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FRINGE '96 Workshop: ERS SAR Interferometry, 30 September - 2 October 1996
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FRINGE 96

Weather Effects on SAR Backscatter for Agricultural Surfaces

Stephen HobbsCollege of Aeronautics,
Cranfield University, Cranfield,
Bedford, MK43 0AL, GB
s.e.hobbs@cranfield.ac.uk
http://www.cranfield.ac.uk/coa

Abstract

Weather is a significant perturbing factor on radar backscatter from natural surfaces but one whose effects have not been carefully studied. We are working to quantify these effects on the backscatter intensity and phase correlation of SAR images. The objectives of the project are to (1) create a dataset with the required ground truth and SAR image data, (2) derive statistical relationships between weather conditions and the observed backscatter variation and phase (de) correlations, and (3) use electromagnetic scattering models to interpret the observations.

Observations of crop growth for typical UK agricultural crops (wheat, beans, oil-seed rape) are made regularly using local test sites (within 5 km of Cranfield University's airfield). Local weather conditions are also being recorded, and these data will be compared with the observed variations in radar backscatter intensity and phase correlation for ERS SAR images. Electromagnetic scattering models will be used to interpret the observations.

Results from a phase coherence simulator and two simple analytical models are presented. These help quantify weather effects on phase correlation and show the importance of weather-independent scatterers on coherence.

The expected outcomes of the project are (1) statistical relationships between backscatter or phase correlation and weather, and (2) models (new or adapted) to help understand the underlying physics. The results may have application in agricultural monitoring, meteorology, and SAR interferometry.

Keywords: SAR, backscatter, phase correlation, coherence, weather, agriculture

Introduction

Radar backscatter from natural surfaces is determined primarily by the moisture content and structure of the scatterers. Both these factors are influenced by weather, and thus a relationship of some sort between weather and radar backscatter is expected. A few observations are reported in the literature of the influence of weather on 0 (e.g. Ulaby et al, 1986, quote a variation of 3 dB due to surface moisture on vegetation) but the author is not aware of any systematic study in this area. Recent developments in the use of backscatter phase as well as intensity highlight the power of the SAR technique. If the relationship between weather and backscatter can be understood for typical surfaces then it should be possible to make even better use of SAR data.

For the last year work has been underway at Cranfield to study the influence of weather on radar backscatter intensity for typical UK agricultural crops. This entails making observations of (1) local weather conditions and (2) crop growth for three test sites, and recording ERS SAR images (the data available are 0, have approximately 25 m resolution, and are accessed using RAIDS (RApid Information Dissemination System, operated by Matra-Marconi, Space, National Remote Sensing Centre Ltd., Defence Research Agency and Logica)). The ERS Tandem Mission gives the opportunity to extend this work to the effect of weather on phase correlation, which is a valuable addition in view of the wide range of applications being developed based on SAR phase measurements.

The next section describes the observations being made and the test sites. The modelling approaches being followed are described, together with some preliminary results from a phase correlation simulation. The final section is a discussion including an outline of the next stages of the project.

Project Database

A key element of this project is the construction of a database on which our models can be developed. The database has three components: (1) observations of crop growth for three test sites, (2) local weather data to allow us to quantify the surface moisture history and general weather conditions, and (3) ERS SAR images of the test sites.

The test sites were chosen to be representative of important agricultural crops in Eastern England and also to sample a variety of plant geometries. A third constraint was that only limited resources were available to undertake the fieldwork. Three test sites are used, all within 5 km of the University (52 04' N, 0 37' W), with crops (1995/96 season) of winter wheat, oil-seed rape and beans. The sampling strategy is relatively rudimentary: plant height and number per unit area are recorded, and a few "representative" plants are brought back to the laboratory for drying to measure their moisture content and dry mass. Photographs of the fields and of individual plants in situ are taken as an additional record. Observations are taken at one or two week intervals through the growing season to harvest. Qualitative observations of the soil condition (moist / dry / cracked / etc.) are also made. The intention of this project is to study the relative effect of weather rather than to provide a high quality absolute database and for this goal it is currently felt that the above sampling regime is adequate, although it is of course possible that later stages of the analysis may point to the need for additional information.

Weather data are recorded using an automatic weather station installed on the airfield at Cranfield University. Variables recorded are air temperature and humidity, incident and net radiation, wind speed and direction, rainfall and soil temperature profile. Data from other stations within about 20 km are available for times when the data quality from the local station is poor.

ERS SAR data have been recorded from RAIDS over the period May 1995 to date. These data are all at approximately 25 m resolution and are related to backscatter intensity. The relative calibration is constant although the absolute calibration is unknown. Participation in the ERS Tandem Mission gives us access to ERS Interferometric SAR image pairs (SLC) over the period June 1995 to July 1996.

Backscatter Modelling

Parallel to the observational work, modelling studies are being carried out to attempt to simulate the effect of weather on SAR backscatter for agricultural crops. Two approaches have been used so far: (1) MIMICS (the backscatter model originally developed at the University of Michigan for forest applications) is being used for studies of backscatter intensity, and (2) a simple phase correlation simulation has been developed. Results from MIMICS are not yet available, but some preliminary results from the phase correlation simulator are presented below.

Phase Correlation Models

Three models have been developed for a preliminary exploration of SAR phase correlation. The first is a Monte Carlo simulator to allow simple weather parameterizations to be applied and the others are simple analytical model to help interpret the results of the simulator.

Monte Carlo Simulator

A simple model to simulate phase correlation dependence on weather has been developed. The model assumes that scatterers within the scattering volume have different responses to weather, e.g. the soil surface may have constant properties, while plant stalks and leaves are moderately or highly sensitive to weather conditions. The model identifies targets within the scattering volume (called pixel hereinafter) as belonging to one of two basic classes: static or weather-dependent. All the static targets are represented by a single equivalent scatterer. The weather-dependent scatterers are represented by one or two equivalent scatterers (to allow for the possibility that more than one type of weather dependence may need to be described). A user of the model specifies the relative strengths of the equivalent scatterers (by defining a |0| value for each). The other parameters chosen by the user represent the effect of weather on the scatterer classes.

Weather effects are modelled by specifying the mean and standard deviation for the changes in phase and magnitude of 0 for each component relative to a "zero weather" case. The signal for zero weather for each pixel is obtained by phasor addition of the electric field vectors for each of the equivalent scatterers, allowing a random phase for the field of each scatterer. Two different weather cases are applied to the zero weather state for each pixel, and the resultant electric field phase for each case is calculated (Figure 1). From the resultant electric field phasors it is possible to calculate the coherence between the two images. The phase for the second weather case is adjusted (by adding 2 radians) to ensure it is within radians of the phase of the first case (this allows a linear correlation between the phases to be calculated).

The model is implemented using a standard spreadsheet (Microsoft Excel v7.0), taking advantage of the built-in random number generator and inverse Normal distribution functions in particular. The model's behaviour has been checked carefully to ensure that it has been implemented correctly using a variety of qualitative and quantitative tests.

Figure 1: Phasor diagram showing the reference ("zero weather") case (dashed line), the two weather cases based on this (Case 1, Case 2), and the resultant phase angles (1, 2) for a single pixel. Note that the static component is common to both weather cases and that the model can be run with one or two variable components.

The current model uses the Monte Carlo method to simulate signals for 100 independent pixels. Figure 2 shows an example of the model's output with only one weather-dependent component for the following parameters:

StaticWeather-Dependent
Weather 1 Weather 2
|0|0.7 0.3
0 magnitude shiftn.a. 00
standard deviationn.a. 00
0 phase shiftn.a. 545
standard deviationn.a. 545

Table 1: Simulation parameters used to produce Figure 2.

Figure 2: Example model output for 100 independent pixels (linear correlation coefficient = 0.974); the simulation parameters are given in Table 1.

A linear correlation coefficient was calculated using the 100 independent pixels simulated. In addition, a check on the mean backscatter intensity for each weather case was also calculated to ensure that it was close to the nominal (user specified) value.

Analytical Models

Two simple analytical models have been developed to interpret the results of the simulator. The first model relates the linear correlation coefficient to the relative phases for the two weather cases, and the second relates the image pair's coherence to the relative strengths of the different scatterer types.

Linear Phase Correlation

A simple analytical model suggested by the general form of the results shown in Figure 2 was developed. This model assumes that the phase of weather case 2 (2) is linearly dependent on the phase of weather case 1 (1) except for being randomly dispersed in a range b about the line 2 = 1, and that 1 is uniformly distributed over the range a (a = for the Monte Carlo simulation). Figure 3 shows the model assumed.

For two variables xi and yi (i = 1 to N), the standard linear correlation coefficient () definition used is:

For the uniform random distribution shown in Figure 3, this expression (in the limit of large N) evaluates to:

For the phase correlation simulator a = , and the maximum size of b is also . This sets a lower limit on of 1/2 (corresponding to a completely random scatter of phases).

Figure 3: The phase correlation distribution on which the analytical model is based. 1 (x-axis) is uniformly distributed between -a and +a; 2 (y-axis) is uniformly distributed between x-b and x+b.

The analytical model is clearly a simplification in that the scatter is not completely uniform in practice. However, a characteristic width corresponding to b can usually be identified. It should be noted that the correlation coefficient is not affected if there is an offset between 1 and 2 (e.g. 2 = 1 + c). Figure 4 shows the dependence of the correlation coefficient on the width of the phase scatter (b) predicted using the analytical model.

Figure 4: Correlation coefficient dependence on the width of the phase scatter predicted by the analytical model.

Coherence

Coherence is easily calculated from the simulation results since there are no unknown systematic corrections which need to be applied. The definition of coherence () is based on the electric field phasors for the two weather cases for each pixel and generated by averaging over the simulated pixels.

The Monte Carlo model developed above assumes that the electric field consists of a static (Ei0, weather independent) component and one or two variable (weather dependent) components. For pixel i (i = 1,2),

where Ei0 is common to both weather cases:

The weather dependent fields are described by

For any pixel, a, b, c, , , are fixed and define the "zero weather" case. a, b, c are given by the square root of the average power scattered by that component (chosen by the simulation's user). The phases , , are uniformly distributed over [-, +). Weather dependence is described by the parameters bi, i, ci, i, each of which is normally distributed with a mean and standard deviation specified by the user (i.e. eight parameters are needed for two weather-dependent components).

In the case of (1) the different field components being independent (implicit in the model's approach), (2) only the scattering phases varying with the weather (i.e. bi = ci = 0), and (3) the scatter being broad (i.e. > 1 cycle), the expression for the coherence averaged over N pixels can be evaluated to a relatively simple result:

where , are random phase angles. This expression shows the importance of the static component (a2) and the number of independent pixels (N) in determining the coherence in the case of large scatter due to weather effects. Physically, "large" scatter corresponds to displacement spreads of the order of half a wavelength or less; such scatter is not unreasonable in windy conditions with many types of vegetation.

Initial Simulation Runs and Preliminary Results

The Monte Carlo model described in the section above was used to study the situation in which the relative strength of the static and variable components varies and in which the backscatter phase shift and standard deviation vary from 0 to 360. The two-component version of the model was used. The strength of the static component was varied from 1 to 0. The weather-dependent component's strength was adjusted to keep the total backscatter intensity equal to 1. The magnitude of the variable component was not weather dependent, and its backscatter phase shift and standard deviation were kept equal to each other as they varied from 0 to 360.

Five runs (using different samples of random numbers) were carried out for each set of parameters to simulate 100 independent pixels per run. The coherence and linear correlation coefficient values obtained for the five runs were used to calculate a mean and standard deviation. The results are shown in Figure 5 (linear correlation coefficient for the phases for six different relative strengths of the static and variable components, static component backscatter intensity = 0.95, 0.80, 0.70, 0.50, 0.25, 0.05) and Figure 6 (coherence for 7 different relative strengths of the static component).

Figure 5: Linear phase correlation as a function of the backscatter phase standard deviation for six different sizes of the static component (0.95, 0.80, 0.70, 0.50, 0.25, 0.05 - in order from top to bottom of the figure for phase standard deviation = 180). The weather-dependent component was set to give a total backscatter intensity of 1. Each point plotted represents the mean (with 1- error bars) of 5 values, where each value is based on 100 independent pixels.

Figure 6: Coherence dependence on scatterer range spread and relative size of the static component. Reading from top to bottom the sizes of the static component are 0.95, 0.75, 0.60, 0.40, 0.25. 0.05, 0.00 (the total backscatter intensity is always 1). Each point plotted represents the mean (with 1- error bars) of 6 values, where each value is based on 100 independent pixels.

Discussion

The main feature of the results in Figures 5 and 6 is the decrease in correlation or coherence from 1 to an asymptotic value as the angle standard deviation increases. The asymptotic value is reached once the angle standard deviation reaches 90 - 120. The scale of this decorrelation phase angle standard deviation can be converted into a standard deviation of the equivalent scatterer's displacement in the slant direction. For ERS SAR, this corresponds to a distance of about 7 mm (/8), i.e. if the variation from pixel to pixel of the slant range to the equivalent scatterer exceeds approximately 7 mm then correlation due to that component is lost. Individual scattering elements in vegetation taller than about 20 cm can easily be displaced by this amount. This raises the question of how well such individual displacements relate to the position of the equivalent scatterer for the whole pixel. The following discussions show that the value of the asymptote can be predicted quantitatively using the analytical models presented above.

Correlation Coefficient

The correlation is small for cases in which the static component is small relative to the variable component. The cases with the static component intensity equal to 25% and 5% of the total overlap significantly while there is a clearer distinction at higher proportions.

The case with the static and variable components equal in size leads to anomalously low correlations for small phase standard deviations since it is possible for the variable component to "fold back" on the static component leaving a resultant with small magnitude. The two different weather cases can then be almost exactly 180 apart in phase and the distribution of phase differences becomes significantly non-Gaussian. Such behaviour is not found for other relative sizes of the components.

The analytical model's results (Figure 4) agree well with the levels of correlation found. For example, the cases with a dominant variable component and high phase standard deviation would expect to show almost completely random behaviour. The analytical model predicts a correlation of 2-0.5 = 0.707 in this case, which is as observed. (Lower correlations can be measured in practice if the phase difference scatter is biassed towards the extremes of the permitted range.)

Coherence

Two aspects of the asymptotic coherence value are predicted well by the analytical model above. The model predicts the mean value of the coherence magnitude to be equal to the fraction of the total power from the static component in the broad scatter case, and also that in the limit of a static component equal to zero and one weather-dependent component the coherence magnitude should be 1/N.

Conclusions

The work presented above provides a framework for the rest of our investigation of the weather dependence of SAR phase correlation. Several specific conclusions can be drawn from the simulations:

  • The relative strength of the static component is important. This implies that weather sensitivity is likely to vary through the growing season.
  • A small spread (/8) due to weather in the position of the equivalent scatterers' slant range is enough to destroy phase correlation due to that component.
  • There is possible synergy between the effects of different types of weather, e.g. precipitation may emphasise scattering from a class of scatterers (e.g. leaves) which is also more susceptible to disturbance by wind.
  • The concept of the "equivalent scatterer" is central to the modelling presented here and should be investigated to understand its applicability. Its variability may be scale-dependent, which implies that there may be different optimum measurement scales for different applications.
  • Coherence is a more useful general measure than the linear correlation coefficient because of its more natural range (0 to 1) and the fact that it uses phase and magnitude information. It may be appropriate to investigate the use of measures of correlation derived specifically for directional data (Batschelet, 1981; Mardia, 1972).

The next stages in the project are to (1) start analysis of ERS SAR data for our test sites, (2) attempt to quantify the physical effects of weather on SAR backscatter using a combination of models and field observations, and (3) use the models above (and MIMICS) to analyse the data.

The expected outcomes of the project are (1) statistical relationships between backscatter or phase correlation and suitable weather parameters, and (2) models (which may be applications of existing models such as MIMICS) to help understand the underlying physics. The results may have application in agricultural monitoring, meteorology, and SAR interferometry (by identifying image pairs likely to exhibit good phase correlation).

Acknowledgements

The work described here has been sponsored by the following organisations: European Space Agency, the Royal Society, AEA Technology plc, the RAIDS consortium, the Engineering and Physical Science Research Council and Cranfield University. The author is grateful for the support of all these organisations.

References

Batschelet, E., 1981:
Circular statistics in biology. Academic Press, London, 371 pages.
Mardia, K.V., 1972:
Statistics of directional data. Academic Press, London, 357 pages.
Ulaby, F.T., Moore, R.K., and Fung, A.K., 1986:
Microwave remote sensing, Active and Passive, Volume 3, From theory to applications. Artech House, Norwood, MA, 2162 pages (Vols. 1 to 3).

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry