Sierra Hydrotech Investigative Report January 1990
1.0 INTRODUCTION The Snowload Committee of El Dorado County has been investigating the possibility of a standardized method based on observed snow-on-ground for applying snowload requirements for structures throughout El Dorado County. The committee contacted Sierra Hydrotech with regard to an analysis of maximum snow-on-ground conditions in the County. Jack Hannaford attended a meeting of the snowload committee on March 16, 1989. Sierra Hydrotech was authorized to conduct an investigation of maximum observed snow-on-ground throughout El Dorado County by Gary Delgado of El Dorado County Building Services. The investigation was to cover both the Western Slope and the Lake Tahoe Basin. This report describes the investigation by Sierra Hydrotech and summarizes the results. 2.0 APPROACH2.1 Objectives It was agreed in discussions with Building Services and the Committee that the primary objective of the investigation would be to develop a relationship between maximum observed snow-on-ground during the historical record of approximately sixty years and site specific physical parameters which could be readily obtained from suitable maps or other records. This would enable the County to make a uniform estimate of maximum snow-on-ground at any given site by knowing selected specific site parameters. Maximum snow-on-ground in the analysis was to be from observations at recognized snow course sites with appropriate records, expressed in terms of inches of snow water content (water equivalent). Consideration was also to be given to a means for estimating maximum snow depth which would correspond to the maximum water content. 2.2 Basic Data As in any investigation of this nature, recognition, selection and editing of an appropriate data base is perhaps the most critical aspect of the work. Since the objective was to relate maximum observed snow-on-ground water content to site specific parameters using the historical record, site specific parameters suitable for analysis had to be identified, defined, and tested for significant correlation. Site specific parameters or variables to estimate snow-on-ground were required to 1) be readily available from an authoritative source, 2) be easily obtained and interpreted by Department personnel, and 3) give uniform results for different interpreters. A number of site specific parameters were investigated, but the two independent variables meeting the above criteria and demonstrating high predictive capability were mean annual precipitation and elevation. The specific parameters used in this investigation were developed as follows.2.2.1 Snow-On-Ground California Department of Water Resources has been responsible for the gathering and publication of data on snowpack water content and depth throughout the state. Data appear in DWR Bulletin 120 on an annual basis. The state and it's cooperators collect snowpack water content in inches and depth in inches at over 400 snow courses throughout the state. Measurements are generally made near February 1, March 1, April 1, May 1, and sometimes June 1 and January 1. At higher elevations, maximum snowpack water content usually occurs on the April 1 measurement. Additionally, a number of radio-reporting snow sensors gather information on snowpack water content, giving continuous records of the accumulation and melt of snowpack. The California Cooperative Snow Survey Program started standardized measurements in 1930, giving 60 years of record to be evaluated. At least from an historical perspective, the maximum observed snow water content would have occurred once in 60 years giving a 1 in 60 chance of occurrence. Data on snowpack water content in inches (i.e., inches depth of water contained in the accumulated pack) and snow depth in inches are archived in computer format at the California Data Exchange Center (CDEC) of the California Department of Water Resources (DWR) in Sacramento. Data for approximately 100 snow courses in the Yuba River, American River, Mokelumne River, Truckee River, Carson River, and Lake Tahoe Basin were accessed by Sierra Hydrotech computer. Records for each snow course were scanned for the three highest observed snowpack water contents. Water contents and depths were assembled into a file for analysis. Most of the data represent elevations in excess of 5,000 feet. Data from outside of the area of immediate geographical interest at lower elevations were also assembled to increase the number of lower elevation observations (i.e., 4,000 to 5,000 feet). Additionally, National Weather Service observations of depth of snow-on-ground were assembled at other low elevation stations. Estimates of maximum water content were made from depths at those stations. 2.2.2 Mean Annual Precipitation It was reasoned that maximum observed water content of snow-on-ground would be highly correlated with the amount of precipitation which normally occurred at the site. Various agencies have prepared "isohyetal maps" or maps showing lines of equal precipitation for various areas in the state. After review of a number of isohyetal maps of the American River and Tahoe Basins, it was concluded that the following three maps would be most suitable for determining 1) mean annual precipitation at each snow course used in analysis, and 2) site specific information for use by El Dorado County in determining snow loads. The first two maps were used to develop a county-wide isohyetal map while the third was used for cross-reference. See Section 4 for reference to these maps and the county-wide isohyetal map.
An estimated value of mean annual precipitation for each snow course was obtained from the subject maps and included as an independent variable in the analysis. 2.2.3 Elevations Each snow course has an elevation determined by DWR. This elevation was assigned as a parameter in the analysis. The logic was that snowpack accumulation at lower elevations would be subject to more melt than that at higher elevations, possibly decreasing the maximum accumulation observed. This would make elevation an appropriate variable in estimating maximum water content of snow-on-ground. 2.2.4 Assembled Data Data for 49 snow courses and observing points have been assembled to represent the West Slope of El Dorado County. Although a number of these courses are actually outside of the county, they are considered to be representative of conditions encountered here. These assembled data appear in Table 1. Data for 24 snow courses representing the Lake Tahoe Basin and Sierra East-side are assembled in Table 2. Again, these courses cover areas outside of El Dorado County, but are considered to be representative of conditions within the Lake Tahoe portion of the county. 3.0 RESULTS 3.1 Form of Relationship The relationship between water content of snow-on-ground and two independent variables, 1) mean annual precipitation, and 2) elevation was developed using a multiple linear regression analysis with certain data transformation. Separate equations relating the variables were investigated and prepared for El Dorado County West Slope and Lake Tahoe Basin. The general form of the equations are:
The logic of this form of equation is:
Although it was observed that maximum water content of snow-on-ground is directly proportional to elevation in a simple correlation, a higher degree of multiple correlation was obtained with some degree of data transformation. It was hypothesized that maximum observed water content is indirectly proportional to the difference between a maximum fixed elevation and the site elevation, and that above some maximum fixed elevation there would no longer be an impact on water content attributable to elevation. Various fixed elevations were investigated, and the 7,500 foot maximum fixed elevation appeared to give the best correlations for both West Slope and Lake Tahoe Basin. An E' value of 0 was used for any snow course elevation above 7,500 feet. The logic was that below some fixed elevation, the maximum snowpack during the accumulation season would be less as a result of warmer temperatures resulting in rain or mixed rain and snow and would also be subject to greater melt between storm events. As a consequence, a lower elevation site with a given mean annual precipitation would have less maximum snowpack accumulation than a high elevation site with the same precipitation. The value "n" gave the opportunity to investigate non-linear relationship between WC and E'. A value of 1.2 for "n" was taken arbitrarily as the best fit value for both West Slope and Lake Tahoe Basin. From a logical standpoint, the form of the equation appears reasonable. Statistically, the results were very good, giving relationships which seem realistic in both form and magnitude. The above equation may be converted from inches water content of snow-on-ground to pounds per square foot of snow-on-ground by multiplying the result in inches of water content by 5.20. 3.2 West Slope Equation The equation relating maximum observed water content of snow-on-ground to mean annual precipitation and elevation for the West Slope portion of El Dorado County is:
WC = 1.663(P) - .00287(7,500 - E)1.2 - 15.12 Where: WC = Water content in inches P = Mean annual precipitation at site in inches E = Site elevation in feet or 7,500 feet if elevation of site exceeds 7,500 feet Most of the West Slope data came from snow courses located at the 5,000 foot elevation and above. Consequently, the numerical relationship derived from the analysis would be most appropriately applied above the 5,000 foot level. Some extrapolation to lower elevations is appropriate. However, a set of minimum snow loads for the lower elevations has been developed for use in conjunction with the above equation. See Section 3.4 and figure 1 for description of the minimum snow loads. 3.3 Lake Tahoe Basin Equation The equation relating maximum observed water content of snow-on-ground to mean annual precipitation and elevation for the Lake Tahoe Basin portion of El Dorado County is :
3.4 El Dorado County Building Services Minimum Snow-On-Ground El Dorado County Building Services has established minimum snow-on-ground for certain elevations on the West Slope and Lake Tahoe Basin. The following table lists minimum snow-on-ground for each 500 foot elevation increase corresponding to Building Services minimum values (which are shown as "(given)").
It might be noted in the above table that there appears to be a discontinuity between minimum snow-on-ground which might be determined for given elevations just to the east or just to the west of the Sierra crest. However, mean annual precipitation amounts near the crest are in the order of 50 to 70 inches, so that large difference in snow-on-ground between adjacent east and west slope sites will not occur as a problem in practice. The minimum snow-on-ground values corresponding to minimum established by El Dorado County Building Services are to apply to specific sites, regardless of whether the equations would give a lower value for a corresponding precipitation and elevation. The equations delineated graphically in the following Section 3.5 reflect these minimum values. 3.5 Graphical Presentation of Results The above equations are presented in graphical form for West Slope in Figure 1 and Lake Tahoe Basin in Figure 2. The top horizontal scale represents maximum water content of snow-on-ground in inches while the bottom horizontal scale represents the maximum water content of snow-on-ground in pounds per square foot. The vertical scale represents mean annual precipitation in inches. The family of lines within the plot represents elevation in feet, with all sites in excess of 7,500 feet elevation represented by the >7,500 foot line. On both Figures 1 and 2, the family of elevation lines has been cut with a series of vertical lines, each representing a specific minimum snow-on-ground condition for that elevation as assigned by Building Services. For example, on the West Slope Plot (Figure 1) minimum snow-on-ground for elevations of 2,000 feet or less would be 20 pounds per square foot, while minimum snow-on-ground for an elevation of 6,000 feet would be 180 pounds per square foot, regardless of mean annual precipitation. In the Lake Tahoe Basin Plot (Figure 2) the minimum elevation line shown is 6,000 feet, as the maximum lake elevation is approximately 6,229 feet. Note that the impact of elevation in Figures 1 and 2 is progressively greater at lower elevations. To use Figures 1 or 2, enter the vertical scale with mean annual precipitation for the given site (from the map of mean annual precipitation for El Dorado County) and proceed horizontally to the site elevation (from U.S.G.S. Quadrangle Sheets delineating elevation contours). Drop vertically from the intersection of the mean annual precipitation-elevation line to the bottom horizontal scale and read snow-on-ground in pounds per square foot. Proceeding along that vertical line to the top of Figures 1 or 2 will give snow-on-ground in inches of water content. 3.6 Maximum Snow Depth Maximum snow depth corresponding to the maximum water content of snow-on-ground was recorded for each snow course entry in the analysis. An average snowpack density of approximately 45 percent for all measurements above the 5,000 foot elevation appears to be quite representative of the data field, regardless of mean annual precipitation or elevation. For snowpack below the 5,000 foot level, it is likely that the maximum snow-on-ground may have resulted from only one or two storms, so that observed densities would be less at lower elevations. Densities of 25 to 35 percent seem representative of the 2,000 to 3000 foot elevation range from miscellaneous observations published by National Weather Service. Consequently, a reduction in density (leading to greater depths, but not greater water contents) would appear appropriate at lower elevations. It is recommended that a snowpack density of 45 percent be used, regardless of precipitation or of elevation above 5,000 feet, to estimate the maximum depth for snow design in El Dorado County. It is suggested that densities as low as 25 percent be used at the 2,000 foot level. Figure 3 represents the relationship between snow-on-ground in pounds per square foot on the vertical scale and corresponding inches in depth on the horizontal scale, with the family of lines in the field representing elevation below 5,000 feet. To use Figure 3, enter the vertical scale with estimated maximum water content of snow-on-ground in pounds per square foot, follow horizontally to the appropriate plotted elevation line, then proceed vertically to the horizontal scale and read depth in inches. 4.0 SITE SPECIFIC DATA 4.1 Site Elevations The Building Department intends to use US Geological Survey 7.5 minute quadrangle maps covering El Dorado County for site location and determination of site elevation. This is a suitable source for determination of elevation, being readily available to both the county and to builders. The interpretation of elevation from quad sheets is fairly straightforward and different interpreters should readily obtain similar results. 4.2 Site Mean Annual Precipitation El Dorado County has no adopted map of mean annual precipitation which has been accepted on a county-wide basis. As a result, the Building Department has requested Sierra Hydrotech to review existing sources of data and to develop from those sources a map suitable to be used by the Building Department for uniform determination of mean annual precipitation for specific building sites. There are a number of isoheytal maps delineating mean annual precipitation which include part or all of El Dorado County. The two maps which appear to be most appropriate to the present needs are:
WEST SLOPE "Lines of Average Annual Precipitation in the Central Valley - North Half" 50 year base period 1910-11 through 1959-60 Compiled by Jim Goodridge California Department of Water Resources April 1966 and Subsequent updates LAKE TAHOE BASIN "Mean Annual Precipitation - Lake Tahoe Basin" 50 year base period 1920-21 through 1969-70 Compiled for Tahoe Regional Planning Agency by Prof. John James, Nevada State Climatologist 1971Material on the above maps was also checked with: "Mean Annual Precipitation in the California Region" Compiled by S.E. Rantz U.S. Geological Survey 1969 Reprinted 1972
Although these maps are not recent publications, they appear to be well researched and representative of specific areas. Note that the 50-year averages for the Goodridge and James maps are for different periods of record, but the two maps developed appear to match reasonably well in areas of overlap. Sierra Hydrotech had previously prepared an isohyetal map for California Department of Water Resources on the 2 mi:inch County Base Map. An isohyetal overlay map had been developed, based on data from Goodridge and Rantz. This map will be published in the "Mountain Counties Report -- El Dorado County" by DWR. It was felt that this overlay was satisfactory for the West Slope, but that Prof. James' work should be incorporated in the Lake Tahoe Basin portion of the map. Sierra Hydrotech has prepared from the Goodridge and James isohyetal maps a county-wide overlay to be used in conjunction with snow-on-ground procedures described in this report. The isohyetal overlay is to be photocopied on the County Base Map. The version of the County Base Map to be used to delineate section numbers for ready identification of locations of specific building sites. The resulting map to be photocopied from the County Base Map and isohyetal overlay is adequate for ready definition of mean annual precipitation for specific sites in any area of the county. Interpolation of inches of mean annual precipitation between specified isohyetal lines on the map is a relatively straightforward process. Section numbers provide for ready identification of specific sites. 4.3 Generalized Snow-On-Ground Map Charles Sinky of the El Dorado County Building Department is currently preparing a map of snow-on-ground in El Dorado County based on the procedures, equations and minimum snow-on-ground values described in this report. This map will be available through the Department for individual use in estimating snow-on-ground. 5.0 SNOW-ON-GROUND DURATION El Dorado County Building Department raised the question of duration of snow-on-ground as it might relate to certain design-load modifications for timber materials and fastenings. Apparently, a 15% increase in stresses in certain timber members and fastenings is permissible under code for a snow-loading not exceeding 60 days duration. The objective of this portion of the investigation was to determine whether or not snow-on-ground loads would exceed 87% of the maximum snow-on-ground loading for over 60 days. The 87% value represents the snow-on-ground, of which maximum snow-on-ground would be 115%, calculated as follows:
Such analysis requires continuous records of snow-on-ground, so that the time-distribution of snowpack may be defined. California Cooperative Snow Surveys, Nevada Cooperative Snow Surveys, and their cooperators, maintain snow-sensor sites throughout the Sierra and other locations. These sites use a pressure measuring device to determine water content of the snowpack at specific locations on a continuously reporting or recording system. Since snow-sensors have not been in the field for a long period of time, there is no record other than 1983 for such heavy snow amounts. Fourteen snow-sensor sites in the American, Tahoe, and adjacent watersheds were determined to have adequate record from the 1983 water year to be useful in estimating duration. A plot was made of the maximum 1983 water content in inches against the number of days which the water content exceeded 87% of the maximum. Although there was some scatter in points, it appears as if 60 days represents a reasonable duration for those sensors with maximum 1983 water content in excess of 60 inches. As maximum water content decreases below 60 inches, duration appears to decrease also. With a maximum 1983 water content of 30 inches, duration appears to be about 30 days. No other years of sensor record appear to give more critical load-duration results. The net result of the analysis is that during the 1983 season (maximum of record), snow-on-ground did not exceed 87% of the maximum snow-on-ground for significantly more than 60 days. In summary, it appears justifiable to permit a 15% increase in the stresses allowed snow loading for certain timber members and fastenings. 6.0 CONCLUSION Definition of water content of snow-on-ground in El Dorado County can be made using the following data:
Using Figures 1 or 2, determination can be made of :
Using Figure 3, depth of snow in inches corresponding to maximum water content in pounds per square foot can be determined. The procedure described in this report should provide a reliable estimate of snow-on-ground corresponding to the maximum snow observed during the past 60 years of record (1930 - 1989). This would represent snow-on-ground in an area without unusual conditions of exposure or drifting. Actual design loads may be substantially modified from observed snow-on-ground as a result of code requirements or other factors as determined by El Dorado County. Analysis of continuously recording snow sensor data confirms that observed snow-on-ground duration justifies application of a 15% increase in design stresses according to code in certain timber members and fasteners.
FIGURE 1 West Slope
FIGURE 2 Tahoe Basin