1. Introduction

Owing to their enormous heat capacity, the oceans are absorbing most of the excess heat trapped in the climate system by the increasing concentrations of greenhouse gases. Ocean heat content can thus be used as a metric to check whether coupled climate models are correctly responding to anthropogenic and natural forcing. However, greater accuracy is needed both for global averages and on smaller scales, as regional patterns of heat content change provide important clues to changes in wind fields and changes in air–sea heat fluxes and inform how local impacts may differ from global impacts. Generating such estimates with accuracy remains a huge challenge (Levitus et al. 2005), largely due to a paucity of data in much of the global ocean, especially south of the equator. Another problem also exists—that of the changing technology used to collect ocean temperature profiles. These changes may result in technology-related biases in estimates of heat content. In the last few years, the rapidly expanding Argo array (Gould et al. 2004) is attempting to rectify many of the past problems in data quality and global coverage by delivering a truly global and highly quality controlled data stream of ocean temperature and salinity.

As the global ocean warms, its thermal expansion contributes to global sea level rise. Attempts to quantify the causes of global sea level rise—ocean thermal expansion, glacier and ice cap/sheet melting, snowpack reduction—are confounded by the problems noted above. While the mean rates of sea level rise over the past 100 years are of great importance, decadal variability is also of interest. Church et al. (2005) show that large volcanic eruptions cool the global ocean and produce a drop in global sea levels. While this volcanic signal is clear in appropriately forced models and the global tide gauge record, it is not as clear in the global thermosteric sea level record (the component of sea level change due to the thermal expansion of the ocean and closely related to ocean heat content), and there are several instances where global sea level is rising but steric sea level is falling, for example, 1980–83 (Fig. 1). Can these curves be reconciled?

Gouretski and Koltermann (2007) used an ocean climatology based on the highest quality data [Nansen casts and conductivity–temperature–depth (CTD) profiles] to compare how different instrument types measured the same ocean regions. Their study identified a clear warm bias in the abundant but low-accuracy data collected by expendable bathythermographs (XBTs). This bias appears to vary from year to year. They also showed its profound impact on estimates of the time history of total ocean heat content. Here we examine the bias identified by Gouretski and Koltermann (2007, hereafter GK) using a different method, diagnose the likely source of the error and recommend a correction.

2. The fall rate problem

XBTs were developed in the early 1960s at the request of the U.S. Navy (Seaver and Kuleshov 1982). The instrument is essentially a thermistor embedded in the nose of a hydrodynamic bulb with two spools of wire: one within the probe and one on the vessel that unwinds as the instrument free-falls from the surface to depth and the vessel steams away from the deployment location. The instrument collects a temperature versus time trace, with the latter converted to reported depth, Z_XBT, using a “fall rate equation”:

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where t is the elapsed time in seconds since the XBT hit the ocean surface.

The bulk of XBT temperature profiles were collected using probes manufactured by Sippican Incorporated (now Lockheed Martin Sippican). Between 1965 and the late 1990s Sippican probes were produced in the United States, after which their manufacture was moved to Mexico. However, the Sippican probe components have remained consistent, consisting of a plastic spool with a zinc nose weight and an afterbody wrapped in plastic-coated copper wire (Sippican 2007, personal communication). One component that has changed significantly is the XBT data system (recording mechanism), changing from analog to digital during the 1980s.

It has long been recognized that depth determination is the most likely source of error in XBT data (Roemmich and Cornuelle 1987). Since the mid-1970s comparison studies between simultaneous XBTs and CTDs have identified systematic errors in the computed XBT depths. Early results suggested that a small negative correction was required for the water above the thermocline, while a much larger positive correction was needed for depths below it (Fedorov et al. 1978; Flierl and Robinson 1977; McDowell 1977; Seaver and Kuleshov 1982). No official correction factor was adopted by Sippican until the early 1990s when Hanawa et al. (1995, hereafter H95) pooled and analyzed recent field intercomparisons against research-quality CTD data. Their comprehensive analysis of the field data unambiguously showed that using the manufacturer’s fall rate equation resulted in deduced depths that were too shallow (and thus produced a cold temperature bias in most of the ocean). H95 recommended a new fall rate equation for Sippican and Tsurumi Seiki Co., Ltd. (TSK) XBTs, but recommended that it not be implemented until arrangements for adequate metadata reporting about the fall rate were put in place. As one reviewer notes: “Many data providers jumped the gun and implemented the correction immediately, leading to ambiguity (corrected/uncorrected) in data from the mid-1990s. Problems persist even to the present day since fall rate metadata are sometimes reported incorrectly.”

It was also recommended that the reported depth for all past XBT profiles for which depth was found using the manufacturer’s original fall rate equation should be corrected to the same effective equation by multiplying by a factor of 1.0336. Thus in the global archives of Boyer et al. (2006), much work was done to provide information on which XBT profiles needed correction (supplied using old manufacturer’s fall rate equation) and which did not (i.e., those reported using the H95 fall rate equation). Despite this and, as noted above, the transition to the new fall rate equation occurred over many years, and not all contributors have provided the necessary or correct metadata.

3. The mean warm bias and its character

The average warm bias of XBTs identified by GK is revealed by differencing the XBT and CTD/bottle based climatologies for the year 1985 (Fig. 3). At nearly all latitudes and in all ocean basins (Fig. 4) we find a warm bias of between 0.05° and 0.3°C. The bias is small but positive (∼0.04°C) near the surface, is a maximum in the tropical thermocline, and is more uniform below that.

One striking feature, though, is that at around 500 m the bias drops to smaller values in deeper waters. The fact that the temperature biases have a depth dependence—small near the surface and a maximum in the strong tropical thermocline—strongly points toward a fall rate error. There is a consistent change in the bias around 500 m (Fig. 4), the maximum depth reached by the T4 probes. This implies that shallow XBTs may have a different bias from deep XBTs. Poleward of about 45°S and 55°N the bias is less clear, and this is likely due to the larger mapping errors associated with strong fronts and currents, smaller vertical temperature gradients reducing the detectability of a depth error, and scarce data in the subantarctic and Arctic regions. In addition, some work suggests that fall rates are affected by ambient densities (e.g., Thadathil et al. 2002), but our data might not be adequate to address this issue.

As fall rate errors are the most likely source of biases in XBTs, the temperature errors are converted into depth reading errors using the local temperature gradient to see whether the resulting error has the right characteristics for a fall rate bias—linearly increasing with depth (Willis et al. 2008). We take into account the strong seasonal cycle and secular temperature trends in the upper ocean by performing the conversion of temperature residual into a depth error estimate profile by profile. Thus, for each identified XBT profile, a mapped equivalent for the right year, location, and season is generated using our bottle/CTD climatology. The resulting temperature residual is then converted to a depth error using the appropriate climatological temperature gradient as follows:

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Here, dZ is the depth error, dT_xbt is the temperature residual and ∂T_clim/∂z is the local climatological temperature gradient.

The individual cast depth errors, like their associated temperature residuals, are dominated by eddy variability and thus massive averaging is required to identify the small shift in the central tendency. Averaged globally and over all years the XBT depth errors do, indeed, show a linear dependence on depth that we argue is diagnostic of a fall rate error (Fig. 5). As suggested by Figs. 3 and 4, shallow XBTs have a significantly larger depth bias than deep XBTs, with depth errors of 10 m near 400-m depth compared to 5 m for deep XBTs. The averaged depth error in CTD and bottle casts is barely distinguishable from zero, which is a reassuring confirmation of the method. Near the surface estimates are noisy as the vertical temperature gradient is small there, and thus the depth error is not well defined. Interestingly, MBTs show a rough 6-m depth error with a structure that is not at all linear in depth. As we do not understand the source of this error in MBTs, we do not attempt to model and remove it. For this reason, we recommend that MBTs be excluded from studies requiring depth accuracy of <5 m.

4. Time dependency

While it is encouraging that the XBT temperature bias appears to be caused by fall rate errors that may be correctable, GK clearly show that this bias is not stable over time. Correction to the archive will only be possible if the data bias across the archive follows a common time history. To explore this possibility, the depth errors were averaged in different ocean basins, and also in different latitude bins. As many agencies stockpile XBTs over periods of 1–2 yr (sometimes longer) our time resolution will be biennial at best, so analyses were carried out in overlapping 2-yr bins.

Remarkably, we find that a common time history does exist in the depth errors (Fig. 6). For example, the diagnosed mean depth errors at 600 m for deep XBTs in the separate ocean basins vary together, with a minimum bias in 1985–90 and maxima in 1978 and 2005 (Fig. 6). The shallow XBTs show a similar variation but with a different magnitude of bias in the later years. Natural ocean variability does not vary uniformly in space (that is with all basins and latitudes in synchronicity) and is unlikely to vary in a way that generates a linearly increasing depth error. Therefore, the most likely source of the common time history in the depth bias of XBTs are subtle manufacturing changes at the XBT factory, which affect the fall rates of entire batches of probes.

At the suggestion of a reviewer we checked the time history of the bias in the northwest Pacific where large numbers of profiles were collected using XBTs manufactured by TSK. This region does, indeed, feature a depth-bias time history that is different from the other basins (Figs. 6d,h), though care must be taken when averaging over a small region as ocean variability may impact the results more.

A correction is fit to the diagnosed depth biases, where the depth error is modeled as a simple multiplicative factor of depth, r, defined such that r = [Z_XBT − Z_true]/Z_XBT.

Attempts were made to include an offset term, as well as a multiplicative factor, but the former was not stable between subsets of the archive. The fit was performed on each profile and then bin averaged. Errors are bootstrapped, whereby 25% of the individual profiles in each pool are randomly sampled to produce a 50-member solution ensemble whose standard deviation is used to determine the error levels. Using a simple multiplicative factor to model depth error results in a remarkably reproducible time history between ocean basins (Fig. 7), though in recent years for deep probes we see some spread between ocean basins that might be due to incorrect metadata about reported fall rates.

Both types of XBTs show small biases (relative to the H95 fall rate) in the early 1970s, just after XBTs came into widespread use. After this period, the bias grows, reaching a 6% error in the late 1970s. After this time, the error quickly returns to near zero when H95 reexamined fall rates and set the new international standard, confirming the accuracy of the H95 results throughout the late 1980s and early 1990s. In the mid-1990s however, we see two distinct changes in the much more numerous deep XBTs—one near 1992 and another larger change in 1999. The latter change may be associated with a shift in manufacturing site from the United States to Mexico.

The diagnosed error factors also help explain the pattern of the mean temperature bias (Fig. 3). When shallow XBTs are very numerous and dominate the global archive (1972–85) their mean depth bias is 5%–6%. After 1990, deep XBTs dominate the archive with a depth bias of only 2.5%. Most of the shallow XBTs deployed globally have a large depth bias, while most deep XBTs had a depth bias roughly half as large. Thus, over the entire archive, temperatures below 500 m have a smaller warm bias than those above. Depth errors, r, diagnosed from EN3, are reported in Table 1 such that

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5. Comparisons with independent methods

Given the complexities and uncertainties of how XBT data are collected (recorder type, ship speed, probe source) and archived (accurate metadata for probe type and fall rate) the derivation of a global correction based simply on year of deployment and depth of measurement would appear naive. Attempting to retrieve the correct metadata to attack this problem in more detail far into the past archive is a very daunting task and it is likely impossible to achieve 100% accuracy. However, the fall rate changes that we have diagnosed since the early 1990s can indeed be independently checked. Based on H95’s recommendations, greatly improved metadata was collected for a larger portion of profiles sent to the global archives from the early 1990s onward. In addition, the XBT data can be checked against independent contemporaneous data—either in situ CTD data or altimetric satellite data. Here we use these methods to check our depth error estimates.

a. Altimetric pseudotemperature method

Another powerful technique for characterizing the XBT bias is analysis of nearby XBT/CTD pairs as described in Willis et al. (2008). The technique is limited by the number of nearby XBT/CTD pairs. Since the early 1990s, however, satellite altimeters have provided global measurements of sea surface height (SSH) variability with excellent spatial and temporal resolution. A number of studies (e.g., Gilson et al. 1998; Willis et al. 2004) have shown that SSH anomalies are strongly correlated with upper-ocean temperature variability. By exploiting this correlation along with improved metadata since the early 1990s, it is possible to use the altimeter data to characterize recent XBT biases in much greater detail than for earlier periods.

The “Upd” product containing gridded SSH anomalies from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) were used for this analysis. This product contains data from several satellite altimeters and includes variability on scales as small as 10 days and 150–200 km (Ducet et al. 2000).

For this part of the analysis, CTD data were obtained directly from both the GTSPP and WOD05 databases, and Argo profile data were obtained from the Argo array of profiling floats (Gould et al. 2004). XBT data were obtained from GTSPP, and, as above, all recommendations about application of the H95 depth correction were followed and probes of unknown type (GTSPP $DPC code 03) also had the H95 correction applied. Data quality flags provided by GTSPP were used to eliminate spurious profiles when available. In addition, a six standard deviation test was performed using profiles in approximate 10° × 10°, geographically similar boxes to eliminate additional gross outliers.

To use the SSH data to test for biases in XBT profiles, local linear regression coefficients were computed between SSH and subsurface temperatures using temperature profiles from CTDs and Argo floats. Argo profiles with spurious pressure values identified by Willis et al. (2008) were excluded from this calculation. The regression coefficients allow subsurface temperature anomalies to be estimated from SSH anomalies as follows:

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where, α(x, y, z) is a local regression coefficient and T_pseudo is the estimate of subsurface temperature anomaly, referred to as the “pseudotemperature” profile.

Regression coefficients were computed in 2° longitude × 1° latitude bins on each 10-m level depth from the surface to 750 m. Temperature anomalies were computed relative to the World Ocean Circulation Experiment (WOCE) Gridded Hydrographic Climatology (WGHC) (Gouretski and Koltermann 2004). Figure 8 shows the correlation coefficient, r, between SSH and temperature anomaly at 400 m. Note that in most regions, r is greater than 0.5.

Once the regression coefficients were computed, pseudotemperature profiles were estimated at the times and locations of all profiles from 1993 through the end of 2006. These “pseudopairs” were then used to examine the dependence of the XBT fall rate bias by probe type and manufacturer. The depth error was then estimated by differencing the observed temperature and the pseudotemperature and normalizing by ∂T_clim/∂z as described above. However, for the pseudopair analysis the WGHC climatology was used to compute ∂T_clim/∂z rather than the bottle/CTD climatology.

The pseudopair technique was first tested for consistency by estimating the depth error for CTD and Argo profiles. Figure 9 shows the median depth difference between CTD profiles and their pseudotemperature pairs, grouped in 1-yr increments from 1993 through 2002. With only a few thousand pairs per year, the depth differences range from 3 to 5 m. Nevertheless, the lack of any time dependence and the proximity to zero suggest that the altimeter data provides a stable, accurate tool for determining depth errors during the altimeter record.

Also shown in Fig. 9 is a pseudopair analysis of Argo data by float type. This serves primarily as a consistency check of the technique as the floats provide most of the data used to determine the regression coefficients, α(x, y, z). Apart from the known bias in a number of Sounding Oceanographic Lagrangian Observer (SOLO) floats from the Woods Hole Oceanographic Institution (Willis et al. 2008), most float types have profiles with nearly zero depth error relative to the pseudopairs, as expected. The Provor and Autonomous Profiling Explorer (APEX) floats with Falmouth Scientific, Inc., (FSI) sensors do show slight offsets below 300 m, but with only 6000 and 1200 pseudopairs, respectively, there are too few of these profiles to determine whether these small offsets are significant.

The pseudopair technique provides an independent estimate of temperature anomaly for each individual profile. However, the altimeter data still do not resolve eddy or internal wave variability on scales smaller than about 150 km and 10 days time. For this reason, significant averaging is still necessary to produce a robust estimate of XBT data errors. Nevertheless, this technique requires fewer pairs than a direct comparison between XBT profiles with nearby CTD and Argo profiles. This is illustrated in Fig. 10, which shows the frequency distribution versus depth of the pair analysis for Sippican Deep Blue XBT probe with H95 coefficients (WMO code 052) compared with nearby Argo profiles, over the 3-yr period from 1 January 2004 through 31 December 2006. Argo profiles were considered to be “nearby” if they fell within 4° longitude, 2° latitude and 90 days of an XBT probe. About 14 000 such pairs were available during this period. The median value and one standard deviation range are highlighted. The frequency distribution of depth errors based on the pseudopair analysis for the same XBT probes is also shown in Fig. 10. Note that the median value is almost identical. However, the large time and space window needed to capture a sufficient number of Argo/XBT pairs results in a larger standard deviation for that technique. For the pseudopair technique, the altimeter data are interpolated to the time and location of the XBT profile, resulting in a one standard deviation range that is about 12 m smaller. This suggests that fewer pairs are needed for the pseudopair analysis technique to converge.

Figure 11 shows the temporal evolution of the depth bias in Sippican Deep Blue XBT probe with manufacturers original fall rate coefficients (WMO 1770 code 051) for each year from 1993 through 2005, based on the pseudopair analysis. About 30 000 of these probes were deployed over the entire period and were more abundant during the 1990s. Note the sharp increase in the bias after 1999, again possibly reflecting changes in manufacturing that occurred after relocation of the main Sippican manufacturing facilities to Mexico.

Table 2 contains the temporal evolution of the depth biases of all probe types of substantial abundance in the GTSPP database computed using the pseudopair technique. As above, the depth error is modeled as a multiplicative factor of depth. Table 2 shows depth error, r, for each probe type and time period. Where there are fewer than 200 probes of a given type in a year, an analysis was not made. The error in r is also computed using the same bootstrap method described above. In general, the pseudopair method confirms the results found in the EN3 analysis (Fig. 12). In particular, the steplike increase in bias among deep XBT probes is confirmed for the abundant Deep Blue probes and the shallow probes. However, for the probes indentified as T7s (Fig. 12b), there is marked divergence from the EN3 correction in certain years and the amplitude is close to that expected if probes are either uncorrected or double corrected with the depth factor 1.0336 suggested by H95. This illustrates a possibly serious problem with the metadata in the archives not being consistent with the fall rates used to determine depth.

It is important to note that the description of XBT biases presented in Table 2 may represent changes in data processing as well as any actual changes in instrument manufacture. In many profiles, ambiguities remain about which fall rate equations were used when the data were submitted to the archives. In the present analysis, we have chosen to adopt the recommendations of GTSPP over whether or not to apply the H95 depth correction factor. However, further refinement of the bias estimate may be possible by considering additional metadata associated with the XBT profiles such as cruise number, data source, or profile history. With a more precise classification of XBT probe type and fall rate equation, bias in these instruments could be better characterized and minimized.

b. Historical and recent in situ field comparisons

It is also possible to compare the EN3-based history of fall rate changes with past field assessments. To do this we convert our slope error into an estimate of the first term, A, in the XBT depth equation (1). The variability in the second-order coefficient B has a much weaker affect on depth estimates than changes in the first-order term A.

If Z_true = A_truet − Bt² and z_XBT = A_XBTt − Bt², where “true” is the actual fall rate parameters, and “XBT” refers to that used in EN3 (the H95 values), then ignoring the small changes in B we can estimate the implied changes in the A term via

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In addition to the field comparisons compiled by H95 in their Table 1, we also examine the additional in situ depth bias estimates listed in Table 3 where depth displacements are converted to an estimate of the A term using the reasoning above.

An in situ CTD/XBT comparison was also carried out in 2001 in the Tasman and Coral Seas. During a high spatial-resolution CTD section, XBTs were dropped during each CTD cast providing a direct cast-by-cast comparison. The results show a clear warm bias in the XBT data (Fig. 13) and, when converted to a depth error, translates to a 3% overestimation of depth, agreeing with our analysis from EN3.

The deduced time history of the fall rate coefficient A for deep XBTs (Fig. 14) based on EN3 agrees very well with most of the published results in the literature where fall rates were actually calculated—the values from H95 Table 1 (numbered), T98, and Snowden et al. (2007, hereafter SGB07). Ironically, the H95 assessment was done at a time when fall rates were faster than at any other time. The reduction of deep XBT fall rates since 1990 is independently confirmed by field intercomparisons (e.g., SGB07), as are the low values in the later 1970s. Before 1975 our estimate does not agree well with the depth errors in the literature, but at this time the number of deep XBTs in the database is quite small. The comprehensive study by Reseghetti et al. (2007, hereafter RBM07) also disagrees with SGB07’s and our results for recent years. However, in their fitting of fall rate parameters to the in situ data, they did not allow for the low values of A found by SGB07, and interestingly found a residual warm bias in their fall rate corrected temperature values. These recent studies raise serious questions, not just about the constancy of the fall rate equation, but also around its form.

6. Summary and discussion

An analysis of temperature and implied depth errors of the XBT profiles in EN3 confirm GK’s findings that there is a time-variable warm bias in the XBT data. Here, we show that this bias is largely due to year-to-year changes in XBT fall rates and that shallow XBTs (T4s) have a different error from deep XBTs (T7s and Deep Blues). We believe it is highly likely that these are due to small changes in the manufacture of XBT probes since the changes are to first order spatially synchronized, have the vertical characteristics of a fall rate error, and are hard to explain in any other way. Our results are largely supported by historical and recent field intercomparisons between XBTs and CTDs, as well as a pseudoprofile technique based on satellite altimetry.

The XBT depth errors can be well modeled as a factor of total reported depth, and we present correction factors for the EN3 data up to 2005 (Table 1). It is crucial to note that these factors apply to XBT profiles that have been adjusted to the H95 fall rate equation. Also, we do not assert that the suggested corrections account for all the bias errors in the archive across all contributing institutions, recorder, and probe-type combinations. Untangling this problem is extremely daunting, given the small amount of metadata for pre-1990 profiles. Our results do suggest, encouragingly, that the bulk of the bias is common across these variations, and thus can be removed to first order. A more careful analysis using more of the available metadata is warranted, and it may be particularly worthwhile to revisit historical XBT/CTD intercomparison datasets to check the form and changing coefficients of the fall rate equation. SGB07 find a depth offset term in their dataset and our Coral Sea data support this. RBM07 find a residual temperature bias. This should also be further studied. In, addition, if XBT data are to be combined in analyses with other data types, some kind of ongoing batch calibration will be necessary, based either on annual field intercomparisons or using the pseudopair method discussed above. These issues present quite a challenge to the community.

Since XBT profiles make up more than 70% of the global temperature profile archive, the impact of these errors on estimates of global ocean heat content changes is large, as shown by GK. Using the spatial interpolation method of Church et al. (2004), and an unbiased XBT/CTD/bottle climatology as a reference, we estimate global ocean thermosteric sea level changes for the upper 700 m (Fig. 15). When corrected for the XBT bias, thermosteric sea level (and the associated ocean heat content) shows much weaker decadal variability in the 1970s and a higher rate of rise for 1961 to 2003 (e.g., compare the fitted linear trends). Though the endpoint values are similar, as found in GK the bias in the XBT data account for a large part of the 1970s decadal change in ocean heat content reported by Levitus et al. (2005). Based on the XBT bias corrections proposed here, Domingues et al. (2008) show that the average heat uptake in the upper 700 m of the ocean, from 1961 to 2003, accounts for a larger portion of sea level rise than previously believed. Their ocean warming and thermal expansion rates are about 50% larger than equivalent rates of earlier estimates (Antonov et al. 2005; Levitus et al. 2005; Ishii et al. 2006).