Calculation of CR fluctuations

Description of the algorithm a.

The input is 1440 of 1-min pressure corrected data from a single day and a single station.

Short gaps (length < 20) are not taken into account for the smoothing. By selecting smoothing (n), the data in the minute t of the day are smoothed as

Xsm(t) = 1/(2n+1)* ∑ [Xmeas(t+i)];    where i = -n, -n+1,...,0,...n-1,n; t=1,2,..., 1440.

Xmeas(t) is count rate/s from NMDB and the station in time t (there are taken into account also data from previous and next day for smoothing at the times near the end of day). The fit is:

Xfit(t) = P1+P2*cos((2*Π*t/1440)+P3)

By the least square method the fitted parameters are P1, P2, P3 (in UT of the maximum).

Results returned are: P1, P2, P3, r , var (daily mean, amplitude, phase of diurnal wave fitted; linear correlation coefficient between the fit and measurements;(measure of quality of fit, or declination from the fit), smoothing parameter n.

Var = 1/(P1*1440)*sqrt(∑ [(Xsm(t)-Xfit(t)]^2}, t=1,..., 1440.

Additionally, the number of missing data (gap) is there too.

The plot shows comparison of the fitted wave and the smoothed data and the results are in the upper right corner of the plot. Table with the fit is also
available.


Description of algorithm b.

The cosmic ray variability has (depending on count rate and thus on statistics) power spectrum density which is different in shape from the white noise just for periodicities above 20 min (Kudela et al., 1996), the inspection of the contribution of different periodicities from T=24 hours down to T=20 min has sense for checking the contributions of possible quasiperiodic contribution to one day of measurements.

For that the 1-min data x(k), k=0,1,..., 1339 are downloaded by the menu on the left hand side of the web site (station and date). The 10 min averages are contructed from one day data set (144 values). The discrete Fourier transform (DFT) is applied for the data supposing the signal is stationary.

Data are normalized y(k)=(x(k)-xaver)/xaver,   where xaver = 1/1440 * ∑ (y(t)) , t=0, 1339

The DFT is computed:

Z(k) = A(k) + i * B(k)

Z(k) = ∑ (y(k)*cos(2*Π*k*n/N))+ i * ∑ (y(k)*sin(2*Π*k*n/N)   n=0,1,..., N-1

PSD(k)= (A(k)² + B(k)²)^1/2

The period corresponding to k is T=24/k in hours. The plot PSD vs T is in the lower panel of the site. By clicking left mouse button the data in digital form can be downloaded and saved. They contain in the heading the identification and parameters of the fit for diurnal variation.

Attachment	Size
CR_fluctuations.pdf	410.5 KB
WP5P6DESCRIPTIONMETHOD.pdf	26.94 KB