The system is presently implemented in the Colorado River Basin, portions of the Sierra Nevada, and portions of the Columbia River Basin.

Water supply is also forecasted with conceptual models. The National Weather Service uses the Extended Streamflow Prediction (ESP) technique as part of the NWS River Forecast System (NWSRFS) to perform long-term forecasts of streamflow. ESP uses current streamflow, soil moisture, and snowpack conditions along with historical time series of precipitation and temperature to estimate future streamflow conditions. Based on the likelihood of future precipitation and temperature time series, the resulting streamflow hydrographs can be analyzed to produce probabilistic forecasts of streamflow peaks, volumes, etc.

Because of the difficulty in accurately estimating precipitation in the mountains, the estimates of the initial conditions provided to the models are often inaccurate. The reliability of ESP forecasts can be increased by using snow water equivalent observations to update model-simulated snow cover conditions. The Snow Estimation and Updating System (SEUS), developed by the National Weather Service, was created for this task. The SEUS utilizes existing ground and airborne snow water equivalent observations, providing better estimates of snowpack conditions for making water supply forecasts (Day, 1990).

Gridded, line, and point data created and used by SEUS is managed by the Geographic Resources Analysis Support System (GRASS) GIS. GRASS is a raster-based public-domain GIS developed for UNIX platforms by the U.S. Army Construction Engineering Research Laboratory (USACERL). GRASS was chosen in the development of SEUS because new functions can be added easily with scripts utilizing GRASS commands or with new commands utilizing GRASS C library routines. SEUS calibration, operational, and administrative processes are simplified by providing a graphical user interface for the user.

For purposes of illustration, the basin "Kings River at Pine Flats", located on the western slope of the Sierra Nevadas in central California (Figure 1), will be used to demonstrate different outputs of SEUS calibration, operation, and updating components. This basin has a drainage area of approximately 1500 square miles, ranges from 900 to 13100 feet in elevation, and averages approximately 32 inches of winter precipitation.

*Figure 1. Basin "Kings River at Pine Flats".*

where,

Z = standardized deviate, x = snow water equivalent observation, = long-term temporal mean, = long-term temporal standard deviation,A gridded snow water equivalent estimate is created by correlating points based on their distance from each other. This requires an estimate of the spatial correlation function of the standardized data. A correlation function was developed for each basin for the first of each month of the snow season using historical station data. This function is expressed as the correlation between each station pair as a function of distance. The equation

where

= correlation coefficient, c,d = regression coefficients, x = distance between pointsis used to fit the data. Figure 2 illustrates this relationship for the Kings River at Pine Flats for the month of January.

*
Figure 2. Correlation-distance function for Kings River at Pine Flats. *

*
*
Given station means and standard deviations and a basin correlation function, point snow water
equivalents can be transformed into standardized deviates and a gridded interpolated field of
standardized deviates can be produced. However, a gridded field of snow water equivalent is
really desired. To transform the standardized deviate grid into a snow water equivalent grid, an
estimate of the mean and standard deviation of the snow water equivalent at each grid point is
needed.

Estimates of the standard deviation of snow water equivalent at a grid point are formed from a mean-standard deviation relationship derived from historical snow water equivalent data for the first of each month of the snow season. The form of this relationship is assumed to be:

where

= standard deviation, a,b = regression coefficients, and = mean.Figure 3 illustrates this relationship for the Kings River at Pine Flats for the month of January.

*
Figure 3. Mean-standard deviation relationship for Kings River at Pine Flats.*

*
*
Using this relationship, transforming a standardized deviate grid into snow water equivalent grid
is now solely a function of the mean snow water equivalent at a point.

Modeling mean snow water equivalent at individual grid points could be extremely computationally intensive given the size of a basin, the grid resolution, and the length of the historical record. As a way of expediently modeling mean snow water equivalent, grid points are lumped into zones based on common snow melt characteristics. First, melt factor classes are formed as a function of aspect, slope, and forest cover. Aspect and slope, both computed from digital elevation data, are combined to form a new surface representing an index of available solar radiation. East and west-facing slopes are assumed to receive the same amount of solar radiation over a day as a horizontal surface. Consequently, for the purposes of SEUS, the available solar radiation is represented by three classes: north, south, and horizontal. Vegetation data is classified into forested and open areas. These solar radiation and vegetation classes produce six melt factor classes.

Melt at a grid point is a function of temperature as well as melt factor. Since temperature is well correlated with elevation, temperature-induced melt is determined by choosing representative elevations within the basin. The GIS is used to derive the range of elevations within the basin, and along with subarea cutoff elevations from the NWSRFS basin model, representative elevations are chosen which define the range of elevation data.

Given these melt factor classes, the list of representative elevations, and the mean areal temperature (MAT) and mean areal precipitation (MAP) time series for the basin, the NWSRFS snow model can compute a mean snow water equivalent for a point within a basin. The melt factors in the snow model are adjusted to represent each melt factor class, the MAT time series is lapsed from its representative elevation to match each required elevation within the basin, and the MAP time series is adjusted to match expected precipitation amounts within the basin. The resulting simulations are used to define a relationship for the melt factor class, mean seasonal precipitation, and mean snow water equivalent weekly from January through June. Mean snow water equivalent surfaces are then produced from these relationships utilizing the snow melt factor surface, the long-term mean October through April precipitation surface, and the elevation surface as shown in Figure 4 for Kings River at Pine Flats for January 22.

*
Figure 4. Mean snow water equivalent surface (in inches) for Kings River at Pine Flats for January
22.*

*
*

*
Figure 5. Standardized deviate surface computed for Kings River at Pine Flats for January 20, 1995.*

*
*
From this gridded field of standardized deviates, a gridded field of snow water equivalent is
created by using the basin's relationship between point long-term means and standard deviations
and the equation defining standardized deviates, recasting it as

or

to determine snow water equivalent. A snow water equivalent field for Kings River at Pine Flats for January 20, 1995, is shown in Figure 6.

*
Figure 6. Snow water equivalent surface (in inches) computed for Kings River at Pine Flats for
January 20, 1995.*

*
*
The operational system can be run either in batch or interactive mode at any time between January
1 and June 22. Typically, the system is first run in batch mode for all the basins, and the resulting
standardized deviate and snow water equivalent surfaces are examined for abnormalities. The
system is then run interactively for these questionable basins, and the user can examine the snow
water equivalent observations and discard those which may be inappropriately biasing the
interpolation. These basins can be rerun, and once the user is satisfied with the new results, the
user can combine these with the existing maps.

In order to account for biases between the pseudo-observed and the estimates of snow water equivalent form the interpolation procedure, regression relationships are developed from the historical data. Pseudo-observed values are estimated for the first of each month for the entire historical record. Similarly, the interpolation procedure is performed for the first of each month throughout the historical record. The GIS is used to compute basin subarea averages from the gridded estimates of snow water equivalent. Regression relationships, which predict pseudo-observed values from basin average snow water equivalent, are developed for the first of each month (Figure 7 illustrates the relationship for Kings River at Pine Flats for first of February). These relationships are used in the operational system to compute estimates of the model snow water equivalent states that can be used for updating.

*
Figure 7. Pseudo-observed versus historic-interpolated snow water equivalent relationship for
Kings River at Pine Flats.*

*
*

The correlation between snow water equivalent observations of any two sites can be a function of other factors besides distance. Other parameters, such as elevation or available solar flux, could also influence the correlation between two stations. A multiple linear regression technique is being examined to account for these additional factors.

An increase in the number of melt factor classes is being investigated. Adding more classes, besides the currently used north, south, and horizontal classes, may provide a better definition of melt. Using forest density, in conjunction with forest cover type, will also be investigated.

A verification system will be implemented to quantify the improvement of runoff forecasts due to the SEUS updating procedure. The method will incorporate techniques developed as part of the National Weather Service Extended Streamflow Prediction (ESP) procedure.

Day, Gerald N., L. E. Brazil, C. S. McCarthy, and D. P. Laurine, "Verification of National Weather Service Expanded Streamflow Prediction Procedure", Proc. on Managing Water Resources During Global Change, American Water Resources Association Symposium, Reno, NV, ASCE, 1992.

Geographic Resources Analysis Support System (GRASS) User's Reference Manual, Version 4.1, U.S. Army Corps of Engineers Construction Engineering Research Laboratory, Champaign, IL, 1993.

McManamon, A. , Szeliga, T. L., Hartman, R. K., Day, G. N., and Carroll, T. R., "Gridded Snow Water Equivalent Estimation Using Ground-based and Airborne Snow Data", Proceedings of Eastern Snow Conference, Quebec City, Quebec, pp 75-81, 1993.

Office of Hydrology, National Weather Service

1735 Lake Drive West

Chanhassen, Minnesota 55317-8582

Telephone (612)361-6610, Facsimile (612)361-6634

email: {rhills,amcmanamon,rhartman}@nohrsc.nws.gov

www: http://www.nohrsc.nws.gov