Holdridge Life Zone Analysis

2. METHODOLOGY AND DATA
2.1 Holdridge Life Zones
In Holdridge (1967) life zones approach (Figure 1), there two assumptions: 1) The temperature and precipitation variables are main factors determining life zones (or biomes). 2) The vegetation is assumed to be independent of animals. According to the assumptions, the primary influences on life zones are those factors that make up climate of the Holdridge system. In this respect, it is not unlike the systems of Köppen (1931) and Thornthwaite (1948), or others.
System of the Holdridge life zones starts by calculating the bio-temperature (BT). Holdridge (1967) defines BT as the temperature in the interval of [0oC, 30oC].
In addition, the long-term precipitation (R) and potential evapotranspiration ratio (PER) are obtained as: (2) where Pi is the total precipitation of i-th month of interesting. (3).
In this study, the potential evapotranspiration (PE) is estimated according to Holdridge (1967) as in Equation (3), but one may estimate it by the other methods such as Penman (1948) and Thornthwaite (1944). After the values of BT, R and PER calculated, so called normal climate conditions at each station then using the chart given in Figure 1, then appropriate life zones can be determined.
2.2. A New Similarity Matrix for Clustering High-Dimensional
Each of the specific clusters is determined by assigning the original point xi to cluster j if and only if i-th row of the matrix M was assigned to cluster j.
On the other hand, Holdridge life zones schme, each data point is defined by a triplet, . Therefore, by applying Equation (4) to obtain D matrix by classical sense is not possible. To solve this problem, the correlation ratio (RS) of Sampson (1984) is suggested instead of equation (4). Given two vectors X and Y, the rank of the vector needs not to be identical; the relationship between these two vectors can be measured by RS as: (8)
Where Tr denotes trace of the matrix in question, and C..s are the covariance matrices. Accordingly, the D matrix in Equation (4) can now be modified for the vector type values as in the following. for and (9)
Where RSi,j is calculated between and .
2.3.