Start | Index | Overview • PREV | UP | Soil temperature of the soil layers is calculated using the formula:
\[ \begin{eqnarray} STMP&=&LAG \cdot STMP0+(1.0-LAG) \cdot (FZ \cdot (AVT-DST0)+DST0) \label{stmp} \end{eqnarray} \]Reference: Williams, J.R., Izaurralde, C.A., 2005. The APEX model, Blackland Research Center Reports, Vol. 2. Blackland Research Center, USDA, Temple, Texas, USA
Daily average soil temperature at the center of each soil layer is simulated for use in nutrient cycling and hydrology. The basic soil temperature equation is shown in Eq \(\eqref{stmp}\) with
\[ \begin{eqnarray} FZ&=&\frac{X1}{X1+\exp(-0.8669-2.0775 \cdot X1)} \\ X1&=&0.5 \cdot \frac{Z(l)+Z(l-1)}{DD} \label{x1} \end{eqnarray} \]where STMP is the soil temperature at the center of a soil layer in �C, Z is the depth from the surface to the bottom of the soil layer l in m, LAG is a coefficient ranging from 0.0 to 1.0 that allows proper weighting of yesterday's temperature STMP0, AVT is the long-term average annual air temperature at the site, DST0 is the soil surface temperature, and DD is the damping depth in m. Thus, given yesterday's temperature, Eq \(\eqref{stmp}\) estimates today's temperature as a function of soil surface temperature, depth, and a lag coefficient. It is assumed that the temperature remains almost constant at the damping depth and is approximately AVT. Obviously, Eq \(\eqref{stmp}\) makes near surface temperatures a strong function of DST0. As depth increases, AVT has more influence until finally at the damping depth, the temperature is within 5% of AVT.
The damping depth is a function of soil bulk density and water content as expressed in the equation
\[ \begin{eqnarray} DD&=&DP \cdot \exp(\ln(\frac{0.5}{DP}) \cdot \frac{1.-WC}{1.+WC} \cdot 2) \\ DP&=&1.+\frac{2.5 \cdot ABD}{ABD+\exp(6.53-5.63 \cdot ABD)} \\ WC&=&0.001 \cdot \frac{ST}{Z(n) \cdot (0.356-0.144 \cdot ABD)} \end{eqnarray} \]where DP is the maximum damping depth for the soil in m, ABD is the average soil bulk density of the profile in t m-3, n is the number of soil layers in the profile, and ST is the water stored in the profile in mm.
To complete the solution of Eq \(\eqref{stmp}\), the soil surface temperature must be estimated. The first step is to estimate the bare soil surface temperature.
\[ \begin{eqnarray} DST&=&0.5 \cdot (TMX+TMN)+(TMX-TMN) \cdot \frac{RA \cdot (1.0-AB)-14.}{20} \label{dst} \end{eqnarray} \]The first term in \(\eqref{dst}\) estimates bare soil temperature to equal average daily air temperature. The second term adjusts the basic estimate using the net radiation as a driver and half the temperature difference as a range. The adjustment changes signs at a net radiation value of 14 MJ m-2 d-1. If the soil surface is not bare, the surface temperature can be affected considerably by the amount of cover (crop residue or snow). This effect can be simulated by combining the estimated bare surface temperature for the day with the previous day's temperature in the second soil layer (the top 10 mm layer is considered too thin for this purpose).
\[ \begin{eqnarray} DST0&=&(1.-BCV) \cdot DST+BCV \cdot STMP(2)) \end{eqnarray} \]where DST0 is the final estimate of soil surface temperature in �C and BCV is a lagging factor for simulating residue and snow cover effects on surface temperature.
This is done using the SnowCoverCalculator SimComponent that can therefore be linked using the outputted SoilTemperature array and delivering the SoilSurfaceTemperature (DST0)
| Content Type | Name | Description | Data Type | Unit | Min Value | Max Value | Default Value |
|---|---|---|---|---|---|---|---|
| constant | cABD | Mean bulk density | DOUBLE | t/m3 | 1.0 | 4.0 | 2.0 |
| constant | cAVT | Constant Temperature of deepest soil layer | DOUBLE | °C | -10.0 | 20.0 | - |
| constant | cDampingDepth | Initial value for damping depth of soil | DOUBLE | m | 1.5 | 20.0 | 6.0 |
| constant | cFirstDayMeanTemp | Mean temperature on first day | DOUBLE | °C | -40.0 | 50.0 | - |
| constant | cSoilLayerDepth | Depth of soil layer | DOUBLEARRAY | m | 0.03 | 20.0 | - |
| input | iDoInitialize | Switch to re-initialize the model with initial values. | BOOLEAN | 1 | - | - | false |
| input | iSoilSurfaceTemperature | Temperature at soil surface | DOUBLE | °C | 1.5 | 20.0 | - |
| input | iSoilWaterContent | Content of water in Soil | DOUBLE | mm | 1.5 | 20.0 | 5.0 |
| out | SoilTempArray | Array of temperature | DOUBLEARRAY | °C | -20.0 | 40.0 | - |
| privat | pSoilLayerDepth | Depth of soil layer plus additional depth | DOUBLEARRAY | m | 0.03 | 20.0 | - |