Application of harmonic analysis in the preliminary prediction of hourly air temperature of Anand station

Introduction

Harmonic Analysis is a branch of mathematics concerned with the representation of Functions or Signals as the superposition of basic waves and the study of generalization of the motions of Fourier series. Applications of harmonic analysis in science and engineering begin with the idea or hypothesis that a phenomenon or signal is composed of a sum of individual oscillatory components.Predicting future meteorological trends based on historical time series data is crucial for agrophysical modeling (Lamorski et al., 2013; Baranowski et al., 2015; Krzyszczak et al., 2017) [4,1,2] . Shekh et al. (2007) [5] analyze the hourly air temperature by two different methods and four different models and they found that the average of daily extreme temperatures is overestimation of hourly air temperatures from actual hourly air temperatures with highest PAE. RMSE and PAE by William and Logan model are higher than by DFS and ANNs. Isikwue1 presented the Application of Harmonic Analysis in the Preliminary Prediction of Air Temperature over Lagos and Abuja, Nigeria. They observed that the variation in hourly air temperature in the two stations is dominated by the first harmonic, thus it fluctuates by one cycle with a period of 24 hours. Harmonic analysis technique has been employed in predicting the hourly air temperatures variations at Anand station in the present study. This study consists of sourcing of the hourly air temperature data, its subsequent analysis using Harmonic Analysis method and results for corresponding Month of Year for 2017-2021.

Source of data

The observed hourly air temperatures data from the year 2017 to 2021 were collected from Automatic Weather Station (AWS) with Soil Property Monitoring System, COSMOS installed by ISRO, Ahmedabad at Agronomy Farm, BACA, AAU, Anand.

Materials and Methods

Data series of the hourly air temperatures of each month of the year 2017 to 2020 were used to find the Fourier coefficients and using their values hourly air temperatures predicted by the Harmonic Analysis for the year 2021. Thus, following Fourier series was developed separately for month-wise using recorded hourly air temperatures.

and no is the number of observations.

Results

Here, Statistical measures were found from the used data series at listed in Table 1. It shows that mean temperatures increasing from January to June & after that trend reversing and going to decrease up to December and value was 21.97°C. At Anand station time of taking observations of minimum and maximum temperature is 7.38hrs and 14.38 hrs. This table shows the air temperatures at 7 & 14 hrs nearly minimum and maximum. Variance in data series was highest in the month of April and second highest in February while variance found lowest in the rainy season in the month of July and second lowest in August. The original observed data of hourly air temperatures for two consecutive days of the year 2021 is plotted in the Figure 1. The patterns show sinusoidal curve. This shows the periodicity in the data with period of 24 hrs. Thus, one can employ the tools of harmonic analysis to predict the hourly air temperatures. The second harmonic has a period of half of the fundamental period that is 12 2 / = P hrs. and third harmonic have

Predicted hourly air temperatures of 7, 14 & 21 th hrs by harmonic analysis for 11 th day of each month for the year 2021 with its observed values and calculated prediction percentage error and mean percentage error calculated given in Table 2. It is observed that the highest prediction perctange error is 1.64 at 21 hrs for month of October and the lowest prediction perctange error is 0.15 at 14 hrs for themonth of February. The less mean prediction percentage error is 0.98 of the February months followed by 1.20, 1.27, 1.28, 1.29, 1.35, 1.38, 1.39 and 1.42 which were less than 10 %. Thus, it shows that the predicted air temperatures are significant to observed air temperatures. The predicted air temperatures are showed in Figures 2 to 13. day for month of August as this months is of rainy season and this model does not take in account of it's cloudy weather effect. First harmonic has biggest amplitude, it's period is one fundamental period of 24 hrs and during this time period second harmonic oscillates two times and so on for other harmonics. Also, the higher harmonics contribute less in the covering of variance. All the values of accounted variations were ranges from 79 to 100%. This shows the high accuracy of predicted hourly air temperatures. The incoming solar radiation flux which is a radiant energy, is the sum of the diffused (the incoming shortwave in the shade) and direct radiations incident on the earth's surface in the form of shortwave radiation. The sunshine hour is an important factor to determine solar irradianceand air temperatures. The sunshine hour is higher in the summer and least in the winter season. Daily extreme temperatures appear to be very much related to solar irradiation. The average monthly maximum temperature is highest in May and lowest in January.

The formula to derive the Solar Irradiance is given as below, Computed Solar Irradiance by above formula are listed with the values of maximum air temperature in Table 4. From the Table 4 it is observed that the highest solar irradiance is 23.74 in April month and the lowest is 12.33 in the September month. There was a strong positive correlation of Maximum air temperature and Solar irradiance i.e. 0.81 at 5% level. It is due to the fact that air temperatures are directly related to the solar irradiance.

Conclusion

Observed hourly air temperatures has sinusoidal curve and its periodic so harmonic analysis can be used for prediction of hourly air temperatures at Anand station. Predicted hourly air temperatures by harmonic analysis were accurate and at par with as computed Mean Percentage Error for 24 hrs. in each month were less than 10 %. Solar irradiance varies with maximum air temperature. This variation is liner and correlation coefficient are 0.81. The monthly variation pattern of solar irradiance and air temperature demonstrates that they have the highest value at summer and lowest in winter. More number of data can improve the accuracy of the predicting task.

Acknowledgement

AcknowledgmentsThe authors are thankful to the Director of Research and DeanPG studies, Anand Agricultural University, Principal and Dean, B. A. College of Agriculture, Anand Agricultural University for approval of the work and technical guidance. Authors also thank the Head of the Department, Basic Science & Humanities Department and Department of Agricultural Meteorology, B.A. College of Agriculture, Anand Agricultural University, Anand.

References

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