Assimilation of global radar backscatter and radiometer brightness temperature observations to improve soil moisture and land evaporation estimates

Remote Sensing of Environment 189 (2017) 194–210

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Assimilation of global radar backscatter and radiometer brightness temperature observations to improve soil moisture and land evaporation estimates H. Lievens a, b, * , B. Martens a , N.E.C. Verhoest a , S. Hahn c , R.H. Reichle b , D.G. Miralles d, a a

Laboratory of Hydrology and Water Management, Ghent University, Ghent, Belgium Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, USA c Department of Geodesy and Geoinformation, Vienna University of Technology, Vienna, Austria d Department of Earth Sciences, VU University, Amsterdam, The Netherlands b

A R T I C L E

I N F O

Article history: Received 18 April 2016 Received in revised form 17 October 2016 Accepted 30 November 2016 Available online xxxx Keywords: ASCAT backscatter SMOS brightness temperature Data assimilation GLEAM Soil moisture Land evaporation

A B S T R A C T Active radar backscatter (s ◦ ) observations from the Advanced Scatterometer (ASCAT) and passive radiometer brightness temperature (TB) observations from the Soil Moisture Ocean Salinity (SMOS) mission are assimilated either individually or jointly into the Global Land Evaporation Amsterdam Model (GLEAM) to improve its simulations of soil moisture and land evaporation. To enable s ◦ and TB assimilation, GLEAM is coupled to the Water Cloud Model and the L-band Microwave Emission from the Biosphere (L-MEB) model. The innovations, i.e. differences between observations and simulations, are mapped onto the model soil moisture states through an Ensemble Kalman Filter. The validation of surface (0–10 cm) soil moisture simulations over the period 2010–2014 against in situ measurements from the International Soil Moisture Network (ISMN) shows that assimilating s ◦ or TB alone improves the average correlation of seasonal anomalies (Ran ) from 0.514 to 0.547 and 0.548, respectively. The joint assimilation further improves Ran to 0.559. Associated enhancements in daily evaporative flux simulations by GLEAM are validated based on measurements from 22 FLUXNET stations. Again, the singular assimilation improves Ran from 0.502 to 0.536 and 0.533, respectively for s ◦ and TB, whereas the best performance is observed for the joint assimilation (Ran = 0.546). These results demonstrate the complementary value of assimilating radar backscatter observations together with brightness temperatures for improving estimates of hydrological variables, as their joint assimilation outperforms the assimilation of each observation type separately. © 2016 Elsevier Inc. All rights reserved.

1. Introduction Understanding the dynamics of the hydrological cycle is essential for predicting the impact of climate change on water scarcity or excess in various parts of the world. A pivotal element of the hydrological cycle is land evaporation (E): the return-flow of moisture from land to atmosphere. Linking the energy, water and carbon cycles, land evaporation influences the general dynamics of precipitation and air temperature, and plays an important role during climate extremes such as droughts or heatwaves (Teuling et al., 2013; Miralles et al., 2014). However, while our ability to monitor precipitation — the other major continental hydrological flux —

* Corresponding author at: Laboratory of Hydrology and Water Management, Ghent University, Ghent, Belgium. E-mail address: [email protected] (H. Lievens).

http://dx.doi.org/10.1016/j.rse.2016.11.022 0034-4257/© 2016 Elsevier Inc. All rights reserved.

has recently improved through dedicated satellite missions, such as the Tropical Rainfall Measuring Mission (TRMM) and the Global Precipitation Measurement (GPM) mission, direct evaporation observations from space are still infeasible, limiting our exploration of global dynamics to the use of land surface models (LSM), reanalysis datasets, or simpler methodologies forced by satellite observations, which are still prone to large uncertainties (Mueller et al., 2013; Miralles et al., 2016; McCabe et al., 2016). The interplay of precipitation and land evaporation is mainly mediated by soil moisture (SM) dynamics, making SM an essential climate variable (World Meteorological Organization, 2006). Past decades have drawn increasing interest towards improving the SM state in land surface models by assimilating independent remote sensing observations (Mecklenburg et al., 2016). At large spatial scales (10–50 km), assimilation studies have mostly focused on microwave satellite observations, which have a frequent revisit time (global coverage every few days) and are highly sensitive to

H. Lievens et al. / Remote Sensing of Environment 189 (2017) 194–210

the Earth’s surface SM content. Depending on the remote sensing technique employed, microwave observations are distinguished between: (1) passive radiometer brightness temperature (TB) observations, e.g. from the Advanced Microwave Scanning Radiometer for Earth observation science (AMSR-E) (Njoku et al., 2003), its successor AMSR2 (Imaoka et al., 2010), the Soil Moisture Ocean Salinity (SMOS) mission (Kerr et al., 2001), and the recently-launched Soil Moisture Active Passive (SMAP) mission (Entekhabi et al., 2010), and (2) active radar backscatter (s ◦ ) observations, e.g. from the two European Remote-Sensing Satellite scatterometers (ERS-1 and ERS-2, Lecomte (1998)), and the series of Meteorological Operational Platform missions (Metop-A, Metop-B, Metop-C) carrying the Advanced Scatterometer (ASCAT) (Figa-Saldaña et al., 2002). As TB and s ◦ observations are indirect proxies of the SM content, radiative transfer models (RTM) are usually applied for SM retrieval prior to the assimilation. Meanwhile, the potential to use microwave-based SM retrievals for improving LSM soil moisture and associated discharge simulations through data assimilation has become widely recognized from regional to continental scales (Brocca et al., 2010; Draper et al., 2012; Matgen et al., 2012; Brocca et al., 2012; De Rosnay et al., 2013; Wanders et al., 2014; Renzullo et al., 2014; Ridler et al., 2014; Lievens et al., 2015b). However, it is less clear whether the assimilation of microwave-based SM yields commensurate improvements of land evaporation (Peters-Lidard et al., 2011; Martens et al., 2016a). Despite the proven record of assimilating soil moisture retrievals, there is an increasing tendency towards the direct assimilation of microwave satellite observations (Reichle et al., 2001; Crow and Wood, 2003; Balsamo et al., 2006; De Lannoy et al., 2013; Han et al., 2014; Lievens et al., 2015a). Retrievals often employ land surface parameters and auxiliary information, such as vegetation, texture and temperature, that are inconsistent with the model simulations. Furthermore, since both retrievals and model simulations rely on similar types of auxiliary information, their errors may be cross-correlated, potentially degrading the system performance (De Lannoy and Reichle, 2016). The direct assimilation of microwave observations has the distinct advantage that it does allow for consistent parameters and auxiliary inputs between the LSM and RTM, avoiding cross-correlated errors. To facilitate the direct assimilation of microwave observations, the LSM needs to be coupled to an RTM. As such, the latter serves as a forward operator for predicting s ◦ or TB by using to the fullest extent information from the LSM, such as soil moisture, vegetation, and temperature. To date, a few studies have evidenced improvements from assimilating satellite TB observations into regional-scale (Lievens et al., 2016) and global-scale (De Lannoy and Reichle, 2016) LSM simulations. However, the assimilation of s ◦ still remains largely unexplored, only being previously applied to local-scale laboratory experiments (Hoeben and Troch, 2000). Nevertheless, it is expected that the direct assimilation of s ◦ shares its preference with TB relative to the assimilation of retrievals. This study evaluates the assimilation of both active radar s ◦ and passive radiometer TB observations for improving estimates of surface SM and associated evaporative fluxes from the Global Land Evaporation Amsterdam Model (GLEAM, Miralles et al., 2011a,b; Martens et al., 2016b). The specific objectives are:

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(a) the assimilation of ASCAT s ◦ observations; (b) the assimilation of SMOS TB observations; and (c) the joint assimilation of ASCAT s ◦ and SMOS TB observations. The overarching objective is to assess the relative skill and complementarity of s ◦ and TB observations in improving simulations of soil moisture and land evaporation. 2. Materials 2.1. ASCAT s ◦ observations Backscatter observations from the real-aperture C-band (5.3 GHz) ASCAT radar sensor on-board the Metop-A satellite were used. Metop-A, launched in October 2006, is flying in a sun-synchronous orbit, achieving global coverage on an approximately daily basis for mid-latitude regions. The radar operates in Vertical–Vertical (VV) polarization and measures a s ◦ triplet at azimuth angles of 45◦ , 90◦ and 135◦ over two ∼550 km swaths, separated by 360 km from the satellite ground track. The incidence angle (h) of the measurements may vary from 25◦ closer to nadir to 65◦ further away. The spatial resolution of the s ◦ measurements equals 50 km for nominal mode, whereas 25 km resolution data are provided in experimental research mode. This study uses the research product (Level 1b SZR), re-sampled to a spatial sampling of 12.5 km in the swath orbit geometry. The processing of the ASCAT s ◦ data included the second-order polynomial correction of azimuthal biases, as were identified over long records of s ◦ observation triplets (Bartalis et al., 2006). Next, the data were normalized to a 40◦ reference incidence angle using again a second-order polynomial (Wagner et al., 1999). The data were further re-sampled from the geometry with 12.5 km pixel spacing to the regular 0.25◦ grid, adopted by GLEAM. To do so, an inverse distance weighting was applied to average the s ◦ observations located within a 12.5 km (half the 25 km resolution) radius from each of the GLEAM grid cell centers using a Haversine formula on a spherical Earth model. The averaging was performed across the s ◦ triplets, combining different azimuth angles, and across ascending and descending orbits of the same day in case of overlap. Finally, the ASCAT data were masked for frozen soils, snow, complex topography, large open water fractions and wetlands. A stringent dual masking was applied using both information from GLEAM forcings and ASCAT product flags. More specifically, the air temperature (Ta) and snow water equivalent (SWE) forcings were used to mask out 3-day windows around time steps with frozen (Ta <0◦ C) or snow (SWE >0 mm) conditions, while only observations with probability flags for frozen soil and snow equal to zero were retained (Dorigo et al., 2015). Complex topography was masked out using a threshold of 2.5◦ on the surface slope, calculated from 90-m Shuttle Radar Topography Mission (SRTM) data, as well as a 10% threshold on the according ASCAT topographic complexity flag (Draper et al., 2012; Dorigo et al., 2015). Finally, observations were masked when GLEAM water fractions or ASCAT wetland probability flags were larger than 10%. 2.2. SMOS TB observations

1. to couple GLEAM with two distinct radiative transfer models, i.e., the Water Cloud Model (WCM, Attema and Ulaby, 1978) and the L-band Microwave Emission from the Biosphere (LMEB) model (Wigneron et al., 2007), for simulating ensembles of s ◦ and TB, and comparing those with observations of ASCAT and SMOS, respectively; and 2. to evaluate the impact of microwave data assimilation on simulations of SM and E by comparison with in situ measurements across the globe. Three assimilation scenarios are examined:

Brightness temperature observations were obtained from the interferometric L-band (1.4 GHz) MIRAS (Microwave Imaging Radiometer using Aperture Synthesis) radiometer on-board SMOS, launched in November 2009. The temporal revisit time of SMOS is ∼3 days, whereas the spatial resolution of the measurements equals ∼43 km (Kerr et al., 2012). The dataset used for this study is the Level 3 CATDS (Centre Aval de Traitement des Données SMOS) TB product (Jacquette et al., 2010) reprocessing version 300 (RE04). The latter is

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a daily, global, multi-angular/multi-polarization product, projected onto the 25 km cylindrical EASE (Equal Area Scalable Earth) version 2.0 grid. This study specifically focuses on horizontal (H)-polarized observations at the nominal 42.5◦ incidence angle of SMOS. The SMOS observations were projected onto the GLEAM grid by nearest neighbour re-sampling. A separate processing was performed for the ascending and descending swaths, given the different statistical properties of the observations (Bircher et al., 2012; Leroux et al., 2014; Verhoest et al., 2015). The latter are mainly resulting from differences in temperature gradients between the ascending (6 am) and descending (6 pm) overpasses (Jackson, 1980). In case a given grid cell was observed by both overpasses on the same day, the ascending observations were selected for the data assimilation. The SMOS data were masked out in a similar way to the ASCAT data. Observations were discarded in a 3-day window around time steps with Ta < 0◦ C and SWE > 0, or if snow, ice, or frozen soil flags were activated in the SMOS product. Complex topography was again masked out using the 2.5-degree threshold on surface slope, derived from SRTM data. The masking process also included GLEAM water fractions (<10%), and SMOS open water, wetland, flood, and heavy rainfall product flags. Finally, the data were also screened for contamination with radio frequency interference (RFI), excluding observations when the RFI probability, as provided in the SMOS product, exceeded 10%.

2.3. In situ validation data The model simulations of soil moisture were compared to in situ measurements of the ISMN (Dorigo et al., 2011, 2013) at the global scale, for the period 2010–2014. The ISMN measurements were initially quality-controlled according to Dorigo et al. (2013) and were further processed to remove outliers from the interval [q25 − 2.5(q75 − q25), q75 + 2.5(q75 − q25)], with q25 and q75 the 25% and 75% quantiles of the station measurements (Martens et al., 2016a). Also, prolonged constant values were removed by screening over 3-day periods with a minimum requirement of 0.0001 m3 / m3 change. Subsequent to the screening, in situ stations were only included if more than 365 daily measurements and satellite observations were available across the 2010–2014 simulation period. The model simulations were compared to measurements within the corresponding depth intervals, i.e. 0–10 cm for the surface, and 10–100 cm for the second layer. The number of available stations differed depending on the soil depth, i.e. 358 for the surface and 634 for the second layer. Note that the larger thickness for the model’s second layer may contribute to the mismatch between the measurements and the model estimates (Section 3.1.1). For instance, in situ measurements taken at the top of this layer (e.g. at 15 cm depth) may not be entirely representative for the average SM conditions over the entire model layer. Simulations of evaporation were compared to in situ flux measurements from the FLUXNET 2015 dataset (Baldocchi et al., 2001). An overview of the stations included in this study is presented in Table A1 in the Appendix. The E measurements were discarded during precipitation events, based on the precipitation forcing used by

GLEAM and tower measurements if available. As for SM, only stations with more than 365 measurements and observations were retained, resulting in 22 stations used for the analysis.

3. Methods 3.1. Model ensemble simulations 3.1.1. GLEAM GLEAM (Miralles et al., 2011a,b) version 3 (Martens et al., 2016b) is a modular set of algorithms designed to estimate the evaporation over land and its various components, i.e. transpiration, interception loss, bare-soil evaporation, snow sublimation and open-water evaporation. The model estimates independently the evaporation from four land cover fractions: bare soil, short (herbaceous) vegetation, tall (woody) vegetation and open water, as well as over a number of vertical soil layers, depending on the land cover. Three soil layers (0– 10 cm, 10–100 cm and 100–250 cm) are simulated, of which all are taken into account for tall vegetation, the first two layers for short vegetation, and only the first layer for bare soil. The final estimates are then given by the weighted average over the different land cover fractions and layers. GLEAM encompasses four modules, respectively focusing upon the calculation of potential evaporation, evaporative stress, the soilwater balance and rainfall interception. The potential evaporation, i.e. the rate of evaporation in the absence of stress, is calculated using the Priestley and Taylor equation (Priestley and Taylor, 1972), and is driven by satellite observations of air temperature and surface net radiation. Evaporative stress, e.g. caused by limited water availability, unhealthy vegetation, heat stress, and other environmental factors, is introduced by multiplying the potential evaporation by an empirical stress factor, ranging from 0 (maximum stress, no evaporation) to 1 (no stress, potential evaporation). The stress factor depends on the moisture state of the soil layers, as well as on the vegetation optical depth (VOD), a proxy for the water content of the leaves (Liu et al., 2013). The volumetric SM states are calculated from the soil–water balance module, which accounts for input of water through rainfall or snowmelt and output as evaporation or drainage. The SM content exerts a strong influence on the stress factor, particularly for water-limited regimes, by decreasing the factor with decreasing SM from a critical value (wc ) to wilting point (wp ), with the parameters derived from survey data provided by the Global Soil Data Task Group (2000) (Table 1). For SM values above wc , it is assumed that there is no water stress. Below wp , vegetation is assumed unable to extract any more water from the soil profile, reducing actual evaporation to zero. The VOD accounts for the effects of seasonal phenological changes (e.g. harvesting, leaf-out periods) or abrupt vegetation changes (e.g. forest fires and clear cuts) on the stress. Finally, interception loss, i.e. the direct vaporisation of rainfall intercepted by vegetation, is simulated using Gash’s analytical model (Gash, 1979; Valente et al., 1997) as a function of precipitation and canopy characteristics (Miralles et al., 2010). The rationale of GLEAM is to maximize the use of remotely sensed drivers of evaporation as static and dynamic forcing datasets. Table 1

Table 1 GLEAM input dataset specifications. Variable

Dataset

Type

Resolution

References

Radiation Precipitation Air temperature Snow water equivalent VOD Cover fractions Soil properties Lightning frequency

CERES L3SYN1DEG TMPA 3B42 v7 AIRS L3RetStdv6.0 GLOBSNOW L3av2 + NSIDC v0.1 CCI-LPRM MOD44B IGBP-DIS LIS/OTD

Satellite Satellite Satellite Satellite Satellite Satellite Survey Satellite

1.00◦ 0.25◦ 1.00◦ 0.25◦ 0.25◦ 250 m 0.25◦ 5 km

Wielicki (1996) Huffman et al. (2007) Aumann et al. (2003) Luojus et al. (2013), Armstrong et al. (2005) Liu et al. (2011, 2013) Hansen et al. (2005) Global Soil Data Task Group (2000) Mach et al. (2007)

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presents an overview of the datasets used in this study. Note that all data were reprocessed to the daily temporal resolution over a global 0.25◦ grid. Data provided at other spatio-temporal resolutions were re-sampled linearly. In this context, it should be mentioned that the TMPA (Multi-satellite Precipitation Analysis) dataset is only available over the [−50◦ , 50◦ ] latitude region, confining our simulations to a quasi-global scale. 3.1.2. Water cloud model Forward backscatter simulations were performed using the Water Cloud Model (Attema and Ulaby, 1978). The first-order WCM, where multiple scattering effects are neglected, represents the total ◦ backscattered power as the sum of vegetation backscatter (sveg , in ◦ dB) and soil backscatter (ssoil , in dB), which is attenuated by the vegetation layer through the two-way attenuation coefficient t2 (−):

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where SM1 corresponds to the first-layer soil moisture simulations by GLEAM. The above formulation of the WCM encompasses four parameters (A, B, C and D). The latter were fitted based on ASCAT s ◦ observations over the period 2008–2011, as to date no literature values are available at large spatial scales. The fitting was performed for each grid cell separately by the Shuffled Complex Evolution algorithm (SCE-UA) (Duan et al., 1992, 1994). The objective function J to be minimized integrates the root mean square error (RMSE) between ◦ ◦ backscatter simulations ssim and observations sobs , together with a parameter penalty term as:   Na N 1   ◦ 2 1  (a0,i − ai )2 ◦ ssim − sobs + Wa , J= N Na sa2 i

◦ ◦ + t2 ssoil . s ◦ = sveg

(1)

The vegetation is represented as a uniform collection of spherical water droplets, held in place structurally by dry matter (Bindlish and Barros, 2001). This allows the vegetation backscatter contribution to be characterized by a bulk vegetation descriptor (Prévot et al., 1993): ◦ sveg

  = AV1 cos h 1 − t2 ,

(2)

with V1 being the bulk vegetation descriptor accounting for direct canopy backscatter and A (−) a fitting parameter. The vegetation attenuation is described as: t2 = exp

−2BV2 , cos h

(3)

with V2 being the bulk vegetation descriptor representing the attenuation, and B (−) a fitting parameter. This study uses the VOD as the vegetation descriptor for both V1 and V2 , as it represents an implicit estimation of the attenuation coefficient t2 , and also aids the coupling of the WCM to GLEAM, which already uses VOD for characterizing the water stress of the vegetation. To describe the soil backscatter contribution, several empirical (e.g. linear regression), semi-empirical (e.g. the Oh model, Oh et al., 1992) and theoretical models (e.g. the Integral Equation Model (IEM), Fung, 1994, or the Advanced IEM, Chen et al., 2003), exist. Although semi-empirical and theoretical models present a more complete description of the scattering phenomena at hand, and have shown their value for small-scale WCM applications (e.g. Lievens and Verhoest, 2011), their application at the global scale is hampered by extensive parameter requirements, e.g. for characterizing surface roughness. Also, their validity range is often confined to specific conditions of surface roughness (Verhoest et al., 2008). A perhaps even larger constraint lays in the fact that theoretical models often show saturation of s ◦ for moist conditions, which is not fully supported by observations (Wolfgang Wagner, personal communication, July, 2016). When forced by model-simulated SM, the degree of saturation reached by the backscatter model will largely depend on the climatology of the SM simulations. If a wet model bias is apparent, simulated s ◦ values may show a much larger saturation comparative to the observations. The associated loss in sensitivity to SM may negatively impact the performance of the data assimilation. To avoid the above mentioned saturation issues, this study makes use of a simple linear approach for modeling the bare soil backscatter as a function of SM: ◦ ssoil = C + D • SM1 ,

(4)

i

(5)

0,i

where N is the number of s ◦ simulations and observations, Na the number of calibrated WCM parameters, Wa the weight-factor given to the parameter penalty term, a i the ith parameter value, and a i,0 the prior value of the ith parameter. The weight-factor Wa was set to 0.01 so that the solution is more strongly constrained by the RMSE term than by the parameter penalty term. The parameter deviation is limited by the variance of a uniform distribution with boundaries [a min , a max ], as in De Lannoy et al. (2013):

sa20,i =

(amax,i − amin,i )2 12

.

(6)

The prior parameter values and boundaries are shown in Table 2. The prior values of the vegetation parameters A (direct vegetation scatter) and B (attenuation) were set to zero, to prioritize bare soil scattering above vegetation scattering, thus minimizing vegetation impacts. The prior values of C and D were based on Verhoest et al. (2008), which reviews a large number of linear soil moisturebackscatter relationships observed from ERS data. The average intercept (C) was found to be ≈ −15 dB, and the average slope (D) ≈40 dB • m3 /m3 (Ds ◦ = 16 dB for DSM = 0.4 m3 /m3 ). The minimum intercept in this study (−35 dB) has been designated as the minimum of the ASCAT observations, whereas the minimum slope (15 dB • m3 /m3 ) corresponds to the minimum slope found in Verhoest et al. (2008). 3.1.3. L-MEB Forward brightness temperature simulations were performed using the L-band Microwave Emission from the Biosphere radiative transfer model (Wigneron et al., 2007). L-MEB is applied to convert the first layer SM simulations by GLEAM into simulations of top of atmosphere (TOA) L-band brightness temperatures (TBTOA,p , in K) at polarization p (H in this study): TBTOA,p = TBau,p + exp (−tatm,p ) TBTOV,p ,

(7)

Table 2 WCM calibration parameters (dimensionless), prior values and boundaries. Parameter

Prior value

Minimum

Maximum

A B C D

0 0 −15 30

0 0 −35 15

5 10 0 60

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H. Lievens et al. / Remote Sensing of Environment 189 (2017) 194–210

in which TBau,p (K) is the upward atmospheric contribution, tatm,p (−) the atmospheric opacity, and TBTOV,p (K) the TB at top of vegetation (TOV). The atmospheric contributions (TBau,p and tatm,p ) are described according to Pellarin et al. (2003). The TBTOV,p (K) is calculated using a first-order tau–omega (t – y) model (Jackson et al., 1982): TBTOV,p = Teff (1− rp ) Cp +Tc (1 − yp ) (1 − Cp ) (1 + rp Cp )+TBad,p rp C2p , (8) with Teff (K) the effective temperature of the soil medium, Tc (K) the vegetation temperature, C p (−) the vegetation transmissivity, yp (−) the scattering albedo, rp (−) the rough surface reflectivity, and TBad,p (K) the downward atmospheric contribution (Pellarin et al., 2003). The effective soil (Teff ) and vegetation (Tc ) temperatures are assumed equal to the air temperature forcings used in GLEAM. The transmissivity of the vegetation is expressed by: 

tveg,p Cp = exp − , cos h

(9)

3.1.4. Ensemble generation The forecast errors required for data assimilation were characterized by running an ensemble of model simulations with 32 stochastic realizations (Reichle and Koster, 2003). These stochastic realizations were obtained by the multiplicative perturbation of model forcings and parameters, for which details are listed in Table 4. The perturbation settings for the surface meteorological forcings are roughly similar to those used in earlier work (De Lannoy and Reichle, 2016). The perturbation to precipitation is by design making use of a lognormal distribution to avoid negative precipitation values. Moreover, this approach also reflects that precipitation errors tend to scale with the magnitude of precipitation. The other variables were perturbed using a normal distribution. The noise standard deviations for the parameter perturbations were optimized by trial and error. To this end, we evaluated important characteristics of the ensemble (Section 4.1), using the metrics described in the following. A first way of evaluating the ensemble is by calculating statistics derived from the moments of its probability density function (De Lannoy et al., 2006):

enspk =

Ne  2 1  yˆ ik − yˆ k , Ne

(13)

i

with tveg,p (−) the vegetation optical depth (VOD) at L-band and h (◦ ) the incidence angle. The optical depth is calculated as a function of the optical depth at nadir tNAD (−) (Wigneron et al., 2007): tveg,p

  2 = tNAD cos2 (h) + ttp sin (h) ,

(10)

where ttp (−) accounts for the influence of the incidence angle, and the optical depth at nadir is given by: tNAD = b1 LAI + b2 ,

(11)

with b1 and b2 structural vegetation parameters, and LAI the green leaf area index (Level 4 MODIS MOD15A2 product). Note that for TB simulations we refrain from using the CCI-LPRM VOD forcing of GLEAM, as the latter is derived from observations at C-band frequency or higher, and may thus not be valid at L-band. The parameterization of the rough surface reflectivity is based on the Q/h formulation by Choudhury et al. (1979):   rp = (QRq + (1 − Q ) Rp ) exp −h cosNrp (h) ,

(12)

with Q (−) the polarization mixing factor (assumed to be 0 at Lband, Wigneron et al., 2001), q the opposite polarization of p, h (−) the surface roughness, Nrp (−) the angular dependence of the surface roughness, and Rp (−) the smooth surface reflectivity. Rp is calculated using the Fresnel equations and depends on the soil dielectric constant, which is related to SM. The latter relationship is described by Mironov et al. (2004). The L-MEB parameters selected in this study mimic the parameters from the ESA Level 2 processor v5.5.1 (Kerr et al., 2012). Table 3 lists the parameter values for the different types of vegetation considered by GLEAM. Table 3 The baseline RTM parameters (dimensionless) for the GLEAM land cover fractions. Vegetation type

b1

b2

NrH

ttH

h

yH

Bare soil Short vegetation Tall vegetation

0.06 0.06 0.30

0 0 0

2 2 2

1 1 1

0.1 0.1 0.3

0 0 0.08

msek =

Ne  2 1  yˆ ik − yk , Ne

(14)

i

 2 enskk = yˆ k − yk ,

(15)

in which enspk is the ensemble spread, msek the ensemble mean squared error and enskk the ensemble skill at time step k. yk and yˆ ik are respectively the observations and observation forecasts, i the ensemble member, and Ne the number of ensembles. The above described ensemble statistics can be used to verify whether two conditions are met (Talagrand et al., 1997; De Lannoy et al., 2006): (1) the difference between the ensemble mean and the observation equals the average ensemble spread over time, that is, ensk ≈ 1, ensp

(16)

where . indicates an average over time, and (2) the observation is statistically indistinguishable from an ensemble member, that is,

ensk Ne + 1 . ≈ √ 2Ne mse

(17)

A second way of evaluating the ensemble is through Talagrand (rank) histograms (Talagrand et al., 1997), which are a useful tool for determining the reliability of ensemble forecasts and for diagnosing errors in its mean and spread (Hamill, 2000). Talagrand histograms Table 4 The ensemble perturbations to model forcings and parameters. The standard deviation is given for a normal (N) or lognormal (LN) distribution. The perturbations were either applied daily to each new model forcing or once at the beginning of the run. Variable

Standard deviation

Distribution

Frequency

Precipitation (mm) Net radiation (W/m2 ) Air temperature (◦ C) VOD (dimensionless) LAI (m2 /m2 ) Residual soil moisture (m3 /m3 ) Wilting point (m3 /m3 ) Field capacity (m3 /m3 ) Saturation (m3 /m3 )

0.5 0.3 0.1 0.1 0.2 0.2 0.2 0.2 0.2

LN N N N N N N N N

Daily Daily Daily Daily Daily Once Once Once Once

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are generated by repeatedly tallying the rank of an observation relative to the ensemble forecasts, sorted from low to high. A reliable ensemble is usually defined by a uniform histogram. A u-shaped histogram indicates a lack of variability in the ensemble, whereas the opposite is designated by an n-shaped histogram. L- and J-shapes are indicators of biased observations and forecasts.

of 0.57 dB (Figa-Saldaña et al., 2002) per azimuth beam. As the s ◦ data were averaged across the azimuth triplet, sR was adjusted with the simplified assumption of uncorrelated errors:

3.2. Data assimilation

with s∗R the observation error standard deviation for the tripletaverage s ◦ , and na the number of azimuth beams (=3). The resultant s∗R used for the data assimilation equals 0.33 dB. The error standard deviation of the SMOS TB observations was characterized as 6 K, according to De Lannoy and Reichle (2016). The relative simplicity of the model error characteristics (Section 3.1.4) and the observation error characteristics is similar to what was used in other studies (De Lannoy and Reichle, 2016). Clearly, the error characteristics specified here are not optimal, and more work is needed to refine them, which may increase the skill improvements achieved by the assimilation system. This work is, however, beyond the scope of the present paper.

3.2.1. The Ensemble Kalman Filter The data assimilation algorithm applied is the Ensemble Kalman Filter (EnKF, Evensen, 1994). The GLEAM state vector to be updated contains the soil moisture content of the first layer (SM1 ), as the observations of ASCAT and SMOS are sensitive to the surface SM content. The second and third layer SM is affected by the data assimilation only through the routing of first-layer SM through the profile by the GLEAM soil–water balance module. The filter is onedimensional, meaning that the SM state of a specific GLEAM grid cell is updated by an observation of s ◦ and/or TB corresponding to the same grid cell. The state vector is: i,f i,f xˆ k = SM1 k ,

(18)

where ˆ. indicates an estimate of the system state, i the ensemble member, f the model forecast, and k the time step. The relationship between the state variable (i.e. SM1 ) and the observation forecast (yˆ ik ) is commonly referred to as the observation system: i,f yˆ ik = hk (xˆ k ),

(19)

with hk the observation operator. For s ◦ assimilation, hk denotes the WCM, whereas for TB assimilation, it corresponds to L-MEB. At time steps for which both s ◦ and TB observations are available, hk includes both the WCM and L-MEB. The EnKF state update equation is given by:   i,f = xˆ k + Kk yk − yˆ ik + vik , xˆ i,a k

(20)

the analyzed (a) state variable for ensemble member i, and with xˆ i,a k Kk the Kalman gain. yk and yˆ ik are respectively the observations and observation forecasts, which can refer to s ◦ and/or TB, depending on the type of observation(s) to be assimilated. Finally, vik is a random realization of the observation error (Burgers et al., 1998). The Kalman Gain Kk in Eq. (20) is calculated from ensemble statistics (Reichle et al., 2002), which has been shown to perform better for a non-linear observation operator hk , compared to the explicit calculation through linearization of the observation system (Pauwels and De Lannoy, 2009). Accordingly, Kk is calculated as:    −1 f , Kk = Cov xˆ k , yˆ k Cov yˆ k , yˆ k + Rk

(21)

  f with Cov xˆ k , yˆ k the ensemble error covariance matrix between  the state variables and observation forecasts, Cov yˆ k , yˆ k the error covariance matrix between the observation forecasts, and Rk the observation error covariance matrix. Note that for the simultaneous assimilation of s ◦ and TB, off-diagonal components of Rk were set to zero, that is, observation errors in s ◦ and TB are assumed uncorrelated. The observation errors of ASCAT s ◦ and SMOS TB were defined with the simplifying assumption of being constant across the globe and over time (De Lannoy and Reichle, 2016). The observation error standard deviation (sR ) for ASCAT was derived from the radiometric accuracy requirement of the instrument, given by a maximum value

1 s∗R = √ sR , na

(22)

3.2.2. Bias correction The EnKF is designed for unbiased observations and forecasts, whereas in reality, biases prevail as the result of differences in representativeness, model shortcomings or observation flaws (Reichle et al., 2004; Wilker et al., 2006; Escorihuela et al., 2010; Sahoo et al., 2013; Al-Yaari et al., 2014a,b). Furthermore, biases in s ◦ and TB may vary seasonally, as they are impacted by vegetation conditions and surface temperature, both exposed to a strong seasonal cycle (De Lannoy and Reichle, 2016; Kornelsen et al., 2015). To remove seasonal biases, this study relied on historical records of ASCAT s ◦ observations (from the period 2008–2014), SMOS TB observations (from the period 2010–2014), and their corresponding WCM/L-MEB forecasts. For every grid cell, the seasonal dynamics of the forecasts and observations were first characterized by taking multi-year averages for each 7-day period of the year. The resulting yearly time series was smoothed by using a 31-day moving average filter, yielding a smooth seasonal cycle for the observations (yk )  ˆ k of s ◦ and TB. Finally, the corresponding seasonal and forecasts y cycles were subtracted from the observations and forecasts, to end up with observation and forecast anomalies that were used in the state update equation as (De Lannoy and Reichle, 2016):     i,f ˆ k + vik . xˆ i,a = xˆ k + Kk (yk − yk ) − yˆ ik − y k

(23)

Separate seasonal cycles were calculated for the ascending and descending orbits of the TB observations, given the different temperature regimes during both overpasses. This separation was not needed for TB simulations, as they relied on daily forcings, nor for s ◦ , which does not depend on temperature. It should be noted that this method corrects for seasonally-varying biases in the first-order moment (i.e. mean), while implicitly assuming that the second-order moment (variability) of the observations is represented by the forecasts (De Lannoy and Reichle, 2016). In addition, Yilmaz and Crow (2013) have shown that such rescaling of the second-order moment may not be justified, particularly at the level of TB, and by extension of s ◦ data. 4. Results 4.1. Model ensemble simulations GLEAM was run in open loop (OL) mode with 1 deterministic realization (no perturbations applied), and in ensemble (ENS) mode with 32 stochastic realizations (perturbations applied), to produce quasiglobal simulations of s ◦ and TB for the period 2007–2014, with the

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Fig. 1. The (a) mean ENS GLEAM–WCM backscatter (s ◦ , in dB) simulations, (b) corresponding ASCAT s ◦ (dB) observations, (c) their temporal correlation R (−) and (d) the ENS standard deviation (dB) of the simulations, averaged over the period 2010–2014.

year 2007 serving as the spin-up period of the model. The following results will only focus on the years 2010–2014, which is the overlap period of ASCAT and SMOS. It should be noted that the period for calibration of the WCM (2008–2011) partially overlaps with the period for validation (2010–2014). A 4-year calibration period was selected to prioritize reliable parameters, while at the same time, we attempted to maximize the validation period over which ASCAT and SMOS operate jointly. Although this violates the condition of an independent validation set, its impact is expected to be minor. Fig. 1 shows the time-mean s ◦ from the calibrated ENS model simulation, the corresponding ASCAT observations, their temporal correlation, and the averaged ensemble standard deviation of the

simulations. Note that for this comparison, simulations were only used over time steps with observations. The coupled GLEAM–WCM framework has large skill in simulating the long-term means of the ASCAT s ◦ observations. The global average bias (observations minus simulations) equals −0.040 dB, whereas the spatial patterns are almost identical. The global averaged temporal correlation between simulations and observations equals 0.633. High correlations (≈0.9) are observed across the Southern Hemisphere, except over tropical rainforest areas, such as the Amazon Basin, the Congo River Basin, and Southeast Asia, and over arid areas, such as the Simpson desert and Namibian desert. Correlations over the Northern Hemisphere are slightly lower, particularly in semi-arid and arid regions

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Fig. 2. The (a) mean ENS GLEAM–L-MEB brightness temperature (TB, in K) simulations, (b) corresponding SMOS TB (K) observations, (c) their temporal correlation R (−) and (d) the ENS standard deviation (K) of the simulations, averaged over the period 2010–2014.

in Mexico and densely forested areas in Southeast Canada. The lower correlations in (semi-)arid zones can be related to more challenging conditions for hydrological modeling. Besides, the backscattered power observed over dry areas is generally low, reducing the signalto-noise ratio of the observations. Also, volume scattering may occur in dry, loose sand (Dorigo et al., 2010), which is not accounted for by the WCM, and systematic orientation of sand ripples and dunes over large areas can lead to systematic azimuth biases in the observations (Bartalis et al., 2006). Dense forests on the other hand obscure the s ◦ contribution of the soil and yield stable vegetation s ◦ over time due to the usually small changes in vegetation conditions. Finally,

the simulated ensemble standard deviation, which is an indicator of the forecast error in the data assimilation, is fairly homogeneous, in the order of 0.3–0.4 dB for most parts of the globe, including tropical areas with tall vegetation, and (semi-)arid areas with low vegetation. Relatively larger variability up to 1 dB is found over temperate areas exposed to a larger ensemble variability in soil moisture with absence of tall vegetation. Fig. 2 illustrates the TB simulations and SMOS observations, their temporal correlation, as well as the average ensemble standard deviation. A large and systematic cold bias is present in the simulations, with an average value of 38.9 K over the globe. Only densely forested

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areas, such as the Southern Hemisphere tropical rainforests and forests in Eastern Canada, are accurately simulated in terms of average magnitude in TB. However, note that the impact of biases on the data assimilation is mitigated by the use of observation and forecast anomalies (Eq. (23)). More importantly, the correlation map in Fig. 2 highlights the skill of the model framework in simulating the temporal dynamics of the SMOS TB observations. The global average correlation equals 0.622, which is very similar to the correlation obtained for s ◦ . Relatively lower correlations are found in the tropics, where simulations and observations of TB display a high temporal stability. Conversely, the Northern Hemisphere reveals correlations in TB which are generally high compared to s ◦ . In contrast to s ◦ , the TB ensemble standard deviation varies significantly across the globe, from about 2 to 15 K (Fig. 2d). Relatively low ensemble variability is observed in areas with low or sparse

vegetation, such as Southwestern Australia, where the variability is mainly driven by variations in soil conditions. Variability increases with increasing vegetation density, as a consequence of uncertainty in LAI. A clear illustration is the gradient found across the Sahel from North to South. Finally, when vegetation saturates the TB, the variability decreases again, down to a level below that of bare soils. That is, uncertainties in LAI no longer impact the ensemble variability, while emissivity contributions from the soil are obscured by the dense vegetation. Hence, the remaining ensemble variability is mainly driven by uncertainties in physical temperature. The ensemble variability was evaluated based on two ensemble verification metrics and Talagrand histograms (see Section 3.1.4). Fig. 3 shows histograms of the verification metrics and Talagrand histograms for the s ◦ and TB ensembles, calculated over the 630 GLEAM grid cells for which in situ measurements of SM and/or E are

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Table 5 Validation metrics of the open loop (OL) and data assimilation (DA) simulations with respect to in situ measurements of soil moisture (SM) and evaporation (E), i.e. the correlation (R, dimensionless), the correlation of the anomalies (Ran , dimensionless) and unbiased RMSE (ubRMSE, in m3 /m3 for SM and mm/day for E). n denotes the number of in situ measurements, and 90%-CI are the 90%-confidence intervals averaged over the OL and DA experiments. Variable

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0.651 0.514 0.057 0.549 0.411 0.044 0.749 0.502 0.753

0.668 0.547 0.056 0.553 0.424 0.043 0.765 0.536 0.708

0.678 0.548 0.054 0.554 0.414 0.043 0.770 0.533 0.696

0.684 0.559 0.054 0.557 0.424 0.042 0.774 0.546 0.690

0.0033 0.0033 0.0002 0.0074 0.0064 0.0003 0.0083 0.0100 0.0072

available. Note that this evaluation was limited to the grid cells used for the validation to reduce computational efforts. Averaged across the 630 sites, the s ◦ and TB ensembles are near-optimal. The√optimal ensk

ensk ≈ 1, and √mse ≈ values of the verification metrics (that is, ensp  Ne +1 ◦ 2Ne = 0.718) are slightly overestimated for both the s ensemble (median values of 1.438 and 0.769) and the TB ensemble (median values of 1.425 and 0.767). Notwithstanding the near-optimal statistics averaged over the 630 sites, the spread of the histograms in Fig. 3 (a) to (d) indicates that, locally, the ensembles are not always well-behaved. The Talagrand histograms, shown in Fig. 3 (e) and (f), are close to uniform, suggesting reliable ensembles. Nevertheless, a considerable number of s ◦ and TB observations are still outside the ensemble envelope, as revealed by the high frequencies at ranks 1 and 33, which likely explains the overestimation of the verification metrics. These unenclosed observations may occur due to several reasons, e.g. simplifications and shortcomings in the LSM and RTM models, such as the negligence of volume-, or multiple/directional scattering effects, errors in the observations, or undetected frost/snow conditions. However, enclosing these observations by increasing the ensemble spread resulted in an amplified n-shape (data not shown), and is therefore not desirable.

4.2. Data assimilation Impacts on SM and E simulations were assessed, considering the assimilation of ASCAT s ◦ and/or SMOS TB observations. This allows for evaluating the skill of each type of observation individually, as well as their complementarity in improving model estimates. As a first test for evaluating the assimilation system, the statistics of the innovations (differences between observations and simulations in the assimilation run) were verified. In an ideal assimilation system, the innovations are characterized by zero bias and zero autocorrelation at time lag one. In this study, the innovations were characterized by mean biases of 0.052 dB for s ◦ and 0.040 K for TB, which are close to the ideal scenario. Mean autocorrelations were slightly larger than zero, i.e. 0.251 for s ◦ and 0.292 for TB, indicating that the model forecast and observation errors are less than optimal. Table 5 presents an overview of the average correlations (R), anomaly correlations (Ran ) and unbiased RMSEs (ubRMSE) over all in situ stations, along with their average 90% confidence intervals (CI), for the different assimilation experiments. The CIs were calculated with an effective sample size (Dawdy and Matalas, 1964; Draper et al., 2012), reducing the degrees of freedom, to account for autocorrelation in the SM and E time series. The calculation of SM and E anomalies was based on the same method as used for calculating anomalies of s ◦ and TB (Section 3.2.2). Overall, modest improvements in metrics were observed by assimilating either s ◦ or TB observations. The joint assimilation of s ◦ and TB performed slightly

better overall than the singular assimilation of either observation type. The first layer SM1 and E evidenced the largest improvements, with statistically significant increases in mean skill (increase in mean R and Ran and decrease in mean ubRMSE across all stations) for each assimilation experiment. For individual stations, a significant increase in Ran at the 10% level from the joint assimilation of s ◦ and TB was observed for 30% of the stations, both for SM1 and E. This relatively low amount of stations is partly due to the autocorrelated nature of SM and E time series, reducing the degrees of freedom, and thus increasing their standard error. Significant decreases in Ran were observed for only 3% of the SM1 stations, and for none of the E stations. A minor impact was found for the second layer SM2 , for which improvements in skill metrics were on the verge of significance. Note that the lower impact for SM2 may partly be due to its large depth interval and associated representativeness problems, and partly to the fact that no direct updating of this layer was performed. The assimilation impacts on SM1 are further examined for each of the in situ stations in Fig. 4. The Ran are shown in Fig. 4 (a), whereas (b), (c) and (d) illustrate the Ran for DA minus Ran for OL, for s ◦ , TB and joint assimilation, respectively. Generally, assimilation improvements (indicated in blue color) tend to be slightly larger in areas covered by short vegetation, and relatively smaller in forested areas (e.g. Eastern United States) and areas prone to (semi-)arid conditions (e.g. Southwestern United States). Deterioration (indicated in red color) is only observed in few locations. Overall, the impact of the assimilation is slightly more pronounced for TB. The joint assimilation of s ◦ and TB alleviated the negative impacts found over some stations when only one of both observation types was used, while further enhancing positive impacts over stations where assimilation of both s ◦ and TB were beneficial. Fig. 5 (a) shows a scatter plot of correlations between in situ SM measurements and ASCAT s ◦ observations versus correlations between in situ SM measurements and SMOS TB observations. The correlation metric is appropriate here because the relationship between SM and s ◦ (or TB) is nearly linear. The colors indicate the temporal mean LAI. This figure illustrates that correlations between in situ SM and L-band TB observations are generally higher than corresponding correlations with C-band s ◦ observations, at least for the sample of in situ stations used in this study. Recall that the latter mainly covers the Northern Hemisphere, and the USA in particular. The lowest correlations for both s ◦ and TB are associated with very low values of LAI found over (semi-)arid regions. As pointed out in Section 4.1, these could be explained by lower signal-to-noise ratios, or volume scattering in dry sandy soils. Also, the vertical mismatch between the in situ sensors and the actual sensing depth of the remote sensing observations may become more important, as SM in the top few centimeters may quickly evaporate or infiltrate to deeper layers in dry regions. Furthermore, the figure also reveals higher TB correlations compared to s ◦ for intermediate values (1–3 m2 /m2 ) of LAI, indicating that the L-band TB observations are less affected

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by vegetation for modest vegetation cover. Correlations for s ◦ and TB tend to converge only for low to intermediate LAI-values (0.5–1 m2 /m2 ). Note that this evaluation is limited to the specific sampling locations available for this study, whereas different results could be obtained in other areas. For instance, in situ measurements are unfortunately lacking over the most densely vegetated areas within the Southern Hemisphere tropical zones. Over these areas, Figs. 1 and 2 revealed relatively higher correlations between simulations and observations of s ◦ than TB, potentially indicating a higher sensitivity of s ◦ to SM. Fig. 5 (b) shows how the assimilation impact (Ran for DA minus Ran for OL) on SM simulations varies with respect to temporal mean LAI, with colors indicating the averaged correlations of s ◦ and TB against in situ SM. This figure demonstrates that assimilation impacts (either positive or negative) are mainly confined to areas with low

mean LAI, where soil scatter or radiance is not obscured by vegetation. Negative impacts associated with low LAI were mainly found over sites for which observations showed low (or even negative) correlations with SM measurements, which were generally located in (semi-)arid regions. The largest positive impacts were observed for sites with low LAI and high ( >0.5) correlations between observations and in situ SM measurements. Analogously to Figs. 4, Fig. 6 shows the Ran and assimilation impacts of s ◦ , TB, and joint observations, for land evaporation. The assimilation impact shows similar spatial patterns between the three different scenarios. For the joint assimilation scenario, deterioration is found only for 2 stations, corresponding to the sites with the largest development of vegetation (temporal mean LAI > 2.5), for which a positive impact on SM by the assimilation is not expected (see Fig. 5). The other 20 stations showed an improvement

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or status quo at least. Hence, our results indicate that evaporation estimates can be improved through the joint assimilation of s ◦ and TB observations.

5. Discussion 5.1. Model ensemble simulations Simulations of ASCAT s ◦ and SMOS TB were carried out by coupling GLEAM to the WCM and L-MEB, respectively. As the global simulation of ASCAT s ◦ is unprecedented, a calibration of WCM parameter values was needed due to the lack of representative values in the literature. The calibration led to an accurate simulation of the temporal mean s ◦ with negligible biases (0.040 dB on average). Conversely, the parameters of L-MEB were derived from the operational ESA Level 2 processor v5.5.1 (Kerr et al., 2012), and led to large biases (38.9 K on average) between simulations and SMOS observations. Several studies have already observed large systematic cold biases in TB simulations when relying on similar parameter sets. For instance, De Lannoy et al. (2013) observed biases against SMOS observations of 10–50 K at the global scale, whereas Lievens et al. (2015a) evidenced a mean bias of 30 K over the Upper Mississippi Basin. Key to the occurrence of bias is the model climatology of the SM simulations that are used as input to the RTM. Several studies have found model simulations to be systematically wetter compared to SMOS retrievals (Al-Yaari et al., 2014a,b). Such wet model bias will propagate into a cold TB bias when relying on the RTM parameters employed by the SMOS processor. Accordingly, a rescaling of the model SM to the climatology of SMOS retrievals prior to input-use in the RTM was found to reduce the mean bias in TB from 30 K to 5 K (Lievens et al., 2015a). In this study, part of the biases induced by SM could be related to the adopted layer depths in GLEAM. More specifically, first-layer GLEAM simulations represent the top 10 cm, whereas SMOS observations are representative of the top few (3–5) centimeters only (Escorihuela et al., 2010), and may thus have a different climatology (e.g. faster dry out). Note that besides SM, other inputs to the RTM or sources of auxiliary information, such as LAI, temperature, or cover fractions, may similarly affect biases in TB. The fact that SM and other auxiliary inputs to the RTM may be biased raises the important question whether use of the ESA Level 2 processor parameters in coupled systems for TB simulation is still justified. Alternatively, RTM parameters, such as the surface roughness h, can be calibrated for better matching the SMOS observations. Generally, calibration studies obtained h-values that are higher and

more dynamic, in the range of 0.1–1.7 (Saleh et al., 2009; Pardé et al., 2011; Renzullo et al., 2011; De Lannoy et al., 2013; Martens et al., 2015; Parrens et al., 2016), compared to those of the ESA Level 2 processor (0.1–0.3). Although the use of calibrated h-values may reduce the long-term bias between simulations and observations of TB, it may also reduce the sensitivity of the TB simulations to SM, as the latter is known to decrease for higher values of h (De Lannoy et al., 2013). In order to preserve the model sensitivity and avoid the introduction of compensation effects due to different SM climatologies and input variables in the h-parameter, we refrained from calibrating the RTM. Instead, TB biases were mitigated by assimilating observation anomalies rather than actual observations. 5.2. Data assimilation The assimilation of ASCAT s ◦ and SMOS TB was found to result in modest but consistent improvements in simulations of surface SM. Averaged across all in situ stations, the increase in skill was statistically significant (at the 10% confidence level), whereas for individual stations, significant improvements were obtained in 30% of the cases. These results are generally in line with the impacts of data assimilation found in literature. Draper et al. (2012) evaluated the assimilation of ASCAT and AMSR-E SM retrievals, either individually or jointly, and found improvements in anomaly correlation of surface SM from 0.47 to 0.56 by the assimilation of ASCAT or AMSRE, and to 0.57 by the assimilation of both, for in situ stations of the SCAN and SNOTEL networks in the USA and OzNET in Australia. Note that the skill after assimilation obtained by Draper et al. (2012) is very similar to the one obtained in this study (Ran = 0.559) by jointly assimilating ASCAT s ◦ and SMOS TB, whereas the skill of the open loop was lower (Ran of 0.47 in Draper et al. (2012) versus 0.514 in this study). De Lannoy and Reichle (2016) showed a larger improvement (increase in Ran of 0.12) by assimilating multi-angular/polarization SMOS TBs. The impact of the assimilation on the second layer SM is only minor in this study, with a maximum increase in Ran from 0.411 to 0.424 averaged across all stations. This impact (increase in Ran of 0.013) is considerably lower than those observed by Draper et al. (2012) and De Lannoy and Reichle (2016), who reported increases in Ran of 0.11 and 0.05, respectively. These larger skill increases compared to the present study may be due to the selection of the in situ stations, as the evaluation of the assimilation is influenced by the quality of the in situ measurements, the development of vegetation, and the occurrence of frost, snow and topographic complexity, amongst others. Also, improvements may be limited because the in

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situ stations are disproportionally located in areas of high-quality rainfall forcing. A second — perhaps more important — reason for the more modest skill improvements in the present study may be related to the setup of the model and data assimilation framework. GLEAM simulates SM for the surface layer (0–10 cm) and second layer (10–100 cm) based on a simple conceptual soil-water balance (Martens et al., 2016b). In this study, only the surface SM was included in the EnKF state-update equation, through which the impact of the assimilation on second layer SM is merely due to updates at the surface that are routed through the profile. Including the second layer SM in the update equation deteriorated the performance of the simulations by increasing the dynamics compared to in situ measurements (data not shown). The latter is arguably due to the large depth increment between the first and second layer, in combination with the

simplicity of the soil–water balance. It is therefore likely that the model and assimilation framework would benefit from a smoother transition between surface and deeper layers, e.g. by adding layers to the profile, and/or by a more physically-based description of moisture distribution through the profile. However, as mentioned in Section 3.1.1, the overall objective of GLEAM is to present a simple observation-driven method tailored to the accurate estimation of land evaporation. Notwithstanding the minor impact of the assimilation on the second layer SM, the simulations of evaporation improved significantly, with an increase in Ran for the joint assimilation from 0.502 to 0.546, averaged across all 22 FLUXNET stations. Previously, Peters-Lidard et al. (2011) observed mixed results by the assimilation of AMSRE soil moisture retrievals, with either improvement or status-quo depending on the retrieval product type. After assimilating SMOS

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retrievals over continental Australia, Martens et al. (2016a) observed a minor impact on estimates of evaporation. In this context, the results of this study are promising, as they highlight the potential of microwave observations to improve evaporative flux estimates as a consequence of improvements in SM simulations. However, future research should investigate if larger improvements can be obtained by revising the model and assimilation system with respect to simulating and updating the SM profile. The results in Section 4.2 allow for evaluating the impact of assimilating ASCAT s ◦ and SMOS TB observations, either separately or jointly. Nevertheless, care should be taken when directly comparing assimilation systems, as their performance may be subject to the level of optimization applied to each of the systems. Although the L-band TB observations were found to be more sensitive to surface SM compared to C-band s ◦ (Fig. 5), the assimilation of the latter performed almost equally well (Table 5). It is hypothesized that the relatively lower sensitivity of s ◦ is offset by the larger number of observations (900 for s ◦ versus 600 for TB over 2010– 2014 averaged across all stations), which might be caused by a more stringent filtering (e.g. of RFI) and the narrower swath width of SMOS. Given that this study only used the H-polarized SMOS observations at the nominal 42.5◦ incidence angle, it is worth noting that the skill of TB assimilation may potentially be improved by extending the assimilation system to accommodate multi-angular/polarization observations (De Lannoy and Reichle, 2016). Finally, it is clear from Table 5 and Figs. 4 and 6 that the joint use of s ◦ and TB leveraged the performance of the assimilation. Besides increasing the number of observations and consequent state updates, the joint assimilation alleviated negative impacts found over some stations for a specific type of observation, while enhancing positive impacts over others.

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and resolution of hydrological estimates, and, by extension, that of numerical weather predictions. Acknowledgment The study is performed in the framework of the HYDRAS+ project (SR/00/302) financed by the Belgian Science Policy (BELSPO), and the ESA ’s Support To Science Element SMOS+ET II project (IPL-POE2015-723-LG-cb-LE). Hans Lievens is a postdoctoral research fellow of the Research Foundation Flanders (FWO). Rolf H. Reichle was supported by funding for the SMAP Science Team. Diego G. Miralles acknowledges the financial support from The Netherlands Organization for Scientific Research through grant 863.14.004. The SMOS data were obtained from the “Centre Aval de Traitement des Données SMOS” (CATDS), operated for the “Centre National d’Etudes Spatiales” (CNES, France) by IFREMER (Brest, France). The authors would like to thank the principal investigators of the International Soil Moisture Network (ISMN). This work used eddy-covariance data acquired and shared by the FLUXNET community, including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, TERN OzFlux, TCOS-Siberia, and USCCC. The FLUXNET eddy-covariance data processing and harmonization was carried out by the ICOS Ecosystem Thematic Center, AmeriFlux Management Project and Fluxdata project of FLUXNET, with the support of CDIAC, and the OzFlux, ChinaFlux and AsiaFlux offices. GLEAM description and data can be found at www.gleam.eu. We thank the Associate Editor and reviewers for their valuable contribution to this paper.

Appendix A. FLUXNET in situ stations 6. Conclusion The potential of microwave remote sensing observations is investigated with respect to improving estimates of GLEAM soil moisture and land evaporation via data assimilation at the quasi-global scale. Two types of observations were studied, i.e. active radar backscatter s ◦ data from ASCAT and passive radiometer brightness temperature TB data from SMOS, distinguishing between three different scenarios: (1) assimilation of s ◦ , (2) assimilation of TB, and (3) joint assimilation of s ◦ and TB. The corresponding improvements were assessed by comparison to in situ soil moisture measurements from the ISMN and evaporative flux measurements from FLUXNET. This study demonstrates that s ◦ observations, to date being unexplored in the frame of land data assimilation, have an equal potential to improve the skill of model simulations of surface soil moisture (Ran increased from 0.514 to 0.547) and land evaporation (Ran increased from 0.502 to 0.536) compared to TB observations (corresponding increases to 0.548 and 0.533). The joint assimilation of s ◦ and TB exploits the relative merits of both types of observations, which further increased the skill to Ran = 0.559 for surface soil moisture and Ran = 0.546 for evaporation. Hence, this study suggests a better performance when combining active and passive remote sensing observations in a data assimilation framework. The contribution of radar backscatter data assimilation to the skill of hydrologic model simulations may have important implications for future land data assimilation studies. A strong asset of some present and future radar missions, such as the Sentinel and Radarsat constellations, is their relatively high spatial resolution, compared to passive microwave observations. Therefore, assimilating backscatter observations has not only the potential to improve the accuracy of simulations but also their level of spatial detail. Future research should thus shed light on how combining coarse-scale passive with fine-scale active microwave observations can enhance the quality

Table A1 List of FLUXNET stations, together with their IGBP land cover, spatial location, and official reference or primary investigator. Station

Land cover

Latitude (◦ )

Longitude (◦ )

Reference

AR-Vir Arcturus AU-ASM AU-Cpr AU-DaP AU-DaS AU-Dry AU-Emr AU-GWW AU-RDF AU-Rig AU-Stp AU-Wom AU-Ync US-ARM US-Ha1 US-SRM US-Ton US-Var US-Whs US-Wkg ZA-Kru

ENF CRO OSH SAV GRA SAV SAV GRA SAV WSA GRA GRA EBF CRO CRO DBF WSA WSA GRA OSH GRA SAV

−28.24 −23.86 −22.28 −34.00 −14.06 −14.16 −15.26 −23.86 −30.19 −14.56 −36.65 −17.15 −37.42 −34.99 36.61 42.54 31.82 38.43 38.41 31.74 31.74 −25.02

−56.19 148.47 133.25 140.59 131.32 131.39 132.37 148.47 120.65 132.48 145.58 133.35 144.09 146.29 −97.49 −72.17 −110.87 −120.97 −120.95 −110.05 −109.94 31.50

Gabriela Posse Schroder (2014) Cleverly (2011) Calperum Tech (2013) Beringer (2013a) Beringer (2013b) Beringer (2013c) Ivan Schroder Craig Macfarlane Jason Beringer Beringer (2014) Beringer (2013d) Arndt (2013) Beringer (2013e) Fischer et al. (2007) Urbanski et al. (2007) Scott et al. (2009) Chen et al. (2007) Ma et al. (2007) Scott et al. (2010) Scott (2010) Bob Scholes

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