| 1 | //#---------------------------------------------------------------------------
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| 2 | //# STAtmosphere.h: Model of atmospheric opacity
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| 3 | //#---------------------------------------------------------------------------
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| 4 | //# Copyright (C) 2004
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| 5 | //# ATNF
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| 6 | //#
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| 7 | //# The code is based on the Fortran code written by Bob Sault for MIRIAD.
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| 8 | //# Converted to C++ by Max Voronkov. This code uses a simple model of the
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| 9 | //# atmosphere and Liebe's model (1985) of the complex refractive index of
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| 10 | //# air.
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| 11 | //#
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| 12 | //# The model of the atmosphere is one with an exponential fall-off in
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| 13 | //# the water vapour content (scale height of 1540 m) and a temperature lapse
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| 14 | //# rate of 6.5 mK/m. Otherwise the atmosphere obeys the ideal gas equation
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| 15 | //# and hydrostatic equilibrium.
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| 16 | //#
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| 17 | //# This program is free software; you can redistribute it and/or modify it
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| 18 | //# under the terms of the GNU General Public License as published by the Free
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| 19 | //# Software Foundation; either version 2 of the License, or (at your option)
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| 20 | //# any later version.
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| 21 | //#
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| 22 | //# This program is distributed in the hope that it will be useful, but
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| 23 | //# WITHOUT ANY WARRANTY; without even the implied warranty of
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| 24 | //# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
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| 25 | //# Public License for more details.
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| 26 | //#
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| 27 | //# You should have received a copy of the GNU General Public License along
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| 28 | //# with this program; if not, write to the Free Software Foundation, Inc.,
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| 29 | //# 675 Massachusetts Ave, Cambridge, MA 02139, USA.
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| 30 | //#
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| 31 | //# Correspondence concerning this software should be addressed as follows:
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| 32 | //# Internet email: Malte.Marquarding@csiro.au
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| 33 | //# Postal address: Malte Marquarding,
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| 34 | //# Australia Telescope National Facility,
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| 35 | //# P.O. Box 76,
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| 36 | //# Epping, NSW, 2121,
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| 37 | //# AUSTRALIA
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| 38 | //#
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| 39 | //# $Id: STAtmosphere.h 1346 2007-04-26 03:24:41Z mar637 $
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| 40 | //#---------------------------------------------------------------------------
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| 41 |
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| 42 | // own includes
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| 43 | #include "STAtmosphere.h"
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| 44 |
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| 45 | // casa includes
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| 46 | #include <casa/Utilities/Assert.h>
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| 47 | #include <casa/Quanta.h>
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| 48 |
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| 49 | // std includes
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| 50 | #include <cmath>
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| 51 |
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| 52 | using namespace casa;
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| 53 | using namespace asap;
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| 54 |
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| 55 | /**
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| 56 | * Default Constructor (apart from optional parameters).
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| 57 | * The class set up this way will assume International Standard Atmosphere (ISA) conditions,
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| 58 | * except for humidity. The latter is assumed to be 50%, which seems more realistic for
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| 59 | * Australian telescopes than 0%.
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| 60 | * @param[in] wvScale water vapour scale height (m), default is 1540m to match MIRIAD's model
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| 61 | * @param[in] maxAlt maximum altitude of the model atmosphere (m), plane parallel layers are spread linearly up to
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| 62 | * this height, default is 10000m to match MIRIAD.
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| 63 | * @param[in] nLayers number of plane parallel layers in the model (essentially for a numberical integration),
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| 64 | * default is 50 to match MIRIAD.
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| 65 | **/
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| 66 | STAtmosphere::STAtmosphere(double wvScale, double maxAlt, size_t nLayers) :
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| 67 | itsHeights(nLayers), itsTemperatures(nLayers),
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| 68 | itsDryPressures(nLayers), itsVapourPressures(nLayers),
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| 69 | itsGndTemperature(288.), itsPressure(101325.), itsGndHumidity(0.5),
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| 70 | itsLapseRate(0.0065), itsWVScale(wvScale), itsMaxAlt(maxAlt), itsObsHeight(200.)
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| 71 | {
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| 72 | recomputeAtmosphereModel();
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| 73 | }
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| 74 |
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| 75 | /**
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| 76 | * Constructor with explicitly given parameters of the atmosphere
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| 77 | * @param[in] temperature air temperature at the observatory (K)
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| 78 | * @param[in] pressure air pressure at the sea level if the observatory elevation is set
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| 79 | * (default is set to 200m) or at the observatory ground level if the elevation
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| 80 | * is set to 0 (Pascals)
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| 81 | * @param[in] humidity air humidity at the observatory (fraction)
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| 82 | * @param[in] lapseRate temperature lapse rate (K/m), default is 0.0065 K/m to match MIRIAD and ISA
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| 83 | * @param[in] wvScale water vapour scale height (m), default is 1540m to match MIRIAD's model
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| 84 | * @param[in] maxAlt maximum altitude of the model atmosphere (m), plane parallel layers are spread linearly up to
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| 85 | * this height, default is 10000m to match MIRIAD.
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| 86 | * @param[in] nLayers number of plane parallel layers in the model (essentially for a numberical integration),
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| 87 | * default is 50 to match MIRIAD.
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| 88 | **/
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| 89 | STAtmosphere::STAtmosphere(double temperature, double pressure, double humidity, double lapseRate,
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| 90 | double wvScale, double maxAlt, size_t nLayers) :
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| 91 | itsHeights(nLayers), itsTemperatures(nLayers),
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| 92 | itsDryPressures(nLayers), itsVapourPressures(nLayers),
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| 93 | itsGndTemperature(temperature), itsPressure(pressure), itsGndHumidity(humidity),
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| 94 | itsLapseRate(lapseRate), itsWVScale(wvScale), itsMaxAlt(maxAlt), itsObsHeight(200.)
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| 95 | {
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| 96 | recomputeAtmosphereModel();
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| 97 | }
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| 98 |
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| 99 | /**
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| 100 | * Set the new weather station data, recompute the model
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| 101 | * @param[in] temperature air temperature at the observatory (K)
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| 102 | * @param[in] pressure air pressure at the sea level if the observatory elevation is set to non-zero value
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| 103 | * (default is set to 200m) or at the observatory ground level if the elevation
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| 104 | * is set to 0 (Pascals)
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| 105 | * @param[in] humidity air humidity at the observatory (fraction)
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| 106 | **/
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| 107 | void STAtmosphere::setWeather(double temperature, double pressure, double humidity)
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| 108 | {
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| 109 | itsGndTemperature = temperature;
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| 110 | itsPressure = pressure;
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| 111 | itsGndHumidity = humidity;
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| 112 | recomputeAtmosphereModel();
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| 113 | }
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| 114 |
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| 115 | /**
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| 116 | * Set the elevation of the observatory (height above mean sea level)
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| 117 | * It affects only interpretation of the pressure supplied as part of the weather data, if this value
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| 118 | * is non-zero, the pressure (e.g. in setWeather or constructor) is that at mean sea level. If the
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| 119 | * observatory elevation is set to zero, regardless on real elevation, the pressure is that at the
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| 120 | * observatory ground level.
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| 121 | *
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| 122 | * By default, 200m is assumed and the pressure should be a mean sea level pressure..
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| 123 | * @param[in] elev elevation in metres
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| 124 | **/
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| 125 | void STAtmosphere::setObservatoryElevation(double elev)
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| 126 | {
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| 127 | itsObsHeight = elev;
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| 128 | recomputeAtmosphereModel();
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| 129 | }
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| 130 |
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| 131 |
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| 132 | /**
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| 133 | * Build the atmosphere model based on exponential fall-off, ideal gas and hydrostatic
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| 134 | * equilibrium. The model parameters are taken from the data members of this class.
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| 135 | **/
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| 136 | void STAtmosphere::recomputeAtmosphereModel()
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| 137 | {
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| 138 | AlwaysAssert(itsGndTemperature > 0, AipsError);
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| 139 | AlwaysAssert(itsPressure > 0., AipsError);
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| 140 | AlwaysAssert((itsGndHumidity >= 0.) && (itsGndHumidity<=1.), AipsError);
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| 141 | AlwaysAssert(itsMaxAlt > 0., AipsError);
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| 142 | AlwaysAssert(itsWVScale > 0., AipsError);
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| 143 |
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| 144 | const double heightStep = itsMaxAlt/double(nLayers());
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| 145 | // molar mass of the air
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| 146 | const double M = 28.96e-3;
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| 147 | // free-fall acceleration
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| 148 | const double g = 9.81;
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| 149 |
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| 150 | const double wvGndSaturationPressure = wvSaturationPressure(itsGndTemperature);
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| 151 | const double gndPressure = itsPressure*exp(-M*g/(QC::R.get().getValue()*itsGndTemperature)*
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| 152 | (itsObsHeight+0.5*itsLapseRate*itsObsHeight*itsObsHeight/itsGndTemperature));
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| 153 | for (size_t layer = 0; layer < nLayers(); ++layer) {
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| 154 | const double height = double(layer)*heightStep;
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| 155 | itsHeights[layer] = height;
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| 156 | itsTemperatures[layer] = itsGndTemperature/(1.+itsLapseRate*height/itsGndTemperature);
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| 157 | const double pressure = gndPressure * exp(-M*g/(QC::R.get().getValue()*itsGndTemperature)*
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| 158 | (height+0.5*itsLapseRate*height*height/itsGndTemperature));
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| 159 | itsVapourPressures[layer] = casa::min(itsGndHumidity*exp(-height/itsWVScale)*wvGndSaturationPressure,
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| 160 | wvSaturationPressure(itsTemperatures[layer]));
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| 161 | itsDryPressures[layer] = pressure - itsVapourPressures[layer];
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| 162 | //std::cout<<"layer="<<layer<<": H="<<itsHeights[layer]<<" T="<<itsTemperatures[layer]<<
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| 163 | // " Pvap="<<itsVapourPressures[layer]<<" Pdry="<<itsDryPressures[layer]<<endl;
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| 164 | }
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| 165 | }
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| 166 |
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| 167 | /**
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| 168 | * Obtain the number of model layers, do consistency check that everything is
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| 169 | * resized accordingly
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| 170 | * @retrun number of model layers
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| 171 | **/
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| 172 | size_t STAtmosphere::nLayers() const
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| 173 | {
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| 174 | const size_t result = itsHeights.size();
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| 175 | DebugAssert(result > 2, AipsError);
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| 176 | DebugAssert(itsTemperatures.size() == result, AipsError);
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| 177 | DebugAssert(itsDryPressures.size() == result, AipsError);
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| 178 | DebugAssert(itsVapourPressures.size() == result, AipsError);
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| 179 | return result;
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| 180 | }
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| 181 |
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| 182 | /**
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| 183 | * Determine the saturation pressure of water vapour for the given temperature.
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| 184 | *
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| 185 | * Reference:
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| 186 | * Waters, Refraction effects in the neutral atmosphere. Methods of
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| 187 | * Experimental Physics, vol 12B, p 186-200 (1976).
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| 188 | *
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| 189 | * @param[in] temperature temperature in K
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| 190 | * @return vapour saturation pressure (Pascals)
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| 191 | **/
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| 192 | double STAtmosphere::wvSaturationPressure(double temperature)
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| 193 | {
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| 194 | if (temperature <= 215.) {
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| 195 | return 0.;
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| 196 | }
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| 197 | const double theta = 300.0/temperature;
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| 198 | return 1e5/(41.51/std::pow(theta,5)*std::pow(10.,9.834*theta-10.0));
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| 199 | }
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| 200 |
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| 201 | /**
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| 202 | * Compute the complex refractivity of the dry components of the atmosphere
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| 203 | * (oxygen lines) at the given frequency.
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| 204 | * @param[in] freq frequency (Hz)
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| 205 | * @param[in] temperature air temperature (K)
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| 206 | * @param[in] pDry partial pressure of dry components (Pascals)
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| 207 | * @param[in] pVapour partial pressure of water vapour (Pascals)
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| 208 | * @return complex refractivity
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| 209 | *
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| 210 | * Reference:
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| 211 | * Liebe, An updated model for millimeter wave propogation in moist air,
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| 212 | * Radio Science, 20, 1069-1089 (1985).
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| 213 | **/
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| 214 | std::complex<double> STAtmosphere::dryRefractivity(double freq, double temperature,
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| 215 | double pDry, double pVapour)
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| 216 | {
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| 217 | // the number of parameters per atmospheric line and the number of lines taken into account
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| 218 | const size_t nLineParams = 7;
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| 219 | const size_t nLines = 48;
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| 220 | // actual tabulated values
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| 221 | const double lines[nLines][nLineParams] =
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| 222 | {{49.452379, 0.12E-6, 11.830, 8.40E-3, 0.0, 5.60E-3, 1.7},
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| 223 | {49.962257, 0.34E-6, 10.720, 8.50E-3, 0.0, 5.60E-3, 1.7},
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| 224 | {50.474238, 0.94E-6, 9.690, 8.60E-3, 0.0, 5.60E-3, 1.7},
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| 225 | {50.987748, 2.46E-6, 8.690, 8.70E-3, 0.0, 5.50E-3, 1.7},
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| 226 | {51.503350, 6.08E-6, 7.740, 8.90E-3, 0.0, 5.60E-3, 1.8},
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| 227 | {52.021409, 14.14E-6, 6.840, 9.20E-3, 0.0, 5.50E-3, 1.8},
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| 228 | {52.542393, 31.02E-6, 6.000, 9.40E-3, 0.0, 5.70E-3, 1.8},
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| 229 | {53.066906, 64.10E-6, 5.220, 9.70E-3, 0.0, 5.30E-3, 1.9},
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| 230 | {53.595748, 124.70E-6, 4.480, 10.00E-3, 0.0, 5.40E-3, 1.8},
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| 231 | {54.129999, 228.00E-6, 3.810, 10.20E-3, 0.0, 4.80E-3, 2.0},
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| 232 | {54.671157, 391.80E-6, 3.190, 10.50E-3, 0.0, 4.80E-3, 1.9},
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| 233 | {55.221365, 631.60E-6, 2.620, 10.79E-3, 0.0, 4.17E-3, 2.1},
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| 234 | {55.783800, 953.50E-6, 2.115, 11.10E-3, 0.0, 3.75E-3, 2.1},
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| 235 | {56.264777, 548.90E-6, 0.010, 16.46E-3, 0.0, 7.74E-3, 0.9},
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| 236 | {56.363387, 1344.00E-6, 1.655, 11.44E-3, 0.0, 2.97E-3, 2.3},
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| 237 | {56.968180, 1763.00E-6, 1.255, 11.81E-3, 0.0, 2.12E-3, 2.5},
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| 238 | {57.612481, 2141.00E-6, 0.910, 12.21E-3, 0.0, 0.94E-3, 3.7},
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| 239 | {58.323874, 2386.00E-6, 0.621, 12.66E-3, 0.0, -0.55E-3, -3.1},
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| 240 | {58.446589, 1457.00E-6, 0.079, 14.49E-3, 0.0, 5.97E-3, 0.8},
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| 241 | {59.164204, 2404.00E-6, 0.386, 13.19E-3, 0.0, -2.44E-3, 0.1},
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| 242 | {59.590982, 2112.00E-6, 0.207, 13.60E-3, 0.0, 3.44E-3, 0.5},
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| 243 | {60.306057, 2124.00E-6, 0.207, 13.82E-3, 0.0, -4.13E-3, 0.7},
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| 244 | {60.434775, 2461.00E-6, 0.386, 12.97E-3, 0.0, 1.32E-3, -1.0},
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| 245 | {61.150558, 2504.00E-6, 0.621, 12.48E-3, 0.0, -0.36E-3, 5.8},
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| 246 | {61.800152, 2298.00E-6, 0.910, 12.07E-3, 0.0, -1.59E-3, 2.9},
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| 247 | {62.411212, 1933.00E-6, 1.255, 11.71E-3, 0.0, -2.66E-3, 2.3},
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| 248 | {62.486253, 1517.00E-6, 0.078, 14.68E-3, 0.0, -4.77E-3, 0.9},
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| 249 | {62.997974, 1503.00E-6, 1.660, 11.39E-3, 0.0, -3.34E-3, 2.2},
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| 250 | {63.568515, 1087.00E-6, 2.110, 11.08E-3, 0.0, -4.17E-3, 2.0},
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| 251 | {64.127764, 733.50E-6, 2.620, 10.78E-3, 0.0, -4.48E-3, 2.0},
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| 252 | {64.678900, 463.50E-6, 3.190, 10.50E-3, 0.0, -5.10E-3, 1.8},
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| 253 | {65.224067, 274.80E-6, 3.810, 10.20E-3, 0.0, -5.10E-3, 1.9},
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| 254 | {65.764769, 153.00E-6, 4.480, 10.00E-3, 0.0, -5.70E-3, 1.8},
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| 255 | {66.302088, 80.09E-6, 5.220, 9.70E-3, 0.0, -5.50E-3, 1.8},
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| 256 | {66.836827, 39.46E-6, 6.000, 9.40E-3, 0.0, -5.90E-3, 1.7},
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| 257 | {67.369595, 18.32E-6, 6.840, 9.20E-3, 0.0, -5.60E-3, 1.8},
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| 258 | {67.900862, 8.01E-6, 7.740, 8.90E-3, 0.0, -5.80E-3, 1.7},
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| 259 | {68.431001, 3.30E-6, 8.690, 8.70E-3, 0.0, -5.70E-3, 1.7},
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| 260 | {68.960306, 1.28E-6, 9.690, 8.60E-3, 0.0, -5.60E-3, 1.7},
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| 261 | {69.489021, 0.47E-6, 10.720, 8.50E-3, 0.0, -5.60E-3, 1.7},
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| 262 | {70.017342, 0.16E-6, 11.830, 8.40E-3, 0.0, -5.60E-3, 1.7},
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| 263 | {118.750341, 945.00E-6, 0.000, 15.92E-3, 0.0, -0.44E-3, 0.9},
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| 264 | {368.498350, 67.90E-6, 0.020, 19.20E-3, 0.6, 0.00E00, 1.0},
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| 265 | {424.763120, 638.00E-6, 0.011, 19.16E-3, 0.6, 0.00E00, 1.0},
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| 266 | {487.249370, 235.00E-6, 0.011, 19.20E-3, 0.6, 0.00E00, 1.0},
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| 267 | {715.393150, 99.60E-6, 0.089, 18.10E-3, 0.6, 0.00E00, 1.0},
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| 268 | {773.838730, 671.00E-6, 0.079, 18.10E-3, 0.6, 0.00E00, 1.0},
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| 269 | {834.145330, 180.00E-6, 0.079, 18.10E-3, 0.6, 0.00E00, 1.0}};
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| 270 |
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| 271 | // convert to the units of Liebe
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| 272 | const double theta = 300./temperature;
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| 273 | const double kPaPVap = 0.001*pVapour;
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| 274 | const double kPaPDry = 0.001*pDry;
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| 275 | const double fGHz = freq * 1e-9;
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| 276 |
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| 277 | // some coefficients
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| 278 | const double ap = 1.4e-10*(1-1.2e-5*std::pow(fGHz,1.5));
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| 279 | const double gamma0 = 5.6e-3*(kPaPDry + 1.1*kPaPVap)*std::pow(theta,0.8);
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| 280 | // initial refractivity
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| 281 | std::complex<double> result(2.588*kPaPDry*theta +
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| 282 | 3.07e-4*(1.0/(1.0+std::pow(fGHz/gamma0,2))-1)*kPaPDry*theta*theta,
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| 283 | (2*3.07e-4/(gamma0*(1+std::pow(fGHz/gamma0,2))*(1+std::pow(fGHz/60,2))) +
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| 284 | ap*kPaPDry*std::pow(theta,2.5))*fGHz*kPaPDry*theta*theta);
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| 285 |
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| 286 | // sum the contributions of all the lines
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| 287 | for (size_t l = 0; l < nLines; ++l) {
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| 288 | const double S = lines[l][1]*kPaPDry*std::pow(theta,3)*exp(lines[l][2]*(1.-theta));
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| 289 | const double gamma = lines[l][3]*(kPaPDry*std::pow(theta,0.8-lines[l][4]) + 1.1*kPaPVap*theta);
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| 290 | const double delta = lines[l][5]*kPaPDry*std::pow(theta,lines[l][6]);
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| 291 | const double x = (lines[l][0]-fGHz)*(lines[l][0]-fGHz) + gamma*gamma;
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| 292 | const double y = (lines[l][0]+fGHz)*(lines[l][0]+fGHz) + gamma*gamma;
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| 293 | const double z = (lines[l][0]+gamma*gamma/lines[l][0]);
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| 294 | result += std::complex<double> (S*( (z-fGHz)/x + (z+fGHz)/y - 2./lines[l][0] +
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| 295 | delta*(1/x-1/y)*gamma*fGHz/lines[l][0]),
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| 296 | S*( (1/x+1/y)*gamma*fGHz/lines[l][0] -
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| 297 | delta*((lines[l][0]-fGHz)/x + (lines[l][0]+fGHz)/y)*fGHz/lines[l][0]));
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| 298 | }
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| 299 |
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| 300 | return result;
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| 301 | }
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| 302 |
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| 303 | /**
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| 304 | * Compute the complex refractivity of the water vapour monomers
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| 305 | * at the given frequency.
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| 306 | * @param[in] freq frequency (Hz)
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| 307 | * @param[in] temperature air temperature (K)
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| 308 | * @param[in] pDry partial pressure of dry components (Pascals)
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| 309 | * @param[in] pVapour partial pressure of water vapour (Pascals)
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| 310 | * @return complex refractivity
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| 311 | *
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| 312 | * Reference:
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| 313 | * Liebe, An updated model for millimeter wave propogation in moist air,
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| 314 | * Radio Science, 20, 1069-1089 (1985).
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| 315 | **/
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| 316 | std::complex<double> STAtmosphere::vapourRefractivity(double freq, double temperature,
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| 317 | double pDry, double pVapour)
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| 318 | {
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| 319 | // the number of parameters per atmospheric line and the number of lines taken into account
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| 320 | const size_t nLineParams = 4;
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| 321 | const size_t nLines = 30;
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| 322 | // actual tabulated values
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| 323 | const double lines[nLines][nLineParams] =
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| 324 | {{22.235080, 0.1090, 2.143, 27.84E-3},
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| 325 | {67.813960, 0.0011, 8.730, 27.60E-3},
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| 326 | {119.995940, 0.0007, 8.347, 27.00E-3},
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| 327 | {183.310117, 2.3000, 0.653, 28.35E-3},
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| 328 | {321.225644, 0.0464, 6.156, 21.40E-3},
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| 329 | {325.152919, 1.5400, 1.515, 27.00E-3},
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| 330 | {336.187000, 0.0010, 9.802, 26.50E-3},
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| 331 | {380.197372, 11.9000, 1.018, 27.60E-3},
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| 332 | {390.134508, 0.0044, 7.318, 19.00E-3},
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| 333 | {437.346667, 0.0637, 5.015, 13.70E-3},
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| 334 | {439.150812, 0.9210, 3.561, 16.40E-3},
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| 335 | {443.018295, 0.1940, 5.015, 14.40E-3},
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| 336 | {448.001075, 10.6000, 1.370, 23.80E-3},
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| 337 | {470.888947, 0.3300, 3.561, 18.20E-3},
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| 338 | {474.689127, 1.2800, 2.342, 19.80E-3},
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| 339 | {488.491133, 0.2530, 2.814, 24.90E-3},
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| 340 | {503.568532, 0.0374, 6.693, 11.50E-3},
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| 341 | {504.482692, 0.0125, 6.693, 11.90E-3},
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| 342 | {556.936002, 510.000, 0.114, 30.00E-3},
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|---|
| 343 | {620.700807, 5.0900, 2.150, 22.30E-3},
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| 344 | {658.006500, 0.2740, 7.767, 30.00E-3},
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|---|
| 345 | {752.033227, 250.000, 0.336, 28.60E-3},
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|---|
| 346 | {841.073593, 0.0130, 8.113, 14.10E-3},
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| 347 | {859.865000, 0.1330, 7.989, 28.60E-3},
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|---|
| 348 | {899.407000, 0.0550, 7.845, 28.60E-3},
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| 349 | {902.555000, 0.0380, 8.360, 26.40E-3},
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| 350 | {906.205524, 0.1830, 5.039, 23.40E-3},
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| 351 | {916.171582, 8.5600, 1.369, 25.30E-3},
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|---|
| 352 | {970.315022, 9.1600, 1.842, 24.00E-3},
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| 353 | {987.926764, 138.000, 0.178, 28.60E-3}};
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| 354 |
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| 355 | // convert to the units of Liebe
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| 356 | const double theta = 300./temperature;
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|---|
| 357 | const double kPaPVap = 0.001*pVapour;
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| 358 | const double kPaPDry = 0.001*pDry;
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| 359 | const double fGHz = freq * 1e-9;
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| 360 |
|
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| 361 | // initial refractivity
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|---|
| 362 | std::complex<double> result(2.39*kPaPVap*theta + 41.6*kPaPVap*theta*theta +
|
|---|
| 363 | 6.47e-6*std::pow(fGHz,2.05)*kPaPVap*std::pow(theta,2.4),
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| 364 | (0.915*1.40e-6*kPaPDry + 5.41e-5*kPaPVap*theta*theta*theta)*
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| 365 | fGHz*kPaPVap*std::pow(theta,2.5));
|
|---|
| 366 |
|
|---|
| 367 | // sum contributions of all the lines
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|---|
| 368 | for (size_t l = 0; l < nLines; ++l) {
|
|---|
| 369 | const double S = lines[l][1]*kPaPVap*std::pow(theta,3.5)*exp(lines[l][2]*(1.-theta));
|
|---|
| 370 | const double gamma = lines[l][3]*(kPaPDry*std::pow(theta,0.8) + 4.80*kPaPVap*theta);
|
|---|
| 371 | const double x = (lines[l][0]-fGHz)*(lines[l][0]-fGHz) + gamma*gamma;
|
|---|
| 372 | const double y = (lines[l][0]+fGHz)*(lines[l][0]+fGHz) + gamma*gamma;
|
|---|
| 373 | const double z = (lines[l][0]+gamma*gamma/lines[l][0]);
|
|---|
| 374 | result += std::complex<double>(S*((z-fGHz)/x + (z+fGHz)/y - 2./lines[l][0]),
|
|---|
| 375 | S*((1./x+1./y)*gamma*fGHz/lines[l][0]));
|
|---|
| 376 | }
|
|---|
| 377 |
|
|---|
| 378 | return result;
|
|---|
| 379 | }
|
|---|
| 380 |
|
|---|
| 381 | /**
|
|---|
| 382 | * Calculate zenith opacity at the given frequency. This is a simplified version
|
|---|
| 383 | * of the routine implemented in MIRIAD, which calculates just zenith opacity and
|
|---|
| 384 | * nothing else. Note, that if the opacity is high, 1/sin(el) law is not correct
|
|---|
| 385 | * even in the plane parallel case due to refraction.
|
|---|
| 386 | * @param[in] freq frequency of interest in Hz
|
|---|
| 387 | * @return zenith opacity (nepers, i.e. dimensionless)
|
|---|
| 388 | **/
|
|---|
| 389 | double STAtmosphere::zenithOpacity(double freq) const
|
|---|
| 390 | {
|
|---|
| 391 | // essentially a numerical integration with the Trapezium method
|
|---|
| 392 | double tau = 0.;
|
|---|
| 393 | for (int layer = int(nLayers()) - 1; layer>=0; --layer) {
|
|---|
| 394 | double dH = 0.;
|
|---|
| 395 | if (layer == 0) {
|
|---|
| 396 | dH = 0.5*(itsHeights[1]-itsHeights[0]);
|
|---|
| 397 | } else if (layer + 1 == int(nLayers())) {
|
|---|
| 398 | dH = 0.5*(itsHeights[nLayers()-1]-itsHeights[nLayers()-2]);
|
|---|
| 399 | } else {
|
|---|
| 400 | dH = 0.5*(itsHeights[layer+1]-itsHeights[layer-1]);
|
|---|
| 401 | }
|
|---|
| 402 | // imaginary part of the total complex refractivity
|
|---|
| 403 | const double nImag = 1e-6*std::imag(dryRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
|
|---|
| 404 | itsVapourPressures[layer])+vapourRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
|
|---|
| 405 | itsVapourPressures[layer]));
|
|---|
| 406 | tau += dH*4.*casa::C::pi/QC::c.get().getValue()*freq*nImag;
|
|---|
| 407 | }
|
|---|
| 408 | return tau;
|
|---|
| 409 | }
|
|---|
| 410 |
|
|---|
| 411 | /**
|
|---|
| 412 | * Calculate zenith opacity for the range of frequencies. Same as zenithOpacity, but
|
|---|
| 413 | * for a vector of frequencies.
|
|---|
| 414 | * @param[in] freqs vector of frequencies in Hz
|
|---|
| 415 | * @return vector of zenith opacities, one value per frequency (nepers, i.e. dimensionless)
|
|---|
| 416 | **/
|
|---|
| 417 | std::vector<double> STAtmosphere::zenithOpacities(const std::vector<double> &freqs) const
|
|---|
| 418 | {
|
|---|
| 419 | std::vector<double> result(freqs.size());
|
|---|
| 420 | for (size_t ch = 0; ch<freqs.size(); ++ch) {
|
|---|
| 421 | result[ch] = zenithOpacity(freqs[ch]);
|
|---|
| 422 | }
|
|---|
| 423 | return result;
|
|---|
| 424 | }
|
|---|
| 425 |
|
|---|
| 426 | /**
|
|---|
| 427 | * Calculate opacity at the given frequency and elevation. This is a simplified
|
|---|
| 428 | * version of the routine implemented in MIRIAD, which calculates just the opacity and
|
|---|
| 429 | * nothing else. In contract to zenithOpacity, this method takes into account refraction
|
|---|
| 430 | * and is more accurate than if one assumes 1/sin(el) factor.
|
|---|
| 431 | * @param[in] freq frequency of interest in Hz
|
|---|
| 432 | * @param[in] el elevation in radians
|
|---|
| 433 | * @return zenith opacity (nepers, i.e. dimensionless)
|
|---|
| 434 | **/
|
|---|
| 435 | double STAtmosphere::opacity(double freq, double el) const
|
|---|
| 436 | {
|
|---|
| 437 | // essentially a numerical integration with the Trapezium method
|
|---|
| 438 | double tau = 0.;
|
|---|
| 439 | const double sineEl = sin(el);
|
|---|
| 440 | for (int layer = int(nLayers()) - 1; layer>=0; --layer) {
|
|---|
| 441 | double dH = 0.;
|
|---|
| 442 | if (layer == 0) {
|
|---|
| 443 | dH = 0.5*(itsHeights[1]-itsHeights[0]);
|
|---|
| 444 | } else if (layer + 1 == int(nLayers())) {
|
|---|
| 445 | dH = 0.5*(itsHeights[nLayers()-1]-itsHeights[nLayers()-2]);
|
|---|
| 446 | } else {
|
|---|
| 447 | dH = 0.5*(itsHeights[layer+1]-itsHeights[layer-1]);
|
|---|
| 448 | }
|
|---|
| 449 | // total complex refractivity
|
|---|
| 450 | const std::complex<double> n = dryRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
|
|---|
| 451 | itsVapourPressures[layer]) +
|
|---|
| 452 | vapourRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
|
|---|
| 453 | itsVapourPressures[layer]);
|
|---|
| 454 | // real and imaginary part of the total complex refractivity scaled appropriately
|
|---|
| 455 | const double nImag = 1e-6*std::imag(n);
|
|---|
| 456 | const double nReal = 1. + 1e-6*std::real(n);
|
|---|
| 457 | // length increment
|
|---|
| 458 | const double dL = dH*nReal/sqrt(nReal*nReal+sineEl*sineEl-1.);
|
|---|
| 459 | tau += dL*4.*casa::C::pi/QC::c.get().getValue()*freq*nImag;
|
|---|
| 460 | }
|
|---|
| 461 | return tau;
|
|---|
| 462 | }
|
|---|
| 463 |
|
|---|
| 464 | /**
|
|---|
| 465 | * Calculate opacities for the range of frequencies at the given elevation. Same as
|
|---|
| 466 | * opacity, but for a vector of frequencies.
|
|---|
| 467 | * @param[in] freqs vector of frequencies in Hz
|
|---|
| 468 | * @param[in] el elevation in radians
|
|---|
| 469 | * @return vector of opacities, one value per frequency (nepers, i.e. dimensionless)
|
|---|
| 470 | **/
|
|---|
| 471 | std::vector<double> STAtmosphere::opacities(const std::vector<double> &freqs, double el) const
|
|---|
| 472 | {
|
|---|
| 473 | std::vector<double> result(freqs.size());
|
|---|
| 474 | for (size_t ch = 0; ch<freqs.size(); ++ch) {
|
|---|
| 475 | result[ch] = opacity(freqs[ch],el);
|
|---|
| 476 | }
|
|---|
| 477 | return result;
|
|---|
| 478 | }
|
|---|
| 479 |
|
|---|
