Gouretski and Koltermann (2007) shows statistics from Expendable Bathythermograph (XBT) vs. Conductivity-Temperature-Depth (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 10-12, 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 25-27, 2010 in Hamburg, Germany.
- The First XBT Science Workshop (XSW-1) was held in Melbourne, Australia, July 7-8, 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 The corrections proposed by Gouretski and Koltermann (2007) are not included here, as they have been superseded by the corrections proposed by Gouretski and Reseghetti (2010).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 situ-altimeter 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/s10872-009-0027-7. 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 1955-2007 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. Deep-Sea Research I, Vol. 57(6), pp. 812-834, 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, 287-300, doi: 10.1175/2010JTECHO773.1 Good depth corrections
- Hamon, M., G. Reverdin, P-Y Le Traon, 2012, Empirical correction of XBT data. Journal of Atmospheric and Oceanic Technology, doi:10.1175/JTECH-D-11-00129.1, 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 Research-I, 62,40-52. 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 side-by-side comparisons, Journal of Atmospheric and Oceanic Technology, 30, 11951225, doi:10.1175/JTECH-D-12-00127.1. 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, 1793-1825, doi:10.1175/JTECH-D-13-00197.1.
**Note:**original CH14-table1, CH14-table2. Updated CH14-table2 February 15, 2017 (personal communication L. Cheng). Updated CH14-table1, CH14-table2, 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 re-computed (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)

`T-corrected = T-observed - 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" depth-depending stretching factor is further modified depending on the deviation of the XBT-profile 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) |
---|---|---|---|---|

Other Types (No Corrections Supplied): |
||||

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 | |

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 1967-2010.
- Depth error offset is provided in Original Table 3 and 2014 Updated Table 3 for different probe types for the years 1967-2010.
- Thermal bias is provided in Original Table 4 and 2014 Updated Table 4 for different probe types for the years 1967-2010.

### 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) |
---|---|---|---|---|

Other Types (No Corrections Supplied): |
||||

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 | |

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 = 2.25x10-3)

`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*time-B*time^2-Offset.`

Where elapsed time (time) for each reported depth by using the original drop-rate equation (`Depth_original = A0*time-B0*time^2`

). For Unknown-FRE 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: Sippican-T4/T6, Sippican-T7/DB, Sippican-T10, Sippican-T5 (This group includes both Sippican-T5 and Unknown-probe-type profiles with maximum depth deeper than 900m), TSK-T7, TSK-T4/T6, TSK-T5, Unknown-Deep (DX, this is for all unknown probe type XBTs with maximum depth deeper than 550m), and Unknown-Shallow (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 time-variable part and temperature-variable part to Hanawa1995 fall rate coefficient:

`A = H95_A+CH14_A_time + CH14_A_temp;`

Where`H95_A=6.691`

with exception of`T5: 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`

Where`Averaged_Temp_100m is 0-100m`

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*0.0070-0.0440; Offset=A*6.3765-40.293`

For Shallow XBTs including T4, T6, T10, T11, SX:`B=A*0.0069-0.0435; Offset=A*=5.7914-37.285`

For T5:`B=A*0.0046-0.0293; Offset= A*10.093-66.4506`

For TSK XBTs:`B=A*0.0034-0.0204;Offset= A*8.3176-55.746`

##### CALCULATE THERMAL BIAS (TBIAS)

Thermal bias Tbias also consists of two parts: time-variable part (Tbias_time) and temperature-variable 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 XBT-T7 profile (reported fall rate equation: A0=6.691, B0=0.00225), the elapse time is given by t = 1486.89-sqrt (2210838.568-444.444*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, 0-100m 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 XBT-T7 profile.

**Depth Error Correction**

Therefore,`CH14_A_temp = 18*0.0025=0.0450`

`CH14_A_time = - 0.0736`

(From CH14-table1)

Then`A=H95_A+CH14_A_time+ CH14_A_temp = 6.691+0.0450-0.0736=6.6624`

;`B=A*0.0070-0.0440=0.0026`

`Offset= A*6.3765-40.293=2.1898`

Therefore, the depth is recalculated as:`Depth_cor=6.6624*time-0.0026*time2-2.1898`

The corrected depth (Depth_cor) when elapsed time is 76.7 is:`Depth_cor=6.6624*76.7-0.0026*76.7*76.7-2.1898=493.5208`

.

That is, the reported depth is larger by 6.4792 meters than expected.**Thermal Bias Correction**`Tbias_time= 0.1016`

(From CH14-table2)`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.`