1. Improving hydrologic simulations Martyn Clark (and many others)

2. Outline Introduction: Why is there a problem? Approach: A more controlled approach to model development and parameter identification Discussion: Strategy to meet project deliverables

3. Subjectivity in model selection: How does the choice of model equations impact simulations of hydrologic processes? Missing processes, inappropriate parameterizations? Subjectivity in selecting/applying models Define a-priori values for model parameters Decide what model parameters we adjust, if any Decide what calibration strategy we implement, if any  Choice of objective function  Choice of forcing data and calibration period Model parameters Decide which processes to include Define parameterizations for individual processes Define how individual processes combine to produce the system-scale response Solve model equations Model structure Subjectivity in parameter identification: How does our choice of model parameters impact simulations of hydrologic processes? Compensatory effects of model parameters (right answers for the wrong reasons)? Climate change studies commonly involve several methodological choices that might impact the hydrologic sensitivities obtained. In particular:

4. 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 considered when 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 –Typically an uncontrolled 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 Key community objectives: Improved representation of observed processes More precise representation of model uncertainty Key community objectives: Improved representation of observed processes More precise representation of model uncertainty

5. Current parameter identification approaches: Are they adequate? Deterministic model calibration –The calibration process is often poorly constrained (e.g., a single objective function) –Parameters for individual model sub-components may be assigned unrealistic values during calibration in order to compensate for unreaslitic parameters in another part of the model or weaknesses in structure and uncertainty in model forcing Regionalization –Basin-by-basin calibration produces parameter sets in different basins that are fitted to the noise in the input-response data –It is difficult to establish regional relationships between calibrated model parameters and basin characteristics A-priori parameter estimation –Many model parameters are not directly observable Key community objective: Physically realistic parameter estimates from headwater catchments to continental scales Key community objective: Physically realistic parameter estimates from headwater catchments to continental scales

6. Outline Introduction: Why is there a problem? Approach: A more controlled approach to model development and parameter identification Discussion: Strategy to meet project deliverables

7. Advocate pursuing the method of multiple working hypotheses Scientists often develop “parental affection” for their theories T.C. Chamberlain 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)

8. many options The modeling decisions include –Choice of processes to include/exclude –Choice of parameterizations for individual processes –Choice of model architecture (how different methods combine to produce the system-scale response) precipitationevaporation vertical percolation surface runoff For example, a possible state equation for the unsaturated zone is............ VIC parameterization... TOPMODEL parameterization Two popular models: Understanding differences among models

9. PRMSSACRAMENTO ARNO/VICTOPMODEL pe S1TS1T S1FS1F S2TS2T S 2 FA S 2 FB q if qbAqbA qbBqbB q 12 ep q sx qbqb q 12 S2S2 S1S1 GFLWR S2S2 S1S1 ep q 12 q sx qbqb ep S 1 TA q sx q if qbqb S 1 TB S1FS1F q 12 S2S2 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. FUSE: Framework for Understanding Structural Errors

10. The multiple-hypothesis framework: A “more controlled” approach to model evaluation 10 Isolate hypotheses Accommodate different decisions regarding process selection Accommodate different options for model architecture Separate the hypothesized model equations from their solutions Evaluate hypotheses Sensitivity analysis (understand reasons for inter-model differences) Extensive evaluation using research data (test internal components of the model) Clever use of routine observing networks (“large sample” hydrology, but not as you know it).

11. Build multiple-hypothesis representation of “treetop to stream” domain 369121518 snow soil Facilitates experimenting with.. 1) Different constitutive functions & parameters Albedo, turbulent heat transfer Soil hydraulic properties 2) Model architecture Surface water – groundwater interactions Sub-grid variability and lateral flow of water

12. Modeling approach Numerical implementation Fine spatial discretization Adaptive sub-stepping with numerical error control (tight tolerance) Fine-grain modularity, with numerical solutions clearly separated from model physics Most subroutines return fluxes and their derivatives, which are used in solver routines Limited use of existing multi- physics codes (e.g., Noah- MP) 12

13. Example modeling decisions 13 Parameterizations –Snow Different snow albedo parameterizations Different thermal conductivity parameterizations Different compaction parametrizations –Turbulent heat transfer Different atmospheric stability parameterizations –Transpiration (from Noah-MP) Different soil stress and stomatal resistance functions –Storage and transmission of liquid water in soil Different forms of Richards’ equation Flexibility in the choice of hydraulic conductivity profile Flexibility in choice of lower boundary condition –Vegetation traits Different parameterizations for veg roughness and displacement height Architecture –Groundwater parameterizations Non-interactive VIC-style, interactive Topmodel style, mixed form of Richards’ equation –Overall model architecture Representation of spatial variability, linkages among components > 100 model parameters

14. Example: Turbulent exchange coefficients

15. Example: Transmission and storage of liquid water within the snowpack

16. Example simulations for Reynolds Creek, Idaho

17. 17 Datasets from: Reba et al. (WRR, 2011) Flerchinger et al. (JHM, 2012)

18. 18

19. Simulations of longwave fluxes above the Aspen grove Comparison of 1)combined surface-atmosphere and canopy-atmosphere longwave radiation fluxes (FUSEv2 model) 2)above-canopy upward longwave observations (Flerchinger, 2012) MODEL OBS (missing data)

20. Simulations of below-canopy windspeed Uses serially-complete forcing from exposed site to enable multi-decade simulations Simulated below-canopy windspeed (red) compared with observed below-canopy windspeed (blue)

21. Partitioning of energy between sensible and latent heat Total sensible heat fluxTotal latent heat flux FUSEv2 simulations Eddy flux observations Two issues: 1)Parameterization uncertainty: impacts of seasonally frozen ground on surface runoff during the melt season and plant-available water in the growing season 2)Architectural uncertainty: non-local sources of soil moisture in the growing season

22. Spatial variability and hydrologic connectivity 22 Hydrologic response units –Different meteorological forcing –Different frozen precipitation multipliers –Different vegetation and terrain properties Hydrologic connectivity –Fluxes in each HRU computed individually –Use dynamic TOPMODEL and DHVSM concepts # to compute flow between HRUs # Modeling approach:  No prognostic water table Baseflow computed based on ratio of total water storage in the soil column to total storage capacity Net baseflow flux (outflow – inflow) added as a sink term to Richards’ equation  Use of HRUs instead of a high-resolution grid With connectivity

23. Distributed simulations – without connectivity

24. Distributed simulations – with connectivity

25. Outline Introduction: Why is there a problem? Approach: A more controlled approach to model development and parameter identification Discussion: Strategy to meet project deliverables

26. Summary of model structure analysis Status: Built a comprehensive multiple-hypothesis “process-based” hydrologic model for the domain treetops to stream –Framework useful to identify a sub-set of “satisfying” modeling options and improve simulations of hydrologic processes –Framework useful for physics-based estimates of uncertainty Multi-physics models (multiple parameterizations for individual processes) not be necessary to quantify model uncertainty – it’s the parameters, stupid! Differences in model architecture are critical Ongoing work: Understand impact of the (subjective) decisions made during model development –Extensive analysis using data from research basins –Attribute inter-model differences to choice of both model parameterizations and model architecture Medium-term goal: Use framework for ensemble continental-scale hydrologic simulations –Improve simulations of hydrologic processes –Quantify model uncertainty from a physical perspective

27. Planned steps for parameter estimation Low dimensional multi-response inference –Identify the “mapping” between different model parameters and different diagnostic signatures of hydrologic behavior –Decompose the high-dimensional problem (prone to compensatory errors) into a set of lower-dimensional sub-problems –Use a mix of local-scale and large-scale signatures to avoid over-fitting to the idiosyncrasies of individual watersheds Focus attention on the parameters in pedotransfer functions (and other transfer functions), rather than the model parameters themselves

28. Key deliverable: multi-model simulations of climate change impacts Model fidelity –Incremental progress: Improve estimates of parameters in a small set of existing models –More noteworthy advance: Improve representation of physical processes using modeling options available in FUSEv2 Model uncertainty –Incremental progress: Use inter-model difference as a proxy for model uncertainty –More noteworthy advance: Quantify uncertainty using a mix of parameter perturbations and model structural choices