Variational Assimilation (VAR) Presented by: Jerry Nunn Hydrologist In Charge West Gulf River Forecast Center October 28, 2003

What is VAR?  Software that produces initial estimates of soil moisture content for SAC-SMA.  Based on variational assimilation popularized by widespread use in meteorology and oceanography.  Solves large-scale inverse problems in dynamic systems via least squares minimization.

Purpose for VAR  Given the latest streamflow observation, MAPX and MAPE estimates, and the initial SAC-SMA state variables: – VAR adjusts the SAC-SMA state variables and the MAPX and MAPE estimates such that the resulting model simulation matches the observed.  Allows the forecaster to start with more accurate SAC – SMA states for forecast runs.  Possible replacement of the current OFS operation; SS-SAC.

VAR  VAR is currently a stand-alone program that runs independent of OFS, however, it uses data stored within OFS. – VAR ingests time series data from OFS in a text format. – VAR also utilizes special decks that include the SAC- SMA parameters and unit hydrograph definitions. – After VAR completes, it outputs time series data that can be ingested back into OFS.

Schematic of VAR

VAR  The software was originally developed on the AWIPS – HP-UX system.  July, Software also made available in Linux format.  WGRFC currently utilizing the Linux version to capitalize on the faster processing speed.

WGRFC VAR Project  Implemented in 2002 – Original project consisted of 6 headwater basins located in eastern Texas  Expanded project in 2003 – Added 10 basins throughout Texas  This was done to account for the varied hydrologic conditions throughout the WGRFC area.

Project Locations

Basin Criteria  Basins selected for the VAR project had to meet the following criteria: – Headwater basin – Basin defined in operational model – Hourly stage data available  Candidate basins also needed to vary in the following areas: – Basin Size (50 – 700 square miles) – Time to peak in the unit hydrograph (4 –80 hours) – Diverse basin shape and geomorphology

WGRFC Project Requirements  Hourly stage data  Hourly MAPX  Climatological MAPE  Calibrated 1 hour SAC-SMA parameters  1 hour unit hydrograph  OFS segment definition

Project Steps  Preparation of historical data sets for observed stage and mean areal precipitation. (WGRFC)  Development of climatological MAPE using Calibration Assistance Program (CAP). (OHD)  Development of 1 hour unit hydrograph. (OHD)  Refinement of SAC-SMA parameters for use in a 1 hour model. (OHD)  Creation of all required OFS components. (WGRFC)

AB_OPT Software  Created by OHD for assistance in the implementation of VAR. – Available in both a HP-UX and Linux version.  Ingests historical stage and MAPX data.  Software estimates long term biases in MAPX and MAPE climatology based upon the historical data.  Uses these biases to develop a 1 hour empirical unit hydrograph and refined SAC-SMA parameters.

Project Analysis  Project Output – 1 hour VAR adjusted time-series (VAR) – 1 hour SAC-SMA time-series (OFS)  Without modification  With forecaster modification – 6 hour operational SAC-SMA time-series (OFS)  All time-series mentioned above are produced and archived hourly for analysis purposes.

VARPOST Forecast Group Output

Future Enhancements  Expansion to non-headwater locations – Routed flow locations – Reservoirs  Inclusion of unit hydrograph theory in the VAR process – Currently VAR will only make modifications based on rainfall, evaporation and sac-sma parameters.

Possible Applications for VAR  Enhancement to RFC Models – Provides a way to maintain the SAC-SMA contents. – Better initialization of SAC-SMA contents will allow for improved forecasts.  Distributed Modeling  Development of new software for use by field offices – (i.e. AB_OPT)

Possible Applications for VAR (cont.)  Flash Flooding – Site Specific – Unattended Models

Contacts  Please contact the following people with any questions relating to VAR: – OHD Team :  Dongjun  Lee – WGRFC Team:  Bob  Tracy