Expendable Bathythermograph (XBT) Corrections in the World Ocean Database

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)

• Thermal_bias_t4t6_vs_year.dat
• Thermal_bias_t7db_vs_year.dat

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.

• Stretch_approx_parameters_t4t6_vs_year.dat
• Stretch_approx_parameters_t7db_vs_year.dat

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).

• tmean_t4t6.dat
• tmean_t7db.dat

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.

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.

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

1. 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).
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, 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.