Improving hydrologic simulations

Martyn Clark (and many others)

Outline

• Introduction: Why is there a problem?

• Approach: A more controlled approach to model development and parameter identification

• Discussion: Strategy to meet project deliverables

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 functionChoice 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:

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

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

Outline

• Introduction: Why is there a problem?

• Approach: A more controlled approach to model development and parameter identification

• Discussion: Strategy to meet project deliverables

Advocate pursuingthe 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)

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• 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)

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• Two popular models:

Understanding differences among models

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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

The multiple-hypothesis framework:A “more controlled” approach to model evaluation

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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).

Build multiple-hypothesis representation of “treetop to stream” domain

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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

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)

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Example modeling decisions

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• 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

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Example: Turbulent exchange coefficients

Example: Transmission and storage of liquid water within the snowpack

Example simulations for Reynolds Creek, Idaho

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

2012)

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Simulations of longwave fluxes above the Aspen groveComparison of

1)combined surface-atmosphere and canopy-atmosphere longwave radiation fluxes (FUSEv2 model)2)above-canopy upward longwave observations (Flerchinger, 2012)

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(missing data)

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)

Partitioning of energy betweensensible and latent heat

Total sensible heat flux Total latent heat flux

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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

Spatial variability and hydrologic connectivity

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• 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

Distributed simulations – without connectivity

Distributed simulations – with connectivity

Outline

• Introduction: Why is there a problem?

• Approach: A more controlled approach to model development and parameter identification

• Discussion: Strategy to meet project deliverables

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

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

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