Variational AssimilationVariational Assimilation(VAR)(VAR)

Presented by:

Jerry Nunn

Hydrologist In Charge

West Gulf River Forecast Center

October 28, 2003

What is VAR?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 VARPurpose 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.

VARVAR

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 VARSchematic of VAR

VARVAR

The software was originally developed on the AWIPS – HP-UX system.

July, 2003 - Software also made available in Linux format.

WGRFC currently utilizing the Linux version to capitalize on the faster processing speed.

WGRFC VAR ProjectWGRFC 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 LocationsProject Locations

Basin CriteriaBasin 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 RequirementsWGRFC Project Requirements

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

Project StepsProject 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 SoftwareAB_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 AnalysisProject 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 OutputVARPOST Forecast Group Output

Future EnhancementsFuture 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 VARPossible 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 Possible Applications for VAR (cont.)(cont.)

Flash Flooding– Site Specific– Unattended Models

ContactsContacts Please contact the following people with any

questions relating to VAR:– OHD Team :

Dongjun Seo Dongjun.Seo@noaa.gov Lee Cajina Lee.Cajina@noaa.gov

– WGRFC Team: Bob Corby Robert.Corby@noaa.gov Tracy Howieson Tracy.Howieson@noaa.gov