Zong-Liang YangHua Su

Guo-Yue Niu

The University of Texas at Austin

Comparison of Two Approaches to Modeling Subgrid Snow Cover Variability

July 25, 2006

www.geo.utexas.edu/climate

Subgrid Snow Cover and Surface Subgrid Snow Cover and Surface TemperatureTemperature

Winter Warm Bias in NCAR Winter Warm Bias in NCAR SimulationsSimulationsCCM3/CLM2 T42 - OBS CCM3/CLM2 T42 - OBS CCSM3.0 T85 - OBS CCSM3.0 T85 - OBS

(Dickinson et al., 2006)(Dickinson et al., 2006)

(Bonan et al., 2002)(Bonan et al., 2002)

Why?

Excessive LW↓ due to excessive low clouds

Anomalously southerly winds

Snow Cover Fraction and Air Snow Cover Fraction and Air TemperatureTemperature

])/(5.2

tanh[0

newsnog

sno

z

hSCF

NEW – OBS

OLD – OBS

The new scheme reduces the warm bias in winter and spring in NCAR GCM (i.e. CAM2/CLM2).

Smaller Snow Cover Warmer Surface

Snow Vegetation

Liston (2004) JCL

• The new SCF scheme improves the simulations of snow depth in mid-latitudes in both Eurasia and North America.

New Snow Cover Fraction Scheme

Eurasia (55-70°N,60-90°E) North America (40-65°N,115-130°W)

Representations of Snow Cover and Representations of Snow Cover and SWESWENatureClimate Modeling Remote Sensing

1. A land grid has multiple PFTs plus bare ground.

2. Energy and mass balances.

3. For each PFT-covered area, on the ground, one mean SWE, one SCF. Canopy interception and canopy snow cover.

1. Pixels.

2. Integrated signals from multi-sources (e.g., snow, soil, water, vegetation), depending on many factors (e.g., view angle, aerosols, cloud cover, etc).

3. Each pixel, MODIS provides one SCF. AMSR provides one SWE.

PFT

GroundSCF

Interception

SWE

SCF

Interception

SWE

Theory of Sub-grid Snow CoverListon (2004), “Representing Subgrid Snow Cover Heterogeneities in Regional and Global Models”. Journal of Climate.

The snow distribution during the accumulation phase can be represented using a lognormal distribution function, with the mean of snow water equivalent and the coefficient of variation as two parameters.

The snow distribution during the melting phase can be analyzed by assuming a spatially homogenous melting rate applied to the snow accumulation distribution.

Liston (2004) JCL

CV values are assigned to 9 categories.

Liston (2004) JCL

Liston (2004) JCL

The Coefficient of Variation (CV)

Relationship Between Snow Cover & SWEAccumulation phase: SCF is constant =1; SWE is the cumulative value of

snowfall.

Melting phase: The SCF and SWE relationship can be described by equations (1) and (2), with the cumulative snowfall, snow distribution coefficient of variation (CV) and melting rate as the parameters.

)1(

*5.0)(

)(

2)(

)()2

(*5.0)(

)2

(*5.0)(

22

2

2

CVLn

uLn

DLnz

dtexerfc

DDz

erfcuDD

zerfcD

mDm

x

t

mmDm

ma

Dmm

(1) Snow Cover Fraction

(2) SWE

Liston (2004) JCL

SCF-SWE in Different Methods

Liston (2004) JCL

Questions:

Can we derive CV values from MODIS and AMSR?How is the CV method compared to “traditional”

methods?

Each curve represents a distinct SCF-SWE relationship in melting season

Datasets

Daily SWE from AMSR Oct 2002–Dec 2004

Daily Snow Cover Fraction from MODIS Oct 2002–Dec 2004 (MOD10C1 CMG 0.05º × 0.05º)

GLDAS 1˚×1˚ 3-hourly, near-surface meteorological data for 2002–2004

A Flowchart for Deriving a Grid-scale SCF

Three records for each sub-grid:

snow cover fraction,

cloud cover fraction,

confidence index

Upscale 0.05º snow cover data to a coarse grid (0.25º, 0.5º or 1º) using the upscaling algorithm described above; Average SWE to the same grid.

Quality check the snow cover and SWE data for each analyzed grid and for each day to make sure there are no missing data or no cloud obscuring SCF data.

Steps to Derive CV

Compare MODIS SCF and AMSR SWE at the same grid

Estimate snowfall at the same grid from other sources

Optimize CV by calibrating the theory-derived SCF against the MODIS SCF through a Nonlinear-Discrete Genetic Algorithm

Design a SCF retrieving algorithm from SWE, CV, µ, Dm

Recursive method:

If snowfall at day t is zero, use

Snowmelt starts from the first day when SCF is less than 1. This criteria can be relaxed to a smaller value like 0.9 because the MODIS data may underestimate SCF in forest-covered areas.

)()2

(*5.0)( mmDm

ma DDz

erfcuDD

to calculate Dm, then use to calculate SCF)2

(*5.0)( Dmm

zerfcD

If snowfall µt at day t is larger than zero, and Dm is the cumulative melting rate at day t-1, then

if µt>Dm, then the cumulative snowfall as the mean of snow distribution, μ, would be replaced by µ+µt-Dm, and follow the same method in (1) to calculate SCF;

if µt≤Dm, then directly follow the method in (1) to calculate SCF

(1)

(2)

This SCF retrieving algorithm is used to derive grid- or PFT-specific CV based on SCF data and SWE data with Genetic Algorithm Optimization.

Retrieving SCF from SWE, CV,μand Dm

1°× 1° Grid (46–47°N, 107–108°W) Grassland in Great Plains 6 January–23 March, 2003

Characterizing Sub-grid-scale Variability of Snow Water Equivalent Using MODIS and AMSR Satellite Datasets

Sn

ow

Wat

er E

qu

ival

ent

(mm

)

Days from November 1, 2002

AMSR

Optimization

RMSE = 16 mm

Coefficient of Variation (CV) = 1.38

In the optimization, the relationship between snow cover fraction and SWE follows the stochastic scheme of Liston (2004).

The optimized CV value is used in CLM (next slide).

Modeling SWE at Sleeper’s River, Vermont Using CLM with a Stochastic Representation of Sub-grid Snow Variability

CV=1.38 CV=0.8Blue: Simulated Red: Observed

Values of CV in CLM

Barren Land

Vegetated Land

PFT Type1 PFT Type2

PFT Type3 PFT Type4

Geographic Distribution of CV in CLM

CV

Baseline

Tanh

AMSR Obs

Snow Density

Monthly SWE from 2002 to 2004

Daily SCF for Northwest U.S. 2002-2004

CV

Baseline

Tanh

MODIS Obs

Snow Density

CV

Baseline

Tanh

MODIS Obs

Snow Density

Daily SCF for High-latitude Regions 2002-2004

CV - Baseline

Snow density - Baseline

Tanh - Baseline

Daily Trad for Northwest U.S. 2002-2004

CV - Baseline

Snow density - Baseline

Tanh - Baseline

Daily Trad for High-latitude Regions 2002-2004

Summary

1) The high latitude wintertime warm bias in NCAR climate model simulations can be caused by an improper parameterization of snow cover fraction.

2) A procedure is developed to estimate CV using MODIS and AMSR data.

3) The CV method (i.e. stochastic subgrid snow cover scheme) is implemented in CLM and the results are promising.

4) The density-dependent SCF scheme is sensitive to the parameters used.

5) We will look at coupled land-atmosphere simulations using

CAM3.