FRINGE 96
Weather Effects on SAR Backscatter for Agricultural Surfaces
Stephen Hobbs   College 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, oilseed 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 weatherindependent 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 MatraMarconi, 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, oilseed 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 weatherdependent. All the static targets are represented by
a single equivalent scatterer. The weatherdependent 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 builtin 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 weatherdependent component for the following
parameters:
 Static  WeatherDependent

  Weather 1
 Weather 2 
^{0}  0.7  0.3

^{0} magnitude shift  n.a.
 0  0 
standard deviation  n.a. 
0  0 
^{0} phase shift  n.a.
 5  45 
standard deviation  n.a. 
5  45 
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 x_{i} and y_{i} (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} (xaxis) is uniformly
distributed between a and +a; _{2} (yaxis) is uniformly
distributed between xb 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 (E_{i0}, weather independent)
component and one or two variable (weather dependent) components.
For pixel i (i = 1,2),
where E_{i0} 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 b_{i}, _{i},
c_{i}, _{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 weatherdependent 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. b_{i} = c_{i} =
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 (a^{2}) 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 twocomponent
version of the model was used. The strength of the static component
was varied from 1 to 0. The weatherdependent 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 weatherdependent 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 nonGaussian. 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 weatherdependent 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 scaledependent,
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
