Regional groundwater prediction model using automatic parameter calibration SCE method for a coastal plain of Seto Inland Sea

Water Resour Manage (2007) 21:947–959DOI 10.1007/s11269-006-9066-7

OR IGINAL ART ICLE

Regional groundwater prediction model using automaticparameter calibration SCE method for a coastal plain ofSeto Inland Sea

Bin He · Keiji Takase · Yi Wang

Received: 21 September 2005 / Accepted: 9 June 2006 / Published online: 21 July 2006C© Springer Science + Business Media B.V. 2006

Abstract Operational groundwater prediction models vary in complexity, but most of themhave parameters for which values must be estimated. In the present study, the proposedregional groundwater prediction model was based on a nonlinear water balance model, whichis very easy to be used once its parameters were determined. The traditional procedure of themodel calibration was done manually using a trial and error process of parameter adjustments.In this case, the goodness-of-fit of the calibrated model is based on a visual judgment bycomparing the simulated and the observed data. It requires considerable training or experienceand is also typically laborious and time consuming. Thus, this paper proposed an approach,which considered the possibilities of using a nonlinear optimization technique – the ShuffledComplex Evolution (SCE) method to calibrate the groundwater model. The applicabilityof this technique was demonstrated with a case study for a coastal plain in Japan. Theperformance of the groundwater model with SCE method was evaluated by comparing themeasured and predicted data.

Keywords Regional groundwater . SCE . Parameter calibration . Water balance model

1. Introduction

Groundwater is an important water supply for industrial, agricultural and residential use inthe coastal plain of the Seto Inland Sea, Japan. The increasing concerns over agriculturalwater use, surface water reliability and groundwater storage changes in the coastal plainhave increased the demand for a sustainable groundwater management (Takase, 2000). Pre-vious studies in the coastal plain have shown that the groundwater level fluctuation andlong term trends depend on the groundwater recharge, which is a function of precipitation,

B. He · Y. WangUnited Graduate School of Agricultural Sciences, Ehime University, Matsuyama 790-8566, Japane-mail: [email protected] or: [email protected]

K. TakaseFaculty of Agriculture, Ehime University, Matsuyama 790-8566, Japan

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948 Water Resour Manage (2007) 21:947–959

evapotranspiration, and pumped water (Madan et al., 1999). Predicting seasonal or annualgroundwater fluctuation by groundwater models is an issue of great practical relevance inthe coastal plain. For groundwater simulation, the numerical modeling has been broadly ap-plied in many researches. Whereas, the quantitative information on hydraulic properties andspatial characteristics, which are required for numerical groundwater modeling, are oftenpoorly known for many measurement stations. In that case, the conceptual model underlyinga water balance computation in basin scale is preferred (Nels et al., 2004). Furthermore, moreattentions have been given to evaluate the use and productivity of water at the basin-scale bytreating each basin as a whole unit of study (Molden, 1997). Some general conceptual andanalytic frameworks have been successfully put forth for the physically dynamic water bal-ance to estimate a basin’s fluxes (Eagleson, 1978). In this study, a conceptual water balancemodel was also employed for estimating the regional groundwater, which changes graduallyin topographically flat plain.

Moreover, parameter calibration is laborious and time-consuming for groundwater model-ing and the calibration quality can influence all of the analysis and interpretations that follow(Gupta et al., 2003). The traditional and widespread manual calibration approach, whichuses the trial and error process, requires considerable training and experience (Johnston andPilgrim, 1976). In the calibration process, the tedious issues, such as deciding which param-eters to vary and differentiating the low-quality data, will be faced and challenged in modelcalibration process (Patrice et al., 1996). Thus, it is necessary to use a parameter optimizationmethod for the groundwater model calibration. In recent decades, the nonlinear parameteroptimization method, which is a mathematical algorithm to estimate parameters for nonlinearmodels, has been successfully used in hydrological models’ calibration (Duan et al., 1992,1993, 1994; Nittaya, 2001).

In this article, the automatic optimization Shuffled Complex Evolution (SCE) method,which is a new heuristic global optimization scheme, has been integrated in the conceptualgroundwater model. It combined the strength of the downhill simplex procedure of Nelder andMead (Nelder and Mead, 1965) with the concepts of controlled random search (Price, 1987),competitive evolution (Holland, 1975) and complex shuffling. This method has become themost popular parameter optimization method among hydrologists (Newsha, 2004; Wang,1991; Wheeter et al., 1993). Whereas, in all the previous studies, the literatures about theconceptual water balance model for estimating regional groundwater by using the SCEparameter optimization technique is scarce. The abovementioned reasons have all contributedto the motivation for calibrating the parameters of the conceptual regional groundwater modelby using the SCE automatic parameter optimization algorithm in this study.

2. Site description

The study site chosen for this study is located in the Dogo plain in the Shikoku Island, Japan(Figure 1). It is surrounded by mountains in the south, north, east, and by the Seto Inland Seain the west. It is an important natural and economic resource for the Shikoku Island due toits great scenic beauty, excellent water quality, and recreational opportunities. In the Dogoplain, the Shigenobu River is the main river and the groundwater is composed by one largegroundwater flow along the Shigenobu River and another groundwater flow along the IshiteRiver. As for the groundwater flow along the Shigenobu River, it gathers the groundwaterin the background watershed of the Shingenobu River. The joint groundwater flow, whichfinally flows into the Seto Inland Sea, comes from two sources. One is the groundwaterfrom the lyo city’s background watershed to the Seto Inland Sea on the left-bank side of the

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Water Resour Manage (2007) 21:947–959 949

Fig. 1 Map of the study site showing the location of the basin and gauging stations in it

Shigenobu river’s downstream, and another is the groundwater from the Ishite River on theright-bank side of the Shigenobu River’s downstream. On the other hand, the groundwateralong the Ishite River partly flows into the Seto Inland Sea on the left bank side and partlyjoins the groundwater with the groundwater along the Shigenobu River on the right bank side.In the Dogo Plain, the precipitation is the main source of groundwater recharge. Averageannual precipitation of the past 105 years from 1900 to 2004 is 1,350 mm, which is abouttwo third of the average annual precipitation in Japan. Average annual precipitation of thepast 30 years from year 1974 to year 2003 is 1,305 mm, which shows a decreasing tendencyby comparing with the average annual precipitation from year 1900 to 2003. The annualpotential evapotranspiration calculated by Penman equation from the data of Matsuyamameteorological station is about 1,150 mm. It is only 200 mm fewer than the above-mentionedannual precipitation (1,350 mm) and it is in a gradual increasing tendency to date. It showsthe serious water shortage condition in the Dogo plain. The groundwater will continue to playan important role in the future water supply because the surface water resources are limited,especially in dry seasons. Based on the measured hydrogeologic and meteorological data inthe coastal Dogo plain, the conceptual groundwater model will be constructed to predict thefluctuation of the regional average groundwater level.

3. Data collection

Various types of data are needed for developing a regional groundwater model. Table 1 showsthe list of the dataset, which is required for the conceptual groundwater model of the Dogoplain in this study. The whole plain has been divided into four blocks, which includes theShigenobu River upstream block (Block 1), the Shigenobu River midstream block (Block 2),the Shigenobu River downstream block (Block 4), and the Ishite River block (Block 3),

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Table 1 Name, type and spatial attribute of the dataset which are used in this study

Data name Data type Spatial attribute

Meteorological data Gauging station, monitoring site PointTopographic data Elevation, slope, hillshade, etc. Grids

Elevation contour, catchment boundary LineHydrological data Stream, river, lake, etc. Line

Flow direction, catchment area GridsRainfall, runoff, evapotranspiration Grids

Geological data Urban area, solid geology PolygonSlope line, etc. Raster (grid)

Land use data Land use boundary Vector (shape file)Soil number Attribute table

Agriculture data Agriculture boundary LineLand cover Grids

Social-economic data Statistical information GirdsBase map View figures, etc. Image

respectively (Figure 2). For each block, the land use, industrial use water, agricultural usewater and meteorological information will be input into the regional groundwater model andgroundwater level of each block could be simulated as the output of the regional groundwatermodel which will be discussed in the following sections. Subdividing the whole plain into fourblocks is based on the geological information, groundwater flow direction, river or streamdistribution, and irrigation area distribution of each block. For each block, the topographicalelevation changes gradually and the average regional elevation can be calculated from thedigital elevation mesh map.

4. Regional groundwater model

The elements expressing the water input and output in each block are discussed as followsand the main components in the model are shown in Figure 3.

4.1. Input elements

(1) Rainfall. Rainfall is the main input element for the paddy field and other fields in surfaceregions.

(2) Discharge from the background watershed and other blocks. The river dischargefrom each block’s background watershed flows into that block and some of it would beused as irrigation water for the paddy field. Thus, this part of river discharge would be aninput element of the paddy field sub-model. The intake water for irrigation from riverswas supposed to be proportional to the discharge as shown in Equation (1).

QIRR = CIRR · Q (1)

where, QIRR is the intake water for irrigation; CIRR is the coefficient of intake waterfrom rivers; Q is river discharge.

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Fig. 2 Schematic figure of the block distribution in the Dogo plain. (a) Schematic figure of the block distri-bution in the Dogo Plain. (b) Detailed block distribution for the Dogo plain (Block 1: the Shigenobu Riverupstream block; Block 2: the Shigenobu River midstream block; Block 3: the Ishite River block; Block 4: theShigenobu River downstream block)

Furthermore, it was also supposed that the river discharge supplies water to subsurfaceregion as influent water as shown in Equation (2).

QINT = CINT · (Q − QIRR) (2)

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RainRain

Epapotranspiration

Dogo Irrigation Water

BP BO

CUO

CLO

S2

CL2

Groundwater Region

PercolationB2

CU3

CL3

Soilevaporation

HU3

wolft

uO reta

wd

nu

orG

)kc

o lb t

x en

oT(

HL2

wolft

uO re

viR

)kc

olb t

xen

oT(

Pumping WaterFor Industrial Use(To Sea)

Subsurface Region

InfiltrationSoilevaporation

Paddy Field Other Fields

InfiltrationSoilevaporation

HLO

HUOCUP

CLP

HLP

HUP

CIRR(Intake from river)

Inflow from mountainous area

Pumping Waterfor Agricultral Use

Surface and Subsurface Discharge (To next block)w

olftu

O revi

R )

kcol

b txe

n o

T(

Surface Discharge

S3

CINT: Influent waterfrom river

Sp So

Fig. 3 Schematic figure of groundwater model in each block of Dogo plain

where, QINT is the influent water from river discharge; CINT is the coefficient of theinfluent water from rivers.

(3) Dogo irrigation water. Diverted water amount for the Dogo plain’s irrigation throughthe reservoir are measured and reported by the management office of the reservoir. Thus,the daily data of Dogo irrigation water is available and can be directly input into thewater balance model.

4.2. Output elements

(1) Potential Evaporation (PE). The epvapotranspiration is a part of output element for thepaddy field and other fields and it will revert to atmosphere. If there was no sufficient waterfor evapotranspiration in surface region (paddy field and other fields), it was supposedthat the evapotranspiration would occur in subsurface or groundwater regions. In thisstudy, the Penman equation was used to calculate the potential evaporation, which isshown in the following equation.

E p = (� · Rn + γ · Ea)/(� + γ ) (3)

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Table 2 The list of symbols

Symbols Meaning of symbols

E p The Potential Evapotranspiration (mm/d)S The daily sunshine time (mm/d)Rn The total solar radiation (mm/d)α Coefficient (0.05)n/N The daily sunshine rationσ The Stefen coefficientes The saturated moisture pressure (mm Hg)ea The actual moisture pressure (mm Hg)u The wind speed (m s−1)Ta The value of average temperature (k)γ The dry moisture coefficient (0.49 mm Hg)� The curve angle of saturated moisture pressure curve (mm Hg/ ◦C)

where

Rn = (1 − α) · (S − σ ) · T 4a · (0.56 − 0.09

√ea) · (0.1 + 0.9 · n/N ) (4)

Ea = 0.35 · (1 + 0.537u) · (es − ea) (5)

Other symbols are presented in Table 2. To calculate the PE, the data of temperature,wind velocity, humility, daily sunshine time, etc., can be collected from the Japan WeatherAssociation (JWA).

(2) Pumped water for industrial and domestic use. The pumped water from groundwaterregion for industrial and domestic use will directly flow into the Seto Inland Sea.

(3) Pumped water for agricultural use from groundwater region. The pumped waterfor agricultural use from groundwater region is an input element for paddy field andcontributes again to the inflow to rivers and infiltration.

(4) River outflow. The input element of paddy field and other fields has two output ways.One is the infiltration to the subsurface region and another one is to flow as surfacedischarge and finally convert to a part of river discharge. The inflow to subsurface regionis also output as subsurface discharge to rivers and as percolation into groundwaterregions.

(5) Groundwater outflow. The percolation from the subsurface region to groundwater re-gion will be the input element for groundwater region. The output element of ground-water region will flow into the groundwater region of next block. In addition, some ofthe groundwater in the Ishite River block and all of the groundwater in the Down-streamblock will flow into the Seto Inland Sea.

Furthermore, the outflow from each region was calculated by the following equation:

QOUTi = CUi · (Si − HUi ) + CLi · (Si − HLi ) (6)

where, QOUTi is the outflow from each region; CUi and CLi are the flow coefficients foreach region; HUi and HLi are the height of flow-out hole for each region; Si is the waterstorage of each region.

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The infiltration and percolation were also calculated by the following equation:

QIPi = Bi · Si (7)

where, QIPi is the infiltration or percolation; Bi is the infiltration or percolation coefficientin each region.

4.3. Model parameter calibration by the SCE method

There are many parameters in this conceptual groundwater model (Figure 3) such as: CLP,CUP: flow coefficient for paddy field sub-model (Unit: day−1); CLO, CUO: flow coef-ficient for other fields sub-model (Unit: day−1); CL2: flow coefficient for surface regionsub-model (Unit: day−1); CL3, CU3: flow coefficient for groundwater region sub-model(Unit: day−1); HLP, HUP, HLO, HUO, HL2, HU3: height of out-let in each sub-model(mm); BP, BO, B2: infiltration coefficient in each sub-model (Unit: day−1); CIRR: coef-ficient of water-supply from river for agricultural use (Unit: none); CINT: coefficient ofwater infiltrating to subsurface or groundwater region (Unit: none); CG3: coefficient ofgroundwater flowing from 3rd block to 4th block (Unit: none). It is desirable to decide theseparameters by observations as much as possible. However, it is time and money consum-ing to do this work. In this study, the SCE method was employed to calibrate the modelparameters.

SCE method is a typical effective numerical method of nonlinear optimization algorithmto automatically calibrate hydrological models. The flow chart of the SCE algorithm has beenshown in the Figure 4. In the present regional groundwater model, the SCE method servesas a general purpose global optimization strategy designed to handle the various responseproblems encountered in the calibration of groundwater model. The initial selection of a‘population’ of points distributed randomly throughout the feasible parameter space can bedecided from the initial part of regional groundwater model. Then the population is parti-tioned into several ‘complexes’, each consisting of 2n + 1 points, where n is the number ofoptimized parameters. Each complex ‘evolution’ of the population will be independently ina manner that is based on the downhill simplex algorithm. The selected population is peri-odically ‘shuffled’ and new complexes will be formed so that the information gained by theprevious complexes can be shared. The evolution and shuffling steps will be repeated untilthe prescribed convergence criteria of the regional groundwater model are satisfied. Thus,the calibration algorithm of the regional groundwater model begins by randomly selectinga population of feasible points that are sorted and partitioned into a number of communi-ties (complexes), each one containing at least 2n + 1 points. Then each of the complexes isallowed to evolve in the direction of global improvement, using competitive evolution tech-niques that are based on the downhill simplex method. At periodic stages in the evolution, theentire set of points is shuffled and reassigned to new complexes to enable information shar-ing. Lastly, the algorithm will stop optimization step when the error function of the regionalgroundwater model can be satisfied as the ideal value. With the SCE parameter optimizationmethod, the proposed regional groundwater model will be calibrated to fit with the measuredgroundwater level by adjusting model parameters to minimize the squared residual betweenthe observed and simulated groundwater level. As the output of the regional groundwatermodel, the estimated regional groundwater level of each block will be simulated from theinput dataset.

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START

INITIAL PARAMETERS & ENVIRONMENT SETS

GENERATE SCE OPTIMIZATION SOLUTION

OBJECT FUNCTION VALUE

CREAT RANDOMS TO GENERATE

OPTIMIZED PARAMETERS

RUN GW SIMULATION MODDEL

OUTPUT ERROR & COMPUTE ERROR FUNCTION

NOT YET SATISFIED

OUTPUT AND PLOT PARAMETERS &

SIMULATED RESULTS

SATISFIED

NOT YET SATISFIED

SATISFIED

Fig. 4 Flow chart of the SCE Algorithm

5. Results and discussion

5.1. Calibration of the model

The objective of the calibration is to obtain daily groundwater level estimation from the modelas close as possible to measured groundwater level. In this study, there are 76 parameterstotally but not all of these parameters will be calibrated and optimized in the regional ground-water model. Some parameters have known values or can be partly decided by empiricallyestimation based on the long-term observation. Others would be calibrated and optimizedby the Shuffled Complex Evolution (SCE) method, which is a typical nonlinear optimiza-tion method. Furthermore, to simplify the complicated problem and minimize the number ofmodel parameters, the parameters of the paddy field and other fields are supposed to be samein all blocks but other parameters are different in each block. In addition, the flow coefficientof the up-outlet for paddy field and other field are supposed to be 1.0 (CUP = 1.0, CUO =1.0). Finally, 41 parameters will be used in the calibration process in all blocks for this Dogoplain study.

The groundwater level (HGC: m) can be calculated by dividing the groundwater storageheight (S3: mm) by the effective porosity of each block. The measured groundwater level of

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Table 3 List and maximum values (Minimum values of all the parameters are zero) of theparameters which are used in the calibration process

Layer Parameter 1st Block 2nd Block 3rd Block 4th Block

Surface regionPaddy field

HUP 150CLP 0.50HLP 100BP 0.75

Other fieldHUO 150CLO 0.75HLO 2.5BO 0.25

Subsurface regionCL2 0.75 0.75 0.75 1.00HL2 200 75 75 200B2 0.50 0.50 0.25 0.25

Groundwater regionCU3 0.50 0.75 0.50 0.50HU3 5000 5000 5000 5000CL3 0.10 0.10 0.10 0.15

CoefficientsCIRR 1.00 1.00 1.00 1.00CINT 1.00 1.00 1.00 1.00CG3 / / 0.50 /

each block is the regional average value, which would be discussed in the following section.The equation of error function (Equation (8)) is the sum of square error between the measuredgroundwater level and predicted groundwater level. The final objective is to minimize theerror using the optimized parameters by the SCE algorithm.

ERR =4∑

Block=1

N∑Day=1

(HGC − HGM)2 (8)

where, HGC is the calculated groundwater level, HGM is the measured groundwater level,and N is the number of observation days. The above objective function was used to help avoidbecoming trapped in local minima as do all other random search techniques by reducing misfitbetween measured and observed groundwater level to a minimum. The list and typical rangeof parameters, which are used in the calibration process, are shown in Table 3. The finalcalibrated values of parameters, which are used in the calibration process, are shown inTable 4.

5.2. Groundwater level simulation

The comparison between the measured groundwater and predicted groundwater, using theoptimized parameters by the SCE method is shown in Figure 5. Clearly, the proposed ground-water model has both strong and weak points, which influence its application under variousconditions. For each block, the groundwater level would be obtained from the well record

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Table 4 The final calibrated values of parameters which are used in the calibration process

Layer Parameter 1st Block 2nd Block 3rd Block 4th Block

Surface regionPaddy field

HUP 29.1CLP 0.16HLP 21.8BP 0.16

Other fieldHUO 68.2CLO 0.02HLO 0.60BO 0.10

Subsurface regionCL2 0.14 0.49 0.22 0.07HL2 23.3 18.7 25.3 54.5B2 0.07 0.30 0.03 0.01

Groundwater regionCU3 0.20 0.48 0.06 0.08HU3 167.0 700.0 21.1 975.0CL3 0.07 0.04 0.01 0.00

CoefficientsCIRR 0.03 0.29 0.08 0.78CINT 0.32 0.86 0.41 0.46CG3 / / 0.48 /

but many of these data records have missing data, which would be found from the Figure 5.In this case, the average measurement groundwater level is a key issue and it will constitutethe observed values for calibration and optimization of the model parameters. To decide therepresentative measurement groundwater level of each block, the average groundwater levelfor each block has been obtained by averaging all the measurement groundwater level. Bycomparing the averaged and measured groundwater level, the measured groundwater whichis most close to the average groundwater level would be decided and it will be chosen as theaveraged measurement groundwater level in that block.

From the Figure 5, it can be clearly found that the predicted groundwater level agreedwell with the measured groundwater level in all blocks, and thus it is judged to express awater cycle of the plain by using the water balance model with the SCE optimization method.Thus on the positive side, the proposed groundwater model provides a reliable, independentestimate of areal groundwater level fluctuation based on relatively few, generally accessibledata. The major weakness of the model is its relatively poor simulation of daily groundwaterfluctuation in the Ishite Block. There are some periods, which could not reproduce a temporaryrise or fall of the measured groundwater level in the Ishite Block. The reason is that the inputdatum of both the pumped water for industrial, agricultural, domestic, and the Dogo irrigationwater for agricultural use are all monthly average value. Thus, the better groundwater levelreproduction is expected if more detailed daily or hourly database would be available in thefuture.

Figure 5 indicates the importance of temporal distribution of precipitation in generatingrecharge to groundwater region. The highest groundwater elevation of four blocks during this4-year period was at 1.63 m below the soil surface during a short time from 16 to 21 August,

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Fig. 5 The comparison between the measured and predicted groundwater level in four blocks of the plain

2003. Obviously, there is no period for groundwater to remain at a constant high level. Fromthe observation data, the groundwater tables ranged from 2 to 5 meters. Once the soil’s waterstorage capacity was exceeded, water started draining and replenishing the groundwater. Mostgroundwater recharge occurred during the late-winter and early spring because of the watersupply as precipitation, melting snow and ice. Annual groundwater levels generally reachedtheir maximum level during this period. The utilization of the complete observation networkdata and more detailed dataset may improve the accuracy of the conceptual groundwatermodel.

6. Conclusions

In this paper, the distributed regional groundwater level of the coastal Dogo plain has beenstudied by using the meteorological and hydrogeological data. A distributed, three layers,conceptual groundwater model was used to estimate the patterns of groundwater level fluctu-ation. The model presented in this paper can be a useful tool for estimating areal groundwaterrecharge under a wide variety of circumstances. The most important conclusions from theresearch were the following:

1. The predicted and measured groundwater elevation agreed well. The model highlightsthe physical relationships that exist between the model variables in the calculation ofgroundwater and the water balance components in the plain. It also considered the pumpedwater for industrial and agricultural irrigation use that in turn affects the groundwater leveland, consequently, the rate of groundwater level fluctuation change.

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2. The predicted groundwater level was not so agreeable with the measured one in some partof periods. With more detailed and accurate database, it is capable to predict the betterresults. The performance of the SCE optimization method is satisfactory and it depends,less or more, on the available database. That also proved that the groundwater model withthe SCE parameter optimization was more effective in real-world applications, especiallyin problem of basin scale regional groundwater estimation. Further study will be carriedout to assess the impacts of hydrological changes and mitigation alternatives, and supportdecision making on balancing various water needs.

Acknowledgements The research was financially supported by the Sasakawa Scientific Research Grant fromThe Japan Science Society. The authors thank for their supports. The authors also thank to the YondenConsultants Company for their suggestion and data collection during the research. We also are grateful for thethoughtful comments by two anonymous reviewers and the editor to improve the manuscript.

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Regional groundwater prediction model using automatic parameter calibration SCE method for a coastal plain of Seto Inland Sea