# Canopy Resistance

Studies in canopy resistance have shown that the canopy resistance for a well-watered reference crop can be estimated by dividing the minimum surface resistance for a single leaf by one-half of the canopy leaf area index (Jensen et. al, 1990):

$$r_c=r_\Box/(0.5*LAI)$$                                                                     2:2.2.8

where $$r_c$$ is the canopy resistance (s m$$^{-1}$$), $$r_{\Box}$$is the minimum effective stomatal resistance of a single leaf (s m$$^{-1}$$), and $$LAI$$ is the leaf area index of the canopy.

The distribution of stomates on a plant leaf will vary between species. Typically, stomates are distributed unequally on the top and bottom of plant leaves. Plants with stomates located on only one side are classified as hypostomatous while plants with an equal number of stomates on both sides of the leaf are termed amphistomatous. The effective leaf stomatal resistance is determined by considering the stomatal resistance of the top (adaxial) and bottom (abaxial) sides to be connected in parallel (Rosenburg, et al., 1983). When there are unequal numbers of stomates on the top and bottom, the effective stomatal resistance is calculated:

$$r_{\Box}=\frac{r_{\Box -ad}*r_{\Box-ab}}{r_{\Box-ab}+r_{\Box-ad}}$$                                                                                   2:2.2.9

where $$r_{\Box}$$ is the minimum effective stomatal resistance of a single leaf     (s m$$^{-1}$$), $$r_{\Box-ad}$$ is the minimum adaxial stomatal leaf resistance (s m$$^{-1}$$), $$r_{\Box-ab}$$ and is the minimum abaxial stomatal leaf resistance (s m$$^{-1}$$). For amphistomatous leaves, the effective stomatal resistance is:

$$r_{\Box}=\frac{r_{\Box-ad}}{2}=\frac{r_{\Box-ab}}{2}$$                                                                              2:2.2.10

For hypostomatous leaves the effective stomatal resistance is:

$$r_{\Box}=r_{\Box-ad}=r_{\Box-ab}$$                                                                           2:2.2.11

Leaf conductance is defined as the inverse of the leaf resistance:

$$g_{\Box}=\frac{1}{r_{\Box}}$$                                                                                                  2:2.2.12

where $$g_{\Box}$$ is the maximum effective leaf conductance (m s$$^{-1}$$). When the canopy resistance is expressed as a function of leaf conductance instead of leaf resistance, equation 2:2.2.8 becomes:

$$r_c=(0.5*g_{\Box}*LAI)^{-1}$$                                                                 2:2.2.13

where $$r_c$$ is the canopy resistance (s m$$^{-1}$$), $$g_{\Box}$$ is the maximum conductance of a single leaf (m s$$^{-1}$$), and $$LAI$$ is the leaf area index of the canopy.

For climate change simulations, the canopy resistance term can be modified to reflect the impact of change in CO$$_2$$ concentration on leaf conductance. The influence of increasing CO$$_2$$ concentrations on leaf conductance was reviewed by Morison (1987). Morison found that at CO$$_2$$ concentrations between 330 and 660 ppmv, a doubling in CO$$_2$$ concentration resulted in a 40% reduction in leaf conductance. Within the specified range, the reduction in conductance is linear (Morison and Gifford, 1983). Easterling et al. (1992) proposed the following modification to the leaf conductance term for simulating carbon dioxide concentration effects on evapotranspiration:

$$g_{\Box,CO_2}=g_{\Box}*[1.4-0.4*(CO_2/330)]$$                                     2:2.2.14

where $$g_{\Box,CO_2}$$ is the leaf conductance modified to reflect CO$$_2$$ effects (m s$$^{-1}$$) and CO$$_2$$ is the concentration of carbon dioxide in the atmosphere (ppmv).

Incorporating this modification into equation 2:2.2.8 gives

$$r_c=r_{\Box}*[(0.5*LAI)*(1.4-0.4*\frac{CO_2}{330})]^{-1}$$                        2:2.2.15

SWAT+ will default the value of CO$$_2$$ concentration to 330 ppmv if no value is entered by the user. With this default, the term $$(1.4-0.4*\frac{CO_2}{330})$$reduces to 1.0 and the canopy resistance equation becomes equation 2:2.2.8.

When calculating actual evapotranspiration, the canopy resistance term is modified to reflect the impact of high vapor pressure deficit on leaf conductance (Stockle et al, 1992). For a plant species, a threshold vapor pressure deficit is defined at which the plant’s leaf conductance begins to drop in response to the vapor pressure deficit. The adjusted leaf conductance is calculated:

$$g_{\Box}=g_{\Box,mx}*\lfloor1-\Delta g_{\Box,dcl}(vpd-vpd_{thr})\rfloor$$ if $$vpd>vpd_{thr}$$  2:2.2.16

$$g_{\Box}=g_{\Box,mx}$$                                                      if $$vpd \le vpd_{thr}$$            2:2.2.17

where $$g_{\Box}$$ is the conductance of a single leaf (m s$$^{-1}$$), $$g_{\Box,mx}$$ is the maximum conductance of a single leaf (m s$$^{-1}$$), $$\Delta g_{\Box,dcl}$$is the rate of decline in leaf conductance per unit increase in vapor pressure deficit (m s$$^{-1}$$ kPa$$^{-1}$$), $$vpd$$ is the vapor pressure deficit (kPa), and $$vpd_{thr}$$ is the threshold vapor pressure deficit above which a plant will exhibit reduced leaf conductance (kPa). The rate of decline in leaf conductance per unit increase in vapor pressure deficit is calculated by solving equation 2:2.2.16 using measured values for stomatal conductance at two different vapor pressure deficits:

$$\Delta g_{\Box,dcl}=\frac{(1-fr_{g,mx})}{(vpd_{fr}-vpd_{thr})}$$                                                                         2:2.2.18

where $$\Delta g_{\Box,dcl}$$ is the rate of decline in leaf conductance per unit increase in vapor pressure deficit (m s$$^{-1}$$ kPa$$^{-1}$$), $$fr_{g,mx}$$ is the fraction of the maximum stomatal conductance, $$g_{\Box,mx}$$, achieved at the vapor pressure deficit $$vpd_{fr}$$, and $$vpd_{thr}$$ is the threshold vapor pressure deficit above which a plant will exhibit reduced leaf conductance (kPa). The threshold vapor pressure deficit is assumed to be 1.0 kPa for all plant species.
