Soil moisture perturbation technique for COSMO and implementation in COSMO suite Petroula Louka & Flora Gofa Hellenic National Meteorological Service Chiara Marsigli ARPA-SIM

Reasoning The interaction between the surface and the lower troposphere determines the development of fluxes close to the ground. Soil moisture is of primary importance in determining the partition of energy between surface heat fluxes, thus affecting near-surface forecasts. The ensemble forecasts usually suffer of a lack of variability among the members, which is typically worse near the surface rather than higher in the troposphere. The aim of this task is to ameliorate this deficiency by implementing a technique for perturbing soil moisture conditions and explore its impacts on the variability of the members for the different forecasted surface parameters (e.g. 2m air temperature, precipitation, etc.).

Soil Moisture Perturbation technique General steps HNMS developed the technique based on the method proposed by Sutton and Hamill (2004), using calculations of Houtekamer (1993) and using theory based on Bjornsson and Venegas (1997). Use daily soil moisture data for a certain period with soil moisture variability for continuous years, in order to have some sort of “climatology” and calculate daily deviations. Implement an EOF (Empirical Orthogonal Function) analysis to identify the variability appearing in the deviation data. Calculate perturbations and create an EPS.

Soil Moisture Perturbation technique Soil moisture “climatology” and deviations Daily soil water content data were provided by DWD COSMO-EU surface analysis through web interface (communication with Andreas Röpnack et al.) The period selected for the dataset, was three months (Apr-May- Jun) for three years ( ). This period can provide the necessary soil moisture variability. These data were extracted at the 8 different levels in the soil, namely 1, 2, 6, 18, 54, 162, 486, 1458 cm It was decided to apply the technique to all levels. For each of these data sets, a 30-day moving average was calculated together with the corresponding daily deviations from the mean.

Example of deviations from the mean 15/04/2007 Positive dev: daily>average => Wetter daily than average conditions 1 st soil layer

Soil Moisture Perturbation technique EOF analysis Routine calculating EOFs [Ziemke J.R. based on Kutzbach (1967)] has been adopted to work for large data files. This calculation is based on the general aspect of EOF analysis, i.e. the determination of different “categories” that characterize the data behavior from the most important to the least important features. Using the eigen-analysis method. Calculation problem: The daily deviation data files are large representing approximately 450,000 grid points (lines) and have to be diagonalized during the EOF analysis leading to matrices with dimensions (450,000x450,000). Such huge matrices are not easy to be handled as they require a very large stack memory. For this reason it was necessary to find solutions to overcome this problem.

Time-dependent EOF analysis An alternative and efficient method to overcome this problem was to inverse the matrices, i.e. if initially there are M lines (grid points) and N days, with N << M, it is possible to end up with NxN matrices that would lead to much less computationally intensive problem (von Storch and Hannoschock, 1984; Legler, 1984). This reduction would lead to time-dependent EOFs. Thus instead of solving the problem in space: where R the covariance matrix of the data F(M,N): and C and Λ are the space eigenvectors and the corresponding eigenvalues, respectively. we solve the problem in time: where L the covariance matrix: and B corresponds to the time eigenvectors.

Space-dependent EOF analysis From the time-dependent EOF analysis the space-dependent eigenvectors, C, were calculated based on Bjornsson & Venegas: which means the space dependent eigenvectors are calculated from the above equations by dividing with (sqrt (λ i )). The matrix C, we will end up with, will have dimensions NxM, which means that its 1st column will correspond with the space leading eigenvector for every ni point, the 2nd column will correspond to the second leading eigenvector and so on up to the M EOF category we have kept.

Soil Moisture Perturbation technique Random perturbations Houtekamer (1993) proposed a method to create an ensemble using an EOF analysis combined with sets of random numbers. The perturbations are calculated from: In order to solve the equation a method for creating random numbers was used – based on Box-Muller method for generating random deviates with normal distribution (Press et al., 1992). where d are the random numbers. Each line corresponds to each point in space and the sum is over the 244 EOF categories (if all are kept).

Random perturbations The perturbations have been added to the soil moisture field to be perturbed in the SREPS domain. In order to obtain the new soil moisture (SM) field, a constrain has been applied so that the perturbations are up to 50% less than the original SM field. The original (control, SM_ctrl) run, corresponds to one member of COSMO-SREPS, nested on IFS without physics perturbations. SM_ctrl refers to a 48-hour run starting on Three 48-hour tests have been performed, each of them dependent on the random numbers obtained starting from a different dummy number (dum): –Test 1. PL_dum0 : in this case no random numbers=1. –Test 2. PL_dum-1. –Test 3. PL_dum-5. These 3 tests could correspond to 3 different members in the ensemble.

PL_dum0 PL_dum-1PL_dum-5 Difference with CNTRL SM – level1 +24h Positive values correspond to wetter soil layer for the CTRL run. The areas with positive values seem to be more than those with negative values at t+24h. For the particular date it seems that the method leads mostly to differences over East and some parts of West Europe although there are also differences in smaller areas elsewhere.

Difference with CNTRL SM – level3 +24h PL_dum0 PL_dum-1PL_dum-5 For the 3 rd soil layer, it seems that the dependence on the set of random numbers used is larger. For the particular date it seems that the method leads to differences over smaller as well as over some other areas than within the 1 st soil layer.

Difference with CNTRL SM – level1 +48h PL_dum0 PL_dum-1PL_dum-5 At t+48h, the differences with the CTRL are greater and appear generally over the whole domain. There are also some changes among the results from the tests with various random numbers used (which could lead to different members of an ensemble).

Difference with CNTRL SM – level3 +48h At t+48h, the differences with the CTRL are greater. Again, for the 3 rd soil layer, it seems that the dependence on the set of random numbers used is large, especially between dum-1 and dum-5. PL_dum0 PL_dum-1PL_dum-5

PL_dum5 Difference with CNTRL T2m +24h PL_dum0 PL_dum-1PL_dum-5 At t+24h, it seems that there are negative differences, i.e., colder new conditions compared to the CTRL run in many parts of the domain, although, there are also some small positive values (warmer new conditions). It seems that the dependence on the set of random numbers used is large, especially between dum-1 and dum-5.

PL_dum5 Difference with CNTRL T2m +48h PL_dum0 PL_dum-1PL_dum-5 At t+48h, it seems that there are larger negative differences, i.e., colder new conditions compared to the CTRL run in many parts of the domain, although, there are also some small positive values (warmer new conditions). It seems that the dependence on the set of random numbers used is large, especially between dum-1 and dum-5.

Difference with CNTRL Accumulative Precipitation +24h PL_dum0 PL_dum-1PL_dum-5 At t+24h, it seems that there are mainly small differences (positive or negative), between the CTRL run and the new runs. It seems that there is a dependence on the set of random numbers used.

Difference with CNTRL Accumulative Precipitation +48h PL_dum0 PL_dum-1PL_dum-5 At t+48h, the differences (positive or negative) between the CTRL run and the new runs are larger, appearing in larger areas of the domain. It seems that there is a dependence on the set of random numbers used.

Difference with CNTRL Latent heat flux +24h PL_dum0 PL_dum-1PL_dum-5 At t+24h, it seems that there are negative values (i.e., the new runs result to larger LHF than the CTRL) over large parts of the domain and some positive over smaller parts of the domain. It is not clear whether these areas are related with positive differences of precipitation, but it seems that they are related with the warmer conditions resulted by the new runs.

Difference with CNTRL Sensible heat flux +24h PL_dum0 PL_dum-1PL_dum-5 At t+24h, it seems that there are positive values (i.e., the new runs result to smaller SHF than the CTRL) over large parts of the domain and some negative over smaller parts of the domain. It seems that the positive differences are related with the warmer conditions resulted by the new runs and the negative differences of LHF over the same areas as expected.

Remarks – Suggestions A technique for creating soil moisture perturbations has been adopted for COSMO ensemble system. Implementation of the technique has been performed with 3 tests and the results have been compared with the control run. Soil moisture fields at different layers, 2m temperature, accumulative precipitation, latent and sensible heat fluxes were investigated. The first results showed: –Differences among the tests and between the tests and the control run. This is necessary when creating an ensemble system as spread among members is required. –Areas of the domain with larger latent heat fluxes are related with smaller sensible heat fluxes and larger 2m temperature as expected. Obviously, more tests of the same kind are required for different dates in order to end up with solid results. It is planned to combine these perturbations with different convective schemes. The technique will be adopted for operational use.

References Bjornsson Halldor and Silvia A. Venegas. "A manual for EOF and SVD analyses of climate data", McGill University, CCGCR Report No. 97-1, Montréal, Québec, 52pp., 1997."A manual for EOF and SVD analyses of climate data" Houtekamer, P.L. (1993). Global and local skill forecasts. Mon. Wea. Rev., 121, Kutzbach J.E. (1967). Empirical eigenvectors of sea-level pressure, surface temperature and precipitation complexes over North America. J. Appl. Meteorol., 6, Magnusson, L., E. Kallen, and J. Nycander (2008). Initial state perturbations in ensemble forecasting. Nonlinear Processes in Geophysics, 15, Press, W.H., S.A. Teulosky, W.T. Vetterling and B.P. Flannery (1992). Numerical Recipies in Fortran nd ed. Cambridge Univ. Press, pp 280. Sutton and Hamill (2004). Impacts of perturbed soil moisture conditions on short range ensemble variability. von Storch, H., and G. Hannoschock (1984). Comments on "Empirical Orthogonal Function Analysis of Wind Vectors over the Tropical Pacific Ocean". Bulleting of the Meteorological Society of America, 65, 162. (Appeared as a letter to the editor concerning: Legier D.M. (1983). Empirical Orthogonal Function Analysis of Wind Vectors over the Tropical Pacific Region. Bulleting of the Meteorological Society of America, 64, )