Soil Temperature

$T_{soil}(z,d_n)=\overline T_{AA} +A_{surf}exp(-z/dd)sin(\omega_{tmp}d_n-z/dd)$ 1:1.3.2

where $T_{soil}(z,d_n)$is the soil temperature (C) at depth z(mm)and day of the year $d_n$ , $\overline T_{AA}$is the average annual soil temperature (C), $A_{surf}$is the amplitude of the surface fluctuations (C), $dd$ is the damping depth (mm) and $_{tmp}$is the angular frequency. When $z=0$ (soil surface), equation 1:1.3.2 reduces to $T_{soil}(0,d_n)=\overline T_{AA} + A_{surf}sin(\omega_{tmp}d_n).$As $z$, equation 1:1.3.2 becomes $T_{soil}(\infty,d_n)=\overline T_{AA}$.

$T_{soil}(z,d_n)=\lambda*T_{soil}(z,d_n1)+[1.0-\lambda]*[df*[\overline T_{AAair}-T_{ssurf}]+T_{ssurf}]$

where $T_{soil}(z,d_n)$is the soil temperature(C) at depth $z$(mm)and day of the year $d_n$,$\lambda$is the lag coefficient (ranging from 0.0 to 1.0) that controls the influence of the previous day's temperature on the current day's temperature , $T_{soil}(z,d_n-1)$ is the soil temperature (C) in the layer from the previous day, $df$ is the depth factor that quantifies the influence of depth below surface on soil temperature , $\overline T_{AAair}$is the average annual temperature (C), and $T_{ssurf}$is the soil surface temperature on the day. SWAT+ sets the lag coefficient ,$\lambda,$to 0.80. The soil temperature from the previous day is known and the average annual air temperature is calculated from the long-term monthly maximum and minimum temperatures reported in the weather generator input (.wgn) file. This leaves the depth factor, $df$, and the soil surface temperature, $T_{ssurf}$, to be defined.

$df=\frac{zd}{zd+exp(-0.867-2.078*zd)}$ 1:1.3.4

where $zd$ is the ratio of the depth at the center of the soil layer to the damping depth:

$zd=\frac{z}{dd}$ 1:1.3.5

where $z$ is the depth at the center of the soil layer (mm) and $dd$ is the damping depth (mm).

From the previous three equations (1:1.3.3, 1:1.3.4 and 1:1.3.5) one can see that at depths close to the soil surface, the soil temperature is a function of the soil surface temperature. As the depth increases, soil temperature is increasingly influenced by the average annual air temperature, until at the damping depth, the soil temperature is within 5% of $\overline T_{AAair}$.

The damping depth, $dd$, is calculated daily and is a function of the maximum damping depth, bulk density and soil water. The maximum damping depth, $dd_{max}$, is calculated:

$dd_{max} = 1000+\frac{2500\rho_b}{\rho_b+686exp(-5.63\rho_b)}$ 1:1.3.6

where $dd_{max}$ is the maximum damping depth (mm), and $b$ is the soil bulk density ($Mg/m^3$). The impact of soil water content on the damping depth is incorporated via a scaling factor,, that is calculated with the equation:

$\varphi=\frac{SW}{(0.356-0.144\rho_b)*z_{tot}}$ 1:1.3.7

where $SW$ is the amount of water in the soil profile expressed as depth of water in the profile (mm $H_{2}O$), $_b$ is the soil bulk density ($Mg/m^3$), and $z_{tot}$ is the depth from the soil surface to the bottom of the soil profile (mm).

The daily value for the damping depth, $dd$, is calculated:

$dd=dd_{max}*exp[ln(\frac{500}{dd_{max}})*(\frac{1-\varphi}{1+\varphi})^2]$ 1:1.3.8

where $dd_{max}$ is the maximum damping depth (mm), and is the scaling factor for soil water. The soil surface temperature is a function of the previous day’s temperature, the amount of ground cover and the temperature of the surface when no cover is present. The temperature of a bare soil surface is calculated with the equation:

$T_{bare}=\overline T_{av}+\varepsilon_{sr}*\frac{(T_{mx}-T_{mn})}{2}$ 1:1.3.1.9

where $T_{bare}$ is the temperature of the soil surface with no cover (C),$\overline T_{av}$ is the average temperature on the day (C), $T_{mx}$ is the daily maximum temperature (C), $T_{mn}$ is the daily minimum temperature (C), and $_{sr}$ is a radiation term. The radiation term is calculated with the equation:

$\varepsilon_{sr}=\frac{H_{day}*(1-\alpha)-14}{20}$ 1:1.3.10

where $H_{day}$ is the solar radiation reaching the ground on the current day ($MJ m^{-2}d^{-1}$), and is the albedo for the day. Any cover present will significantly impact the soil surface temperature. The influence of plant canopy or snow cover on soil temperature is incorporated with a weighting factor, $bcv$, calculated as:

$bcv=max*\{{{\frac{CV}{CV+exp(7.563-1.297X10^-4*CV)}}}, \frac{SNO}{SNO+exp(6.055-0.3002*SNO)}\}$ 1:1.3.11

where $CV$ is the total aboveground biomass and residue present on the current day (kg ha$^{-1}$) and SNO is the water content of the snow cover on the current day (mm $H_2O$ ). The weighting factor, $bcv$, is 0.0 for a bare soil and approaches 1.0 as cover increases.

$T_{ssurf}=bcv*T_{soil}(1,d_n-1)+(1-bcv)*T_{bare}$ 1:1.3.12

where $T_{ssurf}$ is the soil surface temperature for the current day (C), $bcv$ is the weighting factor for soil cover impacts, $T_{soil}(1,d_n-1)$ is the soil temperature of the first soil layer on the previous day (C), and $T_{bare}$ is the temperature of the bare soil surface (C). The influence of ground cover is to place more emphasis on the previous day’s temperature near the surface.