| | 78 | = Plant canopy structure in complex environment = |
| | 79 | |
| | 80 | The detailed simulations of a complex environment e.g. of urban areas require modelling of the plant canopy (PC) in detail of the individual treetops. The PIDS allows to initialize model PALM-4U with arbitrary structure of the plant canopy leave area density (LAD) and basal area density (BAD). This allows to describe the complete 3D structure of individual trees and shrubs as well as the structure of tree clusters. |
| | 81 | |
| | 82 | == Integration of plant canopy and radiative transfer model (RTM) == |
| | 83 | |
| | 84 | While the dynamical effects of such complex vegetation structure can be treated in the way described above, the interaction with radiation requires a deep integration with RTM. This integration is described in detail in RTM documentation. The direct, diffuse, and reflected short wave and lond wave radiation is partialy absorbed by individual grid boxes of PC and transformed to sensible heat flux inside the vegetation. This heat flux is consequently transformed to increase of the corresponding air mass. The PC also emmits the long wave radiation according its current local temperature. |
| | 85 | |
| | 86 | == Calculation of plant canopy latent heat fluxes == |
| | 87 | |
| | 88 | An important part of the heat balance in the urban canopy represent the latent heat fluxes from the vegetation. The RTM |
| | 89 | explicitly computes the radiation balance for each grid cell of the volumetric plant canopy which allows to calculate the |
| | 90 | evapotranspiration of this vegetation. |
| | 91 | |
| | 92 | The evapotranspiration of the resolved vegetation is modelled using the Jarvis-Stewart method [#stewart1998 (Stewart, 1988)] implemented |
| | 93 | following [#daudet1999 Daudet et al. (1999)] as |
| | 94 | {{{ |
| | 95 | #!Latex |
| | 96 | \begin{align*} |
| | 97 | & E = \Omega E_\mathrm{eq} + (1 - \Omega) E_\mathrm{imp} , |
| | 98 | \end{align*} |
| | 99 | }}} |
| | 100 | where ''E'',,eq,, is the equilibrium evaporation per leaf unit area, ''E'',,imp,, the imposed evaporation per leaf unit area and ''Ω'' is the |
| | 101 | decoupling factor. These variables are modeled as |
| | 102 | {{{ |
| | 103 | #!Latex |
| | 104 | \begin{align*} |
| | 105 | & l_\mathrm{v} L_\mathrm{eq} = \frac{R_\mathrm{n}\frac{q_\mathrm{s}}{\gamma}}{\frac{q_\mathrm{s}}{\gamma}+2}, \\ |
| | 106 | & l_\mathrm{v} E_\mathrm{imp} = {\rho} c_p g_\mathrm{s} e_{p,d}, \\ |
| | 107 | & \gamma\Omega = \frac{\frac{q_\mathrm{s}}{\gamma}+2}{\frac{q_\mathrm{s}}{\gamma}+2+ 2g_\mathrm{b} /g_\mathrm{s}}, |
| | 108 | \end{align*} |
| | 109 | }}} |
| | 110 | where ''R_n'' is the net radiation calculated by the RTM for each grid cell containing vegetation, ''e'',,d,, = ''e'',,s,, − ''e'' is the water |
| | 111 | vapor pressure deficit in the air (with ''e'',,s,, and ''e'' being the water vapor pressure at saturation and the water vapor pressure, |
| | 112 | respectively), ''q'',,s,, = ''∂e'',,s,,'' /∂T '' is the partial derivative of the water vapor saturation pressure with respect to temperature, ''γ = (c'',,p,,'' p)/(0.622 l'',,v,,'')'' is the psychrometric constant, ''g'',,b,, is the leaf boundary layer conductance and ''g'',,s,, is the stomatal conductance. |
| | 113 | The leaf boundary layer conductance is parametrized as [#daudet1999 (Daudet et al., 1999)] |
| | 114 | {{{ |
| | 115 | #!Latex |
| | 116 | \begin{align*} |
| | 117 | & g_\mathrm{b} = 0.01{\text{U}} + [0.0071]\mathrm{ms}^{-1}. |
| | 118 | \end{align*} |
| | 119 | }}} |
| | 120 | The stomatal conductance is parameterized after [#daudet1999 Stewart (1988)]: |
| | 121 | {{{ |
| | 122 | #!Latex |
| | 123 | \begin{align*} |
| | 124 | & g_\mathrm{s} = g_\mathrm{s,max} f_1(SW_\downarrow) f_2(T) f_3(e_d) f_4(RSWC), |
| | 125 | \end{align*} |
| | 126 | }}} |
| | 127 | where ''g'',,s,max,, is the maximum value of the stomatal conductance and ''f'',,1,,''–f'',,4,, dimensionless empirical functions that express the dependence of the conductance on the incoming shortwave radiation ''SW↓'', air temperature ''T'' , water pressure deficit ''e'',,d,, and the relative soil water content ''RSWC''. |
| | 128 | |
| | 129 | After computing the evaporation per unit leaf area ''E'', the latent heat flux from leaves per the unit volume of vegetation is calculated by multiplication by the leaf area density ''LAD'' |
| | 130 | {{{ |
| | 131 | #!Latex |
| | 132 | \begin{align*} |
| | 133 | & LE = l_\mathrm{v} E LAD |
| | 134 | \end{align*} |
| | 135 | }}} |
| | 136 | and the sensible heat flux is the residual of the energy balance, neglecting the storage. |
| | 137 | |
