An Assessment of the XBT Fall-Rate Equation in the Southern Ocean
1. Introduction
Among the water properties sampled and analyzed in the oceans, temperature represents the largest part of the available data. That is in part due to the relatively simple and inexpensive measurement methods used. In this sense much of the existing temperature data in the Southern Ocean were measured using expendable bathythermographs (XBT), originally developed for military use during the 1960s but widely deployed for upper-ocean scientific research, especially after the 1970s (e.g., Gouretski and Reseghetti 2010; Cheng et al. 2011, hereinafter CH11; Abraham et al. 2013; IPCC 2013). Because of its popular use by the scientific community, XBT data hold great relevance for marine studies, weather forecasting, and projections of future ocean and climate conditions (Wijffels et al. 2008). In fact, studies indicate that 38% of all upper-ocean temperature in the World Ocean Database 2013 (WOD13) was provided by XBTs deployed from 1970 to 2001 (Boyer et al. 2013). Although Argo floats have been dominating temperature and salinity profiles in the global ocean for the last two decades (Argo 2000), scientific studies still rely on XBT transects when studying variability of surface and subsurface currents, ocean and climate modeling, data assimilation, and climate change (Giese et al. 2011). Moreover, regular and dense spatial and temporal sampling cannot currently be obtained using any other observational equipment or system (Boyer et al. 2013), because of the high costs associated with other methods.
The raw XBT profile consists of a set of electrical resistance measurements as a function of elapsed time (e.g., CH11). These resistance values are converted into temperature values by applying the Steinhart–Hart equation (Georgi et al. 1980) and, ultimately, the FRE establishes a relationship between elapsed time and depth. Thus, water properties such as viscosity and density and their variability may affect the descending speed of the XBTs (Seaver and Kuleshov 1982), causing significant errors in depth estimation.
Hanawa et al. (1995, hereinafter H95) proposed the first global correction scheme accepted by the scientific community. The H95 correction scheme relied on the comparison of 285 XBT profiles with simultaneous measures taken by a conductivity–temperature–depth (CTD) at approximately the same place. According to Hanawa and Yasuda (1992), when CTD and XBT measurements are conducted repeatedly over an observational line, a pseudowaving of the isotherms (“XBT wave”) appears on the vertical temperature profile (cross section). This is related to the depth error in XBT data, since CTDs have a more accurate thermistor (e.g., 
In the last decade, many studies have tried to estimate and remove XBT biases from XBT datasets in order to use those data for climate studies (e.g., Wijffels et al. 2008; Ishii and Kimoto 2009; Levitus et al. 2009; Gouretski and Reseghetti 2010; Good 2011; CH11; Gouretski 2012; Hamon et al. 2012; Cheng et al. 2014, hereinafter CH14). CH14 compiled a summary of all cited methods, broadly indicating the existence of systematic errors in XBT measures that have various sources, not to mention a significant variation within probe type, time, and acquisition system used. These different XBT biases can be generally grouped in (i) depth errors caused by an inaccurate FRE, (ii) pure thermal bias (dT), and (iii) start-up transient (offset; after first usage, offset will appear in roman font.), combined with spikes and random unexpected occurrences (CH11). The source of the start-up transient error is said to be both electrical, when the error is caused by a late adjustment of the thermistor to the surrounding water temperature (CH11), and external, since it is directly related to the launch height (Bringas and Goni 2015) and also dependent on the conditions at the moment of the launch, such as sea state and ship motion, which may affect the probe’s angulation when hitting the water (Abraham et al. 2013). Concerning random errors, spikes are mostly caused by electrical sources, such as the recording system used, faulty ground connection, and wire leakage (Reseghetti et al. 2007); however, random errors can also be related to atmospheric conditions (e.g., lightning interference, wire shorting against a ship’s hull caused by unfavorable or strong wind) and sometimes ship speed (Bailey et al. 1994). Research efforts are currently underway to improve our understanding of the depth offset term sources (Cheng et al. 2016).
Conversely, fall-rate errors estimates can have mechanical sources, such as probe weight and dimensions, shape, nose roughness, and year of fabrication (Seaver and Kuleshov 1982; Green 1984). Moreover, external factors may also intervene, such as sea state conditions and the water column thermohaline characteristics (Thadathil et al. 2002). Systematic errors in the depth estimate are function of water temperature, since water viscosity is directly dependent on temperature, affecting the probe motion/velocity (Kizu et al. 2005; CH14). Following this line, several studies have investigated how regional hydrographic characteristics may influence FRE’s performance. Most of those studies, however, cover tropical or subtropical areas, such as the Australian coast (Ridgway et al. 2002), North Pacific (Kizu et al. 2005) and the Mediterranean Sea (Reseghetti et al. 2007). With respect to the high-latitude oceans, there is still need for specific research on the topic.
While some studies have been undertaken (Pennington and Weller 1981; Wisotzki and Fahrbach 1991; Thadathil et al. 2002; Hutchinson et al. 2013), they all recommend further analysis in these high-latitude regions to account for the XBT bias properly. One of the main issues would be that weaker vertical temperature gradients tend to reduce the detectability of depth errors (Wijffels et al. 2008). For instance, Thadathil et al. (2002) observed that XBT probes had also a tendency to overestimate their depth values in polar and subpolar regions south of Tasmania while using H95 correction scheme. That is due to the much colder temperatures (and higher water viscosity) that the probes are exposed when compared to the study of H95, which used data from only tropical waters to correct the coefficients. Furthermore, while analyzing XBT–CTD pairs south of Africa, Hutchinson et al. (2013) have also proposed that because of the higher viscosity of the relatively cooler waters of the Southern Ocean, the probes suffer more friction, thus reducing their falling speed. Hence, when XBTs perform a slower descent than the one expected by the FRE provided by the manufacturer, it does result in temperature readings shallower than the real. This may lead to considerably warmer conditions than those revealed by a CTD at the same level. According to Hutchinson et al. (2013), these differences can be observed when taking into account the manufacturer’s FRE coefficients, but they are even more pronounced when taking into account H95 coefficients.
Recent observations have suggested that the Southern Ocean is warming faster than other regions of the World Ocean (e.g., Gille 2002, 2008). However, data from XBTs are relatively dominant in this region, accounting for 45% of all casts between 1980 and 2000 and for 20% between 1980 and 2015. Thus, it is unclear whether this faster warming signal would be partially caused by depth overestimates in available XBT data or in fact by an uneven response to global climate change (Hutchinson et al. 2013). On the other hand, exactly because the Southern Ocean is indeed undersampled, some authors argue its contribution to global ocean heat content is being underestimated (Durack et al. 2014; Cheng and Zhu 2014; Cheng et al. 2017). In any case, although XBT data without bias corrections are still suitable for many scientific applications, only corrected data should be used for climate research (Cheng et al. 2016). Therefore, it is of utmost importance that the errors associated with XBTs are correctly estimated in the Southern Ocean and that the available data are corrected for the extreme conditions found in this environment so that the magnitude of the variability in the region can be properly understood.
Finally, although some studies have observed a decrease in the FRE coefficients in cooler waters as a result of an increase in its viscosity (Gouretski and Reseghetti 2010), this effect has not yet been properly quantified. Thus, quantifying the depth bias in high-latitude regions is important for accurate corrections in the Southern Ocean and, ultimately, reliable global ocean heat content (OHC) estimates.
This study aims to identify and quantify the errors in depth estimation of XBTs in relatively densely observed areas of the Southern Ocean, evaluating a regional FRE that potentially offers a more consistent correction to the unique and extreme features of that region. To that end, this work is organized as follows: Section 2 describes the data and methods used in this study. Section 3 addresses the (i) FRE analysis and depth bias, (ii) pure thermal bias, (iii) viscosity comparisons, and (iv) their implications for the OHC estimates. Finally, section 4 summarizes our conclusions and findings.
2. Data and methods
a. Finding XBT–CTD pairs
To investigate and quantify XBT biases in the Southern Ocean, XBT and CTD data located south of 60°S were extracted from WOD13 and matched in order to find time–space pairs. Only XBT profiles within a maximum radius distance of 12.5 nm (or 0.2° of latitude/longitude) and a temporal difference of less than 10 h from a given CTD profile were admitted as collocated pairs (Hutchinson et al. 2013). Initially, the data pairs were grouped within the three choking points of the Antarctic Circumpolar Current, where the data density and space–time distribution are expected to be less sparse: Drake Passage (DRA, 59), south of Africa (AFR, 36) and south of Tasmania (AUS, 62) (Fig. 1), summing up to a total of 157 pairs. The dataset spans from 1984 to 2013, and the pairs are spaced in time as 70 (1984–93), 25 (1994–2003), and 62 (2004–13).
Map displaying the location of all collocated XBT (red dots) and CTD (black dots) considered in this study: (left) DRA (59 pairs), (center) AFR (36 pairs), and (right) AUS (62 pairs). The color shade indicates the sea surface temperature field for the region.
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
Both CTD and XBT profiles were subject to quality control (Reseghetti et al. 2007). Following the same procedure of earlier correction methods (H95; DiNezio and Goni 2011; Hutchinson et al. 2013), a nonlinear median filter was used to eliminate spikes and, subsequently, a low-pass linear Hanning filter was performed to smooth smaller erroneous signals on both XBT and CTD profiles. In addition, the values were also manually checked to ensure that all data below significant spikes, not previously flagged as bad, were also removed. Although they often seem to be good to use, those values are very likely to contain significant biases (Anderson 1980; Hutchinson et al. 2013). Originally, this study started with 633 XBT–CTD pairs, being 245 from DRA, 156 from AFR, and 232 from AUS. Thus, this process can indeed be very rigorous and conservative, given that approximately 75% of all pairs in the database were eliminated from the analysis.
Figure 2 demonstrates examples from DRA of the type of pairs considered in this study and the ones that were discarded. Ideal pairs are those where the XBT wave is identified without the major displacement of the entire XBT profile as represented by the left panel. Individual FRE coefficients for XBT profiles in this group are calculated by minimizing the standard deviations of the temperature differences between the given XBT–CTD pair, which is called the “brute force” algorithm (CH11). In this procedure, both temperature casts are compared through previously established elapsed time windows (instead of depth as used in previous methods), aiming to find the best fit of coefficients for each pair. The corresponding corrected profiles are shown in green for ideal, accepted, and rejected profiles. In the middle panel, there is an example of profiles that have presented a larger displacement of the XBT profile but were still considered in the analysis, since the CH11 method was able to satisfactorily correct them. Finally, the right panel exhibits one of the rejected pairs of profiles that do not quite correspond to the CTD profile at any depth, making it impossible for the method to perform any correction. Profiles with more than 1°C difference or with curves presenting fairly different behaviors fall into that last category.
Examples of collocated XBT–CTD pairs. Temperature XBT (blue), CTD (red), and corrected XBT (green) profiles are displayed in sequence, representing (left) an ideal pair, (middle) a not ideal but still in the range of acceptance pair, and (right) a rejected pair. All three profiles are from AUS.
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
b. Calculating new FRE coefficients
To identify and quantify XBT biases in the Southern Ocean, new FRE coefficients were calculated from the side-by-side pairs using the method proposed by CH11. One of the most important changes of this method in comparison with the SIP FRE is the introduction of the offset term, which is also called the start-up transient.
The final coefficients A and B and the offset for the XBT dataset were calculated by the weighted mean of the individual coefficients obtained for each of the pairs. The weights were the depths of each XBT profile, giving more importance to deeper recordings, since the bias may be different above and below the thermocline (if present) (Seaver and Kuleshov 1982). Initially, we looked at the possibility of using the geographical distance and time span within pairs as the weight to compute the mean. The results, however, proved not to be significantly different from using depth as the recommended method. Moreover, CH14 have defined a time–space window of one month and 1° of latitude/longitude as their threshold for the World Ocean Database 2009 dataset search for pairs in a similar analysis, which is a much wider time–space range when compared to the intervals of search considered in this study (10 h per 0.2°).
The offset term, although shown as an average, was applied individually to each of the profiles. That is mostly because CH11 noticed a probe-to-probe difference of the transient term even when the probes were launched at the same time and under the same conditions. In addition, besides all of the error sources for the offset term described in section 1, its strong relation with launch height ought to be well investigated in order to make an assumption such as the regional average of that term. However, launch height was unavailable in the metadata for most of the XBT profiles and hence this study did not have enough pairs to make a statistically significant analysis regarding the offset term.
Analyzing the temperature itself (CH11) instead of temperature gradients (H95) allows for an independent account of dT and the depth bias. The corrections of dT are not part of the depth estimates when using CH11, being largely dependent on temperature (Cheng et al. 2016) and time (Reverdin et al. 2009). However, Hutchinson et al. (2013) assumed that some of the depth bias might contaminate temperature bias estimates in the Southern Ocean as well, which is also considered in this study.
Essentially, the larger the temperature vertical gradient, the larger the temperature total bias (Reseghetti et al. 2007). Since the temperature vertical gradients in the Southern Ocean are really small and the absolute temperature values are generally quite low (Wijffels et al. 2008; Hutchinson et al. 2013), dT values are expected to be low as well (i.e., the weight of dT in the overall correction is expected to be low). Moreover, previous studies also indicate that different recording systems might have a major effect on temperature bias.
Pure thermal bias in this analysis is corrected by adding the time-dependent dT values proposed by CH14. The launch year instead of the fabrication year was used as an approximation, because it was not possible to access this specific information from the metadata provided by World Ocean Database for the large majority of the XBT–CTD pairs (Cowley et al. 2013).
c. Viscosity analysis
As to exemplifying the probe’s behavior across different viscosity fields, we compared the mean kinematic viscosity profile of the Southern Ocean pairs used in this study with the mean viscosity profile of the NOAA AX97 XBT high-density line, located in the tropical region off the Brazilian coast around 20°S, 30°W. This specific XBT dataset is made freely available on the Atlantic Oceanographic and Meteorological Laboratory, and the line is funded by the NOAA Office of Climate Observations, the Brazilian Research Council (CNPq) and the Brazilian Navy Hydrographic Office (DHN/CHM).
d. Ocean heat content estimates
This study compares the performance of the different FREs here considered, as to evaluate the potential impact of the XBT probe’s descent speed variation and corresponding depth estimates on OHC regional values.
3. Results and discussion
a. FRE performance analysis: Depth bias
To test the new coefficients, we performed comparisons between the following corrections:
SIP FRE, named uncorrected.
CH11 method or the new coefficients obtained, named corrected.
It is noticeable that the new A coefficients are closer to the SIP FRE coefficients than to H95’s classic global correction. The DRA and AFR A coefficients differ from SIP by less than and equal to 1%, respectively. On the other hand, AUS differs by −4% from the original A value and from the whole dataset by −2%. Thadathil et al. (2002) when analyzing 16 XBT–CTD pairs south of Tasmania also observed that the manufacturer’s FRE seems to work well in cold Antarctic waters, possibly because of viscosity changes. Those waters offer more resistance to the probe that falls slower, which also reduces the A value (SIP A < H95 A). Admitting that the probe motion is dependent on water temperature, they suggested that the FRE coefficients should also depend on latitude. Conversely, for some of the profiles, B coefficients reached the boundaries of the previously defined search window, and hence those cases provided no sufficient information to get an accurate estimate of B —that happens as a consequence of the temperature profile being too homogeneous (common in the deeper and high-latitude waters), which makes determining different values of B increasingly more difficult.
Nevertheless, the differences among the coefficients suggest that the depth differences are significant, which means that the temperature of the region can be affecting the probes’ descent. To further investigate this issue, Fig. 3 depicts the mean depth bias of the uncorrected (black), corrected (gray), and H95 corrected (white) profiles for each region, and also for the Southern Ocean as a whole. The depth bias for the Southern Ocean is clearly positive, which supports the claim that the XBT probes fall slower than modeled by the SIP FRE while in colder (high viscosity) waters, thus overestimating depth values. Regionally, the result is generally the same: the depth bias for DRA is mostly positive, showing very few layers with a negative bias and, in AUS, it is positive as a whole. On the other hand, AFR does not present a clear behavior, exhibiting negative values in a number of different layers, mainly at shallower depths. In general, the differences tend to get smaller when using CH11 correction, but in several layers across the regions, the manufacturer’s correction scheme provides better results.
Mean depth differences for each 50-m depth layer for (a) DRA, (b) AFR, (c) AUS XBT–CTD pairs, and (d) for the Southern Ocean. Estimates were made for uncorrected (black), corrected (gray), and H95 corrected XBT (white), and standard deviations are represented by the error bars (gray). Manufacturer’s tolerance is also shown (dashed black line).
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
These averaged differences are smaller than the manufacturer’s tolerance of ±5 m or 2% (whichever is greater; Lockheed Martin Sippican Inc.) and are similar in range to those reported in Hutchinson et al. (2013) and Thadathil et al. (2002), which also indicated an overall positive depth bias for the Southern Ocean south of Africa and south of Tasmania, respectively. This may be related either to the relatively small vertical temperature gradients or as a result of sampling two different water masses within the same collocated pair (Hutchinson et al. 2013). Since most of the negative biases found in the present study are above 400 m and in AFR, it is possible the data might have been influenced by the Agulhas Return Current eddies or that the number of pairs was not numerous enough (36) to address this particularly energetic region. Considering that the presence of a thermocline can sharpen the gradients and lead to very large temperature differences within a few meters, one should also consider this possibility, even in the Southern Ocean.
In Fig. 4 the mean temperature differences and profiles along depth were visually inspected to analyze depth consistency. Figure 4 (top panels) shows mean temperature differences (XBT − CTD) between CTD and H95 corrected (black), uncorrected (red), and corrected (green) XBT for each of the three regions. Temperature differences were calculated by subtracting the XBT temperature from the CTD profile, where positive (negative) values indicate that the XBT temperature at a certain depth was higher (lower) than the CTD temperature value, which can also mean that in those cold waters the XBT probe falls slower than expected.
Mean temperature differences and profiles for Drake, Africa, and Australia. (top) Differences between CTD and uncorrected XBT (red), corrected XBT (green), and the classic H95 correction (black). (bottom) Uncorrected (red), corrected (green), H95 corrected (black) XBT, and CTD (blue) mean profiles for the three regions. The standard error for the corrected XBT at each depth is shown in the top panel (gray shadowed areas).
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
In general, it is noticeable that the adjustment provided by the CH11 method is efficient in reducing differences between the XBT and CTD profiles for all the regions assessed, except for the first 200 m in AFR. In AUS and AFR, the differences are quite close to zero for most of the profile. Above 200-m depth in AFR, the terms proposed for pure temperature bias correction do not seem correct or sufficient, possibly because it is a very energetic region with high incidence of eddies and mesoscale features that may not have been completely excluded from the dataset during the filtering and averaging procedures (Hutchinson et al. 2013). In DRA, the corrected profile is farther from the CTD profile than both the H95 and uncorrected profiles below 500 m. Considerable temperature differences between the XBT and CTD measurements within the thermocline are common and well reported, but very little is known about differences in this deeper layer. CH11 found significant but small biases (less than 0.18°C) that would still remain both within the thermocline regions and at the 450–650-m depth, where the temperature gradients would be varying irregularly with depth. It has been suggested that more detailed studies are needed in order to clarify the processes that might be affecting this specific layer (CH11).
For most XBT–CTD pairs in the dataset, the XBT temperature value was lower than the recorded value by the CTD at that same depth. Table 2 compares the mean temperature bias and standard deviations between depth-corrected-only and depth/temperature-corrected profiles. The difference between DRA, AUS, and the Southern Ocean was roughly the same (~0.1°C), while the results for AFR were inconclusive. The total bias for corrected DRA, AFR, and AUS was −0.02 ± 0.01, 0.003 ± 0.04, and −0.02 ± 0.01°C, respectively. These results are in partial agreement with Hutchinson et al. (2013), who also reported an overall warm bias south of Africa (reaching 0.13°C) but observed a minor cooling bias south of the Polar Front, around 200 m. That particular bias was associated with the presence of Antarctic Surface Water (AASW, or Winter Water) at the subsurface, which sharpens vertical gradients, especially during late summer. This suggests that a seasonal analysis should be conducted at DRA and AUS to verify whether that was also the case. Finally, Fig. 4 (bottom panels) exhibits the mean temperature profiles. The data seem to be in good agreement without extraneous profiles, except for a significant shift that corresponds to an increase of standard deviation (Table 3) in H95 corrected data for AUS.
Total temperature mean bias (°C) between the XBT and CTD (XBT − CTD) recordings for each of the SO sections considered and for the whole dataset, accounting for depth corrected only (D) and depth and temperature corrected profiles (D&T). Significant differences were obtained through a t test at the 95% confidence level.
Total RMS of temperature mean differences (°C) between the XBT and CTD (XBT − CTD) recordings according to correction schemes for each of the SO sections considered and for the whole dataset; D and D&T as in Table 2. Significant differences were obtained through a t test at the 95% confidence level.
When analyzing the whole dataset, the CH11 method (green) seems to be the best correction for the XBT profiles once the differences keep oscillating around zero—except in the temperature minimum layer, where CH11 has the worst performance (Fig. 5). The upper-layer results are less straightforward, but the offset term clearly makes a difference in the fitting. The differences tend to stay very close to zero, suggesting that the processes that are occurring at the studied regions balance each other out or that a greater number of pairs are able to attenuate this signal. An exception is observed at depths below 500 m, where there seems to be a shift and XBT profiles are warmer than CTD profiles on average. The total temperature mean bias for the Southern Ocean dataset after corrections is −0.017°C ± 0.008, which opposes the result of Hutchinson et al. (2013), but bear in mind they used a specific area in their study.
Southern Ocean analysis of temperature profiles, showing CTD profiles (blue), and uncorrected (red), corrected (green), and H95 corrected (black) XBT profiles. (left) The mean temperature profiles, and (right) the mean differences between the XBT and CTD profiles. The standard error for the corrected XBT at each depth is shown in the right panel (gray shadowed areas).
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
In summary, depth correction analysis provides evidence sustaining that XBTs are falling slower than expected in the Southern Ocean. At the same time, the CH11 method seems to improve the consistency over depth for all the regions analyzed (except for AFR, which showed inconclusive results) and for the Southern Ocean as a whole. Thus, it is fair to consider it the most fitting depth correction method.
b. Temperature bias
In the Southern Ocean, temperature errors are mostly due to pure thermal bias, since there is very little stratification that leads to a homogenized water column. However, prior to correcting the pure thermal bias, and after depth corrections, temperature differences were checked for consistency. Figure 6 (top left) shows the average temperature differences adjusted according to the linear regression equation found for the Southern Ocean dataset, defined as 
(top left) Robust fit of dT errors with (bottom left) the corresponding norm plot of residuals. The linear regression trend line for a 95% confidence interval is shown in the top-left panel (solid black). (right) Depth (red) and temperature (blue) corrections are shown independently.
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
The differences seem to be larger in the surface than in deeper waters, which is in agreement with previous studies (Reseghetti et al. 2007; CH11; CH14) and suggests that 
Considering that XBT temperature biases are generally positive on a global scale, especially within XBT profiles from the 1980s and 1990s (Gouretski and Reseghetti 2010; Abraham et al. 2013), the generally negative results raise attention. Therefore, it is quite important to analyze how these temperature biases differ among different latitudes. For instance, CH14 have analyzed the temperature bias behavior across different latitudes and depths, concluding that residuals are still larger at lower latitudes, although zonal gradients tend to decrease after corrections are applied. Such observations are significant for profiles that are less homogenous, meaning that they tend to contain smaller temperature biases than other regions of the global ocean. This also provides insight for the good performance observed for the SIP FRE on the Southern Ocean. Since no pure thermal bias correction is added, final estimates are free from a potential temperature bias overcorrection, thus improving the overall performance.
To analyze the performance of each correction scheme and to validate these claims, we computed the mean RMS along the temperature differences (see Table 3) for both before and after temperature corrections. CH14 temperature correction terms improve estimates by approximately 0.01°C for DRA and AUS, summing up approximately 0.02°C when taking into account the whole dataset. AFR does not show significant changes.
When comparing uncorrected and corrected data within the depth- and temperature-corrected profiles, the differences were significant for DRA at the 95% confidence level, meaning the SIP FRE is able to estimate depth in this area with relatively small errors. For AUS, the CH11 method improves the adjustment by 0.02°C when comparing the RMS, and the differences are also significant, within 5%. The H95 correction presented the worst performance between the three, varying in relation to the corrected data up to 0.02 in AUS, 0.01 in AFR, and 0.10 in DRA. These results become even more solid if the number of pairs by section comes into question. AUS and DRA have 62 and 59 pairs, respectively, making their estimates more significant when compared to the AFR section, which has a total of 36 pairs. At the same time, 59 pairs do not seem to be enough to analyze XBT FRE variability in the DRA, since the discrepancies are larger, even when considering corrected data. Regarding the entire dataset, the CH11 method improves the adjustment by 0.02°C when compared to both SIP FRE and the classic H95 correction scheme.
Overall, the results show that the CH11 method is the best correction scheme, but it is likely that the final data contain a temperature error leading to a negative temperature bias for the Southern Ocean. The findings also support the claim that the SIP FRE coefficients might not be adequate for the extreme conditions of the Southern Ocean but, at the same time, they indicate that the SIP coefficients tend to perform better in high latitudes than in lower latitudes.
c. Viscosity field comparison
To clarify how the probe’s descent is varying across different viscosity fields, Fig. 7 compares the mean kinematic viscosity profile of the Southern Ocean pairs with the mean viscosity profile of the NOAA AX97 XBT high-density line, located in a tropical region near Trindade Island (20°S, 30°W). In the right panel (Trindade Island), the range of viscosity variations is wider, which leads to the conclusion that this environment presents sharper temperature gradients and thus a well-formed thermocline as expected. The Southern Ocean (left) mixed layer normally displays a different behavior than the tropics: the intense winds make the formation of a thermocline very difficult (Talley et al. 2011), resulting in a more homogenous ocean also from the viscosity perspective. This may impact not only the velocity with which the probe descends, as discussed previously, but also the sensitivity of the methods used to estimate this velocity (CH11). The FRE coefficients found for the AX97 dataset using the same method produced a fall-rate equation in the form of 
Mean kinematic viscosity profiles of (left) the 157 Southern Ocean pairs used in this study and (right) the NOAA AX97 XBT high-density line, located in a tropical region off the Brazilian coast toward Trindade Island (20°S, 30°W).
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
While using the CH11 method, it is quite usual for the coefficient 
The comparison between the different XBT elapsed times in the Southern Ocean and in the tropics (Fig. 8, left panel) indicates that the XBT probe falls slower in the former. For 20°S, the behavior is exactly the opposite, further supporting that viscosity is playing an important role in the probe’s descent when in the Southern Ocean, even though our overall results are showing a small temperature negative bias.
Time elapse calculated using the viscosity profiles of the (left) Southern Ocean and (right) AX97 line. Uncorrected (gray), corrected (green), and actual results using Stokes law (red).
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
Thus, it seems that the higher viscosity of the Southern Ocean does influence the XBT probes to fall slower, leading to positive depth biases for most of the profiles. Regarding the temperature bias, although the results point to an overall negative bias, this might be related to either depth or temperature error sources. Considering the depth correction’s consistent results and the XBT/CTD profiles’ close shape, the latter remains most likely.
d. Ocean heat content
In terms of OHC, our results also agree with previous authors in the sense that XBT bias and its dominance in the dataset between the 1980s and the early 2000s might be impacting the observed warming for the Southern Ocean (Hutchinson et al. 2013). Since a considerable bias is clear on the XBT dataset also in the Southern Ocean, this could lead to a spurious shift in the long-term OHC trend, especially considering that the main observational system from 2000 onward is based on Argo floats (e.g., Argo 2000; Wijffels et al. 2008).
Figure 9 displays the calculated OHC values grouped into 1° latitude bins using the Southern Ocean coefficients defined by corrected (black), uncorrected (purple), and H95 corrected XBT data (white), and CTD data (light blue). This approach explains why OHC does not gradually increase northward in this dataset. Although, OHC shows a consistent increase toward the north, the 63°S latitude bin breaks this trend. That is mainly because it has only 14 pairs in comparison to 71 and 37 pairs from the previous bins.
OHC relative to the area occupied by the pairs. OHC was calculated for XBT profiles corrected with mean coefficients A and B, and individual offset (black), uncorrected (purple), and H95 corrected (white), and CTD profiles (gray). The error bars indicate a 95% confidence interval.
Citation: Journal of Atmospheric and Oceanic Technology 35, 4; 10.1175/JTECH-D-17-0086.1
The comparison of both FREs with the CTD data does not indicate very significant differences in the estimation of OHC between CH11 and uncorrected profiles (confidence interval of 95%). It is noticeable that both the recommended method and the SIP FRE are achieving a similar correction range. The best performance, on average, is from the CH11 method. However, despite the corrections, both equations overestimate OHC for the upper layer by approximately 10%. It seems that both FREs tend to overestimate negative values of heat content as well, since in latitude 65°S the OHC calculated by them was smaller than the CTD. This behavior could indicate a possible balance in the overall OHC if more pairs were available. While H95’s method was not shown to be a good and comprehensive method for the Southern Ocean, performing worse than SIP FRE in all previous tests, for OHC its performance was not far from the other correction schemes.
The analysis of the averaged values indicates that the H95 method overestimates OHC the most, with a value of 4.79 ×
These results do not mean that the current OHC is being significantly overestimated as a whole, but it does indicate that the appropriate correction of the historical XBT data and more sampling will help to improve OHC estimates. Unarguably, more paired high-quality profiles are needed in order to make a full assessment of the OHC XBT biases for the Southern Ocean, as the relatively less data available for that region might also be a source of negative biases.
4. Summary and conclusions
Since the global ocean is warming (e.g., Lyman et al. 2010) and the Southern Ocean seems to be warming even faster (Gille 2002), the quantification of the XBT depth bias in high-latitude regions is critical for accurate corrections of a large portion of the available Southern Ocean temperature dataset and thus, ultimately, reliable global ocean heat content estimates. In that sense this study has investigated the XBT bias in the Southern Ocean, aiming to identify and quantify the errors of depth of XBTs in three sections across the Antarctic Circumpolar Current, proposing new FRE coefficients that would offer a more consistent correction to the unique and extreme features of this region.
In partial agreement with previous studies that also contributed in accounting for the XBT bias in the Southern Ocean (e.g., Thadathil et al. 2002; Hutchinson et al. 2013), our results show that the overall depth offset was positive, leading to overestimating depth values. CH11 was generally the best correction scheme for depth. Moreover, the viscosity field analysis also indicates that the higher viscosity of the Southern Ocean does influence the probes to fall slower than expected by the manufacturer.
On the other hand, the temperature bias for the same dataset was negative, at first contradicting the results for depth bias. Considering that the depth bias might be contaminating the temperature bias, since it is difficult to isolate the latter from the depth bias dominance, the expected result would be an overall positive temperature bias. However, imperfections in XBT–CTD comparisons and the fact that XBT profiles are generally closer in shape to CTDs suggests that this cooling may also be related to a temperature bias error. In addition, temperature biases tend to be small in higher latitudes, providing an explanation for the good performance of SIP FRE in those areas, since it does not include a time-dependent pure thermal bias correction.
Regarding OHC estimates, the magnitudes of these biases translate into an overall overestimation of heat for the Southern Ocean of approximately 10%. Although these findings indicate that the Southern Ocean observed warming and that a warming trend might not be as pronounced as expected, these results should be taken carefully. The undersampling of the Southern Ocean might also be a cause of underestimation of OHC (Durack et al. 2014), which would balance or overcome the XBT bias impacts.
Finally, it is important to emphasize that XBTs comprise a considerable part of the global temperature dataset and that science still relies on this relatively simple equipment for a wide range of ocean, climate, and modeling studies. In particular, for the Southern Ocean, XBTs compose almost 50% of all data available between 1970 and 1980. In that sense it is critical to develop a better understanding of XBT biases and behavior to use this valuable and significant source of data in climate sciences. A possibility yet to be explored—since the higher the latitude, the more the vertical velocity of the probe seems to decrease—would be attributing regional weights to the existing correction schemes. A temperature bias correction also related to latitude may also lead to future improvement.
Acknowledgments
This study is a contribution to the activities of the Brazilian High Latitudes Oceanography Group (GOAL; www.goal.furg.br), which is part of the Brazilian Antarctic Program (PROANTAR). GOAL has been funded by and/or has received logistical support from the Brazilian Ministry of the Environment (MMA); the Brazilian Ministry of Science, Technology, Innovation and Communication (MCTIC); and the Council for Research and Scientific Development of Brazil (CNPq) through grants from the Brazilian National Institute of Science and Technology of the Cryosphere (INCT-CRIOSFERA; 573720/2008-8), POLARCANION, NAUTILUS, and CAPES/CMAR2 projects (556848/2009-8, 405869/2013-4, 23038.001421/2014-30). N. R. Santos acknowledges the graduate fellowship funded by the CAPES Foundation. M. Cirano and M. M. Mata were supported by grants from CNPq and CAPES. Finally, we thank Dr. L. Cheng for his availability and interest during the development of this study, and the NOAA World Ocean Database and all scientists who participated in the data collection and made it freely available through the respective databases.
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