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Suggest pagesCategory:Functions and models in forest inventory
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| − | 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 [[ | + | The direct observation of some [[:Category:Single tree variables|tree variables]], such as [[Stem volume|tree volume]], but also [[Tree height|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 [[Diameter at breast height|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: |
| − | 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 | + | *[[height curve]]s which predict the tree height from <math>dbh:height=f(dbh)</math> and |
| − | + | *[[volume functions]] which predict tree volume from <math>dbh</math> or from <math>dbh</math> and height or from other sets of independent variables: | |
| + | **<math>volume=f(dbh)</math>, or | ||
| + | **<math>volume=f(\mbox{dbh, height})</math>, or | ||
| + | **<math>volume=f(\mbox{dbh, upper diameter, height})</math>. | ||
| + | |||
| + | In order to build these models, one needs to define a mathematical function that shall be used during [[Linear regression|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. | ||
[[Category:Forest mensuration]] | [[Category:Forest mensuration]] | ||
Latest revision as of 10:32, 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
- \(volume=f(\mbox{dbh, height})\), 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.
Pages in category "Functions and models in forest inventory"
The following 4 pages are in this category, out of 4 total.
