GEO GRA P HICAL RESEA RCH

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1 GEO GRA P HICAL RESEA RCH Vol129, No12 Feb1, 2010, 3, (, ) :, (Multi2Parameter Sensitivity and Uncertainty Analysis, MPSUA) Monte Carlo, GL U E, MPSUA,,, MPSUA,, SCE2UA MPSUA, : ; ; ; SCE2UA ; : (2010) ,, [1,2 ] [3 ],,, Duan [4,5 ], : SCE2UA ( Shuffled Complex Evolution) [4 7 ],,,, SCE2UA, [ 5 ],,,,,, : ; : : ( ) ; : (19782),,, 3 : (19542),,,, E2mail : ac1cn

2 264 29, (factor pert urbation) [8 ], ;,,,,,, [ 9,10 ], [11 ] ( MPSA : Multi2Parameter Sensitivity Analysis) Monte Carlo, ( N ),, ( ), N,,, [12 ] Monte Carlo, Markov Chain Monte Carlo (MCMC) [13,14 ] MCMC Metropolis [13 ],, [ 15,16 ] ( ty Estimation, GL U E) Generalized Likelihood Uncertain2, GL U E Monte2Carlo, MPSA GL U E ( Multi2Parameter Sensitivity and U ncertainty Analysis, MPSUA), MPSUA, SCE2UA MPSUA, MPSUA 2 ( 1) MPSA GL U E SCE2UA,, 1 Fig11 Multi2Parameter Sensitivity and Uncertainty Analysis (MPSUA) and parameter optimization

3 2 : (MPSA) [11 ] ( 2) : (1) ; (2), ; (3),, N ; (4) N, ; (5) ( R), N,, ; (6) :, (, ),,,,,, ( ), ;, : N 33 % 50 % 66 % 212 GL UE GL U E GL U E (equifinality) ( behavioural model space) [ 15 ] GL U E Monte Carlo,,, (non2behavioural) 0 [ 15 ] Nash Sutcliffe Nash2Sutcliffe [17 ] 213 SCE2UA SCE2UA 4 [4 7 ] : (1) ; (2) /, ; (3) ; (4) (complex shuffling) SCE2UA 3 SCE2UA, Duan, [6 ] [ 17 ] (, ), 13846km 2, ( , ; ) 1 DTVGM Tab11 Parameters in the monthly hydrological model g g Kr / mont h KA W A WO 5 30 mm

4 (MPSA) Fig1 2 Flow chart illustrating MPSA (after Choi, 1999) 3 SCE - UA Fig13 Flow chart of SCE2UA algorithm (after Duan, 1992) (CCE : Competitive Complex Evolution algorithm) D TV GM [17 ],, D TV GM D TV GM Monte2Carlo N = 10000, MPSA 4,,,, 4 SD ( Nash2Sutcliffe [13 ] ), SD 1,, 5 : KA W g 1 Kr g 2 A WO, ( ),, GL U E Nash2Sutcliffe N S EC Monte2Carlo N S EC, 5, N S EC 95 % 0174, : 13, ( 1), N S EC %, ; N S EC N S EC %, ,,

5 2 : ( ) Fig14 Multi2parameter sensitivity analysis (Baihe River basin), 2 (NSEC) ( 6 : (NSEC ) ( KA W g1),,, 1 1,,, AWO ;, A WO : D TV GM 5 (NSEC ) Fig15 Accumulated density of the likelihood (NSEC2represents Nash2Sutcliffe efficient coefficient) 313 SCE2UA, 3 ( KAW g1

6 ( ) Fig16 Dotty maps of parameter against likelihood (Baihe River basin) Kr), SCE2UA : AWO = 25 mm, g2 = 014 :, : OB F = w IV F + (110 - w) NS EC (1), IV F, ; NSEC ; w, 015, 2 NSEC = 0174, NSEC = 0182 NSEC GL U E, SCE2UA D TV GM 2 SCE2UA Tab12 Parameter optimization results using SCE2UA algorithm IVF NSEC g1 Kr KAW Monte2Carlo MPSUA,,, ;,,,,

7 2 : 269, D TV GM,,,, MPSUA Beven,, 10000, 6 % ( 600 ) NSEC NSEC, 6 %,, : [ 1 ] Gupta Hoshin V, Sorooshian Soroosh, Hogue Terri S,et al1 Advances in automatic calibration of watershed Mod2 els1 In : Duan Q1 et al1 ( Eds), Calibration of Watershed Models, Water Sci1 and Appl1 6, A GU, Washington, DC, 2003, [ 2 ] Schultz G A, Engman E T1 ( Eds1) Remote Sensing in Hydrology and Water Management1 Springer Verlag Berlin Heidelberg, Germany, [ 3 ] Rozos Evangelos, Ef stratiadis Andreas, Nalbantis Ioannis, et al1 Calibration of a semi2distributed model for con2 junctive simulation of surface and groundwater flows1 Hydrological Sciences Journal, 2004, 49 (5) : [ 4 ] Duan Q Y1 Global optimization for watershed model calibration1 In : Duan Q1 et al1 ( Eds), Calibration of Water2 shed Models, Water Sci1 and Appl1 6, A GU, Washington, DC, 2003 : [ 5 ] Duan Q, Sorooshian S, Gupta V K1 Effective and Efficient Global Optimization for Conceptual Rainfall2Runoff Models1 Water Resour1 Res1, 1992, 28 (4) : [ 6 ] Duan Q, Sorooshian S, Gupta V K1 Optimal Use of t he SCE2UA Global Optimization Met hod for Calibrating Wa2 tershed Models1 J1 of Hydrol1, 1994, 158 : [ 7 ] Duan Q, Gupta V K,Sorooshian S1 A Shuffled Complex Evolution Approach for Effective and Efficient Global Op2 timization1 J1 Optim1 Theo1 and It s Appl1, 1993, 76 (3) : [ 8 ] McCuen Richard H1 Modeling hydrologic change : statistical met hods1 Lewis publishers, 2003, [ 9 ] White K L, Chaubey I1 Sensitivity analysis, calibration, and validations for a multisite and multivariable SWA T model1 Journal of t he American Water Resources Association, 2005, 41 : [10 ] Lenhart T, Eckhardt K, Fohrer N,et al1 Comparison of two different approaches of sensitivity analysis1 Physics and Chemistry of t he Eart h, 2002, 27 : [ 11 ] Choi J, Harvey J W, Conklin M1 Use of Multi2parameter sensitivity analysis to determine relative importance of factors influencing natural attenuation of mining contaminants1 In : Proceedings of the Toxic Substances Hydrology Program Meeting, Charleston, SC, (D1 Morganwalp, ed1 )1 1999, [ 12 ] Thorsen M, Refsgaard J C, Hansen S, et al1 Assessment of uncertainty in simulation of nitrate leaching to aqui2 fers at catchment scale1 Journal of Hydrology,2001, 242 : [ 13 ] Ajami N K, Duan Q Y, Sorooshian S1 An integrated hydrologic Bayesian multimodel combination framework : Confronting input, parameter, and model structural uncertainty in hydrologic prediction1 Water Resources Re2 search, 2007, 43 (1), doi : / 2005wr [ 14 ] Feyen L, Vrugt J A, Nuallain B O, et al1 Parameter optimisation and uncertainty assessment for large2scale stre2 amflow simulation wit h t he L ISFLOOD model1 Journal of Hydrology, 2007, 332 : [ 15 ] Beven Keit h, Freer Jim1 Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using t he GL U E met hodology1 Journal of Hydrology,2001, 249 :

8 [ 16 ] Demarty J, Ottl C, Braud I, et al1 Contraining a physically based Soil2Vegetation2Atmosphere Transfer model with surface water content and thermal infrared brightness temperature measurements using a multiobjective ap2 proach, Water Resour1 Res1, 2005, 41, W01011, doi : / 2004WR [ 17 ],, 1 1, 2004, 23 (2) : A multi2parameter sensitivity and uncertainty analysis method to evaluate relative importance of parameters and model perf ormance WAN G Gang2sheng, XIA J un, CH EN J un2feng ( Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing , China) Abstract :A Multi2Parameter Sensitivit y and U ncertaint y Analysis ( M PSU A) met hod is developed to evaluate t he relative importance of parameter s and model performance. The idea of MPSUA is to couple the Generalized Likelihood Uncertainty Estimation ( GL U E) with the Multi2Parameter Sensitivity Analysis (MPSA) based on Monte Carlo simulation. The implementation of MPSA includes t he following step s : (1) Running t he model using randomly generated parameter set s ; (2) Comp uting t he objective f unction values, which are defined as t he sum of squared errors between observed and simulated values. The ob2 served values are t he outp ut f rom model simulations using t he median of t he characteristic range for each parameter. (3) Identif ying t he acceptable and unacceptable parameter set s by comparing t he objective f unction values to a given criterion, e. g., t he 50 % division of all sorted objective f unctions. The objective f unction value which is less t han t he criterion is classified as accep table, ot herwise it is classified as unacceptable. ( 4) Measuring t he separating degree between two cumulative distribution curves for "acceptable" and " unac2 ceptable" parameters. Larger discrepancy means higher sensitivit y. The case st udy in t he Chaobai River Basin of Nort h China showed t hat the model performance can be evaluated based on MPSUA, even t hough the optimum parameter values were unknown. For exam2 ple, t he same model could reach a higher modeling precision for t he Chaohe River Basin t han t hat for t he Baihe River Basin. Such a difference in model performance is likely caused by bot h t he uncertainty f rom model struct ure and t he uncertainty f rom inp ut data. The consistency between parameter optimization by SCE2UA algorit hm and MPSUA also illust rated t he ratio nalit y of t he met hodology applied in t his paper. Furt her st udies can take into account multiple objectives into t he MSPUA. Key words :model performance ; parameter ; sensitivity analysis ; SCE2UA algorithm ; Cha2 ohe and Baihe river basins in Nort h China