The difference_ops module.

This module implements averaging and differencing functions for data on a C-grid.

New at 0.4.2

1. Non-dimension coords are treated consistently with dimensional coords.

2. Support for non-xy-periodic grid.

3. Support for UM-style grid staggering.

4. Generic derivatives and grid-conforming functions grid_conform_xy(), d_by_dxy_field_native() and d_by_dxy_field() are available for xy direction.

New at 0.2

1. Specify spatial derivatives of variables at input. Derivatives are split into the d_by_dx_field() and d_by_dx_field_native() (and similarly for y, z) . The latter just perform a centred difference and update the grid specification for that dimension (so, for example, a derivative of a field on x_u points will be on x_p points. The former calls the latter then intterpolates to the required output grid.

New at 0.1

1. Relocated to monc_utils.data_utils.

Detailed Module Contents

The entire module is documented below.

difference_ops.py.

Created on Wed Apr 17 21:03:43 2019

Difference operators for C-grid data.

Note: written for MONC grid

v[i ,j ,k] – + – v[i+1,j ,k] – + | | | | | | | | p[i ,j ,k] – u[i ,j ,k] – p[i+1,j ,k] – u[i+1,j,k] | | | | | | | |

v[i ,j-1,k] – + – v[i+1,j-1,k] – +

The 0th point is a p point. We have decided this is at dx/2, dy/2

roll(f, +1) shifts data right, so is equivalent to f[i-1] (or j-1).

For optional UM grid: + – v[i ,j+1,k] – + – v[i+1 ,j ,k] –+ | | | | | | | | u[i ,j ,k]– p[i ,j ,k] – u[i+1,j ,k] – p[i+1,j ,k] – u[i+2,j,k] | | | | | | | | + – v[i ,j ,k] – + – v[i+1 ,j ,k] –+

The 0th point is a p point. We have decided this is at dx/2, dy/2

roll(f, +1) shifts data right, so is equivalent to f[i-1] (or j-1).

@author: Peter Clark

monc_utils.data_utils.difference_ops.set_difference_ops_options(opts)

monc_utils.data_utils.difference_ops.exec_fn(fn: Callable, field: DataArray, axis: int) → DataArray

Execute function using map_overlap with overlap on selected axis.

Parameters:

• fn (function) – DESCRIPTION.

• field (xarray.DataArray) – DESCRIPTION.

• axis (int) – DESCRIPTION.

Return type:

new xarray.DataArray

monc_utils.data_utils.difference_ops.last_dim(z)

Remove all but last dimension of z. (Deprecated)

Parameters:

z (n-dimensional array.) –

Return type:

last dimension of z.

@author: Peter Clark

monc_utils.data_utils.difference_ops.interpolate_z(field, znew)

Interpolate field znew.

Parameters:

• field (xarray nD field) –

• znew (xarray coordinate new z.) –

Return type:

field on znew levels

@author: Peter Clark

monc_utils.data_utils.difference_ops.interp_aux_coords(field, dim, newfield, target_dim)

Intorpolat non-dimensional coords to new dimension.

Parameters:

• field (xarray.DataArray) – nD field.

• dim (char) – dimension in field. e.g. ‘x_p’

• newfield (xarray.DataArray) – field with new aux_coords associated with dim.

• target_dim (char) – new dimension in field. e.g. ‘x_v’

Returns:

newfield – copy of field with target_dim coords.

Return type:

xarray.DataArray

monc_utils.data_utils.difference_ops.grid_conform_xy(field, target_dim)

Force field to target grid by averaging if necessary. This works on x or y grid. This replaces grid_conform_x and grid_conform_y

Parameters:

• field (xarray) – Any multi-dimensional xarray with x dimension ‘x_u’ or ‘x_p’. Any other x dimensionm treated as ‘x_p’. OR Any multi-dimensional xarray with y dimension ‘y_v’ or ‘y_p’. Any other y dimensionm treated as ‘y_p’.

• target_xdim (str) – Dimension name ‘x_u’ or ‘x_p’ OR ‘y_v’ or ‘y_p’

Returns:

field on target x or y grid.

Return type:

xarray

monc_utils.data_utils.difference_ops.grid_conform_x(field, target_xdim)

Force field to target x grid by averaging if necessary.

Parameters:

• field (xarray) – Any multi-dimensional xarray with x dimension ‘x_u’ or ‘x_p’. Any other x dimensionm treated as ‘x_p’.

• target_xdim (str) – Dimension name ‘x_u’ or ‘x_p’

Returns:

field on target x grid.

Return type:

xarray

monc_utils.data_utils.difference_ops.grid_conform_y(field, target_ydim)

Force field to target y grid by averaging if necessary.

Parameters:

• field (xarray) – Any multi-dimensional xarray with y dimension ‘y_v’ or ‘y_p’. Any other y dimensionm treated as ‘y_p’.

• target_xdim (str) – Dimension name ‘y_v’ or ‘y_p’

Returns:

field on target y grid.

Return type:

xarray

monc_utils.data_utils.difference_ops.grid_conform_z(field, z_w, z_p, target_zdim)

Force field to target x grid by interpolation if necessary.

Parameters:

• field (xarray) – Any multi-dimensional xarray with z dimension ‘z_w’ or ‘z_p’.

• z_w (xarray coord.) –

• z_p (xarray coord.) –

• target_xdim (str) – Dimension name ‘z_w’ or ‘z_p’

Returns:

field on target x grid.

Return type:

xarray

monc_utils.data_utils.difference_ops.grid_conform(field, z_w, z_p, grid: str = 'p')

Force field to target grid by interpolation if necessary.

Parameters:

• field (xarray) – Any multi-dimensional xarray with z dimension ‘z_w’ or ‘z_p’.

• z_w (xarray coord.) –

• z_p (xarray coord.) –

• grid (str | tuple(str)) – grid identifier ‘p’| ‘u’| ‘v’| ‘w’ or tuple (xdim, ydim, zdim).

Returns:

field on target grid.

Return type:

xarray

monc_utils.data_utils.difference_ops.d_by_dxy_field_native(field, dim_dir)

Differentiate field in x direction on native grid.

Parameters:

field (xarray nD field) –

Return type:

field on native grid

monc_utils.data_utils.difference_ops.d_by_dx_field_native(field)

Differentiate field in x direction on native grid.

Parameters:

field (xarray nD field) –

Return type:

field on native grid

monc_utils.data_utils.difference_ops.d_by_dx_field(field, z_w, z_p, grid: str = 'p')

Differentiate field in x direction.

Parameters:

• field (xarray nD field) –

• z_w (xarray coordinate) – zcoord on w levels - needed if changing vertical grid.

• z_p (xarray coordinate) – zcoord on p levels - needed if changing vertical grid.

• grid (str | tuple of 2 strings) – destination grid (Default = ‘p’)

Return type:

field on required grid

@author: Peter Clark

monc_utils.data_utils.difference_ops.d_by_dy_field_native(field)

Differentiate field in y direction on native grid.

Parameters:

field (xarray nD field) –

Return type:

field on native grid

monc_utils.data_utils.difference_ops.d_by_dy_field(field, z_w, z_p, grid: str = 'p')

Differentiate field in y direction.

Parameters:

• field (xarray nD field) –

• z_w (xarray coordinate) – zcoord on w levels - needed if changing vertical grid.

• z_p (xarray coordinate) – zcoord on p levels - needed if changing vertical grid.

• grid (str | tuple of 2 strings) – destination grid (Default = ‘p’)

Return type:

field on required grid

@author: Peter Clark

monc_utils.data_utils.difference_ops.d_by_dxy_field(field, z_w, z_p, dim_dir, grid: str = 'p')

Differentiate field in x direction.

Parameters:

• field (xarray nD field) –

• z_w (xarray coordinate) – zcoord on w levels - needed if changing vertical grid.

• z_p (xarray coordinate) – zcoord on p levels - needed if changing vertical grid.

• dim_dir (char) – Direction to differentiate: ‘x’ or ‘y’.

• grid (str | tuple of 2 strings) – destination grid (Default = ‘p’)

Return type:

field on required grid

@author: Peter Clark

monc_utils.data_utils.difference_ops.d_by_dz_field_native(field)

Differentiate field in z direction on native grid.

Parameters:

field (xarray nD field) –

Return type:

field on native grid

monc_utils.data_utils.difference_ops.d_by_dz_field(field, z_w, z_p, grid: str = 'p')

Differentiate field in z direction.

Parameters:

• field (xarray nD field) –

• z_w (xarray coordinate) – zcoord on w levels - needed if changing vertical grid.

• z_p (xarray coordinate) – zcoord on p levels - needed if changing vertical grid.

• grid (str | tuple of 2 strings) – destination grid (Default = ‘p’)

Return type:

field on required grid

@author: Peter Clark

monc_utils.data_utils.difference_ops.padleft(f, zt, axis=0)

Add dummy field at bottom of nD array.

Parameters:

• f (nD field) –

• zt (1D zcoordinates) –

• axis=0 (Specify axis to extend) –

Return type:

extended field, extended coord

@author: Peter Clark

monc_utils.data_utils.difference_ops.padright(f, zt, axis=0)

Add dummy field at top of nD array.

Parameters:

• f (nD field) –

• zt (1D zcoordinates) –

• axis=0 (Specify axis to extend) –

Return type:

extended field, extended coord

@author: Peter Clark