# Presentation: 284655

## 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.

**Notes:**
Re 2nd Bullet:
The ETA model uses a 3-D VAR algorithm.
The VAR has more or less become the “de facto” data assimilation being used now in the NWS.

## 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.

**Notes:**
SS-SAC operation is based on Kalman filters and such has some limitations.
Main limitation is that the SS-SAC (Space State Sacramento Soil Moisture Accounting) is complicated to use (it has many parameters) and is susceptible to MAPX biases.
It is my understanding that CNRFC has tried SS-SAC in the past.
VAR is not based on Kalman filters.  VAR allows for the SAC-SMA parameters and UHG are completely transferable and VAR is not very susceptible to time-varying biases in MAPX which were limitations of the Kalman filters used in 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.

**Notes:**
A schematic of the program flow is on the next slide.
If successful, VAR will likely be added as an operation to OFS and not remain stand-alone.

## Schematic of VAR

**Notes:**
Definition or Clarification:  QINH is a discharge time series functionally equivalent to QIN, except that missing values are allowed.
The 3rd yellow box on the left (FCST) is a rating table lookup (STG in, QINH out).

## VAR

- 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 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.

**Notes:**
Billy Finn (now with USIBWC) began the project.
Refer to next slide for a picture of the basins involved.

## Project Locations

**Notes:**
Basins in red are the original 6 project basins.
Basins in blue are the additional 10 project basins added this year.
Basins in yellow are possible expansion sites if OH can use ab_opt to obtain better calibration results.  Right now there have not been enough flood cases to develop a reliable uhg and sac parameter with ab_opt.

## 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

**Notes:**
Thing to note on the range for the time to peak:
Range goes to 80 hours, however, most project sites are more in the 4-24 hour range.  
Much more of a short fuse situation.
A couple of points/limitations to remember:
VAR runs hourly but not always with an up-to-date dataset. The 4-hour data dump cycle for GOES data and the 1 to 1 1⁄2 hour delay in processing MAPX may conspire to preclude a timely input dataset.

## WGRFC Project Requirements

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

**Notes:**
We use climatological MAPE because of inaccuracies and inconsistencies from “real time” MAPE. The few MAPE sites we have tend to have ASOS equipment which lacks sunshine sensors. Even though an empirical relation has been developed between cloud cover and sunshine (CBRFC) we find climatological MAPE values just as useful.

## Project Steps

- Preparation of historical data sets for observed stage and mean areal precipitation. (WGRFC)
- Development of climatological MAPE using _C_alibration _A_ssistance _P_rogram (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)

**Notes:**
The historical datasets used are USGS streamflow values and WGRFC xmrg data from 1996 through 2002.

## 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.

**Notes:**
AB_OPT = Adjoint Based Optimizer. Contact D.J. Seo for details.

## 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.

**Notes:**
Note that the UHG defined for VAR and the UHG in the OFS may be different.
Analysis has not yet begun. We do not have a large enough historical collection of VAR vs OFS to start.

## VARPOST Forecast Group Output

**Notes:**
Yellow line up to current time is the observed data.
Yellow line in the future in the var forecast.
Blue line is the OFS 1 hour model output. NOTE: there are actually two blue lines – one with mods and one without. But since there are no mods in this example the two lines completely overlap.
Pink line is the operation 6 hour model output.
(This is a different model than the 1 hour because the SAC-SMA and UHG have been recalibrated.)

## 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.

**Notes:**
Clarification about the 2nd point:  VAR assumes the UHG is “right”. It makes no account of non-uniform precipitation. This is one weakness that WGRFC (with its highly convective precipitation regime year-round) would very much like to address.

## 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 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