Skip to content

Interpolation Operators

Operators for interpolating fields between staggered grid points (T, U, V, X).

finitevolx.Interpolation1D

Bases: Module

1-D averaging operators on an Arakawa C-grid.

Parameters:

Name Type Description Default
grid ArakawaCGrid1D

The underlying 1-D grid.

 required
Source code in finitevolx/_src/operators/interpolation.py 
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
class Interpolation1D(eqx.Module):
    """1-D averaging operators on an Arakawa C-grid.

    Parameters
    ----------
    grid : ArakawaCGrid1D
        The underlying 1-D grid.
    """

    grid: ArakawaCGrid1D

    def T_to_U(self, h: Float[Array, "Nx"]) -> Float[Array, "Nx"]:
        """Interpolate T-point -> U-point (east face).

        h_on_u[i+1/2] = 1/2 * (h[i] + h[i+1])

        Parameters
        ----------
        h : Float[Array, "Nx"]
            Scalar at T-points.

        Returns
        -------
        Float[Array, "Nx"]
            Scalar interpolated to U-points.
        """
        out = interior(avg_x_fwd_1d(h), h)
        return out

    def U_to_T(self, u: Float[Array, "Nx"]) -> Float[Array, "Nx"]:
        """Interpolate U-point -> T-point (cell centre).

        u_on_h[i] = 1/2 * (u[i+1/2] + u[i-1/2])

        Parameters
        ----------
        u : Float[Array, "Nx"]
            Velocity at U-points.

        Returns
        -------
        Float[Array, "Nx"]
            Velocity interpolated to T-points.
        """
        out = interior(avg_x_bwd_1d(u), u)
        return out

T_to_U(h)

Interpolate T-point -> U-point (east face).

h_on_u[i+1/2] = 1/2 * (h[i] + h[i+1])

Parameters:

Name Type Description Default
h Float[Array, Nx]

Scalar at T-points.

 required

Returns:

Type Description
Float[Array, Nx]

Scalar interpolated to U-points.
Source code in finitevolx/_src/operators/interpolation.py 
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
def T_to_U(self, h: Float[Array, "Nx"]) -> Float[Array, "Nx"]:
    """Interpolate T-point -> U-point (east face).

    h_on_u[i+1/2] = 1/2 * (h[i] + h[i+1])

    Parameters
    ----------
    h : Float[Array, "Nx"]
        Scalar at T-points.

    Returns
    -------
    Float[Array, "Nx"]
        Scalar interpolated to U-points.
    """
    out = interior(avg_x_fwd_1d(h), h)
    return out

U_to_T(u)

Interpolate U-point -> T-point (cell centre).

u_on_h[i] = 1/2 * (u[i+1/2] + u[i-1/2])

Parameters:

Name Type Description Default
u Float[Array, Nx]

Velocity at U-points.

 required

Returns:

Type Description
Float[Array, Nx]

Velocity interpolated to T-points.
Source code in finitevolx/_src/operators/interpolation.py 
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
def U_to_T(self, u: Float[Array, "Nx"]) -> Float[Array, "Nx"]:
    """Interpolate U-point -> T-point (cell centre).

    u_on_h[i] = 1/2 * (u[i+1/2] + u[i-1/2])

    Parameters
    ----------
    u : Float[Array, "Nx"]
        Velocity at U-points.

    Returns
    -------
    Float[Array, "Nx"]
        Velocity interpolated to T-points.
    """
    out = interior(avg_x_bwd_1d(u), u)
    return out

finitevolx.Interpolation2D

Bases: Module

2-D averaging operators on an Arakawa C-grid.

Parameters:

Name Type Description Default
grid ArakawaCGrid2D

The underlying 2-D grid.

 required
Source code in finitevolx/_src/operators/interpolation.py 
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
class Interpolation2D(eqx.Module):
    """2-D averaging operators on an Arakawa C-grid.

    Parameters
    ----------
    grid : ArakawaCGrid2D
        The underlying 2-D grid.
    """

    grid: ArakawaCGrid2D

    # ------------------------------------------------------------------
    # T-point -> faces / corners
    # ------------------------------------------------------------------

    def T_to_U(self, h: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """T-point -> U-point (east face), x-average.

        h_on_u[j, i+1/2] = 1/2 * (h[j, i] + h[j, i+1])

        Parameters
        ----------
        h : Float[Array, "Ny Nx"]
            Scalar at T-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Scalar interpolated to U-points.
        """
        out = interior(avg_x_fwd(h), h)
        return out

    def T_to_V(self, h: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """T-point -> V-point (north face), y-average.

        h_on_v[j+1/2, i] = 1/2 * (h[j, i] + h[j+1, i])

        Parameters
        ----------
        h : Float[Array, "Ny Nx"]
            Scalar at T-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Scalar interpolated to V-points.
        """
        out = interior(avg_y_fwd(h), h)
        return out

    def T_to_X(self, h: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """T-point -> X-point (NE corner), bilinear average.

        h_on_q[j+1/2, i+1/2] = 1/4 * (h[j,i] + h[j,i+1] + h[j+1,i] + h[j+1,i+1])

        Parameters
        ----------
        h : Float[Array, "Ny Nx"]
            Scalar at T-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Scalar interpolated to X-points (corners).
        """
        out = interior(avg_xy_fwd(h), h)
        return out

    # ------------------------------------------------------------------
    # X-point -> face points
    # ------------------------------------------------------------------

    def X_to_U(self, q: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """X-point (corner) -> U-point (east face), y-average.

        q_on_u[j, i+1/2] = 1/2 * (q[j+1/2, i+1/2] + q[j-1/2, i+1/2])

        Parameters
        ----------
        q : Float[Array, "Ny Nx"]
            Scalar at X-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Scalar interpolated to U-points.
        """
        out = interior(avg_y_bwd(q), q)
        return out

    def X_to_V(self, q: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """X-point (corner) -> V-point (north face), x-average.

        q_on_v[j+1/2, i] = 1/2 * (q[j+1/2, i+1/2] + q[j+1/2, i-1/2])

        Parameters
        ----------
        q : Float[Array, "Ny Nx"]
            Scalar at X-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Scalar interpolated to V-points.
        """
        out = interior(avg_x_bwd(q), q)
        return out

    # ------------------------------------------------------------------
    # Face points -> T-point
    # ------------------------------------------------------------------

    def U_to_T(self, u: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """U-point -> T-point, x-average.

        u_on_h[j, i] = 1/2 * (u[j, i+1/2] + u[j, i-1/2])

        Parameters
        ----------
        u : Float[Array, "Ny Nx"]
            Velocity at U-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Velocity interpolated to T-points.
        """
        out = interior(avg_x_bwd(u), u)
        return out

    def V_to_T(self, v: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """V-point -> T-point, y-average.

        v_on_h[j, i] = 1/2 * (v[j+1/2, i] + v[j-1/2, i])

        Parameters
        ----------
        v : Float[Array, "Ny Nx"]
            Velocity at V-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Velocity interpolated to T-points.
        """
        out = interior(avg_y_bwd(v), v)
        return out

    def X_to_T(self, q: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """X-point (corner) -> T-point, bilinear average.

        q_on_h[j, i] = 1/4 * (q[j+1/2,i+1/2] + q[j-1/2,i+1/2]
                             + q[j+1/2,i-1/2] + q[j-1/2,i-1/2])

        Parameters
        ----------
        q : Float[Array, "Ny Nx"]
            Scalar at X-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Scalar interpolated to T-points.
        """
        out = interior(avg_xy_bwd(q), q)
        return out

    # ------------------------------------------------------------------
    # Face/center -> X-point (corner)
    # ------------------------------------------------------------------

    def U_to_X(self, u: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """U-point -> X-point (corner), y-average.

        u_on_q[j+1/2, i+1/2] = 1/2 * (u[j, i+1/2] + u[j+1, i+1/2])

        Parameters
        ----------
        u : Float[Array, "Ny Nx"]
            Velocity at U-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Velocity interpolated to X-points.
        """
        out = interior(avg_y_fwd(u), u)
        return out

    def V_to_X(self, v: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """V-point -> X-point (corner), x-average.

        v_on_q[j+1/2, i+1/2] = 1/2 * (v[j+1/2, i] + v[j+1/2, i+1])

        Parameters
        ----------
        v : Float[Array, "Ny Nx"]
            Velocity at V-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Velocity interpolated to X-points.
        """
        out = interior(avg_x_fwd(v), v)
        return out

    # ------------------------------------------------------------------
    # Cross-face (bilinear 4-point)
    # ------------------------------------------------------------------

    def U_to_V(self, u: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """U-point -> V-point (cross-face bilinear, 4-point).

        u_on_v[j+1/2, i] = 1/4 * (u[j,   i+1/2] + u[j+1, i+1/2]
                                 + u[j,   i-1/2] + u[j+1, i-1/2])

        Parameters
        ----------
        u : Float[Array, "Ny Nx"]
            Velocity at U-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Velocity interpolated to V-points.
        """
        out = interior(avg_xbwd_yfwd(u), u)
        return out

    def V_to_U(self, v: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
        """V-point -> U-point (cross-face bilinear, 4-point).

        v_on_u[j, i+1/2] = 1/4 * (v[j+1/2, i] + v[j-1/2, i]
                                 + v[j+1/2, i+1] + v[j-1/2, i+1])

        Parameters
        ----------
        v : Float[Array, "Ny Nx"]
            Velocity at V-points.

        Returns
        -------
        Float[Array, "Ny Nx"]
            Velocity interpolated to U-points.
        """
        out = interior(avg_xfwd_ybwd(v), v)
        return out

T_to_U(h)

T-point -> U-point (east face), x-average.

h_on_u[j, i+1/2] = 1/2 * (h[j, i] + h[j, i+1])

Parameters:

Name Type Description Default
h Float[Array, 'Ny Nx']

Scalar at T-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Scalar interpolated to U-points.
Source code in finitevolx/_src/operators/interpolation.py 
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
def T_to_U(self, h: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """T-point -> U-point (east face), x-average.

    h_on_u[j, i+1/2] = 1/2 * (h[j, i] + h[j, i+1])

    Parameters
    ----------
    h : Float[Array, "Ny Nx"]
        Scalar at T-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Scalar interpolated to U-points.
    """
    out = interior(avg_x_fwd(h), h)
    return out

T_to_V(h)

T-point -> V-point (north face), y-average.

h_on_v[j+1/2, i] = 1/2 * (h[j, i] + h[j+1, i])

Parameters:

Name Type Description Default
h Float[Array, 'Ny Nx']

Scalar at T-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Scalar interpolated to V-points.
Source code in finitevolx/_src/operators/interpolation.py 
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
def T_to_V(self, h: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """T-point -> V-point (north face), y-average.

    h_on_v[j+1/2, i] = 1/2 * (h[j, i] + h[j+1, i])

    Parameters
    ----------
    h : Float[Array, "Ny Nx"]
        Scalar at T-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Scalar interpolated to V-points.
    """
    out = interior(avg_y_fwd(h), h)
    return out

T_to_X(h)

T-point -> X-point (NE corner), bilinear average.

h_on_q[j+1/2, i+1/2] = 1/4 * (h[j,i] + h[j,i+1] + h[j+1,i] + h[j+1,i+1])

Parameters:

Name Type Description Default
h Float[Array, 'Ny Nx']

Scalar at T-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Scalar interpolated to X-points (corners).
Source code in finitevolx/_src/operators/interpolation.py 
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
def T_to_X(self, h: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """T-point -> X-point (NE corner), bilinear average.

    h_on_q[j+1/2, i+1/2] = 1/4 * (h[j,i] + h[j,i+1] + h[j+1,i] + h[j+1,i+1])

    Parameters
    ----------
    h : Float[Array, "Ny Nx"]
        Scalar at T-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Scalar interpolated to X-points (corners).
    """
    out = interior(avg_xy_fwd(h), h)
    return out

U_to_T(u)

U-point -> T-point, x-average.

u_on_h[j, i] = 1/2 * (u[j, i+1/2] + u[j, i-1/2])

Parameters:

Name Type Description Default
u Float[Array, 'Ny Nx']

Velocity at U-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Velocity interpolated to T-points.
Source code in finitevolx/_src/operators/interpolation.py 
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
def U_to_T(self, u: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """U-point -> T-point, x-average.

    u_on_h[j, i] = 1/2 * (u[j, i+1/2] + u[j, i-1/2])

    Parameters
    ----------
    u : Float[Array, "Ny Nx"]
        Velocity at U-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Velocity interpolated to T-points.
    """
    out = interior(avg_x_bwd(u), u)
    return out

U_to_V(u)

U-point -> V-point (cross-face bilinear, 4-point).

u_on_v[j+1/2, i] = 1/4 * (u[j, i+1/2] + u[j+1, i+1/2] + u[j, i-1/2] + u[j+1, i-1/2])

Parameters:

Name Type Description Default
u Float[Array, 'Ny Nx']

Velocity at U-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Velocity interpolated to V-points.
Source code in finitevolx/_src/operators/interpolation.py 
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
def U_to_V(self, u: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """U-point -> V-point (cross-face bilinear, 4-point).

    u_on_v[j+1/2, i] = 1/4 * (u[j,   i+1/2] + u[j+1, i+1/2]
                             + u[j,   i-1/2] + u[j+1, i-1/2])

    Parameters
    ----------
    u : Float[Array, "Ny Nx"]
        Velocity at U-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Velocity interpolated to V-points.
    """
    out = interior(avg_xbwd_yfwd(u), u)
    return out

U_to_X(u)

U-point -> X-point (corner), y-average.

u_on_q[j+1/2, i+1/2] = 1/2 * (u[j, i+1/2] + u[j+1, i+1/2])

Parameters:

Name Type Description Default
u Float[Array, 'Ny Nx']

Velocity at U-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Velocity interpolated to X-points.
Source code in finitevolx/_src/operators/interpolation.py 
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
def U_to_X(self, u: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """U-point -> X-point (corner), y-average.

    u_on_q[j+1/2, i+1/2] = 1/2 * (u[j, i+1/2] + u[j+1, i+1/2])

    Parameters
    ----------
    u : Float[Array, "Ny Nx"]
        Velocity at U-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Velocity interpolated to X-points.
    """
    out = interior(avg_y_fwd(u), u)
    return out

V_to_T(v)

V-point -> T-point, y-average.

v_on_h[j, i] = 1/2 * (v[j+1/2, i] + v[j-1/2, i])

Parameters:

Name Type Description Default
v Float[Array, 'Ny Nx']

Velocity at V-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Velocity interpolated to T-points.
Source code in finitevolx/_src/operators/interpolation.py 
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
def V_to_T(self, v: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """V-point -> T-point, y-average.

    v_on_h[j, i] = 1/2 * (v[j+1/2, i] + v[j-1/2, i])

    Parameters
    ----------
    v : Float[Array, "Ny Nx"]
        Velocity at V-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Velocity interpolated to T-points.
    """
    out = interior(avg_y_bwd(v), v)
    return out

V_to_U(v)

V-point -> U-point (cross-face bilinear, 4-point).

v_on_u[j, i+1/2] = 1/4 * (v[j+1/2, i] + v[j-1/2, i] + v[j+1/2, i+1] + v[j-1/2, i+1])

Parameters:

Name Type Description Default
v Float[Array, 'Ny Nx']

Velocity at V-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Velocity interpolated to U-points.
Source code in finitevolx/_src/operators/interpolation.py 
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
def V_to_U(self, v: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """V-point -> U-point (cross-face bilinear, 4-point).

    v_on_u[j, i+1/2] = 1/4 * (v[j+1/2, i] + v[j-1/2, i]
                             + v[j+1/2, i+1] + v[j-1/2, i+1])

    Parameters
    ----------
    v : Float[Array, "Ny Nx"]
        Velocity at V-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Velocity interpolated to U-points.
    """
    out = interior(avg_xfwd_ybwd(v), v)
    return out

V_to_X(v)

V-point -> X-point (corner), x-average.

v_on_q[j+1/2, i+1/2] = 1/2 * (v[j+1/2, i] + v[j+1/2, i+1])

Parameters:

Name Type Description Default
v Float[Array, 'Ny Nx']

Velocity at V-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Velocity interpolated to X-points.
Source code in finitevolx/_src/operators/interpolation.py 
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
def V_to_X(self, v: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """V-point -> X-point (corner), x-average.

    v_on_q[j+1/2, i+1/2] = 1/2 * (v[j+1/2, i] + v[j+1/2, i+1])

    Parameters
    ----------
    v : Float[Array, "Ny Nx"]
        Velocity at V-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Velocity interpolated to X-points.
    """
    out = interior(avg_x_fwd(v), v)
    return out

X_to_T(q)

X-point (corner) -> T-point, bilinear average.

q_on_h[j, i] = 1/4 * (q[j+1/2,i+1/2] + q[j-1/2,i+1/2] + q[j+1/2,i-1/2] + q[j-1/2,i-1/2])

Parameters:

Name Type Description Default
q Float[Array, 'Ny Nx']

Scalar at X-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Scalar interpolated to T-points.
Source code in finitevolx/_src/operators/interpolation.py 
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
def X_to_T(self, q: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """X-point (corner) -> T-point, bilinear average.

    q_on_h[j, i] = 1/4 * (q[j+1/2,i+1/2] + q[j-1/2,i+1/2]
                         + q[j+1/2,i-1/2] + q[j-1/2,i-1/2])

    Parameters
    ----------
    q : Float[Array, "Ny Nx"]
        Scalar at X-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Scalar interpolated to T-points.
    """
    out = interior(avg_xy_bwd(q), q)
    return out

X_to_U(q)

X-point (corner) -> U-point (east face), y-average.

q_on_u[j, i+1/2] = 1/2 * (q[j+1/2, i+1/2] + q[j-1/2, i+1/2])

Parameters:

Name Type Description Default
q Float[Array, 'Ny Nx']

Scalar at X-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Scalar interpolated to U-points.
Source code in finitevolx/_src/operators/interpolation.py 
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
def X_to_U(self, q: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """X-point (corner) -> U-point (east face), y-average.

    q_on_u[j, i+1/2] = 1/2 * (q[j+1/2, i+1/2] + q[j-1/2, i+1/2])

    Parameters
    ----------
    q : Float[Array, "Ny Nx"]
        Scalar at X-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Scalar interpolated to U-points.
    """
    out = interior(avg_y_bwd(q), q)
    return out

X_to_V(q)

X-point (corner) -> V-point (north face), x-average.

q_on_v[j+1/2, i] = 1/2 * (q[j+1/2, i+1/2] + q[j+1/2, i-1/2])

Parameters:

Name Type Description Default
q Float[Array, 'Ny Nx']

Scalar at X-points.

 required

Returns:

Type Description
Float[Array, 'Ny Nx']

Scalar interpolated to V-points.
Source code in finitevolx/_src/operators/interpolation.py 
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
def X_to_V(self, q: Float[Array, "Ny Nx"]) -> Float[Array, "Ny Nx"]:
    """X-point (corner) -> V-point (north face), x-average.

    q_on_v[j+1/2, i] = 1/2 * (q[j+1/2, i+1/2] + q[j+1/2, i-1/2])

    Parameters
    ----------
    q : Float[Array, "Ny Nx"]
        Scalar at X-points.

    Returns
    -------
    Float[Array, "Ny Nx"]
        Scalar interpolated to V-points.
    """
    out = interior(avg_x_bwd(q), q)
    return out

finitevolx.Interpolation3D

Bases: Module

3-D averaging operators on an Arakawa C-grid.

Operates on the horizontal (y, x) plane for each z-level. Array shape is [Nz, Ny, Nx].

Parameters:

Name Type Description Default
grid ArakawaCGrid3D

The underlying 3-D grid.

 required
Source code in finitevolx/_src/operators/interpolation.py 
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
class Interpolation3D(eqx.Module):
    """3-D averaging operators on an Arakawa C-grid.

    Operates on the horizontal (y, x) plane for each z-level.
    Array shape is [Nz, Ny, Nx].

    Parameters
    ----------
    grid : ArakawaCGrid3D
        The underlying 3-D grid.
    """

    grid: ArakawaCGrid3D

    def T_to_U(self, h: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
        """T -> U (x-average) over all z-levels.

        h_on_u[k, j, i+1/2] = 1/2 * (h[k, j, i] + h[k, j, i+1])
        """
        out = interior(avg_x_fwd_3d(h), h)
        return out

    def T_to_V(self, h: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
        """T -> V (y-average) over all z-levels.

        h_on_v[k, j+1/2, i] = 1/2 * (h[k, j, i] + h[k, j+1, i])
        """
        out = interior(avg_y_fwd_3d(h), h)
        return out

    def U_to_T(self, u: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
        """U -> T (x-average) over all z-levels.

        u_on_h[k, j, i] = 1/2 * (u[k, j, i+1/2] + u[k, j, i-1/2])
        """
        out = interior(avg_x_bwd_3d(u), u)
        return out

    def V_to_T(self, v: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
        """V -> T (y-average) over all z-levels.

        v_on_h[k, j, i] = 1/2 * (v[k, j+1/2, i] + v[k, j-1/2, i])
        """
        out = interior(avg_y_bwd_3d(v), v)
        return out

T_to_U(h)

T -> U (x-average) over all z-levels.

h_on_u[k, j, i+1/2] = 1/2 * (h[k, j, i] + h[k, j, i+1])

Source code in finitevolx/_src/operators/interpolation.py 
352
353
354
355
356
357
358
def T_to_U(self, h: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
    """T -> U (x-average) over all z-levels.

    h_on_u[k, j, i+1/2] = 1/2 * (h[k, j, i] + h[k, j, i+1])
    """
    out = interior(avg_x_fwd_3d(h), h)
    return out

T_to_V(h)

T -> V (y-average) over all z-levels.

h_on_v[k, j+1/2, i] = 1/2 * (h[k, j, i] + h[k, j+1, i])

Source code in finitevolx/_src/operators/interpolation.py 
360
361
362
363
364
365
366
def T_to_V(self, h: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
    """T -> V (y-average) over all z-levels.

    h_on_v[k, j+1/2, i] = 1/2 * (h[k, j, i] + h[k, j+1, i])
    """
    out = interior(avg_y_fwd_3d(h), h)
    return out

U_to_T(u)

U -> T (x-average) over all z-levels.

u_on_h[k, j, i] = 1/2 * (u[k, j, i+1/2] + u[k, j, i-1/2])

Source code in finitevolx/_src/operators/interpolation.py 
368
369
370
371
372
373
374
def U_to_T(self, u: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
    """U -> T (x-average) over all z-levels.

    u_on_h[k, j, i] = 1/2 * (u[k, j, i+1/2] + u[k, j, i-1/2])
    """
    out = interior(avg_x_bwd_3d(u), u)
    return out

V_to_T(v)

V -> T (y-average) over all z-levels.

v_on_h[k, j, i] = 1/2 * (v[k, j+1/2, i] + v[k, j-1/2, i])

Source code in finitevolx/_src/operators/interpolation.py 
376
377
378
379
380
381
382
def V_to_T(self, v: Float[Array, "Nz Ny Nx"]) -> Float[Array, "Nz Ny Nx"]:
    """V -> T (y-average) over all z-levels.

    v_on_h[k, j, i] = 1/2 * (v[k, j+1/2, i] + v[k, j-1/2, i])
    """
    out = interior(avg_y_bwd_3d(v), v)
    return out