Eric Grimit

1. Toward State-Dependent Moisture Availability Perturbations in a Multi-Analysis Ensemble System with Physics Diversity Eric Grimit

2. Soil 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.

3. Soil Moisture Perturbations 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.

4. Soil Moisture Perturbations Current UWME+ Physics Configuration UWME UWME+ 1) Albedo 2) Roughness Length 3)Moisture Availability

5. Soil Moisture Perturbations New Soil Moisture Initial Conditions 0-10 cm soil moisture fraction comparison NCEP 20-km RUC • 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.

6. Soil Moisture Perturbations 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?)

7. Soil Moisture Perturbations 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

8. Soil Moisture Perturbations 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 = US U = 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)

9. Soil Moisture Perturbations RUC Soil Moisture Fraction Standard Deviation and Control Soil Moisture Fraction Standard Deviation Soil Moisture Fraction Control – NCEP 20km RUC 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

10. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #1 Soil Moisture Fraction Control + Perturbation #1 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

11. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #2 Soil Moisture Fraction Control + Perturbation #2 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

12. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #3 Soil Moisture Fraction Control + Perturbation #3 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

13. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #4 Soil Moisture Fraction Control + Perturbation #4 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

14. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #5 Soil Moisture Fraction Control + Perturbation #5 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

15. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #6 Soil Moisture Fraction Control + Perturbation #6 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

16. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #7 Soil Moisture Fraction Control + Perturbation #7 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

17. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations Soil Moisture Fraction Perturbation #8 Soil Moisture Fraction Control + Perturbation #8 90-samples (1200 UTC, 6 Dec – 14 Mar 2005) (1200 UTC, 15 Mar 2005)

18. Soil Moisture Perturbations 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.

19. Original Results Slides

20. Soil Moisture Perturbations RUC Soil Moisture Fraction Standard Deviation 60-samples (0000 UTC, Jan-Feb 2005) 16-samples (0000 and 1200 UTC, 1-8 March 2005)

21. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 60-samples (0000 UTC, Jan-Feb 2005) 16-samples (0000 and 1200 UTC, 1-8 March 2005)

22. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 60-samples (0000 UTC, Jan-Feb 2005) 16-samples (0000 and 1200 UTC, 1-8 March 2005)

23. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 60-samples (0000 UTC, Jan-Feb 2005) 16-samples (0000 and 1200 UTC, 1-8 March 2005) Unperturbed (0000 UTC 2 March 2005)

24. Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 60-samples (0000 UTC, Jan-Feb 2005) 16-samples (0000 and 1200 UTC, 1-8 March 2005) Unperturbed (0000 UTC 2 March 2005)