Calibration, Uncertainty and Regional Analysis of Conceptual Rainfall - Runoff models

Howard Wheater1 , Neil McIntyre1 and Thorsten Wagener2 1Department of Civil and Environmental Engineering Imperial College London 2Department of Civil and Environmental Engineering Pennsylvania State University

GWADI Workshop Roorkee Feb-March 2005 Historical development of modelling methods

1930s Unit hydrograph (Metric models) I I 1960s Conceptual models II I I 1970s Physics-based models I I I I I I 1980s Stochastic analysis I I I I

GWADI Workshop Roorkee Feb-March 2005 Conceptual Models

Assumed model form In general, parameters have no direct (measurable) physical significance Optimisation required for parameter identification

GWADI Workshop Roorkee Feb-March 2005 Fitting a conceptual model

• Manual, subjective

or

• Automatic, objective

GWADI Workshop Roorkee Feb-March 2005 Automatic fitting of a conceptual model

• Specify performance measure(s) (objective functions OFs) • For p model parameters pose problem of minimisation or maximisation of (p+1) dimensional response surface • Classic optimisation methods include Rosenbrock, Simplex • Advanced methods include Shuffled Complex Evolution (SCE-UA)

GWADI Workshop Roorkee Feb-March 2005 Problems in optimisation

• Multiple local optima on the objective function surface • Interdependence of parameters gives difficulties due to production of valleys (or ridges) in objective function • Insensitive directions in parameter space, e.g. if parameter redundant due to a threshold value • Search hampered by boundaries in parameter values • Saddle points • Different scales of parameters

GWADI Workshop Roorkee Feb-March 2005 The reason? Model complexity exceeds the information content of the data The result? Non -uniqueness: many combinations of parameter values provide equally good fits to the data Hence model parameters cannot be uniquely associated with physical catchment characteristics

GWADI Workshop Roorkee Feb-March 2005 The solutions:

• Reduce model complexity • Increase the information content of the data • Abandon the concept of a unique best-fit model

GWADI Workshop Roorkee Feb-March 2005 Model structural analysis

Towards parsimoneous model structures

GWADI Workshop Roorkee Feb-March 2005 evapotranspiration precipita tio n (rain, snow)

snow a ccumula tion (snow water storage)

snowmelt

inte rce ption a nd surfa ce moiste ning

soil water supply overland soil surface storage flo w channel storage (depression storage...) and routing infiltra tion

soil moisture re cha rge (ca pilla ry wa te r) inte rflow basin gravity water storage and flow discharge including macropore flow ca pilla ry rise percolation

baseflow groundwater in upper horizons (shallow, perched) deep percolation delayed baseflow groundwater in deeper horizons (large scale aquifers...)

GWADI Workshop Roorkee Feb-March 2005 Rainfall-Runoff Modelling Toolbox

GUI

HYBRID MODEL ARCHITECTURE OPTIM IZATION MODULES AET

VISUAL ER P MOISTURE ANALYSIS ROUTING T ACCOUNTING Q MODULES MODULE PET MODULE

OFF-LINE DATA PROCESSING MODULES MOISTURE STATUS

GWADI Workshop Roorkee Feb-March 2005 aek rk

u1 cmax k u2k storage capacity

ck sk

10F(c)

aek rk c3 k(quick)

+ cmd c4 d k alpha

+ qk

k(slow) aek rk

msk-1/c msk−1 τ rk rk v (tk ) msk/c GWADI Workshop Roorkee Feb-March 2005 uk=0.5(msk+msk-1)*rk aek rk k(quick)

u1k cmax u2k b alpha storage capacity + qk ck sk

10F(c) k(slow)

GWADI Workshop Roorkee Feb-March 2005 GUI

(GLUE) GLUE GLUE CLASS REGIONAL CONFIDENCE VARIABLE PLOTS SENSITIVITY LIMITS UNCERTAINTY ANALYSIS

MULTI- (MO) 2-D AND 3-D DOTTY OBJECTIVE PARETO SURFACE PLOTS (MO) CONFIDENCE PLOTS ANALYSIS LIMITS

(MO) DYNAMIC A POSTERIORI (MO) NORMALIZED IDENTIFIABILITY PARAMETER PARAMETER PARAMETER ANALYSIS DISTRIBUTIONS RANKINGS RANGES

GWADI Workshop Roorkee Feb-March 2005 MONTE CARLO ANALYSIS OF MODEL STRUCTURE AND PERFORMANCE

With current computing power, it is possible to use Monte Carlo simulation techniques to generate many realisations of model performance, by sampling at random from the feasible parameter space. Using this approach, techniques are now available to explore model performance, parameter sensitivity and parameter identifiability This allows the analysis of a given model structure, and a means of tailoring a model structure to a particular application.

GWADI Workshop Roorkee Feb-March 2005 Monte Carlo Analysis Toolbox

GUI

(GLUE) GLUE GLUE CLASS REGIONAL CONFIDENCE VARIABLE PLOTS SENSITIVITY LIMITS UNCERTAINTY ANALYSIS

MULTI- (MO) 2-D AND 3-D DOTTY OBJECTIVE PARETO SURFACE PLOTS (MO) CONFIDENCE PLOTS ANALYSIS LIMITS

(MO) DYNAMIC A POSTERIORI (MO) NORMALIZED IDENTIFIABILITY PARAMETER PARAMETER PARAMETER ANALYSIS DISTRIBUTIONS RANKINGS RANGES

GWADI Workshop Roorkee Feb-March 2005 DOTTY PLOTS AND IDENTIFIABILITY ANALYSIS

A simple plot of performance vs parameter value for a given parameter using all Monte Carlo results can show whether the parameter is identifiable, at least in a univariate sense (parameter interactions are considered separately).

GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 DYNAMIC IDENTIFIABILITY ANALYSIS

GWADI Workshop Roorkee Feb-March 2005 PURPOSE SYSTEM

CONCEPTUALIZATION DATA

MODEL COMPLEXITY

REQUIRED SUPPORTED

PERFORMANCE UNCERTAINTY

SUFFICIENT ACCEPTABLE

GWADI Workshop Roorkee Feb-March 2005 Model Performance Versus Parameter Uncertainty

GWADI Workshop Roorkee Feb-March 2005 Increasing the information content of the data:

multi-criteria analysis

GWADI Workshop Roorkee Feb-March 2005 MULTIPLE OBJECTIVE FUNCTIONS

A single objective function cannot capture all of the many performance attributes that an experienced hydrologist might look for in evaluating model performance, and uses only a limited part of the total information content of a hydrograph. When used in calibration it will tend to bias model performance to match a particular aspect of the hydrograph

GWADI Workshop Roorkee Feb-March 2005 MULTIPLE OBJECTIVE FUNCTIONS

A single objective function: • cannot capture the many performance attributes that an experienced hydrologist might look for • uses only a limited part of the total information content of a hydrograph • when used in calibration it will tend to bias model performance to match a particular aspect of the hydrograph

GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 A multi-criteria approach overcomes these problems (Wheater et al., 1986, Gupta et al., 1998, Boyle et al., 2001, Wagener et al., 2001). For a single output problem (e.g. a stream hydrograph), different parts of the time series can be selected, e.g. rising limb, recession, low flow periods, to examine different aspects of model performance. These can be matched to the sensitivity of different components of the model (Wheater et al, 1986), or arbitrarily selected (Boyle et al., 2001).

GWADI Workshop Roorkee Feb-March 2005 Good trade off 1 Poor trade off 1 1 1

0. 8 0. 8 0. 8 0. 8

0. 6 0. 6 0. 6 0. 6

FSB0. 40. 4 FSB 0. 40. 4

0. 20. 2 0. 20. 2

0 0 0 0 0 0 0.20.2 0.40.4 0.60.6 0.80.8 1 1 0 0 0.20.2 0.40.4 0.60.6 0.80.8 1 1

NSE NSE

cwi_leak model structure pd4_2pmp model structure at North Esk at Dalmore Weir at Bogie at Redcraig

GWADI Workshop Roorkee Feb-March 2005 • Trade-offs generally occur • A successful model will minimise the trade-offs between alternative criteria • The user must decide what compromise to make

GWADI Workshop Roorkee Feb-March 2005 Abandoning the concept of a unique best-fit model

• Consider a population of models • Define the likelihood that they are consistent with the available data

GWADI Workshop Roorkee Feb-March 2005 REGIONAL SENSITIVITY ANALYSIS Spear and Hornberger (1980)

Spear and Hornberger classified the realisations as "behavioural" or "non- behavioural", and used this classification to explore parameter sensitivity. Parameters were sensitive if there was a significant difference between the set of behavioural and non-behavioural parameters

GWADI Workshop Roorkee Feb-March 2005 1 1 F(θ | B) i θ F( j | B)

F(θ ) θ j F( i ) θ F( j | B ) θ F( i | B ) cumulative distribution cumulative distribution 0 0 θ θ i j

GWADI Workshop Roorkee Feb-March 2005 This approach was extended by Freer et al. (1996); instead of 2 classes, the model realisations are split into 10 groups of equal number, ranked according to their objective function performance, and the cumulative distributions can be plotted to indicate parameter sensitivity

GWADI Workshop Roorkee Feb-March 2005 PREDICTION UNCERTAINTY AND GENERALIZED LIKELIHOOD UNCERTAINTY ANALYSIS (GLUE)

Uncertainties arise in model structure, parameter values and data. A popular approach to estimate and propagate modelling uncertainty is the GLUE procedure (Beven and Binley, 1992; Freer et al., 1996; Beven, 1998), which extends the RSA method discussed above.

GWADI Workshop Roorkee Feb-March 2005 The simulations are classified as behavioural or non-behavioural, and the latter are rejected. The likelihood measures of the behavioural set are scaled and used to weight the predictions associated with individual behavioural parameter sets. The modelling uncertainty is then propagated into the simulation results as confidence limits of any required percentile

GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 Regional analysis

GWADI Workshop Roorkee Feb-March 2005 REGIONALISATION

GAUGED CATCHMENT 1 I 1 θ 1 ,Φ θ 1 1

I2 GAUGED θ Φ LOCAL 2, 2 REGIONAL CATCHMENT 2 Φ* UNGAUGED MODEL θ MODEL 2 CATCHMENT* STRUCTURE STRUCTURE

I N N θ ,Φ N θ N GAUGED CATCHMENT N

θ*

I*

Q*

GWADI Workshop Roorkee Feb-March 2005 C2 C1 C2 C2 C222 C1 92 C22 32 0 12 8C192 2 C23 C21 C20 C18 C10 C0 C1 C1 C1 C1 C1 8 52 1 C0 C04 72 62 C1 C12 C097 C03 42 3 C10 C08 C15 C0 C16 = GAUGINGC11 C06 C17 2 C12 C05 2 C07 C04 2 STATION C01 40 kmC14 C13 C09 C03 N C02 C06 C05 = GAUGING STATION C01

40 km GWADI Workshop Roorkee Feb-March 2005 NO. STATION LOCATION RIVER IHDTM DTM MEAN REF. NGR AREA FLOW (km2) (m3 s-1) * C01 39053 Horley Mole TQ 527 143 91.63 1.31 C02 39069 Kinnersley Manor Mole TQ 526 146 146.17 2.09 C03 39068 Dorking Castle Mole TQ 518 150 317.2 3.61 C04 39079 Weybridge Wey TQ 506 164 903.05 6.68 C05 39011 Tilford Wey SU 487 143 391.24 3.19 C06 39078 Farnham Wey (N) SU 483 146 192.59 0.71 C07 39016 Kennet SU 464 170 1037.38 9.52 C08 39027 Pang SU 463 176 175.68 0.61 C09 39025 Enbourne SU 456 164 141.98 1.29 C10 39114 Frilsham Pang SU 453 173 90.06 0.15 C11 39115 Pang SU 455 171 108.94 0.20 C12 39019 Shaw SU 446 168 235.25 1.69 C13 39103 Newbury Kennet SU 447 167 543.73 4.52 C14 39028 Dun SU 432 168 99.84 0.71 C15 39101 Ramsbury Aldbourne SU 428 171 53.03 0.20 C16 39077 Poulton Farm Og SU 419 169 63.98 0.30 C17 39037 Marlborough Kennet SU 418 168 136.43 0.83 C18 39073 Cirencester Churn SP 402 202 83.17 0.74 C19 39020 Bibury Coln SP 412 206 107.37 1.32 C20 39042 Lechdale Leach SU 422 199 77.61 0.75 C21 39006 Newbridge Windrush SP 440 201 361.97 3.24 C22 39034 Cassington Evenlode SP 444 209 427.25 3.66 C23 39105 Wheatley Thame SP 461 205 531.54GWADI 3.63 Workshop Catchment Details. (* data obtained from the National River Flow Archive at www.nerc-Roorkee Feb-March 2005 wallingford.ac.uk). CATCHMENT UNIT DESCRIPTION CHARACTERISTIC

AREA km2 Catchment drainage area LDP km Longest drainage path BFIHOST - Baseflow index derived using the HOST classification SPRHOST % Standard percentage runoff derived using the HOST classification FARL - Index of flood attenuation due to reservoirs and lakes PROPWET - Index of proportion of time that soils are wet DPLBAR km Index describing catchment size and drainage path configuration DPSBAR mkm-1 Index of catchment steepness ASPBAR - Index representing the dominant aspect of catchment slopes ASPVAR - Index describing the invariability in aspect of catchment slopes RMED-1D mm Median annual maximum 1-day rainfall RMED-2D mm Median annual maximum 2-day rainfall RMED-1H mm Median annual maximum 1-hour rainfall SAAR mm 1961-90 standard-period average annual rainfall SAAR4170 mm 1941-70 standard-period average annual rainfall URBEXT1990 - FEH index of fractional urban extent for 1990 URBCONC - Index of concentration of urban and suburban land cover URBLOC - Index of location of urban and suburban land cover

Description of catchment characteristics (after Institute of Hydrology,GWADI 1999 Workshop). Roorkee Feb-March 2005 CATCHMENT LOCATION RIVER SPRHOST BFIHOST NO. CLAY C02 KinnersleyManor Mole 41.5 0.445 C03 DorkingCastle Mole 40.7 0.436 C01 Horley Mole 40.2 0.464 C09 Wheatley Thame 38.2 0.485 C23 Brimpton Enbourne 32.8 0.5 MIXED (1) C22 Cassington Evenlode 24.1 0.699 C04 Weybridge Wey 23 0.723 C08 Pangbourne Pang 22 0.72 C14 Hungerford Dun 21.3 0.768 MIXED (2) C07 Theale Kennet 18.7 0.767 C05 Tilford Wey 18.3 0.795 C21 Newbridge Windrush 17.2 0.79 C12 Shaw Lambourn 16.1 0.839 MIXED (3) C13 Newbury Kennet 13.6 0.848 C18 Cirencester Churn 13.5 0.844 C06 Farnham Wey (North) 12.8 0.865 C20 Lechlade Leach 12.3 0.864 C19 Bibury Coln 12.1 0.858 CHALK C15 Ramsbury Aldbourne 6.1 0.955 C17 Marlborough Kennet 5 0.959 C16 Poulton Farm Og 4.6GWADI 0.97 Workshop Catchment clusters. Roorkee Feb-March 2005 1

0.9

0.8

0.7

0.6 Nash-Sutcliffe Efficiency (NSE) Efficiency Nash-Sutcliffe

0.5

0.4 CWI_2PAR IC1_2PAR PDM_2PAR IC1_LEAK PDM_LEAK Model Structure Dorking Castle Pangbourne Tilford Marlborough

Model Structure Performance with Respect to the Nash-Sutcliffe Efficiency. GWADI Workshop Roorkee Feb-March 2005 s u =0.5(s +s )*r rk k−1 k k k-1 k rk,tk ⋅ volc tau(tk ) rt(q)

%q Q

rt(s)

GWADI Workshop Roorkee Feb-March 2005 Catchment tau Refp mf rt(q) rt(s) %(q) RMSE NSE Number C02 38.06 1.33 0.44 1.84 218.23 0.78 1.175 0.730 C03 2.82 4.48 0.93 2.78 497.51 0.77 0.796 0.740 CLAY C01 0.55 9.71 0.48 1.64 251.43 0.71 1.131 0.740 C09 6.26 2.77 1.23 3.01 191.97 0.81 0.373 0.790 C23 6.98 2.66 1.35 7.42 53.61 0.89 0.657 0.730 C22 29.04 1.44 1.02 7.10 56.02 0.62 0.290 0.870 MIXED C04 15.38 3.41 0.62 3.90 241.36 0.56 0.244 0.800 1 C08 26.81 1.79 1.65 3.27 106.56 0.15 0.070 0.890 C14 30.83 1.10 1.52 21.51 135.08 0.35 0.108 0.920 C07 26.95 1.76 1.14 7.98 91.16 0.25 0.191 0.880 C05 35.21 1.47 0.88 2.56 173.76 0.40 0.239 0.760 MIXED C21 12.76 2.90 0.76 11.72 59.10 0.36 0.183 0.900 2 C12 20.66 1.81 1.38 92.42 108.46 0.23 0.108 0.910 C13 25.92 2.27 0.88 52.18 216.52 0.81 0.169 0.890 C18 12.32 1.97 1.25 24.89 35.98 0.31 0.247 0.900 C06 29.28 1.22 1.19 2.12 106.64 0.31 0.149 0.810 MIXED C20 36.00 1.90 0.66 13.46 22.30 0.24 0.412 0.770 3 C19 18.11 2.89 0.66 32.69 68.38 0.61 0.273 0.870 C15 4.01 1.43 17.27 51.31 73.29 0.95 0.218 0.750 CHALK C17 21.39 1.41 17.59 18.62 69.40 0.37 0.241 0.820 C16 2.68 1.52 15.08 38.31 53.60 0.07 0.265 0.780

Parameter values and model fits for the CWI_2PAR model. GWADI Workshop Roorkee Feb-March 2005 1.8

1.6

1.4

1.2

1 mf 0.8

0.6

0.4

0.2

0 34 35 36 37 38 39 40 SMDBAR

Overall RMSE best fit mf versus SMDBAR. GWADI Workshop Roorkee Feb-March 2005 For a given model structure, parameter sets are generated (either based on random sampling of the feasible parameter space assuming a uniform distribution, or some known or assumed prior distribution) and the model is run using a Monte Carlo procedure

GWADI Workshop Roorkee Feb-March 2005 0.9

0.8

0.7

0.6

0.5 %(q) 0.4

0.3

0.2

0.1

0 0.4 0.5 0.6 0.7 0.8 0.9 1 BFIHOST

Overall RMSE best fit %(q) versus BFIHOST for all catchmentsGWADI. Workshop Roorkee Feb-March 2005 MODEL MOST SIGNIFICANT CATCHMENT DESCRIPTOR (CORRELATION PARAMETER COEFFICIENT) tau DPSBAR (-0.27) BFIHOST (0.19) RMED-1H (0.13) ASPVAR (-0.12) refp BFIHOST (-0.53) PROPWET (0.42) FARL (-0.42) ASPVAR (0.32) mf BFIHOST (0.53) AREA (-0.32) FARL (0.54) PROPWET (-0.05) rt(q) BFIHOST (0.53) DPSBAR (0.47) PROPWET (-0.38) FARL (0.27) rt(s) BFIHOST (-0.62) PROPWET (-0.38) DPSBAR (-0.38) ASPBAR (0.37) %(q) BFIHOST (-0.54) ASPBAR (0.32) RMED-1H (-0.23) volc BFIHOST (0.58) DPSBAR (0.54) ASPBAR (-0.44) SAAR (0.25)

GWADI Workshop Roorkee Feb-March 2005 tau = -0.4648 (DPSBAR) - 37.5915 (ASPVAR) - 4.2586 (RMED-1H) + 99.5594 (R2 = 0.514) refp = -1.1997 (BFIHOST) - 12.7610 (PROPWET) + 0.2643 (ASPVAR) - 0.2687 (FARL) + 7.0517 (R2 = 0.342) mf = -13.3104 (PROPWET) - 0.3199 (BFIHOST) + 0.00013 (AREA) + 4.9492 (FARL) + 0.8636 (R2 = 0.647) rt(q) = 29.0766 (BFIHOST) - 0.1514 (DPSBAR) -14.1469 (PROPWET) - 3.8213 (R2 = 0.741) rt(s) = -315.0290 (BFIHOST) + 1016.5670 (PROPWET) + 0.01487 (ASPBAR) - 0.0619 (DPSBAR) + 25.6877 (R2 = 0.685)

%(q) = -1.0597 (BFIHOST) + 0.00019 (ASPBAR) - 0.0031 (RMED-1H) + 1.3342 (R2 = 0.733) volc = -0.00698 (BFIHOST) – 0.00004 (DPSBAR) – 0.000004 (ASPBAR) + 0.01065 GWADI Workshop 2 (R = 0.754) Roorkee Feb-March 2005 PARAMETER CALIBRATED ESTIMATED

tau 29.2828 25.1805 refp 1.2182 1.2975 mf 1.1864 0.8528 rt(q) 2.1170 8.0050 rt(s) 106.6432 106.5143 %(q) 0.3130 0.3959 volc 0.0017 0.0021 Calibrated and regionally estimated parameter values for the Farnham catchment (C06).

GWADI Workshop Roorkee Feb-March 2005

Performance Calibrated Estimated Measure RMSE 0.149 0.189 NSE 0.81 0.69 Model performance measures for the calibrated and estimated model parameters for the Farnham catchment.

GWADI Workshop Roorkee Feb-March 2005 A Generic Framework for the Identification of Parsimonious Rainfall-Runoff Models

Thorsten Wagener and Howard S. Wheater Imperial College GWADI Workshop Roorkee Regionalised model fits for the Farnham catchmentFeb-March (C06) 2005 In conclusion:

• recent developments in stochastic analysis, including multi-objective and dynamic analysis, are opening up new horizons in hydrological modelling • these ideas were developed for simple models but are now being applied to complex physics based models • significant progress is being made in the regionalisation of hydrological models - and catchment analysis GWADI Workshop Roorkee Feb-March 2005 Performance of PDM model in estimating flood magnitudes from generalised parameter estimates (after Lamb et al., 2000)

Return period (yrs) 1.0 2.0 2.33 5.0 10.0 20.0

Mean error (%)222324252627

S.D. (%) 181819202123 Count Count

% Error % Error GWADI Workshop Roorkee Feb-March 2005 Some current research challenges:

The spatial dimension: • Spatial-temporal rainfall modelling • Semi-distributed catchment modelling (spatial structures and data conditioning) • Fully-distributed catchment modelling (parameterisation and scale)

GWADI Workshop Roorkee Feb-March 2005 Single site rainfall models

Cell duration

Cell intensity Cell

Storm

Cell arrivals

…..total (observed) intensity Storm arrivals is sum of cell intensities

GWADI Workshop Roorkee Feb-March 2005 Extreme value analysis - B-L random eta - Heathrow, July Hourly maxima

GWADI Workshop Roorkee Feb-March 2005 Launching rain events over catchment

generate • sequence of durations of rain events (2 types) and inter- event dry periods in semi-Markov process • orientations of leading and trailing edges of each event • other event parameters (including velocity) from fitted joint distribution • rain band wide enough to cover catchment for given event duration and velocity simulate • ‘within-event’ model within rain band

GWADI Workshop Roorkee Feb-March 2005 Data (lhs) and simulation (below) - winter

GWADI Workshop Roorkee Feb-March 2005 •

Spatial-temporal disaggregation, river Lee daily to hourly data GWADI Workshop Roorkee Feb-March 2005 Rainfall-Runoff Modelling Toolbox RRMT

Barbara Orellana Department of Civil and Environmental Engineering Imperial College London [email protected]

GWADI Workshop Roorkee Feb-March 2005 Rainfall-Runoff Modelling Toolbox

GUI

HYBRID MODEL ARCHITECTURE OPTIM IZATION MODULES AET

VISUAL ER P MOISTURE ANALYSIS ROUTING T ACCOUNTING Q MODULES MODULE PET MODULE

OFF-LINE DATA PROCESSING MODULES MOISTURE STATUS

GWADI Workshop Roorkee Feb-March 2005 http://ewre.cv.imperial.ac.uk

The Matlab-based RRMT and MCAT Toolboxes can be downloaded free for research users. Please note that Matlab software is required for their implementation.

GWADI Workshop Roorkee Feb-March 2005 Nash Sutcliffe Efficiency Catchment Wetness index Coefficient of Determination Ye et al. Model Structure Root Mean Squared Error Penman Absolute Bias Catchment Moisture Deficit Heteroscedastic Maximun Likelihood Bucket Structure Est. Penman Version RMSE Segmentation A No Soil Moisture Accounting RMSE Segmentation B Probability Distribution of Soil Moisture RMSE High Flows Stores RMSE Low Flows…

Shuffled Complex Evolution Algorithm Uniform Random Search

Conceptual Reservoir Two Conceptual Reservoir in Parallel Three Conceptual Reservoir in Parallel Leaky Aquifer Model Structure No Routing Component Macro-pore approach, single reservoir Macro-pore approach, parallel structure GWADITransfer Workshop Function Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005 GWADI Workshop Roorkee Feb-March 2005