A new method has been developed to define the diurnal cycle by harmonic analysis. First, the monthly/hourly mean OLR values are calculated for each month and for each 2.5 degree latitude/longitude grid box from the original hourly values. Fourier expansion is then performed on the time series of 24 monthly/hourly mean values and the summation of the first 3 harmonics is then defined as the 'first guess' of the diurnal cycle.
When the diurnal cycle is defined this way, however, alias is introduced because of the combined effect of the temporal sampling pattern of the ERBS which is on an orbit precessing through a diurnal cycle in 36 days and the existence of strong variability around the 36-day period in the atmosphere (Madden-Julian Oscillations). Daily NOAA AVHRR OLR data is used to simulate and remove this sampling alias. First, the hourly ERBS observations are simulated by assuming that there is no diurnal cycle and that the 24 hourly OLR values are the same as the daily mean obtained from the NOAA OLR. This simulated ERBS data are then applied to define the diurnal cycle through the same procedure as for the real ERBS data and the results are defined as the sampling alias. The monthly mean diurnal cycle is finally defined by removing the sampling alias from the 'first guess'.
This method is applied to derive the OLR diurnal cycle for a 64-month period from November 1984 to February 1990. Generally speaking, the diurnal cycle over land shows a maximum shortly after the noon and a minimum in the early morning (~06LST). The amplitude presents regional variations, with the largest observed over the Sahel desert (~50W/m^2). Over oceanic areas with no clouds, the amplitude of the OLR diurnal cycle is relatively small (<10W/m^2) while over oceanic areas with clouds, it shows larger amplitude with minimum observed in the early morning (~03LST).
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