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Land surface assimilation
March 2001
By Jean-François Mahfouf and Pedro Viterbo
European Centre for Medium-Range Weather
Forecasts
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5 Soil moisture initialisation using SYNOP observations
5.1 The ECMWF method
The land surface scheme developed by Viterbo and Beljaars (1995) was introduced operationally in August 1993 and all soil prognostic variables were initialized to first-guess values. One of the main differences with respect to the previous ECMWF land surface scheme (Blondin 1991) is the absence of climatological relaxation for deep soil temperature and water content. During May-June 1994, the soil reservoirs were drying out, leading to surface air temperature errors increasingly positive, and in comparison with other models, such as the German Weather Service (constrained by climatological soil moisture), forecast skill was deteriorating (Viterbo and Courtier 1995). The downward drift of soil moisture appears to be linked to excess incoming solar radiation primarily caused by underprediction of clouds. Furthermore, the excessive warming at the lower troposphere affected the forecast performance, as shown in Fig. 2 . The 500 hPa geopotential day 2 forecast averaged over Europe is presented for April to June 1994. The ECMWF forecast (dashed line) has a positive bias from late April onwards.
Analysis increments of specific humidity at the lowest model level during May 1994 show positive values over Europe with maxima reaching 2.5 g/kg. The atmospheric analysis tries to compensate for the model bias by moistening and cooling the lower atmosphere. Therefore, the low level humidity increments can be used to identify areas where the soil is too dry. Knowing the analysis increment of specific humidity
, the
correction of soil moisture to be applied the root zone 
is assumed to be proportional :
|
(8) |
with
t = 6 hours,
and the subscripts a and f refer to analysis and forecast values, repsectively.
The relaxation coefficient D is constant in space and time and
corresponds to a specific humidity analysis increment of 1.5 g/kg filling
150 mm of water in the soil in 9 days. The fraction of vegetation 
in the
above formula guarantees that the scheme is not active over deserts. No
increments are produced in the presence of snow, and the analysed soil moisture
contents 
a are limited by the field capacity and permanent
wilting point thresholds. The integrated soil water increments are distributed
in each of the three soil layers following the model root extraction. This
nudging scheme was implemented operationally in December 1994. It supplies
soil moisture to maintain evaporation in areas of excessive radiation at
the surface, caused, among other factors, by insufficient cloud cover. Fig.
3 compares the day 3 forecast errors in screen level day time temperature
and humidity, averaged over Europe. Three experiments are compared: Operations,
FWDC, where no initialisation of soil water is applied and the diagnostic
cloud scheme is used; IWDC, initial soil water method using the technique
described above, diagnostic cloud scheme, and; IWPC, initial soil water
method and prognostic cloud scheme. The errors in both temperature and humidity
are dramatically reduced when the initialization of soil water is used,
and they are reduced even further when the radiation forcing at the surface
is improved by the use of the prognostic cloud scheme. Note that the soil
water was reset to field capacity at 3 July, in a quick effort to correct
the large systematic errors in the model; this explains the much reduced
operational errors after that date. The reduction of near surface warm dry
bias removes the bias at the tropospheric geopotential, impacting favourably
on the root mean square (rms) of the tropospheric geopotential over land
areas. Examples for the geopotential rms at 500 hPa over Europe and at 200
hPa over North America are shown in Fig.
4 .
Similar techniques are used operationally at Météo-France (Coiffier et al. 1987) and at the Canadian Meteorological centre Mailhot et al. 1997). Recently, Yang et al. (1994) have proposed to improve this method by using both informations of temperature and specific humidity. previous forecast errors with coefficients depending on vegetation type. Unfortunately the method proposed is biased, because a correction of soil moisture is applied even if the forecast of atmospheric low level parameters is perfect; this may lead to a long term drift.
5.2 Possible improvements
Mahfouf (1991) and Bouttier et al. (1993a, 1993b) have proposed an optimal interpolation scheme for the assimilation of soil moisture using information of both temperature and relative humidity at two metres, which can be formaly written:
|
(9) |
The optimal coefficients
and 
minimise the analysis
variance and are related to the forecast error statistics. They are model
dependent and the success of the method depends on their accurate estimation.
Mahfouf (1991) has used a Monte-Carlo
technique with a one-column model, where soil moisture is perturbed randomly
in a range of possible values. One conclusion of this study is that the
coefficients and strongly depend upon the
diurnal cycle (information on soil moisture from atmospheric parameters
can be extracted more easily during day time in clear sky conditions) and
upon the vegetation cover (over bare soil, corrections are applied to the
superficial reservoir and when the vegetation cover is important soil corrections
are applied over the whole root zone).
Bouttier et al. (1993a) proposed a first parametrization of the optimum
coefficients, recently generalized by Giard and Bazile (2000). In order to
be used, this initialisation method requires an analysis of temperature
and relative humidity at two metres (Navascues 1997); the analysis increments
should be zero in those situations where parameters in the boundary layer
are not informative about soil moisture, e.g. strong advection, and low
radiative forcing at the surface.Once the optimal coefficients are derived, the sequential assimilation can easily be implemented in current operational data assimilation systems; however, it assumes linear relationships between atmospheric increments and corrections to be applied in the soil which is not a good approximation for most of the physical parametrizations. Another option is the variational method, which seems a priori more suitable to the analysis of soil moisture due to the non-linearities of the problem and to the importance of the time distribution of observations (surface variables are strongly affected by the diurnal cycle). Mahfouf (1991) and more recently Callies et al. (1998) used a 1D-Var approach to estimate the initial soil moisture of a one-column model that best fit observations of temperature and relative humidity during a diurnal cycle. The variational method was applied by Rhodin et al. (1999) to a regional weather forecast model over a five-day spring period. The optimal soil moisture minimises the following cost-function:
|
(10) |
In the above formula
, 
, 
and
, represent, respectively, the screen level temperature
and relative humidity, and their assumed observational errors, and the subscripts
oi and fi represent the observation i and the
forecast value interpolated to the point i; the summation is done
over the total number of observation observation points, N. Mahfouf
(1991) has validated the two methods described above with a one-column version
of the Météo-France forecast model using data from the HAPEX-MOBILHY
1986 field experiment. Data from this campaign provided at various locations
simultaneous information about soil moisture content and low-level atmospheric
parameters, i.e. temperature, relative humidity, wind speed. When using
observations of temperature and relative humidity, both the sequential and
variational technique converge towards the neutron probe estimates of soil
moisture, starting from arbitrary initial values of soil moisture (Fig. 5 ).
Mahfouf (1991) assumed that there is a priori no useful information in the first-guess which is certainly incorrect with an operational model of some skill; in realistic applications a background term should be added to the cost-function.
Results show that for clear-sky situations both methods retrieve soil moisture contents close to each other and to the observations. The variational method is more efficient but non-linearities of the problem make the efficiency of the convergence dependent on the initial start of the minimisation. When the fraction of vegetation is large, soil moisture in the root zone is retrieved more accurately than surface soil moisture. The examination of the cost-function (Fig. 6 ) shows the existence of a secondary minimum (corresponding to ambiguity in the response, the same surface evaporation can be obtained with totally differents water contents in the soil reservoirs) as well as a plateau where surface evaporation is not sensitive to modifications in soil moisture (above field capacity, evaporation is assumed to take place at a potential rate, therefore it is no more controlled by the surface).
), (B) represents the moist guess
(
), and the square is the searched state (reference).
(From Mahfouf 1991).
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