WIMOVAC Canopy Processes Module

Canopy structure

Light interception & energy budget

A precise description of the pattern of radiation distribution within any plant canopy is difficult because of the necessity of taking account of detailed canopy architecture, the angular distribution of the incident radiation and the spectral properties of the leaves {Jones, 1992 #1954}. Campbell (1986), Campbell and Norman (1989) {Campbell, 1977 #1937; Campbell, 1986 #1752}and Monteith and Unsworth (1990) {Monteith, 1991 #1810} have shown that there are however useful simplifications that give adequate precision for most purposes including the modelling of photosynthesis and productivity.

One such common simplifying assumption is that the canopy stand is horizontally uniform so that radiation is constant in any horizontal layer. The average irradiance is then expected to decrease exponentially with increasing depth according to Beer’s Law {Monsi, 1953 #1972} which assumes that the canopy is a uniform absorber of light and acts like a column of dilute coloured solution.

In most real canopies leaves assume a range of orientations, with some canopies having predominantly, but not entirely, horizontal leaves (planophile) whilst others have predominantly vertical leaves (erectophile), but many other distributions are found. It is often possible to approximate actual leaf angle distributions by simplified geometrical treatments. One commonly used geometrical simplification is the spherical distribution in which leaves are assumed to have an equal probability of any orientation. A more general function in which leaf angles can accommodate canopies with a tendency towards the erect or the horizontal, as necessary, is the ellipsoidal distribution. With the ellipsoidal distribution a single parameter, c (the ratio of the horizontal axis of the ellipsoid to the vertical) is used to describe the shape of the distribution. The spherical distribution therefore becomes a special case of the ellipsoidal in which c =1. Extinction coefficients are more generally useful in modelling light climates than are leaf angle distributions {Jones, 1992 #1954} and wimovac uses the ellipsoidal leaf angle distribution model (Equation 68) to directly calculate the expected foliar absorption/extinction coefficient (k) from the auxiliary variable input of c , derived from the model parameter database, and the solar zenith angle (q ) calculated in the macroclimate light sub module. The canopy extinction coefficient (k) is therefore assumed to characterise light interception and distribution for the model canopy and is used extensively in the calculation of sunlit and shaded leaf areas in the canopy (Equation 69, Equation 70) and the attenuation of light in a vertical profile from the top of the canopy to lower layers.

To evaluate the significance of changes inferred at the leaf level to the canopy level, wimovac offers three distinct models of canopy microclimate structure:

i). The first is a simplified model which treats the canopy as two populations of leaves, sunlit and shaded as proposed by Norman (1980) and Forseth (1991){Forseth, 1991 #1757}. Norman (1980) made a simplifying assumption in his analysis that the diffuse radiation, either upward or downward, at each canopy layer was uniform. This is true in fact only for a canopy with horizontal Lambertian leaves, however, once the uniformity of diffuse radiation was assumed Norman (1980) could use a discrete version of the Kubelka-Munk equations {Kubelka, 1931 #1985} which could be solved analytically to give a simple but useful canopy model. The division of leaves into sunlit and shaded classes was shown by Norman (1980){Norman, 1980 #1221} to provide a substantial improvement in prediction over models which simply assumed an exponential decline in light through homogeneously lit canopy layers. By dynamically calculating the leaf areas of sunlit and shaded leaves (Equation 69, Equation 70) and the mean irradiance of these two populations (Equation 72, Equation 73), the mean assimilation rate for each leaf population and consequently the total canopy photosynthesis can be obtained (Equation 76). Sunlit leaves are assumed to receive direct (I_dir) and diffuse (I_diff) solar radiation from the macroclimate light module whilst shaded leaves are assumed to receive only diffuse light and that produced by multiple scattering by leaves (I_scat).

Diurnal patterns of i). Sunlit and shaded leaf area. ii). Sunlit, shaded and total canopy assimilation

The proportion of sunlit and shaded leaves in the canopy is determined by the canopy extinction coefficient (k) and the solar zenith angle (q ) and so changes dynamically with time of day and day of year. Total canopy assimilation, transpiration and conductance are obtained by summing the rates of individual leaf classes on a ground area basis and then numerically integrating, using the Euler method as given in Cheney and Kincade (1985){Cheney, 1985 #1989} and Spain (1992),{Spain, 1992 #1278} to obtain total canopy rates for a desired time interval (Equation 84). A detailed analysis of Norman's (1980) approach to canopy structure, and the parameters used by wimovac are as given in Long. (1991) and Long & Drake. (1992).

Equations from Norman (1980) and Forseth (1991). {Johnson, 1993 #1919}

ii). In overcast conditions, there will be little variation in the irradiance level in a horizontal plane at the top of the canopy. However for clear skies with strong sunflecks in the canopy there will be considerable horizontal variation in irradiance level and consequently a need for layering of diffuse light absorption. This has been well documented by Reynolds et al. (1992) with a suggested error of up to 15% ascribed to the single layer, two leaf class model proposed by Norman (1980). Wimovac provides a multiple layered approach to calculating the direct and diffuse components of canopy light microclimate in which the multiple layer canopy is considered as 2-n discrete layers, each layer containing an equal fraction of the total canopy leaf area index (LAI) where n is selectable by the user. Within each layer Wimovac calculates the proportion of sunlit and shaded leaves and the direct and diffuse radiation in the layer (Equation 77, Equation 78). This approach makes the common assumption that no light is transmitted through the leaves, and there are two good reasons for making this assumption {Stockle, 1985 #1984}. First, transmitted light is unlikely to exceed 10% of PAR and is probably nearer to 5% {Jones, 1992 #1954} and second there is a decline in the photosynthetic quality as irradiance is transmitted. The main error associated with this approach is likely to occur in bright light where the irradiance transmitted by leaves in direct sunlight could be of similar magnitude to the diffuse irradiance such that a term is ignored which has a similar magnitude to a term that is included. However, in such a situation, the canopy photosynthetic rate will be high and dominated by photosynthesis of leaves in direct sunlight and so the relative error is likely to be small.

Multi-layer canopy model. i). Cumulative sunlit leaf area index (F_sun) with depth into the canopy for a range of light extinction coefficients (k) ii).Canopy layer assimilation rate. J_day=190, F_sum=3.

In addition to treating the canopy light microclimate in a multiple layer fashion wimovac also includes a multi-layer treatment of many other leaf and canopy properties including leaf temperature and vapour pressure deficit (VPD) according to Monteith (1973), leaf nitrogen concentration (either set manually or using an optimisation algorithm), stomatal conductance according to Harley et al. (1987), wind speed according to Reynolds (1992), and transpiration according to Monteith (1973) for each of the canopy layers and leaf classes (Figure 27, Figure 28). This provides reasonable scope to explore the importance of physical and material gradients observed in natural canopies which are seldom included in vegetation models.

Equations from Reynolds et al. (1992) and Johnson (1993). {Johnson, 1993 #1919}

iii). In agricultural and planted forest systems, plants are commonly in rows. The preceding canopy light microclimate models assume a symmetrical distribution of foliar elements about the azimuth and before canopy closure this assumption can lead to serious overestimation of light interception in row crops where spacing and orientation have an important influence on the light microclimate of a canopy {Boote, 1989 #1917; Boote, 1994 #1918}. In order to investigate the importance of canopy row spacing and architecture on intercepted solar radiation the algorithm originally proposed by Goudriaan (1977) and modified by Boote (1989) and Boote and Pickering (1994) has been incorporated into Wimovac.{Goudriaan, 1977 #1797} Row spacing, width and orientation may all be specified as optional auxiliary properties of the canopy and assimilation, conductance, transpiration and energy budgets calculated for the sunlit and shaded leaf classes within the canopy. However practical difficulties with parameterisation of this type of canopy model precludes its general use in the context of this thesis.

Conductance

A number of mathematical models of stomatal conductance have been used in simulations of gas exchange and energy budgets of plant canopies and communities. Often their complexity has precluded simple interpretation {Hall, 1981 #1986} and in the absence of a true mechanistic understanding of stomatal function there is a requirement for relatively simple phenomenological models which adequately describe stomatal behaviour. The Ball et al. (1987) model and later derivatives by Harley et al. (1992) and Leuning (1995) offer a suitable approach at the leaf level but are unable to work directly at the canopy level. Fortunately the scaling mechanisms used to scale up from leaf to canopy photosynthesis may also be applied to stomatal conductance. Canopy conductance (g_c) can therefore be obtained by summing the total stomatal conductance of all leaf classes within the canopy model (Equation 85). For the sunlit/shaded canopy model this implies calculating g_s for sunlit and shaded leaves, multiplying by the instantaneous leaf area index for each leaf type and summing the values. Similarly for the multiple layer model g_s is calculated for sunlit and shaded leaves within each canopy layer, these values are then multiplied by the leaf area index of each leaf type within the layer and summed for all canopy layers. Numerical integration using the Euler method may then be used to take this instantaneous rate of canopy conductance (g_c) and calculate the total canopy conductance (g_c,tot) over any given time interval required (Equation 86).

The structure of the canopy models which allows simulation of environmental gradients in light, temperature and other photosynthetic characteristics with depth in the canopy allows the effects of these properties to be propagated to individual leaf classes within the canopy. Consequently the summing process (Equation 85) allows incorporation of leaf level stomatal sensitivities into canopy level calculations in a straightforward and clearly defined manner.

Microclimate property profiles

A number of leaf properties in wimovac may be expressed as continuous physical or chemical gradients with respect to leaf type or vertical position in the canopy. This forms the basis for the definition of individual leaf classes within the canopy models mentioned earlier, and any leaf property may be expressed in this manner. For the simple sunlit/shaded leaf canopy model this equates to sunlit and shaded leaves having potentially different photosynthetic characteristics (J_max, V_c,max and L_N), temperature (T_leaf) and incident solar radiation (I). In the multiple layer model properties may change with vertical position in the canopy, represented by the canopy layer, as well as the leaf type (sunlit or shaded).

Canopy gradients may be either manually specified, in the model parameter database, or calculated on the basis of additional canopy structure processes included in the canopy microclimate module. Currently wimovac contains microclimate sub modules for the estimation of photosynthetic properties (V_cmax, J_max and R_d) via leaf nitrogen content (Equation 87), wind speed (Equation 89) and humidity (Equation 91) for each canopy leaf class in the canopy models.

A decreasing leaf nitrogen concentration with depth in the canopy has been observed {Field, 1983 #1934; Field, 1986 #1988; Hirose, 1986 #1892; Hirose, 1987 #1889} and it has been proposed that this may reflect the optimisation of daily canopy assimilation. Field (1983) suggested that the optimal canopy nitrogen profile may therefore be expressed as a simple exponential distribution within the canopy, on the basis that this reflects the attenuation of light (Beers law) used in the irradiance component of many canopy models (Equation 87). This approach assumes, probably correctly, that light is the predominant determinant of optimum nitrogen concentration for any given canopy layer. In practice the exponential distribution model (Equation 87) works by taking the nitrogen concentration at the top of the canopy, as specified in the model parameter database (default 3g m^-2), and attenuating this value using the canopy extinction coefficient (k) and the cumulative leaf area index from the top of the canopy (F_sum) to calculate the expected nitrogen concentration for any given canopy layer. Unfortunately this simple approach does not differentiate between sunlit and shaded leaf classes within canopy layers. Sunlit and shaded leaves are therefore assumed to have the same nitrogen concentration and this may be the most serious objection to using this simple approach. Given that the allocation of a given leaf to the sunlit or shaded types is dynamic and will depend upon time of day and day of year it is difficult to access the likely magnitude of error associated with this approach.

Field (1986) also proposed that the profile of nitrogen within a canopy may be described by using an optimum seeking cost/benefit algorithm which calculates the optimum nitrogen concentration for an individual leaf under any given set of environmental conditions. This optimisation approach has been incorporated into wimovac and works by examining a range of leaf nitrogen concentrations from 0 to 100 g m^-2 whilst looking for a maximum turning point at which the highest assimilation rate for a given set of microclimate conditions is achieved. A turning point occurs in this analysis because although Field (1986) assumes leaf nitrogen is linearly related to the photosynthetic properties (Equation 61 to Equation 63) V_cmax, J_max and R_d the effects of these properties on net assimilation are not linear. At higher nitrogen concentrations the increase in gross assimilation (benefit) due to increases in nitrogen concentration, and consequent increases in V_cmax and J_max, is smaller than occurs at lower nitrogen concentrations. Whilst the increases in dark respiration R_d, (the cost) of supporting the additional nitrogen in the leaf, increases by the same amount irrespective of nitrogen concentration.

Incorporation of nitrogen concentration effects at the leaf level via V_cmax and J_max allows other leaf level physical responses to relative humidity, temperature and importantly CO₂ concentration to be taking into account in the optimisation processes. In practice the Field (1986) optimisation routine appears to work reasonable well under a broad range of conditions {Harrison, 1994 #1991} however under certain light and extremes of temperature the optimisation routine predicts unreasonably large optimum leaf nitrogen concentrations (>20 g m^-2). This either results from failure of the fundamental assumption that plants optimise assimilation or more likely that photosynthesis is not the only factor that should be taken into account when performing the optimisation calculations. There are almost certainly costs other than dark respiration (R_d), such as the energy required to obtain nitrogen from the soil and the energy required to maintain leaf protein which should be incorporated. If any of these terms is non linear with respect to leaf nitrogen concentration they are likely to have a profound effect on the calculated nitrogen optimum. Currently wimovac imposes a species specific maximum allowable leaf nitrogen concentration which moderates the behaviour of the optimisation routines to alleviate this problem.

The calculation of all assimilation rates for nitrogen concentrations in the range of 0 to 100 g m^-2 in sufficiently small intervals to allow accurate calculation of the maxima associated with the Field (1986) approach is prohibitively time consuming, especially when the model is used in the context of the multiple layer canopy model in which iteration must be used to calculate stable values of A and g_s and g_s, E_c and T_leaf. Consequently a sophisticated optimisation method is used here in which a modified form of the bisection method is used {Cheney, 1985 #1989}. This minimises the number of calculations required by bracketing the likely maxima at higher and lower nitrogen concentrations and working towards the maxima in initially large steps until the approximate position has been determined and only then using smaller steps to identify the exact position of the maxima. Even with this algorithm operation of the nitrogen optimisation routines may be very time consuming in longer runs of plant growth and so its use tends to be limited to comparative studies with simpler models of nitrogen distribution within the canopy.

Multiple layer canopy microclimate model. i). Exponential leaf nitrogen concentration (L_N) profiles for a range of nitrogen extinction coefficients. ii).Exponential wind speed (u_layer) profiles for a range of wind speed extinction coefficients. Note a minimum speed of 0.5 m s^-1 is set to prevent very small boundary layer conductance’s from being calculated. iii). Canopy air relative humidity (h_s) profile. iv). Optimum leaf nitrogen concentration surface (L_N) with respect to ambient CO₂ concentration and leaf temperature (T_leaf).

Wind speed (u) is an important determinant of leaf transpiration and energy budget, via its effects on the boundary layer conductance term (Equation 48, Equation 49) of these processes. Two models of windspeed are incorporated in wimovac: i). The first approach assumes a simple exponential decline of windspeed through the canopy from a fixed value (u) at a measurement height above the canopy (Equation 90.). This approach although simple to parameterise does not adequately reflect the windspeed profiles observed in many plant canopies. ii). A more realistic model uses the experimental observation that windspeed increases with height above open ground or above plant canopies with the rate of increase being fastest near the ground or the top of the canopy {Jones, 1992 #1954}. The shape of the windspeed profile is assumed to be such that over open ground the logarithm of height (ln z) is linearly related to the windspeed at that height (u_layer). Over vegetation windspeed has been shown to be non linear when u is related to ln z {Jones, 1992 #1954} (Equation 88) however u has been shown to be linearly related to ln (z-d) where d is the apparent reference height-zero plane displacement. In the model d is therefore used to represent the depth into the canopy that the wind profile extrapolates and is related to the structure of the canopy itself. Reasonable empirical approximations of d and z (z_o) for a range of relatively dense vegetation types (Campbell 1977) are d=0.64h, z_o=0.13h where h is the vegetation height.

The erratic turbulence structure within plant canopies and the complexities introduced by the distribution of sources and sinks for heat, mass and momentum make the application of physically correct diffusion gradient analogues for many canopy properties difficult {Jones, 1992 #1954}. A number of simplified models based upon assumed exponential distribution functions do exist for these properties however. One such property model, that is included in wimovac, is the relative humidity gradient model described by Equation 91. in which the relative humidity in a given canopy layer (h_s,layer) is assumed to be 100% at the bottom of the canopy declining to an unfixed but greater than or equal to ambient air relative humidity value, at the top of the canopy, according to the relative humidity extinction coefficient (k_r) and the canopy layer (j) to total number of canopy layers (N) ratio. The experimental and theoretical justification for this approach is questionable but represents a uncomplicated method of incorporating relative humidity gradients into the model.

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