deltametrics.mobility.calculate_reworking_fraction

deltametrics.mobility.calculate_reworking_fraction(chmap, landmap, basevalues=None, basevalues_idx=None, window=None, window_idx=None)

Calculate the reworking fraction.

Uses a method similar to that described in Wickert et al 2013 [1] to measure the reworking of the fluvial surface with time. This requires an input channel map, land map, as well as defining the base maps to use and the time window over which you want to look.

The reworking fraction is calculated as:

\[f_{R} = 1 - \frac{N'_{B,T}}{A \cdot f_{d,B}}\]

where \(f_{R}\) is the reworking fraction, \(N'_{B,T}\) is the number of unreworked cells in the transient map, \(A\) is the area of fluvial surface, and \(f_{d,B}\) is the dry fraction of the base map.

\(N'_{B,T}\) is calculated as:

\[N'_{B,T} = \sum_{i=1}^{m_r} \sum_{j=1}^{n_c} \left[ \left(\sum_{\beta = B+1}^{T} K'_{\beta} \right) \equiv 0 \right]\]

where \(m_r\) and \(n_c\) are the number of rows and columns in the base map, \(K'_{\beta}\) is the channel mask at time \(\beta\) when \(\beta\) is used for each time step after the baseline time. This results in \(N'_{B,T}\) being the number of cells that are not reworked at some transient time \(T\) relative to the base time \(B\).

[1]

Wickert, Andrew D., John M. Martin, Michal Tal, Wonsuck Kim, Ben Sheets, and Chris Paola. “River channel lateral mobility: Metrics, time scales, and controls.” Journal of Geophysical Research: Earth Surface 118, no. 2 (2013): 396-412.

Parameters:

• chmap (list, xarray.DataArray, numpy.ndarray) – Either a list of 2-D deltametrics.mask, xarray.DataArray, or numpy.ndarray objects, or a t-x-y 3-D xarray.DataArray or numpy.ndarray with channel mask values.

• landmap (list, xarray.DataArray, numpy.ndarray) – Either a list of 2-D deltametrics.mask, xarray.DataArray, or numpy.ndarray objects, or a t-x-y 3-D xarray.DataArray or numpy.ndarray with land mask values.

• basevalues (list, int, float, optional) – List of time values to use as the base channel map. (or single value)

• basevalues_idx (list, optional) – List of time indices to use as the base channel map. (or single value)

• window (int, float, optional) – Duration of time to use as the time lag (aka how far from the basemap will be analyzed).

• window_idx (int, float, optional) – Duration of time in terms of indices (# of save states) to use as the time lag.

Returns:

fr – A 2-D array of the reworked fraction values, array is of shape len(basevalues) x time_window so each row in the array represents the overlap values associated with a given base value and the columns are associated with each time lag.

Return type:

ndarray