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, 17931825.
doi: http://dx.doi.org/10.1175/JTECH-D-13-00197.1

Generally, CH14 method

- 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).
- 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, 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 18°C, and temperature at
500m (Temp) is 11°C.
The two variables can be easily calculated by using this XBT-T7 profile.

- 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. - 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.