Calibration of a distributed irrigation water management model using remotely sensed evapotranspiration rates and groundwater heads

CALIBRATION OF A DISTRIBUTED IRRIGATION WATERMANAGEMENT MODEL USING REMOTELY SENSED

EVAPOTRANSPIRATION RATES AND GROUNDWATER HEADSy

RAJ KUMAR JHORAR1*, A.A.M.F.R. SMIT2, W.G.M. BASTIAANSSEN3 AND C.W.J. ROEST2

1Chaudhary Charan Singh Haryana Agricultural University, Soil and Water Engineering, Hisar, Haryana, India2Alterra Green World Research, Department of Water and Environment, Environmental Sciences Group, Wageningen University and Research Centre,

Wageningen, The Netherlands3Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands

ABSTRACT

Parameters of the distributed irrigation water management model FRAME are determined by an inverse method using

evapotranspiration (ET) rates estimated from the SEBAL remote sensing procedure and in situ measurement of groundwater

heads. The model simulates canal and on-farm water management as well as regional groundwater flow. The calibration is

achieved in two phases. The data on ETwere introduced with the primary intent of improving predictions of ET through better

estimated soil hydraulic parameters. During the first phase, soil hydraulic parameters sensitive to ETwere optimized. As per the

canal running schedule in the study area, the daily values of ET data were synthesized into 16 time periods with 15 periods each

of 24 days and one period of 5 days. Use of cumulative (annual basis) ET data results in better estimates of soil hydraulic

parameters as compared to temporal (24-day period basis) ET data due to possible errors in other input data. During the second

phase of calibration, aquifer drainable porosity and maximum allowable groundwater extraction were optimized against

groundwater heads for five years. The calibration was very successful in about 70% of the study area with a coefficient of

correlation between simulated and observed groundwater levels of more than 80%. Subsequently the model is validated against

groundwater heads for nine years. Copyright # 2009 John Wiley & Sons, Ltd.

key words: parameter estimation; distributed irrigation management models; remote sensing; evapotranspiration; groundwater; India

Received 14 July 2008; Revised 9 June 2009; Accepted 9 June 2009

RESUME

Les parametres du modele FRAME de gestion de l’eau d’irrigation distribuee sont determines par la methode inverse en

utilisant l’evapotranspiration (ET) estimee par la procedure SEBAL de teledetection et la mesure in situ des niveaux des eaux

souterraines. Le modele simule la gestion de l’eau dans le canal et sur l’exploitation, ainsi que le flux des eaux souterraines dans

la region. L’etalonnage est realise en deux phases. La donnee ET a ete introduite avec l’intention premiere d’ameliorer les

previsions de ET grace a une meilleure estimation des parametres hydrauliques du sol. Au cours de la premiere phase, les

parametres hydrauliques des sols sensibles a ET ont ete optimises. Pour le tour d’eau dans le canal sur la zone d’etude, les

valeurs quotidiennes de ETont ete synthetisees en 16 periodes, 15 periodes de 24 jours et une periode de cinq jours. L’utilisation

du cumul annuel de ET conduit a de meilleures estimations des parametres hydrauliques du sol par rapport aux donnees ET sur

periodes de 24 jours en raison d’eventuelles erreurs dans les autres donnees d’entree. Au cours de la deuxieme phase de

l’etalonnage, la porosite de l’aquifere exploitable et l’allocation maximum d’eaux souterraines ont ete optimisees sur cinq ans

en fonction du niveau des eaux souterraines. L’etalonnage a ete un grand succes dans environ 70% de la zone d’etude avec un

coefficient de correlation entre les niveaux simules et observes des eaux souterraines de plus de 80%. Par la suite, le modele est

valide pour le niveau des eaux souterraines sur neuf ans. Copyright # 2009 John Wiley & Sons, Ltd.

mots cles: estimation des parametres; modeles de gestion de l’irrigation distribuee; teledetection; evapotranspiration; eaux souterraines; Inde

IRRIGATION AND DRAINAGE

Irrig. and Drain. 60: 57–69 (2011)

Published online 9 December 2009 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/ird.541

*Correspondence to: Raj Kumar Jhorar, Chaudhary Charan Singh Haryana Agricultural University, Soil and Water Engineering, Hisar, Haryana, India- 125004. E-mail: [email protected] d’un modele de gestion de l’eau d’irrigation utilisant l’evapotranspiration teledetectee et le niveau des eaux souterraines.

Copyright # 2009 John Wiley & Sons, Ltd.

INTRODUCTION

Agro-hydrological models are effective tools to help

planners and managers to diagnose different water manage-

ment policy options (Droogers and Kite, 1999; D’Urso et al.,

1999; Singh et al., 2006). However for practical use, the

values of model parameters related to vegetation, soil and

hydrology are not known a priori at the regional scale that

the models are applied (Boyle et al., 2000; Blasone et al.,

2008). Therefore, reliable estimation of the parameters is

required before these models can be applied to solve natural

resource problems (Gupta et al., 1998; Hanson et al., 1999).

Unfortunately, the parameter identification problem is not

straightforward due to many factors including model

structure, too high correlation between different parameters,

too large observation errors for the system response and too

large errors in the input data. In many cases, parameter

uncertainty can be reduced by reducing the number of

parameters to be estimated (Yeh and Soon, 1981) as well as

by using additional system response data during optimiz-

ation (Franks et al., 1998). Therefore, it is desirable to

include as many system responses as possible in the

calibration process. Moreover, calibration of a model against

an output, of which prediction is utilized for performance or

scenario analysis, is important for reliable model appli-

cation. For instance, estimating parameters using one output

may give quite poor results for a different output (Wallach

et al., 2001; Yan and Han, 1991). The objective of this study

is to calibrate a distributed irrigation water management

model, referred to as FRAME (Boels et al., 1996) using

information on both remotely sensed evapotranspiraton

ETRS rates and in situ measurements of groundwater heads.

The data on ETRS fluxes are introduced with the primary

intent of improving predictions of ETa through better

estimated spatial variation of soil hydraulic parameters

across an irrigation scheme.

STUDY AREA

The proposed approach of using ETRS data determined from

satellite remote sensing to calibrate a distributed irrigation

water management model has been applied to the Sirsa

Irrigation Circle in Haryana, north-west India. The Sirsa

Irrigation Circle is located in the western part of Haryana

state and covers an area of about 4800 km2 (Jhorar, 2002).

The area is characterized by arid climate with an annual

average rainfall of 310mm and average annual reference

evapotranspiration of 1720mm. The soil texture varies from

loamy sand to sandy loam with some sandy soil occurring in

patches. The Sirsa Irrigation Circle is served by an extensive

network of irrigation canals. Introduction of canal water

supply in the Sirsa Irrigation Circle triggered rising

groundwater levels in the north-west and south-east where

groundwater quality was poor. Over-exploitation of ground-

water in the central part, where groundwater quality was

good, caused a decline in the groundwater levels. The water

management-related problems encountered in this area are,

therefore, representative of a typical irrigation command,

i.e. rising water levels in the saline groundwater zone and

declining water levels in the fresh groundwater zone.

DISTRIBUTED IRRIGATION WATERMANAGEMENT MODEL

The distributed irrigation water management model,

referred to as FRAME (Boels et al., 1996), is composed

of two existing model packages, SImulation of Water

management in Arid REgions (SIWARE) for canal and on-

farm water management (Sijtsma et al., 1995) and the

Standard Groundwater Model Package (SGMP) for regional

groundwater flow (Boonstra and de Ridder, 1990). Both

these models are linked on a time step basis. Keeping in view

the rostering policy of water distribution among different

canals in the study area, the entire year was divided into 16

periods with 15 periods of 24 days each and one period of

5 days to have exactly a calendar year. SIWARE computes

water balance components for the top system and provides

net recharge data to SGMP (Figure 1). To facilitate

computation of water and salt components in a spatially

distributed manner, SIWARE requires that the study area be

schematized into a number of sub-areas known as

calculation units (CU). The study area was divided into

46 CUs (Figure 2a). Each CU is assumed to be uniform with

respect to soil parameters, and climatic, hydrological and

water supply conditions. Each CU can have heterogeneity in

crops. It is assumed that soil water between field capacity

(ufc) and wilting point (uwp) is available for crop ET.Water in

excess of field capacity is assumed to drain to downward

layers as deep percolation. In addition to water stored in the

root zone, 50% of the water stored in a predefined depth

located below the root zone (referred to as the capillary

zone) is also considered to be available for plants. Daily

actual evapotranspiration (ETa) is related to potential

evapotranspiration (ETp) as under

ETa ¼ asmETp (1)

Value of the soil moisture availability factor asm [-]

depends on total available soil moisture uTAM (ufc� uwp) and

actual available soil moisture uASM for all the layers in the

root zone and capillary zone and is given by

if uASM � buTAM asm ¼ 1 (2a)

if uASM < buTAM asm ¼ uASM=ðbuTAMÞ (2b)

Copyright # 2009 John Wiley & Sons, Ltd. Irrig. and Drain. 60: 57–69 (2011)

DOI: 10.1002/ird

58 R. K. JHORAR ET AL.

The parameter b depends on crop type (threshold leaf

water potential at which stomata close cc, bar), soil salinity

(osmotic potential co, bar) and ETp:

b ¼ 0:51ETp

ðcc þ co � 0:1Þ (3)

Groundwater abstraction is simulated based on the deficit

in canal water supply and subject to the maximum limit of

installed capacity of tubewells in different CUs. The net

recharge to the aquifer consists of leakage losses from the

irrigation system, on-farm percolation losses and ground-

water abstraction.

SGMP computes regional groundwater flow and in return

provides groundwater levels in the aquifer to SIWARE.

Depending on the desired accuracy and the availability of

geo-hydrological parameters, SGMP requires that the area

be schematized into a nodal network. The nodal network

designed for the study area consisted of 37 internal nodes

and 24 boundary nodes (Figure 2b). The groundwater heads

are computed based on recharge and abstraction rates

occurring at each internal node as computed by SIWARE

and the resultant of the lateral aquifer flows.

METHODOLOGY

Identification of parameters to be adjusted

The integrated regional water management model

FRAME has a large number of parameters. In simple cases,

it may be possible to estimate all the model parameters. In

Figure 1. Schematic view of link between SIWARE and SGMP. The symbol hgw stands for head of groundwater, dgw for depth of groundwater and L for netrecharge/leakage. The schematization of the study area in sub-regions for SIWARE is termed as calculation units (CU) and that for SGMP as nodes

Figure 2. Subdivision of Sirsa Irrigation Circle into (a) Calculation unitsfor SIWARE model and (b) Nodal areas for SGMP model


DOI: 10.1002/ird

CALIBRATION OF A DISTRIBUTED IRRIGATION WATER MANAGEMENT MODEL 59

general, however, this is not possible due to the large

computation times and non-availability of sufficient

accurate observations. One approach is to carry out a

sensitivity analysis of the model and to adjust only the most

sensitive parameters. Another approach is to start with an

estimation of a few parameters and then add further

parameters if they improve the model predictive quality

(Wallach et al., 2001). The present study makes use of both

approaches. First a sensitivity analysis was carried out to

identify the most sensitive parameters, thereafter the

parameters which indeed helped to improve the model

predictive quality were added. The other parameters were

fixed to the values determined during the previous

calibration study (Boels et al., 1996).

Parameter optimization criteria

A model should be validated for the types of applications

for which it is intended. Thus, performance criteria as well

as calibration and validation schemes should be tailored to

the objective of study (Refsgaard, 1997). The ultimate

objective of this study is to use the FRAME model to test

different water management scenarios at regional scale.

Actual evapotranspiration rate ETa and groundwater levels

(head) hgw are of prime importance for this study. Therefore,

the model parameters were calibrated to obtain a good fit

between model-simulated evapotranspiration ETSIWARE and

ETRS and observed groundwater levels hgwo and simulated

groundwater levels hgw.

Let ETSIWARE(b, ti) and hgw (b, tj) be the calculatedvalues of ETa and hgw, respectively, at time ti and tjcorresponding to a trial vector of selected parametervalues {b}, where {b} is the n-dimensional vectorcontaining the parameters that are optimized simul-taneously. The inverse problem is then to find anoptimum combination of parameters {b0} that minimizesthe following objective functions:

FðbÞ ¼X

wi ETRSðtiÞ � ETSIWAREðb; tiÞf g½ �2 (4)

FðbÞ ¼X

vj hgwoðtjÞ � hgwðb; tjÞ� �� 2

(5)

whereF is the objective function,wi and vi are the weighting

factors accounting for data points. Equation (4) is used to

calibrate model parameters sensitive to ETa and and

Equation (5) is used to calibrate model parameters sensitive

to hgw. The summation in Equation (4) is over time only as

parameters of SIWARE were estimated independently for

individual calculation units, while the summation in

Equation (5) is over both time and space as the parameters

of SGMP were estimated simultaneously for all the nodes.

There are many possible ways to choose the weighting

factors and their choice can affect the optimized parameter

set (Weiss and Smith, 1998). In the case of random

observation errors only, according to maximum likelihood

the weighting factor should be equal to the inverse of the

standard deviation of the observation error. Jhorar et al.

(2002) noted that assignment of weight, inversely pro-

portional to the magnitude of the observation, implies that

every observation has equal contribution to the objective

function, irrespective of its magnitude. This is particularly

important for erroneous data. Therefore the weighting

factors for different observations were assigned inversely

proportional to the magnitude of different observations.

Parameter estimation procedure

The calibration was achieved in two phases. During the

first, ETRS data were used to calibrate the parameters of

FRAME towhich ETa rates are sensitive. As ETRS rates from

remote sensing analysis were obtained for the year 1990

only, this year was selected for the first phase of calibration.

During the second phase, hgw data were used to calibrate

drainable porosity of the aquifer. The years 1977–81 were

selected for the second phase of calibration. Accordingly,

during the first phase Equation (4) and during the second

phase Equation (5) was used. Initial values of parameters

were taken from the previous study (Boels et al., 1996) and

during parameter optimization a reasonable parameter range

around these values was specified. The inverse problem was

solved using the parameters estimation program PEST

(Doherty et al., 1995).

PEST (Parameter ESTimation) is a non-linear parameter

estimation program which can easily be linked via templates

to anymodel (Doherty et al., 1995). PEST runs the particular

model, compares the model results with target values (e.g.

observations), adjusts selected parameters using an optim-

ization algorithm, and runs the model again (Figure 3). The

Figure 3. Overview of the parameter estimation procedure employed usingPEST and the simulation models SIWARE/FRAME


DOI: 10.1002/ird


optimization algorithm used by PEST is derived from

Gauss–Marquardt–Levenberg, which starts with searching

mainly along the steepest gradient of the objective function

surface and gradually switches to a direction based on a

second-order approximation of the objective function

surface (Marquardt, 1963; Press et al., 1989; Doherty

et al., 1995). Experience in soil water flow modelling shows

that the Gauss–Marquardt–Levenberg method is very

efficient in optimization, in the sense of a minimum amount

of model calls (Cooley, 1985; Clausnitzer and Hopmans,

1995; Finsterle and Pruess, 1995; Olsthoorn, 1998). The

PEST program partly circumvents the possibility of ending

up at local minima by evaluating the objective function with

a number of Marquardt values (Doherty et al., 1995). After

completing the parameter estimation process, PEST

calculates 95% confidence limits for the adjustable

parameters. Parameter confidence limits are calculated on

the basis of same linearity assumptions which are used to

derive the equations for parameter improvement imple-

mentation in each PEST optimization iteration (see Doherty

et al., 1995). The parameter’s specified upper and lower

bounds are not taken into account while calculating the

confidence intervals. Thus the upper and lower confidence

limits can lie well outside a parameter’s allowed domain.

Because the study area modelled is divided into 46 CUs,

which are explicitly parameterized, the number of parameter

values characterizing the study area would be very high. It is

neither possible nor meaningful to optimize all these

parameter values simultaneously (Eckhardt and Arnold,

2001). Therefore, during the first phase of calibration,

parameters were estimated independently for each of the 46

CUs. During the first phase, the SGMPmodel was prevented

from simulating groundwater levels. Observed groundwater

levels were specified to avoid any effect of simulated

groundwater depth on ETa. In the FRAME model a

maximum of eight different soil types may be specified.

Therefore, before the second phase of calibration, all the

CUs were categorized into different subgroups depending on

the optimized/assigned parameter values in phase one. To

each subgroup, a particular soil code was assigned in the

input file containing the optimized parameters. During the

second phase of calibration, the parameters optimized

during the first phase were kept constant and values of

aquifer drainable porosity were optimized for the internal

nodes.

Observations for calibration

As stated earlier, the calibration was carried out using

observations on actual evapotranspiration and groundwater

heads. Remote sensing techniques have been shown to be

promising in assessing regional patterns of actual evapo-

transpiration ETa (Moran and Jackson, 1991). A large

number of remote sensing ETa algorithms have been

developed (Bastiaanssen et al., 1999). In this study, the

SEBAL (Surface Energy Balance Algorithm for Land)

algorithm was used to determine actual evapotranspiration

from remote sensing measurements ETRS. SEBAL (Bas-

tiaanssen et al., 1998, 2005) requires spatially distributed

visible, near-infrared and thermal infrared data. For this

study AVHRR (Advanced Very High Resolution Radio-

meter) images of the NOAA-11 (National Oceanic and

Atmospheric Administration) satellite for 23 cloud-free days

were used. The images have a spatial resolution of

1.1� 1.1 km and can be freely downloaded. The basic

procedure as employed in SEBAL is to solve the energy

balance during satellite overpass to compute instantaneous

evaporative fraction for cloud-free days. The evaporative

fraction is defined as the latent heat divided by the net

available energy. In the older version of SEBAL, the

instantaneous evaporative fraction is considered similar to

its 24-h counterpart (Kustas et al., 1994). For cloudy days,

known values of evaporative fraction together with routine

weather data were used to compute ETa. This results in a

1.1 km grid of ETRS obtained under all weather conditions

(Farah et al., 2004).

The groundwater levels in the study area were monitored

through a network of observation wells twice a year (June

and October). The period of measurements coincided with

the general trend of deepest (June – before rainy season) and

shallowest (October – end of monsoon) water levels.

RESULTS AND DISCUSSION

Prior analysis of calibration strategy

A prior analysis of the optimization process was carried

out to decide the parameters that can be optimized with the

proposed methodology. During this analysis the ETa data

used were generated with forward FRAME simulations and

corrupted with random error. The ETa data with added error

were then used in the objective function (Equation (4)) to

optimize different combinations of the sensitive parameters

(ufc: field capacity, uwp: wilting point and Zcz: thickness of

capillary zone) (Table I).

First only the most sensitive parameter, i.e. ufc, was

optimized. Thereafter, a combination of different parameters

(ufc and uwp, ufc and Zcz, ufc, uwp and Zcz) was optimized. The

95% confidence interval (CI) was used as a means of

comparing the certainty with which different parameter

values were estimated by PEST (Doherty et al., 1995).

Inclusion of both ufc and uwp in the optimization process

resulted in unreliable estimates of parameter values as

indicated by unacceptably high CI as compared to the

parameter estimate (Table I). Moreover, there was no

significant impact on the minimization of the objective


DOI: 10.1002/ird


function. This was due to the high correlation (0.997)

between ufc and uwp. Inclusion of ufc and Zcz in the

optimization process, on the other hand, improved the

objective function, with the optimized values being

identified with acceptable CI values. Also the correlation

(0.591) between ufc and Zcz was not too high. The general

notion (Wallach et al., 2001) that adjusting additional

parameters always reduces the adjustment error (objective

function) is not supported by the results of this study. When

uwp was added for adjustment along with ufc and Zcz, the

minimum value of the objective function was more than that

obtained when only ufc and Zcz were optimized. This

indicates that inclusion of highly correlated parameters in

the optimization process could further prevent global

minima being found. A high correlation between ufc and

uwp requires that one of these parameters should be assigned

a fixed known value. Therefore, during parameter optim-

ization, uwp was independently assigned a fixed value

depending on the available soil textural information for the

study area. Based on the prior analysis of the optimization

process, during the first phase of calibration only ufc and Zczwere optimized using ETRS rates.

Calibration of selected model parameters usingETRS rates

The ETa data as obtained from remote sensing ETRS were

summarized into 16 model time steps to have a one-to-one

correspondence with the FRAME-simulated ETa, i.e.

ETSIWARE. Initial optimization runs indicated that ETRS

for time steps 6, 7 and 8 (days of the year 102–173) was

much higher than the simulated value i.e. ETSIWARE. It may

be noted that time step 6 coincides with the specified date of

harvest of most winter crops and the sowing of summer

crops. A further analysis of the remotely sensed biomass (not

presented here) during different time steps also indicated a

sudden drop in biomass production for the period 4–6 (days

of the year 73–125), showing that most of the fields became

fallow due to harvest of winter crops. Since during time steps

5–8 there was not much rainfall, higher evaporation from

these fallow lands is unlikely to occur. This suggests that

ETRS for time steps 6–8 is an overestimate of ETa. Contrary

to time steps 6–8, ETSIWARE during time step 9 was higher

than ETRS. During time step 9, a considerable amount of

rainfall occurred during 1990. Moreover, because of cloud

cover there was no satellite image available during this

period. ETRS under this condition was estimated based on

images available during the beginning of time step 8 and end

of time step 11. Therefore, it is likely that during time step 9,

ETRS could not capture the effect of rainfall on ETa. Keeping

in mind the above known discrepancies between ETa and

ETRS, during the parameter optimization runs the ETRS data

for time steps 6–9 were not used. First, the parameter

optimization process was carried out using temporal ETRS

rates for 12 time steps. Thereafter, cumulative ETRS (please

note that hereafter ‘ET’ in boldface represents cumulative

value of evapotranspiration and ‘ET’ in normal face

represents temporal value of evapotranspiration) for the

12 time steps were used. The reason for this choice is

explained later. The optimized values of (ufc -uwp) are

presented in Table II.

Parameter estimation using temporal ETRS data

As can be observed from Table II (columns 2 and 3), for

some of the CUs the optimized parameter values are at the

upper bound of the specified range. This indicates that there

is some temporal discrepancy between ETRS and ETSIWARE

under the specified conditions of crop and water supply.

There could be many reasons for this discrepancy. In the

FRAME model, similar crop growth parameters are

specified for all the CUs implying plant growth is similar

in all CUs, while in reality this is different. However, care is

taken for the actual area under different crops that may be

different in different CUs. During simulations, the specified

irrigation dates for a particular crop were the same for all the

Table I. Results of prior optimization runs to decide the number of parameters to be adjusted

Number run Optimized parameter(s) Optimized valuea � 95% CI Correlation coefficient Objective functionb

1 ufc 0.23� 0.03 — 44762 ufc 0.25� 0.41 {ufc, uwp}¼ 0.997 4474

uwp 0.13� 0.383 ufc 0.24� 0.04 {ufc, Zcz}¼ 0.591 4007

Zcz 0.45� 0.184 ufc 0.19� 0.59 {ufc, uwp}¼ 0.998 4470

uwp 0.07� 0.52 {ufc, ZCZ}¼ 0.684Zcz 0.52� 0.27 {uwp, ZCZ}¼ 0.654

aReference value ufc¼ 0.26 (cm3 cm�3), uwp¼ 0.11 (cm3 cm�3) and ZCZ¼ 0.50m; CI¼ confidence interval.bStarting value of objective function¼ 5837.


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CUs and it was assumed that the total area under that

particular crop is irrigated on the specified date. In reality,

the irrigation to a particular crop is completed over a period

of time depending on the farmer’s rotation for canal water

supply. Also in the FRAME simulation study, the potential

evapotranspiration ETp values specified were the same for

all the CUs while in reality microclimatic conditions could

cause spatial differences in ETp. Another major source for

the temporal discrepancy between ETRS and ETSIWARE

could be that during the simulation study, canal water

Table II. Optimized values of total available soil moisture (ufc� uwp) and thickness of capillary zone (Zcz) along with available soil texturalinformation for different calculation units (CUs). Simulated annual groundwater use and annual rainfall (P) are also included to explain theirrole in the fitted parameter values. For soil texture symbols see Table III

CU Based on temp. ETRS Based on cum. ETRS Soil texture P (mm) Simulated groundwateruse (mm)

ufc� uwp (–) Zcz (m) ufc� uwp (–) Zcz (m)

1 0.360 0.90 0.223 0.20 LS/SiL 328 42 0.164 0.31 0.140 0.20 LS/ SiL 403 403 0.360 1.20 0.157 0.20 LS 403 354 0.173 0.20 0.148 0.20 LS 403 755 0.360 0.68 0.150 0.20 LS 328 156 0.360 0.78 0.227 0.30 SiL 328 107 0.360 1.00 0.209 0.30 S/LS/SL/SiL 328 138 0.360 1.20 0.174 0.20 LS 403 309 0.360 1.20 0.156 0.20 LS 403 2510 0.154 0.18 0.137 0.20 LS 455 16211 0.209 0.29 0.204 0.30 LS, SiL 455 2112 0.121 0.10 0.112 0.20 S/ LS/ SL 570 513 0.108 0.12 0.097 0.10 S/SL 570 2514 0.137 0.10 0.133 0.20 S/LS/ SL 570 4115 0.137 0.10 0.122 0.20 LS/ SiL 570 2316 0.133 0.54 0.125 0.30 S/ LS/ SL/ SiL 455 6617 0.140 0.10 0.121 0.20 S/LS /SL 570 1818 0.070 1.20 0.087 0.10 S/LS 570 4719 0.115 0.12 0.107 0.20 S/ SL/ LS 570 7420 0.146 0.19 0.132 0.30 LS/SiL 455 11621 0.261 1.20 0.203 0.30 LS/ SiL 216 23122 0.114 0.10 0.111 0.30 S/ LS/ SiL 547 32223 0.320 0.18 0.108 0.20 S/ SL/ SiL 570 16424 0.199 0.68 0.320 0.30 SiL 89 11825 0.183 0.99 0.320 0.30 LS/ SiL/ SiCL 268 18026 0.115 1.20 0.131 0.30 LS/SiL 547 56227 0.215 0.29 0.207 0.30 LS/ SiL 216 22528 0.320 0.93 0.210 0.30 SL/SiL 216 12129 0.129 1.20 0.153 0.30 SiL/ SiCL 547 20830 0.320 0.50 0.320 0.20 S/LS/SL/SiCL 268 14031 0.320 0.16 0.320 0.20 S/LS/SL/SiCL 89 8832 0.164 0.56 0.111 0.10 S/ SL 268 12433 0.400 0.43 0.400 0.10 S/ LS/ SL/ SiL 268 6734 0.320 0.62 0.225 0.30 SiCL 547 11335 0.320 0.89 0.224 0.30 SiL/ SiCL 216 6436 0.320 0.54 0.320 0.30 LS/ SiCL 291 6837 0.360 0.93 0.360 0.46 LS 291 4238 0.156 0.10 0.156 0.20 LS/ SL 547 3939 0.147 0.10 0.150 0.20 LS/ SL 547 4540 0.129 0.10 0.121 0.10 S/LS/ SL 547 5941 0.113 0.15 0.104 0.10 S/LS/ SL 547 8942 0.360 0.36 0.360 0.20 — 291 3043 0.360 0.40 0.360 0.20 — 291 5044 0.360 0.71 0.360 0.20 — 291 5145 0.360 0.51 0.360 0.20 — 291 2846 0.360 0.65 0.360 0.20 — 291 56

Note: The numbers in boldface indicate the values which were fitted to the upper bound as specified during optimization.


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allocation to different CUs was based on strict official rules

(based on cultivable command area). A study from Pakistan

(Wahaj, 2001), where a similar irrigation system and canal

water allocation rules are followed, showed that the actual

allocation may deviate from designed rules. All the above

factors could cause temporal variations in ETa, which may

not be captured in simulations. Therefore, as a next step,

accumulated annual ETRS (excluding time steps 6–9, as

explained earlier) was used to optimize the different

parameters.

Parameter estimation using cumulative ETRS data

The results of the optimized values of (ufc� uwp) using

cumulative ETRS data are again presented in Table II. In the

northern part of the study area (CUs 1–20), the fitted values

of (ufc� uwp) follow the soil textural information and are in

good agreement with the reported values for different

textures (Table III). For example, CUs 1, 6 and 7 have heavy-

textured soils (Table I) as compared to CUs 2–5 and 8–10.

The same is reflected in the fitted values of (ufc� uwp). On

the other hand, for some CUs (see for example CUs 26 and

29, column 4: Table II), the fitted values of (ufc� uwp) are

lower than expected values (Table III) as per soil textural

information (column 6: Table II). In the year 1990, CUs 22,

24, 25, 26, 29 and 30 had more than 40% of their area under

rice during the summer season. For the rice crop, fields are

kept flooded and ETa does not depend on soil hydraulic

parameters, i.e. (ufc� uwp), in this study. Therefore, in

principle, for areas where rice is a major crop, ETRS cannot

be used inversely to identify soil hydraulic parameters.

Under such situations,ETRS for the non-rice-growing period

may be used. However, as pointed out earlier, this option was

not implemented in this study considering the temporal

discrepancy between ETRS and ETSIWARE. Moreover, during

the winter season, one may expect less moisture stress and as

observed in another study (Jhorar et al., 2002), the moisture

stress period is more appropriate to identify soil hydraulic

parameters using ETa rates. Therefore, the CUs having rice

as major crops were assigned parameter values optimized for

other CUs with similar soil texture.

Contrary to the above situation, the fitted values of

(ufc� uwp) for some of the CUs are still at the upper bound.

The problem of parameters being fitted to the upper bound is

now concentrated in the CUs in the south-western and south-

eastern part of the study area (see Figure 2(a) and Table II). In

order to further examine this discrepancy in those particular

regions, cumulative values ofETSIWARE andETRS (excluding

time steps 6–9) for all the CUs were compared. Figure 4(a)

presents the 1: 1 comparison of ETSIWARE and ETRS.

The ETSIWARE is based on the fitted values of parameters

reported in columns 4 and 5 of Table II. This comparison

between ETSIWARE and ETRS should neither be taken as a

proof of good or poor calibration nor should it be used to

draw conclusions that ETRS was a good or poor estimate of

ETa. This is because both ETRS and ETSIWARE were used in

the objective function (Equation (4)) and close match

between them only shows the capability of PEST to force

model parameters to have as good a match as possible.

Therefore, based on Figure 4(a), no conclusions should be

drawn on the accuracy of either ETRS estimates or ETSIWARE

simulations.

In general ETSIWARE was within 10% of the ETRS.

However, serious underpredictions were observed for some

of the CUs. The CUs for which a notable deviation was

observed are among those for which the optimized values of

(ufc� uwp) were fitted at the upper bound (Table II, column

4). A possible reason could be a shortage in the specified

water supply conditions for these CUs. Neglecting any likely

deviations in the actual allocation of canal water among

different CUs from that allocated according to the designed

rules in the model, groundwater use and specified rainfall

Table III. Reported values of plant available water capacity (ufc� uwp) for different soil textural groups encountered in the Sirsa IrrigationCircle

Soil texture Bulk density ufc� uwpa (–)

(g cm�3) USDA (1955) b Agarwal andKhanna (1983) c

Bastiaanssenet al. (1996)

Sand (S) 1.6 0.08 0.12 0.04Loamy sand (LS) 1.6 — 0.13 0.18Sandy loam (SL) 1.5 0.12 0.14 0.15Silt loam (SiL) 1.4 0.17 0.25 —Silty clay loam (SiCL) 1.3 — 0.23 0.019

aReported values by USDA and Agarwal and Khanna are on mass basis.bQuoted by Miller and Donahue (1990).cAgarwal and Khanna (1983) reported an empirical relationship for available water capacity as a function of sand, silt and clay percentage. The sand, silt andclay percentage of typical soil profiles (aggregated for 1 m depth) as reported by Ahuja et al. (2001) was used to compute (ufc� uwp).


DOI: 10.1002/ird


could be the major source of discrepancy in the supply

conditions. This is particularly true for areas where

considerable groundwater use takes place, as the amount

of groundwater use is decided by the farmers and no actual

measurements were available. Therefore, these CUs were

also assigned parameter values optimized for other CUs with

similar soil texture. In order to further investigate the

possibility of uncertainty in groundwater use, the FRAME

model was used to simulate groundwater depth for the

period 1977–90 without previous calibration against

groundwater heads. The CUs 24 and 31 (Figure 2a), which

showed maximum deviation in ETRS and ETSIWARE

(Figure 4a), are underlain by groundwater nodes 22 and

27 (see Figure 2b). The simulated groundwater depth along

with observed groundwater depth is shown in Figure 5. The

simulated groundwater depth in the nodes underlain with

CUs for which ETSIWARE was underpredicted was consist-

ently shallower than that observed (Figure 5). A possible

reason could be that more groundwater was being used in the

overlying CUs than specified in the simulation study.

Because of the limited number of total soil types that can

be defined in the FRAME model input, all the CUs were

categorized into different subgroups depending on opti-

mized parameter values. The CUs which showed parameter

estimation problems during their individual parameter

optimization processes were assigned to different subgroups

based on soil textural information. ETSIWARE, as simulated

with grouped parameters, andETRS were compared to check

any discrepancy resulting due to categorization of CUs into

different subgroups. In general, the discrepancy between

ETSIWARE as simulated with grouped parameters and ETRS

was less than 10% (see Figure 4b) except for some outlier

CUs as discussed before. The maximum discrepancy

between ETSIWARE and ETRS was observed for the same

CUs where the specified rainfall and groundwater use

amounts are questionable. Therefore, the categorization of

CUs in different subgroups was considered acceptable.

Uncertainty in groundwater extraction

For CUs in the south-western part which indicated

uncertainty in specified groundwater use, the maximum

limit on groundwater use, as specified in the model input,

was adjusted before the second phase of calibration, i.e.

calibration against groundwater levels. Before calibrating

drainable porosity of the aquifer, an attempt was made to

correct the uncertainty in groundwater use. Two factors, i.e.

ETRS and groundwater levels, governed the adjustment of

the specified groundwater extraction limit. The maximum

limit on groundwater extraction was increased if ETSIWARE

was less than ETRS and also if the simulated groundwater

depth was shallower than the observed groundwater depth.

The maximum limit on groundwater extraction was also

increased for CUs where simulated groundwater levels in the

underlying nodes showed a rising trend, while observed

groundwater levels showed a declining trend. This resulted

in an increase in the specified maximum limit of

groundwater extraction up to three times for some of the

Figure 4. Comparison of cumulative (excluding time steps 6-9) evapotran-spiration for different calculation units as estimated from remote sensingETRS and simulated ETSIWARE (a) after parameter optimization (b) after

grouped parameters

Figure 5. Simulated (line) and observed (points) groundwater depth dgw forthe period 1977 to 1990. The simulated dgw is the result of model runs priorto calibration against groundwater levels to show the uncertainty in speci-

fied amounts of groundwater use


DOI: 10.1002/ird


CUs. Before adjustment of the maximum limit on

groundwater extraction, the specified limit was based on

fixed norms (e.g. groundwater abstraction from a shallow

tubewell was taken as 0.0145 millionm3 yr�1). These

standard norms may not be applicable for the CUs where

rice was a major crop and good quality groundwater was

available at relatively shallower depth.

Calibration of selected model parameters usinggroundwater heads

The optimized values of drainable porosity are presented

in Table IV. These values lie within the range of values

reported for the study area (Boonstra et al., 1996). The

coefficient of correlation between simulated and observed

groundwater depth and root mean square error (RMSE) were

computed for the calibration and validation period and are

presented in Table IV. The FRAME model reproduced the

observed tendencies in groundwater level behaviour quite

satisfactorily in the calibration period (1977–81). Cali-

bration was very successful in about 70% of the study area,

with a correlation coefficient between simulated and

observed groundwater levels of more than 0.80. In about

28% of the study area the calibration was considered

sufficient, with a correlation coefficient between 0.50 and

0.80. Figure 6 shows the comparison between simulated and

Table IV. Optimized values of drainable porosity for different nodes in the Sirsa Irrigation Circle along with the coefficient of correlationbetween simulated and observed groundwater depth and root mean square error (RMSE) for the calibration (1977–81) and validation (1982–90) period

Number node Drainable porosity (–) Coefficient of correlation RMSE (m)

Calibration Validation Calibration Validation

1 0.11 0.97 0.83 1.04 2.302 0.14 0.98 0.95 0.83 1.323 0.11 0.98 0.28 0.86 3.164 0.04 0.99 0.98 0.69 1.455 0.06 0.99 0.99 0.64 2.116 0.15 0.99 0.97 0.39 0.987 0.18 0.97 0.93 0.39 1.368 0.23 0.91 0.98 0.71 0.899 0.21 0.98 0.97 0.67 0.5110 0.09 0.98 0.94 0.56 0.9211 0.06 0.99 0.98 1.41 1.6712 0.05 0.98 0.96 0.94 1.8613 0.07 0.98 0.96 0.41 1.3414 0.12 0.95 0.96 0.97 1.2715 0.25 0.97 0.88 0.73 0.5416 0.15 0.62 0.13 0.78 1.2217 0.13 0.98 0.88 0.48 1.4118 0.07 0.97 0.94 1.00 1.4419 0.06 0.97 0.72 0.86 1.7320 0.17 0.84 0.30 1.20 1.1021 0.25 0.54 0.12 0.82 0.6522 0.06 0.68 0.40 0.61 0.9623 0.04 0.75 �0.12 1.50 0.8424 0.02 0.33 0.07 1.62 1.6725 0.02 0.68 0.61 1.14 1.0626 0.14 0.73 �0.22 0.64 1.6327 0.04 0.90 0.27 0.56 1.0828 0.04 0.93 0.09 0.38 2.0629 0.08 0.44 0.31 0.82 2.3730 0.04 0.74 0.43 1.35 1.6931 0.25 �0.53 0.93 1.63 0.5332 0.25 0.80 0.96 0.80 2.5933 0.25 0.71 0.83 0.57 0.5734 0.25 0.97 0.87 0.40 0.9435 0.18 0.97 0.98 0.29 0.4936 0.06 0.96 0.80 0.58 1.9737 0.05 0.91 0.99 0.74 0.63


DOI: 10.1002/ird


observed groundwater levels for six selected nodes for the

validation period (1982–90). In the northern part of the study

area where the groundwater levels were rising continuously,

the validation results were very successful (see nodes 4 and

9, Figure 6). In the central part of the study area, the

validation results were relatively less successful (see nodes

26 and 27, Figure 6). There are different reasons for the

relatively less successful validation in the central part. As

already mentioned, because of the rice crop, the soil

hydraulic parameters for this region could not be estimated

using ETRS data. Another reason is the uncertainty with

respect to rainfall amounts and groundwater pumping.

Future modelling studies, therefore, should include spatially

distributed rainfall data from the TRMM satellite or other

satellite platforms. Finally, in the south-eastern part of the

study area, where the groundwater levels were also rising

continuously, the validation results were again successful

(see nodes 35 and 37, Figure 6). Overall good agreement was

obtained between the simulated and observed tendencies of

groundwater fluctuations in the study area. It may thus be

concluded that the calibrated FRAMEmodel could be used

to evaluate alternative water management scenarios by

studying their effects on ETa and regional groundwater

levels.

CONCLUDING REMARKS

Parameter estimation by inverse methods always faces the

problem of parameter uncertainty. Therefore, it is difficult to

say whether the identified model parameters are right or

wrong and no proof of their validity is possible at the spatial

scale of model application. However, they can be judged as

appropriate or inappropriate. Such a judgement should take

into account the goals of the study and may benefit

considerably from the qualitative information about the data

set. The optimized values of (ufc� uwp) appear to be

acceptable when compared with reported values for similar

soil textural classes. However, under actual conditions there

could be considerable variations within a soil textural class.

The optimized values of (ufc� uwp) were more reliable when

cumulative evapotranspiration rather than temporal evapo-

transpiration was used in the objective function. This means

that when input data are of questionable quality, the

selection of the temporal scale for observations in the

objective function is of critical consideration. For areas

where rice is a major crop, evapotranspiration rates for only

the non-rice-growing periods should be used to inversely

identify soil hydraulic parameters using evapotranspiration

rates.

Assuming no error in the model structure in representing

reality, other major factors responsible for likely parameter

uncertainty in this study could be: crop parameters used,

spatial variability in crop development, differences in canal

water allocation and groundwater use and unaccounted

spatial variations in rainfall. Spatial variability in crop

development at different crop stages can be assessed from

multispectral satellite data (Menenti et al., 1996). Uncer-

tainty in groundwater use may be checked with the help of

observed groundwater levels and ET rates from remote

sensing, as was done in this study. In case actual canal water

allocation differs considerably from design rules, actual

measurements for different sub-areas must be used, at least

during the calibration phase. The way rainfall from a

particular rain-gauge station was assigned to nearby CUs

could also be a major factor for parameter uncertainty. For

example, CU 23 lies between two rain-gauge stations

(station numbers 2 and 4). Observed annual rainfall for year

1990 at rain-gauge station 2 was 570mm and that at rain-

gauge station 4 was 89mm. Additional optimization runs

indicated that when CU 23 was assigned to station 2, the

fitted value of (ufc� uwp) was 0.108 and when assigned to

station 4, the fitted value of (ufc� uwp) was at the specified

upper bound of 0.32. Considering available soil texture

information for CU 23, none of the above fitted values

appears to be realistic. It is most likely that CU 23 may have

neither received as low rainfall as observed at station 4 nor as

high rainfall as observed at station 2. Considering the spatial

variability in the observed rainfall, a denser network of rain-

gauge stations would be highly desirable for this kind of

study. Moreover, a more appropriate approach would be to

further verify the optimized parameters values using multi-

year data on ETRS.

Figure 6. Simulated (lines) and observed (points) groundwater depth dgwbelow soil surface for the validation period (1982–1990) in selected nodes of

the Sirsa Irrigation Circle


DOI: 10.1002/ird


Use of cumulative ETRS data in the objective function

resulted in only one observation being available for the

parameter estimation process. Fundamental to the adopted

inverse procedure is that soil hydraulic parameters are fitted in

such a way that the ability of the model to reproduce ETRS is

optimized. This resulted in ETSIWARE being very close to

ETRS. In reality, such a good match can only, if at all, be

achievedunder thecondition thatbothdataandmodelareerror

free. The use of only one observation, however, may not

always reproduce hydrologically realistic parameters. More-

over, the number of observations clearly has a positive impact

on parameter identifiability (Jhoraret al., 2002).Despite some

inconsistencies in the temporal evapotranspiration estimates

by the simulation model and remote sensing, using the fitted

values of (ufc� uwp) to predict groundwater behaviour, good

agreement was achieved between predicted and observed

groundwater levels. Moreover, the information on ET helped

to remove the uncertainty in the specified groundwater

abstraction conditions. Therefore, it can be concluded that use

of remotely sensed evapotranspiration rates would be an

important input for the calibration of water management

simulation models.

Management of conjunctive use is hydrologically com-

plex, especially because groundwater extractions are hardly

known about and depend on the farmers’ decisions and

perceptions. Depending on rainfall, groundwater quality and

crop water needs, a farmer will decide whether or not to use

groundwater. Hence, data on irrigation applications and

groundwater extractions are scant. Environmental safe-

guarding of the extensive irrigation systems in South Asia –

and the Indo-Gangetic Plain in particular – is fundamental

for sustainable food production and economies of rural

communities. A good water resources planning tool that

adequately reproduces the state conditions at the regional

scale for a long period, is paramount for making productive

use of water resources in a sustainable fashion. This paper

shows that remote sensing and groundwater observations are

effective data sets for swiftly calibrating distributed

irrigation water management models.

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Documents

Calibration of a distributed irrigation water management model using remotely sensed evapotranspiration rates and groundwater heads