A comparison of two off-line soil analysis schemes for assimilation of screen level observations

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008jd011077, 2009 A comparison of two off-line soil analysis schemes for assimilation of screen level oservations J.-F. Mahfouf, 1 K. Bergaoui, 2 C. Draper, 3 F. Bouyssel, 1 F. Taillefer, 1 and L. Taseva 4 Received 1 Septemer 2008; revised 9 Novemer 2008; accepted 21 January 2009; pulished 18 April [1] Two analysis schemes are developed within an off-line version of the land surface scheme ISBA for the initialization of soil water content and temperature in numerical weather prediction models. The first soil analysis is ased on optimal interpolation that is currently operational in a numer of weather centers. The second soil analysis is an extended Kalman filter (EKF) which will allow the assimilation of satellite oservations. First, it is shown, y comparing the Kalman gain of oth analysis schemes, that it is possile to assimilate screen level temperature and relative humidity in an off-line system. This is of great interest for future comined assimilations of conventional and satellite data. The reduced computing time in running the land surface scheme outside the atmospheric model makes Kalman filter approaches compatile with operational requirements. The methodology for coupling the land surface data assimilation with the atmospheric analysis system is explained in order to highlight the existing feedacks etween the two systems (in comparison to fully decoupled land data assimilation systems). The linearity of the oservation operator Jacoians estimated y finite differences and the relevance of the soil prognostic variales to e initialized are assessed. Finally, the two systems are compared over western Europe for the month of July 2006 y assimilating screen level temperature and relative humidity every 6 h. The EKF has een simplified y keeping the covariance matrix of ackground errors constant. The two soil analysis schemes ehave similarly in response to screen level atmospheric errors. The EKF is superior in identifying situations where the near-surface atmosphere is sensitive to soil perturations, which leads to etter use of oservations. Over France, the capaility of oth systems to moisten the soil when rain events are asent from the forcing is demonstrated. Citation: Mahfouf, J.-F., K. Bergaoui, C. Draper, F. Bouyssel, F. Taillefer, and L. Taseva (2009), A comparison of two off-line soil analysis schemes for assimilation of screen level oservations, J. Geophys. Res., 114,, doi: /2008jd Introduction [2] The initialization of soil variales is known to significantly influence numerical weather forecasts over oth the short and medium ranges [Beljaars et al., 1996; Bélair et al., 2003, Ferranti and Vitero, 2006; Drusch and Vitero, 2007; Drusch, 2007]. Statistical techniques developed for atmospheric and oceanic analyses such as optimal interpolation (OI) [Mahfouf, 1991], variational assimilation [Bouyssel et al., 1999], or ensemle Kalman filter (EnKF) [Reichle et al., 2002] have een adapted to continental surfaces. The OI method is widely used operationally in Numerical Weather Prediction (NWP) models [Giard and Bazile, 2000; Mahfouf et al., 2000; Bélair et al., 2003; 1 GAME, CNRM, Météo-France, CNRS, Toulouse, France. 2 Institut National de la Météorologie, Tunis, Tunisia. 3 Department of Civil and Environmental Engineering, University of Melourne, Melourne, Victoria, Australia. 4 National Institute of Meteorology and Hydrology, Bulgarian Academy of Sciences, Sofia, Bulgaria. Copyright 2009 y the American Geophysical Union /09/2008JD Rodriguez et al., 2003]. This method uses short-range forecast errors of screen level parameters (temperature and relative humidity) to correct soil prognostic variales (temperature and volumetric water content). The roustness of the method stems from the density of the gloal surface oservational network (SYNOP reports). However, a major drawack is that screen level forecast errors are not always caused y initial errors in soil variales. In response to this, several empirical thresholds have een defined in the OI approach to prevent undesirale soil corrections. Another frequent criticism of the OI method is that screen level parameter errors are more closely linked to surface turulent fluxes than to actual soil variales (and in particular water content). This has recently een demonstrated y Drusch and Vitero [2007], who showed that while the ECMWF soil analysis improves the forecast skill for oundary layer variales it does not improve the modeled soil moisture content (relative to oservations from the Oklahoma Mesonet Network). A similar conclusion was made y van den Hurk et al. [2008] on the asis of examination of the water udget components from the ECMWF soil analyses at several locations over Europe, within the European Land 1of21

2 Data Assimilation System (ELDAS) project. Additionally, systematic model ias compensations, which are not detrimental for NWP, could hamper other applications such as hydrological modeling, land caron monitoring or climatic trend analyses. In order to improve the analysis of soil variales for NWP with respect to the current status, it is necessary to (1) assimilate oservations that have a more direct link to soil variales than 2 m parameters and (2) force land surface schemes with more accurate radiative and precipitation fields. The goal of this paper is to present the preliminary steps undertaken at Météo-France toward achieving the aove. [3] Regarding the first item, the OI technique of Mahfouf [1991] is not flexile enough to easily account for new oservation types. Indeed, the statistics required to compute the optimal interpolation coefficients were produced from a set of single column Monte Carlo experiments which only considered 2 m temperature and relative humidity oservations, and the analytical expressions of Giard and Bazile [2000] and Douville et al. [2000] would need to e rederived for new oservation types. In contrast, the variational and Kalman filter assimilation techniques are more generalized, and would e etter ale to handle new oservation types. Mahfouf [1991] showed the feasiility of a variational assimilation. This preliminary study has een extended y Bouyssel et al. [1999] with a single column model, and y Rhodin et al. [1999] with a threedimensional model. The major drawack of variational methods is their high computational cost. Hess [2001] proposed an extended Kalman filter (EKF) in which the Kalman gain matrix is computed y finite differences through perturing the soil initial conditions. Since the control variale was reduced to the root zone soil moisture, only one additional integration of the NWP model was required to estimate dynamical optimal interpolation coefficients, and this approach has een used operationally at the German Weather Service since Balsamo et al. [2004] have successfully tested this methodology in the Météo-France limited area model Aire Limitée Adaptation Dynamique développement International ALADIN [Bunová et al., 1995]. However, the additional model run required to compute the Kalman gain matrix was considered too expensive for operational applications at Météo-France. With a single column model, Seuffert et al. [2004] demonstrated that the EKF can simultaneously assimilate screen level oservations and microwave L and rightness temperatures (the latter are informative of superficial soil moisture). This feasiility study shows that it will e possile to exploit the potential of the satellite retrievals of soil moisture and/or low-frequency microwave rightness temperature for near-real-time applications. [4] An alternative method to derive improved soil temperatures and moisture contents is to force off-line land surface schemes with accurate radiative and precipitation forcing. This methodology is only possile over regions that are covered y high-density oservational networks (precipitation radars and rain gauges), such as North America and western Europe [van den Hurk, 2002; Mitchell et al., 2004; Smith et al., 2004; Haets et al., 2008], although gloal initiatives do exist: the Gloal Land Data Assimilation System (GLDAS), the Gloal Soil Wetness Project (GSWP), and the Land Information System (LIS). The assimilation of screen level oservations is not possile in an off-line systems forced with screen level analyses or forecasts of atmospheric parameters. However, Balsamo et al. [2007] showed that such an assimilation is made possile y using a higher atmospheric forcing level: with the forcing applied at etween 20 and 50 m they successfully assimilated screen level variales and satellite radiances using an EKF. This approach is promising as the computational cost of the estimation of the Kalman gain y finite differences is greatly reduced in an off-line land surface scheme (compared to the full atmospheric model). [5] In this paper we compare two soil analysis systems: one ased on an EKF scheme, and one on the OI approach. The comparison is done with an off-line version of the Météo-France land surface scheme. The two soil analysis methods are presented in section 2, the experimental setup is descried in section 3, and preliminary results are presented in section 4 for the first day of analysis, with an emphasis on the oservation operator Jacoians and the Kalman gain matrix. Results from the two soil analysis schemes are analyzed and compared over a month in section 5. Finally, the conclusions and perspectives offered y the new EKF system are discussed in section Soil Analysis Schemes [6] The soil analysis schemes have een developed for the ISBA land surface scheme [Noilhan and Planton, 1989; Noilhan and Mahfouf, 1996], which is used in the Météo- France atmospheric numerical models to descrie the heat, moisture, and momentum exchanges etween the continental surfaces and the surface oundary layer. ISBA is ased on the force-restore equations of Deardorff [1977, 1978], and the two-layer version (ISBA-2L) is used here. The ISBA scheme has een externalized from the atmospheric models using the implicit coupling technique descried y Best et al. [2004]. The externalized module, called Surface Externalized (SURFEX) (P. Le Moigne, SURFEX, Arome training course, Poiana Brasov, 2005 availale at enales the application of the same code to different models, as well as off-line validations Simplified Extended Kalman Filter [7] Using the classical notations of data assimilation proposed y Ide et al. [1997], the analysis equation for the extended Kalman filter is: x a t ¼ x t þ BH T HBH T 1 þ R y o t H x 0 where B is the covariance matrix for the ackground errors, and R is the covariance matrix for the oservation errors. The superscripts a,, and o indicate the analyses, ackground, and oservations, respectively, and the time t (in suscript) indicates the end of the assimilation window. In the following experimental setup the assimilation window Dt is 6 h, which is the same as the atmospheric assimilation window. The cycling of the ackground error covariance matrix B (which is neglected at this stage) will enale the comined assimilation of oservations availale at different temporal frequencies [Mahfouf, 2007; Rüdiger et al., 2007]. ð1þ 2of21

3 Tale 1. Empirical Criteria Defined to Reduce the Optimal Interpolation Coefficients in the Formulation of Giard and Bazile [2000] a Field Minimum Threshold (Value) [8] For this study, the control vector x contains the four main prognostic variales of the ISBA-2L model: the superficial water content w g, the mean (root zone) soil water content w 2, the surface temperature T s, and the mean surface (i.e., deep soil) temperature T 2 (the interception reservoir, soil ice water content, and snow water equivalent are excluded from the present analysis). The oservation vector y o contains the screen level temperature T 2m and relative humidity RH 2m, which are mapped onto the model grid y a horizontal optimal interpolation scheme, Code d Analyse Nécessaire à ARPEGE pour ses Rejets et son Initialisation (CANARI [Taillefer, 2002]). The oservation operator H is the product of the model state evolution from time t 0 = t D t to time t (the oservation time), and the conversion of the model state into an oservation equivalent. Thus, the Jacoian H of the oservation operator is: H t0 Maximum Threshold (Value) This approach is equivalent to the simplified 2D-Var descried y Balsamo et al. [2004], except that the increments are applied at the end of the assimilation window instead of at the eginning (saving a model integration starting from the analysis state, as also noted y Hess [2001]). Since the oservation operator H includes a model propagation, the actual B matrix used in the Kalman gain is implicitly evolved y the linearized model. The elements of the Jacoian matrix are estimated y finite differences, y individually perturing each component x j of the control vector x y a small amount dx j. A given Jacoian element writes: H ij ¼ y i x þ dx j yi ðþ x dx j Dependency 10-m wind speed (m/s) 0 (1) 10 (0) L Precipitation flux (mm/6 h) 0 (1) 0.3 (0) L Soil ice amount (mm) 0 (1) 5 (0) L Snow fraction (%) 0 (1) e (0) L Condensation flux (mm/6 h) 0 (1) e (0) L Cloud cover (%) 0 (1) 100 (0.25) P a The minimum and maximum thresholds correspond to the values y which the coefficients are multiplied (in parentheses). Between these thresholds, either linear (L) or power law (P) variations are imposed. e is an aritrary infinitesimal positive value. The value dx j must e small enough to accurately approximate the derivative, ut not too small that roundoff errors occur. Balsamo et al. [2004] considered perturations of the same size as analysis increments since their land surface scheme was coupled to the full atmospheric model (infinitesimal initial soil changes could trigger clouds and precipitation, resulting in a finite atmospheric response leading to noisy Jacoians). The ð2þ ð3þ mapping of the oservations onto the model grid effectively performs the necessary spatial interpolations outside of the soil analysis module, so that the soil analysis can e done on a set of independent columns (reducing the computational cost of calculating the Jacoians to an affordale level) Optimal Interpolation Scheme [9] For the optimal interpolation scheme, the analogous equations to equation (1) are: w a g ¼ w g þ a 1 T2m o T 2m þ a2 RH2m o RH 2m ð4þ w a 2 ¼ w 2 þ 1 T2m o T 2m þ 2 RH2m o RH 2m Ts a ¼ T s þ m 1 T2m o T 2m þ m2 RH2m o RH 2m T2 a ¼ T 2 þ n 1 T2m o T 2m þ n2 RH2m o RH 2m The analytical formulation of a i and i proposed y Giard and Bazile [2000] depend mostly on the diurnal cycle and the vegetation fraction. These coefficients are reduced in conditions where near-surface atmospheric forecast errors are assumed not to e produced y soil errors (precipitation, clouds, strong wind, snow on the ground,...), as summarized in Tale 1. The coefficients m 1 and n 1 are constant at 1 and 1/(2p), and m 2 = n 2 = 0. These values were proposed y Coiffier et al. [1987] for a previous land surface scheme, and were retained when the ISBA scheme was introduced into the operational Météo-France NWP models Coupling of Atmospheric and Land Data Assimilation Systems [10] The soil analysis schemes descried aove have een coded within the externalized surface module, SURFEX. Contrary to most off-line land surface schemes, the first atmospheric level is not considered to e at 2 m for temperature and humidity, and at 10 m for wind speed. Instead it is imposed higher up, at the first level of atmospheric computations (around 17 m), and variales are vertically interpolated from the surface (as computed y the land surface scheme) to the height of the imposed atmospheric values, following Monin-Oukhov similarity theory [e.g., Geleyn, 1988]. This setup retains the dependence of the screen level parameters on soil variales that is required for the assimilation of the former, as is illustrated in Figure 1. When the forcing height is aove screen level, a change in surface (or soil) variales from x 1 to x 2 will lead to a change at screen level from a reference value y 1 to a pertured value y 2, allowing the estimation y finite differences of a nonzero Jacoian H. When the forcing height is at screen level, the corresponding values y 1 are not affected y changes at the surface or in the soil, leading to zero Jacoians. Oviously, the lack of coupling with the full planetary oundary layer reduces the influence of soil variales on the surface oundary layer. This study will confirm previous findings of Balsamo et al. [2007], and Mahfouf [2007], who noticed that the reduced sensitivity does not hamper the soil analysis from ehaving as ð5þ ð6þ ð7þ 3of21

4 Figure 1. Estimation of the Jacoian of the oservation operator for screen level parameters (defined as y) with respect to soil variales (defined as x) according to the height of the forcing level in an off-line soil analysis scheme. The solid curve is a schematic reference profile in the surface layer, and the dashed curve is a pertured profile through changes at the surface. (left) The possiility of having nonzero Jacoian elements when the forcing level is aove 2 m. (right) Screen level parameters are unchanged when the forcing level is at 2 m leading to zero Jacoian elements. expected. Another important difference with respect to typical off-line land surface models is that the precipitation and radiation fluxes are not taken from analyses (using either surface or satellite oservations), ut are provided y short-range forecasts from the atmospheric model to which SURFEX is coupled (and for which the soil analysis is designed). This choice allows the soil analysis to correct for forcing errors (in particular of the precipitation field), as in current operational systems designed for NWP applications. The availaility of accurate forcing over specific regions will e accounted for in a suitale manner in future versions of the soil analysis (see Balsamo et al. [2005] for preliminary results in that direction). [11] Figure 2 shows how the atmospheric and soil analyses are coupled at the frequency of the atmospheric temporal window (usually 6 h). Oservations from the surface meteorological network are used in a horizontal a a screen level analysis to generate T 2m and RH 2m on the model grid. The externalized land surface scheme is run using atmospheric forcing produced y a short-range forecast from the NWP model using the same configuration as the off-line land surface scheme (in terms of land cover, soil texture dataases, and soil/vegetation processes), since the soil analysis will attempt to compensate for any inconsistencies in the configuration. In practice, hourly values of the atmospheric forcing are interpolated to each time step of the land surface scheme. This off-line reference simulation produces values of T 2m and RH 2m which are, y design, very close to those produced y the land surface scheme coupled with the atmospheric model. For the EKF, pertured off-line integrations are performed y separately modifying each control variale x j at the initial time y a small amount dx j (so that the total numer of pertured runs is the dimension of the control vector x). These pertured simulations produce pertured values of screen level temperature and relative humidity that are used to compute the Figure 2. Coupling strategy of the off-line soil analysis using an externalized land surface scheme with atmospheric modeling and analysis systems. 4of21

5 Figure 3. Surface oservational network over the ALADIN-France domain used to perform screen level temperature and relative humidity analyses. The lack squares correspond to the GTS SYNOP stations, and the small grey circles correspond to the French network RADOME of automatic weather stations. elements of the Jacoian matrix y finite differences (see equation (3)). Then, the analysis equation can e solved (in practice using a Cholesky decomposition for the matrix inversion of the EKF), and the resulting soil analyses are used to launch the atmospheric forecast for the next assimilation window. Even though the atmospheric forcing is not changed during a given assimilation window y the soil modifications, the changes in the soil are reflected in the atmospheric forcing of the next window. This experimental setup is suitale for data that are frequently availale, such as SYNOP reports. This methodology can also e applied to the assimilation of satellite data that are availale less frequently than 6-hourly (e.g., superficial soil moisture, leaf area index), provided ackground errors are transported in time y relaxing the current hypothesis of a constant B matrix, as shown y Mahfouf [2007] and C. Draper et al. (An EKF assimilation of AMSR-E soil moisture into the ISBA land surface scheme, sumitted to Journal of Geophysical Research, 2008). By keeping the matrix B constant, an implicit equilirium etween its decrease through the analysis step and its increase through model error in the forward propagation step is assumed. [12] In this paper, the soil analyses are run completely decoupled from the atmospheric model (i.e., without running atmospheric data assimilations). This setup is acceptale for a feasiility study, ut for operational applications the off-line soil analysis will e coupled to the atmospheric model through the cycling descried in Figure Experimental Setup [13] The analysis schemes have een tested for July 2006, over the ALADIN-France domain, which covers most of western Europe with a 9.5 km grid ( points). The screen level temperature T 2m and relative humidity RH 2m fields were generated y a 6-hourly optimal interpolation system (CANARI system), which uses oservations from GTS SYNOP, SHIP, BUOY reports, and the French RADOME network of automatic weather stations (around 2000 per analysis cycle). The domain of interest and the density of the oservational network are displayed in Figure 3. The density of availale surface oservations varies sustantially from one European country to another: The French RADOME network has around 1000 stations (spaced approximately 30 km apart) and Switzerland and Germany also have a high density of surface weather stations, however the networks over Spain and Italy are relatively sparse. At Météo-France, the screen level analysis and the soil OI analysis are performed operationally in the gloal NWP model Action de Recherche Petite Echelle Grande Echelle (ARPEGE). Since 2005 the ALADIN model has its own atmospheric (3D-Var) data assimilation system [Fischer et al., 2005] ut 5of21

6 Tale 2. Setup Values of the Bidimensional Optimal Interpolation (CANARI) of Screen Level Temperature T 2m and Relative Humidity RH 2m Over the ALADIN-France Domain Parameter Symol Value Correlation length for T 2m (km) L T2m 80 Correlation length of RH 2m (km) L RH2m 85 Background error for T 2m (K) s T2m 1.2 Background error for RH 2m (%) s RH2m 13 Oservation error for T 2m (K) o s T2m 1.4 Oservation error for RH 2m (%) o 10 this does not include a soil analysis at Météo-France, and the setup parameters and initial soil values (on 1 July 2006 at 0000 UT) were otained from the ARPEGE soil analysis. [14] The univariate screen level analysis uses homogeneous and isotropic horizontal structure functions with a correlation model r(r) defined as: rðþ¼exp r r 2L s RH2m where r is the horizontal distance etween two points, and L is a correlation length. This choice was ased on a study of innovation statistics from the gloal NWP model ARPEGE [Ivatek-Sahdan, 2001]. In the future, a revised correlation model with etter spectral density properties should e evaluated [Daley, 1991]. The numerical values of the correlation lengths, and the standard deviations of the ackground and oservation errors are given in Tale 2 (see Ivatek-Sahdan [2002] for their tuning). The value of the correlation length (around 80 km) is likely etter suited to the regions with lower density of surface stations. For each grid point, a maximum of 30 stations within a radius of 500 km is used to solve the inversion of the linear OI system. The quality control for screen level oservations is ased on the size of the innovation, and on a uddy check (comparison of a given oservation to the average of neary oservations). Oservations are flagged as suspicious and rejected if the innovation qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is larger than 2.5 times the standard deviation ðs o Þ 2 þðs Þ 2. Finally, oservations in mountainous areas are rejected, ecause of representativity concerns, if the station altitude is aove 1500 m, or if the difference etween model orography and station height is larger than 500 m. [15] Short-range forecasts were run with a 46-level version of the ALADIN-France model (the 2006 operational configuration), and hourly outputs of horizontal wind components, specific humidity, temperature at the lowest model level (around 17 m), surface pressure, accumulated precipitation, and radiative fluxes (downward longwave and shortwave components) were stored. These quantities have then een used to force the land surface scheme ISBA within the externalized module SURFEX. [16] The computation of the Kalman gain matrix elements requires the specification of oservation and ackground error covariance matrices R and B. We have imposed diagonal matrices, and set the diagonal elements to 1 K and 10% for temperature and relative humidity at 2 m (assumed analysis errors from CANARI), and to 2 K for ð8þ the ackground errors of T s and T 2. The ackground errors of w g and w 2 were set to 0.1 (w fc w wilt ), where w fc and w wilt are the volumetric water content at field capacity and at permanent wilting point, which depend on soil texture [Noilhan and Mahfouf, 1996]. 4. Preliminary Results [17] Below, the two analyses schemes are examined on the 1 July, while the soil conditions for the two schemes are similar, and the results will e used to design the comparisons presented in the following section, and also for interpreting the analysis results Jacoians of Oservation Operator [18] First, the elements of the Jacoian matrix H are examined, focusing on their realism and their order of magnitude. The components of the pertured control vector x 0 are determined y e i, which is set to 10 4 for the volumetric water content (w g and w 2 ) and 10 5 for temperature (T s and T 2 ): x 0 i ¼ x ið1 þ e i Þ ð9þ To check that these perturations are small enough to reproduce the tangent-linear ehavior of the oservation operator, ut not so small that round-off errors occur, the Jacoians computed with negative and positive e i are compared. The Jacoians of T 2m and RH 2m with respect to w g and w 2 are presented in Figure 4, corresponding to the four 6-h values computed for each assimilation window during the first day of analysis. Almost all of the points are aligned along the one-to-one diagonal (i.e., the Jacoians estimated with positive and negative perturations have very similar values), indicating that the finite difference estimates are within the linear regime of the oservation operator. The agreement etween the mean and the standard deviation of each sample also confirms that the Jacoians are not effected y the sign of the initial perturation. [19] The sensitivity of T 2m (RH 2m ) with respect to soil moisture is mostly negative (positive) which means that an increase in soil moisture will reduce (increase) the screen level temperature (relative humidity). This is physically explained y a reduction (augmentation) of the surface sensile heat flux with a corresponding increase (decrease) in the surface evapotranspiration flux. Indeed, the sensitivity of the Bowen ratio to soil moisture is the main physical mechanism y which screen level oservations are affected y soil variales. Examination of the diurnal cycle reveals that the largest Jacoians are otained for the two daytime assimilation windows: 0600 to 1200 UTand 1200 to 1800 UT (not shown). 2m /@w 2 2m /@w 2, there are a numer of points along the zero y axis, indicating that in these instances there was no sensitivity to the negative perturations, while the positive perturations produced Jacoians with significant values. For these locations, the soil moisture w 2 is close to the wilting point w wilt, which is the lower limit for transpiration flux in the ISBA scheme [Noilhan and Mahfouf, 1996]. In this case a reduction in the root zone soil moisture has no impact on the screen level variales since transpiration will remain negligile, yet an increase in the root zone soil moisture has a nonnegligile 6of21

7 Figure 4. Examination of the linearity of the elements of Jacoian matrix of the oservation operator. The scatterplots show values of (top 2m 2, (top 2m 2, (ottom 2m g, and (ottom 2m g otained in finite differences with small negative and positive perturations. The mean and the standard deviation of each sample are displayed on each plot for the negative perturation (ottom right of each plot) and for the positive perturation (top left of each plot). The Jacoians are computed for four 6-h assimilation windows on 1 July 2006 (157,668 values). impact on screen level variales, since the transpiration will e slightly increased. Since the wilting point is not a physical limit for are soil evaporation in ISBA there are no data along the zero y axis in the scatterplots 2m /@w g 2m /@w g. [20] The mean values of the Jacoians are one order of magnitude lower for w g than for w 2, revealing that the assimilation system will e more effective in modifying the root zone soil moisture than the superficial values. The water holding capacity of the soil, defined y the difference etween the field capacity w fc and the wilting point w wilt,is around 0.1 m 3 /m 3, for the textural classification of the ISBA scheme. The standard deviations of the Jacoians are around 20 K 2m /@w 2, and 3.5 2m /@w 2, which 7of21

8 Tale 3. Jacoians of Screen Level Temperature and Relative Humidity With Respect to Initial Soil Temperatures 6 h Earlier Computed in Finite Differences With Small Positive and Negative Soil Perturations a Jacoian Element Mean Standard Deviation Minimum 2m /@T s (+) (K/K) m /@T s ( ) (K/K) m /@T 2 (+) (K/K) (0.174) m /@T 2 ( ) (K/K) m /@T s (+) (%/K) m /@T s ( ) (%/K) m /@T 2 (+) (%/K) (1.114) m /@T 2 ( ) (%/K) a Statistics (mean and standard deviation, maximum and minimum values) are computed over a sample of 157,668 values for 1 July Positive perturations are indicated y plus signs, and negative perturations are indicated y minus signs. Values in parentheses correspond to the standard deviation otained when excluding the largest outlier. (assuming linearity) convert to deviations of 2 K and 35%, respectively, over the full range of the soil water holding capacity. Extreme values of Jacoians (some eing outside the ranges of the scatterplots) do not lead to sustantially larger changes, since the validity of the linear regime reaks down at these points. [21] Statistics for the Jacoians with respect to soil temperatures (T s and T 2 ) calculated with positive and negative perturations are summarized in Tale 3. There is a general agreement etween the mean and standard deviation for each set of Jacoians. The very large and quite different values of the extremes for each sign of perturation reflect the nonlinear ehavior at particular locations. For two 2m /@T 2 2m /@T s, the mismatch of a single extreme value (125.3 in one case and 1817 in the other case) leads to differing standard deviations etween the two sets of Jacoians. However, when these two outliers are excluded from the statistics, the standard deviations (given y values in parentheses in Tale 3) are almost identical for the two samples. The similarity of the two distriutions has also een verified y comparing the median, the first and the third quantiles (not shown). The Jacoians with respect to the surface temperature T s are 7 times smaller than those with respect to the mean surface temperature T 2 (representative of a deeper soil layer). This is similar to the results for soil moisture (larger values for the root zone than for the near surface). [22] The analysis of the Jacoians should e repeated if aspects of the oservation operator (including the land surface scheme) are modified (for example, if the vertical interpolation scheme for the surface layer or the plant stress function are updated) Kalman Gain Matrix [23] To assess the pertinence of using SURFEX for assimilating screen level oservations, the dynamically computed EKF coefficients (Kalman gain matrix elements) have een compared to the analytical OI coefficients (of Giard and Bazile [2000]), which were derived from an ensemle of single-column simulations in which the land surface was fully coupled to the planetary oundary layer. For SURFEX to e useful for the assimilation, it must reproduce the sensitivity of screen level parameters with respect to soil variales, even though it includes only a surface atmospheric layer. Since the link etween screen level and soil variales is provided through turulent surface fluxes, the OI and EKF coefficients experience a strong diurnal cycle. In the analytical Météo-France OI formulation, this dependency is incorporated using a function of the solar zenith angle, as proposed y Douville et al. [2000] for the ECMWF soil analysis. The rejection criteria used in the analytical formulation is given in Tale 1. For 1 July 2006 at 1200 UT, the active thresholds (those less than one) are mapped in Figure 5. The wind threshold is intended to account for strongly advective situations in which the surface is decoupled from the overlying atmosphere, so that local soil corrections ased on screen level forecast errors ecome inappropriate. In the current formulation, the OI coefficients are maximum for zero wind speed and zero when the wind speed is aove 10 m/s. This lower ound has no real physical justification, and it implies that the coupling etween the surface and the oundary layer is maximum in free convective situations. The mean value of the wind reduction over the domain is 0.5. Frozen soil areas are located over the Alps and will prevent soil corrections in this part of Europe. Over precipitating areas (mostly in Central Europe), the OI coefficients will e negligile since the reduction factor is close to zero. Cloudy regions, in which the surface radiative forcing is decreased, encompass the precipitating areas and regions of strong winds (British Islands, Central Europe), with smoother transitions and a maximum reduction factor of [24] Figure 6 compares the OI and EKF coefficients 1 and 2 (link etween screen level innovations and soil moisture corrections in the root zone) for 1 July 2006 at 1200 UT. The coefficients are multiplied y the soil depth to give the correction in mm of water (and allow a comparison with the other components of the water udget). Over clear sky areas (western part of the domain), the maximum values of the OI coefficients are around 8 mm/k for 1, and 70 mm for 2, with slight reductions induced y the wind threshold. The corresponding EKF coefficients have a similar order of magnitude, ut are lower y a factor of 2 for 2. Regions with the largest values of the OI coefficients are located over clear-sky areas with low wind speed values (e.g., Germany, Normandy and Aquitaine regions in France). The OI coefficients are strictly zero over a significant fraction of Central Europe (Austria, Hungary, Slovakia, Bosnia), and are reduced in regions of nonprecipitating clouds (Poland, Scotland), and low vegetation cover (Spain). [25] Maps of the soil wetness index SWI, defined as: SWI ¼ w 2 w wilt w fc w wilt ð10þ and the vegetation cover shown in Figure 7, reveal that within clear sky regions, the areas with the largest EKF coefficients (particularly for 1 ) are associated with high fraction of vegetation cover and low values of SWI (e.g., Poland). This is due to the parameterization of plant transpiration in the ISBA scheme: the surface canopy resistance has a nonlinear dependency on the root zone soil moisture, with the greatest variations close to the wilting 8of21

9 Figure 5. Maps of active empirical rejection criteria reducing the magnitude of the optimal interpolation coefficients in the formulation of Giard and Bazile [2000] for 1 July 2006 at 1200 UT: (top left) wind threshold, (top right) precipitation threshold, (ottom left) frozen soil ice threshold, and (ottom right) cloud cover threshold. point [see Balsamo et al., 2004, Figure 1]. Smaller EKF coefficients occur over clear sky areas characterized y moister soils (e.g., Massif Central), or lower vegetation cover (Ierian peninsula). The vegetation dependency is also evident in the OI coefficients, ut with much stronger contrasts (e.g., the OI coefficient 2 is roughly ten times smaller over Spain than over France). The EKF coefficients also show reductions associated with cloudy and precipitating areas, as well as frozen soils. The rainy region over Slovakia leads to negligile values of the EKF coefficients. Over other rainy regions, the EKF coefficients are reduced without eing strictly zero (e.g., Bosnia). Over Poland, the presence of clouds produces low OI coefficients, whereas the dynamical approach gives high values induced y rather dry soils. There is no ovious signature of a wind speed dependency in the EKF coefficients. On the other hand, the EKF approach creates new areas of negligile values for 1 and 2 (Central Spain, Ero river valley, Vendée region, Maghre region), which are associated with root zone soil moisture values elow the wilting point (see Figure 7). This comparison demonstrates the superiority of a dynamical estimation of the Kalman gain matrix y the EKF, since the gain is modified y the meteorological forcing (clouds, precipitation), and also y the soil moisture conditions. In contrast, these nonlinearities, which cannot e descried y the OI approach, require additional controls when soil 9of21

10 Figure 6. Kalman gain matrix elements 1 (w 2 increments with respect to T 2m innovations) and 2 (w 2 increments with respect to RH 2m innovations) (top) from the optimal interpolation (OI) formulation of Giard and Bazile [2000] and (ottom) from the dynamical estimation of an extended Kalman filter (EKF) on 1 July 2006 at 1200 UT. Units are mm/k for 1 and mm for 2. moisture increments Dw are added to the ackground state to produce the final OI analysis. The analysis state w 2 a is prevented from ecoming lower than the wilting point, or higher than the field capacity: w a 2 ¼ w 2 þ max Dw; lw wilt w 2 w a 2 ¼ w 2 þ min Dw; w fc w 2 if Dw < 0 ð11þ if Dw > 0 ð12þ In the operational configuration [Giard and Bazile, 2000] l is set equal to the vegetation cover veg. In the current setup this value is set to one, as will e justified in section 5. Figure 6 also compares favoraly to Figure 7 presented in Balsamo et al. [2004] for which the ISBA scheme was fully coupled to the atmospheric ALADIN model. [26] The effect of the diurnal cycle is examined y comparing histograms of the coefficients 1 and 2 at 1200 and 1800 UT (Figure 8). At 1200 UT, the two distriutions have similar shapes for 1, with the largest mode of the distriution corresponding to very low values, and a tail etween 9 and 10 mm/k. At 1200 UT, the mean values of 2 for the EKF are a factor of 2 smaller than for the OI. For the OI, a significant fraction of the distriution is made up of large values (aove 40 mm), and also small negative values (this is counter intuitive, since soil drying is not expected to generate moistening of the lower atmosphere; this is caused y the dependence of the soil thermal inertia on soil moisture). Both distriutions have a mode close to zero. The OI has a greater density of values close to zero, ecause of its stricter rejection criteria (see Figure 6). Both distriutions have a second mode, at approximately 20 mm for the EKF, and at approximately 40 mm for the OI. The mode at aout 10 mm in the OI distriution is due to areas of low vegetation cover. At 1800 UT, oth of the OI distriutions are much sharper, since the coefficients are reduced (y roughly 50%), ecause of the analytical dependency on the diurnal cycle (which provides a smooth transition toward low nighttime values). It is interesting to notice that there is no corresponding decrease from 1200 to 1800 UT in the EKF formulation. In fact, there is an increase in the largest values, particularly 10 of 21

11 Figure 7. (left) Fractional vegetation cover and (right) soil wetness index in the root zone over the ALADIN-France domain on 1 July for 2, leading to more skewed EKF distriutions. This is due to the large surface turulent fluxes etween 1200 and 1800 UT, which make the transition toward the low nighttime values much sharper than is descried y the analytical formulation of the OI approach. [27] The mean and standard deviation of a i, m i, and n i are summarized in Tale 4 for the assimilation window corresponding to their largest values (daytime for a i, and nighttime for m i and n i ). The OI values of a 1 and a 2 are roughly 15 and 25 times larger, respectively, than those from the EKF. In general, the a i are much smaller than the corresponding i, ecause of the different reservoir depths for the surface layer (10 mm) and the root zone (etween 500 and 3000 mm). The original OI coefficients of Giard and Bazile [2000] were too large, ecause of an overestimation of the soil ackground errors used in the Monte Carlo method of Mahfouf [1991] to span the range of soil moisture conditions (see a detailed explanation y Douville et al. [2000]). At Météo-France, the i coefficients have een empirically reduced y a factor of 6 for operational applications, however, this correction has not een applied to a i. Since the volume of water in the superficial reservoir is much smaller, its initialization is less critical: it rapidly adjusts toward the root zone soil moisture and it also responds quickly to precipitation forcing. The EKF coefficients explicitly demonstrate the weak link etween screen level forecast errors and the superficial soil moisture content. Similarly, over a 6-h assimilation window the link etween the screen level forecast errors for the mean surface temperature T 2 is stronger than that for the surface temperature T s. Therefore, the aritrary values of m 1 and n 1 are respectively too large and too small in the OI. The temperature dependency of relative humidity (negative correlation) is evident in the EKF, with nonzero negative values for m 2 and n 2. Finally, soil temperature corrections should e greatest when the radiative forcing is weak (as proposed in the ECMWF formulation). Since the mean surface temperature T 2 has longer time scales than T s, the elements of the Kalman gain matrix show that screen level forecast errors can provide nonnegligile corrections to the former Preliminary Conclusions [28] In summary, we have shown that computation of the Jacoians for the oservation operator y finite differences provides a reasonale estimate of the Kalman gain. Both the dynamical (EKF) and analytical (OI) coefficients are greatest for the root zone soil moisture w 2, and have comparale orders of magnitude. The EKF gives slightly lower values, since it accounts for additional (nonlinear) controls (e.g., explicit dependency with the soil moisture content) that are not descried y the OI. Short-range screen level forecast errors are most informative of the root zone soil moisture during the daytime, and of the mean surface (i.e., deep soil) temperature during the nighttime. The other prognostic variales in the ISBA scheme have a much weaker influence on the screen level variales. The empirical corrections made to the surface variales, w g and T s, in the Météo-France OI soil analysis are larger than those made y the EKF. These variales are mostly driven y radiative and precipitation forcing with short temporal scales. The correction to the temperature T s (T 2 ) from equation (5) (equation (6)) is overestimated (underestimated) y the OI scheme y a factor of 5, compared to the EKF approach, with a strong diurnal cycle (lower values during the day). In winter the soil temperature initialization may e more important, particularly during periods of freezing and thawing [Balsamo et al., 2006]. The hierarchy of the sensitivity of the prognostic variales otained here is relevant to the assimilation of screen level oservations, and should e reevaluated (y calculating the Kalman gain) when new oservation types 11 of 21

12 Figure 8. Histogram distriutions of the Kalman gain matrix elements 1 and 2 relating screen level innovations of T 2m and RH 2m to w 2 soil moisture increments for the (left) EKF and (right) OI formulations over the ALADIN-France domain for 1 July 2008 at 1200 and 1800 UT. The size of each sample is 39, of 21

13 Tale 4. Mean and Standard Deviation Statistics of the Kalman Gain Elements a Gain Element Time Window (UT) Mean (EKF) Standard Deviation (EKF) Mean (OI) Standard Deviation (OI) a 1 (mm/k) a 2 (mm) m 1 (K/K) m 2 (K) n 1 (K/K) n 2 (K) a Gain elements relate screen level innovations (index 1 for temperature in K and index 2 for relative humidity) to superficial soil moisture increments (a 1 and a 2 ), surface temperature increments (m 1 and m 2 ), and mean surface temperature increments (n 1 and n 2 ) otained y the dynamical EKF approach and specified from the analytical OI approach for the time window (6-h period) where they are maximum on 1 July are considered (such as satellite derived soil moisture contents). Since the Jacoians for the screen level variales with respect to w g and T s are an order of magnitude lower than those for w 2 and T 2 respectively, the control vector in the EKF has een reduced to include w 2 and T 2 only. Reduction of the control vector leads to significant gains in computing time. For the OI scheme, the four prognostic variales are included to remain consistent with the Météo- France operational configuration. 5. Comparison of the Two Analysis Schemes [29] The OI and EKF soil analysis schemes have een compared for the month of July 2006 over the ALADIN- France domain. As previously mentioned, the experimental setup of the OI scheme is close to that of the operational ARPEGE gloal model. This is true for the spatial interpolation of screen level oservations, and also for the soil analysis with two exceptions: [30] 1. The climatological relaxation of soil moisture toward the GSWP climatology (at one degree resolution) with a 2-month time constant has not een applied here. In the gloal system, the relaxation is intended to prevent the soil analysis from drifting toward unrealistic states in data sparse regions. Over Europe the density of the oservational network is sufficient that this constraint is unnecessary. Climatological relaxation is undesirale in soil analysis schemes, since it damps the interannual soil variaility, which can reduce any atmospheric anomalies induced or reinforced y soil conditions [Beljaars et al., 1996; Douville, 2003]. [31] 2. Since the OI coefficients are not dependent on soil moisture, upper and lower ounds on the magnitude of the increments are imposed, as descried in section 4.2. The lower ound for the analyzed root zone moisture content is set to the wilting point w wilt, rather than veg w wilt, where veg is the fractional vegetation cover within the grid ox (equation (10)). Preliminary tests showed excessive soil drying where the are soil fraction is nonnegligile with the operational setup. Given that the wilting point is the physiological limit for plant water extraction from the root zone, and the root zone is not depleted y are soil evaporation (in the ISBA scheme), there is no strong justification for imposing a threshold value of veg w wilt. [32] In addition to running SURFEX simulations with the assimilation of screen level parameters every 6 h, an open loop run has een performed in which the land surface evolves according to the ALADIN forcing without any soil analysis. The open loop integration provides a reference to indicate how the surface water alance is affected y the soil analyses Screen Level Analysis [33] To understand the ehavior of the soil analysis the increments produced y the CANARI analysis at 2 m (the input to the soil analysis) are examined first. [34] Since soil moisture corrections are only significant at 1200 and 1800 UT, the mean screen level analysis increments over July 2006 are plotted at these times in Figure 9. Most of the domain is characterized y negative increments for relative humidity, indicating that over large areas, the ALADIN short-range forecasts are too moist during the daytime. With the exception of Poland, Hungary, and Great Britain, the largest areas of negative humidity increments coincide with positive temperature increments. The moist ias is aout 2% and the cold ias is aout 0.2 K, with maximum values over the major mountainous areas of the domain, reaching 7% for humidity, and 0.5 K for temperature. In contrast, along the coastlines the model has a dry and warm ias which is most pronounced over the Mediterranean asin. Maximum values are roughly 5% for relative humidity and 0.2 K for temperature. These errors are caused y representativity prolems for the coastal weather stations, due to sea reeze effects. Averaged over the whole domain, the mean screen level analysis increments are uniased, with values of 0.038% for relative humidity, and K for temperature. However, there are mean temporal iases at the grid points. These iases, which are larger for humidity, will affect the soil moisture increments. The ratio of ackground error to oservation error is larger for relative humidity than for temperature (Tale 2), generating larger corrections to the former Soil Moisture Analyses Monthly Accumulated Values [35] In agreement with the screen level analysis increments (the model is generally too moist and too cold except along coastal regions where it is too dry and too warm), there is a tendency for oth soil analyses to dry out the root zone over the ALADIN-France domain, except for coastal regions which are moistened. The total soil moisture increments produced during the month of July y oth soil analyses (expressed in mm) are shown in Figure 10. The spatial structure of the increments is consistent etween the 13 of 21

14 Figure 9. Mean screen level analysis increments averaged over the month of July 2006 at 1200 and 1800 UT for (left) relative humidity in % and (right) temperature in K. OI and the EKF: there is strong moistening over Italy, the coastal regions of Spain and Portugal, the Netherlands, Denmark, the east coast of the British Islands, and Poland; there is drying over Central Europe, and over regions with significant orography (Alps, Massif Central, Pyrenees). There are no increments over the French and Swiss Alps for the OI, ecause of the threshold criterion for soil ice. This region also has low increments for the EKF, demonstrating its aility to dynamically identify regions where the soil conditions have little sensitivity to the atmosphere. The very dry regions identified on 1 July 2006 (Ero river valley, north Italy, Provence region, Central Spain) are not corrected y the EKF scheme over July, whereas the OI scheme produces large corrections in regions where the model has a dry and warm ias. The variaility of the dynamical coefficients in the EKF introduces smaller-scale structure into the soil increments. Regions of significant negative increments (central Europe) correspond to areas where the accumulated evaporation plus runoff minus precipitation in the open loop run is large (not shown). [36] Figure 11 shows histograms of the soil moisture increments for w 2 in mm, together with the accumulated precipitation (SP) and evaporation plus runoff (S (E + R)) over July 2006 from the open loop integration. The histograms for the w 2 increments are slightly skewed toward positive values, with a larger standard deviation for the OI scheme (62 mm) than for the EKF scheme (44 mm), and also larger positive extremes (250 mm against 160 mm). These numers are comparale to the S (E + R) component, which has a mean value of 80 mm. They are also similar to those present in the exponential distriution of SP, for which most values are elow 100 mm and the mean is 50 mm. This indicates that the soil moisture corrections from the analysis schemes are an important contriution to the surface water udget. This may e due in part, to the fact that soil analyses are totally decoupled from the atmospheric analysis, so that soil changes cannot affect the atmospheric forcing to reduce screen level errors. The use of a large root zone ackground error s w2 also contriutes to this imalance. This value was chosen to match that used in the ECMWF soil analysis, and is also consistent with the current operational OI scheme at Météo-France: s w2 of 10% of the SWI allows a correction of roughly 23 mm for a soil depth of 2.3 m (the average depth over the ALADIN-France domain) for each assimilation cycle. Given that there are two corrections per day, a monthly correction of 1400 mm is possile, which is clearly excessive. This prolem partly stems from a weakness of the two-layer version of the ISBA scheme which does not distinguish etween the depth of the root zone and the total soil depth which is presumaly deeper. With the three-layer version of ISBA [Boone et al., 1999] soil moisture corrections would occur in a shallower root zone. The chosen value of s w2 is more representative of a typical error from the precipitation forcing than from the surface evaporation component. Since the precipitation forcing in July 2006 is elow average (modeled ut also oserved), soil moisture errors during this period are more likely to come from surface evaporation for which a ackground error of 2 mm per cycle would e more realistic. Some aspects of the CANARI screen level analysis could also e revised (e.g., specification of a lower ackground error for relative humidity, and lacklisting of some coastal stations). However, these considerations do not jeopardize the pertinence of comparing the two analysis schemes. 14 of 21

15 Figure 10. Total soil moisture increments in the root zone (mm) accumulated over the month of July 2006 produced (left) y the EKF soil analysis and (right) y the OI analysis Time Series [37] To etter examine the ehavior of the two soil analyses, the temporal evolution of w 2 at eight model grid points is plotted (Figure 12). The grid points are chosen so as to cover a range of climatological regimes and soil analysis ehavior. They include two continental regions (Poland, Slovakia), one mountainous region (Austria), three Mediterranean regions (Algeria, Spain, Italy) and two oceanic regions (England, France). The soil moisture evolution from each analysis is compared to the open loop run at each of these locations, to highlight the contriution of the analysis increments. The soil moisture evolution is expressed in SWI, since the land surface scheme is only sensitive to the screen level variales when the SWI is etween 0 and 1. Since the ackground error for w 2 is specified as a factor (0.1) of the SWI, this evolution is implicitly normalized y s w2. There are nonnegligile accumulated increments, for at least one soil analysis scheme, at each of these locations. [38] 1. In Poland, the soil is initially quite dry, and the negative screen level temperature increments increase soil moisture throughout the month. This moistening is consistent etween the two schemes, although there is a tendency for the EKF to produce larger positive corrections (etween day 5 and 10 and after day 28). Indeed, the OI scheme is more sensitive to humidity innovations which have an opposite signal (moist ias at 2 m). [39] 2. In Slovakia, the initial quite wet soil (SWI = 0.6) is dried down consistently y oth schemes, and the soil moisture reaches the wilting point (SWI = 0) after one month of assimilation. Equation (11) prevents the OI scheme from adjusting w 2 elow w wilt, whereas for the EKF this is prevented y the Jacoians eing reduced to zero. [40] 3. Austria is characterized y strong negative (positive) increments in 2-m relative humidity (temperature), leading to a significant soil drying through the month (the SWI decreases from 0.95 to 0.4). Since the soil is close to field capacity at the eginning of the month, the EKF coefficients are lower than in dryer conditions. There is also a period (etween days 20 and 25) when the EKF scheme leads to positive increments while the OI scheme does not generate soil corrections. [41] 4. In Algeria, the total accumulated increments have opposite signs etween the two soil analysis schemes: the OI adds water and the EKF removes water. Relative humidity increments indicate that the soil is too dry, while the temperature increments indicate that the soil is too moist, and these contradictory signals are interpreted differently y the OI and the EKF. The OI is more sensitive to the moistening (noticed etween day 3 and 5, and from day 21). During the first 3 days the EKF does not produce significant soil increments (compensation etween the two screen level errors), ut from day 3 to 8 oth schemes produce drying. After day 8, the soil moisture in the EKF is elow the wilting point, and the Jacoians ecome negligile. Indeed, the moistening signal after day 22 (in the OI scheme) that would have occurred in the EKF if the SWI had een positive, does not occur. Therefore, the soil moisture remains low with negligile sensitivity to screen level variales. [42] 5. Spain is associated with positive RH 2m increments and strong positive T 2m increments, so that the temperature signal (model iased cold) has the strongest effect on the increments. The greater sensitivity of the EKF coefficients in dry conditions, and the reduced magnitude of the OI coefficients for w 2 in the presence of low vegetation cover, 15 of 21

16 Figure 11. (top) Histogram distriutions of accumulated soil moisture increments in the root zone for July 2006 otained from the OI and the EKF analysis schemes compared to (ottom) corresponding distriutions of the accumulated surface water udget components otained during an open loop integration (only precipitation amounts aove 1 mm are included). lead to larger negative increments with the EKF scheme, particularly around day 12. [43] 6. In Italy, the Pô river valley has the maximum positive increments over the whole domain for the OI scheme (more than 300 mm). There is a significant dry and cold ias at this location (induced y a local sea reeze), and the OI scheme increases the SWI from a small negative value to close to one, after one month of assimilation. For the EKF scheme, there is no sensitivity to the screen level variales, since the initial soil moisture value for w 2 is elow the wilting point, and so the soil moisture evolves as in the open loop run. At this location the OI scheme spanned the total soil water availaility range in one month. [44] 7. In England, the accumulated soil increments have opposite signs after one month in oth systems, as occurred over Algeria. This location has a moist ias, and a slight warm ias. The smaller (larger) weight given in the EKF for humidity (temperature) errors, together with a different reactions to filtering clouds and precipitation (less stringent in the EKF) which occur frequently in this part of the domain, are responsile for the opposing corrections. [45] 8. In France, the model is too dry and too warm, and oth analyses are similar, with positive increments, although larger corrections are applied y the EKF ecause of the dominance of the temperature signal. Between day 18 and 22, important corrections are associated with rain that is asent from the forcing (see section 5.2.3) Comparison With a Hydrological Model Over France [46] Figure 13 shows the soil moisture variations DW 2 over the whole soil column during the month of July 2006 over France, from four systems. The first is the hydrological system SIM [Haets et al., 2008] which is an off-line threelayer version of ISBA run at 8 km resolution over France, 16 of 21

17 Figure 12. Temporal evolution of the root zone soil wetness index (SWI) during the month of July 2006 at selected points (located y their latitude and longitude) for an open loop run (lack dashed curves), an optimal interpolation analysis (lack solid curves), and an extended Kalman filter analysis (grey curves). Indications on total soil moisture increments from screen level innovations is provided (e.g., T(+) = soil moistening from T 2m innovations). 17 of 21

18 Figure 13. Soil water content variations over the total soil depth (mm) for the month of July 2006 produced y the hydrological system SIM, an open loop run (OPEN LOOP), an optimal interpolation analysis (OI), and an extended Kalman filter (EKF) analysis over France. using a high-quality forcing data set, including precipitation, radiation, and atmospheric parameters [Quintana- Seguí etal., 2008]. This is considered to e the est estimate of the surface water udget components (noted SIM). The three others are the open loop ISBA run (noted OL), the OI soil analysis (noted OI), and the EKF soil analysis (noted EKF). [47] The SIM and OL runs can e used to compare the accumulated precipitation minus runoff and evaporation, regardless of the soil moisture content at the eginning of the period of interest. Changes to the water udget induced through soil analysis increments are estimated y comparing the analysis runs with the open loop run. For a given experiment i the water udget is: DW i 2 ¼ SPi SE i SR i þ SI i ð13þ The soil moisture increments SI are zero in the open loop run. Ideally, discrepancies etween the open loop run and SIM (errors in the precipitation and evaporation minus runoff) should e compensated y the soil moisture increments produced y the analyses. That is: SI i S P SIM P OL S E SIM E OL S R SIM R OL ð14þ where i is either OI or EKF [48] In the SIM run, the greatest soil moisture depletion (from evaporation and runoff) occurs over eastern France, and along the English Channel coast. Mountainous areas incurred slightly more soil drying than other regions. Increases in soil moisture (a signature of precipitation events) occurred in southeast France, in the Aquitaine region, and in northwest France (along an axis from Nantes to Paris). The open loop run has a numer of similarities with SIM, although the soil moisture reduction during the month is larger, and the regions of soil moisture increase in western France have incorrect spatial extents. Also, the 18 of 21