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Introduction
The forecast of screen-level variables T2m, RH2m is studied with relation to soil moisture initialization. A set of simple experiments allows to assess the sensitivity of 2m forecast fields to a perturbation of the initial mean soil moisture Wp. The perturbation of the guess is used to evaluate the observation matrix H in the 2d-var assimilation.
The screen-level sensitivity to the soil moisture perturbation is varying with the meteorological situation and the soil state, which is the most desirable feature of the variational soil moisture analysis. This variability has also consequences on the validity of an "horizontal decoupling" hypothesis and on the clear evaluation of the gain matrix K. In fact, where the soil has lower vertical influence, the lateral influence of adjacent gridpoint, as well as the occurrence of noise, may become important. Different perturbations of the control variable Wp have been tried. A satisfactory evaluation is obtained with a double chess-like perturbation to increase the horizontal decoupling between gridpoints. The use of a Laplacian smoothing on the coefficients is sufficient to filter out the noisy patterns without varying the main structures of K.
This study is necessary to design a perturbation strategy for 2d-var assimilation of screen-level parameters for mean soil moisture analysis. The gain matrix K resulting from the linear variational method is examined on the ALADIN-France domain.
The perturbation of the control variable Wp
The importance of the initial perturbation comes from the use of 2d-var in the full 3d Aladin model, and the multiple interactions not simply related to the vertical soil-atmosphere feedback. Anyway, it has to be stressed that even for the Single Column Model (SCM), the perturbation of Wp has to be carefully chosen in order to take into account the sensitivity zone, especially the range between field capacity and wilting point (Mahfouf, 1991 and Bouttier, 1993).
The magnitude of the perturbation is also an important issue : it has to be small in order to satisfy the linear hypothesis but large enough to prevent the occurrence of large noisy patterns.
Particularly to this latter point, the occurrence of noise in screen-level forecast under cyclonic conditions can be shown in the "horizontal decoupling" experiment performed on the ALADIN-France domain (see also the previous Newsletter report for details), in figures 1 and 2.
Figure 1.(a), ( b) and (c ): Horizontal decoupling test in clear sky condition. This test shows the sensitivity of 2m temperature (b) and relative humidity (c) to a well known initial perturbation box of mean soil moisture content Wp (a).
Figure 2.(a), ( b) and (c ): Same as Figure 1 for a box placed near to the north-eastern side of the domain (meteorological perturbed conditions).
It arises that a secondary effect of the soil moisture initialization causes the noise to appear on locations far from the initial soil moisture perturbation, in both cases. The occurrence of noise in the 2m trajectory was also shown in a previous report and it is mainly addressed to extra sensitivity of 2m parameterization in meteorological perturbed conditions. In the evaluation of the K matrix this feature is undesirable and has to be removed.
The choice of gridpoint perturbation for Wp
The perturbation of Wp can have different forms. The tests are performed on a real first-guess situation (2000/06/16 12 UTC) with a 6-hour assimilation time-window. The initial soil moisture presents several dry and wet peaks and allows to point out the area where a lower sensitivity to perturbation is expected. Three different perturbation methods are presented and are defined as:
- Coherent
When a certain quantity is added homogeneously to the initial soil moisture. In this case, the result of the evaluation of the K matrix is shown in figure 3a. The evaluation of K can be averaged over several perturbed runs or members to add statistical strength to the final K (figure 3b). A drawback of this choice is that the perturbation is rather strong (~30 mm of water added over a ~107 km2 domain) and can reduce the horizontal decoupling between gridpoints, especially in case of weak vertical correlation.
- Conditional
When the perturbation is added or subtracted according to a condition on the initial guess value (typically, if the soil wetness index is lower than 0.5 the perturbation is added). The reason for such perturbations lies in the search for screen-level sensitivity to soil moisture in the range between wilting point and field capacity. This has been widely used in different tests (when masking is applied), but the occurrence of noise is quite strong (figure 3c).
- Chess-type
When the perturbation is added and subtracted in adjacent gridpoints in order to have a chess-like perturbed fields (Hess, 2001). This has the advantage to increase the horizontal decoupling between gridpoints without changing the overall soil water content on the domain. On the other hand the occurrence of large noise in the response is found in the 2m fields (figure 3d). A better response is found considering 2 opposite perturbations of this type to evaluate the K matrix. This setup allows to distinguish the noisy patterns from the low sensitive zone (figure 3e) and it is therefore considered for further study.
Figure 3. Evaluation of the mean soil moisture perturbation strategy. K matrix for T2m (Wp correction) for given perturbations : (a) coherent, (b ) coherent (average of 10 members), (c ) conditional, (d) chess-type (1 member) and (e) chess-type (2 members).
The masking of sensitive zones
The masking is a technical solution adopted by the operational OI (Optimal Interpolation) analysis (CANARI-ARPEGE/ALADIN) in order to avoid spurious corrections of the mean soil moisture during atmospherical perturbed conditions, such as precipitation events, reduced solar radiation flux or strong lateral advection.
The magnitude of the OI coefficients was evaluated on 1d experiments by a Monte-Carlo method, looking at the correlation between Wp and screen-level parameters, T2m and RH2m. A set of regressions with physiographic parameters (vegetation fraction, Leaf Area Index, soil texture) and model fields provided the value of the OI coefficients (Bouttier et al. 1993, Giard and Bazile, 2000). A masking function is used to cut off the soil moisture correction when some thresholds are over-passed (see Table 1). This has been tuned to stop the analysis when the correlation between soil and screen-level parameters errors is weak. Now, in the ideal case, where all the dependencies are kept into account (too complex to put in operation), the OI coefficient would range continuously between 0 (no information transfer) and the maximum correction (e.g. on a summer day with clear sky condition) without need of masking.
In operational context the OI coefficients transfer the 2m errors of temperature and relative humidity into soil moisture corrections on a limited range of combinations of local physiographic and meteorological situations, explicitly treated in their formulation.
test on first-guess fields |
test on relative or absolute differences between 6-hours forecast from initial and perturbed fields |
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Total cloud cover r = 0.05 | |
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Convective cloud cover r = 0.05 | |
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Precipitation s = 0.3 mm |
Convective precipitation a = 0.01 mm |
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Stratiform precipitation a= 0.01 mm | |
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Solar radiation flux r=0.01 a = 1.0 Wm2 | |
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Solar time duration s = 6 h (min) |
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Snow depth a = 0.05 m | |
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Frozen soil water content s = 5.0 mm |
Frozen soil water content a = 0.05 mm |
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10m wind speed s = 10 m/s |
10m wind speed r = 0.10 a = 0.05 m/s |
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Evaporation s = 0.001 mm (min) |
Table 1: Masking condition in the operational OI surface analysis and analogues in 2d-var.
Figure 4.(a) Evaluation of OI coefficient for T2m (Wp correction) and (b ) equivalent 2d-var gain matrix.
Nevertheless we can think that in such cases the information content from 2m observations is not negligible although small, and the variational approach should allow to gain a consistent correction of the soil moisture. The statistical properties of OI coefficients, in fact, do not allow a full local description whenever the relation between soil moisture and screen-level parameters is not linearizable on a general case (not case dependent).
Although masking in 2d-var has been developed it was used only for tests (comparisons 2d-var versus OI). A combination of a careful choice of the perturbation and of spatial smoothing to get rid of the remaining noise has been studied.
The Laplacian smoothing
The Laplacian smoothing is used to filter the remaining noisy patterns on the K coefficients. The basic Laplacian smoothing is based on the Laplacian flow :
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The discrete implementation is achieved by multiplying the Laplacian operator mask L(i,j) :
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where I(x,y) is the original image and L(i,j) is the Laplacian operator mask. This method gives a smoother image of a given 2d field.
For application on a geographical case the map factor MAP(x,y), the prescribed smoothing length R, the gridpoint dimensioning (X,Y) and the land-sea mask LSM(x,y), have to enter the formulas and be kept into account, therefore the formulation of the Laplacian mask operator is:
L(x,y) = 1/4 x r2 x MAP(x,y) ; r2 = min ( R2, X2 , Y2) (3)
The resulting smoothed field I(x,y) is the summation of the gradients in x and y divided by the squared gridpoint dimension, respectively X2 and Y2 . In the following formulation a generic notation is used :
where i, j=+1 / 0 / -1,so that:
I = I + L x { [ (I(+,0) - I) + (I(-,0) -I) ] / X2 + [ (I(0,+) - I) + (I(0,-) -I) / Y 2 ] } (4)
A small value of the smoothing length preserves the main structures of the field filtering only very high resolution features. Tuning for an ALADIN gridpoint dimensioning of X =Y = 9.92 km led to the choice : R = 2.5 km and 3 cycles of smoothing.
The same smoothing is applied to the analysed field for consistency. This technique is preferable to the thresholds masking for noise removal, as it has smaller impact and easier tuning.
Optimization of the K matrix in 2d-var
As a general warning from the performed test, the degree of horizontal decoupling is dependent from the choice of perturbation of the control variable. Coherent and anti-correlated gridpoint perturbations (chess-type) have different responses in real situation. The evaluation of the K matrix is obtained here with a double chess-like perturbation and Laplacian smoothing. Figure 5 shows the result when applying the method on a real case (16 June 2000).
Figure 5.: K matrix for 2000/06/16 12 UTC as result of chess-type perturbation (2 members) and Laplacian smoothing. (a ) K value for T2m (Wp correction), (b ) K value for RH2m (Wp correction).
Figure 6.: Soil Wetness Index for 2000/06/16 12 UTC ( ARPEGE/ALADIN oper.).
The appearance of strong and weak correction peaks is found to well match the previous soil state and can be compared with the operational analyzed soil wetness index (figure 6).
Conclusions and perspectives
The configuration for testing the 2d-var on a real assimilation cycle has been reached. The validation phase will now focus on 4 periods of 2-3 weeks with 2d-var assimilation of Wp using a 24-hours time-window. A 6-hours cycle is maintained for the assimilation of the other soil variables Ts, Ws, Tp. Some more tests for Tp may also be considered.
Over other benefits of the variational approach, it is also likely that moving to a 24h assimilation period would be beneficial to the stability of analysis (more observations coherently assimilated). Problems highlighted in previous tests as coastal moistening during anti-cyclonic periods, will be probably reduced by some technical constraints adopted in the latest version of the 2d-var, like limiting divergent analysis corrections.
The perspective of using the method in the frame of the ELDAS project will guide further tests towards the assimilation of other fields, like analyzed precipitation and satellite data.
List of figures
The list of figures can be seen here.
References
Bouttier F., J.F. Mahfouf and J. Noilhan, 1993: Sequential Assimilation of Soil Moisture from Atmospheric Low-Level Parameters. Part I: Sensitivity and Calibration Studies. J. of Appl. Met., 32, 1335-1351.
Bouttier F., J.F. Mahfouf and J. Noilhan, 1993: Sequential Assimilation of Soil Moisture from Atmospheric Low-Level Parameters. Part II: Implementation in a Mesoscale Model. J. of Appl. Met., 32, 1352-1364.
Bouyssel F., V. Cassé and J. Pailleux, 1999: Variational surface analysis from screen level atmospheric parameters. Tellus, 51A, 453-468.
Douville H., P. Viterbo, J.F. Mahfouf and A. Beljaars, 2000: Evaluation of Optimum Interpolation and Nudging Technique for Soil Moisture Analysis using FIFE Data. Mon. Wea. Rev., 128, 1733-1756.
Giard D. and E. Bazile, 2000: Implementation of a new assimilation scheme for soil and surface variables in a global NWP model. Mon. Wea. Rev., 128, 997-1015.
Hess, R., 2001: Assimilation of screen level observations by variational soil moisture analysis Meteorol. Atm. Phys. 77, 145-154.
Noilhan J. and J.F. Mahfouf, 1997: The ISBA Land Surface parameterization scheme. Global and Planetery Change, 13, 145-159
Mahfouf J.F., 1991: Analysis of Soil Moisture from Near-Surface Parameters: A Feasibility Study. J. of Appl. Met., 30, 1534-1547.
Rhodin, A., F. Kucharski, U. Callies, D.P. Eppel and W. Wergen, 1999: Variational analysis of effective soil moisture from screen level atmospheric parameters; application to a short-range forecast; Quart. J. Roy. Meteor. Soc. 125, 2427-2448.
