Chapter 5 Geospatial Modeling

5.1 Rationale

5.2 SEBAL modeling for evapotranspiration

5.3 Penman-Monteith method for

evapotranspiration

5.4 Runoff modeling

5.5 Recharge modeling

5.6 Weighed Overlay Analysis using GIS

5.1 Rationale

This chapter is designed to provide detailed information about the models and

algorithms used to retrieve information on different parameters of this study. The

models and algorithms include SEBAL, ArcCN-Runoff, Recharge Model and

Weighed Overlay Analysis technique.

Geospatial modeling is a platform designed to facilitate spatial analysis of remote

sensing data using GIS environment. This ranges from simple map making to

complex algorithms. Apart from in-built models we can create and redesign our own

models in ERDAS Imagine and ArcGIS as per our requirement like recharge and

SEBAL model used in this study.

Hydro-geospatial modeling is a set of algorithms and models that generate spatial

information on various components of hydrological cycle. In GIS few modules have

been incorporated especially for dealing with key variables of hydrology e.g. Arc-

hydro, Arc-swat and spatial analysis module with sub modules for groundwater and

hydrology.

5.2 SEBAL modeling for evapotranspiration

SEBAL algorithm was developed by Bastiannssen et al. (1998) and has been applied

to Landsat ETM+ and TM images in the present study, along with weather data to

compute seasonal and annual evapotranspiration. SEBAL can be processed using a

79 |

number of programs such as ERDAS Imagine, MATLAB, and ArcGIS by

(Bastiannssen et al. 1998; Chemin 2003; French et al. 2005; Brata et al. 2006; Khalaf

and Donoghue 2012; Mendonca et al. 2012). ArcGIS has been chosen for this study

for its least complicated procedural algorithms. ArcGIS is a geospatial software

package and does not require a complicated mathematical modeling background. It

allows manipulation, plotting of functions, data implementation of algorithms,

creation of raster data sets in simple and understandable formats like tiff and img

format. Figure 5.1 presents a diagrammatic view of ET retrieval from satellite data.

Figure 5.1 Schematic representation of SEBAL to retrieve evapotranspiration.

Among all the models used in the present research SEBAL is most complex with

more than 30 computational steps. Landsat data used in SEBAL algorithm is

available monthly except for two monsoon months were cloud cover is more than

80%. SEBAL computes an instantaneous ET flux for the satellite over pass time. This

instantaneous ET is then converted to daily and monthly ET by various computational

steps in SEBAL. The ET flux is calculated for each pixel of the image as a “residual”

of the surface energy budget equation:

Vegetation Indices

Net Radiation

SEBAL Metrological data

ET

Landsat satellite data (TM, ETM)

Radiation Balance

Soil heat flux

80 |

𝛌𝐄𝐓 = 𝐑𝐧 −𝐇 − 𝐆 − −−−−−− (𝟓.𝟏)

Where; λET is the latent heat flux, Rn is the net radiation flux at the land surface, H is

the sensible heat flux to the atmosphere and G is the soil heat flux, all expressed in

(Wm-2). The surface energy budget is further explained in various sections of this

chapter.

5.2.1 Net radiation budget (Rn)

Net radiation budget is the amount of radiation left after all the outgoing radiation

fluxes are subtracted from the incoming radiation fluxes. It is equal to the sum of the

net shortwave and longwave radiation, calculated from the following equation:

𝐑𝐧 = (𝟏 − 𝛂)𝐒↓ + 𝐋↓ − 𝐋↑(𝟏 − 𝛆𝐨)𝐋↓ − − − − − −− (𝟓.𝟐)

Where; S↓ is shortwave radiation reaching the earth’s surface (Wm-2), α is broad band

surface albedo (dimensionless) and L↓ and L↑ are incoming and outgoing longwave

radiations (Wm-2) respectively and εo is the surface thermal emissivity

(dimensionless).

5.2.2 Instantaneous incoming short wave radiation (S↓)

The Incoming shortwave radiation is the direct and diffuse solar radiation flux that

actually reaches the earth’s surface (Wm-2). It is computed using solar constant, solar

incidence angle, a relative Earth-Sun distance and atmospheric transmissivity by the

following equation:

𝐒↓ = 𝐆𝐬𝐜 × 𝐜𝐨𝐬𝛉 × 𝐝𝐫 × 𝛕 −−−−−−− (𝟓.𝟑)

Where; Gsc is the solar constant (1367 Wm-2), cosθ is the cosine of the solar

incidence angle which is calculated from sun elevation data provided with the image,

dr is the inverse squared relative Earth-Sun distance (Appendix 1.1) and τ is the

atmospheric transmissivity (Equ. 5.10).

𝐝𝐫 = 𝟏 + 𝟎.𝟎𝟎𝟑𝐜𝐨𝐬 �𝐉𝐃𝟐𝛑𝟑𝟔𝟓

� − − − − − (𝟓.𝟒)

Where; JD is Julian day and values for dr range from 0.97 to 1.03 and is

dimensionless (Appendix 1.1).

81 |

5.2.3 Albedo (α)

Surface albedo is defined as the ratio of the reflected radiation to the incident

shortwave radiation.

𝛂 =𝛂𝐚 − 𝛂𝐭𝐨𝐚

𝛕𝟐− − − − − −− (𝟓.𝟓)

Whereas; Values for αa is path radiance range between 0.025 and 0.04 and for

SEBAL a value of 0.03 is given Bastiaanssen (2000), αtoa is albedo at top of

atmosphere (Equ. 5.8) and τ is atmospheric transmissivity (Equ. 5.10).

TM and ETM+ Sensor (QCALMIN =1 and QCALMAX =255)

Band no.

Landsat seven Landsat five

Low Gain High Gain

Lmin Lmax Lmin Lmax Lmin Lmax

Band 1 -6.20 293.70 -6.20 191.60 -1.52 169

Band 2 -6.40 300.90 -6.40 196.50 -2.84 333

Band 3 -5.00 234.40 -5.00 152.90 -1.17 264

Band 4 -5.10 241.10 -5.10 157.40 -0.51 221

Band 5 -1.00 47.50 -1.00 31.06 -0.37 30.2

Band 6 0.00 17.04 3.20 12.65 1.237 15.303

Band 7 -0.35 16.54 -0.35 10.80 -0.15 16.5

Band 8 -4.70 243.1 -4.70 158.30 NA NA

Table 5.1 ETM+ and TM post-calibration dynamic spectral ranges (Source: Chander et al. 2009).

Surface albedo is computed using following computational steps in SEBAL, Spectral

radiance (Lλ) is calculated from following equation:

𝐋𝛌 = {(𝐋𝐌𝐀𝐗𝛌 − 𝐋𝐌𝐈𝐍𝛌)

(𝐐𝐂𝐀𝐋𝐌𝐀𝐗 − 𝐐𝐂𝐀𝐋𝐌𝐈𝐍)} × {𝐐𝐂𝐀𝐋 − 𝐐𝐂𝐀𝐋𝐌𝐈𝐍} + 𝐋𝐌𝐈𝐍𝛌 − − − (𝟓.𝟔)

Where; Lλ (Wm-2sr-1μm-1) is the spectral radiance calculated using band information

from file for each band of image λ represents band number. QCAL is the quantized

calibrated pixel value in DNs, QCALMIN is the minimum quantized calibrated pixel

82 |

value (DN=0) corresponding to LMINλ, QCALMAX is the maximum quantized calibrated

pixel value (DN=255) corresponding to LMAXλ, LMINλ is the spectral radiance that is

scaled to QCALMIN in Wm-2sr-1μm-1, and LMAXλ is the spectral radiance that is scaled to

QCALMAX in Wm-2sr-1μm-1. Table 5.1 provides band-specific parameters and the

Landsat imagery.

The reflectivity for each band (ρλ) is computed by equation 5.7. The reflectivity of a

surface is defined as the ratio of the reflected radiation flux to the incident radiation

flux.

𝛒𝛌 =𝛑𝐋𝛌

𝐄𝐒𝐔𝐍𝛌 × 𝐜𝐨𝐬𝛉 × 𝐝𝐫− − − − −−− (𝟓.𝟕)

Where; ρλ is reflectivity, Lλ is the spectral radiance, dr is inverse squared Earth-Sun

distance in astronomical units, ESUNλ is the mean solar exo-atmospheric irradiances,

and cosθ is the solar zenith angle in degrees. Table 5.2 gives the solar exo-

atmospheric spectral irradiances (ESUNλ) for Landsat images.

Band1 Band2 Band3 Band4 Band5 Band6 Band7 Band8

ESUNλ Landsat5 1983 1796 1536 1031 220.0 NA 83.44 NA Landsat7 1997 1812 1533 1039 230.8 NA 84.90 1362

ωλ Landsat5 0.293 0.274 0.233 0.157 0.033 NA 0.011 NA Landsat7 0.293 0.274 0.231 0.156 0.034 NA 0.012

Table 5.2 Solar atmospheric spectral irradiances (ESUNλ) and weighting coefficient (ωλ) for different Landsat TM and ETM+ images (Source: Chander et al. 2009).

The reflectivity calculations depend on the inverse squared Earth-Sun distance (dr)

which varies by each image and can be calculated using image date and Julian day

calculator. Albedo at top of atmosphere αtoa is calculated using following equation:

𝛂𝐭𝐨𝐚 = 𝚺 (𝛚𝛌 × 𝛒𝛌) −−−−−−− (𝟓.𝟖)

Where; ρλ is reflectivity and ωλis a weighting coefficient for each band given in Table 5.2 and can also be calculated as follows:

𝛚𝛌 =𝐄𝐒𝐔𝐍𝛌𝚺 𝐄𝐒𝐔𝐍𝛌

− − − − − −− (𝟓.𝟗)

83 |

Atmospheric transmissivity is defined as the fraction of incident radiation that is

transmitted by the atmosphere and it represents the effects of absorption and reflection

occurring within the atmosphere. This effect occurs to incoming radiation and to

outgoing radiation and is thus squared in Equ. (5.10). It includes transmissivity of both

direct solar beam radiation and diffuse (scattered) radiation to the surface. We calculate

τ assuming clear sky and relatively dry conditions using an elevation-based relationship

from (Allen et al. 1998).

𝛕 = 𝟎.𝟕𝟓 + 𝟐 × 𝟏𝟎−𝟓 × 𝐙 − − −− −−− (𝟓.𝟏𝟎)

Where; Z is the elevation from mean sea level (m); for Gajwel watershed (Z) = 573

m, τ=0.76 and τ2=0.5776.

5.2.4 Instantaneous incoming longwave radiation (L↓)

The incoming long wave radiation is the downward thermal radiation flux from

the atmosphere. It is calculated using the Stefan-Boltzmann equation:

𝐋↓ = 𝛆𝐚 × 𝛔 × 𝐓𝐚𝟒 − − − − −−− (𝟓.𝟏𝟏)

Where εa is atmospheric emissivity (dimensionless), σ is Stefan-Boltzmann constant

(5.67×10-8 Wm-2 K-4), Ta is the air temperature (°K) and εa is calculated based on the

equation developed by Bastiannssen (1995):

𝛆𝐚 = 𝟎.𝟖𝟓 × −𝐥𝐧𝛕 − −− − −−− (𝟓.𝟏𝟐)

5.2.5 Instantaneous outgoing long wave radiation (L↑)

The outgoing long wave radiation is the upward thermal radiation leaving the surface.

It is calculated using Stefan-Boltzmann equation:

𝐋↑ = 𝛆𝐨 × 𝛔 × 𝐓𝐬𝟒 − − − − − −− (𝟓.𝟏𝟑)

Where; εo is the surface emissivity, σ is Stefan-Boltzmann constant (5.67×10-8 Wm-2

K-4) and Ts is the surface temperature (°K) which calculated from radiance of thermal

bands using Plank’s Equation (Equ. 5.14).

84 |

5.2.6 Thermal emissive band for Landsat images

The thermal band, Band 6 is calibrated using the internal calibrator where it is

converted from spectral radiance to effective at-satellite temperature (Chander and

Markham 2003). The effective at-satellite temperature of the imaged earth surface

assumes unit emissivity where the conversion formula is presented in Equ. 5.14.

Where T is the effective at satellite temperature in Kelvin, K1 and K2 is the calibration

constants and Lλ is the spectral radiance of thermal band. The surface temperature

(Ts) is computed using the following modified Plank’s Equation:

𝐓𝐬 =𝐊𝟐

𝐥𝐧 �𝐊𝟏𝐋𝛌

+ 𝟏�− − − − − −(𝟓.𝟏𝟒)

Where; Lλ is the spectral radiance of band 6 and K1 and K2 (Wm-2sr-1μm-1) are

calibration constants for Landsat given in Table 5.3.

Satellite K1 K2

Landsat7 ETM+ Band6 666.09 1282.71

Landsat5 TM Band6 607.76 1260.56

Table 5.3 Landsat ETM+ and TM thermal band calibration constants (Source: Chander et al. 2009).

5.2.7 Surface emissivity (εo)

Emissivity is defined as the ratio of the energy radiated by an object at a given

temperature to the energy radiated by a black body at the same temperature. Since

the thermal radiation of the surface is observed in the thermal bands of satellite

data, one can compute the surface temperature if the emissivity of the land

surface is estimated. In SEBAL, surface emissivity is estimated using NDVI and an

empirically-driven method (van de Griend and Owe 1993):

𝛆𝐨 = 𝟏.𝟎𝟎𝟗 + 𝟎.𝟎𝟒𝟕𝐥𝐧(𝐍𝐃𝐕𝐈) −−−−−−− (𝟓.𝟏𝟓)

Where; NDVI >0; otherwise, emissivity is assumed to be zero as in case of water.

Equation 4.10 is restricted to measurements conducted in the range of NDVI=0.16-

0.74. NDVI is calculated as a ratio of the difference in reflectance for the near

infrared band (NIR) and the red band (R) to their sum as (Goetz 1997):

85 |

𝐍𝐃𝐕𝐈 =𝐍𝐈𝐑 − 𝐑𝐍𝐈𝐑 + 𝐑

− − − −−−− (𝟓.𝟏𝟔)

NDVI is calculated based on reflectance (R), instead of the brightness (DN) values of

the original bands.

5.2.8 Soil heat flux (G)

Soil heat flux is the rate of heat storage in the soil as a result of the temperature

gradient between the soil surface and the underlying soil layers. The

temperature gradient varies with the fractional vegetation cover and the leaf area

index (LAI), as light interception from and shadow formation on the bare soil

determine relative heating of the bare soil surface. Soil heat flux can be measured

using following equation if thermal conductivity of soil is known:

𝐆 = 𝛌𝐬∆𝐓𝐬∆𝐙

− − − − −−−−(𝟓.𝟏𝟕)

Where; λs is thermal conductivity of soil, ΔTs is temperature difference between T0

andT1, and 𝛥𝛥z is the depth difference between Z1 and Z1.

Due to lack of spatial information about thermal conductivity of soil the empirical

relationship developed by Bastiaanssen (1995) has been applied, it calculates soil heat

flux as a function of Rn, NDVI, broad band albedo and surface temperature:

𝐆 = 𝐑𝐧 − �𝐓𝐬 − 𝟐𝟕𝟑

𝛂� {𝟎.𝟎𝟎𝟑𝟖𝛂 + 𝟎.𝟎𝟎𝟕𝟒𝛂𝟐}{𝟏 − 𝟎.𝟗𝟖𝐍𝐃𝐕𝐈𝟒} −−− (𝟓.𝟏𝟖)

Where; Rn is net radiation (Wm-2), Ts is surface temperature (°K) (Equ. 5.14), α

is broad band surface albedo and NDVI is vegetation index normalized differential

vegetation index.

5.2.9 Sensible heat flux (H)

Sensible heat flux is the rate at which energy loss from soil through convection and

diffusion process as a result of temperature difference between the surface and the

lowermost overlaying atmosphere. It is estimated from surface temperature, surface

roughness and measured wind speed by following method:

86 |

𝐇 =𝛒𝐚𝐂𝐩𝐝𝐭𝐫𝐚𝐡

− −− − −−− (𝟓.𝟏𝟗)

Where; ρa is air density (kgm-3), air density calculated on line from temperature in 0F

and elevation from mean sea level in feet, CP is air specific heat (1004 Jkg-1K-1). dT

(K) is the temperature difference (Ts–Ta) between two heights (Z1 and Z2). Ts=

surface temp, Ta= air temp rah is the aerodynamic resistance to heat transport.

𝐫𝐚𝐡 = 𝐥𝐧(𝐙𝟐𝐙𝟐

)

µ × 𝐤− − − − −−− (𝟓.𝟐𝟎)

Where; Z1 and Z2 are heights in meters above the zero plane displacement (d) of the

vegetation, µ is the friction velocity (ms-1) which quantifies the turbulent velocity

fluctuations in the air, and k is von Karman’s constant (k = 0.41), µ is the friction

velocity. Values for µ are obtained from the wind speed at the blending height a value

of 100 m was assumed in this study. In SEBAL model, fixed values of Z1= (0.1 m)

and Z2 (2 m) were preferred for present research.

µ = 𝐥𝐧𝐤µ𝐱

𝐙𝐱𝐙𝐨𝐦�

− − − − −−− (𝟓.𝟐𝟏)

Where; k is von Karman’s constant, µx is the wind speed at blending height (ms-1) at

blending height Zx, and Zom is the momentum roughness length (m). Zom is a measure

of the drag and skin friction for the layer of air that interacts with the surface.

The friction velocity µ at the weather station is calculated for neutral atmospheric

conditions. The assumption of neutral conditions for the weather station is reasonable

if the weather station is surrounded by well-watered vegetation. The calculation of µ

requires a wind speed measurement (ux) at a known height (zx) at the time of the

satellite image. The momentum roughness length (Zom) is empirically estimated from

leaf area index.

𝐙𝐨𝐦 = 𝟎.𝟎𝟏𝟖 𝐋𝐚𝐢 − − − − − −(𝟓.𝟐𝟐)

Where; Lai is leaf area index derived from satellite image by following equation:

87 |

𝐋𝐚𝐢 = −�𝟎.𝟔𝟗 − 𝐬𝐚𝐯𝐢

𝟎.𝟓𝟗 �𝟎.𝟗𝟏

− −− − −−(𝟓.𝟐𝟑)

The temperature difference dt is calculated from following equation:

𝐝𝐭 = 𝐇𝐫𝐚𝐡𝛒𝐚𝐂𝐩

− − − − − −− (𝟓.𝟐𝟒)

In this equation H and dt are both unknown but are directly related to one another as

well as to the value of rah. Therefore, dt is calculated at two extremes, the wettest and

driest pixels, by assuming values for H at these reference pixels. The wettest pixel is

the pixel where H~0, i.e. all the available energy (Rn-G) is converted λET or dt

becomes zero. The driest pixel is the where λET~0, so that H= Rn-G or dt is

maximum. The wettest pixels (coldest pixels) are selected in a well-watered

agricultural field i.e., at pixels with high NDVI but with low temperature, while the

driest pixels (pixels with highest estimated temperature) are selected at pixels with

high temperature but with low NDVI and albedo. Water bodies should be avoided

during the selection of either pixels due to the problem of lag in stored heat (G) into

the body that may not be available at the same instant as Rn or H. Once the wettest

and the driest pixels have been selected, temperatures are noted from surface

temperature image as Tcold and Thot and locations of the pixels are also noted.

Values of Rnhot, Ghot, and rahhot are recorded at the place and Thot is located from

the net radiation map, soil heat flux map and aerodynamic resistance map

respectively. As the latent heat flux is assumed to be equal to zero at the hottest pixel,

the sensible heat flux therefore is equal to the net available energy:

𝐇𝐡𝐨𝐭 = 𝐑𝐧𝐡𝐨𝐭 − 𝐆𝐡𝐨𝐭 − − − − − −− (𝟓.𝟐𝟓)

Temperate difference (dt) is then calculated from the following equation:

𝐝𝐭𝐡𝐨𝐭 =𝐡𝐡𝐨𝐭 × 𝐫𝐚𝐡𝐡𝐨𝐭𝛒𝐚 × 𝟏𝟎𝟎𝟒

− − −− −−− (𝟓.𝟐𝟔)

Where; dthot Values of Tcold, Thot, and dthot are known and may be used to apply

the following equation:

𝐓𝐡𝐨𝐭 − 𝐓𝐜𝐨𝐥𝐝 = 𝐝𝐭 = 𝐚 + 𝐛𝐓𝐬 − −− − −−− (𝟓.𝟐𝟕)

88 |

By making this linear relationship between Ts and dt, a and b may be calculated

from slope and intercept as shown in Figure 5.2 below:

Figure 5.2 Temperature difference between surface and air temperature.

After solving for “a” and “b”, the sensible heat flux (H) for the whole image is

calculated iteratively until convergence in the successive value is found. Finally, the

latent heat flux (λET) is computed for each pixel as a residual term of the surface

energy balance. An equivalent amount of instantaneous ET is also calculated by

dividing the latent heat flux by the latent heat of vaporization (λ).

5.2.10 Latent heat of flux (λET)

Latent heat flux is the rate of latent heat loss from the surface as a result of

evapotranspiration. It can be computed for each pixel using following relationship:

𝛌𝐄𝐓 = 𝐑𝐧 − 𝐇 − 𝐆 − − −−−−− (𝟓.𝟐𝟖)

Where; λET is an instantaneous value for the time of the satellite overpass (Wm-2).

An instantaneous value of ET in equivalent evaporation depth is computed as:

𝐄𝐓𝐢𝐧𝐬𝐭 = 𝟑𝟔𝟎𝟎 𝛌𝐄𝐓𝛌

− − − − −−− (𝟓.𝟐𝟗)

Where; ETinst is the instantaneous ET (mm hr-1), 3600 is the time conversion from

seconds to hours, and λ is the latent heat of vaporization or the heat absorbed when a

kilogram of water evaporates (Jkg-1).

Tcold Thot Ts 0

dthot

dt

89 |

5.2.11 Daily Net Radiation (Rn24)

Net radiation is aggregated as daily net radiation (Rn-day) based on Bastiannssen et al.

(1996) approach:

𝐑𝐧𝟐𝟒 = (𝟏 − 𝟏.𝟏𝛂)𝐑𝐬↓𝟐𝟒 − 𝟏𝟏𝟎𝛕𝐝𝐚𝐲 − − − − − −− (𝟓.𝟑𝟎)

Where; Rs↓24 is daily atmospheric transmissivity for radiation calculated using

Angstrom formula as follows:

𝛕𝐝𝐚𝐲 = 𝟎.𝟐𝟓 + 𝟎.𝟓 𝐧𝐍− −− −−−− (𝟓.𝟑𝟏)

Where; n is the actual duration of sunshine and N is maximum possible sunshine or

day light hour (Appendix 1.1).

𝐑𝐬↓𝟐𝟒 = 𝐆𝐬𝐜𝐄𝐨𝐂𝐨𝐬𝛅𝐂𝐨𝐬𝛗𝟐𝟒𝛑�𝐒𝐢𝐧𝛚𝐗

𝛑𝟏𝟖𝟎

�𝛚𝐬 − 𝐂𝐨𝐬𝛚𝐬 − − − −− (𝟓.𝟑𝟐)

Where; Gsc is the solar constant (1367 Wm-2), Eo is the eccentricity correction factor,

δ is solar declination, θ is latitude and ωx is the sun set or rise hour angle in radians

(Appendix 1.1).

5.2.12 Daily/monthly Actual ET

The daily actual ET is calculated based on the combination of above equations:

𝐄𝐓𝟐𝟒 = 𝐑𝐧𝟐𝟒𝟐𝟖.𝟓𝟖𝟖

− − − − −−− (𝟓.𝟑𝟑)

Where; Rn-day is the daily net radiation in Wm-2.

Monthly ET values were attained by summing up the daily ET (ET24) data of the

respective month in ArcGIS. This monthly data was summed up to seasonal and annual

actual ET. A monthly ET map that covers an entire growing season is often valuable.

This can be derived from the daily ET data by extrapolating the ET24 to the

monthly/seasonal actual evapotranspiration.

5.2.13 Assumptions and uncertainties Induced by of SEBAL algorithm

There are four assumptions that SEBAL makes within the algorithm:

90 |

The sensible heat flux range and the evaporative fraction are anchored by the “hot”

pixel in the very dry terrain where latent heat flux reaches zero and the “cold” pixel

in very moist terrain where sensible heat flux is zero. The determination should be

made very carefully.

Difference in temperature (dt) is assumed to be linearly related to radiometric

surface temperature. The relation between the surface and air temperature and their

gradient is significantly affected by the vegetative properties. The surface heat flux

fractions such as the evaporative fraction and relative ET, throughout the day are

assumed constant.

SEBAL is comprised of computational steps some of which require decision-making

by the user such as the selection of the dry and wet indicator pixels, determination of

prediction algorithms for surface roughness, selection of ground-based weather

data and development of prediction equations for surface to air temperature

differences.

These decisions are crucial and challenging in that they do not only influence accuracy

of the SEBAL output but they also require a good theoretical knowledge of regional

energy and radiation balance modeling, regions microclimate, local bio-physical

environment, e.g. vegetation cover, soil physical conditions, etc. and physics of the

SEBAL algorithm.

5.3 Penman-Monteith method for evapotranspiration

Reference ET is the rate of ET from hypothetical reference crop with assumed height

crop of 0.12 m, a fixed surface resistance of 70 sec m-1, and an albedo of 0.23,

resembling the ET from an extensive surface of green grass of uniform height, actively

growing, well-watered, and completely shading the ground (Allen et al. 1998). Daily

reference ET may also be calculated using FAO Penman-Monteith equation (Appendix

1.1):

𝐄𝐓𝐫𝐞𝐟 =𝟎.𝟒𝟎𝟖∆(𝐑𝐧 − 𝐆) + 𝛄 𝟗𝟎𝟎

𝐓 + 𝟐𝟕𝟑𝐮𝟐(𝐞𝐬 − 𝐞𝐚)𝚫 + 𝛄(𝟏 + 𝟎.𝟑𝟒𝐮𝟐)

−−−−−−− (𝟓.𝟑𝟒)

91 |

Where; ETref is reference crop ET (mm day-1), Rn is net radiation at the crop surface

(MJ m-2 day-1), Go is soil heat flux density (MJ m-2 day-1), T is mean daily temperature

at 2 m height (°C), u2 is wind speed at 2 m height (m s-1), es is saturation vapour

pressure (KPa), ea is actual vapour pressure (KPa), (es-ea) is saturation vapour pressure

deficit (KPa), Δ is slope of vapour pressure curve (KPa °C-1), and 𝛾𝛾 is the

psychrometric constant (KPa °C-1). The monthly actual ET is then determined based on

the assumption that the daily relative ET at date of image acquisition remains the same

for the whole period of the month (Appendix 1.1).

5.3.1 Slope vapour pressure curve (Δ)

The slope of the relationship between saturation vapour pressure and temperature is a

requirement for the calculation of ET. It is given by the following relationship (Allen et

al. 1998):

𝚫 =𝟒𝟎𝟗𝟖 �𝟎.𝟔𝟏𝟎𝟖𝐞𝐱𝐩� 𝟏𝟕.𝟐𝟕𝐓𝐚

𝐓𝐚 + 𝟐𝟕𝟑.𝟑��

(𝐓𝐚 + 𝟐𝟕𝟑.𝟑)𝟐 − − − − − −− (𝟓.𝟑𝟓)

Where; Ta is the mean air temperature in degree celsius.

5.3.2 Psychrometric constant (𝛾𝛾)

The Psychrometric constant is used for the calculation of ET. It is given by the

following relationship (Allen et al. 1998):

𝛄 =𝐂𝐩 × 𝐏𝛆 × 𝛌

− − −− −−− (𝟓.𝟑𝟔)

Where; P atmospheric pressure (KPa),latent heat of vaporization (MJkg-1), Cp specific

heat at constant pressure(MJ kg-1 °C-1), ratio molecular weight of water vapour/dry air

= 0.622

5.3.3 Mean saturation vapour pressure (es)

Saturation vapour pressure is related to air temperature; therefore it can be calculated

using this meteorological element based on the following equation:

𝐞° = 𝟎.𝟔𝟏𝟎𝟖𝐞𝐱𝐩 �𝟏𝟕.𝟐𝟕𝐓𝐚𝐓𝐚 + 𝟐𝟕𝟑.𝟑

� − − − − − −− (𝟓.𝟑𝟕)

92 |

𝐞𝐬 =𝐞°(𝐓𝐦𝐚𝐱) + 𝐞°(𝐓𝐦𝐢𝐧)

𝟐− − − − −−− (𝟓.𝟑𝟖)

5.3.4 Actual vapour pressure (ea)

The actual vapour pressure ea is the saturation vapour pressure at dew-point

temperature that is defined as the temperature to which the air needs to be cooled to

make the air saturated. It is estimated by following method (Allen et al. 1998).

𝐞𝐚 =𝐞°(𝐓𝐦𝐢𝐧)𝐑𝐇𝐦𝐚𝐱

𝟏𝟎𝟎 + 𝐞°(𝐓𝐦𝐚𝐱)𝐑𝐇𝐦𝐢𝐧𝟏𝟎𝟎

𝟐− − − − −−− (𝟓.𝟑𝟗)

Where; RHmean is the mean relative humidity defined as the average between maximum

relative humidity (RHmax) and the minimum relative humidity (RHmin).

5.3.5 Soil heat flux (G)

The soil heat flux, G, is the energy that is utilized in heating the soil. G is positive

when the soil is warming and negative when the soil is cooling. It is estimated by

following empirical relationship (Allen et al. 1998).

𝐆𝐦𝐨𝐧𝐭𝐡,𝐢 = 𝟎.𝟎𝟕 �𝐆𝐦𝐨𝐧𝐭𝐡,𝐢+𝟏−𝐆𝐦𝐨𝐧𝐭𝐡,𝐢−𝟏� − − − −− −− (𝟓.𝟒𝟎)

Where; Tmonth,i is the mean air temperature of month i, Tmonth,i-1 is the mean air

temperature of previous month, and Tmonth,i+1 is the mean air temperature of next

month, all expressed in degrees celsius.

5.3.6 Net radiation (Rn)

The net radiation is the difference between the incoming and the outgoing radiation of

both short and long wavelengths. It is the balance between energy absorbed, reflected,

and emitted by the earth’s surface or the difference between incoming net shortwave

(S) and the net outgoing longwave (L) radiation. It is normally positive during the

daytime and negative during the night times.

𝐑𝐧 = (𝐒 − 𝐋) −−−−−−− (𝟓.𝟒𝟏)

93 |

Where; S and L are expressed in (MJ m-2 day-1). Daily net radiation, humidity and

wind speed data was collected from ICRISAT, Hyderabad.

5.3.7 Actual evapotranspiration (ETa)

Actual evapotranspiration is calculated using crop coefficient approach, by multiplying

the reference crop ET (ETref) by a crop coefficient (Kc)

𝐄𝐓𝐚 = 𝐄𝐓𝐫𝐞𝐟 × 𝐊𝐜 − − − − −−− (𝟓.𝟒𝟐)

Where; ETa is daily actual ET, ETref is daily reference ET and Kc is crop coefficient.

Crop coefficient values are derived from (Allen et al. 1998) and local crop condition of

the area. The monthly actual ET is then determined based on the assumption that the

daily ET.

5.4 Runoff modeling

The amount of water that flows over the land when the soil is infiltrated to full capacity

by precipitation is termed as runoff. Runoff is an essential component of water budget;

runoff estimation is prerequisite for planning and management of water resources.

With non-availability of discharge data runoff is estimated by several methods, among

them, Soil Conservation Service curve number (SCS-CN) renamed as Natural

Resources Conservation Services Curve Number (NRCS-CN) method is the most

popular and widely used worldwide (Melesse and Shih 2002; Bo et al. 2011; Soulis et

al. 2009; Hernandez-Guzman and Ruiz-Luna 2013).

The process of runoff estimation is further alleviated by application of GIS based

runoff modeling. ArcCN-Runoff an extension to Arcmap in .dll format developed by

Zhan and Huang (2004) is used to estimate spatial distribution of runoff. The model

was developed to facilitate watershed runoff modeling for ungauged watersheds. The

model is simple and works on the NRCS curve number method with rainfall, soil

(HSG) and land use as basic input parameters.

This approach involves the use of simple empirical formulas and readily available tables.

The NRCS-CN method continues to be most satisfactory when used for different types of

hydrologic problems that were designed to solve evaluating the effects of land use changes.

94 |

The advantage of this method is its simplicity, predictability, stability and its reliance on

only one parameter namely the curve number (CN). Curve numbers range from 0 to 100;

higher curve numbers represent higher proportion of surface runoff and lower curve

numbers represents lower proportion runoff. The main input required to the NRCS-CN

method is watershed boundary, Land use data, HSG data and knowledge of antecedent

moisture condition to estimate daily runoff.

In the NRCS runoff estimation method, the ratio of amount of actual retention to watershed

storage is assumed to be equal to the ratio of actual direct runoff to the effective rainfall i.e.

total rainfall minus initial abstraction (Melesse and Shih 2002): 𝐅𝐒

=𝐐

𝐏 − 𝐈− − − − −−−−−−(𝟓.𝟒𝟑)

Where; where F actual retention, S is potential maximum watershed storage, Q is

runoff, P is precipitation and I initial abstraction, all expressed in mm.

The amount of actual retention is expresses mathematically by following relationship

(Melesse and Shih 2002):

𝐅 = (𝐏 − 𝐈) − 𝐐 − −−−−−−−(𝟓.𝟒𝟒)

The empirical relationship between actual retention (mm); S is potential maximum

watershed storage (mm) is expressed mathematically by following relation (Melesse

and Shih 2002; Bo et al. 2011):

𝐈 = 𝟎.𝟐𝐒 − − − − −−−−−−− (𝟓.𝟒𝟓)

By substituting equation 5.45 into equation 5.43 and 5.44 following empirical

relationship is derived:

𝐐 ={𝐏 − 𝟎.𝟐𝐒}𝟐

𝐏 + 𝟎.𝟖𝐒− − − − −−−−−−− (𝟓.𝟒𝟔)

The equation 5.46 is used to calculate depth of runoff and the parameter S of equation

5.46 is related to CN by following empirical relation (Melesse and Shih 2002):

𝐒 = 𝟐𝟓𝟒 �𝟏𝟎𝟎𝐂𝐍

− 𝟏� − − − − −−−−(𝟓.𝟒𝟕)

Where; CN is curve number (dimensionless).

95 |

Antecedent moisture condition has a significant effect on runoff, considering this aspect

NRCS developed three AMC conditions viz., AMC I, AMC II and AMC III. Prior to

estimating runoff for a rainfall event, the curve numbers should be adjusted based on the

season and total 5-day antecedent precipitation. The curve numbers for AMC II condition

for hydrologic soil cover complexes are selected are designed on (USDA 1972) and curve

number adjustments for antecedent soil moisture conditions AMC I and AMC III can be

derived from AMC II by following relationships (Bo et al. 2011) .

𝐂𝐍𝐈 =𝟒.𝟐𝐂𝐍𝐈𝐈

(𝟏𝟎 − 𝟎.𝟎𝟓𝟖𝐂𝐍𝐈𝐈)−−−−− (𝟓.𝟒𝟖)

𝐂𝐍𝐈𝐈𝐈 =𝟐𝟑𝐂𝐍𝐈𝐈

(𝟏𝟎 − 𝟎.𝟏𝟑𝐂𝐍𝐈𝐈)−−−−− (𝟓.𝟒𝟗)

Basic input parameters used in runoff modeling include daily rainfall data which was

obtained from MRO and TRMM data sources. This precipitation data was used to design 5-

day AMC and on the basis of daily rainfall analysis, it was observed that the watershed

supports both AMCI and AMCII conditions. Therefore, new CN’s were designed based on

local hydro-metrological conditions of the watershed. Apart from precipitation data, the

land use in the study area was systematized into eight land use groups which mainly

compose agriculture land including (paddy fields, other rainfed crops and orchids), forests,

waste lands, built-up and water bodies. In the study area all three the soil groups fall in

group “C” of hydrological soil group. Details of land use and “HSG” are given in chapter

four (section: 4.4.7.1; 4.4.7.2)

5.4.1 ArcCN-Runoff modeling

The ArcCN-Runoff tool, an extension of the ArcGIS software for generating curve

number and runoff (Zhan and Huang 2004), was added to the ArcGIS desktop software

and activated. Then the HSG and land use map were imported, dissolved and a new

layer called “Landsoil” was generated. Finally, the CN value was obtained and

adjusted according to local watershed condition, and the runoff depth was calculated in

the ArcCN-Runoff tool. The daily runoff values for one hydrological year (June 2008-

May 2009) for the study area were computed by multiplying the runoff depth by the

area. The daily runoff data was then merged to seasonal and annual thematic maps

96 |

using ArcGIS. The detailed, stepwise operation of the runoff calculation by the

ArcCN-Runoff tool in ArcGIS can be found in Zhan and Huang (2004).

ArcCN-Runoff tool is freely available for users and allows users to select among

several options to best fit their data needs, such as adjusting the CN values to the basin

slopes and improving the ability of users to analyze time series data.

Figure 5.3 Flow chart showing ArcCN-Runoff modeling (Source: Zhan and Huang 2004).

5.4.2 Advantages and disadvantages in NRCS-CN method

The advantages are:

It is a simple, predictable and stable conceptual method for the estimation of direct

runoff depth.

It relies on only one parameter the runoff curve number, which varies as a function of

four major runoff producing watershed properties; hydrologic soil group, land use and

treatment class, hydrologic surface condition and antecedent moisture condition.

It is the only methodology that features readily grasped and reasonably well

documented inputs.

It is a well-established method, having been widely accepted for use in various

countries.

Subclass

Hydgrp

Intersect

Land use.shp

Landsoil.shp

To determine runoff for each Land use

Index.dbf

CN Runoff

Runoff Vol

Soil.shp

97 |

The disadvantages are:

For lower curve numbers and/or rainfall depths, the method is very sensitive to curve

number and antecedent moisture condition.

The method is best suited for agricultural sites, for which it was originally intended,

and has since been extended to urban sites. The method rates fairly in applications to

range sites, and generally does poorly in application to forest sites. The implication

here is that the method is best suited for storm rainfall-runoff estimates in streams with

negligible baseflow, i.e., those for which the ratio of direct runoff to total runoff is

close to one.

The method has no explicit provision for spatial scale effects. Without catchment

subdivision and associated channel routing, its application to large catchments (greater

than 250 km2) should be viewed with caution.

5.5 Recharge modeling

A simple recharge model was prepared using “Model Builder Tool” in ArcGIS. The

spatial model records the processes, such as buffering or overlaying themes required to

convert input data into an output map. Large models can be built by connecting several

processes together. In Model Builder, a spatial model is represented as a diagram that

looks like a flow chart (see the illustration below in Figure 5.4). It has nodes

representing input data, spatial functions that do the processing and output data. It has

arrows connecting the nodes that show the sequence of processing in the model. The

model is much more than a static diagram; it stores all the properties and instructions

necessary to run the model in ArcGIS. The same model can be applied to different

geographic areas by changing the input data. Model can be easily modified the model

to explore "what if" scenarios and obtain different solutions. Model Builder has the

tools needed to create, modify and run a model. Model Builder uses ArcGIS to manage

the input and output data. In most cases, the input data is added as a theme in ArcGIS.

From ArcGIS, the Model Builder can be started to load an existing model or create a

new model. When the model is run, the output data is created and displayed in your

ArcGIS project. Data from precipitation (MRO and TRMM), SEBAL and ArcCN-

Runoff was used as input to the model.

98 |

Recharge was computed using simple water balance method in which ET and runoff

were subtracted from precipitation to generate recharge. Figure 5.4 gives details of the

present recharge model.

𝐑 = 𝐏 − (𝐄𝐓 + 𝐐) −−−−−−− (𝟓.𝟓𝟎)

Where; R is rainfall recharge, P is Precipitation ET is ET and Q is runoff.

ArcGIS based Recharge Model primarily involves three input datasets generated from

TRMM/MRO, SEBAL and ArcCN-Runoff data. SEBAL (details given in section 5.1)

generates the ET data component for recharge modeling.

Precipitation data from both TRMM and point data are converted to spatial format

and exported to runoff model and acts as one of the input parameter to runoff. The ET

data in seasonal and annual spatial format is exported to recharge model and acts a

one of the components to estimate recharge.

Figure 5.4 Flow chart for recharge modeling.

Runoff input data generated using ArcCN-Runoff (details given in 5.2) which

involves NRCS curve method based on land use and soil data. Runoff data is

generated on daily basis which is then converted into seasonal and annual spatial

theme using GIS modeling. This seasonal and annual spatial data is then used as an

input in recharge modeling. Rainfall spatial variability data was taken into the

recharge model based on spatial variability of precipitation derived from TRMM or

ET-S1 ET-Total

ET-S2

ET-Total

Compute discharge

Compute Recharge (Water balance method)

Runoff

Generate Runoff

Runoff Total Discharge

Rainfall

Recharge

99 |

point data by MRO. Finally a simple water balance approach was used to compute

seasonal and annual rainfall recharge (in mm) for the watershed.

5.6 Weighed Overlay Analysis

Weighed Overlay Analysis technique has been widely used in deciphering groundwater

potential zones by workers like Dar et al. 2011; Rashid et al. 2012; Gumma and

Pevalic 2013. Weighed overlay analysis was performed in ArcGIS spatial analysis

module, all the surface and sub-surface datasets that govern the groundwater

prospecting, viz., geology, geomorphology, land use/land cover, soil, lineament

density, drainage density, slope and aquifer thickness were converted to raster format

followed by assigning respective theme weight and class rank as shown (Appendix

1.2). In first step the weighed overlay analysis was performed on surface indicators

viz., Geology + Geomorphology + Lineament density + Land use + Soil + Slope +

Drainage density using “Spatial Analyst Module” in ArcGIS. The output map was

named as GWP-S1 with values ranging from 1-4 where value 1 corresponds to poor

GWP-S1 zone, value 2 corresponds to moderate GWP-S1 zone, value 3 corresponds to

good GWP-S1 zone and the value 4 represents very good GWP-S1 zone. In second

step GWP-S1 thematic map was overlaid with aquifer thickness map named as GWP-

S2 using “Spatial Analyst Module” of ArcGIS. Value 1 corresponds to poor GWP-S2

zone, value 2 corresponds to moderate GWP-S2 zone, value 3 corresponds to good

GWP-S2 zone and the value 4 represents very good GWP-S2 zone.

The output of both surface indicators (GWP-S1) and subsurface indicators (GWP-S2)

were then assigned equal weight which corresponds to different groundwater potential

zones and classified into four categories from poor (GWP1), moderate (GWP2), good

(GWP3) and very good (GWP4). Finally the groundwater potential map of the study

area was prepared showing the groundwater scenario of the study area. The areal extent

of different groundwater potential zones and details of different parameters that govern

the groundwater potential of the area are discussed in chapter seven (section 7.1).

100 |