Combined assimilation of screen-level observations and radar-derived precipitation for soil moisture analysis

Transcription

1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: , April 2011 A Combined assimilation of screen-level observations and radar-derived precipitation for soil moisture analysis Jean-François Mahfouf a *andvojtěch Bližňák b,c a Météo-France/CNRS, CNRM/GAME, Toulouse, France b Charles University in Prague, Faculty of Science, Department of Physical Geography and Geoecology, Prague, Czech Republic c Institute of Atmospheric Physics, Prague, Czech Republic *Correspondence to: Jean-François Mahfouf, GAME/CNRM (Météo-France/CNRS), 42 Av. G. Coriolis, Toulouse Cedex 1, France. jean-francois.mahfouf@meteo.fr A methodology is proposed in order to combine information from radar precipitation with other observations (e.g. screen-level temperature and relative humidity) in a soil analysis scheme based onanextendedkalmanfilter.apreliminary study is performed over the Czech Republic for one month in July 2008 using threehour rainfall accumulations derived from two C-band radars and a land-surface scheme forced by short-range forecasts from a limited-area model. The Jacobian matrix of the observation operator is examined to make optimal choices for the estimation of the Kalman gain matrix. It is shown that the size of the perturbation for computing Jacobian matrix elements with finite differences has to be carefully chosen, since too small values lead to unphysical negative elements whereas too large values reduce the spatial variability considerably. After a log-transform of the precipitation field, the corresponding errors are more compatible with the Gaussian hypothesis of the Kalman filter. However, at locations where model rainfall is underestimated, positive soil moisture increments are much too low. Finally, two methods for combining the assimilation of screen-level observations with radar precipitation are compared. A first evaluation shows more accurate soil analyses (leading to reduced screen-level parameter forecast errors) when both sources of information are considered to correct soil moisture contents. Avenues for improving the specification of observation and model errors of the precipitation field are also discussed. Copyright c 2011 Royal Meteorological Society Key Words: data assimilation; weather prediction; land surface schemes Received 17 June 2010; Revised 18 January 2011; Accepted 18 January 2011; Published online in Wiley Online Library 4 March 2011 Citation: Mahfouf J-F, Bližňák V Combined assimilation of screen-level observations and radar-derived precipitation for soil moisture analysis. Q. J. R. Meteorol. Soc. 137: DOI: /qj Introduction The importance of soil moisture initialization for weather and seasonal forecasting has been recognized through many numerical sensitivity studies (Viterbo and Courtier, 1995; Dirmeyer, 2003; Zhang and Frederiksen, 2003; Koster et al., 2004; Fischer et al., 2007). However, the lack of direct measurements of root-zone soil moisture in real time over large domains makes this initialization difficult. For operational weather applications, two main techniques are currently used in numerical prediction models. The first method consists of running an offline landsurface scheme (similar to the one coupled to the atmospheric model) with the best available atmospheric forcing in terms of precipitation, radiative fluxes, wind, temperature and humidity. This approach has been chosen Copyright c 2011 Royal Meteorological Society

2 710 J. F. Mahfouf and V. Bliznak for example at the National Centers for Environmental Prediction (NCEP) with the North American Land Data Assimilation System (NLDAS; Mitchell et al., 2004) and the Global Land Data Assimilation System (GLDAS; Rodell et al., 2004). Since forcing data come from various origins (conventional, satellite, radar) consistency checks are necessary (e.g. the short-wave downward radiation should have low values when it rains). This method is efficient for correcting model forecast errors coming from precipitation and radiation fluxes. On the other hand, other sources of errors in the prediction of surface evaporation fluxes cannot be corrected with such a method (e.g. inadequate prescription of land-surface parameters, such as soil depth or minimum stomatal resistance). The second method is based on data-assimilation techniques developed within the atmospheric and oceanographic communities and adapted to land-surface models. An optimal interpolation technique developed by Mahfouf (1991) that uses short-range forecast errors of near-surface temperature and humidity is operational in a number of operational services: Météo-France (Giard and Bazile, 2000), Environment Canada (Bélair et al., 2003) and the European Centre for Medium-Range Weather Foreacasts (Douville et al., 2000) among others. The physical link between soil variables and near-surface parameters is given by the surface turbulent fluxes (since soil moisture exerts a strong control on the evaporative fraction). Such a method allows one to correct for errors in precipitation and evaporation fluxes, but has more difficulties when turbulent fluxes are affected by downward radiation-flux errors (Hu et al., 1999; Douville et al., 2000). An advantage of the second method is that it is applicable globally since, despite the fact that the surface observational network is not uniform, the spatialization of nearsurface temperature and humidity observations is easier than that of surface precipitation, which requires data from dense networks (rain-gauge and radar products) that are not currently exchanged on the global telecommunication system. Satellite missions with microwave instruments at low frequencies (< 10 GHz) that have recently been launched provide useful information on superficial soil moisture contents. Promising results in terms of forecast skill scores have been obtained in a number of feasibility studies with simplified data-assimilation methods (Drusch 2007; Scipal et al., 2008; Dharssi et al., 2010; Mahfouf, 2010). Data from microwave instruments have also been assimilated with more advanced methods, but not yet in the numerical weather prediction (NWP) context (Crow and Wood, 2003; Reichle et al., 2007, Draper et al., 2009, among others). However, their rather coarse spatial and temporal resolutions (40 km footprint with a three-day revisit time), together with other limitations (screening by dense vegetation, loss of information on deep layers by rainy events, limited accuracy, reduced vertical soil-penetration depth), makes their use in operational weather-prediction models non-trivial, particularly in high-resolution limitedarea models. The present study is a preliminary step in order to reconcile the two methods for soil moisture analysis. In areas where no precipitation analyses are available, the soil analysis should rely on screen-level observations and satellite-derived soil moisture. In areas where precipitation analyses are available, this additional source of information should be used on top of other relevant observations. In order not to discard the information provided by the atmospheric short-range forecast in terms of surface rainfall (which also preserves consistency between meteorological quantities and radiative fluxes), precipitation analyses allow one to compute innovations (differences between observations and model counterparts) for correcting soil moisture reservoirs, as already proposed by Balsamo et al. (2005) within the European Land Data Assimilation System (ELDAS) project. A strong advantage of precipitation analyses over specific regions compared with satellite observations is their better spatial and temporal resolutions (in particular when provided by a weather radar network). Over limited-area domains, precipitation analyses are likely to be the most valuable information for improving soil moisture contents in NWP models. The soil analysis is presented in section 2 with the necessary modifications to account for precipitation observations. The experimental set-up described in section 3 is used to examine the best method for computing the Jacobian matrix of the observation operator (section 4). Section 5 compares results from experiments in which the land-surface scheme is run with either model or radar rainfall forcings. Then, a number of assimilation experiments are performed and analysed. In section 6, conclusions from this study and future plans, in particular regarding the specification of precipitation errors, are given. 2. Description of the surface analysis The soil temperature and moisture contents are evolved by the two-layer land-surface scheme Interactions Soil- Biosphere-Atmosphere (ISBA) based on the force-restore method (Noilhan and Planton, 1989; Noilhan and Mahfouf, 1996). This scheme is available within a surface externalized (SURFEX) modelling platform (Le Moigne, 2009) together with an extended Kalman filter (EKF). The EKF has already been evaluated for the assimilation of screenlevel observations (Mahfouf et al., 2009), remotely sensed superficial soil moisture (Draper et al., 2009) and leaf-area index (Albergel et al., 2010). Here we use a simplified version of the EKF in which the background covariance matrix P f does not evolve with time. We define a vector of observations composed of two subsets: y (1) (observations already considered in the EKF such as screen-level temperature and relative humidity: T 2m and RH 2m )andy (2) (precipitation observations). If the two observation sets are uncorrelated, they can be assimilated sequentially as shown by Ehrendorfer (2007): x a(1) = x f + K (1) (y (1) H (1) x f ), (1) K (1) = P f H (1)T ( H (1) P f H (1)T + R (1)) 1, (2) P a(1) = P f, (3) x a = x a(1) + K (2) (y (2) H (2) x a(1) ), (4) K (2) = P a(1) H (2)T ( H (2) P a(1) H (2)T + R (2)) 1, (5) using the classical notations of the Kalman filter (Ide et al., 1997). The superscripts a and f correspond to the analysed and forecast values respectively. In this study, the control vector x contains two prognostic variables: the volumetric superficial soil moisture content w g (representative of a depth d 1 = 1cm) and the volumetric root-zone soil moisture content w 2 (representative of a depth d 2 varying between 50 cm and 3 m).

3 Radar Precipitation use in Soil Moisture Analysis 711 In the following, we rewrite equations (4) and (5) for the assimilation of precipitation data. We assume that a precipitation analysis (accumulated amount over the assimilation window) is available on the model grid: y (2) = PR o (expressed in mm). The observation vector is reduced to a scalar because the land-surface assimilation problem is solved as a set of independent columns. The landsurface scheme ISBA is forced by short-range forecasts from an atmospheric model that produces a model counterpart of observations in terms of accumulated precipitation: H (2) x a(1) = PR b.sincepr b is a forcing term it does not explicitly depend upon the model state x, but on the other hand the land-surface prognostic variables (soil moisture contents and soil temperatures) depend upon PR b. The covariance matrix of forecast errors H (2) P f H (2)T that describes precipitation errors reduces to a scalar (σ f ) 2 and has to be compared with the observation precipitationvariance error R (2) = (σ o ) 2. The error covariance between the precipitation and the soil prognostic variables can be written as P f H (2)T = (x x t )(y (2) y (2) t ) T, (6) where the subscript t stands for the true value and the overline the averaging operator. By introducing the Jacobian matrix J = x/ y (2), the previous expression can be approximated by P f H (2)T = J(y (2) y (2) t )(y (2) y (2) t ) T = J(σ f ) 2. (7) Finally, one can write the analysis increments x as with x = J α (PR o PR b ), (8) α = (σ f ) 2 (σ f ) 2 + (σ o ) 2. (9) From the above equation, soil moisture corrections can be estimated once the errors associated with the precipitation observation and the precipitation forecast are known, on top of the Jacobian matrix J. This Jacobian matrix represents the sensitivity of the prognostic variables with respect to the observations, i.e. the inverse sensitivity given by the observation operator H. With an offline land-surface scheme the rainfall rate is imposed as a forcing, so there is no sensitivity of this field to the state vector. On the other hand, changes to the precipitation forcing have a direct effect on the soil moisture reservoirs w g and w 2 of the state vector x. In section 4, we explain how the Jacobian matrix J can be estimated with finite differences within SURFEX. We also discuss the underlying assumption of Gaussian errors implied by the EKF and the consequences for the precipitation field, which is known to have non-gaussian errors (Errico et al., 2000). Another point of discussion will be the specification of precipitation forecast errors (which could be derived from an ensemble of short-range forecasts). It is interesting to notice from Eq. (8) that the soil moisture corrections depend upon the model precipitation error over the assimilation window. The proportionality factor (noted γ i ; see Eqs (10) and (11)) depends on the accuracy of modelled and observed precipitation fields and increases when observations become more accurate. It also Figure 1. Positions of two Czech weather radars are indicated by triangles ( B for Brdy and S for Skalky) with the topography at 0.1 resolution expressed in metres. Brdy and Skalky are located in Bohemia and Moravia respectively. The Sudeten mountains are located along the border with Poland, the Carpathian mountains are located along the border with Slovakia, and the Sumava forest is located along the southern border with Germany. depends upon the ability of the soil layers to infiltrate any water excess produced at the surface through the Jacobian matrix J (to be discussed more thoroughly in section 4). The analysis equations for w g and w 2 can be summarized as w g = α 1 T 2m + α 2 RH 2m + γ 1 PR, (10) w 2 = β 1 T 2m + β 2 RH 2m + γ 2 PR, (11) where w are the analysis increments, T 2m, RH 2m,and PR are the innovations (observation departures) and α i, β i and γ i are the elements of the Kalman gain matrix. 3. Description of the experimental design The above methodology has been set up over the Czech Republic domain shown in Figure 1 for the month of July The domain has a horizontal resolution of 0.1 in both directions with 70 points in the x direction and 26 points in the y direction. Surface orography and physiographic parameters (soil and vegetation properties) are taken from the ALADIN/France NWP model (Bubnova et al., 1995; Giard and Bazile, 2000; Fischer et al., 2005). Since the horizontal resolution of the ALADIN/France model is 9.5 km, the nearest grid-point approach has been chosen to interpolate the data on the regular latitude/longitude grid of the domain. Surface precipitation, downward radiative fluxes, near-surface temperature, wind and humidity from ALADIN/France short-range forecasts (6 h sampled every 3 h) have been used to force the land-surface scheme ISBA over the chosen month with a 15 min model time step. Radar-derived rainfall estimates corrected by rain-gauge stations have been used for improving the soil moisture analysis of the ISBA land-surface scheme. The data are derived from reflectivity measurements of two Czech C-band weather radars located at Skalky and Brdy (triangles in Figure 1). A merging method proposed by Sokol (2003) combines radar and rain-gauge daily values by a spatial kriging of the radar bias. Sokol and Bližňák (2009) have shown good agreement between this radar product and climatological observations over 6 years. In the present study, hourly radar accumulated precipitation data at 1 km resolution have

4 712 J. F. Mahfouf and V. Bliznak been upscaled to the model grid resolution of 0.1 (binning technique) and accumulated over 3 h. Figure 2 displays the monthly accumulated rainfall rates (July 2008) from the NWP ALADIN model and the radar over the experimental domain. The difference between the two accumulated amounts (which represents the model monthly bias) is also shown in Figure 2(c). Radar data have been merged with ALADIN precipitation fields in order to provide a forcing data set over the whole domain of computation. Where the radar data are missing (spatially and temporally) they are replaced by ALADIN values. This merged product will be used to force the ISBA scheme by a direct-insertion method, which consists of replacing the model value by the measured counterpart (Rodell and Houser, 2004). The accumulated precipitation from ALADIN shows a number of reasonable features consistent with the radar patterns. The smallest amounts below 75 mm are located over the western and southeastern parts of the country, whereas the highest values above 150 mm are located in the northeastern part of the country near the border with Poland (Sudeten mountains). On the other hand, the small amounts (below 50 mm) in the north central part of the domain identified by the radar correspond to a region with large amounts in ALADIN (above 100 mm). Similarly, maximum accumulations above 100 mm west of the Skalky radar location (Moravia region) are not simulated by the ALADIN model. The map of differences shows that, in general, model rainfall accumulations are overestimated over the western part of the Czech Republic and underestimated over the eastern part. Orographic precipitation values near the highest mountain ranges (Sudeten mountains and Carpathian mountains) correspond to the largest model overestimations (above 100 mm). By restricting the comparison to grid points for which radar data are available, the standard deviation of the difference between the two fields is 13 mm day 1 over the monthofjulywithameanvalueof95mmforaladinand 92 mm for the radar. These values will be compared with the corrections imposed by the soil analysis over the same period. 4. Jacobian matrix of soil moisture with respect to precipitation A reference simulation has been performed where the ISBA scheme is run over the month of July 2008 forced by ALADIN precipitation forecasts (EXP1). Then a number of perturbed simulations have been run by imposing a small perturbation δpr to the precipitation forcing PR with a constant rainfall rate at each time step in order to compute the elements of the Jacobian matrix J. When considering two control variables w g and w 2 and a precipitation observation PR, the elements are computed with finite differences w PR w(pr + δpr) w(pr). (12) δpr The variables w from the perturbed and reference simulations are compared after each 6 h model integration. Several positive perturbations δrr of 10 5, 10 4 and 10 3 mm s 1 have been considered, leading respectively to accumulated amounts δpr over a 6 h period t of 0.216, 2.16 and 21.6 mm of liquid water added at the surface (δpr = δrr t). The use of positive perturbations allows nonzero sensitivities even when the model does not produce rain over a given 6 h period. The Jacobian matrix elements have been expressed in both physical space and log-transformed space (to be justified later) Evaluation in physical space The Jacobian matrix elements are expressed in (mm mm 1 ) where each soil moisture reservoir is scaled by its actual depth and the rainfall rate is expressed in accumulated amounts. These non-dimensional elements represent the fraction of liquid water that is retained by each reservoir after a 6 h period. Intuitively they should vary between 0 and 1. Mean Jacobian matrix elements for the month of July are presented in Figure 3 for the three values of δrr previously chosen. For the superficial soil reservoir w g, minimum values are noticed along the border with Poland where accumulated rainfall amounts are maximum. Similarly, the low values in the north central part of the Czech Republic are associated with large model precipitation amounts. Maximum values located southeast and northwest of the domain correspond to precipitation minima. Since the water-holding capacity for w g is limited to values lower than about 5 mm (soil depth times soil porosity), in areas with significant precipitation amounts the surface reservoir can easily reach saturation. Part of the water excess δpr is thus removed from the soil column by runoff, leading to only small changes of the water reservoir w g with respect to a reference simulation. When the precipitation forcing is weaker or the soil drier, a given water excess δpr canremaininthesoil,leadingtoa significant increase in w g after 6 h and consequently to rather large sensitivities. Even though the patterns look similar for the three values of δrr, small-scale structures are present with the smallest value 10 5 and the spatial variability is very much reduced with the largest value 10 3.Asexplained later, the behaviour of the land-surface scheme can become unrealistic when δpr is too small, in particular over regions where the radiative forcing is large. At these locations, the water losses can be larger than the imposed perturbation, leading to negative Jacobian matrix elements. For the deep soil reservoir w 2, an increase of δpr reduces the contrast between large values noticed in areas with the highest rain amounts and small values associated with areas experiencing the lowest rain amounts. The positive correlation between w 2 / PR and PR is physically understandable by the fact that, when increasing precipitation amounts, more water can be retained by the deep soil reservoir. The threshold value that was important for explaining the behaviour of w g / PR does not hold for w 2 since the water amounts required to reach saturation or field capacity for soil depths varying between 1000 and 2000 mm are much larger than the size of the imposed precipitation perturbations. The probability density functions (PDFs) of the Jacobian matrix elements w 2 / PR and w g / PR for the three perturbation values (Figure 4) show narrower distributions for increasing sizes. In particular, with δrr = 10 3,each distribution is strongly skewed (towards the mode 1.0 for w 2 and 0.1 for w g ). For δrr = 10 5, negative values are noticed. They correspond to locations where the model does not rain in the reference. At such locations, a small amount of drizzle is imposed by the perturbed rain forcing that fills the canopy interception reservoir for which evaporation is at the potential rate. Since the evaporative demand can be

5 Radar Precipitation use in Soil Moisture Analysis 713 (c) Figure 2. Monthly accumulation of surface precipitation for July 2008 from the NWP ALADIN model (top panel) and derived from C-band weather radars (middle panel). The lowest panel is the difference between radar and model accumulations. Plotted isolines are 100, 50, 25, 5, 5, 25, 50 and 100 mm with shaded areas below 50 mm. This figure is available in colour online at wileyonlinelibrary.com/journal/qj rather large in such areas (strong radiative forcing), the explicit numerical resolution of this prognostic equation can produce negative values of the reservoir at the end of each time step. Such (small) negative values are put back to zero by extracting water from the superficial soil reservoir. This numerical artefact is a negative runoff that will reduce the amount of water in the soil (for both superficial and total reservoirs). For larger values of δrr, the amount of water added to the interception reservoir per time step is greater than the potential evaporation rate (i.e. this reservoir cannot become totally empty at the end of each time step). From the above results, the Jacobian matrix elements appear to have similar spatial patterns when computed with finite differences with perturbations of various sizes. There

6 714 J. F. Mahfouf and V. Bliznak (c) (d) (e) (f) Figure 3. Jacobian matrix elements of soil moisture content with respect to surface precipitation (in mm mm 1 ) for various sizes of precipitation perturbation (first row: 10 5 mm s 1, second row: 10 4 mm s 1, third row: 10 3 mm s 1 ). The left column corresponds to the superficial soil moisture reservoir w g and the right column corresponds to the deep soil moisture reservoir w 2. are close similarities with δrr = 10 5 and δrr = 10 4,but the Jacobian matrix elements present more noisy patterns for w g with the smallest size of perturbation and can exhibit unrealistic negative values. With the value δrr = 10 3,the Jacobian matrix elements are biased towards corrections to the deep reservoir w 2 at the expense of the surface reservoir w g. The spatial variability is significantly reduced with high (resp. low) values for w 2 (resp. w g ) when the precipitation forcing is large. It is also reduced with low (resp. high) values for w 2 (resp. w g ) when the precipitation forcing is weak. This is understandable by the fact that in most regions such large perturbations dominate the reference value (δpr > PR). Since the runoff process has a strong impact on the relationship between precipitation and soil moisture variations, it explains why no real linear regime is evident from this study of the Jacobian matrix elements. Nevertheless, the behaviour obtained with δrr = 10 4 appears to be a good compromise between too small perturbations, which lead to noisy patterns and can produce unphysical values, and too large perturbations, which dominate the total precipitation forcing PR + δpr Evaluation in log-transformed space The EKF equations assume that model and observations errors follow a normal distribution. Knowing that

7 Radar Precipitation use in Soil Moisture Analysis 715 wg 1E 5 w2 1E 5 (c) (e) (mm/mm) wg 1E (mm/mm) wg 1E 3 (d) (f) (mm/mm) w2 1E (mm/mm) w2 1E (mm/mm) (mm/mm) Figure 4. Histograms of Jacobian matrix elements of w g and w 2 with respect to surface precipitation in physical space (PR) estimated every 6 h for July Each row corresponds to a different value of the rain perturbation imposed for estimating the Jacobian matrix with finite differences: first row δrr = 10 5 mm s 1, second row δrr = 10 4 mm s 1, third row δrr = 10 3 mm s 1. precipitation errors are hardly Gaussian (Errico et al., 2000), a change of variable is proposed by defining x = ln(pr + 1) as in the study of Mahfouf et al. (2007). In that case the soil analysis increments can be written as w = [ w PR (PRf + 1) ] (σ f x )2 (σ f x )2 + (σ o x )2 (x o x b ), (13) where the standard deviation σ x should provide more comprehensive information on the statistical distribution of errors. The corresponding PDF Jacobian matrix elements are displayed in Figure 5. From Eq. (13), the unit of these elements is mm. A number of similarities can be found to the distributions examined in physical space, such as negative values for δrr = 10 5 and less spread for w g with δrr = However, the distributions are more alike when varying the size of the perturbation, in particular for the deep reservoir w 2. The exponential shape of the distributions reflects that of the precipitation field, since In this expression and in similar ones, the precipitation PR is given in mm over a 6 h period. the physical Jacobian matrix elements are multiplied by (PR + 1) in order to get their log-transform counterpart. From these distributions, the transformation in log-space looks appealing, since it exhibits less dependence on the size of the perturbation than that in physical space. In order to choose one formulation versus another, the sums of pseudo-analysis increments for the deep reservoir w 2 from respectively Eqs (8) and (13) have been computed based on the difference between ALADIN and radar accumulations every 6 h. We have then compared these estimates with the differences in soil moisture obtained after a one-month integration of ISBA with ALADIN (EXP1) and radar precipitation forcing fields (EXP2). This comparison is shown in the scatter-plot diagrams of Figure 6. We have considered a model error σ f that is twice the value of the observation error σ o in both log-space and physical space. The computation of the increments in physical space leads to a total correction in the soil that is closer to the actual soil moisture difference induced by the two forcing datasets than in the log-transformed space. Indeed the logtransformed space gives more weight to occurrences in which the model overestimates rainfall rates and reduces the differences when the model underestimates rainfall rates. Therefore areas with a precipitation deficit over the month

8 716 J. F. Mahfouf and V. Bliznak wg 1E w2 1E (c) wg 1E 4 (d) w2 1E (e) wg 1E 3 (f) w2 1E Figure 5. Histograms of Jacobian matrix elements of w g and w 2 with respect to surface precipitation in log-transformed space (ln(pr + 1)) estimated every 6 h for July Each row corresponds to a different value of the rain perturbation imposed for estimating the Jacobian matrix with finite differences: first row δrr = 10 5 mm s 1, second row δrr = 10 4 mm s 1, third row δrr = 10 3 mm s 1. only show small positive soil moisture increments. Such distortion of the precipitation field in order better to match a Gaussian distribution of errors appears to be detrimental in terms of water budget. This comparison also supports the use of a precipitation perturbation δrr of 10 4 mm s 1, since a lower value reduces the size of the Jacobians and thus the agreement with the soil moisture differences. A larger value improves the agreement slightly but at the expense of reducing the spatial variability of the Jacobian matrix elements, as noticed in Figure 3. In the remaining part of this study, data-assimilation experiments requiring knowledge of J are undertaken using surface precipitation in physical space and a precipitation perturbation δrr of 10 4 mm s 1 for computing the Jacobian matrix elements with finite differences. 5. Experiments and results A set of five experiments summarized in Table 1 has been performed. The reference simulation (EXP1) corresponds to a one-month integration of ISBA using forcing data provided by short-range forecasts from the ALADIN model (including precipitation). This reference run has been used in the previous section for the computation of the Jacobian Table I. Summary of experiments. Name Rain forcing T2m/RH2m assimilation assimilation assimilation EXP1 ALADIN no no EXP2 RADAR no no ANA1 ALADIN yes no ANA2 ALADIN yes yes ANA3 ALADIN + RADAR yes no matrix with finite differences, together with three perturbed runs (for which the precipitation forcing has been increased by a small amount) that will not be discussed further in this section. Then a second experiment (EXP2) similar to EXP1 has been performed in which the precipitation from the ALADIN model was replaced by the one derived from the weather radars. This experiment is similar to a direct-insertion method. The third experiment (ANA1) corresponds to an assimilation of screen-level temperature and relative humidity (available every 6 h from an optimal interpolation using SYNOP observations) in the ISBA scheme with the EKF. The experimental set-up is similar

9 Radar Precipitation use in Soil Moisture Analysis 717 using radar rainfall-rate observations (experiment ANA2) as given by Eqs (10) and (11). The radar precipitation error σ o is assumed to be half the model precipitation error σ f. Despite some arbitrariness in this choice, it is very likely that the radar-derived product is more accurate than the NWP product. Finally a last experiment (ANA3) is an alternative solution for combining screen-level observations with radarderived rainfall rates. In order to avoid the computation of the Jacobian matrix, which needs to be done carefully, the precipitation forcing is replaced by a weighted average between observed and modelled values according to their relative accuracy following optimal interpolation theory, i.e. PR a = α PR o + (1 α) PR b, (14) where the optimal coefficient α is given by Eq. (9) with the same error specification for σ f and σ o as in experiment EXP2. With respect to the direct-insertion method, this approach has the advantage of not discarding the precipitation produced by the model and proposing a forcing field depending upon the errors of each piece of information. A drawback, similar to that for the direct-insertion method, is the fact that some inconsistencies may arise between the blended forcing precipitation field PR a and other forcing fields obtained from the forecast model (radiation fluxes in particular) Results from experiments EXP1, EXP2 and ANA1 Figure 6. Monthly accumulated soil moisture increments for the deep soil reservoir w 2 against soil moisture differences in w 2 between experiments EXP2 (radar rain) and EXP1 (model rain) after one month. The upper panel corresponds to the use of rain increments in physical space (PR) and the lower panel corresponds to the use of rain increments in log space (ln(pr + 1)). Increments are computed for various sizes of the perturbation δrr for the Jacobian matrix element computation with finite differences 10 5,10 4 and 10 3 mm s 1. to that described in Mahfouf et al. (2009) with few modifications. In particular, background errors have been set to 0.01 m 3 m 3 for the deep soil reservoir. Values for screenlevel temperature observation error have been set to 1.5 K and those for screen-level relative-humidity observation error to 10%. A background check is performed on screenlevel observations. They are rejected when innovations are larger in absolute value than 5 K for temperature and 30% for relative humidity. Moreover we have taken advantage of the availability of radar rainfall to avoid using screenlevel observations when precipitation is observed and not modelled. When the sum of model and radar rainfall is larger than 1 mm per 6 h, increments generated by the EKF are set to zero. The EKF set-up for the assimilation of screen-level observations (experiment ANA1) has been modified to account for additional soil moisture corrections In order to examine the influence of the precipitation forcing on soil moisture evolution, the soil moisture contents w 2 from EXP2 and EXP1 produced at the end of the forecasting period (1 August 2008 at 0000 UTC) are compared in Figure 7. Since both experiments start from the same initial conditions, the soil moisture difference mostly reflects differences in accumulated precipitation forcings. This is indeed what can be seen when comparing Figures 7 and 2(c). The two figures exhibit similar spatial patterns but with smaller values for soil moisture changes. The differences come from the runoff and evaporation components in the two experiments, since in areas with larger (resp. smaller) precipitation amounts, higher (resp. lower) evaporation and runoff fluxes take place as the soil is wetter (resp. drier). Figure 7 shows the soil moisture content difference between experiments ANA1 and EXP1 on 1 August 2008 at 0000 UTC. This difference is close to the soil moisture accumulated increments produced by the EKF assimilation scheme during the month of July 2008 in response to temperature and relative humidity screen-level forecast errors. If the soil analysis was mainly correcting for errors in the precipitation forcing, the differences between experiments ANA1 and EXP1 and experiments EXP2 and EXP1 should be similar. The comparison between Figure 7 and reveals a number of locations where this it the case, although the effect is not systematic. First the size of the increments is about the same order of magnitude as the soil moisture changes induced by precipitation differences (around 25 mm, with few locations above and below 50 mm). The soil has dried down in ANA1 in agreement with the precipitation excess noticed over the western part of the domain. The Sudeten mountains is another region in which the soil moisture decrease induced by screen-level variables is consistent with the model precipitation excess. It is over this region that the largest negative differences take place between

10 718 J. F. Mahfouf and V. Bliznak Figure 7. Soil moisture differences for the deep reservoir w 2 at 0000 UTC on 1 August 2008 between a simulation with radar precipitation (EXP2) and a simulation with ALADIN precipitation (EXP1) (upper panel). The lower panel shows similar deep soil moisture differences between an EKF soil assimilation using screen-level observations (ANA1) and a simulation (open loop) with ALADIN precipitation (EXP1). Plotted isolines are 100, 50, 25, 5, 5, 25, 50 and 100 mm with shaded areas below 50 mm. This figure is available in colour online at wileyonlinelibrary.com/journal/qj experiment ANA1 and the reference. The Moravia region is characterized by a precipitation deficit with the ALADIN model that leads to soil moisture increases between EXP2 and EXP1. The assimilation of screen-level variables in the EKF also produces a moistening around 10 mm in this region, but the spatial patterns do not match precisely. The same features can be noticed in the northeastern part of the country along the border with Poland. Regions of strong disagreement between the two soil moisture difference fields appear along the Austrian border near longitude 15 E. Indeed, experiment ANA1 leads to a soil moisture decrease around 50 mm, whereas to compensate for the model precipitation deficit an amount of 25 mm should have been added at that particular location. Conversely, along the Sumava forest (southwestern region along the German border) a significant soil moisture increase of 25 mm has been produced by the EKF that is only consistent with the precipitation differences near (49 N, 35 E). Drusch and Viterbo (2007) also found that, in the global ECMWF model over specific areas, screen-level observations hardly compensate for precipitation errors. The soil moisture differences generated by the EKF increments have smaller scale features than those produced by the differences between the precipitation forcings, since they depend not only upon the spatial scale of the screen-level analysis increments but also on the Jacobian matrix of the observation operator (for T 2m and RH 2m ), which can have weak horizontal correlations at some locations because soil columns are assumed to be independent Results from combined data-assimilation experiments ANA2 and ANA3 We examine results from experiments in which both screen-level observations and radar precipitation have been included to modify the soil moisture contents of the ISBA scheme. The precipitation corrections are included differently on top of an EKF assimilation of screen-level observations: experiment ANA2 adds a soil moisture increment at the analysis time proportional to

11 Radar Precipitation use in Soil Moisture Analysis 719 Figure 8. Soil moisture differences for the deep reservoir w 2 at 0000 UTC on 1 August 2008 between an EKF soil assimilation using screen-level observations and radar precipitation with Jacobian matrix elements (ANA2) and a simulation (open loop) with ALADIN precipitation (EXP1) (upper panel). The lower panel presents similar differences but experiment ANA2 is replaced by an EKF soil assimilation using screen-level observations and radar precipitation with modified rainfall forcing (ANA3). Plotted isolines are 100, 50, 25, 5, 5, 25, 50 and 100 mm with shaded areas below 50 mm. This figure is available in colour online at wileyonlinelibrary.com/journal/qj the precipitation difference, whereas ANA3 forces the surface scheme during each forecast period with a precipitation field that is a weighted average between the two precipitation fields (according to their respective accuracy). The soil moisture values at the end of the one-month period are compared with the ones obtained when assimilating only screen-level observations (experiment ANA1). The patterns shown in Figure 8 are consistent between the two experiments, since the same information is added to the land-surface scheme but in a different manner. These soil moisture corrections are also in agreement with the largest precipitation differences noticed in Figure 2, in particular the negative values along the Sudeten mountains, the Carpathian mountains and most of Bohemia and the positive values in Moravia. Experiment ANA3 (resp. ANA2) produces stronger moistening (resp. drying) in regions of model precipitation deficit (resp. excess) than experiment ANA2 (resp. ANA3). This can be understood by the fact that the Jacobian matrix element w 2 / PR has its largest values over regions associated with intense model rainfall events (Figure 3). These differences are more clearly noticeable in Figure 9, which presents the time evolution of the mean soil moisture w 2 (expressed in mm) averaged over the Czech Republic domain for July Rainfall accumulated differences (model minus radar) are also displayed in order better to understand the behaviour of the five experiments. Indeed, even though the mean accumulated difference at the end of the month is only 3 mm, the month can be divided into two contrasted periods: the ALADIN precipitation is strongly underestimated during the first ten days, in association with strong convective events, whereas the rest of the month is characterized by a small systematic overestimation. This explains the differences in soil moisture behaviour between EXP1 and EXP2. The soil moisture is drier by about 10 mm in EXP1 with respect to EXP2 up to day 12, then gradually its evolution gets closer to EXP2

12 720 J. F. Mahfouf and V. Bliznak Mean soil moisture content EXP1 EXP2 ANA1 ANA2 ANA Days Rain accumulation difference Figure 9. Mean total soil moisture content evolution over the Czech Republic in July 2008 for the five experiments summarized in Table 1 (top panel). The bottom panel is the evolution of mean accumulated rain differences (ALADIN minus radar) over the same domain for the same period. Days with almost similar mean values at the end of the month. The assimilation of screen-level observations only (ANA1) increases soil moisture values significantly between day 11 and day 17, placing them between experiments EXP1 and EXP2. During the last ten days, the EKF leads to a strong drying of the soil by about 20 mm because during this period the model is systematically colder and moister in the surface boundary layer than reflected by screenlevel observations. The combined assimilation based on additional soil increments (ANA2) exhibits moister soils than in experiment ANA1 between day 3 and day 10; then from this date, since the model precipitation bias changes sign, the soil moisture decreases more rapidly than with the assimilation of screen-level observations only. The combined assimilation based on modified precipitation forcing (ANA3) has a similar trend compared with ANA2. The moistening during the first half of the month is larger whereas the drying when the model precipitation is in excess is much smaller. In experiment ANA3, the soil moisture content at the end of the month is closer to experiment ANA1 than to experiment ANA Preliminary evaluation The previous analysis of the five experiments described in Table 1 has revealed different behaviour in terms of soil moisture content according to the precipitation forcing (EXP1, EXP2), the use of additional information (screenlevel observations, radar rainfall; ANA1, ANA2, ANA3) and the methodology for combining them (additional soil increments, modified forcing). However, nothing can be said about improvements or degradations of the landsurface modelling system. As a preliminary evaluation of theskillofthefiveexperiments,giventhefactthattheonly available observations over the Czech domain are screenlevel analyses of T 2m and RH 2m,wehaveexaminedthe mean error in these parameters for the month of July Mean errors in 2 m temperature and relative humidity are presented for the five experiments in Figure 10 in terms of improvement in percent with respect to the reference simulation (EXP1). This simulation is characterized by a small negative cold bias in temperature of 0.10K and a small positive bias in humidity of 3.2%. Such a cold and moist bias explains why on average the assimilation of screen level dries out the soil over the domain of interest. These biases are rather small, partly because they exhibit a strong diurnal cycle (Draper et al., 2011). The use of radar precipitation (EXP2) in the forcing reduces the biases slightly with respect to EXP1, by 20% for T 2m and 4% for RH 2m. This result indicates that an improved precipitation forcing has a positive impact on surface turbulent fluxes that can reflect on screen-level variables. The assimilation of screen-level variables only (ANA1) also provides an improvement but with larger reductions with respect to EXP1 (35% for T 2m and 7% for RH 2m ). This comes from the design of such an assimilation, but it must be emphasized that the comparison is made against observations before their assimilation (background departures). The combined assimilation ANA2 shows that the beneficial individual impact of each source of information adds up to provide alargerbiasreductionwithrespecttoexp1thaneither EXP2 or ANA1 (42% for T 2m and 9% for RH 2m ). Finally, the inclusion of radar precipitation as a forcing term instead of increments on top of an EKF of screen-level observations

13 Radar Precipitation use in Soil Moisture Analysis 721 T2m bias reduction (%) RH2m bias reduction (%) EXP1 EXP2 ANA1 ANA2 ANA3 Experiment EXP1 EXP2 ANA1 ANA2 ANA3 Experiment Figure 10. Reduction in mean errors of screen-level temperature (upper panel) and relative humidity (lower panel) averaged over the Czech Republic in July 2008 for the experiments presented in Table 1 against a control experiment (open loop) EXP1. provides the best results (53% for T 2m and 11% for RH 2m ). This is understandable by the fact that the background trajectory has already been improved with this methodology, whereas precipitation errors are only corrected at analysis time (end of the time window) in experiment ANA2. The above preliminary results are encouraging in the sense that short-range forecast errors of the ISBA scheme are reduced when including additional information from either screenlevel observations or radar precipitation. The methodologies proposed for a combined usage of these two sources of data lead to the best results. The use of a weighted averaged precipitation forcing appears to be superior to the use of soil moisture increments proportional to the precipitation error. Such a result is encouraging for future applications, given the fact that the computation of the Jacobian matrix elements with finite differences needs to be performed carefully. This will have to be confirmed by additional studies, since this approach can introduce inconsistencies between the precipitation field and the other forcing fields. 6. Conclusions and perspectives A methodology for including precipitation observations in a land data-assimilation system basedonanekfconsidering screen-level temperature and relative humidity (and also potentially, but not tested here, satellite-derived soil moisture) has been proposed following Balsamo et al. (2005). Instead of replacing the model forecast by a precipitation analysis as is commonly done in offline land-surface models (e.g. NLDAS and GLDAS), the model precipitation is not discarded but used to compute innovations. Then these innovations are projected on to the model state variables according to the confidence given to the model and observed precipitation fields and also to the sensitivity (Jacobian matrix) of the model state to precipitation perturbations included as forcing terms in the land-surface scheme. A study of sensitivity to the choice of precipitation perturbation for computing the Jacobian matrix elements with finite differences has been undertaken. It appears that too small values lead to unrealistic negative perturbations and that too large perturbations damp the spatial variability originating from the precipitation forcing. For the superficial soil reservoir, Jacobian matrix elements are reduced in areas having large precipitation amounts, by the runoff process. On the other hand, for the deep soil reservoir, the largest sensitivity is found in areas where rainfall is the most intense. The use of a log-transformed precipitation field leads to an easier specification of model and observation errors, and to less dependence of the Jacobian matrix elements on the size of the perturbation. However, this can jeopardize the soil water budget, leading to significant corrections only when the model overestimates precipitation. A simpler methodology is also examined, in which a merged precipitation product (weighting factor depending upon the accuracy of each component) is used as an improved forcing on top of an EKF assimilation of screen-level observations. A preliminary study has been undertaken over the Czech Republic in July 2008, where the precipitation forcing provided by the ALADIN NWP model is significantly different from the observed counterparts derived from two C-band radars. The comparison of soil moisture simulations of the land-surface scheme ISBA forced by ALADIN and radar precipitation has revealed that the assimilation of screen-level observations in the EKF only partly compensates for this error in the surface water budget, since these data are also sensitive to surface evaporation errors and other sources of errors. The capability of the combined EKF assimilations to correct the deep soil moisture content has been verified for this one-month period. A preliminary comparison against screen-level observations has revealed that the combined assimilations lead to the largest reduction in mean errors. With this measure of skill, the assimilation integration using the merged precipitation product has smaller errors than the assimilation integration based on additional soil moisture increments with Jacobian matrix elements. In order to demonstrate further the beneficial impact of precipitation observations on soil moisture analysis, it will be necessary to undertake a comparison with independent in situ measurements (e.g. soil moisture content) and also to launch numerical weather forecasts with ALADIN and examine skill scores. It is planned to study the two methodologies over France, where a network of soil moisture measurements and various near-real-time precipitation analyses are available. Moreover, the soil analyses could be used to initialize the Météo-France convection-permitting NWP model AROME (2.5 km grid mesh; Seity et al., 2010) and compare forecast skill scores. An area of improvement for this revised soil analysis scheme lies in the better specification of observation and model errors for the precipitation field, which have been rather crudely specified in the present study. The spatial variance of radar precipitation upscaled from 1 km to 10 km could be an indicator of both random errors and precipitation type. Regarding model precipitation errors, it is likely that ensemble data assimilation and/or prediction systems would be very useful for providing reasonable estimates to the soil analysis scheme. Finally, the same methodologies will be considered for observed