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Assessment of Crop Water Deficit and Estimation of Yield of Wheat in Greater Dinajpur Region Using MODIS Data
FINAL REPORT
SUJIT KUMAR BALA A.K.M. SAIFUL ISLAM
December 2010
Institute of Water and Flood Management (IWFM)
Bangladesh University of Engineering and Technology (BUET) Dhaka-1000, Bangladesh
Assessment of Crop Water Deficit and Estimation of Yield of Wheat
in Greater Dinajpur Region Using MODIS Data
FINAL REPORT
SUJIT KUMAR BALA A.K.M. SAIFUL ISLAM
December 2010
Institute of Water and Flood Management (IWFM) Bangladesh University of Engineering and Technology (BUET)
Dhaka-1000, Bangladesh
ii
Table of Contents Page No.
Table of Contents ........................................................................................................................... ii
List of Tables .................................................................................................................................. v
List of Figures ............................................................................................................................... vi
List of Symbols ............................................................................................................................. ix
List of Abbreviations .................................................................................................................... xii
Executive Summary .................................................................................................................... xiii
Chapter 1: Introduction .................................................................................................................. 1
1.1 Background .............................................................................................................................. 1
1.2 Objectives of the Study ............................................................................................................ 2
1.3 Outline of Methodology ........................................................................................................... 3
Chapter 2: Literature Review ......................................................................................................... 5
2.1. Application of remote sensing for crop monitoring and yield estimation ............................... 5
Chapter 3: Study Area .................................................................................................................... 9
3.1. Description of the Study Area ................................................................................................. 9
3.1.1. Location ............................................................................................................................ 9
3.1.2 Climate .............................................................................................................................. 9
3.2. Data ....................................................................................................................................... 10
3.2.1 Remote Sensing Data ...................................................................................................... 10
3.2.2. Field Data ....................................................................................................................... 11
2.3 Secondary Data .................................................................................................................. 13
3.3 Image Processing and Wheat Area Classification .................................................................. 13
Chapter 4: Methodology of estimating evapotranspiration using SEBAL Algorithm ................. 16
4.1 SEBAL Method ...................................................................................................................... 16
4.2 Solar Zenith Angle ................................................................................................................. 17
4.3 Solar Declination .................................................................................................................... 17
4.4 Equation of Time .................................................................................................................... 17
4.5 Local Apparent Time (LAT) .................................................................................................. 18
4.6 Hour Angle ............................................................................................................................. 18
4.7 Solar zenith angle ................................................................................................................... 18
4.8 Bio Physical Parameters ......................................................................................................... 19
4.8.1 Normalized Difference Vegetation Index (NDVI) .......................................................... 19
4.8.2 Soil Adjusted Vegetation Index (SAVI) ......................................................................... 19
4.8.3 Leaf Area Index (LAI) .................................................................................................... 21
iii
4.8.4 Displacement height (d) .................................................................................................. 21
4.8.5 Surface roughness (zo) ..................................................................................................... 22
4.8.6 Surface Roughness for Momentum Transport (zom) ....................................................... 24
4.8.7 Surface Roughness for Heat Transport (zoh) ................................................................... 24
4.9 Net Radiation (Rn) .................................................................................................................. 24
4.10 Soil Heat Flux (G) ................................................................................................................ 28
4.11 Sensible Heat Flux (H) ......................................................................................................... 30
4.11.1 Aerodynamic resistance to heat transport ..................................................................... 31
4.11.2 Friction velocity ( *u ) .................................................................................................... 31
4.11.3 Blending height (UB) ..................................................................................................... 31
4.11.4 Monin Obukhov Length(L). .......................................................................................... 31
4.11.5 Correction factors. ......................................................................................................... 32
4.12 Instantaneous Latent Energy Flux ........................................................................................ 34
4.13 Evaporative Fraction ............................................................................................................ 34
4.14 Total daily net radiation ....................................................................................................... 35
4.14.1 Daily terrestrial solar radiation ...................................................................................... 35
4.14.2 Average Daily Incoming Shortwave Radiation (S↓day) ................................................. 36
4.14.3 Average Daily Net Longwave Radiation ...................................................................... 36
4.15 Daily Evapotranspiration ...................................................................................................... 37
Chapter 5: Estimation of Evapotranspiration ............................................................................... 39
5.1 Cosine of Solar Zenith Angle [cos (θz)] ................................................................................ 39
5.2 Reflectance and Temperature ................................................................................................. 40
5.3 Albedo .................................................................................................................................... 40
5.3.1 Planetary Broadband Albedo .......................................................................................... 40
5.3.2 Broadband Surface Albedo ............................................................................................. 40
5.4 Instantaneous Surface Temperature ....................................................................................... 41
5.5 Biophysical Parameters .......................................................................................................... 43
5.5.1 Normalized Difference Vegetation Index (NDVI) .......................................................... 43
5.5.2 Soil Adjusted Vegetation Index (SAVI) ......................................................................... 44
5.5.3 Leaf Area Index (LAI) .................................................................................................... 45
5.5.4 Displacement height (d) .................................................................................................. 46
5.5.5 Surface Roughness for Momentum Transport ................................................................ 47
5.6 Instantaneous Net Radiation (Rn). ......................................................................................... 49
5.6.1 Net Shortwave Radiation ................................................................................................ 50
5.6.2 Net Longwave Radiation ................................................................................................. 52
5.7 Soil Heat flux: ........................................................................................................................ 53
iv
5.8 Sensible heat Flux. ................................................................................................................. 54
5.8.2 Spread Sheet Calculation - Estimation of constants a & b for determination of dT (Ts-Ta) .............................................................................................................................. 56
5.8.3 Final Iteration for the determination of Sensible heat ..................................................... 56
5.9 Instantaneous Latent Heat flux. .............................................................................................. 61
5.10 Evaporative Fraction ............................................................................................................ 62
5.11 Net Daily Radiation .............................................................................................................. 63
5.11.1 Daily terrestrial solar radiation ...................................................................................... 63
5.11.2 Average Daily Net Longwave Radiation ...................................................................... 65
5.12 Evapotranspiration ............................................................................................................... 65
5.13 Spatial Distribution of Evapotranspiration ........................................................................... 66
5.14 Comparison of SEBAL with FAO Penman Monteith .......................................................... 69
5.14.1 FAO Penman-Monteith equation .................................................................................. 69
5.14.2 Comparison of ET using SEBAL and Penman Monteith methods ............................... 73
Chapter 6: Crop Growth Monitoring and Yield Estimation ......................................................... 76
6.1 Spatial Distribution of wheat during the growing season ...................................................... 76
6.2 Correlation between NDVI and production ........................................................................... 78
Chapter 7: Conclusions ................................................................................................................ 81
7.1 Conclusions ............................................................................................................................ 81
7.2 Recommendations .................................................................................................................. 82
REFERENCES ............................................................................................................................. 83
APPENDIX A: ILWIS script developed for running the SEBAL algorithm ............................. 87
v
List of Tables
Page No.
Table 3.1: List of MODIS Images downloaded for the study ...................................................... 11
Table 5.1: Derived components of dry and wet pixel for the study region. ................................. 56
Table 5.2: Derived components, constants and other data used in the spreadsheet iterative calculation to estimate ‘a’ and ‘b’ ............................................................................... 58
Table 5.3: Spread sheet iteration table for determining the constants ‘a’ and ‘b’. ....................... 58
Table 5.4: Calculation for crop co-efficient of wheat (Source: Rahman et al. (2008)) ................ 72
Table 5.5: Mean value of atmospheric parameters and ET of wheat using Penman Monteith method during the growing season. ............................................................. 73
Table 5.6: Mean value of various components of surface energy fluxes and ET of wheat using SEBAL method during the growing season. ..................................................... 74
Table 6.1: Wheat Coverage Area during 2007-2008 growing season ........................................ 76
Table-6.2: Upazila-wise Yield and maximum NDVI during the growing season. ...................... 78
vi
List of Figures Page No.
Figure 3.1: Location map of the study area ................................................................................... 9
Figure 3.2 Monthly maximum and minimum temperature (0C) at Dinajpur district ................... 10
Figure 3.3: Mean monthly rainfall at Dinajpur district ................................................................ 10
Figure 3.4: location of the wheat fields (red diamond) in Dinajpur, Panchagarh and Thakurgaon district. ..................................................................................................... 12
Figure 3.5: Ground truthing Farmers’ wheat fields under study area. ......................................... 12
Figure 3.6: Changes of NDVI in the growing season of the selected fields. The dark bold line shows the average value of the changes of NDVI. ............................................... 14
Figure 3.7: (a) NDVI value over the study area and (b) NDVI value over the wheat cultivable area on the 25 January 2008 (Day of the year is 25). ................................. 15
Figure 3.8: Location map of the wheat fields in the study area during growing season of 2007-2008. ................................................................................................................... 15
Figure 4.1: Components of the Energy Balance .......................................................................... 16
Figure 4.2: Solar declination angle. ............................................................................................. 17
Figure 4.3: Flow chart of methodology to derive Soil Adjusted Vegetation Index ..................... 20
Figure 4.4: Vertical distribution of wind profile over vegetation.. .............................................. 21
Figure 4.5: Surface resistance of crop canopy and energy balance of crop canopy & soil. ......... 23
Figure 4.6: Surface Atmosphere Energy Exchange ..................................................................... 25
Figure 4.7: Solving for constants using wet and dry pixels ......................................................... 33
Figure 4.8: Flow chart of Iterative process to calculate Sensible Heat Flux ................................ 34
Figure 5.1: Cosine of Solar Zenith Angle on 25 January 2008 .................................................... 39
Figure 5.2: Broad band Surface Albedo ....................................................................................... 41
Figure 5.3: Instantaneous Surface Temperature ........................................................................... 42
Figure 5.4: NDVI Map for the study region for the date 25 January 2008 .................................. 43
Figure 5.5: Soil line concept for computing the value of ‘γ’ ....................................................... 44
Figure 5.6: SAVI map for studying biophysical parameters of the region. ................................. 45
Figure 5.7: Leaf Area Index (LAI) map for the study area. ......................................................... 46
Figure 5.8: Displacement Height map for the study area. ............................................................ 47
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Figure 5.9: Map of Surface roughness length of momentum transport. ...................................... 48
Figure 5.10: Map of surface roughness length for Heat transport ............................................... 49
Figure 5.11: Net Radiation Map (Wm-2). ..................................................................................... 50
Figure 5.12: Net shortwave radiation map for the study area. ..................................................... 52
Figure 5.13: Net Longwave Radiation Map (Wm-2). ................................................................... 53
Figure 5.14: Soil heat flux (Wm-2). .............................................................................................. 55
Figure 5.15: Two Dimensional Scatter Plot between Surface Temperature and Albedo for determination of Dry Pixel .......................................................................................... 57
Figure 5.16: Two Dimensional Scatter Plot between Surface Temperature and NDVI for determination of Wet Pixel .......................................................................................... 57
Figure 5.17: Plot of dT over surface temperature Ts for determining the constant ‘a’ and ‘b’ ................................................................................................................................ 59
Figure 5.18: Difference between surface and air temperature (dT map in K). ............................ 60
Figure 5.19: Instantaneous Sensible heat flux (Wm-2) map for the study area ............................ 60
Figure 5.20: Histogram of sensible heat flux values for the study area. ...................................... 61
Figure 5.21: Instantaneous Latent heat flux in Wm-2 estimated as residual term of energy balance. ........................................................................................................................ 62
Figure 5.22: Evaporative fraction map estimated for the satellite pass instant. ........................... 63
Figure 5.23: Daily terrestrial solar radiation in MJm-2day-1. ........................................................ 64
Figure 5.24: Average daily incoming shortwave radiation in Wm-2 ............................................ 65
Figure 5.25: Single day Evapotranspiration of the day of 25 January 2008 for the study area. ............................................................................................................................. 66
Figure 5.26: Change of Evapotranspiration (mm/day) for the study area .................................... 67
Figure 5.27: Change of Evapotranspiration (mm/day) for the wheat field .................................. 68
Figure 5.28: Explaining the reference crop ETo and crop evapotranspiration ETc ...................... 70
Figure 5.29: Growth stages and changes of Kc values ................................................................. 71
Figure 5.30: Growth stages and changes of Kc values of wheat .................................................. 72
Figure 5.31: Comparison of Evapotranspiration (mm/d) between SEBAL and Pennman Montieth ...................................................................................................................... 74
Figure 5.32: Comparison of Kc values determined from field experiment with values determined using both SEBAL and Penman Montieth methods. ................................ 75
viii
Figure 6.1: Changes of the NDVIs of the wheat for the growing season of 2007-2008. ............. 77
Figure 6.2: Correlation between wheat yield (t/ha) and median value of NDVI during the peak growth (DOY=25) for each Upazila of the study area. ....................................... 79
Figure 6.3: Correlation between wheat Production (ton) and no of wheat pixels in the Upazila ......................................................................................................................... 80
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List of Symbols
ρp : Unitless planetary reflectance
δ : Solar declination angle
ω : Hour angle
ε0 : Broadband surface emmissivity
εa : Emmisivity of atmosphere
σ : Stefan-Boltzmann constant
aρ : density of the moist air (Kgm-3)
ψh : Monin-Obukhov stability correction for heat transport
ψm : Monin-Obukhov stability correction for momentum transport
Λ : Evaporative fraction
Λinst : Instantaneous evaporative fraction
vλ : Latent heat of vaporization in MKg-1
sw : Sunrise hour angle
φ : Latitude
τday : Single way transmissivity
ε' : Net emissivity between atmosphere and ground
f : Cloudiness factor 0C : Degree Celsius
θ : Solar zenith angle
Lλ : Spectral radiance at the sensor's aperture
a : Is a constant taken as 1.16
ae : Correlation coefficient, default=0.34
as+bs : fraction of the extraterrestrial radiation reaching the ground in a
complete clear day
be : Correlation coefficient, default=-0.14
d : Earth-Sun distance in astronomical units
ESUNλ : ESUNλ Mean solar exo-atmospheric irradiances
T : Effective at-satellite temperature in Kelvin
K2 : Calibration constant 2 =1282.71 Kelvin
K1 : Calibration constant 1= 666.09 w/(m-2 * ster * µm)
dn : Julian day.
da : Day angle
x
Et : Equation of time
Lc : Longitude
N : Day length
L : Adjustment factor(0.5)
C1 : Is a constant taken as 0.13 for computing LAI
C2 : Is a costant taken as 0.35 for computing LAI
z : Height with respect to surface
zst : Standard height for the wind speed measurement
c1 : Is a constant taken as -5.5 for Zom formula
c2 : Is a constant taken as 5.8 for Zom formula
d : Displacement height
h : Vegetation height
c : Free parameter equal to 20.16
Cp : air specific heat at constant pressure (JKg-1K-1)
rah : Aerodynamic resistance to heat transport between reference and surface
level(sm-1)
zo : Surface roughness
Zom : Surface roughness for momentum transport
Zoh : Surface roughness for heat transport
k : Von Karman’s constant(0.41)
Rn : Net Radiation
S↓ : Shortwave incoming
S↑ : Shortwave outgoing
L↓ : Long wave incoming
L↑ : Long wave outgoing
r0 : is the broadband surface albedo
Trad : Radiometric temperature
Ts : Surface temperature
Ta : Air temperature
as+bs : fraction of the extraterrestrial radiation reaching the ground in a
complete clear day
n : Sunshine hours
N : Day length in hours
S0↓ : extraterrestrial radiation [MJm-2day-1]
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ed : vapor pressure [mbar],
G : Soil heat flux(W/m-2)
H : H is the Sensible heat flux (W/m-2)
rah : Aerodynamic resistance to heat transport in(sm-1)
Zref : The reference height for the determination of wind speed.
*u : Friction velocity in (ms-1)
Ub : Wind velocity at ZB taken as 100 meter(ms-1).
uref : Wind speed at reference height Zref(ms-1).
ZB : Blending height
L : Monin obukhov length
Χh : Correction factor for heat transport
ΧM : Correction factor for momentum transport
LE : Latent energy flux
g : Gravitational constants
Eo : Eccentricity correction factor for a day(constant) .
SC : Solar constant exo
dayS ↓ : The daily exoterrestrial solar radiation
↓dayS : The average daily incoming solar radiation
sa : Terrestrial radiation reaching on a complete overcast day(0.25)
as+bs : Total fraction of terrestrial radiation reaching the ground, where bs is
0.5.
Lday : Average daily Net long wave radiation
Ta,mean : Mean daily air temperature
ae : Correlation coefficient, default=0.34
be : Correlation coefficient, default=-0.14
ed,mean : Average vapor pressure
es,mean : Average saturation vapor pressure
Rnday : Total daily Net radiation
c1 : Conversion factor surface Albedo taken as 1.1
xii
List of Abbreviations BCA : Bangladesh Country Almanac
BMD : Bangladesh Meteorological Department
DAE : Department of Agricultural Extension
DN : Digital number
DVI : Difference Vegetation Index
EOS : Earth Observing System
EVI Enhanced Vegetation Index
GIS : Geographic Information System
ILWIS : Integrated Land and Water Information System
IPVI : Infrared Percentage Vegetation Index
LAT : Local apparent time
LAI : Leaf Area Index
MAX : maximum
MIN : Minimum
MODIS : Moderate Resolution Imaging Spectroradiometer
MSAVI : Modified Soil Adjusted Vegetation Index
MVC : Maximum-value compositing
NASA : National Aeronautics and Space Administration
NDVI : Normalized Difference Vegetation Index
NIR : Near Infrared
PVI : Perpendicular Vegetation Index
RS : Remote Sensing
RVI : Ratio Vegetation Index
SAVI : Soil Adjusted Vegetation Index,
SEBAL : Surface Energy Balance algorithm for land.
SRDI : Soil Resource Development Institute
TDVI : Transformed Difference Vegetation Index
TVI : Transformed Vegetation Index
TSAVI : Transformed Soil Adjusted Vegetation Index
VI : Vegetation Index
WDVI : Weighted Difference Vegetation Index
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Executive Summary The increasing demand of food management, monitoring of the crop growth and forecasting its
yield well before harvest is very important. Early yield prediction together with monitoring of
crop development and its growth are being identified with the help of satellite and remote
sensing images. Studies using remote sensing data along with field level validation reported high
correlation between vegetation indices and yield. In recent years, there has been a growing
cultivation of cereal crops including wheat in the North West region of Bangladesh especially in
the greater Dinajpur region which consists of three districts: Dinajpur, Panchagarh and
Thakurgaon. However, it is difficult to quantify the exact area of wheat cultivation using
traditional ground based measurements. However, remote sensing can provide most real time
information about the wheat coverage area and can estimate the probable yield.
In this context, this study has been carried out to estimate crop yield of wheat at field level using
remote sensing data for the greater Dinajpur region of Bangladesh. The study area lies between
latitude 20029’56.06”N to 26047’55.91”N and longitude 87048’4.09”E to 92048’0.59”E. The
main objectives of this study are to identify spatial coverage area of wheat using remote sensing
data and validate it through field based survey, to estimate evapotranspiration of wheat during
the growing period and detect the crop water deficit using remote sensing data, to develop
relationship between vegetation indices such as Normalized Difference Vegetation Index
(NDVI) and yield to predict regional yield of wheat.
Field data of wheat for the growing season from November 2007 to March 2008 was collected
from the farmers through successive field visits in the study area. A total of 40 farmers were
interviewed and their fields were digitized. A hand held GPS was used to digitize fields and for
ground-truthing of the wheat fields. Data on administrative boundary were collected from the
Data Base Bangladesh Country Almanac (BCA). Data on crop information was collected from
the Department of Agricultural Extension (DAE) at Sadar Upazila of Dinajpur district. Climatic
data was collected from Bangladesh Meteorological Department (BMD).
Surface reflectance and land surface temperature data of the Moderate Resolution Imaging
Spectroradiometer (MODIS) were used. A time series data product of MODIS with a temporal
resolution of 8 days and a spatial resolution of 500m for spectral band and 1 km for thermal
band data were used to study yield and evapotranspiration of wheat. A total of 13 images were
downloaded from December 2007 to March 2008 during the growing season of wheat.
xiv
Integrated Land and Water Information System (ILWIS 3.4) software was used for image
processing and spatial analysis. Images were geo-referenced using software MODIS Re-
projection Tool (MRT). MODIS images were validated for wheat area from bare land,
settlement, water bodies, agricultural crops, etc. through establishing mean wheat growth curve
using data from selected 40 farmers’ fields. The chronological changes of vegetation indices
(e.g. NDVI) after wheat plantation were studied through spatial and temporal distribution for the
study area. Using the NDVI indicator developed from time series MODIS satellite images, the
phonological growth of wheat has been monitored during the Rabi season (November to March)
of 2007-2008 for the greater Dinajpur region of Bangladesh. The median value of NDVI for
various Upazila varies from 0.563 to 0.603 with a mean of 0.584 during the growing season. The
wheat field has been successfully delineated (masked) using the chronological changes of
vegetation indices (NDVI) from the selected farmers’ field. This information was used for
estimation of evapotranspiration of the crop and its yield.
As mentioned above, satellite images provide a powerful tool for the identification of crops and
determine crop water requirement which is effective for land use and water management. The
estimation of evapotranspiration using remote sensing data is another very important component
for effective water management. The exchanges of radiative heat and moisture fluxes affect the
biosphere and various irrigation process, and estimation of crop water demand and also the rate
of evapotranspiration. A study was conducted to estimate the daily evapotranspiration through
remote sensing for the greater Dinajpur region of Bangladesh. Surface Energy Balance
Algorithm (SEBAL) was used to estimate evapotranspiration by balancing all energy
components such as sensible heat flux, net radiation, soil heat flux and latent heat of
evaporation. The average values of evapotranspiration for the study area using SEBAL and
Penman Monteith method were found 2.7 mm/day and 2.44 mm/day respectively. The actual
evapotranspiration calculated from the SEBAL method was compared with the theoretical ET of
reference crop using the Penman Monteith method. Crop coefficient, Kc was determined during
the growing season of wheat by comparing ET from the above two methods. This study
successfully demonstrate the capability of estimating evapotranspiration and crop coefficient of
wheat using remote sensing data which can be used as useful tool for crop water management.
An attempt was undertaken to correlate the crop health using NDVI indices with the yield.
Using the Upazila wise yield data from the Department of Agricultural Extension (DAE) a
correlation was developed between yield of wheat and maximum values of NDVI. In the study
xv
area, the yield of wheat varies from 1.04 ton/ha to 2.5 ton/ha with a mean value of 2.19 ton/ha.
A strong correlation was found (R2=0.71) between the wheat production and satellite
represented wheat area. It can be inferred that satellite data can be used as effective tool for crop
monitoring and yield estimation of wheat.
However, the results of this study can be improved by using high resolution satellite images,
continuous collection of evapotranspiration data through Lysimeter experiments, installation of
more meteorological stations for weather parameters and collecting production and yield from
farmers’ fields etc.
1
Chapter 1: Introduction
1.1 Background
Remote sensing technology is an effective tool for monitoring agricultural crops, assess growth,
estimate evapotranspiration (ET), predict yield, etc. Now days, food security issue has taken a
global dimension and emerged as a very important one for an overpopulated country like
Bangladesh, application of remote sensing technique in agriculture sector needs full attention.
The recent food price hike fueled its urgency. The farmers of Bangladesh have gone for
intensive cultivation of cereal crops including wheat in this Rabi crop year of 2008. The
production of wheat continued to grow from the late 1990s due to favorable price. The present
price trends of wheat accelerated the process of intensive wheat cultivation. The future prospect
of cultivation of wheat in Bangladesh, at present, is quite bright especially in greater Dinajpur
region of Bangladesh. The airy information says that wheat cultivation acreage area has been
increased resulting in higher wheat production in the country. But it is difficult to quantify the
increased wheat acreage area and production on real time basis using conventional techniques.
Conventional techniques to such jobs are based on ground-based field visits, data collection for
crop and reports which are often subjective, costly and time consuming and also bear large
errors for incomplete ground observations (Reynolds et al. 2000).
On the other hand, satellite and remote sensing images are capable of doing these jobs very
effectively. In recent years, studies using remote sensing data done at field level reported high
correlation between NDVI and yield. Assessment and monitoring of vegetation parameters like
NDVI and crop vigor and green biomass may be ascertained through use of remote sensing.
Therefore, NDVI can be used to estimate yield before harvesting (Groten 1993, Liu & Kogan,
2002 and Rasmussen 1997). Ali et al. (1987) and Choudhury et al. (1990) investigated
hydrological and agricultural applications using AVHRR data in Bangladesh. Nessa (2005) in
her M. Phil Thesis studied the use of NDVI for monitoring of rice growth and its production in
Bangladesh with NOAA satellite data. Bala and Islam (2008) in their recently completed
research project have shown the effectiveness of use of remote sensing technology for prediction
of yield of potato in Bangladesh. Islam et al. (2008) also have shown the applicability of remote
sensing technology in establishing the scale of disaster like green mass destruction over the
mangrove forest of Bangladesh just after the SIDR. However, to the best of our knowledge, no
2
research works have been carried out in Bangladesh on the determination wheat coverage area
and yield estimation through remote sensing data.
In the past, remote sensing data has been used for estimating NDVI and correlate with
evapotranspiration (Kerr et al.1989, Kite et al. 2000, Lo 1993, Srivastava, 1997, Sun et al.,
2004). But, recent approaches use remote sensing data to directly calculate ET at basin scale by
solving energy balance equations such as, SEBAL-Surface Energy Balance Algorithm for Land
(Bastiaanssen, 1998), SEBS-Surface Energy Balance System (Su, 2002), RESP-Regional
Evapotranspiration through Surface Energy Partitioning (Ambast, 2002) etc. Significant
progress has also been made in accuracy of remote sensing models in the calculation of regional
ET using both imagery and meteorological data. Initially the surface ET is divided into soil
evaporation and vegetation transpiration (Mo et al., 2004) from the one layered model (the land
surface is seen as a uniform surface) to the present two or multi-layered model (the land surface
is seen as soil pixel and vegetation pixel). Many research studies have been found which
estimate ET to identify crop water stress and evaluate the performance of irrigated agricultural
processes. Yi et al. (2007) has shown application of MODIS data to detect crop water deficit
during winter wheat growing period along the lower reaches of the Yellow river, China. Tang et
al. (2007) has calculated regional evapotranspiration using MODIS data and compare it with
point based field measurements. Abdalla et al. (2007) has estimated evapotranspiration of arid
regions of USA using airborne remote sensing data. Di Bella et al. (2000) applied multiple
regression analyses to relate ET estimated from water balance technique with NDVI data from
AVHRR sensor and mapped ET of the Pampa region of Argentina. Using SEBAL method ,
performances of irrigation system of paddy crop in Sri Lanka has been assessed (Bandara,
2006). It has been found that the remote sensing data could be a viable cost effective tool of
sufficient accuracy to provide many useful information of an irrigation system.
1.2 Objectives of the Study
The specific objectives of this study are:
i) to identify spatial coverage area of wheat using remote sensing data and
validate it through field based survey.
ii) to estimate ET of wheat during the growing period and detect the crop water
deficit using remote sensing data.
iii) to develop relationship between NDVI and yield data from farmers field.
3
iv) to predict regional yield of wheat in the study area using the relationship
developed based on NDVI and field data.
This research work on finding out of ET and NDVI of wheat from remotely sensed image and
their correlation for understanding its effect on yield may pave the way for better understanding
of water management issues on wheat yield as well as its prediction using remote sensing
technique. Thus, this study is very important for the applied field like agricultural science of the
country.
1.3 Outline of Methodology
In this study, spatial distribution of wheat during the growing season of 2007-2008 (November
to April) will be estimated from satellite data for the greater Dinajpur region. Meteorological
data of Dinajpur region would be collected from the BMD. Field level yield and
evapotranspiration data will be collected in cooperation with the Wheat Centre at Dinajpur.
Satellite images will be used for the study include TERRA MODIS surface reflectance
(resolution 250m and 500m) and Land surface temperature, LST (resolution 1km). TERRA
MODIS images will be freely downloaded from internet. Topographic map of the area will be
collected for geo-referencing. GPS will be used for ground-truthing of farmer’s field. ILWIS 3.4
and Arc GIS 9.2 software will be used for image processing and analysis.
The preliminary crop calendars will be collected for the study area from Depart of Agricultural
Extension (DAE). The images will be classified in ERDAS using unsupervised classification
algorithm. A TERRA MODIS image will be re-projected using the software MRT. The satellite
image will be processed in a GIS environment and an NDVI map will be generated using band 2
(NIR) and band 1 (RED). The field polygons will be imported into ILWIS. The polygons will be
then rasterized. Crossing the field raster images with the NDVI image would generate field level
NDVIs. Then, these field level NDVIs will be plotted for the whole growing season of wheat.
Phenological curves based on the field level NDVIs data will be developed to identify
characteristics of wheat crop. Based on this crop phenology, wheat coverage map will be
generated for the study area. This map will be used for further study such as estimation of
evapotranspiration, determination of crop coefficient, and estimation of yield etc.
4
This study will calculate of the surface ET in greater Dinajpur region based on energy balance
equation using MODIS imagery and meteorological data. To match the remotely sensed ET with
point observed ET from field, a sinusoidal relationship will be adopted to calculate the spatial
distribution of diurnal ET using IDW (Inverse Distance Weighting). The mean value of a 3x3
pixel area, including the observed point value is calculated as the pixel value for comparison
with observed point data. Finally, other observed data precluding the verified aforementioned
was used to validate the remote sensed ET in the study area. Crop stress detection during the
growing season of wheat will be determined by comparing actual ET from satellite data with the
Potential ET (FAO 56, 1998) of wheat.
A correlation will be establish between maximum NDVI and Upazila wise yield data from
Department of Agricultural Extension (DAE). Using this relationship, the aerial average yield
for the greater Dinajpur region will be estimated for the growing season.
5
Chapter 2: Literature Review
2.1. Application of remote sensing for crop monitoring and yield estimation
Remote sensing provides the status of the health of vegetation. The spectral reflectance of a crop
field depends on phenology, stage type and crop health and they could be well monitored using
multi-spectral sensors. Thus remotely sensed data can be used in GIS for further analysis to
provide field level information of ownership and management practices. Objective, standardized
and possibly cheaper/faster methods that can be used for crop growth monitoring and early crop
yield estimation are imperative. Many empirical models have been developed to try and estimate
yield before harvesting. However, most of the methods require data that are not easily available.
The models complexity, their data demand, and methods of analysis, render these models
impractical, especially at field level. Remote sensing images provide access to spatial
information at global scale; of features and phenomena on earth on an almost real-time basis and
estimate crop yield. Estimation of crop yield is usually done by detecting the land cover change
seasonally and annually. Seasonal change provides information of agricultural change, while
annual change indicates land cover or land use change, which may be called as real change.
Many studies were done at field level and reported high correlation between NDVI and yield.
However, most of these studies were done under research conditions involving very small plots
with spectral data being collected with ground-based platforms extended over the plots or low
flying platforms. Such conditions enable a large degree of control over many extraneous factors
and normally result in high quality data and excellent correlation between the measured and
remote sensed data (Staggenborg & Taylor, 2000). Quarmby et al. (1993) showed that NDVI
can be used to estimate yield from a test field in Greece and Verma et al (1998), working on
gram, found high correlation between NDVI and dry matter. The potential of regression models
to estimate crop yield more accurately under variable management conditions was clearly
established. Estimation of crop yield at the regional scale from MODIS (Medium resolution
imaging spectroradiometer) data using the data assimilation method was done by Shunlin et al.
(2004). MODIS data products included leaf area index (LAI) and enhanced vegetation index
(EVI). The crop growth models of DSSAT were used in the study, which were driven by
weather, soil and crop management data. Some of the variables of the models were adjusted
through data assimilation algorithms for accurate prediction of crop yields.
6
The Canadian Wheat Board adopted NOA AVHRR maximum value of NDVI for the purpose of
crop condition assessment and yield prediction. Spring wheat estimates for the 1991 and 1992
growing season with NDVI showed that early season estimates were within 5% of official
estimates released 3 months following the harvest of wheat. Yang et al. (2000) reported that
NDVI can predict grain yields with 89% accuracy, while can account 80% of variability in grain
yields. Murthy et al.(1994) showed relationship of yield and NDVI at different phenological
stages of rice. Their estimates of rice yields using time composite NDVI in comparison with
crop cutting experiments are found to be promising in accuracy with less than 10% deviation
from actual yield.
Satellite remote sensing techniques can provide resource managers an efficient and economical
means of acquiring timely data for the development and management of our natural resources.
Remote sensing and its associated image analysis technology provide access to spatial
information on a planetary scale. Ibrahim et al. (1994) estimated paddy yield from the Landsat-5
Thematic Mapper (TM) data in the Sungai Besar area in the state of Selandgor, Malaysia. The
yield estimated derived from the satellite data were found to be 30% higher than the field
estimates. It happened due to the difference in the paddy phenology cycle at the time the satellite
data were acquired and the time the field measurements were taken.
2.2. Application of remote sensing for estimation of Evapotranspiration
A number of scientists contribute to develop algorithms of the estimation of evapotranspiration
of crop using remote sensing data. Bastiaanssen et al, (1998) formulated the new surface Energy
Balance Algorithm for Land (SEBAL). The new algorithm estimates the spatial variation of
most essential hydro-meteorological parameters empirically which requires only field
information on short wave atmospheric transmittance, surface temperature and vegetation and
vegetation height. This algorithm doesn’t involve numerical simulation models and calculates
fluxes independently from Land cover and can handle thermal infrared images at a resolution
between few meters to few kilometers. The empirical relationship is adjusted to different
geographical conditions and regions and time of image acquisition. Norman et al. (1995)
developed a two layer model of turbulent exchange that includes the view geometry and
associated with directional radiometric surface temperature is developed and evaluated by
comparison of model prediction with field measurement. Boegh, et al (2002) evaluated
evapotranspiration rates and surface conditions using Landsat TM to estimate atmospheric
resistance and surface resistance. Michael (2003) estimated of absolute surface temperature by
7
satellite remote sensing. Venturini et al, (2004) did comparison of evaporative fractions
estimated from AVHRR and MODIS sensors over South Florida. Rivas and Caselles (2004)
simplified equation to estimate spatial reference evapotranspiration from remote sensing-based
surface temperature and local standard meteorological data. Boegh and Soegaard (2004)
presented a remote sensing based method for calculating evapotranspiration rates using standard
meteorological field data and radiometric surface temperature recorded for bare soil, maize and
wheat canopies in Denmark. Di Bella et al, (2004) estimated evapotranspiration estimation using
NOAA AVHRR imagery in the Pampa region of Argentina. Pamela et al. (2005) computed
evapotranspiration on western U.S. rivers estimated using the Enhanced Vegetation Index from
MODIS and data from eddy covariance and Bowen ratio flux towers. Loheide and Gorelick
(2005) developed a local-scale, high-resolution evapotranspiration mapping algorithm (ETMA)
with hydroecological applications at riparian meadow restoration sites was studied. El-magd and
Tanton (2005) carried out study on remote sensing and GIS for estimation of irrigation crop
water demand. Jing et al. (2004) studied distributed hydrological model for mapping
evapotranspiration using remote sensing inputs. Mekonnen(2005) assessed Catchment Water
Balance Using GIS and Remote Sensing in Roxo, Portugal . Lin (2005) estimated satellite based
regional-scale evapotranspiration in the Hebei Plain of Northeastern China using the Surface
Energy Balance System (SEBS) model. This model was developed to estimate land surface
fluxes using remotely sensed data and available meteorological observations. Weligepolage
(2005) studied estimation of spatial and temporal distribution of evapotranspiration by satellite
remote sensing in Hupselse Beek, the Netherlands. French et al. (2005) studied surface energy
fluxes with the Advanced Spaceborne Thermal Emission and Reflection radiometer (ASTER) at
the Iowa 2002 SMACEX site (USA). Zhang et al. (1995) developed an integrated algorithm for
estimating regional latent heat flux and daily evapotranspiration by using remote-sensing data
and ground-based data.
Boegha et al, (2004) incorporated remote sensing data in physically based distributed agro-
hydrological modeling. Hailegiorgis, (2006) did remote sensing analysis of summer time
Evapotranspiration using SEBS algorithm Regge and Dinkel, The Netherlands The study has
been carried out using summer time Landsat images, meteorological and groundwater data for
attaining the desired objective. The physically based advanced surface energy balance algorithm
(SEBS) (Su, 2002) was applied for assessing the spatial and temporal variation of AET. The
Surface Energy Balance Algorithm for Land (SEBAL) images was used to determine the actual
evapotranspiration of acquisition day Landsat ETM+ images. Reduan (2004) studied multi-
8
sensor approach to evapotranspiration mapping and STREAM Model Validation in the Perfume
River Basin, Hue, Vietnam. In this study, a spatial hydrological model called STREAM was
used where it require minimum levels of input data. McCabe and Wood (2006) studied scale
influences on the remote estimation of evapotranspiration using multiple satellite sensors.
Understanding the role of landscape heterogeneity and its influence on the scaling behavior of
surface fluxes as observed by satellite sensors with different spatial resolutions is studied. Batra
et al. (2006) carried out studies on the estimation and comparison of evapotranspiration from
MODIS and AVHRR sensors for clear sky days over the Southern Great Plains. Wang et al.
(2006) estimated evaporative fraction from a combination of day and night land surface
temperatures and NDVI.
9
Chapter 3: Study Area
3.1. Description of the Study Area
3.1.1. Location
The study was conducted in the greater Dinajpur region of Bangladesh. The study area is located
between 87°57´ E to 89°26´ E and 25°10´ N to 26°39´ N. The greater Dinajpur region consists
of three districts: Dinajpur, Panchagarh and Thakurgaon. There are 7 Upazilas in Dinajpur
district, 5 Upazilas in Panchagarh and 5 Upazilas in Thakurgaon districts. Figure 3.1 shows the
location map of the study area.
Figure 3.1: Location map of the study area
3.1.2 Climate
Dinajpur has a tropical wet and dry climate under the Koppen climate classification. The district
has a distinct monsoonal season, with an annual average temperature of 25 °C (77 °F) and
monthly means varying between 18 °C (64 °F) in January and 29 °C (84 °F) in August. Figure
3.2 shows the mean monthly maximum and minimum temperature of Dinajpur district.
10
Figure 3.2 Monthly maximum and minimum temperature (0C) at Dinajpur district
This district has a distinct monsoon season with yearly rainfall of 1979 mm. The mean monthly
rainfall distribution of Dinajpur district is shown in Figure 3.3. Majority of rainfall occurred
during the monsoon season.
Figure 3.3: Mean monthly rainfall at Dinajpur district
3.2. Data
3.2.1 Remote Sensing Data
In this study MODIS images acquired by TERRA instrument were used. MODIS, the Moderate
Resolution Imaging Spectroradiometer satellite was launched on 18 December 1999 as part of
NASA’s Earth Observing System (EOS). A product of the average of 8 days reflectance
11
“Surface Reflectance 8-Day L3 Global 250m” were used for the winter season of 2007-2008.
The images can be freely downloaded from the Earth Observing System Data Gateway by using
Warehouse Inventory Search Tool (WIST). The spatial resolution of this product is
approximately 250 m, and atmospheric correction has already been carried out. The MODIS
data sets can be found in a sinusoidal coordinates system where Bangladesh is located at 26th
row and 6th column of a global tile system. MODIS has 36 bands of which band 1 (red) and band
2 (NIR) are aggregated with a spectral range from 620 nm to 876 nm.
In total 13 images were downloaded from the MODIS Website (http://modis.gsfc.nasa.gov/)
covering a period from 3 December 2007 to 5 March 2006, while 12 imaged were processed for
the study. Downloaded images are shown in the Table 3.1. Day after plantation has been
calculated based on field data. It was found from successive field visit to the study area that
plantation of wheat has started from middle of November. In this study, 15 November 2007 has
been considered as plantation date of wheat for this study area.
Table 3.1: List of MODIS Images downloaded for the study
No Date Julian date Days after plantation 1 03-Dec-2007 337 18 2 11-Dec-2007 345 26 3 19-Dec-2007 353 344 27-Dec-2007 361 39 5 01-Jan-2008 001 47 6 09-Jan-2008 009 55 7 17-Jan-2008 017 63 8 25-Jan-2008 025 71 9 02-Feb-2008 033 79 10 10-Feb-2008 041* 87 11 18-Feb-2008 049 95 12 26-Feb-2008 057 203 13 05-Mar-2008 065 111
* Image of Julian date 041 was excluded due to clouds
3.2.2. Field Data
Primary data on wheat for the season December 2007 to March 2008 was collected from the
farmers’ fields through interviews. The interviews were conducted on farmers’ fields. Visits
were made to villages and farmers who grew wheat during the Rabi 2007-2008 cropping season.
Interviews were carried out during the field visits. A total of 40 farmers were interviewed and
their fields were digitized. The farmers’ fields were selected randomly at three remote corners of
12
Dinajpur, Thakurgaon and Panchagarh distritcts. Figure 3.4 shows the locations of the farmers’
field in the study area where farmers’ fields are shown in red diamond symbols.
Figure 3.4: location of the wheat fields (red diamond) in Dinajpur, Panchagarh and Thakurgaon district.
Selected farmers’ fields were digitized by using a hand held GPS. A photograph taken during the field ground truthing of farmers’ field (Figure 3.5).
Figure 3.5: Ground truthing Farmers’ wheat fields under study area.
13
2.3 Secondary Data
Data on land and land use in the form of shape files (geomorphologic units, water shade,
drainage lines and water bodies, and communication system and other shape files) were
collected from the Data Base Bangladesh Country Almanac BCA. Data on crop information
were collected from the Department of Agricultural Extension at Dinajpur district. Climatic data
were collected from Bangladesh Meteorological Department (BMD).
3.3 Image Processing and Wheat Area Classification
MODIS data/images have been geo-referenced using MODIS Re-projection Tool (MRT) and
analyzed using ILWIS software (ILWIS, 2010). Normalized Vegetation Index (NDVI) is the
most commonly used vegetation index. It varies from +1 to -1. NDVI value of zero means no
green vegetation and NDVI values close to +1 (0.8 to 0.9) indicates the highest possible density
of green leaves.
At a selected 40 farmers’ field points from the starting of wheat plantation up to the harvest time
for 12 images were extracted. The chronological changes of NDVI value after plantation for the
40 farmers’ field has been plotted in Figure 3.6. The mean changes of NDVI are marked by dark
black lines which can represent as the phonological curve of wheat. It can be found from the
mean curve that the peak occurred on 25 January 2008 which is approximately 71 days from the
plantation date. The peak of the mean curve was found as 0.6 with a range varies from 0.49 to
0.65. A rule based supervised classification technique has been applied to identify wheat
growing area are as follows:
65.049.0 <<= NDVIAreaWheat (3.1)
14
Figure 3.6: Changes of NDVI in the growing season of the selected fields. The dark bold line shows the average value of the changes of NDVI.
Figure 3.7(a) shows the NDVI values on the study area on the 25 January 2008. Figure 3.7(b)
shows the NDVI values only for the wheat field based on the rule based classification techniques
as discussed earlier. Figure 3.8 shows map of only the wheat fields in the study area during
growing season of 2007-2008. This map was later used to mask satellite images to separate the
wheat growing areas and other areas.
15
Figure 3.7: (a) NDVI value over the study area and (b) NDVI value over the wheat cultivable area on the 25 January 2008 (Day of the year is 25).
Figure 3.8: Location map of the wheat fields in the study area during growing season of 2007-2008.
16
Chapter 4: Methodology of estimating evapotranspiration using
SEBAL Algorithm
4.1 SEBAL Method
Surface Energy Balance Algorithm for Land (SEBAL) single source model (Bastiaanssen et al.,
1998) has been applied to simulate the surface energy fluxes. SEBAL is a relatively new
parameterization of surface heat fluxes based on spectral satellite measurements. The SEBAL
has been applied for the estimation of surface heat fluxes and evaporation, using satellite data in
the visible, near infrared, and thermal infrared spectral range. The SEBAL parameterization is
an iterative and feedback-based numerical procedure that deduces the radiation, heat and
evaporation fluxes. SEBAL has been applied to many case studies in Europe and Asia, and is
regarded as one of the most logical and precise methods in evaporation estimation at present.
SEBAL method is based on the energy balance principle as shown in Figure 4.1. The energy
coming from the sun and atmosphere in form of short and long wave radiation is
dissipated/transformed on the ground. The total available energy Rn is then used for several
purposes: heat up the soil (soil heat flux)., heat up the surface transfer to the environment
(sensible heat flux) and transform water into vapour (latent heat flux). The energy balance
equation in its most simplistic form stands:
(L.E)flux heat latent (H)flux heat sensible (G)flux heat soil (Rn)radiation Net ++= ........ (4.1)
Figure 4.1: Components of the Energy Balance
In the next, sub-sections different components of estimating evaporation using SEBAL have
been discussed.
17
4.2 Solar Zenith Angle
The maximum instantaneous solar radiation outside the atmosphere, measured at an average
Sun-Earth distance and perpendicular to the solar rays is equal to 1367 watt/m2. The amount of
energy at the top of the atmosphere is a function of the solar zenith angle at certain latitude and
time and the distance between Sun and Earth.
Figure 4.2: Solar declination angle.
4.3 Solar Declination
The position of the sun during summer and winter is described by solar declination angle (δ) in
radians
( ) ( ) ( )( ) ( ) ( )dadada
dadada3sin00148.03cos002697.02sin0000907.0
2cos006758.0sin070257.0cos399912.0006918.0+−
+−+−=δ.…(4.2)
( )36521 π
−= na dd ……..…(4.3)
4.4 Equation of Time
The axial rotation of the Earth along with the revolution of the earth in the elliptical orbit around
the sun causes slight irregularities (maximum 16 minutes) in the calculation of sun’s position
18
and determination of local time. Correction can be made through the equation of time (Et in
radians, eq.3.7)
E t =0.000075+0.001868cos ( )da -0.032077sin ( )da -0.014615cos ( )da2 -0.04089sin ( )da2 ………….(4.4)
4.5 Local Apparent Time (LAT)
When the Universal time is given the LAT is calculated from
6060*4 tc EL
UTCLAT ++= …………(4.5)
LAT and UTC are in hour (decimal) and L c is the longitude.
4.6 Hour Angle
The hour angle is directly computed from the LAT as
( )180
1215 πω −= LAT …………(4.6)
LAT is in hours and ω is given in radians.
4.7 Solar zenith angle
The solar zenith angle θ is given by
)cos()cos()cos()sin()sin()cos( ωδφδφθ += …………(4.7)
At the hour of sunset θ =90 0 and then the sunset hour angle sω is given as;
cos ( )sω =-tan ( )φ tan ( )δ
The day length is given by equation 4.7.
N=52 cos 1− ( ) ( )( )δφ tantan− …………(4.8)
19
4.8 Bio Physical Parameters
In order to estimate the bio physical parameter required for the SEBAL algorithm, a statistical
method was adopted. The bio-physical parameter have been defined using following vegetation
indices, primarily calculated using band reflectance of Red and NIR
4.8.1 Normalized Difference Vegetation Index (NDVI)
The Normalized Difference Vegetation Index (NDVI) is a measure of the amount and vigor of
vegetation at the surface. The reason NDVI is related to vegetation is that healthy vegetation
reflects very well in the near infrared part of the spectrum. Green leaves have a reflectance of 20
% or less in the 0.5 to 0.7 range (green to red) and about 60 percent in the 0.7 to 1.3 µm range
(near infrared). The value is then normalized to -1<=NDVI<=1 to partially account for
differences in illumination and surface slope. The index is defined by equation 3.12
RNIRRNIRNDVI
+−
= …………(4.9)
4.8.2 Soil Adjusted Vegetation Index (SAVI)
SAVI is the Soil Adjusted Vegetation Index, which was introduced by Huete (1988). This index
attempts to be a hybrid between the ratio-based indices and the perpendicular indices. The
reasoning behind this index acknowledges that the isovegetation lines are not parallel, and that
they do not all converge at a single point. The initial construction of this index was based on
measurements of cotton and range grass canopies with dark and light soil backgrounds, and the
adjustment factor 'L' was found by trial and error until a factor that gave equal vegetation index
results for the dark and light soils was found. The result is a ratio-based index where the point of
convergence is not the origin. The correction factor was found to vary between 0 for very high
densities to 1 for very low densities. The standard value typically used in most applications is
0.5, which is for intermediate vegetation densities. Negative SAVI indicates presence of water.
Figure 4.3 depicts the process involved in the computation of SAVI .
( )( )LRNIRRNIRLSAVI
++−+
=1 …………(4.10)
20
Figure 4.3: Flow chart of methodology to derive Soil Adjusted Vegetation Index
The feature space plot of reflectance values of NIR band versus RED band shows a distinctive
line which represents the bare soils in the image and termed as the soil line. The equation of line
can be expressed by equation 3.13.
βγρρ += REDNIR …. ………(4.11)
Usually γ is closed to unity and β lies in the range from -0.1 to 0.1. The soil line extends from
darker soils with low RED and NIR image Intensity to upper region of brighter soils with high
levels of RED and NIR image Intensity. The Iso-vegetation lines are said to be parallel to the
soil line. The points which lie closer to the soil line are partially vegetated whereas the points
which stay farther away from the line are purely vegetated. The weighted difference vegetation
index (WDVI) and correction factor L are given by equation 4.14 and 4.15.
RNIRWDVI .γ−= ……………..…(4.12)
L = 1-2a.NDVI.WDVI …..................(4.13)
21
4.8.3 Leaf Area Index (LAI)
The leaf area index LAI represents the total biomass and is indicative of crop yield, canopy
resistance and heat flux. The LAI is defined as the ratio of the total area of all leaves on a plant
to the ground area covered by the plant. If a plant has only one layer of leaves and these would
cover the ground exactly, then the LAI would be 1. For crops such as maize the LAI goes up
during the growing season to values ranging between 2 and 5.
2
1
CCSAVILAI −
= ………(4.14)
4.8.4 Displacement height (d)
Over plant communities of uniform height 'h' , the turbulent boundary layer behaves as if the
vertically distributed elements of the community were located at a certain distance 'd' from the
ground (Figure 4.4).
Figure 4.4: Vertical distribution of wind profile over vegetation..
'd' is called the "zero plane displacement" or "displacement height" level of the flow and is in
general a major fraction of the plant height 'h'. Taking 'd' into account, the wind profile equations
are corrected for the shifted origin.
22
⎟⎟⎠
⎞⎜⎜⎝
⎛×=
0
lnzzAu ………………(4.15)
where 'z 'indicates the height with respect to the surface, a change in variable is proposed to
account for the "zero plane displacement" of the vegetation.
dzz st −= …………….(4.16)
where 'zst' is the standard height for wind speed measurement. Displacement height 'd' is a major
part of the plant height. The model is based on the LAI map and requires only one coefficient
that was adjusted to fit a wide range of field results.
⎥⎥⎦
⎤
⎢⎢⎣
⎡ −−=
−
LAICehd
LAIC
1
111 ……………..(4.17)
4.8.5 Surface roughness (zo)
It is a fraction of the crop height used as a physical reference for momentum and heat flux
calculations. 'zo' affects the shear stress between crop and atmosphere, which determines surface
fluxes and the actual and potential evapotranspiration.
23
Figure 4.5: Surface resistance of crop canopy and energy balance of crop canopy & soil.
The roughness of the ground surface affects momentum, heat, and water vapor exchanges
between land and atmosphere. The Figure 4.5 indicates that partially covered soil has separated
latent heat flux (LE) and sensible heat flux (H) for bare soil and canopy. The soil moisture
regulation of latent heat flux from the bare soil is expressed physico-mathematically by means
of the bare soil resistance, rsoil. The mechanical friction between land and atmosphere, and
buoyancy processes controlling the vapor removal from soil to atmosphere are expressed in the
aerodynamic resistance to vapor transport, rav. The canopy's resistance to releasing water vapor
varies with the stomatal aperture and is expressed in the canopy resistance, rc, being physically
determined by soil moisture conditions, among others. Because the atmospheric heat transfer
processes differ from the transport of water vapor, the resistance to heat transfer, rah, differs from
rav . The LE and H fluxes depend further on the vertical differences of vapor pressure (esat - eact )
and temperature (Tzoh - Tair), respectively. The total flux from a sparse canopy is the sum of the
individual LE and H fluxes, weighted by the fractional vegetation cover. The total LE flux is
usually parameterized by an effective bulk surface resistance to evaporation, rs, which comprises
rsoil, and rc, and a surface temperature, To, which comprises Tzoh of soil and canopy.
Surface roughness is an essential component of aerodynamic resistance to momentum transport,
heat transport, and water vapor transport. Total shear stress is formed by local drag over flat
homogeneous surfaces and by form drag due to terrain topography. Because irrigated fields are
24
usually flat, local drag induced by the presence of crops and wind shelters is the governing
factor and form drag due to undulating terrain and mountains has less impact.
4.8.6 Surface Roughness for Momentum Transport (zom)
The surface roughness for momentum transport (zom) is defined mathematically as the plane
where the wind speed becomes zero. The value of zom is related to surface geometry, i.e., the
vertical extent in relation to the horizontal extent of landscape elements. Two models to
determine zom are, a simple relation discussed by Bastiaanssen et al. (1998), and a more complex
procedure by Verhoef et al. (1997). The values of zom are not critical to the overall procedure to
calculate evapotranspiration.
( )NDVICCExpZ om 21 += (Bastiaanssen et.al., 1998)…………(4.18)
( )( )hh ukuom e
dhZ ψ−
−=
*/ (Verhoef et al., 1997) ..................(4.19)
where h is the vegetation height, d the displacement distance, k von Karman’s constant (always
equal to 0.41), u* friction velocity, ψh a vegetation influence function and uh wind speed at the
top of the canopy.
4.8.7 Surface Roughness for Heat Transport (zoh)
The scalar roughness height for heat transfer, hz0 , is calculated from equation 4.19.
( )100 exp/ −= kBzz mh …..……(4.20)
kB-1 is a parameter normally called excess resistance for heat transfer which is used to compare
zom and zoh. 1−B is the inverse Stanton number, a dimensionless heat transfer coefficient. kB-1 is
taken as 2.3 for well grown homogeneous vegetation.
4.9 Net Radiation (Rn)
Figure 4.6 show the simplified surface atmosphere energy exchange, showing main long and
short wave radiation components, sensible heat flux H and latent heat flux LE. The main balance
equation is LE = Rn – G – H, where incoming components are positive and outgoing are counted
25
as negative. The net radiation is the sum of the incoming and outgoing short and long wave
components.
Figure 4.6: Surface Atmosphere Energy Exchange
Net radiation Rn is the dominant term in the EBE, since it represents the source of energy that
must be balanced by the thermodynamic equilibrium of the other terms. The net radiation can
also be expressed as an electromagnetic balance of all incoming and outgoing fluxes reaching
and leaving a flat horizontal and homogeneous surface as:
Rn = S↓–S↑ + L↓ -L↑ …………………..(4.21)
Where, S means shortwave (0.3 – 3 µm) and L expresses the longwave radiation (3-µm100).
The arrows show the direction of the flux entering ↓ or leaving ↑ the system. Eq. (4.20) is
very convenient from the data acquisition point of view, since each term can be determined by
available models, or can be obtained directly from instruments at ground stations. Remote
sensors measure “outgoing radiation” only. Characterized by the reflective properties of the
terrestrial bodies, so “incoming fluxes” must be derived through alternative methods. The
incoming shortwave radiation or global radiation, S ↓, has to be measured at ground stations by
means of pyranometers these instruments usually work in all visible broadband range (usually
0.305 – 2.4 µm). This range comprises almost 96% of the spectral interval of the solar
irradiance.
The outgoing shortwave radiation is the portion of the visible energy, energy which is reflected
back of the atmosphere. It is characterized by the albedo. As albedo is a reflective property that
26
can be evaluated from remote sensors, the shortwave radiation balance is given by equation
4.21.
∆S = S↓ - S ↑ = (1- r0) S ↓ …………….(4.22)
A blackbody having a kinetic temperature (temperature measured by a thermometer inside the
body) T0 [K] emits a wavelength energy that corresponds to Planck’s Law.
⎥⎦
⎤⎢⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛=
1exp 25
1
o
bb
TC
CL
λλ
λ ……………..(4.23)
Lλbb is the blackbody energy emission in (W m-2µm-1) and λ is the wavelength in [µm]. C1 and
C2 are planks constant and have value 3.74x108 and 1.44x104 respectively. A blackbody is a
physical abstraction that does not exist in nature. Terrestrial materials behave more as grey
bodies, meaning that part of the received energy is reflected back to the atmosphere. In the
thermal range, the relation between black and grey bodies is simplified by a property called
emissivity. A blackbody has a constant emissivity equal to one for all wavelengths. For natural
bodies, the thermal emission depends on the emissivity ε = F(λ).
)()( obb
o TLTL λλλ ε= ………………..(4.24)
Integration of L over all wavelengths leads to:
∫∞
==0
4)()( ooobb
o TdTLTL σελε λλ …………….….(4.25)
A remote sensor working within a spectral range (in the atmospheric window) of the thermal
channels measures only a portion of L (To)↑ but also for H, the expression for the outgoing
longwave radiation reads:
4)( ooo TTL σε= ………………...…(4.26)
εo must be measured in situ or derived from surface properties, and To is derived from the
radiant temperature Trad in combination with the estimated value of εo.
27
radoo TT 4/1−= ε ………………...…..(4.27)
The incoming longwave radiation cannot be derived from remote sensors, but must be
determined from ground data. It is variable with cloudiness (water vapor), air temperature and
atmospheric constituents. For clear skies, the notion of effective thermal infrared emissivity of
the atmosphere (εa) introduces an overall emission value for all constituents.
Then, having the air temperature Ta at screen level, L↓ is estimated as:
4
aaTL σε↓= …………………(4.28)
A portion of this energy reaching a terrestrial object is reflected back to the atmosphere. Since
εo describes the emissivity of a body in the thermal range. (1-εo) accounts for the reflection.
The final expression for Rn is given by equation 3.32.
44
04 )1()1( ooaaaaon TTTSrR σεσεεσε −−−+↓−= …………………(4.29)
The daily short wave radiation is measured at agrometerological stations with pyranometers, an
instrument that requires careful calibration and maintenance and for this reason; solar radiation
data are usually not available in standard stations. If sunshine hour data are available
(periheliometers) in most of the cases the daily incoming shortwave radiation S↓ [MJm-2day-1]
can be obtained from relation 3.33.
↓+↓= oss SNnbaS )(
………...…..(4.30)
In equation 3.33 as fraction is the extraterrestrial radiation reaching the ground in a complete
overcast day (when n=0) and as+bs fraction is the extraterrestrial radiation reaching the ground in
a complete clear day (n=N). S0↓ is the extraterrestrial radiation in MJm-2day-1.Local
instrumentation can be used to estimate as and bs for local conditions. The net shortwave
radiation ∆S is estimated as Eq. (3.25), assuming an average daily albedo. The daily long wave
radiation exchange between the surface and the atmosphere is very significant, since on average
28
the surface is warmer than the atmosphere and also ε0>εa, there is usually a net loss of energy as
thermal radiation from the ground.
The apparent emissivity of the atmosphere is usually estimated with equations based on vapor
pressure and temperature at the standard meteorological stations. For clear skies a common
formulation is (Brutsaert, 1975);
7/1
24.1 ⎟⎟⎠
⎞⎜⎜⎝
⎛=
a
da T
eε
…………. (4.31)
Ta is the air temperature [K], ed is the vapor pressure [mbar], everything measured at screen
level.
4.10 Soil Heat Flux (G)
There are two types of transport processes in the soil; conduction and convection. Soil heat flux
through a porous medium includes heat transport through each soil component: water, air,
minerals and organic matter. De Vries (1963) developed the theory based on the effective
thermal conductivity of soil components.
Heat is transported through the soil not only by conduction through the solid part but also by
convective movement of water and air. This process was also treated in De Vries (1975) who
lumped the transport by the separate components together in a mix-convective heat flow process.
Then, the summation of two terms, one considering the thermal conductivity of the soil without
fluid movement (Qc) and the other considering the movement of air and water through it (Qa)
explain the whole process.
dzdT
QQG soilsac λ−=+= ………. (4.32)
Where dT soil/dz is the gradient of temperature in the soil with depth, and λs is the apparent
thermal conductivity that combines all thermal conductivities of the different soil substances and
processes. G mapping requires some empirical formulation since soil heat flux cannot be
29
directly read from satellite sensors. Bastiaanssen et al. (1994) have evaluated the effect of
surface temperature, albedo and incoming shortwave radiation on the evaluation of G. The
evaluation of G is usually presented as a ratio G/Rn. The instantaneous G/Rn function depends
on pixel size, location and time. Over a period of one day, the integrated soil heat flux is usually
considered as negligible.
The remote sensing derivable variables that best explain the soil heat transport behavior are
albedo, surface temperature and land cover vegetation indexes. Net radiation must also be
included. It should be noted, however, that slopes and aspects need to be taken into account for
proper application.
Bastiaanssen et al. (1994) introduced an equation (eq.3.36) based on their own research (Egypt
and applied in HAPEX-EFEDA experiment) and other soil researchers.
( )( )42 98.0162.032.0100
)15.273(NDVIrr
rT
RnG
ooo
o −+−
= ………… (4.33)
Where r0 is the average albedo (approx, 1.1r0) when the soil heat flux is directly downward.
Note that T0 is the surface temperature in Kelvin. Equation 3.36 explains reasonably well the
wide range of a variability of the soil heat fluxes on clear days even in rich relief terrain, mainly
for low NDVI values.
Very simple approaches neglect the value of G for very dense canopies or give a fixed
percentage of the incoming solar global radiation. Seguin (1983) showed the simplest
approaches used by several authors based on this fixed relation.
G = 0 for very dense vegetation.
G/Rn = 0.1 for normal vegetation …………. (4.34)
0.2 < G/Rn ≤ 0.3 for bare soil
Different empirical studies have shown that the daytime ratio G/Rn is related to, among other
factors, the amount of vegetation present (De Bruin and Holtstag, 1982). Thus, an approximation
of G can be achieved by assuming that it is a fraction of Rn dependent on the spectral estimates
of surface vegetation cover. Jackson et al. (1987) used an exponential relation (eq.3.38).
30
]13.2exp[58.0 NDVIRnG
−= ..……… (4.35)
Where NDVI is a spectral index that estimates the amount of vegetation present based on the
normalized difference between near-infrared (NIR) and red reflectance. Kustas and Daughtry
(1990) proposed two linear expressions equation 3.39 and 3.40.
G/Rn = 0.325 – 0.208 NDVI ……….. (4.36)
G/Rn = 0.294 – 0.0164 NDVI ……….. (4.37)
Clothier et al. (1986) suggested a similar relation between G, Rn and NIR/Red reflectance given
by equation 3.41.
G/Rn = 0.295 – 0.0133 NIR/RED ………. (4.38)
4.11 Sensible Heat Flux (H)
The sensible heat flux (H) is the flow of energy through air as a result of the temperature
gradient. Since the Surface temperature during the day is usually much higher than the air
temperature, the sensible heat flux is normally directed upwards during the day. During the night
the situation is reversed. Close to the surface Sensible heat transport takes place most by
diffusive processes, whereas at some distance away from the surface, turbulent transport
becomes dominant. The mathematical formulation of the sensible heat flux is based on the
theory of mass transport of heat and momentum between the surface and the near surface
environment. The expression can be written as;
ah
aopa r
TTCH
−= ρ ……..................(4.39)
31
4.11.1 Aerodynamic resistance to heat transport
This is the resistance to heat transport between surface and air, rah varies with wind speed and
with the intensity and direction of sensible heat itself, therefore the iterative computation is the
only solution its estimation.
⎥⎥⎦
⎤
⎢⎢⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛ −= h
oh
refah Z
dZku
r ψln1
*
………………..(4.40)
4.11.2 Friction velocity ( *u )
The determination of the heat transfer phenomena requires the description of the turbulent wind
profile near the surface. The lateral transfer of momentum in the interior of the flux is done
through molecular and turbulent eddy activity. This action creates shear stress that is directly
proportional to the speed of the eddy 'u*' usually called eddy velocity or friction velocity.
Mom
B
B
zdzuk
uψ−⎟⎟
⎠
⎞⎜⎜⎝
⎛ −=
ln
** ……………….(4.41)
4.11.3 Blending height (UB)
Blending height is the height at which the wind speed is no longer influenced by surface is given
by equation 3.46.
⎟⎟⎠
⎞⎜⎜⎝
⎛
−−−−
=)ln()ln()ln()ln(
omref
omBrefB ZdZ
ZdZuu …………….(4.42)
4.11.4 Monin Obukhov Length(L).
The monin obukhov length, is the ratio between the energy produced by Forced mechanical
convection and the energy produced by the thermal convection,’L’ is negative under stable
conditions. Observation shows ‘L’ depends on sensible heat flux, what leads to an iterative
process to account for buoyancy effects and is given by.
HgkTuc
L spa
..... 3
*ρ= ………….........(4.43)
32
4.11.5 Correction factors.
As per Monin –Obukhov similarity theory, the dimensionless temperature and wind speed
gradients are the function of dimensionless height. Because it is rather difficult to measure
vertical gradients accurately, it is convenient to integrate the correction factors between two
levels, by which only observation of temperature and wind speed at these levels is required. And
they are separately applied with momentum and heat transfer. Suffix ‘m’ and ‘h’ in the equations
3.48 to 3.51 denotes correction factors for momentum and heat transfer respectively.
25.0
161 ⎟⎠⎞
⎜⎝⎛ −
−=L
dZx B
m ………………...(4.44)
( ) ( ) ( )2
arctan22
1ln
21
ln22 πψ +−⎥
⎦
⎤⎢⎣
⎡ ++⎥⎦
⎤⎢⎣⎡ +
= mmm
m xxx
………………..(4.45)
25.0
161 ⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=
LdZ
x refh ……………….(4.46)
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡ +=
21
ln22
hh
xψ ………………(4.47)
By combining the above equations we get the relation.
………….(4.48)
SEBAL uses the extreme pixels of the image called dry and wet pixels to develop a relationship
between surface temperature (T0) and the difference between (To-Ta) given in the form of;
To-Ta = dt = a+b×To ……………………(4.49)
Where ‘a’ and ‘b’ are constants and once they are determined for each and every pixel the “dt” is
expressed using the surface temperature. Selection of wet pixel and dry pixel is done based on
the temperature-albedo and the NDVI-albedo relationship in a particular image. Usually a pixel
with low temperature and high NDVI is selected as the wet pixel and a pixel with low albedo,
low NDVI and high temperature is selected as the dry pixel. For the wet pixel it is assumed that
the sensible heat flux is zero and therefore according to To-Ta= dt, dt is equal to zero (Figure
⎥⎦
⎤⎢⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛ −=− h
oh
ref
paao Z
dZuCk
HTT ψρ
ln*
33
4.7). For the dry pixel the condition dt = dtmax and the sensible heat flux was put the maximum
value of the difference between net radiation and soil heat flux.
ahpa r
dtCH max
max ρ= ………..(4.50)
Figure 4.7: Solving for constants using wet and dry pixels
In order to determine constants ‘a’ and ‘b’ the term ‘rah’ has to be determined. Determination of
‘rah’ which is an implicit function of sensible heat flux is the most complicated issue in the
whole energy balance procedure. The term ‘rah’ varies with the intensity and direction of H itself
and other variables such as wind speed. Determination of ‘rah’ can only be done by solving the
set of equations iteratively. Once the wet and dry pixels are determined the values of To-wet, To-
dry, Rn-dry, Go-dry, Zom-dry and dh-dry, are obtained from the corresponding maps. The
suffixes dry and wet represent the pixel value of the dry and wet pixels respectively. The values
of the wind speed (Ub) at blending height and the surface roughness for heat transport (zoh) are
used in the calculation. Initially the correction factors ψh and ψm were taken as ‘0’ and Hmax=Rn-
dry-Gdry in first loop which was runned to obtain the values of ‘a’ and ‘b’. The dT map was
calculated as dT=a+b*Ts. Using the dT map the iterative process was started for the study area
with the above set of equations. The iterative process is run until a constant value of the
parameters is reached upon. Figure 4.8 shows the flow chart of the iterative process executed for
determining the sensible heat flux map.
34
Figure 4.8: Flow chart of Iterative process to calculate Sensible Heat Flux
4.12 Instantaneous Latent Energy Flux
Having estimated all the other components in the energy balance equation, the Latent Energy
flux (LE) was calculated for each pixel of the image as a 'residual' term.
LE = Rn-G-H .............................(4.51)
All the components in the equations are instantaneous values and expressed in units of W/m-2
4.13 Evaporative Fraction
Evaporation from the surface over land usually displays a pronounced diurnal variation.
Inspection of illustrations of the daily cycle of the surface energy budget suggests that this
variation is often quite similar to that of several other components in this budget. The point of
interest is that if only one or a few instantaneous estimates of the evaporation are available, it
may be possible to infer its diurnal variation from the known variation of some other component
of the surface energy budget by assuming self-preservation in the diurnal evolution of this
budget. "Self-preservation" means that relative partition of energy flux among its main
35
components remains the same. If this assumption is valid, the evaporative fraction (EF) can be
taken as a constant through the day.
The ratio of latent energy to the available energy (Rn-G) is defined as the evaporative fraction
( Λ ).
GRLE
ninst −
=Λ ……..................(4.52)
The evaporative fraction is based on the instantaneous surface energy fluxes and is calculated as
expressed in the equation given below.
GRHGR
n
nins −
−−=Λ ………………..(4.53)
4.14 Total daily net radiation
It is the result of the energy balance between the incoming and outgoing long and shortwave
radiation on the Earth' surface during one day. Positive fluxes indicate radiation reaching the
surface and negative leaving it. The mathematical equation that expresses this balance is:
daydaydaydaydayn LLSSR ↑−↓+↑−↓=− ………………...(4.54)
Assuming that the instantaneous Albedo derived from the visible channels is proportional to the
average daily Albedo:
daydayodayn LSrCR +↓×−=− )1( 1 ………………..(4.55)
C1 is the conversion factor for surface Albedo. It is the ratio between the average daily Albedo to
the instantaneous Albedo as it is derived from the visible band image. A default value 1.1 can be
taken.
4.14.1 Daily terrestrial solar radiation
The maximum instantaneous solar radiation outside the atmosphere, measured at an average
Sun-Earth distance, and perpendicular to the solar rays is equal to 1367 watt/m2. The daily
terrestrial solar radiation as defined as 24 hour average of the total energy reaching the top of the
atmosphere at the point of consideration.
36
)tan.(sin.sin...24 'sso
exoday wwESCS −=↓ δφ
π ………………(4.56)
( )36521 π
−= na dd ……………...(4.57)
( ) ( ) ( ) ( )( ) ( )dada
dadadada3sin00148.03cos002697.0
2sin0000907.02cos006758.0sin070257.0cos399912.0006918.0+−
+−+−=δ
……………....(3.62)
).2sin(.000077.0).2cos(.000719.0)sin(.00128.0)cos(.034221.000011.10 dadadadaE ++++=
)]tan().tan(cos[ δφ−= arws ……………...(4.58)
4.14.2 Average Daily Incoming Shortwave Radiation (S↓day)
The solar radiation reaching the ground is a function of geometric and atmospheric factors such
as date of the year, latitude, sunshine fraction and atmospheric gaseous components. Due to the
highly temporal and spatial variation of the atmospheric components, the determination of the
incoming shortwave radiation reaching the ground is usually done by means of atmospheric-
solar models in combination with ground data collection. The incoming shortwave radiation or
global radiation, 'S↓', is measured at ground stations by means of instruments called
"pyranometers". These instruments usually work in the entire visible broadband range (usually
0.305 - 2.4 µm). This range comprises almost 96% of the spectral solar irradiance.
exodaydayday SS ↓
↓ = ..5741.11 τ ……………….(4.59)
).( Nnba ssday +=τ . ………………(4.60)
4.14.3 Average Daily Net Longwave Radiation
There is a significant exchange of radiant energy between the earth's surface and the atmosphere
in form of radiation at longer wavelengths (3-100 µm). The average daily net longwave radiation
is given by: The value of Lday can be determined with appropriate instruments (net longwave
radiometer) and is the most accurate method since direct information is available. For stations
not having a net longwave radiometer but information on standard daily averaged
meteorological parameters, the exchange of long-wave radiation Lday between vegetation and
soil on the one hand, and atmosphere and clouds on the other, can be represented by the
following radiation law:
37
( )4,
' 273... +−= meanaday TfL σε ………………...(4.61)
Where Lday is given in Wm-2 and net emissivity can be derived from the relation;
10. ,' meandee
eba +=ε …………………(4.62)
'ae' and 'be' are correlation coefficient and their value ranges from 0.34 to 0.44 and -0.14 to –
0.25 respectively.
meansmean
meand eRH
e ., .100
= ………………...(4.63)
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+=
2.237.27.17
exp.108.6,
.,
meana
meanameans T
Te ………………..(4.64)
The cloudiness factor 'f' is equal to 1 in case of a perfect clear day and 0 in a complete overcast
day.
Another easy approximation of average daily net longwave radiation, can be done through the
formula given by De Bruin, 1982.
τ.110−=dayL ………………...(4.65)
4.15 Daily Evapotranspiration
Assuming that the daily value of evaporative fraction is approximately equal to the
instantaneous value, the daily value of latent energy flux (LE24) was calculated in the following
manner.
When 24Λ≈Λ ins
( ) )( 24242424 oninson GRGRLE −Λ=−Λ= ………………….(4.66)
38
Where Rn24 is the 24 hours net radiation and the 24 hour value of soil heat flux (Go) is usually
ignored in this equation for simplicity. Hence the expression for the daily evapotranspiration
(ET24) can be expressed as.
v
nins
v
RLEETλλ
242424
Λ== ………………(4.67)
The final equation that is used to evaluate the daily evaporation is based on the evaporative
fraction:
w
nins RET
ρλ.1064.8 24
7
24Λ×
= ……….……(4.68)
In equation 3.74 daily net radiation is given in Wm-2, λ is 2.47x106 JKg-1 and ρw is 1000 kgm-3.
The final form of equation is given by equation number 3.75.
588.28
2424
nins RET
Λ= …..…………(4.69)
39
Chapter 5: Estimation of Evapotranspiration
5.1 Cosine of Solar Zenith Angle [cos (θz)]
The steps involved in calculation of solar zenith angle are given in section 4.5. Solar zenith
angle is required for calculation of reflectance from different bands. The other parameters
required for the calculation of solar zenith angle are latitude map, longitude map, day angle,
equation of time, local apparent time and solar declination. The data required to calculate these
parameters are the coordinate details of the area, Julian day and image acquisition time.
Appendix gives the ILWIS script for calculating the above parameters. The cosine of solar
zenith angle was nearly constant (0.53497 to 0.54676) for the entire study area and the reason
for this can be attributed for the small extent of the study region. Figure 5.1 shows solar zenith
angle of the study area on 25 January 2008.
Figure 5.1: Cosine of Solar Zenith Angle on 25 January 2008
40
5.2 Reflectance and Temperature
The reflective and thermal bands of the MODIS sensor were converted into reflectance and
temperature maps using the calibration coefficients and solar zenith angle derived in the above
section. Band 1,2,3,4,5,6 and 7 were converted into reflectance and band 31 and 32 were
converted into temperature (discussed in section 4.4 & 4.5). The temperature is known as
brightness temperature or radiant temperature because it is measured at the top of the
atmosphere by the satellite. Temperature map was re-sampled to the reflective band resolution
for all future analysis.
5.3 Albedo
5.3.1 Planetary Broadband Albedo
The planetary broad band albedo is the ratio of the scattered radiation reflected at the top of the
atmosphere to the incoming radiation reaching it measured in the solar effective wavelength
range of 0.3 and 3 µm (visible). Since the sensors are built in narrow bands called "atmospheric
windows", the classical approach to derive broadband reflection is to apply a linear conversion
affecting the narrow reflection measured in each channel by a weight factor that counts for the
reflected solar radiation in the close non-measured visible wavelength. Satellites measure the
spectral reflectance in narrow bands at the top of the atmosphere. The conversion of multiple
narrow band reflectances to a single broadband reflectance is a weighting procedure in which the
spectral incoming solar radiation of each band is proportional to the weighting factors.
Albedo (rp)=ref_band1*0.160+ref_band2*0.291+ref_band3* 0.243+ref_band4*0.116+
ref_band5*0.112+ref_band7*0.018- 0.0015 ………(5.1)
5.3.2 Broadband Surface Albedo
It is the hemispherical surface reflectance of shortwave radiation between wavelengths of 0.3
and 3 µm. Energy balance equation is evaluated at the earth’s surface hence ro is required instead
of rp. Reflected radiation at the surface is affected by the atmosphere therefore a simple linear
correction is applied to convert rp to ro.
2min /)( τppo rrr −= ………………..(5.2)
The instantaneous transmittance ‘τ’ is assumed to be equal to daily transmittance ‘τday’ and
computed from the formula:
41
⎟⎠⎞
⎜⎝⎛ +=
Nnba ssday *τ ………………(5.3)
Where, as=0.25, and bs=0.5, n is the sunshine hours and is taken as 8, N is the day length and is
taken as 12. Transmittance is computed as 0.5833. Figure 5.2 shows the broadband surface
albedo map using the computed values of rp and τ.
Figure 5.2: Broad band Surface Albedo
5.4 Instantaneous Surface Temperature
Surface temperature is derived from radiant temperature (Trad) in combination with the estimated
value of surface emissivity (εo) from the relation:
41
o
rado
TT
ε= ………………..(5.4)
42
Thermal infrared surface emissivity (εo) is the efficiency with which the surface emits longwave
radiation at a given temperature in the 3 to 100 µm spectral range. Surface emissivity map is
calculated using the relation:
εo = 1.009 + 0.047 ln(NDVI) ………………..(5.5)
The relation is only valid for NDVI values over 0.16. Therefore, for NDVI values below 0.16
(usually bare soils) an exception has to be made and the emissivity is set to 0.92. A second
exception is made for NDVI values below –0.1 (usually water), in this case it is set to 1. Using
the radiant temperature and the computed value of surface emissivity, the surface temperature
map is derived as shown in Figure 5.3.
Figure 5.3: Instantaneous Surface Temperature
43
5.5 Biophysical Parameters
The various Biophysical parameters determined for the computation are presented in this
section.
5.5.1 Normalized Difference Vegetation Index (NDVI)
The Normalized Difference Vegetation Index (NDVI) is a measure of the amount and vigor of
vegetation at the surface. The magnitude of NDVI is related to the level of photosynthetic
activity in the observed vegetation. In general, higher values of NDVI indicate greater vigor and
amounts of vegetation. The NDVI value for the study region was calculated from equation 3.x
and the valued varied from 0.1667 to 0.78960 on 25 January 2008 as shown in Figure 5.4.
Figure 5.4: NDVI Map for the study region for the date 25 January 2008
44
5.5.2 Soil Adjusted Vegetation Index (SAVI)
SAVI is the Soil Adjusted Vegetation Index, which was introduced by Huete (1988). This index
attempts to be a hybrid between the ratio-based indices and the perpendicular indices. The
reasoning behind this index acknowledges that the iso vegetation lines are not parallel, and that
they do not all converge at a single point.
( )( )LRNIRRNIRLSAVI
++−+
=1 ……………(5.6)
‘γ’ was computed from the slope of the soil line and was found to be 1.15 as shown in Figure
5.5. WDVI and L were derived as explained in section 4.5.2 and subsequently SAVI map was
generated.
Figure 5.5: Soil line concept for computing the value of ‘γ’
SAVI map generated for the study is given in Figure 5.6 and shows a variation in value in the
range of 0.07560 to 0.64012 on 25 January 2008. The SAVI value was adjusted to remove the
negative values in order to avoid the complications in future calculations.
45
Figure 5.6: SAVI map for studying biophysical parameters of the region.
5.5.3 Leaf Area Index (LAI)
LAI represents the total biomass and is indicative of crop yield, canopy resistance and heat flux.
Leaf area index (LAI) is ratio of the total area of all leaves on a plant to the area of ground
covered by the plant. The leaf area index is computed using the equation 4.17. Figure 5.7 shows
the adjusted value (negative value removed) of leaf area index for the study region. The LAI
values varied from 0.00001 to 1.66707 on 25 January 2008.
46
Figure 5.7: Leaf Area Index (LAI) map for the study area.
5.5.4 Displacement height (d)
Displacement height was calculated based on the LAI map and required only one coefficient that
was adjusted to fit a wide range of field results. The relation to derive displacement height is
explained in section 4.5.4. The value of displacement height for the study region varied from
0.00714 to 0.82984 on 25 January 2008 as shown in Figure 5.8.
47
Figure 5.8: Displacement Height map for the study area.
5.5.5 Surface Roughness for Momentum Transport
The length zom is defined as the roughness length for momentum transport. The roughness length
zom is usually a very small number, in the order of 0.01 m or less. zom is determined using the
relation given Bastiaanssen et al. (1998), and the value for the study region varied from 0.01071
to 0.039839 on 25 January 2008. Figure 5.9 shows the Zom map for the study area.
The surface roughness length for heat transport (Zoh) was calculated using equation 4.23. Figure
5.10 shows the Zoh map for the study area.
48
Figure 5.9: Map of Surface roughness length of momentum transport.
49
Figure 5.10: Map of surface roughness length for Heat transport
5.6 Instantaneous Net Radiation (Rn).
The net radiation is the sum of the incoming and outgoing short and long wave components
given as
Rn = S↓–S↑ + L↓ -L↑. ……………….(5.7)
Figure 5.11 shows the Rn map for the study area.
50
Figure 5.11: Net Radiation Map (Wm-2).
5.6.1 Net Shortwave Radiation
Net shortwave radiation is the algebraic sum of the incoming shortwave radiation and outgoing
shortwave radiation and can be written as Snet= S↓–S↑ . This can also be determined from the
relation Snet = (1- ro) S ↓, where ro is the broadband albedo. The broadband surface albedo map
is derived in the above section and shown in Figure 5.2.
The incoming shortwave radiation or global radiation, S ↓, has to be measured at ground stations
by means of pyranometers working in all visible broadband range (usually 0.305 – 2.4 µm). But
due to the non-availability of this information following relation was used to determine the value
of shortwave incoming radiation.
exoground SS ↓=↓ *τ …………………...…(5.8)
51
The approach is to calculate the transmittance at ground stations having solarimeters. 'S↓' map is
obtained by multiplying the transmittance map by the 'S↓exo'. However the instantaneous
transmittance ‘τ’ is assumed to be equal to daily transmittance ‘τday’ and computed by :
5833.01285.025.0 =⎟
⎠⎞
⎜⎝⎛ ×+=
⎟⎠⎞
⎜⎝⎛ ×+=
day
SSday Nnba
τ
τ ……………………….(5.9)
exo
ground
SS
↓
↓=τ ……………………(5.10)
θτ
CosESCgroundS
o ××↓
= …………………..(5.11)
The value of solar constant ‘SC’ is taken as 1367 watt/m2 and Eo is taken as 0.9892. Since cos θ
is a map, the incoming shortwave radiation is derived as a map. Using this derived incoming
shortwave radiation map and the Albedo map, the net shortwave radiation is computed as shown
in Figure 5.12.
52
Figure 5.12: Net shortwave radiation map for the study area.
5.6.2 Net Longwave Radiation
Net longwave radiation is the algebraic sum of the incoming longwave radiation and outgoing
longwave radiation and can be written as Lnet= L↓–L↑.
4
aaTL σε↓= …………………..(5.12)
440 )1( ooaa TTL σεσεε +−↑= ………………...(5.13)
The detail explanation of the above equations are given in section 4.5.2. The unknowns in this
equation are the apparent emissivity of the atmosphere εa and the air temperature Ta while other
components are derived in the above sections. Air temperature was collected from the
meteorological station. In order to calculate the emissivity of air, two meteorological inputs
namely Relative humidity (RH) and air temperature were used. The calculation required to
estimate the emissivity of air is given in appendix 1 and the same was estimated to be
53
0.849.With the computed value of emissivity of air and taking Stefan boltzmann constant (σ) as
5.67x10-8 Watt m-2 K-2 the longwave incoming radiation was estimated to be 355.20 Watt m-2.
The parameters required for long wave outgoing radiation such as surface emissivity and surface
temperature is computed in the sections above. Figure 5.13 shows the upwelling long wave
radiation and was found to range from -70.58 to -44.82 Wm-2 on 25 January 2008 for the study
area.
Figure 5.13: Net Longwave Radiation Map (Wm-2).
5.7 Soil Heat flux:
The evaluation of G is usually presented as a ratio G/Rn. The instantaneous G/Rn function
depends on the pixel size, location and time. Over a period of one day the integrated soil heat
flux is usually considered as negligible. Different empirical studies have shown that the time
ratio G/Rn is related to the amount of vegetation present. The empirical equation for G/Rn
(Bastiaanssen et al. 1998) was used to estimate Soil Heat flux.
54
( ) ( )( )42 98.0162.032.0100
15.237NDVIrr
rT
RG
ooo
o
n
−+−
= …………….(5.13)
Where ro is the average albedo (approx 1.1ro) When the soil heat flux is directly downward. To is
the surface temperature in Kelvin. Surface temperature (To), the surface emissivity 0ε , and
NDVI have been calculated in the above sections. The maximum soil heat flux value for the
study area was estimated as 28.35 Wm-2 on 25 January 2008.
5.8 Sensible heat Flux.
The mathematical formulation of the sensible heat flux is based on the theory of mass transport
of heat and momentum between the surface (boundary) and the near surface environment. The
transport equation for sensible heat flux applicable in EBE theory is:
( )ah
aspa r
TTCH −= ρ ….………(5.14)
Figure.5.14 shows the sensible heat flux of the study area.
55
Figure 5.14: Soil heat flux (Wm-2).
5.8.1 Selection of Dry and Wet Pixel for the Determination of dT (Ts-Ta)
The dry and wet pixels were identified using the criteria described in the methodology. (4.5.4).
Scatter plot between Surface Temperature and Albedo (Figure 5.15) was made to find the dry
pixel. Another scatter plot between surface temperature and NDVI was constructed to find the
wet pixel.
The different estimated values of derivative components for the dry and wet pixel is given in
Table 5.1.
56
Table 5.1: Derived components of dry and wet pixel for the study region.
Derived Components Wet pixel Dry Pixel
Net Radiation 389.3546 W/m2 395.3427 W/m2
Surface Temperature 285.54 K 289.59 K
Soil Heat Flux 18.4738 W/m2 27.49775 W/m2
Displacement Height 0.7618 m 0.00714 m
Surface Roughness for Momentum Transport (zom)
0.21233 m 0.01452 m
5.8.2 Spread Sheet Calculation - Estimation of constants a & b for determination of dT (Ts-Ta)
The iterative process for the determination of ‘a’ and ‘b’ constants in-order to compute dT
(difference between surface and air temperature) is built as a spread sheet calculation. The
spreadsheet calculation is shown in Table 5.2. The derived components, constants and
meteorological data required for the calculation is provided in a tabular form (Table 5.3). After
the iteration the value of dTmax was estimated as 16.14 K. Considering a linear relation between
dT and surface temperature the value of constants a and b was computed as
-1517.18291 and 5.29483 respectively.
Using the value of a and b computed in the above iteration process a map of dT was developed
as shown in Figure 5.17. The dT map is an important input for the determination of sensible
heat.
5.8.3 Final Iteration for the determination of Sensible heat
Since Sensible Heat Flux is an implicit function of components that contains it therefore an
iterative process is run to derive the final value.
57
Figure 5.15: Two Dimensional Scatter Plot between Surface Temperature and Albedo for determination of Dry Pixel
Figure 5.16: Two Dimensional Scatter Plot between Surface Temperature and NDVI for determination of Wet Pixel
58
Table 5.2: Derived components, constants and other data used in the spreadsheet iterative calculation to estimate ‘a’ and ‘b’
Constants & Derived Components
Value Unit Remarks
To-wet 285.54 K Wet pixel temperature
To-dry 289.59 K Dry pixel temperature
Rn-dry 395.34265 Wm-2 Net radiation-dry pixel
Gs-dry 27.49775 Wm-2 Soil heat flux-dry pixel
zom -dry 0.01452 m Roughness length for momentum transport-dry pixel
Displ-dry 0.00714 m Displacement distance-dry pixel
u blend 3.026359 ms-1 Wind speed at blending height
Hmax 368.8449 Wm-2 Hmax=Rndry-Gdry
ρair 1.12 kgm-3 Air density
Cp 1004.16 Jkg-1K-1 Air specific heat
k 0.41 Karman constant
g 9.81 ms-2 acceleration due to gravity
z blend 100 m blending height
z ref 5 m reference height
zoh 0.0014558 m roughness length for heat transport
Table 5.3: Spread sheet iteration table for determining the constants ‘a’ and ‘b’.
Read from
maps Values Steps ψm ψh Ustar rah dTmax L Xh Xm ψh ψm To-wet 285.54 1 0.000 0.000 0.140 141.407 46.376 -0.608 7.164 3.393 4.784 4.533 To-day 289.59 2 4.784 4.533 0.306 28.738 9.425 -6.298 3.996 1.923 2.889 2.905 Qn-day 395.34265 3 2.889 2.905 0.209 61.217 20.077 -1.993 5.325 2.532 3.789 3.661 Gs-day 27.49775 4 3.789 3.661 0.246 44.446 14.577 -3.260 4.709 2.247 3.395 3.325 Zom-dry 0.01452 5 3.395 3.325 0.228 51.510 16.893 -2.602 4.981 2.373 3.574 3.477 Displ-dry 0.00714 6 3.574 3.477 0.236 48.247 15.823 -2.877 4.858 2.316 3.494 3.409 U-blend 3.02636 7 3.494 3.409 0.232 49.693 16.297 -2.750 4.913 2.341 3.530 3.439 hmax 368.8449 8 3.530 3.439 0.234 49.040 16.083 -2.806 4.889 2.330 3.514 3.426 rhoa 1.12 9 3.514 3.426 0.233 49.332 16.179 -2.781 4.900 2.335 3.521 3.432 cp 1004.16 10 3.521 3.432 0.233 49.201 16.136 -2.792 4.895 2.333 3.518 3.429 k 0.41 g 9.81 zblend 100 B 5.2948 zref 5 A -1517.182 zoh 0.0015
59
Figure 5.17: Plot of dT over surface temperature Ts for determining the constant ‘a’ and ‘b’
60
Figure 5.18: Difference between surface and air temperature (dT map in K).
The iteration process is carried with initial value of ψm (correction factor for momentum
transport) and ψh (correction factor for heat transport) as zero then subsequently computing the
maps of Friction Velocity (U*), Aerodynamic resistance for heat transport (Rah), Sensible Heat
(SH), Monin Obukhov Length (L), xm, ψm, xh, ψh in sequential order. The value of ψm and ψh at
the end of the first iteration is taken for the next iteration. This iterative process is run till a
constant value of sensible heat is reached. Figure 5.19 shows the final map of sensible heat
derived after 6 runs of the iterative process. Sensible heat flux ranged from 0.57258 to
603.54044 Wm-2 for the study area on 25 January 2008. Histogram of sensible heat flux (Figure
5.20) shows a normal distribution of values.
Figure 5.19: Instantaneous Sensible heat flux (Wm-2) map for the study area
61
Figure 5.20: Histogram of sensible heat flux values for the study area.
5.9 Instantaneous Latent Heat flux.
After the estimation of net radiation, soil heat flux and sensible heat, the instantaneous latent
heat flux was calculated as a residual term of the energy balance equation in W/m-2.The value of
latent heat flux ranged from 0 to 388 Wm-2 for the study area on 25 January 2008. The map of
latent heat flux is shown in Figure 5.21.
62
Figure 5.21: Instantaneous Latent heat flux in Wm-2 estimated as residual term of energy balance.
5.10 Evaporative Fraction
After developing the latent heat map, net radiation map and soil heat flux map, evaporative
fraction is estimated as discussed in section 4.11. Evaporative fraction for the study area ranged
from -0.80521 to 0.99852 on 25 January 2008 and is shown in Figure 5.22.
63
Figure 5.22: Evaporative fraction map estimated for the satellite pass instant.
5.11 Net Daily Radiation
Daily net radiation is the integration of all the instantaneous values of net radiation for the
whole day, there are separate set of formulas for its estimation.
5.11.1 Daily terrestrial solar radiation
The daily terrestrial solar radiation was computed using the relations explained in section 4.12.1.
Day angle map was created using the Julian day value; this map is used to compute the
eccentricity correction factor and the solar declination values. The sunrise hour angle map was
developed using the latitude map and solar declination map. Using the above derived
components the daily terrestrial solar radiation was computed as a map in megajoules m-2 day-1,
given in Figure 5.23. The value of daily terrestrial solar radiation was nearly constant and ranged
from 24.29973MJm-2day-1 to 25.08052MJm-2day-1 for the study area on 25 January 2008.
64
Figure 5.23: Daily terrestrial solar radiation in MJm-2day-1.
65
Figure 5.24: Average daily incoming shortwave radiation in Wm-2
5.11.2 Average Daily Net Longwave Radiation
The average daily net longwave radiation was calculated using the meteorological data. Mean
relative humidity for the satellite overpass day was recorded as 80% and the mean air
temperature was taken as 180C. Using the meteorological data the average daily net longwave
radiation was estimated to be -65.09 Wm-2. Also using the relation provided be De Bruin 1987,
the net longwave radiation was estimated to be -64.166 Wm-2.
5.12 Evapotranspiration
Once the evaporative fraction map and daily net radiation map was developed, the daily
evapotranspiration map was estimated from the relation given in 4.13. The evapotranspiration
value ranged from -2.85432 to 4.21735 on 25 January 2008 and is shown in Figure 5.25.
66
Figure 5.25: Single day Evapotranspiration of the day of 25 January 2008 for the study area.
5.13 Spatial Distribution of Evapotranspiration
Using SEBAL methods evapotranspiration has been estimated for the study area during the
wheat growing season. Figure 5.26 shows the spatial distribution map of evapotranspiration of
all the crops for the study area. Figure 5.27 shows the spatial distribution map of
evapotranspiration of only for the wheat fields for the study area. It has been found that
evapotranspiration of wheat has been increasing with time and the highest evapotranspiration
was found after the 95 days of plantation.
67
26 days (DOY = 345) 34 days (DOY=353) 39 days (DOY=361)
47 days (DOY=001) 55 days (DOY=009) 63 days (DOY=017)
71 days (DOY=025) 79 days (DOY=033) 95 days (DOY=049)
103 days (DOY=057) 111 days (DOY=065)
Figure 5.26: Change of Evapotranspiration (mm/day) for the study area
68
26 days (DOY = 345) 34 days (DOY=353) 39 days (DOY=361)
47 days (DOY=001) 55 days (DOY=009) 63 days (DOY=017)
71 days (DOY=025) 79 days (DOY=033) 95 days (DOY=049)
103 days (DOY=057) 111 days (DOY=065)
Figure 5.27: Change of Evapotranspiration (mm/day) for the wheat field
69
5.14 Comparison of SEBAL with FAO Penman Monteith
5.14.1 FAO Penman-Monteith equation
In 1948, Penman combined the energy balance with the mass transfer method and derived an
equation to compute the evaporation from an open water surface from standard climatological
records of sunshine, temperature, humidity and wind speed. This so-called combination method
was further developed by any researchers and extended to cropped surfaces by introducing
resistance factors. A consultation of experts and researchers was organized by FAO in May
1990, in collaboration with the International Commission for Irrigation and Drainage and with
the World Meteorological Organization, to review the FAO methodologies on crop water
requirements and to advice on the revision and update of procedures. The panel of experts
recommended the adoption of the Penman-Monteith combination method as a new standard for
reference evapotranspiration and advised on procedures for calculation of the various
parameters. By defining the reference crop as a hypothetical crop with an assumed height of
0.12 m having a surface resistance of 70 s m-1 and an albedo of 0.23, closely resembling the
evaporation of an extension surface of green grass of uniform height, actively growing and
adequately watered, the FAO Penman-Monteith method was developed. The method overcomes
shortcomings of the previous FAO Penman method and provides values more consistent with
actual crop water use data worldwide. From the original Penman-Monteith equation and the
equations of the aerodynamic and surface resistance, the FAO Penman-Monteith method to
estimate ETo can be derived as follow:
….………(4.14)
Where, ETo reference evapotranspiration [mm day-1],
Rn net radiation at the crop surface [MJ m-2 day-1],
G soil heat flux density [MJ m-2 day-1],
T mean daily air temperature at 2 m height [°C],
u2 wind speed at 2 m height [m s-1],
es saturation vapour pressure [kPa],
ea actual vapour pressure [kPa],
es-ea saturation vapour pressure deficit [kPa],
∆ slope vapour pressure curve [kPa °C-1],
γ psychrometric constant [kPa °C-1].
70
Crop evapotranspiration can be calculated from climatic data and by integrating directly the crop
resistance, albedo and air resistance factors in the Penman-Monteith approach. As there is still a
considerable lack of information for different crops, the Penman-Monteith method is used for
the estimation of the standard reference crop to determine its evapotranspiration rate, i.e., ETo.
Experimentally determined ratios of Etc /ETo, called crop coefficients (Kc), are used to relate ETc
to ETo or ETc = Kc * ETo. Figure 5.28 explains the component of the estimation of
evapotranspiration using Penman-Montieth equation.
Figure 5.28: Explaining the reference crop ETo and crop evapotranspiration ETc
The value of crop coefficient (Kc) changes with the growth stages of crop. Typically, a cereal
crop e.g. wheat follows four growth stages: initial, crop development, mid season and late
season. The initial stage runs from planting date to approximately 10% ground cover. The length
of the initial period is highly dependent on the crop, the crop variety, the planting date and the
climate. During the initial period, the leaf area is small, and evapotranspiration is predominately
in the form of soil evaporation. The crop development stage runs from 10% ground cover to
effective full cover. Effective full cover for many crops occurs at the initiation of flowering. The
mid-season stage runs from effective full cover to the start of maturity. The start of maturity is
often indicated by the beginning of the ageing, yellowing or senescence of leaves, leaf drop, or
71
the browning of fruit to the degree that the crop evapotranspiration is reduced relative to the
reference ETo. The mid-season stage is the longest stage for perennials and for many annuals,
but it may be relatively short for vegetable crops that are harvested fresh for their green
vegetation. The late season stage runs from the start of maturity to harvest or full senescence.
The calculation for Kc and ETc is presumed to end when the crop is harvested, dries out
naturally, reaches full senescence, or experiences leaf drop. A summary of different stages of
crop development and typical values of Kc were presented in Figure 5.29.
Figure 5.29: Growth stages and changes of Kc values
Rahman et al. (2008) conducted a study using Lysimeter to determine crop coefficient values of
wheat in Joydebpur, Bangladesh. The reference crop evapotranspirations (ET0) for Joydebpur
was estimated for wheat and presented in the Table 5.4. Knowing crop ET and ET0 of different
development stages, the crop coefficient (Kc) values of wheat were determined. These crop
coefficient values are slightly different from those recommended by FAO (Doorenbos and
Pruitt, 1977) which is also presented in the table.
72
Table 5.4: Calculation for crop co-efficient of wheat (Source: Rahman et al. (2008))
Crop growth stage
Duration
(days)
Crop ET
(mm)
Reference crop ET (ET0)
(mm)
Crop
coefficient
(Lysimeter)
FAO recommended
Kc values
Initial 15 19.5 46.64 0.42 0.30
Development 25 46.5 59.80 0.78 0.70
Midseason 40 114.0 101.0 1.13 1.05
Late season 30 64.0 132.0 0.48 0.65
In this study, Kc values were determined based on the Rahman et al. (2008) study. The values
of Kc used for different development stage of wheat are calculated and plotted in the Figure
5.30.
Figure 5.30: Growth stages and changes of Kc values of wheat
Penman Monteith Equation was used to determine the evapotranspiration of the study area for
the reference crop. These values were determined for the days when satellite images were
available to compare the evapotranspiration values using energy balance equation. A number of
meteorological parameters such as daily maximum temperature (0C), minimum temperature
73
(0C), wind speed (knot), sunshine hours (hour/day), relative humidity (%) and Mean Sea level
pressure (mbar) from the nearest meteorological station. Within the study area, the only
meteorological station is located in the Dinajpur district. The values of different meteorological
parameters presented in the Table 5.5 for the specific days when satellite images were available.
Based on these meteorological parameters, ET0 of the reference crop was calculated using
Penman Monteith formula. These values of evapotranspiration (Et0) were multiplied by the crop
coefficient (Kc) to determine the evapotranspiration (Etc) of wheat. The values of
evapotranspiration using the Penman Monteith equation can be considered as the possible
maximum water crop can use for evapotranspiration.
Table 5.5: Mean value of atmospheric parameters and ET of wheat using Penman Monteith method during the growing season.
Days after plan.
Mean Temp
Min Temp
Max Temp
Humidity
Wind speed
Sunshine Hr.
MSL Pressure
ET Ref. Crop, Et0
Crop Coeff., kc
ET Crop, Etc
(days) (0C) (0C) (0C) (%) (Knot) (hr/d) (mbar) (mm/d) - (mm/d) 18 21.64 14.90 28.39 73.71 1.20 7.93 1014.64 2.61 0.75 1.96 26 19.40 12.83 25.97 77.57 1.26 7.06 1015.74 2.24 0.9 2.02 34 18.49 11.46 25.53 72.86 1.37 7.06 1014.23 2.31 1 2.31 42 17.54 10.74 24.33 78.14 1.59 4.63 1012.57 2.05 1.15 2.36 47 17.38 11.38 23.38 81.25 1.50 4.93 1012.40 1.93 1.15 2.22 55 18.93 11.49 25.37 87.00 1.26 7.17 1015.31 2.20 1.15 2.53 63 17.76 11.47 24.06 70.14 1.63 5.00 1013.60 2.38 1.15 2.74 71 17.15 12.74 21.56 78.43 1.83 3.17 1012.13 1.99 1.15 2.2979 15.01 11.11 18.91 75.86 1.99 3.09 1012.07 1.97 1.15 2.2787 15.34 9.57 23.11 81.00 1.63 8.39 1014.63 2.67 1.05 2.80 95 20.60 14.41 25.79 71.00 1.74 7.41 1013.30 3.30 0.93 3.07
103 21.45 14.39 28.51 72.71 1.53 8.21 1011.66 3.57 0.76 2.71 111 23.72 18.17 29.27 65.71 1.91 7.11 1010.97 4.02 0.1 0.40
5.14.2 Comparison of ET using SEBAL and Penman Monteith methods
The mean values of evapotranspiration using SEBAL methods of the study area were calculated
over the study area for the specific days when satellite images were available. A summary of the
mean values of evapotranspiration using SEBAL method over the study area was presented in
Table 5.6. ET was calculated from the energy components such as net radiation, soil heat flux,
sensible heat flux and evaporative fraction which were also presented in the table. NDVI and
Land Surface Temperature were calculated from MODI images using spectral and thermal bands
respectively.
74
Table 5.6: Mean value of various components of surface energy fluxes and ET of wheat using SEBAL method during the growing season.
Days after plan.
ET NDVI Sensible Heat Flux
Net Radiation
Soil Heat Flux
Evaporative Fraction
Land Surface Temp.
(days) (mm/d) (Wm-2) (Wm-2) (Wm-2) (0C) 18 1.50 0.39 167 324 27 0.43 19.77 26 1.97 0.36 115 312 25 0.60 18.39 34 2.20 0.35 95 315 23 0.67 17.14 42 2.49 0.38 77 321 24 0.74 17.73 47 2.36 0.43 89 324 25 0.70 18.54 55 2.54 0.56 92 359 23 0.72 15.8863 3.17 0.45 35 353 25 0.89 15.2871 1.91 0.59 179 383 22 0.50 14.50 79 2.63 0.48 139 386 27 0.61 15.85 87 3.32 0.46 131 427 34 0.66 19.38 95 4.37 0.42 88 470 41 0.79 20.99
103 3.95 0.53 148 492 42 0.67 21.83 111 3.17 0.51 214 498 48 0.52 23.59
The mean ET of wheat over the study area using SEBAL and Penman Montieth were compared
during the growing season. Figure 5.31 shows time series plot of mean ET of wheat determined
from energy balance and Penman Monteith method. It has found that after 80 days from the
plantation the ET calculated from SEBAL method showed higher values than Penman Monteith
method. However, the possible ET for the reference crop (Et0) shows similar trends which was
presented as dashed line in the plot. Therefore, the Kc values used from the Lysimeter
experiments conducted by Rahman et al. (2008) at Jaydebpur can’t be used here.
Figure 5.31: Comparison of Evapotranspiration (mm/d) between SEBAL and Pennman Montieth
75
Penman Monteith method provides theoretical values of evapotranspiration whereas SEBAL
method gives the actual evapotranspiration. The crop coefficient (Kc) was determined by making
ratios of actual evapotranspiration calculated from the SEBAL method with the
evapotranspiration of reference crop (ET0) from Penman Monteith method. Figure 5.32 shows a
comparison between crop coefficients determined from the SEBAL and Penman Monteith
method and that of from the Lysimeter experiments conducted by Rahman et al. (2008). The
mean Kc value found from SEBAL method was 1.20 whereas that of from Lysimeter
experiments was 1.13 during the mid-season. The crop coefficient estimated by SEBAL method
was found higher of a value of 0.07 (6%) than the Kc estimated using Lysimeter experiments.
Abou El-Mag et al. (2003) has mentioned that in field Lysimeters lacks acceptability when
applied to the field or large irrigation schemes where conditions are very variable. He found that
the estimated mean real time Kc value of 1.16 (±1-3% error) using SEBAL method was higher
than the standard Kc value of 1.1 identified by FAO-56 using Lysimeter. Hence, the crop
coefficient values developed in this study using SEBAL method was found more realistic than
that suggested by a single Lysimeter experiments. However, further analysis with high
resolution satellite images can provide more accurate information on the crop evapotranspiration
and crop coefficient values.
Figure 5.32: Comparison of Kc values determined from field experiment with values determined using both SEBAL and Penman Montieth methods.
76
Chapter 6: Crop Growth Monitoring and Yield Estimation
6.1 Spatial Distribution of wheat during the growing season
Growth of the wheat has been monitored using satellite images. Time series MODIS data has
data over the study area were to determine NDVI which represents health of the crop. A spatial
distribution maps were developed over the study area using NDVI values. These maps were
masked only for the wheat growing area. The masking techniques were mentioned in details in
the Chapter 3. These masked images were shown the spatial distribution of the wheat crop over
the study area. Figure 6.1 shows spatial distribution of the wheat growing areas in the study area
for the whole growing season of 2007-2008 (November to April). As mentioned earlier that
plantation of wheat started at the middle of November with an average growing season of 110
days. Harvesting occurred at the second week of March of the following year. Chronological
changes of the NDVI values over the study area supports this information. It has been found that
peak value occurred around 71 days (Day of the Year, DOY =25) after the plantation. Changes
of the NDVI clearly indicate the growth pattern and extend of wheat over the study area. Using
this information, the wheat coverage area was calculated for the study area. The total wheat
coverage area was found 1118 km2 whereas the non-wheat agricultural area was found 5391km2.
Table 6.1 presents no of pixels and coverage area for wheat and non-wheat crops over the study
area during the 2007-2008 growing seasons.
Table 6.1: Wheat Coverage Area during 2007-2008 growing season
Landuse No of pixels Area (km2)Non wheat area 95848 5391Wheat growing area 19818 1118
77
26 days (DOY = 345) 34 days (DOY=353) 39 days (DOY=361)
47 days (DOY=001) 55 days (DOY=009) 63 days (DOY=017)
71 days (DOY=025) 79 days (DOY=033) 95 days (DOY=049)
103 days (DOY=057) 111 days (DOY=065)
Figure 6.1: Changes of the NDVIs of the wheat for the growing season of 2007-2008.
78
6.2 Correlation between NDVI and production
An attempt was made to correlated wheat production with the maximum NDVI values. Upazila-
wise wheat yield data has been collected for the study area from the Department of Agricultural
Extension (DAE). The maximum value of NDVI has been calculated for each Upazila using the
supervised classified images. A summary of the yield, area, production and maximum NDVI
value of the growing season for each Upazila have been presented in Table 6.2. It has been
found that the total productions of wheat are 83,255, 31,485 and 132,275 tons and average yields
are 2.18, 2.06 and 2.33 tons/hactor for Dinajpur, Panchagarh and Thakurgaon district,
respectively. A correlation was established between Upazila wise yield and maximum NDVI as
shown in Figure 6.2. The coefficient of determination between yield and maximum NDVI was
found 0.32. Although there has been no significant correlation has been found between these
two variables, the trend is found positive.
Table-6.2: Upazila-wise Yield and maximum NDVI during the growing season.
District Upazila Median NDVI
Area (ha) Yield (ton/ha)
Production (ton)
Total Pixel
Dinajpur Birgonj 0.603 9875 2.45 24187 1967 Khansama 0.585 2830 2.40 6792 769 Bochagonj 0.599 4465 2.35 10492 574 Kaharol 0.598 5095 2.40 12228 1052 Chirir Bandar 0.588 1160 2.36 2737 630 Dinajpur Sadar 0.585 1530 2.46 3764 537 Parbitipur 0.570 830 1.20 992 291 Birol 0.585 6510 2.45 15924 698 Nawabgonj 0.580 775 2.40 1860 308 Fulbari 0.571 1065 2.12 2263 62 Birampur 0.563 520 2.45 1274 74 Ghoraghat 0.583 230 2.23 512 331 Hakimpur 0.568 220 1.04 230 13 Panchagar Tetulia 0.572 830 1.90 1577 189 Panchagar Sadar 0.569 4200 2.20 9240 155 Atwari 0.582 4380 2.12 9286 1016 Boda 0.572 2420 2.10 5082 570 Debigonj 0.581 3150 2.00 6300 793 Thakurgaon Thakugaon Sadar 0.591 15500 2.00 31000 4007 Baliadangi 0.599 11500 2.50 28750 1954 Ranishankail 0.597 9500 2.50 23750 1450 Haripur 0.603 8500 2.40 20400 843 Pirgonj 0.592 12500 2.27 28375 1535
79
Figure 6.2: Correlation between wheat yield (t/ha) and median value of NDVI during the peak growth (DOY=25) for each Upazila of the study area.
However, a significant correlation was found between the total production and median number
of pixel which represents wheat field. Median values were used for NDVI to avoid the bias in
mean due to any outlier data. The coefficient of determination between total production (tons) of
wheat and median value of the number of wheat pixels was found as 0.708. Figure 6.3 shows the
total wheat production (tons) in each Upazila and the respective median value of the number of
wheat pixels.
It is clear from the above analysis that more and accurate information of yield from the field
were essential to establish a correlation between yield and crop health which is represented by
NDVI. However, remote sensing technology can successfully determine the crop coverage area
and able to gross estimate the production of the crop.
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Figure 6.3: Correlation between wheat Production (ton) and no of wheat pixels in the Upazila
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Chapter 7: Conclusions
7.1 Conclusions
This study has been conducted to determine the applicability of remote sensing technology to
monitor the growth of what and establish a relationship between crop growth and its yield.
Using time series MODI images during the growing season of 2007-2008, the growth of wheat
was monitored over the greater Dinajpur region which consists of three districts: Dinajpur,
Thakurgaon and Panchagaor. Normalized Vegetation Index was calculated to identify the health
of the crop over the study area. By using field level farmers information, these images were
masked based to identify only the wheat coverage area from the other agricultural area. Spatial
distribution maps over the study area was developed using wheat and non-wheat area masks.
The spatial and temporal plots of the changes of NDVI of the masked area (which represents
wheat area) are found analogous to the field information. The plantation of wheat started at the
middle of November with an average growing season of 110 days. Harvesting occurred at the
second week of March of the following year. Chronological changes of the NDVI values over
the study area were also support this information. It has been found that peak value of NDVI
occurred around 71 days (Day of the Year, DOY =25) after the plantation. The total wheat
coverage area was found 1118 km2 whereas the non-wheat agricultural area was found 5391km2
during the 2007-2008 growing seasons.
The remote sensing images were further used to determine the evapotranspiration of the crop in
order to identify the crop coefficients and crop water requirements. The Surface energy balance
algorithm for land (SEBAL) model was used to estimate the evapotranspiration of wheat. Both
spectral and thermal bands of MODIS were used to estimate ET. The auxillary data in which
there were relative humidity (RH), temperature, sunshine hours, wind speed etc which were
taken from the only meteorological station at Dinajpur.
The mean values of the components of the energy balance over the study were varies within the
following ranges during the growing season of wheat:
1. The minimum net radiation estimated is 312 w/m2 and maximum was 498 w/m2. 2. The minimum Soil heat flux is 48 w/m2 and maximum is 22 w/m2.
3. The minimum Sensible heat flux is 35 w/m2 and maximum was 214 w/m2.
4. The minimum Evapotranspiration value was 1.5 mm/day and maximum 4.4 mm/day.
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The spatial distribution map of the actual evapotranspiration over the study area was developed
during the growing season. The mean ET of wheat over the study area using SEBAL was
compared with ET using Penman Monteith method. Penman Monteith method provides
theoretical values of evapotranspiration whereas SEBAL method gives the actual
evapotranspiration. The crop coefficient (Kc) was determined by making ratios of actual
evapotranspiration calculated from the SEBAL method with the evapotranspiration of reference
crop (ET0) from Penman Monteith method. The mean Kc value found from SEBAL method was
1.20 whereas that of from Lysimeter experiments conducted by Rahman et al. (2008) was 1.13
during the mid-season. The crop coefficient estimated by SEBAL method was found higher of a
value of 0.07 (6%) than the Kc estimated using Lysimeter experiments. On the basis of the
following results it is clearly evident that it is possible to determine the evapotranspiration of the
study area using energy balance equation.
An attempt was undertaken to correlate the crop health using NDVI indices with the yield.
Using the Upazila wise yield data from the Department of Agricultural Extension (DAE) a
correlation was developed between yield of wheat and maximum values of NDVI. It has been
found that the total productions of wheat are 83,255, 31,485 and 132,275 tons and average yields
are 2.18, 2.06 and 2.33 tons/hactor for Dinajpur, Panchagarh and Thakurgaon district,
respectively. The coefficient of determination between yield and maximum NDVI was found
0.32. However, a strong correlation was found (R2=0.71) between the wheat production and
satellite represented wheat area. It can be conclude that satellite images can successfully
determine the coverage area and spatial distribution of the wheat during the growing season.
7.2 Recommendations
The following recommendations can be made from this study-
i) The research results should be verified conducting more research studies considering
several wheat cultivation seasons in the greater Dinajpur region as well as in other
wheat growing areas of Bangladesh.
ii) The research results could be tuned more accurately, if remote sensing image of
higher resolution for the study area could be used.
iii) Information of the yield from many farmers’ field is essential to develop a significant
correlation between yield and crop health monitored by remote sensing images.
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APPENDIX A: ILWIS script developed for running the SEBAL algorithm
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Note: Calculation is conducted for MODIS image on 3rd December, 2007 (DOY=337)
Importing satellite imagery and sub-setting
Surface Reflectance
// import image of h25 and v 06 of surface reflectance of band 1 import tiff('mod09a1.a2007337.h25v05.sur_refl_b01'.tif,'b01_h25_2007337') // import image of h26 and v 06 of surface reflectance of band 1 import tiff('mod09a1.a2007337.h26v05.sur_refl_b01'.tif,'b01_h26_2007337') // glue of two maps of h26 and h25 with v06 to make band 1 image for 2007 at 337 b01_2007337:=MapGlue(b01_h25_2007337,b01_h26_2007337,replace) // similar lines of code will be used for band 2 to 7 of Surface reflectance….. Land Surface temperature from thermal bands // import day time Land Surface Temperature of h25v06 grid import tiff('MOD11A2.A2007337.h25v05.LST_day_1km'.tif,'day_h25_2007337') day_h25_cor_2007337:=IFF(day_h25_2007337=0,?,day_h25_2007337) // import day time Land Surface Temperature of h26v06 grid import tiff('MOD11A2.A2007337.h26v05.LST_day_1km'.tif,'day_h26_2007337') day_h26_cor_2007337:=IFF(day_h26_2007337=0,?,day_h26_2007337) //combined LST of day time day_2007337:=MapGlue(day_h25_cor_2007337,day_h26_cor_2007337,replace) // import night time Land Surface Temperature of h25v06 grid import tiff('MOD11A2.A2007337.h25v05.LST_night_1km'.tif,'night_h25_2007337') night_h25_cor_2007337:=IFF(night_h25_2007337=0,?,night_h25_2007337) // import night time Land Surface Temperature of h26v06 grid import tiff('MOD11A2.A2007337.h26v05.LST_night_1km'.tif,'night_h26_2007337') night_h26_cor_2007337:=IFF(night_h26_2007337=0,?,night_h26_2007337) //combined LST of night time night_2007337:=MapGlue(night_h25_cor_2007337,night_h26_cor_2007337,replace) // combined LST of day and night time lst_2007337:=IFUNDEF(day_2007337,?,IFUNDEF(night_2007337,?,(day_2007337+night_2007337)/2)) // LST in degree centigrade lst_deg_2007337:=lst_2007337*0.02-273 Land Surface Emissivity //importing Surface emissivity from band 31 and 32 // emissivity of band 31 for the h25v06 grid
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import tiff('MOD11A2.A2007337.h25v05.Emis_31'.tif,'Emis_31_h25_2007337') Emis_31_h25_cor_2007337:=IFF(Emis_31_h25_2007337=0,?,Emis_31_h25_2007337) // emissivity of band 31 for the h26v06 grid import tiff('MOD11A2.A2007337.h26v05.Emis_31'.tif,'Emis_31_h26_2007337') Emis_31_h26_cor_2007337:=IFF(Emis_31_h26_2007337=0,?,Emis_31_h26_2007337) // combined emissivity of band 31 Emis_31_2007337:=MapGlue(Emis_31_h25_cor_2007337,Emis_31_h26_cor_2007337,replace) // emissivity of band 32 for the h25v06 grid import tiff('MOD11A2.A2007337.h25v05.Emis_32'.tif,'Emis_32_h25_2007337') Emis_32_h25_cor_2007337:=IFF(Emis_32_h25_2007337=0,?,Emis_32_h25_2007337) // emissivity of band 32 for the h26v06 grid import tiff('MOD11A2.A2007337.h26v05.Emis_32'.tif,'Emis_32_h26_2007337') Emis_32_h26_cor_2007337:=IFF(Emis_32_h26_2007337=0,?,Emis_32_h26_2007337) // combined emissivity of band 31 Emis_32_2007337:=MapGlue(Emis_32_h25_cor_2007337,Emis_32_h26_cor_2007337,replace) // combined emissivity for both band 31 and band 32 Emis_2007337:=IFUNDEF(Emis_31_2007337,?,IFUNDEF(Emis_32_2007337,?,(Emis_31_2007337+Emis_32_2007337)/2)) // Broad band emissivity Emisv_2007337:=Emis_2007337*0.0020+0.49 //Subsetting for the study area (dinajpur) lst_500m_2007337.mpr := MapResample(lst_deg_2007337,dinaj_geo_500m.grf,nearest) emsi_500m_2007337.mpr := MapResample(Emisv_2007337,dinaj_geo_500m.grf,nearest)
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Calling Script for SEBAL method
// Net Radiation assuming cloud free conditions //***************** Calculate Net Radiation****************************** run net_rad 2007337 //***************** Calculate Soil Heat Flux ***************************** run soil_heat_flux 2007337 //***************** Calculate Sensible Heat Flux ************************* run sensible_heat_flux 2007337 //***************** Calculate Daily Net Radiation************************* run daily_net_rad 2007337 //***************** Calculate Latent Heat Flux and daily Evapotranspiration*** run evapotranspiration 2007337 //************** End of Script***************************************** Net Radiation // Net Radiation assuming cloudfree conditions //***************** Short Wave***************************** //latitude in degree latitudemap{dom=VALUE.dom;vr=-180.0000:180.0000:0.00001}:=IFF(lst_dinaj_2007337,crdy(transform(mapcrd(lst_dinaj_2007337),latlon)),0) //longitude in degree longitudemap{dom=VALUE.dom;vr=-180.0000:180000.0:0.00001}:=IFF(lst_dinaj_2007337,crdx(transform(mapcrd(lst_dinaj_2007337),latlon)),0) //ones for creating maps and keeping the precision upto 5 decimal point ones{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=longitudemap-longitudemap // dn = 337 for Julian date 337 of 2007 // Day angle in radians da:=ones+2*PI*(337-1)/365 // E0 E0:=ones+1.00011+0.034221*COS(da)+0.00128*SIN(da)+0.000719*COS(2*da)+0.000077*SIN(2*da)
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// declination angle in radians delta:=ones+0.006918-0.399912*COS(da)+0.070257*SIN(da)-0.006758*COS(2*da)+0.000907*SIN(2*da)-0.002697*cos(3*da)+0.00148*SIN(3*da) //Equation of time in hours Et:=ones+(0.000075+0.001868*COS(da)-0.032077*SIN(da)-0.014615*COS(2*da)-0.04089*SIN(2*da))*(229.18/60) // Local apparent time in hour LAT:=ones+8.708+longitudemap*4/60+Et // hour angle in radians omega:=ones+15*(LAT-12)*PI/180 // cosine of Solar zenith angle cos_theta:=ones+SIN(delta)*SIN(latitudemap*PI/180)+COS(delta)*COS(latitudemap*PI/180)*COS(omega) // solar zenith angle in Degrees solzen:=ACOS(cos_theta)*180/PI // Instantaneous terrestrial solar radiation Kin_TOA:=ones+1367*E0*cos_theta // reading from the S_down map for tower point, Kin_TOA = 1127.349 Wm-2 // reading from the data file Kin_o = 860 // transmissivity tau:=ones+8/12 // Kin will be Kin:=ones+tau*Kin_TOA // outgoing shortwave radiation Kout:=ones+ro_dinaj_2007337*Kin // Net shortwave radiation Knet:=ones+Kin-Kout //***************** Long Wave************************************************ //Stefan Boltzman constant //Sigma:=ones+5.67*(10^-8) // Reading Instantaneous air temperature in [°C] for tower Ta:=ones+21.74 // Instantaneous Relative humidity[%]
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Rh:=ones+73.75 //es saturated water vapor pressure at Ta [milibar] es:=ones+(5.108*EXP(17.27*Ta/(Ta+237.3))) //ea water vapor pressure derived from relative humidity RH [milibar] ea:=ones+(es*Rh/100) //e apparent atmospheric emissivity as defined by Brutsaert (1975) e:=ones+1.24*(ea/(Ta+273))^(1/7) //Ld instantaneous incoming longwave radiation [watt/m^2] following equation //1. Brutsaert Equation Ld:=ones+e*5.67*(10^-8)*(Ta+273)^4 // Outgoing LW radiation [watt/m^2] //NDVI map NDVI{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(band02_dinaj_2007337-band01_dinaj_2007337)/(band02_dinaj_2007337+band01_dinaj_2007337) //Surface emissivity [-] map emis:=ones+IFF(NDVI>0.16,1.009+0.047*ln(NDVI),IFF(NDVI>-0.1,0.92,1)) // Outgoing Reflected radiation Lo_ref:=ones+(1-emis)*Ld // kinetic temperature of the body is "lst_dinaj_2007337" as map // Outgoing Surface radiation Lo_sur:=ones+emis*5.67*(10^-8)*lst_dinaj_2007337^4 // Total outgoing radiation Lo:=ones+Lo_sur+Lo_ref // Net Longwave radiation Lnet:=Ld-Lo // **********Net radiation************************** Rnet:=ones+Knet+Lnet // ********************* End of Script************************** Soil Heat Flux // Soil Heat Flux using MODIS data // Red is band-1 and NIR is band 2 Red:=band01_dinaj_%1.mpr
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NIR:=band02_dinaj_%1.mpr // compute NDVI NDVI{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(NIR-Red)/(NIR+Red) // plot soil line and find the value of gamma //gamma= 1.15 WDVI{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=NIR-1.15*Red L_factor{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=1-2*1.6*NDVI*WDVI SAVI{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(NIR-Red)*(1+L_factor)/(NIR+Red+L_factor) // For LAI equation for Savanna area // using grass & bush land type from table c1=0.14 and c2=0.3 LAI{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=IFF(((SAVI-0.14)/0.3)>0,((SAVI-0.14)/0.3),0.00001) // fPAR fPAR{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=IFF(NDVI>(-0.161/1.275), (-0.161+1.275*NDVI),0.00001) //surface roughness map for momentum z0m{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=EXP(-5.5+5.8*NDVI) //surface roughness map for heatmap z0h{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=z0m/10 //Displacement height LAI_fact{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(20.6*LAI)^0.5 displ{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=1.0*(1-(1-EXP(-LAI_fact))/LAI_fact) // Soil heat Flux // Bastiaanssen (1998) // default value of c1 = 1.1 G0_bas{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=Rnet*((lst_dinaj_%1-273.15)/(ro_dinaj_%1.mpr*100))*(0.32*(1.1*ro_dinaj_%1.mpr)+0.62*(1.1*ro_dinaj_%1.mpr)^2)*(1-0.978*NDVI^4) // Kustan and Norman Equation G0_kus:=0.35*cos_theta*Rnet*EXP(-0.6*LAI/((2*cos_theta)^0.5))
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// difference map G_dif{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=G0_bas-G0_kus // Select Bastiaanssen equation for soil heat flux G0{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=G0_bas Iteration Calling Script for Sensible Heat Flux // Sensible Heat Flux using MODIS data //initialize system //ones to create map psiM{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=ro_dinaj_%1-ro_dinaj_%1 psiH{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=ro_dinaj_%1-ro_dinaj_%1 // find sensible heat flux, H using iteration run sensible_heat_flux_script_2 %1 run sensible_heat_flux_script_2 %1 run sensible_heat_flux_script_2 %1 run sensible_heat_flux_script_2 %1 run sensible_heat_flux_script_2 %1 run sensible_heat_flux_script_2 %1 run sensible_heat_flux_script_2 %1 Sensible Heat Flux // Sensible Heat Flux using MODIS data //ones to create map ones{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=ro_dinaj_%1-ro_dinaj_%1 // Values from previously calculated in spread sheet for "a" and "b" //T0_wet:= 285.54 //T0_dry:= 289.59 //Rn_dry:= 395.34265 //Gs_dry:= 27.49775 //Z0M_dry:= 0.01452 //d_dry:= 0.00714 //u_blend:= 3.026363 //H_max:= 368.8449 //p_air:=1.12 //Cp:=1004.16 //k:=0.41 //g:=9.81 //z_blend:=100 //z_ref:=5 //z0H:= 0.0015 //a:= -1517.18201 //b:= 5.29483
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ub{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=2.0*((ln(100-displ)-ln(z0m))/(ln(5-displ)-ln(z0m))) del_T{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=IFF((-1517.18201+5.29483*lst_dinaj_%1)<0,0,(-1517.18201+5.29483*lst_dinaj_%1)) u_s{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(0.41*ub) /(ln((100-displ)/z0m)-psiM) rah{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(ln((5-displ)/z0h)-psiH)/(0.41*u_s) H{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=1.12*1004.16*del_T/rah L{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=-(1.12*1004.16*(u_s^3)*lst_dinaj_%1)/(0.41*9.81*H) xm{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(1-16*(100-displ)/L)^(1/4) xh{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:= (1-16*(5-displ)/L)^(1/4) psiM{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:= 2*ln(0.5+0.5*xm^1)+ln(0.5+0.5*xm^2)-2*ATAN(xm)+0.5*PI psiH{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:= 2*ln(0.5+0.5*xh^2) Daily Net Radiation // Daily Net Radiation assuming cloud free conditions // Sunrise hour angle ws{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=ACOS(-TAN(latitudemap*PI/180)*TAN(delta)) // total hours for a perfect clear day N_day{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=ws*360/(15*PI) // n = bright sunshine hour per day = N_day s // Sunshine fraction (Sf) = (n/N) is given as 1 in our data set // daily incoming shortwave radiation at the top of atmosphere (megajules m-2 day-1) Kin_day_TOA{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(24/PI)*(1367*0.0036)*E0*COS(latitudemap*PI/180)*COS(delta)*(sin(ws)-ws*cos(ws)) //daily incoming shortwave radiation (w/m2) Kin_day{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=11.5741*(0.25+0.5*(1.0))*Kin_day_TOA
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// daily atmospheric transmittance , here n/N is 1 tau_day{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=ones+(0.25+0.5*(1.0)) //daily net long wave radaition //L_day:=110*tau // daily net radiation // taking c1=1.1 Rnet_day{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=(1-1.1*ro_dinaj_%1)*Kin_day-110*tau Evapotranspiration // Daily Evapotranspiration using SEBAL algorithm and MODIS data //calcluate latent heat flux LE0{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=Rnet-G0-H //evaporation fraction map Ef{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=1.0*LE0/(LE0+H) // Daily amount of evapotranspiration E_day_%1{dom=VALUE.dom;vr=-10000.0000:10000.0000:0.00001}:=Ef*8.64*(10^7)*Rnet_day/(2.47*(10^6)*1000)
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