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 8th, 2007

Measurement Methods

Photos: A. Slater

SNOTEL and Precipitation Gauges Snow Board

Measurement Methods

Photos: A. Slater

Sonic Snow Depth Sensor

Measurement MethodsAlter

Wyoming

DFIR

Nipher

Photos: NCAR

Measurement Methods

Photos: A. Slater

Pyranometer and Stevenson Screen

Other Data Sources

CAIC TowerBerthoud Pass

Photos: A. Slater

Snow courses & weather networks

9

Field campaigns

10

11

12

MODIS in the West

• Yampa Basin, Colorado

MissingCloudSnowSnow-Free

MODIS in the West

MissingCloudSnowSnow-Free

• Yampa Basin, Colorado

MODIS in the West

• Important period often cloud contaminated

• No mass information included (?)

• Calibration potential

• SWE inversion?

MissingCloudSnowSnow-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

SWESM

Historical Data

Past Future

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

SWESM

Historical Data Forecasts

Past Future

SNOW-17 / SAC 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 PredictabilityModel solutions to the streamflow forecasting problem…

Historical Simulation

Q

SWESM

Historical Data Forecasts

Past Future

SNOW-17 / SAC SNOW-17 / SAC

Sources of PredictabilityModel 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 conceptualizationof 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 scaleif there is good data available

Data Requirements:PrecipitationTemperatureHumidityIncoming shortwave radiationDownwelling longwave radiationWind speedPressure

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

sss mpdt

dS−= state equation (conservation of mass)

accm

accms TT

TTpp

>≤

=0 assume precipitation either rain or snow

assume melt depends on temperature alone( ) meltmelt

melts TTTT

TTm

>−

≤=κ

0

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 = 1.0CV 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

xSNOTEL

1. Xt

- = AXt-1 + Bft

2. Kt = P(P + R)-1

3. Xt

+ = Xt

- + Kt(zt – Xt

- )

• 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 = 2x = 2

Optimized Assimilation: Scalar Example

Our Observations say : Z = 4

Obs. error variance : R = 2z= 1

Optimized Assimilation: Scalar Example

222

111

zxa +=

Combined Model and Observations say :

X+ = 6 + (2/(2+1)) x (4 – 6)

Our Analysis is X+ = 4.66

Analysis variance : 2a= 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 – assimilate @ 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)