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*Figure 7: $\sigma^0_E$, $\gamma^0_E$, and $\gamma^0_T$ can be selected on the right-hand side of the graphic.*
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When comparing $\gamma^0_E$ and $\gamma^0_T$ in the plot we can clearly see the impact of the radiometric correction in the mountainous areas. This correction is necessary, because for slopes facing towards the sensor, a larger ground area contributes to the backscatter value of a slant range resolution cell, than for slopes lying in the opposite direction. This results in significant brightness changes, where foreshortening areas appear brighter and lengthening areas darker. $\gamma^0_T$ adjusts the backscatter to represent what it would be if the terrain was flat, thus reducing these effects. This significantly reduces the impact of the terrain on the backscatter values, allowing for more accurate comparisons across different terrain types and locations. The correction is done by using a DEM to determine the local illuminated area at each radar position. The above illustrated approach is also referred to as terrain flattening because in the resulting image, mountains appear flat. As $\gamma^0_T$ is corrected for geometric and radiometric distortions, it is also referred to as Normalized Radar Backscatter (NRB) and is the current standard for Analysis-Ready-Backscatter (ARD).
Copy file name to clipboardExpand all lines: chapters/courses/microwave-remote-sensing/05_in_class_exercise.qmd
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```{python}
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import numpy as np
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import xarray as xr
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import intake
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import matplotlib.pyplot as plt
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import hvplot.xarray # noqa
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import hvplot.xarray # noqa: F401
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import holoviews as hv
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```
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Can you see some patterns when analyzing the different wavelengths and polarizations?
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Remember again that we deal with a logarithmic scale. A measurement of 10 dB is 10 times brighter than the intensity measured at 0 dB, and 100 times brighter at 20 dB. The most notable difference is that the offset between cross- and co-polarised signals becomes larger at low LAI and lower at higher LAI. This might indicate the effect of volume scattering in forested areas where co- and cross-polarization render backscattering values more equal. You will study the differences among cross- and co-polarized backscattering in more detail in the homework exercise.
*Figure 4: Lake Neusiedl $\sigma^0_E$ with a temporal filter applied.*
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Let´s observe the histograms of the two plots. Especially in the region around the lake, it is clear that the distribution is now less dispersed and more centered around a central value.
We can plot the posterior probabilities of flooding and non-flooding again and compare these to pixel's measured $\sigma^0$. For reference we model the flood and non-flood posteriors (`model_posteriors`) over a range of $\sigma^0$ values. **Hover** on a pixel to calculate the posterior probability.
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