All the four polarizations are used to retrieve the soil moisture using all the three models. First, results for HH polarization from the three (CT, CD and DI) model are described. Then, the results from CT models are discussed in detail for spatial and temporal behavior. Followed by the discussion of retrieval error from all the three models and for all the four polarizations, along with the sensitivity analysis (effect of number of available data and uncertainty in the BC).

#### 4.1. Results for σ_{HH}

The retrieved soil moisture from the three models are compared with field measured soil moisture for the 50 plots through Taylor diagram, presented in

Figure 4. The standard deviations are represented through their ratio over the standard deviations of the observations, and hence should ideally be equal to 1. The observed correlation coefficient from all the three model is similar and range between 0.4 to 0.8 for most of the plots. CT and CD models showed the normalized standard deviation relatively closer to the ideal value of 1, while DI model showed relatively higher value for most of the plots. CT and CD models outperformed the DI model for almost all the plots. No significant difference is observed between the performance of CT and CD models.

The comparison of the SM retrieved from the CT model using RADARSAT-2

σ_{HH} (HH polarization BC) with the SM measured in 50 plots is shown in

Figure 5. The error indices (correlation, bias, and RMSE) comparing the retrieved soil moisture with the measured soil moisture along with the number of data points for each plot are presented in

Table 3. Histogram of these indices is presented in

Figure 6. The retrieved soil moisture showed a good comparison with the field measured soil moisture. The bias showed approximately uniform distribution with a mean and median approximately equal to 0. Approximately half of the plots showed absolute bias lesser than 0.03. The nil average bias observed from 50 plots, can be assumed to hold good for the up-scaled soil moisture. Most of the plots (approximately 70%) showed RMSE lesser than 0.09, with the median equal to 0.07. Correlation for more than 80% of the plots is higher than 0.4, with a median of 0.61. Similar range of correlation is observed in [

41] over National Airborne Field Experiment (NAFE) 2005 by retrieving the SM using the change detection approach with the ENVISAT Advanced Synthetic Aperture Radar (ASAR) Global Monitoring (GM) data which has the spatial resolution of 1 km. Though a slightly higher RMSE was observed in [

41] with RMSE of 0.14 and 0.15

m^{3}/m^{3} for croplands and pastures respectively. Study by [

42] using the change detection and ENVISAT ASAR GM data over Oklahoma also reported the same range of correlation.

A relatively poor performance of the CT model in few plots (3, 4, 5, 11, 16, 23, 43, 44) can be attributed to the fact that these plots often had extensive irrigation, sometimes resulting in ponding like condition. The ponding type condition decreases the roughness and hence decreases the BC, which is opposite of the general trend,

i.e., increase in soil moisture results in the increase in BC. Another possible reason might be the enhanced impact of difference in sensing depth between field and RADARSAT-2 measurements in irrigated areas [

43]. Poor performance in the plot no. 19 could be attributed to the fact that it is situated in a foothill. Though correction for topography is performed, it can still be improved by a higher resolution DEM. Most of the plots having higher bias showed a significant correlation coefficient suggesting the effect of scaling the relative soil moisture into the absolute soil moisture using the soil information. This is consistent with the finding of [

14], where scaling the

RSM into

SM with the help of soil information resulted in a bias dependent on soil type. The major source of error in the soil information could be due to the erroneous delineation of the soil classes and error coming from the pedo-transfer function. A better soil map could reduce this bias and hence provide a lower RMSE.

Spatial behavior of the retrieved soil moisture for all the 30 RADARSAT-2 images is shown in the

Figure 7. The soil moisture shows a significant variability both in space and as well as in time, with the soil moisture ranging from 0.06 to 0.32 (

m^{3}/m^{3}). Relatively higher soil moisture is observed in the valley of the watershed. Agricultural part of the study area shows a relatively higher variation in SM compared to the forested part, which is consistent with the observed temporal variation (maximum–minimum) of 7.4 dB and 5.4 dB in

σ_{HH} for the agricultural and forested part of the study area respectively. The relatively low variation observed in the SM in forested part could be due to the low vegetation penetration capability of C band. Temporal behavior of SM is also compared with the district average monthly precipitation provided by the Indian Meteorological Department (IMD) (

http://www.imd.gov.in/section/hydro/distrainfall/districtrain.html).

Figure 8 shows the temporal variation of the mean retrieved SM using the CT model along with the monthly rainfall. For all the four years, the peak rainfall is observed around the month of September–November and minimum rainfall around December–February. The monthly rainfall showed a bi-modal behavior, showing a second peak around the month of March–May. The cumulative annual rainfall for the year 2010, 2011, 2012 and 2013 are 900.5 mm, 758.8 mm, 529.5 mm, and 678.9 mm respectively. Year 2012 received lowest rainfall during the study period. The soil moisture showed a temporal behavior similar to the one shown by monthly rainfall with soil moisture for the December–March being relatively low. The soil moisture for the month of May–October was usually high except year 2012 which was a relatively dry year as shown by the monthly rainfall. A trend of decreasing soil moisture in the dry months (December 2009 to February 2010) is observed which is consistent with the fact that these months observed very low rainfall. Approximately, monthly rainfall lesser than 50 mm resulted in a decrease in soil moisture in time, and a monthly rainfall higher than 100 m showed the increasing trend. For the monthly rainfall between 50 mm and 100 mm, the trend was found to be dependent on the initial condition of soil moisture.

#### 4.3. Impact of Vegetation and Roughness

The three models considered in the study assume negligible impact of the temporal variation in the vegetation and soil roughness. For C-band, at an incidence angle of around 15 degree this assumption is reasonable [

44,

45]. At an incidence angle higher than 15 degree, the temporal variation of soil roughness and vegetation might impact the BC. The impact will be relatively higher for a relatively higher incidence angle. Studies using the change detection approach observed that the major source of SM retrieval error is the noise of the backscatter measurements and the impact of seasonal vegetation cover is about one order of magnitude smaller.

Taconet

et al. [

46] suggested that for wheat canopy, at an incidence angle of 21 degree, BC requires a correction of 1 dB per 1

kg/m^{2}. The biomass for the agricultural plots in the study area are less than approximately 3

kg/m^{2}. A sensitivity analysis is performed to evaluate the impact of uncertainty in the BC on the soil moisture retrieval accuracy. The time series of BC is perturbed with random variable having normal distribution with zero mean and a given standard deviation. Same perturbed time series is used in retrieving the soil moisture from the three models.

Figure 10 shows the RMSE in retrieving the soil moisture for different level of standard deviation (std.) of error in the BC for the three models and all the four polarization. DI model showed significant increase in the RMSE with the increase in the standard deviation of error, which could be due to the reason that it normalize the data with one data point and any error in that particular data point will introduce the error in entire time series of retrieved soil moisture. CD and CT showed the similar behavior showing a marginal increase (RMSE increased approximately from 0.07 to 0.10 for the increase in standard deviation of error from 0 to 3.5 respectively) in the RMSE with the increase in standard deviation of error.

The retrieval of soil moisture can be improved by accounting for the contribution of vegetation in BC by using Water Cloud model [

47]. Such a correction requires crop specific parameters, and a crop map at the watershed scale. Since, no crop map is available for the study area, and data only from the lower incidence angle is used which can penetrate the modest vegetation, no correction for vegetation is applied in the current work. Kim

et al. [

48] estimated the vegetation water content from Radar Vegetation Index (RVI) based on a linear regression model. The RVI is less impacted by environmental condition [

49], and is defined as,

where,

σ is BC in linear unit and subscripts refer to the polarization. RVI can be used as a proxy to quantify the impact of higher and lower stages of vegetation. To quantify the effect of the different stages of vegetation, the RMSE for the retrieved soil moisture is computed for the lower and higher values of RVI. For each plot, RVI is classified into two groups by using the threshold of median. Then, RMSE are computed separately for these two group for all the 50 plots. Two tailed Welch’s t-test is used to compare if the expected value of RMSE for lower and higher vegetation are statistically identical. The computed t-statistic for the test is 1.586 with

p-value of 0.116. It means that at 5% significance level the mean are identical. This could be explained by a relatively lower incidence angle of RADARSAT-2 images used in the study. It can be concluded that the error introduced by not correcting for vegetation might be bringing relatively lower uncertainty compared to other sources (e.g., soil information).

RMSE for each image is computed by comparing the retrieved SM from HH polarization using the CT model. Temporal behavior of the computed RMSE along with the mean (averaged over 50 plots) RVI is presented in

Figure 11. Mean RVI shows the seasonal cropping patters observed in the study area, with peak observed around September in all the four years. A moderate correlation of 0.45 is observed between the time series of RVI and RMSE. This could be probably due to the presence of different types of vegetation resulting in differences in scattering behavior, including other factors (soil roughness, soil parameters and soil wetness). However, a relatively higher value of RMSE is observed when there is a seasonal peak in the RVI. This suggests that the moderate relationship between the RVI and RMSE can not be used to quantify the retrieval error, however the RVI can be used to identify the images having the relatively higher vegetation biomass and mask them. Four images belonging to the seasonal peak value of mean RVI are masked which have RMSE of 0.094, 0.086, 0.079

m^{3}/m^{3}.

Using Integral Equation Model (IEM) [

6], the behavior of

σ_{HH} is modeled in terms of incidence angle and soil roughness mean standard deviation height (

H_{rms}) by assuming the exponential correlation function and a correlation length of 6 cm and SM equal to 0.20

m^{3}/m^{3}.

H_{rms} is assumed to vary from 0.6 to 1.2 cm. Simulated behavior of

σ_{HH} is shown in

Figure 12. It can be seen from the figure, the minimum variation in the

σ_{HH} due to the

H_{rms} is observed at an incidence angle of about 17 degree, and higher or lower incidence angle than this results in a relatively higher variation of

σ_{HH}. At an incidence angle of 23 degree, which is used in the current study, a saturation of

σ_{HH} is observed at higher value of

H_{rms} than 1.0 cm. A variation of 2.12 dB in

σ_{HH} is observed for

H_{rms} varying from 0.6 to 1.2 cm, and the variation reduces to 0.5 dB for the range from 0.8 to 1.2 cm. It should be noted that though the absolute value of BC depends upon the SM, the difference in BC due to the

H_{rms} is independent of SM [

50]. A similar impact of variability in soil roughness was observed by using the IEM model [

51]. From

Figure 10, it can be inferred that an error of 1 dB standard deviation in BC results in increase in RMSE by 0.01

m^{3}/m^{3} approximately. Often agricultural field experiences

H_{rms} > 0.6 cm [

52–

56], except soil with a higher (more than 50%) slit content as reported in [

50,

57]. In the study area, all soil tillages correspond to medium or high roughness and therefore the impact of temporal variation in soil roughness can be neglected.

To investigate the validity of assumption of maximum SM being equal to field capacity and minimum SM being equal to 0.5 of wilting point, frequency distribution of field measured SM is analyzed. It is observed that the field measured SM remains lower than the field capacity for 92% of the cases, and higher than the 0.5 of wilting point for 87% of the cases. A possible reason for SM falling outside the range of 0.5 of wilting point and field capacity could be the calibration error of 0.031

m^{3}/m^{3} observed in the theta probe. For few field plots which were irrigated close to the satellite acquisition date, SM exceeded the field capacity and is observed to be closer to saturation value. The assumption that maximum soil moisture can be assumed to be equal to the field capacity might not hold true in the case of very dry or very wet region, and would need suitable change in the maximum soil moisture which can be calibrated as a function of field capacity for that region. Moran

et al. [

4] reported that the use of difference between dry and wet season

BC can normalize the effects of surface roughness and topography. In the current study, since a CDF approach is used, which normalize the

BC not only using the wet and dry season

BC but using the entire measured time series, the impact of surface roughness and topography can be reduced considering that the RADARSAT-2 images are at approximately same incidence angle. The CT approach has the advantage that it can work in the case of relationship between

SM and

BC being nonlinear and avoids the identification of dry and wet season images. The CT approach also explicitly account for the soil type, by normalizing using the field capacity and wilting point map. This is similar to the normalization performed by Dobson and Ulaby [

58] using the field capacity only, the current approach being different in the sense that it uses wilting point also for the normalization. The normalization with the wilting point ensures the lower range of soil moisture into a physical range. Since current approach does not require any calibration parameter, it has the potential to be applied globally in the case of modest vegetation.

#### 4.4. Validation at SMOS Scale

The soil moisture retrieved from RADARSAT-2 is up-scaled to the coarse scale to compare with the soil moisture from SMOS. The up-scaling is performed for the eight strategies mentioned in

Table 2. The correlation coefficient and RMSE for the comparison are shown in

Figure 13. To analyze the impact of SMOS pass direction (ascending/descending) the comparison is performed separately for only ascending pass data, for only descending pass data and for all the passes. The descending pass of SMOS showed a better comparison (a relatively higher correlation coefficient and a relatively lower RMSE) for all the eight strategies. Strategy number 3, 4, 7 and 8 outperformed the other strategies (a relatively higher correlation coefficient and a relatively lower RMSE) and the difference among these four best strategies (3, 4, 7 and 8) is very minimal. The best strategies showed a RMSE of approximately 0.051

m^{3}/m^{3} and a correlation coefficient of approximately 0.88. The common factor among these four strategies is land cover, which means that the land cover is the significant factor while aggregating the soil moisture from the scale of RADARSAT-2 to the scale of SMOS. This is consistent with the fact that SMOS level 2 did have the contribution from the forest area [

59,

60]. The under performance of ascending overpass is explained by the presence of radio frequency interferences. It is useful to note that this result can not be generalized for other regions.

The comparison of RADARSAT-2 retrieved SM with SMOS retrieved SM offers the opportunity to make a multi-scale (local to regional) validation with independent sources. However, the spatial resolution and representative depth is different. SM retrieved from RADARSAT-2 is upscaled based on the approach proposed by Al Bitar

et al. [

40] to bring it to the spatial resolution of SMOS. Representative depth of SM from RADARSAT-2 is typically representative of 0–2 cm [

7] and from SMOS is typically representative of 0–5 cm [

61]. Other studies associate more a 0-3 cm representative depth for soil moisture from L-band radiometers (SMOS, SMAP, Aquarius) [

62,

63]. The difference in representative depth might introduce the difference in estimated SM [

64,

65]. Nevertheless, the correlation between soil moisture at these depths is high [

66]. To remove the impact of representative depth a bias correction using CDF matching is performed. In addition, at L-band and in passive mode (radiometer) the impact of vegetation is expected to be lower than C-band acquisitions [

67]. Finally the comparison at SMOS scale offers the opportunity to make a multi-scale (local to regional) validation with independent sources.