Randy Hills1, Ann McManamon1, and Robert K. Hartman1

Snow Estimation and Updating System (SEUS)


The National Weather Service Office of Hydrology has developed a methodology to generate real-time, gridded snow water equivalent estimates using ground-based and airborne snow data collected over the Western United States. The gridded snow water equivalent estimates incorporate the spatial variability of the snowpack induced by the orographic effect in the West. The Snow Estimation and Updating System (SEUS) uses a geographic information system to store, analyze and display the spatial data necessary to perform the estimation. The gridded information is used to derive snowmelt characteristics and to develop long-term mean snow water equivalent data. A conceptual hydrologic model is used in the development of many of the parameters needed during this calibration step. The point snow water equivalent data are interpolated into a gridded product using data derived during the calibration step. Basin boundaries are used to identify the area included within each basin so that the gridded data can be analyzed to determine the average snow water equivalent over subareas within each basin. The estimates are used to update the snow water equivalent states of National Weather Service River Forecast System snow model.

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


In the Western United States, a significant portion of the annual runoff is generated from snowmelt. Accurate estimates of the snowpack can greatly enhance seasonal water supply forecasts, which are useful in estimating hydropower generation, planning reservoir releases, and determining water allocations. Regression techniques work well in estimating snowmelt in average years, however, these techniques tend to be inaccurate in extreme years.

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).


SEUS consists of four components: calibration, operational, updating, and administration. The calibration component analyzes historical snow observation data and develops the parameters needed to estimate snow water equivalent operationally. The operational component utilizes these calibration parameters, along with near real-time snow observation data, to determine gridded snow water equivalent. The updating component computes new snow water equivalent states for the conceptual snow model based on the weighted contributions of the historic simulated snow states and the estimates of the snow states developed using historic snow observations. The administration component manages individual user calibration and operational data.

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.

BasinKings River at PineFlats

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


The purpose of SEUS is to interpolate point snow water equivalent data into gridded estimates of snow water equivalent. A direct interpolation of point snow water equivalent in the West, however, does not account for orographic effects. One possible method to account for these effects is to transform point snow water equivalents into point standardized deviates using the following equation:

	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


 		=	correlation coefficient,
	c,d	=	regression coefficients,
	x	=	distance between points
is 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:



		=	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.


Estimates of the mean snow water equivalent at a grid point are derived by modeling snow accumulation and ablation, taking into account the precipitation and site characteristics of the grid point. The GIS and an existing, calibrated, NWSRFS snow model are used to estimate gridded snow water equivalent weekly through the snow season.

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.

Meansnow waterequivalent

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


A gridded field of snow water equivalent is computed by first creating a gridded field of standardized deviates. This field is developed using the standardized deviate definition, snow water equivalent observations, the basin's correlation-distance function, and an interpolation procedure detailed in Day (1990). The interpolation routine uses all available observations in a pre-defined area within and around each basin (previously, a maximum of twenty observations were used), computing the standardized deviate for each grid point within the basin. A standardized deviate field for Kings River at Pine Flats for January 20, 1995, is shown in Figure 5.

Standardized deivatesurface

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


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.

Snowwater equivalentsurface

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.


All of the information needed to estimate snow water equivalent is now available, however, the snow water equivalent estimated using the interpolation procedure may not be consistent with the snow water equivalent states in the conceptual snow model. Historical estimates of the snow water equivalent needed by the model are generated by computing the model states which would have been necessary on a specific date in order for the model to simulate the seasonal runoff that was actually observed. These estimates are called pseudo-observed snow water equivalent, and they represent the best estimate of the optimal snow water equivalent model states. Pseudo-observed snow water equivalents are developed for each basin subarea which has been calibrated for NWSRFS.

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.

Psuedo-observed vshistoric

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


The NWS is adding a new snow operation, SNOW-43, to NWSRFS to enhance the updating capability of the current snow accumulation and ablation model, SNOW-17. SNOW-43, a state-space version of SNOW-17, uses a Kalman filtering updating procedure which optimally combines observed snow water equivalent estimates from SEUS with simulated states generated by the SNOW-17 model. The procedure uses error estimates from both processes to update the snow model states. SEUS will be modified to compute an error estimate of a subarea mean snow water equivalent value along with the currently estimated subarea mean snow water equivalent.

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., "A Methodology for Updating a Conceptual Snow Model with Snow Measurements", NOAA Technical Report NWS 43, Department of Commerce, Silver Spring, MD March 1990.

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.

1National Operational Hydrologic Remote Sensing Center
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