The Linear Directional Mean can be used to analyze the direction of the body of a line object, and a general line feature usually points in one direction, that is, from the start point to the end point. It can be used to represent some information in practice, such as the trajectory of a vehicle, each turn represents a journey, or the trajectory of a hurricane. Of course, there are some lines that have no direction, such as contour lines. There is also a kind of line segment, which may have azimuth value, but no direction value. For example, the fault line reflects the extension direction and extension scale of the fault. The general description of this kind of fault line is "with northwest-southeast orientation", but it does not have specific direction.
Application case
- Compares two or more sets of lines. For example, by studying the migration of elk and moose in river valleys, wildlife biologists can calculate the migration paths of these two species to obtain the direction and trend of their migration.
- Compare the elements of different periods. For example, ornithologists can calculate the trend of falcon migration month by month. Many animal studies now strap data collection instruments such as GPS to samples, but when there are too many samples, they become disorganized. The directional average can summarize the flight paths of multiple individuals and smooth the daily migration. This makes it easy to know which months the birds travel fastest and when the migration ends.
- Dynamic and static data can be compared, such as assessing logging conditions in a forest to understand wind patterns and directions in the weather conditions in the area.
- In the study of Glaciology, the analysis of ice scratches can indicate the way a glacier moves.
- In criminal research, it can be used to identify the general direction of car theft and stolen vehicle recovery.
Function entrance
- Spatial Statistical Analysis tab-> Measuring Geographic Distributions-> Linear Directional Mean. （iDesktopX）
- Toolbox-> Spatial Statistical Analysis-> Measuring Geographic Distributions-> Linear Directional Mean. (iDesktopX)
Main parameters
Source data: Set the vector Line Dataset to be analyzed.
Group Field: a field that classifies analysis features. After classification, each group of objects will have an ellipse. Group Field can be of integer, date or string type. If the field value in the Group Field is blank, the element is excluded from the analysis.
Weight Field: Set a numeric field as Weight Field, for example, if a traffic accident grade field is used as Weight Field, the result ellipse can reflect not only the spatial distribution of accidents, but also the severity of traffic accidents.
- Ignore direction order for start and end points：
- Unchecked (default): The order of the start and end points is used when calculating the directional average. The line is directional (start to end).
- Check: The order of the start and end points is ignored when calculating the directional average. Lines are not directional (start to end or end to start have the same meaning).
Mean Center: Set Reserved Fields of Result Data and Statistics Type of field value in the field list box.
Result Settings: Set the Datasource and Dataset Name where the Result Data will be saved.
Explanation of results
When the run is complete, a new feature class is created that contains a line feature centered at the Mean Center point of the centroids of all Input Data:, with the length of the line feature equal to the average length of all Input Data:. And its bearing or direction is the average bearing or direction of all Input Data:.
The attribute values for the new line feature are as follows:
- AverageX and AverageY-Mean Center X and Y coordinates
- AverageLength-Average line length
- CompassAngle-Compass angle (clockwise rotation based on true north)
- Directional Mean-Directional mean (counterclockwise rotation based on due east)
- Circle Variance (used to measure how much the line direction or orientation deviates from the average of the directions)
Other estimates are easier to understand, but this tool introduces a concept called the circular variance, which is a similar concept to the standard deviation, which is the degree of variation in the direction of the data you're trying to analyze. The circular variance ranges from 0 to 1. If all the analyzed data have exactly the same (or very similar) orientation, the circular variance will be small (close to 0). When the direction of the input data spans the entire compass, the circular variance will be large (close to 1). The larger the circular variance, the more pronounced the change in direction between the data analyzed.
Instance
The following figure shows some rivers and tributaries at the junction of Pingdu City and Jimo City in Shandong Province. The direction of these rivers is measured and described by calculating the average value of linear direction. The result of the calculation is the red line in the figure. The segment is centered at the Mean Center point of the centroids of all rivers, the length of the segment is equal to the mean length of all rivers, and the bearing or direction is the mean bearing or direction of all rivers.
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