Parameter identification and calibration of the Xin’anjiang model using the surrogate modeling approach

Abstract

Practical experience has demonstrated that single objective functions, no matter how carefully chosen, prove to be inadequate in providing proper measurements for all of the characteristics of the observed data. One strategy to circumvent this problem is to define multiple fitting criteria that measure different aspects of system behavior, and to use multi-criteria optimization to identify non-dominated optimal solutions. Unfortunately, these analyses require running original simulation models thousands of times. As such, they demand prohibitively large computational budgets. As a result, surrogate models have been used in combination with a variety of multi-objective optimization algorithms to approximate the true Pareto-front within limited evaluations for the original model. In this study, multi-objective optimization based on surrogate modeling (multivariate adaptive regression splines, MARS) for a conceptual rainfall-runoff model (Xin’anjiang model, XAJ) was proposed. Taking the Yanduhe basin of Three Gorges in the upper stream of the Yangtze River in China as a case study, three evaluation criteria were selected to quantify the goodness-of-fit of observations against calculated values from the simulation model. The three criteria chosen were the Nash-Sutcliffe efficiency coefficient, the relative error of peak flow, and runoff volume (REPF and RERV). The efficacy of this method is demonstrated on the calibration of the XAJ model. Compared to the single objective optimization results, it was indicated that the multi-objective optimization method can infer the most probable parameter set. The results also demonstrate that the use of surrogate-modeling enables optimization that is much more efficient; and the total computational cost is reduced by about 92.5%, compared to optimization without using surrogate modeling. The results obtained with the proposed method support the feasibility of applying parameter optimization to computationally intensive simulation models, via reducing the number of simulation runs required in the numerical model considerably.

Keywords

Xin’anjiang model / parameter calibration / multi-objective optimization / surrogate modeling

References

[1] AkhtarM, AhmadN, BooijM J (2008). The impact of climate change on the water resources of Hindukush-Karakorum-Himalaya region under different glacier coverage scenarios. J Hydrol (Amst), 355(1–4): 148–163

[2] BehzadianK, KapelanZ, SavicD, ArdeshirA (2009). Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks. Environ Model Softw, 24(4): 530–541

[3] BennettD A, XiaoN C, ArmstrongM P (2004). Exploring the geographic consequences of public policies using evolutionary algorithms. Ann Assoc Am Geogr, 94(4): 827–847

[4] BevenK, FreerJ (2001). Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology. J Hydrol (Amst), 249(1–4): 11–29

[5] BevenK J (2006). A manifesto for the equifinality thesis. J Hydrol, 320: 18–36

[6] BingemanA, KouwenN, SoulisE D (2006). Validation of hydrological processes in a hydrological model. J Hydrol Eng, 11(5): 451–463

[7] BiondiD, FreniG, IacobellisV, MascaroG, MontanariA (2012). Validation of hydrological models: conceptual basis, methodological approaches and a proposal for a code of practice. Phys Chem Earth A/B/C, 42–44: 70–76

[8] BliznyukN, RuppertD, ShoemakerC, RegisR, WildS, MugunthanP (2008). Bayesian calibration and uncertainty analysis for computationally expensive models using optimization and radial basis function approximation. J Comput Graph Statist, 17(2): 270–294

[9] BroadD R, DandyG C, MaierH R (2005). Water distribution system optimization using metamodels. J Water Resour Plan Manage, 131(3): 172–180

[10] BroadD R, MaierH R, DandyG C (2010). Optimal operation of complex water distribution systems using metamodels. J Water Resour Plan Manage, 136(4): 433–443

[11] CaoK, BattyM, HuangB, LiuY, YuL, ChenJ F (2011). Spatial multi-objective land use optimization: extensions to the non-dominated sorting genetic algorithm-II. Int J Geogr Inf Sci, 25(12): 1949–1969

[12] ClarkM P, McMillanH K, CollinsD B G, KavetskiD, WoodsR A (2011). Hydrological field data from a modeller’s perspective.Part 2: process-based evaluation of model hypotheses. Hydrol Processes, 25(4): 523–543

[13] de VosN J, RientjesT H M (2008). Multiobjective training of artificial neural networks for rainfall-runoff modeling. Water Resour Res, 44(8): W08434, doi: 10.1029/2007WR006734

[14] di PierroF, KhuS T, SavicD, BerardiL (2009). Efficient multi-objective optimal design of water distribution networks on a budget of simulations using hybrid algorithms. Environ Model Softw, 24(2): 202–213

[15] DuanQ Y, SorooshianS, GuptaV (1992). Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour Res, 28(4): 1015–1031

[16] DumedahG (2012). Formulation of the evolutionary-based data assimilation, and its implementation in hydrological forecasting. Water Resour Manage, 26(13): 3853–3870

[17] DumedahG, BergA A, WinebergM, CollierR (2010). Selecting model parameter sets from a trade-off surface generated from the non-dominated sorting genetic algorithm-II. Water Resour Manage, 24(15): 4469–4489

[18] DunnS M, FreerJ, WeilerM, KirkbyM J, SeibertJ, QuinnP F, LischeidG, TetzlaffD, SoulsbyC (2008). Conceptualization in catchment modeling: simply learning?Hydrol Processes, 22(13): 2389–2393

[19] FeniciaF, SavenijeH H G, MatgenP, PfisterL (2008). Understanding catchment behavior through stepwise model concept improvement. Water Resour Res, 44(1): W01402, doi: 10.1029/2006WR005563

[20] FriedmanJ H (1991). Multivariate adaptive regression splines. Ann Stat, 19(1): 1–67

[21] GanT Y, BiftuG F (1996). Automatic calibration of conceptual rainfall-runoff models: optimization algorithm, catchment conditions, and model structure. Water Resour Res, 32(12): 3513–3524

[22] GoelT, VaidyanathanR, HaftkaR T, ShyyW, QueipoN V, TuckerK (2007). Response surface approximation of Pareto optimal front in multi-objective optimization. Comput Methods Appl Mech Eng, 196(4–6): 879–893

[23] GuoJ, ZhouJ, ZouQ, SongL, ZhangY (2013b). Study on multi-objective parameter optimization of Xin’anjiang model. Journal of China Hydrology, 33(1): 1–7 (in Chinese)

[24] GuoJ, ZhouJ Z, ZouQ, LiuY, SongL (2013a). A novel multi-objective shuffled complex differential evolution algorithm with application to hydrological model parameter optimization. Water Resour Manage, 27(8): 2923–2946

[25] GutmannH M (2001). A radial basis function method for global optimization. J Glob Optim, 19(3): 201–227

[26] HuangK, LiuX, LiX, LiangJ, HeS (2013). An improved artificial immune system for seeking the Pareto front of land-use allocation problem in large areas. Int J Geogr Inf Sci, 27(5): 922–946

[27] JiangY, LiX Y, HuangC C (2013). Automatic calibration a hydrological model using a master-slave swarms shuffling evolution algorithm based on self-adaptive particle swarm optimization. Expert Syst Appl, 40(2): 752–757

[28] JonesD R, SchonlauM, WelchW (1998). Efficient global optimization of expensive black-box functions. J Glob Optim, 13(4): 455–492

[29] JonesJ P, SudickyE A, McLarenR G (2008). Application of a fully-integrated surface-subsurface flow model at the watershed-scale: a case study. Water Resour Res, 44(3): W03407, doi: 10.1029/2006WR005603

[30] KavetskiD, ClarkM P (2011). Numerical troubles in conceptual hydrology: approximations, absurdities, and impact on hypothesis-testing. Hydrol Processes, 25(4): 661–670

[31] KavetskiD, KuczeraG, FranksS W (2006). Bayesian analysis of input uncertainty in hydrological modeling: 1.theory. Water Resour Res, 42: W03407, doi: 10.1029/2005WR004368

[32] KhuS T, MadsenH (2005). Multiobjective calibration with Pareto preference ordering: an application to rainfall-runoff model calibration. Water Resour Res, 41(3): W03004, doi: 10.1029/2004WR003041

[33] KhuS T, WernerM G F (2003). Reduction of Monte-Carlo simulation runs for uncertainty estimation in hydrological modeling. Hydrol Earth Syst Sci, 7(5): 680–692

[34] KongF Z, LiL L (2006). Application of digital elevation model in Xinanjiang model. Journal of China University of Mining & Technology, 35(3): 393–396 (in Chinese)

[35] KourakosG, MantoglouA (2009). Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models. Adv Water Resour, 32(4): 507–521

[36] LeeK T, HungW C, MengC C (2008). Deterministic insight into ANN model performance for storm runoff simulation. Water Resour Manage, 22(1): 67–82

[37] LiH, ZhangY, ChiewF H S, XuS (2009). Predicting runoff in ungauged catchments by using Xinanjiang model with MODIS leaf area index. J Hydrol (Amst), 370(1–4): 155–162

[38] LindströmG, JohannsonB, PerssonM, GardelinM, BergströmS (1997). Development and test of the distributed HBV-96 hydrological model. J Hydrol (Amst), 201(1–4): 272–288

[39] LiuD, YuZ, HaoZ, YangC, JuQ (2007). Groundwater simulation in the Yangtze River basin with a coupled climate-hydrologic model. Journal of China University of Geosciences, 18(Special issue): 155–157

[40] LüH S, HouT, HortonR, ZhuY, ChenX, JiaY, WangW, FuX (2013). The streamflow estimation using the Xinanjiang rainfall runoff model and dual state-parameter estimation method. J Hydrol (Amst), 480: 102–114

[41] MadsenH (2000). Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. J Hydrol (Amst), 235(3–4): 276–288

[42] McCabeM F, FranksS W, KalmaJ D (2005). Calibration of a land surface model using multiple data sets. J Hydrol (Amst), 302(1–4): 209–222

[43] McIntyreN, Al-QurashiA (2009). Performance of ten rainfall-runoff models applied to an arid catchment in Oman. Environ Model Softw, 24(6): 726–738

[44] McLachlanG J, DoK-A, AmbroiseC (2004). Analyzing Microarray Gene Expression Data. Hoboken, New Jersey: John Wiley & Sons, Int, 213–216

[45] McMillanH K, ClarkM P, BowdenW B, DuncanM, WoodsR A (2011). Hydrological field data from a model’s perspective.Part 1: diagnostic tests for model structure. Hydrol Processes, 25(4): 511–522

[46] MoriasiD N, ArnoldJ G, Van LiewM W, BingnerR L, HarmelR D, VeithT L (2007). Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE, 50(3): 885–900

[47] MugunthanP, ShoemakerC A (2006). Assessing the impacts of parameter uncertainty for computationally expensive groundwater models. Water Resour Res, 42(10): W10428, doi: 10.1029/2005WR004640

[48] NashJ E, SutcliffeJ V (1970). River flow forecasting through conceptual models part I — A discussion of principles. J Hydrol (Amst), 10(3): 282–290

[49] PushpalathaR, PerrinC, MoineN L, AndréassianV (2012). A review of efficiency criteria suitable for evaluating low-flow simulations. J Hydrol (Amst), 420–421: 171–182

[50] QuS, BaoW, ShiP, YuZ, LiP, ZhangB, JiangP (2012). Evaluation of runoff responses to land use changes and land cover changes in the upper Huaihe river basin, China. J Hydrol Eng, 17(7): 800–806

[51] QuirósE, FelicísimoÁ M, CuarteroA (2009). Testing multivariate adaptive regression splines (MARS) as a method of land cover classification of TERRA-ASTER satellite images. Sensors (Basel), 9(11): 9011–9028

[52] RazaviS (2013). Developing efficient strategies for automatic calibration of computationally intensive environmental models. Thesis of University of Waterloo, Waterloo, Ontario, Canada

[53] RazaviS, TolsonB A, BurnD H (2012). Review of surrogate modeling in water resources. Water Resour Res, 48(7): W07401, doi: 10.1029/2011WR011527

[54] ReedP, MinskerB S, GoldbergD E (2003). Simplifying multi-objective optimization: an automated design methodology for the nondominated sorted genetic algorithm–II. Water Resour Res, 39(7): 1196, doi: 10.1029/2002WR001483

[55] RegisR G, ShoemakerC A (2007). A stochastic radial basis function method for the global optimization of expensive functions. INFORMS J Comput, 19(4): 497–509

[56] ReichertP, WhiteG, BayarriM J, PitmanE B (2011). Mechanism-based emulation of dynamic simulation models: concept and application in hydrology. Comput Stat Data Anal, 55(4): 1638–1655

[57] RitterA, Muñoz-CarpenaR (2013). Performance evaluation of hydrological models: statistical significance for reducing subjectivity in goodness-of-fit assessments. J Hydrol (Amst), 480: 33–45

[58] SinghS K, BárdossyA (2012). Calibration of hydrological models on hydrologically unusual events. Adv Water Resour, 38: 81–91

[59] SkaggsT H, BarryD A (1997). The first-order reliability method of predicting cumulative mass flux in heterogeneous porous formations. Water Resour Res, 33(6): 1485–1494

[60] SongX, KongF (2010). Application of Xin’anjiang model coupling with artificial neural networks. Bulletin of Soil and Water Conservation, 30(6): 135–138 (in Chinese)

[61] SongX, KongF, ZhanC, HanJ (2012a). Sensitivity analysis of hydrological model parameter using a statistical theory approach. Advances in Water Science, 23(5): 642–649 (in Chinese)

[62] SongX, KongF, ZhanC, HanJ (2012b). Hybrid optimization rainfall-runoff simulation based on Xin’anjiang model and artificial neural network. J Hydrol Eng, 17(9): 1033–1041

[63] SongX, KongF, ZhanC, HanJ, ZhangX (2013). Parameter identification and global sensitivity analysis of Xin’anjiang model using meta-modeling approach. Water Sci Eng, 6(1): 1–17

[64] SongX, ZhanC, KongF, XiaJ (2011). Advances in the study of uncertainty quantification of large-scale hydrological modeling system. J Geogr Sci, 21(5): 801–819

[65] SongX, ZhanC, XiaJ (2012c). Integration of a statistical emulator approach with the SCE-UA method for parameter optimization of a hydrological model. Chin Sci Bull, 57(26): 3397–3403

[66] SongX, ZhanC, XiaJ, KongF (2012d). An efficient global sensitivity analysis approach for distributed hydrological model. J Geogr Sci, 22(2): 209–222

[67] SrinivasuluS, JainA (2006). A comparative analysis of training methods for artificial neural network rainfall-runoff models. Appl Soft Comput, 6(3): 295–306

[68] TangY, ReedP, WagenerT (2006). How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration?Hydrol Earth Syst Sci, 10(2): 289–307

[69] TrautmannH, RudolphG, Dominguez-MedinaC, SchutzeO (2013). Finding evenly spaced Pareto fronts for three-objective optimization problems. In: SchutzeO, CoelloC A, TantarA, TantarE, BouvryP, MoralP D, LegrandP eds. EVOLVE–A Bridge between Probability Set Oriented Numeric, And Evolutionary Computation II. Heidelberg: Springer-Verlag, 89–105

[70] van WerkhovenK, WagenerT, ReedP, TangY (2009). Sensitivity-guided reduction of parametric dimensionality for multi-objective calibration of watershed models. Adv Water Resour, 32(8): 1154–1169

[71] VrugtJ A, GuptaH V, BastidasL, BoutenW, SorooshianS (2003b). Efficient and efficient algorithm for multiobjective optimization of hydrologic model. Water Resour Res, 39(8), doi: 10.1029/2002WR001746

[72] VrugtJ A, GuptaH V, BoutenW, SorooshianS (2003a). A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrological model parameters. Water Resour Res, 39(8), doi: 10.1029/2002WR001642

[73] VrugtJ A, GuptaH V, NuallainB, BoutenW (2006). Real-time data assimilation for operational ensemble streamflow forecasting. J Hydrometeorol, 7(3): 548–565

[74] WagnerT, EmmerichM, DeutzA, PonweiserW (2010). On expected-improvement criteria for model-based multi-objective optimization. In: SchaeferR, CottaC, KolodziejJ, RudolphG, ed. Parallel Problems Solving from Nature (PPSN) XI, Part I, LNCS 6238. Berlin: Springer, 718–727

[75] WangQ J (1991). The genetic algorithm and its application to calibrating conceptual rainfall-runoff models. Water Resour Res, 27(9): 2467–2471

[76] WheaterH S (2002). Progress in and prospects for fluvial flood modeling. Phil Trans R Soc Lond A, 360(1796): 1409–1431

[77] XuC Y (1999). Estimation of parameters of a conceptual water balance model for ungauged catchments. Water Resour Manage, 13(5): 353–368

[78] XuD M, WangW C, ChauK W, ChenC T, ChenS Y (2013). Comparison of three global optimization algorithms for calibration of the Xinanjiang model parameters. J HydroInf, 15(1): 174–193

[79] YanS, MinskerB (2006). Optimal groundwater remediation design using an adaptive neural network genetic algorithm. Water Resour Res, 42, W05407, doi: 10.1029/2005WR004303

[80] YanS, MinskerB (2011). Applying dynamic surrogate models in noisy genetic algorithms to optimize groundwater remediation designs. J Water Resour Plan Manage, 137(3): 284–292

[81] YangX H, MeiY, SheD X, LiJ Q (2011b). Chaotic Bayesian optimal prediction method and its application in hydrological time series. Comput Math Appl, 61(8): 1975–1978

[82] YangX H, SheD X, YangZ F, TangQ H, LiJ Q (2009). Chaotic Bayesian method based on multiple criteria decision making (MCDM) for forecasting nonlinear hydrological time series. International Journal of Nonlinear Sciences and Numerical Simulation, 10(11–12): 1595–1610

[83] YangX H, ZhangX J, HuX X, YangZ F, LiJ Q (2011a). Nonlinear optimization set pair analysis model (NOSPAM) for assessing water resource renewability. Nonlinear Process Geophys, 18(5): 599–607

[84] YaoC, LiZ, YuZ, ZhangK (2012). A prior parameter estimates for a distributed, grid-based Xinanjiang model using geographically based information. J Hydrol (Amst), 468–469: 47–62

[85] YapoP O, GuptaH V, SorooshianS (1998). Multi-objective global optimization for hydrologic models. J Hydrol (Amst), 204(1–4): 83–97

[86] YuZ, LüH, ZhuY, DrakeS, LiangC (2010). Long-term effects of vegetation on soil hydrological processes in vegetation-stabilized desert ecosystem. Hydrol Processes, 24(1): 87–95

[87] ZhanC S, SongX M, XiaJ, TongC (2013). An efficient integrated approach for global sensitivity analysis of hydrological model parameters. Environ Model Softw, 41: 39–52

[88] ZhangQ, LiuW, TsangE, VirginasB (2010). Expensive multiobjective optimization by MOEA/D with Gaussian process model. IEEE Trans Evol Comput, 14(3): 456–474

[89] ZhangX S, SrinivasanR, Van LiewM (2009). Approximating SWAT model using artificial neural network and support vector machine. J Am Water Resour Assoc, 45(2): 460–474

[90] ZhaoR J (1984). Watershed Hydrological Modeling. Beijing: Water Conservancy and Electric Power Press, 106–130(in Chinese)

[91] ZhaoR J (1992). The Xin’anjiang model applied in China. J Hydrol (Amst), 135(1–4): 371–381

[92] ZhaoR J, LiuX R (1995). The Xin’anjiang model. In: SinghV P ed. Computer Models of Watershed Hydrology. Colorado: Water Resources Publications, 215–232

[93] ZouR, LungW S, WuJ (2007). An adaptive neural network embedded genetic algorithm approach for inverse water quality modeling. Water Resour Res, 43(8): W08427, doi: 10.1029/2006WR005158

[94] ZouR, LungW S, WuJ (2009). Multiple-pattern parameter identification and uncertainty analysis approach for water quality modeling. Ecol Modell, 220(5): 621–629

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg