# Presentation: 929361

## Parameterization and Parameter Estimation of 

**Koray K. Yilmaz****	****	****Maitreya Yadav**
**Hoshin Gupta****	****	****	****Thorsten Wagener**
- _[koray@hwr.arizona.edu](mailto:koray@hwr.arizona.edu)__, __[hoshin.gupta@hwr.arizona.edu](mailto:hoshin.gupta@hwr.arizona.edu)__,__	__[thorsten@engr.psu.edu](mailto:thorsten@engr.psu.edu)__, __[muy125@psu.edu](mailto:muy125@psu.edu)_** **** **

**NWS OFFICE OF HYDROLOGIC DEVELOPMENT**
**Annual Meeting, 01/20/2006**

**Parameterization and Parameter Estimation of **
**Distributed Models For Flash Flood and River Prediction**

## Objectives

-  **Distributed parameter estimation - automated and/or semi-automated  **
**	****(e.g. regularization)**

-  **A priori methods for parameter estimation in un-gauged basins using direct ****	****inference from watershed properties and statistical regression analysis**

**Objectives**

## Work Completed Until Previous Annual Presentation (01/17/05)

**Work Completed ****Until Previous Annual Presentation ****(01/17/05)**

** ****Hydrology Laboratory-Research Modeling System (HL-RMS) was implemented ****	****at the University of Arizona and tested **

** ****Literature review of the frameworks developed for incorporating watershed **
**	****physical properties (i.e. geology, soil properties, remote sensing)**
**	****to model structure identification and parameter estimation **

## Integrated Strategy (Presentation 1/17/05)

- INVARIANTS

- MODEL

- DYNAMIC
- RESPONSE
- BEHAVIOR

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

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

**DATA**
**ASSIMILATION**

**TOP-DOWN**

**BOTTOM-UP**

**WATERSHED**
**A PRIORI KNOWLEDGE**

**DYNAMIC              TO STATIC**

**STATIC                  TO DYNAMIC**

**Integrated Strategy (Presentation 1/17/05)**

## Work Completed During Current Project Year (01/17/05–01/20/06)

**Work Completed ****During Current Project Year ****(01/17/05–01/20/06)**

** ****Hydrology Laboratory-Research Modeling System (HL-RMS) was linked to a ****	****automated optimization algorithm called “MOSCEM” (Multi Objective ****	****Shuffled Complex Evolution – Metropolis) – enables optimization of a ****	****priori parameter **_**multipliers**_

** ****A model diagnostic interface was developed using MATLAB****®**** environment**

** **_**A study was undertaken to**_** : **
** ****Analyze the consistency**** between the a-priori parameter information and the information contained in the input-output data, using **_***multi-objective optimization***_
** ****Analyze the relationship**** between the **_***uncertainty in the soil hydraulic parameters***_** and the uncertainty in the hydrologic model parameters**
** ****Create an uncertainty framework**** to constrain ensemble predictions in ungauged watersheds **_***utilizing watershed indices***_

## Model Diagnostics

**Model Diagnostics**

**Sandy**

**Clayey**

**Blue River**

_**SOIL TEXTURE**_

** ****HL-RMS **
**    ****with a priori (Koren et al. 2000) **
**    ****model parameters**

## Constraining Parameters of HL-RMS (Distributed Model)

**Constraining Parameters of HL-RMS (Distributed Model)**

**Reduce the high dimensionality**
** ****of the optimization problem**

**a priori information**

**Optimization using MOSCEM**

**Allow MULTIPLIERS to vary within a range, so that model parameters are physically meaningful**

**Assume spatial pattern of **
**model parameters are well-defined by**
**a priori framework of Koren et al. (2000)**

**Optimize the a-priori parameter grid MULTIPLIERS using Input-Output response information**

**Blue River**

## Multi-Objective Optimization Setup

**Multi-Objective Optimization Setup**

| O | observed flow |
| --- | --- |
| M | model simulated flow |
| θ | Model parameter multiplier |

| Gd |   Scaling function for FDATA |
| --- | --- |
| Gp |   Scaling function for FPAR |

| σd |   error deviation of flow measurement (driven) |
| --- | --- |
| σn |   error deviation of flow measurement (non-driven) |

| Wd |   Scaling function for driven flow |
| --- | --- |

| P |   Number of optimized parameter multipliers |
| --- | --- |

| D | Driven flow time steps |
| --- | --- |
| N | Non-Driven flow time steps |

|  |   Weighting parameter |
| --- | --- |

## e

**Error Variance of Streamflow Measurements**

** **_**Wavelet filtering/denoising**_**  **

_**Mother Wavelet**_
**Symlet8**

_**Denoising Method**_
**Level thresholding**

**Time Step (hours)**

**e**

**FLOW TIME SERIES**

## Error Variance of Streamflow Measurements

**Error Variance of Streamflow Measurements**

**BARON FORK  BASIN**

** **_**Wavelet filtering/denoising**_**  **

_**Mother Wavelet**_
**Symlet8**

_**Denoising Method**_
**Level thresholding**

**BARON FORK BASIN**

**FLOW TIME SERIES**

## Multi-Objective Optimization

**Multi-Objective Optimization**

## Multi-Objective Optimization

_**MODEL PARAMETER GRID MULTIPLIER SENSITIVITY TO DATA**_

**Parameter Grid Multiplier**

_**BARON FORK RIVER**_

**Parameter**

**Multi-Objective Optimization**

## Multi-Objective Optimization

**Feasible Space**

**Objective Function**

**Low**

**High**

_**MODEL PARAMETER GRID MULTIPLIER SENSITIVITY TO DATA**_

_**BARON FORK RIVER**_

**Multi-Objective Optimization**

**Parameters**

**Data**

## Multi-Objective Optimization

**Baron Fork River – Calibration Period**

**Multi-Objective Optimization**

** **_**Comparison of observed and simulated flows**_**  **

## Multi-Objective Optimization

**Baron Fork River – Verification Period**

**Multi-Objective Optimization**

** **_**Comparison of observed and simulated flows**_**  **

## Multi-Objective Optimization

**Multi-Objective Optimization**

**Until Now...**

**Sacramento Model**
**Conceptual **
**Parameters**

**DATA**

**Soil Hydraulic**
** ****Parameters**

**Soil Texture**

**Pedotransfer **
**Functions**

**Koren **
**Equations**

**Calibration**

**Next...**

**Incorporate Uncertainty**

## Analysis of Uncertainty in Soil Hydraulic Parameters 

**USDA Soil Texture Triangle**

**Analysis of Uncertainty in Soil Hydraulic Parameters **

| LEVEL “0”
 INFO | SOIL HYDRAULIC 
PARAMETERS |  | MODEL PARAMS |
| --- | --- | --- | --- |
| % SAND | θsat | θfld | UZTWM |
| %CLAY | Ψsat | θwlt | UZFWM |
| CN | Ψfld | μ | UZK |
| Ds | Ψwlt |  | ZPERC |
|  | b |  | REXP |
|  | Ks |  | PFREE |
|  |  |  | LZTWM |
|  |  |  | LZFPM |
|  |  |  | LZFSM |
|  |  |  | LZPK |
|  |  |  | LZSK |

**PEDOTRANSFER**
**FUNCTIONS**

**PEDOTRANSFER**
**FUNCTIONS**

**KOREN**
** ****EQUATIONS**

**CN  : Curve Number**
**Ds   : Stream Channel Density**
**θ****      : Soil moisture content**
**Ψ****     : Matric potential**
**Ks   : Hydraulic conductivity @ saturation**
**μ      : Specific Yield**

## Analysis of Uncertainty in Soil Hydraulic Parameters 

**USDA Soil Texture Triangle**

**Analysis of Uncertainty in Soil Hydraulic Parameters **

| LEVEL “0”
 INFO | SOIL HYDRAULIC 
PARAMETERS |  | MODEL PARAMS |
| --- | --- | --- | --- |
| % SAND | θsat | θfld | UZTWM |
| %CLAY | Ψsat | θwlt | UZFWM |
| CN | Ψfld | μ | UZK |
| Ds | Ψwlt |  | ZPERC |
|  | b |  | REXP |
|  | Ks |  | PFREE |
|  |  |  | LZTWM |
|  |  |  | LZFPM |
|  |  |  | LZFSM |
|  |  |  | LZPK |
|  |  |  | LZSK |

**PEDOTRANSFER**
**FUNCTIONS**

**PEDOTRANSFER**
**FUNCTIONS**

**KOREN **
**EQUATIONS**

**CN  : Curve Number**
**Ds   : Stream Channel Density**
**θ****      : Soil moisture content**
**Ψ****     : Matric potential**
**Ks   : Hydraulic conductivity @ saturation**
**μ      : Specific Yield**

## Analysis of Uncertainty in Soil Hydraulic Parameters 

**Analysis of Uncertainty in Soil Hydraulic Parameters **

**Propagation of Uncertainty through Pedotransfer Functions**

## Analysis of Uncertainty in Soil Hydraulic Parameters 

| Feasible Parameter Ranges |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Upper | 300 | 150 | 0.75 | 350 | 5 | 0.8 | 500 | 1000 | 400 | 0.05 | 0.35 |
| Lower | 10 | 5 | 0.10 | 5 | 1 | 0 | 10 | 10 | 5 | 0.001 | 0.01 |

**Analysis of Uncertainty in Soil Hydraulic Parameters **

**Propagation of Uncertainty through Model Parameters**

## Open Question? 

**Open Question? **

**The presented approach is so far based on the use of small scale**
**data to parameterize the model. The approach is thus**
**limited by the type of information contained in this data, e.g. **
**problem with recession.**
**How can we include watershed scale behavior to constrain **
**the model at ungauged sites?**

## Constrain Ensemble Predictions 

**Constrain Ensemble Predictions **

**The regionalization of model parameters is limited by model structural**
**problems, problems of formulating the calibration task, data error etc.**
**A different approach is the regionalization of watershed behavior!**

**Pilot study using 30 UK watersheds.**

## Initial test regionalizing two characteristics:

**Initial test regionalizing two characteristics:**
**[1] The Runoff Ratio (Runoff/Precipitation)**
**[2] Mean slope of the flow duration curve (FDC Slope)**

**Watershed characteristics used are DPSBAR (topographic slope)**
**and BFIHOST, a baseflow index derived from physical characteristics.**

## Using a simple 5-parameter hydrologic model as test case:

**Using a simple 5-parameter hydrologic model as test case:**
**(Remember that the approach is generally model independent!)**

**We ran a Uniform Random Sampling selecting 10,000**
**Parameter sets from the a priori feasible space.**

## We can constrain the feasible parameter and therefore the output space

**We can constrain the feasible parameter and therefore the output space**
**using the regionalized dynamic behavior at the ungauged site:**

## We can combine different constraints to achieve even ‘sharper’ predictions:

**We can combine different constraints to achieve even ‘sharper’ predictions:**

## Conclusions

**Conclusions**

**Investigated a structured & logical Multi-Criteria Approach **
**	****to assimilating Information into a distributed hydrologic model: **
**  ****A-priori Watershed Properties information (local information)**
**  ****Watershed Input-Output Response information (global information)**

**Includes a way to handle estimates of uncertainty:**
**  ****Watershed Soil Property uncertainty**
**  ****Streamflow Data uncertainty**

**Towards ensemble predictions in gauged and ungauged watersheds utilizing information derived at different scales**

## Future Work

**  ****Improved Handling of Multipliers**
**     ****- Currently highly effected by the outliers in the a priori parameter grids**
**     ****- Will look into clustering, non-linear transformation techniques**
**  ****Procedures for Diagnosing & Fixing Model Deficiencies**
**  ****Constraining hydrologic model behavior in ungauged basins within an uncertainty framework using regionalized watershed behavior**
**  ****More Complete Treatment of Uncertainty**
**    ****- Uncertainty arising from the pedotransfer functions**
**    ****- other aspects such as input, model structure uncertainty**

**Future Work**

## Recent References for more Information

** ****Wagener, T. and Gupta, H.V. 2005. Model identification for hydrological forecasting under uncertainty. *****Stochastic Environmental Research and Risk Analysis*****. DOI 10.1007/s00477-005-0006-5.**
** ****Yadav, M., Wagener, T. and Gupta, H.V. Regionalization of dynamic watershed behavior. In Andréassian, V., Chahinian, N., Hall, A., Perrin, C. and Schaake, J.  (eds.) **_**Large sample basin experiments for hydrological model parameterization Results of the MOdel Parameter Estimation Experiment (MOPEX) Paris (2004) and Foz de Iguaçu (2005) workshops**_**. IAHS Redbook.** **In Press.**
** ****McIntyre, N., Lee, H., Wheater, H.S., Young, A. and Wagener, T. 2005. Ensemble prediction of runoff in ungauged watersheds. *****Water Resources Research*****, 41, W12434, doi: 10.1029/2005WR004289.**
**Wagener, T. and Wheater, H.S. 2006. Parameter estimation and regionalization for continuous rainfall-runoff models including uncertainty. *****Journal of Hydrology*****. In Press. (*****Available online 2 September 2005*****)**
** ****Hogue, T.S., Yilmaz, K., Wagener, T. and Gupta, H.V. Modeling ungauged basins with the Sacramento model. In Andréassian, V., Chahinian, N., Hall, A., Perrin, C. and Schaake, J.  (eds.) **_**Large sample basin experiments for hydrological model parameterization Results of the MOdel Parameter Experiment (MOPEX) Paris (2004) and Foz de Iguaçu (2005) workshops**_**. IAHS Redbook.** **In Press.**

**Recent References for more Information**