Soil roughness strongly influences processes like erosion, infiltration, moisture and evaporation of soils as well as growth of agricultural plants. An approach to soil roughness based on active-passive microwave covariation is proposed in order to simultaneously retrieve the vertical RMS height (s) and horizontal correlation length (l) of soil surfaces from simultaneously measured radar and radiometer microwave signatures. The approach is based on a retrieval algorithm for active-passive covariation including the improved Integral Equation Method (I2EM). The algorithm is tested with the global active-passive microwave observations of the SMAP mission. The developed roughness retrieval algorithm shows independence of permittivity for > 10 [-] due to the covariation formalism. Results reveal that s and l can be estimated simultaneously by the proposed approach since surface patterns of non-vegetated areas become evident on global scale. In regions with sandy deserts, like the Sahara or the outback in Australia, determined and confirm rather smooth to semi-rough surface roughness patterns with small vertical RMS heights and corresponding higher horizontal correlation lengths

Akbar, Ruzbeh

Entekhabi, Dara

Fluhrer, Anke

Jagdhuber, Thomas

O'Neill, Peggy

O'Neill, Peggy E.

OPUS Augsburg

Simultaneous retrieval of surface roughness parameters for bare soils from combined active–passive microwave SMAP observations

Simultaneous retrieval of surface roughness parameters from combined active-passive SMAP observations

OPUS - Augsburg University Publication Server

Soil roughness strongly influences processes like erosion, infiltration, moisture and evaporation of soils as well as growth of agricultural plants. An approach to soil roughness based on active-passive microwave covariation is proposed in order to simultaneously retrieve the vertical RMS height (s) and horizontal correlation length (l) of soil surfaces from simultaneously measured radar and radiometer microwave signatures. The approach is based on a retrieval algorithm for active-passive covariation including the improved Integral Equation Method (I2EM). The algorithm is tested with the global active-passive microwave observations of the SMAP mission. The developed roughness retrieval algorithm shows independence of permittivity for e_s > 10 [-] due to the covariation formalism. Results reveal that s and l can be estimated simultaneously by the proposed approach since surface patterns of non-vegetated areas become evident on global scale. In regions with sandy deserts, like the Sahara or the outback in Australia, determined s and l confirm rather smooth to semi-rough surface roughness patterns with small vertical RMS heights and corresponding higher horizontal correlation lengths

Institute of Transport Research:Publications

SIMULTAENOUS RETRIEVAL OF SURFACE ROUGHNESS PARAMETERS FROM COMBINED ACTIVE-PASSIVE SMAP OBSERVATIONS  Anke Fluhrer1, Thomas Jagdhuber1, Ruzbeh Akbar2, Peggy O’Neill3, Dara Entekhabi2  1German Aerospace Center, Microwaves and Radar Institute, P. O. BOX 1116, 82234 Weßling, Germany. 2Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139 USA. 3Hydrological Science Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA.  ABSTRACT  Soil roughness strongly influences processes like erosion, infiltration, moisture and evaporation of soils as well as growth of agricultural plants. An approach to soil roughness based on active-passive microwave covariation is proposed in order to simultaneously retrieve the vertical RMS height (s) and horizontal correlation length (l) of soil surfaces from simultaneously measured radar and radiometer microwave signatures. The approach is based on a retrieval algorithm for active-passive covariation including the improved Integral Equation Method (I2EM). The algorithm is tested with the global active-passive microwave observations of the SMAP mission. The developed roughness retrieval algorithm shows independence of permittivity for 𝜀𝑠 > 10 [-] due to the covariation formalism. Results reveal that s and l can be estimated simultaneously by the proposed approach since surface patterns of non-vegetated areas become evident on global scale. In regions with sandy deserts, like the Sahara or the outback in Australia, determined 𝑠 and 𝑙 confirm rather smooth to semi-rough surface roughness patterns with small vertical RMS heights and corresponding higher horizontal correlation lengths.  Index Terms— radar, radiometer, RMS height, correlation length, covariation, I2EM  1. INTRODUCTION  Soil roughness as a boundary property between the pedosphere and the atmosphere is an essential variable in numerous physical processes which are related to water, energy and nutrient flux and exchange [1]. It plays an indispensable role in soil moisture sensing from active and passive microwave techniques, one of the key state variables in the global water cycle having significant impact on the global weather and climate system [2]. Due to their critical role in land surface dynamics, both soil moisture and soil roughness affect the brightness temperature 𝑇𝑏𝑃 [K] and backscatter |𝑆𝑃𝑃|2 [dB] characteristics of natural surfaces measured by radiometers and radars, respectively. While 𝑇𝑏𝑃 can be expressed as a function of soil moisture, soil roughness and effective surface temperature for bare soils [3], |𝑆𝑃𝑃|2 is only dominated by surface soil moisture and soil roughness for the case of bare soils [4], at polarization 𝑃, respectively. In the last decades, soil roughness is regarded as a subordinate variable in the field of microwave remote sensing despite its importance in several environmental applications such as land surface modeling for soil erosion [1]. The two fundamental parameters which describe the soil surface roughness are the standard deviation of the surface height variation (or RMS height) denoted by 𝑠 [cm] with its related autocorrelation function (ACF), and the surface correlation length denoted by 𝑙 [cm]. In order to estimate 𝑠 and 𝑙 concurrently and independent of permittivity we link active and passive microwave signatures through their covariation.   2. DATASET  Global data from NASA’s Soil Moisture Active Passive (SMAP) mission launched in 2015 is applied for this study. We used the SMAP L1B Radar Half-Orbit Time-Ordered low resolution backscatter |𝑆𝑃𝑃|2 [5], the SMAP L1C Radiometer Half-Orbit Time-Ordered Brightness Temperatures 𝑇𝑏𝑃 [6], the physical soil temperature 𝑇 and soil moisture extracted from the SMAP L3SM_P products [7], all posted on a 36 km Equal-Area Scalable Earth-2 (EASE-2) grid [8, 9]. The period of study with SMAP data covers the months from 04/14/2015 to 07/07/2015 until the failure of the SMAP radar sensor [9].  For filtering of the retrieval results to non-vegetated areas we used the vegetation optical depth (VOD) posted on a 36 km EASE-2 grid from the SMAP dataset processed with the multi-temporal dual-channel retrieval algorithm (MT-DCA) [9], and the surface condition quality flags for snow and frozen ground from the SMAP L3 Radiometer Global and Northern Hemisphere Daily 36 km EASE-Grid Freeze/Thaw State [10].  3. METHODS  In order to combine microwave measurements from radar and radiometers independently of permittivity, their covariation with soil moisture is utilized [11, 12, 13]. We introduced the formulation for active-passive covariation already in [13]. The basic of this method are the data-based 𝛽𝑃𝑃 𝐷𝑎𝑡𝑎 and the model-based 𝛽𝑃−𝑃𝑃𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  covariation parameters for simultaneous retrieval of surface roughness parameters 𝑠 and 𝑙 [13].  3.1. Formulation of Active-Passive Microwave Covariation  The fundamental formulation of active-passive microwave covariation is based on Kirchhoff’s law of energy conservation and derived in [12]. The covariation-based retrieval formulation includes the emissivity 𝐸𝑃 [-] and backscattering |𝑆𝑃𝑃|2 [-] characteristics of bare surfaces and is proposed here for active-passive soil roughness retrieval at L-band. The relationship between the backscattering coefficient of the active radar (|𝑆𝑃𝑃|2) and the emissivity (𝐸𝑃 =  𝑇𝑏𝑃/𝑇) based on brightness temperatures 𝑇𝑏𝑃  [K] of the passive radiometer is functionally linear and can be expressed by the two parameters 𝛼 and 𝛽, with 𝛼 [-] being the intercept and 𝛽 [-] being the slope of a linear regression (1) [8]. 𝑇𝑏𝑃/𝑇 =  𝛼 + 𝛽 ∗  |𝑆𝑃𝑃|2  (1) For bare soils the intercept 𝛼 is 1, due to the fact that vegetation is absent [12].  Based on (1), the 𝑃-polarized covariation parameter can be calculated with (2), which stems from [11] and [14], and is the inversion of the active-passive covariation forward model for bare soils presented in [12]: 𝛽 =𝐸𝑃−1|𝑆𝑃𝑃|2  =   𝑇𝑏𝑃𝑇 − 1|𝑆𝑃𝑃|2 , (2) with 𝑇 [K] as physical surface temperature mostly from about the top 5 [cm] of the soil but variable with soil moisture and temperature profiles. Thus, the slope 𝛽 describes the covariation between emissivity and backscatter for bare soils due to soil roughness. One restriction is that both sensors, radar and radiometer, need to have the same spatial resolution in order to observe the same roughness scale. Plus, since microwave-retrieved soil surface roughness is dependent on the wavelength of the observation system, the surface roughness parameters 𝑠 and 𝑙 are estimated in units of wavelength and subsequently need to be scaled by the wave number 𝑘 =2𝜋/𝜆 to the unit of meters.  3.1.1. Data-based Retrieval of covariation The data-based covariation parameter 𝛽𝑃𝑃 𝐷𝑎𝑡𝑎 [-] for polarization 𝑃 is calculated according to (2). As input parameters for active-passive microwave signatures (𝑇𝑏𝑃 , 𝑇 and |𝑆𝑃𝑃|2) we used the datasets from the SMAP mission (cf. 2.).  3.1.2. Definition of Forward Model for covariation The model-based covariation parameter 𝛽𝑃−𝑃𝑃𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  [-] for respective polarization 𝑃 and type of ACF calculated with the proposed covariation-based retrieval algorithm (2), is dependent on surface roughness parameters 𝑠 and 𝑙. We defined a range of values for the surface roughness parameter 𝑠 from 0.05 cm to 10 cm in 0.1 cm steps, and 𝑙 from 1 cm to 21 cm in 1.0 cm steps. Besides 𝑠 and 𝑙, input parameter for active-passive microwave signature simulations is the permittivity 𝜀𝑠, retrieved from soil moisture information by a pedo-transfer function like [15]. Within the first presentation of this active-passive retrieval algorithm in [13], the covariation parameter 𝛽𝑃−𝑃𝑃𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  is the ratio of Fresnel and Bragg roughness loss terms. However, sensitivity analyses revealed unsatisfying results for the retrieval of surface correlation length 𝑙. The reason could be the missing incoherent part of surface scattering within the Fresnel roughness loss term. Hence, we revised our approach for simultaneous retrieval of surface roughness parameters and used the I2EM for simulations of active and passive microwave bare soil interactions. The reason for employing the I2EM is its physics basis and analytical formalism for backscatter and emissivity based on surface roughness parameters 𝑠 and 𝑙, frequency, incident angle and permittivity [16, 17]. Due to its analytical formalism, I2EM is preferred over more computationally intensive numerical methods such as the Numerical Maxwell Model in 3-D (NMM3D) [17].  3.2. Estimation of Surface Roughness Parameters 𝒔 and 𝒍  As described in [13], we determine the best fit between model- and data-based covariation parameters in order to estimate surface roughness parameters 𝑠 and 𝑙. Hence, we calculate the differences for horizontal as well as vertical polarizations and add up the respective results for both polarizations. We then receive a look-up-table (LUT) with the dimensions of the pre-defined ranges of roughness parameters 𝑠 and 𝑙. The position of the global minimum of the LUT corresponds to the best-fitting values for surface roughness parameters 𝑠 and 𝑙 [13].  4. RESULTS  4.1. Sensitivity analyses on permittivity with I2EM  Besides surface roughness parameters 𝑠 and 𝑙 permittivity 𝜀𝑠 is the other input parameter into the I2EM for calculation of backscatter and emissivity. In order to determine the influence of 𝜀𝑠 on surface roughness parameter retrievals we conducted several sensitivity analyses. For instance, we compared the full range of physically possible permittivity values with the calculated model-based covariation parameter 𝛽𝑃−𝑃𝑃𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  for both polarizations. As depicted in Figure 1, results show that for higher permittivity values the 𝛽𝑃−𝑃𝑃𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  is at constant level and only exhibits changes for 𝜀𝑠 approximately lower than ten. Hence, with increasing 𝜀𝑠 the I2EM computed backscatter and emissivity are more and more insensitive to permittivity which in turn applies to the I2EM-based retrieval of surface roughness parameters 𝑠 and 𝑙. Figure 1. Influence of permittivity on model-based covariation parameter 𝜷𝑷−𝑷𝑷𝑴𝒐𝒅𝒆𝒍𝑨𝑪𝑭 from backscatter and emissivity values of I2EM assuming a Gaussian ACF. (A) Results for 𝜷𝑯−𝑯𝑯𝑴𝒐𝒅𝒆𝒍𝑨𝑪𝑭, (B) Results for 𝜷𝑽−𝑽𝑽𝑴𝒐𝒅𝒆𝒍𝑨𝑪𝑭; Model input parameters: vertical RMS height of 0.5 cm, 1.5 cm and 2.5 cm, horizontal correlation length of 4 cm, 7 cm and 10 cm.   4.2. Global surface roughness retrieval with SMAP data  Figure 2 illustrates the retrieval results for surface roughness parameters 𝑠  and 𝑙 calculated with the proposed covariation-based approach assuming a Gaussian ACF. Pixels with VOD > 0.12 or with more than one day covered by snow or frozen ground during the investigation period or with > 5 % water fraction are masked to guarantee analyzes exclusively for bare soils. Results for surface roughness parameter 𝑠 are in the range from 0.05 m to 7 cm with most frequent heights (~60.3 %) between 0.05 cm to 4 cm. In Figure 2A the smallest RMS heights are found within the Sahara whereas largest heights are reached at the edges of the Sahara or in Australia due to sparse vegetation (e.g. shrublands). Results for surface roughness parameter 𝑙 are between 1 cm and 21 cm with most lengths (~75.4 %) from 2 cm to 6 cm. Lowest horizontal correlation lengths are estimated, for instance, in the Sahara or in the southern part of Australia. Largest lengths can be found in the north western part of Australia as well as in Kazakhstan and Mongolia (cf. Fig. 2B).  Figure 2. Global time-averaged (April-July 2015) results for estimated surface roughness parameters 𝒔 (A) and 𝒍 (B) assuming a Gaussian ACF and using SMAP active and passive microwave observations. Inset shows histogram of the estimated parameter.  By taking a closer look at both roughness parameters, results show opposed retrievals for vertical RMS heights and horizontal correlation lengths. This means, in regions with smallest RMS-heights the corresponding autocorrelation lengths are largest and vice versa. Furthermore, retrieval results for 𝑠 and 𝑙 indicate rather smooth surface structures in regions with deserts, like the Sahara in Africa, the outback in Australia or the northern part of the Gobi in Mongolia, and rather rough surface structures at the edges of deserts, like south of the Sahara or the outback. Sensitivity analyses based on comparisons of initial and retrieved values for surface roughness parameter 𝑠 and 𝑙 with varying deviation on the I2EM computed input parameters confirmed the feasibility and accuracy of the proposed covariation-based approach with correlations between input and output 𝑠-values from 77 % to 98 %. Compared to presented surface roughness results for 𝑠 and 𝑙 in [13], further analyses revealed that the revised covariation-based approach proposed in this study outperforms the initially introduced retrieval algorithm in [13] (based on Fresnel and Bragg roughness loss terms) especially regarding the estimation of the horizontal correlation length.  5.  CONLCUSION  In this study, we presented a covariation-based retrieval algorithm to simultaneously determine surface roughness parameters (𝑠, 𝑙) from combined polarimetric radar and radiometer microwave signatures of the SMAP mission. The analyses for bare soil areas on the globe confirm that surface roughness parameters 𝑠 and 𝑙 can be calculated simultaneously over large sparsely and non-vegetated areas, compared to field-based techniques, and for each individual active-passive acquisition pair (no time series needed). Admitting, this requires nearly identical spatial resolutions for radar and radiometer acquisitions in order to observe roughness at the same scale. The utilization of the covariation parameter 𝛽 combined with the forward model I2EM to retrieve 𝑠 and 𝑙 concurrently provides the advantage of a quasi-permittivity-independent algorithm for non-arid soils (𝜀𝑠 > 10 [-], cf. Fig. 1). Furthermore, the model basis (I2EM) of the approach enables the application of varying autocorrelation functions (ACF). Hence, calculations for 𝑠 and 𝑙 can also be performed for an exponential or 𝑛-exponential ACF and will be further investigated. Despite the rather coarse resolution of the SMAP datasets (~36 km) the retrieval results for 𝑠 and 𝑙 can be used as larger-scale indicators of global soil surface patterns. In regions with rather smooth surface structures, like sandy deserts (e.g. parts of Sahara or Gobi), the estimated surface roughness parameters are also indicating rather smooth surface structures with small vertical RMS heights and corresponding higher horizontal correlation lengths.  ACKNOWLEDGEMENTS  We are grateful to MIT for supporting this research with the MIT-Germany Seed Fund „Global Water Cycle and Environmental Monitoring using Active and Passive Satellite-based Microwave Instruments”.  REFERENCES  [1] Marzahn, P., Ludwig, R. (2009). “On the derivation of soil surface roughness from multi parametric PolSAR data and its potential for hydrological modeling.” In: Hydrol. Earth Syst. Sci., 13, pp. 381-394. [2] McColl, K.A. et al. (2017). “The global distribution and dynamics of surface soil moisture.” In: Nature Geoscience, 10(2), p.100. [3] Srivastava, P. et al. (2014). “Evaluation of Dielectric Mixing Models for Passive Microwave Soil Moisture Retrieval Using Data From ComRAD Ground-Based SMAP Simulator.” In: Selected Topics in Applied Earth Observations and Remote Sensing, IEEE, vol. 99, pp. 1-10. [4] Entekhabi, D. et al. (2010). “The Soil Moisture Active Passive (SMAP) Mission.” In: Proc. IEEE, 98, 704–716, doi:10.1109/JPROC.2010.2043918. [5] SMAP data 2015 (NASA). Dataset: SMAP_L1B_S0_ LoRes_V2. Retrieved from ASF DAAC 7 December 2015. doi: 10.5067/J4SZZV52B88J. [6] Chan, S., Njoku, E.G., Colliander, A. (2016). SMAP L1C Radiometer Half-orbit 36 km EASE-grid Brightness Temperatures, Version 3. Global Projection. NASA  National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado USA. https://doi.org/10.5067/E51BSP6V3KP7. 08.30.17. [7] O'Neill, P.E. et al. (2016). SMAP L3 Radiometer Global Daily 36 km EASE-Grid Soil Moisture, Version 4. Global Projection. NASA National Snow and Ice Data Center Distributed Active Archive Center, Boulder, Colorado USA. https://doi.org/10.5067/OBBHQ5W22HME. 08/30/2017. [8] Entekhabi, D. et al. (2014). “Soil Moisture Active Passive (SMAP). Algorithm Theoretical Basis Document L2 & L3 Radar/Radiometer Soil Moisture (Active/Passive) Data Products.” [9] Konings, A.G., Piles, M., Das, N., Entekhabi, D. (2017): L-band vegetation optical depth and effective scattering albedo estimation from SMAP. In: Remote Sensing of Environment, Vol. 198, pp. 460-470, https://doi.org/10.1016/j.rse.2017.06.037. [10] Xu, X. et al. (2016). SMAP L3 Radiometer Northern Hemisphere Daily 36 km EASE-Grid Freeze/Thaw State, Version 1. Global Projection. Boulder, Colorado USA. NASA National Snow and Ice Data Center Distributed Active Archive Center. https://doi.org/10.5067/RDEJQEETCNWV. 08.30.17. [11] Saatchi, S., Njoku, E., Wegmüller, U. (1993). “Synergism of active and passive microwave data for estimating bare soil surface moisture.” ESA/NASA Int. Workshop Passive Microwave Remote Sens. Res. Related to Land-atmosphere. Interactions, Saint-Lary, France, Jan. 11-15, pp. 205-224. [12] Jagdhuber, T. et al. (2018). “Physics-Based Modeling of Active and Passive Microwave Covariations Over Vegetated Surfaces.” In: IEEE Transactions on Geoscience and Remote Sensing, doi:10.1109/TGRS.2018.2860630. [13] Fluhrer, A. et al. (2018). "Physics-Based Retrieval of Surface Roughness Parameters for Bare Soils from Combined Active-Passive Microwave Signatures.” IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium, Valencia, pp. 337-340. doi: 10.1109/IGARSS.2018.8519563. [14] Jagdhuber, T. et al. (2016). “Physically-based retrieval of SMAP active-passive measurements covariation and vegetation structure parameters.” International Geoscience and Remote Sensing Symposium (IGARSS), vol. 2016-11-1, pp. 3078-3081. [15] Mironov, V.L., Kosolapova, L.G.,Fomin, S.V. (2009). “Physically and mineralogically based spectroscopic dielectric model for moist soils,” In: IEEE Trans. Geosci. Remote Sens., 47(7), pp. 2059–2070. [16] Ulaby, F.T. et al. (2014). “Microwave radar and radiometric remote sensing.” University of Michigan. Press Ann Arbor. [17] Fung, A.K. et al. (2012). “An Improved IEM Model for Bistatic Scattering From Rough Surfaces.” In: Journal of Electromagnetic Waves and Applications, 16, 689–702. doi:10.1163/156939302X01119. 

Simultaenous Retrieval of Surface Roughness Parameters from Combined Active-Passive SMAP Observations

Crossref

Simultaneous Retrieval of Surface Roughness Parameters from Combined Active-Passive SMAP Observations

An active-passive microwave retrieval algorithm for simultaneous determination of soil surface roughness parameters (vertical RMS height (s) and horizontal correlation length (l)) is presented for bare soils. The algorithm is based on active-passive microwave covariation including the improved Integral Equation Method (I2EM) and is tested with global SMAP observations. Estimated retrieval results for s and l are overall consistent with values in the literature, indicating the validity of the proposed algorithm. Sensitivity analyses showed that the developed roughness retrieval algorithm is independent of permittivity for es > 10 [-]. Furthermore, the physical model basis of this approach (I2EM) allows application of different autocorrelation functions (ACF), such as Gaussian and exponential ACFs. Global roughness retrieval results confirm bare areas in deserts such as Sahara or Gobi. However, the type of ACF used within roughness parameter estimation is important. Retrieval results for the Gaussian ACF describe a rougher surface than retrieval results for the exponential ACF. No correlations were found between roughness results and the amount of precipitation or the soil texture, which could be due to the coarse spatial resolution of the SMAP data. The extension of this approach to vegetated soils is planned as an add-on study

Simultaneous Retrieval of Surface Roughness Parameters for Bare Soils from Combined Active-Passive Microwave SMAP Observations

NASA Technical Reports Server

SIMULTAENOUS RETRIEVAL OF SURFACE ROUGHNESS PARAMETERS FROM 
COMBINED ACTIVE-PASSIVE SMAP OBSERVATIONS 
 
Anke Fluhrer1, Thomas Jagdhuber1, Ruzbeh Akbar2, Peggy O’Neill3, Dara Entekhabi2 
 
1German Aerospace Center, Microwaves and Radar Institute, P. O. BOX 1116, 82234 Weßling, Germany. 
2Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139 USA. 
3Hydrological Science Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA. 
 
ABSTRACT 
 
Soil roughness strongly influences processes like erosion, 
infiltration, moisture and evaporation of soils as well as 
growth of agricultural plants. An approach to soil roughness 
based on active-passive microwave covariation is proposed 
in order to simultaneously retrieve the vertical RMS height 
(s) and horizontal correlation length (l) of soil surfaces from 
simultaneously measured radar and radiometer microwave 
signatures. The approach is based on a retrieval algorithm for 
active-passive covariation including the improved Integral 
Equation Method (I2EM). The algorithm is tested with the 
global active-passive microwave observations of the SMAP 
mission. The developed roughness retrieval algorithm shows 
independence of permittivity for 𝜀𝑠 > 10 [-] due to the 
covariation formalism. Results reveal that s and l can be 
estimated simultaneously by the proposed approach since 
surface patterns of non-vegetated areas become evident on 
global scale. In regions with sandy deserts, like the Sahara or 
the outback in Australia, determined 𝑠 and 𝑙 confirm rather 
smooth to semi-rough surface roughness patterns with small 
vertical RMS heights and corresponding higher horizontal 
correlation lengths. 
 
Index Terms— radar, radiometer, RMS height, 
correlation length, covariation, I2EM 
 
1. INTRODUCTION 
 
Soil roughness as a boundary property between the 
pedosphere and the atmosphere is an essential variable in 
numerous physical processes which are related to water, 
energy and nutrient flux and exchange [1]. It plays an 
indispensable role in soil moisture sensing from active and 
passive microwave techniques, one of the key state variables 
in the global water cycle having significant impact on the 
global weather and climate system [2]. Due to their critical 
role in land surface dynamics, both soil moisture and soil 
roughness affect the brightness temperature 𝑇𝑏𝑃 [K] and 
backscatter |𝑆𝑃𝑃|
2 [dB] characteristics of natural surfaces 
measured by radiometers and radars, respectively. While 𝑇𝑏𝑃 
can be expressed as a function of soil moisture, soil roughness 
and effective surface temperature for bare soils [3], |𝑆𝑃𝑃|
2 is 
only dominated by surface soil moisture and soil roughness 
for the case of bare soils [4], at polarization 𝑃, respectively. 
In the last decades, soil roughness is regarded as a 
subordinate variable in the field of microwave remote sensing 
despite its importance in several environmental applications 
such as land surface modeling for soil erosion [1]. The two 
fundamental parameters which describe the soil surface 
roughness are the standard deviation of the surface height 
variation (or RMS height) denoted by 𝑠 [cm] with its related 
autocorrelation function (ACF), and the surface correlation 
length denoted by 𝑙 [cm]. In order to estimate 𝑠 and 𝑙 
concurrently and independent of permittivity we link active 
and passive microwave signatures through their covariation.  
 
2. DATASET 
 
Global data from NASA’s Soil Moisture Active Passive 
(SMAP) mission launched in 2015 is applied for this study. 
We used the SMAP L1B Radar Half-Orbit Time-Ordered low 
resolution backscatter |𝑆𝑃𝑃|
2 [5], the SMAP L1C Radiometer 
Half-Orbit Time-Ordered Brightness Temperatures 𝑇𝑏𝑃 [6], 
the physical soil temperature 𝑇𝑃𝐻𝑌𝑆 and soil moisture 
extracted from the SMAP L3SM_P products [7], all posted 
on a 36 km Equal-Area Scalable Earth-2 (EASE-2) grid [8, 
9]. The period of study with SMAP data covers the months 
from 04/14/2015 to 07/07/2015 until the failure of the SMAP 
radar sensor [9].  
For filtering of the retrieval results to non-vegetated areas we 
used the vegetation optical depth (VOD) posted on a 36 km 
EASE-2 grid from the SMAP dataset processed with the 
multi-temporal dual-channel retrieval algorithm (MT-DCA) 
[9], and the surface condition quality flags for snow and 
frozen ground from the SMAP L3 Radiometer Global and 
Northern Hemisphere Daily 36 km EASE-Grid Freeze/Thaw 
State [10]. 
 
3. METHODS 
 
In order to combine microwave measurements from radar and 
radiometers independently of permittivity, their covariation 
with soil moisture is utilized [11, 12, 13]. We introduced the 
formulation for active-passive covariation already in [13]. 
The basic of this method are the data-based 𝛽𝑃𝑃 
𝐷𝑎𝑡𝑎 and the 
model-based 𝛽𝑃−𝑃𝑃
𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  covariation parameters for 
https://ntrs.nasa.gov/search.jsp?R=20190028772 2019-09-26T19:38:22+00:00Z
simultaneous retrieval of surface roughness parameters 𝑠 and 
𝑙 [13]. 
 
3.1. Formulation of Active-Passive Microwave 
Covariation 
 
The fundamental formulation of active-passive microwave 
covariation is based on Kirchhoff’s law of energy 
conservation and derived in [12]. The covariation-based 
retrieval formulation includes the emissivity 𝐸𝑃 [-] and 
backscattering |𝑆𝑃𝑃|
2 [-] characteristics of bare surfaces and 
is proposed here for active-passive soil roughness retrieval at 
L-band. The relationship between the backscattering 
coefficient of the active radar (|𝑆𝑃𝑃|
2) and the emissivity 
(𝐸𝑃 =  𝑇𝑏𝑃/𝑇) based on brightness temperatures 𝑇𝑏𝑃  [K] of 
the passive radiometer is functionally linear and can be 
expressed by the two parameters 𝛼 and 𝛽, with 𝛼 [-] being 
the intercept and 𝛽 [-] being the slope of a linear regression 
(1) [8]. 
𝑇𝑏𝑃/𝑇 =  𝛼 + 𝛽 ∗  |𝑆𝑃𝑃|
2  (1) 
For bare soils the intercept 𝛼 is 1, due to the fact that 
vegetation is absent [12].  
Based on (1), the 𝑃-polarized covariation parameter can be 
calculated with (2), which stems from [11] and [14], and is 
the inversion of the active-passive covariation forward model 
for bare soils presented in [12]: 
𝛽 =
𝐸𝑃−1
|𝑆𝑃𝑃|
2  =   
𝑇𝑏𝑃
𝑇𝑃𝐻𝑌𝑆
 − 1
|𝑆𝑃𝑃|
2 , 
(2) 
with 𝑇𝑃𝐻𝑌𝑆 [K] as physical surface temperature from the top 
5 cm layer of the soil. 
Thus, the slope 𝛽 describes the covariation between 
emissivity and backscatter for bare soils due to soil 
roughness. One restriction is that both sensors, radar and 
radiometer, need to have the same spatial resolution in order 
to observe the same roughness scale. Plus, since microwave-
retrieved soil surface roughness is dependent on the 
wavelength of the observation system, the surface roughness 
parameters 𝑠 and 𝑙 are estimated in units of wavelength and 
subsequently need to be scaled by the wave number 𝑘 =
2𝜋/𝜆 to the unit of meters. 
 
3.1.1. Data-based Retrieval of covariation 
The data-based covariation parameter 𝛽𝑃𝑃 
𝐷𝑎𝑡𝑎 [-] for 
polarization 𝑃 is calculated according to (2). As input 
parameters for active-passive microwave signatures (𝑇𝑏𝑃 , 
𝑇𝑃𝐻𝑌𝑆 and |𝑆𝑃𝑃|
2) we used the datasets from the SMAP 
mission (cf. 2.). 
 
3.1.2. Definition of Forward Model for covariation 
The model-based covariation parameter 𝛽𝑃−𝑃𝑃
𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  [-] for 
respective polarization 𝑃 and type of ACF calculated with the 
proposed covariation-based retrieval algorithm (2), is 
dependent on surface roughness parameters 𝑠 and 𝑙. We 
defined a range of values for the surface roughness parameter 
𝑠 from 0.05 cm to 10 cm in 0.1 cm steps, and 𝑙 from 1 cm to 
21 cm in 1.0 cm steps.  
Besides 𝑠 and 𝑙, input parameter for active-passive 
microwave signature simulations is the permittivity 𝜀𝑠, 
retrieved from soil moisture information by a pedo-transfer 
function like [15]. 
Within the first presentation of this active-passive retrieval 
algorithm in [13], the covariation parameter 𝛽𝑃−𝑃𝑃
𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  is the 
ratio of Fresnel and Bragg roughness loss terms. However, 
sensitivity analyses revealed unsatisfying results for the 
retrieval of surface correlation length 𝑙. The reason could be 
the missing incoherent part of surface scattering within the 
Fresnel roughness loss term. Hence, we revised our approach 
for simultaneous retrieval of surface roughness parameters 
and used the I2EM for simulations of active and passive 
microwave bare soil interactions. The reason for employing 
the I2EM is its physics basis and analytical formalism for 
backscatter and emissivity based on surface roughness 
parameters 𝑠 and 𝑙, frequency, incident angle and permittivity 
[16, 17]. Due to its analytical formalism, I2EM is preferred 
over more computationally intensive numerical methods such 
as the Numerical Maxwell Model in 3-D (NMM3D) [17]. 
 
3.2. Estimation of Surface Roughness Parameters 𝒔 and 𝒍 
 
As described in [13], we determine the best fit between 
model- and data-based covariation parameters in order to 
estimate surface roughness parameters 𝑠 and 𝑙. Hence, we 
calculate the differences for horizontal as well as vertical 
polarizations and add up the respective results for both 
polarizations. We then receive a look-up-table (LUT) with 
the dimensions of the pre-defined ranges of roughness 
parameters 𝑠 and 𝑙. The position of the global minimum of 
the LUT corresponds to the best-fitting values for surface 
roughness parameters 𝑠 and 𝑙 [13]. 
 
4. RESULTS 
 
4.1. Sensitivity analyses on permittivity with I2EM 
 
Besides surface roughness parameters 𝑠 and 𝑙 permittivity 𝜀𝑠 
is the other input parameter into the I2EM for calculation of 
backscatter and emissivity. In order to determine the 
influence of 𝜀𝑠 on surface roughness parameter retrievals we 
conducted several sensitivity analyses. For instance, we 
compared the full range of physically possible permittivity 
values with the calculated model-based covariation 
parameter 𝛽𝑃−𝑃𝑃
𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  for both polarizations. As depicted in 
Figure 1, results show that for higher permittivity values the 
𝛽𝑃−𝑃𝑃
𝑀𝑜𝑑𝑒𝑙𝐴𝐶𝐹  is at constant level and only exhibits changes for 
𝜀𝑠 approximately lower than ten. Hence, with increasing 𝜀𝑠 
the I2EM computed backscatter and emissivity are more and 
more insensitive to permittivity which in turn applies to the 
I2EM-based retrieval of surface roughness parameters 𝑠 and 
𝑙. 
Figure 1. Influence of permittivity on model-based covariation 
parameter 𝜷𝑷−𝑷𝑷
𝑴𝒐𝒅𝒆𝒍𝑨𝑪𝑭 from backscatter and emissivity values of 
I2EM assuming a Gaussian ACF. (A) Results for 𝜷𝑯−𝑯𝑯
𝑴𝒐𝒅𝒆𝒍𝑨𝑪𝑭, (B) 
Results for 𝜷𝑽−𝑽𝑽
𝑴𝒐𝒅𝒆𝒍𝑨𝑪𝑭; Model input parameters: vertical RMS 
height of 0.5 cm, 1.5 cm and 2.5 cm, horizontal correlation length 
of 4 cm, 7 cm and 10 cm.  
 
4.2. Global surface roughness retrieval with SMAP data 
 
Figure 2 illustrates the retrieval results for surface roughness 
parameters 𝑠  and 𝑙 calculated with the proposed covariation-
based approach assuming a Gaussian ACF. Pixels with VOD 
> 0.12 or with more than one day covered by snow or frozen 
ground during the investigation period or with > 5 % water 
fraction are masked to guarantee analyzes exclusively for 
bare soils. 
Results for surface roughness parameter 𝑠 are in the range 
from 0.05 m to 7 cm with most frequent heights (~60.3 %) 
between 0.05 cm to 4 cm. In Figure 2A the smallest RMS 
heights are found within the Sahara whereas largest heights 
are reached at the edges of the Sahara or in Australia due to 
sparse vegetation (e.g. shrublands). Results for surface 
roughness parameter 𝑙 are between 1 cm and 21 cm with most 
lengths (~75.4 %) from 2 cm to 6 cm. Lowest horizontal 
correlation lengths are estimated, for instance, in the Sahara 
or in the southern part of Australia. Largest lengths can be 
found in the north western part of Australia as well as in 
Kazakhstan and Mongolia (cf. Fig. 2B). 
 
Figure 2. Global time-averaged (April-July 2015) results for 
estimated surface roughness parameters 𝒔 (A) and 𝒍 (B) assuming 
a Gaussian ACF and using SMAP active and passive microwave 
observations. Inset shows histogram of the estimated parameter. 
 
By taking a closer look at both roughness parameters, results 
show opposed retrievals for vertical RMS heights and 
horizontal correlation lengths. This means, in regions with 
smallest RMS-heights the corresponding autocorrelation 
lengths are largest and vice versa. Furthermore, retrieval 
results for 𝑠 and 𝑙 indicate rather smooth surface structures in 
regions with deserts, like the Sahara in Africa, the outback in 
Australia or the northern part of the Gobi in Mongolia, and 
rather rough surface structures at the edge of deserts, like 
south of the Sahara or the outback in Australia. 
Sensitivity analyses based on comparisons of initial and 
retrieved values for surface roughness parameter 𝑠 and 𝑙 with 
varying deviation on the I2EM computed input parameters 
confirmed the feasibility and accuracy of the proposed 
covariation-based approach with correlations between input 
and output 𝑠-values from 77 % to 98 %. 
Compared to presented surface roughness results for 𝑠 and 𝑙 
in [13], further analyses revealed that the revised covariation-
based approach proposed in this study outperforms the 
initially introduced retrieval algorithm in [13] (based on 
Fresnel and Bragg roughness loss terms) especially regarding 
the estimation of the horizontal correlation length. 
 
5.  CONLCUSION 
 
In this study, we presented a covariation-based retrieval 
algorithm to simultaneously determine surface roughness 
parameters (𝑠, 𝑙) from combined polarimetric radar and 
radiometer microwave signatures of the SMAP mission. The 
analyses for bare soil areas on the globe confirm that surface 
roughness parameters 𝑠 and 𝑙 can be calculated 
simultaneously over large sparsely and non-vegetated areas, 
compared to field-based techniques, and for each individual 
active-passive acquisition pair (no time series needed). 
Admitting, this requires nearly identical spatial resolutions 
for active radar and passive radiometer acquisitions in order 
to observe roughness at the same scale. The utilization of the 
covariation parameter 𝛽 combined with the forward model 
I2EM to retrieve surface roughness parameters 𝑠 and 𝑙 
concurrently provides the advantage of a quasi-permittivity-
independent algorithm for non-arid soils (𝜀𝑠 > 10 [-], cf. Fig. 
1). Furthermore, the model basis (I2EM) of the approach 
enables the application of varying autocorrelation functions 
(ACF). Hence, calculations for 𝑠 and 𝑙 can also be performed 
for an exponential or n-exponential ACF and will be further 
investigated. 
Despite the rather coarse resolution of the SMAP datasets 
(~36 km) the retrieval results for 𝑠 and 𝑙 can be used as larger-
scale indicators of global soil surface patterns. In regions with 
rather smooth surface structures, like sandy deserts (e.g. parts 
of Sahara or Gobi), the estimated surface roughness 
parameters are also indicating rather smooth surface 
structures with small vertical RMS heights and corresponding 
higher horizontal correlation lengths. 
 
ACKNOWLEDGEMENTS 
 
We are grateful to MIT for supporting this research with the 
MIT-Germany Seed Fund „Global Water Cycle and 
Environmental Monitoring using Active and Passive 
Satellite-based Microwave Instruments”. 
 
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Simultaenous Retrieval of Surface Roughness Parameters from Combined Active-Passive SMAP Observations

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