Representing Model Error in Ensemble DA

Chris Snyder (NCAR)NCAR is supported by the National Science Foundation

Representing Model Error in Ensemble DA

Results from:

Soyoung Ha (NCAR)

Judith Berner (NCAR)

Josh Hacker (NPS)

Introduction

Parameterized physical processes crucial at both meso- and convective scales

– Model errors relatively more important than at synoptic and global scales

Meso- and convective-scale motions incompletely observed– E.g., lots of v obs but few of T at convective scale– DA scheme must use info from model dynamics to infer unobserved

variables– DA scheme should therefore account for forecast-model errors

Introduction (cont.)

For ens. DA, natural to represent model error during forecast step– Multi-physics: Members uses distinct suites of physical parameterizations– Multi-parameter: Single physics suite, but parameters within

parameterizations vary among members– Stochastic backscatter: Include noise in tendencies at each time step (iid!)

Can also represent in analysis step– Additive noise that depends on observations (Dowell and Wicker 2009)– Inflation of various flavors: “inflate” deviations of ensemble members about

mean before assimilation

Introduction (cont.)

Here, focus on mesoscale aspects, esp. surface observations

Tests on CONUS domain– WRF/ARW, 45 km– Forecasts from GFS ensemble ICs every 3 days over 3 winter months– Evaluation against obs

Three schemes1. Multi-physics. 10 distinct parameterization suites

2. Stochastic backscatter. Noise has spatially uniform variance

3. Limited multi-physics, multi-parameter (LMP2). 3 parameterization suites plus perturbations to one parameter in each of microphys, Cu, PBL, SW rad.

Comparison of Model-Error Treatments in EF

– Stochastic backscatter better than multiphysics at 700 hPa; multiphysics better than backscatter near surface

Comparison of Model-Error Treatments in EF

Courtesy Josh Hacker. See Hacker et al (2011), Berner et al (2011)

Difference in CRPS, 2-m TDifference in CRPS, 700 hPa T

WRF/DART

Data Assimilation Research Testbed (DART)– Provides EnKF algorithm(s)– General framework, used for several other models– Parallelizes efficiently to 100’s of processors– See http://www.image.ucar.edu/DAReS/DART/

WRF/ARW is forecast model

Suite of observation operators– Includes Doppler radar and various GPS; no radiances

Capable of assimilation on multiple, nested domains simultaneously

Assimilation of Surface Observations

Experimental design:– CONUS domain, 45-15 km nested configuration– 3-hourly analyses, with continuous cycling for June 2008– Assimilate conventional obs and METAR observations– Evaluate against (independent) mesonet observations

Also tested “multiphysics” configuration– 10 different suites of physical parameterizations

EnKF details– 50 members– ~800-km localization– Adaptive inflation

Assimilation of Surface Observations (cont.)

Accounting for model error improves analyses and 3-h forecasts

(NOT assimilated)

Adaptive Inflation

If forecast spread is too small, “inflate” ensemble deviations:

xi = (xi - E(x)) + E(x),where dim() = dim(x), i.e. inflation for each state variable,

spatially and temporally varying. (Anderson 2009)

Estimate with a Bayesian update: p( | y) = p(y | ) p().Requires assumption that cor() = cor(x).

Accounts for numerous sources of uncertainties

Assimilation of Surface Observations (cont.)

Compensation between different model-error treatments– Need less inflation when using multi-physics ensemble

Control physics Multi-physics

Which Approach?

Multi-physics and backscatter perform comparably for surface obs

Multiphysics:– Represents “structural” model error and differences among members are

often differences in bias/climate– System is demanding to maintain as model and parameterizations evolve– V. v. demanding to improve all 10 suites– What to do in ensemble DA when members have different state variables?

Backscatter:– Represents random variations in grid-scale effects from sub-grid variability– Single model configuration, so easy to maintain and feasible to improve

Which Approach?

Multi-physics and backscatter perform comparably for surface obs

Multiphysics:– Represents “structural” model error and differences among members are

often differences in bias/climate– System is demanding to maintain as model and parameterizations evolve– V. v. demanding to improve all 10 suites– What to do in ensemble DA when members have different state variables?

Backscatter:– Represents random variations in grid-scale effects from sub-grid variability– Single model configuration, so easy to maintain and feasible to improve

We favor backscatter at present.

Issues at the Convective Scale

Environment may be wrong because of model error/bias or because of random IC error at larger scale

– Easy to conflate model error and larger-scale IC error– Crucial to consider extended periods or many cases

Where there is convective instability, expect error growth rates to increase rapidly as scale decreases

– Backscatter may be especially effective

Backscatter for advected substances?

AFWA MEPS Ensemble Configurations

AFWA’s Mesoscale Ensemble Prediction System (MEPS)Member Physical parameterizations

Surface Microphysics PBL Cumulus LW_RA SW_RA

1 Thermal Kessler YSU KF RRTM Dudhia

2 Thermal WSM6 MYJ KF RRTM CAM

3 Noah Kessler MYJ BM CAM Dudhia

4 Noah Lin MYJ Grell CAM CAM

5 Noah WSM5 YSU KF RRTM Dudhia

6 Noah WSM5 MYJ Grell RRTM Dudhia

7 RUC Lin YSU BM CAM Dudhia

8 RUC Eta MYJ KF RRTM Dudhia

9 RUC Eta YSU BM RRTM CAM

10 RUC Thompson MYJ Grell CAM CAM

LMP2 Details

Perturbation magnitude chosen s.t. differences in forecast comparable to those

produced in previous perturbed-parameter experiments

Member Microphys Cu PBL SW Rad Notes

1 WSM5 KF YSU Dudhia AFWA control (member 10)

2 n0r=2e9 dRad = 0.0 a_r=0.3 swrad_scat=2.5

3 n0r=2e6 dRad = -500 a_r=0.1 swrad_scat=1.0

4 n0r=8e6 dRad = 500 a_r=0.15 swrad_scat=0.02

5 Thompson Grell MYJ Dudhia

AFWA member 11 (modified to include Thompson)

6 mu_r=0.5 maxens=4 epsq2=0.02 swrad_scat=0.02 7 mu_r=-0.5 maxens2=4 epsq2=0.25 swrad_scat=2.5

8 Eta_new BMJ YSU CAM AFWA Member 17 9 N0r0=2e6 EFMNT=0.8 a_r=0.3 A=0.95

10 N0r0=2e9 EFMNT=0.6 a_r=0.1 A=1.05