source: trunk/src/STAtmosphere.cpp @ 1715

Last change on this file since 1715 was 1715, checked in by Max Voronkov, 14 years ago

changed pressure to the mean sea level to match miriad, bugfix, C++ code is now exposed to python
File size: 21.0 KB
Line 
1//#---------------------------------------------------------------------------
2//# STAtmosphere.h: Model of atmospheric opacity
3//#---------------------------------------------------------------------------
4//# Copyright (C) 2004
5//# ATNF
6//#
7//# The code is based on the Fortran code written by Bob Sault for MIRIAD.
8//# Converted to C++ by Max Voronkov. This code uses a simple model of the
9//# atmosphere and Liebe's model (1985) of the complex refractive index of
10//# air.
11//#
12//# The model of the atmosphere is one with an exponential fall-off in
13//# the water vapour content (scale height of 1540 m) and a temperature lapse
14//# rate of 6.5 mK/m. Otherwise the atmosphere obeys the ideal gas equation
15//# and hydrostatic equilibrium.
16//#
17//# This program is free software; you can redistribute it and/or modify it
18//# under the terms of the GNU General Public License as published by the Free
19//# Software Foundation; either version 2 of the License, or (at your option)
20//# any later version.
21//#
22//# This program is distributed in the hope that it will be useful, but
23//# WITHOUT ANY WARRANTY; without even the implied warranty of
24//# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General
25//# Public License for more details.
26//#
27//# You should have received a copy of the GNU General Public License along
28//# with this program; if not, write to the Free Software Foundation, Inc.,
29//# 675 Massachusetts Ave, Cambridge, MA 02139, USA.
30//#
31//# Correspondence concerning this software should be addressed as follows:
32//#        Internet email: Malte.Marquarding@csiro.au
33//#        Postal address: Malte Marquarding,
34//#                        Australia Telescope National Facility,
35//#                        P.O. Box 76,
36//#                        Epping, NSW, 2121,
37//#                        AUSTRALIA
38//#
39//# $Id: STAtmosphere.h 1346 2007-04-26 03:24:41Z mar637 $
40//#---------------------------------------------------------------------------
41
42// own includes
43#include "STAtmosphere.h"
44
45// casa includes
46#include <casa/Utilities/Assert.h>
47#include <casa/Quanta.h>
48
49// std includes
50#include <cmath>
51
52using namespace casa;
53using namespace asap;
54
55/**
56 * Default Constructor (apart from optional parameters).
57 * The class set up this way will assume International Standard Atmosphere (ISA) conditions,
58 * except for humidity. The latter is assumed to be 50%, which seems more realistic for
59 * Australian telescopes than 0%.
60 * @param[in] wvScale water vapour scale height (m), default is 1540m to match MIRIAD's model
61 * @param[in] maxAlt maximum altitude of the model atmosphere (m), plane parallel layers are spread linearly up to
62 *            this height, default is 10000m to match MIRIAD.
63 * @param[in] nLayers number of plane parallel layers in the model (essentially for a numberical integration),
64 *            default is 50 to match MIRIAD.
65 **/
66STAtmosphere::STAtmosphere(double wvScale, double maxAlt, size_t nLayers) :
67   itsHeights(nLayers), itsTemperatures(nLayers),
68   itsDryPressures(nLayers), itsVapourPressures(nLayers),
69   itsGndTemperature(288.), itsPressure(101325.), itsGndHumidity(0.5),
70   itsLapseRate(0.0065), itsWVScale(wvScale), itsMaxAlt(maxAlt), itsObsHeight(200.)
71{
72  recomputeAtmosphereModel();
73}
74
75/**
76 * Constructor with explicitly given parameters of the atmosphere
77 * @param[in] temperature air temperature at the observatory (K)
78 * @param[in] pressure air pressure at the sea level (Pascals)
79 * @param[in] humidity air humidity at the observatory (fraction)
80 * @param[in] lapseRate temperature lapse rate (K/m), default is 0.0065 K/m to match MIRIAD and ISA
81 * @param[in] wvScale water vapour scale height (m), default is 1540m to match MIRIAD's model
82 * @param[in] maxAlt maximum altitude of the model atmosphere (m), plane parallel layers are spread linearly up to
83 *            this height, default is 10000m to match MIRIAD.
84 * @param[in] nLayers number of plane parallel layers in the model (essentially for a numberical integration),
85 *            default is 50 to match MIRIAD.
86 **/
87STAtmosphere::STAtmosphere(double temperature, double pressure, double humidity, double lapseRate,
88               double wvScale, double maxAlt, size_t nLayers) :
89   itsHeights(nLayers), itsTemperatures(nLayers),
90   itsDryPressures(nLayers), itsVapourPressures(nLayers),
91   itsGndTemperature(temperature), itsPressure(pressure), itsGndHumidity(humidity),
92   itsLapseRate(lapseRate), itsWVScale(wvScale), itsMaxAlt(maxAlt), itsObsHeight(200.)
93{
94  recomputeAtmosphereModel();
95}
96               
97/**
98 * Set the new weather station data, recompute the model
99 * @param[in] temperature air temperature at the observatory (K)
100 * @param[in] pressure air pressure at the sea level (Pascals)
101 * @param[in] humidity air humidity at the observatory (fraction)
102 **/
103void STAtmosphere::setWeather(double temperature, double pressure, double humidity)
104{
105  itsGndTemperature = temperature;
106  itsPressure = pressure;
107  itsGndHumidity = humidity;
108  recomputeAtmosphereModel();
109}
110
111/**
112 * Set the elevation of the observatory (height above mean sea level)
113 * By default, 200m is assumed.
114 * @param[in] elev elevation in metres
115 **/
116void STAtmosphere::setObservatoryElevation(double elev)
117{
118  itsObsHeight = elev;
119  recomputeAtmosphereModel(); 
120}
121
122
123/**
124 * Build the atmosphere model based on exponential fall-off, ideal gas and hydrostatic
125 * equilibrium. The model parameters are taken from the data members of this class.
126 **/
127void STAtmosphere::recomputeAtmosphereModel()
128{
129  AlwaysAssert(itsGndTemperature > 0, AipsError);
130  AlwaysAssert(itsPressure > 0., AipsError);
131  AlwaysAssert((itsGndHumidity >= 0.) && (itsGndHumidity<=1.), AipsError);
132  AlwaysAssert(itsMaxAlt > 0., AipsError);
133  AlwaysAssert(itsWVScale > 0., AipsError);
134 
135  const double heightStep = itsMaxAlt/double(nLayers());
136  // molar mass of the air
137  const double M = 28.96e-3;
138  // free-fall acceleration
139  const double g = 9.81;
140 
141  const double wvGndSaturationPressure = wvSaturationPressure(itsGndTemperature);
142  const double gndPressure = itsPressure*exp(-M*g/(QC::R.get().getValue()*itsGndTemperature)*
143                   (itsObsHeight+0.5*itsLapseRate*itsObsHeight*itsObsHeight/itsGndTemperature));
144  for (size_t layer = 0; layer < nLayers(); ++layer) {
145       const double height = double(layer)*heightStep;
146       itsHeights[layer] = height;
147       itsTemperatures[layer] = itsGndTemperature/(1.+itsLapseRate*height/itsGndTemperature);
148       const double pressure = gndPressure * exp(-M*g/(QC::R.get().getValue()*itsGndTemperature)*
149                   (height+0.5*itsLapseRate*height*height/itsGndTemperature));
150       itsVapourPressures[layer] = casa::min(itsGndHumidity*exp(-height/itsWVScale)*wvGndSaturationPressure,
151                                             wvSaturationPressure(itsTemperatures[layer]));
152       itsDryPressures[layer] = pressure - itsVapourPressures[layer];                                     
153       std::cout<<"layer="<<layer<<": H="<<itsHeights[layer]<<" T="<<itsTemperatures[layer]<<
154           " Pvap="<<itsVapourPressures[layer]<<" Pdry="<<itsDryPressures[layer]<<endl;
155  }
156}
157 
158/**
159 * Obtain the number of model layers, do consistency check that everything is
160 * resized accordingly
161 * @retrun number of model layers
162 **/
163size_t STAtmosphere::nLayers() const
164{
165  const size_t result = itsHeights.size();
166  DebugAssert(result > 2, AipsError);
167  DebugAssert(itsTemperatures.size() == result, AipsError);
168  DebugAssert(itsDryPressures.size() == result, AipsError);
169  DebugAssert(itsVapourPressures.size() == result, AipsError); 
170  return result;
171}
172
173/**
174 * Determine the saturation pressure of water vapour for the given temperature.
175 *
176 * Reference:
177 * Waters, Refraction effects in the neutral atmosphere. Methods of
178 * Experimental Physics, vol 12B, p 186-200 (1976).
179 *   
180 * @param[in] temperature temperature in K
181 * @return vapour saturation pressure (Pascals)
182 **/
183double STAtmosphere::wvSaturationPressure(double temperature)
184{
185  if (temperature <= 215.) {
186      return 0.;
187  }
188  const double theta = 300.0/temperature;
189  return 1e5/(41.51/std::pow(theta,5)*std::pow(10.,9.834*theta-10.0));
190}
191
192/**
193 * Compute the complex refractivity of the dry components of the atmosphere
194 * (oxygen lines) at the given frequency.
195 * @param[in] freq frequency (Hz)
196 * @param[in] temperature air temperature (K)
197 * @param[in] pDry partial pressure of dry components (Pascals)
198 * @param[in] pVapour partial pressure of water vapour (Pascals)
199 * @return complex refractivity
200 *
201 * Reference:
202 * Liebe, An updated model for millimeter wave propogation in moist air,
203 * Radio Science, 20, 1069-1089 (1985).
204 **/
205std::complex<double> STAtmosphere::dryRefractivity(double freq, double temperature,
206                     double pDry, double pVapour)
207{
208  // the number of parameters per atmospheric line and the number of lines taken into account
209  const size_t nLineParams = 7;
210  const size_t nLines = 48;
211  // actual tabulated values
212  const double lines[nLines][nLineParams] =
213    {{49.452379,    0.12E-6, 11.830,  8.40E-3, 0.0,  5.60E-3,  1.7},
214     {49.962257,    0.34E-6, 10.720,  8.50E-3, 0.0,  5.60E-3,  1.7},
215     {50.474238,    0.94E-6,  9.690,  8.60E-3, 0.0,  5.60E-3,  1.7},
216     {50.987748,    2.46E-6,  8.690,  8.70E-3, 0.0,  5.50E-3,  1.7},
217     {51.503350,    6.08E-6,  7.740,  8.90E-3, 0.0,  5.60E-3,  1.8},
218     {52.021409,   14.14E-6,  6.840,  9.20E-3, 0.0,  5.50E-3,  1.8},
219     {52.542393,   31.02E-6,  6.000,  9.40E-3, 0.0,  5.70E-3,  1.8},
220     {53.066906,   64.10E-6,  5.220,  9.70E-3, 0.0,  5.30E-3,  1.9},
221     {53.595748,  124.70E-6,  4.480, 10.00E-3, 0.0,  5.40E-3,  1.8},
222     {54.129999,  228.00E-6,  3.810, 10.20E-3, 0.0,  4.80E-3,  2.0},
223     {54.671157,  391.80E-6,  3.190, 10.50E-3, 0.0,  4.80E-3,  1.9},
224     {55.221365,  631.60E-6,  2.620, 10.79E-3, 0.0,  4.17E-3,  2.1},
225     {55.783800,  953.50E-6,  2.115, 11.10E-3, 0.0,  3.75E-3,  2.1},
226     {56.264777,  548.90E-6,  0.010, 16.46E-3, 0.0,  7.74E-3,  0.9},
227     {56.363387, 1344.00E-6,  1.655, 11.44E-3, 0.0,  2.97E-3,  2.3},
228     {56.968180, 1763.00E-6,  1.255, 11.81E-3, 0.0,  2.12E-3,  2.5},
229     {57.612481, 2141.00E-6,  0.910, 12.21E-3, 0.0,  0.94E-3,  3.7},
230     {58.323874, 2386.00E-6,  0.621, 12.66E-3, 0.0, -0.55E-3, -3.1},
231     {58.446589, 1457.00E-6,  0.079, 14.49E-3, 0.0,  5.97E-3,  0.8},
232     {59.164204, 2404.00E-6,  0.386, 13.19E-3, 0.0, -2.44E-3,  0.1},
233     {59.590982, 2112.00E-6,  0.207, 13.60E-3, 0.0,  3.44E-3,  0.5},
234     {60.306057, 2124.00E-6,  0.207, 13.82E-3, 0.0, -4.13E-3,  0.7},
235     {60.434775, 2461.00E-6,  0.386, 12.97E-3, 0.0,  1.32E-3, -1.0},
236     {61.150558, 2504.00E-6,  0.621, 12.48E-3, 0.0, -0.36E-3,  5.8},
237     {61.800152, 2298.00E-6,  0.910, 12.07E-3, 0.0, -1.59E-3,  2.9},
238     {62.411212, 1933.00E-6,  1.255, 11.71E-3, 0.0, -2.66E-3,  2.3},
239     {62.486253, 1517.00E-6,  0.078, 14.68E-3, 0.0, -4.77E-3,  0.9},
240     {62.997974, 1503.00E-6,  1.660, 11.39E-3, 0.0, -3.34E-3,  2.2},
241     {63.568515, 1087.00E-6,  2.110, 11.08E-3, 0.0, -4.17E-3,  2.0},
242     {64.127764,  733.50E-6,  2.620, 10.78E-3, 0.0, -4.48E-3,  2.0},
243     {64.678900,  463.50E-6,  3.190, 10.50E-3, 0.0, -5.10E-3,  1.8},
244     {65.224067,  274.80E-6,  3.810, 10.20E-3, 0.0, -5.10E-3,  1.9},
245     {65.764769,  153.00E-6,  4.480, 10.00E-3, 0.0, -5.70E-3,  1.8},
246     {66.302088,   80.09E-6,  5.220,  9.70E-3, 0.0, -5.50E-3,  1.8},
247     {66.836827,   39.46E-6,  6.000,  9.40E-3, 0.0, -5.90E-3,  1.7},
248     {67.369595,   18.32E-6,  6.840,  9.20E-3, 0.0, -5.60E-3,  1.8},
249     {67.900862,    8.01E-6,  7.740,  8.90E-3, 0.0, -5.80E-3,  1.7},
250     {68.431001,    3.30E-6,  8.690,  8.70E-3, 0.0, -5.70E-3,  1.7},
251     {68.960306,    1.28E-6,  9.690,  8.60E-3, 0.0, -5.60E-3,  1.7},
252     {69.489021,    0.47E-6, 10.720,  8.50E-3, 0.0, -5.60E-3,  1.7},
253     {70.017342,    0.16E-6, 11.830,  8.40E-3, 0.0, -5.60E-3,  1.7},
254     {118.750341,  945.00E-6,  0.000, 15.92E-3, 0.0, -0.44E-3,  0.9},
255     {368.498350,   67.90E-6,  0.020, 19.20E-3, 0.6,  0.00E00,  1.0},
256     {424.763120,  638.00E-6,  0.011, 19.16E-3, 0.6,  0.00E00,  1.0},
257     {487.249370,  235.00E-6,  0.011, 19.20E-3, 0.6,  0.00E00,  1.0},
258     {715.393150,   99.60E-6,  0.089, 18.10E-3, 0.6,  0.00E00,  1.0},
259     {773.838730,  671.00E-6,  0.079, 18.10E-3, 0.6,  0.00E00,  1.0},
260     {834.145330,  180.00E-6,  0.079, 18.10E-3, 0.6,  0.00E00,  1.0}};
261     
262  // convert to the units of Liebe
263  const double theta = 300./temperature;
264  const double kPaPVap = 0.001*pVapour;
265  const double kPaPDry = 0.001*pDry;
266  const double fGHz = freq * 1e-9;
267 
268  // some coefficients
269  const double ap = 1.4e-10*(1-1.2e-5*std::pow(fGHz,1.5));
270  const double gamma0 = 5.6e-3*(kPaPDry + 1.1*kPaPVap)*std::pow(theta,0.8);
271  // initial refractivity
272  std::complex<double> result(2.588*kPaPDry*theta +
273         3.07e-4*(1.0/(1.0+std::pow(fGHz/gamma0,2))-1)*kPaPDry*theta*theta,
274         (2*3.07e-4/(gamma0*(1+std::pow(fGHz/gamma0,2))*(1+std::pow(fGHz/60,2))) +
275          ap*kPaPDry*std::pow(theta,2.5))*fGHz*kPaPDry*theta*theta);
276         
277  // sum the contributions of all the lines
278  for (size_t l = 0; l < nLines; ++l) {
279       const double S = lines[l][1]*kPaPDry*std::pow(theta,3)*exp(lines[l][2]*(1.-theta));
280       const double gamma = lines[l][3]*(kPaPDry*std::pow(theta,0.8-lines[l][4]) + 1.1*kPaPVap*theta);
281       const double delta = lines[l][5]*kPaPDry*std::pow(theta,lines[l][6]);
282       const double x = (lines[l][0]-fGHz)*(lines[l][0]-fGHz) + gamma*gamma;
283       const double y = (lines[l][0]+fGHz)*(lines[l][0]+fGHz) + gamma*gamma;
284       const double z = (lines[l][0]+gamma*gamma/lines[l][0]);
285       result += std::complex<double> (S*( (z-fGHz)/x + (z+fGHz)/y - 2./lines[l][0] +
286                                  delta*(1/x-1/y)*gamma*fGHz/lines[l][0]),
287               S*( (1/x+1/y)*gamma*fGHz/lines[l][0] -
288               delta*((lines[l][0]-fGHz)/x + (lines[l][0]+fGHz)/y)*fGHz/lines[l][0]));       
289  }
290 
291  return result;
292}
293
294/**
295 * Compute the complex refractivity of the water vapour monomers
296 * at the given frequency.
297 * @param[in] freq frequency (Hz)
298 * @param[in] temperature air temperature (K)
299 * @param[in] pDry partial pressure of dry components (Pascals)
300 * @param[in] pVapour partial pressure of water vapour (Pascals)
301 * @return complex refractivity
302 *
303 * Reference:
304 * Liebe, An updated model for millimeter wave propogation in moist air,
305 * Radio Science, 20, 1069-1089 (1985).
306 **/
307std::complex<double> STAtmosphere::vapourRefractivity(double freq, double temperature,
308                     double pDry, double pVapour)
309{
310  // the number of parameters per atmospheric line and the number of lines taken into account
311  const size_t nLineParams = 4;
312  const size_t nLines = 30;
313  // actual tabulated values
314  const double lines[nLines][nLineParams] =
315    {{22.235080,  0.1090, 2.143, 27.84E-3},
316     {67.813960,  0.0011, 8.730, 27.60E-3},
317     {119.995940,  0.0007, 8.347, 27.00E-3},
318     {183.310117,  2.3000, 0.653, 28.35E-3},
319     {321.225644,  0.0464, 6.156, 21.40E-3},
320     {325.152919,  1.5400, 1.515, 27.00E-3},
321     {336.187000,  0.0010, 9.802, 26.50E-3},
322     {380.197372, 11.9000, 1.018, 27.60E-3},
323     {390.134508,  0.0044, 7.318, 19.00E-3},
324     {437.346667,  0.0637, 5.015, 13.70E-3},
325     {439.150812,  0.9210, 3.561, 16.40E-3},
326     {443.018295,  0.1940, 5.015, 14.40E-3},
327     {448.001075, 10.6000, 1.370, 23.80E-3},
328     {470.888947,  0.3300, 3.561, 18.20E-3},
329     {474.689127,  1.2800, 2.342, 19.80E-3},
330     {488.491133,  0.2530, 2.814, 24.90E-3},
331     {503.568532,  0.0374, 6.693, 11.50E-3},
332     {504.482692,  0.0125, 6.693, 11.90E-3},
333     {556.936002, 510.000, 0.114, 30.00E-3},
334     {620.700807,  5.0900, 2.150, 22.30E-3},
335     {658.006500,  0.2740, 7.767, 30.00E-3},
336     {752.033227, 250.000, 0.336, 28.60E-3},
337     {841.073593,  0.0130, 8.113, 14.10E-3},
338     {859.865000,  0.1330, 7.989, 28.60E-3},
339     {899.407000,  0.0550, 7.845, 28.60E-3},
340     {902.555000,  0.0380, 8.360, 26.40E-3},
341     {906.205524,  0.1830, 5.039, 23.40E-3},
342     {916.171582,  8.5600, 1.369, 25.30E-3},
343     {970.315022,  9.1600, 1.842, 24.00E-3},
344     {987.926764, 138.000, 0.178, 28.60E-3}};
345
346  // convert to the units of Liebe
347  const double theta = 300./temperature;
348  const double kPaPVap = 0.001*pVapour;
349  const double kPaPDry = 0.001*pDry;
350  const double fGHz = freq * 1e-9;
351 
352  // initial refractivity
353  std::complex<double> result(2.39*kPaPVap*theta + 41.6*kPaPVap*theta*theta +
354            6.47e-6*std::pow(fGHz,2.05)*kPaPVap*std::pow(theta,2.4),
355            (0.915*1.40e-6*kPaPDry + 5.41e-5*kPaPVap*theta*theta*theta)*
356             fGHz*kPaPVap*std::pow(theta,2.5));
357             
358  // sum contributions of all the lines
359  for (size_t l = 0; l < nLines; ++l) {
360       const double S = lines[l][1]*kPaPVap*std::pow(theta,3.5)*exp(lines[l][2]*(1.-theta));
361       const double gamma = lines[l][3]*(kPaPDry*std::pow(theta,0.8) + 4.80*kPaPVap*theta);
362       const double x = (lines[l][0]-fGHz)*(lines[l][0]-fGHz) + gamma*gamma;
363       const double y = (lines[l][0]+fGHz)*(lines[l][0]+fGHz) + gamma*gamma;
364       const double z = (lines[l][0]+gamma*gamma/lines[l][0]);
365       result += std::complex<double>(S*((z-fGHz)/x + (z+fGHz)/y - 2./lines[l][0]),
366                           S*((1./x+1./y)*gamma*fGHz/lines[l][0]));
367  }
368 
369  return result;
370}
371
372/**
373 * Calculate zenith opacity at the given frequency. This is a simplified version
374 * of the routine implemented in MIRIAD, which calculates just zenith opacity and
375 * nothing else. Note, that if the opacity is high, 1/sin(el) law is not correct
376 * even in the plane parallel case due to refraction.
377 * @param[in] freq frequency of interest in Hz
378 * @return zenith opacity (nepers, i.e. dimensionless)
379 **/
380double STAtmosphere::zenithOpacity(double freq) const
381{
382  // essentially a numerical integration with the Trapezium method
383  double tau = 0.;
384  for (int layer = int(nLayers()) - 1; layer>=0; --layer) {
385       double dH = 0.;
386       if (layer == 0) {
387           dH = 0.5*(itsHeights[1]-itsHeights[0]);
388       } else if (layer + 1 == int(nLayers())) {
389           dH = 0.5*(itsHeights[nLayers()-1]-itsHeights[nLayers()-2]);
390       } else {
391           dH = 0.5*(itsHeights[layer+1]-itsHeights[layer-1]);
392       }
393       // imaginary part of the total complex refractivity
394       const double nImag = 1e-6*std::imag(dryRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
395             itsVapourPressures[layer])+vapourRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
396             itsVapourPressures[layer]));
397       tau += dH*4.*casa::C::pi/QC::c.get().getValue()*freq*nImag;
398  }
399  return tau;
400}
401
402/**
403 * Calculate zenith opacity for the range of frequencies. Same as zenithOpacity, but
404 * for a vector of frequencies.
405 * @param[in] freqs vector of frequencies in Hz
406 * @return vector of zenith opacities, one value per frequency (nepers, i.e. dimensionless)
407 **/
408std::vector<double> STAtmosphere::zenithOpacities(const std::vector<double> &freqs) const
409{
410  std::vector<double> result(freqs.size());
411  for (size_t ch = 0; ch<freqs.size(); ++ch) {
412       result[ch] = zenithOpacity(freqs[ch]);
413  }
414  return result;
415}
416
417/**
418 * Calculate opacity at the given frequency and elevation. This is a simplified
419 * version of the routine implemented in MIRIAD, which calculates just the opacity and
420 * nothing else. In contract to zenithOpacity, this method takes into account refraction
421 * and is more accurate than if one assumes 1/sin(el) factor.
422 * @param[in] freq frequency of interest in Hz
423 * @param[in] el elevation in radians
424 * @return zenith opacity (nepers, i.e. dimensionless)
425 **/
426double STAtmosphere::opacity(double freq, double el) const
427{
428  // essentially a numerical integration with the Trapezium method
429  double tau = 0.;
430  const double sineEl = sin(el);
431  for (int layer = int(nLayers()) - 1; layer>=0; --layer) {
432       double dH = 0.;
433       if (layer == 0) {
434           dH = 0.5*(itsHeights[1]-itsHeights[0]);
435       } else if (layer + 1 == int(nLayers())) {
436           dH = 0.5*(itsHeights[nLayers()-1]-itsHeights[nLayers()-2]);
437       } else {
438           dH = 0.5*(itsHeights[layer+1]-itsHeights[layer-1]);
439       }
440       // total complex refractivity
441       const std::complex<double> n = dryRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
442                                                      itsVapourPressures[layer]) +
443                                      vapourRefractivity(freq,itsTemperatures[layer],itsDryPressures[layer],
444                                                      itsVapourPressures[layer]);
445       // real and imaginary part of the total complex refractivity scaled appropriately
446       const double nImag = 1e-6*std::imag(n);
447       const double nReal = 1. + 1e-6*std::real(n);
448       // length increment
449       const double dL = dH*nReal/sqrt(nReal*nReal+sineEl*sineEl-1.);
450       tau += dL*4.*casa::C::pi/QC::c.get().getValue()*freq*nImag;
451  }
452  return tau; 
453}
454
455/**
456 * Calculate opacities for the range of frequencies at the given elevation. Same as
457 * opacity, but for a vector of frequencies.
458 * @param[in] freqs vector of frequencies in Hz
459 * @param[in] el elevation in radians
460 * @return vector of opacities, one value per frequency (nepers, i.e. dimensionless)
461 **/
462std::vector<double> STAtmosphere::opacities(const std::vector<double> &freqs, double el) const
463{
464  std::vector<double> result(freqs.size());
465  for (size_t ch = 0; ch<freqs.size(); ++ch) {
466       result[ch] = opacity(freqs[ch],el);
467  }
468  return result;
469}
470
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