# Influence of Atmosphere Near-Surface Layer Properties on Development of Cloud Convection

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## Abstract

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## 1. Introduction

- the vertical component of the pressure disturbance gradient is ignored;
- the solution is sought for in the Boussinesq approximation, where the undisturbed air density is assumed to be constant;
- the solution is sought for in the form of the stationary two-dimensional wave.

_{0}in the sub-cloud layer:

## 2. Definition of Problem

## 3. Equations of Thermal Convection or Moist Unsaturated Air

## 4. Parameters of Convection on Condensation Level

- If the near-surface dew point deficit equals the second critical value ${d}_{0}={\left({d}_{0}\right)}_{\mathrm{cr}2}$, the condensation level temperature excess of a buoyant parcel will be negative (Figure 1a)$${\Delta}_{\mathrm{c}}T=-\frac{\left(\mathsf{\alpha}\Delta \mathsf{\gamma}+\mathsf{\beta}b\right){\Delta}_{0}T+2\mathsf{\beta}\Delta \mathsf{\gamma}{\Delta}_{0}s}{\mathsf{\alpha}\Delta \mathsf{\gamma}-\mathsf{\beta}b}=-{\left({\Delta}_{\mathrm{c}}T\right)}_{\mathrm{max}}<0,$$
- If the near-surface dew point deficit is ${\left({d}_{0}\right)}_{\mathrm{cr}1}<{d}_{0}<{\left({d}_{0}\right)}_{\mathrm{cr}2}$, then the condensation level temperature excess of a buoyant parcel is negative, but its absolute value is lesser in magnitude than the maximal value $-{\left({\Delta}_{\mathrm{c}}T\right)}_{\mathrm{max}}<{\Delta}_{\mathrm{c}}T<0$, while the rising flow velocity at the same level is positive. In this case, the rising sub-cloud flow will break through the level of condensation: this promotes the cloud convection development (Figure 1b).
- If the near-surface dew point deficit equals the first critical value ${d}_{0}={\left({d}_{0}\right)}_{\mathrm{cr}1}$, then the condensation level temperature excess of a buoyant parcel equals zero ${\Delta}_{\mathrm{c}}T=0$, and the rising flow velocity equals ${w}_{\mathrm{c}}=w\left({z}_{\mathrm{t}}\right)$ (lesser than maximum), that is, the velocity equals the value at the level ${z}_{\mathrm{t}}$ of equalization of temperatures:$${w}_{\mathrm{c}}^{2}=g\left(\mathsf{\alpha}\Delta \mathsf{\gamma}-\mathsf{\beta}b\right){z}_{\mathrm{t}}\left(2{z}_{\mathsf{\rho}}-{z}_{\mathrm{t}}\right){\mathrm{sin}}^{2}kx$$$${w}_{\mathrm{c}}^{2}=g\frac{{\Delta}_{0}T}{\Delta \mathsf{\gamma}}\left[\mathsf{\alpha}{\Delta}_{0}T+\mathsf{\beta}\left(2{\Delta}_{0}s+b\frac{{\Delta}_{0}T}{\Delta \mathsf{\gamma}}\right)\right]{\mathrm{sin}}^{2}kx.$$

## 5. Cloud Convection

## 6. Artificial Stimulation of Convection

## 7. Discussion of the Results

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Distributions of rising flows velocity and temperature excess of a buoyant parcel with altitude depending on different near-surface dew point deficits. Graphs are shown schematically for moist unsaturated air. (

**a**) ${d}_{0}={\left({d}_{0}\right)}_{\mathrm{cr}2}$, ${\Delta}_{\mathrm{c}}T=-{\left({\Delta}_{0}T\right)}_{\mathrm{max}}$, ${w}_{\mathrm{c}}=0$; (

**b**) ${d}_{0}<{\left({d}_{0}\right)}_{\mathrm{cr}2}$, $-{\left({\Delta}_{0}T\right)}_{\mathrm{max}}<{\Delta}_{\mathrm{c}}T<0$, ${w}_{\mathrm{c}}>0$, $\partial w/\partial z<0$; (

**c**) ${d}_{0}={\left({d}_{0}\right)}_{\mathrm{cr}1}$, ${\Delta}_{\mathrm{c}}T=0$, ${w}_{\mathrm{c}}={w}_{\mathrm{max}}$; (

**d**) ${d}_{0}<{\left({d}_{0}\right)}_{\mathrm{cr}1}$, ${\Delta}_{\mathrm{c}}T>0$, ${w}_{\mathrm{c}}>0$, $\partial w/\partial z>0$.

**Figure 2.**Interaction between sub-cloud and cloud convections. Left—in a dry atmosphere, when the dew point deficit in the surface layer is equal to d

_{0}= 9.0 °C; right—in a moist atmosphere, when the dew point deficit in the surface layer is equal to d

_{0}= 2.0 °C.

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**MDPI and ACS Style**

Abshaev, M.T.; Zakinyan, R.G.; Abshaev, A.M.; Al-Owaidi, Q.S.K.; Kulgina, L.M.; Zakinyan, A.R.; Wehbe, Y.; Yousef, L.; Farrah, S.; Al Mandous, A.
Influence of Atmosphere Near-Surface Layer Properties on Development of Cloud Convection. *Atmosphere* **2019**, *10*, 131.
https://doi.org/10.3390/atmos10030131

**AMA Style**

Abshaev MT, Zakinyan RG, Abshaev AM, Al-Owaidi QSK, Kulgina LM, Zakinyan AR, Wehbe Y, Yousef L, Farrah S, Al Mandous A.
Influence of Atmosphere Near-Surface Layer Properties on Development of Cloud Convection. *Atmosphere*. 2019; 10(3):131.
https://doi.org/10.3390/atmos10030131

**Chicago/Turabian Style**

Abshaev, Magomet T., Robert G. Zakinyan, Ali M. Abshaev, Qasim Shakir Kadhim Al-Owaidi, Ludmila M. Kulgina, Arthur R. Zakinyan, Youssef Wehbe, Latifa Yousef, Sufian Farrah, and Abdulla Al Mandous.
2019. "Influence of Atmosphere Near-Surface Layer Properties on Development of Cloud Convection" *Atmosphere* 10, no. 3: 131.
https://doi.org/10.3390/atmos10030131