# Presentation: 134203

## Advancing Hydrologic Ensemble Forecasting using Distributed Watershed Models

- Thorsten Wagener, Chris Duffy, Patrick Reed, Yong Tang, Katie Goodwin and Maitreya Yadav

- NWS Talk May 2006

- http://www.engr.psu.edu/ce/Divisions/Hydro/hydro.html

## Overall Objective

- To provide reliable forecasts of hydrologic variables for different water resources tasks, at gauged and ungauged locations, including estimates of uncertainty.
- Understanding how to build and work with a new generation of more complex distributed hydrologic models.

## Outline

- Background
- Model Building
- Calibration
- Observations/Hydrologic Theory
- Simulation

## UNCERTAINTY

## MODEL BUILDING

- MODEL

- DYNAMIC
- RESPONSE
- BEHAVIOR

**CONCEPTUAL STRUCTURE**
**FUNCTIONAL FORM**
**PARAMETER VALUES**

**WATERSHED CHARACT.**
**SYSTEM INVARIANTS**
**A PRIORI KNOWLEDGE**

**MODEL BUILDING**

- FORECASTING

- UNCERTAINTY

## Model Building Questions

- How to build distributed watershed models?
- What is the necessary degree of coupling of processes?
- What are appropriate levels of complexity for different water resources tasks?
- What are efficient ways of domain decomposition?

## Duffy et al. Approach

- 	To develop physically-based, multi-scale model for water, solute, sediment, and energy budgets in complex large-scale hydrologic systems
**MOTIVATION****:**
- to simplify complex, large-scale spatio-temporal models
- to study or uncover new and emergent physical phenomena in _coupled hydrologic systems_
- to provide reliable water, solute and energy budgets
- to estimate recharge, bank storage, ephemeral stream losses, climate and landuse effects across river basins
- to provide predictive tools for water resource forecasting

## Integrated Hydrologic Model (PIHM)

## Unstructured Grid - TINs

-  Flexibility in **fitting a complex-shaped domain **
**Ability to grade** from small to large elements over a relatively short distance
**Decrease in number of nodes**

## Nested Triangulation

-  **Seamless assimilation** of forcings and parameters at **different resolutions**
**Combine** **large-scale simulations with nested mesoscale forecasts**

**Weber River Watershed**

## General System

## Modular Modeling System (MMS)

- Background: In 1992, The USGS (George Leavesley) released a Unix-based Modular Modeling System (MMS) that incorporated their _Performance and Results Measurement System_ (PRMS) surface runoff model.
- A more generic framework, (Leavesley et al., 1996) where different modules and model structures can be selectively combined to form an _‘__**optimal**__’_ integrated model for environmental and water resources analysis.

## Major Components of MMS

- _pre-process component_
- tools to build and analyzes the input data.
- _model component_
- tools to apply the different models.
- _post-process component_
- tools to analyze the output statistically and graphically and pass the output to the decision support system or other software.

## Set-up

- A schematic showing the different conceptual components of the Modular Modeling System (MMS) (*Adapted from Leavesley et al. 1983*)

## Susquehanna River                             Basin GeoDataBase

- Climate
- Temperate (controlled by polar front, prevailing westerlies & Atlantic)
- Orographic effects (P:35-45”, ET:15-50”)
- Drainage
- 71,410 km2
- Main channel: 714 km
- Headwaters: Finger lake uplift and Appalachian mountain and plateau
- Mouth: Chesapeake Bay, MD
- Physiography
- Appalachian plateau
- Ridge & Valley
- Piedmont
- Hydrogeology
- Flat/folded sandstone and shale
- Some carbonate valleys
- Some igneous dikes, sills, and fractures

## Conceptual Hydrologic Model: Susquehanna River

## Initial Results

## Weak or Strong Coupling?

- Interception
- Snowmelt
- Evapotranspiration

- Overland flow
- Subsurface
- Channel routing

## DATA ASSIMILATION & MODEL CALIBRATION

- MODEL

- DYNAMIC
- RESPONSE
- BEHAVIOR

**INPUT**
**STATE**
**OUTPUT**

**CONCEPTUAL STRUCTURE**
**FUNCTIONAL FORM**
**PARAMETER VALUES**

**DATA ASSIMILATION & MODEL CALIBRATION**

- FORECASTING

- UNCERTAINTY

## Background

## Model Calibration/D.A. Questions

- What are efficient optimization algorithms for highly complex models?
- How can parallel computing frameworks be used for efficient model calibration?
- What are appropriate calibration strategies for distributed watershed models?

## Comparison of 3 Multi-objective Population-based Search Algorithms

- Epsilon Nondominated Sorted Genetic Algorithm-II
- Developed by Kollat and Reed (2005)
- Extension of Deb et al. (2002)
- Multiobjective Shuffled Complex Evolution Metropolis
- Developed by Vrugt et al. (2004)
- Extension of Yapo et al. (1998)
- Strength Pareto Evolutionary Algorithm-II
- Developed by Zitzler et al. (2001)
- Extension of Zitzler & Thiele (1999)

## What are efficient optimization algorithms for highly complex models?

- Testing of the efficiency and effectiveness of different multi-objective optimization algorithms resulted in improved understanding of how complex a problem can be solved in what time and with what reliability.
- Test case: Sacramento model with Leaf River Data

**RMSE(T): Box-Cox Transformed RMSE**

**RMSE(R): RMSE of raw data**

## Reliability?

- Binary metric top ranking ratios
- SPEA2 has the highest binary metric top ranking ratio (i.e., it is the most reliable algorithm)

## Convergence?

- Dynamic unary metrics (best runs)
- ε-NSGAII’s best trial run is superior to those of SPEA2 and MOSCEM-UA

## How can parallel computing frameworks be used for efficient model calibration?

## What are appropriate calibration strategies for distributed watershed models?

- Main problem: The ‘open’ calibration of complex distributed hydrologic models is too complex. How can the calibration problem be simplified?
- For the Sacramento/HLRMS framework.
- For PIHM.

## Juniata River Basin

## Sacramento/HLRMS Model Scenarios

## Sensitivity Analysis

- Which parameters dominate
- the model response?

## SensitivityAnalysis

- Sacramento Model
- at Saxton

## Hierarchical Calibration

- ANNUAL

- HOURLY

- COARSE

- DETAILED

- DATA

- MODEL

## OBSERVATIONS & HYDROLOGIC THEORY

- MODEL

- DYNAMIC
- RESPONSE
- BEHAVIOR

**INPUT**
**STATE**
**OUTPUT**

**WATERSHED CHARACT.**
**SYSTEM INVARIANTS**
**A PRIORI KNOWLEDGE**

**OBSERVATIONS & HYDROLOGIC THEORY**

- FORECASTING

- UNCERTAINTY

## Observations/Hydrol. Theory Questions

- How can our understanding about the link between watershed structure and watershed behavior be used to constrain hydrologic predictions?
- A new approach to the ungauged basins problem?
- How can we use our understanding about watershed function to decompose the model domain?

## Predictions in Ungauged Basins – October 1970

## Slide 36

## Regionalizing Watershed Behavior

## Slide 38

## Ensemble Evaluation?

- RELIABILITY: How much of the observations are contained by the ensemble?
- SHARPNESS: How wide are the ensemble prediction ranges?

## Reliability and Sharpness

- Coquet@Morwick

## Reliability and Sharpness                              per Flow Percentile

- Reliability Values

- Sharpness Values

## Multiple Response Characteristics as Constraints

- All 19 indices used as constraint on ensemble predictions

- Dove@Kirkby Mills

- Reliability = 80%
- Sharpness = 75%
- Behavioral = 1%

## Tillingbourne@Shalford

- Rainfall

- Elevation

- Hydrogeology

## Next Step: Using U.S. MOPEX Data

## SIMULATION

- MODEL

- DYNAMIC
- RESPONSE
- BEHAVIOR

- FORECASTING

**STREAMFLOW**
**INUNDATED AREAS**
**WATER QUALITY**

**SIMULATION**

- UNCERTAINTY

**CONCEPTUAL STRUCTURE**
**FUNCTIONAL FORM**
**PARAMETER VALUES**

## Simulation Questions

- How can we estimate the reliability of forecasts?
- How can we create ensemble (probabilistic) predictions of inundated areas?
- What is needed for long term simulations incl. climate change impacts (droughts & floods)?

## Probabilistic Inundation and Hazard Maps

## Acknowledgements

- Partial support for this work was provided by SAHRA under NSF- STC grant EAR-9876800, and the National Weather Service Office of Hydrology under grant numbers NOAA/NA04NWS4620012,UCAR/NOAA/COMET/S0344674, NOAA/DG 133W-03-SE-0916. We thank The British Atmospheric Data Center for providing the temperature data (http://badc.nerc.ac.uk/home/index.html).

## References

- Yang, T., Reed, P. and Wagener, T. 2006. How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration? *Hydrology and Earth System Sciences*. In Press.
- Wagener, T. and Gupta, H.V. 2005. Model identification for hydrological forecasting under uncertainty. *Stochastic Environmental Research and Risk Assessment*. DOI 10.1007/s00477-005-0006-5.
- Ajami, N.K., Gupta, H.V., Wagener, T. and Sorooshian, S. 2004. Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system. *Journal of Hydrology*, 298(1-4), 112-135.
- Yang, T., Reed, P. and Kollat, J. 2006. ... . *Advances in Water Resources*, in Review.
- Yadav, M., Wagener, T. and Gupta, H.V. 2006. Regionalization of constraints on hydrologic watershed behavior . *Advances in Water Resources*, in Preparation.
- Wagener, T. and Kollat, J. Visual and numerical evaluation of hydrologic and environmental models using the Monte Carlo Analysis Toolbox (MCAT). *Environmental Modeling and Software*, in Press pending minor Revisions.
- Vrugt, J.A., Gupta, H.V., Dekker, S.C., Sorooshian, S., Wagener, T. and Bouten, W. 2006. Confronting parameter uncertainty in hydrologic modeling: Application of the SCEM-UA algorithm to the Sacramento Soil Moisture Accounting model. *Journal of Hydrology*, In Press.
- Wagener, T. and Wheater, H.S. 2006. Parameter estimation and regionalization for continuous rainfall-runoff models including uncertainty. *Journal of Hydrology*, 320(1-2), 132-154.