The soil analysis scheme is based on an "local" optimum interpolation technique as described in Mahfouf (1991) and Douville et al. (2001). The analysis increments from the screen-level analysis are used to produce increments for the water content in the first three soil layers (correponding to the root zone) :

(12.8)

and for the first soil temperature layer :

(12.9)

The coefficients

and

are defined as the product of optimum coefficients

and

minimising the variance of analysis error and of empirical functions

and

reducing the size of the optimum coefficients when the coupling between the soil and the lower boundary layer is weak.

(12.10)

and

(12.11)

with

(12.12)

where

represents the correlation of background errors between parameters

and

.

The statistics of background errors have been obtained from a series of Monte-Carlo experiments with a single-column version of the atmospheric model where initial conditions for soil moisture have been perturbed randomly. They were obtained for a clear-sky situation with strong solar insolation. Empirical functions are aimed to reduce soil increments when atmospheric forecast errors contain less information about soil moisture. To obtain negligible soil-moisture corrections during the night and in winter,

is a function of the cosine of the mean solar zenith angle

, averaged over the 6 h prior to the analysis time :

(12.13)

The optimum coefficients are also reduced when the radiative forcing at the surface is weak (cloudy or rainy situtations). For this purpose, the atmospheric transmittance

is computed from the mean downward surface solar radiation forecasted during the previous 6 hours

as :

(12.14)

where

is the solar constant.

The empirical function

is expressed as :

(12.15)

with

and

.

The empirical function

reduces soil moisture increments over mountainous areas :

(12.16)

where

is the model orography,

=500 m and

=3000 m.

Furthermore, soil moisture increments are set to zero if one of the following conditions is fufilled:

1) The last 6 h precipitation exceeds 0.6 mm

2) The instantaneous wind speed exceeds 10 m s^-1

3) The air temperature is below freezing

4) There is snow on the ground

To reduce soil moisture increments over bare soil surfaces, the standard deviations and the correlations coefficients are also weighted by the vegetation fraction

, where low and high vegetation cover are defined in Chapter 7 of the Physics Documentation.

The statistics of forecast errors necessary to compute the optimum coefficients are given in Table 12.1.

The correlations have been produced from the Monte-Carlo experiments. The standard deviation of background error for soil moisture

is set to 0.01 m³m^-3 on the basis of ECMWF forecasts differences between day 1 and day 2 of the net surface water budget (precipitation minus evaporation minus runoff).

The standard deviation of analysis error

is given by the screen-level analysis from :

(12.17)

From the values chosen for the screen-level analyis

and

%.

Soil moisture increments

are such that they keep soil moisture within the wilting point

and the field capacity

values, i.e. :

• if

then

• if

then

Finally the coefficients providing the analysis increments are :

(12.18)

and

(12.19)

The coefficient

is such that soil temperature is more effective during night and in winter, when the temperature errors are less likely to be related to soil moisture. This way, 2 m temperature errors are not used to correct soil moisture and soil temperature at the same time.

Table 12.1 Statistics of background errors for soil moisture derived from Monte-Carlo experiments
Coefficient	Value
	-0.82
	-0.92
	-0.90
	0.83
	0.93
	0.91
	1.25 K
	9.5 %
	-0.99

In the 12 h 4D-Var configuration, the soil analysis is performed twice during the assimilation window and the sum of the increments is added to the background values at analysis time.

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22.03.2002

DATA ASSIMILATION

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12.3 Soil analysis