1

Downscaling of SMAP soil moisture using land surface temperature 1

and vegetation data 2

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Bin Fang and Venkataraman Lakshmi 7

School of Earth Ocean and Environment, University of South Carolina Columbia 8

SC 29208 USA 9

Corresponding author bfang@geol.sc.edu 10

Rajat Bindlish 11

Hydrological Sciences Branch, NASA Goddard Space Flight Center Greenbelt MD 12

20771 USA 13

Thomas J Jackson 14

Hydrology and Remote Sensing Laboratory, Beltsville Agricultural Research 15

Center, USDA-ARS Beltsville MD 20705 16

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https://ntrs.nasa.gov/search.jsp?R=20180004874 2020-08-01T07:38:44+00:00Z

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ABSTRACT 1

Remotely sensed soil moisture retrieved by the Soil Moisture Active and Passive (SMAP) sensor 2

is currently provided at a 9 km grid resolution. Although valuable, some applications in weather, 3

agriculture, ecology and watershed hydrology require soil moisture at a higher spatial resolution. 4

In this study, a passive microwave soil moisture downscaling algorithm based on thermal inertia 5

theory was improved for use with SMAP and applied to a data set collected at a field experiment. 6

This algorithm utilizes a NDVI (Normalized Difference Vegetation Index) modulated relationship 7

between daytime soil moisture and daily temperature change modeled using output variables from 8

the Land Surface Model (LSM) of the NLDAS (North America Land Data Assimilation System), 9

and remote sensing data from MODIS (Moderate-Resolution Imaging Spectroradiometer) and 10

AVHRR (Advanced Very High Resolution Radiometer). The reference component of the 11

algorithm was developed at the NLDAS grid size (12.5 km) to downscale the SMAP Level 3 12

radiometer-based 9 km soil moisture to 1 km. The downscaled results were validated using data 13

acquired in SMAPVEX15 (Soil Moisture Active Passive Validation Experiment 2015) that 14

included in situ soil moisture and PALS (Passive Active L-band System) airborne instrument 15

observations. The resulting downscaled SMAP estimates better characterize soil moisture spatial 16

and temporal variability and have better overall validation metrics than the original SMAP soil 17

moisture estimates. Additionally, the overall accuracy of the downscaled SMAP soil moisture is 18

comparable to the PALS high spatial resolution soil moisture retrievals. The method demonstrated 19

in this manuscript downscales satellite soil moisture to produce a 1 km product, which is not site 20

specific and could be applied to other regions of the world using the publicly available 21

NLDAS/GLDAS (Global Land Data Assimilation System) data. 22

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1.0 INTRODUCTION 1

Soil moisture is a key variable for studies that include land atmosphere interactions, 2

hydrology, extreme weather prediction and water resource management. During recent decades, 3

passive microwave satellite remote sensing has provided reliable soil moisture estimates over 4

many regions of the world using space-borne sensors. These satellite observations began in the 5

late 1970s with the Scanning Multichannel Microwave Radiometer (SMMR) - a C-band sensor 6

(Guha and Lakshmi, 2004) and the Special Sensor Microwave Imager (SSM/I) at 19, 37 and 85 7

GHz (soil moisture was derived using 19 GHz) (Lakshmi et al., 1997a, b, c) and were followed by 8

the Advanced Microwave Scanning Radiometer - EOS (AMSR-E) - a C-band sensor (Njoku et al., 9

2003) and the L band sensors - Soil Moisture and Ocean Salinity (SMOS) (Kerr et al., 2001) and 10

Aquarius (Bindlish et al., 2015). The most recent observing system is the NASA 1.4 GHz Soil 11

Moisture Active Passive Sensor (SMAP) launched in 2015, which provides soil moisture retrievals 12

on a 9 km Earth grid with greater sensitivity to soil moisture as compared to the prior higher 13

frequency sensors (Chan et al., 2018). Algorithms for soil moisture retrievals from the 14

aforementioned passive microwave sensors are now well-established and validated (Schmugge et 15

al., 1994; Narayan at al., 2004; Jackson et al., 2010, 2012; Kerr et al., 2016; Lakshmi et al., 2004, 16

2013; Bolten et al., 2003; Bindlish et al. 2015; and Chan et al., 2016, 2018). 17

Although reliable, these passive microwave radiometers have coarse resolutions (~25 – 40 18

km) (Njoku et al., 2003; Entekhabi et al., 2010; Jackson et al., 2012; Bindlish et al., 2015). Soil 19

moisture at a spatial resolution of 10s of km derived from the space-borne sensors mentioned above 20

cannot satisfy all of the science and application needs in the areas of ecology, agriculture, weather 21

and watershed hydrology. There is a growing need for soil moisture observations at higher spatial 22

resolutions (on the order of 1-10 km) and this has led to the development of a number of approaches 23

4

that integrate coarse resolution microwave remote sensing data or retrievals with high-resolution 1

information. Peng et al. (2017) conducted an extensive review of different soil moisture 2

downscaling approaches and classified them into three groups – 3

(1) Satellite observations from various platforms (instruments). 4

(2) Physical relationships between soil moisture and other geophysical variables, such as 5

topography, soil and vegetation properties. 6

(3) Mathematical modeling approaches, such as statistical methods and data assimilation. 7

In this study, we focus on an approach that would fall into category 1, viz., – using soil moisture 8

retrievals from various satellite instruments. Category 1 is independent of modeling and is solely 9

based on observations, thereby providing an independent measure of soil moisture. 10

Within category 1, there is a group of downscaling methodologies that integrate passive 11

microwave soil moisture with remotely sensed land surface variables derived from visible/infrared 12

sensors. The general advantage of using visible/infrared sensors is a much higher spatial resolution 13

(order of 1-5 km) as compared to microwave sensors (order to 10s of km). In addition, the data are 14

readily available on a frequent global basis. Such approaches are based on the assumptions that 15

there are physical relationships between soil moisture and other land variables, which include land 16

surface temperature, vegetation, evapotranspiration (ET) and soil properties (Carlson et al., 2007; 17

Zhao et al., 2013). 18

The general approaches (for using the visible/infrared sensors) include the following 19

examples: The Disaggregation Based on Physical And Theoretical scale Change (DISPATCH) 20

method was developed based on the relationship between soil moisture and Soil Evaporation 21

Efficiency (SEE) to downscale SMOS soil moisture developed by Merlin et al. (2010), Merlin et 22

al. (2013) and Merlin et al. (2015). Merlin et al. (2008) used soil moisture indices, Evaporative 23

5

Fraction (EF) and Actual Evaporative Fraction (AEF). Fang et el. (2013), Fang and Lakshmi 1

(2014b) compared different algorithms for computing SEE and applied them for downscaling 2

AMSR-E soil moisture using NLDAS model data. Colliander et al. (2017) developed a model 3

based on MODIS derived SEE for downscaling SMAP soil moisture. Another downscaling 4

algorithm based on polynomial regression between MODIS NDVI, Land Surface Temperature 5

(LST) and brightness temperature (TB) has been applied to SMOS soil moisture (Song et al., 2014; 6

Piles et al., 2009, 2011). Peng et al. (2016) developed a downscaling model based on a vegetation 7

temperature index. Choi and Hur (2012) and Sánchez-Ruiz et al. (2014) used MODIS NDVI and 8

LST to downscale AMSR-E and SMOS soil moisture. Kim et al. (2012) implemented an algorithm 9

that uses a linear relationship between Soil Wetness Index (SWI) and soil moisture. Peng et al. 10

(2015) developed an improved algorithm using a Vegetation Temperature Condition Index (VTCI) 11

instead of the SWI. Other soil moisture downscaling approaches include: Narayan et al. (2006, 12

2008), Mascaro et al. (2010, 2011), Pablos et al. (2016), Montzka et al. (2016). 13

In the present work, we modified and applied an existing algorithm that exploits the 14

vegetation – land surface temperature – soil moisture relationship (Fang et al., 2013; Fang and 15

Lakshmi, 2014b, 2014c). This algorithm is attractive because (a) It employs a simple relationship 16

that uses readily available satellite data and model outputs, (b) Does not require any parameters 17

that need site or climate specific calibration, and (c) Has shown good results when applied to the 18

C-band AMSR-E brightness temperatures over the state of Oklahoma as well as the smaller region 19

Little Washita Watershed. 20

In this study, the soil moisture downscaling algorithm proposed by Fang et al. (2013) was 21

applied to SMAP 9 km soil moisture retrievals obtained coincident to the time of the SMAPVEX15 22

campaign PALS airborne observations (Colliander et al., 2017). This study improved the 23

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downscaling algorithm with modifications, as well as for the first time, implemented the algorithm 1

over semi-arid region in Arizona. 2

The validation of downscaled soil moisture estimates can be challenging. The most robust 3

evaluation requires high-density in situ soil moisture observations over the study area. In this 4

investigation, we utilized a unique data set collected in SMAPVEX15. This data set includes 5

concurrent high-resolution soil moisture obtained using an aircraft-based microwave radiometer 6

Passive Active L-band System (PALS) that facilitated the direct comparison of the SMAP 7

downscaled soil moisture. 8

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2.0 STUDY AREA AND DATA 10

2.1 SMAPVEX15 11

The SMAPVEX15 field campaign was conducted in summer 2015 at the United States 12

Department of Agriculture Agricultural Research Service’s (USDA-ARS) Walnut Gulch 13

Experimental Watershed (WGEW) and nearby sites in Southeastern Arizona. The WGEW 14

(center coordinates of 31.71oN, 110.68oW) covers approximately 150 km2 within the Upper San 15

Pedro River Basin. The major land cover of WGEW consists of brush and grass rangeland and 16

has been the site of previous field experiments (Colliander et al., 2017) that have been conducted 17

over this area. WGEW is located in a semi-arid climate zone where the majority of precipitation 18

occurs during June – September as convective storms with highly variable spatial distributions. 19

The entire SMAPVEX15 domain, WGEW and the other two study sites (Empire Ranch and 20

Santa Rita) are shown in Figure 1. 21

A full description of SMAPVEX15 is provided in Colliander et al. (2017). Key data sets 22

include the permanent in situ network, temporary stations added for the campaign, and aircraft 23

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brightness temperature collected with the PALS. These data were used by Colliander et al. 1

(2016) to produce soil moisture maps at a grid scale of 500 m. For the campaign, the aircraft-2

based measurements were performed concurrently with SMAP morning overpasses. Data were 3

collected between August 2 -18, 2015. 4

2.2 Data 5

2.2.1 NLDAS 6

The NLDAS contains land-surface model datasets which are temporally and spatially 7

consistent and quality-controlled forcing data and model outputs. NLDAS provides land surface 8

forcing data sets including surface fluxes, soil moisture and snow cover at 1/8o (12.5 km) 9

resolution covering North America. Past studies have evaluated and discussed accuracy and 10

uncertainties of NLDAS variables (Cosgrove et al., 2003; Mitchell et al., 2004; Robock et al., 11

2003; Schaake et al., 2004). The data was downloaded from http://ldas.gsfc.nasa.gov/nldas/. In 12

this study, two NLDAS Phase-2 model variables: surface skin temperature and soil moisture at 13

0-10 cm soil layer at SMAP overpass times were extracted for building the downscaling model. 14

These variables are computed from the National Oceanic and Atmospheric Administration Noah 15

model, which is the land component of the National Centers for Environmental Prediction meso-16

scale Eta model (Chen et al., 1996; Koren et al., 1999; Ek et al., 2003; Mitchell et al., 2004; Xia 17

et al., 2013). 18

2.2.2 MODIS/AVHRR 19

The MODIS sensors are onboard NASA satellites Terra and Aqua which were launched in 20

1999 and 2002, respectively, for monitoring and understanding global processes and dynamics of 21

land, air and atmosphere, such as temperature, vegetation indices and land cover on a daily basis 22

(Wan et al., 1997; Lakshmi et al., 2001). These sensors have a total of 36 visible/infrared bands 23

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ranging from 0.4-14.4 µm at different spatial resolutions from 250 m - 1 km. In order to construct 1

the downscaling model, the 0.05o (5 km) spatial resolution Climate Modeling Grid daily NDVI 2

data was downloaded from NASA LTDR (Long Term Data Record) website 3

https://ltdr.nascom.nasa.gov/ and upscaled to match the NLDAS grid size 1/8o (12.5 km) by using 4

bilinear interpolation method. The LTDR Version 5 NDVI data consists of a collection from 5

AVHRR instruments on NOAA satellites N07~N19 (AVH13C1, 1981-present) (Tucker, 1979). In 6

addition, the 1 km daily Aqua and Terra MODIS LST (MYD11A1, MOD11A1) and 1 km 7

biweekly Aqua MODIS NDVI (MYD13A2) were downloaded from the online data pool Land 8

Processes Distributed Active Archive Center at https://lpdaac.usgs.gov/. 9

2.2.3 SMAP 10

The SMAP provides estimates of the moisture content of the 0 - 5 cm soil layer for 11

vegetation water content ≤ 5 kg/m2. It is in a near polar and sun-synchronous orbit with a revisit 12

every 2-3 days. Both morning (6 a.m.) and afternoon (6 p.m.) products are available. The SMAP 13

soil moisture is derived from brightness temperature observations provided by an L-band 14

radiometer (1.41 GHz) and the native spatial resolution of the instrument is nominally 40 km 15

(Entekhabi et al., 2014). Data products are available beginning in March 31, 2015. 16

The standard SMAP soil moisture products are provided on a 36 km fixed Earth grid 17

(Chan et al., 2016) and the SMAP Enhanced soil moisture product is on a 9 km grid (Chan et al., 18

2018). Enhanced Level-3 radiometer global daily 9 km soil moisture retrievals (Data set ID: 19

SPL3SMP_E) as well as 36 km retrievals (Data set ID: SPL3SMP) in EASE (Equal Area 20

Scalable Earth) - grid were acquired from National Snow and Ice Data Center website: 21

https://nsidc.org/data/SPL3SMP_E/versions/1. The Level-3 soil moisture retrievals are global 22

daily composites of the SMAP Level-2 data. In this study, the SMAP soil moisture retrievals of 23

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morning overpasses were selected for implementing downscaling model, as they coincided with 1

the acquisition times of PALS airborne observations and field soil moisture sampled 2

measurements during SMAPVEX15. 3

In addition to the SMAPVEX15 study domain, in this study we also wanted to investigate 4

the downscaled soil moisture heterogeneity over a larger area. Therefore, the entire state of 5

Arizona was selected for downscaling and mapping. As an illustration of the spatial variability 6

that might be expected, Figure 2 shows the Level 3 10 km 3-day accumulated precipitation (mm) 7

derived from GPM (Global Precipitation Measurement) IMERG (Integrated Multi-satellitE 8

Retrievals for GPM) product acquired from https://pmm.nasa.gov/data-access/downloads/gpm, 9

between August 7 - 18, 2015 over Arizona and the SMAPVEX15 domain. Major rainfall 10

occurred in northwestern and southeastern Arizona followed by more scattered rainfall events. 11

The change of soil moisture heterogeneity at finer spatial scale after downscaling is expected to 12

be characterized in this study. 13

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2.2.4 PALS 15

The PALS instrument provides L-band (1.413 GHz) radiometer TB data at H (Horizontal) 16

and V (Vertical) polarizations and L-band (1.26GHz) radar backscatter coefficients at four 17

polarizations (Colliander et al., 2017). The PALS was to provide high spatial resolution TB maps 18

that could be used to validate the original concept of SMAP that combined active passive sensing 19

for soil moisture retrieval. PALS data were acquired for 5 flight lines coincident with SMAP 20

morning overpasses on August 2 - 18, 2015. The PALS observations cover a domain of three 21

adjacent SMAP 36 km grids and the nominal spatial resolution is at 500 m. More details on these 22

products can be found in Colliander et al. (2017). 23

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2.2.5 In situ observations 1

The ground observations consist of the existing network of precipitation gauges and soil 2

moisture sensors, a temporary network of soil moisture stations, field sampled gravimetric soil 3

moistures as well as other land surface parameter measurements such as vegetation and surface 4

roughness. The in situ soil moisture measurements were recorded every 20 minutes at a depth of 5

5 cm using Stevens Water Hydra Probe from July to October 2015, while the field sampled soil 6

moistures were collected using dielectric-based probes at three locations for each site from August 7

2 – 18. An overall root mean square error (RMSE) of 0.02 m3/m3 of the SMAPVEX15 ground 8

measurements was achieved (Colliander et al., 2017; Cai et al., 2017). The in situ measurements 9

were used to validate 1 km downscaled and 9 km SMAP soil moisture estimates in this study. 10

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3.0 METHODOLOGY 15

3.1 Soil Moisture Downscaling Model 16

Thermal inertia theory as utilized here refers to the time-dependent response of an object 17

to the variation of temperature. The volumetric heat capacity of soil increases when the soil 18

layer becomes wetter, corresponding to a smaller diurnal temperature variation. During the soil 19

moisture – temperature variation relationship modeling, it is assumed that the soil moisture at a 20

particular time (e.g., morning) is inversely proportional to the daily temperature change. This soil 21

moisture can be approximated by the temperature difference between the two overpasses of 22

SMAP on the same day. In addition, the presence of vegetation in terms of NDVI will influence 23

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the soil moisture-temperature relationship. Based on the studies by Carlson et al. (1995), Gillies 1

et al. (1997) Wan et al. (1997) and Mallick et al. (2009), the remotely sensed variables NDVI-2

surface temperature (Ts) relationship has a triangular shape which changes into a polygonal when 3

the vegetation is under water stress (Schmugge et al., 1974; Choudhury et al., 1979; Carlson et 4

al., 1995; Gillies et al., 1997; Minacapilli et al., 2009; Hong et al., 2009; Merlin et al., 2010; 5

Lakshmi et al., 2011). The triangular shape formed by three vertices, which corresponds to the 6

vertex A of dry bare soil with low NDVI and high Ts, and the vertex B of moist bare soil with 7

low NDVI and low Ts, as well as the vertex C of high NDVI and low Ts on well-watered surface. 8

The edge AB represents the dry edge corresponding to low ET, while the edge BC represents the 9

wet edge of high ET. 10

Based upon previous studies, the soil moisture in the morning is negatively related to 11

daily temperature difference (Fang and Lakshmi, 2014a). This fact was also used to estimate soil 12

moisture by a triangle method (Schmugge et al., 1974; Carlson et al., 1995). For a single month, 13

the relationship between soil moisture and temperature difference for a given NDVI range can be 14

expressed by the following linear regression model 15

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𝜃𝜃(𝑖𝑖, 𝑗𝑗) = 𝑎𝑎0 + 𝑎𝑎1∆𝑇𝑇𝑠𝑠(𝑖𝑖, 𝑗𝑗) (1) 17

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Where, for a NLDAS grid (𝑖𝑖, 𝑗𝑗), 𝜃𝜃(𝑖𝑖, 𝑗𝑗) is the NLDAS soil moisture in the morning at 6:00 a.m. 19

and ∆𝑇𝑇𝑠𝑠(𝑖𝑖, 𝑗𝑗) is the NLDAS temperature difference between the two MODIS overpass times 20

(1:30 a.m. / p.m.) of the same day. This relationship was built at the scale of the NLDAS grid 21

using the NLDAS soil moisture and surface skin temperature variables from all August months 22

between 1981 - 2016. The daily NDVI derived from AVHRR, MODIS data were combined, 23

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upscaled and matched-up to the NLDAS grids by using a nearest neighbor method. The NDVI 1

were binned into 5 classes based on the range of NDVI values in Arizona, 4 classes with the 2

interval of 0.1 from 0 - 0.4, and 1 class from 0.4 - 1, which resulted in five regression fit lines in 3

the 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 scatterplots shown in Figure 3. The regression equations at the specific NLDAS 4

spatial resolution were applied on a daily basis to the 1 km MODIS grids within that NLDAS 5

grid. The 1 km soil moisture was then computed from the 1 km MODIS LST using the 6

regression equation corresponding to the proper NDVI class. 7

The SMAP soil moisture observations are retrieved from the microwave radiometer, 8

which is a different satellite platform from the optical imaging sensor MODIS. In order to solve 9

this issue, the 1 km soil moisture computed from the MODIS LST products should be corrected 10

by removing the difference between original SMAP soil moisture retrievals and MODIS LST 11

computed uncorrected soil moistures using the following equation 12

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𝜃𝜃(𝑠𝑠, 𝑡𝑡) = 𝜃𝜃�(𝑠𝑠, 𝑡𝑡) + [𝛩𝛩 − 1𝑁𝑁∑𝜃𝜃�𝑁𝑁] (2) 14

Where, 𝜃𝜃(𝑠𝑠, 𝑡𝑡) stands for a 1 km bias corrected SMAP soil moisture at the MODIS grid 15

(𝑠𝑠, 𝑡𝑡). 𝛩𝛩 is the 9 km SMAP soil moisture in the morning overpass. 𝜃𝜃�𝑁𝑁 are the N of uncorrected 1 16

km SMAP soil moisture grids that fall in the 9 km SMAP grid 𝛩𝛩. 17

The downscaled soil moisture has the following characteristics: (a) the soil moisture at 1 18

km can be computed by the relationship between soil moisture and daily temperature variation, 19

(b) the bias between SMAP and MODIS derived soil moisture can be eliminated at the low 20

resolution, and (c) the 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 relationship varies in response to different vegetation conditions. 21

3.2 Data Processing 22

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The Inverse Distance Weighting (IDW) method was applied for upscaling of LTDR and 1

PALS data. It is a nonlinear interpolation technique using the weighted average of the values 2

surrounding the predicted location. The IDW method assumes the influence of each measured 3

point reduces as the distance increases, hence the weight becomes smaller. For any grid 𝑍𝑍𝑙𝑙𝑙𝑙 at 4

low spatial resolution to be upscaled from high resolution grids 𝑍𝑍ℎ𝑖𝑖, it can be computed by using 5

𝑍𝑍𝑙𝑙𝑙𝑙 =∑ 𝑍𝑍𝑛𝑛

ℎ𝑖𝑖

𝑑𝑑ℎ𝑖𝑖,𝑙𝑙𝑙𝑙𝑛𝑛

∑ 1𝑑𝑑ℎ𝑖𝑖,𝑙𝑙𝑙𝑙

𝑛𝑛 (3) 6

The n of high spatial resolution neighbor grids 𝑍𝑍ℎ𝑖𝑖 were used to generate the new grid at 7

low spatial resolution 𝑍𝑍𝑙𝑙𝑙𝑙. n is determined by the number of 𝑍𝑍ℎ𝑖𝑖 grids that fall in the 𝑍𝑍𝑙𝑙𝑙𝑙. 𝑑𝑑ℎ𝑖𝑖,𝑙𝑙𝑙𝑙 is 8

the distance between the centroids of 𝑍𝑍ℎ𝑖𝑖 and 𝑍𝑍𝑙𝑙𝑙𝑙. 9

In a few occasions, the 1 km grid may overlap with more than one 12.5 km grid (2~4 10

adjacent grids at most) so multiple modeled 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 relationship equations from the overlapped 11

12.5 km grids should be applied on the 1 km MODIS LST for calculating soil moisture. We 12

applied an averaging method based on the proportion of each overlapped NLDAS grid to solve 13

this issue. 14

𝜃𝜃�′ = 1𝑛𝑛∑ 𝑃𝑃𝑛𝑛 ∗ 𝜃𝜃�𝑛𝑛′ (4) 15

Where, 𝜃𝜃�′ is the adjusted uncorrected 1 km soil moisture, n is the number of 12.5 km 16

grids overlapped the 1 km grid. 𝑃𝑃 is the proportion in percentage of each 12.5 km grid 17

overlapped the 1 km grid, and 𝜃𝜃�𝑛𝑛′ is the soil moisture value calculated by each 12.5 km grid 18

corresponded 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 relationship equation. 19

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3.3 Validation 21

14

The original and downscaled SMAP soil moisture data were evaluated using in situ soil 1

moisture observations acquired from SMAPVEX15 campaign, which are point estimates at the 2

permanent and temporary network stations, as well as the upscaled PALS soil moisture retrievals 3

at 1 km and 9 km resolutions. The in situ soil moisture measurements that fall in each 1 km/ 9 4

km soil moisture grid were averaged for comparison. The statistical variables include R2, slope, 5

unbiased RMSE, bias and p-value from significance test of Pearson correlation coefficient. In 6

order to compare the three estimated soil moisture products: 1 km / 9 km SMAP soil moisture 7

and PALS soil moisture through the sampling days in SMAPVEX15, results were analyzed using 8

the histogram plots showing distribution form, Empirical Cumulative Distribution Function 9

(ECDF) plots as well as time series plots showing mean and standard deviation. 10

11

4.0 RESULTS AND DISCUSSION 12

4.1 𝜽𝜽 - ∆𝑻𝑻𝒔𝒔 relationship 13

NLDAS data from 1981-2016 were used to estimate the model function between 𝜃𝜃 and ∆𝑇𝑇𝑠𝑠 14

which is modulated by NDVI. Three NLDAS grids were selected to demonstrate the relationships 15

for the three SMAPVEX15 study sites: Walnut Gulch, Empire Ranch and Santa Rita. From Table 16

1, the 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 regression fit lines are negatively correlated for all three sites. Walnut Gulch has 17

better R2 (0.5 - 0.809) than the other two sites. The R2 do not vary much as NDVI increases. From 18

the Figure 3, the ranges of slope for the three sites are -106.127 to -66.565, -66.239 to -47.302, 19

-79.861 to -66.478, respectively. The ranges of slope for Walnut Gulch and Santa Rita are smaller 20

than for Empire Ranch. The NDVI-based classes differentiate the data pairs and the five regression 21

fit lines line up well from top to bottom which correspond to the NDVI classes from the highest to 22

the lowest. From the scatterplot, given any ∆𝑇𝑇𝑠𝑠 value, the soil moisture corresponding to the 23

15

highest NDVI class (>0.4) are approximately 0.1 m3/m3 wetter than the lowest class (NDVI<0.1). 1

The results show that the NDVI - 𝑇𝑇𝑠𝑠 triangle principle is applicable in this study domain and can 2

be used to downscale the SMAP soil moisture estimates. With regard to the significance of the 3

correlations between 𝜃𝜃 and ∆𝑇𝑇𝑠𝑠 , the results show that the p-values of the correlations of all NDVI 4

classes from all three sites are much smaller than a significance level of 0.01. 5

4.2 1 km downscaled soil moisture 6

Figure 4 shows the soil moisture maps for the 1 km downscaled, the SMAP 9 km and the 7

SMAP 36 km products 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 , 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃36𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 , as well as difference between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 8

𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 respectively for the five sampling days (8th, 10th, 13th, 16th, 18th of August, 2015). It can be 9

seen that the soil moisture distribution pattern was consistent between the downscaled 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 10

the original product 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, while the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 displayed greater spatial variability. However, if we 11

compare the difference between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 through all five days, we find that the 12

distribution patterns of the two products exhibited discrepancies, especially in central and 13

southeast Arizona where the soil moisture pattern was more complex. In these regions, 𝜃𝜃36𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 did 14

not show any wetting or dry-down zones, which were found in the two finer resolution estimates. 15

The 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 images demonstrated greater spatial heterogeneity of soil moisture over the 16

SMAPVEX15 domain. The 500 m resolution PALS L-band radiometer soil moisture was retrieved 17

using a version of the SMAP baseline algorithm (Single Channel Algorithm-Vertical Polarization) 18

(Jackson et al., 1993, 2010) and upscaled to 1 km in order to compare directly with the 1km 19

downscaled SMAP soil moisture. Figure 5 shows that the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 compares well with the upscaled 20

1 km PALS soil moisture 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 and SMAP 9 km soil moisture 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 for the five sampling days. 21

The black grids over each map outline the 9 km grid boundaries for easier visualization of the 22

downscaled soil moisture heterogeneity within the coarser resolution grid. It can be summarized 23

16

that within each 9 km grid, the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 displayed soil moisture features in more detail than the 1

original 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, as well as similar spatial distribution pattern with 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. For instance, the spatial 2

heterogeneity was more visible near the boundaries between the San Pedro River basin and Santa 3

Cruz River Basin and Whitewater Draw Basin. However, the overall range of soil moisture values 4

for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 was generally lower than that of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 . When compared for each day, the 5

discrepancies between the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 could be noted in Figure 5. Looking at the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 6

product, two dry zones in middle west and east were apparent on August 8, as well as a wet zone 7

with a belt shape on August 16 which were not observed in 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆maps. Some small and isolated 8

spots showed stronger drying or wetting trends than surrounding areas in 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆, which were not 9

present in 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. Additionally, the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 showed greater contrast between the highest and lowest 10

soil moisture values than 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 . As opposed to this, the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 showed better 11

consistency on the other two days August 10 and 18. 12

The comparisons between uncorrected 1 km soil moisture 𝜃𝜃�1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 calculated from 13

downscaling model and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are shown in Figure 6. Better correlations were found in August 14

16 and 18, with unbiased RMSE (µbRMSE) = 0.026 and 0.019, bias = 0.03 and 0.025, respectively. 15

More scattered characteristic was noted especially on August 8, which had µbRMSE of 0.043 and 16

bias of 0.048. Such inconsistency between 𝜃𝜃�1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 might have influences on the 17

downscaled soil moisture. 18

Figure 7 shows the frequency distribution histogram of the three soil moisture products. It 19

can be summarized that the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 had more similar shape and data ranges as 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 than 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, 20

which had skewed or bimodal shapes on August 10, 13 and 16 and narrower ranges of the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 21

for corresponding days. Additionally, more similar data ranges and shapes of soil moisture values 22

17

between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 were observed in August 13 and 18, while 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 had narrower ranges 1

than 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 for the other three days. 2

The ECDF curves for the three soil moisture products 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 for the five 3

SMAPVEX15 sampling days of descending overpasses are displayed in Figure 8. It was found 4

that the ECDF curves of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 had better agreement with 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 than 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 , which might 5

indicate the improved accuracy of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. However, the inconsistency between PALS and SMAP 6

was noted from three days: August 8, 10 and 16, of which 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 had limited improvement of 7

𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. 8

The overall mean and standard deviation values of the three soil moisture products as well 9

as the in situ measurements are shown as a time series in Figure 9. From the top graph, it can be 10

observed that the mean values of in situ were always drier than the other three data sets, whereas 11

the mean values of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 were closer to either 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or in situ than the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. In addition, 12

August 13, 16, and 18 were found to have better agreement among the four data sets than August 13

8 and 10. Examining the bottom graph, the standard deviations of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 were 14

approximately 0.02 m3/m3 lower than either the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or in situ. The 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 was more consistent 15

with 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 on August 13 and 18, while it was more consistent with in situ observations 16

for the other three days. 17

4.3 Validation 18

Table 2 and Figure 10 shows the results of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 validated using 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. 19

The following observations can be made based on the validation results in Table 1: (1) the R2 of 20

the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are higher and they range 0.189 – 0.697 for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and ranges 0.003 - 0.597 for the 21

𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, (2) the slopes for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are slightly higher for August 8, 10 and 18. They range 0.518 22

- 1.552 for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and range 0.07 - 1.915 for the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, (3) the µbRMSEs and the biases are 23

18

improved on four days for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 over the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, ranging 0.009 - 0.02 m3/m3 and -0.002 - 1

0.01 m3/m3, respectively. The range of µbRMSEs for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 meets the criteria that RMSE < 2

0.04 m3/m3 for validated SMAP soil moisture estimates. Additionally, the p-values of the Pearson’s 3

correlation coefficient for the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are all much smaller than the significance level 𝛼𝛼 = 0.05, 4

indicating significant correlations between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. Examining the scatterplots in Figure 5

10, it appears that the locations of the highest density data points in the 1 km plots correspond to 6

the locations of points in 9 km plots. From this figure, it is also seen that there is a relatively better 7

consistency between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 . However, it should be noted that there is an obvious 8

underestimation trend for either 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 or 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 when comparing to the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆. In addition, it is 9

observed that the PALS soil moisture values cover a wider range (approximately 0.05 - 0.25 m3/m3) 10

than either the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆(approximately 0.1 - 0.2 m3/m3), which probably indicates greater 11

soil moisture spatial variability. This fact corresponds to what is observed in Figure 5, 7 and 9. 12

Table 3 and Figure 11 illustrates the validation results for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆and 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 using the in 13

situ measurements. In this validation, only the 9 km 𝜃𝜃 grids having more than 8 in situ points 14

within their boundaries were considered. For the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, the R2 range 0.255 - 0.733 and µbRMSEs 15

range 0.006 - 0.044 m3/m3, comparing with the R2 range of < 0.001 - 0.353 and µbRMSEs range 16

of 0.03 - 0.088 m3/m3 for validation results of 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 . It can be concluded that the validation 17

metrics of the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 show an obvious improvement over 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and the RMSE range of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 18

meets the criteria < 0.04 m3/m3 for SMAP soil moisture. The improvement may also be observed 19

in the slope values as well as the plots shown in Figure 11, where the scatter points for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 are 20

closer to the 1-1 diagonal line. The p-values for the Pearson’s correlation coefficient for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 21

are significant at the 𝛼𝛼 = 0.05 significance level. Additionally, the bias range of -0.029 - < 0.001 22

m3/m3 for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 also indicates the underestimation tendency as compared to the in situ data. 23

19

The downscaling algorithm had varying performance on different days. One explanation 1

could be that the precipitation during SMAPVEX15 may have an impact on the performance of 2

the downscaling algorithm. As Figure 2 shows, it rained more between August 7 and 12 than after 3

August 13, which corresponded to the relatively higher µbRMSE for August 8, 10 and 13 and 4

validation results using in situ data in Figure 11. Additionally, the downscaled 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 might not 5

be sensitive to the wetting trends in the central and southern regions (August 8 and 10 in Figure 6

5). Similarly, another inconsistency was noted in the regions showing very dry condition in the 7

eastern part of SMAPVEX15 for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 in August 8, 10 and 16. However, these features were not 8

fully captured in these regions for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. In addition, the spatial heterogeneity between 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 9

and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 observed for the day with less amount of rain (August 18) had better agreement than 10

the other days. Secondly, the bias of 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 might also influence the downscaling model 11

performance, as the downscaled 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 was corrected by 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆. So, if the original SMAP soil 12

moisture is biased, the uncertainties will be passed down to the downscaled product. 13

There is a contradictory issue that the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 validation of August 18 had the worst R2 14

but the best µbRMSE. One possible explanation could be 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 validation of this day had 15

narrower data range and lower variance than the other days. Additionally, better validation 16

metrics: R2 and µbRMSE for 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 using in situ data were shown for August 18 than for other 17

days in Figure 11 and Table 3 and therefore we are confident that the algorithm still performs 18

well for August 18. 19

The PALS soil moisture was retrieved from the high spatial resolution L-band TB provided 20

by the aircraft system using the SCA (Single Chanel Algorithm), which calculated soil moisture 21

from single wavelength (L-Band) radiometer observations as well as other ancillary data such as 22

soil properties, comparing with the 1 km downscaled SMAP soil moisture estimated from multiple 23

20

spaceborne observations (visible/infrared spectroradiometer derived LST and NDVI products as 1

well as coarse resolution microwave radiometer derived soil moisture). The uncertainties in the 2

soil moisture retrieval algorithm likely contributed to weaker results for the SMAP downscaled 3

soil moisture estimates than the PALS retrievals. 4

This investigation introduced several improvements to the soil moisture downscaling 5

algorithm proposed by Fang et al. (2013). First, the original algorithm used only three NDVI 6

classes for building the NDVI corresponded 𝜃𝜃-∆𝑇𝑇𝑠𝑠 model. The revised algorithm divides this into 7

5 classes with the increment of 0.1, which better characterizes the NDVI modulated 𝜃𝜃-∆𝑇𝑇𝑠𝑠 8

relationship. Second, the original algorithm used the “drop-in-bucket” method for upscaling data 9

to coarser resolution, while the revised algorithm applies an IDW interpolation technique that 10

considers the distance between the new and fine resolution grid. And third, we applied an 11

averaging method to improve the accuracy of the calculated 1 km soil moisture grids which 12

overlap multiple 12.5 km (NLDAS) grids. Finally, we are now computing the downscaled soil 13

moisture corresponding to the SMAP descending 6:00am overpass rather than calculating a daily 14

averaged soil moisture. 15

Fang et al. (2013) point out that there were four limitations mentioned in the original 16

downscaling algorithm. We have attempted to overcome these limitations in the current 17

investigation. First, it is often very difficult to recover the cloud-contaminated pixels and the 18

current cloud-remover algorithms may cause uncertainties. In this study, we selected MODIS 19

data for the sampling days of SMAPVEX15 campaign site (it rarely rained during the latter part 20

of the campaign) for testing the downscaling algorithm. Second, the downscaling model was 21

built using 5 km AVHRR NDVI data, while the model was applied on 1 km MODIS NDVI data. 22

The AVHRR NDVI and MODIS NDVI data of overlapping period (since 2001) are at different 23

21

spatial resolutions. Third, this article is a new application (our past application has been in 1

Oklahoma) of the improved soil moisture downscaling algorithm by Fang et al. (2013). The 2

validation results for downscaled soil moisture indicate the improvement of accuracy over the 3

downscaled AMSR-E soil moisture in Fang et al. (2013) paper. Additionally, we also worked to 4

improve the downscaling model performance, using IDW technique. Finally, as mentioned 5

above, the other soil moisture related variables are often difficult to acquire. For example, the 6

related variables, including soil properties, topography and land cover information can be 7

acquired at very small scale of regions, which cannot fulfill the demands of providing soil 8

moisture estimates of wider range. So, we need to use the simplified downscaling model based 9

on the thermal inertia theory between temperature difference, soil moisture and vegetation. 10

Cosh et al. (2004) noted several inconsistency issues between the downscaled remotely 11

sensed soil moisture and in situ observations. First, the remote sensing data sets provide the soil 12

moisture data for an ellipsoidal region at a kilometer scale, as opposed to the in situ ground 13

observations that record the soil moisture at the point scale. There are also potential mismatches 14

in the sensing depth among all the soil moisture data sets. The brightness temperatures sensed by 15

the passive microwave sensor (SMAP) and MODIS, soil moisture output from NLDAS, as well 16

as the soil moisture measured by the SMAPVEX15 stations are all at different depths. The 17

passive microwave sensors typically penetrate a few centimeters, while the MODIS penetrates 18

only a few of millimeters, which are then compared with the NLDAS output soil moisture at 0-19

10 cm depth and the SMAPVEX15 ground measurements at 5 cm depth. Based on a previous 20

study, the satellite-based soil moisture is expected to be noisier than LSM data (Fang et al., 21

2016). The actual contributing domain used to compute the SMAP L3 soil moisture product is at 22

33 km rather than 9 km. So, the discrepancy between assumed or grid resolution and actual 23

22

resolution could be a source of error, especially in the regions of strong heterogeneity. Due to a 1

lack of a long-term monitoring of very high spatial resolution of land surface variables, the 2

NLDAS outputs as well as AVHRR and MODIS products were upscaled to 12.5 km for 3

downscaling the microwave soil moisture to 1 km. The spatial heterogeneity at 1 km within each 4

12.5 km grid during the model implementation was also ignored. 5

6

5.0 CONCLUSIONS 7

This study implemented a soil moisture downscaling algorithm with the SMAP Level 3 8

Radiometer Enhanced 9 km daily soil moisture product and validated the results using airborne 9

PALS radiometer and in situ soil moisture measurements from the SMAPVEX15 field campaign 10

in Arizona. This algorithm was developed based on a vegetation modulated daytime soil 11

moisture - daily surface temperature change relationship. The algorithm uses only three 12

variables: surface temperature, soil moisture and NDVI, as it is usually difficult to obtain high 13

spatial resolution data for other soil moisture related variables, such as precipitation, soil 14

properties and ET. The modeled relationship was applied on 1 km MODIS Aqua/Terra LST data 15

to compute 1 km soil moisture, which was then bias corrected by SMAP 9 km soil moisture. 16

Data from the five sampling days with aircraft coverage during the SMAPVEX15 campaign 17

were used for soil moisture and validation along with in situ data sets. It was found that soil 18

moisture spatial variability as well as dry-down and wetting trends were better characterized by 19

the downscaled estimates than the original 9 km SMAP estimates. The 1 km downscaled and 9 20

km SMAP soil moisture estimates were validated using the SMAPVEX15 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 retrievals and 21

the in situ measurements. The validation metrics of 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 showed overall better consistency 22

with the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 than the 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, with R2 increased by 0.169, µbRMSE decreased by 0.002 m3/m3 23

23

and bias decreased by 0.004 m3/m3. The downscaled soil moisture estimates also compared well 1

with the in situ soil moisture over the SMAPVEX15 study domain. The validation metrics for 2

𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 has the following improvements on 𝜃𝜃9𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆: R2 improved by 0.293, µbRMSE decreased by 3

0.037 m3/m3 and bias decreased by 0.03 m3/m3. The p-values indicated significant correlations 4

between the 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆and 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 and in situ measurements. Additionally, the overall 5

RMSE ranges of the downscaled SMAP validated by either 𝜃𝜃1𝑘𝑘𝑘𝑘𝑆𝑆𝑆𝑆𝑃𝑃𝑆𝑆 or in situ data meet the criteria 6

for retrieval accuracy that RMSE < 0.04 m3/m3. Based on these results, we believe the 7

downscaling approach applied to SMAP soil moisture data is reliable and accurate for the 8

conditions evaluated and expect to implement the algorithm for providing a daily high spatial 9

resolution soil moisture product to the Contiguous United States. 10

With respect to these issues, future studies might include: (1) Other methodologies or 11

data sets that could be used to improve the 𝜃𝜃 - ∆𝑇𝑇𝑠𝑠 correlation. Also, other land surface variables, 12

such as evapotranspiration (ET) and soil evaporative efficiency could be considered. (2) 13

Calibrated hydrological models could be helpful to provide correction for the SMAP soil 14

moisture retrievals (Sridhar et al., 2013). (3) Confidence in the soil moisture validation results 15

could be increased by having more in situ soil moisture stations within each soil moisture 16

retrieval grid for better representation of the spatial heterogeneity of the soil moisture. 17

18

24

FIGURES AND TABLES 1

2

Table 1. R2 of NLDAS soil moisture of top layer (m3/m3) at 6:00 a.m. versus daily surface skin temperature 3 (K) difference (1:30 p.m. - 1:30 a.m.) corresponding to NDVI classes from 0-1 in August for the three 4 SMAPVEX15 sampling sites: Walnut Gulch, Empire Ranch and Santa Rita. 5

Site NDVI Class R2 Slope

Walnut Gulch

0-0.1 0.528 -78.143

0.1-0.2 0.517 -77.023

0.2-0.3 0.5 -66.565

0.3-0.4 0.574 -78.334

> 0.4 0.809 -106.127

Empire Ranch

0-0.1 0.348 -53.090

0.1-0.2 0.294 -47.302

0.2-0.3 0.62 -66.239

0.3-0.4 0.47 -54.967

> 0.4 0.499 -61.209

Santa Rita

0-0.1 0.504 -79.861

0.1-0.2 0.366 -66.478

0.2-0.3 0.594 -75.577

0.3-0.4 0.638 -76.962

> 0.4 0.572 -79.173 6

25

Table 2. Statistical variables of validating (with upscaled PALS soil moisture) downscaled 1 km and 1 original 9 km SMAP soil moisture of descending overpass (6:00 a.m.) from five sampling days in August 2 2015 (The * symbol denotes p-value < |0.001|). 3

4 5

Date SM Dataset

Number of

Points R2 Slope µbRMSE

(m3/m3) Bias

(m3/m3) p-value

08/08 1 km 4477 0.697 1.552 0.02 0.002 *

9 km 70 0.597 1.915 0.022 0.004 0.259

08/10 1 km 4514 0.544 1.279 0.009 0.004 *

9 km 70 0.538 1.514 0.011 0.001 0.933

08/13 1 km 4544 0.429 1.128 0.011 0.01 0.003

9 km 69 0.209 1.006 0.018 0.018 0.024

08/16 1 km 4586 0.438 1.517 0.01 -0.002 *

9 km 70 0.103 0.854 0.003 0.003 0.713

08/18 1 km 4523 0.189 0.518 0.009 -0.001 *

9 km 70 0.003 0.07 0.013 0.007 0.106

26

Table 3. Statistical variables of validating (with in situ data) downscaled 1 km and original 9 km SMAP 1 soil moisture of descending overpass (6:00 a.m.) from five sampling days in August 2015. The validation 2 soil moisture data set is acquired from SMAPVEX15 in situ soil moisture sites (The * symbol denotes < 3 |0.001|). 4

5 6

Date SM Dataset

Number of

Points R2 Slope µbRMSE

(m3/m3) Bias

(m3/m3) p-value

08/08 1 km 48 0.409 0.236 0.044 -0.029 *

9 km 11 0.088 -0.126 0.088 -0.079 0.375

08/10 1 km 39 0.255 0.27 0.032 -0.023 0.001

9 km 11 * 0.004 0.081 -0.068 0.979

08/13 1 km 42 0.454 0.419 0.013 * *

9 km 11 0.353 -0.217 0.06 -0.035 0.054

08/16 1 km 44 0.443 0.352 0.02 -0.009 *

9 km 11 0.091 0.044 0.04 -0.024 0.368

08/18 1 km 39 0.733 0.705 0.006 -0.002 *

9 km 11 0.131 0.132 0.03 -0.023 0.274

27

1

2

Figure 1. Location of the study sites: (1) Walnut Gulch; (2) Empire Ranch and Santa Rita. Permanent in 3 situ soil moisture stations from the three study sites are denoted in red dots. 4

5

28

1

Figure 2. 10 km GPM (IMERG) 3-day accumulated Level 3 precipitation (unit: mm) from August 7-18, 2 2015 at Arizona (top row) and SMAPVEX15 (bottom row). 3 4

29

1 2 Figure 3. NLDAS surface soil moisture (m3/m3) at 6:00 a.m. versus daily surface skin temperature (K) 3 difference (1:30 p.m. - 1:30 a.m.) in August for the three SMAPVEX15 sampling sites: Walnut Gulch, 4 Empire Ranch and Santa Rita. The 𝜃𝜃 − ∆𝑇𝑇𝑠𝑠 point pairs are classified into 5 classes, based on the MODIS 5 NDVI value corresponding to each NLDAS grid. 6

7

30

1 2 Figure 4. SMAP Level 3 radiometer soil moisture (m3/m3) retrievals of 1 km downscaled, 9 km, 36 km, 3 and difference between 1 km and 9 km of descending overpasses (6:00 a.m.) in Arizona of the five 4 SMAPVEX15 sampling days. 5 6

31

1 2 Figure 5. 1 km downscaled SMAP soil moisture vs. 1 km upscaled PALS soil moisture and 9 km original 3 SMAP soil moisture retrievals of descending overpasses (6:00 a.m.) at SMAPVEX15 field (center 4 coordinates: 31.71oN, 110.68oW), from the five SMAPVEX15 sampling days. Boundaries of the Upper 5 San Pedro River Basin and San Pedro River are depicted in black and blue lines. The black grids outline 6 the 9 km grid boundaries. 7

8

32

1 2 Figure 6. Uncorrected 1 km soil moisture calculated from downscaling model comparing with 9 km 3 SMAP soil moisture of descending overpasses (6:00 a.m.) from the five SMAPVEX15 sampling days. 4 5

33

1 Figure 7. Soil moistures for 1 km downscaled SMAP, 1 km upscaled PALS and 9 km original SMAP soil 2 moistures of descending overpasses (6:00 a.m.) in SMAPVEX15 field from the five sampling days. 3

4

34

1

Figure 8. The empirical cumulative distribution function 𝑓𝑓(θ) of the 1 km downscaled SMAP, 1 km 2 upscaled PALS and 9 km original SMAP of descending overpasses (6:00 a.m.) for the five SMAPVEX15 3 sampling days. 4

5

35

1 2 Figure 9. Time series of the overall mean and standard deviation values of the 4 soil moisture data sets: 1 3 km downscaled SMAP, 1 km upscaled PALS and 9 km original SMAP of descending overpasses (6:00 4 a.m.) as well as in situ soil moisture measurements. 5

6

36

1

2 3 Figure 10. Validation scatterplots of 1 km downscaled and 9 km original SMAP soil moisture (m3/m3) 4 comparing with upscaled 1 km / 9 km PALS soil moisture (m3/m3). Warmer color in 1 km comparison plots 5 indicates higher density of scatter points. 6

7

37

1 2 Figure 11. Validation scatterplots of 1 km downscaled and 9 km SMAP soil moisture estimates (m3/m3) at 3 6:00 a.m. overpasses comparing with in situ soil moisture measurements for the five SMAPVEX15 4 sampling days. Comparison was made when there was a minimum of 8 in situ observations in each 1 km / 5 9 km SMAP soil moisture grid. 6

7

38

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