Gouretski and Koltermann (2007) shows statistics from Expendable Bathythermograph (XBT) vs. ConductivityTemperatureDepth (CTD)/reversing thermometer instrument comparisons which reveal a warm bias in XBT temperatures. This bias varies over time and depths, and may be due to both errors in the calculation of depth and in measurement of the temperature. An important deviation from the majority of existing correction schemes is that depth correction varies with depth.
Workshops and Reports
 A NOAA sponsored XBT Fall Rate Workshop was held in Miami, FL, March 1012, 2008 to discuss this problem. Results of that meeting came to no conclusion as to the best way to correct the bias.
 A second XBT Fall Rate Workshop was held August 2527, 2010 in Hamburg, Germany.
 The First XBT Science Workshop (XSW1) was held in Melbourne, Australia, July 78, 2011. Information on the meeting and presentations from the meeting*
Publications
A number of papers with estimates of corrections have been published or submitted to scientific journals. The corrections proposed in some of these works are provided here to facilitate intercomparison by the scientific community. The corrections proposed by Gouretski and Koltermann (2007) are not included here, as they have been superseded by the corrections proposed by Gouretski and Reseghetti (2010).
 Gouretski, V. V., and K. P. Koltermann, 2007, How much is the ocean really warming? Geophysical Research Letters, L01610, doi:10.1029/2006GL027834
 Wijffels, Susan E., Josh Willis, Catia M. Domingues, Paul Barker, Neil J. White, Ann Gronell, Ken Ridgway, John A. Church, 2008: Changing Expendable Bathythermograph Fall Rates and Their Impact on Estimates of Thermosteric Sea Level Rise. J. Climate, 21, 56575672. doi: http://dx.doi.org/10.1175/2008JCLI2290.1 Wijffels et al. depth corrections: Table 1 (in situ comparison), Table 2 (in situaltimeter comparison).
 Ishii, M. and M. Kimoto, 2009: Reevaluation of Historical Ocean Heat Content Variations With An XBT depth bias Correction. J. Oceanogr. 65, 287299, doi:10.1007/s1087200900277. Ishii and Kimoto depth corrections. New corrections in conjunction with version 6.12* analysis of ocean temperature and salinity.
 Levitus, S, J. Antonov, T. Boyer, Global ocean heat content 19552007 in light of recently revealed instrumentation problems (Geophys. Res. Lett. , 36, L07608, doi:10.1029/2008GL037155). Levitus et al. temperature corrections; updated temperature corrections: September, 2010; April, 2011; July, 2019
 Gouretski, V. and F. Reseghetti, 2010, On depth and temperature biases in bathythermograph data: Development of a new correction scheme based on analysis of a global ocean database. DeepSea Research I, Vol. 57(6), pp. 812834, doi:10.1016/j.dsr.2010.03.011
 Good, S.A, 2011,Depth biases in XBT data diagnosed using Bathymetry data ,Journal of Atmospheric and Oceanic Technology, 28, 287300, doi: 10.1175/2010JTECHO773.1 Good depth corrections
 Hamon, M., G. Reverdin, PY Le Traon, 2012, Empirical correction of XBT data. Journal of Atmospheric and Oceanic Technology, doi:10.1175/JTECHD1100129.1, in press. Hamon et al. depth and temperature corrections
 Gouretski, V., 2012, Using GEBCO digital bathymetry to infer depth biases in the XBT data, Deep Sea ResearchI, 62,4052. Gouretski depth and temperature corrections
 Cowley, R., S. Wijffels, L. Cheng, T. Boyer, S. Kizu: Biases in Expendable BathyThermograph data: a new view based on historical sidebyside comparisons, Journal of Atmospheric and Oceanic Technology, 30, 11951225, doi:10.1175/JTECHD1200127.1. XBT pairs database used in study.
 Lijing Cheng, Jiang Zhu, Rebecca Cowley, Tim Boyer, and Susan Wijffels, 2014: Time, Probe Type, and Temperature Variable Bias Corrections to Historical Expendable Bathythermograph Observations. J. Atmos. Oceanic Technol., 31, 17931825, doi:10.1175/JTECHD1300197.1. Note: original CH14table1, CH14table2. Updated CH14table2 February 15, 2017 (personal communication L. Cheng). Updated CH14table1, CH14table2, coefficients for T5 added, June 28, 2017 (personal communication L. Cheng).
Correction Methods
XBT probe types T4/T6, T7/deep blue and T5
Temperature
T(corrected) = T(xbt)  thermal_bias
The values of thermal bias for T7/DB, T4/T6, and T5 are provided in table 1, table 2, and table 3 respectively.
Depth
Z(corrected) = Z(xbt) * stretch_factor
The stretch values for T7/DB and T4/T6 at 1m depth interval is provided in table 4, table 5, and table 6 respectively.
XBT probe type T10
Temperature
T(corrected) = T(xbt)  thermal_bias
Depth
Z(corrected) = Z(xbt)  depth_bias
Where, depth_bias = 1* (coeff1+coeff2*Z(xbt))
The values of coeff1, coeff2 and thermal_bias for T10 probe are provided in table 7.
Gouretski and Reseghetti Correction Steps
Step 1
All XBT sample depths are recomputed (if necessary) according to the SIPPICAN FRE
Step 2
XBT observed temperature is corrected for thermal bias according to the time (year) of the observation (see thermal_bias correction files)
Tcorrected = Tobserved  Thermal_Bias
Step 3
Depth correction factor ("stretching") is calculated using the following formula (as in Gouretski and Reseghetti, 2010, but with different numerical values of the coefficients).
nominal_stretching(Z) = b + a/Z  c*Z**2
For numerical values of a, b, and c see stretching parameter files.
Step 4
This "nominal" depthdepending stretching factor is further modified depending on the deviation of the XBTprofile mean temperature (tmean_profile) from the "nominal" mean temperature (tmean_nominal). (Values of tmean_nominal are given in mean_temperature files).
Here mean temperature refers to the mean temperature within the respective layer between the ocean surface and the sample depth (Z) for which the correction is calculated.
delta = tmean_profile(Z)  tmean_nominal(Z)
final_stretching (Z) = nominal_stretching(Z) + delta*0.0015
Step 5
"Observed" (Sippican) XBT sample depth is now finally corrected:
Z_corrected = Z*final_stretching(Z)
V. Gouretski, 31 May 2010, KlimaCampus, Hamburg
Thermal Gradient Correction Steps
Step 1: Identify appropriate correction
Corrections are provided for T4/T6 (Sippican), T7/Deep Blue (Sippican), TSK T6 and TSK T7/Deep Blue.
If the manufacturer is not given the deploying country and year of deployment and maximum depth should be used to identify probe type.
Deploying Country
TSK types are applied to: Japan, Taiwan, Korea, Thailand, China. All other countries are designated Sippican.
Table 1 contains the information on earliest to market and depth cutoffs for each probe type.
Probe Type  Earliest Date to Market (dd/mm/yyyy)  Nominal Depth (m)  Depth Cutoff (m)  Approximate Percentage in WOD09 (of Total XBTs) 

Sippican T4  6/14/1965  460  550  49.00% 
Sippican T6  4/14/1968  460  550  
Sippican T7  6/20/1967  760  950  29.70% 
Sippican Deep Blue  4/20/1981  760  950  
TSK T6  7/1/1972  460  550  12.40% 
TSK T7  4/1/1978  760  950  1.10% 
TSK Deep Blue  8/1/1997  760  950  
Other Types (No Corrections Supplied):  
Sippican T5  6/3/1971  1830  2500  0.80% 
Sippican Fast Deep  9/25/1991  1000  2500  0.25% 
Sippican T10  3/24/1972  200  350  5.50% 
TSK T10  1/1/1979  200  350  
TSK T5  8/1/1971  1000  2500  0.07% 
Probes designated TSK T4 use TSK T6 (TSK does not make T4s). All Sparton XBTs use Sippican corrections.
In the paper, the following additional corrections were applied to other probe types for the Global Ocean Heat Content (GOHC) calculation:
Where a correction was not available for a particular year, T4/T6 corrections were used for T7/DB probes and vice versa for Sippican types. The equivalent Sippican correction was used for TSK types. Sippican T4/T6 corrections were applied to all T10, T11, and unknown types with terminal depth < 550 m. Sippican T7/DB corrections were applied to Sippican Fast Deeps and unknown types with terminal depth ›= 550 m and < than 1005m. Corrections were not applied to T5s or to probes with depths ›= 1005m. XBT data from 1996 to the present with no depth equation information were not included in the GOHC calculation.
Step 2
Convert to Hanawa (1995) fall rates if required.
Step 3
Apply the corrections:
Cowley thermal gradient (TG) corrections:
Z(corrected) = (Z(Hanawa)*(1  Depth_error_slope))  Depth_error_offset
T(corrected) = T(original)  Thermal_bias
Where Z(Hanawa) is obtained by applying the Hanawa correction to the observed depth and T(original) is the observed temperature.
 Depth error slope is provided in Original Table 2 and 2014 Updated Table 2 for different probe types for the years 19672010.
 Depth error offset is provided in Original Table 3 and 2014 Updated Table 3 for different probe types for the years 19672010.
 Thermal bias is provided in Original Table 4 and 2014 Updated Table 4 for different probe types for the years 19672010.
Cheng Correction Steps
Step 1: Identify appropriate correction
Corrections are provided for T4/T6 (Sippican), T7/Deep Blue (Sippican), TSK T6 and TSK T7/Deep Blue.
If the manufacturer is not given the deploying country and year of deployment and maximum depth should be used to identify probe type.
Deploying Country
TSK types are applied to: Japan, Taiwan, Korea, Thailand, China. All other countries are designated Sippican.
Table 1 contains the information on earliest to market and depth cutoffs for each probe type.
Probe Type  Earliest Date to Market (dd/mm/yyyy)  Nominal Depth (m)  Depth Cutoff (m)  Approximate Percentage in WOD09 (of Total XBTs) 

Sippican T4  6/14/1965  460  550  49.00% 
Sippican T6  4/14/1968  460  550  
Sippican T7  6/20/1967  760  950  29.70% 
Sippican Deep Blue  4/20/1981  760  950  
TSK T6  7/1/1972  460  550  12.40% 
TSK T7  4/1/1978  760  950  1.10% 
TSK Deep Blue  8/1/1997  760  950  
Other Types (No Corrections Supplied):  
Sippican T5  6/3/1971  1830  2500  0.80% 
Sippican Fast Deep  9/25/1991  1000  2500  0.25% 
Sippican T10  3/24/1972  200  350  5.50% 
TSK T10  1/1/1979  200  350  
TSK T5  8/1/1971  1000  2500  0.07% 
Probes designated TSK T4 use TSK T6 (TSK does not make T4s). All Sparton XBTs use Sippican corrections.
In the paper, the following additional corrections were applied to other probe types for the Global Ocean Heat Content (GOHC) calculation:
Where a correction was not available for a particular year, T4/T6 corrections were used for T7/DB probes and vice versa for Sippican types. The equivalent Sippican correction was used for TSK types. Sippican T4/T6 corrections were applied to all T10, T11, and unknown types with terminal depth < 550 m. Sippican T7/DB corrections were applied to Sippican Fast Deeps and unknown types with terminal depth ›= 550 m and < than 1005m. Corrections were not applied to T5s or to probes with depths ›= 1005m. XBT data from 1996 to the present with no depth equation information were not included in the GOHC calculation.
Step 2
Convert to Hanawa (1995) fall rates if required.
Step 3
Apply the corrections
Cowley et al Cheng Corrections
Back calculate time from depth, t = q  (q2  z/bh)0.5
Where q = ah/(2 * bh) and time t is in seconds.
And ah,bh are the fall rate coefficients used (Hanawa : ah = 6.691, bh = 2.25x103)
Z(corrected) = a*t  b*t2  c
Where a,b are provided in Table 2, Table 3, and c which is the depth offset term is provided in Table 4.
T(corrected) = T(original)  Thermal_bias
Thermal _bias for Cheng corrections is provided in Table 5.
CH14 Method Steps

Recalculates the depth by using the following fall rate equation:
Depth_cor=A*timeB*time^2Offset.
Where elapsed time (time) for each reported depth by using the original droprate equation (Depth_original = A0*timeB0*time^2
). For UnknownFRE profiles, Hanawa et al. (1995) (A0=6.691, B0=0.00225) should be applied before applying this depth bias correction, if necessary. Original FRE for T5 (A0=6.828, B0=0.00182), T10 (A0=6.301, B0=0.00216). 
Corrects each temperature measurement (
Temp_original
) by using:Temp_cor = Temp_original  Tbias
. 
The corrections are made for 9 different XBT groups according to probe types: SippicanT4/T6, SippicanT7/DB, SippicanT10, SippicanT5 (This group includes both SippicanT5 and Unknownprobetype profiles with maximum depth deeper than 900m), TSKT7, TSKT4/T6, TSKT5, UnknownDeep (DX, this is for all unknown probe type XBTs with maximum depth deeper than 550m), and UnknownShallow (SX, this is for all unknown probe type XBTs with maximum depth shallower than 550m).
Details
CALCULATE FALL RATE COEFFICIENTS (A, B, OFFSET)
Fall rate coefficient (A) is obtained by adding a timevariable part and temperaturevariable part to Hanawa1995 fall rate coefficient:
A = H95_A+CH14_A_time + CH14_A_temp;
WhereH95_A=6.691
with exception ofT5: H95_A=6.828
;T10: H95_A=6.301
;
CH14_A_time
is presented in CH14_table1 for 9 groups;
CH14_A_temp
is calculated according to the following equation:
For Deep XBTs including T7, Deep Blue, DX:
CH14_A_temp= Averaged_Temp_100m * 0.0025
For Shallow XBTs including T4, T6, T10, T11, SX:
CH14_A_temp= Averaged_Temp_100m * 0.0050
For T5:
CH14_A_temp= Averaged_Temp_100m * 0.0044
WhereAveraged_Temp_100m is 0100m
averaged ocean temperature calculated by using this corresponding XBT profile.
Fall rate coefficients (B
and Offset
) are obtained according to A:
 For Deep XBTs including T7, Deep Blue, DX:
B=A*0.00700.0440; Offset=A*6.376540.293
For Shallow XBTs including T4, T6, T10, T11, SX:
B=A*0.00690.0435; Offset=A*=5.791437.285
For T5:
B=A*0.00460.0293; Offset= A*10.09366.4506
For TSK XBTs:
B=A*0.00340.0204;Offset= A*8.317655.746
CALCULATE THERMAL BIAS (TBIAS)
Thermal bias Tbias also consists of two parts: timevariable part (Tbias_time) and temperaturevariable part (Tbias_temp):
Tbias= Tbias_time + Tbias_temp
Tbias_time is presented in CH14_table2 for 9 groups;
Tbias_temp is calculated as:
For Deep XBTs including T7, Deep Blue, DX:
Tbias_temp =Temp * 0.0014 + 0.0139
For Shallow XBTs including T4, T6, T10, T11, SX:
Tbias_temp = Temp * 0.00167 + 0.0115
For T5:
Tbias_temp = Temp * 0.0026 + 0.0227
Where Temp is each individual temperature measurement in a XBT profile.
EXAMPLE
In case of a XBTT7 profile (reported fall rate equation: A0=6.691, B0=0.00225), the elapse time is given by t = 1486.89sqrt (2210838.568444.444*d), where d is a reported depth. When d
is 500 meters, the elapsed time becomes 76.7 seconds. Assuming that the observation was made at the center of 1970, 0100m averaged temperature (Averaged_Temp_100m
) is 18°C, and temperature at 500m (Temp
) is 11°C. The two variables can be easily calculated by using this XBTT7 profile.

Depth Error Correction
Therefore,CH14_A_temp = 18*0.0025=0.0450
CH14_A_time =  0.0736
(From CH14table1)
ThenA=H95_A+CH14_A_time+ CH14_A_temp = 6.691+0.04500.0736=6.6624
;
B=A*0.00700.0440=0.0026
Offset= A*6.376540.293=2.1898
Therefore, the depth is recalculated as:
Depth_cor=6.6624*time0.0026*time22.1898
The corrected depth (Depth_cor) when elapsed time is 76.7 is:
Depth_cor=6.6624*76.70.0026*76.7*76.72.1898=493.5208
.
That is, the reported depth is larger by 6.4792 meters than expected. 
Thermal Bias Correction
Tbias_time= 0.1016
(From CH14table2)
Tbias_temp= Temp * 0.0014 + 0.0139 = 11*0.0014+0.0139=0.0293
Tbias= Tbias_time+ Tbias_temp = 0.1016 +0.0293=0.1309
Therefore, the temperature measurement at 500m (Temp_original) is corrected by removing this bias:Temp_cor = Temp_original  0.1309.