*Refractivity N*ð Þ¼ 1*:*53*Humidity* þ 0*:*17 *Pressure* þ 5*:*68*Temperature* � 1617*:*97 (20)

The above equation can be used to accurately predict the variation of refractivity, given the values of the meteorological parameters. **Table 4** shows these results obtained from the multiple linear regression. The values for the predicted refractivity (Predicted N) was gotten from Eq. (20) by substituting the values of the meteorological parameters. This equation is more straight forward that the equation recommended by ITU as all the variables and coefficients are all linear with respect to refractivity.

**Figure 7** shows the trend of refractivity calculated from Eq. (8) with that of predicted refractivity, calculated from Eq. (20). The residual error seen from **Table 5** shows relatively constant values (in agreement with our MLG conditions), and a small deviation from the original values of refractivity.

From **Table 4** probability values (p-values) of the parameters are all less than the significance level (5% = 0.05; 95% confidence level), this shows that the variation agrees with the alternative hypothesis and shows a trend relating the independent variables to the dependent variables.

**Figure 7.** *Comparison plot of annual refractivity and predicted refractivity.*


*The Role of Statistical Methods and Tools for Weather Forecasting and Modeling DOI: http://dx.doi.org/10.5772/intechopen.96854*

#### **Table 5.**

*Residual output derived from the results of the coefficients, showing the predicted refractivity values compared to the refractivity values to give the residuals.*

Results from **Figure 7** show the minimal error between the predicted refractivity and the calculated refractivity. **Table 5** shows the values for both as well as the residual error between them. This shows that the error is small and thus, Eq. (20) can be adopted for the prediction of refractivity for the study area. This equation can be modified and refractivity N can be gotten in terms of other parameters like the saturated vapor pressure and the atmospheric vapor pressure.

## **4. Conclusion**

There are myriads of ways in which weather can be forecasted and this arises from the understanding of basic meteorological parameters and how they behave in the atmosphere; and also from the understanding of the role of statistics in climate research [21]. Research in this area has been reviewed to give a better understanding of the different techniques for analyzing trends; which include, Linear Regression (Multiple and Simple), the Mann-Kendall trend test [22, 23] (to test for trends in a time series variation), the Angstrom-Prescott model for estimating solar radiation as well as the python implementation of some various techniques.

The multiple linear regression technique was applied to model an equation to accurately predict the trend for refractivity in the study location, the simple linear regression technique has been explained as well as accurate methods for its application in the predicting/estimation of the Angstrom-Prescott coefficients. These coefficients can be gotten for specific regions and can be accurately applied to predict solar radiation in that region.

Results from the multiple linear regression gave an accurate model for the prediction of refractivity in the region after the residual error between the calculated refractivity and predicted refractivity was minimal.

The Mann-Kendall original and seasonal test has been applied to analyze the maximum temperature in Calabar, Nigeria for the annual and seasonal (dry and wet
