1. Snow Properties Relation to Runoff
Presentation by Karl Rittger
This work is supported by Naval Postgraduate School Award N and NASA Cooperative Agreement NNG04GC52A
We investigate the relationship of snow-covered area (SCA) to snow water equivalent (SWE) in Sierra Nevada watersheds with varying latitudes, orientations, and elevations. In addition to snow-covered area, we estimate the spatial distribution of snow water equivalent. The correlations of these estimates with streamflow are evaluated for each of the watersheds.

2. Motivation
In snowmelt dominated river basins, snow properties near peak accumulation are used to assess spring and summer runoff. Forecast models rely on estimates of the water stored in the snowpack to determine the contribution of snowmelt to runoff.
Current operational runoff forecasts (DWR & NWS) assume stationary relationship between sparse point measurements of snow water equivalent and runoff
Spring runoff forecasts use snow course measurements taken near the 1st of each month
Analysis of snow course measurements show non-stationarity ie. trends
Howat and Tulaczyk (2005) find decreasing and increasing SWE trends dependent on both latitude and elevation
In the mathematical sciences, a stationary process is a stochastic process whose probability distribution is the same for all times or positions. As a result, parameters such as the mean and variance, if they exist, also do not change over time or position.
As an example, white noise is stationary. However, the sound of a cymbal crashing is not stationary because the acoustic power of the crash (and hence its variance) diminishes with time.
Stationarity is used as a tool in time series analysis, where the raw data are often transformed to become stationary, for example, economic data are often seasonal and/or dependent on the price level. Processes are described as trend stationary if they are a linear combination of a stationary process and one or more processes exhibiting a trend. Transforming this data to leave a stationary data set for analysis is referred to as de-trending.

3. Snow Water Equivalent in the Sierra Nevada

4. Can we improve runoff forecasting by integrating remote sensing sources?
Snow Covered Area
From satellites
MODIS
Daily at 500m
Landsat
Every 16 days at 30m
Snow Water Equivalent
Telemetered pillows
Daily measurements

5. Spring Runoff in the Sierra Nevada for the last 100 years
Based on monthly unimpaired runoff volumes, we selected a set of years during the Landsat TM historical record ( ) that encompass 80% of the range of variability in runoff during the last century.
An average family uses 0.25 to 1.0 acre-feet a year

6. Study Area – Location and Topography

7. Topographic Characteristics
Elevation
American lower
Kern higher
Aspect
Kern south facing
Slope
Similar
Kern slightly steeper

8. Spring Runoff for each Watershed
We estimate the fraction of snow in each 30 m pixel for the American, San Joaquin and Kern watersheds for five years that represent the minimum, quartiles and maximum April, May, and June unimpaired runoff. Recent years have produced similar variability in runoff, and fractional snow cover is estimated from MODIS for these years at 500 m resolution.

9. Satellite Spectral Bands
Landsat
MODIS

10. Landsat Thematic Mapper (TM and ETM+)
TM RGB, sensor description
Satellite sources include MODIS which provides daily imagery at 500m spatial resolution, and Landsat which provides imagery every 16 days at 30m spatial resolution. In California’s Sierra, daily snow pillow measurements of snow water equivalent are the main source of in-situ information.

11. Moderate Resolution Imaging Spectroradiometer (MODIS)
MODIS RGB, sensor description

12. Top of Atmosphere Reflectance for Landsat
Lλ = "gain" * QCAL + "offset“ Lλ = ((LMAXλ - LMINλ)/(QCALMAX-QCALMIN)) * (QCAL-QCALMIN) + LMINλ

13. 6S radiative transfer code (http://6s.ltdri.org)
Developed by the Laboratoire d'Optique Atmospherique. The code permits calculations of near-nadir (down-looking) aircraft observations, elevated surfaces, non lambertian surface conditions, absorbing gases, Rayleigh scattering, and aerosol scattering effects. The spectral resolution is 2.5 nm.
Primarily used for LUTs for MODIS
Kotchenova et al. 2006
Kotchenova and Vermote 2007
List of other atmospheric radiative transfer codes
Largest errors w/ polarization

14. Physical Background
Fraction of photons from target reach satellite sensor.
Typically 80% at 0.85 µm and 50% at 0.45µm
Photons lost though absorption and scattering
Absorption from
Aerosols (small) or atmospheric gasses
Principally O3, H2O, O2, CO2, CH4, N2O
Scattering

15. Surface Reflectance using 6S
Signal perturbed by gaseous absorption and scattering by molecules and aerosols
Absorption by atmospheric gases:
O3, H2O, O2, CO2,CH4, and N2O
Graphs from 6S

16. Surface reflectance to TOA reflectance for Landsat

17. Solar Zenith and Elevation

18. Snow Covered Area from Spectral Unmixing
Fractional snow covered area is estimated using multiple endmember spectral unmixing from MODSCAG and TMSCAG at 500m and 30m respectively. These algorithms are based on MEMSCAG (Multiple Endmember Snow Covered Area and Grain Size) and use MODIS bands 1-7 or TM bands 1-5 & 7(Painter et al, 2003, RSE). Landsat TM saturates frequently saturates over snow in visible bands. Saturation in Bands 1-3 are modeled as 100% snow whereas saturation in 1 or 2 of the bands are modeled with 5 or 4 bands respectively to estimate fractional SCA. Landsat TM surface reflectance is modeled using 6S and accounts for elevation.
Roberts et al, 1998
Painter et al, 2003

19. SWE from snow pillows San Joaquin 3/8/2004

20. (Roughly?) Estimating SWE for a River Basin
Fassnacht et al, 2003
Hypsometric Interpolation with inverse weighted distance interpolation of the residuals
Spreads snow into the ocean
Blended SWE
Multiply by SCA
Snow water equivalent is interpolated from snow pillows using the Hypsometric method with inverse weighted distance interpolation of the residuals (Fassnacht et al, 2003, WWR).
Difficult to assess accuracy w/o ground truth

21. Results from 2004 near peak SWE

22. SCA and Elevation
SCA in the San Joaquin is very similar in varying size snow years as is the high elevation Kern, whereas SCA in the American differs greatly from year to year. Therefore, larger runoff years have deeper and/or denser snowpack at high elevations.

23. SWE and Elevation
Interpolation methods are limited by data input. The interpolated SWE maps shown above for the San Joaquin incorrectly depict higher depths of snow at lower elevations than at higher elevations. The lower elevation snow pillows measure more snow due to the orographic effect which is not accounted for by the interpolation. A greater number and better placement of snow pillows allow the American and Kern to be modeled more realistically.

24. Snow Covered Area totals
Landsat
MODIS

25. Snow Water Equivalent totals
Kern
American
San Joaquin
Kern
American
San Joaquin

26. Correlation of SCA, SWE and blended SWE with Runoff
We find significant values of rho for SWE and blended SCA x SWE for 30 m resolution and significant values of rho for blended SCA x SWE at 500 m resolution. These tests show that snow products at higher resolution give more information about spring runoff than lower resolution data. They also show that snow products that take advantage of both in-situ measurements and remote sensing are more informative.

27. Conclusion
Although snow water equivalent interpolations are influenced by data availability, when combined with remote sensing it can be useful in predicting stream flow. These techniques can provide water managers with more accurate volumes of water stored in snowpack
Further work will investigate alternative interpolation methods as well as utilize space-time interpolated MODIS snow cover to provide basin SWE estimates over the season