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

2. 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.

3. 15 March 2005Soil 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. 15 March 2005Soil Moisture Perturbations 1) Albedo 2) Roughness Length 3) Moisture Availability UWME UWME+ Current UWME+ Physics Configuration

5. 15 March 2005Soil Moisture Perturbations 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 RUC 0-10 cm soil moisture fraction comparison

6. 15 March 2005Soil 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. 15 March 2005Soil 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 = XX T = USV T (USV T ) T = USV T VSU T = US 2 U T 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. X T X ~ m x m X T X = (USV T ) T (USV T ) = VSU T USV T = VS 2 V T Now we have a manageable eigenvector-eigenvalue problem to solve. (X T X) V = V S 2

8. 15 March 2005Soil 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 = USV T 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. xx T = L -1 yy T L -T = L -1 CL -T ~ I (assuming a large sample) C = USU T ~ LL T L ~ US 1/2 y ~ U S 1/2 x (Nx1) ~ (Nxk)(kxk)(kx1)

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

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

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

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

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

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

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

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

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

18. 15 March 2005Soil 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. 15 March 2005Soil Moisture Perturbations RUC Soil Moisture Fraction Standard Deviation 16-samples (0000 and 1200 UTC, 1-8 March 2005)60-samples (0000 UTC, Jan-Feb 2005)

21. 15 March 2005Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 16-samples (0000 and 1200 UTC, 1-8 March 2005)60-samples (0000 UTC, Jan-Feb 2005)

22. 15 March 2005Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 16-samples (0000 and 1200 UTC, 1-8 March 2005)60-samples (0000 UTC, Jan-Feb 2005)

23. 15 March 2005Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 16-samples (0000 and 1200 UTC, 1-8 March 2005)60-samples (0000 UTC, Jan-Feb 2005) Unperturbed (0000 UTC 2 March 2005)

24. 15 March 2005Soil Moisture Perturbations Example EOF-based Soil Moisture Fraction Perturbations 16-samples (0000 and 1200 UTC, 1-8 March 2005)60-samples (0000 UTC, Jan-Feb 2005) Unperturbed (0000 UTC 2 March 2005)