Changing vegetation and trend analysis

A piece of homogeneous vegetation can be treated as a point, so it can have dynamic analysis, or trend analysis. However, to carry enough information, this point has to be put into multi-variable space. Thus, vegetation can be expressed as an identity, or a position vector in multidimensional space. Furthermore, vegetation is a resource competing system. All plant species compete for limited resources, and demands of all species can not exceed the available resources. This can be expressed as geometric sum of all species equal to one: Y₁²+Y₂²+..Y_m² =1, therefore, all the plant species can be treated mutual orthogonal. When using position vector to represent vegetation, the magnitude of the vector carries the information of the total biomass, while the direction of the vector carries the information of composition of vegetation, thus the position vector has to be standardized. The vegetation growth based on cell duplication, exponential growth, is expressed as Y_k=Y₀*e^rk. The combination of e^r can be called intrinsic changing trend. Not knowing the value of e^r, changing trend can be expressed by empirical growth rate, present state over past, T_k=Y_k/Y_k-1. This trend can be used to monitor the vegetation changes and project the future states: Y_k+1=Y_k*T_k.