Fixed the full integration methods

atmosphericModel.py

@@ -1,7 +1,7 @@
 #!/usr/bin/env Python3
 import numpy as np
 from scipy import integrate
-
+from pdb import set_trace
 
 '''
 @ Author:		Joost van den Born 
@@ -755,6 +755,7 @@ class dispersion(Observatory):
 			different atmosphere layers.
 			Recommended use with the US Standard Atmosphere from 1976.
 			USSA1976 data generated from code supplied by http://www.pdas.com/atmos.html
+			The method described in eq. 3 in Auer & Standish (2000) is used for the calculation.
 		'''
 		if not R0:
 			R0 = self.rc
@@ -770,19 +771,26 @@ class dispersion(Observatory):
 		
 		# Integration of the refraction integral over the atmosphere layers.
 		for _n in [n1, n2]:
+			_Dens 	= np.asarray(_Dens)
+			_h 	 	= np.asarray(_h) 
+			_R 		= R0 + _h * 1000
 			
-			_refractionIntegralList = []
-			_nList 					= []
+			# Gladstone-Dale relation between refractive index and density
+			_n_h = 1 + (_n - 1) / _Dens[0] * _Dens 
 
-			for _i in range(len(_h)):
-				_R 	 = R0 + _h[_i]*1000
-				_n_h = 1 + (_n - 1) / _Dens[0] * _Dens[_i] # Gladstone-Dale relation between refractive index and density
-				_nList.append(_n_h)
-				_refractionIntegralList.append( (_n * R0 * np.sin(z0))/(_n_h*np.sqrt((_n_h*_R)**2 - (_n * R0 * np.sin(z0))**2 )) )
-			_dn = (_nList[0] - _nList[-1]) / ((len(_h)-1))
+			# Calculation of the zenith angle for given height and refractive index, from the refractive invariant
+			_z 		= np.arcsin( (_n * R0) / (_n_h * _R) * np.sin(z0) )
 			
-			_rList.append(np.sum(np.degrees(np.asarray(_refractionIntegralList) * _dn)))
+			# Calculation of log space derivative of n and r
+			_lnn = np.log(_n_h)
+			_lnr = np.log(_R)
+			_dlnn = np.asarray([_lnn[i+1] - _lnn[i] for i in range(len(_lnn)-1)])
+			_dlnr = np.asarray([_lnr[i+1] - _lnr[i] for i in range(len(_lnr)-1)])
+			_dz   = np.asarray([(_z[i] - _z[i+1]) for i in range(len(_z)-1)])
 
+			# Calculation of the integrand in eq. 3 in Auer & Standish
+			_Integrand = -1*(_dlnn/_dlnr) / (1 + _dlnn/_dlnr) * _dz
+			_rList.append(np.degrees(np.sum(_Integrand)))
 		return _rList[0] - _rList[1]
 
 
@@ -1182,19 +1190,29 @@ class refraction(Observatory):
 			_Dens = rhoData
 			_h 	  = heightData
 
-		_refractionIntegralList = []
-		_nList 					= []
 		z0 						= np.deg2rad(z0)
+		_Dens 	= np.asarray(_Dens)
+		_h 	 	= np.asarray(_h) 
+		_R 		= R0 + _h * 1000
 		
-		# Integration of the refraction integral over the atmosphere layers.
-		for _i in range(len(_h)):
-			_R 	 = R0 + _h[_i]*1000
-			_n_h = 1 + (n0 - 1) / _Dens[0] * _Dens[_i] # Gladstone-Dale relation between refractive index and density
-			_nList.append(_n_h)
-			_refractionIntegralList.append( (n0 * R0 * np.sin(z0))/(_n_h*np.sqrt((_n_h*_R)**2 - (n0 * R0 * np.sin(z0))**2 )) )
-		_dn = (_nList[0] - _nList[-1]) / ((len(_h)-1))
+		# Gladstone-Dale relation between refractive index and density
+		_n_h = 1 + (n0 - 1) / _Dens[0] * _Dens 
 
-		return np.sum(np.degrees(np.asarray(_refractionIntegralList) * _dn))
+		# Calculation of the zenith angle for given height and refractive index, from the refractive invariant
+		_z 		= np.arcsin( (n0 * R0) / (_n_h * _R) * np.sin(z0) )
+		
+		# Calculation of log space derivative of n and r
+		_lnn = np.log(_n_h)
+		_lnr = np.log(_R)
+		_dlnn = np.asarray([_lnn[i+1] - _lnn[i] for i in range(len(_lnn)-1)])
+		_dlnr = np.asarray([_lnr[i+1] - _lnr[i] for i in range(len(_lnr)-1)])
+		_dz   = np.asarray([(_z[i] - _z[i+1]) for i in range(len(_z)-1)])
+
+		# Calculation of the integrand in eq. 3 in Auer & Standish
+		_Integrand = -1*(_dlnn/_dlnr) / (1 + _dlnn/_dlnr) * _dz
+
+
+		return np.degrees(np.sum(_Integrand))