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

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

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

Measurement Methods Photos: A. Slater SNOTEL and Precipitation GaugesSnow Board

Measurement Methods Photos: A. Slater Sonic Snow Depth Sensor

Measurement Methods Alter Wyoming DFIR Nipher Photos: NCAR

Measurement Methods Photos: A. Slater Pyranometer and Stevenson Screen

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

9 Field campaigns

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

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

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

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

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

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

Historical Simulation Q SWE SM Historical Data PastFuture SNOW-17 / SAC Sources of Predictability 1.Run hydrologic model up to the start of the forecast period to estimate basin initial conditions; Model solutions to the streamflow forecasting problem…

Historical Simulation Q SWE SM Historical DataForecasts PastFuture SNOW-17 / SAC 1.Run hydrologic model up to the start of the forecast period to estimate basin initial conditions; 2.Run hydrologic model into the future, using an ensemble of local-scale weather and climate forecasts. Sources of Predictability Model solutions to the streamflow forecasting problem…

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

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

Snow Modelling 1)Detailed physically-based conceptualization of snow processes 2)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

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

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

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 Sub-grid model (after Liston, 2004): CV Parameter = 1.0 CV Parameter = 0.1 Example simulations where sub-grid SWE parameterized with probability distributions

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

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

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

Example: Direct Insertion & Nudging 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 x SNOTEL

1.X t - = AX t-1 + Bf t 2.K t = P(P + R) -1 3.X t + = X t - + K t (z t – X t - ) 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 Optimized Assimilation: General Case

Optimized Assimilation: Scalar Example Our Model predicts : X - = 6 Model error variance : P =  2 x = 2

Optimized Assimilation: Scalar Example Our Observations say : Z = 4 Obs. error variance : R =  2 z = 1

Optimized Assimilation: Scalar Example Combined Model and Observations say : X + = 6 + (2/(2+1)) x (4 – 6) Our Analysis is X + = 4.66 Analysis variance :  2 a = 0.66 Analysis Variance

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

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

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

The End (thank you)