Root zone soil moisture from the assimilation of screen level variables and remotely sensed soil moisture

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010jd013829, 2011 Root zone soil moisture from the assimilation of screen level variables and remotely sensed soil moisture C. S. Draper, 1,2 J. F. Mahfouf, 3 and J. P. Walker 1,4 Received 8 January 2010; revised 25 October 2010; accepted 23 November 2010; published 29 January [1] In most operational NWP models, root zone soil moisture is constrained using observations of screen level temperature and relative humidity. While this generally improves low level atmospheric forecasts, it often leads to unrealistic model soil moisture. Consequently, several NWP centers are moving toward also assimilating remotely sensed near surface soil moisture observations. Within this context, an EKF is used to compare the assimilation of screen level observations and near surface soil moisture data from AMSR E into the ISBA land surface model over July Several issues regarding the use of each data type are exposed, and the potential to use the AMSR E data, either in place of or together with the screen level data, is examined. When the two data types are assimilated separately, there is little agreement between the root zone soil moisture updates generated by each, indicating that for this experiment the AMSR E data could not have replaced the screen level data to obtain similar surface turbulent fluxes. For the screen level variables, there is a persistent diurnal cycle in the model observations bias, which is not related to soil moisture. The resulting diurnal cycle in the analysis increments demonstrates how assimilating screen level observations can lead to unrealistic soil moisture updates, reinforcing the need to assimilate alternative data sets. However, when the two data types are assimilated together, the near surface soil moisture provides a much weaker constraint of the root zone soil moisture than the screen level observations do, and the inclusion of the AMSR E data does not substantially change the results compared to the assimilation of screen level variables alone. Citation: Draper, C. S., J. F. Mahfouf, and J. P. Walker (2011), Root zone soil moisture from the assimilation of screen level variables and remotely sensed soil moisture, J. Geophys. Res., 116,, doi: /2010jd Introduction [2] Model root zone soil moisture can exert a strong influence on atmospheric boundary layer forecasts, through influencing the partitioning of incoming energy into latent and sensible heat fluxes, and of precipitation into infiltration and runoff. If not suitably constrained, an NWP model s land surface state will drift away from the true climate, and most NWP centers prevent this by updating their model land surface variables according to forecast errors in screen level temperature (T 2m ) and relative humidity (RH 2m ): for example, at the European Centre for Medium Range Weather Forecasting (ECMWF) [Douville et al., 2000], the German Weather Service [Hess et al., 2008], Météo France [Giard and Bazile, 2000], the Meteorological Service of Canada [Bélair et al., 2003], and the UK Met Office [Best and 1 Department of Civil and Environmental Engineering, University of Melbourne, Melbourne, Victoria, Australia. 2 Now at GAME, CNRM, Météo France/CNRS, Toulouse, France. 3 GAME, CNRM, Météo France/CNRS, Toulouse, France. 4 Now at Department of Civil Engineering, Monash University, Clayton, Victoria, Australia. Copyright 2011 by the American Geophysical Union /11/2010JD Maisey, 2002]. The assimilation of screen level observations has been shown to effectively decrease errors in boundary layer forecasts [Douville et al., 2000; Hess, 2001; Drusch and Viterbo, 2007]. However, from the inception of this approach it was recognized that these improvements would not necessarily be due to an improved representation of the model surface [Douville et al., 2000; Hess, 2001]. By targeting the low level atmosphere, rather than the actual land surface states, the land surface variables are adjusted in response to screen level errors that are not always related to the surface, for example due to inaccuracies in the land surface flux parameterizations or the radiation physics. Consequently, the assimilation of screen level variables often degrades modeled soil moisture [Douville et al., 2000; Hess, 2001; Drusch and Viterbo, 2007]. [3] The recent launch of the Soil Moisture and Ocean Salinity (SMOS) satellite [Kerr et al., 2001], and the development of soil moisture retrieval algorithms for preexisting microwave remote sensing missions [Wagner et al., 1999; Owe et al., 2001; Bartalis et al., 2007], offers a possible opportunity to improve the realism of modeled soil moisture. These sensors observe the soil moisture in the near surface soil layer, which interacts with the underlying soil layers through diffusion processes, potentially offering a more 1of13

2 direct observation of root zone soil moisture [Calvet and Noilhan, 2000]. Several studies have demonstrated that model root zone soil moisture can be improved by assimilating remotely sensed near surface soil moisture data [e.g., Walker and Houser, 2001; Crow and Wood, 2003; Drusch, 2007; Reichle et al., 2007]). For NWP, remotely sensed soil moisture data offers the additional advantage over screenlevel data of providing close to global coverage without reliance on ground based observation networks, which are expensive to maintain. However, there are also considerable uncertainties associated with the use of remotely sensed soil moisture data. Most notably, the extent to which the nearsurface soil layer represents the underlying soil moisture profile is not well understood. [4] This paper compares the analysis of root zone soil moisture in an NWP model from the assimilation of screenlevel observations and remotely sensed near surface soil moisture, using data from the Advanced Microwave Scanning Radiometer (AMSR E). An Extended Kalman Filter (EKF) is used to assimilate the observations into an off line version of the land surface model, Interactions between Surface, Biosphere, and Atmosphere (ISBA) [Noilhan and Planton, 1989; Noilhan and Mahfouf, 1996], used in Météo France s limited area model, Aire Limitée Adaptation Dynamique développment International (ALADIN [Bubnova et al., 1995]). Since the assimilation of screen level observations reduces low level atmospheric forecast errors in part by adjusting the land surface states to compensate for model errors, it is not straightforward that improving the realism of the model soil moisture will immediately lead to improved atmospheric forecast skill (of principal interest to NWP centers). Hence the two data types are also assimilated together to test whether this can improve both the low level atmosphere and soil moisture forecasts. [5] This work builds directly on two previous studies. Mahfouf et al. [2009] analyzed the soil moisture and temperature in ALADIN using a simplified EKF assimilation of T 2m and RH 2m. They showed that the simplified EKF is superior to the Optimal Interpolation (OI) scheme currently used operationally to analyze ALADIN s surface state from the same observations, while also allowing the assimilation of new data types. Draper et al. [2009a] then demonstrated the application of this method to the assimilation of AMSR E soil moisture data, and also extended the simplified EKF into a full EKF by introducing the temporal evolution of the background error matrix. 2. Method 2.1. EKF Assimilation [6] The EKF as formulated by Draper et al. [2009a] is used here. Adopting the notation of Ide et al. [1997], the EKF equations for the ith model state forecast and update at time step t i are: and x b ðt i Þ ¼ M i 1 ½x a ðt i 1 ÞŠ ð1þ x a ðt i Þ ¼ x b ðt i ÞþK i y o i H i x b ðt i Þ where x indicates the model state vector and y is the observation vector. The superscripts a, b, and o indicate the ð2þ analysis, background, and observations, respectively. M is the nonlinear state forecast model, and H is the nonlinear observation operator (mapping the model state into the observation state space). The observations are 6 h later than the analysis, and following Hess [2001] and Balsamo et al. [2007] the observation operator is an integration of the forecast model over the length of the assimilation window. K is the Kalman gain, given by: K i ¼ P f ðt i ÞH T i H i P f ðt i ÞH T 1 i þ R i ð3þ where P and R are the covariance matrices of the model background and observation errors, respectively. H is the linearization of H, obtained by finite differences (see Draper et al. [2009a] for details). The defining feature of the EKF is that the background model error is also evolved through a series of model forecasts and updates: P f ðt i Þ ¼ M i 1 P a ðt i 1 P a ðt i Þ ¼ ði K i H i ÞP f ðt i Þ ÞM T i 1 þ Q ð t i 1Þ ð4þ where Q is the error covariance matrix for the (additive) model forecast error, and M is the linearization of M, also obtained by finite differences. [7] Draper et al. [2009a] found that introducing the evolution of the background error (equations (4) and (5)) did not generate substantial differences in the EKF assimilation of soil moisture, compared to the simplified form of Mahfouf et al. [2009]. Despite this, the EKF is used here since it incurs no additional cost if M is approximated based on the perturbed model simulations made prior to the analysis to estimate H (neglecting any changes in M due to the analysis update). The impact of this approximation to M was tested by comparing the assimilation results obtained with the approximate M to a reference run in which M was estimated using perturbed model integrations made after the analysis update. For 1 July 2006, the mean absolute difference between the approximate and reference M was small (O(10 3 ) and O(10 5 ) for the daytime and nighttime assimilation cycles, respectively). As a result, after 2 weeks of assimilating T 2m, RH 2m, and near surface soil moisture (using the CMB experimental setup described below), the mean absolute difference between the two estimates of root zone soil moisture was m 3 m 3. This is several orders of magnitude less than the impact of the assimilation: the mean absolute difference between w 2 from the reference assimilation and an open loop simulation after 2 weeks was around m 3 m 3. Hence the approximation of M based on the perturbed model simulations made prior to the analysis is considered acceptable, and has been used here ISBA Land Surface Scheme [8] The land surface model in ALADIN is a two layer version of the ISBA model [Noilhan and Planton, 1989; Noilhan and Mahfouf, 1996]. Soil moisture is defined in the model by two storages: the superficial soil moisture, w 1 (defined over the depth of bare soil evaporation, d 1 = 0.01 m), and the total soil moisture, w 2 (defined over the total soil depth d 2, which varies between 0.24 and 3.8 m over the ð5þ 2of13

3 European domain). There is no distinction between the root zone and total soil depth, and so the root zone is effectively modeled over the total depth. Horizontal subsurface flows are neglected (each grid is modeled independent from its neighbors), and the vertical liquid moisture dynamics are described by the force restore method of Deardorff [1977]. For w i less than 1 =@t ¼ C 1 w d 1 C 2 P g E g w 1 w 2 =@t ¼ 1 C 3 P g E g E tr w d 2 max 0; w 2 w fc [9] The first term in each equation represents the forcing: precipitation (P g ), and bare soil evaporation (E g ) affect both layers, while transpiration (E tr ) acts on w 2 only. For a given energy input the evapotranspiration terms are dependent on w 2 and w 1 : w 2 controls the stomatal resistance to transpiration, while w 1 controls the bare soil evaporation via the surface humidity. The second term in each equation represents the restore term. In equation (6) w 1 is restored toward an equilibrium value (w eq ), representing the balance between gravitational drainage and capillary rise from w 2, and calculated from w 2 and the saturation water content. In equation (7) the restore term represents gravitational drainage, proportional to the volume of moisture exceeding field capacity (w fc ). The coefficients (C 1, C 2, and C 3 ) are soil texture specific [see Noilhan and Mahfouf, 1996], t represents the time scale (1 day), and r w is the density of liquid water. [10] This study is motivated by the potential to improve the land surface analysis used in ALADIN, and so ISBA has been run in an environment that resembles the operational ALADIN model as closely as possible (referred to as ISBA ALADIN). The assimilation experiments have been performed on the (approximately) 9.5 km irregular grid used by ALADIN, and all model parameters, forcing, and initial conditions have been taken from ALADIN. The off line ISBA model was forced at the first atmospheric model layer (17 m) to allow an off line assimilation of screen level observations, following [Balsamo et al., 2007]. The surface analysis is designed to be semicoupled to ALADIN, so that ALADIN is updated with each soil moisture analysis, before the subsequent forcing for the next off line assimilation cycle is generated (see Mahfouf et al. [2009] for further details). However, for this initial investigation the feedback between the soil moisture updates and the atmospheric forecasts has been neglected, and the forcing was generated once at the start of the experiments Data [11] The T 2m and RH 2m fields assimilated in this study were taken from ALADIN s screen level analysis. A bidimensional OI scheme is used to analyze screen level variables in ALADIN every 6 h, based on screen level observations from GTS SYNOP, SHIP, BUOY reports, and the French RADOME network. Approximately 2000 observations each of T 2m and RH 2m are ingested per analysis cycle, although the density of the observations varies across the model domain. For a model grid not affected by observations, the ð6þ ð7þ analysis equals the background field (i.e., an ALADIN forecast). [12] The near surface soil moisture data were retrieved from C band AMSR E brightness temperatures by the Vrije Universiteit Amsterdam (VUA) in collaboration with NASA GSFC [Owe et al., 2008]. AMSR E provides global coverage in less than 2 days [Njoku et al., 2003], from both the ascending (1330 LT), and descending (0130 LT) overpasses. Regions affected by frozen ground cover, dense vegetation, and/or radio frequency interference have been screened out, leaving an average spatial coverage for the European domain of 49% for each overpass. [13] The AMSR E soil moisture observations have been rescaled to fit the model climatology, by matching the Cumulative Distribution Function (CDF [Reichle and Koster, 2004]) of the observations to that of the w 1 forecasts from ALADIN over 2006, as in the work by Draper et al. [2009a] (ALADIN fields were available for 2006 only). The CDFs for each model grid were estimated using the data from the surrounding one degree area to compensate for the truncated time period used, following Reichle and Koster [2004]. The CDF matching has been performed separately for each overpass. As discussed by Draper et al. [2009a], there are differences in the seasonal cycle of the near surface soil moisture from ALADIN and AMSR E, and the seasonal cycle of the AMSR E data was adjusted to that of ALADIN before applying the CDF matching. This is an extremely conservative approach, since it removes any seasonal scale anomalies in the model observation difference by assuming that the model seasonal cycle is correct (note that the single year of data available for the rescaling is insufficient to identify such anomalies) Assimilation Experiments [14] Four assimilation experiments have been conducted over July 2006: (1) CTR, an open loop simulation with no assimilation (the control); (2) SLV, assimilation of screenlevel variables (T 2m and RH 2m ); (3) AMS, assimilation of AMSR E w 1 ; and (4) CMB, a combined assimilation of T 2m, RH 2m, and AMSR E w 1. The results of each experiment have been compared by examining the net monthly soil moisture increments, and the impact of the analysis on the fit between the subsequent model forecasts and the observations (for all of the observed variables). In ISBA, w 1 is defined over a thin surface layer, giving it a very short time scale (perturbations are lost within a day) and limiting its influence on other model variables. Consequently, the accurate initialization of w 1 is not important, and while w 1 was included in the update vector in these experiments (but not in the work by Mahfouf et al. [2009]), results have been reported for w 2 only. [15] The observation error covariances are based on Mahfouf et al. [2009] and Draper et al. [2009a]. For the screen level variables, observed error variances of (10%) 2 and (1 K) 2 have been used, following Mahfouf et al. [2009]. These are the analysis errors used by Météo France s screenlevel analyses, from which the observations have been taken. For the AMSR E w 1 observations, an error variance of (0.05 m 3 m 3 ) 2 has been used, following Draper et al. [2009a]. This value was based on published root mean square error estimates for the VUA NASA AMSR E nearsurface soil moisture product, specifically on Wagner et al. [2007] (0.06 m 3 m 3 from one location in Spain), Rüdiger 3of13

4 et al. [2009] (0.06 m 3 m 3 at one location in France), and Draper et al. [2009b] (0.03 m 3 m 3 at 10 locations in Australia). The errors for each observation type were assumed to be independent from each other. While this assumption is clear for the w 1 data, it will neglect some correlation between T 2m and RH 2m, for example due to representivity errors (note that T 2m and RH 2m are observed by different sensors, and so their observation errors are not aliased). [16] For the EKF both the additive model forecast error, Q, and the initial background model error, P, must be defined, although beyond the first few assimilation cycles P is largely determined by Q. P and Q were assumed to be diagonal, and both have been defined as a fraction of the difference between the soil moisture at field capacity (w fc ) and at the wilting point (w wilt ), following Mahfoufetal. [2009] and Balsamo et al. [2007]. For w 2 the error variance in Q was set at (0.02 (w fc w wilt )) 2. Over the depth of w 2 this amounts to applying a mean error of 4 mm of water every 6 h, giving 16 mm d 1 of water applied across the soil layer. This is slightly more than the approximate NWP surface water budget error of 10 mm d 1 quoted by Douville et al. [2000]. The initial w 2 error variance in P was set at (0.2 (w fc w wilt )) 2, equivalent to approximately 40 mm. With these values, the EKF rapidly (within a few assimilation cycles) reduced the mean w 2 error in P to approximately 20 mm for the SLV experiment. This value is consistent with empirical error estimates for w 2. For example, comparisons of ISBA w 2 forecasts to in situ soil moisture observations have yielded root mean square error estimates of 28 mm [Muñoz Sabater et al., 2007], 20 mm [Calvet and Noilhan, 2000], and 23 mm, 32 mm, and 15 mm [Calvet et al., 1998], at various locations in France. Additionally, this value is slightly larger than the (static) w 2 background error used by Mahfouf et al. [2009]. Recall that the observation errors have also been taken from Mahfouf et al. [2009], who in turn based their model and observation errors on those used to derive the update coefficients for the current operational OI surface analysis in ALADIN [Mahfouf et al., 2009]. [17] The mean w 2 error of 20 mm in P is equivalent to 0.01 m 3 m 3, which is much smaller than the errors typically expected from a land surface model, and 5 times less than the assumed AMSR E observation error. This apparently small error is due to the unrealistic soil moisture behavior in ISBA ALADIN associated with its poorly specified soil parameters. Since there is no distinction between the root zone and total soil depth, the root zone is defined over the total depth, with a mean of 2.3 m. To compensate for the overly deep root zone, the water holding capacity (w fc w wilt ) in ISBA ALADIN is specified to be unrealistically small (mean (w fc w wilt ): m 3 m 3 ). For comparison, the ECMWF model has a 1 m deep root zone, and a (w fc w wilt ) close to 0.2 m 3 m 3 for a medium soil texture [Balsamo et al., 2009]. These misspecified soil parameters reduce the soil moisture variability in ISBA, since a given volume of moisture forcing (P E), or any error in that forcing, is dispersed across the too deep layer. For example, applying a 20 mm error to the ECMWF root zone would result in a volumetric error of 0.02 m 3 m 3 (note that this is still 0.1 (w fc w wilt )), rather than the 0.01 m 3 m 3 value obtained here. [18] The model errors for w 1 are more difficult to define, partly due to the difficulty of observing soil moisture over such a thin layer. However, sensitivity tests showed that the w 1 error also has much less impact on the analysis results than the other errors. The model w 1 error (in m 3 m 3 ) are expected to be greater than those in w 2, since the surface layer has more active soil moisture dynamics and a greater exposure to the atmospheric forcing (errors). The model w 1 error variance has then been set to give a mean w 1 background error standard deviation approximately double the mean w 2 error standard deviation in P. This was achieved using an error variance of (0.2 (w fc w wilt )) 2 for both the initial P and Q. For Q this is equivalent to adding an error of 0.8 mm d 1, which is approximately one third of the mean daily bare soil evaporation forecasts. However, w 1 has a very short memory, and so the mean w 1 error variance in P was (0.24 mm) 2, only slightly larger than the added Q. 3. Results 3.1. Dependence Between w 2 and the Observations [19] Figure 1 shows the Jacobians of the observation operator for the 0000 and 1200 UTC analysis updates on 1 July 2006, for each assimilated variable. For the screenlevel observations the Jacobian maps show the expected dependency on evapotranspiration, with the largest Jacobians occurring during the day where transpiration is most sensitive to w 2. As outlined by Mahfouf et al. [2009], the ISBA surface canopy resistance to transpiration is nonlinearly dependent on the root zone soil moisture, with stronger dependencies close to the wilting point, so that w 2 influences the screen level variables most strongly in clear sky regions with a high fraction of vegetation cover and dry soils. The mean screen level Jacobians for each of the four daily assimilation cycles in Table 1 shows reduced screen level Jacobians for UTC and UTC, although there was still a small response since both time periods include some daylight. The exception is the UTC Jacobian for RH 2m, which had a relatively large mean (80%(m 3 m 3 ) 1 (compared to %(m 3 m 3 ) 1 for the subsequent assimilation cycles) suggesting a rapid humidity response at sunrise. [20] For the w 1 observation operators, w 2 directly influences w 1 in equation (6) only via the w 1 restore term representing the balance between gravitational drainage and capillary rise. However, there is a strong and unexpected similarity between the Jacobians of the observation operators for w 1 and for the screen level variables in Figure 1. The w 1 model Jacobians in Table 1 were also highest during the daytime, when they had a strong spatial correlation to the screen level observation operators in Figure 1, highlighting that the greatest influence of w 2 on w 1 does not arise from the direct restore term, but from an indirect relationship via evapotranspiration. As discussed by Draper et al. [2009a], this dependency arises from the influence of transpiration on the surface temperature: increased w 2 increases transpiration, which reduces the surface temperature, thus reducing the depletion of w 1 by bare ground evaporation, giving a relative increase in w 1, and a positive dependency of w 1 and w 2. This relationship is likely to be due to the use of a single surface temperature for both the soil and vegetation surface in ISBA, rather than a true physical relationship between transpiration 4of13

5 Figure 1. Maps of the observation operator Jacobians for modeled w 2 and observed (top) T 2m, (middle) RH 2m, and (bottom) w 1, for (left) UTC and (right) UTC on 1 July and bare soil evaporation. During the night the mean w 1 Jacobian in Table 1 was close to half the daytime values, and its spatial variability was consistent with the w 1 restore term in equation (6) [Draper et al., 2009a]. [21] To highlight how the observation operator and the error covariances combine to translate the observations into updates to w 2, the relative information content for each observation type is included in Table 1. The relative information content, calculated following Balsamo et al. [2007] and Cardinali et al. [2004], measures the sensitivity of the analysis updates to each observed variable, scaled by the net sensitivity to all observations. To isolate the impact on w 2 (rather than w 1 ), the relative information content was calculated from an additional experiment in which only w 2 was 5of13

6 Table 1. Mean of the Observation Operator Jacobians Relating w 2 to Each Observation Type, as Well as the Information Content for Each Observation Type Relative to the Daily Total, for Each of the Four Daily Assimilation Cycles for the CMB Experiment (With w 2 Updated Only) a T2m RH2m w (0.01) 0.8 (0.10) 0.16 ( ) (0.25) 1.1 (0.10) 0.30 (0.01) (0.27) 1.7 (0.24) 0.33 ( ) (0.01) 0.1 (0.00) 0.17 (0.01) a Information content for each observation type relative to the daily total is given in parentheses. analyzed (otherwise identical to CMB). This neglects any cross correlation between the model w 1 and w 2 errors, and so likely underestimated the true impact of the w 1 data. However, the limited impact on w 2 of evolving the model error covariances obtained by Draper et al. [2009a] suggests that this will not significantly influence the results. The relative information content in Table 1 shows that nearly all of the information in the CMB assimilation was derived from the screen level observations during periods of active evapotranspiration. In total, 96% of the daily information content was derived from T 2m and RH 2m data during the day (1200 and 1800 UTC) together with RH 2m in the early morning (0600 UTC), and just 2% was derived from the AMSR E data. [22] It was noted in section 2.4 that the misspecification of the soil parameters in ISBA suppresses the variability of w 2, so that the mean w 2 error of 20 mm corresponds to a volumetric error of only 0.01 m 3 m 3, 5 times lower than the observation error. To test whether the low information content of the w 1 data is related to the large ratio of the observed and modeled errors, an additional experiment has been conducted in which the observation error for AMSR E was artificially reduced to 0.02 (close to the model w 1 error). In this experiment the analyzed w 2 was still dominated by the signal from the screen level variables, with the relative information content of the AMSR E data increased to only 11%. The low information content of the w 1 observations in the CMB experiment is then principally related to the relative sensitivity of the forecasts of the observed variables to w 2, rather than the choice of error specification used here Observation Increments [23] Histograms of the mean monthly difference between the open loop forecasts and the observations across the model domain are shown in Figure 2 (for the assimilated variables this is equivalent to the observation increment). For consistency the screen level increments have been excluded from the mean at locations where AMSR E data were screened out. While the spatial mean observation increment for the screen level variables was close to zero ( 0.01 K and 0.3%), which might suggest there was no significant model observation bias, there is considerable spread in the distributions of the increments (giving standard deviations of 0.5 K and 3.6%), indicating significant biases at some locations. The distributions of the observation increments for T 2m and RH 2m are approximately mirror images, indicating a consistent signal from w 2. Both are skewed, with T 2m (RH 2m ) having a longer positive (negative) tail, suggesting a cool and moist model bias. [24] Compared to the mean monthly errors described above, the diurnal cycle in the observation increments for the screen level variables was rather large. The largest increments occurred in the early morning, when the observations suggest a cool and moist model bias (mean monthly increments at 0600 UTC: 0.56 K and 3.5%). As each day proceeded, this cool and moist bias was initially reduced (mean increments at 1200 UTC: 0.09 K and 1.6%), and then reversed in the evening (mean increments at 1800 UTC: 0.29 K and 0.6%, and at 0000 UTC: 0.33 K and 3.2%). This diurnal cycle in the observation increments cannot be easily attributed to errors in w 2, and almost certainly had another cause. In particular, the largest biases occurred early in the morning at 0600 UTC, when only RH 2m has an intermediate sensitivity to w 2 (and T 2m has very little sensitivity) in Table 1. [25] In contrast to the screen level observations, which were not explicitly bias corrected, the AMSR E observation increments are distributed more symmetrically, with less spread (standard deviation of 0.028%). However, the distribution slightly favors positive values, with a mean of m 3 m 3, indicating a tendency for the model to be drier than the observations. Additionally, the normalization of the AMSR E data explicitly removed any systematic diurnal differences between the model and the observations, Figure 2. Histograms of the mean observation minus CTR forecast over July 2007 for (a) w 1 (m 3 m 3 ), (b) RH 2m (%), and (c) T 2m (K). 6of13

7 Figure 3. Histograms of the w 2 analysis increments accumulated over July 2006 (mm) from the (a) AMS, (b) SLV, and (c) CMB assimilation experiments. so that the mean observations increments at 00 and 1200 UTC were similar, at m 3 m 3 and m 3 m 3, respectively Analysis Increments [26] Histograms of the total volume of moisture added to w 2 from the assimilation of AMSR E (AMS), screen level variables (SLV), and both (CMB) over July 2006 are shown in Figure 3. For all experiments the analysis increments could be quite large, with the tails of the distributions reaching ± 200 mm/month (in comparison the monthly mean precipitation was 50 mm). For SLV, the skewed T 2m and RH 2m observation increments generated an asymmetrical distribution of analysis increments, with a slightly negative mode, giving a small negative mean reduction in w 2 ( 5.5 mm/month), and considerable spread (standard deviation: 57 mm/month). The AMS analysis increments had the opposite behavior, with a stronger tendency to add moisture to the surface. The mode of the distribution for the AMS analysis increments is centered on zero, however the positive tail reaches approximately 200 mm/month, double the negative tail ( 100 mm/month). The net magnitude of the increments was generally smaller than for SLV (giving a standard deviation of 49 mm/month), although the strong positive skew generated a net addition of moisture (mean of 7.1 mm/month). [27] The maps of the net monthly w 2 analysis increments for the AMS and SLV experiments in Figure 4 show very little spatial agreement between the mean increments added by each. While they both removed moisture across most of arid Spain and North Africa, there is little agreement over central and east Europe, where SLV in general decreased w 2, while AMS increased it. It is interesting to note that the regions of strongest moisture reduction by SLV correspond to locations where the AMSR E data was screened out due Figure 4. Maps of the w 2 analysis increments (mm) accumulated over July 2006 by the (a) AMS and (b) SLV assimilation experiments. 7of13

8 Figure 5. Maps of the w 2 analysis increments (mm) accumulated over July 2006 for each of the four daily assimilation cycles for the SLV assimilation. Each plot is labeled with the time of the analysis. to mountainous terrain and/or dense vegetation. The lack of consistency between the net monthly SLV and AMS analysis increments has also been confirmed by a scatterplot (not shown), and the (spatial) correlation coefficient between the net monthly increments for each experiment is just 0.1. Additionally, the temporal correlation at individual locations between the increments applied by SLV and AMS were also consistently low (<0.25) across the model domain. [28] Consistent with the very low information content of the w 1 data in Table 1, the analysis increments for the CMB experiment were only slightly changed from those for SLV by the inclusion of the AMSR E data. In Figure 3 the inclusion of the positively skewed AMSR E data in the CMB experiment slightly reduced the asymmetry of the SLV distribution, by both decreasing the frequency of the negative mode, and increasing the occurrence of positive increments. The result is a slight reduction in the negative mean increment of 1.1 mm/month, and a larger spread in the distribution (standard deviation: 59 mm/month). The map of the net monthly analysis increments from the CMB experiment has not been included in Figure 4, since it cannot be visually distinguished from the SLV map. [29] Figure 5 shows maps of net analysis increments for each of the four daily assimilation cycles (at 0000, 0600, 1200, and 1800 UTC) for the SLV experiment, demonstrating how the diurnal cycle in the screen level observation incre- 8of13

9 1200 UTC and 1800 UTC, which balanced out the earlier moisture reductions. Additionally, the regions where the strongest early morning moisture reduction occurred, correspond to regions of strong wetting 6 h later. For example, in northern Poland moisture was removed by the UTC analysis, and then added back in by the UTC analysis, with the same pattern occurring 6 h later in northern France. Plots of the analysis increments on individual days indicate that the systematic addition and removal of moisture at the same location consistently occurred throughout the month (rather than being an artifact of the calculation of the monthly mean). Figure 6. Diurnal cycle in the mean monthly observation minus model forecast over July 2006 for (a) T 2m (K), (b) RH 2m (%), and (c) w 1 (m 3 m 3 ) for the CTR (black solid line), SLV (black dashed line), AMS (gray solid line), and CMB (gray dashed line) experiments. The horizontal axes are in hours. ments was translated into w 2 updates. The SLV assimilation had a strong tendency to remove moisture in the morning, initially in the east of the domain at 0000 UTC, and then in the west at 0600 UTC, giving net negative monthly increments of 22 mm and 1.2 mm at 0000 UTC and 0600 UTC. As each day progressed, moisture was then added back into w 2, giving net positive increments of 17 mm and 5 mm at 3.4. Impact of the Experiments on the Observation Increments [30] Time series of the mean difference between the forecasts and observations for each experiment are shown in Figures 6 and 7, with the mean diurnal cycle and the mean daily time series plotted separately. Supporting the earlier assertion that the diurnal cycle in the screen level observation increments is not related to w 2, the SLV assimilation did not significantly affect this diurnal cycle, and it is difficult to distinguish between the SLV and CTR experiments in Figure 6. At many individual locations the SLV assimilation reduced the screen level biases during one phase of the diurnal cycle, while enhancing the biases during the opposite phase. In the current ALADIN surface OI scheme the surface temperature and moisture states are both updated from the screen level observations. Since the deep layer soil temperature (T 2 ) is sensitive to the screen level observations Figure 7. Mean daily observation minus model forecast for each day in July 2006 for (a) T 2m (K), (b) RH 2m (%), and (c) w 1 (m 3 m 3 ) for the CTR (black solid line), SLV (black dashed line), AMS (gray solid line), and CMB (gray dashed line) experiments. 9of13

10 Table 2. RMSD Between the Observations and Model Forecasts Over July 2006 for Each Assimilation Experiment a Time T 2m (K) RH 2m (%) w 1 (m 3 m 3 ) CTR 1.26 (0.8) 9.41 (6.0) SLV 1.21 (0.7) 9.05 (5.5) AMS 1.25 (0.8) 9.60 (6.2) CMB 1.21 (0.7) 9.05 (5.5) a The RMSD of the mean daily forecast and observed values are shown in parentheses for the screen-level variables. (specifically T 2m ) at night [Mahfouf et al., 2009], a possible explanation for the persistence of the diurnal biases is that it was caused by the exclusion of T 2 from the update vector. However, additional experiments have confirmed this is not the case. [31] At the daily time scale the SLV assimilation did generate reductions in the screen level biases that are evident in Figure 7. For the first two thirds of the month, the observations were warmer and drier than the model and SLV removed moisture, while at the end of the month the screen level biases were reversed and SLV added moisture to the surface. During both periods SLV generated a clear reduction in the daily mean biases in Figure 7, by up to 0.1 K and 1.0%. For both variables these maximum reductions are equivalent to about half of the mean daily CTR bias. [32] In contrast to SLV, the w 1 observation increments were consistently positive (both spatially and temporally), and AMS had a strong tendency to add moisture to w 2. The AMS assimilation reduced the daily mean w 1 observation increments by close to m 3 m 3 on most days (which is again about half of the mean daily bias for CTR). However, there are two periods of mean negative daily observation increments, and AMS was slow to respond to these, resulting in larger negative observation increments than for the CTR simulation. Even though the net monthly w 2 analysis increments for AMS were generally smaller than those from SLV, the AMS assimilation had a much greater impact on the forecasts of the screen level variables, due to the more consistent direction of the AMS increments. In Figure 6 the addition of moisture by AMS decreased the warm and dry model biases at the end of the day, while increasing the cool and moist biases at the start of the day. The net effect across the day in Figure 7 was of moistening and cooling, by a maximum of approximately 0.2 K and 1.5% (double the impact of SLV). [33] For most of the month the AMS and SLV experiments generated opposing w 2 analysis increments. The cool and moist screen level model biases for the first two thirds of the month were reduced by SLV and increased by AMS, while the warm and dry biases at the end of the month were reduced by both AMS and SLV. The w 1 observation increments were consistently reduced by AMS, while SLV had a minimal impact, slightly increasing the biases at the start of the month, and then reducing them at the end of the month. For the CMB experiment, it is again difficult to distinguish between the CMB and SLV results in Figure 6, while the daily mean observation increments in Figure 7 were drawn slightly toward the AMS results. [34] To quantify the overall impact of each assimilation on the forecasts of the observed variables, Table 2 shows the monthly Root Mean Square Difference (RMSD) between the observations and the model background for each experiment (for the assimilated observations this is the standard deviation of the observation increments). The rather small RMSD for the screen level observations is partly due to the use of the ALADIN screen level analysis (rather than the direct use of the observations) in these assimilation experiments, since in regions with sparse observations the analysis will strongly resemble the model. For example, about half of the screen level observations ingested by the screen level analysis were over France, where the RMSD of the CTR observation increments was 1.62 K and 10.3%, considerably higher than the figures in Table 2. The SLV assimilation only slightly reduced the T 2m and RH 2m RMSD; by about 5% of the original CTR RMSD. This relatively small impact is thought to be a consequence of the diurnal cycle in the observation increments, since this was the greatest contributor to the screen level RMSD, and it was not amended by the assimilation. Taking the RMSD of the daily forecast and observed screen level observations (shown in brackets in Table 2) slightly increased the relative impact of the assimilation, giving an improvement of close to 8% of CTR. The SLV assimilation had little impact on the RMSD for w 1.In contrast the AMS assimilation slightly reduced the w 1 RMSD, while also very slightly reducing the T 2m RMSD and increasing the RH 2m RMSD. The disparity between the T 2m and RH 2m results for AMS is likely due to the sensitivity of RH 2m to w 2 in the early morning (recall that AMS increased the early morning cool and moist model bias). The CMB assimilation retained the small reductions in the screenlevel RMSD generated by SLV, while also slightly reducing the w 1 RMSD. 4. Discussion [35] A series of experiments has been conducted to compare the soil moisture analyses generated by assimilating screen level observations and remotely sensed soil moisture from AMSR E. For the screen level observations, the observation increments were dominated by a persistent and substantial diurnal cycle, so that on most days the SLV assimilation removed moisture early in the morning before adding moisture back to w 2 later in the day. This diurnal cycle cannot be easily attributed to soil moisture errors in the model, and almost certainly has another cause, demonstrating how the assimilation of screen level data can adjust the surface to compensate for errors unrelated to soil moisture, emphasizing the need to develop alternate data sets for land surface assimilation. Additionally, despite the substantial diurnal cycle in the analysis increments, assimilating the (6 hourly) screen level observations did not reduce the diurnal cycle in the observation increments, although the daily mean biases were slightly reduced. Consequently, the net reduction in the screen level observation increments induced by the SLV assimilation was very small. [36] For assimilating the AMSR E data, the Jacobians of the observation operators for w 1 show that over 6 h the restore term in equation (6) only very weakly restores w 1 toward w 2, and that the strongest relationship between them is an indirect link via evapotranspiration (thought to arise 10 of 13

11 from the use of a single surface energy budget in ISBA for vegetation and bare soil). The observation increments for w 1 were more consistent than those for the screen level observations, so that the net analysis increments accumulated by assimilating one month of AMSR E data were of similar, although slightly smaller, magnitude than those from assimilating the screen level observations. However, when the two data types were assimilated together, the w 1 observations contributed only a small fraction (2%) of the observation information content, and the CMB assimilation maintained a strong similarity to the SLV assimilation. This result highlights the importance of conducting experiments assimilating novel data sets within the context of the currently assimilated data: from the results of the AMS experiment alone it would have been easy to overestimate the impact of assimilating w 1 observations into ISBA. Even if the information content of the AMSR E data is normalized by the data coverage, it is still an order of magnitude less than that of the screen level observations. This differs from Balsamo et al. [2007], who found that the information content of a single C band brightness temperature observation was greater than that of the screen level observations, when assimilated into the ISBA model coupled to the Canadian Global Environmental Multiscale system using a simplified EKF. This difference is likely due to the very low AMSR E observation error of 3 K used in that study, equivalent to a volumetric soil moisture error of approximately 0.01 m 3 m 3 over bare soil [see, e.g., Jackson and Schmugge, 1991], while the remaining error statistics were similar to those used here. [37] In many instances the AMSR E and screen level observations indicated opposing directions of w 2 analysis increments, so that when each data type was assimilated separately, there was no clear consistency between the soil moisture analyses produced by each. Additionally, assimilating each data type did not in general improve the model fit to the other data type, indicating that for these experiments the screen level observations could not have been substituted with AMSR E data to achieve similar corrections to the low level atmospheric forecasts. If this is extrapolated to regions with scarce screen level data, it suggests that the AMSR E data may not be immediately useful for NWP. However, when both data types were assimilated together, the EKF was able to slightly improve the fit between the model and both observation types, and the combined assimilation of T 2m, RH 2m, and w 1 gave the lowest overall RMSD between the observations and the model forecasts. However, these reductions were extremely modest, and the RMSD was reduced by less than 5% of the CTR value for all observed variables using the 6 hourly statistics (and by about 8% for the daily mean screen level statistics). As noted earlier, the relatively small impact on the screen level forecasts is believed to be due to the inability of the 6 hourly assimilation cycle to reduce the diurnal cycle of the observation increments, while the relatively small impact on the w 1 forecasts is consistent with the weak coupling between the near surface and root zone soil moisture in ISBA. Despite the modesty of the improvements to the RMSD, these results are believed to reflect a true reduction in the observation increments, since the statistics were based on a very large sample size (for the screen level observations, approximately 250,000 observations were used). If this result can be substantiated once the diurnal cycle in the screen level observations has been addressed (ideally using a longer experiment period than was used here), this implies that assimilating remotely sensed soil moisture together with screen level observations has the potential to improve the realism of the NWP land surface without degrading the low level atmospheric forecasts. [38] The disparity between the analysis increments generated by assimilating each data type could have several causes. It may indicate a conflict between the assimilated data sets; there is certainly a conflict in the treatment of the biases in each. The AMSR E data have been very strongly bias corrected to remove systematic differences to the model, including any diurnal or seasonal cycles in the modelobservation bias, based on the assumption that the model is bias free (as is common practice in the off line land surface assimilation community). The presence of a small positive bias in the AMSR E data, even after this bias correction, could indicate a failure of the CDF matching algorithm used to normalize the observations. In contrast the screen level observations have not been bias corrected (nor are they currently corrected in Météo France s operational land surface assimilation). While the monthly averaged modelobservation bias for the screen level variables is close to zero, there are strong and systematic differences between their diurnal cycles and strong biases at some locations. Additionally, the accuracy of remotely sensed soil moisture is not well established, and the conflict between the two data sets could also be associated with inaccuracies in the AMSR E data. Consequently, experiments are underway to test the assimilation of near surface soil moisture from active microwave ASCAT observations into ISBA [Mahfouf, 2010]. [39] Alternatively, the disparity between the SLV and AMS experiments could also have been caused by systematic errors in the model forecasts of the observed variables, particularly since several previous studies over heavily instrumented sites have pointed toward this result [Douville et al., 2000; Hess, 2001; Drusch and Viterbo, 2007]. Validating the assimilation results against independent data (specifically from flux towers and in situ soil moisture sensors) would help to resolve this issue, however such a validation would require a longer experimental period than was possible for this study. [40] The T 2m, RH 2m, and w 1 observation errors (of 1 K, 10% and 0.05 m 3 m 3, respectively) used here are thought to be approximately correct, to the extent that spatially and temporally uniform errors can represent the true values. These observation errors are consistent with the root mean square of the observation increments in Table 2: if the observations increments are partitioned equally between the model and observations (i.e., the background and observation errors are assumed to be independent and have equal mean squares), the error standard deviation for each would be 0.9 K for T 2m, 7% for RH 2m (slightly lower than the RH 2m observation error used), and 0.05 m 3 m 3 for w 1. The selection of the model errors is more difficult, since there has been little work to validate ISBA ALADIN. Additionally, the soil moisture climatology of ISBA ALADIN is unrealistic, and in particular the variability in w 2 is suppressed by the misspecification of the soil parameters described in section 2.4. In addition to difficulties related to the bias correction of the observed soil moisture, this lack of realism in the modeled soil moisture also necessitates that the expected 11 of 13