A toy hydrologic model Martyn Clark and Dmitri Kavetski

1. A toy hydrologic model MartynClark and Dmitri Kavetski

2. Numerical modeling as a decision-making process • Some modeling decisions can be based on relatively well understood physical principles • Explicitly simulate snow surface energy exchanges rather than simulating melt “just” as an empirical function of temperature? • Other modeling decisions more ambiguous • How should saturation-excess runoff be represented? • What about macropore flow – is it significant or even dominant, and, if so, how should it be represented? • What is the best way to quantify (unknown) bedrock topography/permeability on sub-surface water retention? • Other modeling decisions are more pragmatic, based on the computer budget and other considerations • What is the best way to represent the spatial variability of snow depth across a hierarchy of scales? • Is the application of Beer’s Law to a single canopy layer sufficient to simulate the transmission of shortwave radiation through the forest canopy, or are more sophisticated methods required?

3. Current approaches to model development:Are they adequate? • Scrutiny during model development • Ideally, a discerning model developer will carefully scrutinize each modeling decision and thoughtfully evaluate alternatives • However, although multiple alternatives may be consideredwhen a model is developed, it is typical that only one approach is implemented and tested (or one approach is reported). • Model evaluation along the axis of complexity • Top-down approach, etc. • Effectively restricts the investigation to a single branch of the model development tree • Rejectionist frameworks, e.g., GLUE • A BYO approach to model evaluation • Model inter-comparison experiments • Weak methods for model evaluation (not focused on processes) • Difficult to attribute inter-model differences to specific processes

4. T.C. Chamberlain Advocate pursuingthe method of multiple working hypotheses • Scientists often develop “parental affection” for their theories • Chamberlin’s method of multiple working hypotheses • “…the effort is to bring up into view every rational explanation of new phenomena… the investigator then becomes parent of a family of hypotheses: and, by his parental relation to all, he is forbidden to fasten his affections unduly upon any one” • Chamberlin (1890)

5. Multi-hypothesis frameworks formodel development and refinement • The term “multi-hypothesis framework” describes any modeling framework that facilitates experimenting with different ways to represent the behavior of a system • Key requirements of a multi-hypothesis framework • Accommodate different decisions regarding process selection and representation • Accommodate different options for model architecture, representing the connectivity among different model components • Ability to separate the hypothesized model equations from their solutions • The modular approach must account for frequent interdependencies among different modeling decisions Clark, M.P., D. Kavetski, and F. Fenicia, 2011: Pursuing the method of multiple working hypotheses for hydrological modeling. Water Resources Research, 47, W09301, doi:10.1029/2010 WR009827

6. uninfluenced influenced saturated 3 6 9 12 15 18 Requirement 1: Accommodate different decisions regarding process selection and representation Consider an example conceptual model of hydrological processes

7. vertical percolation surface runoff precipitation evaporation many options . . . . . . . . . . . . VIC parameterization . . . TOPMODEL parameterization Requirement 1: Accommodate different decisions regarding process selection and representation • The modeling decisions include • Choice of state variables • Choice of processes to include/exclude • Choice of parameterizations for individual processes • For example, a possible state equation for the unsaturated zone is • Two popular models:

8. Requirement 2: Accommodate different options for model architecture Consider the “mosaic” approach to representing heterogeneity in vegetation, as in the VIC model … and contrast against other model architectures: • should different vegetation types compete for the same soil moisture? • should the architecture allow for sub-grid variability in soil moisture, to simulate the co-variability between vegetation type and water availability?

9. Requirement 3: Ability to separate the hypothesized model equations from their solutions • Many hydrologic models use ad-hoc approaches to add/subtract model fluxes from model stores in a pre-determined sequence • For example, the Sacramento model implementation is: • Compute evaporation and subtract it from tension storages • Add precipitation to the upper zone tension storage • Compute baseflow and subtract it from the lower zone storage • If precipitation was in excess of the upper zone tension storage (in step 2), then add the excess precipitation to the upper zone free storage • Compute drainage from the upper zone and move it to the lower zone • Compute surface runoff and update water storage in the impervious area. • This approach is known as “operator splitting” (OS) which allows applying specialized numerical approximations to each individual process • Numerical approximations intertwined with model equations • Unless numerical error control is implemented (very unusual), model predictions computed using the OS approach may depend on the order of processing individual model fluxes • creates an undesirable arbitrariness in model construction and behavior

10. Requirement 3: Ability to separate the hypothesized model equations from their solutions • Critically: Lack of attention applied to numerical error control • Though seemingly mundane, the numerical approximation technique has a profound impact on model behavior.. … yes, even when data is inexact and model is poor! • Recent references: • Numerical artefacts: • Clark and Kavetski (WRR2010) Ancient numerical daemons of hydrological modeling. Part 1 – Fidelity and efficiency. • Kavetski and Clark (WRR2010) Ancient numerical daemons of hydrological modeling. Part 2 – Impact on model application • Kavetski and Clark (HP2011) Numerical troubles in conceptual hydrology: Approximations, absurdities and hypothesis-testing • Time resolution effects (with discussion of causes): • Kavetski, Fenicia and Clark (WRR2011) Impact of data resolution on conceptual hydrological modeling: Experimental insights

11. Requirement 3: Ability to separate the hypothesized model equations from their solutions • Critically: Lack of attention applied to numerical error control • Though seemingly mundane, the numerical approximation technique has a profound impact on model behavior.. … yes, even when data is inexact and model is poor!

12. FUSE: Framework for Understanding Structural Errors e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

13. Define development decisions: unsaturated zone architecture e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

14. Define development decisions: saturated zone / baseflow e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

15. Define development decisions: vertical drainage e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

16. Define development decisions: surface runoff e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

17. Build unique models: combination 1 e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

18. Build unique models: combination 2 e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

19. Build unique models: combination 3 e p PRMS SACRAMENTO e p qsx S1TA qif S1F S1TB qif S1T S1F q12 q12 qb S2 qbA S2T S2FA S2FB qbB TOPMODEL ARNO/VIC e p e p qsx S1 S1 q12 q12 qb qsx S2 qb S2 GFLWR HUNDREDS OF UNIQUE HYDROLOGIC MODELS ALL WITH DIFFERENT STRUCTURE Clark, M.P., A.G. Slater, D.E. Rupp, R.A. Woods, J.A. Vrugt, H.V. Gupta, T. Wagener, and L.E. Hay (2008) Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research, 44, W00B02, doi:10.1029/2007WR006735.

20. Configure model analysis/inference software • Copy the BATEA directory to a convenient place • The “convenient place” will henceforth and hereafter be known as the “KORE_INSTALLATION” (e.g., D:/) • Set paths for your local file system • Open [KORE_INSTALLATION]BATEA\exe\bateau_fpf_director.dat and define the correct path to the template file (i.e., replace D:/ with KORE_INSTALLATION) • Open the template file defined in bateau_fpf_director.dat, and define the KORE_INSTALLATION (i.e., replace D:/ with whatever is correct) • Define the forcing data • Open file Applications\MOPEX\INF_DAT\MOPEX.INF.DAT (in directory [KORE_INSTALLATION]BATEA\) and set the name of the data file (line 3) and indices defining the start of warm-up and inference period and the end of the inference period (last line). • Define the model • Open file Applications\MOPEX\FUSEsettings\fuse_zDecisions-004.txt (in directory [KORE_INSTALLATION]BATEA\) , and define your desired modeling decisions • Start analysis/inference • Click on the appropriate executable in [KORE_INSTALLATION]BATEA\exe

21. Demonstration • Quasi-Newton optimization • Optimization menu, select Quasi-Newton • Manual Calibration • ManualC menu, select ChangeActiveD • Click DNYX button (top right) and move slider bars • Model analysis – parameter x-sections • Analyse menu, select GridObjFunk • Split-sample analysis • Save parameter file (ManualC menu, select writeParFile) and close BATEA • Modify the indices defining the start/end of the inference period: last line in file Applications\MOPEX\INF_DAT\MOPEX.INF.DAT • Start-up BATEA again and load parameter file (ManualC menu, select loadParFile) • Experiment with a different model • Define desired modeling decisions in “fuse_zDecisions-004.txt” (in directory [KORE_INSTALLATION]BATEA\Applications\MOPEX\FUSEsettings\) , and re-start BATEA • Save model simulations • ManualC menu, select writeAllDataFile

22. Exercise • Select a model and basin, calibrate the model using one time period, and evaluate the calibration using a different time period. • Repeat the exercise for a different model structure and/or different basin. • Document your observations.

23. QUESTIONS ???