[efdb01a] | 1 | #!/usr/bin/env python |
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| 2 | # -*- coding: utf-8 -*- |
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[991df6a] | 3 | #******************************************************************************* |
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| 4 | # @Author: Anne Philipp (University of Vienna) |
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| 5 | # |
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| 6 | # @Date: March 2018 |
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| 7 | # |
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| 8 | # @Change History: |
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[54a8a01] | 9 | # |
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[991df6a] | 10 | # November 2015 - Leopold Haimberger (University of Vienna): |
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| 11 | # - migration of the methods dapoly and darain from Fortran |
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| 12 | # (flex_extract_v6 and earlier) to Python |
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| 13 | # |
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| 14 | # April 2018 - Anne Philipp (University of Vienna): |
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| 15 | # - applied PEP8 style guide |
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| 16 | # - added structured documentation |
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| 17 | # - outsourced the disaggregation functions dapoly and darain |
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[ff99eae] | 18 | # to a new module named disaggregation |
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[991df6a] | 19 | # |
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| 20 | # @License: |
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| 21 | # (C) Copyright 2015-2018. |
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| 22 | # |
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| 23 | # This software is licensed under the terms of the Apache Licence Version 2.0 |
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| 24 | # which can be obtained at http://www.apache.org/licenses/LICENSE-2.0. |
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| 25 | # |
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| 26 | # @Module Description: |
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[54a8a01] | 27 | # disaggregation of deaccumulated flux data from an ECMWF model FG field. |
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[991df6a] | 28 | # Initially the flux data to be concerned are: |
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| 29 | # - large-scale precipitation |
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| 30 | # - convective precipitation |
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| 31 | # - surface sensible heat flux |
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| 32 | # - surface solar radiation |
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| 33 | # - u stress |
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| 34 | # - v stress |
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| 35 | # Different versions of disaggregation is provided for rainfall |
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| 36 | # data (darain, modified linear) and the surface fluxes and |
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| 37 | # stress data (dapoly, cubic polynomial). |
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| 38 | # |
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| 39 | # @Module Content: |
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| 40 | # - dapoly |
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| 41 | # - darain |
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[ae88f7d] | 42 | # - IA3 |
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[991df6a] | 43 | # |
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| 44 | #******************************************************************************* |
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[efdb01a] | 45 | |
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| 46 | # ------------------------------------------------------------------------------ |
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| 47 | # MODULES |
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| 48 | # ------------------------------------------------------------------------------ |
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| 49 | |
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| 50 | # ------------------------------------------------------------------------------ |
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| 51 | # FUNCTIONS |
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| 52 | # ------------------------------------------------------------------------------ |
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| 53 | def dapoly(alist): |
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[708c667] | 54 | """Cubic polynomial interpolation of deaccumulated fluxes. |
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| 55 | |
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| 56 | Interpolation of deaccumulated fluxes of an ECMWF model FG field |
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| 57 | using a cubic polynomial solution which conserves the integrals |
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| 58 | of the fluxes within each timespan. |
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| 59 | Disaggregation is done for 4 accumluated timespans which |
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| 60 | generates a new, disaggregated value which is output at the |
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| 61 | central point of the 4 accumulation timespans. |
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| 62 | This new point is used for linear interpolation of the complete |
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| 63 | timeseries afterwards. |
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| 64 | |
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| 65 | Parameters |
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| 66 | ---------- |
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| 67 | alist : :obj:`list` of :obj:`array` of :obj:`float` |
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| 68 | List of 4 timespans as 2-dimensional, horizontal fields. |
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| 69 | E.g. [[array_t1], [array_t2], [array_t3], [array_t4]] |
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| 70 | |
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| 71 | Return |
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| 72 | ------ |
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| 73 | nfield : :obj:`array` of :obj:`float` |
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| 74 | Interpolated flux at central point of accumulation timespan. |
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| 75 | |
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| 76 | Note |
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| 77 | ---- |
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| 78 | March 2000 : P. JAMES |
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| 79 | Original author |
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| 80 | |
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| 81 | June 2003 : A. BECK |
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| 82 | Adaptations |
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| 83 | |
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| 84 | November 2015 : Leopold Haimberger (University of Vienna) |
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| 85 | Migration from Fortran to Python |
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| 86 | |
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| 87 | """ |
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| 88 | |
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[efdb01a] | 89 | pya = (alist[3] - alist[0] + 3. * (alist[1] - alist[2])) / 6. |
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| 90 | pyb = (alist[2] + alist[0]) / 2. - alist[1] - 9. * pya / 2. |
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| 91 | pyc = alist[1] - alist[0] - 7. * pya / 2. - 2. * pyb |
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| 92 | pyd = alist[0] - pya / 4. - pyb / 3. - pyc / 2. |
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| 93 | nfield = 8. * pya + 4. * pyb + 2. * pyc + pyd |
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| 94 | |
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| 95 | return nfield |
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| 96 | |
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| 97 | |
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| 98 | def darain(alist): |
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[708c667] | 99 | """Linear interpolation of deaccumulated fluxes. |
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| 100 | |
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| 101 | Interpolation of deaccumulated fluxes of an ECMWF model FG rainfall |
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| 102 | field using a modified linear solution which conserves the integrals |
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| 103 | of the fluxes within each timespan. |
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| 104 | Disaggregation is done for 4 accumluated timespans which generates |
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| 105 | a new, disaggregated value which is output at the central point |
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| 106 | of the 4 accumulation timespans. This new point is used for linear |
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| 107 | interpolation of the complete timeseries afterwards. |
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| 108 | |
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| 109 | Parameters |
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| 110 | ---------- |
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| 111 | alist : :obj:`list` of :obj:`array` of :obj:`float` |
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| 112 | List of 4 timespans as 2-dimensional, horizontal fields. |
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| 113 | E.g. [[array_t1], [array_t2], [array_t3], [array_t4]] |
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| 114 | |
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| 115 | Return |
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| 116 | ------ |
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| 117 | nfield : :obj:`array` of :obj:`float` |
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| 118 | Interpolated flux at central point of accumulation timespan. |
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| 119 | |
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| 120 | Note |
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| 121 | ---- |
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| 122 | March 2000 : P. JAMES |
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| 123 | Original author |
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| 124 | |
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| 125 | June 2003 : A. BECK |
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| 126 | Adaptations |
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| 127 | |
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| 128 | November 2015 : Leopold Haimberger (University of Vienna) |
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| 129 | Migration from Fortran to Python |
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| 130 | """ |
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| 131 | |
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[efdb01a] | 132 | xa = alist[0] |
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| 133 | xb = alist[1] |
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| 134 | xc = alist[2] |
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| 135 | xd = alist[3] |
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| 136 | xa[xa < 0.] = 0. |
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| 137 | xb[xb < 0.] = 0. |
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| 138 | xc[xc < 0.] = 0. |
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| 139 | xd[xd < 0.] = 0. |
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| 140 | |
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| 141 | xac = 0.5 * xb |
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| 142 | mask = xa + xc > 0. |
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| 143 | xac[mask] = xb[mask] * xc[mask] / (xa[mask] + xc[mask]) |
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| 144 | xbd = 0.5 * xc |
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| 145 | mask = xb + xd > 0. |
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| 146 | xbd[mask] = xb[mask] * xc[mask] / (xb[mask] + xd[mask]) |
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| 147 | nfield = xac + xbd |
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| 148 | |
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| 149 | return nfield |
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[ae88f7d] | 150 | |
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| 151 | def IA3(g): |
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[708c667] | 152 | """ Interpolation with a non-negative geometric mean based algorithm. |
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| 153 | |
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| 154 | The original grid is reconstructed by adding two sampling points in each |
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| 155 | data series interval. This subgrid is used to keep all information during |
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| 156 | the interpolation within the associated interval. Additionally, an advanced |
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| 157 | monotonicity filter is applied to improve the monotonicity properties of |
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| 158 | the series. |
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| 159 | |
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| 160 | Note |
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| 161 | ---- |
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| 162 | Copyright 2017 |
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| 163 | Sabine Hittmeir, Anne Philipp, Petra Seibert |
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| 164 | |
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| 165 | This work is licensed under the Creative Commons Attribution 4.0 |
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| 166 | International License. To view a copy of this license, visit |
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| 167 | http://creativecommons.org/licenses/by/4.0/ or send a letter to |
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| 168 | Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. |
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| 169 | |
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| 170 | Parameters |
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| 171 | ---------- |
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| 172 | g : :obj:`list` of :obj:`float` |
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| 173 | Complete data series that will be interpolated having |
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| 174 | the dimension of the original raw series. |
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| 175 | |
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| 176 | Return |
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| 177 | ------ |
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| 178 | f : :obj:`list` of :obj:`float` |
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| 179 | The interpolated data series with additional subgrid points. |
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| 180 | Its dimension is equal to the length of the input data series |
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| 181 | times three. |
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| 182 | |
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| 183 | |
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| 184 | References |
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| 185 | ---------- |
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| 186 | For more information see article: |
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| 187 | Hittmeir, S.; Philipp, A.; Seibert, P. (2017): A conservative |
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| 188 | interpolation scheme for extensive quantities with application to the |
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| 189 | Lagrangian particle dispersion model FLEXPART., |
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| 190 | Geoscientific Model Development |
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[ae88f7d] | 191 | """ |
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| 192 | |
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| 193 | ####################### variable description ############################# |
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| 194 | # # |
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| 195 | # i - index variable for looping over the data series # |
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| 196 | # g - input data series # |
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| 197 | # f - interpolated and filtered data series with additional # |
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| 198 | # grid points # |
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| 199 | # fi - function value at position i, f_i # |
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| 200 | # fi1 - first sub-grid function value f_i^1 # |
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| 201 | # fi2 - second sub-grid function value f_i^2 # |
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| 202 | # fip1 - next function value at position i+1, f_(i+1) # |
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| 203 | # dt - time step # |
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| 204 | # fmon - monotonicity filter # |
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| 205 | # # |
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| 206 | ########################################################################### |
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| 207 | |
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| 208 | |
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| 209 | import numpy as np |
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| 210 | |
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| 211 | # time step |
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[0e2f93e] | 212 | dt = 1.0 |
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[ae88f7d] | 213 | |
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| 214 | ############### Non-negative Geometric Mean Based Algorithm ############### |
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| 215 | |
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| 216 | # for the left boundary the following boundary condition is valid: |
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| 217 | # the value at t=0 of the interpolation algorithm coincides with the |
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| 218 | # first data value according to the persistence hypothesis |
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[0e2f93e] | 219 | f = [g[0]] |
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[ae88f7d] | 220 | |
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| 221 | # compute two first sub-grid intervals without monotonicity check |
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| 222 | # go through the data series and extend each interval by two sub-grid |
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| 223 | # points and interpolate the corresponding data values |
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| 224 | # except for the last interval due to boundary conditions |
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[0e2f93e] | 225 | for i in range(0, 2): |
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[ae88f7d] | 226 | |
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| 227 | # as a requirement: |
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| 228 | # if there is a zero data value such that g[i]=0, then the whole |
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| 229 | # interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0 |
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| 230 | # according to Eq. (6) |
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[0e2f93e] | 231 | if g[i] == 0.: |
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| 232 | f.extend([0., 0., 0.]) |
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[ae88f7d] | 233 | |
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| 234 | # otherwise the sub-grid values are calculated and added to the list |
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| 235 | else: |
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| 236 | # temporal save of last value in interpolated list |
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| 237 | # since it is the left boundary and hence the new (fi) value |
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| 238 | fi = f[-1] |
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| 239 | |
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| 240 | # the value at the end of the interval (fip1) is prescribed by the |
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| 241 | # geometric mean, restricted such that non-negativity is guaranteed |
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| 242 | # according to Eq. (25) |
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| 243 | fip1=min( 3.*g[i] , 3.*g[i+1] , np.sqrt(g[i+1]*g[i]) ) |
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| 244 | |
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| 245 | # the function value at the first sub-grid point (fi1) is determined |
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| 246 | # according to the equal area condition with Eq. (19) |
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[0e2f93e] | 247 | fi1 = 3./2.*g[i]-5./12.*fip1-1./12.*fi |
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[ae88f7d] | 248 | |
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| 249 | # the function value at the second sub-grid point (fi2) is determined |
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| 250 | # according Eq. (18) |
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[0e2f93e] | 251 | fi2 = fi1+1./3.*(fip1-fi) |
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[ae88f7d] | 252 | |
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| 253 | # add next interval of interpolated (sub-)grid values |
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| 254 | f.append(fi1) |
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| 255 | f.append(fi2) |
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| 256 | f.append(fip1) |
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| 257 | |
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| 258 | # compute rest of the data series intervals |
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| 259 | # go through the data series and extend each interval by two sub-grid |
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| 260 | # points and interpolate the corresponding data values |
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| 261 | # except for the last interval due to boundary conditions |
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[0e2f93e] | 262 | for i in range(2, len(g)-1): |
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[ae88f7d] | 263 | |
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| 264 | # as a requirement: |
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| 265 | # if there is a zero data value such that g[i]=0, then the whole |
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| 266 | # interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0 |
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| 267 | # according to Eq. (6) |
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[0e2f93e] | 268 | if g[i] == 0.: |
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[ae88f7d] | 269 | # apply monotonicity filter for interval before |
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| 270 | # check if there is "M" or "W" shape |
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[0e2f93e] | 271 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
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| 272 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
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| 273 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
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[ae88f7d] | 274 | |
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| 275 | # the monotonicity filter corrects the value at (fim1) by |
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| 276 | # substituting (fim1) with (fmon), see Eq. (27), (28) and (29) |
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| 277 | fmon = min(3.*g[i-2], \ |
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| 278 | 3.*g[i-1], \ |
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| 279 | np.sqrt(max(0,(18./13.*g[i-2] - 5./13.*f[-7]) * |
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| 280 | (18./13.*g[i-1] - 5./13.*f[-1])))) |
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| 281 | |
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| 282 | # recomputation of the sub-grid interval values while the |
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| 283 | # interval boundaries (fi) and (fip2) remains unchanged |
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| 284 | # see Eq. (18) and (19) |
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[0e2f93e] | 285 | f[-4] = fmon |
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| 286 | f[-6] = 3./2.*g[i-2]-5./12.*fmon-1./12.*f[-7] |
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| 287 | f[-5] = f[-6]+(fmon-f[-7])/3. |
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| 288 | f[-3] = 3./2.*g[i-1]-5./12.*f[-1]-1./12.*fmon |
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| 289 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
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[ae88f7d] | 290 | |
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| 291 | f.extend([0.,0.,0.]) |
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| 292 | |
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| 293 | # otherwise the sub-grid values are calculated and added to the list |
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| 294 | else: |
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| 295 | # temporal save of last value in interpolated list |
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| 296 | # since it is the left boundary and hence the new (fi) value |
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| 297 | fi = f[-1] |
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| 298 | |
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| 299 | # the value at the end of the interval (fip1) is prescribed by the |
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| 300 | # geometric mean, restricted such that non-negativity is guaranteed |
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| 301 | # according to Eq. (25) |
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[0e2f93e] | 302 | fip1 = min( 3.*g[i] , 3.*g[i+1] , np.sqrt(g[i+1]*g[i]) ) |
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[ae88f7d] | 303 | |
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| 304 | # the function value at the first sub-grid point (fi1) is determined |
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| 305 | # according to the equal area condition with Eq. (19) |
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[0e2f93e] | 306 | fi1 = 3./2.*g[i]-5./12.*fip1-1./12.*fi |
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[ae88f7d] | 307 | |
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| 308 | # the function value at the second sub-grid point (fi2) is determined |
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| 309 | # according Eq. (18) |
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[0e2f93e] | 310 | fi2 = fi1+1./3.*(fip1-fi) |
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[ae88f7d] | 311 | |
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| 312 | # apply monotonicity filter for interval before |
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| 313 | # check if there is "M" or "W" shape |
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[0e2f93e] | 314 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
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| 315 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
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| 316 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
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[ae88f7d] | 317 | |
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| 318 | # the monotonicity filter corrects the value at (fim1) by |
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| 319 | # substituting (fim1) with fmon, see Eq. (27), (28) and (29) |
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| 320 | fmon = min(3.*g[i-2], \ |
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| 321 | 3.*g[i-1], \ |
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| 322 | np.sqrt(max(0,(18./13.*g[i-2] - 5./13.*f[-7]) * |
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| 323 | (18./13.*g[i-1] - 5./13.*f[-1])))) |
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| 324 | |
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| 325 | # recomputation of the sub-grid interval values while the |
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| 326 | # interval boundaries (fi) and (fip2) remains unchanged |
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| 327 | # see Eq. (18) and (19) |
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[0e2f93e] | 328 | f[-4] = fmon |
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| 329 | f[-6] = 3./2.*g[i-2]-5./12.*fmon-1./12.*f[-7] |
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| 330 | f[-5] = f[-6]+(fmon-f[-7])/3. |
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| 331 | f[-3] = 3./2.*g[i-1]-5./12.*f[-1]-1./12.*fmon |
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| 332 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
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[ae88f7d] | 333 | |
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| 334 | # add next interval of interpolated (sub-)grid values |
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| 335 | f.append(fi1) |
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| 336 | f.append(fi2) |
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| 337 | f.append(fip1) |
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| 338 | |
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| 339 | # separate treatment of the final interval |
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| 340 | |
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| 341 | # as a requirement: |
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| 342 | # if there is a zero data value such that g[i]=0, then the whole |
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| 343 | # interval in f has to be zero to such that f[i+1]=f[i+2]=f[i+3]=0 |
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| 344 | # according to Eq. (6) |
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[0e2f93e] | 345 | if g[-1] == 0.: |
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[ae88f7d] | 346 | # apply monotonicity filter for interval before |
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| 347 | # check if there is "M" or "W" shape |
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[0e2f93e] | 348 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
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| 349 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
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| 350 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
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[ae88f7d] | 351 | |
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| 352 | # the monotonicity filter corrects the value at (fim1) by |
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| 353 | # substituting (fim1) with (fmon), see Eq. (27), (28) and (29) |
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| 354 | fmon = min(3.*g[-3], \ |
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| 355 | 3.*g[-2], \ |
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| 356 | np.sqrt(max(0,(18./13.*g[-3] - 5./13.*f[-7]) * |
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| 357 | (18./13.*g[-2] - 5./13.*f[-1])))) |
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| 358 | |
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| 359 | # recomputation of the sub-grid interval values while the |
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| 360 | # interval boundaries (fi) and (fip2) remains unchanged |
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| 361 | # see Eq. (18) and (19) |
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[0e2f93e] | 362 | f[-4] = fmon |
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| 363 | f[-6] = 3./2.*g[-3]-5./12.*fmon-1./12.*f[-7] |
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| 364 | f[-5] = f[-6]+(fmon-f[-7])/3. |
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| 365 | f[-3] = 3./2.*g[-2]-5./12.*f[-1]-1./12.*fmon |
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| 366 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
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[ae88f7d] | 367 | |
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| 368 | f.extend([0.,0.,0.]) |
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| 369 | |
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| 370 | # otherwise the sub-grid values are calculated and added to the list |
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| 371 | # using the persistence hypothesis as boundary condition |
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| 372 | else: |
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| 373 | # temporal save of last value in interpolated list |
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| 374 | # since it is the left boundary and hence the new (fi) value |
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| 375 | fi = f[-1] |
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| 376 | # since last interval in series, last value is also fip1 |
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| 377 | fip1 = g[-1] |
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| 378 | # the function value at the first sub-grid point (fi1) is determined |
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| 379 | # according to the equal area condition with Eq. (19) |
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| 380 | fi1 = 3./2.*g[-1]-5./12.*fip1-1./12.*fi |
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| 381 | # the function value at the second sub-grid point (fi2) is determined |
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| 382 | # according Eq. (18) |
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| 383 | fi2 = fi1+dt/3.*(fip1-fi) |
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| 384 | |
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| 385 | # apply monotonicity filter for interval before |
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| 386 | # check if there is "M" or "W" shape |
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[0e2f93e] | 387 | if np.sign(f[-5]-f[-6]) * np.sign(f[-4]-f[-5]) == -1 \ |
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| 388 | and np.sign(f[-4]-f[-5]) * np.sign(f[-3]-f[-4]) == -1 \ |
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| 389 | and np.sign(f[-3]-f[-4]) * np.sign(f[-2]-f[-3]) == -1: |
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[ae88f7d] | 390 | |
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| 391 | # the monotonicity filter corrects the value at (fim1) by |
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| 392 | # substituting (fim1) with (fmon), see Eq. (27), (28) and (29) |
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| 393 | fmon = min(3.*g[-3], \ |
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| 394 | 3.*g[-2], \ |
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| 395 | np.sqrt(max(0,(18./13.*g[-3] - 5./13.*f[-7]) * |
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| 396 | (18./13.*g[-2] - 5./13.*f[-1])))) |
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| 397 | |
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| 398 | # recomputation of the sub-grid interval values while the |
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| 399 | # interval boundaries (fi) and (fip2) remains unchanged |
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| 400 | # see Eq. (18) and (19) |
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[0e2f93e] | 401 | f[-4] = fmon |
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| 402 | f[-6] = 3./2.*g[-3]-5./12.*fmon-1./12.*f[-7] |
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| 403 | f[-5] = f[-6]+(fmon-f[-7])/3. |
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| 404 | f[-3] = 3./2.*g[-2]-5./12.*f[-1]-1./12.*fmon |
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| 405 | f[-2] = f[-3]+(f[-1]-fmon)/3. |
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[ae88f7d] | 406 | |
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| 407 | # add next interval of interpolated (sub-)grid values |
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| 408 | f.append(fi1) |
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| 409 | f.append(fi2) |
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| 410 | f.append(fip1) |
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| 411 | |
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| 412 | return f |
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