HOW WELL DOES A MODEL REPRODUCE

Transcription

1 HOW WELL DOES A MODEL REPRODUCE HYDROLOGIC RESPONSE? Lessons from an inter-model comparison Riddhi Singh, Basudev Biswal Department of Civil Engineering Indian Institute of Technology Bombay, India 2018 SWAT Conference, IIT Madras January 10-12, 2018

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3 Catchments are complex systems Kelleher et al. 2013, PhD Dissertation 3

4 The goal of modelling efforts is to abstract these complex systems to as to enable: 1. Hypothesis testing 2. Prediction: floods & droughts, climate change Image: (left) (right) 4

5 Streamflow e 1 e 2 e 3 A goodness-of-fit statistic or objective functions quantifies the distance between model output and observations X t M f (, X t 1, I t 1 ) O t M g (, X t 1, I t 1 ) Obs t Obs t MODEL (M) I t O t e t Obs t O t O t State update (X t ) Time, t Total error E(,Obs, X o ) f (e 1,e 2,...,e t,...) Common objective functions such as the NSE, RMSE, or percentage bias collapse this information into a single value 5

6 Most common objective function lead to un-identifiability of one or more model parameters Generally, parameters that fit the peaks well are identified by squared error metrics. All simulations yield an RMSE value of 0.60! Only some parameters are identifiable using RMSE. Wagener et al. 2003, DYNIA, Hydrological Processes 6

7 Streamflow Challenges in model structure and parameter identification RMSE f e1 e2 e t ( ), ( ),..., ( ) 1. Loss of information of time series errors in a single value. 2. Squared error metrics tend to focus on fitting the peak flows 3. No clear guidelines for cutoffs of high versus low performance O t e 1 e 2 e 3 Time, t Obs t Equifinality of model structures and parameters 7

8 Recent studies suggest a modular approach to model building Clark et al., 2015, SUMMA, WRR 8

9 Beyond NSE: including hydrologic signatures in model assessment Pareto dominance based multiobjective optimization yields the highest level of consistency among all formulations. Single Multiple Shafi and Tolson, 2015, Optimizing hydrological consistency by incorporating hydrological signatures into model calibration objectives, WRR 9

10 Our study: compare model performance for a proposed routing structure Pure overland flow (POF) Reality Biswal and Singh, 2017, AWR Mixed surface-subsurface flow (MSSF) Image source: The two flow components can then be modelled separately. 10

11 Discharge [day -1 ] The geomorphic hydrological response model (GHRM) Pure overland flow (POF) Mixed surface subsurface flow (MSSF) Time [day] Biswal and Singh, 2017, AWR 15

12 Soil Moisture Accounting Module Unit hydrograph [mm/day] Unit hydrograph [mm/day] Snow Module Unit hydrograph [mm/day] We create two model structures based on GHRM and compare it against a liner reservoir type routing Effective rainfall generation* P, T Geomorphology driven Quick flow GHRM Linear routing AE No T>T t* T>T b* Yes C max * M S(t) b* ER1 ER2 Yes No M=min(S s, (T-T b *) x D*) ER Snow Storage, S s ER ER v * s α * Time [days] Slow flow v d * v s*, v d * v s * Time [days] Q q Q s Q GHRM-NS Q ER α * Quick flow linear reservoir K q * Slow flow linear reservoir K s * Q q Q s Q C(t) Time [days] *The probability distributed model Routing Biswal and Singh, 2017, AWR 7

13 Flow Flow Indicator 2 Flow Identifying the behavioral parameter space using multiple ecologically relevant indicators Models Effective rainfall Linear Quick flow Water balance parameters Routing parameters Uniform random sampling Simulations Multiple indicator analysis PDM Effective rainfall GHRM Slow flow POF Uniform random sampling Θ 1,routing x 3 Uniform random sampling Time Pareto front PDM Effective rainfall MSSF GHRM-NS Θ snow, soil x 5 Θ 2,routing x 3 Uniform random sampling Time Indicator 1 PDM GHRM GHRM-NS PDM Only MSSF Θ 2, routing (no split) x 2 Time Biswal and Singh, 2017, AWR 13

14 Using multiple objectives allows us to obtain envelopes of streamflow for each model Biswal and Singh, 2017, AWR 14

15 Indicator 2 We find significant spatial variation in the contribution of each model to the Pareto optimal set Multiple indicator analysis Pareto front Indicator 1 PDM GHRM GHRM-NS Biswal and Singh, 2017, AWR Contribution to Pareto set [%] Linear GHRM GHRM-NS Watershed Note: clusters are delineated for groups of 3 or more watersheds 15

16 NSE performance of the three model structures was comparable Biswal and Singh, 2017, AWR 16

17 A multi-dimensional assessment of model performance 1 Linear 2 GHRM 3 GHRM-NS Biswal and Singh, 2017, AWR 17

18 Partitioning of flow varies significantly between linear routing and geomorphological routing CDF [-] CDF [-] CDF [-] Watershed location is shown by a circle and color denotes the model with maximum contribution to the Pareto sets Alpha [-] Biswal and Singh, 2017, AWR Alpha [-] Linear GHRM Alpha [-] Cumulative distribution of split parameter across the Pareto optimal sets shows very different behavioral ranges for the linear and geomorphic models. 18

19 Q ave [mm/day] The recession behavior changes considerably between linear and geomorphology based models Simulations for the Pareto optimal set with the best NSE value for each model Linear GHRM GHRM-NS Observed dq/dt [mm/day] dq/dt [mm/day] dq/dt [mm/day] Watershed location is shown by a circle and color denotes the model with maximum contribution to the Pareto sets Biswal and Singh, 2017, AWR 19

20 Q ave [mm/day] Q ave [mm/day] Q ave [mm/day] The recession behavior changes considerably between linear and geomorphology based models Simulations for the Pareto optimal set with the best NSE value for each model Linear GHRM GHRM-NS Observed Watershed location is shown by a circle and color denotes the model with maximum contribution to the Pareto sets Thank you! dq/dt [mm/day] dq/dt [mm/day] dq/dt [mm/day] Biswal and Singh, 2017, AWR 20