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The high spatio-temporal variability of soil moisture is the result of atmospheric forcing and redistribution processes related to terrain, soil, and vegetation characteristics. Despite this high variability, many field studies have shown that in the temporal domain soil moisture measured at specific locations is correlated to the mean soil moisture content over an area. Since the measurements taken by Synthetic Aperture Radar (SAR) instruments are very sensitive to soil moisture it is hypothesized that the temporally stable soil moisture patterns are reflected in the radar backscatter measurements. To verify this hypothesis 73 Wide Swath (WS) images have been acquired by the ENVISAT Advanced Synthetic Aperture Radar (ASAR) over the REMEDHUS soil moisture network located in the Duero basin, Spain. It is found that a time-invariant linear relationship is well suited for relating local scale (pixel) and regional scale (50 km) backscatter. The observed linear model coefficients can be estimated by considering the scattering properties of the terrain and vegetation and the soil moisture scaling properties. For both linear model coefficients, the relative error between observed and modelled values is less than 5 % and the coefficient of determination (R^{2}) is 86 %. The results are of relevance for interpreting and downscaling coarse resolution soil moisture data retrieved from active (METOP ASCAT) and passive (SMOS, AMSR-E) instruments.

Soil moisture is highly variable in space and time. Soil moisture patterns are spatially organized phenomena, influenced by geology and topography, land cover and climate [

As a result of large scale atmospheric forcing, temporal soil moisture variations can be expected to be similar across different spatial scales, from meters to hundreds of kilometres. At local scale these atmospheric-driven temporal variations are modulated by small-scale hydrologic processes related to terrain, soil, and vegetation characteristics. Experimental work based on

The questions of whether, where and how coarse resolution satellite data can be used at finer scales are important because, within the next few years, only coarse resolution (25-50 km) soil moisture data derived from spaceborne radiometer and scatterometer systems can be expected to be operationally available [

Given that soil moisture has an important influence on radar backscatter measurements at all spatial scales, it is hypothesized that temporally stable soil moisture patterns lead to temporally stable radar backscatter patterns. To verify this hypothesis, long-term backscatter time series acquired by the Advanced Synthetic Aperture Radar (ASAR) flown on board of the European satellite ENVISAT are analysed in this paper. ASAR can be operated in Wide Swath (WS) mode to cover a much wider swath (swath width of 405 km) than in conventional strip-map mode (swath width of 100 km). In this way, large areas can be more frequently imaged and long backscatter time series can be more easily constructed.

The concept of temporal stability was introduced by [

Let us consider a soil moisture network with _{r}_{j}

where _{p}_{i}_{i}^{2} depending on the employed measurement technique (see [

and calculated the mean and standard deviation of _{i,j}_{i,j}_{i}_{i}_{i,j}_{p}_{r}_{i,j}^{2}) of station soil moisture with the regional mean over the 610 km^{2} Little Washita Watershed located in Oklahoma, USA, was larger than 0.75 for the majority of the sites. Grayson and Western [^{2} values of more than 0.9 in the 10.5 ha Tarrawarra catchment near Melbourne, Australia.

Given temporally stable soil moisture patterns, time-invariant relationships can be used for estimating regional soil moisture _{r}_{p}^{2} large Sahelian site located in the Gourma region in Mali. Not only in ^{2}) and found that a linear model was well suited to describe the relationship between 1 km^{2} and 40 × 40 km^{2} soil moisture fields. One can hence write

where _{rp}_{rp}_{rp}_{rp}

Instead of confining _{r}

In subareas of region ℛ where large-scale atmospheric forcing has a dominant control on soil moisture, the upscaling model (4) is expected to give good results. On the other hand, at points (

where the reverse sequence of the subscripts now indicates that the soil moisture content at point (_{r}_{pr}_{pr}_{rp}_{rp}

Estimates of the regional soil moisture content _{r}_{pr}_{pr}

Over bare soil and moderately vegetated terrain, radar backscatter is sensitive to soil moisture. In such areas it can be expected that the temporal persistence of soil moisture patterns is reflected in the spatio-temporal behaviour of the radar backscattering coefficient. For a better quantitative understanding of this effect, a model relating backscatter across two spatial scales is derived in the following.

Radar backscatter from land surfaces is a complex function of sensor parameters (frequency, polarization, incidence angle) and external factors given by the dielectric (soil moisture, vegetation water content) and geometric (surface roughness, plant structure) properties of the imaged terrain [

Change detection methods rest upon the idea that reference images representing dry soil conditions are subtracted from each radar image to implicitly account for surface roughness and land cover patterns [

where ^{0}_{dry}^{0} to changes in soil moisture ^{0}_{dry}^{0}_{dry}

While soil moisture ^{0}_{dry}^{0}_{dry}^{0}_{dry}^{0}, the time ^{0}_{dry}^{0}_{dry}^{0}_{dry}^{0}_{dry}

The change detection model (8) has successfully been applied to coarse-resolution (50 km) ERS scatterometer measurements on a global scale [

For the discussion of spatio-temporal trends two spatial scales are considered, one denoted by local scale and one by regional scale. The local scale is represented by an area ℒ of size _{l}_{r}. It is assumed that the region ℛ is much larger than the local area ℒ, i.e. _{r}_{l}

where the subscripts

By substituting the downscaling

and pulling _{r}

where

Using ^{0}_{l}^{0}_{r}

where the coefficients

This derivation suggests that the backscattering coefficients at local and regional scale are linearly related, whereas the linear model coefficients ^{0}_{dry}^{0}_{dry}_{lr}_{lr}^{0}_{dry,l}_{l}

As discussed, the coefficients _{lr}_{lr}

While the coefficient _{lr}_{lr}_{lr}_{lr}

The test site is a region of 4200 km^{2} that surrounds the 1285 km^{2} REMEDHUS network area located in the centre of the Duero basin, Spain, where the University of Salamanca has been operating

The area is characterized by a Mediterranean climate with mean annual precipitation of 385 mm and mean annual evapotranspiration of around 908 mm. The geological substrate mainly consists of sandstones, conglomerates and fluvial deposits. The soils within the test site area are dominated by sandy textures. The area is intensively used for farming. The main crops are cereals and grapes. A network of 20 permanent time domain reflectometry (TDR) soil moisture stations is spread over the test site area. At each station two-wire TDR probes (Tektronix 1512C) were installed at 5 cm, 25 cm, 50 cm and 100 cm depths. Only the values taken at 5 cm were used in this study. Comprehensive laboratory analyses of soil samples were carried out to calibrate the TDR measurements and to assess soil properties at each station (texture, porosity, etc.). After the calibration phase, readings have been taken fortnightly since spring 1999. The land cover map and the location of the TDR stations are shown in

The network has repeatedly served for soil moisture process studies [

Backscatter time series can be obtained from SAR instruments that are capable of acquiring imagery with a high spatial resolution independent of cloud cover and light conditions. However, many spaceborne SAR systems are characterized by short duty cycles (acquisition time per satellite orbit) and small swath width (< 100 km). Therefore, long and dense time series of several dozens or more SAR images covering the same area are generally not available. Coverage can be much improved by increasing the duty cycle and/or by using ScanSAR technology to image a wide swath [

For this study, ScanSAR data acquired by the European satellite ENVISAT have been used. ENVISAT was launched on February 28, 2002 by the European Space Agency and circles the earth in a polar 35-days repeat orbit at an altitude of around 800 km and an inclination of 98.5°. The satellite carries the Advanced Synthetic Aperture Radar (ASAR) which is operated at a frequency of 5.331 GHz (C-band). ASAR has two ScanSAR modes which cover a swath of 405 km width [

Pre-processing of the ASAR WS data consisted of several steps including georeferencing, radiometric calibration and normalisation. ASAR data require georeferencing with respect to earth curvature and terrain for further processing [

where

The soil moisture scaling properties of the REMEDHUS network were studied by [_{i,j}_{r}_{P}_{P}_{r}^{2} and the standard error of the estimate (SEE) which is the standard deviation of the residuals.

The theoretical discussion in section 2 suggested that within a time period [^{2}. The local scale is 150 m which corresponds to the spatial resolution of ASAR WS mode. By performing a linear regression analysis for each 150 m pixel across the images from the selected time period, the spatial patterns of the model coefficients ^{2}, and the standard error of estimate (SEE) are calculated. To study seasonal vegetation effects, the linear regression was performed for each month based on ASAR data from all years (2003-2006). To make sure that at least 20 images were available for the regression, a relative long time window of Δ

At this stage, the parameters describing the fit of the linear backscatter scaling model (16) are known. These empirical results are sufficient for accepting or rejecting the main hypothesis of this study that temporally stable soil moisture patterns lead to temporally stable backscatter patterns. However, it is also of interest to investigate how well the model developed in section 2.2. can predict the backscatter scaling coefficients _{lr}_{lr}^{0}_{dry}^{0}_{l}

where the brackets indicate the mean. If ^{0}_{l}^{0}_{dry}_{l}_{l}^{0}_{dry,l}_{l}^{0}_{dry,l}_{lr}_{lr}_{lr}_{lr}

The modelled parameters were then compared to the observed values of ^{2} and the root mean square error (RMSE).

The soil moisture scaling parameters _{lr}_{lr}_{lr}_{lr}_{lr}_{lr}_{pr}_{pr}

Soil moisture data from the 20 soil probes installed at 5 cm of the REMEDHUS network are plotted in time together with the spatial mean in _{p}_{r}

_{pr}_{pr}_{pr}

A first impression about the relationship between local and regional backscatter can be obtained from scatter plots such as shown in ^{0}_{l}^{0}_{r}^{0}_{l}^{0}_{r}^{0} to soil moisture.

Because of the important role of _{l}_{l}_{r}_{l}^{0}_{dry}

Because of this absence of seasonal effects in

All further calculations will therefore be based on all available ASAR WS images.

Spatial images of the coefficient of determination (R^{2}) and the standard error of estimate (SEE) of the linear backscatter scaling model (16) are shown in ^{2} in general is high over agricultural areas and other sparsely vegetated terrain with values up to about 0.8. The correlation decreases with increasing vegetation density and becomes smaller than 0.2 over dense forests and urban areas. The standard error of estimate shows very similar spatial patterns. Over areas characterised by relatively stable backscatter (and hence low R^{2}) SEE may be as low as 0.6 dB which corresponds to the noise of the ASAR Wide Swath measurements. With decreasing vegetation density SEE increases. One important reason for this is that over bare or sparsely vegetated terrain, backscatter shows a pronounced incidence angle dependency. Therefore, uncertainties related to the normalisation ^{0}(30) over these areas compared to more densely vegetated areas. Also, agricultural activities such as ploughing or harvesting may cause outliers. Nevertheless, SEE does not exceed 2 dB even over agricultural fields characterised by a steep ^{0}(

As expected, the backscatter scaling parameters ^{0}_{dry}

_{l}

This can be more clearly observed in _{lr}_{lr}^{2} = 0.86 for both

Having confirmed the validity of the backscatter scaling model, _{lr}_{lr}

The retrieved maps of _{lr}_{lr}_{lr}_{lr}_{lr}_{lr}_{lr}_{lr}_{lr}_{lr}_{lr}_{lr}

Finally, the ASAR derived backscatter scaling coefficients are compared to the ones derived from the ^{2} for the _{pr}_{lr}_{pr}_{lr}_{pr}_{lr}

The spatio-temporal distribution of soil moisture is the result of highly non-linear atmospheric and hydrological processes. Similarly, backscatter observed by radar instruments is a complex function of vegetation and soil parameters. Yet, quite regular spatio-temporal patterns emerge out of these nonlinear processes. This study demonstrates that temporally stable soil moisture patterns lead to temporally stable radar backscatter patterns. This means that time-invariant relationships can be used for connecting soil moisture and radar backscatter measurements across different spatial scales. The analysis of

To gain a better understanding of the underlying physical phenomena, a model was developed to explain the magnitude of the observed backscatter scaling coefficients ^{2} = 0.86) and a low relative error of 5 % for both parameters respectively. This suggests that the model captures the main physical effects well. The model was subsequently used to estimate soil moisture scaling parameters _{lr}_{lr}_{lr}_{lr}_{pr}_{pr}_{lr}_{pr}

An important application of the methods developed in this study lies in the interpretation of coarse resolution soil moisture data derived from METOP ASCAT at sub-pixel level. By analysing long ENVISAT ASAR image time series it is possible to identify those sub-pixel areas that contribute to the soil moisture signal observed by ASCAT. Furthermore, ASAR retrieved scaling coefficients may be used for downscaling ASCAT soil moisture data. Because active and passive microwave measurements deal, in principle, with the same physical phenomena [

ENVISAT ASAR data have been kindly provided by the European Space Agency (ESA) through ENVISAT-AO 356. The study has been carried out within the framework of EUMETSAT's Satellite Application Facility in Support to Operational Hydrology and Water Management (H-SAF) and the SHARE project funded by the European Space Agency (ESA). Financial support by the Austrian Science Fund (FWF) through project MISAR (P16515-N10), the Austrian Research Promotion Agency (FFG) through projects ENVISAT-AO 356 and EO-NatHaz (ALR-OEWP-CO-413/07) and the Austrian Academy of Sciences through project ÖH 31 is acknowledged. The study was also supported by the Spanish Research Programme through project MIDAS-5 (ESP2007-65667-C04-04).

Study area. The left map shows the land cover and location of the

Relative soil moisture measured at 5 cm depth at 20 time domain reflectometry (TDR) stations within the REMEDHUS network and their mean (bold black diamonds) in the period 2003-2005.

Scatter plots of point versus regional scale soil moisture (5 cm) for three selected stations of the REMEDHUS network.

Scatter plots of local versus regional scale backscatter for four selected points representative of the land cover classes cropland, herbaceous plants, forest, and urban area.

Seasonal behaviour of the backscatter scaling coefficient

Coefficient of determination R^{2} (left) and standard error of estimate (SEE) expressed in decibels (right) of the linear backscatter scaling model. The forest and settlement polygons from the land cover map are overlain over the images for orientation purposes.

Comparison of observed (left) and modelled (right) backscatter scaling coefficients

Sensitivity (left) and dry backscatter reference (right). The unit of both parameters is decibels.

Scatterplots of observed and modelled backscatter scaling coefficients

Soil moisture scaling parameters _{lr}_{lr}

Scatterplots of soil moisture scaling coefficients derived from _{pr}_{lr}_{pr}_{lr}

Soil scaling parameters computed from the relative soil moisture data collected at 20 stations of the REMEDHUS network: soil composition, mean relative difference _{i,j}_{i,j}_{pr}_{pr}^{2}), and standard error of the estimate (SEE).

_{i,j} |
_{i,j} |
_{pr} |
_{pr} |
^{2} |
_{lr} |
_{lr} | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

75.1 | 16.4 | 8.5 | -47.50 | 9.26 | -0.04 | 1.43 | 0.69 | 0.09 | 0.03 | 0.93 | |

67.2 | 13.7 | 19.1 | -32.60 | 18.32 | 0.02 | 2.03 | 0.79 | 0.10 | 0.01 | 0.97 | |

81.5 | 12.0 | 6.5 | -29.89 | 18.13 | -0.04 | 0.93 | 0.89 | 0.03 | -0.02 | 1.03 | |

85.1 | 9.6 | 5.3 | -27.76 | 26.17 | 0.10 | 0.34 | 0.49 | 0.03 | 0.02 | 0.96 | |

79.7 | 10.2 | 10.1 | -27.13 | 27.17 | 0.03 | 1.26 | 0.75 | 0.07 | -0.02 | 1.04 | |

70.4 | 11.5 | 18.2 | -22.98 | 14.88 | 0.02 | 0.77 | 0.69 | 0.05 | -0.08 | 1.16 | |

90.2 | 6.3 | 3.5 | -18.28 | 15.37 | 0.01 | 1.08 | 0.78 | 0.05 | -0.02 | 1.04 | |

89.8 | 5.9 | 4.3 | -16.38 | 37.73 | 0.06 | 0.85 | 0.73 | 0.05 | 0.08 | 0.83 | |

85.1 | 11.3 | 3.7 | -16.27 | 20.45 | 0.00 | 0.73 | 0.57 | 0.06 | 0.02 | 0.96 | |

60.9 | 16.9 | 22.2 | -14.99 | 20.66 | 0.03 | 1.38 | 0.85 | 0.05 | 0.02 | 0.97 | |

66.8 | 21.0 | 12.2 | -12.12 | 23.17 | -0.02 | 0.90 | 0.84 | 0.04 | -0.09 | 1.18 | |

87.1 | 9.3 | 3.6 | -8.48 | 19.47 | 0.02 | 0.61 | 0.65 | 0.04 | -0.03 | 1.05 | |

91.2 | 5.7 | 3.1 | 5.54 | 22.37 | -0.04 | 0.86 | 0.77 | 0.04 | -0.06 | 1.13 | |

82.3 | 6.4 | 11.3 | 9.85 | 25.04 | 0.03 | 0.80 | 0.77 | 0.04 | 0.02 | 0.95 | |

46.8 | 20.8 | 32.4 | 14.79 | 12.17 | -0.03 | 0.94 | 0.49 | 0.09 | -0.06 | 1.13 | |

81.6 | 8.3 | 10.1 | 18.02 | 16.12 | 0.00 | 1.17 | 0.89 | 0.04 | 0.06 | 0.88 | |

49.8 | 24.9 | 25.3 | 29.04 | 39.59 | 0.01 | 1.10 | 0.92 | 0.03 | -0.07 | 1.15 | |

62.5 | 16.8 | 20.8 | 38.26 | 43.75 | -0.07 | 1.09 | 0.82 | 0.05 | -0.05 | 1.10 | |

78.8 | 13.5 | 7.7 | 48.70 | 25.93 | 0.00 | 0.51 | 0.84 | 0.02 | 0.00 | 1.01 | |

86.1 | 5.7 | 8.3 | 110.78 | 46.90 | -0.10 | 1.22 | 0.81 | 0.06 | 0.28 | 0.44 | |

75.9 | 12.3 | 11.8 | 0.03 | 24.13 | 0.00 | 1.00 | 0.75 | 0.05 | 0.00 | 1.00 | |

13.1 | 5.6 | 8.4 | 36.41 | 10.40 | 0.05 | 0.37 | 0.12 | 0.02 | 0.08 | 0.16 |