Thermal Lag problems in Slocum CTDs

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Thermal Lag problems in Slocum CTDs a MATLab
correction algorithm(OR why does our salinity
data have so many outliers?)
Charlie Bishop PhD Candidate Memorial University
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Upcast vs. Downcast

• Hypothesis The profiles (Temp, Salinity) of
  consecutive downcast and upcast should be the
  same.

Reality Mismatching of down/upcast
profiles. Source Thermal Lag in conductivity
cell. Corrections Methods by Lueck Picklo
(1990) and Morison et al (1994) to correct for
thermal lag.
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The Problem

• During the Slocum's downcast, the probe moves
  from warm to cold waters through a sharp
  thermocline. As it is lowered, the heat stored in
  the sensor body diffuses into the water being
  sampled in the vicinity of the conductivity
  sensor, artificially raising conductivity, and
  consequently salinity. Conversely, when the probe
  moves upward from cold to warm waters,
  conductivity and salinity are artificially
  lowered.
• The existence of a systematic offset in salinity
  between down and upcast is in agreement with the
  theory of thermal-lag affecting SBE CTDs crossing
  sharp temperature gradients. Much work has been
  done to attempt to resolve the thermal-lag
  problem

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Salinity spiking in our SBE19 CTD
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Correcting for Thermal Lag in Conductivity Cell
Using a recursive filter as applied by Morrison
et al (1994) to estimate the temperature inside
the conductivity cell
T(n) -bTn-1 a(Tn Tn-1)
where T is the corrected temperature inside the
cell, n is the sample index, and the constants a
and b are given by
a 4fnat/(1 4fnt) b 1 2a/a
where fn is the Nyquist frequency
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Some Definitions

• Alpha initial magnitude of the thermal fluid
  anomaly.
• Tau relaxation time constant of the error
• Nyquist frequency half the sampling frequency
  of a discrete signal processing system. It is
  sometimes called the folding frequency, or the
  cut-off frequency of a sampling system.

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MATlab algorithm

• First developed by Morison/Lueck et al (1990s).
• Adapted to ARGO profilers by Johnson et al
  (2006).
• Adapted by Bishop et al. (Me!) for Slocum glider
  CTDS (2007)
• Matlab file called thermallagcorrection.m (will
  be added to the website)

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MATlab algorithm

• function temp_for_salinity_calculationthermallagc
  orrection(temp,alpha,tau,nyquist)
• algorithm to correct for thermal lag in
  conductivity. based on morison et al (1994)
• usage temp_for_salinity_calculationthermalla
  gcorrection(temp,alpha,tau,nyquist)
• you must specify alpha, tau and the nyquist.
• the output "temp_for_salinity_calculation"
  can then be used with conductivity values
• for new salinity calculations
• a(4nyquistalphatau)/(1(4nyquisttau)) a
  and b are parameters for the correction
• b1-(2a)/alpha
• initialize so that it dosnt grow inside the
  loop. save a lot of time
• temp_correctionzeros(length(temp),1)
• for i2length(temp) the main loop
• temp_correction(i)-btemp_correction(i-1)a(temp
  (i)-temp(i-1))
• end

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How to use it

• 1st calculate a new temperature data set, use the
  function like so
• temp_for_salinity_calculationthermallagcorrecti
  on(temp,alpha,tau,nyquist)
• 2nd the output "temp_for_salinity_calculation"
  can then be used with original conductivity
  values for new salinity calculations using the
  seamat toolbox like us
• Salinity sw_salt(cond,T,P)
• where T is our new temperature values, P is
  pressure and cond is conductivity

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Wait a secondWhat are our values for Alpha and
Tau? You tell me!

• We can create an iterative loop in Matlab to vary
  values of alpha and tau.
• For every combination of alpha and tau, we can
  correct temperature series, calculate salinity,
  and then compare the downcast temperature to
  upcast temperature using an RMS calculation.
• Or we can use standard literature values,
  calculated for a SBE25 instrument
• Alpha_sbe25 0.028 deg C, Tau_sbe25 10 s
• For comparison, glider values were
• Alpha_glider 0.11 deg C, Tau_glider 7.12 s

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Another method to calculate Alpha and Tau

• Both Lueck and Picklo and Morison et al. state
  that empirical formulas can be used to calculate
  values for alpha and tau in cases where it is
  difficult to determine them directly. These
  formulas were based on data gathered from a SBE9
  CTD and the equations are

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If it actually works we get this
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References

• Gregory C. Johnson, John M. Toole, and Nordeen G.
  Larson. Sensor Corrections for Sea-Bird SBE-41CP
  and SBE-41 CTDs. Journal of Atmospheric and
  Oceanic Technology, 241117-1130, June 2007.
• E.P. Horne and J.M. Toole. Sensor response
  mismatches and lag correction techniques for
  temperature-salinity profilers. Journal of
  Physical Oceanography, 101122-1130, 1980.
• J. Morison, R. Andersen, N. Larson, E. D'Asaro,
  and T. Boyd. The Correction for thermal-lag
  effects in Sea-Bird CTD data. Journal of
  Atmospheric and Oceanic Technology, 111151-1164,
  1994.
• Rolf G. Lueck and James J. Picklo. Thermal
  Inertia of Conductivity Cells Observations with
  a Sea-Bird Cell. Journal of Atmospheric and
  Oceanic Technology, 7756-768, 1990.

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