Category:Functions and models in forest inventory
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==General observations== | ==General observations== | ||
| − | 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: | + | 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: |
| − | *height curves which predict the tree height from <math>dbh: | + | *height curves 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: | *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(dbh)</math>, or | ||
**<math>volume=f(\mbox{dbh, height})</math>, or | **<math>volume=f(\mbox{dbh, height})</math>, or | ||
**<math>volume=f(\mbox{dbh, upper diameter, height})</math>. | **<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, 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. | 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. | ||
| − | This category contains all articles about mathematical functions and models in forest inventory. | + | |
| + | '''This category contains all articles about mathematical functions and models in forest inventory.''' | ||
[[Category:Forest mensuration]] | [[Category:Forest mensuration]] | ||
Revision as of 19:15, 18 February 2011
General observations
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, 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.
This category contains all articles about mathematical functions and models in forest inventory.
Pages in category "Functions and models in forest inventory"
The following 4 pages are in this category, out of 4 total.
