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← Revision 5 as of 2010-06-15 12:18:41 ⇥
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| $\sigma^0(f,\theta)$ }}} as a function of frequency and incidence angle. The backscatter coefficient describes how much of the transmitted energy is backscattered from the surface media. |
$\sigma^0(f,p,\theta)$ }}} as a function of frequency, polarization and incidence angle. The backscatter coefficient describes how much of the transmitted energy is backscattered from the surface media. |
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| A useful representation of the intensity is the logarithmic transformation to the [[http://en.wikipedia.org/wiki/Decibel| decibel unit]] {{{#!python img_dB=10*log10(img) }}} |
= Exercise = This [[attachment:ASAR_seaice_mixed_20080421_f32_1000x1000|ASAR image]] shows different sea ice types. Investigate the statistic of normalized backscatter value. |
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| The PDF of the image above can be estimated from the number of occurrence of grey levels in the ''B'' intervals between ''q'' and ''q+dq'' and displayed using {{{#!python hist(img,bins=50) }}} with the resolution ''B'' for 50 ''bins'' (intervals). {{attachment:seaice_histogram.png}} The measurements that form an image show statistical fluctuations. The image is characterised by a probability density function (PDF). The PDF ''f'' describes the probability of the occurrence of a discrete grey level ''q'' in the range of grey levels ''Q''. {{{#!latex $\sum_{q=1}^Qf_q=1$ }}} = Exercise = This [[attachment:ASAR_seaice_mixed_20080421_f32_1000x1000|ASAR image]] shows different sea ice types. Investigate the statistic of normalized backscatter value. What is the mean for the two prevalent sea ice types? Try to fit the image PDF with a superposition of two gamma distributions (ADVANCED EXERCISE). |
* What is the mean for the two prevalent sea ice types? Select homogeneous regions to answer this question. * Try to fit the image PDF with a superposition of two gamma distributions (ADVANCED EXERCISE). |
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| img=reshape(fromfile('ASAR_seaice_mixed_20080421_f32_1000x1000.dat',dtype=float32),(1000,1000)) close('all') ql(img,vmin=0,vmax=0.3) colorbar() title('Sea ice radar backscatter intensity') |
sigma0=reshape(fromfile('ASAR_seaice_mixed_20080421_f32_1000x1000.dat',dtype=float32),(1000,1000)) |
Radar backscatter statistics
The received power (intensity) of a radar system is proportional to the (normalized) radar backscatter coefficient
latex error! exitcode was 2 (signal 0), transscript follows:
as a function of frequency, polarization and incidence angle. The backscatter coefficient describes how much of the transmitted energy is backscattered from the surface media.
A (calibrated) ASAR image img(y,x)=I is made of the measured intensities I which can be directly related to the backscatter coefficient. A value of zero means that no energy is reflected from the surface whereas a value of one means the total reflection.
Exercise
This ASAR image shows different sea ice types. Investigate the statistic of normalized backscatter value.
- What is the mean for the two prevalent sea ice types? Select homogeneous regions to answer this question.
- Try to fit the image PDF with a superposition of two gamma distributions (ADVANCED EXERCISE).
from pylab import *
sigma0=reshape(fromfile('ASAR_seaice_mixed_20080421_f32_1000x1000.dat',dtype=float32),(1000,1000))