Harmonic Analysis of Atmospheric Pressure(Case Study: Over Tehran and Babolsar)

Atmospheric pressure among meteorological elements, is the only element that it’s relatively little changes can cause major changes of weather. Atmospheric pressure due to being influenced by diurnal temperature changes and by solar and lunar attractions has both diurnal and semidiurnal cycles (Ahrens, 2010). Fourier analysis method has been applied to those atmospheric elements including pressure that have periodic nature. Some researchers believe that more than one harmonic is necessary to analyze air pressure and other meteorological variables time series.
Data and In this case study, this method was applied to atmospheric pressure time series of Tehran-Mehrabad as a station in the interior of Iranian plateau and of Babolsar as a station in coastal lowland region of Caspian Sea in 47-year period of 1961-2007. We also examined some other characteristics of atmospheric pressure for the two stations in the above mentioned period. According to Glickman (2000), harmonic analysis is “a statistical method for determining the amplitude and period of certain harmonic or wave components in a set of data with the aid of Fourier series. Harmonic analysis has been used in meteorology, for example, to determine periodicities in climatic data”.
Annual average of QFF in Babolsar for period 1961-2007 is 1015.8 hPa. Low values of standard deviation (SD=0.72) and of coefficient of variation (CV=0.07) is indicative of low variability of annual averages of QFFs in Babolsar. Corresponding values for Tehran are 1017.3 hPa, 0.98, and 0.10 that confirm a bit more variability in this station. Figure 4 compares observed monthly averages of QFF in both stations with estimated values by first 3 and 4 harmonics. First three harmonics cover 99% of total variance in both stations.
Highest variability of monthly averages of QFF for the both stations was found in February. The only significant trend was found for annual averages of QFF over Tehran with r = - 0.55. First two harmonics show very well periodic variations of mean monthly sea level pressure (QFF) in both stations. Contribution of variance of first harmonic to total variance in Tehran (Babolsar) is 96.7% (93.9%) and of first two harmonics is 99.6% (99.4%). Best fitted frequency model for mean monthly QFF, among linear, exponential, power, polynomial, and logarithmic ones, was a fourth order polynomial with significant coefficient of correlation (r=0.475) for Tehran and a fifth order polynomial with significant coefficient of correlation (r=0.69) for Babolsar.
Analysis of QFF at synoptic hours showed dominance of first harmonic (diurnal cycle) over second harmonic (semidiurnal cycle) in Tehran and vice versa in Babolsar. First and second harmonics covered 56% and 43% of total variance in Tehran and 47% and 52% in Babolsar respectively. Furthermore phases of first two harmonics were -22.5 and -1.2 in Tehran and -41.1 and -7.1 in Babolsar.