Frequency analysis of daily rainfalls

Rainfall has periodic and stochastic properties. By using the technique of fourier transform, we can elaborate on the frequency of rainfall daily into the shape of the spectrum of daily rainfall that was presented in the relationship between the amplitude of the daily rainfall (mm) with daily rainfall period (days).

In the example was given of data time series of daily rainfall data of length 512 days.

Figure 1. Daily rainfall of daily rainfall stations Purajaya, Lampung Indonesia with long data 512 days (1977) daily precipitation frequency analysis

From this data generated image as follows,

Figure 2. The spectrum of daily precipitation from station Purajaya to the length of data N = 512 daily.

Based on the spectrum of daily precipitation over a significant period produced 253 used to calculate the frequency of significant to simulate or create a daily rainfall of synthetic or artificial Purajaya station. This can be seen in the picture below,

Figure 3. Daily rainfall measured and calculated/synthetic from Purajaya station.

Figure 3 shows the 2 (two) daily precipitation series, namely the daily rainfall compared to synthetic/artificial rainfall measured by a coefficient of correlation daily of 0,9813.

To see the value of the coefficient of correlation, then it can be said that the synthetic daily rainfall that is created or the countless very close to the measured daily rainfall.

The results of calculation by using fourier analysis can be seen from the output file ' fourier. out '.

The Program for this spectrum analysis, for the purposes of the research faculty and students, you can get it for free using this link. The Program is run using input data that is a power of 2, which is a sequence of 16, 32, 64, 128, 256, 512, 1024, ..., 8192. For use with data that is larger than 8192 you can contact ahmadzakaria@unila.ac.id.

As for the fourier analysis using least squares you can also download complete program FTRANS and the FOURIER TRANSFORM of this link.

File output program also include images with eps (postscript) format, so if you want to open the picture file, you should download and install Ghostscripts and Ghostview.