CH14 method to correct XBT Depth and Temperature bias:
Refer to:
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: http://dx.doi.org/10.1175/JTECH-D-13-00197.1
Generally, CH14 method
(1). Recalculates the depth by using the following fall rate equation:
Depth_cor=A*time-B*time^2-Offset. where elapse 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).
(2). Corrects each temperature measurement (Temp_original) by using: Temp_cor =
Temp_original – Tbias.
(3). The corrections are made for 9 different XBT groups according to probe types:
Sippican-T4/T6, Sippican-T7/DB, Sippican-T10, Sippocan-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).
In details:

Calculate fall rate coefficients (A, B, Offset):
(i) 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.
(ii) 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):
(i). 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 elapse time becomes 76.7
seconds. Assuming that the observation was made at the center of 1970, 0-100m
averaged temperature (Averaged_Temp_100m) is 18oC, and temperature at 500m
(Temp) is 11oC. The two variables can be easily calculated by using this XBT-T7
profile.
(1). For 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.
(2). For 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.