Master of Arts
in
Geography
by
Tammy Renee Johnson

Committee in charge:

December 1998

INTRODUCTION

Table 1

Station-Year Maximum Dataset

To determine station-year maximum SWE values and timing, I reduced the monthly dataset in the following ways: stations were selected for time series analyses that had at least 3 measurements per year and 10+ years of measurements covering 30+ years.  These data also had to meet the following quality assurance: the day of maximum SWE was not simply the last day measured unless that month was the average month of melt and it was an average-to-wet year.  This criterion discouraged false snowmelt timing calculations due to sampling bias, yet accounted for precipitation variability and associated snowmelt fluctuations.

Seasonal maximum SWE and the month of maximum SWE were computed for each station, then these values were normalized by dividing yearly amounts by station averages.  This resulting wetness factor can be compared to other stations in various latitudes and elevations with different SWE levels.  Where a station-year’s maximum SWE occurred in more than one month, the later month was selected as the timing of melt.

Maximum Dataset Quality Assurance

Whereas the monthly dataset quality assurance was fairly straightforward, the time of maximum SWE dataset was much more difficult to substantiate.  I felt that it was important to distinguish any possible snowmelt timing and maximum accumulation trends, since snowmelt timing is predicted to change so drastically in a doubled carbon dioxide atmosphere.

Usually four monthly sampling days were used to determine a time of maximum snow accumulation and an amount.  The effect of monthly sampling on a regression analysis of trends in date of maximum accumulation had to be determined, and trends in sample dates further complicated the analysis.  However, a trending sample time cast further doubt as to the validity of these results.

Fortunately, extensive snow sensor and precipitation measurements in the Sierra Nevada led to three different methods to verify that these trends were meaningful.  About 100 daily snow sensor stations have measurements spanning a couple of decades.  This was useful in two ways.  First, 47 of these stations are located adjacent to snow course stations so comparisons can be made for yearly maximum SWE and monthly estimates.  Second, the effect of trends in sample dates can be calculated by comparing the real maximums, as recorded by the daily instruments, with any other results generated by sub-sampling this daily dataset.  With these data I compared various sample days’ (in time from the first-of-the-month) effects on the month of maximum SWE determination.

The third test, which also determined the effect of a trending sample day, was to compare DWR first-of-the-month corrected SWE values with the original SWE measurements.  These are data based on the measurements but corrected to what the SWE probably would have been on the first of the month.  Adjusted SWE is calculated by multiplying precipitation between the sample day and the first by a correction factor.

Adjusted SWE = measured SWE * precipitation * correction factor
          Precipitation is positive if the day sampled is before the first.
          Correction factors are unique for each snow-rain station pairing.

Sampled Station Bias

Analyses were separated into 100 meter elevation bins to both diminish station sampling bias and to exploit the spatial snow course clarity that is missing from the river data.

Daily Snow Sensor Experiment

I used the daily snow sensor data to determine the effects of a trending sampling schedule on the time-series regressions.  With daily data, I could create monthly datasets with various sampling schedules to check the effects of earlier sampling.  However, first I quality checked the sensor data and found that it contained many obvious errors.  I rejected the obviously erroneous data and ran a cubic spline interpolation to fill in the missing daily data.  A cubic spline is a segmented function consisting of third-degree polynomial functions joined together so that the whole curve and its first and second derivatives are continuous.  Missing dates were filled-in with the appropriate spline function.

Using validated daily sensor data, actual seasonal maximum SWE and the month of maximum SWE was calculated for each station.  Then these real values were compared to sensor estimates using only monthly sampling to check the effects of monthly sampling.  Finally, errors were calculated for both maximum SWE and the month of maximum SWE and fit to the number of days of earlier or later sampling.  These errors associated with the 15 days before and after the real maximum first-of-the-month measurement were used to calculate the effect of the earlier sample timing.

I considered each day in the real maximum SWE month as the monthly sample day.  This value was compared to the remaining monthly measurements, which were first-of-the-month values.  This represented a perfect monthly dataset with the exception of one month off by a set number of days.

The SWE value for any day was compared to the next highest, first-of-the-month, monthly SWE value to decide which of those two measurements would be classified as the maximum SWE value and month.

The error associated with a given number of days from the first could then be calculated by subtracting its results with the actual maximum SWE and month of maximum SWE values.  The differences were fitted with the number of days from the first to determine the error due to an inconsistent sampling schedule.

For example, daily snow sensor SWE data, dates and station information were run through a program to calculate these numbers listed in Table 2 for station 162 in May 1991.  Station 162 is on the east side of the Sierra Nevada, in the Tuolumne river basin at 2562 meters above sea level.  The second highest first-of-the-month SWE value is 26.6 inches and occurs in April.  The actual highest measurement recorded is 27.0, which is recorded in the table with the 2nd day before the first (April 30^th).

Example of Sampling Effects Calculations

Table 2

The following explains the program that calculated the error, or difference values.  It was not used to adjust any results, but only to indicate potential errors due to the sampling scheme.

The first step in the process was to filter the daily data and interpolate missing values.  The day of the month and the month numbers were pulled out of the date, and these numbers were grouped so that all measurements after the 15^th of the month are grouped with the following month.  Years are also adjusted to water years in this way.  The days until the first-of-the-month are then calculated.  I accounted for varying monthly length but I didn’t calculate exact February leap year days, so February 29^th readings will appear to be on the first of March.

Then I simulate perfect monthly sampling by pulling all SWE values on the first of each month.  The highest monthly SWE value and month are then stored.  To compare the errors associated with various sample days, the next highest first-of-the-month measurements and months are also recorded.  Finally, the actual highest daily SWE measurements for each station-year are recorded.

The resulting error in maximum SWE is the difference between the actual highest SWE value and the monthly measurement.  The monthly SWE used is either the maximum month daily SWE amount (the one being tested for timing effects) or the second highest first-of-the-month maximum SWE value (whichever is highest).  All of these results are positive or zero, indicating how much lower the SWE result is from the real maximum SWE.

Sampling effects on snowmelt timing were calculated similarly.  The month of snowmelt timing error was called zero if the given daily SWE measurement was higher than the second highest first-of-the-month SWE measurement.  In this case a measurement was as accurate as the “perfect” one for determining the timing of maximum SWE, despite when it was collected.  However, if the SWE value dropped below the next highest monthly sample value, it was inaccurate.  The error was determined by how many months the result was off.  I subtracted the second month from the real maximum SWE month, so positive numbers indicate false earlier melt.

The errors were fit to the number of days from the first-of-the-month to calculate the maximum SWE and month of maximum SWE change as the sample time changes.  All station-years were used to calculate average sample timing effects.

Climate Changes

Climate cycles or steps were checked by a method similar to the discontinuous station procedure, but instead of taking differences from means of yearly group averages, each station's standardized wetness was analyzed.  Calculating means before and after every station-year, and subtracting the difference did this.

The first and last 10 years with data are not considered in the difference of before and after means analyses because of severe edge effects.  Very high or very low differences indicate climate change.

Time-Series Regressions

All station measurements were standardized to station means to account for changing station elevations with time.  Estimated slopes were further standardized to changes per 50 years for comparison.  Percent changes and absolute changes were computed for monthly, maximum and the timing of maximum for river basins above and below 2400m and 100-meter elevation bins.  River basin changes are mapped throughout the Sierra Nevada and elevation bin changes are plotted.

RESULTS

Sample Timing Effects

Monthly sample timing has very little effect on measured maximum SWE.  The average bias is a 0.3% reduction per day sampled after the first.  The monthly sampled maximum will always be either less than or equal to the true maximum.  However, there is a greater effect on the calculated timing of maximum SWE.  Monthly sampling and earlier sample timing cause a false later maximum SWE timing change of 0.8 days over the 50-year period.  When broken into elevation bins, the greatest schedule change of 7.2 days amounts to a false later melt of 2.1 days.   Although 80% of the monthly sample days identify the correct maximum SWE month, monthly sampling creates melt-timing errors with 3.4 times more erroneous earlier melt months than false later ones.

An examination of the sample data indicates that on the first-of-the-month with maximum SWE, the sampling error indicates false earlier melt.  The snow is actually melting later.  This is probably because the SWE levels tend to drop faster than they accumulate throughout the season.  The result is that monthly measurements are more likely to catch the upside (earlier) rather than the steeper downside.  Earlier sampling appears to be catching more times near this peak.

These slight changes were not corrected in the analyses.  Instead, results staying within 5% of the maximum SWE and within 2 days per 50 years for snowmelt timing were considered to be unchanged.

River Basin Trends

Regressions on time of station data from individual river basins below 2400 meters consistently indicate less maximum SWE or no change (Figure 2).  Downward maximum SWE trends of 5% to 25% per 50 years are supported by 95% confidence in the Trinity, Feather, Lake Tahoe, American and Mokelumne basins.  The Tule’s estimated change of 33% less SWE per 50 years lacks confidence because there is only one station that survived the data quality filters.  It has 31 observations.

Above 2400 meters, most river basins show upward maximum SWE trends.  The southern east-draining Walker, Mono Lake and Owens basins all show significant maximum SWE increases of 15% to 25%.  The west-draining American, Stanislaus and Merced also indicate more snow accumulation.

Snowmelt timing changes in the lower elevations consistently indicate earlier melt or no change.  Nine of the 15 basins’ trends are supported with 95% confidence.  The Scott and Trinity River basins in the northwestern corner are melting two and three weeks earlier, respectively

At higher elevations, snowmelt has also tended to occur earlier, with six basins showing a clear change in the time of maximum snow accumulation.  Only one of these indicated later melt, the east-draining Owens, which is estimated to be melting a week and a half later than it did 50 years ago.

Monthly estimated changes for the basins are summarized in Table 3 and all estimates supported by 95% confidence are in bold.  The basins are arranged by latitude, with the west-draining basins listed first, followed by the east-draining results.  All 15 lower elevation, monthly basin trends with strong statistical confidence indicate decreasing SWE levels.  Of the six higher elevation estimates with good confidence, four suggest increasing SWE trends.  Three of these basins are located on the east-draining side of the range.