Soil moisture perturbation technique for COSMO Petroula Louka & Flora Gofa Hellenic National Meteorological Service [email protected]@hnms.gr, [email protected]@hnms.gr.

Soil moisture perturbation technique for COSMO

Petroula Louka & Flora Gofa

Hellenic National Meteorological Service

[email protected], [email protected]

12th COSMO General Meeting

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).


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.


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.


Example of deviations from the mean

15/04/2007

Positive dev: average<daily

=> Wetter average than

daily conditions

1st soil layer



15/04/2007



daily conditions

2nd soil layer



15/04/2007



daily conditions

3rd 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 files from the major to the minor “parts”.

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).


EOF categories - Variance percentage

0

2

4

6

8

10

12

14

0 60 120 180 2400

5

10

15

20

25

30

35

0 60 120 180 240

0

5

10

15

20

25

30

35

0 60 120 180 240

1st soil layer 2nd soil layer

3rd soil layer


Soil Moisture Perturbation technique Random perturbations

In order to create perturbations possessing the same structure as the daily deviations, a perturbation method was used:

244

1

N

iiiij d

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.


dyyedyyp 22

2

1

211 2cosln2 xxy

212 2sinln2 xxy

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:


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.

perturbation

Perturbations (kg/m2)

layer 1cm layer 2cm layer 6cm

1 -0.2500 0.1451 0.3711

2 -0.1135 -0.1266 -0.2680

3 -0.1149 0.0967 0.1238

4 -0.0597 0.3479 -0.8977

5 0.0260 -0.3341 -0.7927

6 -0.1952 0.0898 0.1984


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.


Soil moisture input fields1st soil 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.


Soil moisture +12h fields1st soil 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.


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.

1st soil layer

Difference between original and new

forecasted values and corresponding

percentage

Difference

Percentage


Soil moisture input fields3rd soil 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.


Soil moisture +12h fields3rd soil layer (6 cm)


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.


3rd soil layer



percentage

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.

Difference

Percentage



2m Temperature+12h forecast

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.


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.

Difference

2m temperature



percentage

Percentage



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 (wetter) month.


Precipitation


forecasted values

Positive values indicate that the original run has more precipitation than the new run.

The differences over Greece are of the order of 1mm.

Difference


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.


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.)

Soil moisture perturbation technique for COSMO Petroula Louka & Flora Gofa Hellenic National Meteorological Service [email protected]@hnms.gr, [email protected]@hnms.gr.

Documents

daily soil moisture

average wetter average

daily conditions

general aspect of eof

data sets

dwd cosmoeu surface

corresponding daily

large data files