Toward State-Dependent Moisture Availability Perturbations in a Multi-Analysis Ensemble System with...

Toward State-Dependent Moisture Availability Perturbations in a Multi-Analysis

Ensemble System with Physics Diversity

Eric Grimit

15 March 2005Soil Moisture Perturbations

The Importance of Soil Moisture

Near-surface soil moisture fraction controls the partitioning of surface sensible and latent heat fluxes.Thus, it has a large effect on atmospheric circulations at a broad range of spatio-temporal scales.

Soil moisture changes can be responsible for seasonal precipitation anomalies.Soil moisture impacts the atmospheric boundary layer structure and its evolution over a diurnal cycle.Soil moisture is known to be a crucial factor in convective initiation.


Soil Moisture in MM5

In the default configuration of MM5, climo summer and winter values of near-surface (0-10 cm) volumetric soil moisture fraction (w) are assigned for each land use category type.

These climo w-values are assumed to represent the moisture available (M) for evaporation into the atmosphere.

No state-dependence or uncertainty included for these parameters.


vertical Cloud 36-km 12-km shlw. SST Land UseIC ID# Soil diffusion Microphysics Domain Domain cumls. Radiation Perturbation Table

MRF 5-Layer Y Simple Ice Kain-Fritsch Kain-Fritsch N cloud standard standard

avn plus01 MRF LSM Y Simple Ice Kain-Fritsch Kain-Fritsch Y RRTM SST_pert01 LANDUSE.plus1

cmcg plus02 MRF 5-Layer Y Reisner II Grell Grell N cloud SST_pert02 LANDUSE.plus2

eta plus03 Eta 5-Layer N Goddard Betts-Miller Grell Y RRTM SST_pert03 LANDUSE.plus3

gasp plus04 MRF LSM Y Shultz Betts-Miller Kain-Fritsch N RRTM SST_pert04 LANDUSE.plus4

jma plus05 Eta LSM N Reisner II Kain-Fritsch Kain-Fritsch Y cloud SST_pert05 LANDUSE.plus5

ngps plus06 Blackadar 5-Layer Y Shultz Grell Grell N RRTM SST_pert06 LANDUSE.plus6

tcwb plus07 Blackadar 5-Layer Y Goddard Betts-Miller Grell Y cloud SST_pert07 LANDUSE.plus7

ukmo plus08 Eta LSM N Reisner I Kain-Fritsch Kain-Fritsch N cloud SST_pert08 LANDUSE.plus8Perturbations to

moisture availability,

albedo, and

roughness length

ACMEcore+

CumulusPBL

ACME

1) Albedo

2) Roughness Length

3) Moisture Availability

UWME

UWME+

Current UWME+ Physics Configuration


New Soil Moisture Initial Conditions

Began using a soil moisture analysis from NCEP’s Rapid Update Cycle (RUC) model in January.

In response to the comparisons with SNOTEL obs and model tests performed in summer/fall 2004.

MM5 updates the moisture availability as precipitation falls during the run.Supposed to account for evaporation & runoff as well, but suspect!

Renders the climo moisture availability perturbations obsolete.

NCEP 20-km RUC0-10 cm soil moisture fraction comparison


State-Dependent Moisture Availability Perturbations

Options:(1) ensemble DA – state-dependent covariances (Reichle et al. 2002)

Would efficiently utilize the very limited set of real-time soil moisture observations.

• Could also use other variables (temp, wind, mx ratio) if they correlate.

However, do not really have the non-linear model M to find the new background estimates of moisture availability.

• Cannot run RUC and RUC land-surface model (LSM) locally.• May use UWME+ with “dump-bucket” model.

Subject to large errors.• Could modify UWME+ to use MM5’s NOAH LSM on all members.

Option for future consideration.

(2) EOF method – climatological covariances (Sutton and Hamill 2004)

Easier.

Variable snow cover, transient precipitation could have enormous impact on EOFs – what period to use?

Soil moisture fraction is non-Gaussian (Beta?)


Calculating the EOF-based Perturbations

RUC soil moisture analysis ~ 225 x 301 = N

X = matrix of m column vectors (of length N) with row-means removed

X ~ N x m

The covariance matrix is:

C = XXT = USVT(USVT)T = USVTVSUT = US2UT

C ~ N x N

Finding the EOFs of C directly is impractical, in general.

However, C has a big null space. Take advantage of it.

XTX ~ m x m

XTX = (USVT)T(USVT) = VSUTUSVT = VS2VT

Now we have a manageable eigenvector-eigenvalue problem to solve.

(XTX) V = V S2


Calculating the EOF-based Perturbations

Now that we have V and S, we can find U easily (keeping only k leading singular values/vectors, where k < m).

X = USVT

XV = USU = XVS-1

U ~ N x k

U contains the EOFs of C.

x = column vector of k Gaussian random numbers

Use linear transformation, y = L x, to get the correlated random numbers.xxT = L-1yyTL-T = L-1CL-T ~ I (assuming a large sample)

C = USUT ~ LLT

L ~ US1/2

y ~ U S1/2 x(Nx1) ~ (Nxk)(kxk)(kx1)


RUC Soil Moisture Fraction Standard Deviation and Control

90-samples (1200 UTC, 6 Dec – 14 Mar 2005)

Soil Moisture Fraction Standard Deviation Soil Moisture Fraction Control – NCEP 20km RUC

(1200 UTC, 15 Mar 2005)


Example EOF-based Soil Moisture Fraction Perturbations


Soil Moisture Fraction Perturbation #1 Soil Moisture Fraction Control + Perturbation #1

(1200 UTC, 15 Mar 2005)





(1200 UTC, 15 Mar 2005)


Summary

Soil moisture fraction perturbation amplitude/structure was very sensitive to the time period used in the EOF methodology.

SVs tied to precipitation location over the time period.With 60-days, the perturbations appeared too large/noisy.

With 16-samples (8-days), the perturbations appeared too weak/localized.

Would using a longer climo even be a good idea?

Use an intermediate-length (say, 30-day) period?

Gaussian assumption probably increases the noise.Fisher-Z transform? (statistical engineering problem)

Ultimately, we would like to have moisture availability perturbations with state-dependent covariances.

Resources not currently in place to do this (e.g., automated soil moisture observation ingestion, appropriate M, cycling)

If these resources are put in place, why stop at moisture availability?Might as well use such an EnKF system for perturbations to all fields.

Original Results Slides


RUC Soil Moisture Fraction Standard Deviation

16-samples (0000 and 1200 UTC, 1-8 March 2005)60-samples (0000 UTC, Jan-Feb 2005)




Unperturbed (0000 UTC 2 March 2005)

Toward State-Dependent Moisture Availability Perturbations in a Multi-Analysis Ensemble System with...

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