Kevin and Kyra Moon EE 670 December 1, 2011

 Background ◦ Motivation ◦ Problem  Theoretical model for backscatter  Simulations  Estimators ◦ ML ◦ MAP  Example of estimators  Results  Conclusion

 In the highest part of Greenland, the snow never melts ◦ Called the dry snow zone ◦ Used frequently for calibration purposes  However, some annual variation in the backscatter has been detected which is consistent from year to year

 We decided to test if received backscatter values could predict changes in permittivity  The answer to this would provide insight into possible causes for the annual variation ◦ If backscatter cannot predict changes in permittivity, then it is likely there are other factors affecting the annual variation

 We created a model relating permittivity to backscatter (at least for snow)  Because knowing the temperature helps us predict the permittivity more accurately, we found a relationship between temperature and permittivity ◦ This model required an intermediate step relating temperature to snow density and snow density to permittivity

 We then ran a simulation to see if backscatter could predict permittivity.  We assumed that the underlying temperature data was weighted based on real data

 Randomly generated temperatures using the histogram ◦ Normalized the histogram ◦ Calculated the cumulative distribution function ◦ Generated uniformly distributed random numbers between 0 and 1 ◦ Assigned each random number the temperature value corresponding to the same index as the closest value of the cdf that was still less than the random number

 For a given temperature, the snow density, permittivity, and corresponding backscatter were calculated using the earlier equations  The backscatter was then corrupted with additive white Gaussian noise ◦ This simulated real noise between the ground and the satellite receiver, including atmospheric and instrumental noise

(or equivalently, permittivity or backscatter) True value Received value What ML would estimate (minimize distance from received) What MAP would estimate (this value is a lot more likely, even if the distance from received is further)

 MAP has superior performance to ML because there is more information available  However, neither estimator is a good predictor of permittivity based on received backscatter values  It is likely that the annual variation noticed in Greenland is caused by more than just changes in permittivity