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1. Soil Thermal Properties

For any type of soil, the temperature rises when it gains heat and falls when it loses heat. However, for different types of soil, such as dry and wet soil, the extent of temperature increase and decrease is different when the same amount of heat is gained or lost, mainly due to the different thermal properties of the soil. The thermal properties of soil include soil heat capacity, thermal conductivity, and thermal diffusivity.

1. Heat Capacity

There are three physical quantities that describe the heat capacity of soil: heat capacity, mass specific heat, and volume specific heat.

• Heat Capacity: Represents the amount of heat required to raise or lower the temperature of an object by 1℃. It is denoted by C and the unit is J/℃.
• Mass Specific Heat: Represents the amount of heat required to change the temperature of a unit mass of a substance by 1℃. It is denoted by Cm and the unit is J/(kg·℃).
• Volume Specific Heat: Represents the amount of heat required to change the temperature of a unit volume of a substance by 1℃, also known as volumetric heat capacity. It is denoted by CV and the unit is J/(m3·℃).

The relationship between mass specific heat and volume specific heat is: ρCm=CVJY (3-2) where ρ is the soil density.

From the definition, it can be seen that the larger the heat capacity of the soil, the more heat it needs to absorb or release to raise or lower its temperature by 1℃. Conversely, if the heat absorbed and released is equal, then the temperature change of soil with a large heat capacity is small, meaning the temperature change is more moderate.

So, which soils have a large heat capacity and which have a small heat capacity? Due to the different material composition, density, and water content of various soils, their heat capacity varies greatly. For example, the volume specific heat of dry kaolin is 840J/(m3·℃), and when the water content in the soil increases to 50% and 100%, their volume specific heat increases to 2090J/(m3·℃) and 3350J/(m3·℃) respectively. This is because the heat capacity of air is small, while the heat capacity of water is large, more than 3000 times that of air. Therefore, the main factors affecting the heat capacity of soil are the proportion of water and air in the soil. When soil moisture increases, the air content in the soil decreases and the heat capacity increases; when soil moisture decreases, the air content in the soil increases and the heat capacity decreases. In addition, when the soil water content remains unchanged, the heat capacity also decreases with the increase of soil porosity. For example, after plowing, the soil porosity increases, and if the soil water content does not increase, the heat capacity becomes smaller, and the temperature rises rapidly when heat is gained.

2. Thermal Conductivity

When there is a temperature difference between objects in nature, heat transfer occurs, and the direction of heat flow is always from high temperature to low temperature. The ability of an object to transfer heat is represented by thermal conductivity. The same rule applies to soil, and the ability of soil to transfer heat is also represented by thermal conductivity. Thermal conductivity, also known as heat conductivity, is denoted by λ, and its definition is the amount of heat transferred per unit time through a unit horizontal cross-sectional area when the temperature vertical gradient is 1℃/m, and the unit is J/(℃·m·s). In other words, when the thickness of a layer of soil is 1m and the temperature difference between the two sides is 1.0℃, the amount of heat transferred per second between two corresponding unit areas.

A high thermal conductivity of soil indicates that the soil has a strong ability to transfer heat, with a fast rate of heat transfer, and more heat is transferred within the same period of time. When the vertical temperature gradient is the same, soil with high thermal conductivity allows heat to easily penetrate into deeper layers or receive heat from deeper layers, resulting in smaller temperature changes in the surface soil. For example, compared to dry soil, moist soil has a smaller diurnal temperature difference at the surface. If the thermal conductivity of the soil is low, the opposite is true.

So, what factors are related to the magnitude of soil thermal conductivity? The magnitude of soil thermal conductivity depends on the composition of the soil and the proportion of its components. As shown in Table 3.3, the thermal conductivity of solid components in the soil is the highest, that of air is the lowest, and the thermal conductivity of water is in between, but still 28 times that of air. Usually, the solid components of the soil rarely change, so under certain soil conditions, the main factors affecting thermal conductivity are soil porosity and soil moisture content. Soil thermal conductivity decreases with the increase of soil porosity, as shown in Figure 3.5, and increases with the increase of soil moisture. In addition, the organic matter content in the soil also affects thermal conductivity. Generally, an increase in organic matter content can reduce thermal conductivity because the increase in organic matter content increases soil porosity.

3. Thermal diffusivity

Thermal diffusivity refers to a physical quantity that indicates how fast the soil temperature changes under certain heat gain or loss conditions, usually denoted by K. Its magnitude is directly proportional to soil thermal conductivity and inversely proportional to soil heat capacity, with the unit being m²/s. It can be expressed by the following formula:

K=λ/CVs (3-3)

where K is the thermal diffusivity; λ is the thermal conductivity; CVs is the volumetric heat capacity.

Since soil thermal diffusivity is directly proportional to soil thermal conductivity and inversely proportional to soil volumetric heat capacity, the greater the soil thermal conductivity and the smaller the soil volumetric heat capacity, the greater the soil thermal diffusivity, and the faster the soil temperature changes. Conversely, the smaller the soil thermal conductivity and the larger the soil volumetric heat capacity, the smaller the soil thermal diffusivity, and the slower the soil temperature changes.

Let's look at the factors affecting the magnitude of soil thermal diffusivity. From formula (3-3), it can be seen that any factors affecting soil thermal conductivity and soil volumetric heat capacity will affect the magnitude of soil thermal diffusivity, such as the amount of soil organic matter, soil porosity, and soil moisture. However, the relationship between soil thermal diffusivity and soil moisture B(%) is quite complex because changes in soil moisture content affect both soil thermal conductivity and soil volumetric heat capacity, thus the impact on soil thermal diffusivity is not a simple linear relationship. According to experiments and observations, when soil moisture is relatively low, soil thermal diffusivity increases with the increase of soil moisture. But when soil moisture exceeds a certain value, because the increase in thermal conductivity is not significant, while the volumetric heat capacity still increases linearly with moisture, soil thermal diffusivity actually decreases.

For soils with high thermal diffusivity, such as moist clay, during the day, when solar radiation energy is obtained, it quickly transfers the heat from the surface to the deeper layers of the soil, so the surface temperature does not become too high; at night, when the soil surface loses heat due to effective ground radiation, it can quickly transfer heat from the deeper layers to the surface, preventing the surface temperature from becoming too low at night. Therefore, the ground temperature of such soil is less likely to reach extreme values (i.e., too high during the day and too low at night), which is very beneficial for crop growth. On the contrary, if the soil's thermal diffusivity is very small, such as dry peat soil, during the day, it is not easy to quickly transfer the heat from the surface to the deeper layers, causing the surface temperature to become too high; at night, it is not easy to transfer heat from the deeper layers to the surface, causing the surface temperature to become too low at night. Therefore, such soil is prone to extreme temperatures, making crops growing on it very susceptible to the threat of frost damage or heat damage.

II. Daily and Annual Changes in Soil Temperature

Due to the Earth's rotation and revolution, the solar radiation reaching the ground exhibits periodic diurnal and annual variations, and consequently, soil temperature also shows corresponding periodic diurnal and annual changes. This periodic variation in temperature can be described using amplitude and phase. Amplitude refers to the difference between the highest and lowest temperatures within a certain period. Phase refers to the time at which the highest and lowest temperatures occur.

1. Diurnal Variation {|###|} The continuous change of soil temperature over a 24-hour period is referred to as the diurnal variation of soil temperature, as shown in the figure below: {|###|} {|###|} {|###|} Observations indicate that soil temperature reaches a maximum and a minimum within a day, with the difference between the two being the diurnal temperature range. Generally, the highest temperature at the soil surface occurs around 13:00, while the lowest temperature occurs just before sunrise. After noon, although solar radiation gradually weakens, the solar radiation energy absorbed by the soil surface is still greater than the heat lost through long-wave radiation, molecular conduction, and evaporation. This means the heat balance at the soil surface remains positive, so the temperature continues to rise until around 13:00, when the heat balance is achieved, and the heat accumulation reaches its maximum, resulting in the highest temperature. Afterward, the soil surface gains less heat than it loses, causing the temperature to gradually decrease. By the next day, just before sunrise, the heat balance is achieved again, and the heat accumulation is at its minimum, resulting in the lowest temperature of the day. {|###|}The magnitude of the diurnal temperature range at the soil surface is mainly influenced by the following factors: {|###|}{|###|}Solar Altitude: This is the most fundamental factor affecting soil surface temperature. In seasons and regions where the solar altitude at noon is high, the diurnal variation of solar radiation is significant, leading to a larger diurnal temperature range at the soil surface. Generally, the solar altitude at noon decreases with increasing latitude, so the diurnal temperature range at the soil surface also decreases with increasing latitude. In mid-latitude regions, the solar altitude at noon varies significantly with the seasons, resulting in a larger seasonal variation in the diurnal temperature range at the soil surface. {|###|}Soil Thermal Properties: Soils with high thermal conductivity transfer more heat to deeper layers when the surface gains heat and transfer more heat from deeper layers to the surface when the surface cools, resulting in a smaller diurnal temperature range at the surface. Soils with low thermal conductivity have a larger diurnal temperature range at the surface. Soils with high heat capacity have a smaller diurnal temperature range, while those with low heat capacity have a larger diurnal temperature range. {|###|}Soil Color: Dark-colored soil surfaces have a larger diurnal temperature range than light-colored soil surfaces. This is due to the difference in reflectivity of solar radiation between the two types of soil. {|###|}Topography: Topography mainly affects turbulent heat exchange. Compared to flat land, elevated areas have better ventilation and more vigorous turbulent exchange, making it harder for temperatures to rise during the day and drop at night, resulting in a smaller diurnal temperature range than flat land. In contrast, depressions have weaker turbulent exchange, making it harder for heat to dissipate during the day. At night, in addition to radiative cooling, cold air flows down slopes and accumulates in depressions, further cooling the ground, resulting in a larger diurnal temperature range at the soil surface in depressions compared to flat land. {|###|}Weather: The diurnal temperature range at the soil surface is larger on clear days than on cloudy days. This is because clouds weaken solar radiation during the day, reducing ground warming, and emit more atmospheric counter-radiation at night, reducing effective ground radiation. Therefore, the diurnal temperature range at the soil surface is smaller on cloudy days. {|###|} In reality, the diurnal temperature range of soil is the result of the combined influence of the above factors. {|###|} 2. Annual Variation {|###|} The annual variation of soil surface temperature is mainly determined by the annual variation of solar radiation energy. In mid- and high-latitude regions of the Northern Hemisphere, the monthly average highest soil surface temperature generally occurs in July to August, while the monthly average lowest temperature occurs in January to February. These lag behind the months with the strongest solar radiation (summer solstice) and the weakest solar radiation (winter solstice), as shown in the figure below: {|###|} {|###|}

The difference between the highest and lowest monthly average temperatures in a year is called the annual temperature range or annual amplitude.

The annual range of soil surface temperature increases with latitude. For example, the annual range in Guangzhou (23°08′N) is 15.9°C; in Beijing (39°57′N) it is 34.7°C; and in Qiqihar (47°20′N) it is 47.8°C. This is due to the increase in the annual variation of solar radiation with increasing latitude.

The natural cover of soil (vegetation and snow cover) has a significant impact on the annual range of soil temperature. The annual range of bare soil temperature is greater than that of soil under natural cover during summer and winter.

Other factors such as soil thermal properties, topography, and weather conditions have similar effects on the annual range as they do on the daily range.

III. Soil Temperature Wave Equation

Since the periodic daily and annual variation curves of soil temperature are very regular and exhibit a sinusoidal pattern, they can be described using the soil temperature wave equation. Assuming the soil structure is uniform and infinitely deep, the temperature at any depth below the surface at any given time can be represented by equation (3-4):

T(z,t)=T+A(0)e-z/Dsin(ωt-z/D) (3-4)

In the equation, T(z,t) represents the soil temperature at depth z and time t, measured in °C; T is the average surface temperature (°C); A(0) is the amplitude of the surface temperature wave (i.e., the maximum temperature is T+A(0), and the minimum temperature is T-A(0)); ω is the angular frequency of the soil temperature curve, ω=2π/τ, where τ is the period (e.g., the period for daily soil temperature variation is 24h, and for annual variation it is 365d); z is the observation depth; t is the observation time, when T＝T, t＝0, meaning the observation time when the soil temperature equals the average surface temperature is taken as the starting point; D is the damping depth of the soil temperature, measured in meters.

From the above temperature wave equation, the general patterns of soil temperature variation can be derived:

• If the soil depth increases arithmetically, the amplitude of the soil temperature decreases geometrically.
• The times at which the highest and lowest soil temperatures occur are delayed with increasing depth.

IV. Vertical Distribution of Soil Temperature

Due to the continuous exchange of heat between different layers of the soil day and night, the vertical distribution of soil temperature has certain characteristics. Based on observation results, the vertical distribution of soil temperature can be categorized into three types: solar radiation type, radiation type, and transitional type.

• The solar radiation type is characterized by a decrease in soil temperature with increasing depth. This type generally occurs during the day and in summer, when the soil surface heats up first after receiving solar radiation, and heat is transferred from the surface to the lower layers. The vertical distribution of soil temperature at 13:00 in a day and in July of a year can be taken as representative, as shown in the following figure: Vertical distribution of soil temperature diurnal variation
  

  Vertical distribution of soil temperature

• The radiation type is characterized by an increase in soil temperature with increasing depth. This type generally occurs at night and in winter, caused by the surface of the soil radiating and cooling first, with heat being transferred from the lower layers to the surface. The vertical distribution of soil temperature at 01:00 in a day and in January of a year can be taken as representative.
• The transitional type has characteristics of both the solar radiation type and the radiation type in the vertical distribution of soil temperature in the upper and lower layers, respectively. This type generally occurs during the transition periods between day and night (or between winter and summer), with the vertical distribution of soil temperature at 09:00, 19:00, and in April and October taken as representative.