Simultaneous retrieval of global scale Vegetation Optical Depth, surface roughness, and soil moisture using X-band AMSR-E observations

Remote Sensing of Environment 234 (2019) 111473

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Simultaneous retrieval of global scale Vegetation Optical Depth, surface roughness, and soil moisture using X-band AMSR-E observations

T

L. Karthikeyana,b,c,∗, Ming Panb, Alexandra G. Koningsd, María Pilese, Roberto Fernandez-Morane, D. Nagesh Kumarc, Eric F. Woodb a

Centre of Studies in Resources Engineering, IIT Bombay, Powai, Mumbai, India Department of Civil and Environmental Engineering, Princeton University, New Jersey, USA c Department of Civil Engineering, Indian Institute of Science, Bangalore, India d Department of Earth System Science, Stanford University, Stanford, USA e Image Processing Lab (IPL), Universitat de València, Valencia, Spain b

ABSTRACT

The radiative transfer scheme implemented for the retrieval of soil moisture from passive microwaves is a function of scattering, polarization mixing and attenuation effects of soil and vegetation. Theses factors are usually represented by Vegetation Optical Depth (VOD), vegetation scattering albedo, and surface roughness parameter, along with soil moisture. The VOD is the degree to which vegetation attenuates the microwave radiation. It has generally the dominant effect from vegetation, whereas scattering is negligible and close to zero. The surface roughness (which varies in space but not much in time) is until recently, often assumed to be a global constant. In this work, we attempted to simultaneously retrieve the VOD, the surface roughness parameter, and the soil moisture at the global scale using the Level 3 daily 0.25° X-band brightness temperatures of the Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) sensor. The methodology, coined as the Simultaneous Parameter Retrieval Algorithm (SPRA), is based on the premise that the vegetation dynamics undergo slower temporal changes than the soil moisture - an assumption, which is successfully used in the past for microwave radiometric retrievals at lower frequencies. Results indicate that the SPRA produces the VOD retrievals with reduced high-frequency noise when compared to the baseline Land Parameter Retrieval Algorithm (LPRM) retrievals. This effect assisted in identifying the influence of precipitation and cropping patterns on the temporal dynamics of the VOD. Good agreement is observed between the mean SPRA VOD and canopy height data (global correlation = 0.75). The spatial patterns of surface roughness parameter agree well with the roughness product (HR map) developed using Soil Moisture Ocean Salinity (SMOS) sensor based data (global correlation = 0.57). Validation of SPRA and LPRM soil moisture products with in-situ observations over the Contiguous United States (CONUS) indicated an improvement in mean ubRMSE with SPRA product (SPRA-0.11 m3/m3 and LPRM-0.18 m3/m3) and comparable mean Pearson correlations between the two products (SPRA-0.36 and LPRM-0.38). Further, a precipitation based consistency evaluation of SPRA and LPRM soil moisture retrievals indicated better skill of the SPRA product over India.

1. Introduction Knowledge of global hydrological, energy, and carbon cycles, along with their interactions, is essential for climate and Earth system studies. In this process, satellite remote sensing, particularly using passive radiometers, has immensely supported the researchers over the years. Soil moisture, due to its presence at the land-atmosphere interface, is an essential variable for modeling these processes. Over the past four decades, research in microwave remote sensing has made significant strides towards obtaining accurate soil moisture information at global scales (Karthikeyan et al., 2017b). Improved knowledge of soil moisture leads to a better understanding of the occurrence of precipitation (Koster et al., 2004; Tuttle and Salvucci, 2016), variability of air temperature (Schwingshackl et al., 2017), and an improved modeling of heatwaves (Hauser et al., 2016), droughts (Luo and Wood, 2007) and

∗

floods (Grillakis et al., 2016). The passive microwave remote sensing of soil moisture involves a retrieval algorithm, that converts satellite brightness temperatures (TB ) to surface soil moisture as a function of the location specific surface properties. Currently, NASA's Soil Moisture Active Passive (SMAP), ESA's Soil Moisture Ocean Salinity (SMOS) and JAXA's Advanced Microwave Advanced Microwave Scanning Radiometer 2 (AMSR2) satellite missions are operational in the domain of passive microwave sensors, which have the ability to obtain soil moisture at the global scale. The past missions that had the ability to retrieve soil moisture include Scanning Multichannel Microwave Radiometer (SMMR), Special Sensor Microwave Imager (SSM/I), Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), WindSAT, Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E), and Aquarius missions. In the context of these missions, several

Corresponding author. Centre of Studies in Resources Engineering, IIT Bombay, Powai, Mumbai, India. E-mail addresses: [email protected], [email protected] (L. Karthikeyan).

https://doi.org/10.1016/j.rse.2019.111473 Received 6 April 2019; Received in revised form 11 September 2019; Accepted 12 October 2019 0034-4257/ © 2019 Elsevier Inc. All rights reserved.

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retrieval algorithms are proposed in the literature (Bindlish et al., 2003; Drusch et al., 2001; Feldman et al., 2018; Kerr et al., 2012; Koike, 2013; Konings et al., 2016; Li et al., 2010; Njoku and Chan, 2006; Njoku and Li, 1999; O'Neill et al., 2018; Owe et al., 2008; Pan et al., 2014; Wigneron et al., 2007). These algorithms vary among themselves in terms of the inherent assumptions and the manner in which the ancillary information is provided/estimated. Readers may refer to Karthikeyan et al. (2017a), Mladenova et al. (2014), and Wigneron et al. (2017) for a review of passive microwave soil moisture retrieval algorithms. During the process of retrieving soil moisture from passive microwave measurements, one has to address the effects of scattering and attenuation of vegetation, and attenuation/polarization-mixing due to surface roughness, among other variables. The scattering effect of vegetation is characterized by a parameter called the single scattering albedo ( ). Its value is influenced by the type of vegetation and leaf structure (Kurum, 2013). Although is observed to be varying according to spatio-temporal dynamics of land cover (Konings et al., 2016), its value is generally assumed to be polarization independent (particularly over natural vegetation rather than croplands), constant or a function of land cover, and close to zero in the soil moisture retrieval algorithms (implying minimal effect of scattering on the retrievals) (Kerr et al., 2012; Pan et al., 2014; Van de Griend and Owe, 1994; Wigneron et al., 2004). The attenuation from vegetation cover is parameterized by a variable called the Vegetation Optical Depth (VOD), which closely relates to the water content in foliage and woody components of the above ground biomass to different degrees, depending on the frequency (Chaparro et al., 2019; Liu et al., 2013; Momen et al., 2017). It is observed to be responsive to the vegetation type and its seasonal dynamics, and plays a similar role – yet records complementary information – to that of the optical vegetation indices such as the Normalized Difference Vegetation Index (NDVI), which saturates for dense forests, and the Enhanced Vegetation Index (EVI) (Jones et al., 2011; Piles et al., 2017; Tian et al., 2016). Apart from its usage in the soil moisture retrieval process, the knowledge of VOD is essential due to the fact that the spatio-temporal land cover changes in the vegetation dynamics influence the hydrologic responses, and also in the exchange of carbon dioxide and water vapor at land-atmosphere interface (Schlesinger and Jasechko, 2014). Several studies investigated the role of VOD in assessing the crop dynamics (Chaparro et al., 2018; Lawrence et al., 2014; Patton and Hornbuckle, 2013), forest height (Rahmoune et al. 2013, 2014), vegetation fraction (Guan et al., 2012), Leaf Area Index (LAI) (Wigneron et al., 2007), plant drought response (Konings and Gentine, 2017), sap flow (Schneebeli et al., 2011), and carbon cycle (Brandt et al., 2018; Chaparro et al., 2019; Fan et al., 2019). Typically, the VOD is estimated either from ancillary data (such as NDVI, O'Neill et al. (2015)) or by using dual polarized TB or by using multiple incidence angles (in the case of Soil Moisture Ocean Salinity – SMOS sensor) (Kerr et al., 2012; Meesters et al., 2005; Pan et al., 2014) to simultaneously retrieve VOD and soil moisture. In the former case, the errors in ancillary sources may propagate into the VOD estimates, which in turn can affect the quality of soil moisture retrievals. In the latter case, due to a highly-correlated nature of TB across the two polarizations, the VOD retrievals are prone to noise (Konings et al., 2016). Since the VOD estimated this way is directly fed (unaltered) to the soil moisture retrieval algorithm, we hypothesize that the VOD's noise propagates into the soil moisture retrievals, prompting the need for addressing this issue in the VOD retrievals. The idea of VOD undergoing slower temporal transition is also implemented successfully in the SMOS's new multi-orbit soil moisture retrieval algorithm (Al Bitar et al., 2017). Furthermore, the microwave emissions from the soil are also influenced by the soil surface roughness conditions, which can be frequency and polarization dependent (Shi et al., 2005). As the roughness increases, the emissivity increases resulting in higher TB , which ultimately degrades their sensitivity to soil moisture variations (Choudhury

et al., 1979; Montpetit et al., 2015). Hence, evaluating the effect of surface roughness is essential for accurate soil moisture retrieval. Generally, surface roughness (h) is modelled as described by a statistical distribution (usually exponential or Gaussian) with physical parameters representing the spatial auto-correlation length (L), the root-meansquare (RMS) height (hs), and an autocorrelation function (Mo et al., 1982; Tsang et al., 1985). Given the limitation of obtaining these observations at the global scale, semi-empirical models are proposed (Choudhury et al., 1979; Shi et al., 2002; Wang and Choudhury, 1981; Wigneron et al., 2007), which estimate the attenuation due to roughness in microwave emissions from the soil. Traditionally, these semi-empirical roughness parameters are either assumed to be constant globally or assume a fixed value for a particular land cover type (Fernandez-Moran et al., 2017b; Njoku and Li, 1999; O'Neill et al., 2012; Paloscia et al., 2015). In this context, several field experiments – limited to certain land cover classes at local scale – are helpful in obtaining physically the surface roughness parameter values (Fernandez-Moran et al., 2015; McNairn et al., 2015; Panciera et al., 2014). However, these values may not be applicable at the global scales due to the possibility of the existence of multiple land cover types within a satellite footprint. Studies by Parrens et al. (2016) and Wang et al. (2015) indicate the spatial variability of roughness across different land cover classes. Given this heterogeneous nature, Fernandez-Moran et al. (2017a) and Fernandez-Moran et al. (2017b) have calibrated the surface roughness parameters in an attempt to improve the accuracy of SMOS soil moisture retrievals. Furthermore, the roughness values can also exhibit spatial variability within a land cover type owing to the spatial heterogeneity of soil and vegetation (within the land cover type), and the influence of changes in agricultural practices (McNairn et al., 2015). Hence, given the challenges in estimating the roughness parameter and the impact of assumptions above (regarding roughness parameters) on the quality of soil moisture retrievals brings us the need to derive a spatially varying global surface roughness map. In this paper, we attempt to simultaneously estimate the VOD, soil moisture, and surface roughness, using the AMSR-E X-band TB measurements. The methodology is termed as Simultaneous Parameter Retrieval Algorithm (SPRA). The algorithm is generic by nature and can be implemented in the operational soil moisture missions AMSR2, SMOS, and SMAP. AMSR-E provides global scale TB data spanning ~10 years (2002–2011). There is a considerable rise in the usage of satellite soil moisture observations in climate studies (Jung et al., 2010; Miralles et al., 2014b), understanding land-atmosphere interactions (Hirschi et al., 2014; Lei et al., 2018; Miralles et al., 2014a), droughts (Hao et al., 2018; Nicolai-Shaw et al., 2017), assimilation studies (Gruber et al., 2019; Reichle et al., 2007; Rodríguez-Fernández et al., 2019), and in monitoring vegetation (Liu et al., 2013) among other works. Given these applications, the information provided by AMSR-E is deemed to be valuable. Therefore, efforts should be invested towards developing better retrieval algorithms that can assist the efforts towards developing long-term satellite soil moisture (Dorigo et al., 2017) and vegetation observations (Liu et al., 2011). Given its long data record, AMSR-E observations have been successfully used to evaluate several retrieval algorithms in the past (Du et al., 2016; Jones et al., 2011; Njoku and Chan, 2006; Njoku et al., 2003; Owe et al., 2008; Pan et al., 2014). Among these products, the Land Parameter Retrieval Algorithm (LPRM) based soil moisture product is widely used in the literature. LPRM algorithm – developed by Vrije Universiteit Amsterdam (VUA) and NASA (De Jeu and Owe, 2003; Owe et al. 2001, 2008) – retrieves soil moisture, VOD, and surface temperature (Holmes et al., 2009) concurrently. The algorithm utilizes the analytical solution proposed by Meesters et al. (2005) to retrieve VOD, which makes the technique to be independent of ancillary vegetation information in the process of retrieving soil moisture. Besides, the LPRM algorithm assumes vegetation and soil surface related parameters to be polarization independent and global constants. In the current study, we utilized the AMSR-E LPRM 2

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soil moisture and VOD retrievals as baseline data, based on previous comparison studies (Dorigo et al., 2010; Draper et al., 2009; Hain et al., 2011; Rüdiger et al., 2009; Tuttle and Salvucci, 2016), to carry out comparisons with the SPRA retrievals. The remainder of the manuscript is structured as follows. Section 2 presents the SPRA method. Section 3 presents the datasets used for obtaining the retrievals as well as for the analysis of results. Section 4 describes the application of SPRA to AMSR-E X-band TB data and the manner in which the retrieved VOD, soil moisture, and surface roughness products are analyzed. Section 5 presents the analysis and performance of the three retrieved products. Section 6 concludes with some remarks and future work.

(Meesters et al., 2005). The optimal soil moisture and VOD are found by iterating over the full soil moisture range and comparing the predicted brightness temperature with the observed value on an instantaneous basis (Owe et al., 2008). The process of estimating VOD and soil moisture in this work is based on the time series motivation proposed by Konings et al. (2016) in their Multi Temporal – Dual Channel Algorithm (MT-DCA) algorithm. During the simultaneous retrieval of VOD and soil moisture using dual-polarized observations at every single overpass (such as performed by the LPRM), the retrievals can be sensitive to noise due to highly correlated nature of brightness temperatures (Konings et al., 2016). This problem can be addressed by including additional observations either from multangular measurements on the same day (in case of the SMOS (Soil Moisture Ocean Salinity) sensor) or, if these are not available, by using multiple overpasses (such as in this work and the MT-DCA). In the current work, we assume the vegetation changes very slowly and the VOD remains constant over a time window (of width w). Hence, for a w day period with w × 2 AMSRE TB measurements (dual polarized observations of a single pass), there will be w × 2 radiative transfer equations and w + 1 unknowns: w soil moisture retrievals (one per day) and one VOD retrieval. This is an overconstrained problem, where a least squares solution is usually pursued through optimization. It is important to assess the width of the time window within which the VOD can be assumed constant. A smaller window may not ensure robust and smooth VOD retrievals, and a larger window may result in the violation of constant VOD assumption. Given the correlated nature of TB across polarizations, it is necessary to assess the number of observations required for obtaining robust retrievals. For this, the Degrees of Information (DoI) (Konings et al., 2015) are computed for the screenshot of AMSR-E dual polarized TB measurements, which are found to be 1.89 per observation set. This value indicates that we can robustly estimate one parameter using dual polarized observations of AMSR-E on a particular day at a location. Given the temporal resolution of AMSR-E to be one day, w can be as small as two overpasses (resulting in DoI to be 1.89 2 = 3.78) to retrieve two soil moisture values and one VOD value (that remains constant over the two days). The VOD retrievals thus obtained are still found to be noisy (results not shown here), which are still deemed to be unnatural. Hence, the width of the window is set to seven days. Since AMSR-E has an average revisit time of 1–2 days (per overpass) across the globe (Njoku et al., 2003), the number of overpasses in seven days window ranges between 4-7, resulting in DoI range of 7.56–13.23. The minimum DoI occurs closer to the equator due to lesser number of overpasses (Njoku et al., 2003). Although this can affect the SPRA retrievals, given that the equatorial belt is covered with dense forests (Broxton et al., 2014), the soil moisture retrievals in these regions are anyway unreliable. Further, this choice of window is reasonable, given the vegetation characteristics vary at a weekly basis (Wigneron et al., 2000). Besides, the multitemporal retrieval approach has previously been successfully applied to the Aquarius sensor (Konings et al., 2016; Rötzer et al., 2017), which has an average temporal resolution of seven days. Let {TBg , t T gB: g = {H , V }, t = 1,2, …, n} be a time series of AMSR-E X-band brightness temperatures. Given a value of roughness parameter (h) (the procedure of estimating h is described in Section 2.3), the following procedure is adopted for the simultaneous retrieval of VOD and soil moisture at a location across moving time windows:

2. Methodology 2.1. Retrieval approach In the current work, we used the radiative transfer scheme proposed by Mo et al. (1982), which estimates the brightness temperature above canopy (TBg ) in g polarization, where g = {H , V } , as a combination of contributions from canopy and soil (underneath the canopy), using the following equation.

TBg = TS erg

v

+ TC (1

)(1

v)

+ TC (1

)(1

v )(1

erg )

v

(1)

where, TS and TC are soil and canopy temperatures (in K) respectively, which are assumed to be approximately equal (TS TC ); erg is the polarization dependent rough soil emissivity; v is the vegetation transmissivity; is the single scattering albedo. Due to the minimal effect of atmospheric opaqueness on the TB at low frequencies, the atmosphere is assumed to be transparent. The parameter erg is estimated using the model developed by Wang and Choudhury (1981) (Eq. (2)). This model has two components, smooth soil emissivity (esg ), and roughness effects. esg is the representative variable of soil moisture. It is estimated using the Fresnel's equations (Landau and Lifshitz, 1960) with soil dielectric constant as the main input, which is computed from the soil moisture content using the model proposed by Wang and Schmugge (1980). The roughness effects are characterized by two parameters h – a dimensionless roughness factor, and Q – a polarization mixing factor.

erp = 1

((1

Q ) Rsq + QRsp)exp( h cosn

)

(2)

is where, p and q are the two polarizations (horizontal and vertical); the rough soil emissivity in p polarization; Rs is the reflectivity of smooth soil (reflectivity is related to emissivity as, R = 1 e ); is the angle of incidence (in radians); n is the factor that influences the angular dependence of emissivity. v , which accounts for attenuation of emissions passing through the canopy layer, is related to the VOD ( ) using the following equation (Eq. (3)).

erp

v

= exp

cos

(3)

Under this model setup, the three variables, τ, h, and soil moisture, remain unknown. From this point, the terms VOD and τ are used interchangebly throughout the manuscript. The following sections present first the methodology adopted for the simultaneous estimation of VOD and soil moisture, followed by h parameter.

1) Set the time window t = j: j + w 1, and select the associated time period's TBg, t values. Consider the radiative transfer equation shown t = f ( t , t , TSt , h) , in Eq. (1) represented in functional form as TBg,,sim g, t where, TB, sim is the simulated brightness temperature in p polarization on tth day (or overpass), TSt is the surface temperature parameter on tth day (estimated from the Ka band TB as described in Appendix B.3). Every timestep in the selected window yields two radiative transfer equations, one for horizontal and the other for vertical polarizations. The optimization minimizes the error between

2.2. Estimation of VOD and soil moisture The radiative transfer scheme (Section 2.1) implemented here is similar to that of other dual-channel algorithms (e.g. Crow et al. (2005)), including the LPRM retrieval algorithm, although LPRM does consider a minimal atmospheric effect. The difference in the two retrieval algorithms centers on the retrieval of VOD and h parameter. As mentioned earlier, LPRM solves Eq. (1) analytically to express VOD as a function of microwave polarization difference and soil emissivity 3

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simulated and observed dual polarized brightness temperatures (Eq. (4)), resulting in the VOD {ˆ t = j: j + w 1} and the soil ˆ : t = j: j + w 1} retrievals in the selected time moisture { ˆt window. Repeat this process for the entire time series i.e., j = 1: n w + 1. j+w 1

t (TBg,,sim

Objective Function = min t=j

TBg, t )

minimal effect on the contribution ratio. Fig. 1(b and c) are the contribution ratio values marginally averaged with respect to h and ω parameters respectively across various parameter combinations for H polarization. Similar plots are developed from V polarization equation as well Fig. 1(e and f). Fig. 1(b) indicates that changing h parameter induces significant nonlinear variability in the ratio across all the scenarios of Q and n. So, assuming a location independent h parameter can significantly alter the TB simulations. On the contrary, varying ω does not have such a prominent effect on the ratio values (Fig. 1(c)). Although an increase in ω increases the contribution ratio, the rate of increase is much lesser compared to the variability noticed in the h case (Fig. 1(b)). The inclusion of variability in Q and n parameters induced nonlinear and linear bias in the cases of h and ω parameters respectively. The contribution ratio reduces with an increase in the value of Q parameter at lower h parameter values, and Q parameter remains insensitive (convergence of contribution ratio values) at high h parameter values. The n parameter has noticeable effect on the contribution ratio. Since n parameter has an inverse effect on the rough soil emissivity, it's increase results in a decrement of contribution ratio. Unlike the case of Q parameter convergence of contribution could not be achieved making the n parameter to be relatively more sensitive in simulating the TB . Even under changing Q and n parameters, the variability of h parameter has a dominant effect on the contribution ratio compared to that of ω parameter. In summary, these results indicate that h parameter has greater sensitivity compared to that of ω parameter. At high vegetation, due to the presence of both VOD and h parameters, the TB is affected by the combination of these two parameters, thus making it impossible to totally separate their respective contributions (a problem of equifinality). Due to this combined effect, Fernandez-Moran et al. (2015), Parrens et al. (2017), and Patton and Hornbuckle (2013) have noticed the VOD retrievals to be influenced by temporally varying roughness conditions (that occur due to plowing, rain etc.). Furthermore, several works, with a focus on retrieving accurate soil moisture retrievals, have combined the vegetation and roughness effects to a single parameter (Pan et al., 2014; Parrens et al., 2017; Wigneron et al., 2017). However, such a parameter is sensitive to the roughness effects, rendering combined parameter retrievals less useful for monitoring the vegetation (Wigneron et al., 2017). Furthermore, Njoku and Chan (2006) suggested using multi temporal analysis to separate the roughness effects from vegetation. Considering these developments, it is determined that it is important to retrieve a spatially varying and temporally constant surface roughness parameter (h). Based on the sensitivity analysis the value of ω is assumed to be fixed (equal to 0.06), and Q, and n are assumed to be equal to 0.127, and 1 respectively to maintain consistency with the values assumed for Xband frequency in the LPRM algorithm (Mladenova et al., 2014). It has to be noted that LPRM algorithm assumes a constant value of h equal to 0.18 globally.

2

g = {p, q}

(4)

2) The above step is repeated for the next time window (1 day ahead) and this continues throughout the entire time series. The moving window scheme results in multiple values of soil moisture and VOD at a particular time step (or overpass) as neighboring windows overlap. These values are averaged to obtain a single value per time ˆ :t = 1: n} and soil step resulting in the times series of VOD { ˆt ˆ : t = 1: n} . moisture { ˆt 2.3. Estimation of spatially varying roughness parameter h 2.3.1. Need for spatially varying roughness parameter h In the previous section, the procedure of retrieving the VOD and the soil moisture requires specification of the surface roughness (h) parameter along with single scattering albedo ω parameter. Apart from these, there are additional parameters Q (polarization mixing ratio) and n (exponent of cosine term) in the roughness equation (Eq. (2)). Konings et al. (2016) developed (MT-DCA) to retrieve concurrently soil moisture, VOD along with spatially varying ω, and implemented on Aquarius and SMAP (Konings et al., 2017) sensors. In their work, authors have retrieved the ω parameter by keeping other parameters h and n in the roughness equation (omitting the Q parameter) as constants. there have also been efforts to calibrating these parameters in the context of SMOS mission (Fernandez-Moran et al. 2015, 2017b). In view of these developments, it is important to assess the sensitivity of roughness parameter (h) and vegetation parameter (ω), along with other parameters Q and n on the simulated values of TB . To explore this aspect, we conducted the following experiment. In order to test the sensitivity of parameters, the following ranges of parameters are considered: h = [0,3.5] (351 equally spaced values), = [0,0.2] (201 equally spaced values), Q = {0,0.125, 0.2} , and n = { 1,0,1,2} . These parameters are assumed to be polarization independent. In addition, the VOD is varied between = [0.1, 1.2] (12 equally spaced values). Consider the radiative transfer equation (Eq. )(1 (1)), wherein the first (TS erg v ) and the second terms (TC (1 v) ) quantify the contributions from soil interacting with canopy and direct vegetation respectively. The former contains the combined effect of soil and vegetation parameters, and the second contains the effect of vegetation parameter alone. For each one of the aforementioned parameters’ combinations (resulting in 10,159,344 cases), Eq. (1) is used to simulate the total TB to estimate the contribution ratio between the sum of first and second terms, and TB is computed (considering a fixed soil moisture value of 0.2 m3/ m3 and surface temperature of 284 K). This contribution ratio will help us to understand how the parameter variability is affecting to the total TB in a way that greater is the variation in contribution ratio as a parameter is varied, greater will be the sensitivity of the parameter in simulating TB . Fig. 1 presents the results pertaining to this experiment. Fig. 1(a and d) depict this ratio in terms of changing h, ω, and τ (keeping Q = 0.127 and n = 1, which are the parameters used in the LPRM algorithm) for H and V polarizations respectively. It can be noticed that the contribution ratio is higher for V polarization (Fig. 1(d)) compared to that of H polarization (Fig. 1(a)). This indicates that the ground reflected vegetation scattering effects could be more prominent in the latter case. It is noticed that an increase in roughness in areas with low vegetation results in a higher contribution ratio. Its effect is gradually reducing and increasing as the vegetation increases. On the other hand, varying ω has

2.3.2. Retrieval of roughness parameter h For the retrieval of the h parameter, another layer of optimization is implemented outside of soil moisture/VOD retrievals. The search space of h is fixed as 0–3.5. At a particular location, the following procedure describes the retrieval of h parameter. 1) Initialize the value of h, obtain the time series of VOD and soil moisture using the method presented in Section 2.2, in order to simulate the time series of dual polarized brightness temperatures using Eq. (1). 2) The optimization is performed to obtain an optimal surface roughness parameter hoptim , with an objective of minimizing the error between the time series of simulated and observed brightness temperatures (Eq. (5)).

4

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)(1 Fig. 1. Experiment to assess the sensitivity of parameterization of radiative transfer model. (a) contribution ratio (ratio between TS erg v +TC (1 v ) and the total TB ) of varying h and ω w.r.t τ (Q = 0.127, n = 1) for H polarization; contribution ratio of (b) h parameter and (c) ω parameter w.r.t varying Q and n parameters for H polarization; (d–f) same as (a–c) but for V polarization. soil moisture and surface temperature values of 0.2 m3/ m3 and 284 K respectively are assumed here. n

Objective Function = min t = 1 g = {p, q}

i (TBg,,sim

TBg )

covered with major land cover categories. Each of these time series is supplemented with daily precipitation information (procured from MSWEP Version 2 dataset (Beck et al., 2017a; Beck et al., 2017)), in order to assess the variability of the VOD and soil moisture retrievals with regard to precipitation conditions. The VOD and soil moisture retrievals are analyzed in Sections 5.1 and 5.3 respectively by computing their mean and standard deviation and comparing them with that of the LPRM products. In addition, the VOD time series plots are supplemented with the time series of NDVI, which are obtained from MODIS Aqua MOD13C1 v006 16 days 0.05° resolution product (Dian, 2015) resampled to AMSR-E grid scale (0.25° resolution). Although VOD (vegetation water content) and NDVI (vegetation greenness) correspond to different aspects of vegetation, their comparison in terms of temporal patterns may provide an idea about the quality of VOD retrievals. The variation of mean SPRA VOD across each of the LULC categories is determined by plotting the error bars (which show the mean and the standard deviation information) using the 10 years (2001–2010) composite of MODIS MCD12Q1 LULC product (Broxton et al., 2014), which is resampled to quarter degree resolution from native 0.5 km resolution. The VOD, as determined before (Konings et al., 2017; Rahmoune et al., 2013; Vittucci et al., 2016), can be related to the canopy height value. Hence, in order to assess the extent of their relationship, the mean SPRA VOD retrievals are compared with the mean canopy height dataset developed by Simard et al. (2011) across different land cover classes. The global surface roughness map, which is obtained as one of the outcomes of SPRA, is analyzed for its spatial variability by comparing it with the roughness product (denoted as ‘HR map’ from here on) developed by Fernandez-Moran et al. (2017a). This map is used as an input for the SMOS-IC soil moisture and vegetation optical thickness retrieval algorithm (Fernandez-Moran et al., 2017a). SMOS-IC is a new retrieval algorithm applied to SMOS L-band (1.4 GHz) observations. It is provided in the 25 km EASE 2.0 grid. Details about generation of HR map are presented in Appendix B.3. For this study, the HR map is resampled to equidistant cylindrical projection prior to the analysis. Later on, we looked into the factors that affect the spatial variability of

2

(5)

The VOD and the soil moisture are retrieved using the method presented in Section 2.2, using hoptim . Thus, at the end of this procedure, one can simultaneously retrieve the VOD, the surface roughness parameter, and the soil moisture at a location. The schematic of the algorithm is presented in Appendix A (Figure A.1) This algorithm is termed as the Simultaneous Parameter Retrieval Algorithm (SPRA). From this point forward, the retrievals pertaining to this approach will be referred to as the SPRA retrievals. 3. Data The datasets used in the current work are summarized in Table 1. Further details about these datasets is presented in Appendix B. 4. Application and analysis The SPRA is applied pixel-wise on the land area globally. At a particular location, the optimization scheme is initiated on the AMSR-E X-band descending pass TB (Appendix B.1). Information about criterion implemented to filter unreliable soil moisture retrievals in the presence of snow, frozen soil, active rain, and Radio Frequency Interference (RFI) is presented in Appendix B.2. The descending pass (equatorial crossing time 1:30 a.m.) observations are selected due to better thermal equilibrium conditions of soil surface, overlying vegetation, and near surface air (Owe et al., 2008). As mentioned in Section 2.2, the width of the moving window is set to 7 days. Initially, the surface roughness parameter is retrieved (using the methodology presented in Section 2.3), which is then used to retrieve the time series of VOD and soil moisture (using the methodology presented in Section 2.2). The VOD and soil moisture retrievals obtained from SPRA are analyzed in terms of their temporal dynamics when compared to the LPRM retrievals. For this, the time series plots corresponding to seven locations (Table 2) are selected across the world randomly that are 5

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Knowles et al. (2006)

Holmes et al. (2009) Simard et al. (2011) Broxton et al. (2014) ESA-CCI-SM-v4.2. (2018) and USGS (1996) Fernandez-Moran et al. (2017b) Dorigo et al. (2011) Beck et al. (2017a); Beck et al., 2017 Pai et al. (2014) Dian (2015)

19 June 2002 to 27 September 2011

19 June 2002 to 27 September 2011 Static dataset; 2005 Composite; 2001–2010 Static dataset (for 1996) Static dataset; 2011–2013 19 June 2002 to 27 September 2011 2004–2005 19 June 2002 to 27 September 2011 2004–2005

Table 2 Selected locations where the time series of the VOD and the soil moisture obtained from SPRA and LPRM retrievals are analyzed along with daily precipitation. Location

Latitude

Longitude

Land Cover

Congo Kenya South Australia North Australia North East China West India South East US

2.125°N 2.125°N 32.375°S 12.875°S 42.375°N 23.625°N 30.625°N

18.625°E 36.875°E 123.375°E 133.125°E 112.125°E 70.875°E 87.375°W

Evergreen Broadleaf Forest Mixed Forests Open Shrubland Savannas Grasslands Croplands Natural Vegetation Mosaic

surface roughness, by assessing the inter-dependencies between surface roughness, mean SPRA VOD, and topographic complexity information (ESA-CCI-SM-v4.2, 2018). This analysis is carried out by plotting 2-D density plots among these datasets. Lastly, we assessed the accuracy of the SPRA soil moisture with respect to the LPRM soil moisture by validating the two datasets in two ways 1) using in-situ soil moisture observations over the Contiguous United States (CONUS) region, and 2) by assessing consistency with precipitation information over India. The in-situ observations corresponding to 792 stations spread across the CONUS covering the duration of AMSR-E runtime are procured from International Soil Moisture Network (ISMN) (Dorigo et al., 2017). Details about the stations considered and processing of the observations are presented in Appendix B.4. The temporal performance of the two products is evaluated using ubRMSE and Pearson correlation (R) metrics. Along with in-situ validation, it is also important to assess the accuracy of soil moisture products in data poor regions. To address this issue, the SPRA soil moisture product is determined for its consistency with local precipitation conditions. The comparison is made by considering the AMSR-E LPRM soil moisture product as a reference. The methodology is based on the observation made by Salvucci (2001), who demonstrated that soil moisture retrievals and precipitation at a location plotted as E [P SM ] curve, where P is the local precipitation, depict a a characteristic sigmoidal convex-concave curve. Tuttle and Salvucci (2016) assessed that this curve behavior can be mimicked by estimating mutual information between soil moisture and precipitation. In their analysis, they determined that while comparing two soil moisture products at a location, the product which has higher mutual information with respect to precipitation depicts better curve behavior of E [P SM ], thus making the product relatively more accurate at that location. Karthikeyan and Nagesh Kumar (2016) made improvements to this technique wherein a new dependency measure called the CopulaKernel Density Estimator based Mutual Information (CKDEMI) is proposed. In their method, CKDEMI measure is coupled with a couple of bootstrap strategies to result in a “best choice soil moisture product” map. Through this technique, the consistency of any two soil moisture products with precipitation can be determined, and the “best choice soil moisture product” map provides locations where either one of the two products or both or none of the two soil moisture products have accurate retrievals. Further details on this technique can be obtained from Karthikeyan and Nagesh Kumar (2016). The SPRA and LPRM soil moisture products are assessed for their accuracy over India, which is devoid of dense in-situ soil moisture networks. As a reference, the IMD gridded precipitation data (Pai et al., 2014) is used for this analysis (Appendix B.4). For this analysis, IMD data coinciding with the AMSR-E duration is considered. 5. Results and discussion

NDVI

Surface temperature Canopy height Land use land cover (LULC) Topographic complexity HR Map In-situ soil moisture (CONUS) Precipitation

AMSR-E X-band Level 3 daily descending pass dual polarized quarter degree gridded (0.25° × 0.25°) data AMSR-E's Ka band (36.5 GHz) TB Geoscience Laser Altimeter System (GLAS) aboard ICESat (Ice, Cloud, and land Elevation Satellite) MODIS 5.1 MCD12Q1 product ESA-CCI v3.2 ancillary information SMOS International Soil Moisture Network Multi-Source Weighted-Ensemble Precipitation (MSWEP) Data India Meteorological Department (IMD) MODIS (Aqua MOD13C1 v006) product Satellite brightness temperature data

Citation Duration Source Name of the Dataset

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Table 1 Summary of datasets used in the current work.

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Fig. 2 presents the time series of SPRA and LPRM VOD retrievals 6

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Fig. 2. Time series of VOD retrievals of the SPRA (shown in blue), the LPRM (shown in red) product, and the LPRM product smoothened with moving window filter of width seven days (shown in green) at selected locations for two-year period, 2004–05. Each plot also contains daily precipitation (shown in brown; axis on the right) and NDVI (shown in magenta; axis on the right) of the location observed during the said period. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

along with NDVI and precipitation at seven locations (Table 2). The timeseries plots also contain seven days moving average of LPRM VOD timeseries (VOD MA). In general, it is observed that the SPRA VOD retrievals have reduced high frequency variability compared to the LPRM retrievals. The plots indicate that the SPRA VOD retrievals do not appear to have similarity with that of VOD MA timeseries. At several points, the SPRA VOD could detect the change in VOD due to precipitation, whereas the VOD MA timeseries failed to do the same. Some examples are July 2004 rainfall events in Southern Australia pixel, January 2005 rainfall event in Kenya pixel, July 2005 rainfall event in North East China, etc. There is consistency in the temporal patterns of VOD and NDVI. In the case of Congo pixel, the VOD patterns are more dynamic, which is not the case with the NDVI timeseries. This could be due to the saturation effect of NDVI in the densely vegetated regions (Huete et al., 2002). The patterns of agreement with NDVI are much stronger in the case of SPRA VOD retrievals. This is evident in Kenya, South Australia, North Australia, and South East US pixels. In the case of North Australia pixel, post rainfall season (April 2005), the greenness (NDVI) and the

vegetation water content (VOD) have gradually reduced till the beginning of next rainfall during October 2005. In the case of South East US, the SPRA VOD retrievals agree well with NDVI timeseries due to their reduced temporal variability. In the case of West India pixel, the agriculture takes place prominently in two phases, one during the monsoon period (June–September), and another during the post-monsoon period (October–April). The patterns of increase and decrease in the VOD agree with that of NDVI during the monsoon period. There is an agreement between SPRA VOD and NDVI during the senescence stages of the crop (end of March to April in 2004 and 2005). However, there is a disagreement in the VOD temporal patterns with NDVI during the sowing period, and growth stages post monsoon (from October 2004 to mid-January 2005). It may be noted that agriculture during the post monsoon period relies on groundwater resources in this region (CRIDA, 2011; Swain et al., 2012). This could have resulted in an increase in VOD during this period. Notably, the VOD patterns of SPRA are different from that of LPRM in the case of North East China and West India pixels, specifically during July 2005 and May 2005 respectively. The temporal patterns of 7

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VOD SPRA and VOD MA timeseries during the periods, as mentioned above are also different. Since SPRA uses a moving window based optimization scheme and also retrieves surface roughness parameter, there could be an effect due these features on the SPRA VOD timeseries (SPRA retrieved surface roughness parameter values of 0.47 and 0.97 for North East China and West India pixels respectively). The increase in both SPRA and LPRM VOD during May 2005 in West India pixel could be attributed to groundwater irrigation-based pre-monsoon agricultural activities in the region. Apart from the effects of growth stages of vegetation (such as from tilling to senescence stages in crops) (Meyer et al., 2018), the temporal dynamics of VOD can also be affected by the events of precipitation. A precipitation event increases the vegetation water content of the plant and thus the VOD through both growth in response to increased water availability and through an increase in the relative water content per unit biomass associated with increased plant water uptake, although the duration of such effect is dependent on the type of vegetation. The SPRA VOD retrievals are observed to be more sensitive to the precipitation events. Such a relation is observed at several cases in these time series. Following the precipitation events occurred at the end of March 2005 and July 2005 at North Australia and North East China sites respectively, a sudden increase followed by a gradual decrease in the SPRA VOD time series is noticed. This could be due to wetting of the canopy supported by continuous drying due to the lack of rainfall. Interestingly, in the case of West India pixel, the increase in SPRA VOD since the beginning of monsoon months (June 2004 and July 2005) is spread over a larger duration. This could be attributed to agricultural activities in the region. The seasonal variability of the North Australia site is depicted clearly in the SPRA time series. Further, SPRA could identify the rainfall durations by retrieving high VOD correctly, which are not identified by the LPRM retrievals. Precipitation during April 2005 and June 2005 of South Australia and North East China respectively are examples of this observation. The mean and the standard deviation of the SPRA and the LPRM VOD retrievals are presented in Fig. 3. The standard deviation is estimated from the residual timeseries obtained by removing seven days moving average timeseries from the original timeseries. This is done to emphasize the residual variance of timeseries. There exists similarity in terms of the magnitude of the mean VOD between the two products in most regions of the world. This is expected due to the fact that the present method tries to reduce only the high variability in the VOD

retrievals, which may not result in significant changes in the mean value of the retrievals. The SPRA VOD dataset has produced expected general vegetation dynamics across the world. The VOD values are highest in the tropical and boreal forests and lowest in the arid climate regions. The Tundra region has slightly lower VOD values, due to the presence of a low vegetation. The distinction between the arid region located in Rajasthan, India (the Thar Desert, having low VOD) and agriculturally intense areas surrounding this region (in the Northern India; having intermediate VOD) is evident from the figure, indicating the sensitivity of the VOD product to the spatial vegetation dynamics. In the case of mountainous terrains such as the Andes, which are primarily covered with moderate to low vegetation cover with shrublands, grasslands and barren land cover, the VOD values are found to be in the range of 0.03–0.67. However, the upper Andes (in Peru, Ecuador, and Colombia), and the Himalayas, which are dominated by evergreen broadleaf and mixed forests have comparatively higher VOD retrievals. In general, it is observed that the mean VOD retrievals are slightly lower than that of LPRM retrievals in the dense vegetation regions of the needleleaf, broadleaf, and mixed forest classes. In the case of standard deviation maps (see Fig. 3(b and d)), the values of SPRA VOD retrievals are less than that of the LPRM VOD retrievals, indicating the effect of reduced variability in the SPRA VOD retrievals. This effect is prominent in the tropical savanna region between the Sahara Desert and the Congo basin in Africa. There is also a reduced variability of the VOD retrievals in some of the boreal landscapes covered with savannas in Canada (Quebec) and Russia. Even in the case of tropical forests, low variability in the VOD retrievals is observed, which could be due to the low seasonal effect on the vegetation conditions throughout the year. However, the SPRA VOD retrievals produced slightly higher standard deviation than the LPRM retrievals in the sparsely vegetated areas, mostly in the Sahara region, the Middle East, the Tibetan plateau, Shrublands in South Africa, and East Australia. The error bars (depicting the mean and the standard deviation) of the SPRA VOD retrievals across different land cover classes are presented in Fig. 4. It is observed that the forests with woody vegetation have a high value of median VOD compared to other classes. There is a noticeable distinction in the VOD values of broadleaf and needleleaf categories, which is attributable to the differences in leaf structure in these classes. The evergreen forests have greater variability in VOD compared to deciduous forests. Despite the lack of leaf-off period in the

Fig. 3. Mean (a, c) and standard deviation (b, d) of the VOD retrievals obtained from the SPRA and the LPRM algorithm. The standard deviation is computed for residual VOD timeseries obtained by subtracting seven day moving window average from the original timeseries. 8

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5.2. Roughness characterization The global map of retrieved surface roughness values is presented in Fig. 6. The roughness values are found to be influenced primarily by the vegetation and terrain characteristics of a location. As a result, the tropical rain forests have high roughness, which, as mentioned before, increases the TB (due to increased emissivity), and thus reduces the sensitivity to soil moisture dynamics (Choudhury et al., 1979; Montpetit et al., 2015). Hence, the soil moisture retrievals in these regions can be unreliable. The roughness values are observed to be moderately high in the mountainous regions such as, the Himalayas, the Alps, the Rockies, the Caucasus, and the Pyrenees mountains, which incidentally are covered with vegetation. In the case of the Andes mountains, the southern part, which has barren lands, is retrieved with low roughness, whereas the northern part covered with dense vegetation has higher roughness. This indicates that the vegetation plays a bigger role, followed by the terrain characteristics, in determining the roughness factor. This effect of vegetation on the roughness can be supported by Fig. 1, wherein it is determined that vegetation and roughness effects interact with each other. In the case of regions of intense agriculture, such as the Ganges basin (India), the Pampas (Argentina), and the interior plains of North America, the roughness values are varying between 1.0-1.6. Apart from the lower density of vegetation, the seasonality in cultivation might have resulted in such a range of retrieved roughness parameters in these regions. Lastly, low roughness values (< 1.0) are observed in the barren areas of the world. The values in these areas could be directly impacted by the slow varying factors such as soil texture and terrain characteristics. It is expected that the roughness value will be insensitive to moisture dynamics as they vary at a smaller time scale. Fig. 7 presents the SPRA roughness values compared with HR. It can be noticed from Fig. 7(a) that similar patterns exist between the two datasets with respect to their mean spatial distribution across different land cover classes. There is a difference in the range of roughness values between the two datasets, which is expected due to the variations in a) the sensor microwave frequency (AMSR-E X-band and SMOS L-band) and overpass times (AMSR-E), b) retrieval procedure, c) roughness and albedo parameterization, and d) differences in the time of acquisition between the two datasets. Despite these differences, a global cross correlation (Pearson) of 0.57 is obtained between the two datasets. Given such reasonable correlation, it can be speculated that the variations due to the aforementioned factors have a greater effect of bias than the nonlinear interactions in the two sets of roughness retrievals. Further, the higher magnitude of roughness values in X-band retrievals (SPRA) compared to L-band retrievals (HR) is in agreement with observations made by Kerr (1996). In addition, similar spatial variability of roughness across the biomes is observed by Wang et al. (2015) (for AMSR-E C-band data) and Parrens et al. (2016) (for SMOS L-band data). Fig. 7 presents the boxplots of land cover wise spatial variability of the two datasets. It can be seen that woody vegetation has the highest roughness, followed by croplands, savannas, shrublands, and grasslands, with barren areas having the lowest value of roughness. In the case of evergreen forests, the distinction in the distribution of roughness values between needleleaf and broadleaf forests is evident, which can be attributed to the differences in the leaf structures of the two biomes. A similar distinction, although minor, can also be made in the case of deciduous forests. The evergreen broadleaf forest category has the highest median roughness value. The leaf structure and the lack of seasonality could have resulted in such high value. The closed shrublands, due to the presence of vegetation on a larger area, have expectantly higher roughness than that of the open shrublands. The roughness effects are more prominent in the forested classes in the SPRA dataset compared to the HR map. This could be attributed to the fact that the X-band TB of AMSR-E has lesser ability, compared to the Lband TB of SMOS, to penetrate through heavily forested areas, which

Fig. 4. Plot of error bars (indicating mean and standard deviation) of retrieved VOD values across different land cover biomes, along with mean VOD value in each category, shown as red square. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5. Scatter plot of the mean canopy height versus the mean VOD (retrieved using SPRA) across different land cover classes.

evergreen forests, they have greater variability in VOD compared to the deciduous forests. This could be due to larger uncertainties in these regions due to multiple scattering effects of microwave emissions. Croplands and cropland/natural vegetation mosaic have a large spread in the VOD values, which could be due to the existence of different crop varieties (thus different plant structure) and inherent seasonal patterns within these classes. Furthermore, the highest spread in the VOD values is observed in the open shrubland category, which could be attributed to varying proportions of grass and woody vegetation components (Liu et al., 2011). Fig. 5 presents scatter plot of the mean canopy height (Simard et al., 2011) and the mean SPRA VOD plotted across different land cover categories. The plot indicates positive dependency (with concavity) between these two variables, with higher values observed with the forests. The plot also depicts a bit of saturation in the VOD at high canopy heights. Also, an overall spatial correlation of 0.75 (between mean canopy height and mean VOD on all land pixels) shows the extent to which the SPRA is able to retrieve the woody component biomass (which canopy height corresponds to).

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Fig. 6. Global scale surface roughness (h) map obtained from the SPRA. The white regions in the map are the areas where retrievals could not be performed.

results in signals to contain mostly the information about vegetation rather than soil. Also, there can be some uncertainty sourced from the algorithm's optimization scheme towards retrieving the soil moisture in these regions, given the broad range of values (0–3.5) considered for the retrieval of h parameter. Although the median values of roughness parameter of grasslands and croplands coincide in SPRA roughness map, interestingly, the croplands – despite their heterogeneous nature in crop varieties, seasonal patterns, which includes soil tillage periods – have lesser variability in roughness parameter. This result is in contrast with the larger spread of VOD values retrieved under these classes (Fig. 5). From this, it can be said that the surface roughness parameter is less sensitive than the VOD in capturing the seasonal fluctuations of vegetation. Also, given the coarse resolution of the AMSR-E footprint, the tillage effects could have little influence on the roughness

parameter. In addition, the temporal invariability of the roughness parameter might also have contributed to this outcome. Fig. 8 presents the 2-D joint probability density plots between the surface roughness, the elevation, and the average SPRA VOD. From Fig. 8(a), it is observed that topographic complexity has little effect on the surface roughness value. With approximately 80% of the land pixels having topographic complexity less than 10%, the surface roughness values are spread over their complete range in this domain. However, for the areas of higher topographic complexity (> 20%, constituting mountain ranges such as the Alps, the Andes, the Caucasians, the Himalayas, and the Rockies), the surface roughness values are concentrated in the range of 0.83–1.34. This result is consistent with the observations made by Parrens et al. (2016) and Wang et al. (2015). The joint density between the mean VOD and the topographic complexity

Fig. 7. Land cover wise comparison between the SPRA roughness and SMOS HR map (Note the scale difference between the two vertical axes).

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Fig. 8. Joint density between (a) surface roughness and topographic complexity; (b) SPRA VOD and topographic complexity; and (c) surface roughness and SPRA VOD. (Note that the scale of topographic complexity in (a) and (b) is curtailed to 0–25% in order to focus on non-white density portion).

Fig. 9. Time series of the SPRA and the LPRM soil moisture retrievals at selected locations for the period 2004–05. Each plot also contains daily precipitation information.

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Fig. 10. Mean (a, c) and standard deviation (b, d) of soil moisture retrievals obtained from the SPRA and the LPRM algorithms. The standard deviation is computed for residual soil moisture timeseries obtained by subtracting seven day moving window average from the original timeseries.

(see Fig. 8(b)) indicate little dependence between them, although the areas of high complexity (> 20%) are retrieved with a higher VOD, which is attributable to the presence of dense forests in the regions. Fig. 8(c) illustrates the inter-dependency between surface roughness and VOD.

positive sign. However, the presence of a large number of lakes/ponds in these regions is probably still leading to an overestimation of soil moisture and this should be addressed in future versions of the algorithm. Also, there can be uncertainties in soil moisture retrievals due to the presence of dense vegetation. Further validation needs to be carried out to obtain deeper insights in this regard. The effect of SPRA roughness can be observed in North East China and West India pixels’ soil moisture timeseries in Fig. 9. The former pixel has SPRA roughness of 0.47, and the latter has SPRA roughness of 0.97. Both of these values are greater than the LPRM roughness value of 0.18. Since these regions have relatively lower vegetation conditions compared to the boreal forests, the roughness effects have a prominent effect on soil moisture dynamics. This could be the reason for an overall wet bias in SPRA soil moisture timeseries compared to that of LPRM soil moisture in these two pixels. Despite the extent of influence of vegetation on surface roughness, it would be interesting to explore the positive effects of using the SPRA roughness map in the LPRM algorithm instead of existing assumption of constant roughness parameter value (h = 0.18). The drier regions across the world (e.g., Sahara) are retrieved with slightly higher soil moisture values. The source of uncertainty pertaining to this issue needs to be examined in future. In the case of standard deviations, in general, the SPRA dataset is found to have a lower variability of soil moisture than that of the LPRM retrievals. The effect is more pronounced in the regions of where low variability in the VOD has been achieved (e.g. boreal landscapes, and Eastern USA) (see Fig. 3(b)), indicating its impact on the variability of soil moisture retrievals.

5.3. Soil moisture characterization Fig. 9 presents the time series of SPRA and LPRM soil moisture datasets at selected locations, plotted along with the precipitation. It can be observed from the plots that the SPRA soil moisture retrievals are responsive to the precipitation cycles. In the case of South Australia, North Australia, and North East China pixels, the SPRA could retrieve periods of persistent precipitation with higher soil moisture, which are not retrieved by the LPRM product. The SPRA product also exhibited reduced soil moisture content over the prolonged duration of dry periods. In the case of West India site, the signals of groundwater irrigation during the beginning of Rabi season (October/November) are captured by the SPRA product. Fig. 10 presents the mean and standard deviation of soil moisture retrieved from the SPRA and the LPRM. The standard deviation is estimated from the residual timeseries obtained by removing seven days moving average timeseries from the original timeseries. Although the SPRA soil moisture map has retained the general spatial characteristics, it has distinct features compared to that of the LPRM product. Noticeably, the boreal landscapes in higher latitudes, portions of Southeast Asia, Bolivia and Eastern USA are drier in the SPRA soil moisture product compared to the LPRM retrievals. This could be attributed to lower SPRA VOD retrievals in these regions, which increase the transmissivity and thus can result in colder estimated TB , leading to lower moisture content. Although the SPRA roughness is in general higher in these regions, the presence of dense vegetation has a greater impact on the roughness retrievals (evident from Fig. 8(c)). Due to this reason, the roughness retrievals could have minimal effect on the soil moisture in this region. Moreover, given the LPRM retrievals tend to overestimate the soil moisture when compared to the in-situ observations (Champagne et al. 2010, 2012; Chen et al., 2013; Draper et al., 2009; Jackson et al., 2010; Leroux et al., 2014; van der Velde et al., 2015; Wagner et al., 2007; Zeng et al., 2015), the lower values of soil moisture means portrayed by the SPRA in higher latitudes can be seen as a

5.3.1. Validation of SPRA soil moisture product The top row of Fig. 11 presents the ubRMSE of SPRA and LPRM soil moisture products computed with respect to in-situ observations (ISMN) over the CONUS region. The two ubRMSE maps share a similar pattern with better soil moisture retrievals in the central CONUS. This is expected due to the sparse vegetation existing in this region. The accuracy is degraded in western and eastern CONUS due to the presence of dense vegetation and complex topography. The mean values of ubRMSE are found to be 0.11 m3/m3 and 0.18 m3/m3 for SPRA and LPRM respectively. SPRA has improved the accuracy of soil moisture retrievals in the central and south-western CONUS regions, which resulted in an improvement in average ubRMSE value. The bottom row of 12

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Fig. 11. Validation of SPRA and LPRM soil moisture products over CONUS region with in-situ observations using ubRMSE and correlation (R) metrics.

Fig. 11 presents the correlation of SPRA and LPRM soil moisture products computed with respect to in-situ observations (ISMN) over the CONUS region. Similar spatial patterns are noticed as that of ubRMSE maps. The mean values of correlation are found to be 0.36 and 0.38 for SPRA and LPRM respectively. However, the cross correlation in the region of Nevada, which is predominantly covered with Grasslands and Open Shrublands has slightly degraded in the case of SPRA thereby affecting its correlation values in this region. The ranges of performance metrics observed here are in agreement with the results obtained from Karthikeyan and Nagesh Kumar (2016). The usage of X-band frequency of AMSR-E could have resulted in low values of average correlation for

both the datasets. With the advent of L-band radiometers with improved sensor design in SMOS and SMAP missions, the accuracy of soil moisture retrievals has improved significantly over the recent years (Colliander et al., 2017; Ma et al., 2019). In the near future, new mission concepts such as the Copernicus Microwave Imaging Radiometer (CIMR, Kilic et al. (2018)) based on multi-frequency (L, C, X, Ka/Ku) observations, open the path for enhanced products. Fig. 12 presents the best choice soil moisture product map upon validating the SPRA and the LPRM soil moisture products using IMD precipitation information over India. Over a total of 4632 quarter degree grids over India, 159 grids – primarily located in the snow-fed areas of Jammu and Kashmir – the validation could not be carried out due to lack of data. The results indicate that the SPRA soil moisture product is found to be more consistent with precipitation information over ~70% (3137 grids cells) of the land area, the LPRM soil moisture product is found to be more consistent over ~13% (593 grid cells) of the land area. Over ~16% (703 grid cells) of the land area have both the products performing well, and only 40 grids cells have none of the two products having more consistent soil moisture retrievals with regard to the precipitation data. The dominating influence of the SPRA soil moisture product indicates the improvement achieved in terms of the consistency against precipitation information. There is an underlying pattern by which the selection of products is carried out. For example, if we look at Fig. 11 in tandem with the land use land cover map and elevation maps of India (refer to Fig. 8 in Karthikeyan and Nagesh Kumar, 2016), the ridge line (in Northern India) between low lying croplands and high-elevation savannas, woody savannas, and grasslands, is depicted in the best choice soil moisture product map wherein the SPRA product performs better in the former case and the LPRM product performs better in the latter case. The rest of India, which is mostly covered with croplands and cropland/natural vegetation mosaic classes, the SPRA soil moisture product is observed to be more consistent. Together, these two land cover classes occupy about 63% of the total land area, of which ~78% of the grids are selected with the SPRA soil moisture product, ~8% of the grids with LPRM product, and ~14% of the grids where both products perform well, and ~0.21% of independent grids. With these observations, we find that the SPRA soil moisture product performs well under moderate vegetation conditions and the LPRM product performs well under extreme vegetation (barren or densely vegetated) conditions.

Fig. 12. Best choice soil moisture product map of India. The product selection is carried out by checking their consistency with precipitation information (Karthikeyan and Nagesh Kumar, 2016).

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6. Conclusions

correlation = 0.57) with the HR map derived from L-band SMOS data (Fernandez-Moran et al., 2017b), despite the difference in the range of roughness values between the two datasets. This result indicates that all attributable differences between the two datasets may mostly cause a bias effect on the roughness retrievals rather than nonlinear interactions. The soil moisture obtained from the SPRA is also investigated by comparing it to baseline AMSRE LPRM retrievals. Due to lower VOD values, the SPRA soil moisture retrievals in the high latitudes are lower than the LPRM retrievals. At the global scale, the temporal patterns of the SPRA soil moisture retrievals indicate a higher sensitivity to precipitation patterns. Two different soil moisture product evaluation strategies are implemented in this work: 1) validation with ISMN in-situ observations over the CONUS region and 2) assessing the consistency with precipitation information over India. In both cases, LPRM product is considered as a reference. The in-situ validation revealed that SPRA retrieved soil moisture with better ubRMSE and comparable correlations with respect to LPRM product (mean ubRMSE: SPRA-0.11 m3/m3, LPRM-0.18 m3/m3; mean correlation: SPRA-0.36 and LPRM-0.38). In terms of consistency with the precipitation information, SPRA soil moisture indicated a significant improvement over India with over ~70% of the land area getting selected with the SPRA product over the LPRM product. Since the SPRA VOD retrievals could reduce the effect of the high frequency noise, the product will be analyzed in terms of detecting drought events, and deforestation (e.g. Southern Amazon) that occurred during the AMSR-E time period. The sensitivity analysis of model parameters revealed a greater sensitivity of n parameter in the roughness equation. The effects of including this parameter in the retrieval process need to be evaluated in future. Since SPRA is generic in its usage, it has potential in its applicability on the operational passive microwave sensors, SMOS, AMSR2, and SMAP.

In this study, we attempted to simultaneously retrieve the VOD, the surface roughness parameter, and the soil moisture at the global scale using the Level 3 daily AMSR-E X band brightness temperature observations. In the process, we developed a method, called the Simultaneous Parameter Retrieval Algorithm (SPRA), with a premise that the vegetation dynamics undergo slower temporal changes than the soil moisture, an assumption, which is successfully applied in passive microwave retrieval algorithms before (Konings et al. 2016, 2017; Rötzer et al., 2017). The SPRA is applied to each land pixel, to retrieve time series of VOD and soil moisture and a temporally constant surface roughness value. The mean VOD exhibited expected spatial patterns across the globe, with values influenced by the land cover distribution. Noticeable differences exist in the VOD values as the leaf structure varied. There is a reduction in the standard deviation of the SPRA VOD retrievals at most locations, when compared to the LPRM data, due to the implementation of a multi-temporal moving window scheme in the algorithm. Comparison of mean VOD retrievals with the tree height information (global cross correlation = 0.75) indicates the contribution of foliage in the total value of the VOD. At this stage, to the best of our knowledge, it is difficult to carry out a global scale direct validation of the VOD retrievals. However, an indirect validation with the tree height data can be attempted, if the water content of the woody component can be separated (Brandt et al., 2016; Tian et al., 2017) from the total value of the VOD. An assessment of the time series of the VOD retrievals at selected locations showcased the seasonality and also the strong influence of the precipitation patterns on the SPRA retrievals. In the case of croplands (India site), there is an added effect of agricultural patterns influencing the dynamics of the VOD. Due to the reduced variability, the effects of these factors are noticeable through the SPRA product. The surface roughness retrievals are found to be affected by the vegetation patterns and the topographic complexity across the globe. The roughness values are high in the regions of dense vegetation, rendering the soil moisture in these areas to be unreliable. Moderate roughness values are noticed in the mountainous regions covered with vegetation. Low roughness values are retrieved in the barren lands. In the case of regions where agriculture is practiced, the roughness values are less affected by factors such cropping patterns, seasonality – which have an influence on the VOD retrievals – along with the tillage (Fernandez-Moran et al., 2015). This could be due to the coarse resolution of the AMSR-E footprint, and the temporal invariability of the roughness parameter at that resolution. Further, the spatial patterns of the retrieved roughness map are comparable (global

Acknowledgements The work reported in this paper is done while the first author was a visiting scholar at Princeton University under the Fulbright-Nehru India Doctoral Research program (Grant Id: 15160292). Additional support for the research is from NASA Grants NNX14AH92G (Soil Moisture Cal/ Val Activities as a SMAP Mission Science Team Member). The support from these programs is gratefully acknowledged. All data used in the analysis area available in literature and are appropriately cited in this manuscript. The complete global datasets of the SPRA are available upon request to the first author ([email protected]).

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Appendix A. Schematic of the SPRA

Figure A.1. Schematic of the Simultaneous Parameter Retrieval Algorithm (SPRA) implemented to simultaneously retrieve the VOD, the surface roughness (h), and soil moisture at a location

Appendix B. Data B.1 AMSR-E brightness temperature data The Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E), onboard the National Aeronautical and Space Administration's (NASA) Aqua satellite was launched in 2002 (Kawanishi et al., 2003). The polar orbiting satellite radiometer, equipped with six dual-polarized frequencies (6.92, 10.65, 18.7, 23.8, 36.5, and 89.0 GHz), achieves global coverage every day. The measurements are made at 55° incidence angle with respect to the Earth's surface. Although the sensor is operational, higher power requirements lead to shutdown of the sensor in 2011, resulting in total record length of ~10 years. In the current work, the Level 3 daily quarter degree gridded (0.25° × 0.25°) TB data (version 3) (Knowles et al., 2006) of X-band frequency (10.65 GHz), dated from 19 June 2002 to 27 September 2011, is considered as the primary input to the retrieval process. The X-band frequency is selected for the study due to the minimal effect of radio frequency interference (RFI) on the measurements (Njoku et al., 2005). The gridding of TB is carried out using Level 2 swath data, with squared inverse distance weighted interpolation method. The information pertaining to morning overpass (descending orbit) is used for the analysis, which better ensures thermal equilibrium existing between canopy and soil layers (O'Neill et al., 2015). B.2 Data Screening Following conditions are implemented by using information from other channels of AMSR-E to filter data that may not be suitable for retrieving soil moisture, 1) active rains if TBV,89.0GHz < 249K or TBH,89.0GHz TBH,23.8GHz > 1K (Grody and Basist, 1996), 2) snow/frozen soils if TBV,36.5GHz < 250K and TBV,36.5GHz TBV,18.7GHz < 3K (Grody and Basist, 1996), and 3) RFI if TBV,10.65GHz < TBH,10.65GHz or TBH,18.7GHz < TBH,10.65GHz 5K or TBV,18.7GHz < TBV,10.65GHz 5K (Njoku et al., 2005). Although it is known that dense vegetation will affect the microwave emissions from soil, these areas are not filtered in this current work due to the lack of a well-defined threshold for the VOD.

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B.3 Other datasets Surface temperature (TS ): The land surface temperature used in the retrieval process is derived from AMSR-E's Ka band (36.5 GHz) TB using methodology proposed by Holmes et al. (2009). For the descending pass, the surface temperature is estimated using, TS = 0.893 × TBV, Ka + 44.8 relation (as used in LPRM for night-time observations). The following datasets are used for analyzing the results. Canopy height: The global tree height map developed by Simard et al. (2011) is used in the current analysis. The canopy heights are derived at 1 km native spatial resolution for the year 2005 using Geoscience Laser Altimeter System (GLAS) aboard ICESat (Ice, Cloud, and land Elevation Satellite). The data is acquired from https://webmap.ornl.gov/ogc/dataset.jsp?ds_id=10023, wherein the data is aggregated (using averaging) to the AMSR-E quarter degree resolution. Given this data falls within the time period of AMSR-E, use of this data will be relevant in the current work. Land Use Land Cover (LULC) map: The LULC map, developed by the United States Geological Survey – Land Cover Institute (USGS – LCI) (Broxton et al., 2014), is a composite of 10 years (2001–2010; the time period which nearly coincides with that of AMSR-E) of MODIS 5.1 MCD12Q1 land cover type information. The map has seventeen land cover categories, which are defined under International Geosphere-Biosphere Programme (IGBP). The data is available at a native resolution of 0.5 km, which is also resampled to AMSR-E quarter degree grid system. Topographic Complexity: The topographic complexity information (V01.1) obtained from European Space Agency Climate Change Initiative (ESA CCI) phase II – soil moisture product's ancillary datasets (ESA-CCI-SM-v4.2, 2018), is developed using the USGS 30-s Global Elevation Data (GTOPO30) (USGS, 1996). The elevation data is normalized between 0 to 100, and is resampled to quarter degree grid system (aligned with that of AMSR-E, using nearest neighborhood technique, ESA-CCI-SM-v4.2, 2018). Multi-Source Weighted-Ensemble Precipitation (MSWEP) Data: The MSWEP is a global scale gridded precipitation dataset available from 1979 to 2016, at three hourly temporal 0.1° × 0.1° spatial resolutions (Beck et al. 2017a, 2017b). The dataset is prepared from multiple precipitation data sources, such as rain gauges, satellites, and reanalysis products. In the current work, the Version 2 dataset of daily precipitation (procured from http://www.gloh2o.org/) is used at selected locations across the globe (details regarding these locations are presented in Section 4) for the period 2004–2005. HR Map: This map is based on previous calibration studies which used in situ information (Fernandez-Moran et al., 2017b) and modelled data (Parrens et al., 2016) in order to provide representative roughness values for different cover types (Table B.1), which are based on the International Geosphere-Biosphere Programme (IGBP) classification. In order to account for the heterogeneity present in pixels, HR is calculated by linear weighting the roughness contribution according to the percentage of each IGBP class within the pixel based on the values provided in Table B.1. In order to obtain the percentage of each IGBP class inside the pixel, we used the 0.5 km resolution LULC product (Broxton et al., 2014). NDVI Data: MODIS MOD13C1 version 6 product provides Normalized Difference Vegetation Index (NDVI) on Climate Modeling Grid (CMG) of 0.05° resolution (Dian, 2015). The data is prepared as a cloud free composite at 16 days temporal resolution. NDVI timeseries for the duration 2004–2005 are extracted for six selected locations (Table 2) in order to compare with corresponding SPRA and LPRM timeseries. Table B.1

Representative roughness values for different cover types to generate HR map S. No.

Class

Roughness Value (SMOS-IC)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Evergreen needle leaf forest Evergreen broadleaf forest Deciduous needle leaf forest Deciduous broadleaf forest Mixed forests Closed shrublands Open shrublands Woody savannas Savannas Grasslands Permanent wetland Croplands Urban and built-up Cropland/Natural Vegetation Mosaic Snow and ice Barren and sparsely vegetated

0.30 0.47 0.43 0.46 0.43 0.27 0.17 0.35 0.23 0.12 0.19 0.17 0.21 0.22 0.12 0.02

B.4 Data using for the evaluation of soil moisture products International Soil Moisture Network (ISMN) Data: Observations from ARM (24), COSMOS (2), FLUXNET-AMERIFLUX (2), PBO-H2O (58), SCAN (174), SNOTEL (374), SOILSCAPE (64), USCRN (90), and USDA-ARS (4) networks (numbers in parenthesis indicate the number of stations) are considered for the analysis. These observations are corrected filtered based on quality flags indicated by the ISMN (Dorigo et al., 2011). All the observations are temporally aggregated to daily scale and spatially aggregated to the quarter degree grid system of this study using unweighted arithmetic mean. The 792 stations resulted in 551 grid cells containing station data over the CONUS. India Meteorological Department (IMD) Precipitation: The precipitation data procured from IMD (Pai et al., 2014) is a quarter degree dataset available over India for a period of 113 years (1901–2013) at daily scale. The gridding is carried out using information from 6995 rain gauge stations spread across the country. Given the high density of station data, along with stringent quality checks, it is assumed that this dataset is the most appropriate source of precipitation information over India. Further, it is assumed that precipitation information is accurate and all attributable differences in E [P SM ] curve behavior occur only due to soil moisture product accuracy.

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