Double Mass Analysis

Description

Double mass analysis cumulates two variables on separate x and y axes to detect possible breakpoints that might be the result of inhomogeneity (Kohler 1949). Unfortunately, a double mass plot by itself suffers from subjectivity. This tool enhances the methodology used by the Interactive Double Mass Analysis program developed by the Office of Hydrological Development at the National Oceanic and Atmospheric Administration (NOAA 1999). Dendro Tools constructs the double mass plot, but then uses simple linear regression and user-specified input information to detect breakpoints (see "Breakpoint Parameters" below for further details). All breakpoints are specified in the output file and shown in the double mass data plot (see "Output Double Mass Analysis" below).

Input

File
Select the input data by clicking on "Browse" and navigating to the proper file.

Input Data Format
Year / Data

Each "/" is a tab (i.e., data should be tab-delimited). Missing Data should be denoted as "-99".

Start Row
Enter the row number where the main data to be processed begin in the input file selected above. An example of how row numbers are entered is shown in Figure 2 located in the Running Dendro Tools topic.

Variable 1 Column Number
This input is the column number where the data for the first variable are located in the input file selected above. An example of how column numbers are entered is shown in Figure 2 located in the Running Dendro Tools topic.

Variable 2 Column Number
This input is the column number where the data for the second variable are located in the input file selected above. An example of how column numbers are entered is shown in Figure 2 located in the Running Dendro Tools topic.

Start Year
Enter the year to start the analysis.

End Year
Enter the year to end the analysis.

Output

File
Select or enter the name of the file where the results will be stored.

Header
Information entered here will be output in the first line of the output file.

Breakpoint Parameters

Initial Points to Analyze per Segment
Enter the minimum number of points that will be used to estimate a least squares line of best fit associated with the double mass plot (default value = 9). This regression line and a prediction interval computed using the "Probability Criterion" below are used to identify breakpoints.

Probability Criterion
Select the probability criterion that will be used to compute a prediction interval (default = 0.05 or a 95% prediction interval). This prediction interval is used to identify breakpoints. The detection of breakpoints is performed by first reading the number of initial points to analyze and then computing a least squares line of best fit. The resulting regression line is then used to predict the next data point. If this prediction is within the prediction interval, then no breakpoint is assumed. The new data point is then used with the previous data points to calculate a new line of best fit and the process repeats. If the prediction breaches the prediction interval in either the positive or negative direction, then a breakpoint is assumed.

Output Double Mass Analysis

How to Read the Output
Once the double mass analysis tool has been run, the number of breakpoints is output along with a time series of the cumulated data for each variable. An asterisk (*) is denoted in the "Breakpoint" column if a breakpoint was detected, and any breakpoint denoted by Dendro Tools represents the end of a line segment (i.e., if a breakpoint occurs at 1915, the line segment ends at 1915 and a new line segment begins at 1916). A double mass plot is then generated with any breakpoints denoted as red stars (Fig. 1). Hovering the mouse arrow over a red star or blue dot will display the year when that red star or blue dot occurs.

Figure 1. Two breakpoints, denoted as red stars, were detected in a double mass plot displayed above. The user can hover the mouse over each red star or blue dot in order to see the year when it occurs. Each star represents the end of a line segment, as detected by Dendro Tools.