CORRECTTHERMALLAG Correct CTD conductivity and temperature sequence from thermal lag effects.
Syntax:
[TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, COND_INSIDE, TEMP_OUTSIDE, PARAMS)
[TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, COND_INSIDE, TEMP_OUTSIDE, FLOW_SPEED, PARAMS)
Description:
[TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, COND_INSIDE, TEMP_OUTSIDE, PARAMS)
corrects thermal lag in a CTD profile sequence with constant flow speed
(pumped CTD) given by vectors TIMESTAMP (sampe timestamp), COND_INSIDE
(conductivity inside CTD cell) and TEMP_OUTSIDE (temperature outside CTD
cell), returning vectors COND_OUTSIDE (conductivity outside CTD cell) and
TEMP_INSIDE (temperature inside CTD cell). TIMESTAMP, COND_INSIDE,
TEMP_OUTSIDE, COND_OUTSIDE and TEMP_OUTSIDE all have the same dimensions.
The correction parameters are given in a two element vector PARAMS,
with the error magnitude (alpha), and the error time constant (tau).
A detailed description of these parameters may be found in the references
listed below (Lueck 1990).
[TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, DEPTH, PITCH, COND_INSIDE, TEMP_OUTSIDE, PARAMS)
performs the same correction but for a CTD profile with variable flow
speed (unpumped CTD), given by FLOW. FLOW should be a vector with the
same dimensions as COND_INSIDE and TEMP_OUTSIDE, with the flow speed
inside the CTD cell in m/s. The correction parameters are given in a
four element vector PARAMS, with the offset and the slope of the error
magnitude (alpha_o and alpha_s), and the offset and the slope of the
error time constant (tau_o and tau_s). A detailed description of these
parameters may be found in the references listed below (Morison 1994).
Notes:
This function is a recoding of the function by Tomeu Garau with the same
name. He is the true glider man. Main changes are:
- Moved flow speed computation to a separate function COMPUTECTDFLOWSPEED.
- Added support for pumped CTD profiles (constant flow speed).
References:
Garau, B.; Ruiz, S.; G. Zhang, W.; Pascual, A.; Heslop, E.;
Kerfoot, J.; and Tintoré, J.; 2011:
Thermal Lag Correction on Slocum CTD Glider Data.
Journal of Atmospheric and Oceanic Technology, vol. 28, pages 1065-1071.
Morison, J.; Andersen, R.; Larson, N.; D'Asaro, E.; and Boyd, T.; 1994:
The Correction for Thermal-Lag Effects in Sea-Bird CTD Data.
Journal of Atmospheric and Oceanic Technology, vol. 11, pages 1151-1164.
Lueck, R. G.; and Picklo, J. J.; 1990:
Thermal Inertia of Conductivity Cells: Observations with a Sea-Bird cell.
Journal of Atmospheric and Oceanic Technology, vol. 7, pages 756–768.
Lueck, R. G.; 1990:
Thermal Inertia of Conductivity Cells: Theory.
Journal of Atmospheric and Oceanic Technology, vol. 7, pages 741–755.
Examples:
% Constant flow speed (pumped CTD) profile:
[temp_inside, cond_outside] = ...
correctThermalLag(timestamp, cond_inside, temp_outside, params)
% Variable flow speed (unpumped CTD) profile:
[temp_inside, cond_outside] =
correctThermalLag(timestamp, cond_inside, temp_outside, ...
flow_speed, params)
See also:
FINDTHERMALLAGPARAMS
COMPUTECTDFLOWSPEED
Authors:
Joan Pau Beltran <joanpau.beltran@socib.cat>0001 function [temp_inside, cond_outside] = correctThermalLag(varargin) 0002 %CORRECTTHERMALLAG Correct CTD conductivity and temperature sequence from thermal lag effects. 0003 % 0004 % Syntax: 0005 % [TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, COND_INSIDE, TEMP_OUTSIDE, PARAMS) 0006 % [TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, COND_INSIDE, TEMP_OUTSIDE, FLOW_SPEED, PARAMS) 0007 % 0008 % Description: 0009 % [TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, COND_INSIDE, TEMP_OUTSIDE, PARAMS) 0010 % corrects thermal lag in a CTD profile sequence with constant flow speed 0011 % (pumped CTD) given by vectors TIMESTAMP (sampe timestamp), COND_INSIDE 0012 % (conductivity inside CTD cell) and TEMP_OUTSIDE (temperature outside CTD 0013 % cell), returning vectors COND_OUTSIDE (conductivity outside CTD cell) and 0014 % TEMP_INSIDE (temperature inside CTD cell). TIMESTAMP, COND_INSIDE, 0015 % TEMP_OUTSIDE, COND_OUTSIDE and TEMP_OUTSIDE all have the same dimensions. 0016 % The correction parameters are given in a two element vector PARAMS, 0017 % with the error magnitude (alpha), and the error time constant (tau). 0018 % A detailed description of these parameters may be found in the references 0019 % listed below (Lueck 1990). 0020 % 0021 % [TEMP_INSIDE, COND_OUTSIDE] = CORRECTTHERMALLAG(TIMESTAMP, DEPTH, PITCH, COND_INSIDE, TEMP_OUTSIDE, PARAMS) 0022 % performs the same correction but for a CTD profile with variable flow 0023 % speed (unpumped CTD), given by FLOW. FLOW should be a vector with the 0024 % same dimensions as COND_INSIDE and TEMP_OUTSIDE, with the flow speed 0025 % inside the CTD cell in m/s. The correction parameters are given in a 0026 % four element vector PARAMS, with the offset and the slope of the error 0027 % magnitude (alpha_o and alpha_s), and the offset and the slope of the 0028 % error time constant (tau_o and tau_s). A detailed description of these 0029 % parameters may be found in the references listed below (Morison 1994). 0030 % 0031 % Notes: 0032 % This function is a recoding of the function by Tomeu Garau with the same 0033 % name. He is the true glider man. Main changes are: 0034 % - Moved flow speed computation to a separate function COMPUTECTDFLOWSPEED. 0035 % - Added support for pumped CTD profiles (constant flow speed). 0036 % 0037 % References: 0038 % Garau, B.; Ruiz, S.; G. Zhang, W.; Pascual, A.; Heslop, E.; 0039 % Kerfoot, J.; and Tintoré, J.; 2011: 0040 % Thermal Lag Correction on Slocum CTD Glider Data. 0041 % Journal of Atmospheric and Oceanic Technology, vol. 28, pages 1065-1071. 0042 % 0043 % Morison, J.; Andersen, R.; Larson, N.; D'Asaro, E.; and Boyd, T.; 1994: 0044 % The Correction for Thermal-Lag Effects in Sea-Bird CTD Data. 0045 % Journal of Atmospheric and Oceanic Technology, vol. 11, pages 1151-1164. 0046 % 0047 % Lueck, R. G.; and Picklo, J. J.; 1990: 0048 % Thermal Inertia of Conductivity Cells: Observations with a Sea-Bird cell. 0049 % Journal of Atmospheric and Oceanic Technology, vol. 7, pages 756–768. 0050 % 0051 % Lueck, R. G.; 1990: 0052 % Thermal Inertia of Conductivity Cells: Theory. 0053 % Journal of Atmospheric and Oceanic Technology, vol. 7, pages 741–755. 0054 % 0055 % Examples: 0056 % % Constant flow speed (pumped CTD) profile: 0057 % [temp_inside, cond_outside] = ... 0058 % correctThermalLag(timestamp, cond_inside, temp_outside, params) 0059 % % Variable flow speed (unpumped CTD) profile: 0060 % [temp_inside, cond_outside] = 0061 % correctThermalLag(timestamp, cond_inside, temp_outside, ... 0062 % flow_speed, params) 0063 % 0064 % See also: 0065 % FINDTHERMALLAGPARAMS 0066 % COMPUTECTDFLOWSPEED 0067 % 0068 % Authors: 0069 % Joan Pau Beltran <joanpau.beltran@socib.cat> 0070 0071 % Copyright (C) 2013-2016 0072 % ICTS SOCIB - Servei d'observacio i prediccio costaner de les Illes Balears 0073 % <http://www.socib.es> 0074 % 0075 % This program is free software: you can redistribute it and/or modify 0076 % it under the terms of the GNU General Public License as published by 0077 % the Free Software Foundation, either version 3 of the License, or 0078 % (at your option) any later version. 0079 % 0080 % This program is distributed in the hope that it will be useful, 0081 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0082 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0083 % GNU General Public License for more details. 0084 % 0085 % You should have received a copy of the GNU General Public License 0086 % along with this program. If not, see <http://www.gnu.org/licenses/>. 0087 0088 error(nargchk(4, 5, nargin, 'struct')); 0089 0090 % Parse input arguments. 0091 switch(nargin) 0092 case 4 0093 % Constant flow speed (pumped CTD). 0094 [timestamp, cond_inside, temp_outside, params] = ... 0095 varargin{1:4}; 0096 constant_flow = true; 0097 case 5 0098 % Variable flow speed (unpumped CTD). 0099 [timestamp, cond_inside, temp_outside, flow_speed, params] = ... 0100 varargin{1:5}; 0101 constant_flow = false; 0102 end 0103 0104 if constant_flow 0105 % Select full CTD rows 0106 % The positive time test is needed to deal with odd data from initial 0107 % lines in Slocum segment files. 0108 valid = (timestamp(:) > 0) ... 0109 & ~any(isnan([cond_inside(:) temp_outside(:)]), 2); 0110 time_val = timestamp(valid); 0111 temp_val = temp_outside(valid); 0112 cond_val = cond_inside(valid); 0113 % Extract parameter values: 0114 alpha = params(1); 0115 tau = params(2); 0116 else 0117 % Select full CTD rows 0118 % The positive time test is needed to deal with odd data from initial 0119 % lines in Slocum segment files. 0120 valid = (timestamp(:) > 0) ... 0121 & ~any(isnan([cond_inside(:) temp_outside(:) flow_speed(:)]), 2); 0122 time_val = timestamp(valid); 0123 temp_val = temp_outside(valid); 0124 cond_val = cond_inside(valid); 0125 flow_val = flow_speed(valid); 0126 % Extract parameter values: 0127 alpha_offset = params(1); 0128 alpha_slope = params(2); 0129 tau_offset = params(3); 0130 tau_slope = params(4); 0131 % Compute dynamic thermal error and error time parameters for variable flow 0132 % speed. The formula is given in the references above (Morison 1994). 0133 alpha = alpha_offset + alpha_slope ./ flow_val(1:end-1); 0134 tau = tau_offset + tau_slope ./ sqrt(flow_val(1:end-1)); 0135 end 0136 0137 0138 % Compute the coefficients of the correction formula. 0139 % Definitions in references use the Nyquist frequency (half the sampling 0140 % frequency). This might be wrong in the original implementation by Tomeu 0141 % Garau, where the sampling frequency was used. 0142 % These are three equivalent formulas for coefficients. 0143 dtime = diff(time_val); 0144 % sampling_freq = 1 ./ dtime; 0145 % nyquist_freq = 0.5 * sampling_freq; 0146 % coefa = alpha .* (4 * nyquist_freq .* tau) ./ (1 + 4 * nyquist_freq .* tau); 0147 % coefb = 1 - 2 * (4 * nyquist_freq .* tau) ./ (1 + 4 * nyquist_freq .* tau); 0148 % coefa = 2 * alpha ./ (2 + dtime .* beta); % from SBE Data Processing. 0149 % coefb = 1 - 2 .* coefa ./ alpha; 0150 coefa = 2 * alpha ./ (2 + dtime ./ tau); % same using tau instead of beta. 0151 coefb = 1 - 4 ./ (2 + dtime ./ tau); 0152 0153 0154 % Compute the sensitivity of conductivity with respect to temperature. 0155 % Approximation suggested by SeaBird at section 6 of SBE Data Processing 0156 % User's Manual: Data Processing Modules, Cell Thermal Mass. 0157 % Software Release 7.16a and later. Date: 01/18/08 0158 % dc_dt = 0.1 .* (1 + 0.006 .* (temp - 20)); 0159 dcond_dtemp = (0.088 + 0.0006 * temp_val); 0160 0161 % Compute auxiliary vector of consecutive temperature differences. 0162 dtemp = diff(temp_val); 0163 0164 % Compute conductivity and temperature correction using the recursive formula 0165 % proposed in references. Loop unfolding seems impractical. 0166 cond_correction = zeros(size(time_val)); 0167 temp_correction = zeros(size(time_val)); 0168 for n = 1:numel(time_val)-1, 0169 % Compute corrections for next depth level. 0170 cond_correction(n+1) = ... 0171 - coefb(n) * cond_correction(n) + coefa(n) * dcond_dtemp(n) * dtemp(n); 0172 temp_correction(n+1) = ... 0173 - coefb(n) * temp_correction(n) + coefa(n) * dtemp(n); 0174 end 0175 0176 % Apply corrections to valid values in original sequences, 0177 % preserving invalid values in the output. 0178 temp_inside = nan(size(timestamp)); 0179 cond_outside = nan(size(timestamp)); 0180 temp_inside(valid) = temp_val - temp_correction; 0181 cond_outside(valid) = cond_val + cond_correction; 0182 0183 end