Category:Functions and models in forest inventory

Revision as of 10:07, 28 October 2013

The direct observation of some tree variables, such as tree volume, but also tree height, is time consuming and therefore expensive. Thus, we may establish a statistical relationship between the target variable and variables that are easier to observe such as dbh. These relationships are formulated as mathematical functions which are used as prediction models: they allow us predicting the value of the target variable (dependent variable) once the value of the easy-to-measure variable (independent variable) is known. In forest inventory, two important models exist: height curves which predict the tree height from dbh: height = f(dbh) and volume functions which predict tree volume from dbh or from dbh and height or from other sets of independent variables: volume = f(dbh), or volume = f(dbh, height), or volume=f(dbh, upper diameter, height). In order to build these models, one needs to define a mathematical function that shall be used, and one needs to select a set of sample trees at which all variables (the dependent variable and the independent variables) are observed. Then, the model has to be fitted to the sample data in a way that prediction errors are minimized. The resulting function with the best fit is then used as prediction model. The statistical technique used to fit a mathematical function to a set of data points is called regression. While this topic is covered in detail in the forest biometry module, here we give a brief summary only.