polaris.ocean.vertical.elevation.elevation_range_weights

polaris.ocean.vertical.elevation.elevation_range_weights(z_interface, layer_mass, min_level_cell, max_level_cell, z_top, z_bot)[source]

Get the mass per unit area of the part of each layer within an elevation range

The range is given in geometric elevation while the integral it weights is in mass, so the geometric overlap thickness

\[w_k = \max\left(0, \min(z^{int}_k, z_{top}) - \max(z^{int}_{k+1}, z_{bot})\right)\]

is computed from z_interface and used only as the fraction \(w_k / h_k\) of the layer, which is then applied to layer_mass. A layer lying entirely within the range therefore contributes its whole mass, and the geometric coordinate enters only through the partial layers at the boundaries.

The whole column, top:bottom, is the one range in which every valid layer is whole, so its overlap fraction is one, no z_interface is read and none need be passed.

Parameters:

  • z_interface (xarray.DataArray or None) – The elevation of layer interfaces, needed for any range but the whole column

  • layer_mass (xarray.DataArray) – The mass per unit area of each layer, from polaris.ocean.model.get_layer_mass(). Passing differences of z_interface instead recovers the purely geometric weights.

  • min_level_cell (xarray.DataArray) – The zero-based index of the topmost valid layer of each column

  • max_level_cell (xarray.DataArray) – The zero-based index of the bottommost valid layer of each column

  • z_top (float) – The upper bound of the range in m, positive up, or inf for the free surface of each column

  • z_bot (float) – The lower bound of the range in m, positive up, or -inf for the seafloor of each column

Returns:

weights (xarray.DataArray) – The mass per unit area of the overlap of each layer with the range, zero outside the valid layers of a column

Raises:

ValueError – If a range with a finite bound is asked for without z_interface