Abstract
<p/>In crop micrometeorology the transfer of radiation, momentum, heat and mass to or from a crop canopy is studied. Simulation models for these processes do exist but are not easy to handle because of their complexity and the long computing time they need. Moreover, up to now such models can only be run on mainframe computers. This study aims at developing a more elegant mathematical analysis that both deepens the understanding of the processes involved, and enables the writing of more efficient computer programs.<p/>To model the radiation regime, Goudriaan (1977) divided the crop canopy into several layers. The radiation at each layer was classified into downward and upward flux densities, assigned to nine contiguous zones in a hemisphere. Then a set of equations was derived for these radiation components and an efficient iteration method was developed to solve them. The solutions gave a detailed description of the distribution of the radiation in a canopy, from which the zonal reflectance from a canopy can also be obtained. In addition, by computer experimentation a so- called reciprocity relation was found between a direct light source and the reflected radiance from vegetation. This relation has potential applications in remote sensing techniques. Remaining problems are: (a) the computation of the radiation profiles in a canopy needs much execution time; (b) azimuthal variations of bidirectional reflectance from a canopy cannot be simulated; and (c) the mathematical proof of the reciprocity relation was not found.<p/>In Chapters 2 and 3, the downward and upward radiation from all directions in a hemisphere are represented by radiation vectors and the interactions of the radiation with a horizontally homogeneous canopy layer are represented by reflectance and transmittance matrices. In Chapter 2, the physical process of the reflection and transmission of radiation by a multi-layer canopy is examined under vector-matrix notation. The radiation vector incident upon the top of a canopy, may be directly reflected from the first layer forming a component of the reflected radiation vector from the top of the canopy; or it may, for instance, be transmitted through the first layer, reflected from the second layer, and transmitted again through the first layer, forming another component of the reflected radiation vector. Not every reflection-transmission series, called a radiation path, results in a component of the reflected radiation vector but there is an infinite number of such paths. It is proven in Chapter 2 that the reciprocity relation holds if each radiation path contributing to the reflection vector can be reversed and also result in a component of the reflected radiation vector. It is shown that this reversibility of the radiation paths is generally true for reflection whereas for transmission a vertically uniform canopy and a black soil surface are required.<p/>In Chapter 3, the radiation equations are rewritten as a set of difference equations with vectors as variables and matrices as coefficients. Then two differential equations for downward and upward radiation vectors are derived, where the coefficients are interception, backward and forward scattering matrices, which are the three basic matrices characterizing the interactions of a horizontally homogeneous canopy with radiation vectors. These two differential equations are, in fact, the vector-matrix version of the Kubelka-Munk equations, which are two scalar differential equations for total downward and upward radiation intensities in a canopy with horizontal Lambertian leaves. The extended Kubelka-Munk equations can describe the directional transfer of radiation in a canopy with non-Lambertian leaves and any leaf inclination distribution. This is more realistic than Suits' (1972) model containing, principally, only vertical and horizontal leaves. The azimuthal variations are included by extending the corresponding vectors and matrices. The analytical solutions for profiles of the downward and upward radiation vectors are found by means of a standard matrix method and also the bidirectional reflectance from a canopy is thus obtained. In spite of the availability of the analytical solution to the bidirectional reflectance from a canopy, however, the azimuthal resolution is still restricted by the execution time. Thus, for leaf canopies without azimuthal preference a special method reducing the dimensions of the relevant matrices, and an approximate method based on the radiation path method presented in Chapter 2 are developed. The approximate method allows the resolution of 10 degrees in azimuth as well as in inclination, and calculates the bidirectional reflectance from a canopy within an acceptable execution time.<p/>In Chapters 4 to 7, profiles of temperature, humidity, sensible and latent heat flux densities in a canopy are studied in detail. Because the derived equations for sensible and latent heat flux densities are coupled with each other, they must be solved simultaneously. This leads to the following problems: (a) it costs much execution time and space so the program cannot be executed on a microcomputer; (b) distinction of sunlit and shaded leaves within each layer would require to split each layer into several sublayers according to different irradiation levels and thus increase further the execution time and space; (c) the analytical expressions for total sensible and latent heat flux densities above a canopy are not available so that it is not possible to find relationships between the parameters used in the multi-layer model and those used in the single- layer model (Penman- Monteith approach), viz. the canopy resistance and the excess resistance.<p/>In Chapter 4, the sensible and latent heat flux densities are replaced by the enthalpy flux density H, which is the sum of the sensible and latent heat flux densities, and by the saturation heat flux density J, which is a weighted difference between the sensible heat flux density and the latent heat flux density. This weight is done in such a way that the resulting equations for H and J are now mutually independent, so that the computation of the relevant profiles is greatly simplified. Two uncoupled electrical analogues for H and J, respectively, are designed, which are the counterparts of the coupled electrical analogue for the sensible and latent heat. The computation of the J profile is further simplified by recurrent formulas. Moreover, in terms of H and J, the well known Penman's formulas are expressed in a unified form applicable to both single- and multi-layer models, which provides a bridge between these two models.<p/>In Chapter 5, a method to distinguish sunlit and shaded leaves is developed based on the two uncoupled electrical analogues for H and J and on the recurrent formulas developed in Chapter 4. Goudriaan's (1977) simulation program MICROWEATHER is then rewritten in BASIC. A complete list of the program and the symbols used in the program is given in the Appendix. This program in BASIC gives the same detailed description of the crop micrometeorology as MICROWEATHER does, while it can be executed on a microcomputer. The agreement between the results of these two<br/>programs is good.<p/>In Chapter 6, Monteith's (1963) extrapolation method to obtain representative surface values of temperature and vapour pressure is extended by replacing the vapour pressure profile by the dew- point temperature profile. Thus, the canopy resistance can be obtained directly by graphical means. Two basic parameters of the single-layer model, the canopy resistance and the excess resistance, are clearly presented in this way.<p/>In Chapter 7, the canopy resistance and the excess resistance are calculated from the parameters used in the multi-layer model by means of the unified Penman's formulas developed in Chapter 4. The formulas derived for these two resistances show that both of them contain aerodynamic and physiological components. It is shown that however, for a dense canopy with a dry soil surface, the canopy resistance contains mainly physiological components and is approximately equal to the resistance value calculated as all stomatal resistances of the leaves connected in parallel; the excess resistance contains mainly aerodynamic components and is a simple function of the friction velocity. In this case, therefore, the canopy resistance and the excess resistance can be estimated easily in 'terms of the parameters used in the multi-layer model.<p/>In the discussion in Chapter 8, it is emphasized that the method to calculate bidirectional reflectance from a canopy developed in Chapter 3 can have important applications in remote sensing of vegetation, because it allows to study the effects of different leaf inclination distributions and non-Lambertian leaves. The results should be compared with data sets on the bidirectional reflectance from various vegetation canopies to see the practical significance of these two factors. The simulation program for crop micrometeorology developed for microcomputers (Chapter 5) can be used for short grass, where Goudriaan's MICROWEATHER has difficulties with the execution time caused by the small time coefficient of the model. The model can be further developed to simulate the evapo-transpiration from a canopy wetted by rainfall, and it could be incorporated into a pest and plant disease model. The results obtained on the canopy resistance and excess resistance (Chapter 7) justify the applicability of the single-layer model for a dense canopy. But for a sparse canopy the influence of the soil surface cannot be neglected, and the double-layer model one represents the canopy and the other represents the soil surface should be used. This version of the micrometeorological simulation program may be included in a crop growth model such as BACROS (de Wit et al., 1978).
Original language | English |
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Qualification | Doctor of Philosophy |
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Award date | 26 Sept 1984 |
Place of Publication | Wageningen |
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DOIs | |
Publication status | Published - 26 Sept 1984 |
Keywords
- agronomy
- agricultural meteorology
- microclimate
- plants
- boundaries
- microclimatology
- vegetation
- interactions
- computer simulation
- simulation
- simulation models
- mathematical models
- research