Crop micrometeorology : a simulation study

This monograph presents the results of a detailed study in micrometeorology; one of the sciences that play an important role in production ecology. The purpose is to explain the microweather as a function of the properties of plant and soil, and of the weather conditions prevalent at some height above the canopy. So many, partly interacting, factors are involved in micrometeorology that a quantitative evaluation of their combined effect can only be successfully achieved with the aid of a simulation technique.In Chapters 2, 3 and 4 the submodels, that are the basic elements of the micrometeorological system, are described and discussed. In Chapter 5 the programming aspects are considered and in Chapter 6 some results of the composite model are given, together with an evaluation. The parameter values that are needed in the submodels are almost exclusively taken from literature sources. The structure of the submodels on the contrary is specially developed for this study to attain compatibility of these submodels and an optimal balance between accuracy and simplicity.In Chapter 2 some models are given for the radiation in plant canopies for different circumstances and assumptions.For horizontal leaves the extinction of radiant fluxes of one wavelength is exactly exponential, both for black and scattering leaves. The numerical model shows that for non-horizontal leaves the extinction is usually close to exponential. Only for low inclinations of direct radiation does the exponential profile underestimate the extinction in the top layers. The values of the extinction and reflection coefficients can be approximately calculated with a few simple equations, based on a generalization of the results for horizontal leaves. Ross (1975) had already shown that the leaf angle distribution can be approximately characterized by a single number. My evaluation shows that the values of the reflection and extinction coefficients are successfully estimated by the model and the simplified equations. The daily trends and the difference between the visible and the near-infrared regions are well represented by the model. The numerical results of the model show a reciprocity relation with interesting theoretical aspects and important implications for the remote sensing technique for example. The equations for the thermal radiation field can be kept simple because the temperatures of the leaves and the soil surface are considered as state variables.An extension of the model to a scattering coefficient of unity explains the radiance distribution of the standard overcast sky (SOC). Another model extension shows the effect of a deviation from the foregoing simplifying assumption that the reflection and transmission coefficients of the individual leaves should be equal. Subsequently it is shown that over the range from a regular to a clustered leaf arrangement, the reflection and extinction coefficients in a canopy decrease, as well as the difference between extinction of visible and near-infrared radiation. Both effects are also found in literature. The modelling of light interception by plants in rows shows that the loss of diffuse light between the rows is not too serious. Simplifying formulations are derived and evaluated for this situation.The models presented in this chapter are general enough on the one hand and their results are sufficiently simplified on the other to be successfully applicable in simulation models for photosynthesis and transpiration of plant stands.In Chapter 3 the energy and mass balances of single leaves, of the soil, of the canopy and of the air inside the canopy are evaluated by a partitioning of the incoming radiant energy over the leaves and the soil surface according to the theory of Chapter 2. The distribution of the available energy between transpiration or evaporation, sensible heat loss, heat storage and photosynthesis is derived from the specific properties of plants and soil, and from the aerial conditions. The plant water content, which feeds back on the stomatal resistance, is found by integration of calculated transpiration and water uptake from the soil. The uneven distribution of the radiation over the leaves and the presumed vertical gradients of air temperature and humidity require a classification of the leaves with respect to height and to incidence of radiation. The fluxes of heat and water vapour from the leaves and the soil surface are released into the air. The aerial profiles of temperature and humidity are found by integration of the net fluxes with respect to time for each horizontal layer inside the canopy.The soil temperatures are found by a similar procedure. Here the driving force is the soil heat flux at the surface. In the soil the diffusivity for heat is taken as constant. To obtain the values of the turbulent exchange in the air the theory of Chapter 4 is used.In Chapter 4 the turbulent echange in the air inside and above the canopy is calculated.In Section 4.2 the frequently observed logarithmic wind profile is used as a basis for the calculation of the exchange coefficient above the canopy. When there is a vertical temperature gradient in the air, the logarithmic wind profile is disturbed and the values of the exchange coefficient have to be modified. The relations that express this effect, are taken from literature and reformulated for the purpose of application in the simulation model. An important result is that the formation of an inversion layer (in which the turbulent exchange is reduced or even blocked) above the canopy during the night when the net radiation is negative, can be understood and described. In Section 4.3 the turbulent exchange inside the canopy is calculated. It is found that the profiles of both wind speed and exchange coefficient are reasonably well approximated by an exponential extinction with depth. The values of the extinction coefficient derived theoretically are in good agreement with experimental data. When temperature gradients exist in the canopy the exchange coefficient is corrected in a similar way to above the canopy. There is a lower limit for the exchange coefficient when the wind speed drops to zero, as might occur under an inversion, so that the exchange inside the canopy is then maintained. In Section 4.4 the aerodynamic macrocharacteristics, i.e. the zero plane displacement <em>d</em> and the roughness length <em>_Zo</em> , are expressed in the aerodynamic microcharacteristics and geometry of the crop. The theoretical results for grassland, maize and a coniferous forest appear to agree well with the aerodynamic macrocharacteristics found experimentally. From a model analysis of the effect of spatial variability it is concluded in Section 4.5 that the one-dimensional scheme is adequate as long as one is only interested in horizontally averaged figures, Temporal variations such as those caused by gustiness of wind may have quite important effects on mean values of temperature and humidity.In Chapter 5 the programming aspects are discussed. In Section 5.2 first the initialization problem is discussed, which can be solved by the concept of the cyclic equilibrium. One spatial boundary of the system is chosen deep enough in the soil to eliminate the influence of the daily heat wave, and the other one is not taken higher than 3 in above the ground surface to keep horizontal advection as small as possible. The method of conversion of the weather data measured at this level is also given. In Section 5.3, the usefulness of the hierarchical approach as well as the conditions for its application are discussed. Some examples are given. Section 5.4 gives a survey of some solution techniques together with their merits and drawbacks for different problems (see also Fig. 27). The choice of the programming language is explained. In Section 5.5 a technique is given by which the number of computations in a simulation program for a stiff system is greatly reduced. This method is employed in the micrometeorological simulation program. The listings of the programs are printed in Section 5.6.Chapter 6 gives the results of the composite model. The daily courses of some typical output variables are simulated for a specific case and explained with the submodels. Here (wet soil) the simulated soil evaporation amounted to about one third of the total evapotranspiration. The dew on the leaves mainly consisted of over-distilled soil water. During the night an inversion situation developed. A water stress in the afternoon resulted in a serious depression of the rate of CO ₂ -assimilation.The sensitivity analysis (Section 6.3) showed that slow sensors may be used to record input weather data, because hourly averages are sufficiently accurate. An exception must be made for wind speed since wind gustiness may seriously affect the simulated results. Incoming solar radiation should preferably be recorded in the diffuse and the direct components separately. Amount of dew and duration of leaf wetness cannot be calculated by an easy rule. The numerous complex relations must be integrated in a simulation program to evaluate their combined effect. The compartmentalization of the soil in ten layers was sufficiently accurate, for the canopy space only three layers seemed sufficient. Among the plant properties, the scattering coefficient of the leaves is of great importance. Other important factors are the cuticular resistance, especially when the leaf area index is high, and the stomatal resistance behaviour. Compared to these factors, the leaf angle distribution is of only minor importance, (already found by de Wit (1965)) so that Ross' characterization (Section 2.3.3) is certainly sufficiently accurate. For a closed canopy the leaf area index has little influence on CO ₂ -assimilation. and transpiration and the aerodynamic crop characteristics are of moderate importance.The thermal properties of the soil have a large effect on the amplitude of the soil heat flux and hence on the amplitude of the soil temperature variation, but their phases are only little influenced. The effect of the thermal soil properties on the profile in the air is negligible in the daytime, but much larger during the night.The variation of the exchange coefficient with height is one of the predominant factors for the shape of the profiles of temperature and humidity in the air in the canopy space. The temporal variation of wind speed and exchange coefficient is also an important factor.In Section 6.4 the model results are compared with the measurements of micrometeorological factors in a maize crop for three different days. The profiles of net radiation, wind speed and leaf resistances are in sufficient agreement. However, the simulated profiles in the air showed a substantial deviation from the measured profiles.In Section 6.4.4 it is shown that this deviation is largely due to an overestimation of the relative turbulence intensity and to neglect of the effect of wind gustiness. A more correct implementation of both of them reduces the differences to much smaller values. Micrometeorological research should be concentrated on the physical knowledge of these phenomena where it is still lacking. The presented model is a sound and reliable basis for the calculation of the different components of microweather inside a crop. Its results can be fruitfully applied to simulation of crop growth and development, and of some of its pests and diseases.In future the model should be extended to other situations like grassland. Its results should be summarized in simple formulae as was done for the radiation models. A next step will be the bridging of the gap between where the crop is grown and meteorological observation site. Still it is good to realize that prediction of crop growth and yield by simulation is certainly a problem of weather forecasting, but even more a problem of understanding the physiology of plant growth.