[4773] | 1 | ! radiation_optical_depth_scaling.h - Cloud optical-depth scaling for Tripleclouds |
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| 2 | ! |
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| 3 | ! (C) Copyright 2016- ECMWF. |
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| 4 | ! |
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| 5 | ! This software is licensed under the terms of the Apache Licence Version 2.0 |
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| 6 | ! which can be obtained at http://www.apache.org/licenses/LICENSE-2.0. |
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| 7 | ! |
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| 8 | ! In applying this licence, ECMWF does not waive the privileges and immunities |
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| 9 | ! granted to it by virtue of its status as an intergovernmental organisation |
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| 10 | ! nor does it submit to any jurisdiction. |
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| 11 | ! |
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| 12 | ! |
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| 13 | ! Author: Robin Hogan |
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| 14 | ! Email: r.j.hogan@ecmwf.int |
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| 15 | ! |
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| 16 | ! Modifications |
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| 17 | ! 2017-07-14 R. Hogan Incorporate gamma distribution option |
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| 18 | ! |
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| 19 | ! This file is intended to be included inside a module to ensure that |
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| 20 | ! this simple routine may be inlined |
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| 21 | |
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| 22 | !--------------------------------------------------------------------- |
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| 23 | ! Compute the optical depth scalings for the optically "thick" and |
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| 24 | ! "thin" regions of a Tripleclouds representation of a sub-grid PDF of |
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| 25 | ! cloud optical depth. Following Shonk and Hogan (2008), the 16th |
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| 26 | ! percentile is used for the thin region, and the formulas estimate |
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| 27 | ! this for both lognormal and gamma distributions. |
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| 28 | pure subroutine optical_depth_scaling(nreg, frac_std, do_gamma, od_scaling) |
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| 29 | |
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| 30 | use parkind1, only : jprb |
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| 31 | |
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| 32 | ! Number of regions |
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| 33 | integer, intent(in) :: nreg |
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| 34 | |
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| 35 | ! Fractional standard deviation of in-cloud water content |
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| 36 | real(jprb), intent(in) :: frac_std |
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| 37 | |
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| 38 | ! Do we do a lognormal or gamma distribution? |
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| 39 | logical, intent(in) :: do_gamma |
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| 40 | |
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| 41 | ! Optical depth scaling for the cloudy regions |
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| 42 | real(jprb), intent(out) :: od_scaling(2:nreg) |
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| 43 | |
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| 44 | if (nreg == 2) then |
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| 45 | ! Only one clear-sky and one cloudy region: cloudy region is |
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| 46 | ! homogeneous |
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| 47 | od_scaling(2) = 1.0_jprb |
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| 48 | else |
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| 49 | ! Two cloudy regions with optical depth scaled by 1-x and |
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| 50 | ! 1+x. |
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| 51 | ! Simple version which fails when fractional_std >= 1: |
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| 52 | !od_scaling(2) = 1.0_jprb-cloud%fractional_std(jcol,jlev) |
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| 53 | ! According to Shonk and Hogan (2008), 1-x should correspond to |
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| 54 | ! the 16th percentile. |
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| 55 | if (.not. do_gamma) then |
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| 56 | ! If we treat the distribution as a lognormal such that the |
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| 57 | ! equivalent Normal has a mean mu and standard deviation sigma, |
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| 58 | ! then the 16th percentile of the lognormal is very close to |
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| 59 | ! exp(mu-sigma). |
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| 60 | od_scaling(2) & |
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| 61 | & = exp(-sqrt(log(frac_std**2+1))) / sqrt(frac_std**2+1) |
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| 62 | else |
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| 63 | ! If we treat the distribution as a gamma then the 16th |
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| 64 | ! percentile is close to the following |
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| 65 | od_scaling(2) = exp(-frac_std*(1.0_jprb + 0.5_jprb*frac_std & |
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| 66 | & *(1.0_jprb+0.5_jprb*frac_std))) |
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| 67 | end if |
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| 68 | |
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| 69 | ! Ensure mean optical depth is conserved |
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| 70 | od_scaling(3) = 2.0_jprb-od_scaling(2) |
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| 71 | end if |
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| 72 | |
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| 73 | end subroutine optical_depth_scaling |
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