[8463d78] | 1 | #!/usr/bin/env python3 |
---|
[efdb01a] | 2 | # -*- coding: utf-8 -*- |
---|
[991df6a] | 3 | #******************************************************************************* |
---|
| 4 | # @Author: Anne Philipp (University of Vienna) |
---|
| 5 | # |
---|
| 6 | # @Date: March 2018 |
---|
| 7 | # |
---|
| 8 | # @Change History: |
---|
[54a8a01] | 9 | # |
---|
[991df6a] | 10 | # November 2015 - Leopold Haimberger (University of Vienna): |
---|
| 11 | # - migration of the methods dapoly and darain from Fortran |
---|
| 12 | # (flex_extract_v6 and earlier) to Python |
---|
| 13 | # |
---|
| 14 | # April 2018 - Anne Philipp (University of Vienna): |
---|
| 15 | # - applied PEP8 style guide |
---|
| 16 | # - added structured documentation |
---|
| 17 | # - outsourced the disaggregation functions dapoly and darain |
---|
[ff99eae] | 18 | # to a new module named disaggregation |
---|
[6f951ca] | 19 | # - added the new disaggregation method for precipitation |
---|
[991df6a] | 20 | # |
---|
| 21 | # @License: |
---|
[6f951ca] | 22 | # (C) Copyright 2014-2019. |
---|
| 23 | # Anne Philipp, Leopold Haimberger |
---|
[991df6a] | 24 | # |
---|
[44174de] | 25 | # SPDX-License-Identifier: CC-BY-4.0 |
---|
| 26 | # |
---|
[6f951ca] | 27 | # This work is licensed under the Creative Commons Attribution 4.0 |
---|
| 28 | # International License. To view a copy of this license, visit |
---|
| 29 | # http://creativecommons.org/licenses/by/4.0/ or send a letter to |
---|
| 30 | # Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. |
---|
[991df6a] | 31 | # |
---|
[6f951ca] | 32 | # @Methods: |
---|
[991df6a] | 33 | # - dapoly |
---|
| 34 | # - darain |
---|
[ae88f7d] | 35 | # - IA3 |
---|
[991df6a] | 36 | #******************************************************************************* |
---|
[6f951ca] | 37 | '''Disaggregation of deaccumulated flux data from an ECMWF model FG field. |
---|
| 38 | |
---|
| 39 | Initially the flux data to be concerned are: |
---|
| 40 | - large-scale precipitation |
---|
| 41 | - convective precipitation |
---|
| 42 | - surface sensible heat flux |
---|
| 43 | - surface solar radiation |
---|
| 44 | - u stress |
---|
| 45 | - v stress |
---|
| 46 | |
---|
| 47 | Different versions of disaggregation is provided for rainfall |
---|
| 48 | data (darain, modified linear) and the surface fluxes and |
---|
| 49 | stress data (dapoly, cubic polynomial). |
---|
| 50 | ''' |
---|
[efdb01a] | 51 | |
---|
| 52 | # ------------------------------------------------------------------------------ |
---|
| 53 | # MODULES |
---|
| 54 | # ------------------------------------------------------------------------------ |
---|
| 55 | |
---|
| 56 | # ------------------------------------------------------------------------------ |
---|
| 57 | # FUNCTIONS |
---|
| 58 | # ------------------------------------------------------------------------------ |
---|
| 59 | def dapoly(alist): |
---|
[708c667] | 60 | """Cubic polynomial interpolation of deaccumulated fluxes. |
---|
| 61 | |
---|
| 62 | Interpolation of deaccumulated fluxes of an ECMWF model FG field |
---|
| 63 | using a cubic polynomial solution which conserves the integrals |
---|
| 64 | of the fluxes within each timespan. |
---|
| 65 | Disaggregation is done for 4 accumluated timespans which |
---|
| 66 | generates a new, disaggregated value which is output at the |
---|
| 67 | central point of the 4 accumulation timespans. |
---|
| 68 | This new point is used for linear interpolation of the complete |
---|
| 69 | timeseries afterwards. |
---|
| 70 | |
---|
| 71 | Parameters |
---|
| 72 | ---------- |
---|
[6f951ca] | 73 | alist : list of array of float |
---|
[708c667] | 74 | List of 4 timespans as 2-dimensional, horizontal fields. |
---|
| 75 | E.g. [[array_t1], [array_t2], [array_t3], [array_t4]] |
---|
| 76 | |
---|
| 77 | Return |
---|
| 78 | ------ |
---|
[6f951ca] | 79 | nfield : array of float |
---|
[708c667] | 80 | Interpolated flux at central point of accumulation timespan. |
---|
| 81 | |
---|
| 82 | Note |
---|
| 83 | ---- |
---|
| 84 | March 2000 : P. JAMES |
---|
| 85 | Original author |
---|
| 86 | |
---|
| 87 | June 2003 : A. BECK |
---|
| 88 | Adaptations |
---|
| 89 | |
---|
| 90 | November 2015 : Leopold Haimberger (University of Vienna) |
---|
| 91 | Migration from Fortran to Python |
---|
| 92 | |
---|
| 93 | """ |
---|
| 94 | |
---|
[efdb01a] | 95 | pya = (alist[3] - alist[0] + 3. * (alist[1] - alist[2])) / 6. |
---|
| 96 | pyb = (alist[2] + alist[0]) / 2. - alist[1] - 9. * pya / 2. |
---|
| 97 | pyc = alist[1] - alist[0] - 7. * pya / 2. - 2. * pyb |
---|
| 98 | pyd = alist[0] - pya / 4. - pyb / 3. - pyc / 2. |
---|
| 99 | nfield = 8. * pya + 4. * pyb + 2. * pyc + pyd |
---|
| 100 | |
---|
| 101 | return nfield |
---|
| 102 | |
---|
| 103 | |
---|
| 104 | def darain(alist): |
---|
[708c667] | 105 | """Linear interpolation of deaccumulated fluxes. |
---|
| 106 | |
---|
| 107 | Interpolation of deaccumulated fluxes of an ECMWF model FG rainfall |
---|
| 108 | field using a modified linear solution which conserves the integrals |
---|
| 109 | of the fluxes within each timespan. |
---|
| 110 | Disaggregation is done for 4 accumluated timespans which generates |
---|
| 111 | a new, disaggregated value which is output at the central point |
---|
| 112 | of the 4 accumulation timespans. This new point is used for linear |
---|
| 113 | interpolation of the complete timeseries afterwards. |
---|
| 114 | |
---|
| 115 | Parameters |
---|
| 116 | ---------- |
---|
[6f951ca] | 117 | alist : list of array of float |
---|
[708c667] | 118 | List of 4 timespans as 2-dimensional, horizontal fields. |
---|
| 119 | E.g. [[array_t1], [array_t2], [array_t3], [array_t4]] |
---|
| 120 | |
---|
| 121 | Return |
---|
| 122 | ------ |
---|
[6f951ca] | 123 | nfield : array of float |
---|
[708c667] | 124 | Interpolated flux at central point of accumulation timespan. |
---|
| 125 | |
---|
| 126 | Note |
---|
| 127 | ---- |
---|
| 128 | March 2000 : P. JAMES |
---|
| 129 | Original author |
---|
| 130 | |
---|
| 131 | June 2003 : A. BECK |
---|
| 132 | Adaptations |
---|
| 133 | |
---|
| 134 | November 2015 : Leopold Haimberger (University of Vienna) |
---|
| 135 | Migration from Fortran to Python |
---|
| 136 | """ |
---|
| 137 | |
---|
[efdb01a] | 138 | xa = alist[0] |
---|
| 139 | xb = alist[1] |
---|
| 140 | xc = alist[2] |
---|
| 141 | xd = alist[3] |
---|
| 142 | xa[xa < 0.] = 0. |
---|
| 143 | xb[xb < 0.] = 0. |
---|
| 144 | xc[xc < 0.] = 0. |
---|
| 145 | xd[xd < 0.] = 0. |
---|
| 146 | |
---|
| 147 | xac = 0.5 * xb |
---|
| 148 | mask = xa + xc > 0. |
---|
| 149 | xac[mask] = xb[mask] * xc[mask] / (xa[mask] + xc[mask]) |
---|
| 150 | xbd = 0.5 * xc |
---|
| 151 | mask = xb + xd > 0. |
---|
| 152 | xbd[mask] = xb[mask] * xc[mask] / (xb[mask] + xd[mask]) |
---|
| 153 | nfield = xac + xbd |
---|
| 154 | |
---|
| 155 | return nfield |
---|
[ae88f7d] | 156 | |
---|
| 157 | def IA3(g): |
---|
[708c667] | 158 | """ Interpolation with a non-negative geometric mean based algorithm. |
---|
| 159 | |
---|
| 160 | The original grid is reconstructed by adding two sampling points in each |
---|
| 161 | data series interval. This subgrid is used to keep all information during |
---|
| 162 | the interpolation within the associated interval. Additionally, an advanced |
---|
| 163 | monotonicity filter is applied to improve the monotonicity properties of |
---|
| 164 | the series. |
---|
| 165 | |
---|
| 166 | Note |
---|
| 167 | ---- |
---|
[6f951ca] | 168 | (C) Copyright 2017-2019 |
---|
[708c667] | 169 | Sabine Hittmeir, Anne Philipp, Petra Seibert |
---|
| 170 | |
---|
| 171 | This work is licensed under the Creative Commons Attribution 4.0 |
---|
| 172 | International License. To view a copy of this license, visit |
---|
| 173 | http://creativecommons.org/licenses/by/4.0/ or send a letter to |
---|
| 174 | Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. |
---|
| 175 | |
---|
| 176 | Parameters |
---|
| 177 | ---------- |
---|
[6f951ca] | 178 | g : list of float |
---|
[708c667] | 179 | Complete data series that will be interpolated having |
---|
| 180 | the dimension of the original raw series. |
---|
| 181 | |
---|
| 182 | Return |
---|
| 183 | ------ |
---|
[6f951ca] | 184 | f : list of float |
---|
[708c667] | 185 | The interpolated data series with additional subgrid points. |
---|
| 186 | Its dimension is equal to the length of the input data series |
---|
| 187 | times three. |
---|
| 188 | |
---|
| 189 | |
---|
| 190 | References |
---|
| 191 | ---------- |
---|
| 192 | For more information see article: |
---|
| 193 | Hittmeir, S.; Philipp, A.; Seibert, P. (2017): A conservative |
---|
| 194 | interpolation scheme for extensive quantities with application to the |
---|
| 195 | Lagrangian particle dispersion model FLEXPART., |
---|
| 196 | Geoscientific Model Development |
---|
[ae88f7d] | 197 | """ |
---|
| 198 | |
---|
| 199 | ####################### variable description ############################# |
---|
| 200 | # # |
---|
| 201 | # i - index variable for looping over the data series # |
---|
| 202 | # g - input data series # |
---|
| 203 | # f - interpolated and filtered data series with additional # |
---|
| 204 | # grid points # |
---|
| 205 | # fi - function value at position i, f_i # |
---|
| 206 | # fi1 - first sub-grid function value f_i^1 # |
---|
| 207 | # fi2 - second sub-grid function value f_i^2 # |
---|
| 208 | # fip1 - next function value at position i+1, f_(i+1) # |
---|
| 209 | # dt - time step # |
---|
| 210 | # fmon - monotonicity filter # |
---|
| 211 | # # |
---|
| 212 | ########################################################################### |
---|
| 213 | |
---|
| 214 | |
---|
| 215 | import numpy as np |
---|
| 216 | |
---|
| 217 | # time step |
---|
[0e2f93e] | 218 | dt = 1.0 |
---|
[ae88f7d] | 219 | |
---|
| 220 | ############### Non-negative Geometric Mean Based Algorithm ############### |
---|
| 221 | |
---|
| 222 | # for the left boundary the following boundary condition is valid: |
---|
| 223 | # the value at t=0 of the interpolation algorithm coincides with the |
---|
| 224 | # first data value according to the persistence hypothesis |
---|
[0e2f93e] | 225 | f = [g[0]] |
---|
[ae88f7d] | 226 | |
---|
| 227 | # compute two first sub-grid intervals without monotonicity check |
---|
| 228 | # go through the data series and extend each interval by two sub-grid |
---|
| 229 | # points and interpolate the corresponding data values |
---|
| 230 | # except for the last interval due to boundary conditions |
---|
[0e2f93e] | 231 | for i in range(0, 2): |
---|
[ae88f7d] | 232 | |
---|
| 233 | # as a requirement: |
---|
| 234 | # if there is a zero data value such that g[i]=0, then the whole |
---|
| 235 | # interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0 |
---|
| 236 | # according to Eq. (6) |
---|
[0e2f93e] | 237 | if g[i] == 0.: |
---|
| 238 | f.extend([0., 0., 0.]) |
---|
[ae88f7d] | 239 | |
---|
| 240 | # otherwise the sub-grid values are calculated and added to the list |
---|
| 241 | else: |
---|
| 242 | # temporal save of last value in interpolated list |
---|
| 243 | # since it is the left boundary and hence the new (fi) value |
---|
| 244 | fi = f[-1] |
---|
| 245 | |
---|
| 246 | # the value at the end of the interval (fip1) is prescribed by the |
---|
| 247 | # geometric mean, restricted such that non-negativity is guaranteed |
---|
| 248 | # according to Eq. (25) |
---|
[0f89116] | 249 | fip1 = min(3. * g[i], 3. * g[i + 1], np.sqrt(g[i + 1] * g[i])) |
---|
[ae88f7d] | 250 | |
---|
| 251 | # the function value at the first sub-grid point (fi1) is determined |
---|
| 252 | # according to the equal area condition with Eq. (19) |
---|
[0e2f93e] | 253 | fi1 = 3./2.*g[i]-5./12.*fip1-1./12.*fi |
---|
[ae88f7d] | 254 | |
---|
| 255 | # the function value at the second sub-grid point (fi2) is determined |
---|
| 256 | # according Eq. (18) |
---|
[0e2f93e] | 257 | fi2 = fi1+1./3.*(fip1-fi) |
---|
[ae88f7d] | 258 | |
---|
| 259 | # add next interval of interpolated (sub-)grid values |
---|
| 260 | f.append(fi1) |
---|
| 261 | f.append(fi2) |
---|
| 262 | f.append(fip1) |
---|
| 263 | |
---|
| 264 | # compute rest of the data series intervals |
---|
| 265 | # go through the data series and extend each interval by two sub-grid |
---|
| 266 | # points and interpolate the corresponding data values |
---|
| 267 | # except for the last interval due to boundary conditions |
---|
[0e2f93e] | 268 | for i in range(2, len(g)-1): |
---|
[ae88f7d] | 269 | |
---|
| 270 | # as a requirement: |
---|
| 271 | # if there is a zero data value such that g[i]=0, then the whole |
---|
| 272 | # interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0 |
---|
| 273 | # according to Eq. (6) |
---|
[0e2f93e] | 274 | if g[i] == 0.: |
---|
[ae88f7d] | 275 | # apply monotonicity filter for interval before |
---|
| 276 | # check if there is "M" or "W" shape |
---|
[0e2f93e] | 277 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
---|
| 278 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
---|
| 279 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
---|
[ae88f7d] | 280 | |
---|
| 281 | # the monotonicity filter corrects the value at (fim1) by |
---|
| 282 | # substituting (fim1) with (fmon), see Eq. (27), (28) and (29) |
---|
[0f89116] | 283 | fmon = min(3. * g[i - 2], |
---|
| 284 | 3. * g[i - 1], |
---|
| 285 | np.sqrt(max(0, (18. / 13. * g[i - 2] - 5. / 13. * f[-7]) * |
---|
| 286 | (18. / 13. * g[i - 1] - 5. / 13. * f[-1])))) |
---|
[ae88f7d] | 287 | |
---|
| 288 | # recomputation of the sub-grid interval values while the |
---|
| 289 | # interval boundaries (fi) and (fip2) remains unchanged |
---|
| 290 | # see Eq. (18) and (19) |
---|
[0e2f93e] | 291 | f[-4] = fmon |
---|
| 292 | f[-6] = 3./2.*g[i-2]-5./12.*fmon-1./12.*f[-7] |
---|
| 293 | f[-5] = f[-6]+(fmon-f[-7])/3. |
---|
| 294 | f[-3] = 3./2.*g[i-1]-5./12.*f[-1]-1./12.*fmon |
---|
| 295 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
---|
[ae88f7d] | 296 | |
---|
[0f89116] | 297 | f.extend([0., 0., 0.]) |
---|
[ae88f7d] | 298 | |
---|
| 299 | # otherwise the sub-grid values are calculated and added to the list |
---|
| 300 | else: |
---|
| 301 | # temporal save of last value in interpolated list |
---|
| 302 | # since it is the left boundary and hence the new (fi) value |
---|
| 303 | fi = f[-1] |
---|
| 304 | |
---|
| 305 | # the value at the end of the interval (fip1) is prescribed by the |
---|
| 306 | # geometric mean, restricted such that non-negativity is guaranteed |
---|
| 307 | # according to Eq. (25) |
---|
[0f89116] | 308 | fip1 = min(3. * g[i], 3. * g[i + 1], np.sqrt(g[i + 1] * g[i])) |
---|
[ae88f7d] | 309 | |
---|
| 310 | # the function value at the first sub-grid point (fi1) is determined |
---|
| 311 | # according to the equal area condition with Eq. (19) |
---|
[0e2f93e] | 312 | fi1 = 3./2.*g[i]-5./12.*fip1-1./12.*fi |
---|
[ae88f7d] | 313 | |
---|
| 314 | # the function value at the second sub-grid point (fi2) is determined |
---|
| 315 | # according Eq. (18) |
---|
[0e2f93e] | 316 | fi2 = fi1+1./3.*(fip1-fi) |
---|
[ae88f7d] | 317 | |
---|
| 318 | # apply monotonicity filter for interval before |
---|
| 319 | # check if there is "M" or "W" shape |
---|
[0e2f93e] | 320 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
---|
| 321 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
---|
| 322 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
---|
[ae88f7d] | 323 | |
---|
| 324 | # the monotonicity filter corrects the value at (fim1) by |
---|
| 325 | # substituting (fim1) with fmon, see Eq. (27), (28) and (29) |
---|
[0f89116] | 326 | fmon = min(3. * g[i - 2], |
---|
| 327 | 3. * g[i - 1], |
---|
| 328 | np.sqrt(max(0, (18. / 13. * g[i - 2] - 5. / 13. * f[-7]) * |
---|
| 329 | (18. / 13. * g[i - 1] - 5. / 13. * f[-1])))) |
---|
[ae88f7d] | 330 | |
---|
| 331 | # recomputation of the sub-grid interval values while the |
---|
| 332 | # interval boundaries (fi) and (fip2) remains unchanged |
---|
| 333 | # see Eq. (18) and (19) |
---|
[0e2f93e] | 334 | f[-4] = fmon |
---|
| 335 | f[-6] = 3./2.*g[i-2]-5./12.*fmon-1./12.*f[-7] |
---|
| 336 | f[-5] = f[-6]+(fmon-f[-7])/3. |
---|
| 337 | f[-3] = 3./2.*g[i-1]-5./12.*f[-1]-1./12.*fmon |
---|
| 338 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
---|
[ae88f7d] | 339 | |
---|
| 340 | # add next interval of interpolated (sub-)grid values |
---|
| 341 | f.append(fi1) |
---|
| 342 | f.append(fi2) |
---|
| 343 | f.append(fip1) |
---|
| 344 | |
---|
| 345 | # separate treatment of the final interval |
---|
| 346 | |
---|
| 347 | # as a requirement: |
---|
| 348 | # if there is a zero data value such that g[i]=0, then the whole |
---|
| 349 | # interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0 |
---|
| 350 | # according to Eq. (6) |
---|
[0e2f93e] | 351 | if g[-1] == 0.: |
---|
[ae88f7d] | 352 | # apply monotonicity filter for interval before |
---|
| 353 | # check if there is "M" or "W" shape |
---|
[0e2f93e] | 354 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
---|
| 355 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
---|
| 356 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
---|
[ae88f7d] | 357 | |
---|
| 358 | # the monotonicity filter corrects the value at (fim1) by |
---|
| 359 | # substituting (fim1) with (fmon), see Eq. (27), (28) and (29) |
---|
[0f89116] | 360 | fmon = min(3. * g[-3], |
---|
| 361 | 3. * g[-2], |
---|
| 362 | np.sqrt(max(0, (18. / 13. * g[-3] - 5. / 13. * f[-7]) * |
---|
| 363 | (18. / 13. * g[-2] - 5. / 13. * f[-1])))) |
---|
[ae88f7d] | 364 | |
---|
| 365 | # recomputation of the sub-grid interval values while the |
---|
| 366 | # interval boundaries (fi) and (fip2) remains unchanged |
---|
| 367 | # see Eq. (18) and (19) |
---|
[0e2f93e] | 368 | f[-4] = fmon |
---|
| 369 | f[-6] = 3./2.*g[-3]-5./12.*fmon-1./12.*f[-7] |
---|
| 370 | f[-5] = f[-6]+(fmon-f[-7])/3. |
---|
| 371 | f[-3] = 3./2.*g[-2]-5./12.*f[-1]-1./12.*fmon |
---|
| 372 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
---|
[ae88f7d] | 373 | |
---|
[0f89116] | 374 | f.extend([0., 0., 0.]) |
---|
[ae88f7d] | 375 | |
---|
| 376 | # otherwise the sub-grid values are calculated and added to the list |
---|
| 377 | # using the persistence hypothesis as boundary condition |
---|
| 378 | else: |
---|
| 379 | # temporal save of last value in interpolated list |
---|
| 380 | # since it is the left boundary and hence the new (fi) value |
---|
| 381 | fi = f[-1] |
---|
| 382 | # since last interval in series, last value is also fip1 |
---|
| 383 | fip1 = g[-1] |
---|
| 384 | # the function value at the first sub-grid point (fi1) is determined |
---|
| 385 | # according to the equal area condition with Eq. (19) |
---|
| 386 | fi1 = 3./2.*g[-1]-5./12.*fip1-1./12.*fi |
---|
| 387 | # the function value at the second sub-grid point (fi2) is determined |
---|
| 388 | # according Eq. (18) |
---|
| 389 | fi2 = fi1+dt/3.*(fip1-fi) |
---|
| 390 | |
---|
| 391 | # apply monotonicity filter for interval before |
---|
| 392 | # check if there is "M" or "W" shape |
---|
[0e2f93e] | 393 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
---|
| 394 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
---|
| 395 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
---|
[ae88f7d] | 396 | |
---|
| 397 | # the monotonicity filter corrects the value at (fim1) by |
---|
| 398 | # substituting (fim1) with (fmon), see Eq. (27), (28) and (29) |
---|
[0f89116] | 399 | fmon = min(3. * g[-3], |
---|
| 400 | 3. * g[-2], |
---|
| 401 | np.sqrt(max(0, (18. / 13. * g[-3] - 5. / 13. * f[-7]) * |
---|
| 402 | (18. / 13. * g[-2] - 5. / 13. * f[-1])))) |
---|
[ae88f7d] | 403 | |
---|
| 404 | # recomputation of the sub-grid interval values while the |
---|
| 405 | # interval boundaries (fi) and (fip2) remains unchanged |
---|
| 406 | # see Eq. (18) and (19) |
---|
[0e2f93e] | 407 | f[-4] = fmon |
---|
| 408 | f[-6] = 3./2.*g[-3]-5./12.*fmon-1./12.*f[-7] |
---|
| 409 | f[-5] = f[-6]+(fmon-f[-7])/3. |
---|
| 410 | f[-3] = 3./2.*g[-2]-5./12.*f[-1]-1./12.*fmon |
---|
| 411 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
---|
[ae88f7d] | 412 | |
---|
| 413 | # add next interval of interpolated (sub-)grid values |
---|
| 414 | f.append(fi1) |
---|
| 415 | f.append(fi2) |
---|
| 416 | f.append(fip1) |
---|
| 417 | |
---|
| 418 | return f |
---|