Category:Functions and models in forest inventory

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
  • \(volume=f(\mbox{dbh, height})\), or
  • \(volume=f(\mbox{dbh, upper diameter, height})\).

In order to build these models, one needs to define a mathematical function that shall be used during regression analysis, 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.