca. Model-generated soil moisture monthly-data were

collected from the National Oceanic and Atmospheric Administration (NOAA). They were then

compared with four other different factors: precipitation, temperature, groundwater depth, NDVI

index, soil type. After collecting all the data, they were graphically and statistically analyzed to

define their correlation, to suggest which parameter has the strongest influence on soil moisture

and what can be detected by satellite. It was possible to see how both investigated areas

presented a strong correlation of soil moisture with precipitation and temperature, as expected

since they are the inputs for the soil moisture forecasting model, and also with groundwater depth

during winter, when it is shallower. In summer, correlation with groundwater is visible only for the

southern group, where the water level is shallower than in the northern one, fluctuating between 1

and 3 m, a level that can be detected by remote sensing techniques. The NDVI and soil factors did

not show any significant correlation. Essentially, while the influence of precipitation and

temperature was predictable, it was proved how satellite-soil moisture distribution is influenced

also by groundwater, when its depth is close to the thickness of the model’s soil column of 1.6 m.

No significant effect was given by slight changes in lithology or vegetation.

Another task of this work was to increase the scale of gravimetric field soil moisture data from 2012

for validating satellite soil moisture, based on the method developed by Cosh et al. (2004)[4], Cosh

et al. (2006)[5] and Jacobs et al. (2004)[28]. By testing their spatiotemporal stability, it was possible

to define two potential locations representative of the watershed soil moisture conditions. The

comparison between field and satellite soil moisture was not possible, due to the scarcity of field

measurements.

IV

Acknowledgements

I want to thank Prof. Dr. Cristoph Scüth, for giving me the opportunity to work with his team on this

project, for his support and his helpful indications throughout these months.

I am also very grateful to Dr. Laura Foglia, who has given me the chance of a new start, and has

had enough patience to give me precious advices, fetch me with the data I needed, go through my

drafts and always find some time for me inside her busy days.

I would especially like to thank my colleague and friend Dr. Layth Sahib for the idea behind this

project, the support along the way and its great help with suggestions and corrections that helped

me see the completion of my thesis. I know that his office door will always be open for students in

need.

A word of gratitude goes to Susanne Weyand and Dr. Andres Marandi who, although not directly

involved in my project, have been more than willing to help me with their valuable ideas.

I want to include in my thanking also Dr. Olaf Lenz, who has been ready to help me and to share

some of his time with me.

Appreciation goes also to Dr. Michael Cosh who, without even knowing me, has been eager to

share some of his knowledge and his precious opinions with me.

I want to thank Dr. Thomas Harter, Gus Tolley and Steve Orloff, for having shown interest in the

project, giving me the possibility to use some of their data and sending me useful remarks.

My thanks go to my colleague and friend Philipp Schumann, for being such a nice adventure

companion during this thesis, and to Walid and all the TropHEE group for this wonderful

experience which this master has been.

Last but not least, there is my family I want to thank, my brother for having helped me start this

adventure abroad and supported me in these years, and of course my father and mother, for the

far greater moral than economical support they have given me since the first day. Grazie.

V

Table of Contents

Abstract ......................................................................................................................................... III

Acknowledgements ........................................................................................................................ IV

Table of Contents............................................................................................................................ V

List of Figures ............................................................................................................................... VII

List of Tables ............................................................................................................................... VIII

List of Abbreviations ........................................................................................................................ X

1. Aim of the Study ...................................................................................................................... 1

2. Area of Interest ........................................................................................................................ 5

2.1. Geological Setting ........................................................................................................... 10

2.2. Precipitation and Temperature ........................................................................................ 12

2.3. Soil Type ......................................................................................................................... 14

3. Initial Data .............................................................................................................................. 15

3.1. Landsat Images .............................................................................................................. 16

3.2. Groundwater Table Readings ......................................................................................... 19

3.3. Soil Moisture Files .......................................................................................................... 20

3.4. Precipitation and Temperature Data ............................................................................... 22

3.5. Evapotranspiration and Irrigation Estimates .................................................................... 23

3.6. Soil Map.......................................................................................................................... 24

3.7. Field Gravimetric Soil Moisture ....................................................................................... 25

4. Methodology .......................................................................................................................... 27

4.1. Soil Map Simplification .................................................................................................... 27

4.2. Landsat Processing: NDVI Index .................................................................................... 29

4.3. Watershed Detailed Analysis .......................................................................................... 32

4.4. Soil Moisture Grid Files ................................................................................................... 34

4.5. Groundwater Depth Contour Maps ................................................................................. 36

4.6. Precipitation and Temperature Trends ............................................................................ 39

4.7. Evapotranspiration and Pumping Rates .......................................................................... 42

4.8. Statistics of Soil Moisture Spatiotemporal Stability .......................................................... 42

5. Results ................................................................................................................................... 44

5.1. Correlation Coefficient .................................................................................................... 44

5.1.1. Winter + Summer ..................................................................................................... 46

5.1.2. Winter ...................................................................................................................... 46

5.1.3. Summer ................................................................................................................... 47

5.2. Principal Component Analysis ........................................................................................ 48

5.3. Two-Variables Scatter Plots ............................................................................................ 52

5.3.1. Soil Moisture - Precipitation ..................................................................................... 52

VI

5.3.2. Soil Moisture - Temperature..................................................................................... 53

5.3.3. Soil Moisture - NDVI ................................................................................................ 54

5.3.4. Soil Moisture – Groundwater Depth ......................................................................... 55

5.4. Multi-Variables xy-Line Plot............................................................................................. 56

5.5. Ternary Plots .................................................................................................................. 58

5.5.1. Winter ...................................................................................................................... 59

5.5.2. Summer ................................................................................................................... 59

5.6. Spatiotemporal Stability Analysis of Gravimetric Soil Moisture ........................................ 60

6. Conclusions ........................................................................................................................... 64

References ................................................................................................................................... 67

Appendix A ................................................................................................................................... 74

Appendix B ................................................................................................................................... 77

Appendix C ................................................................................................................................... 83

VII

List of Figures

Figure 1: Hydrographic system of the Scott Valley. ......................................................................... 5

Figure 2: Map of the Scott river valley inside the bigger Klamath river watershed. .......................... 6

Figure 3: Land use categories based on the Department of Water Resources (DWR). ................... 8

Figure 4: Map of the irrigation types and of the available irrigation wells ......................................... 9

Figure 5: Valley floor precipitation co-kriging interpolation with anisotropy. ................................... 13

Figure 6: Raw and clipped Landsat image, based on the AOI extension. ...................................... 18

Figure 7: CPC Soil Moisture data provided by the NOAA/OAR/ESRL PSD. .................................. 21

Figure 8: Location of the main meteorological stations covering the AOI. ..................................... 22

Figure 9: Soil map of the AOI. ....................................................................................................... 24

Figure 10: Position of the 16 sites where gravimetric soil moisture probes were installed. ............ 26

Figure 11: Ternary diagram of the soil texture triangle .................................................................. 27

Figure 12: Final soil map obtained after simplifying the original USDA soil map. ........................... 28

Figure 13: Emitted and absorbed radiation pattern by healthy and unhealthy vegetation .............. 30

Figure 14: NDVI-making for the year 2007. ................................................................................... 31

Figure 15: Position of the two areas chosen for the analysis.. ....................................................... 32

Figure 16: Group 1 NDVI images in succession, from 2006 to 2014. ............................................ 33

Figure 17: Group 2 NDVI images in succession, from 2006 to 2014.. ........................................... 34

Figure 18: Processing steps of the raw soil moisture grid files.. .................................................... 35

Figure 19: Observation wells represented by red points and numbers going from 1 to 56.. ........... 36

Figure 20: Groundwater-contour maps processing steps. ............................................................. 37

Figure 21: Groundwater depth contour maps from March and August 2010. ................................. 39

Figure 22: Position of the two groups in respect of the location of the meteorological stations. ..... 40

Figure 23: Precipitation trend of the valley in monthly means ........................................................ 41

Figure 24: Temperature trend of the valley.................................................................................... 41

Figure 25: Scree-plot for Clay loam of group 1. ............................................................................. 49

Figure 26: Scatter plot for the lithology Clay loam of group 1.. ...................................................... 50

Figure 27: Scatter plot for the lithology Clay loam of group 2. ....................................................... 50

Figure 28: Scatter plots of soil moisture against precipitation. ....................................................... 52

Figure 29: Scatter plots of soil moisture against temperature. ....................................................... 53

Figure 30: Scatter plots of soil moisture against NDVI index. ........................................................ 54

Figure 31: Scatter plots of soil moisture against groundwater depth.............................................. 55

Figure 32: Multi-variable xy-line plot for group 1. ........................................................................... 57

Figure 33: Multi-variable xy-line plot for group 2. ........................................................................... 57

Figure 34: Ternary plots for group 1 and group 2. ......................................................................... 58

Figure 35: Mean relative difference plot for the Scott Valley gravimetric soil moisture network.. ... 60

Figure 36: Matrix plot of the Spearman’s ranks for the 21measured weeks.. ................................ 63

VIII

List of Tables

Table 1: List of the initial data with relative source, time span and specifications. ......................... 15

Table 2: TM and ETM+ sensors band designation. ....................................................................... 16

Table 3: OLI and TIRS sensors band designation. ........................................................................ 17

Table 4: Wells spreadsheet. .......................................................................................................... 19

Table 5: Notation of gravimetric soil moisture measuring weeks.. ................................................. 25

Table 6: Names, coding and soil type of the 16 locations of field soil moisture measurement. ...... 25

Table 7: Number of well, for each processed month, offering groundwater measurements. .......... 37

Table 8: Correlation matrix for group 1 (winter & summer) – clay loam. ........................................ 45

Table 9: Correlation matrix for group 1 (winter) – clay loam. ......................................................... 45

Table 10: Correlation matrix for group 1 (summer) - clay loam. ..................................................... 45

Table 11: Correlation matrix for group 2 (winter & summer) - gravelly loam. ................................. 45

Table 12: Correlation matrix for group 2 (winter) - gravelly loam. .................................................. 45

Table 13: Correlation matrix for group 2 (summer) - gravelly loam. ............................................... 45

Table 14: Correlation between soil moisture and the other parameters. ........................................ 47

Table 15: List of eigenvalues and percentage of variance for clay loam of group 1. ...................... 49

Table 16: List of eigenvalues and percentage of variance for clay loam of group 2. ...................... 49

Table 17: Statistical parameters for spatiotemporal stability of the 16 analyzed sites. ................... 61

Table 18: Amount of monthly precipitation for the 21 weeks of field data. ..................................... 63

Table A1: Correlation matrix for group 1 (winter & summer) - gravelly loam……………………… ...74

Table A2: Correlation matrix for group 1 (winter & summer) - loam ............................................... 74

Table A3: Correlation matrix for group 1 (winter & summer) - sandy loam .................................... 74

Table A4:Correlation matrix for group 1 (winter) - gravelly loam .................................................... 74

Table A5:Correlation matrix for group 1 (winter) – loam ................................................................ 74

Table A6: Correlation matrix for group 1 (winter) - sandy loam...................................................... 74

Table A7: Correlation matrix for group 1 (summer) - gravelly loam ............................................... 75

Table A8: Correlation matrix for group 1 (summer) - loam ............................................................. 75

Table A9: Correlation matrix for group 1 (summer) – sandy loam ................................................. 75

Table A10: Correlation matrix for group 2 (winter &summer) - clay loam ....................................... 75

Table A11: Correlation matrix for group 2 (winter &summer) - loam .............................................. 75

Table A12: Correlation matrix for group 2 (winter &summer) - sandy loam.................................... 75

Table A13: Correlation matrix for group 2 (winter) - clay loam ....................................................... 76

Table A14: Correlation matrix for group 2 (winter) - loam .............................................................. 76

Table A15: Correlation matrix for group 2 (winter) - sandy loam .................................................... 76

Table A16: Correlation matrix for group 2 (summer) - clay loam ................................................... 76

Table A17: Correlation matrix for group 2 (summer) – loam .......................................................... 76

IX

Table A18: Correlation matrix for group 2 (summer) – sandy loam ........ ……………………………76

Table B1: List of eigenvalues and percentage of variance for gravelly loam of group 1……………77

Table B2: List of eigenvalues and percentage of variance for loam of group 1. ............................. 78

Table B3: List of eigenvalues and percentage of variance for sandy loam of group 1. .................. 79

Table B4: List of eigenvalues and percentage of variance for gravelly loam of group 2. ................ 80

Table B5: List of eigenvalues and percentage of variance for loam of group 2. ............................. 81

Table B6: List of eigenvalues and percentage of variance for sandy loam of group 2. .................. 82

Table C1: Gravimetric field measurements for the sampled 16 sites, in 21 weeks………………... 83

Table C2: Results of equation 2 for MRD. ..................................................................................... 84

Table C3: Root Mean Square Difference calculation ..................................................................... 85

Table C4: Spearman's rank coefficients. ....................................................................................... 86

X

List of Abbreviations

AMSR-E/AMSR2: Advanced Microwave Scanning Radiometer - Earth

AOI: Area of interest

ASCAT: Advanced Scatterometer

a.s.l.: above sea level

CDEC: California Data Exchange Center

CDWR: California Department of Water Resources

CRN: Climate Reference Network

DWR: Department of Water Resources

ESA: European Space Agency

ESRL: Earth System Research Laboratory

JAXA: Japan Aerospace Exploration Agency

Ma: Million years ago

MRD: Mean Relative Difference

NASA: National Aeronautics and Space Administration

NCDC: National Climatic Data Center

NDVI: Normalized Difference Vegetation Index

NESDIS: National Environmental Satellite, Data, and Information Service

NOAA: National Oceanic & Atmospheric Administration

OSPO: Office of Satellite and Product Operations

PCA: Principal Component Analysis

PSD: Physical Sciences Division

RMSD: Root Mean Square Difference

SCAN: Soil Climate Analysis Network

SD: Standard Deviation

SMOS: Soil Moisture Ocean Salinity

USDA: United States Department of Agriculture

USGS: United States Geological Survey

1

1. Aim of the Study

Soil moisture importance is constantly progressing into several disciplines, from climatology to

hydrogeology and hydrology, and also biology and biogeochemistry (e.g. reservoir management

and water quality). Climatology utilizes soil moisture data for its forecasting (Drusch, 2007)[13], to

sharpen precipitation trend and temperature variations: indeed, the water content of the soil can

help estimating the amount of evaporation and plant transpiration (Jung et al., 2010)[30], being the

result of the water-heat exchange between soil and atmosphere. Soil moisture distribution can

give indications on the hydrological conditions of an area: how much rainfall infiltrates into the soil,

the conditions of vegetation, the depth of groundwater from the surface, the thickness of the root

zone, the amount of runoff, droughts occurrence (Mo et al., 2010)[43]. Hence, it can also be a

useful tool to assess flood hazard, soil erosion and slope failure: dry or wet soils will have specific

runoff coefficients, which define how much rainfall will flow into nearby streams or rivers (Ray et al.,

2010)[54]. In some areas, soil moisture forecasts are also used to schedule irrigation cycles

(Lakhankar et al., 2009a)[34], e.g. smart irrigation.

A better understanding on soil moisture patterns would require a homogeneous network of

measuring stations (since each of them has a spatial scale of few cm) which should have started

collecting data several years ago. While other climatic parameters, like precipitation or

temperature, are supported by numerous stations around the world and organizations managing

their networks, and with datasets that go back to the first half of last century, the situation is

different for soil moisture. Despite the accuracy of field sensors, a widespread and homogeneous

network is still missing, with some exception like the Soil Climate Analysis Network (SCAN,

http://www.wcc.nrcs.usda.gov/scan/)[47] and the Climate Reference Network (CRN,

http://www.ncdc.noaa.gov/crn)[17], let alone to a global scale (Robock et al., 2000)[55]. Occasional

campaigns have hosted short-term data collection in specific regions, but they are not sufficient.

On the other hand, satellite soil moisture offers the advantage of a bigger spatial coverage, 1-40

km (Jackson et al., 2010)[27], and a temporal continuity that spans back to several decades ago,

with the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration

Agency (JAXA) first satellites (Njoku et al., 2003)[50]. Satellite retrieval relies on microwaves to

estimate soil moisture based on the contrast between the dielectric properties of wet and dry soils

(Ulaby et al., 1986[63]; Dobson et al., 1985[11]). As soon as the moisture in the soil increases, its

dielectric constant grows as well, and the water content becomes easier to detect by the

microwave sensors of satellites (Njoku & Kong, 1977)[49]. It is an advantageous methods, which

however suffers from many challenges: the depth it can reach (it is usually limited to the first

meters, depending on the actual moisture of the soil), surface roughness, vegetation cover

(Jackson et al., 2010)[27]. Based on Vinnikov et al. (1996)[71] and Jana (2010)[29], large scale soil

moisture is generally dominated by meteorological forcing (e.g. rainfall and temperature), while

2

land cover, topographic and soil factors gain more importance at a finer scale. Adequate physical-

mathematical description of microwave backscatter interaction with all these influencing factors has

not been perfected yet (Lakhankar et al., 2009)[35]. That being said, remote sensing might still be

the key factor into compensating for the lack of well-structured field networks at a global scale.

This work represents an attempt to enhance the reliability and usefulness of satellite data via a

better understanding of their range of detection of some factors that might influence them more.

One of its first aims was to rely on remote sensing to describe the distribution of soil moisture in the

area of the Scott river basin, in northern California. The Scott river is part of the bigger Klamath

river watershed, and it flows for a total length of approximately 90 km close to the border between

California and Oregon. The climate is temperate, with precipitation that ranges between 500-600

mm/yr, and temperatures that fluctuates between 0 °C and 20°C (usa.com[64]; CDEC,

http://cdec.water.ca.gov/[1]). Scott valley has an altitude of around 800-900 m at its base, but it is

surrounded by mountains that reach 2500 m on the west and 1600 m on the east side.

The chosen source for satellite-soil moisture was the NOAA-NESDIS (National Environmental

Satellite, Data, and Information Service) Soil Moisture Operational Product System. This system

joins together and scales different sources of information: Windsat, with its sensors AMSR-E

(Advanced Microwave Scanning Radiometer – Earth) and AMSR2 inside the Coriolis satellite

(managed by the Naval Research Lab); Soil Moisture Ocean Salinity (SMOS) satellite (from the

European Space Agency, ESA); ASCAT, or Advanced Scatterometer (Zhan et al., 2014)[74]. All

these satellite retrievals are scaled and combined together to enhance the original spatiotemporal

coverage of the data and produce a better global soil moisture map (OSPO[65]). The time interval

of NOAA-NESDIS products can be every six hours or daily, and is mapped with a cylindrical

projection on 0.5°x0.5° grids showing monthly estimations. The surface model behind the

computing of data is the “leaking bucket” soil column, with a thickness of 1.6 m and a mean

porosity of 0.47 (Huang et al., 1996[24]; Fan & van den Dool, 20004[16]). One strong side of this

model is that it is directly dependent on precipitation and temperature data as inputs: these data

come from external sources, respectively the Climate Prediction Center (CPC) monthly global

precipitation over land (Chen et al., 2002)[3], and the monthly global Reanalysis/CDAS 2m air

temperature (Kistler et al., 2001)[32]. On the other hand its small resolution, as well as the difficulty

of displaying natural small scale variations of soil moisture, urges to find a way to make the data

more reliable. Some attempts have already been made to validate soil moisture products by

ground-based sampling with selected algorithms (Njoku et al., 2003[50]; Draper et al., 2009[12];

Jackson et al., 2010[27]; Li et al., 2010[37]).

One goal of the work was to relate satellite-based soil moisture with other environmental

parameters: precipitation, temperature, NDVI index, soil type and groundwater depth. For the

applied method to have a meaningful weight, it was necessary to consider a sufficiently large time

3

span: the interval between the years 2006 and 2014 was considered, with particular focus on

winter and summer seasons.

Precipitation and temperature represent essential factors for the climate of a region, and also for

soil moisture patterns (Kim and Streicker, 1996)[31]. NOAA-NESDIS satellite data, as explained

above, require precipitation and temperature inputs for the model to work (Kistler et al., 2001)[32]:

these inputs have a global scale, and they are modeled, not directly measured. However, when

deciding to relate satellite soil moisture with precipitation and temperature as separate datasets,

this work relied on a different source than the model’s for the latter, the California Data Exchange

Center (CDEC)[1], a network of meteorological stations controlled by the State of California. The

idea behind this choice was to compare two different precipitation data sources, one global and

model-generated (CPC), already included in the soil moisture datum, the other local and field-

measured (CDEC). Hence, it was possible to test the satellite accuracy, to see whether a strong

correlation between satellite soil moisture and field precipitation could be detected or not.

The NDVI index was considered as an accurate way to include the vegetation factor in the

process, because of the influence that vegetation can have on soil moisture spatial variation

(Mohanty et al., 2001[45]; Crow et al., 2012[9]). In order to avoid the effects that plants have on soil

moisture distribution, since in highly vegetated areas soil moisture retrievals are less accurate than

in bare soil areas (Lakhankar et al., 2009)[35], it was necessary to know the location of healthy

vegetation in order to choose the right areas where to conduct detailed analysis, i.e. those without

growing vegetation.

Satellite soil moisture data do not have a sufficiently high resolution to highlight small-scale

differences in lithology (Vinnikov et al., 1996[71]; Jana, 2010[29]), although in reality one soil type

might retain a completely different amount of water than another, even under the same climatic

conditions (Mohanty et al., 2001[45]; Crow et al., 2012[9]). The signal that satellites receive is

usually a result of several inputs from different soil types, joined together by the large scale of the

signal (Crow et al., 2001)[8]. Therefore an attempt was made to differentiate moisture data for each

soil type, to see whether or not it could be possible to delineate unique behaviors for the lithologies

in the area.

Groundwater has also a strong influence on soil moisture, and vice versa. They are usually

connected by a strong correlation for which, when the groundwater table is shallow, soil water

content rises, while when the water table is deep the soil is more depleted in water. Considering

the small resolution of soil moisture data, this correlation could be hard to detect: in winter months

it could be completely covered by strong precipitations, although groundwater reaches a closer

level to the surface; in summer, temperature might be the unique controlling factor, due to the lack

of rainfall and a deeper water level. Hence, another task was to test these assumptions, trying to

4

find some relationship between soil moisture and groundwater both in winter and summer season,

even with such low-resolution data.

Another approach towards the validation of satellite data is their association with field

measurements. However, before the actual comparison, it is required to fix the difference in scales

between the two datasets (km for satellite, cm for field samples; Evett and Parkin, 2005[14]). This

important task, necessary for the successive enhancement of the ground truth of remote sensing

records, was the second main goal of this work. The first steps towards the upscaling to a

watershed level have been made by Famiglietti et al. (1999)[15] and Mohanty et al. (2000)[44]. For

the same purpose, this work considered a data-collecting campaign of gravimetric soil moisture

performed in 2012 in the Scott Valley. Its spatial scale is in the order of 100-200 km2, which is a

suitable scale to examine sub-footprint-scale soil moisture spatial scaling (Crow et al., 2012)[9]. In

order to increase the scale of field data, the method proposed by Cosh et al. (2004)[4], Jacobs et

al. (2004)[28], Cosh et al. (2006)[5], and Cosh et al. (2008)[6] was applied: it implies the validation

of temporal and spatial stability of soil moisture over a certain area (Guber et al., 2008)[20] by the

calculation of some statistical parameters on the dataset: the mean relative difference with

standard deviation (Vachaud et al., 1985[68]; Grayson & Western, 1998[19]; Pachepsky et al.,

2005[52]), which give information about which observed site presented soil moisture-trend stability

throughout the observation period, and which therefore is a function of the dataset’s spatial

variability; and the Spearman’s rank coefficients (Vachaud et al., 1985)[68], related to pairs of

observation time (Vanderlinen et al., 2012)[70], which express the trend of soil moisture in terms of

temporal stability along the whole area. When proved how the dataset, and therefore the soil water

content, can remain stable over a certain time and place, that would become representative for the

whole area, therefore increasing the initial scale of the soil moisture datum to a larger one, making

it suitable to be compared with satellite data. Indeed, that site should have soil water contents

which are close to the average of the watershed, making it possible to address it as a “catchment

average soil moisture monitoring site” (Grayson & Western, 1998)[19].

5

2. Area of Interest

The Scott Valley (Figure 1) is a drainage basin which is part of the Scott River watershed in

Northern California, U.S.A., near the California-Oregon border (Figure 2). It lies between

122°45’/123° longitude and 41°15’/41°40’ latitude. It extends within the Klamath Mountains with a

length of approximately 43 km in direction N-S and a width of 20.4 km in direction E-W at its

widest. Its upstream part, in the S, has a width of just hundreds of meters, while moving

downstream towards N, the valley reaches an average width of 8 to 10 km. The total area is

around 180 km2. The altitude inside the valley ranges from 900 m upstream to 820 m downstream.

The mountains at the edges, on

the other hand, can reach

altitudes of more than 2400 m on

the W (Marble, Salmon, Trinity

Alps and Scott Mountain), and

1500 m ca. on the E. Western

mountains are covered with

mixed-conifer forest, while the

eastern range by brush and

western juniper, together with

frequent woodland-grass. This

difference in vegetation is mainly

due to different amounts of

precipitation and different

bedrocks.

The Scott river (Figure 1) flows

through the valley’s middle-east,

with a gentle slope, between 1°

and 2° (Scott Valley study plan,

2008)[23], drawing a sinuous

channel whit bars, islands, side and/or off-channel habitats. It starts flowing in the southern part of

the valley, with different tailing sub-watersheds: these tailings are mainly constituted by large

boulders with a high hydraulic conductivity and a rapid connectivity to the river. Particularly in late

summer and early fall, this part of the river is often disconnected, mainly because of the highly-

permeable sub-watershed. At its final part the river proceeds northwest, it slightly increases the

slope angle and flows into the Klamath river (Figure 2), for a total length of 97 km.

The central river body is fed by eight main tributaries (Figure 1): Sugar, French, Etna, Patterson,

Kidder, Mill, Shackleford, and Moffett Creeks, which contribute to the overall stream flow for the

Figure 1: Hydrographic system of the Scott Valley (Yokel, 2011).

6

50.3% of its entire capacity. Other smaller tributaries could be mentioned, but they are mostly

ephemeral small streams that during summer see their water sink into the coarser permeable

gravel (Mack, 1958)[38]. The Scott river provides an important spawning habitat for salmon fish

inside the Klamath basin.

Figure 2: Map of the Scott river valley inside the bigger Klamath river watershed (USBR[39]).

7

There are two main settlements, the towns of Fort Jones and Etna, for a total population in the

area of around 8,000 people. The main activities are represented by agriculture, with the cultivation

of alfalfa and grain, and farming. The main land use (Figure 3), as per Foglia et al. (2013)[18], is:

- Alfalfa and grain crops (70.5 km2), which rotate regularly inside each field with a 8 years-

cycle, of which one random year is dedicated to grain, the others to alfalfa. The main

irrigation methods are flood (the main water source is surface runoff), center-pivot

sprinklers and wheel-line sprinklers (the main water source is the aquifer). A general

evolution, in the last twenty years, from wheel-line to center pivot method must be pointed

out (Figure 4).

- Farming land (67.1 km2).

- Natural vegetation, high water meadow, riparian vegetation (57.27 km2), which have seen a

sharp drop in the last years, with the consequent increase of the stream temperatures in

summer, due to lack of trees shadowing effect.

- Barren soil, paved surfaces and settlements (6.86 km2).

Irrigation is limited to some periods of the year, which are different from one field to another. The

water amount is dependent on seasonal precipitation, temperature and pumping rates. Most

pumping occurs during summer, while groundwater recharge mostly happens between late winter

and early spring. However, more pumping in summer usually means more irrigation of fields: this

could allow a higher recharge rates through irrigated fields, mainly alfalfa’s.

In summer, the flow rate of the river is between 25,000 and 125,000 m3/d, and in order to keep on

flowing on the surface it relies strongly on groundwater return flow (i.e. base flow); hence, the

irrigation source depends almost entirely on groundwater pumping. In winter, the river flow can

exceed 1,000,000 m3/d (Foglia et al., 2013)[18]. It was estimated that groundwater pumping

interests the upper 60 meters of the alluvial fill.

Based on the information provided by the California Department of Water Resources (CDWR),

several wells have been dug in the valley, both for pumping and monitoring purposes (Figure 4):

- Domestic wells, 1,302

- Irrigation wells, 240

- Industrial wells, 3

- Public/Municipal wells, 4

- Other (monitoring, tests, etc.), 152

Based on the results obtained by the soil-water budget model performed by Foglia et al.

(2013)[18], the amount of annual recharge from irrigation should be around 46 Mm3/yr.

Groundwater pumping is 25% larger, around 55 Mm3/yr. All other non-irrigated land use types, e.g.

dry land farming and riparian vegetation, recharge the system with 26 Mm3/yr ca., thanks to winter

precipitation. Alfalfa requires a higher amount of water (840 mm/yr) than grains (358 mm/yr) for

8

irrigation, because of its higher evapotranspiration rates and the longer harvesting season. Pasture

fields are irrigated more intensively than alfalfa, but with a lower annual irrigation rate (755 mm/yr).

Figure 3: Land use categories based on the Department of Water Resources (DWR) 2000 map and updated for 2011 using suggestions from GWAC and local landowners (Foglia et al., 2013[18]).

9

Figure 4: Map of the irrigation types and of the available irrigation wells for version 2 of the integrated hydrologic model

by Foglia et al. (2013)[18]. Locations have been refined by inspection and may not coincide with those reported by the California Department of Water Resources. The irrigation type reflects 2011 conditions.

10

2.1. Geological Setting

The Scott Valley is inside the metamorphic complex of the Klamath Mountains Province, of

Paleozoic/Mesozoic origin, composed by the stacking of different metamorphosed marine facies

interrupted by plutons and magmatic intrusions, mostly metamorphosed too after the orogeny that

involved the province in Late Jurassic/Early Cretaceous. The modern alluvial basin is much more

recent, of Quaternary origin, formed around 2 Ma by basin and range extensional tectonics.

The extensional tectonics of the region is part of the much bigger Basin and Range Province of

North America, extending from northern Mexico through the U.S. and into Canada, for a distance

of approximately 3,000 km. This geological province is a continental rift zone, composed by a

series of ranges and basins with a main N/NE-S/SW orientation, expanding the crust in a E-W

direction with a rate of approximately 1-5 cm/yr. The main topography of such a tectonic setting is

represented by valleys, i.e. grabens or half-grabens, and by ranges, i.e. horsts. The valleys are

usually bordered by normal faults that can cut deep into the crust, with a listric geometry at the

bottom. Different evidences exist of such an extensional tectonics. Heat flow underneath the region

is three times higher than the mean for stable continental crust. The seismic activity concentrates

on the same N-S direction of the supposed extensional axis, with focal mechanisms of normal

faults-solution joined in the S with strike-slip faults (mainly due to the presence and influence of the

San Andreas faulting system). Furthermore, seismic refraction shows an anomalous thin crust

below the region and low p-waves velocity, indicative of a shallow hot mantle. The current E-W

direction extensional phase started around 10-6 Ma; the previous one, with direction NE-SW,

began around 20 Ma.

* * *

Going from top to bottom through the valley main rock sequence, it is possible to find:

- Recent alluvium, made by alluvial-fans, stream-channels and flood-plain deposits. It is the

most important aquifer in the valley.

- Pleistocene sediments, interfingering with volcanic rocks placed after the thinning of the

upper crust due to extensional tectonics, and as a result of the subduction process off the

Western North American coast. These volcanic products fall inside the activity of the

Cascade Volcanic Range. These sediments do not constitute an important aquifer.

- Deformed pre-Silurian to Jurassic metamorphic and magmatic rocks, in downward

succession (Mack, 1958)[38]:

Ultrabasic (serpentine) and felsic intrusive rocks (granodiorite) (Late Jurassic/Early

Cretaceous);

Greenstones of the Copley Greenstone formation (Devonian) or the Applegate

group (Triassic);

11

Chancelulla formation of Hinds (Silurian);

Abrams mica schists and Salmon hornblende schists (pre-Silurian).

- Crystalline bedrock, e.g. Trinity and Rail Creek terrane.

Bedrock terranes in the Scott Valley are progressively younger, going from east to west. Among

them the Trinity and Rail Creek terrane, in the southeastern part of the valley, mainly represented

by plagiogranites, is the oldest tectonic unit of North America which can be found in a convergent

margin. On top of it, going from 450 Ma to 130 Ma, a succession of younger terranes were

deposited, starting from Abrams’s original sequence of sandstone, shale and limestone. They were

occasionally intruded by magmatic plutons, of mafic (pyroxenite to gabbro) composition. The

different orogenic phases caused the metamorphism of these units. Abrams strata were converted

to mica schist and quartzite.

During Silurian, the area underwent a subsidence process that led to the deposition of the

Chancellula’s transgressive marine sequence of sandstone, chert, shale and limestone, lying in

unconformity on top of the Abrams and Salmon formations.

Following a successive uplifting phase, from Devonian through Triassic, metamorphism proceeded

along with a new period of intense volcanism, involving the extrusion of andesitic and basaltic lava

and the expulsion of pyroclastic material. These products were converted into greenstones and

greenstone schists by metamorphism.

In Late Jurassic/Early Cretaceous, between 174 and 138 Ma, a new orogenic phase called

Nevadan orogeny interested all the western coast of the modern U.S.: this brought a new

metamorphic signature on the older rocks together with a new magmatic activity, characterized by

the intrusion of peridotite and granodiorite, which persisted even after the orogeny closure.

In Middle Cretaceous, the mountains subsided again under sea level, just to be uplifted again in

Late Cretaceous.

During Miocene, no further uplift was recorded, and the mountains were slowly but progressively

eroded, forming broad valleys. Around 4 Ma, in the Pliocene, a new uplifting phase increased the

erosive action of rivers, which dug narrow and deep valleys between the mountains. This uplift

produced is correlated with tilting and faulting of the Western Cascades ranges. Between these

ranges, along two main faults, the Greenhorn and the western Scott Valley fault, the tectonic

graben of which the Scott Valley is the westernmost portion was formed (Elder, personal

communication, 2009). The activity along these two faults has progressively modified the original

course of the Scott River, which originally flowed with a S-N direction, intersecting the Klamath

river more to the E than nowadays. The same activity has also forced the river to sharply turn W in

the northern part of the valley (Mack, 1958)[38].

12

The alluvium, which is the uppermost and most recent rock type in the valley, can be differentiated

between the valley center and its rims. The rim alluvium is mainly composed by alluvial fan

deposits of sandy and silty clay with well-rounded granodiorite, serpentine, chert and quartzite

boulders, of western-mountains origin, with a total thickness of around 15-30 m. The mountains on

the western side, which rise sharply from the valley floor up to 2000 m or more, have discharged

more sediments than the eastern side mountains, which rise more gently and to a lower altitude:

hence, the western side presents much more distinct, steeply sloping alluvial fans than on E.

The central alluvium is composed by alluvial fan deposits, stream channels and floodplain

deposits, mainly connected to the actual course of the river, with a thickness between 0 and 120

m, at the western part of the valley. This thickness usually decreases towards N and S or at the

margins, while it gets thicker towards the center. Fan and stream deposits can vary their

percentage of fine clay and sand in respect to the coarser part, made of gravel and boulders. The

floodplain deposits, are generally composed by fine material. e.g. fine sand, silt and clay.

Gravel and sand deposits represent the most conductive facies of the soil sequence, therefore they

are supposed to be highly connected through all the aquifer system, and not sharply separated by

clay layers or lenses. However, the presence of clay horizons was recorded by different cross

sections of the area, therefore some parts of the aquifer may present also conditions of semi-

confinement (Foglia et al., 2013)[18].

2.2. Precipitation and Temperature

Precipitation in the Scott Valley follows a general trend with a SW-NE direction (Figure 5), mainly

because the highest mountains on the southern and western side collect most of the rainfall, which

then progressively falls inside the valley. The mean annual precipitation is around 662.7 mm/yr

(usa.com[64]), with the rainy period going from October to March/April, when rainfall can reach

peaks of more than a 110 mm/month, especially in December and January. This value is exceeded

abundantly on the western mountain chain, where precipitation can range between 152 cm/yr and

203 cm/yr (although a consistent part of it is represented by snow). The shield effect of the western

chain reduces the amount of rain that can reach the eastside mountains, whit values between 300

and 400 mm/yr (Scott Valley study plan, 2008)[23]. The lowest precipitation amount is recorded

between July and September, with an average of 10.1 mm/month.

Snowfall usually occurs between middle October and middle April, with an annual average of 127.5

mm/yr. Above an altitude of 1700 m a.s.l., snow cover is a prevailing factor (Scott Valley study

plan, 2008)[23]. Especially on the western side, in winter, mountain caps are usually covered by

snow, which melts in springs when temperatures raise steadily above 21°C (Foglia et al.,

2013)[18]. Snowmelt is an essential source of water during spring and summer: this water

13

penetrates through the rock fractures, enhancing the permeability of rocks; then, it flows down the

mountains and reaches the surface again with several springs that supply water to all those

streams that feed and recharge the Scott river. The average temperature in the Scott Valley is

around 11.27 °C (usa.com[64]). The highest peaks in summer are reached between July and

August, with maximums that can reach 32.6 °C and minimums that can fall to 10 °C, for a mean of

21.3 °C. The coldest period of winter is usually between December and January, when maximums

reach 7.85 °C and minimums can fall down below 0°C.

Figure 5: Valley floor precipitation co-kriging interpolation with anisotropy (Foglia et al., 2013)[18].

14

2.3. Soil Type

Soil is mostly represented by the alluvium in the valley floor and debris fans on mountain slopes.

- Flood plains: they are gently sloped (less than 3%) and poorly drained. They usually record

a shallow groundwater level, and are often subject to floods when this level exceeds the

river’s. They have a fine texture and are composed of stratified loam, sandy loam, silty loam

and clay loam, in different successions.

- Alluvial fans: they are more steeply sloping (up to 15%) and are well drained. The grain size

is coarser, with layering of gravelly loam, sandy loam and loam. These fans are typical of

the tributaries of the Scott River.

- Mountain slopes: the soil here is usually thinner, very well drained and with an average

coarse texture. It has been principally accumulated from the erosion of the granitic material

of the mountain range.

The river bed is made mostly by cobble, upstream, and by sand, downstream; the remaining

course is mainly represented by gravel (Sommarstrom et al., 1990)[59].

15

3. Initial Data

Different sets of data were collected at the beginning of the work (Table 1):

- Two Landsat images, for summer and winter (Figure 6), for each processed year from 2006

to 2014 (source: USGS, U.S. Geological Survey[67]).

- Groundwater table monthly readings from 56 wells along the valley, from March 2006 to

March 2014 (source: volunteering program).

- Satellite soil moisture monthly grid files (Figure 7), from 1948 to present, providing a set of

contour lines, each representing a value of water depth in mm (source: NOAA[60]). Two

files per year were considered, correspondent to the selected months to process.

- Daily precipitation from 1990 to 2011, averaged between three different meteorological

stations along the valley (source: NCDC, National Climatic Data Center[17], Figure 8).

Monthly readings from 2012 to present, averaged between two stations of the valley

(source: CDEC [1]).

- Soil map of the valley (Figure 9) with specifications for each soil type (source: U.S.

Department of Agriculture, [48]).

- Monthly temperature, from 1936 to present (source: CDEC[1])

- Evapotranspiration and irrigation rates for the valley (source: University of California,

Davis), computed by a soil-water budget model (Foglia et al., 2013)[18].

- Gravimetric field soil moisture data, in centibar, from April 2012 to September 2012, out of 8

different locations in the valley (source: University of California, Davis. See Figure 10).

Table 1: List of the initial data with relative source, time span and specifications.

Initial data Data source Time span Notes

Landsat images USGS 1972-present

Two images, for summer and

winter, from 2006 to 2014

(30 meters)

Groundwater table Volunteering program 03/2006-03/2014 Data collected from 56 wells

(meters)

Soil moisture NOAA 1948-present Satellite computed grid files, each

with contour lines (mm) (0.5°x0.5°)

Precipitation NCDC - CDEC 1936-present (CDEC) Data collected from 3/2

meteorological station, (in)

Temperature CDEC 1936-present (CDEC) Data collected from 2

meteorological station (°F)

Soil map USDA - Shapefile indicating the different

soil facies and slope disposition

Actual Et & irrigation

Scott Valley soil-water budget

model

(U.C. Davis)

10/1990-09/2011 Single value for each cell of the

modeled area (m3/month)

Gravimetric field soil moisture

data U.C. Davis April 2012-September 2012

Measurements from 8 different

locations for 21 weeks

(centibar)

16

3.1. Landsat Images

The Landsat project[36] is one of the biggest enterprises for the collection of satellite images of the

Earth’s surface. The program started in 1972 with the launch of the satellite Landsat 1 and is still

running with the launch, in 2013, of the newest Landsat 8.

Landsat sensors can detect reflected and emitted energy from the Earth in different wavelengths of

the electromagnetic spectrum (from gamma rays to radio waves): this range includes visible light

and infrared spectrum, which cannot be seen but can be felt as heat. This energy is digitally stored

by the satellite and later on forwarded to different ground stations (18 centers around the world)

that process the data and store it in specific archives. For this project, data collected by three

different satellites were used: Landsat 5, 7 and 8, each with its own sensor.

TM sensor (Landsat 5 & 7) consists of seven spectral bands with a spatial resolution of 30 m, with

the exclusion of band six, whose original resolution is 120 m, which is later re-sampled to 30 m

pixels. The size of each picture is approximately 170 km N-S and 183 km E-W (Table 2).

ETM+ sensor (Landsat 7) consists of eight spectral bands with a spatial resolution of 30 m, except

for band six and eight. The picture size is the same as for TM sensor (Table 2).

OLI and TIRS sensors (Landsat 8) consist of nine spectral bands with a resolution of 30 m, except

for band eight, plus two other bands, ten and eleven, with a resolution of 100 m, which are useful

for a high quality surface temperature assessment. The picture size is the same (Table 3).

Table 2: TM and ETM+ sensors band designation[65].

Tematic Mapper (TM)

and

Enhanced Tematic

Mapper Plus

(ETM+)

Landsat 5 & 7

Spectral Bands Wavelenght (μm) Resolution (m) Use

Band 1: blue-green 0.45-0.52 30 Bathymetry, distinction of soil from

vegetation

Band 2: green 0.52-0.61 30 Plant vigor assessment

Band 3: red 0.63-0.69 30 Vegetation slopes assessment

Band 4: near IR 0.76-0.90 30 Biomass content and shoreline

definition

Band 5: mid-IR 1.55-1.75 30 Moisture content of soil and

vegetation – penetrates cloud

Band 6: thermal 10.40-12.50 120 Estimated soil moisture

Band 7: mid-IR 2.08-2.35 30 Mapping hydrothermally altered

rocks

Band 8: panchromatic

(ETM+, Landsat 7) 0.52-0.90 15 “sharpening” multispectral images

17

Table 3: OLI and TIRS sensors band designation[65].

Operational Land

Imager (OLI)

And

Thermal Infrared

Sensor (TIRS)

Landsat 8

Spectral Bands Wavelenght (μm) Resolution (m) Use

Band 1: coastal/arosol 0.43-0.45 30 Coastal zone observation

Band 2: blue 0.45-0.51 30 Bathymetry, distinction of soil from

vegetation

Band 3: green 0.53-0.59 30 Plant vigor assessment

Band 4: red 0.64-0.67 30 Vegetation slopes assessment

Band 5: near-IR 0.85-0.88 30 Vegetation boundary between land

and water

Band 6: SWIR 1 1.57-1.65 30 Plant drought stress and fire-

affected vegetation

Band 7: SWIR 1 2.11-2.29 30 Plant drought stress and fire-

affected vegetation

Band 8: panchromatic 0.50-0.68 15 “sharpening” multispectral images

Band 9: cirrus 1.36-1.38 30 Cirrus clouds detection

Band 10: TIRS 1 10.60-11.19 100 Thermal differences in water

currents, estimating soil moisture

Band 11: TIRS 2 11.50-12.51 100 See band 10

The months selected for this work were (under brackets are the days when the satellites have

taken the picture):

- February 2006 (23rd)

- August 2006 (26th)

- March 2007 (22nd)

- August 2007 (29th)

- March 2008 (8th)

- August 2008 (31st)

- March 2009 (27th)

- August 2009 (18th)

- March 2010 (14th)

- August 2010 (5th)

- March 2011 (1st)

- August 2011 (8th)

- February 2012 (24th)

- August 2012 (18th)

- April 2013 (23rd)

- August 2013 (13th)

- February 2014 (21st)

- August 2014 (31st)

The criterion for this choice was to select, for each year, the summer and winter month which were

the richest on data. The days under brackets were chosen because they offered the best quality

among the available pictures, with scarce cloud cover and low interference (Figure 6).

18

Figure 6: Example of raw Landsat image (left), and processed Landsat (right) after clipping to the AOI extension. The

AOI outline is highlighted on the right picture (source: USGS).

19

3.2. Groundwater Table Readings

Within the Scott Valley, 56 observation wells are available. The location of 49 of them is to be

considered confidential, as well as the measurements coming from them; the other seven are

managed by the Department of Water Resources (DWR), and their information is freely accessible.

The records used in this work came from a volunteering project of data collection. Measurements

of groundwater depth were taken monthly since March 2006. Not all 56 wells offered a

measurement every month, but each time step had enough points to produce a groundwater

contour map via interpolation (see Chapter 4.5).

These values were originally organized in spreadsheets (Table 4) with the wells code-name,

location, altitude, opening’s height from the surface, exact date when the measurements were

taken, depth of groundwater from the surface and its absolute elevation.

Table 4: Wells spreadsheet, with all information about their position and that of the groundwater table, plus the days

when measurements were taken.

20

3.3. Soil Moisture Files

NOAA institute provides soil moisture data in the form of monthly grid files with an extension of

0.5°x0.5° that cover the entire globe and range back to January 1948. Any month can be selected

with the requested extent, given by two values of latitude and two of longitude. These data are

computed by a numerical model, they are not obtained by direct measurement. The main influence

on this model comes from large scale climatic trends of wind, temperature and precipitation: that is

why, on a small scale, these data appear monotonous and following a constant trend; it is at a

larger scale that they show a greater variability.

Hence, it is probable that they will not show any influence given by terrestrial elements like a river

or a change in lithology, because their resolution is not high enough to represent them. They will

more probably show variations due to those elements that are big enough to influence the climate

of a region, e.g. a mountain range, the sea, a big river or a lake.

The format of the downloadable data is grid file, or gif., depending on the needs of the user: these

files can be handled as images in all GIS or remote sensing programs, in order to be

georeferenced and associated to other maps. The output presents a sequence of contour lines,

where each line indicates a unique value of soil moisture in mm of water depth (Figure 7).

The soil moisture values are estimated by using the one-layer “bucket” hydrological model

developed by Huang et al. (1996)[24], Van den Dool et al. (2003)[69] and Huang et al. (2006)[25].

This model is driven by some input data: precipitation, taken from the Climate Prediction Center

(CPC) monthly global precipitation over land, generated from more than 17,000 gauges worldwide

(Chen et al., 2002)[3], and temperature, taken from monthly global Reanalysis/CDAS 2m air

temperature (Kistler et al., 2001)[32]. Precipitation and temperature from these sources are global

and gridded at 0.5° resolution, the same resolution as the final soil moisture grid files. As output,

the model gives values of soil moisture, evaporation and runoff. Evaporation is dependent on

monthly temperature. Runoff is divided into surface runoff, base runoff and loss to groundwater

which, as in operational hydrological practice, are all parameterized in terms soil moisture and

rainfall. The model runoff was originally adjusted by considering few small streams in Oklahoma for

1961-1990. This procedure requires the fitting of five empirical coefficients. One of them is the

effective holding capacity of 76 cm of water. This value, when related to a common porosity of

0.47, corresponds to a soil column of 1.6 m, represented by a “leaky” bucket (Fan et al., 2004)[16].

21

Figure 7: CPC Soil Moisture data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site

at http://www.esrl.noaa.gov/psd/data/gridded/[60]. The base colors of the first two images were just references of the soil moisture range, but were not considered, since each line presented its own labeling.

22

3.4. Precipitation and Temperature Data

The AOI is covered by several meteorological stations that collect, on a daily and monthly basis,

different climatic parameters, from temperature to wind speed and direction, snow cover, etc.

(Figure 8). Three of them are also equipped to collect precipitation data. Their information is

available online [1]. The three stations are named:

- Fort Jones RS (FJN) Lat: 41.60000 – Lon: -122.85000; Elevation: 830.6 m.

- Callahan (CAL) Lat: 41.31700 – Lon: -122.80000; Elevation: 970.78 m.

- Etna Mountain (ETN) Lat: 41.40000 – Lon: -123.00100; Elevation: 1798.3 m.

Figure 8: Location of the main meteorological stations covering the AOI.

23

Precipitation data were taken from two different sources: CDEC meteorological stations database

and NCDC[17]. Both these sources relies on data coming from the three meteorological stations of

Callahan, Fort Jones and Etna. The last one covers only time until 2011, but its data had been

integrated together with the first two stations into a spreadsheet of the NCDC with daily readings

and monthly averages of the single stations and of the valley, for the years between 2006 and

2011. This document contained single measurements from each location, plus the mean of the

valley, obtained by averaging their values. Callahan and Fort Jones, instead, had up to date

measurements, therefore they were used to get values for the years going from 2012 to 2014.

Their data were retrieved from the CDEC online portal[1].

Temperature data were also obtained from CDEC. Two stations offered temperature readings in

monthly averages, Callahan and Fort Jones. These values were joined together to give a unique

entry, indicative of the whole valley.

3.5. Evapotranspiration and Irrigation Estimates

In 2013, a soil-water budget model of the Scott River valley was developed by Foglia et al.,

(2013)[18], from the University of California, Davis, to estimate irrigation amount (as a combination

of both surface water and groundwater used for irrigation), actual evapotranspiration, recharge and

pumping throughout the valley. This model runs daily from October 1990 to September 2011 and it

divides the AOI in single fields, calculating the quantities mentioned above for each of them.

24

3.6. Soil Map

The soil map of the area (Figure 9) was made by the U.S. Department of Agriculture. Its

boundaries follow those of the soil-water budget model by Foglia et al. (2013)[18]. This boundaries

are supposed to confine all alluvial deposits at the surface, and at the same time they include only

those areas where there is no steep topographic gradient (not more than 3%): a steeper gradient

was not considered, since this could have affected considerably the variability of moisture in the

soil, reducing the validity of satellite data too (Charpentier et al., 1992[2]; Jacobs et al., 2004[28]).

The surface covered by this model is 202.34 km2.

Figure 9: Soil map of the AOI, based on the classification given by U.S. Department of Agriculture.

The original map (Figure 9) was very detailed, differentiating soil classes not only based on their

lithology and grain size, but also on the percentage of slope angle they lay onto. By looking at its

legend, it is possible to distinguish different soil facies. The USDA provides explanatory cards for

each soil class, where the facies as well as their ideal profile and lithologies are accurately

described. These cards were later on used to simplify this map (see Chapter 4.1).

25

3.7. Field Gravimetric Soil Moisture

The dataset contained gravimetric soil moisture measurements taken in 2012 from different points

of the AOI. The data were collected by using Watermark sensors, electrical resistance sensing

devices used to measure the soil-water tension. This tension changes constantly with different

water contents in the soil. A current is then applied to the sensors to obtain a resistance value,

which is correlated to centibars of soil-water tension (www.irrometer.com[26]). A total of 23 weeks

were covered by sampling: indeed, one day per week was regularly selected for the collection of

data, from April 27th to September 27th; those days are shown in Table 5. Because some sites

lacked measurements for the first and last week, only 21 of them were considered, from May 4th to

September 20th. 8 sites were available (Figure 10), and for each of them two sets of data were

provided (for a total of 16), corresponding to two different but close positions. Each set contained a

reading for each foot of depth down to 8 feet, except few exceptions. In Table 6 are displayed the

coding of the different sites, which was used in the next steps of the project.

Table 5: Notation of the measured weeks. Only 21 weeks

out of the original 23 were selected, the excluded being the last week of April and September.

Weeks notation Day of the

measurement

1 May 4th

2 May 10th

3 May 16th

4 May 23rd

5 May 30th

6 June 6th

7 June 13th

8 June 20th

9 June 27th

10 July 5th

11 July 11th

12 July 18th

13 July 26th

14 August 2nd

15 August 9th

16 August 16th

17 August 23rd

18 August 30th

19 September 6th

20 September 13th

21 September 20th

Table 6: Original names of the 16 different locations

where gravimetric soil moisture was measured, with their coding adopted in this work, and the soil type they lay on.

Site name Site coding Soil type

Sweezy Wheel line 1 SWL1 Sandy loam

Sweezy Wheel line 2 SWL2 Sandy loam

Plank Wheel line 1 PWL1 Loam

Plank Wheel line 2 PWL2 Loam

Morris Pivot 1 MRP1 Loam

Morris Pivot 2 MRP2 Loam

Menne Pivot 1 MP1 Out of boundaries

Menne Pivot 2 MP2 Out of boundaries

Hanna Wheel line 1 HWL1 Clay loam

Hanna Wheel line 2 HWL2 Clay loam

Harris Pivot 1 HP1 Gravelly loam

Harris Pivot 2 HP2 Gravelly loam

Fawaz Pivot 1 FP1 Loam

Fawaz Pivot 2 FP2 Loam

Harris Wheel line 1 HWL1 Loam

Harris Wheel line 2 HWL2 Sandy loam

26

Figure 10: Position of the 16 sites where gravimetric soil moisture probes were installed during 2012. Each point

represents the two locations with the same name that are very close to each other.

27

4. Methodology

4.1. Soil Map Simplification

The original soil map, provided by the U.S.D.A. (Figure 9), was considered too accurate for the

purpose of this work, since the low resolution of satellite data does not allow them to clearly

distinguish all soil types (Crow et al., 2001)[8]: not only diverse classes were differentiated based

on variations in lithology, grain size or facies; inside the same soil type further distinctions were

offered depending on the arrangement of the soil on a slope and the latter’s angle. This detailed

characterization was not needed, considering that the resolution of satellite soil moisture is quite

small. The most useful approach was then to join those classes that shared the same lithology and

grain size (e.g. clay), dismissing the slope angle and the facies classification. From a starting

condition of 49 different soil types, four of them were highlighted (Figure 12), chosen in a way that

each covered a relatively large portion of the AOI (this could have helped in relating the soil

information with the large scale of soil moisture data):

- Clay loam

- Loam

- Sandy loam

- Gravelly loam

All four classes referred to the same kind of grain

size, loamy, with a secondary component whose

grain size goes from clay to gravel. Loam is indeed a

particular lithology defined by different percentages

of sand, silt and clay: the combination of these three

components defines the loam soil type (Figure 11).

By looking at the disposition inside the AOI of these

classes, loam and clay loam were more frequent in

the middle of the alluvial plain, while sandy and

gravelly loam were closer to the surrounding hills,

where streams lose their carrying capacity and

deposit the coarser sediment.

Figure 11: Ternary diagram of the soil texture triangle

showing the different USDA-based soil texture classifications (Twarakavi et al., 2010)[62]

28

Figure 12: Final soil map obtained after simplifying the original USDA soil map.

29

4.2. Landsat Processing: NDVI Index

Two Landsat images per year were downloaded from the USGS website, one in winter and the

other in summer. The main reason why satellite images were included in the analysis was to

calculate from them the NDVI index for the area.

The NDVI is one of the most important remote sensing tool to evaluate whether an area contains

green vegetation or not. It mainly works by collecting the reflected solar radiation by vegetation in

the near-infrared and visible wavelength (http://earthobservatory.nasa.gov[46]). Any object, when

stricken by solar light, absorbs part of it and reflect the rest. The same statement also works for

plants, which need light to feed the photosynthesis process. The pigment inside leaves,

chlorophyll, is responsible for absorbing a lot of the visible light spectrum (from 0.4 to 0.7 μm),

reflecting back just 5% of the original radiation. On the other hand, the same leaves do not need

near-infrared wavelengths (0.7-11 μm) therefore they reflect most of them, around 50% of the

striking radiation (Figure 13).

It is clear now the following: the more green leaves a plant has, which indicate it is healthy, the

more it will absorb visible light and reflect near-infrared. On the contrary, a stressed plant (because

of lack of water, scarcity of nutrients in the soil, dry climate, etc.) will record a stronger reflection of

visible light and weaker reflection of near-infrared. Assumptions can be made not only on single

plants, but also on vegetation in general: a weak reflection of near-infrared can be generated by

scarce vegetation, maybe consisting of grassland, tundra or desert. A strong reflection of near-

infrared may be produced instead by any type of forest.

Specific satellites can measure the intensity of reflected radiation from the Earth: by getting the

amount of visible and near-infrared reflected radiations, they are able to quantify the photosynthetic

capacity of the vegetation in a generic pixel of the satellite image. This capacity is represented by

an index, the Normalized Difference Vegetation Index (NDVI), which is given by Equation 1:

(1)

where: NDVI = Normalized Difference Vegetation Index

NIR = Near-Infrared wavelength

VIS = Visible wavelength

30

Healthy and dense vegetation will produce a high NIR and a low VIS, therefore the index will go

towards 1. Stressed or scarce vegetation will produce instead a lower NIR and a higher VIS,

therefore the index will move towards -1. No green leaf should leave a value close to 0

(http://earthobservatory.nasa.gov[46]).

Figure 13: Scheme explaining the emitted and absorbed radiation pattern by healthy and unhealthy vegetation, in terms

of near infrared and visible wavelength. Green leaves absorb almost all visible light and reflect almost half of near-infrared radiation (left-side); stressed vegetation, instead, absorbs less visible light and reflects less near-infrared

radiation (right-side, http://earthobservatory.nasa.gov[46]).

The first step to generate an NDVI distribution map of the AOI was to download the Landsat image

from USGS[67]. Depending on the satellite that provided it (Landsat 5, 7 or 8, see Chapter 3.1), the

number of bands constituting the image changed. These bands were first joined together into a

single image. That was used to create two different NDVIs for summer and winter season. The

necessary bands for generating a NDVI image are the red and the near-infrared: for Landsat 5 and

7 this means bands 3 and 4, while for Landsat 8 this means bands 4 and 5.

When considering a single picture taken at a unique time, the NDVI allows the user to visualize the

conditions of vegetation (values from -1 to +1) at that moment. In this case, the two NDVI images

from summer and winter of the same year were joined together, in order to have also knowledge

on changes in vegetation during the year (Figure 14). The concept behind it is the same as before:

a negative value or close to -1 will indicate receding vegetation around one spot, while a positive

value or close to +1 will represent growing vegetation. This knowledge was fundamental in the next

step of the project, when selecting random points of the AOI, where to deepen the analysis on soil

moisture. Indeed, this work considered as a backing assumption that areas with high NDVI indexes

were to be avoided, because dense and healthy vegetation might have influenced the soil moisture

31

distribution, making it not representative anymore. On the other hand, areas with low NDVI indexes

were supposed to include more truthful soil moisture values.

Figure 14: NDVI-making for the year 2007. Starting from the two Landsat seasonal images in 2007, from March and

August, the single NDVI maps were generated (white color indicates healthy vegetation, dark colors indicate stressed plants). The two maps were then joined to create a single NDVI image for the whole year, giving indications about

vegetation changes from winter to summer (purple color indicates steady or unhealthy vegetation, green color indicates strong and growing vegetation). It must be pointed out how also snow, by reflecting almost all visible light, records a very

low index and therefore a purple color, like in the western portion of the map, as shown by the final picture.

32

4.3. Watershed Detailed Analysis

The next step was to select some specific areas where to conduct the analysis in order to

understand what relationships does the soil moisture have with the other collected parameters.

Some requirements had to be fulfilled before making this choice:

- Two groups of points had to be selected, one in the N and the other in the S of the valley, in

order to represent as much of the AOI as possible

- One point per soil type had to be found, hence four points for each group, for a total of eight

points (Figure 15)

- All points had to fall inside fields with a mean low NDVI index during the 9 analyzed years.

This means that in ideal conditions, at a specific point, the NDVI image of every year should

give a low value, indicator of not-growing vegetation. Considering how this valley is mainly

dedicated to agriculture, where fields are regularly irrigated, it was impossible to find any

point showing a negative NDVI index for all years; therefore it was decided to look at the

average behavior of the fields and, if they showed a predominance of negative indexes,

they were considered suitable for the purpose.

Figure 15: Position of the two areas chosen for the analysis. Each area includes four points, one for each soil type.

33

Figure 15 shows the location of the chosen points for each group. Figure 16 and Figure 17 show

instead the variation of the NDVI index from 2006 to 2014 for both groups: blue-dark blue color

indicates a negative index, therefore stressed or steady vegetation; a white-bright yellow color

stands for a positive index, hence healthy and growing plants. As previously said, NDVI images are

generated from two bands, near-infrared and red. After the images were created, it was necessary

to assign to the three color channels, red, green and blue, their respective band. In order to get the

same color distribution as shown in the pictures below, the chosen association was:

- Red = band 1 (red)

- Green = band 1 (red)

- Blue = band 2 (near-infrared)

Figure 16: Group 1 NDVI images in succession, from 2006 to 2014. Blue areas indicate low NDVI index, and they were

preferred to the yellow areas for the points selection. Not all years recorded a low index in those specific points, but bluish colors were recorded for more years than yellowish tonalities.

34

Figure 17: Group 2 NDVI images in succession, from 2006 to 2014. Blue areas indicate low NDVI index, and they were

preferred to the yellow areas for the points selection. Not all years recorded a low index in those specific points, but bluish colors were recorded for more years than yellowish tonalities.

4.4. Soil Moisture Grid Files

Satellite soil moisture data were provided by NOAA[60] as grid files, each with its own set of

contour lines that cut the AOI in different slices. All downloaded pictures had the same bounding

coordinates:

- Latitude: 41.3 N/41.7 N

- Longitude: 123 W/122.71 W

However, at the beginning they had no spatial reference, therefore they had to be georeferenced,

before associating it with any other map of the area. Hence, they were put into an ArcGIS 10.2.2®

project and georeferenced based on the coordinate system NAD 1983, UTM zone 10N. After this

step, the pictures were cut based on the outlines given by the hydrological model proposed by

Foglia et al. (2013)[18], in order to leave just the relevant parts of the original image. As final step,

the contour lines were digitized and each assigned with its own value of soil moisture in mm of

water depth (Figure 18).

35

As previously said, this source of data has a small resolution and is really dependent on climatic

trends affecting the area (Figure 5). By looking at Figure 18, which shows a processed month

taken as example (March 2008), it can be noticed how the lines follow a more or less constant

trend with the same orientation, and the soil moisture values decrease by a constant factor going

from SW to NE: this trend is to be considered constant for the entire time range of the analysis.

Figure 18: Processing steps of the raw soil moisture grid files. The original image was first georeferenced, then cut

based on the AOI shape, and eventually its contour lines were digitized and given a unique value of soil moisture in mm. The base colors of the first two images are just original references of the soil moisture range, but they were not

considered, since each line presented its own labeling.

36

4.5. Groundwater Depth Contour Maps

In order to generate groundwater contour maps of the area, the spreadsheet with the well

information and readings was used as starting point (see Chapter 3.2). The well coordinates were

used to represent them as points, as shown in Figure 19, where they were labeled with increasing

numbers going from 1 to 56. This labeling is not to be considered the official coding of the wells:

that is confidential, as well as their precise location.

Figure 19: Observation wells represented by red points and numbers going from 1 to 56. The base map is the ASTER

GDEM of the area. The AOI is shown here, with its boundaries as a black line.

After creating the points, they were assigned one value for the well absolute elevation in meters

a.s.l. and one for the groundwater depth (m below the surface). In order to represent each of the

37

selected analyzed months, different point Shapefiles were generated for the different times, for a

total of 17 Shapefiles (two months for nine years except Summer 2014, which was not available

yet when this work was completed), as explained by the flow chart in Figure 20: every Shapefile

contained only those wells that offered a reading for that specific month, as shown in Table 7.

Figure 20: Groundwater-contour maps processing steps: from the original spreadsheet, the “All wells” file was extracted,

with information about wells position and absolute elevation. Then a Shapefile containing the wells was created. By replicating it for the number of months to process, and joining the data of groundwater depth to it, the result were17

Shapefiles, one for each month: each of them contained a set of wells/points with a value of groundwater depth.

Table 7: Number of wells, from the original 56, for each processed month, offering groundwater depth measurements.

Month to process n. of wells available

February 2006 39/56

August 2006 35/56

March 2007 35/56

August 2007 28/56

March 2008 34/56

August 2008 38/56

March 2009 40/56

August 2009 44/56

March 2010 44/56

August 2010 41/56

March 2011 39/56

August 2011 33/56

February 2012 36/56

August 2012 35/56

April 2013 36/56

August 2013 36/56

February 2014 35/56

38

Eventually, the 17 Shapefiles were suitable to apply an interpolation method for generating a

contour map of groundwater depth from the surface. The interpolation process required first the

setting of the x, y, z fields: the well coordinates were used as x and y, while the groundwater depth

from surface was used as z field. Different methods were tested and compared, to see which one

was the most representative of the reality of the area:

- Inverse Distance Weighting (IDW)

- Kriging

- Spline

- Natural Neighbor

- Nearest Neighbor.

After a phase of trial and error, Kriging was chosen as the best method to apply on this area, its

suitability for displaying groundwater depth variations being already defined by previous case

studies (Kumar & Remadevi, 2006)[33]. Kriging is directly derived from the regionalized variable

theory. It depends on expressing spatial variation of water depth in terms of its variogram, and it

minimizes the prediction errors which are themselves estimated (Oliver & Webster, 2007)[51]. Its

spatiotemporal random function, which is necessary to predict, as far as possible, the natural

variations of a parameter, yields maps with lower estimation variances, while allowing forecasting

and hindcasting (Rouhani & Hall, 1989)[56]. Furthermore, in the specific case of this work, the

Kriging method delivered groundwater levels, along the valley, which did not lay too far away from

the original well readings, which were measured values. Hence its results seemed not to

exceedingly avert the modeling from the ground truth. An example of the application of Kriging to

the AOI is shown in Figure 21, considering winter and summer of 2010.

39

Figure 21: Groundwater depth (meters below surface) contour maps from March (left) and August 2010 (right) as

examples. Each contour line represents a groundwater level from the surface, starting from 0 m. The crosses along the map represent the observation wells, while the thicker black line represents the AOI borders.

4.6. Precipitation and Temperature Trends

Precipitation data were taken from two different sources: CDEC[1] meteorological stations

database and National Climatic Data Center (NCDC)[17]. All these data were joined together,

converted from inches/month to mm/month, then the mean of the stations (Callahan, Fort Jones

and Etna from 2006 to 2011, only the first two from 2012 to 2014) was selected as

representative for the valley (Figure 23).

However, by looking at the position of the two groups of points in Figure 22, it is possible to

notice how group 1, in the N, is very close to Fort Jones Station. It seemed therefore more

truthful to assign to it the values of rainfall coming from that station, instead of giving it the mean

value from all the stations. Group 2, instead, being its position in between the three

meteorological stations, was assigned the average of values coming from all of them (Figure

23).

Temperature data were obtained from CDEC by considering two stations only, Callahan and

Fort Jones, those having up to date available data. All values were converted from °F to °C

(Figure 24). As seen before for precipitation, a difference between the two groups was

40

considered, based on their position (Figure 22): group 1 was assigned the values coming from

Fort Jones, while group 2 was given the mean of the two stations.

Figure 22: Position of the two analyzed areas in respect of the location of the meteorological stations.

41

Figure 23: Precipitation trend of the valley in monthly means, after the values from Callahan, Etna and Fort Jones were

averaged and converted into mm.

Figure 24: Temperature trend of the valley for group 1, which received only Fort Jones measurements, and group 2,

whose values were defined after Callahan and Fort Jones measures were averaged and converted into mm.

42

4.7. Evapotranspiration and Pumping Rates

In order to get these values, the original data from the hydrological integrated model of Foglia et al.

(2013)[18] were retrieved: a series of grid files, one for each month to analyze, was extracted from

the model. The model provided daily (or monthly aggregated) value of evapotranspiration and

pumping for each cell, within the boundaries of the model.

4.8. Statistics of Soil Moisture Spatiotemporal Stability

Spatiotemporal stability analysis is a useful tool to upscale field data of soil moisture to a

watershed level by finding few locations with representative conditions for the whole area, which

could be later on used as reference for a comparison with satellite data. To increase the scale of

field soil moisture from a cm (Evett and Parkin, 2005)[14] to a km scale, a very dense network of

measuring stations should be present. The statistical method, instead, defines the area’s trend by

the means coming from some “representative” sites. The requirement that these sites have to fulfill

is to have a soil moisture trend that is stable over time and space. The spatiotemporal stability

analysis can tell which sites maintain a consistent temporal relationship with the watershed

average, with only a small variability. This method of analysis was tested for a time period of two

months (Cosh et al., 2004)[4], without the possibility to exclude seasonality effects due to the short

time, and 21 months (Cosh et al., 2006)[5]. However, Martìnez-Fernandez & Ceballos (2005)[41]

stated that, under Mediterranean conditions, approximately one year of measurements was

required to determine the representative points, with a mean relative difference close to zero and

smallest standard deviation. Martìnez-Fernandez & Ceballos (2003)[40] proved how also time

periods of 3 years could see the maintenance of temporal stability of soil moisture, because the

sites maintained their rank in the mean relative difference curve for that time, and Cosh et al.

(2008)[6] tested the same method for 3.5 years.

The first step was to generate a mean relative difference (MRD) plot, based on the mode by

Vachaud et al. (1985)[68], Grayson & Western (1998)[19], Pachepsky et al. (2005)[52]. MRD gives

information about the spatial stability of the data set. It is defined by Equation 2:

t

j j

jjii

S

SS

t 1

,1 (2)

where: jiS , = soil moisture value of the jth sample at the ith site of n sites within the study region

(cbar).

43

jS = soil moisture computed average among all sites for a given date and time, j ( j =1 to t)

(cbar).

This value is important to evaluate how close the site’s measurements are to the average of a

bigger area, or how much they differ.

The original field database presented eight different locations, with two samples each, taken at

slightly separated points (Figure 10): these two points were considered as sites of their own,

therefore 16 different positions were accounted for the calculation of the MRD (16 = n, therefore i

goes from 1 to 16). 21 days (t = 21, therefore j goes from 1 to 21) out of a total of 23 available were

considered for the analysis (Table 5), since the first and the last day (respectively April 27th and

September 27th) of the time range did not present any measurement for the locations SWL1,2 and

PWL1,2 (Table 6). It must be remembered how each day represents a week, since measurements

were regularly taken one single day for 23 consecutive weeks from April to September.

All sites presented a soil moisture value for the first 8 feet (2.44 m) of soil: in this work only the first

6 were considered (1.83 m), since the satellite soil moisture values were calibrated to a soil column

of only 1.6 m. The mean out of these 6 feet was used for the calculation. A matrix was assembled,

with the 16 sites as rows and the 21 weeks as columns, and the cells were filled with the soil

moisture means of 6 feet. Equation 2 (see page 42) was then applied, obtaining values between -1

and 1. For each site, the mean and the standard deviation of its set of measurements was then

calculated. These two statistical parameters were eventually used to produce and xy-error graph,

where each site’s MRD was plotted against its rank (see Chapter 5.6): the rank indicates how high

is the level of moisture in the soil in respect to the general average.

The second step for modifying the scale of field soil moisture was to test its temporal stability. This

was achieved by calculating the Spearman’s rank coefficient. This coefficient does not deal with

the raw soil moisture data, but with the sites rankings (i.e. how dry or wet a soil is), calculating their

correlation from one week to the other, and therefore assessing the temporal stability of the

dataset. It is defined by Equation 3 (Vachaud et al., 1985[4]; Cosh et al., 2004[4]):

)1(

)(6

12

1

2',,

nn

RR

rs

n

i

jiji

(3)

where: Ri, j = rank of the soil moisture, Si, j, at location i on day j, for a total of n days.

Ri,j = rank of the same location i for day j’ when the sites are ranked in order from dry to

moist, and each assigned a number.

The same matrix as for the MRD calculation was used as a starting point, then the Spearman’s

ranks were calculated for all values.

44

5. Results

All collected data were joined together into spreadsheets, separating the two groups of points

(Figure 15) and the four different soil types. The two seasons, summer and winter, were instead

considered together, in order to better display the difference in conditions from one time to the

other. From such organized set of data, statistical and graphical analysis, were performed.

5.1. Correlation Coefficient

In order to understand what kind of relationship exists between precipitation, soil moisture,

groundwater depth, NDVI index, temperature, a correlation coefficient analysis was performed.

This coefficient gives as result numbers that express the strength of the correlation between

variables, and whether that is positive or negative (Rummel, 1976)[57]. A perfect and positive

correlation between two parameters would give a value of +1, a perfectly negative correlation

would result in a value of -1; in both cases the two variables would be completely dependent from

each other. When the result is 0, it means that the variables are independent, hence when one

increases, the other can decrease or increase too. In the specific case, the crucial point was to find

out more about correlations between soil moisture and the other parameters, to see if there was a

trend when considering both seasons together or separately, or if just precipitation and

temperature effect could be detected by this method.

Correlation matrices have been calculated for each group for winter and summer, and for clay loam

and gravelly loam. Results are presented in Table 8 - Table 13. Table 14, instead, summarizes all

the results.

45

Table 8: Correlation matrix for group 1 (winter & summer) – clay loam.

Prec. Soil

m.

Grw

depth

NDVI Temp

Prec. 1

Soil m. 0.9 1

Grw depth -0.5 -0.75 1

NDVI -0.59 -0.44 0.34 1

Temp -0.88 -0.78 0.52 0.66 1

.

Table 9: Correlation matrix for group 1 (winter) – clay

loam.

Prec. Soil

m.

Grw

depth

NDVI Temp

Prec. 1

Soil m. 0.71 1

Grw depth -0.02 -0.64 1

NDVI -0.27 0.16 -0.22 1

Temp -0.52 0.02 -0.46 0.63 1

Table 10: Correlation matrix for group 1 (summer) - clay

loam.

Prec. Soil

m.

Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.68 1

Grw depth -0.3 -0.41 1

NDVI -0.18 -0.21 0.37 1

Temp. -0.24 0.24 0.13 0.27 1

Table 11: Correlation matrix for group 2 (winter & summer) - gravelly loam.

Prec. Soil

m.

Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.88 1

Grw depth -0.30 -0.45 1

NDVI -0.80 -0.61 -0.02 1

Temp. -0.92 -0.79 0.16 0.85 1

Table 12: Correlation matrix for group 2 (winter) - gravelly

loam.

Prec. Soil m. Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.68 1

Grw depth -0.46 -0.62 1

NDVI -0.46 0.041 0.12 1

Temp. -0.73 -0.12 0.09 0.67 1

Table 13: Correlation matrix for group 2 (summer) -

gravelly loam.

Prec. Soil

m.

Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.099 1

Grw depth -0.22 -0.66 1

NDVI -0.08 0.58 -0.6 1

Temp. -0.57 -0.007 -0.15 -0.21 1

46

5.1.1. Winter + Summer

(Table 8, Table 11) Both groups show strong positive correlation between soil moisture and

precipitation, and a slightly weaker negative correlation with temperature. In general, the more it

rains, the wetter the soil is; inversely, the higher is the temperature, the drier is the soil. Since

precipitation and temperature are the two input parameters in the satellite-soil moisture model

(their sources are respectively the CPC Monthly Global Precipitation and the Monthly Global

Reanalysis/CDAS Temperature, both with a global scale), when comparing soil moisture with the

same data sources, it would be logical to find a strong correlation. However this work compared

soil moisture with precipitation and temperature values coming from another source, the CDEC

stations network database, with a watershed scale. A different result than the one obtained with the

correlation matrix would mean that the model does not support different data sources than its own.

On the other hand, this high correlation can be a proof that NOAA’s soil moisture data can be

reliable from a precipitation and temperature point of view, even when comparing them with finer

scaled measurements.

Group 1 records also a medium negative correlation linking soil moisture and groundwater depth,

while this is not the case for group 2. Since this does seem to get along neither with the results

obtained for single seasons nor with the groundwater readings, for they show a mean shallower

table around group 2 (which should mean a clearer correlation), this relationship is discussed

further for the single seasons.

A rule connecting both soil moisture and NDVI is difficult to find, since the latter represents a very

punctual information dependent on several factors, therefore with the potential to change radically

from one field to the next, or from one soil type to another. Indeed, if a certain point was irrigated, it

could show a positive correlation between soil moisture and NDVI; otherwise this correlation would

be very weak. The general trend is a negative relationship connecting the two factors, although

very weak and, when considering group 2, only for one soil type (gravelly loam, Table 11)

5.1.2. Winter

(Table 9, Table 12) The two groups show a medium positive correlation between soil moisture and

precipitation, mainly due to the high amount of rainfall in this season that positively contributes to

the moisture of the soil. They also record a medium negative correlation linking soil moisture to

groundwater depth. Groundwater is shallower in winter and it gets closer to the detection limit of

the satellite, therefore its relationship with soil moisture becomes stronger. On the other hand,

there is almost no association of soil moisture with temperature, since the latter sharply drops in

this season, nor with NDVI, since winter is not the harvesting season and the index gets closer to

0. All soil types maintain similar ratios but for gravelly loam in group 1 (see Appendix A), which

shows a slightly stronger negative correlation with NDVI.

47

5.1.3. Summer

(Table 10, Table 13) Group 1 shows a medium positive correlation between soil moisture and

precipitation, although the amount of rainfall in summer is very low, while group 2 does not have it.

Since both groups were assigned relatively similar values of rainfall, this difference in correlation

strength must be due to soil moisture differences: as average, group 2 recorded higher soil water

content than group 1; this difference might make it harder, in the second group, to detect a

relationship connecting the two parameters.

Group 2 shows a medium to weak negative correlation with groundwater depth. Considering that

weak summer rainfalls were not a decisive factor for the soil wetness, the main influence could

have come from groundwater, which was relatively shallow, showing low fluctuations between the

two seasons. This relatively stable groundwater table could have been fed by slow water infiltration

in winter or by higher irrigation rates in summer, but also by snow melting during spring (group 2 is

closer to the mountains, in a narrower part of the valley). As explained before, a shallower

groundwater is easier to detect by satellites, therefore the correlation should be stronger. The

same conditions were not recorded for group 1, which had a much deeper groundwater table in

summer. Connection amid soil moisture and NDVI is not relevant for group 1, and weakly positive

for gravelly loam, loam and sandy loam of group 2 (see Appendix A): then, the higher the NDVI,

the more is the water content in the soil. This might be interpreted as irrigated, thus healthy

vegetation that positively contributes to soil moisture. Excluding the NDVI, the different soil types

show similar trends (see Appendix A).

Table 14: Correlation between soil moisture and the other parameters for group 1 and 2, for summer and winter together

and for the two separate seasons.

GROUP 1 GROUP 2

Winter + Summer

- Strong positive correlation with precipitation

- Strong/Medium negative correlation with temperature

- Medium negative correlation with groundwater depth

- Loam and sandy loam: Medium/Weak negative correlation

with NDVI

Winter + summer

- Strong positive correlation with precipitation

- Strong/Medium negative correlation with temperature

- Clay loam and gravelly loam: Weak negative correlation with

NDVI

Winter

- Medium positive correlation with precipitation

- Medium negative correlation with groundwater depth

- Gravelly loam: Weak negative correlation with NDVI

Winter

- Medium positive correlation with precipitation

- Medium/Weak negative correlation with groundwater depth

Summer

- Medium positive correlation with precipitation

Summer

- Medium negative correlation with groundwater depth

- Gravelly loam and loam: Weak positive correlation with NDVI

48

5.2. Principal Component Analysis

The Principal Component Analysis (PCA) is useful in reducing the original number of variables of a

multi-variable dataset to a smaller one, by highlighting the most important, or “principal

components”: these will have the largest possible variances within the dataset (Davis, 1986[10];

Harper, 1999[22]). When considering the dataset as a cluster of points, the principal component

first axis passes through the centroid of the cluster and minimizes the square of the distances of

each point to that line: along this line (called eigenvector) the maximum variation of data can be

found. The second principal component axis (an eigenvector too) must be completely uncorrelated

to the first one and perpendicular to it. The principal components are described also by a peculiar

eigenvalue, a number that defines the importance of a component. Each of the variables has its

own eigenvalue: the highest one is for the most significant component. Hence, an eigenvalue

represents the percentage of variance that a component has. When the first variables of the set

cover already most of this percentage, the remaining ones can be ignored: this would mean losing

data, but they should not be relevant for the result. This work deals with five different parameters,

hence five different components. The first thing that had to be done before performing the PCA

was to normalize the data set, because each parameter was expressed in a different unit. Hence,

each value was modified by applying Equation 4:

(4)

xxy

Where: y = standardized value

x = original value

x = arithmetic mean

σ = standard deviation

The eigenvalues were thus calculated for the modified dataset (Table 15 and Table 16). Figure 26

and Figure 27 show a representative example of PCA results, relative to lithology “clay loam” of

both groups. The other lithologies can be found in the Appendix B.

49

Table 15: List of eigenvalues and percentage of

variance for the five variables of the dataset, after performing the PCA for the lithology Clay loam of group

1.

Eigenvalue % variance

Precipitation 3.59 71.93

Soil moisture 0.76 15.25 Groundwater depth 0.47 9.35

NDVI 0.15 3.02

Temperature 0.02 0.45

Table 16: List of eigenvalues and percentage of

variance for the five variables of the dataset, after performing the PCA for the lithology Clay loam of group

2.

Eigenvalue % variance

Precipitation 3.4 68

Soil moisture 1.04 20.94

Groundwater depth 0.39 7.92

NDVI 0.1 2.09

Temperature 0.05 1.03

Table 15 and Table 16 show that more than 85% of the variance is covered by precipitation and

soil moisture. Precipitation is the main input for soil moisture model, therefore it was expected it

would represent the main eigenvector. Soil moisture represents axis 2, perpendicular to it. To help

choosing the principal components, a Scree plot was generated (Figure 25), which displays the

eigenvalues associated with a component or factor in descending order versus the number of the

component or factor [72]. The blue line, representing the percentage of variance, shows a break in

slope immediately after the second principal component which, together with the first, covers most

of the variance.

Figure 25: Scree-plot for Clay loam of group 1, showing how much data variance, in %, do the different variables

represent. When the line slope breaks, most of the variance is covered and the principal components can be defined.

0 1 2 3 4 5

Component

0

8

16

24

32

40

48

56

64

72

Eig

enva

lue %

50

Figure 26: Scatter plot for the lithology Clay loam of group 1. The horizontal axis represents precipitation, while the

vertical axis represents soil moisture. The points are the different months, while the green lines are the biplots, which show towards which direction the variables increase, and help understanding their mutual relationship. Different clusters of points are grouped together, and the main conditions inside are highlighted as bullet points. For the other soil types

and groups, see Appendix B.

Figure 27: Scatter plot for the lithology Clay loam of group 2. The horizontal axis represents precipitation, while the

vertical axis represents soil moisture. For the other soil types and groups, see Appendix B.

51

In the resulting scatter plots (Figure 26, Figure 27) all months are plotted as points, in the

coordinate system given by the two main components. Additionally in the graph, the biplots are

displayed (green lines): they help visualize the direction towards which the different variables

increase or decrease and their correlation, which reflects the results seen with the correlation

matrix analysis (see Chapter 5.1). The statements below are valid for both groups, except when

specified:

- Strong positive correlation between soil moisture and precipitation (see Table 8, Table 11).

- Negative correlation between soil moisture and groundwater depth, although this is

stronger in group 1 than in group 2 (the biplots for group 1 are almost on the same line).

The same result was displayed with the correlation matrix (Table 8, Table 11).

- Negative correlation between soil moisture and NDVI/Temperature (Table 8, Table 11).

- Very strong negative correlation between precipitation and temperature.

- Weak positive correlation between temperature and groundwater depth.

The biplots were also useful to understand the conditions ruling the positioning of the points. By

looking at Figure 26 and Figure 27, two main groups of points can be distinguished along the

biplots of precipitation and temperature. The differences are listed as bullet points next to the group

bubbles. There is a clear distinction between summer (right side) and winter months (left side).

Summer is characterized by high temperature and NDVI and deeper groundwater depth, as well as

low soil moisture and precipitation. Winter records instead high soil moisture and precipitation,

shallow groundwater, low temperature and NDVI.

52

5.3. Two-Variables Scatter Plots

A series of xy-graphs was created in order to have a further understanding of the relationship

between soil moisture and the other parameters, and to find out if some other influences, apart

from precipitation and temperature, could be detected on soil moisture trends. The lithology loam

has been plotted in all graphs.

5.3.1. Soil Moisture - Precipitation

Figure 28: Scatter plots of soil moisture against precipitation for group 1 (left) and group 2 (right). Also shown is the trend

line, with r2 value, while the outliers are labeled.

Both groups (Figure 28) show a clear positive correlation with precipitation: the more it rains, the

higher is the soil moisture. This value was generally higher in winter months and lower in summer,

therefore a clear separation between summer (bottom-left) and winter cluster (top-right) can be

seen. This strong positive relationship shows that satellite-based soil moisture worked well with

precipitation data of much more detailed resolution (CDEC meteorological stations) than those of

the soil moisture model. Soil moisture in winter records a much larger scattering than in summer

months.

The two groups also produce the same outliers, April 2013 and February 2014. April 2013

recorded the lowest precipitation amount for a winter month during the 9 analyzed years, although

soil moisture was supported by a relatively wet winter, therefore it did not drop below the average.

February 2014, instead, produced a very low soil moisture value, mainly due to a very cold winter

with below average rainfalls.

53

5.3.2. Soil Moisture - Temperature

Figure 29: Scatter plots of soil moisture against temperature for group 1 (left) and group 2 (right). Also shown is the trend

line, with r2 value, and highlighted are the outliers.

Correlation between soil moisture and temperature is negative (Figure 29): the higher is the

temperature, the lower is the wetness of the soil. Summer months are localized thus on the top-left

of the graph, while winter months are scattered at its bottom. The same concept seen for

precipitation also works for temperature: the correlation, although not very strong, indicates that the

soil moisture model worked well also with different sources of data than those used for the model

itself, since also temperature values came from CDEC stations.

Outliers for group 1 are February 2006 and February 2014. While February 2014 low soil moisture

is to be attributed to the low precipitation and temperatures of the previous months, as previously

seen for Figure 28, not only February 2006 recorded a high amount of rainfall, but the month

before was one of the most rainy in the record of last years, with more than 170 mm of

precipitation; this sharply increased the soil moisture value, shifting the point to the right of the

graph (Figure 29, left).

Group 2 presents, as outliers, February 2014, like in group 1, and February 2012, the latter

characterized by low temperatures and precipitation below the average for that month, around 20

mm.

54

5.3.3. Soil Moisture - NDVI

Figure 30: Scatter plots of soil moisture against NDVI index for group 1 (left) and group 2 (right).

Correlation with NDVI (Figure 30) does not present the same strong results as previously seen

both for precipitation and temperature. One reason is probably that the NDVI index is not a

parameter included in the soil moisture model. The situation could be further complicated since the

NDVI index represents a very punctual information and each month is strongly influenced by

several factors: whether the field is cultivated or not, the different crops, whether it is irrigated or

not at that specific time, how much precipitation it receives compared to the others, the occurrence

of fires, sunlight exposition, together with possible interferences on the satellite (Gutmann,

1999)[21]. That is why, although a general division between summer and winter months can be

traced, points from the same season do not cluster closely together. On the conditioning that an

irrigated area can have on soil moisture, Panciera et al. (2009)[53] stated how cropped areas

exhibited persistently wetter-than-average conditions, and forested areas exhibited drier-than-

average conditions, while grassland sites were more representative of the area average soil

moisture conditions. An important assumption is that, as an average, higher NDVI indices were

recorded in summer than in winter, which could be due to the harvesting time coinciding with

summer for most of the crops, and with the higher amounts of irrigation in the same period. Only in

few cases the indices are negative values, which would represent the ideal condition of not-

growing vegetation: this high average should have been caused mainly by the spread irrigation

activity occurring in summer. Between the two groups, a stronger scattering of winter months is

visible for group 1, while a better division between summer and winter is possible in group 2.

55

5.3.4. Soil Moisture – Groundwater Depth

Figure 31: Scatter plots of soil moisture against groundwater depth for group 1 (left) and group 2 (right).

These graphs (Figure 31) show the groundwater depth from the surface (with a descending

vertical axis) in relation to soil moisture. Group 1 shows a general negative correlation: the

shallower the groundwater, the higher the soil water content. That is mostly possible because this

group presents a clear difference in depth between winter and summer groundwater, which

defines the gradient of the trend: indeed, the depth for this group ranges from 2 m to 7 m.

On the other hand, group 2 does not offer the same clear correlation: winter and summer months

are often mixed, because the groundwater level did not fluctuate much during the year, so the

differences between winter and summer are rather small. This lack of fluctuation might have been

caused by several reasons, like a more intense irrigation regime on the area, which increases the

infiltration rate in the soil during summer. In this direction, the integrated hydrological model by

Foglia et al. (2013)[18] assigned to the corresponding fields a mean amount of 0.04 m3/month

irrigated water between February 2006 and August 2011. Even the upstream position of group 2,

in a narrower sector of the valley, could be the reason why surface water had less time and

space to infiltrate down to a greater depth than a couple of meters. Furthermore, this side of the

valley presents a lower density of pumping wells than the northern side, which could be why

group 1 displays a higher scattering of values. However, based on Foglia et al. (2013)[18], group

1 area was assigned a mean irrigation amount for the same time period of 0.10 m3/month.

This distribution of values is important to clarify why group 2 hosts a good correlation between

soil moisture and groundwater depth also in summer (Table 13) while group 1 does not: while the

soil moisture model is based on a soil column of 1.6 m thickness, with a porosity of 0.47 (Fan et

56

al., 2004)[16], the groundwater level in this group ranges between 1.5 m to 3 m ca. Because the

soil types considered here can have a different porosity than 0.47 (loam has a mean porosity

between 0.3 and 0.44, source: Missouri Department of Natural Resources-Soil Type

Determination Guideline [42]) and the soil succession can be heterogeneous, the 1.6 m value

should not be considered as fixed, but with a certain level of oscillation.

5.4. Multi-Variables xy-Line Plot

These graphs (Figure 32, Figure 33) allow to present all five different parameters together. By

plotting all of them as percentages, their relationships become clearer, and it is possible to

compare their trends over time, to see if they are regular or with any interference.

Group 1 shows:

- A perfectly opposite trend between soil moisture and temperature but almost the same

trend with precipitation.

- A general opposite trend between soil moisture and groundwater, which gets more

confused past the year 2011.

- A negative correlation between soil moisture and NDVI, starting from 2007.

Group 2 shows:

- The same relationship of group 1 regarding soil moisture with temperature and

precipitation.

- A relationship between soil moisture and groundwater that is not well defined, since

groundwater fluctuations between winter and summer for this group are weaker, therefore

summer and winter levels can be very similar. Other methods result clearer in showing

this relationship (correlation matrix and ternary plots, see Chapter 5.1 and 5.5).

- NDVI and soil moisture have a relatively defined negative correlation, until 2012.

57

Figure 32: Multi-variable xy-line plot for group 1, relating together the five analyzed parameters, expressed as

percentages, with time on the x-axis, where the unit is in month; however, only the processed months are labeled.

Figure 33: Multi-variable xy-line plot for group 2, relating together the five analyzed parameters, expressed as

percentages, with time on the x-axis, where the unit is in month; however, only the processed months are labeled.

58

5.5. Ternary Plots

The main purpose of the ternary plots (Figure 34) is to correlate together precipitation and soil

moisture, which are the two main components along which most of the dataset variability lay (as

per the PCA, see Chapter 5.2), with groundwater depth, which is an important correlated factor,

as per the correlation matrix analysis (see Chapter 5.1). All the values plotted in the graphs were

first converted into percentages, by considering the highest value recorded in the dataset as

100%, and all soil types were joined:

- For groundwater depth and soil moisture, the highest value recorded in the 17 analyzed

months was taken as 100%. These values are shown next to the corresponding axis titles

in the plots

- For precipitation, the highest value recorded in all months between 2006 and 2014 was

considered as the maximum percentage, this month being December 2012 with a rainfall

of 182,4 mm.

In both groups, there is a sharp separation between summer and winter months, having summer

a much lower precipitation rate than winter (less than 10% of the total for summer, between 20

and 40% for winter). Precipitation is therefore the main responsible for the vertical distribution of

points. Groundwater and soil moisture are together responsible for the horizontal distribution of

points. Soil moisture stretches from 25% to 60% for both groups. Groundwater depth ranges

between 10 and 50% for winter months, and amid 50 and 70% for summer months, therefore it is

the major responsible for the horizontal distribution of the points.

Figure 34: Ternary plots for group 1 (left) and group 2 (right), plotting together groundwater depth, soil moisture and

precipitation as %. The blue dots represents the different months for all soil types, the black lines are the main trends of the points, the red lines in group 2 plot are instead the secondary trends. The outliers are labeled.

59

5.5.1. Winter

Winter trend in group 1 shows how the soil moisture, in a precipitation change of around 20%

(from 20% until 38%), moves for the 25% of its range (from 30% to 55%) together with a

variation of groundwater depth from 10% to 50%.

In group 2, the same winter trend has percentages of precipitation between 20% to 35%, of soil

moisture from 30% to 50%, and groundwater depth from 15 to 55%.

This distribution for both groups demonstrates how most of the variability of soil moisture is well

represented by an even larger distribution of groundwater values, while precipitation do not

show the same resolution, since all soil moisture variability is expressed by a range of only 15-

20% of precipitation values. This clear correlation between soil moisture and groundwater

should be supported by the shallower level of the latter, around the satellite’s detection limit:

indeed, the 10/15-50% of the maximum depth would mean 0.9 m to 4,7 m for group 1, and 0.5

m to 1.6 m for group 2. Group 1 maximum value seems to be too deep: hence, the correlation

may be given by the large variability of depth in terms of values, which allows the points to

distribute over a long segment of the graph and to produce a trend line with soil moisture. This

would mean that few large values of groundwater depth inside the dataset can influence the

trend and the actual correlation. Hence, only group 2 seems suitable to represent the

relationship linking groundwater depth and soil moisture.

5.5.2. Summer

Summer trend in both groups has a weaker slope than winter’s, mainly due to a deeper

groundwater table (between 40-45% and 70%) and to lower amounts of rainfall (for a maximum

of 10%), with a soil moisture varying between 25% and 40-45%. Still, group 2 displays a slightly

better slope than group 1, perhaps as evidence that its shallower groundwater is more suitable

to represent a correlation with soil moisture.

Analyzing group 2, there is also a secondary opposite trend for both winter and summer (Figure

34, right). Based on it, for an increase in precipitation, there is a decrease in soil moisture. This

goes together with a lowering of the groundwater level, which might be one explanation. This

statement is though weak when considering winter, since an increase in precipitation should rise

groundwater, even because there is less pumping in that season. Therefore the secondary

trend is considered only for summer, since an increase in precipitation then would represent

only few mm of rainfall, which would not affect much soil moisture, potentially reduced, instead,

by a drop in groundwater, more common in summer due to higher pumping rates. Considering

these assumptions, this trend might be seen as another evidence for a relationship between

satellite-soil moisture and groundwater level, although in opposite conditions than those seen

for the major trend. Hence, group 2 should be considered as the more proper to express this

correlation.

60

5.6. Spatiotemporal Stability Analysis of Gravimetric Soil Moisture

The spatiotemporal stability analysis is a useful statistical tool to upscale field measurements of

soil moisture, with a spatial validity of only few cm (Evett and Parkin, 2005)[14], to a watershed

level, with a validity of some km. The necessary steps are the calculation of the mean relative

difference (MRD), with standard deviation (SD) and root mean square difference (RMSD) (Cosh

et al., 2012)[7] for all measured sites, to assess the spatial stability of the area, and the

computation of the Spearman’s rank coefficients for the measured period, to assess the

temporal stability of the area. The matrices for the calculation can be found in Appendix C.

The graph of Figure 35 plots the MRD for the 16 sites where gravimetric field soil moisture was

measured, against the sites ranks, which indicate how dry or wet compared to the valley’s

average the sites are. Also plotted as error bar is the SD for each site with a multiplier of one,

which displays how spread out their dataset is from the average. The exact data are also listed

in Table 17. With this graph, the more representative sites of the soil moisture average for the

entire watershed can be highlighted: based on the assumption behind it, when a site’s MRD is

close to zero, then its mean is close to the overall average; a small SD indicates also a low

variance of this estimate (Cosh et al., 2004[4]; Cosh et al., 2006[5]).

Figure 35: Mean relative difference plot for the Scott Valley gravimetric soil moisture network. The error bars are ± 1

standard deviation. The 0 line represents the average for the whole valley.

61

Table 17: Statistical parameters for assessing spatiotemporal stability of the 16 analyzed sites. The included

parameters are Mean Relative Difference (MRD), Standard Deviation (SD) and Root Mean Square Difference (RMSD).

Site MRD SD RMSD

SWL1 -0.65 0.14 40.74

SWL2 -0.59 0.23 39.97

PWL1 -0.58 0.21 35.92

FP2 -0.46 0.19 32.37

MP1 -0.44 0.19 25.76

HWL2 -0.39 0.34 24.92

HWL1 -0.31 0.33 27.78

HP1 -0.28 0.15 20.74

MP2 -0.23 0.5 31.95

HRWL1 -0.03 0.39 18.31

FP1 0.01 0.57 34.42

PWL2 0.39 0.54 27.55

HRWL2 0.4 0.88 57.96

HP2 0.48 0.63 38.43

MRP2 1.18 0.46 68.33

MRP1 1.49 0.56 90.53

The high variability of MRD values between the different locations may be due to different

reasons: the low spatial density of the measuring sites, around one point per 11.25 km2, which

makes the results more sensitive to non-local effects such as precipitation (Vanderlinen et al.,

2012)[70]; the temporal scale; discrete soil properties, since the sites can be on different soil

types; vegetation, which during the growing season may affect the stability due to heterogeneous

transpiration (Teuling and Troch, 2005)[61]. However, also time-stable sites having a non-zero

MRD could represent the area’s average, provided that their offset from the mean value is known

(Grayson and Western, 1998)[19].

That being said, by analyzing Figure 35 and Table 17, HRWL1 and FP1 are the sites with the

closest MRD to the average (respectively -0.03 and 0.01). However, FP1 presents larger SD

(0.57) and root mean square difference (RMSD = 34.42), therefore HRWL1 was preferred,

because it shows a higher temporal stability due to the less inherent error from a lower SD, equal

to 0.39 (Guber et al., 2008[20]; Schneider et al., 2008[58]) and the lowest RMSD (18.31).

62

Site HP1 is not far from the average, with a MRD of -0.28, its SD is the second lowest of the set

(0.15) and the RMSD is equal to 20.74. Both sites are inside the valley, on the alluvium, with a

very low angle of slope: Jacobs et al. (2004)[28] defined locations with a mild slope (0.9 to 1.7%)

as those exhibiting time-stable features with MRD close to zero. In the same direction, Grayson &

Western (1998)[19] expected that sites in field-neutral locations may represent field means.

However, the same slope condition are common for other sites as well, therefore other factors

were considered too to explain this differentiation. The two sites lay on different soil types:

HRWL1 is on loam, HP1 is on gravelly loam. Kim and Stricker (1996)[31] suggested that fine

loamy soil can show stronger effects of soil spatial heterogeneity on components of the water

budget than what happens for a sandy loam soil, for example, or coarser. Another cause of

distinction can be the different irrigation methods: HRWL1 is on a field with wheel line technique,

HP1’s field displays center pivot. A strong influence could be given by the presence of a creek

near HRWL1, which might increase the variability of the site through its seasonal changes. HP1,

on the other hand, is not close to any stream.

* * *

The Spearman’s rank coefficients are values going from 0 to 1, where 0 indicates a lack of

temporal stability for a certain time period, while 1 indicates a stable time: this would mean that

wet areas remain wet and vice versa for dry areas. The results obtained from the calculation of

the ranks, which can be seen in detailed in the Appendix C, were plotted against time in a gray-

scale matrix plot (Figure 36): light colored pixels represent low ranks (close to 0) and unstable

conditions of soil moisture between two crossed weeks; dark pixels, instead, represent high ranks

and stable soil moisture conditions. The lower right and upper left corner are characterized by

relatively dark pixels, indicating correlation coefficients of more than 0.75: this means there is a

strong spatial stability of the average soil moisture across the region between weeks 1 and 6, and

between 11 and 21. On the other hand, the lower left corner is composed by relatively light pixels,

indicating correlation coefficients of less than 0.5 and low stability. Therefore relating weeks 1 to

6 with weeks 10 to 20, the correlation is not good: this might indicate that between weeks 9 and

11 there is a distinct change in moisture conditions.

The rank distribution displays a partial lack in spatiotemporal stability of the average soil moisture

across the region through the complete time measurement. In the first 7 or 8 weeks there is a

relatively stable moisture state, (dark pixels in the upper left corner), followed by a change in

moisture conditions in the middle and eventually, in the latest weeks, by stable conditions again.

This change in conditions in the middle weeks seems to coincide with an above average

precipitation in the month of June (weeks 6 to 9), as shown in Table 18. This would demonstrate

that Spearman’s ranks are strongly influenced by short and possibly heterogeneous rainfall

events, because they give an uneven input to the area, which could affect one part of it and leave

63

relatively unmarked the rest; hence, this kind of stability validation would only have a weight for a

long-term validation (Cosh et al., 2004)[4]. On the same concept, Teuling & Troch (2005)[61]

found out how soil water content stability is reduced by drainage after rainfall. Table 18 is meant

to clarify the relationship between the ranks and precipitation: each week of the analysis is

associated with the corresponding monthly precipitation mean.

Figure 36: Matrix plot representing the Spearman’s ranks for the 21measured weeks. Dark pixels represent a high

rank, hence high temporal stability. White pixels, on the other hand, stand for low rank and low stability.

Table 18: Amount of monthly precipitation for each of the 21 weeks of the data collection campaign of 2012.

Weeks

notation

Week’s

days

Monthly

precipitation (mm)

1 May 4th

3.55

2 May 10th

3 May 16th

4 May 23rd

5 May 30th

6 June 6th

18.54 7 June 13

th

8 June 20th

9 June 27th

10 July 5th

1.27 11 July 11

th

12 July 18th

13 July 26th

14 August 2nd

1.52

15 August 9th

16 August 16th

17 August 23rd

18 August 30th

19 September

6th

0 20 September

13th

21 September

20th

64

6. Conclusions

Validation of satellite-based soil moisture is a key step in the attempt to prove the suitability of

remote sensing products in representing the reality of soil moisture distribution along the Earth.

Remote sensing is, nowadays, the only available solution to the lack of a worldwide distributed

network of soil moisture measuring stations. However, despite being a fast and economical source

of information, satellite data lack in accuracy mainly because of their small resolution. What this

implies is that they are not suitable for detecting small scale environmental components or

heterogeneous climatic events, which might still be relevant for the final soil moisture distribution.

One of the attempts of this work was to test the accuracy of the NOAA/NESDIS soil moisture data

for the Scott river watershed in Northern California (USA), by checking which parameters they are

able to detect, despite being model-generated, not directly measured. Together with soil moisture,

five other different parameters were collected: precipitation, temperature, groundwater depth, NDVI

index, soil type. All of them were joined together, in relation to time. A period of 9 years, from 2006

to 2014, was investigated, with focus on summer and winter season. The analysis was localized in

two small areas inside the watershed, one in the N and the other in the S. The dataset was

processed with the help of GIS techniques, mapping, graphical analysis and statistical testing.

The results showed that satellite-based values are strongly influenced by the original inputs given

by the soil moisture model. Precisely, NOAA’s model requires the input of precipitation and

temperature data from other global prediction databases. In this work, however, data of

precipitation and temperature from CDEC local stations network were considered, which have a

much finer resolution than NOAA’s model records, and they were compared with satellite-soil

moisture in order to find a correlation. Eventually, relationship between soil moisture and

precipitation was still strong, slightly weaker when considering temperature: this indicates that the

model worked well also with finer-scaled data.

No significant interaction between soil moisture and soil type was found, but this was expected

because the soil categories taken into account were not enough dissimilar, but rather varieties of

the loamy soil class. It is not excluded that the effect of lithology changes in soil moisture is crucial,

but satellite resolution did not seem accurate enough to detect it. NDVI was chosen as a crucial

factor for including vegetation into the test: since plants can influence the moisture content in the

soil, it was necessary to avoid as much as possible areas with healthy vegetation. However, the

results were not satisfactory, since no clear correlation between soil moisture values and NDVI

during the tested years could be found. There might be several reasons for this: first, it was difficult

to find locations that had recorded for the whole period a negative index, since the area is

frequently irrigated, being agriculture and pasture the main activities, and high NDVI values can

easily be recorded also in summer, the harvesting period. Second, NDVI is a punctual information,

that might change from one field to the next depending on the land use, irrigation amount, sun

65

exposition, localized precipitation events, etc. Therefore it was a demanding task to try and

correlate two parameters, soil moisture and NDVI, with such a discrepancy in scale. Better results

could be obtained in different environments, where agriculture is not the main activity and natural

vegetation is more dependent on natural factors like precipitation and temperature.

The last parameter to be considered was groundwater depth. Since it is not a surface parameter,

the key aspect to consider was the depth reachable by satellites. Based on the soil moisture-model

specifications, its predictions are based on a soil column of 1.6 m, whit a mean porosity of 0.47.

The results showed an evident interaction between soil moisture and groundwater depth, for both

areas, in winter time, when the groundwater table is shallower. But most importantly, a medium

correlation was detected in summer, but only for the southern group, where fluctuations of

groundwater along the year were not strong, and the level remained more or less constant,

between 1 and 3 m below the surface. This depth could, perhaps, still be reached by satellites:

indeed, the loamy soil of the valley, which is the most frequent soil class, can have different

porosities, between 0.3 and 0.44. Furthermore, the soil succession can easily include different soil

types, thus it can be far from uniform. Hence, the value of 1.6 m should be considered fluctuating

up to a certain level. The fact that group 1 detected a correlation between soil moisture and

groundwater in winter (Table 9), despite its deeper groundwater table (between 0.9 m and 4.7 m),

might be due to the larger range of depths it displayed (Figure 34), compared to group 2. Probably,

a wider distribution of numbers made it possible to “intercept” more soil moisture values and make

the correlation, otherwise impossible for depths of 4 to 5 m. This could be the reason why the

same correlation was not displayed in summer, when the water was even deeper (down to 9.5 m)

but with a smaller range of values. Group 2 was considered more ideal to represent the correlation

(Figure 34), since both seasons presented it (Table 12; Table 13), and the groundwater depth

ranged around values which were closer to the model’s soil column. The right ternary plot in Figure

34 showed a secondary trend in summer, based on which soil moisture decreases together with

groundwater depth also when precipitation increases, because the latter’s influence during this

season is not significant, while the depth of groundwater can still influence the soil moisture

content. Finally, despite the low resolution of satellite data, and the large influence coming from the

model input data, precipitation and temperature, also groundwater effect could be detected, both in

condition of rising and dropping level.

The second step to validate the accuracy of satellite soil moisture is to compare it with field data,

when available. However, the step to overcome before doing this is to fix the difference in scale

between field samples (few cm) and satellite data (several km). For this work, a set of gravimetric

soil moisture measurements from 21 weeks of 2012, between May and September, was selected

to apply the method proposed by Cosh et al. (2004)[4], Jacobs et al. (2004)[28] and Cosh et al.

(2006)[5] for increasing the scale of field soil moisture up to a watershed extent. Following this

method, the spatiotemporal stability of the dataset was evaluated by calculating the mean relative

66

difference, with root mean square difference, and the Spearman’s rank coefficients of 16 different

sites inside the AOI. As a result, it was possible to define two suitable locations to represent the

watershed’s soil moisture variability. The site Harris Wheel line 1 (HRWL1) had the closest mean

to the average of the valley, but a higher standard deviation than Harris Pivot 1 (HP1), the second

chosen site, which had a slightly farther mean from the average but a smaller standard deviation.

The reason for the higher standard deviation of HRWL1 might be the proximity of a stream, which

may contribute to the higher variability of this site’s data, the field’s wheel line irrigation system or

its loamy soil. By analyzing the Spearman’s rank for each week, there was a general stability in soil

moisture distribution, with high stability in the first 6 weeks and in the last 10, indicated by rank

values close to 1. Between weeks 6 to 11, there was a lack in stability, probably due to a rainfall

amount, in the month of June, higher than summer’s average. This result may not necessarily

mean that there was a consistent lack of soil moisture constancy in the valley, but only that

precipitation patterns strongly affect the temporal stability rankings, especially when rainfall events

are short and heterogeneous, because they do not give a uniform input to all the watershed. This

can be a clear indication about how this method is mainly useful into assessing long-term stability

trends, which might overcome the influence coming from short-term climatic events.

The two offered sites, by taking into account the deviation from the average they can imply, could

be used in the future to establish a correlation with soil moisture satellite data. Since this work only

dealt with one year of field measurements, a longer time will be needed for a potentially fitting

correlation between the two data sources.

67

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Appendix A

Table A1: Correlation matrix for group 1 (winter & summer) - gravelly loam

Prec. Soil

m.

Grw

depth

NDVI Temp

Prec. 1

Soil m. 0.91 1

Grw depth -0.53 -0.71 1

NDVI -0.45 -0.5 0.3 1

Temp -0.88 -0.8 0.37 0.46 1

Table A2: Correlation matrix for group 1 (winter &

summer) - loam

Prec. Soil

m.

Grw

depth

NDVI Temp

Prec. 1

Soil m. 0.9 1

Grw depth -0.58 -0.72 1

NDVI -0.69 -0.59 0.42 1

Temp -0.88 -0.78 0.5 0.64 1

Table A3: Correlation matrix for group 1 (winter &

summer) - sandy loam

Prec. Soil

m.

Grw

depth

NDVI Temp

Prec. 1

Soil m. 0.9 1

Grw depth -0.58 -0.71 1

NDVI -0.71 -0.63 0.44 1

Temp -0.88 -0.78 0.5 0.65 1

Table A4:Correlation matrix for group 1 (winter) - gravelly loam

Prec. Soil

m.

Grw

depth

NDVI Temp

Prec. 1

Soil m. 0.71 1

Grw depth -0.32 -0.69 1

NDVI -0.41 -0.51 0.26 1

Temp -0.52 0.03 -0.53 0.37 1

Table A5:Correlation matrix for group 1 (winter) –

loam

Prec. Soil

m.

Grw

depth

NDV

I

Tem

p

Prec. 1

Soil m. 0.71 1

Grw depth -0.27 -0.63 1

NDVI -0.58 -0.24 0.04 1

Temp -0.52 0.03 -0.55 0.68 1

Table A6: Correlation matrix for group 1 (winter) –

sandy loam

Prec. Soil

m.

Grw

depth

NDV

I

Tem

p

Prec. 1

Soil m. 0.71 1

Grw depth -0.28 -0.64 1

NDVI -0.6 -0.31 0.08 1

Temp -0.52 0.03 -0.55 0.66 1

75

Table A7: Correlation matrix for group 1 (summer) - gravelly loam

Prec. Soil m. Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.66 1

Grw depth -0.16 -0.33 1

NDVI 0.47 -0.23 0.13 1

Temp. -0.24 0.21 0.3 -0.77 1

Table A8: Correlation matrix for group 1 (summer) -

loam

Prec

.

Soil

m.

Grw

depth

NDV

I

Temp

.

Prec. 1

Soil m. 0.67 1

Grw depth -0.5 -0.38 1

NDVI -0.46 -0.34 0.18 1

Temp. -0.24 0.23 0.15 -0.46 1

Table A9: Correlation matrix for group 1 (summer) –

sandy loam

Prec

.

Soil

m.

Grw

depth

NDV

I

Temp

.

Prec. 1

Soil m. 0.67 1

Grw depth -0.5 -0.39 1

NDVI -0.49 -0.41 0.2 1

Temp. -0.24 0.23 0.14 -0.44 1

Table A10: Correlation matrix for group 2 (winter &summer) - clay loam

Prec. Soil

m.

Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.88 1

Grw depth -0.27 0.39 1

NDVI -0.72 -0.51 0.031 1

Temp. -0.92 -0.79 0.13 0.77 1

Table A11: Correlation matrix for group 2 (winter

&summer) - loam

Prec

.

Soil m. Grw

depth

NDV

I

Temp

.

Prec. 1

Soil m. 0.88 1

Grw depth -0.25 -0.38 1

NDVI -0.45 -0.25 -0.37 1

Temp. -0.92 -0.79 0.09 0.49 1

Table A12: Correlation matrix for group 2 (winter

&summer) - sandy loam

Prec

.

Soil

m.

Grw

depth

NDVI Temp

.

Prec. 1

Soil m. 0.88 1

Grw depth -0.30 -0.44 1

NDVI -0.54 -0.37 0.21 1

Temp. -0.92 -0.79 0.19 0.51 1

76

Table A13: Correlation matrix for group 2 (winter) - clay loam

Prec. Soil m. Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.68 1

Grw depth -0.47 -0.56 1

NDVI -0.33 0.23 -0.03 1

Temp. -0.73 -0.11 0.15 0.77 1

Table A14: Correlation matrix for group 2 (winter) –

loam

Prec. Soil

m.

Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.68 1

Grw depth -0.47 -0.61 1

NDVI -0.18 0.23 -0.28 1

Temp. -0.73 -0.12 0.06 0.55 1

Table A15: Correlation matrix for group 2 (winter) –

sandy loam

Prec

.

Soil m. Grw

depth

NDV

I

Temp

.

Prec. 1

Soil m. 0.69 1

Grw depth -0.39 -0.55 1

NDVI -0.51 0.08 0.09 1

Temp. -0.73 -0.11 0.05 0.92 1

Table A16: Correlation matrix for group 2 (summer) - clay loam

Prec. Soil

m.

Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.09 1

Grw depth -0.22 -0.66 1

NDVI -0.10 0.21 -0.13 1

Temp. -0.57 -0.01 -0.08 -0.55 1

Table A17: Correlation matrix for group 2 (summer) –

loam

Prec. Soil

m.

Grw

depth

NDVI Temp.

Prec. 1

Soil m. 0.09 1

Grw depth -0.4 -0.55 1

NDVI 0.04 0.52 -0.64 1

Temp. -0.57 -0.03 0.61 -0.35 1

Table A18: Correlation matrix for group 2 (summer) –

sandy loam

Prec

.

Soil m. Grw

depth

NDV

I

Temp

.

Prec. 1

Soil m. 0.10 1

Grw depth -0.18 -0.66 1

NDVI -0.18 -0.46 0.19 1

Temp. -0.57 -0.008 -0.23 -0.33 1

77

Appendix B

Table B1: List of eigenvalues and percentage of variance for the five variables of the dataset, after performing the PCA for

the lithology gravelly loam of group 1.

Eigenvalue % variance

Precipitation 3.45 69.03

Soil moisture 0.73 14.68

Groundwater depth 0.64 12.86

NDVI 0.11 2.29

Temperature 0.06 1.14

Figure B1: Scatter plot for the lithology gravelly loam of group 1 after performing PCA.

78

Table B2: List of eigenvalues and percentage of variance for the five variables of the dataset, after performing the PCA for

the lithology loam of group 1.

Eigenvalue % variance

Precipitation 3.72 74.45

Soil moisture 0.64 12.75

Groundwater depth 0.41 8.28

NDVI 0.17 3.33

Temperature 0.06 1.18

Figure B2: Scatter plot for the lithology loam of group 1 after performing PCA.

79

Table B3: List of eigenvalues and percentage of variance for the five variables of the dataset, after performing the PCA for

the lithology sandy loam of group 1.

Eigenvalue % variance

Precipitation 3.75 75.08

Soil moisture 0.62 12.41

Groundwater depth 0 7.97

NDVI 0.17 3.4

Temperature 0.06 1.2

Figure B3: Scatter plot for the lithology sandy loam of group 1 after performing PCA.

80

Table B4: List of eigenvalues and percentage of variance for the five variables of the dataset, after performing the PCA for

the lithology gravelly loam of group 2.

Eigenvalue % variance

Precipitation 3.53 70.62

Soil moisture 1.09 21.86

Groundwater depth 0.23 4.56

NDVI 0.09 1.91

Temperature 0.05 1.03

Figure B4: Scatter plot for the lithology gravelly loam of group 2 after performing PCA

81

Table B5: List of eigenvalues and percentage of variance for the five variables of the dataset, after performing the PCA for

the lithology loam of group 2.

Eigenvalue % variance

Precipitation 3.02 60.48

Soil moisture 1.41 28.34

Groundwater depth 0.36 7.24

NDVI 0.15 2.93

Temperature 0.05 1

Figure B5: Scatter plot for the lithology loam of group 2 after performing PCA.

82

Table B6: List of eigenvalues and percentage of variance for the five variables of the dataset, after performing the PCA for

the lithology sandy loam of group 2.

Eigenvalue % variance

Precipitation 3.22 64.47

Soil moisture 0.9 18.01

Groundwater depth 0.69 13.73

NDVI 0.14 2.79

Temperature 0.05 0.99

Figure B6: Scatter plot for the lithology sandy loam of group 2 after performing PCA

83

Appendix C

Table C1: Gravimetric field measurements (centibar) for the sampled 16 sites, in 21 weeks.

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Week

Site

39.5

0

36.3

3

22.5

0

16.8

3

16.3

3

5.6

7

10.3

3

8.1

7

37.5

0

21.0

0

14.0

0

29.8

3

16.3

3

13.8

3

20.8

3

18.5

0

12.1

7

9.1

7

11.1

7

12.8

3

11.5

0

SW

L1

40.8

3

27.8

3

20.5

0

16.6

7

18.0

0

12.0

0

13.8

3

32.0

0

27.1

7

18.0

0

13.1

7

17.8

3

12.1

7

28.3

3

21.6

7

16.5

0

11.6

7

9.1

7

26.5

0

17.6

7

11.8

3

SW

L2

66.8

3

52.0

0

36.8

3

21.3

3

5.1

7

19.0

0

5.8

3

25.6

7

36.3

3

25.0

0

7.5

0

14.8

3

27.8

3

12.1

7

27.1

7

21.5

0

13.6

7

15.8

3

6.6

7

20.0

0

13.0

0

PW

L1

106

.17

78.1

7

66.0

0

53.6

7

47.0

0

64.0

0

52.5

0

61.3

3

75.5

0

62.0

0

42.1

7

90.5

0

101

.17

115

.17

105

.50

90.0

0

77.1

7

64.6

7

46.1

7

31.8

3

32.3

3

PW

L2

198

.83

165

.33

154

.33

135

.00

131

.00

133

.17

129

.67

197

.00

190

.33

177

.17

181

.67

161

.83

225

.33

186

.00

129

.17

94.0

0

92.5

0

59.5

0

58.8

3

44.3

3

36.6

7

MR

P1

181

.00

147

.67

127

.00

110

.67

109

.33

127

.00

130

.83

143

.50

147

.33

141

.17

172

.00

173

.67

159

.17

135

.17

109

.67

85.6

7

75.8

3

66.1

7

49.0

0

46.0

0

38.8

3

MR

P2

87.1

7

70.0

0

44.0

0

35.8

3

30.0

0

22.8

3

26.0

0

64.0

0

58.0

0

32.6

7

20.8

3

20.3

3

21.6

7

17.1

7

17.5

0

34.1

7

28.5

0

21.0

0

11.0

0

6.6

7

9.1

7

MP

1

179

.83

151

.00

72.5

0

41.5

0

31.1

7

36.3

3

42.0

0

114

.67

120

.33

53.6

7

30.6

7

24.1

7

25.1

7

18.8

3

27.1

7

42.5

0

25.0

0

12.3

3

4.0

0

2.1

7

7.1

7

MP

2

57.3

3

45.0

0

40.3

3

33.1

7

25.3

3

45.8

3

34.5

0

65.6

7

66.3

3

35.3

3

17.6

7

7.8

3

11.1

7

68.5

0

70.1

7

49.1

7

27.8

3

15.8

3

9.6

7

24.1

7

16.8

3

HW

L1

109

.17

102

.50

95.3

3

83.8

3

61.0

0

41.0

0

32.5

0

47.8

3

46.5

0

28.6

7

19.0

0

16.5

0

9.3

3

25.1

7

24.6

7

16.5

0

12.6

7

8.3

3

3.8

3

11.5

0

8.0

0

HW

L2

86.6

7

54.3

3

37.5

0

39.5

0

36.6

7

31.1

7

41.6

7

32.1

7

37.6

7

41.8

3

45.0

0

50.0

0

47.3

3

49.0

0

34.1

7

43.1

7

34.6

7

21.1

7

18.8

3

13.8

3

14.5

0

HP

1

147

.50

134

.67

118

.33

140

.17

78.3

3

42.5

0

45.6

7

30.5

0

66.6

7

89.5

0

71.0

0

63.1

7

55.3

3

90.6

7

116

.83

112

.00

108

.17

59.0

0

35.5

0

23.5

0

24.8

3

HP

2

118

.00

128

.83

123

.67

121

.50

141

.50

133

.17

80.1

7

53.3

3

46.3

3

37.1

7

32.1

7

27.6

7

28.6

7

28.1

7

26.6

7

25.0

0

22.1

7

21.5

0

19.3

3

20.6

7

18.0

0

FP

1

37.6

7

43.1

7

36.5

0

37.0

0

39.1

7

34.5

0

37.0

0

27.6

7

26.1

7

21.8

3

20.1

7

18.5

0

59.6

7

21.3

3

19.5

0

18.5

0

16.6

7

18.1

7

17.1

7

18.8

3

16.8

3

FP

2

78.5

0

60.1

7

49.1

7

52.8

3

62.0

0

54.6

7

62.8

3

66.5

0

70.3

3

96.1

7

53.5

0

47.3

3

34.8

3

35.0

0

28.8

3

23.8

3

20.5

0

33.0

0

33.6

7

40.1

7

31.6

7

HW

R

L1

199

.00

156

.67

116

.17

124

.33

166

.33

150

.83

180

.83

136

.83

97.1

7

66.6

7

50.0

0

131

.67

123

.67

80.3

3

30.6

7

13.1

7

7.8

3

11.1

7

7.8

3

6.5

0

12.5

0

HW

R

L2

84

Table C2: Results of equation 2 for MRD (see page 42) applied on Table C1 values.

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Week

Site

-0.6

4

-0.6

0

-0.6

9

-0.7

5

-0.7

4

-0.9

0

-0.8

2

-0.8

8

-0.4

8

-0.6

5

-0.7

2

-0.4

7

-0.7

3

-0.7

6

-0.5

9

-0.5

8

-0.6

7

-0.6

7

-0.5

0

-0.4

0

-0.3

9

SW

L1

-0.6

2

-0.6

9

-0.7

2

-0.7

5

-0.7

1

-0.8

0

-0.7

6

-0.5

4

-0.6

2

-0.7

0

-0.7

3

-0.6

8

-0.8

0

-0.5

1

-0.5

7

-0.6

3

-0.6

8

-0.6

7

0.1

8

-0.1

7

-0.3

8

SW

L2

-0.3

8

-0.4

3

-0.4

9

-0.6

8

-0.9

2

-0.6

8

-0.9

0

-0.6

3

-0.4

9

-0.5

8

-0.8

5

-0.7

4

-0.5

4

-0.7

9

-0.4

6

-0.5

1

-0.6

3

-0.4

3

-0.7

0

-0.0

6

-0.3

2

PW

L1

-0.0

2

-0.1

4

-0.0

9

-0.1

9

-0.2

5

0.0

7

-0.0

9

-0.1

1

0.0

5

0.0

5

-0.1

5

0.6

2

0.6

9

0.9

9

1.0

8

1.0

4

1.1

0

1.3

2

1.0

6

0.5

0

0.7

0

PW

L2

0.8

3

0.8

2

1.1

3

1.0

3

1.1

0

1.2

3

1.2

4

1.8

5

1.6

5

1.9

9

2.6

8

1.8

9

2.7

6

2.2

2

1.5

5

1.1

4

1.5

2

1.1

3

1.6

2

1.0

8

0.9

3

MR

P1

0.6

7

0.6

3

0.7

5

0.6

6

0.7

5

1.1

3

1.2

6

1.0

7

1.0

5

1.3

8

2.4

8

2.1

0

1.6

6

1.3

4

1.1

7

0.9

5

1.0

7

1.3

7

1.1

8

1.1

6

1.0

5

MR

P2

-0.2

0

-0.2

3

-0.3

9

-0.4

6

-0.5

2

-0.6

2

-0.5

5

-0.0

7

-0.1

9

-0.4

5

-0.5

8

-0.6

4

-0.6

4

-0.7

0

-0.6

5

-0.2

2

-0.2

2

-0.2

5

-0.5

1

-0.6

9

-0.5

2

MP

1

0.6

6

0.6

6

0.0

0

-0.3

8

-0.5

0

-0.3

9

-0.2

7

0.6

6

0.6

7

-0.0

9

-0.3

8

-0.5

7

-0.5

8

-0.6

7

-0.4

6

-0.0

3

-0.3

2

-0.5

6

-0.8

2

-0.9

0

-0.6

2

MP

2

-0.4

7

-0.5

0

-0.4

4

-0.5

0

-0.5

9

-0.2

3

-0.4

0

-0.0

5

-0.0

8

-0.4

0

-0.6

4

-0.8

6

-0.8

1

0.1

9

0.3

9

0.1

2

-0.2

4

-0.4

3

-0.5

7

0.1

4

-0.1

1

HW

L1

0.0

1

0.1

3

0.3

1

0.2

6

-0.0

2

-0.3

1

-0.4

4

-0.3

1

-0.3

5

-0.5

2

-0.6

2

-0.7

1

-0.8

4

-0.5

6

-0.5

1

-0.6

3

-0.6

5

-0.7

0

-0.8

3

-0.4

6

-0.5

8

HW

L2

-0.2

0

-0.4

0

-0.4

8

-0.4

1

-0.4

1

-0.4

8

-0.2

8

-0.5

4

-0.4

8

-0.2

9

-0.0

9

-0.1

1

-0.2

1

-0.1

5

-0.3

3

-0.0

2

-0.0

6

-0.2

4

-0.1

6

-0.3

5

-0.2

4

HP

1

0.3

6

0.4

8

0.6

3

1.1

1

0.2

6

-0.2

9

-0.2

1

-0.5

6

-0.0

7

0.5

1

0.4

4

0.1

3

-0.0

8

0.5

7

1.3

1

1.5

4

1.9

5

1.1

2

0.5

8

0.1

0

0.3

1

HP

2

0.0

9

0.4

2

0.7

0

0.8

3

1.2

7

1.2

3

0.3

8

-0.2

3

-0.3

6

-0.3

7

-0.3

5

-0.5

1

-0.5

2

-0.5

1

-0.4

7

-0.4

3

-0.4

0

-0.2

3

-0.1

4

-0.0

3

-0.0

5

FP

1

-0.6

5

-0.5

2

-0.5

0

-0.4

4

-0.3

7

-0.4

2

-0.3

6

-0.6

0

-0.6

4

-0.6

3

-0.5

9

-0.6

7

0.0

0

-0.6

3

-0.6

1

-0.5

8

-0.5

5

-0.3

5

-0.2

4

-0.1

2

-0.1

1

FP

2

-0.2

8

-0.3

4

-0.3

2

-0.2

1

-0.0

1

-0.0

8

0.0

9

-0.0

4

-0.0

2

0.6

2

0.0

8

-0.1

5

-0.4

2

-0.3

9

-0.4

3

-0.4

6

-0.4

4

0.1

8

0.5

0

0.8

9

0.6

7

HW

R

L1

0.8

4

0.7

2

0.6

0

0.8

7

1.6

7

1.5

3

2.1

2

0.9

8

0.3

5

0.1

3

0.0

1

1.3

5

1.0

6

0.3

9

-0.3

9

-0.7

0

-0.7

9

-0.6

0

-0.6

5

-0.6

9

-0.3

4

HW

R

L2

85

Table C3: Root Mean Square Difference calculation for values on Table C1. The final RMSD values for each site are shown

in Table 17.

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Week

Site

474

3.7

7

297

2.5

2

250

4.1

7

246

5.7

4

212

1.7

5

290

9.2

5

226

1.2

0

372

2.2

7

118

0.2

1

146

2.2

7

125

3.6

0

683

.60

190

0.4

2

193

3.2

5

888

.16

650

.78

601

.27

350

.00

127

.27

71.5

4

55.9

4

SW

L1

456

1.8

8

397

1.6

3

270

8.3

4

248

2.3

2

197

0.9

9

226

6.1

6

194

0.5

9

138

2.1

4

199

6.9

7

170

0.7

0

131

3.3

1

145

5.1

0

228

1.0

6

868

.41

839

.19

756

.82

626

.04

350

.00

16.4

2

13.1

4

51.0

6

SW

L2

172

5.7

1

150

9.6

5

127

5.0

9

203

9.0

9

327

5.1

8

164

8.7

0

270

9.4

2

189

3.1

6

126

1.7

3

117

2.3

5

175

6.1

3

169

2.9

8

103

0.0

1

208

2.5

9

550

.78

506

.72

529

.96

145

.00

249

.05

1.6

7

35.7

5

PW

L1

4.8

8

160

.97

42.7

9

164

.43

237

.03

19.3

2

29.0

0

61.5

2

13.2

9

7.6

2

52.4

1

119

1.6

9

170

0.7

0

329

0.7

0

301

0.1

2

211

5.0

4

163

8.5

6

135

3.6

3

562

.58

111

.13

178

.33

PW

L2

818

2.7

1

554

7.1

5

668

9.8

8

469

3.6

8

470

6.5

3

541

1.4

4

515

2.5

5

163

38.7

140

37.3

139

06.8

174

92.8

112

0.1

0

273

59.2

164

3.7

1

616

7.1

6

249

8.9

6

311

5.0

4

100

0.1

4

132

3.9

0

530

.92

312

.85

MR

P1

527

4.3

9

322

7.6

6

296

5.7

1

195

1.6

1

220

3.1

3

454

2.2

0

532

1.4

0

552

3.9

0

569

7.1

0

671

2.0

5

150

29.2

138

50.3

984

8.4

9

598

5.2

8

348

4.6

9

173

5.2

4

153

2.4

0

146

6.2

5

705

.01

610

.50

394

.19

MR

P2

449

.79

434

.90

814

.63

939

.81

104

9.4

9

135

2.0

9

101

6.6

8

26.8

0

191

.94

706

.12

816

.41

127

0.6

3

146

3.8

6

165

1.2

4

109

7.9

6

96.9

0

67.0

4

47.2

7

131

.05

213

.89

96.2

9

MP

1

510

6.2

9

361

7.5

2

0.0

0

624

.48

975

.26

541

.53

252

.35

206

9.3

0

235

0.2

3

31.0

6

351

.17

101

2.0

4

120

8.2

9

151

8.5

6

550

.78

2.2

8

136

.60

241

.54

340

.33

365

.77

139

.54

MP

2

260

5.2

5

210

2.6

0

103

7.3

8

111

0.4

2

137

3.6

3

189

.64

546

.88

12.3

2

30.4

8

571

.51

100

7.4

0

231

8.0

2

237

7.5

8

114

.45

381

.47

26.5

9

78.4

0

145

.00

163

.36

8.2

7

4.6

0

HW

L1

0.6

3

135

.63

519

.46

300

.81

1.9

5

346

.12

644

.42

455

.56

642

.83

934

.70

924

.54

155

8.6

0

255

9.7

3

106

5.0

7

674

.38

756

.82

577

.00

381

.88

346

.50

95.8

8

120

.54

HW

L2

471

.25

133

3.7

7

122

7.9

2

728

.44

661

.99

808

.69

263

.05

136

9.7

7

116

8.7

9

302

.98

19.4

2

35.7

5

158

.60

77.4

8

271

.22

0.7

1

4.0

8

45.0

0

13.0

7

55.6

3

20.0

6

HP

1

153

0.7

7

191

9.5

4

209

6.8

8

542

8.3

1

254

.00

292

.55

149

.30

149

5.9

2

26.9

1

915

.69

466

.29

51.6

6

21.1

0

108

0.0

8

438

2.1

6

462

2.5

8

510

9.2

7

968

.77

170

.36

4.8

8

34.2

7

HP

2

92.6

4

144

2.4

2

261

3.7

7

302

6.1

5

625

7.4

7

541

1.4

4

496

.45

251

.02

651

.31

487

.21

297

.20

801

.60

977

.21

878

.26

574

.50

361

.40

210

.85

40.6

4

9.7

0

0.3

9

0.9

6

FP

1

499

9.6

7

227

4.1

0

129

9.0

0

869

.64

539

.59

630

.22

436

.20

172

3.1

1

208

7.3

5

139

9.2

3

854

.95

140

4.6

9

0.0

7

132

9.9

7

969

.41

650

.78

400

.83

94.2

5

27.8

9

6.0

4

4.6

0

FP

2

892

.52

941

.72

546

.39

186

.49

0.1

6

24.3

8

24.4

8

7.1

7

2.3

1

136

3.6

1

16.7

6

74.7

5

629

.70

519

.94

475

.33

407

.11

262

.04

26.2

7

125

.86

356

.27

160

.97

HW

RL

1

821

2.8

9

433

1.2

9

190

3.1

4

334

5.9

0

108

03.0

832

2.7

6

151

16.1

457

7.3

7

640

.72

55.1

6

0.3

5

572

8.6

0

406

2.7

3

507

.66

398

.75

951

.34

832

.56

279

.17

213

.59

218

.79

41.9

8

HW

RL

2

86

Table C4: Spearman's rank coefficients for Table C1, by applying Equation 3 (see page 43).

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Week

1

0.9

3

2

0.7

8

0.8

5

3

0.8

0

0.7

7

0.8

7

4

0.8

3

0.6

0

0.5

5

0.6

0

5

0.9

7

0.8

0

0.5

9

0.5

9

0.6

2

6

0.7

3

0.6

7

0.6

4

0.5

4

0.6

3

0.7

0

7

0.8

6

0.5

8

0.5

7

0.6

4

0.7

0

0.6

3

0.7

5

8

0.6

5

0.6

0

0.4

2

0.4

6

0.7

2

0.6

3

0.4

6

0.7

2

9

0.8

4

0.7

0

0.6

2

0.4

4

0.4

6

0.6

5

0.6

7

0.3

5

0.5

9

10

0.8

7

0.7

9

0.7

7

0.7

0

0.5

7

0.6

3

0.7

5

0.6

4

0.4

5

0.6

6

11

0.9

4

0.7

9

0.7

1

0.7

6

0.8

2

0.6

3

0.6

3

0.7

3

0.5

4

0.5

1

0.6

5

12

0.8

9

0.7

6

0.6

6

0.5

1

0.6

6

0.7

0

0.5

4

0.5

1

0.4

9

0.3

1

0.3

0

0.3

9

13

0.8

8

0.7

5

0.6

4

0.4

9

0.4

1

0.5

9

0.4

9

0.3

2

0.3

2

0.3

8

0.2

3

0.2

4

0.3

1

14

0.7

4

0.7

5

0.8

6

0.8

8

0.7

9

0.7

7

0.7

5

0.6

3

0.3

5

0.3

7

0.6

1

0.5

0

0.3

9

0.6

2

15

0.9

2

0.7

3

0.7

2

0.7

8

0.7

3

0.5

8

0.6

1

0.7

3

0.6

2

0.3

2

0.3

2

0.5

2

0.3

6

0.4

4

0.6

1

16

0.8

9

0.9

1

0.5

7

0.5

9

0.7

4

0.8

2

0.6

8

0.6

6

0.6

6

0.4

8

0.2

0

0.2

7

0.4

8

0.4

1

0.3

0

0.5

2

17

0.9

3

0.8

3

0.8

4

0.5

1

0.6

7

0.8

0

0.8

4

0.6

8

0.6

4

0.6

6

0.6

2

0.4

0

0.4

6

0.5

2

0.3

8

0.2

9

0.4

9

18

0.9

2

0.8

5

0.8

4

0.8

0

0.6

8

0.7

9

0.8

1

0.7

8

0.6

1

0.5

3

0.6

1

0.6

1

0.4

7

0.5

0

0.5

3

0.3

3

0.3

4

0.4

6

19

0.9

3

0.8

7

0.7

7

0.7

5

0.7

7

0.7

2

0.8

4

0.7

9

0.7

5

0.6

3

0.5

6

0.5

1

0.5

5

0.3

8

0.4

1

0.3

9

0.1

6

0.0

8

0.2

5

20

0.9

8

0.9

1

0.8

4

0.7

6

0.7

3

0.7

6

0.7

1

0.8

2

0.7

7

0.7

3

0.6

5

0.5

3

0.5

5

0.5

7

0.3

5

0.3

7

0.3

6

0.1

7

0.0

6

0.2

3

21