# Summary Study on Temperature Calculation Method for Water Accumulation in Permafrost Regions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Thermal Surface Boundary of Water Accumulation

#### 2.1. Unfrozen Surface Boundary

_{0}is the solar absorptivity at the surface. $S\left(1-\mathrm{a}\right)$, ${E}_{a},{E}_{s}$, $H$ and $LE$ are the heat exchange factors at the surface of water, which can be explained by the equations below.

#### 2.2. Frozen Surface Boundary

## 3. Water Temperature

#### 3.1. Empirical Law

#### 3.2. Mathematical Model Method

^{2}), B is the average width of the unit layer (m), ${D}_{Z}$ is the vertical temperature diffusivity (m

^{2}/s), $\mathsf{\rho}$ is the density of water (kg/m

^{3}), the density of water is a function of temperature, C is the specific heat capacity of water [J/kg °C)], ${\phi}_{Z}$ is the solar radiation flux (W/m

^{2}), ${u}_{i}$ is the inflow velocity (m/s), $\text{}{u}_{0}$ is the outflow velocity (m/s), ${Q}_{V}$ is the vertical flow through the upper boundary of the element (m

^{3}/s), N is the surface unit, ${V}_{N}$ is the volume of surface unit (m

^{3}), ${Q}_{V,N-1}$ is the vertical flow through the interface between layer N and layer N-1 (m

^{3}/s), and $\text{}{\phi}_{N}$ is the heat absorbed by the surface water through the water air interface (W/m

^{2}).

## 4. Phase Change in Water Accumulation

#### 4.1. Empirical Law

#### 4.2. Mathematical Model Method

## 5. Heat Exchange between the Bottom of Water Accumulation and the Underlying Soil

## 6. Discussion

_{a}, E

_{s}, H, LE in the figure has the same means as the Equation (1). They include the energy exchange at the interface of water and air, including the energy exchange between water and air, the heat transfer in water accumulation and the energy exchange between soil and water bottom. For the interface of water and air, it is important to calculate the surface energy balance of water, considering the meteorological elements at the surface. For the heat transfer in water accumulation, it is important to conduct an analysis of water temperature stratification, taking into account the buoyancy flow and the solution of melting and freezing of ice. Moreover, the solar short-wave radiation will be absorbed by each water layer as a heat source in the water accumulation. The heat exchange between water accumulation bottom and permafrost below is key to calculating water temperature.

## 7. Conclusions

- (1)
- It is more practical to calculate the water surface temperature by energy balance method, which includes solar short-wave radiation, net long-wave radiation, sensible heat and latent heat. The mechanisms and influence degrees of various factors acting on the surface temperature of water accumulation can be discussed in depth, which is conducive to accurate prediction of water temperature.
- (2)
- The depth and area of water accumulation will affect the water temperature distribution. It is necessary to analyze the variation law of water temperature and its influence on the thermal state of the lower soil layer from the perspective of a water accumulation scale.
- (3)
- Water accumulation in permafrost regions not only affects the environment but also affects the stability of surrounding engineering. Therefore, the impact of water accumulation on soil based on the response of water accumulation to climate under different existing times should be analyzed.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Hu, X.; Peng, E.; Sheng, Y.; Chen, J.; Zhao, X.; Yang, Q.
Summary Study on Temperature Calculation Method for Water Accumulation in Permafrost Regions. *Atmosphere* **2023**, *14*, 964.
https://doi.org/10.3390/atmos14060964

**AMA Style**

Hu X, Peng E, Sheng Y, Chen J, Zhao X, Yang Q.
Summary Study on Temperature Calculation Method for Water Accumulation in Permafrost Regions. *Atmosphere*. 2023; 14(6):964.
https://doi.org/10.3390/atmos14060964

**Chicago/Turabian Style**

Hu, Xiaoying, Erxing Peng, Yu Sheng, Ji Chen, Xiangbin Zhao, and Qifan Yang.
2023. "Summary Study on Temperature Calculation Method for Water Accumulation in Permafrost Regions" *Atmosphere* 14, no. 6: 964.
https://doi.org/10.3390/atmos14060964