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Soil moisture perturbation technique for COSMO

Soil moisture perturbation technique for COSMO. Petroula Louka & Flora Gofa Hellenic National Meteorological Service louka@hnms.gr , fgofa@hnms.gr. Reasoning. The interaction between the surface and the lower troposphere determines the development of fluxes close to the ground.

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Soil moisture perturbation technique for COSMO

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  1. Soil moisture perturbation technique for COSMO Petroula Louka & Flora Gofa Hellenic National Meteorological Service louka@hnms.gr, fgofa@hnms.gr

  2. 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, accumulative precipitation). 12th COSMO General Meeting

  3. Soil Moisture Perturbation technique General points 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 – Principal Component Analysis) analysis to calculate the perturbations in the variability categories appearing in the data. • Create random perturbations. 12th COSMO General Meeting

  4. 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 (2007-2009). 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. 12th COSMO General Meeting

  5. Example of deviations from the mean 1st soil layer 15/04/2007 Positive dev: average<daily => Wetter average than daily conditions 12th COSMO General Meeting

  6. Example of deviations from the mean 2nd soil layer 15/04/2007 Positive dev: average<daily => Wetter average than daily conditions 12th COSMO General Meeting

  7. Example of deviations from the mean 3rd soil layer 15/04/2007 Positive dev: average<daily => Wetter average than daily conditions 12th COSMO General Meeting

  8. 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 files from the major to the minor “parts”. • Using the eigen-analysis way: Where C the covariance matrix of the quantity S: e and λare the eigenvectors and eigenvalues respectively. α, β=1, …, Ν N is e.g. the number of grid points or time series of S. 12th COSMO General Meeting

  9. 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). 12th COSMO General Meeting

  10. EOF categories - Variancepercentage 1st soil layer 2nd soil layer 3rd soil layer 12th COSMO General Meeting

  11. 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, di 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 depends on the random coefficients created. 12th COSMO General Meeting

  12. Method for generating random numbers of normal distribution • In order to create random numbers, the method described in Press et al. (1992) is adopted that calculates normally distributed deviates with zero mean and unit variance. • This uses the Box-Muller method for generating random deviates with normal (Gaussian) distribution: which considers the transformation of x1,x2 by y1 and y2: 12th COSMO General Meeting

  13. Random perturbations • The perturbations are then added/subtracted to the soil moisture field to be perturbed. • 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. 12th COSMO General Meeting

  14. 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 absolute larger perturbation values from the initial field. • A run was performed with these fields just for 12 hours for 01/09/2010 00UTC cycle. 12th COSMO General Meeting

  15. Soil moisture input fields1stsoil layer (1cm) Original field New field Initial values of soil moisture in the first soil layer range between 0 and 3.0 kg/m2 in Greece. The new soil layer has become drier by 0.25 kg/m2. 12th COSMO General Meeting

  16. Soil moisture +12h fields1stsoil layer (1cm) Original run New run The forecasted values (in both cases) show wetter conditions over NE Greece. The new run resulted to a slightly drier 1st soil layer than in the original run. 12th COSMO General Meeting

  17. 1st soil layer Difference between original and new forecasted values and corresponding percentage Difference Positive values indicate that the original run has larger values than the new (drier). The differences over Greece are small between 0.2 and 0.3 kg/m2 corresponding approximately to 8 -15% change from the original run. Percentage 12th COSMO General Meeting

  18. Soil moisture input fields3rdsoil layer (6 cm) Original field New field Initial values of soil moisture in the third soil layer range between 0 and 18 kg/m2 in Greece. The new soil layer has become drier by 0.90 kg/m2. 12th COSMO General Meeting

  19. Soil moisture +12h fields3rdsoil layer (6 cm) Original run New run The forecasted values (in both cases) show wetter conditions over NE Greece. The new run resulted to a drier 3rd soil layer than in the original run. 12th COSMO General Meeting

  20. 3rd soil layer Difference between original and new forecasted values and corresponding percentage Difference Positive values indicate that the original run is higher than the new (drier). The differences over Greece are small between 1 and 1.5 kg/m2 corresponding approximately to 8 -12% change from the original run. Percentage 12th COSMO General Meeting

  21. 2m Temperature+12h forecast Original run New run The effect of the perturbed initial soil moisture fields to the 2m temperature field is small of the order of 0.5 Cº with temperature reaching 30ºC at the South and 26ºC at the NE Greece. The impact may had been greater if in another (wetter) month. 12th COSMO General Meeting

  22. 2m temperature Difference between original and new forecasted values and corresponding percentage Difference Negative values indicate that the original run has lower values than the new (cooler). The differences over Greece are quite small ~0.5Cº corresponding to 2 -3% change from the original run. Percentage 12th COSMO General Meeting

  23. Total precipitation+12h forecast Original run New run 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 (wetter) month. 12th COSMO General Meeting

  24. Precipitation Difference between original and new forecasted values Difference Positive values indicate that the original run has more precipitation than the new run. The differences over Greece are of the order of 1mm. 12th COSMO General Meeting

  25. Next steps • The soil perturbation technique will be applied 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). • Depending on the adequacy of the spread in the ensemble results the same technique may be modified, e.g. • Only in the part of creating the sets of random numbers. • Separating the different soil categories and start the technique from the beginning in order to create different perturbation numbers for each soil category. 12th COSMO General Meeting

  26. References • Houtekamer, P.L. (1993). Global and local skill forecasts. Mon. Wea. Rev., 121, 1834-1846. • Kutzbach J.E. (1967). Empirical eigenvectors of sea-level pressure, surface temperature and precipitation complexes over North America. J. Appl. Meteorol., 6, 791-802. • Magnusson, L., E. Kallen, and J. Nycander (2008). Initial state perturbations in ensemble forecasting. Nonlinear Processes in Geophysics, 15, 751-759. • Press, W.H., S.A. Teulosky, W.T. Vetterling and B.P. Flannery (1992). Numerical Recipies in Fortran 77. 2nd 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, 234-241.) 12th COSMO General Meeting

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