) and a population spike of more than 100,000 above the trend value in 2005.  During the years 2005 -2011, the de-trended population data declines more than 200,000, which indicates a significant decline in the population growth.
We followed the same above approach to de-trend precipitation data. Changing from linear to quadratic or cubic regression does not improve the model. The adjusted R2 for linear, quadratic and cubic models are, 46.76%, 45.19%, and 49.25%, respectively; see supplemental II for the coefficients. Therefore, we choose the linear regression (Figure 4.c). After de-trending the precipitation data, the fitted Gaussian model identified a significant ditch with the minimum value in the year 1983. As shown in Figure 4d, there is a ditch from 600 to -600 and going back to 160 during the years 1980 to 1990.