Soil moisture perturbation technique for COSMO Petroula Louka & Flora Gofa Hellenic National Meteorological Service

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 Based on the method proposed by Sutton and Hamill (2004) and using Houtekamer (1993). 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 calculate the perturbations in the variability categories appearing in the data. Create random perturbations.

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, initially, to the first 3 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 characterise the data behaviour from the most important to the least important features. Using the eigen-analysis way: Where C the covariance matrix of the quantity S: e and λ are the eigenvectors and eigenvalues, respectively. α, β = 1, …, Ν N is e.g. the number of grid points or time series of S.

EOF analysis The daily deviation data files are large representing approximately 450,000 grid points (lines) and have to be diagonalised 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. 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).

Soil Moisture Perturbation technique Random perturbations In order to create perturbations possessing the same structure as the daily deviations, a perturbation method was used: where, j is the j-th perturbation, d i a standard normally distributed random number, i the square root of the eigenvalues and i the corresponding eigenvectors. 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). Therefore, the result also depends on the random coefficients created.

Random perturbations The perturbations should then be added/subtracted to the soil moisture field to be perturbed in the SREPS domain. If using 6 perturbations for each soil layer, the result will be 6 perturbed fields and hence 6 new fields to be used as initial conditions in the suite for each layer, e.g.: perturbation Perturbations (kg/m 2 ) layer 1cmlayer 2cmlayer 6cm

Soil Moisture Perturbation technique Preliminary test The perturbation method was applied to the operational COSMO-GR deterministic model. The first 3 soil layers were perturbed and became drier subtracting the perturbation values from the initial fields. A run was performed with these fields just for 12 hours for 01/09/ UTC cycle.

Soil moisture input fields 3 rd soil layer (6 cm) Original fieldNew field Initial values of soil moisture in the third soil layer range between 0 and 18 kg/m 2 in Greece. The new soil layer has become drier.

Soil moisture +12h fields 3 rd soil layer (6 cm) Original runNew run The forecasted values (in both cases) show wetter conditions over NE Greece. The new run resulted to a drier 3 rd soil layer than in the original run.

3 rd soil layer Difference between original and new forecasted values and corresponding percentage Positive values indicate that the original run is higher than the new (which is drier). The differences over Greece are between 1 and 1.6 kg/m 2 corresponding approximately to % change from the original run. Difference Percentage

Original runNew run Total precipitation + 12h forecast The effect of the perturbed initial soil moisture fields to the accumulative precipitation fields is quite small of the order of 1mm. The impact may had been greater if in another month or looking at another country.

Precipitation Difference between original and new forecasted values Positive values indicate that the original run has more precipitation than the new run. Difference

Remarks – Suggestions A technique for creating soil moisture perturbations has been adopted for COSMO. Preliminary test of the implementation of the technique on the deterministic COSMO-GR model showed impacts on the forecasted soil moisture and small impact on precipitation forecasts over Greece. It is expected that the impact will be greater in the case of another month or in other countries. The soil perturbation technique is going to be applied in testing mode to the initial fields in the CONSENS suite to create e.g. 2 members (1 for drier and 1 for wetter than the initial conditions). It is planned to combine these perturbations with different convective schemes. Depending on the adequacy of the spread in the ensemble results the same technique may be modified, e.g. –Separating the different soil categories and start the technique from the beginning in order to create different perturbation numbers for each soil category. The technique will be adopted for operational use.

References 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, )