Snow Hydrology: A Primer

1. Snow Hydrology:A Primer Martyn P. Clark NIWA, Christchurch, NZ Andrew G. Slater CIRES, Boulder CO, USA

2. Outline • Snow measurement • Hydrological predictability available from knowledge of snow • Snow modelling methods • Energy balance models • Temperature index models • Snow data assimilation • Potential role of remotely sensed snow products

3. Measurement Methods • Snow Water Equivalent • Snow Depth • Precipitation • Meteorology etc. December 8th, 2007

4. Measurement Methods SNOTEL and Precipitation Gauges Snow Board Photos: A. Slater

5. Measurement Methods Sonic Snow Depth Sensor Photos: A. Slater

6. Measurement Methods Alter DFIR Nipher Wyoming Photos: NCAR

7. Measurement Methods Pyranometer and Stevenson Screen Photos: A. Slater

8. Other Data Sources CAIC Tower Berthoud Pass Snow courses & weather networks Photos: A. Slater

9. Field campaigns

13. Missing Cloud Snow Snow-Free MODIS in the West • Yampa Basin, Colorado

14. Missing Cloud Snow Snow-Free MODIS in the West • Yampa Basin, Colorado

15. Missing Cloud Snow Snow-Free MODIS in the West • Important period often cloud contaminated • No mass information included (?) • Calibration potential • SWE inversion?

16. AMSR-E – Microwave Miracles? • Radiances vs. Products • Products tend to be “global” • Statistical vs. Physical inversion • Same old questions: • Validation • Error estimate

17. AMSR-E • Some information exists – can we exploit it? • Global algorithm (Chang) is not ideal

18. Outline • Snow measurement • Hydrological predictability available from knowledge of snow • Snow modelling methods • Energy balance models • Temperature index models • Snow data assimilation • Potential role of remotely sensed snow products

19. Sources of Predictability Model solutions to the streamflow forecasting problem… Historical Data SNOW-17 / SAC Historical Simulation SWE SM Q Past Future • Run hydrologic model up to the start of the forecast period to estimate basin initial conditions;

20. Sources of Predictability Model solutions to the streamflow forecasting problem… Historical Data Forecasts SNOW-17 / SAC SNOW-17 / SAC Historical Simulation SWE SM Q Past Future • Run hydrologic model up to the start of the forecast period to estimate basin initial conditions; • Run hydrologic model into the future, using an ensemble of local-scale weather and climate forecasts.

21. Sources of Predictability Model solutions to the streamflow forecasting problem… Historical Data Forecasts SNOW-17 / SAC SNOW-17 / SAC Historical Simulation SWE SM BETTER INITIAL CONDITIONS = BETTER FORECASTS Q Past Future • Meteorological predictability • Derived from accurate weather forecasts • Hydrological predictability • Derived from knowledge of basin initial conditions

22. Outline • Snow measurement • Hydrological predictability available from knowledge of snow • Snow modelling methods • Energy balance models • Temperature index models • Snow data assimilation • Potential role of remotely sensed snow products

23. Snow Modelling • Detailed physically-based conceptualization • of snow processes • The real world • The art of modelling is to define the complexity of the model that is justified in light of • the data that we have available • the problem we are trying to solve • the environment in which the model is applied

24. Energy balance approaches Accurate at the point scale if there is good data available Data Requirements: Precipitation Temperature Humidity Incoming shortwave radiation Downwelling longwave radiation Wind speed Pressure In operational models data must be interpolated across large distances, and the complexity of energy balance models cannot be justified by the limited data available

25. state equation (conservation of mass) assume precipitation either rain or snow assume melt depends on temperature alone Temperature-index method • The melt factor can be parameterized to • Vary seasonally • Decrease immediately after snowfall events • Increase during rain-on-snow events

26. Sub-grid model (after Liston, 2004): Example simulations where sub-grid SWE parameterized with probability distributions CV Parameter = 1.0 CV Parameter = 0.1 Sub-grid variability in SWE • Important to accurately model the timing of streamflow • Shallow areas of snow melt first, and only contribute melt for a limited period of time; deep areas of snow contribute melt late into summer • Early-season melt controlled by available energy; late-season melt controlled by snow covered area

27. Example snow simulations (parameter sensitivity) South Island, New Zealand Columns: Temperature threshold for snow accumulation Rows: Mean and seasonal amplitude of the melt factor

28. Outline • Snow measurement • Hydrological predictability available from knowledge of snow • Snow modelling methods • Energy balance models • Temperature index models • Snow data assimilation • Potential role of remotely sensed snow products

29. Data Assimilation: The Basics • Improve knowledge of Initial conditions • Assimilate observations at time t • Model “relocated” to new position

30. Example: Direct Insertion & Nudging SNOTEL x • Small basin with SNOTEL type station • Objective : determine basin SWE • Observation is SWE, as is model state • Direct Insertion: Assumes observation is perfect • Newtonian Nudging: Nudges model as suggested by observation

31. Optimized Assimilation: General Case • Predict model states (X) • Get relative weights (K) of model and observations • Update model state as a combination of its own projected state and that of the observations (z) • P = model error • R = observation error Xt- = AXt-1 + Bft Kt = P(P + R)-1 Xt+ = Xt- + Kt(zt – Xt- )

32. Optimized Assimilation: Scalar Example Our Model predicts : X- = 6 Model error variance : P = s2x = 2

33. Optimized Assimilation: Scalar Example OurObservationssay : Z = 4 Obs. error variance : R = s2z= 1

34. Optimized Assimilation: Scalar Example CombinedModelandObservationssay : X+ = 6 + (2/(2+1)) x (4 – 6) Our Analysis is X+ = 4.66 Analysis variance : s2a= 0.66 Analysis Variance

35. NWS SNOW-17 model Generated cross validated ensemble forcing Used cross validated observation ‘estimates’ Withholding experiments Accounted for filter divergence Assimilation shown to produce better results EnKF Example: Snow Assimilation

36. EnKF Example: Snow Assimilation Interpolated SWE Mean & Std. Dev Model Truth

37. White without Red = B.L.U.E • SWE contains red (time correlated) noise • Only want to use “new” information • Example – assimilate @ same timestep • Filter Divergence = potential problem Slater & Clark, 2006

38. Summary • Many snow measurement techniques • Depth versus water equivalent • Key consideration is station representativeness • Snow is an important source of hydrological predictability • Need good models • Need capability to assimilate available observations • Including satellite observations of snow extent (Clark et al., 2006) • Snow modelling methods • Energy balance models limited by intensive data requirements • Temperature index models can work well • Important to account for spatial variability of snow within a model element • Snow data assimilation • Important to use observations to constrain models, so as to capitalize on increases in hydrological predictability possible through knowledge of snow

39. The End (thank you)