Atmospheric phenomena are produced by the combination of atmospheric-origin parameters ( Table 1 ). Table 1 presents eight main phenomena according to these natural atmospheric parameters: thunder, lightning, global warming (GW), wind, evaporation, rain, clouds, and snow.

The following numerical models represent the equations of atmospheric phenomena. They are derived from the physical model in Figure 1 and have no application limits. They are written as follows:

Equation for flash

$E_{Flash}=\left(1+\frac{1}{1+\frac{PM}{\rho R}}\right)\left(1+\frac{PM}{\rho R}\right)$ (1)

Equation for lightning

$E_{Lightning}=1+\left(\frac{1}{1+\frac{PM}{\rho R}}\right)\left(1+3\frac{PM}{\rho R}\right)$ (2)

Equation for global warming

$E_{GW}=1+\frac{PM}{\rho R}\left(1+\frac{2}{1+\frac{PM}{\rho R}}\right)$ (3)

Equation for wind

$E_{Wind}=1+\left(\frac{1}{1+\frac{\rho R}{PM}}\right)\left(3+\frac{\rho R}{PM}\right)$ (4)

Equation for evaporation

$E_{Evaporation}=1+\left(\frac{1}{1+\frac{\rho R}{PM}}\right)\left(2+\frac{\rho R}{PM}\right)$ (5)

Equation for rain

$E_{Rain}=4+\left(\frac{1}{1+\frac{\rho R}{PM}}\right)\left(2+\frac{PM}{\rho R}\right)$ (6)

Equation for cloud

$E_{Cloud}=\frac{PM}{\rho R}+\left(\frac{1}{1+\frac{PM}{\rho R}}\right)\left(1+\frac{PM}{\rho R}\right)$ (7)

Equation for snow

$E_{Snow}=1+\left(\frac{1}{1+\frac{\rho R}{PM}}\right)\left(1+\frac{PM}{\rho R}+\frac{\rho R}{PM}\right)$ (8)

Proof of theorems.

Proof of Theorem 1. Note the fact that $\left(E_{dry}\vee E_{hum}\vee E_{vapor}\right)\to E_{flash}\neg$. Theorem 1 is true if $\left\{x\in ℝ\left|x\cong 275.16\right|\right\}$; $E_{flash}=275.16\neg$;

Proof of Theorem 2. Note that $\left(E_{fier}\vee E_{heat}\vee E_{hum}\right)\to E_{lightning}\neg$. Theorem 2 is true if $\left\{x\in ℝ\left|x\cong 3.9927\right|\right\}$; $E_{lightning}=3.9927\neg$;

Proof of Theorem 3. Note that $\left(E_{hum}\vee E_{vapor}\vee E_{heat}\right)\to E_{GW}$. Theorem 3 is true if $\left\{x\in ℝ\left|276.15\le x\le 294.5\right|\right\}$; $E_{GW}=\left[276.15;294.5\right]$, (minimal global warming) $\neg$ and $\left\{x\in ℝ\left|276.15\le x\le 327\right|\right\}$; $E_{GW}=\left[276.15;327\right]$, (maximum global warming) $\neg$;

Proof of Theorem 4. Note that $\left(E_{dry}\vee E_{heat}\vee E_{air}\right)\to E_{wind}\neg$. Theorem 4 is true if $\left\{x\in ℝ\left|3.997\le x\le 5.43\right|\right\}$; $E_{wind}=\left[3.997;5.43\right]$, (wind at altitude) $\neg$ and $\left\{x\in ℝ\left|x>5.43\right|\right\}$; $E_{wind}>5.43$, (surface wind) $\neg$;

Proof of Theorem 5. Note that $\left(E_{dry}\vee E_{heat}\vee E_{hum}\right)\to E_{evaporation}\neg$. Theorem 5 is true if $\left\{x\in ℝ\left|2.9963\le x\le 4.75\right|\right\}$; $E_{evaporation}=\left[2.9963;4.75\right]$, (heavy water evaporation) and $\left\{x\in ℝ\left|2.9963\le x\le 6.55\right|\right\}$; $E_{evaporation}=\left[2.9963;6.55\right]$, (very heavy water evaporation) $\neg$;

Proof of Theorem 6. Note that $\left(E_{dry}\vee E_{heat}\vee E_{water}\right)\to E_{rain}\neg$. Theorem 6 is true if $\left\{x\in ℝ\left|278.15\le x\le 281.15\right|\right\}$; $E_{rain}=\left[278.15;281.15\right]\neg$, (heavy rain) and $\left\{x\in ℝ\left|281.15<x\le 298\right|\right\}$; $E_{rain}=\left]281.15;298\right]$, (torrential rain) $\neg$;

Proof of Theorem 7. Note that $\left(E_{dry}\vee E_{heat}\vee E_{vapor}\right)\to E_{cloud}\neg$. Theorem 7 is true if $\left\{x\in ℝ\left|274.159\le x\le 275.16\right|\right\}$; $E_{cloud}=\left[274.159;275.16\right]$, (thick cloud cover) $\neg$ and $\left\{x\in ℝ\left|275.16<x\le 291.6\right|\right\}$; $E_{cloud}=\left]275.16;291.6\right]$, (very thick cloud cover) $\neg$;

Proof of Theorem 8. Note that $\left(E_{dry}\vee E_{heat}\vee E_{ice}\right)\to E_{snow}\neg$. Theorem 8 is true if $\left\{x\in ℝ\left|274.1632\le x\le 278.19\right|\right\}$; $E_{snow}=\left[274.1632;278.19\right]$, (heavy snowfall) $\neg$ and if $\left\{x\in ℝ\left|278.19<x\le 294.6\right|\right\}$; $E_{snow}=\left]278.19;294.6\right]$, (very heavy snowfall) $\neg$.