**4.2. Results on the SMEX'02 experiments**

added to the mean values of *s* and *l*. The pseudo random values are drawn from a standard

**•** Case 8: VWC is provided as an input variable and an integration is done over the following

**•** Case 9: VWC is calculated using a SPOT image, based on NDVI values, and an integration is done over roughness and correlation length in the following ranges:0.4 cm< *s* < 1.2 cm and

In Fig.9, preliminary results are presented where the different analyzed cases based on various prior conditions are numbered from 1 to 9. In general, for bare soil (fig. 9), the results showed a sensitivity of the algorithms to the different roughness conditions of each plot with a variability of around 5-7% (excluding the extreme cases). The highest variability among the cases is around 40% and is found when the roughness interval is very small (case 2 and 3). When considering a random function for roughness (case 7) and when performing the retrieval over average values of backscattering coefficients (case 5), the mean different with respect to

For vegetated areas, due to the limited availability of field measurements (field 5N), the evaluation of the performances is still under work. More extensive results for vegetation are

**Figure 9.** Comparison of SM estimates with measured values. Behavior diagram of the described cases.

normal distribution.

3.0 cm < *l* < 10.0 cm.

values: 0.01 <VWC < 6 Kg m2

ground measurements is around 15%.

presented for the SMEX'02 experiments.

.

54 Dynamic Programming and Bayesian Inference, Concepts and Applications

As illustrated in previous paragraphs, the inversion methodologies based on Bayesian approach can be applied to different sensors configurations. In this way different polarizations and/or bands can be exploited to extract soil features. In fact, due to the different way C band or L band signals interact with soil and the above canopy layer, they are sensitive to different surface characteristics. Thus a proper combination of the two bands can help disentangle the effect of vegetation and then improve the estimation of soil moisture. In this paragraph, the results of the Bayesian methodologies are illustrated and the evaluated in terms of:

**Configurations Corn Soybean**

in such kind of plants with broad leaves could dominate [43].

the expected values for soil moisture has been varied as follows:

**•** Whole range of roughness: *s* varying between 0.2 and 5.0 cm.

**•** Low roughness: *s* varying between 0.2 and 1.2 cm; **•** High roughness: *s* varying between 1.2 and 5.0 cm;

carried out by considering the effect of prior information on roughness.

indicated.

of roughness.

showed in fig. 12.

deviations.

C band 0.36 0.127 *0.83 0.032* L band 0.41 0.091 0.42 0.072 C+L band *0.68 0.057 0.82 0.037*

**Table 5.** Correlation coefficients (R), RMSE for the comparison between the different estimates and ground truth values for SM values and for the Bayesian approach. With respect to table 4, in this case, the soybean and corn fields are considered separately. In italics, the values significantly different from the one found in whole data sets are

Similar characteristics are also found in [44], where it is proved that the RMSE is dependent on the level of vegetation of the different fields. Furthermore, in the case of C band, the signal coming from the VWC dominates over the signal coming from soil. In fact, when the vegetation has low value of VWC such as in the case of soybean fields, the C band is able to provide acceptable estimates for soil moisture. In the case of corn fields, the best results is obtained with the combination of C and L band, one sensitive to VWC and the other to the surface contribution. These discrepancies may be ascribed to the fact that in the Bayesian formulation the double bouncing between soil and corn trunk effect is not taken into account. This effect

On the SM estimates derived from combination of C and L band, a further analysis has been

More in details, the range of roughness in the integration of equation which is used to derive

The chosen values for roughness have selected based on prior information on roughness during field measurements. Along with these fixed ranges of roughness, a variable roughness interval has been considered based on the values of backscattering roughness. Higher values of backscattering coefficients on both C and L band have been also associated to high values

The SM estimates derived from C and L band are illustrated in figure 11. When the estimates under these hypotheses are compared, they show an overall variability of around 25%. The results in term of correlation coefficients, are presented in the form of Taylor diagram as

The SM estimates closest due to the ground measurements are those derived from the whole range of roughness and the adapted intervals. The high roughness and the whole range of roughness produces very close results both in terms of correlation coefficients and standard

**R RMSE (cm3/cm3) R RMSE (cm3/cm3)**

Integration of Remotely Sensed Images and Electromagnetic Models into a Bayesian Approach for…

http://dx.doi.org/10.5772/57562

57


When dealing with the different cases due to the prior information, the retrieved values will be compared with the measurements through the Taylor plots [42].

The Bayesian approach has been applied to AirSAR data collected during the SMEX'02 experiments considering C band, L band and combination of C and L data.

The results for the estimation of SM are reported in table 4. As expected the estimation of SM is quite difficult, thus determining values of R varying from 0.47 to 0.80 for the combination of C and L bands. The highest difficulties are found for the detection and correct estimation of extreme values of soil moisture.


**Table 4.** Correlation coefficients (R), RMSE for the comparison between the different estimates and ground truth values for SM values, excluding extreme values.

The retrieval of low values of SM can be difficult as the signal for soil is small and difficult to be disentangled from the vegetation signal. For high values, the signal from soil is strong but in the case of C bands the double bouncing and the effect of absorption from leaves also for L band, typical of narrow leaf plants such as soybean, determine a lower signal reaching the sensor [43]. The L band estimates are the only one able to predict highest values of SM.

Similar analyses were also found in Notarnicola et al. 2006 [39]. In this previous analysis, the methodologies were applied only to few fields of the same data set. With respect to the accuracy reported in Notarnicola et al., 2006 [39], a worsening in the performance is found. In particular the data set includes all the fields in the watershed basin and the fields located in the eastern part which exhibits anomalous values of SM, some very high values around 35% and some values lower than 5%. Considering the available meteorological information, the eastern and western parts of the watershed experienced very different intensity for the rain event where most of the rain event occurred in the western part.

If the watershed is divided in two parts the western and the eastern part the performances of the algorithm for SM retrieval differ significantly. The correlation coefficients are equal to 0.57 and 0.84, not significantly different from those found in [39].

Furthermore, the performances notably change if in the data set the soybean and corn fields are considered separately. The results are reported in table 5.


**Table 5.** Correlation coefficients (R), RMSE for the comparison between the different estimates and ground truth values for SM values and for the Bayesian approach. With respect to table 4, in this case, the soybean and corn fields are considered separately. In italics, the values significantly different from the one found in whole data sets are indicated.

Similar characteristics are also found in [44], where it is proved that the RMSE is dependent on the level of vegetation of the different fields. Furthermore, in the case of C band, the signal coming from the VWC dominates over the signal coming from soil. In fact, when the vegetation has low value of VWC such as in the case of soybean fields, the C band is able to provide acceptable estimates for soil moisture. In the case of corn fields, the best results is obtained with the combination of C and L band, one sensitive to VWC and the other to the surface contribution. These discrepancies may be ascribed to the fact that in the Bayesian formulation the double bouncing between soil and corn trunk effect is not taken into account. This effect in such kind of plants with broad leaves could dominate [43].

On the SM estimates derived from combination of C and L band, a further analysis has been carried out by considering the effect of prior information on roughness.

More in details, the range of roughness in the integration of equation which is used to derive the expected values for soil moisture has been varied as follows:

**•** Low roughness: *s* varying between 0.2 and 1.2 cm;

effect of vegetation and then improve the estimation of soil moisture. In this paragraph, the

When dealing with the different cases due to the prior information, the retrieved values will

The Bayesian approach has been applied to AirSAR data collected during the SMEX'02

The results for the estimation of SM are reported in table 4. As expected the estimation of SM is quite difficult, thus determining values of R varying from 0.47 to 0.80 for the combination of C and L bands. The highest difficulties are found for the detection and correct estimation of

**Configurations Correlation coefficients RMSE (cm3/cm3)**

**Table 4.** Correlation coefficients (R), RMSE for the comparison between the different estimates and ground truth

The retrieval of low values of SM can be difficult as the signal for soil is small and difficult to be disentangled from the vegetation signal. For high values, the signal from soil is strong but in the case of C bands the double bouncing and the effect of absorption from leaves also for L band, typical of narrow leaf plants such as soybean, determine a lower signal reaching the sensor [43]. The L band estimates are the only one able to predict highest values of SM.

Similar analyses were also found in Notarnicola et al. 2006 [39]. In this previous analysis, the methodologies were applied only to few fields of the same data set. With respect to the accuracy reported in Notarnicola et al., 2006 [39], a worsening in the performance is found. In particular the data set includes all the fields in the watershed basin and the fields located in the eastern part which exhibits anomalous values of SM, some very high values around 35% and some values lower than 5%. Considering the available meteorological information, the eastern and western parts of the watershed experienced very different intensity for the rain event where

If the watershed is divided in two parts the western and the eastern part the performances of the algorithm for SM retrieval differ significantly. The correlation coefficients are equal to 0.57

Furthermore, the performances notably change if in the data set the soybean and corn fields

C band 0.47 0.10 L band 0.67 0.05 C + L band 0.80 0.02

results of the Bayesian methodologies are illustrated and the evaluated in terms of:

**•** Root Mean Square Error, RMSE, between the estimates and the ground truth values.

**•** Correlation coefficients, R, between the estimates and the ground truth values

be compared with the measurements through the Taylor plots [42].

56 Dynamic Programming and Bayesian Inference, Concepts and Applications

extreme values of soil moisture.

values for SM values, excluding extreme values.

most of the rain event occurred in the western part.

and 0.84, not significantly different from those found in [39].

are considered separately. The results are reported in table 5.

experiments considering C band, L band and combination of C and L data.


The chosen values for roughness have selected based on prior information on roughness during field measurements. Along with these fixed ranges of roughness, a variable roughness interval has been considered based on the values of backscattering roughness. Higher values of backscattering coefficients on both C and L band have been also associated to high values of roughness.

The SM estimates derived from C and L band are illustrated in figure 11. When the estimates under these hypotheses are compared, they show an overall variability of around 25%. The results in term of correlation coefficients, are presented in the form of Taylor diagram as showed in fig. 12.

The SM estimates closest due to the ground measurements are those derived from the whole range of roughness and the adapted intervals. The high roughness and the whole range of roughness produces very close results both in terms of correlation coefficients and standard deviations.

**5. Conclusions**

SAR signal.

applied to C band, L band and C+L band data.

backscattering coefficients on roughness and vegetation parameters.

algorithms for SM estimation, the following considerations emerge:

**•** The set of prior information has to be selected carefully;

has an impact on the final estimates;

performances with respect to the ground reference data.

The main objective of this chapter is to present the capability of Bayesian approach to estimate SM values starting from SAR backscattering coefficients. Two case studies are presented where SAR acquisitions took place over agricultural fields. The first case study was related to an Argentinean test site developed and equipped for acquisitions of airborne L band SAR called SARAT. The acquisitions were carried out in preparation of the SAOCOM mission. The second case study was related to the experiment SMEX'02 carried out in IOWA in 2002. In this experiment airborne AirSAR images were available and for this reason the retrieval was

Integration of Remotely Sensed Images and Electromagnetic Models into a Bayesian Approach for…

http://dx.doi.org/10.5772/57562

59

Based on the retrieval results, the main goal was then to verify the sensitivity of the SM estimates from the set prior information on roughness and vegetation. All the prior PDFs are set a uniform, non-informative but the set limits of the interval in the integration procedure can determine variation in the final SM estimates. This behavior is expected because the electromagnetic models used in the retrieval approach contain explicitly the dependence of

The effect of prior information ranges from few percentages up to 25% where the highest sensitivity is found in both case studies when too specific and narrow intervals for roughness are used. The highest performances were found for both case studies when the range of roughness is large enough to include most roughness measurements. Moreover, if a prelimi‐ nary assessment on the roughness level is available, the algorithm determines the highest

An interesting feature observed in the case of Argentinean test site is the reduction of errors on the SM estimates when the retrieval is performed on average values of backscattering coefficients from each field. This behavior can be due to the reduction of noise present in the

As main conclusion of this analysis and suggestions in using the proposed the Bayesian

**•** Even in the case of non-information prior PDF, the range of variability of the prior variable

**•** It is preferable to integrate over a large interval of roughness and/or vegetation variables in

**•** As the speckle noise can influence the SM estimates, a proper filter over the SAR image

order to take into account and properly weight all the measured values.

needs to be applied before proceeding to the retrieval approach.

**Figure 11.** Comparison of SM estimates under different roughness hypothesis with ground measurements. "LR" stand for low roughness, "HR" for high roughness, "Whole" for the whole range of roughness and adaptive for adaptive values of roughness.

**Figure 12.** Taylor diagram showing the comparison under different prior hypotheses on roughness. A refers to ground measurements; B to low roughness; C to high roughness; D to whole range of roughness; E adapted rough‐ ness ranges.
