# Presentation: 158010

## Ensemble Snow

**Ensemble Snow**

***Martyn P. Clark***
***Andrew G. Slater***

**CIRES                 University of Colorado**

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## Uncertainties in model inputs (method)

***Uncertainties in model inputs (method)***

- Estimate precipitation
- CDF at each grid cell
- Synthesize ensembles
- from the CDF

- Precipitation

- Cumulative Prob.

- Clark & Slater, in press

-     Conditional CDF
- (ord. least squares)

## Uncertainties in model inputs (method)

- Estimate precipitation
- CDF at each grid cell
- Synthesize ensembles
- from the CDF

- Clark & Slater, in press

## ...ensemble forcing inputs 

***...******ensemble forcing inputs ***

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## Compensatory effects of model parameters

_**Deterministic optimization:**_
- Global minimum in objective function found for each input ensemble

_**Objective function topology:**_
- Objective function defined as the difference between the ensemble mean and observations – plotted for each point in the parameter space

- Clark and Vrugt, submitted

## ...and the effects of state updating (SODA)

- state updates during model simulations reduce persistent errors in model states and identifies “optimum” parameter values that are more physically realistic

- Clark and Vrugt, submitted

## Quantifying uncertainty is a model calibration problem...

- Shift from paradigm of error separation to that of error propagation
- Quantify individual sources of uncertainty and evaluate their impact on the basin response
- Reduce compensatory effects caused by model weaknesses
- Understand and document model assumptions
- Include state updating as part of the calibration strategy
- Diagnose the time series of state updates for clues on model weaknesses
- Reduce compensatory effects caused by parameter interactions
- Understand how different components of the model impact the basin response in similar (or opposing) ways
- Careful choice of objective functions that relate to sensitivities of each process component
- Multi-step (sequential) versus multi-objective calibration strategies
- Use appropriate methods for high dimensional problems
- Reduce the dimensionality of the problem
- Consider the use of transfer functions rather than parameter multipliers

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## 53 Upper C.R.B.  SNOTEL Stations

## Probabilistic Spatial SWE Interpolation

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## Satellite applications: uncertainty in SCA

- Spectral mixture analysis
- Weighed combination of different land cover types that match the satellite reflectance
- Uncertainties:
- Choice of land cover types
- Fractions assigned to each land cover type
*Probabilistic non-linear optimization problem, instead of a radiative transfer problem*

## Uncertainty in choice of land cover types

*(multiple end-member combinations have similar accuracy)*

## Uncertainty in fractional coverage

*Multiple fractional coverage can produce equivalent accuracy*

## ...spatially-explicit probabilistic SCA

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## Ensemble snow data assimilation

- SNOW-17
- Anderson (1973)
- Simple Temperature based model
- Runs Operationally @ the NWS
- Parameters : CBRFC operational code
- Calibrated for streamflow
- Nine state variables used
- Model forced with ensemble of inputs
- Attempt to account for initial conditions uncertainty

## EnKF Sample Results

- Slater & Clark, (2005)

- 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 – assimilate @ same timestep
- Filter Divergence = potential problem

- Slater & Clark, (2005)

## Final Assimilation Results

- Slater & Clark, (2005)

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## Assimilation of snow-covered area data

- Clark et al., in press

## “Toy” snow water balance model

- Sub-grid SWE modeled using probability distributions
- Water balance modeled using a conceptual series of reservoirs
_***Assimilation:***_  Use snow covered area to update snow and water balance state variables

- Clark et al., in press

## Ensemble streamflow simulations...

- Clark et al., in press

## Example impact of SCA assimilation

- Clark et al., in press

## Improvements in streamflow simulation

- Small impact
- Basin continuously snow covered throughout winter
- Melt occurs fairly quickly
*Thus, small time window for which snow covered area information is useful*
- Snow covered area information may be most useful where snow is ephemeral

- Clark et al., in press

## Research foci

- Quantifying model uncertainty
- Uncertainty in model inputs
- Uncertainty in model parameters/structure
- Quantifying uncertainty in observations
- Uncertainty in spatial estimates of SWE from SNOTEL
- Uncertainty in satellite SCA estimates
- Data assimilation methods
- Assimilation of station SWE data
- Assimilation of satellite SCA information
- 1-D versus 3-D assimilation strategies

## 1-D vs. 3-D Assimilation Strategies

- Hydro models are 2D arrays of 1D models
- Spatial information is not propagated by model
- Need methods to supply “obs” for assimilation
- Methods should be able to account for:
- Differences in topography e.g. elevation
- Differences in vegetation cover
- 3-D assimilation relies on spatial model covariance for interpolation
- 1-D assimilation relies on interpolation from methods “outside” the model.

## Key papers

- Clark, M.P., and A.G. Slater, 2006:  Probabilistic quantitative precipitation estimation in 	complex terrain.  *Journal of Hydrometeorology*, in press.
- Slater, A.G., and M.P. Clark, 2006:  Snow data sssimilation via and ensemble 	Kalman filter.  *Journal of Hydrometeorology*, in press.
- Clark, M.P., and Co-authors, 2006:  Assimilation of snow covered area information into 	hydrologic and land surface models.  *Advances in Water Resources*, in press.
- Hay, L.E., and Co-authors, 2006:  A multi-objective, step-wise, automated calibration 	approach applied to hydrologic modeling of a snowmelt-dominated basin in 	Colorado.  *Journal of the American Water Resources Association, *in press*.*
- Clark, M.P., and Co-authors, 2006:  Scientific and societal uses of remotely 	sensed snow 	and ice information.  To appear in the AGU monograph *Research and Economic **	**Applications of Remotely Sensed Data Products*.
- Clark, M.P., and J.A. Vrugt, 2006:  Unraveling uncertainties in hydrologic model 	calibration:  Addressing the problem of compensatory parameters.  Submitted to 	*Geophysical Research Letters*.

## The End

**The End**

**CIRES                 University of Colorado**

- http://sciencepolicy.colorado.edu/hydroclimate/

## Issues with Noah and snow

## Information Supply for Assimilation

## ...how can we use SNODAS output?

_**Problem 1:**_  Treat SNODAS as “observations”
_**Problem 2:**_ Calibration issues.
- SNODAS uses a different simulation model
- Real snow is not *“what the model wants to see”*
- _Solutions:_
- Multi-objective model calibration
- Bias adjustment
_**Problem 3:**_ Quantifying error
- Validation is impossible because all available data is used to produce snow estimates
- SNODAS is a subjective system managed by human analysts—errors may change rapidly
-  _Solutions:_
- Optimize the error term as part of simulation modeling

- Hay et al., submitted