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LandscapeDNDC
1.36.0
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LandscapeDNDC
1.36.0
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Interception capacity \( I_c \) is given by:
\[ I_c = m_{wood, above} \cdot MWWM + LAI \cdot MWFM \]
This function calculates the potential transpiration \(T_{pot}\) (water in kg). Therefore, it is assumed that the loss of water is directly related to the gain of carbon (by photosynthesis):
\[ T_{pot} = \frac {carbon\_uptake \cdot scale}{wue} \]
\[ wue = WUECMAX \cdot \frac {mc}{mco2} \]
\[ scale = 1.3 - 0.0009 \cdot co2 \]
with:
The function assumes an increase in carbon uptake efficiency (a decrease of water loss per unit carbon uptake) with increasing CO2 concentration in the air.
Similar as for non-woody plants, the potential transpiration \(T_{pot}\) for woody plants is assumed to correlate with the gain of carbon by photosynthesis. The water use efficiency, however, is allowed to vary with vapor pressure deficit [1] as well as relative available soil water. This accounts for the frequent observation that the efficiency of carbon uptake increases with increasing evaopration demand and decreasing water supply.
\[ T_{pot} = \frac {\_carbon\_uptake}{wue} \]
\[ wue = \frac {wuec \cdot mc / mco2} {vpd} \]
\[ wuec = (WUECMAX - WUECMIN) \cdot sum( rwa\_{sl} \cdot \frac { h\_{sl} }{rd} ) \]
\[ rwa\_{sl} = \frac { wc\_{sl} - wcmin\_{sl} } {wcmax\_{sl} - wcmin\_{sl}} \]
with:
The potential transpiration stream (in m hr-1) is calculated from canopylayer-specific stomatal conductance and the vapor pressure deficits in each layer [38]. These layered values are added up to scale to the whole-canopy. The canopylayer-specific transpiration \( tr_{fl} \) is thus calculated as:
\( tr_{fl} = \frac{vpd_{fl}}{P_{atm}} \; c_{fl} \; lai_{fl} \)
With stomatal conductance \( c_{fl} \) is either:
\( c_{fl} = GSMIN + relativeconductance_{fl} \; (GSMIN - GSMAX)\)
if stomatal conductance is not directly calculated, or:
\( c_{fl} = GSMIN + frad_{fl} (gs_{fl} - GSMIN)\)
if stomatal conductance has been determined by the Berry Ball method.
with:
This option is chosen in the setup file by selecting transpirationmethod="potentialtranspiration" (see Model options).
Returns the water pressure head [cm] of a specific soil layer: matrix \(h_{m}\) + gravitational/elevation \(h_{g}\). The result is given in cm.
Includes snow and ice formation and melting at the surface and soil layers as well as the resulting soil temperature changes.
All precipitation is assumed to be snow when air temperature is less or equal a given temperature limit (SNOWFALL_TEMPERATURE_LIMIT). It can be intercepted by the canopy, but otherwise accumulates at the soil surface.
When air temperatures (tair) exceeds a limit temperature (TLIMIT = 0 oC), snow melts with a rate depending on air temperature and an empirical parameter MCOEFF:
\[ \Delta \theta_{snow} = MCOEFF \cdot (tair - TLIMIT) \]
Soil ice formation occurs when soil temperature \( T_{soil }\) drops below ice temperature \( T_{ice}\). The amount of ice \(\Delta \theta_{ice}\) that is formed depends on the enthalpy of ice formation \(H_{m}\) and the energy release \( Q_{r}\), which is calculated by the difference between ice and soil temperature multiplied by the heat capacity of the wet soil:
\begin{eqnarray*} Q_r &=& (T_{ice} - T_{soil}) \cdot C_{p,wetsoil} \\ \Delta \theta_{ice} &=& \frac{Q_r}{H_m} \end{eqnarray*}
The change of soil temperature due to energy release is hence given by:
\[ \Delta T = \frac{\Delta \theta_{ice} H_m}{C_{p,wetsoil}} \]
Soil ice melting occurs for \( T_{soil} > 0\)oC. The amount of melted ice and associated energy uptake is given by:
\begin{eqnarray*} Q_u &=& T_{soil} \cdot C_{p,wetsoil} \\ \Delta \theta_{ice} &=& -\frac{Q_u}{H_m} \end{eqnarray*}
The change of soil temperature due to energy uptake is hence given by:
\[ \Delta T = \frac{\Delta \theta_{ice} H_m}{C_{p,wetsoil}} \]
Heat capacity of the (wet) soil \( C_{p,wetsoil}\) is calculated by heat capacity values of its components, i.e., soil organic matter, mineral soil, water and ice (air is neglected):
\begin{eqnarray*} C_{p,wetsoil} &=& C_{p,drysoil} + C_{p,water} + C_{p,ice} \\ C_{p,drysoil} &=& (c_{p,som} \cdot c_{som} + c_{p,min} \cdot (1 - c_{som})) \cdot m_{soil} \\ C_{p,water} &=& c_{p,water} \cdot m_{water} \\ C_{p,ice} &=& c_{p,ice} \cdot m_{ice} \end{eqnarray*}
Ice temperature \( T_{ice}\) depends on the ratio of ice and water mass and the parameter TICE:
\[ T_{ice} = TICE \cdot \frac{m_{ice}}{m_{water}} \]
The unterlying principle is that the energy between radiation, heat flux, and vaporizing water is balanced. It is set up for grass. For higher growing crops it should be adapted by a Penman crop factor in the original version. In the present implementation, the lai fullfils this role to some extend.
The albedo (reflection coefficient) \(a\) is determined by distinguishing
wet soil (water table of more than 0.005mm): \(rfs = 0.05 \)
\[ a = rfs \cdot exp(-0.5\cdot lai) + 0.25 \cdot (1-exp(-0.5\cdot lai)) \]
This equation represents, that the background (soil or water) is shielded by the crop/grass. In [68] the albedo is a fixed parameter. The size of the plant is taken into account by the crop coefficient curve.
Net radiation \( R_n \) is given by:
\[ R_n = (1-a) R_{shortwave} + R_{longwave,in} - R_{longwave,out} \]
Evapotranspiration is separated in a radiation and an aerodynamic term:
\[ PET = PET_r + PET_d = \frac{1}{\lambda} \left( \frac{ \frac{\text{d}p_s}{\text{d}T} R_n}{\frac{\text{d}p_s}{\text{d}T}+\gamma} + \frac{\gamma \lambda E_a}{\frac{\text{d}p_s}{\text{d}T}+\gamma} \right) \]
\(p_2\): vapour pressure at 2m height
Saturated vapour pressure
Saturated vapour pressure \( p_s \) and respective derivative with respect to temperature are given by:
\begin{eqnarray*} p_s &=& 0.61 \cdot \mathrm{e}^{ \left (\frac{17.32 \cdot T}{T + 238.102} \right)} \\ \frac{\text{d}p_s}{\text{d}T} &=& 238.102 \cdot 17.32 \cdot \frac{p_s}{(T + 238.102)^{2}} \end{eqnarray*}
Wind function
The wind function is chosen depending on the surface type.
Bare soil [68] :
\[ f_w = 2.63 \cdot (0.5 + 0.54 v_w) \]
Short grass [68] :
\[ f_w = 2.63 \cdot (1.0 + 0.54 v_w) \]
The Priestley-Taylor evapotranspiration is a simplified Penman method. It is based on the assumption that the radiation driven part of evapotranspiration dominates. Therefore, it uses only the radiation driven part of the Penman equation and an empirical coefficient \( \alpha_{PT}\) = 1.1, which adapts the radiation term for the neglected aerodynamic term:
\[ PET = \alpha_{PT} \frac{1}{\lambda} \frac{R_n s}{s + \gamma} \; , \]
wherein \( \lambda \) and \( \gamma \) refer to the latent heat of vaporization and the psychrometric constant, respecitvely. This method should work well for humid and semi-arid climates. It fails, when net radiation gets negative (as in Dutch winters). It is set up for short grass. If one wants to use it for crops, the result should (originally) be multiplied by a Penman crop factor. Instead , in the present implementation, the lai is inculded in the albedo.
The slope of saturation vapor pressure for changing temperature at the temperature at 2m height is estimated by:
\[ s = vps \cdot \frac{4098}{\sqrt{T + 237.3}} \]
Net radiation \( R_n \) is given by:
\[ R_n = (1-a) R_s + R_{l,in} - R_{l,out} \]
The albedo \(a\) is determined in the same way as for Penman.
For more details, see [68].
Daily potential evapotranspiration \( PET \) [m] after [65] with additions from [73] is calculated depending on temperature by:
\begin{eqnarray*} PET (T > 37.5) &=& -415.85 + 32.24 \cdot 37.5 - 0.43 \cdot 37.5^2 \\ PET (37.5 \ge T > 26) &=& -415.85 + 32.24 \cdot T - 0.43 \cdot T^2 \\ PET (26 \le T) &=& 16 \cdot \left( 10 \cdot \frac{T}{h_i} \right)^{0.49239 + 0.0179 h_i - 0.0000771 h_i^2 + 0.000000675 h_i^3} \end{eqnarray*}
These formulas give monthly values for an average of 12 hours daylight. They are corrected to the appropriate number of hours and devided to a daily value.
Depending on the heat index \( h_i \) there can be a jump at 26degreeC (maybe of 2mm per day).
The method is purely empirical.
The Thornthwaite heat index \( h_i \) is given by:
\[ h_i = \sum_m (0.2 \cdot T_m)^{1.514} \]
The monthly temperature \( T_m \) is derived from the annual mean temperature \( T_a \):
\[ T_m = -0.5 \cdot T_a \cdot cos \left(2 \pi \; \frac{d_m}{d_y} \right) \]
wherein \( d_m \) and \( d_y \) refer to the midmonth day of year and total number of days per year, respectively.
1.8.13