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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In the past decades, many studies on soil moisture retrieval from SAR demonstrated a poor correlation between the top layer soil moisture content and observed backscatter coefficients, which mainly has been attributed to difficulties involved in the parameterization of surface roughness. The present paper describes a theoretical study, performed on synthetical surface profiles, which investigates how errors on roughness parameters are introduced by standard measurement techniques, and how they will propagate through the commonly used Integral Equation Model (IEM) into a corresponding soil moisture retrieval error for some of the currently most used SAR configurations. Key aspects influencing the error on the roughness parameterization and consequently on soil moisture retrieval are: the length of the surface profile, the number of profile measurements, the horizontal and vertical accuracy of profile measurements and the removal of trends along profiles. Moreover, it is found that soil moisture retrieval with C-band configuration generally is less sensitive to inaccuracies in roughness parameterization than retrieval with L-band configuration.

Surface soil moisture plays a crucial role in various hydrological and agronomical processes: the top layer moisture content controls the infiltration rate during precipitation events and therefore largely influences the amount of surface runoff, it drives the crop development, and finally, affects the evapo-transpiration rate and thus the micro-climate and -meteorology.

The retrieval of soil moisture content from Synthetic Aperture Radar (SAR) relies on the dependency of the backscattered radar signal on the surface reflection coefficients of the sensed target [

Apart from soil moisture, the backscattered radar signal shows to be extremely dependent on the roughness state of the sensed surface, in most backscatter models described by the surface root mean square (RMS) height

A series of surface height points (roughness profile) is defined along a 1-dimensional surface transect, mostly sampled by means of meshboard, pin profilometer or laser techniques [

From this profile a linear trend is removed to compensate for the possibility that the measurement device was not aligned perfectly parallel to a horizontal reference surface [

The RMS height

As

This standard parameterization procedure is not absolute: vertical accuracies and horizontal spacings of measured surface points differ for various instruments, causing diverging roughness parameterizations [

As briefly summarized above, the parameterization of roughness from profile measurements is characterized by several problems. An extensive literature review on these surface roughness problems is provided by Verhoest

Many empirical, semi-empirical and theoretical models have been developed to retrieve soil moisture content from the backscattered radar signal. A large number of studies proposed a simple linear empirical relationship between the backscatter coefficient and soil moisture content. Such relationship is easy to apply, however, only valid for a single study site, under the condition that surface roughness remains constant over successive radar acquisitions [e.g., 17, 18]. The mostly used semi-empirical models, developed by Oh

The single scattering approximation of the IEM calculates backscatter coefficients

As soil roughness largely influences the backscattered signal, one can expect that a correct roughness parameterization is indispensable in order to ensure accurate soil moisture retrieval. To assess the impact of roughness parameterization errors on the soil moisture retrieval, a profound sensitivity analysis is performed using the following experimental setup: for different values of soil moisture (5, 15, 25 and 35 vol%), backscatter coefficients are calculated for

As is revealed from

Sensitivity plots to

The sign of the gradients expressed in

Based on the results of Section 3., one can deduce that even small errors in roughness parameterization, particularly of RMS height, may have a large impact on the soil moisture retrieval. This section further elaborates on the roughness parameterization errors that are associated with standard profile measurement techniques and on the influence of these errors on soil moisture retrieval. To be able to individually address the errors involved with each standard parameterization aspect, synthetical surface profiles are generated. Subsection 4.1. demonstrates the method used to generate such profiles.

The main advantage of synthetical profiles is that they can be designed with a predefined RMS height, correlation length, profile length and spacing between series of height points. Moreover, inaccuracies of the instrument measuring a profile may be easily simulated by adding white noise to each point of the series, and topographic height variations along the profile, which in reality may be caused by either an oblique positioning of the instrument or microrelief, may be introduced by adding a linear or undulating trend.

On the designed profiles, standard parameterization techniques can be applied and evaluated quantitatively. In Subsections 4.2. to 4.6., different experiments are set up to demonstrate respectively the influences of the following parameterization aspects: the profile length, the number of profiles over which

In order to assess the influence of roughness parameterization techniques on the soil moisture retrieval, a series of synthetical rough surface profiles is generated. The synthetical 1-dimensional profiles are identified using a first order autoregressive model for an exponential ACF:
_{t}_{t}

The dependency of roughness parameters on profile length has already been described in depth [e.g., 6, 8, 11, 36]: short profiles generally result in an underestimation of both

To assess the influence of profile length on the parameterization of roughness and soil moisture retrieval, extremely long profiles are generated with a Δ

Backscatter coefficients are then calculated for a soil having a specific moisture content and roughness parameters equal to the ones used to generate the extremely long profile. Subsequently, these backscatter coefficients are inverted with IEM^{−1} into soil moisture content, using the roughness parameters from the sampled profiles.

A rough estimate of the soil moisture retrieval error for a surface with given moisture content, roughness state and a certain sensor configuration may also be deduced from

In this experimental setup, it was assumed that an optimal parameterization of roughness requires an extremely large profile, resulting in precise asymptotic roughness parameters (see

According to Bryant

A field experiment is simulated in which roughness parameters are determined by averaging

Next, backscatter coefficients are calculated for given moisture contents, sensor configurations and the roughness parameters used to generate the extremely large profiles, and are subsequently inverted with IEM^{−1} into soil moisture content, using the series of averaged roughness parameters from sampled profiles. Only 4-m profiles are considered in this part of the experiment, as these are frequently used in practice.

Analysis of the soil moisture retrieval error for sampled 4-m profiles from surfaces with (

As can be seen in

The horizontal spacing between discrete height observations along the profile is mostly defined by the instrument used. For laser devices, this spacing commonly ranges between 1 mm [

To assess the impact of the horizontal spacing on the roughness parameterization and soil moisture retrieval, an experiment is set up in which ten 4-m profiles with given set of (

Subsequently, these roughness parameters are used for soil moisture retrieval from backscatter coefficients, obtained for given soil moisture contents and the roughness parameters defined at 1-mm spacing. Finally, the effect of a misinterpretation of the ACF on the soil moisture retrieval is investigated using the calculated roughness data from resampled profiles with 15-mm spacing.

Mean and standard deviations of roughness parameters calculated from ten resampled profiles are shown in

Mean and standard deviations of inverted soil moisture contents for different horizontal spacings and sensor configurations (

The accuracy of instruments that measure discrete surface height points varies from less than 1 mm for non-contact techniques, such as laser profilometers, up to 2.5 mm for instruments that require a destructive contact with the surface, e.g. meshboards and pin profilometers [

To assess the effect of the instrument accuracy on the roughness parameterization and consequently soil moisture retrieval, the following experiment is carried out: a noisy signal, uniformly distributed in [−

The calculated roughness parameters may then be used for inversion of backscatter coefficients obtained with given moisture contents and the predefined roughness parameters from profiles without added noise signal.

The Root Mean Square Errors (RMSE) between roughness parameters calculated on the noisy profiles and predefined roughness parameters are presented in

Soil moisture retrieval errors due to an inaccurate roughness parameterization are presented in

The standard procedure for roughness parameterization includes the removal of a linear trend from a profile to compensate for the fact that the profile transect may be slightly tilted with respect to a horizontal reference surface. However, in case a field shows a slightly undulating surface, corresponding to roughness at very low frequency, it is currently not known whether or not such low-frequency component should be removed from the profile in order to precisely measure the roughness spectrum as it is sensed by a radar signal, particularly for high-frequency radar (e.g. at C-band). As argued by Ulaby

To assess the impact of commonly used detrending techniques on roughness parameterization and soil moisture retrieval, ten 4-m profiles are generated with predefined (

The derived roughness parameter sets are then used to invert backscatter coefficients obtained for the predefined (

Similar tests on profiles with (

Based on this experiment, it cannot be decided whether or not undulations along profiles should be removed prior to roughness parameterization. However, it can be concluded that soil moisture retrieval results may be very different in case undulations are removed through non-linear detrending than in case they are maintained,

Correct surface roughness parameters are of extreme importance in order to accurately retrieve soil moisture from SAR. A sensitivity study of the soil moisture retrieval to RMS height and correlation length reveals that small errors on RMS height generally more affect the soil moisture retrieval than ten times larger errors on correlation length. Therefore, RMS height parameterization requires a higher accuracy than the parameterization of the correlation length. Besides, sensitivity surfaces of respectively

The profile length used during

The number of profiles over which RMS height and correlation length are averaged only has a moderate impact on the final roughness parameters and soil moisture retrieval results. Generally, a higher number of profiles is required for shorter profiles, surfaces with higher correlation lengths, higher soil moisture contents, and L-band HH configuration.

The horizontal spacing between height points measured along a profile is of low influence on the soil moisture retrieval, yet may cause confusion in the determination of the appropriate ACF. A misinterpretation of the slope of the ACF can lead to errors covering the complete range of moisture content.

Instrument inaccuracies up to ±2 mm, typically found for most current instruments, have a negligible impact on the soil moisture retrieval result. However, inaccuracies of ±5 mm may lead to errors ranging from ±0.5 vol% up to ±8 vol%. Such inaccuracies are possible for roughness parameterized using a meshboard and manual digitization.

Probably the most prevailing aspect in the parameterization of roughness is the removal of surface trends. In case the surface is characterized by an undulating trend, a linear removal may lead to retrieval errors up to 25 vol%, as was found on 4-m profiles of (

As shown in this paper, the parameterization of surface roughness is not obvious. In the demonstrated experiments, various aspects were treated individually. However, in practice, different parameterization problems show up simultaneously, through which roughness errors may add up or cancel out. Therefore, future research definitely needs to clarify the errors involved in the entire parameterization and soil moisture retrieval process. Moreover, optimal standard parameterization procedures should be developed in function of the sensor configuration and target properties under study. Finally, being a theoretical study, the obtained results should be corraborated with experimental SAR observations.

The research presented in this paper is funded by the Belgian Science Policy Office in the frame of the Stereo II programme - project SR/00/100.

Backscatter coefficients calculated for different values of RMS height and correlation length and a moisture content of 25 vol% for (a) an ASAR VV configuration and (b) a PALSAR HH configuration.

Sensitivity of the soil moisture retrieval to RMS height (vol%/cm) for an ASAR VV configuration and a moisture content of (a) 5 vol%, (b) 15 vol%, (c) 25 vol%, and (d) 35 vol%.

Sensitivity of the soil moisture retrieval to correlation length (vol%/cm) for an ASAR VV configuration and a moisture content of (a) 5vol%, (b) 15vol%, (c) 25vol%, and (d) 35vol%.

Sensitivity of the soil moisture retrieval to RMS height (vol%/cm) for a PALSAR HH configuration and a moisture content of (a) 5 vol%, (b) 15 vol%, (c) 25 vol%, and (d) 35 vol%.

Sensitivity of the soil moisture retrieval to correlation length (vol%/cm) for a PALSAR HH configuration and a moisture content of (a) 5vol%, (b) 15vol%, (c) 25 vol%, and (d) 35 vol%.

Mean and standard deviations of RMS height and correlation length for different profile lengths, sampled from large profiles with (a) (

Mean and standard deviations of inverted soil moisture contents for different profile lengths. Inverted soil moisture contents are derived using roughness parameters from sampled profiles, originating from large profiles with (

Number of profiles required to obtain a standard deviation of RMS height or correlation length less than 10% of the mean for different profile lengths. Sampled profiles originate from large profiles with (

Mean and standard deviations of inverted soil moisture contents for different numbers of profiles used. Inverted soil moisture contents are derived using roughness parameter series from sampled 4-m profiles, originating from large profiles with (

Mean and standard deviations of inverted soil moisture contents for different horizontal spacings used in the parameterization of roughness from 4-m profiles with (

Autocorrelation functions derived for the same roughness profile with (

Boxplots of inverted soil moisture contents, calculated using roughness parameters from resampled profiles with 15-mm spacing, and exponential (E) and Gaussian (G) autocorrelation functions, for initial moisture contents of 5, 15, 25 and 35 vol%, and all defined sensor configurations, for profiles with (

(a) Original simulated 4-m roughness profile with (

Mean inverted soil moisture contents for different radar configurations, using roughness parameters obtained after (a) linear detrending over the 4-m profile, (b) piecewise 1-m detrending, (c) second-order polynomial detrending and (d) third-order polynomial de-trending of 10 synthetical roughness profiles of (

Mean inverted soil moisture contents for different radar configurations, using roughness parameters obtained after (a) linear detrending over the 4-m profile, (b) piecewise 1-m detrending, (c) second-order polynomial detrending and (d) third-order polynomial de-trending of 10 synthetical roughness profiles of (

Input parameters used for the IEM and the four-component dielectric mixing model.

ENVISAT ASAR configuration | Frequency | 5.3 GHz (C-band) |

Polarization | HH or VV | |

Incidence angle | 23° | |

ALOS PALSAR configuration | Frequency | 1.27 GHz (L-band) |

Polarization | HH or VV | |

Incidence angle | 34.3° | |

| ||

Bulk density | 1.2 g/cm^{3} | |

Specific density | 2.65 g/cm^{3} | |

Sand content | 15% | |

Clay content | 11.4% | |

Temperature | 15°C |

Average values of

Sample spacing | |||||
---|---|---|---|---|---|

‘Truth’ (1 mm) | 2mm | 5mm | 10mm | 15mm | |

1 | 0.99 (0.00) | 0.98 (0.00) | 0.97 (0.01) | 0.96 (0.02) | |

5 | 5.02 (0.04) | 5.15 (0.11) | 5.34 (0.22) | 5.47 (0.40) | |

| |||||

1 | 1.00 (0.00) | 1.00 (0.00) | 1.00 (0.00) | 0.99 (0.00) | |

40 | 40.02 (0.04) | 40.07 (0.21) | 40.20 (0.41) | 40.23 (0.37) | |

| |||||

2 | 1.99 (0.01) | 1.97 (0.01) | 1.93 (0.02) | 1.91 (0.01) | |

5 | 5.07 (0.05) | 5.17 (0.08) | 5.43 (0.19) | 5.76 (0.52) | |

| |||||

2 | 2.00 (0.00) | 2.00 (0.00) | 2.00 (0.01) | 1.99 (0.01) | |

40 | 40.03 (0.05) | 40.16 (0.28) | 40.30 (0.45) | 40.26 (0.58) |

RMSE values of

Correct ( |
RMSE on | |||||
---|---|---|---|---|---|---|

1mm noise | 2mm noise | 5mm noise | ||||

(1 cm,5 cm) | 0.0019 | 0.0316 | 0.0074 | 0.0775 | 0.0443 | 0.3782 |

(1 cm,40 cm) | 0.0017 | 0.1673 | 0.0068 | 0.4764 | 0.0421 | 2.9972 |

(2 cm,5 cm) | 0.0015 | 0.0447 | 0.0043 | 0.0316 | 0.0215 | 0.1265 |

(2 cm,40 cm) | 0.0009 | 0.0707 | 0.0035 | 0.1871 | 0.0219 | 0.9301 |

RMSE values of the retrieved soil moisture contents due to roughness parameterization errors, introduced by instrument noise.

( |
Soil moisture content (vol%) | RMSE (vol%) of retrieved soil moisture due to | |||
---|---|---|---|---|---|

1 mm noise | 2 mm noise | 5 mm noise | |||

(1 cm,5 cm) | 5 | 0.04 | 0.11 | 0.54 | |

(1 cm,5 cm) | 15 | 0.11 | 0.30 | 1.39 | |

(1 cm,5 cm) | 25 | 0.21 | 0.57 | 2.61 | |

(1 cm,5 cm) | 35 | 0.34 | 0.92 | 4.15 | |

| |||||

(1 cm,40 cm) | 35 | 0.39 | 2.08 | 8.31 | |

(2 cm,5 cm) | 35 | 0.24 | 0.26 | 0.51 | |

(2 cm,40 cm) | 35 | 0.23 | 0.46 | 2.76 |

Average values of

| ||||||||
---|---|---|---|---|---|---|---|---|

| ||||||||

1 | 5 | 1 | 40 | 2 | 5 | 2 | 40 | |

| ||||||||

Linear 4-m | 0.99 (0.01) | 4.93 (0.13) | 0.91 (0.07) | 30.09 (7.48) | 1.97 (0.03) | 4.76 (0.25) | 1.80 (0.18) | 31.57 (6.00) |

Piecewise 1-m | 0.92 (0.03) | 3.80 (0.45) | 0.51 (0.04) | 8.31 (1.34) | 1.85 (0.06) | 3.77 (0.40) | 0.98 (0.12) | 7.45 (1.12) |

Second-order | 0.98 (0.02) | 4.67 (0.29) | 0.81 (0.10) | 24.22 (7.40) | 1.94 (0.04) | 4.51 (0.26) | 1.57 (0.19) | 22.00 (7.58) |

Third-order | 0.96 (0.02) | 4.36 (0.30) | 0.64 (0.05) | 15.02 (3.96) | 1.93 (0.03) | 4.37 (0.26) | 1.41 (0.16) | 17.84 (6.18) |

| ||||||||

| ||||||||

Linear 4-m | 2.64 (0.13) | 50.07 (2.25) | 2.78 (0.42) | 54.30 (4.68) | 3.07 (0.26) | 28.13 (8.31) | 3.01 (0.74) | 44.81 (7.06) |

Piecewise 1-m | 0.95 (0.04) | 4.13 (0.49) | 0.58 (0.06) | 9.40 (1.47) | 1.85 (0.05) | 3.79 (0.36) | 1.00 (0.10) | 7.79 (1.47) |

Second-order | 1.32 (0.13) | 13.48 (6.67) | 1.10 (0.35) | 25.47 (8.16) | 2.17 (0.13) | 7.19 (2.03) | 1.88 (0.27) | 28.38 (8.27) |

Third-order | 1.04 (0.04) | 5.33 (0.53) | 0.79 (0.12) | 18.16 (4.72) | 1.95 (0.05) | 4.53 (0.30) | 1.47 (0.12) | 18.81 (5.13) |