Nicolas Baghdadi
email: nicolas.baghdadi@teledetection.fr

Maelle Aubert
email: maelle.aubert@teledetection.fr

Mehrez Zribi

Use of TerraSAR-X Data to Retrieve Soil Moisture Over Bare Soil Agricultural Fields

Keywords: Soil moisture, TerraSAR-X images. I Soil moisture, TerraSAR-X images

The retrieval of the bare soil moisture content from TerraSAR-X data is discussed using empirical approaches. Two cases were evaluated: 1) one image at low or high incidence angle and 2) two images, one at low incidence and one at high incidence. This study shows by using three databases collected between 2008 Q1 and 2010 over two study sites in France (Orgeval and Villamblain) that TerraSAR-X is a good remote sensing tool for the retrieving of surface soil moisture with accuracy of about 3% (rmse). Moreover, the accuracy of the soil moisture estimate does not improve when two incidence angles (26 • -28 • or 50 • -52 • ) are used instead of only one. When compared with the result obtained with a high incidence angle (50 • -52 • ), the use of low incidence angle (26 • -28 • ) does not enable a significant improvement in estimating soil moisture (about 1%).

moisture for values between 5% and 35% [6]. Moreover, σ • in-41 creases with soil surface roughness and follows an exponential 42 or logarithmic behavior (e.g., [4] and [7]). 43 Very few studies analyzed the sensitivity of TerraSAR-X 44 data to bare soil surface parameters. Baghdadi et al. [8] have 45 observed that the radar signal at X-band is slightly more sen-46 sitive to surface roughness at high incidence angle than at low 47 incidence angle. The difference observed between radar signals 48 reflected by the roughest and smoothest areas increases with the 49 radar wavelength. Moreover, results showed that the sensitivity 50 of radar signal to surface roughness is better with PALSAR in AQ7 51 L-band than with TerraSAR-X in X-band and that the C-and 52 X-bands are similar sensitivity results. In this letter, only in 53 situ soil moisture measurements in very wet conditions between 54 25% and 40% are available. Results obtained showed that the 55 backscattering coefficient at X-band is stable when the moisture 56 content ranges between 25% and 35% and that it decreases 57 beyond this threshold. 58 Aubert et al. [9] have showed that the sensitivity of the 59 TerraSAR-X signal to soil moisture is very important at low 60 and high incidence angles. In comparison to results published 61 with C-band SAR data, this sensitivity of the radar signal to 62 soil moisture is higher in X-band. The second important result 63 concerns the potential of the fine spatial resolution of TerraSAR 64 (1 m) in the detection of soil moisture variations at the within-65 plot scale. The spatial distribution of slaking crust could be 66 detected when soil moisture variation is observed between soil 67 crusted and soil without crust. Indeed, areas covered by slaking 68 crust could have greater soil moisture and, consequently, a 69 greater backscattering signal than soils without crust. improves the accuracy of the estimate of surface soil moisture in comparison to only one incidence (low or high). TerraSAR-X sensor has the advantage to acquire on the same study site image pairs at low and high incidence angles within one day.

The goal of this work is to compare the findings with C-and X-band data. At C-band, several studies have shown that the use of two incidence angles provides distinct improvement in the soil moisture estimate, in comparison with results obtained using a single incidence (e.g., [1], [2], and [4]). Moreover, low incidence angle is better than the high incidence angle for estimating soil moisture with C-band SAR data. This letter investigates this research question.

II. STUDY AREA AND DATA SET

A. Study Site

Data were acquired over two mainly agricultural sites (Fig. 1). The Villamblain site is located in the south of Paris, I). 106 The radar data are available in HH polarization, with incidence 107 angles (θ) of 26 • ,2 8 • ,5 0 • , and 52 • . The imaging mode 108 used was spotlight with a pixel spacing of 1 m. Radiometric 109 calibration using multilook ground range detected TerraSAR-X 110 images was first carried out using the following equation [10]: 111

σ • i (dB)=log 10 Ks • DN 2 i -NEBN +10log 10 (sin θ i ). (1)
This equation transforms the amplitude of backscattered sig-112 nal for each pixel (DN i ) into a backscattering coefficient (σ • ) 113 in decibels. Ks is the calibration coefficient, and NEBN is 114 the noise equivalent beta naught. All TerraSAR-X images were 115 then georeferenced using GPS points with a root-mean-square 116 error of the control points of approximately one pixel (i.e., 1 m). 117 This coregistration error was overcome by removing two 118 boundary pixels from each training plot relative to the limits 119 defined by the GPS control points. The mean backscattering 120 coefficients were calculated from calibrated SAR images by 121 averaging the linear σ • values of all pixels within reference 122 fields.

C. Field Data

Simultaneously with TerraSAR-X acquisition, field measurements of soil moisture and surface roughness have been achieved on several bare soil reference fields of at least 2 ha.

In the case of TerraSAR-X in spotlight mode (pixel spacing of 1 m), this corresponds to a surface of 20 000 pixels or more.

The volumetric water content at field scale was assumed to be equal to the mean value estimated from several samples (20-40 measurements per field; Fig. 2) collected from the top 5 cm of soil using the gravimetric method. The soil moistures range from 13% to 40%.

In most studies of microwave measurements carried out over bare soils, the experimental relationship between soil moisture and backscattering coefficient is provided by mean volumetric water contents measured to a soil depth, generally 0-5 cm or 0-10 cm. Indeed, only some studies using theory results are available at X-band. These studies suggest a penetration depth maybe lower than 5 cm. No experimental measurements are made in field condition, and the low penetration depth of X-band is only based on theoretical study. Therefore, the penetration depth of the X-band is not yet well known.

Roughness measurements were made using needle profilometers (1 m long and with 2-cm sampling intervals). Ten roughness profiles were sampled for each training field (parallel and perpendicular to the row direction). From these measurements, the two roughness parameters, i.e., root mean square (rms) surface height and correlation length (L), were calculated using the mean of all correlation functions. The rms surface heights range from 1.1 to 3.3 cm, and the correlation length (L) varies from 2.3 cm in sown fields to 9.3 cm in plowed fields.

III. METHODOLOGY

The retrieval of soil moisture from TerraSAR-X images by means of empirical approaches requires the development of experimental relationships between σ incidence angle (0.43 dB/% for 26 • -28 • and 0.29 dB/% for 163 50 • -52 • ; Fig. 3). For a confidence level of 95%, there are sig-164 nificant relationships between the TerraSAR-X backscattering 165 coefficient and the in situ soil moisture because the p-values are 166 much less than 0.05 (p-value < 2.2 × 10 -16 for HH26 showed lower sensitivities between radar signal and soil mois-170 ture, between 0.2 and 0.3 dB/% for low incidence angles 171 and about 0.1 dB/% for high incidence angles (e.g., [2] and 172 [11]- [13]).

173

The objective of this study is to analyze the influence of 174 incidence angle on the accuracy of the soil moisture estimate. 175 Configurations in HH polarization with single incidence an-176 gle (26 • -28 • or 50 • -52 • ) were studied. Next, multi-incidence 177 TerraSAR-X images acquired at both low and high θ values 178 with one-day-spaced dates and only minor variations in soil 179 characteristics were used to analyze the possible improvement 180 in the soil moisture estimates when two incidences are used. 181 The empirical relationship between the radar backscattering 182 coefficient (σ • ) and the volumetric soil moisture (mv) for bare 183 soil surfaces without taking into account the rms surface height 184 is given by (e.g., [14]; Fig. 3)

185 σ • dB = f (mv, θ) dB = δmv + ξ. (2)
This simplified relationship is valid for mv values between 186 5% and 35% [6]. The coefficient δ is dependent on SAR pa-187 rameters (radar wavelength, incidence angle, and polarization), 188 while the coefficient ξ is controlled by SAR parameters and 189 surface roughness. Experimental data of σ • and mv show slope 190 δ values of about 0.43 dB/% for HH26 • -28 • and 0.29 dB/% for 191 HH50 • -52 • . 192 The relationship obtained between σ • and the rms height 193 independent of row direction, correlation length, and soil mois-194 ture could be written as an exponential relationship of the form 195 σ • dB = g(rms, θ) dB = µe -krms + c [15], [16] or a logarithmic 196 relationship of the form σ

• dB = g(rms, θ) dB = µ ln(rms)+197 c [1]. AQ10 198
With taking into account of both soil roughness and soil 199 moisture, the radar signal in decibel scale may be written as 200

TABLE II INVERSION MODELS FOR ESTIMATING SOIL MOISTURE AND STATISTICS ON THE VALIDATION OF THESE MODELS

the sum of two functions that describe the dependence of the radar signal on soil moisture (f : linear) and surface roughness (g: exponential) (e.g., [1] and [4])

σ • dB = f (mv, θ) dB + g(rms, θ) dB = δ, mv + µ, e -krms + τ ( 3
)
where k is the radar wavenumber (∼ 2 cm -1 for TerraSAR-X).

This equation neglects the effect of the correlation length L on the backscattering coefficient. To take account of the correlation length, Zribi and Deschambre [1] proposed a new roughness parameter Zs, defined by rms 2 /L, which is the product of the rms surface height and the slope of the soil surface (rms/L). Thus, the empirical model linking σ • and Zs could be written as σ • dB = δmv + ηe -kZs + ψ.

In the case of one SAR image characterized by one incidence (θ =26 • -28 • or 50 • -52 • ), inversion model is written as follows:

mv = ασ • (θ)+β. ( 4
)
The use of two incidence angles eliminates the effects of roughness and thus allows linking the backscattering coefficient to the soil moisture only. For two images acquired with low and high incidence angles, the estimate of soil moisture can be obtained by solving (3) for two incidences (substituting the

e -krms of σ • (θ low ) into σ • (θ high ) mv = ασ • (θ low )+βσ • (θ high )+γ. (5)
α and β depend on δ and µ, whereas γ is a function of δ, µ, and τ (in both incidence angles).

The form of ( 5) should be the same if the Zs parameter was used.

The empirical models given in (4) and (5) were then fitted to experimental data acquired in 2008 and 2009 by using the least squares method (cf. Table II). The validation of these models was tested in using the data set of 2010 (13 points for each of the two configurations HH26 • and HH50 • ). The inputs are the mean backscattering coefficients in decibels calculated for each reference field.

IV. RESULTS AND DISCUSSION

The inversion procedures were applied in order to retrieve soil moisture. The results obtained in the validation phase with one low incidence show inversion errors in the estimation of mv of about 3% for incidence angles. The use of high 236 incidences (50 • -52 • ) gives slightly poorer results with an rmse 237 of about 4%. The accuracy of the soil moisture estimate remains 238 unchanged by using TerraSAR-X multi-incidence data (both 239 low and high incidence angles) with an rmse of about 3% 240 (Table II). Fig. 4 shows the good agreement between estimated 241 and measured mv values.

242

In contrast, large errors in the retrieved soil moisture were 243 observed at C-band for a single incidence angle (rmses of about 244 6% for 20 • and 9% for 40 • ) [4]. This is due to the fact that the 245 radar signal is much more sensitive to surface roughness at high 246 radar wavelength. The accuracy is strongly improved with the 247 use of both low and high incidences (rmse of about 3.5%) (e.g., 248 [1], [2], and [4]).

249

The dependence of the radar signal at X-band on surface 250 roughness in agricultural areas was described as weak by 251 several works ( [8], [14], and [17]). Results of these studies 252 show that the influence of surface roughness on the radar signal 253 increases with increasing radar wavelength. Moreover, this 254 dependence is mainly significant for low levels of roughness. 255 At X-band, Baghdadi et al. [4], [8] showed that the sensitivity 256 of σ • to surface roughness becomes weak for rms > 1 cm. 257 Thus, the effect of surface roughness on radar signal becomes 258 weak in X-band, which improves the estimates of soil moisture, 259 particularly for rms > 1 cm. Moreover, the multi-incidence 260 approaches become less effective because the effect of surface 261 roughness that we try to eliminate is relatively weak at X-band 262 compared to C-band.

I. INTRODUCTION

R ADAR SIGNAL is a function of soil moisture and surface roughness in the case of bare soil. The possibility of retrieving these soil parameters was little investigated from X-band synthetic aperture radar (SAR). However, many studies were carried out by using C-band radar data (e.g., [1]- [4]). With the launch of satellites using the X-band (∼9.6 GHz), such as TerraSAR-X and COSMO-SkyMed, the use of X-band data to Q2 derive soil parameters became possible. A radar configuration that minimizes the effects of surface roughness is recommended for a better estimate of soil moisture when using only one incidence angle. The optimal radar incidences in C-band for the retrieval of soil moisture are smaller than 35 • [4].

Soil moisture estimation from SAR images is carried out by using physical or statistical models. Physical approach consists in using a physical model, such as the integral equation model [5], to predict the radar backscattering coefficient from SAR and soil parameters (wavelength, polarization, incidence angle, surface roughness, and soil dielectric constant). Statistical models based on experimental measurements are also often used in soil moisture estimation. For bare soils, the increase of radar signal (σ moisture for values between 5% and 35% [6]. Moreover, σ • in-41 creases with soil surface roughness and follows an exponential 42 or logarithmic behavior (e.g., [4] and [7]).

43

Very few studies analyzed the sensitivity of TerraSAR-X 44 data to bare soil surface parameters. Baghdadi et al. [8] have 45 observed that the radar signal at X-band is slightly more sen-46 sitive to surface roughness at high incidence angle than at low 47 incidence angle. The difference observed between radar signals 48 reflected by the roughest and smoothest areas increases with the 49 radar wavelength. Moreover, results showed that the sensitivity 50 of radar signal to surface roughness is better with PALSAR in AQ7 51 L-band than with TerraSAR-X in X-band and that the C-and 52 X-bands are similar sensitivity results. In this letter, only in 53 situ soil moisture measurements in very wet conditions between 54 25% and 40% are available. Results obtained showed that the 55 backscattering coefficient at X-band is stable when the moisture 56 content ranges between 25% and 35% and that it decreases 57 beyond this threshold. 58 Aubert et al. [9] have showed that the sensitivity of the 59 TerraSAR-X signal to soil moisture is very important at low 60 and high incidence angles. In comparison to results published 61 with C-band SAR data, this sensitivity of the radar signal to 62 soil moisture is higher in X-band. The second important result 63 concerns the potential of the fine spatial resolution of TerraSAR 64 (1 m) in the detection of soil moisture variations at the within-65 plot scale. The spatial distribution of slaking crust could be 66 detected when soil moisture variation is observed between soil 67 crusted and soil without crust. Indeed, areas covered by slaking 68 crust could have greater soil moisture and, consequently, a 69 greater backscattering signal than soils without crust. The goal of this work is to compare the findings with C-and X-band data. At C-band, several studies have shown that the use of two incidence angles provides distinct improvement in the soil moisture estimate, in comparison with results obtained using a single incidence (e.g., [1], [2], and [4]). Moreover, low incidence angle is better than the high incidence angle for estimating soil moisture with C-band SAR data. This letter investigates this research question.

II. STUDY AREA AND DATA SET

A. Study Site

Data were acquired over two mainly agricultural sites (Fig. 1). The Villamblain site is located in the south of Paris, I). 106 The radar data are available in HH polarization, with incidence 107 angles (θ) of 26 • ,2 8 • ,5 0 • , and 52 • . The imaging mode 108 used was spotlight with a pixel spacing of 1 m. Radiometric 109 calibration using multilook ground range detected TerraSAR-X 110 images was first carried out using the following equation [10]: 111

σ • i (dB)=log 10 Ks • DN 2 i -NEBN +10log 10 (sin θ i ). (1)
This equation transforms the amplitude of backscattered sig-112 nal for each pixel (DN i ) into a backscattering coefficient (σ • ) 113 in decibels. Ks is the calibration coefficient, and NEBN is 114 the noise equivalent beta naught. All TerraSAR-X images were 115 then georeferenced using GPS points with a root-mean-square 116 error of the control points of approximately one pixel (i.e., 1 m). 117 This coregistration error was overcome by removing two 118 boundary pixels from each training plot relative to the limits 119 defined by the GPS control points. The mean backscattering 120 coefficients were calculated from calibrated SAR images by 121 averaging the linear σ • values of all pixels within reference 122 fields.

123

Author-produced version of the article published in IEEE Geoscience and remote sensing letters, 2012, 9(3), 512-516. The original publication is available at http://ieeexplore.ieee.org http://dx.doi.org/10.1109/LGRS.2011.2173155

C. Field Data

Simultaneously with TerraSAR-X acquisition, field measurements of soil moisture and surface roughness have been achieved on several bare soil reference fields of at least 2 ha.

In the case of TerraSAR-X in spotlight mode (pixel spacing of 1 m), this corresponds to a surface of 20 000 pixels or more.

The volumetric water content at field scale was assumed to be equal to the mean value estimated from several samples (20-40 measurements per field; Fig. 2) collected from the top 5 cm of soil using the gravimetric method. The soil moistures range from 13% to 40%.

In most studies of microwave measurements carried out over bare soils, the experimental relationship between soil moisture and backscattering coefficient is provided by mean volumetric water contents measured to a soil depth, generally 0-5 cm or 0-10 cm. Indeed, only some studies using theory results are available at X-band. These studies suggest a penetration depth maybe lower than 5 cm. No experimental measurements are made in field condition, and the low penetration depth of X-band is only based on theoretical study. Therefore, the penetration depth of the X-band is not yet well known.

Roughness measurements were made using needle profilometers (1 m long and with 2-cm sampling intervals). Ten roughness profiles were sampled for each training field (parallel and perpendicular to the row direction). From these measurements, the two roughness parameters, i.e., root mean square (rms) surface height and correlation length (L), were calculated using the mean of all correlation functions. The rms surface heights range from 1.1 to 3.3 cm, and the correlation length (L) varies from 2.3 cm in sown fields to 9.3 cm in plowed fields.

III. METHODOLOGY

The retrieval of soil moisture from TerraSAR-X images by means of empirical approaches requires the development of experimental relationships between σ • TerraSAR-X and the measured soil moisture. TerraSAR data acquired in two configurations of incidence angles (∼ 26 • and ∼ 50 • ) were used with ground measurements conducted over bare soil. The sensitivity of TerraSAR signal to soil moisture is the greatest for low incidence angle (0.43 dB/% for 26 • -28 • and 0.29 dB/% for 163 50 • -52 • ; Fig. 3). For a confidence level of 95%, there are sig-164 nificant relationships between the TerraSAR-X backscattering 165 coefficient and the in situ soil moisture because the p-values are 166 much less than 0.05 (p-value < 2.2 × 10 -16 for HH26 showed lower sensitivities between radar signal and soil mois-170 ture, between 0.2 and 0.3 dB/% for low incidence angles 171 and about 0.1 dB/% for high incidence angles (e.g., [2] and 172 [11]- [13]).

173

The objective of this study is to analyze the influence of 174 incidence angle on the accuracy of the soil moisture estimate. 175 Configurations in HH polarization with single incidence an-176 gle (26 • -28 • or 50 • -52 • ) were studied. Next, multi-incidence 177 TerraSAR-X images acquired at both low and high θ values 178 with one-day-spaced dates and only minor variations in soil 179 characteristics were used to analyze the possible improvement 180 in the soil moisture estimates when two incidences are used. 181 The empirical relationship between the radar backscattering 182 coefficient (σ • ) and the volumetric soil moisture (mv) for bare 183 soil surfaces without taking into account the rms surface height 184 is given by (e.g., [14]; Fig. 3)

185 σ • dB = f (mv, θ) dB = δmv + ξ. (2)
This simplified relationship is valid for mv values between 186 5% and 35% [6]. The coefficient δ is dependent on SAR pa-187 rameters (radar wavelength, incidence angle, and polarization), 188 while the coefficient ξ is controlled by SAR parameters and 189 surface roughness. Experimental data of σ • and mv show slope 190 δ values of about 0.43 dB/% for HH26 • -28 • and 0.29 dB/% for 191 HH50 • -52 • . 192 The relationship obtained between σ • and the rms height 193 independent of row direction, correlation length, and soil mois-194 ture could be written as an exponential relationship of the form 195 σ • dB = g(rms, θ) dB = µe -krms + c [15], [16] or a logarithmic 196 relationship of the form σ • dB = g(rms, θ) dB = µ ln(rms)+197 c [1].

AQ10 198
With taking into account of both soil roughness and soil 199 moisture, the radar signal in decibel scale may be written as 200 the sum of two functions that describe the dependence of the radar signal on soil moisture (f : linear) and surface roughness (g: exponential) (e.g., [1] and [4])

σ • dB = f (mv, θ) dB + g(rms, θ) dB = δ, mv + µ, e -krms + τ ( 3
)
where k is the radar wavenumber (∼ 2 cm -1 for TerraSAR-X).

This equation neglects the effect of the correlation length L on the backscattering coefficient. To take account of the correlation length, Zribi and Deschambre [1] proposed a new roughness parameter Zs, defined by rms 2 /L, which is the product of the rms surface height and the slope of the soil surface (rms/L). Thus, the empirical model linking σ • and Zs could be written as σ • dB = δmv + ηe -kZs + ψ.

In the case of one SAR image characterized by one incidence (θ =26 • -28 • or 50 • -52 • ), inversion model is written as follows:

mv = ασ • (θ)+β. ( 4
)
The use of two incidence angles eliminates the effects of roughness and thus allows linking the backscattering coefficient to the soil moisture only. For two images acquired with low and high incidence angles, the estimate of soil moisture can be obtained by solving (3) for two incidences (substituting the e -krms of σ

• (θ low ) into σ • (θ high ) mv = ασ • (θ low )+βσ • (θ high )+γ. (5)
α and β depend on δ and µ, whereas γ is a function of δ, µ, and τ (in both incidence angles).

The form of ( 5) should be the same if the Zs parameter was used.

The empirical models given in (4) and (5) were then fitted to experimental data acquired in 2008 and 2009 by using the least squares method (cf. Table II). The validation of these models was tested in using the data set of 2010 (13 points for each of the two configurations HH26 • and HH50 • ). The inputs are the mean backscattering coefficients in decibels calculated for each reference field.

IV. RESULTS AND DISCUSSION

The inversion procedures were applied in order to retrieve soil moisture. The results obtained in the validation phase with one low incidence show inversion errors in the estimation of mv of about 3% for incidence angles. The use of high 236 incidences (50 • -52 • ) gives slightly poorer results with an rmse 237 of about 4%. The accuracy of the soil moisture estimate remains 238 unchanged by using TerraSAR-X multi-incidence data (both 239 low and high incidence angles) with an rmse of about 3% 240 (Table II). Fig. 4 shows the good agreement between estimated 241 and measured mv values.

242

In contrast, large errors in the retrieved soil moisture were 243 observed at C-band for a single incidence angle (rmses of about 244 6% for 20 • and 9% for 40 • ) [4]. This is due to the fact that the 245 radar signal is much more sensitive to surface roughness at high 246 radar wavelength. The accuracy is strongly improved with the 247 use of both low and high incidences (rmse of about 3.5%) (e.g., 248 [1], [2], and [4]).

249

The dependence of the radar signal at X-band on surface 250 roughness in agricultural areas was described as weak by 251 several works ( [8], [14], and [17]). Results of these studies 252 show that the influence of surface roughness on the radar signal 253 increases with increasing radar wavelength. Moreover, this 254 dependence is mainly significant for low levels of roughness. 255 At X-band, Baghdadi et al. [4], [8] showed that the sensitivity 256 of σ • to surface roughness becomes weak for rms > 1 cm. 257 Thus, the effect of surface roughness on radar signal becomes 258 weak in X-band, which improves the estimates of soil moisture, 259 particularly for rms > 1 cm. Moreover, the multi-incidence 260 approaches become less effective because the effect of surface 261 roughness that we try to eliminate is relatively weak at X-band 262 compared to C-band.

Fig. 1 .

 1 Fig. 1. Location of study sites. (1) Orgeval. (2) Villamblain.

  TABLE I CHARACTERISTICS OF TERRASAR-X IMAGES AND SUMMARY OF GROUND-TRUTH MEASUREMENTS (mv, rms, AND L)At least one research question remained open. It concerns the precision of the soil moisture estimates in bare agricultural soils. The objective of this study is to examine the potential of TerraSAR-X data for retrieving volumetric soil moisture over bare soils. This work evaluates if the use of two incidence angles at X-band [one low (26 • -28 • ) and one high (50 • -52 • )]

  France (latitude 48 • 01 ′ N and longitude 1 • 35 ′ E) with soil composed of 30% clay, 60% silt, and 10% sand. The second site is situated in the Orgeval watershed, located in the east of Paris, France (latitude 48 • 51 ′ N and longitude 3 • 07 ′ E). The soil has a loamy texture, composed of 78% silt, 17% clay, and 5% sand. Both of these two sites are very flat. During the period of February-April (our SAR acquisitions), 99 the main crops are wheat and colza. They cover approximately 100 50% of the agricultural area. The remaining surface corre-101 sponds to plowed soils awaiting future cultivation (corn and 102 potato). 103 B. TerraSAR-X Images 104 Fourteen TerraSAR-X images (X-band ∼9.65 GHz) were 105 acquired during the years of 2008, 2009, and 2010 (Table

Fig. 2 .

 2 Fig. 2. Example of volumetric soil moisture measurements taken on a reference field.

Fig. 3 .

 3 Fig. 3. TerraSAR-X signal versus volumetric soil moisture (measured at a depth of 5 cm). Each point corresponds to the average backscattering coefficient in decibels for one reference field. Thirty points are used for each of the two configurations HH26 • -28 • and HH50 • -52 • (data sets of 2008 and 2009).

Fig. 4 .

 4 Fig. 4. Comparison between the estimated mv values and those measured. The error bars on the measured soil moisture values correspond to one standard deviation.

Fig. 1 .

 1 Fig. 1. Location of study sites. (1) Orgeval. (2) Villamblain.

70 1545 -

 1545 598X/$26.00 © 2011 IEEE Author-produced version of the article published in IEEE Geoscience and remote sensing letters, 2012, 9(3), 512-516. The original publication is available at http://ieeexplore.ieee.org http://dx.doi.org/10.1109/LGRS.2011.2173155TABLE I CHARACTERISTICS OF TERRASAR-X IMAGES AND SUMMARY OF GROUND-TRUTH MEASUREMENTS (mv, rms, AND L)At least one research question remained open. It concerns the precision of the soil moisture estimates in bare agricultural soils. The objective of this study is to examine the potential of TerraSAR-X data for retrieving volumetric soil moisture over bare soils. This work evaluates if the use of two incidence angles at X-band [one low (26 • -28 • ) and one high (50 • -52 • )] improves the accuracy of the estimate of surface soil moisture in comparison to only one incidence (low or high). TerraSAR-X sensor has the advantage to acquire on the same study site image pairs at low and high incidence angles within one day.

  France (latitude 48 • 01 ′ N and longitude 1 • 35 ′ E) with soil composed of 30% clay, 60% silt, and 10% sand. The second site is situated in the Orgeval watershed, located in the east of Paris, France (latitude 48 • 51 ′ N and longitude 3 • 07 ′ E). The soil has a loamy texture, composed of 78% silt, 17% clay, and 5% sand. Both of these two sites are very flat. During the period of February-April (our SAR acquisitions), 99 the main crops are wheat and colza. They cover approximately 100 50% of the agricultural area. The remaining surface corre-101 sponds to plowed soils awaiting future cultivation (corn and 102 potato). 103 B. TerraSAR-X Images 104 Fourteen TerraSAR-X images (X-band ∼9.65 GHz) were 105 acquired during the years of 2008, 2009, and 2010 (Table

Fig. 2 .

 2 Fig. 2. Example of volumetric soil moisture measurements taken on a reference field.

Fig. 3 .

 3 Fig. 3. TerraSAR-X signal versus volumetric soil moisture (measured at a depth of 5 cm). Each point corresponds to the average backscattering coefficient in decibels for one reference field. Thirty points are used for each of the two configurations HH26 • -28 • and HH50 • -52 • (data sets of 2008 and 2009).

Fig. 4 .

 4 Fig. 4. Comparison between the estimated mv values and those measured. The error bars on the measured soil moisture values correspond to one standard deviation.

V 1 ) 2 )

 12 the potential of TerraSAR-X data for 265 estimating soil moisture (mv) over bare soils. TerraSAR-X 266 images collected between 2008 and 2010 over two study sites in 267 France were used. SAR images were acquired at HH polariza-268 tion and for incidence angles of 26 • ,28 • ,50 • , and 52 • . The goal 269 of this work was to compare estimates of mv obtained from 270 various incidence configurations and to find the best sensor 271 configuration in incidence angle for measuring the bare soil 272 moisture. 273 This study tested empirical models for soil moisture inver-274 sion from one incidence (low or high) and multi-incidence 275 TerraSAR-X data (both low and high incidences). The results 276 of this study may be summarized as follows. 277 For a single incidence, the retrieval algorithm performed 278 very well for low and high incidence angles. The rmses 279 for the soil moisture estimate are about 3% for 26 • -28 • 280 and 4% for 50 • -52 • . 281 The accuracy of the soil moisture estimate does not 282 improve when two incidence angles (rmse is about 3%) 283 are used. 284 These results appear promising for the development of sim-285 plified algorithms for retrieving soil moisture from TerraSAR-286 X data and for monitoring temporal moisture changes. TableIII

  287 lists the different observation possibilities for the Orgeval study 288 site within one orbit cycle (11 days). This site could be imaged 8 289 times within 11 days (two images for each following incidence: 290 ∼ 26 • ,3 9 • ,5 0 • , and 58 • ) and 24 times within one month. 291 The soil moisture mapping frequency with low incidence angle 292 (26 • ) or with both low and high incidence angles (26 • and 50 • ) 293 is possible six times within one month. The incidence of 39 • can 294 also be used, which would increase to 12 the TerraSAR-X scene 295 number within one month. This very short revisit time makes 296 TerraSAR-X a very useful source for the soil moisture mapping. 297 Moreover, the increase in the acquisition frequency is much 298 awaited for the soil moisture data assimilation in hydrological 299 modeling. 300 In addition, the very high spatial resolution (metric) of the 301 TerraSAR-X sensor is also very promising for local estimation 302 of soil moisture at the within agricultural field scale. It offers a 303 great potential in terms of improving the quality of soil moisture 304 mapping for catchment areas where the parcels are of small

  • ) is supposed to be linear with the volumetric soil Manuscript received August 11, 2011; revised September 19, 2011; accepted October 17, 2011. This work was supported in part by the CEMAGREF (Agricultural and Environmental Engineering Research) and in part by the ORFEO Program, National Space Study Center (CNES).

	Q3 Q4

N.

Baghdadi

and M. Aubert are with UMR TETIS, CEMAGREF, Q5 34093 Montpellier, France (e-mail: nicolas.baghdadi@teledetection.fr; maelle. aubert@teledetection.fr). M. Zribi is with Centre d'Etudes Spatiales de la BIOsphère, Institut de Recherche pour le Développement, 31401 Toulouse, France. Q6 Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2011.2173155

TABLE II INVERSION

 II MODELS FOR ESTIMATING SOIL MOISTURE AND STATISTICS ON THE VALIDATION OF THESE MODELS

TABLE III TERRASAR

 III -X COVERAGE SIMULATION FOR ORGEVAL SITE BETWEEN SEPTEMBER 2 AND 12, 2010 (ORBIT CYCLE)

The authors would like to thank the German Space Agency 308 (DLR) for kindly providing TerraSAR-X images within the 309 framework of proposals HYD0007 and HYD0542, P. Ansart, Y. Hachouch, and C. Loumagne for their logistic support during the field campaigns, and TerraSAR-X Science Coordinators A. Roth and U. Marschalk for their assistance.

This work was supported in part by the CEMAGREF (Agricultural and Environmental Engineering Research) and in part by the ORFEO Program, National Space Study Center (CNES).

Author-produced version of the article published in IEEE Geoscience and remote sensing letters, 2012, 9(3), 512-516. The original publication is available at http://ieeexplore.ieee.org http://dx.doi.org/10.1109/LGRS.2011.2173155 AUTHOR PLEASE ANSWER ALL QUERIES AQ1 = "In" was changed to "by." Please check if the original thought was retained. AQ2 = Please provide the expanded form of the acronym "COSMO-SkyMed." AQ3 = Please provide the expanded form of the acronym "ORFEO." AQ4 = "French Space Study Center" was changed to "National Space Study Center." Please check if appropriate. AQ5 = Please provide the expanded form of the acronym "UMR TETIS." AQ6 = The acronyms "CESBIO" and "IRD" were defined as "Centre d'Etudes Spatiales de la BIOsphère"

and "Institut de Recherche pour le Développement," respectively. Please check if appropriate. AQ7 = Please provide the expanded form of the acronym "PALSAR." AQ8 = All occurrences of "2.2e -16 " were changed to "< 2.2 × 10 -16 ." Please check if appropriate. AQ9 = Please provide the expanded forms of the acronyms "ERS," "RADARSAT," and "ASAR." AQ10 = This sentence was reworded for clarity. Please check if the original thought was retained. AQ11 = Please check the URL provided in Ref. [10]. Page was not found.

END OF ALL QUERIES

Author-produced version of the article published in IEEE Geoscience and remote sensing letters, 2012, 9(3), 512-516. The original publication is available at http://ieeexplore.ieee.org http://dx.doi.org/10.1109/LGRS.2011.2173155

Author-produced version of the article published in IEEE Geoscience and remote sensing letters, 2012, 9(3), 512-516. The original publication is available at http://ieeexplore.ieee.org http://dx.doi.org/10.1109/LGRS.2011.2173155

I E E E P r o o f

AUTHOR PLEASE ANSWER ALL QUERIES AQ1 = "In" was changed to "by." Please check if the original thought was retained. AQ2 = Please provide the expanded form of the acronym "COSMO-SkyMed." AQ3 = Please provide the expanded form of the acronym "ORFEO." AQ4 = "French Space Study Center" was changed to "National Space Study Center." Please check if appropriate. AQ5 = Please provide the expanded form of the acronym "UMR TETIS." AQ6 = The acronyms "CESBIO" and "IRD" were defined as "Centre d'Etudes Spatiales de la BIOsphère"

and "Institut de Recherche pour le Développement," respectively. Please check if appropriate. AQ7 = Please provide the expanded form of the acronym "PALSAR." AQ8 = All occurrences of "2.2e -16 " were changed to "< 2.2 × 10 -16 ." Please check if appropriate. AQ9 = Please provide the expanded forms of the acronyms "ERS," "RADARSAT," and "ASAR." AQ10 = This sentence was reworded for clarity. Please check if the original thought was retained. AQ11 = Please check the URL provided in Ref. [10]. Page was not found.

END OF ALL QUERIES


Dr Enrico Chiovetto
email: enrico.chiovetto@klinikum.uni-tuebingen.de

Laura Patanè

Thierry Pozzo

Variant and invariant features characterizing natural and reverse whole-body pointing movements

Keywords: Reverse whole-body pointing movements, coordination, principal component analysis, EMG, non-negative matrix factorization, multi-joint coordination

Variant and invariant features characterizing natural

and reverse whole-body pointing movements.

Introduction

Movement accomplishment involves two kinds of variables: context-dependent and invariant variables. Those movement parameters that change the least under multiple kinds of movement transformation (such as translations, rotations or scaling in space) are usually referred to as motor patterns. Specific motor patterns were found characterizing, for instance, point-to-point arm movements [START_REF] Morasso | Spatial control of arm movements[END_REF]Soechting and Flanders, 1991), handwriting tasks (Lacquaniti 1989;[START_REF] Polyakov | A compact representation of drawing movements with sequences of parabolic primitives[END_REF] and locomotion [START_REF] Ivanenko | Five basic muscle activation patterns account for muscle activity during human locomotion[END_REF]. Other investigations [START_REF] Berret | Modular control of pointing beyond arm's length[END_REF][START_REF] Thomas | Kinematic and kinetic constraints on arm, trunk, and leg segments in target-reaching movements[END_REF] have shown that whole-body pointing (WBP) movements to reach a target from a standing position are organized according to a single coordinative structure in the space of the elevation angles, to assure simultaneous forward displacement of the global centre of mass (CoM) and hand trajectory formation.

Conversely, little is known about the motor patterns characterizing the reverse movements, when the displacement of a large number of joints is required to take the whole body back to a standing initial posture. In this case, indeed, the mechanical and sensory contexts result profoundly modified, mainly because of the different contribution of gravity to the dynamics of the movement. It makes therefore sense questioning about what motor patterns are conserved across the reversal of movement direction. Previous investigations characterizing sit-to-stand (STS) and the back-to-sit (BTS) motor tasks (see [START_REF] Papaxanthis | Similar planning strategies for whole-body and arm movements performed in the sagittal plane[END_REF]) revealed general differences between the forward and return movements. Movement duration was significantly longer for downward compared with upward movements and also the shape of the velocity profiles changed: the relative acceleration duration (acceleration duration divided by movement duration during the vertical motion) was smaller for the upward compared with the downward displacement. Such considerations referred however more to high-rather than to low-level movement variables (Lockhart and ting, 2007;[START_REF] Tresch | A balanced view of motor control[END_REF], so that no information of inter-joint coordination could be retrieved from the analysis.

The kinematic behavior characterizing reverse WBP movements cannot be given for granted and many different possible strategies may be expected to regulate joint coordination. The two tasks are indeed drastically different. During the downward movement the motor goal is twofold: one has to point the target with the fingers (pointing sub-task) while balance has to be maintained (postural subtask). During the returning movement instead, the task is mainly postural, as there is not target to point anymore and one has only to assume an upright standing position. Therefore, whereas strict coordination was found during downward movements [START_REF] Berret | Modular control of pointing beyond arm's length[END_REF], the subsequent return to the upright standing position might thus be obtained for instance by means of separate co-variation of the two groups of joints to make the relative body links (respectively those of the arms and those of the trunk plus lower-body) assume a vertical orientation in two consecutive moments.

In this study, we compared the kinematics and electromyographic (EMG) data of a natural WBP with that of the subsequent movement accomplished to return back to the initial standing position. Principal component analysis was applied to the time series describing the temporal evolution of the elevation angles associated with all the body links. Non-negative matrix factorization was moreover applied to the electromyographic signals. Results revealed that elevation angles where highly co-varying in time and that, despite some differences in the global parameters characterizing the different movements (i.e. differences regarding high-level variable associated with the selected motor plans), the level of joint co-variation did not change across movement direction. Differently, muscle organization of the forward whole-body pointing tasks was found to be different with respect to that characterizing the opposite movements. Such results agree with previous findings, according to which the central nervous system (CNS) exploits, dependently on the direction of motion, different motor plans for the execution of whole-body movements. However, in addition, this study shows how such motor plans are translated into different muscle strategies that equivalently assure a high level of covariation in the joint space.

Materials and Methods

Participants

Twelve healthy male subjects (ages 29 ± 4 years, mass 74 ± 9 kg, height 1.77 ± 0.07 m), participated voluntarily to the experiment. All subjects were in good health condition and had no previous history of neuromuscular disease. The experiment conformed to the declaration of Helsinki and informed consent was obtained from all the participants according to the protocol of the local ethical committee.

Protocol

Participants were required to perform a series of whole-body pointing movements toward a target located in front of them (forward movements, F), followed by backward movements to return to the initial standing position (returning movements, R). The target was a wooden dowel (45 cm long, 3 cm of diameter) positioned horizontally with respect to the ground, parallel to the subjects' coronal plane and with its centre intersecting the subjects' sagittal plane. For each participant, the two extremities of the dowel had a vertical distance from the ground equal to 25% of their body height.

Two horizontal target distances (measured starting from the distal end of the participants' great toe) were tested: the first one (D1) corresponded to 15% of participants' height, the second one (D2) to 30%. Participants started from an upright standing position with their hands initially located at the external side of the thighs. All movement, that were assumed to be symmetrical [START_REF] Kaminski | The coupling between upper and lower extremity synergies during whole-body reaching[END_REF], were performed in the sagittal plane, with each side of the body moving together. After verbal instruction that data recording had started, participants had to point to the target with both the index fingers at a comfortable velocity (not too slow or too fast to induce loss of balance). At the end of the pointing movement, they had to stand still on the final pointing position for about two seconds, keeping the fingers close to the extremities of the bar. They had then to return back to the initial upright position.

Target accuracy was not the primary constraint during the experiments and no instruction was given to the participants regarding the strategy to follow to accomplish the task. Forward and return movements were considered separately in the analysis. Each subject performed one block of six valid trial repetitions for each target distance.

Apparatus

Movement kinematics was monitored by means of a Vicon (Oxford, UK) motion capture system. The temporal positions of eleven passive reflective markers attached to the right side of the participant's body were recorded during trial executions. Markers were attached to the lower limb (fifth metatarsophalangeal joint of the foot, lateral malleolus, knee interstitial joint space (lateral condyle of the femur), greater trochanter, iliac crest), arm (the acromion process, lateral epicondyle of the humerus, the styloid process and the tip of the index finger) and head (external canthus of the eye and auditory meatus). This marker configuration allowed schematizing the human body as a multi-joint system made of seven segments (as depicted in Fig. 1): head, trunk (thorax plus abdomen-pelvis), thighs (as a single segment), shanks, feet, upper arms and forearms. Electromyographic activity was monitored by means of an Aurion (Milan, Italy) wireless electromyographic system. EMG data were amplified (gain of 1000), band-pass filtered (10 Hz high-pass and 1 KHz low-pass) and digitized at 1000 Hz. Up to twenty-four different muscles from the right hemibody of each subject were simultaneously recorded: tibialis anterior (Tib), soleus (Sol), peroneus (Per), gastrocnemius lateralis (Gast), vastus lateralis (VL), biceps femoris (BF), vastus medialis (VM), semitendinosus (ST), rectus femoris (RF), semimembranosus (SM), adductor longus (AL), erector spinae (ES, with the electrodes over the longissimus thoracis at the level of the T8 spinal segment), rectus abdominis (RA), gluteus maximus (GM), internal oblique (OI), latissimus dorsi (LD), serratus anterior (Ser), anterior deltoid (DA), posterior deltoid (DP), pectoralis superior (Pect), rhomboid major (Rho), biceps brachii (Bic, short head), triceps brachii (Tri, lateral head) and brachioradialis muscle (Bra). The functional role of each single muscle and the right placement of the electrodes were tested by making subjects perform both isometric and free movements [START_REF] Kendall | Muscles: Testing and Function with Posture and Pain[END_REF].

Data collection and processing

Kinematic data were recorded at a sampling frequency of 100 Hz. They were analysed off-line using customized software written in Matlab (Mathworks, Natick, MA). Before any kind of analysis they were low-pass filtered (Butterworth filter, cut-off frequency of 20 Hz). Markers' velocities and accelerations and were obtained as first and second order derivatives of their spatial positions. Based on the multi-link model described above, the position of the global body centre of mass (CoM) was computed by means of standard methods and by using statistical anthropometric data [START_REF] Winter | Biomechanics and motor control of human movement[END_REF]).

The model and the method used to estimate the whole-body CoM trajectory were already validated in previous studies [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF][START_REF] Stapley | Does the coordination between posture and movement during human whole-body reaching ensure center of mass stabilization?[END_REF]. Marker positions were used to compute the kinematics of the index finger and the time-series of the elevation angles of the different body links.

The absolute value of the jerk associated with the shoulder's marker was computed as the second derivative of its velocity absolute value, and it was used to quantify the smoothness of the movements.

Each elevation angle was defined as the angle between the corresponding body joint with respect to the vertical direction [START_REF] Berret | Modular control of pointing beyond arm's length[END_REF]. The five elevation angles taken into consideration in this study were those relative to the shank (Sh), thigh (Th), trunk (Tr), humerus (Hu) and forearm (Fo). Elevation angles of the feet and head segments were not computed as they were not considered relevant for the analysis. Other standard kinematic parameters were calculated for both the index finger and the CoM: peak velocity (PV), mean velocity (MV), relative time to peak velocity (TPV) defined as the ratio of the duration of acceleration and MD, index of path curvature (IPC = Dev/LD) defined as the ratio of the maximum path deviation (Dev) from a straight line connecting the initial and final finger or CoM positions (linear distance, LD), and curvilinear distance (CD) defined by the integral over time from 0 to MD of the norm of the finger or CoM velocity vector in the sagittal plane. The smoothness of the movement was quantified by computing the maximum peak-to-peak value associated with the jerk of the shoulder marker (and it was indicated with JPP). All the kinematic variables associated with each single trial and single subject were time-interpolated to fit a standard 200-point time base. For both G and R movements, the time instants t 0 , t f and t pv were computed for each trial: t 0 corresponded to the movement onset, at which the velocity profile of the right index finger exceeded 5% of its peak value; t f , the end of the movement, was defined as the instant at which the index finger velocity profile dropped below 5% of its peak value (reached at instant t pv ). Movement duration (MD) was defined as the time interval between t 0 and t f . For the EMG treatment and analysis we followed the same procedures described in [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF]. Briefly, muscle signals were full-wave rectified, normalized in amplitude with respect to their maximum value recorded across all trials and conditions and low-pass filtered with a zero-lag Butterworth filter and a cut-off frequency of 10 Hz. In in order to compute the average muscle activity across trials and subjects, the EMG signals comprised between 300 ms before t 0 and 100 ms after the end of the movement were normalized to a standard time window of 200 samples. Surface EMG electrodes were attached on each muscle by following standard recommendations and procedures, as indicated by [START_REF] Hermens | Development of recommendations for SEMG sensors and sensor placement procedures[END_REF]. Nevertheless, contamination of the EMG muscle signals by the activations of other adjacent muscles could be possible and the amount of such contamination had to be assessed. Cross-correlation analysis between channels revealed that the average peaks of the cross-correlation function in an interval about lag zero never exceeded 0.3. Because of the difficulty of distinguishing between muscle crosstalk and synchronous recruitment of motor units in different muscles (d'Avella et al., 2008;[START_REF] Kilner | A novel algorithm to remove electrical cross-talk between surface EMG recordings and its application to the measurement of short-term synchronisation in humans[END_REF] we did not excluded such muscles from further analyses. Thus, we verified that results obtained by working on different subsets of data in which muscle potentially affected by crosstalk were removed did not change significantly. Finally, we tested the absence of muscle cross-talk also by providing a small control experiment in one single subject. We provided electrical stimulation to the RF muscle of his right leg and recorded the activities of the VL and VM, which are muscles adjacent to the RF and could be the main locus of crosstalk effect. After stimulation, only RF presented clear muscle activation induced by the electric impulse, while for VL and VM no activity was recorded. This observation confirmed that the effect of muscle cross-talk on the global muscle activity could be considered minimal and negligible. Some among the twenty-four muscles recorded during the experiment for every participant showed a change in signal amplitude, because of the imperfect adhesion of the electrodes to the skin. These muscles were excluded from further analyses. The muscles that were eventually considered for analysis for each subject that participated to the experiment are listed in table 1.

Principal Component Analysis (PCA) and Non-Negative Matrix Factorization (NNMF)

PCA was applied, for each single condition, to the kinematic data describing the temporal evolutions of the elevation angles associated with each trial and subject. Because of the large differences of magnitude between angular displacements of the upper versus lower-body joints, PCA based on the correlation matrix was performed. This choice was equivalent to operating an amplitude normalization of the joint displacements, so as to avoid biases in the analysis introduced by the joint displacements with the largest excursions. The number of PCs considered suitable to obtain a good compromise between the goodness of signal reconstruction and the level of physical interpretation of the solution was set according to an objective criterion: after examining the data reconstruction performance (expressed in percentage of variance accounted for) in function of increasing numbers of PCs, only the minimum number of PCs that could explain together at least the 90% of the total variation associated with the original data set [START_REF] Berret | Modular control of pointing beyond arm's length[END_REF][START_REF] Thomas | Kinematic and kinetic constraints on arm, trunk, and leg segments in target-reaching movements[END_REF] was considered. The loadings relative to such PCs were analyzed to understand how variability of the angular displacements was captured by each PC.

PCA was also used to remove the intrinsic noise of measure affecting the EMGs. To this aim, PCA was applied to EMGs and the cumulative percentage of variance accounted for was again computed as a function of the number of PCs considered. The dimensionality D of the dataset was determined according to the 90% criterion mentioned above. EMGs were finally reconstructed and freed of noise by using just the first D extracted PCs. To identify specific patterns of activation characterizing the different muscle datasets, de-noised EMGs were applied a customized version of the NNMF algorithm proposed by [START_REF] Lee | Learning the parts of objects by non-negative matrix factorization[END_REF], and based on the minimization of the cost function below

T N 2 E 2 = ∑ || m(t k ) -∑ c i (t k )w i || k=1 i=1
subject to the constraints 0 ≤ w ij , c i (t) ≤ 1 and where T is the total number of time samples, m(t k ) is a vector of M real numbers whose elements are the activations at the instant t k of the muscles taken into consideration, the c i (t k ) (i=1,2,..,N) are the combination coefficients and the w ij

Statistical analysis

Statistical differences between mean values of kinematic parameters associated with G and R movements and between corresponding kinematic parameters of the index finger and CoM within the same experimental condition were tested by means of paired t-tests. The level of significance at which the null hypotheses were rejected was set at 5%. Normality of parametric distribution was tested (Kolmogorov-Smirnov test). Pearson correlation coefficient (R) was used to assess the level of shape similarity between pairs of kinematic trajectories, PCs or EMG components identified by NNMF.

Results

General kinematic features

Fig. 1 depicts, for each target distance, typical stick diagrams associated with both F and R movements. In all cases, marked displacements of CoM and finger trajectories are evident and both present curvilinear shapes. Their trajectories are qualitatively always straighter and more horizontal at the beginning (end) of the F (R) movements, that is when the subject is closer to the upright standing position. Mean values of the kinematic parameters are reported in table 2. For both distances, the peak velocity of the index finger and the CoM were higher during the F movements than R (p << 0.001) and their acceleration phase (described by the TPV index) was shorter during R (p < 0.001). Movement duration (MD) was significantly smaller when reaching the target than when returning back to the standing position (p << 0.001). For both target distances, the linear and curvilinear distances LD and CD associated with the index finger and the CoM trajectories in the sagittal plan were significantly shorter during F movements (p << 0.001), while the index of path curvature (IPC) was smaller (p << 0.001). Similarly, mean values of the time to peak velocity (TPV) were smaller (p < 0.05 when target was at D1 and p << 0.001 when it was at D2, for both CoM and index finger). In the tasks with highest equilibrium demand, therefore, high differences were found for a parameter describing either postural (when referred to the CoM) or pointing (when referred to the index finger) features. As expected, the computation of the jerk relative to the shoulder's marker computed starting from its velocity absolute value revealed that F movements, which were faster that R movements, were much jerkier than R (p << 0.001).

In summary, remarkable differences between F and R movements were found. F movements were always faster and jerkier than the R ones, and their mean TPV values were always shorter (possibly because of the action of gravity). The index finger and CoM trajectories associated with R movements resulted longer and more curved compared to G movements. Different kinematic features characterized the index finger and the CoM motions during the same movement when strong equilibrium efforts were required during the task.

Elevation angles and PCA

The average time series of the five elevation angles relative to movements with target at short and long distance are reported in Fig. 2. Initially, before reaching the target, all angles are very small or close to zero as subjects stood in upright position. During F movements all the angles change so as to determine the flexion of legs, trunk and arms. Note the mirrored behaviour of the Th angle with respect to Sk and Tr, and the similar trend of Hu and Fo: the two angle associated with the arm on average assume almost the same values, meaning that the arms were mainly kept still and rotate about the shoulder joints. The average time series of the elevation angles describing the return movements were on average similar to those of the forward movements (in Fig. 2 the time series of the returning motion were vertically flipped). Such angular displacements corresponded to extension of all the body segments until reaching a final, upright standing position. PCA over the elevation angles revealed that, when the target was at D1, two principal components could account for more than 90% of the variance associated with both forward and return movements (PC1 more than 80% by itself, see Fig 3 top panel): consequently the components of higher order were excluded from the analysis. When the target was positioned at D2, the co-variation among the different elevation angles increased. More in detail, although the VAF by the first two principal components together did not changed drastically with respect to the movements with target at D1, the contribution provided by PC1 increased notably (% of VAF by PC1 was higher than 90% for both forward and returning movements, see Fig. 3). Note that, within the movements with target at the same distance, the amount of VAF and its distribution among the first two principal components was the same for forward and returning movements. The mean values of the loadings associated with each PC are illustrated in the middle and lower parts of the Fig. 3, for each elevation angle. In PC1, segments of the lower-body (Sh, Th and Tr) were always tightly coupled, during both forward and returning movements and independently of target distance. The upper-body segments always relative to PC1 showed instead a different behaviour, dependent of the target distance. Hu and Fo were found not coupled to the lower-body segments when the target was at D1. At the contrary, they became tightly coupled to the lower-body segments when target was at long distance. The loadings of PC2 showed that, with target at D1, Sk and Hu were highly coupled during forward movement, whereas Sk and Fo were tightly covering when subject moved back to the initial standing position. When target was positions at D2, PC2 just described variability associated with Hu.

The shapes of corresponding principal components associated with F and R movements were compared (Fig. 4). Although the percentage of variance explained by corresponding PCs was the same independently of the direction of motion indeed (Fig. 3A), their shape might reveal very different. This would also indicate different pattern of angular co-variation of the elevation angles during G with respect to R movements. The high values of the correlation coefficients reported in Fig. 4, however, indicated that elevation angles co-varied in a similar way regardless of the direction of movements. The biggest difference between corresponding PCs was a slight temporal lag of the PC relative to the R motion, always anticipating the one relative to G. Such a lag can be explained by the different role played by gravity during the two movements, which results in lower TPV values of finger and CoM during R movements). PCA revealed therefore that the angular synergies at the base of the pattern of co-variation between the different body segments did not change dependently of the direction of motion: the only exceptions were the loadings of Hu and Fo associated with PC2 with target at D1.

Muscle activity and NNMF

In Fig. 5 the ensemble-averaged muscle activities associated with F and R movements are plotted. Such muscle patterns refer to movement accomplished with target at D2. As in [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF] indeed, target distance was not found to play a relevant role on the shape of muscle signals and therefore from now on results we will refer, with no loss of generality, to the movements in which the target was positioned at longest distance. In the left column (F movement) muscles show the wellknown triphasic pattern already described in literature [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF]. A clear anticipatory muscle activity characterized movement initiation prior to t 0 . Deactivation of a group of postural muscles (Sol, BF, ST, ES and SM) was followed by the activation of another group of both lower-limb (Tib, Per, RF, OI) and upper-limb muscles (Serr, DA and Pect). Then, between t 0 and t pv a further set of muscles activated that before either deactivated (Sol, BF, ST, SM) or started becoming active (Gast, VL, VM, Add L, GM, LD, DP and Bra). The second half of the movement, starting after t pv , was characterized by a significant tonic activity and co-contraction that likely contributed to stiffen the body joints to counterbalance the gravity effect. The right column depicts the average muscle activity of R movements. In this case all muscles presented initially, as at the end of the F movements, a high level of tonic activity. Anticipatory changes, however, still interested the time period prior to t 0 . Some postural muscles (such as Tib and RF) together with RA and some upper-limb muscles (Pect, LD, Serr, DA, DP and Tri) deactivated, while other lower-body and trunk muscles (Sol, Gast, VL, BF, VM, ST, SM, SM, ES and GM) activated. Differently from the activity of F movements, the largest part of the muscles (with the exception of Sol) presented no significant bursts of activation in the time period between t o ant t pv but, rather, they were characterized by a deactivation profile that coincided with the natural continuation of the initiation phase starting prior to t o . In the second half of the R movements then, muscles presented just a modest level of tonic activity or presented almost no level of activation at all (as in the case of Tib and DA). Note that in Fig. 5 the level of tonic activity at the end of F movement was equal, for each muscle, to the initial tonic activity associated with R movements. In the figure however they look different just because of a different scale of the vertical axes of the graphs.

The upper limit of the vertical axis of each graph was indeed set equal to the maximum value assumed by the average EMG signal plotted in that graph.

Application of PCA to the average muscle activities of F and R movements presented in Fig. 5 revealed that, in both cases, three PCs could account for more than 90% of their variance. The results of NNMF applied to ensemble-averaged EMG activities freed of noise according to the procedure described in the methods section are shown in Fig. 6. The two panels at the top of the figure show the time course of the combination coefficients c i (t), i=1,2,3 (ordered according to the timing of their peaks) for both movements. The upper-left panel confirms the results already described in [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF] for F movements. Each peak was found playing a dominant role in one of the three time phases associated with the movements (time period prior to t o , period ranging between t o ant t pv and the time period that goes from t pv until the end of the movements). The coefficients c 1 (t) was the one mainly responsible for the initiation phase, c 2 (t) to muscle deactivations in the first time phases and muscle activations in the second phase, and c 3 (t) contributed the most to the final co-contraction of all muscles in the third and last phase of the movement. The contribution of each coefficient to each time phase was not unique as conversely it might have been expected. In fact c 1 (t) contributed partly also to the co-contraction phase, as well as c 3 (t), that activated between t 0 and t pv , played a role also in the braking one. This sharing of multiple contributions from different components by each time phase determined consequently the level of the muscle activations in each one of the three vectors w i (Fig. 6, bottom panel). The coefficients associated with the R movement are illustrated in top-right panel of figure 6. Differently from the F case, in this the contribution of each coefficient resulted slightly modified. Although the contribution of c 1 (t) to muscle activation during the first time phase and the major contribution of c 3 (t) to the muscle tonic activity at the end of the movements, c 2 (t) was not found in this case to contribute to muscle activations in the second phase of the movement anymore, but just to muscle deactivations in the time period preceding t 0 .

In conclusion, EMG analysis extended previous results regarding the tri-dimensional and triphasic muscle organization of forward WBP movements. The existence of two distinct groups of muscle (agonists and antagonists, refer to [START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF] for their definitions) acting synergistically was confirmed also when accomplishing R movements, as well as a tri-dimensional organization of the electromyographic activity. Agonists and antagonists switched roles during the two movements, at least in the first phase of the movement: the role of the agonists indeed, that in F were responsible for movement initiation, was replaced by the action played by the antagonists in R movements. Differently from the antagonist muscles, however, agonists did not played a braking role in the time period between t 0 and t pv , and some of them just maintained a level of non-void tonic activity at the end of the movement. Therefore, despite the muscle organization of R movements was found to be still characterized by a tri-dimensional organization like that associated with the F movements, no more three but two main time phases were found to describe the time course of muscle activations relative to R movements. In the first phase agonist muscles deactivated and antagonist activated to initiate the movement. After this phase no active action was provided by muscles, letting gravity braking the movement "naturally". At the end of the movement (second phase) some muscles kept a non-void level of tonic activity to stabilize posture.

Discussion

In this study we compared the kinematic and electromyographic features of a reverse WBP task, in which subjects had to move back to an initial upright standing position, to those associated with a standard WBP movement in which subjects had to point to a target located in front of them [START_REF] Stapley | Does the coordination between posture and movement during human whole-body reaching ensure center of mass stabilization?[END_REF][START_REF] Pozzo | Coordination between equilibrium and hand trajectories during whole body pointing movements[END_REF][START_REF] Berret | Modular control of pointing beyond arm's length[END_REF][START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF]. To this aim, general kinematic parameters were computed for each movement and PCA was applied to the time series describing the temporal evolution of the elevation angles associated with all the body links during either F or R movements. The shape of the extracted principal components and the values of the relative combination coefficients were then compared. Non-negative matrix factorization was moreover applied to the EMG signals collected from a large number of body muscles to assess their modular organization. It was found that, although the mean values of a set of movement parameters differed significantly dependently on the direction of motion, the pattern of joint co-variation remained instead substantially the same. On average, the waveforms of all the elevation angles simply underwent a reversal in time during R movements with respect of the F movements. Muscle organization of the forward whole-body pointing tasks was found instead to be remarkably different with respect to that characterizing the reverse movements. Our results extend those reported by other previous studies [START_REF] Grasso | Motor patterns for human gait: backward versus forward locomotion[END_REF]Papaxantis et al. 1998) and provide evidence that, although the motor plans and motor programs associated with multi-joint opposite movements in the gravity field are different, at kinematic level they are equally translated in the same pattern of motor co-variation.

total body momentum and to keep the balance more easily). The reasons to believe that the strong covariation in the joint space cannot be casual or due to task constraints (e.g. to the requirements for equilibrium maintenance, similar initial and final body configurations, similar velocities and relatively short pointing movements) are multiple. The easiest to put forward is that, because of the large number of degrees of freedom involved during body movement, the target could be reached in many different ways (e.g. with or without flexion of the knees, with or without trunk bending, by moving first the arms and then the trunk plus lower limbs etc.), as well as subjects might use different coordinative strategies during the pointing and backward motions. To test such a hypothesis we asked one subject to accomplish F and R movements by following well-specific instructions. One of them was, among the others, to reach the target and to get back to the initial standing position by first rotating the knees, followed by the hip and actually the arms. The subject never reported difficulties in accomplishing the constrained tasks, as well as he did not perceive them to be unnatural. PCA applied to the kinematic data associated with multiple movements of this kind revealed that joint coordination decreased remarkably, regardless of the direction of motion (Fig. 7). In comparison to the results displayed in Fig. 3, where one single PC could account for more the 90% of the variance, it is clear from Fig. 7 that three PCs were instead required to satisfy the 90% criterion for F movements with imposed kinematic strategy, two PCs for R movements. Moreover, the shapes of the first two PCs extracted resulted much different from those shown in Fig. 4, as demonstrated by the computation of the average R value (R = 0.37).

The notion of motor pattern is strictly linked to those movement components that are repetitive and stereotypical across several kinds of movement transformations. Motor patterns are moreover thought to be the result of the interaction between central and peripheral influences (biomechanical characteristics and sensory afferent activities). Similarly to our findings, Grasso and colleagues (1998) showed that the kinematic pattern associated with the elevation angles of thigh, shank, ankle and foot was conserved across the reversal of gait direction, at the expense of a complete different pattern of electromyographic activity of the leg muscles. Like reversal of gait direction represents a special kind of movement transformation, the same can therefore hold for R with respect to the F whole-body movements. Our results, therefore, seems to extend those by Grasso and colleagues, at least because of the larger number of body-joints considered. Grasso argued that, in the case of locomotion, conservation of the motor pattern do not arise from biomechanical constraints but may instead reflect a behavioural goal achieved by the central network involved in the control of locomotion. Despite the different neural mechanisms underlying locomotion and pointing tasks therefore, such consideration might however be true also in the case of F and R movements.

The reasons why strong joint coupling is maintained also during R movement may be multiple.

In their work, Berret and colleagues (2009) attributed the strong joint coordination during unconstrained F movements to multiple factors, such as passive mechanical effects [START_REF] Ramos | Postural maintenance during fast forward bending: a model simulation experiment determines the "reduced trajectory[END_REF][START_REF] Eng | Interaction of the reactive moments and center of mass displacement for postural control during voluntary arm movements[END_REF][START_REF] Pozzo | Simulating mechanical consequences of voluntary movement upon whole-body equilibrium: the arm-raising paradigm revisited[END_REF] or attractor dynamics (Mussa- Ivaldi et al. 1988;[START_REF] Mohan | A forward/inverse motor controller for cognitive robotics[END_REF]. Another hypothesis is that joint coupling may be the results of the combination of a low number of muscle synergies. In a study on arm reaching in stroke patients for instance, [START_REF] Cheung | Stability of muscle synergies for voluntary actions after cortical stroke in humans[END_REF] supported evidence according to which cortical signals from M1, premotor, supplementary areas or basal ganglia would function to select and activate fixed muscle synergies specified by the spinal or brainstem networks. The authors showed that the EMG activities recorded from both the unaffected and the stroke-affected arms of the patients were characterized by very similar synergistic organizations, despite differences in motor performance between the arms, in cerebral lesion sizes and locations between patients. Prior to this study, Chiovetto and colleagues (2010) already demonstrated that the electromyographic activity of a whole-body pointing task could be explained by the weighted sum of three functional muscle synergies: one to initiate the movement, one to brake it and a third one to stabilize the final body posture. The authors could thus link together, in a hierarchical view of motor control, the joint coordination characterizing the investigated motor tasks with a basic triphasic muscle pattern having similarities with the control schema of single-joint flexion-extension. Such results were confirmed by this study, which in addition also provided knowledge about the muscle activity of the reverse movement. Again, a triphasic organization might have been expected. However, a tridimensional muscle organization was still found, but made of two instead of three time phases. For R movements indeed the braking phase was not found as it was likely replace by the braking action exerted by gravity and other passive mechanical effects. The change of the mechanical and sensory contexts resulted therefore in a reorganization of the muscle activity that, however, still can provide a reason for the strong joint coupling characterizing also R movements.

In conclusion, the present investigation revealed that, for the accomplishment of complex multi-joint movements carried out under different mechanical and sensory contexts due to the different contribution given by gravity to movement dynamics, the CNS relies on different motor plans and different motor programs. The explanation for the kinematic differences between F and R movements was provided by the EMG analysis, which proved that the gravitational force is included into the motor plan when accomplishing whole-body tasks and consequently modifies the processes controlling movement programming. However, the same coordinative structure was found at kinematic level, where the waveforms of all the elevation angles simply underwent a reversal in time during R movements with respect of the F movements. Additional studied needs therefore to be carried out in the future to clarify better why inter-joint coordination is a so peculiar feature characterizing movement generation. The subject was instructed to rotate sequentially the knees first, followed by hip and arms.

Captions

Table 2: The parameters included in the table are the following: peak velocity (PV), relative time to peak velocity (TPV), mean velocity (MV), movement duration (MD), curvilinear distance (CD), linear distance (LD), index of path curvature (IPC) and maximum peak-to-peak amplitude of the jerk (JPP).

  (i = 1,2,..,.N, j = 1,2,...,M) are the elements of the basic time-invariant vectors of muscle activations (or muscle patterns) w i . The number N of combination coefficients and muscle vectors was set equal to the dimension D provided by PCA performed over the EMGs data set under investigation. The reader can refer to[START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF] for additional details regarding the algorithm implementation and the benefits deriving from the combined use of PCA and NNMF in sequence. It is here enough to remind that, because of the positivity of the processed EMGs, application of NNMF can facilitate the interpretation of the results. In the next section we will present for simplicity only the results relative to NNMF applied to the ensemble-averaged (across trials and subjects) muscle activities of F and R movements with target positioned at long distance (D2). Robustness and invariance of such results with respect to the data sets considered were however tested by applying NNMF separately also to the F and R muscle activities associated with the single subjects. Afterwards comparisons were made with those obtained from the enable-averaged muscle activities. Such test comparisons confirmed that results remained always the same across both F (as already shown in[START_REF] Chiovetto | Tri-dimensional and triphasic muscle organization of wholebody pointing movements[END_REF] and R data sets.

Figure 1 :

 1 Figure 1: Typical stick diagrams of the task performed for the near (D1) and the distant (D2) target

Figure 2 :

 2 Figure 2: Average time series of the five elevation angles. In each graph, time-series of the F (in green)

Figure 3 :

 3 Figure 3: On the top of the figure, the percentages of VAF by the first two principal components

Figure 4 :

 4 Figure 4: The temporal shapes of the first two principle components are compared across movement

Figure 5 :

 5 Figure 5: Ensemble-averaged activity patterns of F (left column) and R (right column) movements.

Figure 6 :

 6 Figure 6: Time courses of the average index finger velocity profiles of F (top-left panel) and R (top-

Figure 7 :

 7 Figure 7: The figure displays the percentages of VAF by the first three principal components

Acknowledgements:

Dr. Chiovetto's research was partly supported by EU grant FP7-ICT-248311 (AMARSI).

Asymmetries were found characterizing, dependently on the direction on motion, CoM and finger kinematic parameters, suggesting differences in the motor plans relative to F and R conditions.

Such results confirm those from previous investigations and relative to other kinds of opposite movements. Similarly to what has been reported in this study, asymmetric hand path and velocity profiles were indeed found during the accomplishment of arm reaching movements in the sagittal plane [START_REF] Atkenson | Kinematic features of unrestrained vertical arm movements[END_REF]Papaxanthis et al. 1998a,b,c;Pellegrini and Flanders, 1998;[START_REF] Papaxanthis | Similar planning strategies for whole-body and arm movements performed in the sagittal plane[END_REF]. Moreover, always in agreement with our results, hand-path curvature was reported to be greater and hand velocity profile to have smaller acceleration duration during an upward movement with respect to a downward movement. Other studies in the literature compared the kinematic behaviour associated with even more complex reverse tasks than simple arm movements.

The existence of kinematic asymmetries was for instance reported also for the case of sit-to-stand (STS) and back-to-sit (BTS) tasks [START_REF] Mourey | Standing up from a chair as a dynamic equilibrium task: a comparisonbetween young and elderly subjects[END_REF][START_REF] Scholz | Effects of varying task constraints on solutions to joint coordination in a sit-to-stand task[END_REF][START_REF] Kerr | Analysis of the sitstand-sit movement cycle in normal subjects[END_REF][START_REF] Schenkman | Whole-body movements during rising to stand from sitting[END_REF][START_REF] Papaxanthis | Similar planning strategies for whole-body and arm movements performed in the sagittal plane[END_REF].

In contrast to the marked differences that we found distinguishing the motor plans of F and R movements, our results provide instead evidence for the existence of common patterns of motor covariation at the kinematic level. This result is not obvious a priori. Because of the intrinsic redundancy characterizing the human body and the different mechanical and sensory contexts characterizing the two movements, different coordinative strategies might have been expected. Moreover, F and R movements are drastically different. The first one is indeed strongly target-oriented, while the second one is more a postural task. Thus, for instance, during F movements high inter-joint coordination (typically characterizing arm reaching) might have been expected. During R movements instead, when the main goal is to recover a stable upright posture, one might have expected a returning motion starting with the extension of the arms followed that of the other body segments (so as to reduce the