The aim of this study is to test a land data assimilation prototype for the production of a global daily root-zone soil moisture analysis. This system can assimilate microwave L-band satellite observations such as those from the future Hydros NASA mission. The experiments are considered in the framework of the Interaction Soil Biosphere Atmosphere (ISBA) land surface scheme used operationally at the Meteorological Service of Canada for regional and global weather forecasting. A land surface reference state is obtained after a 1-yr global land surface simulation, forced by near-surface atmospheric fields provided by the Global Soil Wetness Project, second initiative (GSWP-2). A radiative transfer model is applied to simulate the microwave L-band passive emission from the surface. The generated brightness temperature observations are distributed in space and time according to the satellite trajectory specified by the Hydros mission. The impact of uncertainties related to the satellite observations, the land surface, and microwave emission models is investigated. A global daily root-zone soil moisture analysis is produced with a simplified variational scheme. The applicability and performance of the system are evaluated in a data assimilation cycle in which the L-band simulated observations, generated from a land surface reference state, are assimilated to correct a prescribed initial root-zone soil moisture error. The analysis convergence is satisfactory in both summer and winter cases. In summer, when considering a 3-K observation error, 90% of land surface converges toward the reference state with a soil moisture accuracy better than 0.04 m3 m−3 after a 4-week assimilation cycle. A 5-K observation error introduces 1-week delay in the convergence. A study of the analysis error statistics is performed for understanding the properties of the system. Special features associated with the interactions between soil water and soil ice, and the presence of soil moisture vertical gradients, are examined.
The initialization of soil moisture in numerical weather and climate prediction models has been recognized as being of crucial importance for its feedback with near-surface and tropospheric processes at continental (Beljaars et al. 1996) and regional scales (Ek and Holtslag 2004). In recent years, soil moisture has also been linked with predictability issues on seasonal to interannual time scales (Timbal et al. 2002; Schlosser and Milly 2002; Koster et al. 2004; Yang et al. 2004).
Improving the knowledge of soil water content in the upper surface layer on a global scale is the focus of two future satellite missions: the Soil Moisture and Ocean Salinity (SMOS) mission by the European Space Agency (Kerr et al. 2001), scheduled to fly in 2007, and the Hydrosphere State Mission (Hydros) by National Aeronautics and Space Administration (Entekhabi et al. 2004), intended to fly in 2010. Although the two missions differ in a number of technological aspects, both platforms will carry a microwave L-band radiometer capable of sensing the land surface with negligible contribution from the atmosphere. A common goal for both missions is to provide a 3-day global coverage for superficial soil moisture at a useful resolution for current general circulation models (GCMs). The aim of this work is to investigate the usefulness of such information to constrain and correct root-zone soil moisture in a numerical weather prediction (NWP) context.
Several studies have shown that L band is optimal for the retrieval of land surface soil moisture and freeze/thaw state transition (see Entekhabi et al. 2004 for a review). Seuffert et al. (2003, 2004) have evaluated the impact of including both L-band and conventional screen-level observations in data assimilation schemes with a single-column experiment on field site datasets. Balsamo et al. (2004a) have examined the assimilation of multiple simulated observations showing a large information content in L-band satellite observations for a root-zone soil moisture analysis over North America.
The main objective of this work is to evaluate the impact of the Hydros data in a Land Data Assimilation System (LDAS) with a global Observing System Simulation Experiment (OSSE). A realistic distribution of data is simulated according to the Hydros satellite trajectory. The observations are generated for the Hydros swath coverage for hourly transects. Unlike similar studies involving the use of L-band microwave brightness temperatures over land (Pellarin et al. 2003; H. Gao et al. 2004), a direct assimilation of these observations is considered, without applying a retrieval algorithm. For this purpose a radiative transfer model (RTM) for microwave frequencies is implemented in the LDAS system. The RTM, when combined sequentially to the land surface scheme, is responsible for mapping a land surface state into a microwave brightness temperature (so-called observation operator). The direct assimilation of satellite radiances is currently implemented for multivariate atmospheric data assimilation systems (e.g., Andersson et al. 1994). A main advantage of this approach is the early access to the observations, which allows near–real time analyses, while the main concern is the treatment of observational biases which need to be removed prior to the assimilation. In this experimental framework, the assimilated observations are assumed to be bias free, and error sources related to signal processing, or due to the operation frequency (i.e., Faraday rotation), are supposed to be already corrected.
In section 2, the Hydros satellite mission is briefly described and a simple satellite orbit simulator is presented. Section 3 introduces the land surface scheme (LSS) used at Meteorological Service of Canada (MSC). Section 4 presents the data assimilation method and the choice of the control variable. In sections 5 and 6, the L-band RTM is presented and a set of sensitivity tests is discussed. The input dataset for the global simulations is described in section 7 and the results for a 1-yr-long simulation (1995) are illustrated and commented on. In section 8, results are reported for a set of global OSSE experiments performed in January and July 1995. The analysis convergence and the evolution of the system’s errors are evaluated during the data assimilation cycles. Conclusions and perspectives of the study are presented in section 9.
2. The satellite observations
a. The Hydros satellite mission
The Hydros satellite will fly on a 670-km polar sun-synchronous orbit with an inclination of 98°. A 6-m deployable antenna will perform a conical scan at a constant zenith angle of 39.3° with a rotating speed of 14.6 rpm, resulting in a swath width at the ground of about 1000 km. The onboard instrumentation will include a radiometer, operating at a frequency of 1.41 GHz (21-cm wavelength) with H, V, and U polarizations, and a radar, operating at 1.26–1.29 GHz in HH, VV, and HV polarizations. The footprint resolution will be approximately 40 km for the radiometer and 30 km for the radar. These values are constrained by the antenna beamwidth: 2.6° for the radiometer and 1.9° for the radar. A range and Doppler discrimination technique will allow reaching a final resolution of 10 km for soil moisture and 3 km for freeze/thaw transitions. The radiometer capability to retrieve soil moisture is limited by high values of vegetation water content (VWC; less than 5 kg m−2), while for the radar, studies are in progress to increase the accuracy of retrievals in densely vegetated areas, currently limited to VWC less than 0.5 kg m−2. The depth of the L-band penetration in the soil is between 2 and 5 cm (Jackson and Schmugge 1989), which allows one to infer the root-zone soil moisture given its relationship with superficial soil moisture (Calvet et al. 1998; Calvet and Noilhan 2000).
b. The observation error
Measuring soil moisture from space implies dealing with several error sources, which may be separated in two main components: the satellite instrumental specification and the land surface description. To the first belong technological issues, such as the antenna performance, which has to satisfy the expected gain, and the system geolocation accuracy, which should allow a separation of land surface heterogeneous tiles (i.e., inland water bodies). The second component includes the land surface vegetation and soil descriptions both in terms of ancillary datasets and physical processes. For the modeling components, the LSS and the RTM have to reproduce the land state evolution and the L-band emission with sufficient accuracy.
The brightness temperature measurement error is expected to be less than 1 K. This rather high radiometric accuracy results from the 0.04 m3 m−3 soil moisture accuracy requirement of the Hydros design (Entekhabi et al. 2004). O’Neill et al. (2004) have investigated the feasibility for Hydros to meet the accuracy level in OSSEs, and this is generally verified by field site experiments [i.e., Soil Moisture Experiments 2002 and 2003 (SMEX02, SMEX03), Southern Great Plains 1999 (SGP99)]. In the present study, the Faraday ionospheric effects are assumed to be partially corrected according to Skou (2003), and inland water bodies are not considered.
An overall observation error of 3 to 5 K is therefore considered for assimilating the Hydros simulated brightness temperatures. A soil moisture accuracy requirement of 0.03 (ideal) to 0.05 m3 m−3 (minimum) is also indicated by Walker and Houser (2004) to be beneficial for increasing prediction skills. In the current data assimilation experiments a soil moisture accuracy of 0.04 m3 m−3 is used as a convergence criteria.
c. The satellite orbit simulation
An algorithm is defined to spatially and temporally locate the simulated observations and is described in the following. The Hydros satellite passes are simulated according to Wertz and Larson (1991). The aim is to provide a realistic distribution of data for the assimilation experiments. The Hydros polar sun-synchronous orbit is simulated with a simple Keplerian orbit model that satisfies the prescribed satellite inclination, altitude, and revisit time reported in Entekhabi et al. (2004). A 3-day satellite trajectory is generated and repeated along the time window of each numerical experiment. A circular scan with given amplitude around the satellite’s nadir location is considered to reproduce the expected swath coverage. The simulated observations are stored in hourly transects along the satellite trajectory between an initial time ti = t − 30 min, and a final time tf = t + 30 min, around the hour t (from 0001 to 0000 UTC of the next day). A real footprint has a more complex geometry than a circular disk and requires a geometrical transformation to compare model outputs to observations. In this framework, each simulated observation is supposed to match perfectly the model grid box and no subgrid information is considered.
3. The land surface scheme
The land surface processes are represented by the Interaction Soil Biosphere Atmosphere (ISBA) scheme that has been described in detail by Noilhan and Planton (1989), Noilhan and Mahfouf (1996), and Bélair et al. (2003a, b). The operational version of ISBA at MSC considers the evolution of six prognostic variables for soil and vegetation: Ts is the surface temperature, Tp is the daily mean surface temperature, ws is the superficial volumetric water content, wp and wpi are the total volumetric water contents (liquid and ice phase), and Wr is the vegetation-intercepted water content. In addition, four prognostic variables for the snowpack are considered: Wn is the snow water equivalent, Wnl is the liquid water in the snowpack, ρn is the snow density, and αn is the snow albedo. The soil moisture and temperature variables are operationally analyzed in the regional version of the Global Environmental Multiscale model (GEM; Côté et al. 1998) using an optimum interpolation (OI) technique introduced by Mahfouf (1991). The implementation of the LSS and the analysis technique at the Canadian Meteorological Centre (CMC) are described in Bélair et al. (2003a, b).
At present, a tiles approach to account for inner-grid land cover type variability is not available. The land surface is simply divided into a vegetation fraction (veg) and a bare ground fraction (1 − veg). A single energy budget is considered for bare ground, vegetation, and snow cover. Therefore, only one prognostic variable for surface temperature accounts for vegetation and soil surfaces. Within the hydrological soil depth, a skin layer (the superficial reservoir of arbritary thickness ds = 10−2 m) and a total soil layer containing the root zone (much deeper and with variable thickness d2) are considered. The exchange of heat and water between the soil reservoirs is determined by the force–restore method (Deardorff 1978). The total soil water content, wp, evolves with a time scale of several weeks; thus, its initialization is particularly important for NWP applications. The land surface evapotranspiration, Et, is largely determined by the total soil moisture in the range specified by the field capacity (wfc), which is the maximum soil water content with negligible drainage (beyond which Et is maximum), and the wilting point (wwl) at which phenological activity stops (Et = 0), as defined in Noilhan and Planton (1989). Soil freezing and snowpack evolution are also parameterized as described in Bélair et al. (2003a, b).
The vegetation properties are specified with the United States Geological Survey (USGS) ancillary database, which has a global spatial resolution of about 1 km. The leaf area index (LAI) and the vegetation fraction vary according to day of year and are provided by lookup tables (similar to Giard and Bazile 2000). For soil texture, a high-resolution (i.e., 1 km) multilayer soil characteristics dataset [state soil geographic (STATSGO) dataset; U.S. Department of Agriculture 1994] is used over the United States and a similar dataset is used over Canada (Agriculture Canada Research Branch 1987), whereas a lower-resolution (i.e., 10 km) database is used elsewhere (FAO 1995). The sand and clay percentages are calculated from dominant soil type extracted from the dataset at highest resolution. Area-weighted averages of the native resolution data are performed to obtain the sand and clay fields at target resolution (i.e., 1° latitude) according to Noilhan and Lacarrère (1995).
4. The data assimilation method
A simplified two-dimensional variational data assimilation (2DVAR), described in Balsamo et al. (2004b), is adapted for the assimilation of the L-band microwave brightness temperatures. The analysis state xa is given by the best linear unbiased estimate (BLUE) expression:
where x is the vector containing the variables to analyze, xb is the background state, and y is the observation vector. The terms
are, respectively, named the gain matrix and the innovation vector (difference between the observation and the model forecast in observation space). Here 𝗕 and 𝗥 are, respectively, the background and the observation error covariance matrices; H is the observation operator that maps the model state vector x into observation space and includes the microwave RTM and the LSS.
Under the tangent-linear hypothesis, H can be approximated by its first-order Taylor expansion. The linearized observation operator 𝗛 is then evaluated with a finite-difference approach as proposed by Hess (2001) and examined in Balsamo (2003).
In the LDAS system, the only variable that is analyzed is wp. The other ISBA prognostic variables are not analyzed and left free to evolve during the assimilation cycles. This choice of the control variable is consistent with the ISBA scheme in which the total soil moisture describes the mean soil state and with the penetration depth of the L-band, which is sensitive to the subsurface soil moisture in the first 2 to 5 cm. Furthermore, it is justified by the dominant role of wp in the analysis, as shown in variational studies by Bouyssel et al. (1999). The superficial soil moisture is not corrected by the analysis since it is restored by the land surface integration with a time scale of 1 day. The total soil moisture analysis equation is written as follows:
where ki are the elements of the gain matrix 𝗞 (2), and ΔTh,υb are the brightness temperature observation departures for the horizontal and vertical polarizations given by observation minus model values for a given grid cell (3). The 2DVAR soil moisture analysis assimilates the simulated Tb in a 24-h assimilation time window to produce a daily analysis at 0000 UTC. The convergence of the analysis is tested in extended assimilation cycles during one month. The aim of the data assimilation experiment is to build a realistic global data assimilation framework to evaluate the potential of Hydros (and similarly for SMOS) L-band radiometric observations for soil moisture analysis. Radar observations are not considered. The assimilation experiments use the horizontal and vertical polarization components of the simulated brightness temperatures with an observation error (σo) of 3 K, which accounts for the error of both the radiometric measurement and the land surface microwave emission model. A larger observation error (σo of 5 K) is also considered to evaluate its impact on the system. The correlation between the two observations (expressed by the off-diagonal terms of 𝗥) is unknown and is set to zero for the purpose of this test, even though real observations would probably exhibit a nonzero correlation. Provided the validity of the tangent-linear hypothesis, the analysis error covariance matrix 𝗔, defined in model space, can be written as
where 𝗕 here expresses the uncertainties of the predicted total soil moisture (specified by the error σb). The value of σb is set equal to 5% of the soil moisture active range (between field capacity and wilting point (wfc − wwl), according to Balsamo et al. (2004b). A large value of σb would give an excessive weight to the observations in the analysis. The evolution of the analysis error is computed and monitored within the assimilation cycles by considering the analysis error reduction obtained from (5) as follows:
The dependence of the analysis error reduction on observation error is evaluated in section 8c.
5. The Land Surface Microwave Emission Model
The relationship between soil water and microwave brightness temperature at the surface comes from the soil moisture influence on the dielectric properties of the soil, which in turn affects the surface microwave emissivity (ɛ). The natural land surface emission at microwave frequencies is a vertically integrated quantity that depends on soil parameters (texture properties, temperature, and humidity profiles) over a depth varying according to frequency (about 2–5 cm at L band), and on vegetation parameters (canopy structure, temperature, and water content). For the purpose of this study the Land Surface Microwave Emission Model (LSMEM), developed by Drusch et al. (1999a, 2001), is used. The accuracy of the RTM is evaluated for several case studies at L-band frequency.
The LSMEM simulates the actual complexity of land microwave emission by representing the contribution of each land surface component (with simplifications for the geometrical aspects) and the vertical distributions of the soil and canopy medium. The dielectric constant of the soil–water mixture is calculated from Dobson et al. (1985). The emissivity of a flat stratified surface is computed according to Wilheit (1978). This soil emission model is preferred to single-layer models implementing the Fresnel equation since it requires no assumptions on the microwave sampling depth, which may itself depend on soil moisture and temperature profiles (Raju et al. 1995). The parameterization of Wegmüller and Mätzler (1999) represents the effects of surface roughness on the soil surface emissivity. The contribution of the vegetation is taken into account according to the effective medium theory (Kirdyashev et al. 1979), and the atmospheric oxygen and water vapor absorption are parameterized according to Liebe (1989). At L band, gas absorption is rather small as expected. The solution of the radiative transfer equation is given by Kerr and Njoku (1990)
where the suffix p indicates the polarization, and s and υ stand respectively for soil and vegetation. The terms Tau and Tad are the upward and downward atmospheric temperature contributions, Tsky is the cosmic radiation, τat is the atmospheric optical depth, w* is the effective vegetation single scattering albedo, and τ* is the effective vegetation optical depth (Kirdyashev et al. 1979).
The input parameters required by LSMEM are listed in Table 1. The parameters already needed by ISBA (ancillary data), or those resulting from the land surface integration (prognostic variables), are directly introduced as inputs to LSMEM. In LSMEM, the soil moisture and temperature can be specified for a number of layers allowing for the use of a multilayer LSS. In ISBA the superficial and total soil layer are respectively representative of the fast and slow components of the energy and water budgets.
In the ISBA–LSMEM coupling, two physical soil layer depths are specified: 1) a thin superficial layer of 1 cm, described by ws and Ts, which is superposed onto 2) a deep layer (d2) described by wp and Tp. This assumption is made to bridge the force–restore concept (for which the depth of soil layers is arbitrarily defined) to the explicit soil discretization of the microwave emission model (Wilheit 1978). The soil moisture profile provided to LSMEM consists of two layers with a step-size transition from ws, Ts to wp, Tp at a depth of 1 cm; therefore the choice of vertical discretization (i.e., number of vertical layers) does not change the value of emissivity. When continuous vertical profiles (i.e., interpolated from multilayer LSS) are considered, the number of vertical layers used in the soil emission model should be greater than 50 to ensure the accuracy of the simulated brightness temperature (Wilker et al. 2006).
The vegetation temperature is not explicitly present in ISBA (marked by * in Table 1), but as previously mentioned, Ts accounts for a superficial temperature that includes the canopy and is used for the vegetation temperature. This approximation does not account for separate thermal inertia of each land surface cover type (see definition of CT in Bélair et al. 2003b).
where fsand and fclay are the sand and clay fractions composing soil texture. The soil surface roughness is not available as a 2D field, and for the purpose of this study, a fixed value of 1.2 cm is used in agreement with values proposed by Crow et al. (2005). In LSMEM, the effective vegetation optical depth τ* is calculated for a given zenith angle θ, according to the formulation of Kirdyashev et al. (1979):
where k0 is the wavenumber, VWC is the vegetation water content, ρwater is the water density (assumed constant ρwater = 1000 kg m−3), and ɛwater is the dielectric constant of saline water, calculated according to Klein and Swift (1977), and dependent on water temperature and salinity. The A parameter is a structure coefficient for the vegetation. Since the value of A and its dependence on vegetation-cover type are not largely documented in the literature, at least for low frequencies such as L band, a simpler formulation (Jackson and Schmugge 1991) is used:
where the vegetation opacity varies linearly with the VWC and a vegetation structure coefficient (b).
The vegetation properties with respect to microwave emission are parameterized as in Pellarin et al. (2003), where the VWC linearly depends on the LAI, to follow the leaf phenological cycle. An exception is made for forest canopy, since the branches contain the largest fraction of water (Ferrazzoli and Guerriero 2002) and therefore a constant value is used. A lookup table that consists of five vegetation classes prescribes parameters such as single-scattering albedo, vegetation water content, and vegetation structure coefficient. These parameters are taken from Pellarin et al. (2003) but have been readjusted according to T. Pellarin (2005, personal communication). The parameters in Table 2 are used directly in the radiative transfer Eq. (9) or in the definition of the vegetation optical depth (12). The parameters prescribed from the literature are rather difficult to measure and a calibration using observational datasets and an ensemble-based reanalysis technique (Dunne and Entekhabi 2005) could be necessary when considering global applications.
The land surface heterogeneity is probably the most important property to be considered when modeling L-band microwave emission at the surface (Crow et al. 2005; Drusch et al. 1999b). This is supported by observational evidence and is motivated by the large dynamical range of the response of brightness temperature to soil water content. An obvious situation is the presence of inland water bodies, which appear as cold spots in the brightness temperature fields. The horizontal resolution of the available global land-use databases allows one to identify dominant vegetation types down to 1 km, and water bodies up to a few tens of meters.
In the current setup, the spatial heterogeneity is taken into account to provide a more realistic surface brightness temperature. LSMEM is run for each vegetation type present in the grid cell and for bare soil. The final value of Tb is calculated by a weighted average of the Tib obtained from each of the five cover types (i) specified in Table 2, with a weight given by its fractional cover. The differences in the Tib come essentially from the differences in vegetation parameters, since the soil state underneath and the atmospheric forcing are uniform for each grid cell. In contrast, a precise characterization of the vertical structure of vegetation and soil layers remains extremely difficult because of lack of information.
In ISBA, the effective layer approach is already embedded in its concept, with a combined vegetation/soil temperature and a total soil moisture, defined to be representative of each grid cell. This feature would be desirable within the LDAS system, since each modeling module (LSS and RTM) can evolve independently in order to include scientific advances or new parameterizations. Nevertheless soil moisture and temperature profile issues have to be investigated in order to assess the feasibility of this approach. In the chosen configuration the impact of vertical soil moisture and temperature gradients is examined considering two layers (from ISBA) and a stratified soil emission model (Wilheit 1978). A sensitivity study presented in section 6b shows the implications of choosing the soil emission model (one layer versus two layer), and the effects of vertical gradients on the simulated Tb. The impact of choosing a single soil layer is also evaluated in the assimilation experiments (section 8).
6. A sensitivity study of the L-band surface emission model
The land surface state provided by ISBA is used to prescribe the input parameters to LSMEM. A sensitivity study is performed to investigate the relative importance of the parameters used in LSMEM. Several single-column experiments are performed with a reference setup, where only one parameter is perturbed at a time. The reference and the perturbation (expressed as a percentage of the reference value) are reported in Table 3 together with the mean sensitivity (averaged over 11 vegetation-cover classes) of the H and V components of Tb and for a “dry” and a “wet” reference state. Perturbations try to reflect uncertainties of the various parameters, although some are rather arbitrarily chosen (i.e., single-scattering albedo, vegetation parameter).
a. Sensitivity to surface parameters
The sensitivity is first evaluated for vertically uniform soil moisture and temperature profiles. The perturbation is set between the field capacity (wfc, wet case) and the wilting point (wwl, dry case), which respectively correspond to the maximum and minimum of land surface evapotranspiration flux. To analyze the dependence on vegetation cover, the results for the horizontal and vertical polarization components of Tb are calculated for different vegetation cover percentages and are summarized in Fig. 1. As expected at 1.4 GHz, the largest sensitivity is obtained for the soil moisture followed by soil temperature and vegetation water content. The horizontal polarization component has a larger sensitivity than the vertical. The impact of soil properties such as clay and sand percentage is invariant with vegetation fraction. Vegetation water content is particularly important for large vegetation fractions. Note that the atmospheric absorption for both the oxygen and the water vapor at L band is negligible (i.e., of the order of 0.01 K; not shown).
By comparing the sensitivity for a wet and a dry reference, it is possible to extract further information. The dry soil reference experiments exhibit a larger sensitivity to soil texture (specific and dry bulk densities, sand and clay), while wet reference experiments are relatively more sensitive to surface roughness and vegetation parameters (veg, b, VWC). The increased vegetation sensitivity for wet land surfaces is in agreement with the expected limit of the L-band radiometer for densely vegetated area where the signal from total soil moisture is reduced.
b. Impact of vertical moisture and temperature gradients
To better understand the behavior of the brightness temperature sensitivity to soil moisture and temperature gradients, the experiments previously described and illustrated in Fig. 1 are repeated with the same perturbations (specified in Table 3) applied to a different reference profile with a gradient between the two soil layers considered. Figure 2 illustrates the importance of soil moisture in the superficial layer. A vertical soil moisture gradient is imposed for the previously defined wet and dry states. The case of a dry soil with a thin wet surface (of 1 cm) is plotted in Fig. 2a (i.e., wet over dry). This configuration can be representative of a soil state after a summer precipitation event, when the superficial soil moisture rapidly responds to the rainfall due to its smaller holding capacity. The brightness temperature sensitivity for this case resembles that of the uniformly wet case, Fig. 1b, showing a complex (nonlinear) interaction between the layers that contribute to the microwave land emission. A wet surface is likely to be rapidly restored (i.e., dried out) by moisture-sink processes (runoff, drainage, and evapotranspiration).
The reverse situation (i.e., dry over wet) is also considered (Fig. 2b) although large gradients are less common than in the previous case, since the restore mechanism within ISBA acts to reduce them (capillarity rises). Nevertheless a drying bare soil could present a smaller positive vertical moisture gradient, which would lead to a reduced sensitivity to soil moisture. In the presence of vertical soil moisture gradients, the L-band signature of subsurface soil moisture is significantly reduced with respect to the possible sources of variation, and therefore the observations might be less informative.
The results from the uniform soil moisture and the vertical gradient experiments can be unified by considering a variable superficial soil layer depth ds (for a chosen vegetation cover, veg = 80%). In these experiments the soil moisture gradient is fixed and the depth of the superficial layer (ds) is varying. For an infinitesimal superficial thickness (ds → 0) the setup falls into the uniform moisture cases of Fig. 1 while for a depth ds = 1 cm (as used in ISBA–LSMEM coupling) the sensitivity matches that of Fig. 2. Figure 3 shows that for either positive or negative gradients, the superficial soil moisture slightly attenuates the brightness temperature signal of the underneath moisture state up to a few millimeters. For superficial depths larger than 1 cm, the brightness temperature sensitivity from deep soil moisture is modulated both in magnitude and sign.
This nonlinear behavior of the brightness temperature with increasing soil depth was already observed by Wilheit (1978) and is associated with the interaction of incident and reflected electromagnetic waves in the presence of gradients in the refraction index (i.e., due to a stepwise soil moisture gradient). The resulting emissivity of the soil was shown to have local maxima and minima for depths varying in the range between 0.1λ − 0.5λ (where λ is the radiation wavelength). For L band, this translates into 2–10-cm depth range, which corresponds to that observed in Fig. 3. Negligible Tb signal is observed from soil moisture below 10-cm depth. A larger value of veg (or VWC) reduces the amplitude of the oscillations in Fig. 3 but does not change the behavior (not shown).
The sensitivity to soil temperature profiles is examined in a similar study. The impact of temperature gradients is evaluated with respect to the reference setup of Table 3 where the soil temperature is uniformly set to 288.15 K. One soil layer is perturbed at a time, introducing positive and negative temperature gradients. The variations in the brightness temperature sensitivity to soil moisture (introduced by soil temperature gradients) are evaluated with respect to the results obtained with an isothermal profile (Fig. 1). In analogy with the previous tests, two values are selected to be representative of “cold” and “hot” cases, and are respectively set to 273.15 and 303.15 K (0° and 30°C).
The effect on the sensitivity is rather symmetric and of small magnitude when either varying the superficial or the deep soil temperatures imposing a temperature gradient of ± 15 K between the two layers. The sensitivity values change by 5%–6% (w.r.t. Fig. 1) when varying the superficial layer temperature. The sensitivity is increased for a cold surface (and decreased for a hot surface). A variation of 10%–11% is observed when varying the deep-soil layer temperature, but with opposite effects, and an increased sensitivity for the hot case. The attenuation of the soil moisture signal due to a warmer superficial layer is likely to add to the attenuation due to a dry surface previously shown (Fig. 2b), as the two states are physically related (this may be the case for 6 p.m. satellite passes, particularly over arid regions). On the contrary, a surface colder than the underneath soil can introduce a compensation for the attenuation of a wet surface (favorable for morning satellite passes). Effects of soil temperature profiles are rather linear and do not represent a problem for the analysis.
7. A one-year global land surface simulation
An ISBA offline land surface simulation is performed on the period from 1 July 1994 to 31 December 1995. The length of the simulation allows reaching equilibrium for most of the land surface fields including the total soil moisture wp for which a 6-month spinup period is expected in 1994. The near-surface atmospheric forcing is provided by the Global Soil Wetness Project, second initiative (GSWP-2; Dirmeyer et al. 1999, 2002; X. Gao et al. 2004). The GSWP is a research activity of the Global Land–Atmosphere System Study (GLASS) and the International Satellite Land Surface Climatology Project (ISLSCP). Both projects contribute to the Global Energy and Water Cycle Experiment (GEWEX). GSWP-2 is closely linked to the ISLSCP Initiative II, and covers the period July 1982 to December 1995.
The atmospheric forcing data are provided at a resolution of 1° globally on a domain of 360 × 150 grid points that does not consider latitudes south of 60°S. The GSWP-2 data are based on atmospheric reanalyses [National Centers for Environmental Prediction–Department of Energy (NCEP–DOE) reanalysis] at 3-h intervals. Surface radiation and precipitation fields are corrected using observational data, via a multiplicative factor, while temperature and pressure fields are rescaled according to elevation differences between the reanalysis model topography and that used in GSWP-2. Wind fields are used as provided by GSWP-2. The state variables of surface pressure, air temperature, and specific humidity at 2 m, as well as wind at 10 m, are provided as instantaneous values. The surface radiation and precipitation flux represent 3-h averages. The GSWP-2 forcings are linearly interpolated in time to the ISBA integration time step of 30 min.
The initial conditions for soil temperature and water content are provided by a 35-km version of CMC’s (MSC) GEM model valid at 0000 UTC 1 July 2003 (most recent date available). This initialization is believed to be more realistic than a climatological field and unbiased with respect to ISBA. The global water cycle simulated for 1995 is summarized in Fig. 4. The mean water in the reservoirs (as global average in Fig. 4a) and the water budget (Fig. 4b) are illustrated in order to verify the stability of the simulation and the balance of the hydrological budget. As expected, the ice content has a peak for the boreal winter. The water content has almost an opposite phase, with a peak at the beginning of boreal summer, coincident with large snow melting.
July and January are selected months for the data assimilation experiments as representative for cold and warm seasons. In Fig. 5 the total soil moisture and the snow water equivalent at 0000 UTC 1 January 1995 and 1 July 1995 are shown. Snow-covered regions in the Northern Hemisphere, in Fig. 5a, are also associated to completely frozen soil (not shown), with the exception of the Tibetan Plateau, which appears rather dry (frozen water content below 0.10 m3 m−3). Land grid points covered by snow (with Wn > 1kg m−2) are not considered by the analysis. The total soil moisture fields of Fig. 5 are used in the reference experiment at the beginning of the assimilation cycles presented in the following section.
8. Global Observing System Simulation Experiments
A set of global assimilation experiments is realized for the months of January and July 1995, selected to be representative of a summer and winter period. The GSWP-2 forcing is used to drive the ISBA LSS integration. The LSMEM and satellite-track model are applied sequentially to produce the Hydros L-band simulated observations over the two selected periods. An initial guess for the land surface state is obtained by initializing the soil moisture wp to a medium wetness defined as (wfc + wwl)/2. This initialization corresponds locally to a large error imposed to the total soil moisture at the beginning of the assimilation cycles (as shown later in the upper panels of Figs. 8 and 9). The other ISBA land surface variables are not perturbed. Each assimilation experiment is forced with the GSWP-2 atmospheric dataset without errors (perfect forcing). This setup allows us to evaluate the behavior of the LDAS cycle assuming the availability of an accurate atmospheric forcing. A daily analysis is performed with the simplified 2DVAR assimilation scheme. Each land surface point is analyzed except in the presence of snow-covered or completely frozen soil conditions. As a result, 95% of land points are analyzed for the July case and 53% for January.
The simulated observations, generated by the land surface reference state, are assimilated at the appropriate time in a 2DVAR analysis with a 24-h time window and are cycled for a month. An example of the Hydros hourly transect is produced in Fig. 6 for the morning pass over central Europe valid at 0005 UTC (±30 min) 1 July 1995. The performance of the analysis is monitored during the data assimilation cycles by comparison with the reference run. The initial total soil moisture errors are progressively corrected, as shown in Fig. 7, in terms of mean and RMSE values and in terms of percentage of analyzed points converging at a given accuracy. In the upper panels, the evolution of the mean value of the total soil moisture is shown for the analysis (2DVAR), the control (no analysis), and the reference cycles. The RMSE error evolution along the cycle (Fig. 7, middle panels) is calculated with respect to the reference and shows the impact of the analysis.
An accurate convergence is achieved for most of the analyzed land surface grid points (Fig. 7, bottom panels). Figures 8 and 9 show the area where the RMSE exceeds the 0.04 and 0.08 m3 m−3 thresholds at the beginning, in the middle, and at the end of the assimilation cycles. The analysis errors, monitored along the cycle, show the impact of the assimilated observations, which provides a daily analysis error reduction (6) of about 5% of the background error. The analysis of the total soil moisture achieves a convergence with an accuracy better than 0.04 m3 m−3 over 88.9% of the analyzed points for January and 94.4% for July. The total soil moisture RMSE, calculated with respect to the reference state, is lower than 0.02 m3 m−3 in both the experiments (0.018 m3 m−3 for January 0.014 m3 m−3 for July). The control experiment (without analysis) obtains a significantly slower convergence for the 0.04 m3 m−3 threshold (53.9% for January and 68.0% for July) and reduced accuracy in terms of RMSE (0.049 m3 m−3 for January and 0.036 m3 m−3 for July).
Common areas of slower convergence, in both the assimilation and control experiments, are identified in equatorial latitudes and are particularly well marked over the Indian peninsula. The main reason for this effect is the attenuation of the L-band signal due to superficial soil moisture, which in those areas is filled up by large amounts of precipitation. This effect is observed in the LSMEM sensitivity (section 6b) in the presence of a wet land surface overlapping a dry soil (Fig. 2a). At the end of the July cycle, the correlation between the analysis convergence error and the soil moisture vertical gradient is particularly large where the difference between ws and wp soil moisture reservoirs is larger than 0.10 m3 m−3 (274 points). The normalized vertical soil moisture gradient [expressed as (ws − wp)/wp] and the normalized soil moisture analysis error [(wap − wp)/wp] exhibit a correlation coefficient of 0.99. This behavior can be explained by the Tb sensitivity tests in the presence of moisture gradient (section 6b).
A proof of this is demonstrated by repeating the analysis convergence experiment (July) with a single soil layer (Fresnel model) represented by wp and Tp. In this experiment a much quicker convergence is observed (not shown), with a convergence accuracy obtained in the first 10 days compared to the final accuracy of the previous test (after 30 days). Patterns of slower convergence are absent in this case because soil moisture vertical gradients are rather artificially removed. This test confirms the importance of modeling vertical moisture gradients for extracting information on the root-zone soil moisture. A reduced signal from root-zone soil moisture in the presence of a thin wet surface is also observed when assimilating other sources of observations [i.e., for screen-level temperature and humidity, as shown in Bouyssel et al. (1999)] and is in agreement with results from Calvet and Noilhan (2000).
The soil moisture analysis convergence over equatorial evergreen forests (i.e., Amazon, Congo, Malaysia, etc.) cannot be inferred from Figs. 8 and 9 since the initial error (from the choice a medium wetness) is rather small. A further test from an initially dry state (wp = wwl; not shown) confirms a much slower local convergence of the analysis, which does not meet the soil moisture accuracy after 1-month assimilation, as expected from the reduced soil moisture signal over rain forest (with VWC > 5 kg m−2). However, it can be argued that such large errors introduced in the root-zone soil moisture are not realistic for those areas.
a. Evolution of the superficial soil water content
Although the superficial soil moisture is neither perturbed nor analyzed in the OSSEs, it is strongly related to the total soil moisture by the force–restore mechanism and therefore is likely to be affected by the initial error prescribed for the total soil moisture. Figure 10 shows the evolution of the superficial soil moisture in the OSSEs. In both the assimilation and the control cycles, the initial state presents no error, since the initial soil moisture is equal to the reference. The first three days are characterized by a divergence from the reference values, a consequence of the large error imposed on the initial total soil moisture. The largest deviation is observed on the first day in agreement with the typical time scale of superficial moisture variations. From the fourth day both cycles tend to reconverge toward the reference with a trend similar to that of the total soil moisture shown in Fig. 7. The 2DVAR analysis applied to the total soil moisture content results in a more rapid convergence on the superficial reservoir than the control experiment. Figure 10 illustrates the impact of total soil moisture errors even in the presence of a perfect initialization of superficial soil moisture and the importance of correcting them in the analysis (choice of the control variable).
b. Evolution of the soil ice content
The soil ice reservoir wpi has a large holding capacity, and errors for this quantity cannot be easily removed since the microwave brightness temperature observations are not sensitive to soil ice. The analysis in this case can only remove errors when the exceeding storage is transferred to liquid phase on the melting season. Evidence of this is found in the January OSSE experiment where the soil ice content wpi error (w.r.t. reference) is monitored during the assimilation and control cycles with almost no difference in the two experiments, as shown in Fig. 11. In the Northern Hemisphere, the excess of water introduced by the total soil moisture initialization (set equal to a medium wetness) freezes rapidly during the first week, causing an error in the ice content that is not restored during the rest of the month. Furthermore, this increased ice storage can induce a larger melting, having an impact on the analysis convergence. This is the case for the pattern of nonconvergent points over North America observed in Fig. 8a, which matches well with the areas having a large soil ice melting as shown in Fig. 12. In this situation, the errors of convergence can be entirely attributed to the LSS (background term in the analysis), which stores the initial soil water error preventing the analysis corrections and then redistributes the errors during the cycle. Over North America, the convergence errors mostly related to ice melting can be identified by comparing winter and summer cycles of Figs. 8 and 9.
c. Effect of an increased L-band observation error
The assimilation experiment for the month of July is rerun with an increased observation error reducing the weight given to the observations in the analysis. This test is useful to evaluate the variation of the LDAS performance with a reduced observation accuracy. The observation error in the covariance matrix used to calculate the analysis gain matrix (3) is increased (σo = 5 K; TB5 experiment), with respect to the previous cycle (σo = 3 K; TB3). The comparison of the convergence and the RMSE plots allows us to point out the effects of the observation error, as shown in Fig. 13. The daily analysis error reduction, defined in (6), is about 2% (averaged value) along the cycle. Considering a mean total soil moisture RMSE of 0.04 m3 m−3, the TB5 experiment reaches this threshold on 12 July, compared with 7 July for the TB3 experiment, and 25 July for the control experiment (Fig. 13a). Considering as a threshold two-thirds of the land points converging at an accuracy of 0.04 m3 m−3, this condition is realized on 15 July for the TB5, on 9 July for the TB3, and only on 28 July for the control experiment (Fig. 13b). The increased observation error produces a delay in the cycle performance, estimated at about a week, with a convergence still considerably faster than the control experiment where the atmospheric forcing is the only term contributing to restore the total soil moisture toward the reference.
This paper presents a land data assimilation system for the Hydros simulated brightness temperature developed at the MSC. The ISBA land surface scheme and the LSMEM radiative transfer model are coupled to simulate the L-band land surface emission. A polar orbit simulation of the Hydros satellite passes is used to locate spatially and temporally the observations according to the specified altitude and field of view. The L-band simulated observations are then assimilated at the appropriate time and location with a simplified variational technique having a 24-h window.
Particular attention is given to the observation operator for generating the microwave emission signal from the land surface, since an accurate model is necessary for assimilating this information in NWP models. A sensitivity study for the LSMEM shows the impact of uncertainties in the parameters prescribed for obtaining the microwave brightness temperature. Although the total soil moisture has the largest signal, different combinations of land surface parameters and moisture states may reduce the signal to noise ratio. The effect of superficial moisture and vegetation fraction is particularly evident.
A first set of OSSEs is performed to study the properties of the system. A reference soil moisture is produced by a 1.5-yr integration of the land surface scheme driven by the GSWP-2 near-surface atmospheric forcing, and is used to simulate the L-band emission with ISBA–LSMEM. The Hydros simulated observations are assimilated over a 24-h time window to correct a prescribed soil moisture error. The total soil moisture, which contains the root zone, is analyzed daily while the superficial reservoir, as well as the other land surface variables, are free to evolve during the cycle.
The results of monthly assimilation experiments for July and January show similar convergence toward the reference. The analyzed soil moisture satisfies the 0.04 m3 m−3 volumetric water content accuracy over a large percentage of the analyzed land grid points. The interaction of total soil moisture errors with soil ice errors is highlighted for the winter case. In summer, the attenuation of the microwave emission by wet land surfaces (i.e., hence the lack of sensitivity to wp) is responsible for slowing down the convergence. Considering a single soil layer for microwave emission with a fixed sampling depth would artificially hide this behavior. These experiments highlight the importance of representing soil moisture vertical gradients and the areas where the analysis is likely to be affected. The evolution of the superficial water content is also monitored showing that analysis corrections applied to the total soil moisture determines the convergence of the superficial layer due to the restore mechanism of the ISBA scheme.
An increased Hydros observation error would have an impact on the convergence rate of the analysis. A delay of about one week to reach a given accuracy is observed when the error is increased from 3 to 5 K. For both prescribed observation errors, the analysis produces a convergence significantly faster than when no analysis is performed (i.e., land surface constrained only by a perfect atmospheric forcing).
Additional studies are needed to evaluate the behavior of L-band radiative transfer equation, the specification of some of the ancillary data, and the treatment of areas with snow and frozen soils. The results of this study may be useful for performing further tuning of the ancillary dataset when L-band observations will be available. Although a large number of parameters are needed for the radiative transfer scheme, the soil moisture, the vegetation opacity, and the soil temperature are the most sensitive at least over relatively flat surfaces. The L-band emission from complex orography is not considered here and additional studies are required to evaluate the limit of the present modeling parameterization. The Faraday effect is not explicitly simulated but its contribution is considered in the observation error budget.
The LDAS system at the MSC will consider in the near future the following improvements: A multilayer land surface scheme that will allow a more realistic representation of soil moisture and temperature profiles. For the data assimilation scheme, further developments will apply an ensemble Kalman filter (EnKF), as an upgrade to the simplified variational analysis technique used, which extends the coherence of the analysis beyond the assimilation time window via the update of the background error covariance. A wider range of observations from both conventional ground-based and satellite instruments will be assimilated for constraining the soil moisture. This approach is believed to compensate for weaknesses of single observational sources, both in terms of observation coverage and information content.
The authors wish to thank Dara Entekhabi (PI, Hydros), Eni Njoku, and the Hydros science team for providing material and precious discussions. Matthias Drusch and Thierry Pellarin are acknowledged for providing the radiative transfer models and helpful suggestions. This work has been funded by the Canadian Space Agency, Earth Observation Government Related Initiatives Program (GRIP) project.
Corresponding author address: Gianpaolo Balsamo, ECMWF, Shinfield Park, Reading, Berkshire, RG2 9AX, United Kingdom. Email: email@example.com