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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 54, NO. 1, JANUARY 2016

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Passive Microwave Remote Sensing of Soil Moisture Based on Dynamic Vegetation Scattering Properties for AMSR-E Jinyang Du, Member, IEEE, John S. Kimball, Member, IEEE, and Lucas A. Jones, Student Member, IEEE

Abstract—Accurate mapping of long-term global soil moisture is of great importance to earth science studies and a variety of applications. An approach for deriving volumetric soil moisture using satellite passive microwave radiometry from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) was developed in this study. Unlike the major AMSR-E retrieval algorithms that assume fixed scattering albedo values over the globe, the proposed algorithm adopts a weighted averaging strategy for soil moisture estimation based on a dynamic selection of albedo values that are empirically determined. The resulting soil moisture retrievals demonstrate more realistic global patterns and seasonal dynamics relative to the baseline University of Montana soil moisture product. Quantitative analysis of the new approach against in situ soil moisture measurements over four study regions also indicates improvements over the baseline algorithm, with coefficients of determination (R2 ) between the retrievals and in situ measurements increasing by approximately 16.9% and 41.5% and bias-corrected root-mean-square errors decreasing by about 25.0% and 38.2% for ascending and descending orbital data records, respectively. The resulting algorithm is readily applied to similar microwave sensors, including the Advanced Microwave Scanning Radiometer 2, and its retrieval strategy is also applicable to other passive microwave sensors, including lower frequency (L-band) observations from the National Aeronautics and Space Administration Soil Moisture Active Passive mission. Index Terms—Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E), passive microwave remote sensing, single scattering albedo, soil moisture.

I. I NTRODUCTION

S

OIL moisture is a crucial hydrosphere state variable governing land surface evapotranspiration and energy and carbon transfer between the soil and atmosphere [1]. Accurate mapping of soil moisture and its spatial–temporal variations is of great significance to scientific studies on global water, energy, and carbon cycles, as well as operational applications, including flood and drought monitoring, water resources man-

Manuscript received March 24, 2015; revised June 22, 2015; accepted July 24, 2015. This work was supported by the National Aeronautics and Space Administration Science of Terra and Aqua Program under Grant NNX11AD46G. The authors are with the Numerical Terradynamic Simulation Group, College of Forestry and Conservation, University of Montana, Missoula, MT 59812 USA (e-mail: [email protected]; [email protected]; lucas@ ntsg.umt.edu). Digital Object Identifier 10.1109/TGRS.2015.2462758

agement, and crop yield forecasts [2]–[5]. With the development of remote sensing techniques during the past decades, efforts have been made to retrieve large-scale soil moisture information from satellite observations, particularly those acquired by active/passive microwave sensors [6], [7]. In particular, the ESA Soil Moisture and Ocean Salinity (SMOS) mission and the NASA Soil Moisture Active Passive (SMAP) mission are equipped with L-band sensors designed for soil moisture mapping and are expected to provide global soil moisture retrievals with significant improvements in both accuracy and spatial resolution [1], [8]. Meanwhile, microwave emissions from the earth surface at C-band, X-band, and higher frequencies have been measured routinely for more than a decade from spaceborne instruments such as the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E), which was operational from June 2002 to October 2011 [9], [10], the WindSat passive microwave radiometer, operating since 2006 [11], and the Advanced Microwave Scanning Radiometer 2 (AMSR2) on board the JAXA Global Change Observation Mission 1st-Water satellite, operating since May 2012 [12]. The relatively high-frequency instruments are not optimum for soil moisture monitoring, but their longterm measurements provide valuable opportunities for studying climatic trends and associated impacts to hydrologic and ecological systems [13]; associated efforts for retrieving land surface parameters, including soil moisture, also contribute to our understanding of microwave radiative transfer processes for solving remote sensing inversion problems. The total microwave signal from vegetated soil received by a spaceborne radiometer consists of contributions from a number of emission sources, including cosmic background, atmosphere, vegetation, soil, snow (when present), and water bodies within the sensor footprint [14], [15]. The importance of each emission source can be weighed by considering the penetration ability of the particular microwave frequency being used. For soil moisture inversion problems using C- or X-band observations from AMSR-E, vegetation effects need to be carefully accounted for before reliable soil moisture estimation can be obtained. However, this is difficult when referring to global soil moisture inversion since, for the given sensor configurations, 1) vegetation extinction and scattering properties are determined by complex physical and geometrical properties of leaves, stems, and branches, including their dielectric values, geometric dimensions, density, and distributions [16]–[18]; 2) vegetation properties are spatially and temporally variant due to factors such as vegetation type and condition, growth

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stage, climate, terrain, and human/natural disturbances; and 3) microwave emissions from vegetation may undergo complex scattering processes inside the vegetation canopy and at the vegetation–soil interface [17]. In practice, vegetation effects are normally represented by various simplifying modeling schemes and assumptions regarding complex vegetation emission/scattering processes that enable global soil moisture retrievals. For example, the well-known single-channel algorithm approach employs a simple vegetation correction using an empirical estimation of microwave optical thickness from vegetation water content [19], [20]. Alternatively, several other algorithms, including the NASA standard soil moisture inversion algorithm, the JAXA standard soil moisture algorithm, and the land parameter retrieval model, use polarization ratios of AMSR-E channel brightness temperatures to account for intervening vegetation effects on soil moisture retrievals [9], [10], [15], [21], [22]. All of these approaches focus on the estimation of vegetation optical thickness while assuming negligible or constant vegetation scattering [15]. The constant scattering albedo assumption simplifies the soil moisture inversion problem, but is not fully consistent with theory and ground observations. Vegetation has a large potential range of single scattering albedos based on theoretical simulations, where scattering albedo is dynamic and varies with changes in scatterer physical and geometric properties, including canopy biomass [16]–[18]. Ground-based measurements also indicate that scattering properties vary with vegetation type and growth stages [23]–[25]. In this paper, vegetation scattering properties were evaluated based on AMSR-E brightness temperature (Tb ) observations and in situ soil moisture measurements. An enhanced soil moisture inversion algorithm (henceforth referred to as the revised algorithm) that accounts for dynamic vegetation scattering properties was then implemented in this study using AMSR-E multifrequency Tb observations based on the previously established University of Montana (UMT) soil moisture retrieval algorithm (henceforth referred to as the baseline algorithm) [26].

II. DATA P ROCESSING AND S TUDY S ITES A. AMSR-E Brightness Temperatures AMSR-E was operational on the NASA Aqua satellite from June 2002 to October 2011 [27]. Based on more than nine years of AMSR-E observations, a variety of global land parameter products, including surface soil moisture, have been developed from these data [15], [28]–[30]. Although AMSR-E ceased effective operations in October 2011 due to a failure of the rotational antenna spin mechanism, the accumulated global Earth observations and associated land parameter retrieval products from the sensor are still of great value for understanding microwave radiative transfer processes and supporting science investigations involving mechanisms of global water circulation and climate impacts on ecosystems [31]–[35]. In particular, studies on AMSR-E soil moisture retrieval could also directly benefit science and algorithm development for similar followon missions, including AMSR2, SMOS, and SMAP. AMSR-E measures microwave emissions from the earth surface twice daily for descending/ascending orbital equatorial

crossings at 1:30 A . M ./P. M . local time, with vertically (V) and horizontally (H) polarized Tb retrievals at six frequencies (6.9, 10.7, 18.7, 23.8, 36.5, and 89.0 GHz) [27]. The sensor footprint varies with frequency, whereas the AMSR-E X-band (10.7-GHz) channel used for soil moisture retrieval in this investigation has a 51 km × 29 km footprint. We also employ AMSR-E Version 7 Tb swath data from Remote Sensing Systems that have been spatially resampled and reprojected to a 25-km-resolution global Equal-Area Scalable Earth Grid following previously established methods [36], [37]. Prior to further analysis, the gridded AMSR-E Tb data were subjected to a prescreening process to minimize effects from radio frequency interference, active precipitation, frozen conditions, and permanent ice and snow cover areas using an approach previously established for the UMT land parameter retrieval algorithm [26].

B. Data Sets From ISMN The International Soil Moisture Network (ISMN) (http:// www.ipf.tuwien.ac.at/insitu) is a centralized data hosting facility where in situ soil moisture measurements from operational and experimental monitoring networks worldwide are collected, harmonized, and made available to users [38]. The global distribution of the different soil moisture measurement networks encompasses a broad range of climatic and land cover conditions, as well as soil textures for global scale validation. The ISMN performed preprocessing and quality checks to ensure data consistency and reliability. In particular, for intercomparison and validation of different soil moisture inversion algorithms, 75 calibration sites and 75 other independent validation sites were selected worldwide for the round-robin activity carried out under the ESA Soil Moisture Climate Change Initiative (http://www.esa-soilmoisture-cci.org/). These sites have surface layer (< 10 cm) soil moisture measurements over the 2007–2011 study period, and the selection procedure ensures reliable and representative soil moisture data for a wide variety of vegetation conditions [39], [40]. Additional screening was conducted to select in situ measurement sites more representative of the overlying AMSR-E sensing footprint by examining correlations between H-polarized X-band brightness temperatures and collocated soil moisture measurements from the 75 calibration sites; these results showed 23 sites with correlations higher than 0.4 (absolute value of correlation coefficient), which were then selected for further analysis. For the selected sites, surface soil moisture was measured at 5-cm depth at 19 sites, 2 cm at two sites, 0–8 cm at one site, and 8 cm at one site. The spatial distribution of in situ calibration sites (see Fig. 1) represents five major global land cover types, including Evergreen Needleleaf Forest, Mixed Evergreen and Deciduous Forest, Open Shrubland, Grassland, Cropland, and mixed Cropland and Natural vegetation, as indicated in Fig. 1 by the MODIS global International Geosphere-Biosphere Programme (IGBP) land cover classification [41]. The calibration sites represent a wide range of vegetation conditions and are used to derive empirical formula for estimating vegetation scattering properties.

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Fig. 1. Spatial distribution of the selected (solid black circles) ISMN sites used for developing the revised UMT AMSR-E soil moisture retrieval algorithm; (solid white circles) independent validation site network locations are also denoted, whereas inset maps show detailed subregions surrounding the (white polygons) four soil moisture validation networks used in this study; background images represent the MODIS IGBP global land cover map.

C. Soil Moisture Measurement Network Ground measurements with spatial scales comparable with satellite observations have been used for validating satellite inversion algorithms [21]. In this paper, four globally distributed in situ soil moisture measurement networks were selected for evaluating the baseline and revised UMT algorithms. For this investigation, all available point measurements were averaged within a specific region and similar soil depth at the time closest to that of the AMSR-E overpass to represent regional soil moisture conditions for comparison against the collocated satellite retrievals. The soil moisture network sites used in this study are denoted in Fig. 1 and span a global range of climate and land cover conditions; these sites are also part of the larger ISMN [38]. The Little River (LR) and Little Washita (LW) soil moisture networks represent the U.S. Department of Agriculture Agricultural Research Service research watersheds [21]. The LR watershed (centroid 83.61◦ W, 31.65◦ N) is located in the southeast USA in Georgia. Approximately 36% of the LR watershed is forested, whereas the remaining areas include cropland (40%) and pasture (18%) [21]. The LR watershed has a humid climate with mean annual precipitation of 1203 mm [21]. The LW watershed is located in southwest Oklahoma (centroid 98.1◦ W, 34.95◦ N) and is dominated by rangeland

and pasture. The LW watershed is characterized by a subhumid climate with mean annual rainfall of 750 mm. More detailed descriptions of the LR and LW watersheds are provided elsewhere [21]. The LR and LW watersheds contain a distributed network of continuous soil moisture measurements at 5-cm depth and deeper soil layers that have previously been used for evaluating satellite-based soil moisture products from AMSR-E and SMOS [21], [42]. In this paper, a three-year (from 2003 to 2005) record of in situ soil moisture measurements from the LR and LW watersheds was used for analyzing the baseline and revised UMT retrieval algorithms. The Naqu (NQ) regional soil moisture network (centroid 91.875◦ E, 31.625◦ N) was also used in this study and is located within a 0.25◦ area of the Tibetan Plateau in western China. The NQ network was constructed and has been operated by the Institute of Tibetan Plateau Research of the Chinese Academy of Sciences since August 2010 [43], [44]. The NQ network consists of 56 stations continuously reading soil moisture and temperature at three nested spatial scales (1.0◦ , 0.3◦ , and 0.1◦ ) and four soil depths (0–5, 10, 20, and 40 cm). The monitoring region is characterized by the following: 1) high elevation, with stations located at about 4470–4950 m above sea level; 2) low vegetation biomass, with alpine grasslands covering 93% of the area; and 3) high soil moisture dynamic range caused by

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strong seasonal wetting from the South Asian summer monsoon [43]. The NQ soil moisture measurements at 0- to 5-cm depth and 0.3◦ spatial scale, and extending from August 2010 to September 2011, were used for validating the AMSR-E soil moisture algorithms in this study. The Murrumbidgee Soil Moisture Monitoring Network [45] consists of 38 stations distributed across the Murrumbidgee River Catchment in southern New South Wales, Australia (centroid 146.0915◦ E, 34.842◦ S). Each soil moisture station provides measurements of soil moisture at 0–5 cm (new sites) or 0–8 cm (old sites), 0–30 cm, 30–60 cm, and 60–90 cm every 20 min, as well as other related parameters, including soil temperature and rainfall. In this paper, we focused on the 34 km × 38 km Yanco subregion (abbreviated as YC), which is a semiarid agricultural and grazing area located in the western plains of the Murrumbidgee [46]. The YC has been used for previous airborne soil moisture field campaigns, including the National Airborne Field Experiment 2006 and the Soil Moisture Active Passive Experiments [47]. Two-year (year 2009–2010) data sets describing 0- to 5-cm-depth soil moisture conditions within the YC were selected for this study. III. M ETHODS A. Theoretical Basis 1) Tau–Omega Model: The zero-order radiative transfer model, also known as the Tau–Omega model [14], [48], has been widely used in microwave soil moisture retrieval studies [15]. The Tau–Omega model in the following equation describes the sensor observed microwave emissivity ep as a combination of upward radiation emitted directly from vegetation, upward radiation from underlying soil attenuated by vegetation, and downward radiation emitted from vegetation and reflected by underlying soil and further attenuated by vegetation:     ep = [1 − ωp ][1 − γp ] 1 + Rps γp + 1 − Rps γp γp = exp[−VODp ]

(1)

where the subscript p denotes microwave horizontal or vertical polarization, ω is the single scattering albedo, γ is the one-way transmissivity of the canopy, VOD is the slant path vegetation optical depth, and Rs is the effective reflectivity of bare soil. 2) Vegetation Scattering and Extinction Properties: In the Tau–Omega model, vegetation scattering and extinction properties are characterized by two parameters, i.e., VOD and the single scattering albedo. VOD is particularly sensitive to vegetation water content and has been estimated based on ancillary optical-IR remote sensing observations [19], [49] and from microwave observations at multiple polarizations or frequencies [50]–[53]. In particular, the VOD parameter is derived from multifrequency brightness temperatures as part of the baseline UMT AMSR-E land parameter algorithms and global database [28]; the resulting VOD estimate is derived using an iterative Tb retrieval algorithm that does not rely on optical-IR remote sensing or other ancillary inputs and has been successfully applied for a variety of ecosystem studies, including vegetation phenology and disturbance recovery [53], [54]. The VOD derivation used in baseline UMT algorithm was also applied in this study.

The single scattering albedo, i.e., ω, is another critical parameter in the Tau–Omega model. The ω parameter is conventionally defined as the ratio between the total scattering coefficient and the extinction coefficient of the unit volume of scatterers. The Tau–Omega model is generally valid when scattering is small relative to total extinction; ω is normally considered a small constant value for a given frequency (from L- to X-band), incident angle, and polarization in microwave forward and inverse problems [15]. However, based on electromagnetic theory and modeling [16]–[18], ω can vary significantly in relation to scattering media properties. For example, ω of a tree branch was found to be as high as approximately 0.6 at L-band frequency. Moreover, ω and the Omega–Tau model are actually influenced by multiple scattering effects, which increase at higher microwave frequencies, including AMSR-E Tb channels, and may be also significant for lower L-band frequency observations [17], [18], [55]. Therefore, the “effective scattering albedo,” which is denoted by ω ∗ , has been defined to distinguish from the more restrictive single scattering albedo concept and replace ω in the Omega–Tau model [55]. Here, ω ∗ is associated with single scattering but also parameterizes more complex vegetation scattering effects involving multiple scattering mechanisms and interactions between the canopy and the ground. The explicit form of ω ∗ and its theoretical derivation are described elsewhere [55]. ω ∗ has been found to vary according to vegetation conditions indicated from both ground observations and satellite observations, generally ranging from 0.0–0.12/0.13 [15], [56], which is much lower than the theoretical ω. Ideally, both VOD and ω ∗ should be accurately estimated as a precondition to obtaining reliable soil moisture retrievals. However, due to the large global range of vegetation conditions, the major AMSR-E soil moisture retrieval approaches, including the baseline UMT algorithm, prescribe ω as a constant value. The availability of long-term soil moisture measurements from coordinated regional monitoring networks overlapping with the AMSR-E record provides opportunities for evaluation and potential refinement of the scattering albedo assumption, particularly for moderately to densely vegetated areas. Another assumption commonly made in the Tau–Omega inversion algorithm is that both VOD and ω are polarization independent; this assumption has been verified using coarse scale Tb observations from spaceborne radiometers [57], and it is also applied in our study. B. UMT Baseline Soil Moisture Inversion Algorithm The UMT baseline AMSR-E soil moisture retrieval is derived using an iterative algorithm [26], [58], which uses H- and V-polarized 18.7- and 23.8-GHz brightness temperature data and several microwave indices to derive precipitable water vapor (PWV), surface temperature (Ts), and the fraction of open water inundation (fw) within the sensor footprint. With the estimation of the aforementioned parameters, VOD is retrieved by inverting the land–water emissivity slope index α, given in α=

(ev − ew v) (eh − ew h)

(2)

where ew p is the open water emissivity for V- or H-polarization and is considered constant, and ev is the satellite observed

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emissivity, defined as a weighted combination of the contributions from open water and land; α was found to be sensitive to vegetation and was therefore used to estimate VOD as formulated in   √ −B − B 2 − 4AC (3) VOD = −log 2A where

 d# A = (1 − ω) RVd# − αRH  d# d# d# ∗ B = αed# − e + (1 − ω ) αR − R + 1 − α H V H V w# C = (1 − ω ∗ )(α − 1) + ew# V − αeH .

The # term indicates predefined values for dry bare soil emisd# w# sivity ed# p or reflectivity Rp and open water emissivity (ep ), and ω ∗ is prescribed as a constant (0.06) [26]. The VOD parameter in the UMT algorithm also incorporates surface roughness effects [15], [26]. Based on the two steps above, smooth soil emissivity corrected for atmosphere, fractional open water, and vegetation effects can be estimated by inverting the Tau–Omega model. Soil moisture is then estimated using a theoretical polynomial function derived from the Dobson dielectric model for loamy soils [15]. C. Effective Scattering Albedo Estimation As discussed in Section III-A, unlike ω, which is only affected by vegetation properties and can be directly calculated from electromagnetic theory, estimation of ω ∗ is more complex since it accounts for multiple scattering effects from the land and soil surface reflectivity. In this investigation, we estimate ω ∗ by inverting the Tau–Omega model using accumulated AMSR-E observations and associated UMT land parameter products with in situ soil moisture measurements from a global set of regional station networks. According to (1), ω ∗ can be calculated as   o ep − ep ∗  ωp =  o ep − γp · esp eop = 1 − γp2 · Rps esp = 1 − Rps (4) where eo is the microwave emissivity when vegetation scattering effects can be neglected (or when ω ∗ = 0), and es and Rps here represent the emissivity and reflectivity from smooth bare soil since soil surface roughness effects are incorporated in the UMT VOD or transmissivity (γ) terms. Using (4), an effective scattering albedo data set (henceforth referred to as albedo database) was produced using the following inputs: ep calculated from AMSR-E X-band Tb observations and UMT land surface temperature retrievals, Rps calculated from surface soil moisture measurements at 23 ISMN monitoring stations (see Fig. 1) using the Dobson dielectric model, and γ derived from X-band microwave VOD estimates determined as part of the UMT land parameter retrievals. The resulting database provides the basis for examining spatial and temporal characteristics of ω ∗ at the level of a coarse (∼25-km resolution) AMSR-E grid cell and under variety of land parameter conditions. These results are used to evaluate the constant albedo assumption used

Fig. 2. (a) Relationship between the averaged effective scattering albedo and the vegetation optical thickness (VOD) at X-band with the sample population (N = 15 568) binned into five VOD subgroup levels. The X and Y coordinates of each point are the median of the range and the averaged albedo corresponding to that range within each VOD subgroup, respectively; error bars denote the standard deviation of the albedo values within each corresponding VOD subgroup. (b) Number of sample points for each VOD subgroup levels.

in the baseline UMT algorithms and the potential for using ω ∗ to improve soil moisture retrieval accuracy. The relationship between the X-band VOD derived from the baseline UMT algorithms and ω ∗ is shown in Fig. 2 using the albedo database with a total of 15 568 points grouped into five VOD ranges. The X and Y coordinates of each point in Fig. 2(a) are the median of the range and the averaged albedo corresponding to that range, respectively; error bars denote the standard deviations of the albedo values that belong to the corresponding VOD ranges. The results indicate a general quadratic relationship between VOD and ω ∗ , with most (99.8%) of the sampled albedo values below 0.12. ω ∗ generally increases at higher vegetation biomass and associated VOD levels, with albedo saturation at X-band VOD levels above approximately 1.75. Larger ω ∗ variability is found for lower VOD levels consistent with less vegetation biomass cover. To interpret these findings, two factors need to be considered: 1) vegetation scatterers with larger geometric dimensions and higher dielectric values are generally associated with higher single scattering albedo [16] and contribute to a higher value of ω ∗ ; and 2) more significant multiple scattering effects result in a larger portion

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Fig. 3. Soil moisture estimation errors caused by inaccurate albedo values (absolute albedo errors from 0 to ±0.03 at 0.01 intervals) under different VOD levels ranging from 0.00 to 1.25 at 0.25 intervals. The true soil moisture and albedo values are assumed to be 0.182 cm3 /cm3 and 0.03, respectively.

of the vegetation emission received by the sensor and have an equivalent effect of increasing total microwave vegetation emissions. Thus, multiple scattering tends to lower ω ∗ . Therefore, the final value of ω ∗ is balanced between scatterer properties and multiple scattering effects. For sparse vegetation, scatterer properties are dominant over multiple scattering effects, and a much larger range of ω ∗ is expected due to the large diversity of scatterer properties, including foliage size, shape and density, canopy water content, and dielectric values. As the VOD increases, multiple scattering effects become more significant and counteract increased scattering from vegetation. For very dense vegetation (e.g., VOD ∼ 2.5), multiple scattering effects are overwhelming, and ω ∗ tends to be saturated and relatively stable at approximately 0.06. This finding is also consistent with other independent studies that report similar albedo values over forested areas [59], [60]. Another issue to be considered is how ω ∗ affects the AMSR-E soil moisture retrieval accuracy. This was demonstrated by analyzing retrieval results from the baseline algorithm with erroneous albedo considered. Assuming respective soil moisture and albedo conditions of 0.182 cm3 /cm3 and 0.03, soil moisture estimation errors caused by inaccurate albedo values (absolute errors from 0.0 to ±0.03 at 0.01 intervals) were evaluated under different VOD levels ranging from 0.00 to 1.25 at 0.25 intervals. As illustrated in Fig. 3, underestimated albedo results in overestimation of soil moisture and vice versa. The absolute soil moisture estimation error is directly proportional to the absolute albedo error for a given VOD level. The soil moisture estimation error also increases exponentially at higher VOD levels for a given albedo error level. For example, an albedo error of 0.03 propagates to a soil moisture estimation error larger than 0.04 cm3 /cm3 under moderate to dense vegetation conditions (see Fig. 3). These results indicate that ω ∗ estimation is a significant error source for Tau–Omega model based soil moisture retrievals from satellite passive microwave remote sensing, whereas better representation of ω ∗ can lead to improved soil moisture accuracy. However, this is challenging since ω ∗ is affected by spatially complex and temporally dynamic vegetation properties and multiple scattering effects.

Fig. 4. Relationship between the “true” and estimated effective scattering albedo for (a) moderate vegetation biomass conditions (0.65 < VOD < 1.5; the number of sample points represented is 7867) and (b) dense vegetation biomass conditions (VOD > 1.5; the number of sample points represented is 7525). Diagonal line denotes a 1:1 relationship.

As discussed earlier and in [55], ω ∗ represents multiple surface scattering and ground–vegetation interactions. Therefore, ω ∗ can be described as a function of the satellite observed microwave reflectivity of vegetated soil: Rp = 1 − ep , which is calculated based on the AMSR-E observed Tb and associated land surface air temperature retrievals, and vegetation transmissivity γ calculated from the VOD retrievals, as shown in (1). By considering H-polarization only, the resulting empirical relationships for estimating ω ∗ at X-band (10.7 GHz) are derived based on the albedo database and expressed in the following for respective moderate and dense vegetation conditions: ω ˆ h∗ = 0.033 + 0.379Rh −0.212γh +5.010Rhγh −9.698Rhγh2 , if VOD > 1.5 (5) ω ˆ h∗ = 0.043 + 0.594Rh −0.199γh +1.564Rhγh −2.100Rhγh2 , if 0.65 < VOD ≤ 1.5 (6) where ω ˆ h∗ represents the estimated ωh∗ . As plotted in Fig. 4, ∗ ω ˆ h accounted for 65.8% and 80.9% (R2 ) of variability in the “observed” albedo values derived from the in situ soil moisture measurements, corresponding root-mean-square (RMS) differences of 0.009 (relative RMS difference 15.9%) and 0.004 (relative RMS difference 6.9%) for moderate (0.65 < VOD ≤ 1.5) to high (VOD > 1.5) vegetation biomass cover, respectively. Since ωh∗ has less impact on soil moisture retrieval accuracy

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Fig. 5. Histogram of emissivity difference between theoretically calculated and satellite observed emissivity at X-band and V-polarization for moderate vegetation biomass conditions (0.65 < VOD < 1.5), with normal distribution curve (mean 0.0048 and standard deviation 0.0057) overlaid.

for sparsely vegetated areas while VOD > 0.65 for the majority of points in the albedo database, no relationship for estimating ω ∗ is derived for sparsely vegetated soil conditions (VOD ≤ 0.65). Assuming the regression errors from (5) and (6) follow a normal distribution with mean 0.0 and standard deviation σ (equal to the above RMS difference in value), about 95% of the ωh∗ − 2σ, ω ˆ h∗ + 2σ]. “observed” ωh∗ values are within the range [ˆ Therefore, the previous empirical relationships described in (5) and (6) with known estimation errors provide a first-order estimation of ωh∗ and its value range. The next task is to select the best ωh∗ from the range [ˆ ωh∗ − 2σ, ω ˆ h∗ + 2σ]. D. Optimization of Effective Scattering Albedo An additional optimization process is needed to evaluate the possibility of the potential ωh∗ values so that one optimum ωh∗ used for soil moisture retrieval can be obtained. Different from the previous ωh∗ estimation process that mainly relies on X-band H-polarization observations, the optimization process is based on X-band V-polarized observations involving three steps: first, theoretically estimated V-polarized emissivity eˆv was calculated for the selected ISMN sites using “observed” ωh∗ from the albedo database, corresponding UMT baseline land surface parameters, and ISMN in situ soil moisture measurements with the assumptions ωv∗ = ωh∗ and γv = γh ; second, the theoretical distribution of estimation error of eˆv , which is denoted by εv , where εv = eˆv − ev , is evaluated. The estimation error εv actually reflects the overall uncertainties inherent in the satellite observations and the assumptions made in this study. Finally, the probabilities of a number of possible ωh∗ values within the range [ˆ ωh∗ − 2σ, ω ˆ h∗ + 2σ] are evaluated considering the theoretical distribution of εv . Specifically, eˆv is calculated using eˆv = [1 − ωh∗ ] [1 − γh ] [1 + Rvs γh ] + (1 − Rvs ) γh

(7)

and the corresponding εv is obtained for the selected ISMN sites. To analyze the εv distribution for moderate (0.65 < VOD≤ 1.5) vegetation conditions, the histogram of εv is plotted in Fig. 5 with the distribution of εv approximated by a normal distribution with mean of 0.0048 and standard deviation of 0.0057. Similarly, the distribution of εv for dense vegetation (VOD > 1.5)

is approximated by a normal distribution with mean of 0.0011 and standard deviation of 0.0038. The normal distributions describing εv serve as a tool to evaluate the probability of ωh∗ being within [ˆ ωh∗ −2σ, ω ˆ h∗ +2σ], since each ωh∗ value corresponds to one set of eˆv and εv . In practice, the range [ˆ ωh∗ −2σ, ω ˆ h∗ +2σ] is equally divided into n parts represented by n discrete values. ∗ = (ˆ ωh∗ −2σ)+δ·(2i−1), Taking the ith value, for example, ωh_i ∗ ∗ ±δ. where δ = 2σ/n, and ωh_i represents the small interval ωh_i ∗ ∗ To evaluate ωh_i , εv_i1 and εv_i2 corresponding to ωh_i + δ and ∗ ωh_i −δ, respectively, are calculated using (7) and the AMSR-E observed emissivity. Assuming εv_i1 < εv_i2 , Pi , which is the probability of εv in the interval εv_i1 < εv ≤ εv_i2 , can be calculated from the cumulative distribution function of the normal distribution as Pi = F (εv_i2 ) − F (εv_i1 ) and served as ∗ the weight of ωh_i . Finally, the optimized ωh∗ is obtained from n

∗ ωh_i · Pi i=1 ∗ ωh = . (8) n

Pi i=1

In the following subsection, the established relationships and optimization process for dynamic estimation of ω ∗ are used in place of the prescribed constant albedo in the baseline UMT algorithms to evaluate potential improvements in soil moisture retrieval accuracy. E. Revised UMT Soil Moisture Retrieval Algorithm The revised UMT algorithm is developed from the previous baseline algorithm with one important difference: the dynamic scattering albedo with a range of possible values is considered instead of a predefined constant. Here, ω ˆ h∗ is initially estimated based on (5) and (6). Then, the optimization process described in the previous subsection is iteratively carried out with ωh∗ adjusted sequentially within the range [ˆ ωh∗ − 2σ, ω ˆ h∗ + 2σ] at a step of 2δ or 4σ/n, where n is assigned as 10. The ωh∗ calculation is constrained to be ≥ 0.0. For sparse vegetation (VOD < 0.5), the initial ω ∗ is set as 0.06 and σ as 0.03, so that the commonly reported ωh∗ values from 0.0 to 0.12 can be examined; the εv distribution is assumed to be the same as for moderate vegetation conditions. Once the optimized ωh∗ is determined using (8), smooth soil emissivity for X-band H-polarization corrected for atmosphere, fractional open water, and vegetation effects can be estimated similar to the baseline UMT algorithm, and soil moisture is obtained based on Dobson dielectric model. Another revision over the baseline algorithm is the consideration of spatially variant soil texture instead of fixed soil properties in the previous forward Tb simulations and soil moisture inversion process. Global soil texture data obtained from the global soil properties database described in [61] are necessary for a rigid determination of soil moisture using dielectric models, although the impacts of this revision on algorithm performance are expected to be small. IV. R ESULTS AND VALIDATION A. Global Soil Moisture Distribution Characteristics From AMSR-E In order to evaluate the baseline and revised UMT soil moisture algorithms, general statistics of AMSR-E soil moisture

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Fig. 6. Statistical summary of AMSR-E daily soil moisture retrievals for a representative year (2007), including mean annual soil moisture, annual soil moisture range, excluding upper and lower 2.5 percentiles, and annual soil moisture standard deviation. (a), (c), and (e) are produced from the baseline UMT algorithm, whereas (b), (d), and (f) are from the revised UMT algorithm using a dynamic effective scattering albedo developed from this study, and (g) is the mean VOD at X-band for the year 2007, provided as a reference of the soil moisture retrieval uncertainties.

retrievals from the two algorithms over a representative year (2007) were evaluated, whereas the comparison results are summarized in Fig. 6. These results show the estimated global patterns of annual mean soil moisture conditions from the two

sets of retrieval algorithms. Both sets of retrievals show characteristically wet surface soil moisture conditions in northern high latitude areas as was also found in [7], with drier soil moisture extremes in deserts and semiarid regions, including

DU et al.: PASSIVE MICROWAVE REMOTE SENSING OF SOIL MOISTURE

the African Sahara and central and western desert regions of Australia. However, the soil moisture product developed from this study tends to have larger spatial and temporal dynamic ranges over the global domain; the revised algorithm also produces a more realistic spatial pattern, particularly over more densely vegetated areas, including central Africa and Southern China, where soil moisture tends to be underestimated from the baseline algorithm. The observed annual soil moisture ranges in Fig. 6 were computed by excluding the upper and lower 2.5 percentiles to avoid extreme conditions [15]. Both baseline and revised algorithm results share similar distribution patterns of the soil moisture ranges, although the baseline retrievals are associated with generally drier mean soil moisture conditions relative to the results from the revised algorithm. In particular, the baseline retrievals show larger soil moisture ranges but much lower mean values than the revised algorithm in the central USA; this implies that the baseline algorithm generally predicts drier soil conditions in the area but greater frequency of anomalous spikes in the soil moisture time series relative to the revised algorithm. The standard deviation maps in Fig. 6 illustrate the seasonal variation in estimated soil moisture conditions. Relatively large seasonal soil moisture variations are apparent in both products in regions with distinct wet and dry seasons, including the central USA, Southern Tibet, and India. However, in some areas, such as South America and Southeast Asia, temporal variations tend to be subdued in the baseline retrievals relative to the revised algorithm results, possibly due to soil moisture underestimation. Overall soil moisture from the revised algorithm has more reasonable spatial distributions and temporal dynamics over the global domain, and use of the adjustable albedo tends to avoid anomalous soil moisture spikes in the revised algorithm products. Soil moisture retrieval uncertainties from both algorithms are also related to vegetation biomass conditions since denser vegetation tends to obscure a larger portion of the underlying soil signal. Therefore, Fig. 6 should be interpreted cautiously, particularly for high VOD conditions [e.g., VOD > 1.7 as indicated in dark green and blue in Fig. 6(g)]. B. Comparisons Between AMSR-E Soil Moisture Retrievals and In Situ Measurements For quantitative comparisons, the baseline and revised soil moisture retrievals were compared with independent in situ soil moisture measurements across four regional station networks distributed globally (LW, LR, NQ, and YC) and summarized in Section II. The overall algorithm performance statistics for all four regions and all orbits are summarized in Table I, including bias, bias-corrected RMSE, and coefficient of determination (R2 ). The revised algorithm shows generally favorable performance over the global validation regions and overall higher accuracy than the baseline algorithm. For LW, NQ, and YC, soil moisture results from the revised algorithm corresponded well with the in situ measurements, with R2 values ranging from 0.506 to 0.755 and bias-corrected RMSEs from 0.037 to 0.059 cm3 /cm3 . Compared with the baseline, the revised

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algorithm produced a 5.6% to 34.4% increase in R2 correspondence and 11.9% to 77.4% reduction (0.008 to 0.127 cm3 /cm3 ) in bias-corrected RMSE differences. The revised algorithm, however, does not perform better than the baseline algorithm everywhere. Among all four site networks, LR is where both products agree well with the in situ measurements, whereas the baseline algorithm shows the best performance in ascending orbits. Considering the four site networks as a whole, the revised algorithm demonstrates improved performance, with R2 correspondence between the retrievals and in situ measurements increasing by approximately 16.9% and 41.5% and biascorrected RMSEs decreasing by about 25.0% and 38.2% for ascending and descending orbits, respectively. Incorporation of a dynamic ω ∗ term in the revised retrieval algorithm instead of the prescribed constant albedo used in the baseline algorithm appears to provide improved representation of vegetation scattering effects and more accurate soil moisture retrievals in relation to the independent in situ soil moisture observations. A major drawback of the revised algorithm is that the resulting soil moisture retrieval is biased from approximately −0.061 to 0.072 cm3 /cm3 depending on the validation sites analyzed. Uncertainties in the revised UMT algorithm may be due to one or more factors. First, soil moisture is estimated after other parameters such as land surface temperature and VOD are obtained; these parameters have been validated in independent studies [26], [54], but possible errors, including biases, in these parameters may lead to systematic deviations in the downstream soil moisture retrievals. Second, soil moisture records for each validation region were spatially averaged from multiple distributed point measurements within 0- to 5-cm depth, whereas the X-band AMSR-E retrievals are more sensitive to surface (∼0–1 cm) soil moisture conditions over the region; the inconsistency between satellite and ground measurements in horizontal scale and vertical soil depth could not be completely removed and may also contribute to the observed

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the baseline algorithm can be attributed to underestimation (overestimation) of ω ∗ . V. C ONCLUSION

Fig. 7. Comparison of in situ observed soil moisture and satellite estimated soil moisture with watershed bias corrected (from ascending AMSR-E orbits) produced from the UMT (a) baseline algorithm and (b) revised algorithm for Little River, USA; Little Washita, USA; Naqu, China and Yanco, Australia.

bias. Finally, the revised algorithm is limited in that it does not find the “true” albedo for the retrieval; instead, the albedo is optimized as the weighted average of a group of possible values by considering uncertainties inherent in the assumptions made in the algorithm and instrument measurements. The weighted average strategy is a compromise with albedo spatial and temporal complexity, as well as the limitations of coarse satellite measurements and simplifying model assumptions. Thus, errors cannot be completely eliminated in the retrieval approach. Nevertheless, the revised algorithm retrievals improved the overall performance in terms of better correlation and lower RMSE differences if site-specific bias corrections were applied. The overall relations between bias-corrected soil moisture retrievals from both algorithms and independent ground observations from the validation sites are shown in Fig. 7 for the AMSR-E ascending pass. The baseline soil moisture retrievals show generally lower correspondence and larger error across the global range of soil moisture observations than the revised algorithm results. Since both retrieval algorithms are largely consistent other than their use of a fixed or an adjustable albedo, soil moisture overestimation (underestimation) from

An approach has been developed in this study for global satellite estimation and monitoring of surface soil moisture from the AMSR-E sensor. The major difference between the revised algorithm and our previous study is that a weighted average strategy is adopted based on dynamic albedos instead of a fixed value, and this helps to account for variability in vegetation scattering properties. From this study, the following are found: 1) ω ∗ generally increases with VOD but tends to be saturated under higher vegetation biomass conditions since it is affected by both vegetation scatterer properties and multiple scattering effects; 2) soil moisture estimation errors caused by an inaccurate albedo exponentially increase with VOD, and an albedo error of 0.03 can lead to soil moisture retrieval error larger than 0.04 cm3 /cm3 for moderate to dense vegetation conditions; 3) empirically estimated albedos are well correlated with those derived based on ground soil moisture measurements, with R2 of 65.8% and 80.9% for respective vegetated conditions ranging from 0.65 < τ ≤ 1.5 to τ > 1.5; and 4) based on the weighted average strategy that considers a range of possible relative scattering albedos, soil moisture retrievals from the revised algorithm are improved relative to previous studies, including more realistic soil moisture spatial patterns and seasonal dynamics over the global domain. Quantitative analysis also indicates improved soil moisture performance from the revised algorithm in four global validation regions, with R2 agreement between retrievals and in situ measurements increasing by approximately 16.9% and 41.5% and biascorrected RMSEs decreasing by about 25.0% and 38.2% for the ascending and descending orbits, respectively. However, significant biases (about −0.061 to 0.072 cm3 /cm3 ) are also found in the revised algorithm soil moisture retrievals. The revised algorithm described in this study represents an improvement over the baseline UMT soil moisture product. Continuing efforts to improve the AMSR-E retrieval algorithms are still valuable since the improved retrieval record facilitates better detection and understanding of environmental changes and hydrological and ecological processes. Moreover, this study provides insight into general microwave remote sensing challenges common to other microwave Earth observation missions, including AMSR2, SMOS, and SMAP. ACKNOWLEDGMENT This work was conducted at the University of Montana. The AMSR-E data used in this study are produced by Remote Sensing Systems and sponsored by the NASA Earth Science MEaSUREs DISCOVER Project and the AMSR-E Science Team; the data are available at www.remss.com. AMSR-E data were also provided courtesy of the National Snow and Ice Data Center. The Naqu soil moisture and soil temperature data set used in this study was provided by the Data Assimilation and Modeling Center for Tibetan Multi-spheres, Institute of Tibetan Plateau Research, of the Chinese Academy of Sciences.

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Jinyang Du (M’10) received the Ph.D. degree in geographic information systems and cartography from the Institute of Remote Sensing Applications, Chinese Academy of Sciences, Beijing, China, in 2006. From 2006 to 2007, he was a Visiting Scientist with the Hydrology and Remote Sensing Laboratory, Agricultural Research Service, U.S. Department of Agriculture, Beltsville, MD, USA. He is currently a Research Scientist with the Numerical Terradynamic Simulation Group, University of Montana, Missoula, MT, USA. His research interests include microwave modeling of vegetation, soil and snow signatures, and inversion models for retrieving land surface parameters from remote sensing data. Dr. Du is a member of the American Geophysical Union and the IEEE Geoscience and Remote Sensing Society.

John S. Kimball (M’07) received the Ph.D. degree in bioresource engineering and geosciences from Oregon State University, Corvallis, OR, USA, in 1995. He is currently a Professor of systems ecology with the University of Montana, Missoula, MT, USA. His research interests include integration of ecological theory with satellite remote sensing for better understanding terrestrial ecosystem structure and function, from single plot to global scales. He is a member of the NASA Soil Moisture Active Passive Mission and EOS MODIS and AMSR-E Science Teams and is working toward improved measurement and monitoring of global carbon and water cycles through synergistic use of biophysical process models and satellite remote sensing.

Lucas A. Jones (S’06) received the M.S. degree in remote sensing and forest ecology from the University of Montana, Missoula, MT, USA, in 2007. He is currently working toward the Ph.D. degree in the Numerical Terradynamic Simulation Group, University of Montana. He is also currently a Research Scientist with the Numerical Terradynamic Simulation Group, University of Montana. He was a NASA Earth System Science Fellow from 2010–2013 and conducts research for the AMSR-E and SMAP Science Teams. His research addresses global land carbon and water cycle questions by fusion and uncertainty estimation of land parameters from microwave remote sensing with land surface models. Mr. Jones is a member of the American Geophysical Union and the IEEE Geoscience and Remote Sensing Society.