**3.2 Discussion**

For the annual variation in **Figure 4**, results show that there is a trend in the series as the p-value is less than the significance level (0.05). The positive Z value (observed from *Appendix C*) shows that the series is increasing. We can conclude that the maximum ambient temperature variation is increasing, and it is doing so with significance, the slope of the trend can be observed from the results in *Appendix C.*

For the dry season variation observed in **Figure 5**, results show that there is a trend in the series. The positive Z value of the dry season trend observed from *Appendix E* shows that the series is increasing. We can conclude that the maximum temperature variation in the dry season is increasing significantly as the calculated p-value is less than the significance level (0.05), the slope of the trend can be observed from results in *Appendix E.*

For the wet season variation observed also in **Figure 5**, results show that there is a trend in the series. The positive Z value from *Appendix G* shows that the series is increasing. We can conclude that the maximum temperature variation in the dry season is increasing significantly as the calculated p-value is less than the significance level (0.05), the slope of the trend can be observed from the results in *Appendix G.*

These results are in agreement with Agbo et al. [2] for the same region.

### *3.2.1 Relationship between refractivity and meteorological parameters*

To understand the relationship between refractivity and all parameters relating to it, we adopt Eq. (18) by substituting obtained and calculated data.

From the data obtained at the Nigerian Meteorological Agency (NiMet) Calabar, and adopting Eq. (9) and (10) we obtain the total annual values for the meteorological parameters as;

*P* = 1005.97 hPa; *H* = 85.71%; *T* = 300.28 K; *e* = 30.71 hPa; *es* = 35.94 hPa. Substituting these values into the equations in Eq. (18), we obtain;

$$\begin{aligned} \frac{\partial N}{\partial P} &= 0.258425\\ \frac{\partial N}{\partial T} &= -0.0196183\\ \frac{\partial N}{\partial H} &= 1.48436\\ \frac{\partial N}{\partial \epsilon} &= 4.13672\\ \frac{\partial N}{\partial \epsilon\_i} &= 3.62832 \end{aligned} \tag{19}$$

Results from the gradients of the differential equations in Eq. (19) show that the vapor pressure and saturated vapor pressure contributes more to the variation of refractivity. The relative humidity similarly has a high gradient; this can be physically explained by relating the water vapor content of the atmosphere to the variation of refractivity.

The correlation plot of refractivity and all other meteorological parameters is shown in **Figure 6**. Results agree with that of the differential equations in Eq. (19). As seen in Eq. (19), the correlation plot showed that the atmospheric vapor pressure and relative humidity had high positive relationships with refractivity. The saturated vapor pressure however has a low correlation coefficient compared to the high gradient in Eq. (19); this can be interpreted thus; that the variation of the saturated vapor pressure has a relatively high contribution to the variation of refractivity, but the saturated vapor pressure does not have a similar trend to that of refractivity.

#### *3.2.2 Application of multiple linear regression in climatology*

Multiple linear regression has been applied to relate refractivity with obtained meteorological parameters. The goal is to obtain an equation that relates refractivity *The Role of Statistical Methods and Tools for Weather Forecasting and Modeling DOI: http://dx.doi.org/10.5772/intechopen.96854*

**Figure 6.** *Correlation matrix of atmospheric parameters and refractivity.*

to meteorological parameters through Multiple Linear Regression (MLG). Using Eq. (8) to calculate refractivity, we show results in **Table 3**. As part of the conditions for carrying out multiple linear regression, we have to test for collinearity


### **Table 3.**

*Data of obtained meteorological parameters and refractivity.*


**Table 4.**

*Output of the multiple linear regression showing the coefficients (C) of each parameter and their standard error (*Se*).*

between the independent variables. We see from the correlation matrix in **Figure 6** that the independent variables are not collinear, hence this satisfies the criteria for carrying out MLG.

From our analysis we obtain the coefficients (slopes) of the variables (meteorological parameters) and the intercept from **Table 4** to form the equation below;
