1. Introduction
The historical record of the vertical temperature structure of the subsurface of the ocean is used to estimate the change in the heat content of the oceans over time (e.g., Levitus et al. 2000, 2005; Domingues et al. 2008; Levitus et al. 2009; Ishii and Kimoto 2009), among other applications. A substantial proportion of this record is derived from measurements made using expendable bathythermograph (XBT) instruments. Following their introduction in 1966 the popularity of XBTs grew rapidly and during the 1970s they were used to measure more than a third of the recorded profiles. The number of profiles measured using XBTs continued to increase further through to the mid-1990s. Recently, their use has decreased and profiling floats launched as part of the Argo project (http://www.argo.ucsd.edu and http://wo.jcommops.org/cgi-bin/WebObjects/Argo) have become the dominant source of subsurface ocean data.
The XBT instrument operates by free-falling through the ocean, measuring temperature as it travels. The temperature data are telemetered back to the launch vessel via a wire. The depths at which the measurements are made are not recorded directly. Instead, the time since the XBT entered the water is converted into a depth using a “fall rate equation.” There are a number of different XBT types and manufacturers. The most numerous type is the T4, which measures to a nominal depth of 460 m (Lockheed Martin Corporation 2005). Other common types are the T7 and Deep Blue probes, which both reach 760 m, and the T5 and T10 instruments that measure to 1830 and 200 m, respectively (Lockheed Martin Corporation 2005). The most common manufacturer is Sippican Inc. (now Lockheed Martin Sippican), followed by Tsurumi Seiki (TSK) and then Sparton. Unfortunately, metadata describing the type and manufacturer are unavailable for about 50% of XBTs (Ishii and Kimoto 2009).
A variety of potential sources of bias have been identified for XBT data and these can affect both the temperatures and the depths attributed to the measurements (e.g., see Reseghetti et al. 2007). In particular, a number of previous studies have highlighted issues with obtaining the measurement depths indirectly using a fall rate equation. Hanawa et al. (1995) demonstrated that the fall rate equation provided by the manufacturer for Sippican and TSK T4, T6, and T7 XBTs underestimated the depths. Kizu et al. (2005) found that the depths of TSK T5 temperature measurements were overestimated, although those from the Sippican T5 exhibited almost no bias. New fall rate equations were proposed for the affected instruments.
Gouretski and Koltermann (2007) demonstrated that time-varying biases exist in XBT data, which cause spurious interdecadal variability in estimates of ocean heat content. They highlighted the need for the development of a procedure to account for these biases. One approach is to use a technique that reduces potential depth-related biases such as analyzing average temperature above an isotherm (Palmer et al. 2007; Palmer and Haines 2009). A number of time-varying adjustments have also been published that can be used to correct the data. These are based on comparisons between XBT data and the highest-quality measurements available, such as those made using conductivity–temperature–depth (CTD) sensors.
Various methodologies have been used when developing time-varying corrections for XBT data. Wijffels et al. (2008) calculated two sets of time-varying multiplication factors that can be used to correct the profile depths. For the first set they divided XBTs into “shallow” and “deep” types and generated corrections for each. The second set of corrections, which made use of satellite altimeter data and hence were only defined since 1993, divided XBTs by type and whether the manufacturer-supplied equation or the Hanawa et al. (1995) fall rate equation had been used. The corrections of Ishii and Kimoto (2009) are applied to depths and are proportional to the time since launch of the XBT. Separate sets of corrections are provided for a number of different types and makes of XBTs. Both the second set of corrections of Wijffels et al. (2008) and those of Ishii and Kimoto (2009) include an “unknown” type, consisting of the large proportion of XBTs for which the metadata are incomplete. Wijffels et al. (2008) also divided these unknown XBTs into shallow or deep types. Levitus et al. (2009) calculated corrections to the temperatures at a number of standard depth levels, with no division by type or manufacturer. This methodology allows other types of biases to be corrected in addition to fall rate errors, but does not distinguish between them. Gouretski and Reseghetti (2010) derived depth-independent, time-varying temperature corrections and depth-dependent, time-independent depth corrections, with a set of corrections for T4 and T6 XBTs, and a set for T7s and Deep Blues. In contrast to the other studies that focused only on depth adjustments, they found that the depth biases do not vary strongly from year to year and that the corrections required can be approximated by a time-independent formula. The variety of approaches that have been used is symptomatic of the difficulties with the XBT metadata and the limited amount of information available to diagnose and derive corrections for the biases that might exist in XBT data.
In this study, an attempt is made to isolate biases in XBT depths associated with incorrect fall rates from other potential error sources. The method involves using a bathymetry dataset to derive corrections for estimates of ocean floor depths in shallow regions made using XBT data. As the methodology and data used to obtain these corrections are different to those used in previous studies, these represent an independent assessment of the biases in XBT depths. In section 2, the methodology that has been developed is explained in detail. Then, in section 3, the depth adjustments that have been obtained are described and compared to those proposed by Wijffels et al. (2008), Ishii and Kimoto (2009), and Gouretski and Reseghetti (2010). Finally, in section 4, possible causes of the similarities and differences seen and some of the limitations of the corrections are discussed.
2. Data and methodology
The profile data were obtained from version 2a of the EN3 dataset (available online at http://www.metoffice.gov.uk/hadobs/en3; Ingleby and Huddleston 2007). The XBT observations in this dataset were sourced originally from the World Ocean Database 2005 (WOD05; Boyer et al. 2006) and the Global Temperature and Salinity Profile Program (GTSPP) database (available online at http://www.nodc.noaa.gov/GTSPP/). As part of the EN3 processing a comprehensive set of quality checks are performed. Those observations where the entire profile had been rejected were not used. This should exclude from the analysis profiles that have gross errors in their positions. The processing also included application of the depth corrections of Hanawa et al. (1995) and Kizu et al. (2005) where required. Following Thadathil et al. (2002), some of these corrections had been reduced in cooler water (see Ingleby and Huddleston 2007). To obtain a dataset that is comparable to those analyzed by Wijffels et al. (2008), Ishii and Kimoto (2009), and Gouretski and Reseghetti (2010), this cold water tapering of corrections was removed. Where possible, the types and manufacturers of the XBTs were identified using the metadata supplied with each profile. Profiles purporting to be from the shallower probes were assumed to be of type T5 if their profiles extended beyond 840 m. However, this was not applied to profiles from Deep Blue probes as some are able to reach deeper than this.
An estimate of the depth of the ocean was determined from each XBT profile (DXBT). In the majority of cases this was achieved by finding the maximum depth for which a temperature had been recorded. However, some profiles have repeated values at their base. For these a simple approach was adopted where DXBT was estimated to be the depth at which these repeated values begin. An estimate of the depth of the ocean (DBathy) was also obtained using the General Bathymetric Chart of the Ocean (GEBCO) 30-arc-sec gridded bathymetry (The GEBCO_08 Grid, version 20090202, available online at http://www.gebco.net). The depth at each XBT profile position was determined from the gridded data using bilinear interpolation.
Figure 1 shows an example of the resulting depth data. Here DBathy is plotted against DXBT for all the profiles from the period 1985–87 (black dots). If the two estimates of depth were exactly equal, they would lie on the gray line. The locations at which these profiles were recorded tend to be near coastlines, as shown in Fig. 2. For 4% of these profiles DXBT is greater than DBathy by 200 m or more, which implies that there are large errors in either the bathymetry or the XBT data for a significant proportion of the observations. There are also many points where DXBT is much less than DBathy. These will mostly correspond to situations where the XBT had not reached the floor of the ocean when it stopped measuring, either because it was not designed to reach that depth or because there was a problem such as a wire break. The large number of points in a vertical band between approximately 450 and 480 m corresponds to the maximum depth of the T4 XBT. Other vertical lines mark either the maximum depth of other types of XBT or appear to be common depths at which XBT measurements were stored. Of the data shown in Fig. 1, approximately two-thirds lie in a narrow band defined by |DXBT − DBathy| ≤ 100 m. Therefore, despite the issues that have been noted, a large proportion of the data is potentially of use for diagnosing depth biases.
As only XBTs that reach the bottom of the ocean are of use for this analysis, any profiles that extend to within 10 m of the nominal maximum depth of the instrument used to record them were discarded. Figure 3 (left panel) shows the distribution of the ratio DBathy/DXBT for the remaining data for the Sippican T4 XBT. Owing to the erroneous data points and those where the XBT did not reach the ocean floor, the tails of the distribution do not decrease to zero.
A methodology was developed to obtain from these data a correction that can be applied to the XBT depths so that, on average, they match the bathymetry. Owing to the many data points that are erroneous or do not carry useful information, fitting a line to the data was unsuccessful. Instead, a method that is resistant to the outliers was adopted. To estimate a correction for a particular point in time all the observations that used XBTs from the type and manufacturer of interest were found and the 3 years of data centered on that time were selected. A smoothed histogram of the ratio DBathy/DXBT was then produced: the number of observations with DBathy/DXBT within the range 0.80–0.90 (i.e., within 0.05 of the central value 0.85) was counted to produce the first point of the histogram. This was repeated but with the center of the range shifted upward by 0.002 to form the next point of the histogram. This procedure continued until the central ratio value was 1.10. The mode of the resulting histogram is the multiplication factor that needs to be applied to DXBT to adjust the distribution so that it peaks at ∼DBathy/DXBT = 1. This was repeated so that a correction was obtained for the midpoint of each year between 1968 and 2008. The parameters used in this algorithm (such as the number of years of data used to calculate each correction) were set to the values that best balanced the need to minimize the noisiness of the results while still providing a good representation of the time evolution of the corrections and the structure of the histograms. When calculating corrections for XBTs with unknown type and manufacturer, observations with DXBT between 450 and 480 m were not used. It was found that if this step was not applied, the numerous T4 profiles could dominate the data being analyzed. There were sometimes large numbers of measurements recorded at the same location and with the same depth values (e.g., a series of measurements using XBTs of unknown type and manufacturer at 54.6°N, 11.5°E). To avoid these repeats skewing the results, at each time step only one instance was retained.
The result of applying the corrections to the data is illustrated in the right panel of Fig. 3. This shows a histogram of the same data used for the left panel but after the corrections have been applied to the XBT data. The result of applying the corrections is that the histogram has shifted so that the peak is aligned more closely with 1.0. The mode of the smoothed histogram generated as described above was 0.974 for these data. If the XBT depths were first corrected using the histogram modes as multiplication factors and then a new histogram generated, the mode changed to 1.000.
A bootstrap method was used to estimate the uncertainty in the values of the modes of the distributions that arises from the limited sampling of the underlying distributions. The data used to generate each histogram were randomly resampled (with replacement) to obtain 10 000 alternative realizations of the original data. For each realization a new histogram was calculated and the mode determined. The range that encompassed 99% of the results (leaving 0.5% at each extremity) and the median were calculated from these modes.
The result of performing this analysis was a set of estimates of the multiplication factor required to make, on average, the estimates of ocean floor depth from XBT profiles equal to those from the bathymetry. This type of correction is useful for the situation where the XBTs fell faster or slower than anticipated in the fall rate equation. It is possible that there are also additive errors in the depths, for example due to the XBT being launched from a height that meant it was traveling faster or slower than assumed in the fall rate equation when entering the water. While it was not possible to derive adjustments for these types of error with the data being analyzed, by applying corrections derived using other methods (e.g., those of Gouretski and Reseghetti 2010) to the XBT profiles before performing the analysis, it is possible to assess their performance.
3. Results
There were 19 XBT-type and manufacturer combinations for which there was at least one profile that met the criteria for use, including an “unknown” category. From these, four types of XBT were selected for further investigation: the Sippican T4, the Sippican T7, the Sippican T10, and those XBTs where neither the type nor manufacturer is known. These all have periods during which the number of profiles suitable for use was large, which reduces the uncertainty in the derived corrections. The adjustments required for the remaining XBT types are less well constrained owing to the small number of observations.
Figure 4 (left panel) shows the number of XBT profiles in use across the global oceans for each type (black lines) and in water shallow enough for them to reach the bottom of the ocean (gray shaded areas). While the number of T4, T7, and XBTs with unknown type and manufacturer in use in shallow water are a small proportion of the total in use across the globe, they represent the majority of the T10 measurements. When the numbers of plotted as proportions (Fig. 4, right panel) it is possible to see that while the Sippican T10 measurements represent less than 5% of XBT profiles across the globe (black lines), they form a much larger proportion of those used in shallow water. The same is true for the Sippican T7 for recent years while the Sippican T4 is underrepresented in shallow water compared to the globe during the 1980s.
Figure 5 shows representations of the histograms for each of the four types of XBTs that were selected for further analysis. To display all the histograms on the same plot, each has been scaled so that the maximum value is unity. The scaling factor used is displayed in the lower part of each plot. The red and blue colors show the height of the histograms after scaling and the modes are shown by the black lines. The dotted line indicates the position where DBathy/DXBT = 1. The gray lines show the medians and dashed lines the 99% confidence intervals of the modes found during the bootstrap analysis. The medians found from the bootstrap analysis and the modes of the original data generally follow each other closely. The median values are often close to the edge of the confidence intervals, indicating that the distribution of the modes found in the bootstrap analysis was skewed. The modes of the distributions (referred to from now on as the “corrections”) and the confidence intervals from the bootstrap analysis are listed in Table 1.
For the Sippican T4, the number of observations is greatest in the 1970s and decreases to small values in the 1990s. This is reflected in the size of the confidence intervals, which are larger when the number of observations is small. There were no observations for the Sippican T10 at the begining of the time series and, as with the Sippican T4, there are relatively few toward the end. In contrast, the number of Sippican T7 observations is largest from 1996 onward. The profiles for which the type and manufacturer are unknown are the most numerous. The number peaks in the early 1990s but then decreases to zero, resulting in very large confidence intervals in the most recent years.
The corrections are compared to those proposed by Wijffels et al. (2008), Ishii and Kimoto (2009), and Gouretski and Reseghetti (2010) in Fig. 6. In these plots, the black line shows the corrections obtained in this study, and the gray shading shows the 99% confidence interval. The dashed lines indicate the bounds of these intervals. To aid interpretion of the quality of these corrections when comparing them to those proposed in the previous studies a plus symbol has been plotted for those corrections where the range of the uncertainty limits is less than 0.04. This corresponds roughly to the quoted accuracy of the XBT depths of ±2% (Lockheed Martin Corporation 2005). Note also that care should be taken when interpreting these plots as rapid, short-term changes in corrections may be due to the uncertainty in the results rather than a real change in XBT fall rate.
The Ishii and Kimoto (2009) corrections were converted to an equivalent depth correction using the transform (b − at − I)/(b − at), where a, b are the fall rate coefficients from Hanawa et al. (1995); I is the correction; and t was set to be 30 s, which corresponds to approximately 200-m depth. The interval I ± 0.02 m s−1 was taken to correspond to the 95% confidence interval in the corrections and this was converted to a 99% confidence interval under the assumption that the errors are normally distributed. This confidence interval is shown on the plot using the blue shading. The 99% confidence intervals from Wijffels et al. (2008) are represented in the figure by different shades of green, red, and purple. Also shown (in cyan) are depth correction factors for the T4s and T7s from Gouretski and Reseghetti (2010). These are time invariant, but the correction factor used to adjust each depth value varies considerably with depth and so cannot be represented as a single line in Fig. 6. Therefore, the correction factors that are applied at three different depths are shown. The solid lines show the correction factor at 100-m depth, the dashed lines at 200 m, and the dashed–dotted lines at the full depth of the instrument (460 m for the T4 and 760 m for the T7).
For the Sippican T4, the results from this work and those of Wijffels et al. (2008) and Ishii and Kimoto (2009) demonstrate a similar time evolution of biases in the first half of the time period shown. This consists of an increase in the size of the required adjustment to the depths (as the correction values become further from 1.0), followed by a decrease. This result seems to provide additional confirmation that there is a time-varying bias in the XBT depths. However, there are differences in the magnitudes of the corrections. At the beginning of the time period, the confidence intervals obtained in this work generally encompass the corrections obtained in the other studies. The size of the corrections are generally slightly larger than those of Ishii and Kimoto (2009) during this time. Those of Wijffels et al. (2008) for shallow XBTs (which include the Sippican T4) follow a similar path, except during the mid-1970s when they move to the lower edge of the confidence intervals. From the early 1980s to the early 1990s both the Wijffels et al. (2008) and Ishii and Kimoto (2009) corrections are outside the limits of the confidence intervals. The size of the corrections become very small in both before increasing again, but this occurs earlier in the results from Wijffels et al. (2008). However, since the Wijffels et al. (2008) corrections are derived from all shallow XBTs, which would include types such as the T6 and T10 and probes from other manufacturers, some disagreement with studies that derived corrections for single types of XBT (such as Ishii and Kimoto 2009) should be expected. The results from this study imply that a larger correction to the Sippican T4 XBT depths might be required than previously thought. From 1990, the confidence intervals obtained in this study become very large owing to the reduced amount of data available compared to previous years. The other published corrections lie within these confidence ranges. However, they are not always consistent with each other; for example, the Ishii and Kimoto (2009) corrections do not always fall within the uncertainty ranges from Wijffels et al. (2008).
Owing to the low number of observations, the uncertainties in the corrections for the Sippican T7 are relatively large in the early part of the time period compared to those obtained for the other XBT types. However, some similarity to the time evolution of the corrections obtained by Wijffels et al. (2008) and Ishii and Kimoto (2009) is evident and the uncertainties generally encompass their results. At the end of the time period the uncertainties are smaller and some disagreement in the time evolution is evident. For example, the corrections of Ishii and Kimoto (2009) are at the upper bound of the confidence intervals from this study in 2000, but fall to the lower bound in the most recent year. The corrections for deep XBTs of Wijffels et al. (2008) are at the lower bound of the confidence interval, and those from their second set of corrections also show different changes in bias. Other studies have investigated the depth errors of these XBTs in recent years. Reseghetti et al. (2007) obtained a new fall rate equation for the Deep Blue type of XBT (which is similar to the T7 but suitable for boats traveling at greater speeds). At approximately 200 m the new fall rate equation provides a depth that is greater than the Hanawa et al. (1995) equation by 0.4%. Reverdin et al. (2009) found that depths of T7 and Deep Blue XBT profiles recorded between 1997 and 2007 are overestimated by 1.7% and 1.2% for equatorial and midlatitude regions, respectively, while DiNezio and Goni (2010) calculated that depths were overestimated by 3% for T7 and Deep Blue probes between 2000 and 2007. Therefore, there is still some uncertainty about the size of correction required in recent times for this type of XBT.
According to Gouretski and Reseghetti (2010), XBT depth biases are depth dependent, with the depths overestimated relative to the results of the Hanawa et al. (1995) fall rate equation by a greater amount near the surface than at depth. For the T4s the Gouretski and Reseghetti (2010) correction that is applied at the full depth of the instrument is similar to that found in this study around 1970 and in the mid- to late 1980s. Their correction to a 100-m depth is similar to that found here around 1980. For the T7 the variation of the Gouretski and Reseghetti (2010) corrections with depth is stronger. Their correction at the full depth of the instrument is consistent with the adjustments obtained in this study. Their correction to a 200-m depth is at the lower bound of the confidence intervals obtained in this study and their correction to 100 m is beyond these.
The suggestion of Gouretski and Reseghetti (2010) that the biases vary with depth raises the possibility that the temporal variation in the corrections could be due to changes in observing patterns rather than depth biases. For example, during the 1970s there might have been an increased number of observations in locations where the depth of the ocean is less than 200 m, resulting in an apparent change in the depth bias in the results of this study. To test this theory directly the corrections from Gouretski and Reseghetti (2010) were applied to the estimates of ocean depth from the XBT profiles to give a new estimate of ocean depth (DGR). The methodology described previously was then used to generate histograms of the ratio of DBathy/DGR and 99% confidences intervals. The results of this procedure are shown in Fig. 7. The modes of the histograms are shown by the solid black lines and the confidence intervals as dashed lines. The histogram modes before the Gouretski and Reseghetti (2010) corrections were applied are shown in gray. For the Sippican T4 the corrections have had the effect of reducing the depth biases in the data considerably. However, the temporal variation in the depth biases in the 1970s and 1980s is not removed. For the Sippican T7 the Gouretski and Reseghetti (2010) corrections appear to have overadjusted the data. As with the T4, residual temporal variation in bias is evident. It was found that adjusting the b parameter in the Gouretski and Reseghetti (2010) depth stretching factor equation from 4.6 to 1.6 m removed the apparent overadjustment in recent years (gray circles). While this might seem to suggest a bias in the Gouretski and Reseghetti (2010) corrections, this is approximately equivalent to increasing the XBT depths by 3 m before applying the adjustments and could also point to a systematic bias in the results of this study (see section 4 for a discussion of systematic biases).
The adjustments for the Sippican T10s are generally smaller than for the Sippican T4. Prior to the mid-1970s and from the mid-1990s onward the uncertainties in the corrections derived from the bathymetry are large. Between these times the corrections generally correspond well to those from Ishii and Kimoto (2009). However, they separate between 1977 and 1985 when the corrections from this work increase in size. The corrections from Ishii and Kimoto (2009) for this XBT type are generally constant. As shown in Fig. 4, most T10 observations are made along the coast. Although this is a useful property for this study, it may have had the effect of limiting the amount of data available for the method used by Ishii and Kimoto (2009), resulting in the need for many years of data to be combined in order to obtain the corrections. Therefore, the results from this work complement the Ishii and Kimoto (2009) results as they supply a more detailed view of the time evolution of biases for this XBT type for the earlier part of the time period. For completeness the Wijffels et al. (2008) shallow XBT corrections are shown in the panel for the Sippican T10s in Fig. 6. However, it is likely that the magnitude of these will be dominated by the numerous T4s.
The previously published corrections for the profiles for which type and manufacturer are not known look similar to those for the Sippican T4s and T7s. The corrections found in this study are smaller (closer to 1.0) than the others in the mid- to late 1970s and then larger around 1990. However, it should be noted that the uncertainties in the mid- to late 1970s are larger than in the surrounding years and there are relatively few data from the late 1990s onward, when the corrections become quite erratic. The second set of Wijffels et al. (2008) corrections are defined for only a short period for these XBTs. Initially the corrections for both shallow and deep unknown XBTs are similar in magnitude to the first set of corrections for shallow XBTs. Although the corrections for the unknown shallow XBTs stop, those for the unknown deep XBTs continue for a few years and become much larger than the other estimates. Reasons for differences between the corrections obtained in this work for these “unknown” XBTs compared to the other studies are explored in section 4.
4. Discussion
Broadly speaking, similarity has been observed in the time evolution of the corrections from Wijffels et al. (2008), Ishii and Kimoto (2009), and this study. However, the magnitude of the adjustments are sometimes different. For example, in the early to mid-1980s the previously published corrections for the Sippican T4 are generally weaker than those found in this study, with the exception of the time-invariant corrections of Gouretski and Reseghetti (2010). Similarly, the results for the Sippican T7s agree with those from Ishii and Kimoto (2009) and with the corrections for deep XBTs from Wijffels et al. (2008) within the uncertainty for much of the time series. Differences were noted compared to the results of those studies at the end of the time series, and the magnitude of the corrections are different from Gouretski and Reseghetti (2010). Overall, the results provide further independent confirmation that part of the biases in XBT data are from depth errors. However, additional work is required to find the cause of the disagreements and determine what the adjustments should be. One avenue for future investigation could be the difference in fall rates in warm and cool regions since XBTs fall slower in colder water (Thadathil et al. 2002). Effects such as this could potentially cause discrepancies between the proposed corrections if the data that have been used for each have different regional emphases.
Limitations of the data make exploration of these kind of issues problematic. Lack of data is evident in the constant values in the corrections for the Sippican T10s of Ishii and Kimoto (2009) and in the large uncertainty in many of the corrections derived in this study. Specific avenues for future research relevant to this study that could improve this situation include obtaining improved estimates of the ocean depths from the XBT and bathymetry data, since uncertainties in these will act to broaden the distribution of DBathy/DXBT. For example, there may be XBT data where the profile has not been terminated when the ocean bottom has been hit for which the estimate of ocean depth could be improved. Recorded levels in XBT profiles have a tendency to be spaced coarsely, as shown by the separation of the vertical lines in Fig. 1. Therefore, an avenue for investigation could be to determine whether the accuracy of the depth estimate is related to the level spacing and, if so, to adapt the methodology to take account of this. It may also be possible to improve the method of using the shallowest point of repeated temperature value as the depth estimate.
Part of the uncertainty in the results from this study derives from the reliance on a bathymetry dataset for estimates of the ocean depth. Although the GEBCO bathymetry dataset is gridded at 30-arc-sec spacing, this does not necessarily mean that depth observations were spaced this closely (Goodwillie 2003). Even with such fine grid spacing, there is potential for errors to occur due to the interpolation. However, as long as any errors are random the method of combining many data points together should produce an accurate estimate of the depth bias. If errors are systematic, the results could be biased. This could occur, for example, if the topography of the ocean floor deviates in a consistent way from the assumption of linearity used in the interpolation.
To obtain an indication of whether the depth estimates from the bathymetry data have a systematic bias, global bathymetry data collected during cruises were downloaded from the National Oceanic and Atmospheric Administration (NOAA) National Geophysical Data Center (NGDC; see online at http://www.ngdc.noaa.gov/mgg/geodas/trackline.html). Bathymetry estimates at the locations of the cruise data were also estimated by interpolating the GEBCO data. A histogram of the differences between the cruise and GEBCO bathymetry estimates for locations where the ocean depth is shallower than 760 m was found to peak at 0.5 m (GEBCO estimates are shallower than the cruise data). This is equivalent to just a 0.5% error where the ocean has a depth of 100 m and only 0.07% at 760 m. An indication of the random error in the GEBCO depths is provided by the full width at half maximum of this histogram, which was found to be 2.7 m.
Systematic errors may also occur in the estimation of depth from the XBT profiles, for example, if profiles tended to be terminated before the ocean floor was hit. The biases in XBT depths are relatively small; for example, a 5% error at 400 m depth is 20 m, so it is possible that the combination of systematic errors could be large enough to affect the results.
The Gouretski and Reseghetti (2010) corrections for T7 data were found to overcorrect the data in a reasonably consistent way over the whole time period of study. The overcorrection of approximately 2% would be equivalent to about 15 m at the full depth of the T7, although increasing the XBT depths by just 3 m before applying the corrections was found to be sufficient to successfully remove the differences in recent years. While this seems to suggest a systematic bias, there is no strong indication of this in the other results. The size of the corrections obtained in this study are approximately consistent with those of Wijffels et al. (2008) and Ishii and Kimoto (2009). For the T4s no systematic offset is observed after the Gouretski and Reseghetti (2010) corrections had been applied and although there are some differences in the magnitude of corrections when compared to Wijffels et al. (2008) and Ishii and Kimoto (2009), these are not consistent over the time period. The magnitude of the corrections for the Sippican T10 in Ishii and Kimoto (2009) are consistent with those found in this study. However, while there is no clear signal of a systematic bias in the results, the possibility that one exists must be taken into account when interpreting the results.
Type and manufacturer metadata are unavailable for approximately 50% of the XBT profiles in the historical record (Ishii and Kimoto 2009). If this information could be obtained or inferred from the data, it would considerably improve the amount of information available to calculate corrections. Another motivation for doing this is that although corrections for an unknown type have been calculated, these will only partially correct the data. For example, in 1977 the correction factor for the Sippican T10 was calculated to be 0.992. For the Sippican T4 the correction is 0.952, for the T7 it is 0.972, and for the unknown XBTs the correction is 0.980. Therefore, if one of the XBTs with unknown type and manufacturer was a Sippican T4 or T7, the depths will be undercorrected, while if it was a T10 they will be overcorrected. In terms of depth, if the depth of the measurement from the Hanawa et al. (1995) fall rate equation was 200 m (the maximum depth of the T10), using the correction for the unknown XBTs the new depth would be 196.0 m; while for the T4, T7, and T10 it would be 190.4, 194.4, and 198.4 m, respectively. Similar results can be obtained from the corrections of Ishii and Kimoto (2009), although, as also discussed below, the size of the correction for the unknown type and manufacturer XBTs from this study are likely to be closer to the corrections for the T10s since they are overrepresented in shallow-water data. For the XBT types that go deeper, the size of the differences will increase proportionally with depth. In addition, because of the different depth ranges of the various XBT types there will be a depth dependence to the residual biases if the observations are combined together in some way. However, whether these will be of sufficient magnitude to be an issue will be application dependent. For example, as shown in Fig. 4, most Sippican T10 measurements occurred in coastal regions so it may only be important to accurately correct these data if the application has a focus on these areas.
It has been noted that the corrections for the unknown XBTs in this work are different in some periods to the Wijffels et al. (2008) and Ishii and Kimoto (2009) corrections. This is not surprising since the corrections that are obtained will be related to the mix of instruments used to derive them. This is different according to the ocean basin and depth of water, and also varies with time. To illustrate this, the relative proportions of Sippican T4s, T7s and T10s at different times and in different regions are shown in Fig. 8.
The colors define different 4-yr periods and the symbols denote the ocean basin or depth. The triangles show the proportions that are present in the data that have been used to derive corrections for this study (i.e., profiles that were recorded in water shallower than the maximum depth of the XBT with no other restriction on location). In the period 1979–82 the data consist of 44% T4s, 6% T7s, and 50% T10s. The proportions for the globe as a whole with no restriction on ocean depth (circles) are different and the data are dominated by the T4, which was used for 79% of the profiles. As T10 XBTs reach a shallower depth than the T4, it is unsurprising that they would be used more in the shallow ocean—a characteristic of the data also revealed in Fig. 4.
In the next two 4-yr periods the mix is slightly more similar, with about 60% of the data in shallow water coming from T4s, compared to 85% in the globe as a whole. However, between 1991 and 1994 there was a clear change in the type of instruments being used, with the T7 becoming more important. Although the T4 was still the most common type, they accounted for only 49% of the global set of profiles and 53% in shallow water. By the 1995–98 period the T7 was the most common of the three types of XBT, although they were used in smaller proportions in shallow water. The situation was similar between 1999 and 2002, although the proportion of T7s fell slightly. This evidence of significant differences in the proportions of XBTs in use in shallow water and across all depths calls into question the applicability to the global record of the corrections obtained in this study for the unknown XBTs and it is recommended that they only be used with caution. It should also be noted that there is a possibility that the proportions of each type of XBT in the data selected for analysis in the other studies do not reflect those in the full set of XBT profiles.
Also shown in Fig. 8 are the proportions for the Atlantic and Pacific Oceans (squares and diamonds, respectively) for all depths. The proportions for the Pacific are generally very similar to those for the globe as a whole. The proportions for the Atlantic tend to be different from both the global and shallow values. As the corrections for the unknown XBTs over- or undercorrect depending on the type of XBT that is being corrected, this implies that there will be regional biases remaining in the data no matter which corrections are applied. Therefore, where sufficient data are available, regional corrections for these XBTs would be beneficial. As the majority of profiles are from either a T4 or a T7 XBT, which have different maximum depths, splitting the unknown XBTs according to profile depth (as done by Wijffels et al. 2008) and obtaining different corrections for each category might also reduce this problem.
5. Conclusions
XBT profiles recorded in shallow areas of the oceans have been used to derive time-varying corrections to the depths attributed to the XBT temperature measurements. Owing to data limitations, corrections were presented for only four types of XBT: the Sippican T4; the Sippican T7; the Sippican T10; and an “unknown” type, which is a mix of XBTs for which the type and manufacturer are unknown.
The corrections obtained for the Sippican T4 agree within uncertainty limits with those calculated by Wijffels et al. (2008) and Ishii and Kimoto (2009) prior to 1980. Subsequently, the corrections decrease in size in all three sets of adjustments, but by a smaller amount in the results of this study. A similar time evolution in biases is also observed in all studies for the Sippican T7, although again some differences are observed (e.g., in the early 2000s). Time-invariant corrections proposed by Gouretski and Reseghetti (2010) were found to generally correct the depths of the Sippican T4 XBT well when considering the time period as a whole but were found to overcorrect the depths for the Sippican T7. Temporal variations in depth biases still remained after the corrections were applied. These new results provide independent confirmation that there are time-varying depth biases in XBT data. The areas of strengths and weaknesses that have been highlighted in the corrections proposed in the other studies demonstrate where futher work might be focused in order to improve understanding of the biases.
Corrections obtained in this study for the Sippican T10 between 1976 and 1990, the period when there were many profiles from which to derive corrections, are similar to those of Ishii and Kimoto (2009) except for a period centered on 1981 when the corrections are larger. The corrections of Ishii and Kimoto (2009) are constant during that period so this result provides a first indication of the time evolution of biases at this time for the Sippican T10.
The existence of the large number of XBTs that belong to the unknown type is a problem because it reduces the amount of data available to calculate corrections for the XBTs whose type is known and could lead to some profiles being over- or undercorrected. The corrections obtained in this study for these instruments contain some differences to those previously published. However, it has been demonstrated that the mix of instruments used to obtain XBT profiles recorded in shallow water is different to that in the wider population, so differences are to be expected. As the data used to derive corrections are not representative of the whole dataset, caution is recommended if using these. The proportions of the different types of XBTs used in the Pacific and Atlantic Oceans were also found to differ. Obtaining regional corrections for the unknown XBTs or dividing XBTs by profile depth could help reduce any residual regional biases.
This study has examined only depth biases. Other work, such as by Levitus et al. (2009) and Gouretski and Reseghetti (2010), has suggested that temperature biases also exist. By adding the extra information about depth biases that is provided by the bathymetry data to the information obtained through the more conventional method of comparing XBT profiles to those from other types of instruments it may be possible to better constrain biases in XBT data in the future.
Acknowledgments
Comments from Nick Rayner, Matt Palmer, and the two anonymous reviewers helped to improve this manuscript. This work was supported by the Joint DECC and Defra Integrated Climate Programme–DECC/Defra (GA01101). The GEBCO data used in this study (the GEBCO_08 Grid, version 20090202, see online at http://www.gebco.net) were obtained through the British Oceanographic Data Centre (BODC). Additional bathymetry data were obtained from the NOAA NGDC (see online at http://www.ngdc.noaa.gov/mgg/geodas/trackline.html).
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Comparison of estimates of ocean depth from XBTs (DXBT) and bathymetry (DBathy) for data recorded during the period 1985–87. The line where the two estimates of depth are equal is drawn in gray.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
Location of XBT observations in shallow water during 1985–87, corresponding to the data shown in Fig. 1.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
Histogram of the ratio of the depths estimated from the bathymetry to those estimated from Sippican T4 data in the period 1985–87 (left) before and (right) after application of depth corrections derived in this study.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
(left) The number of Sippican T4, Sippican T7, Sippican T10, and unknown type and manufacturer XBT profiles in use per year across the whole ocean (black lines) and the number in shallow areas that were used in this study (gray shaded areas). (right) The number of XBT profiles of each type as a proportion of the number of XBTs of all types used across the whole ocean (black lines) and the number of each type of XBT used in shallow water relative to the total number of XBTs used in shallow-water areas (gray shaded area).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
Smoothed histograms of the ratios of the depth estimated from bathymetry DBathy to that from XBT data DXBT for four different XBT types. The upper part of each plot shows the histogram values relative to the peak value at each time point (blue and red colors). The modes of the distributions are shown by the solid black lines. The gray lines show the medians and the dashed lines the 99% confidence intervals obtained from the bootstrap analysis. The dotted line indicates where DBathy/DXBT = 1. The gray shaded regions show where there were no data available. The bottom part of each plot shows the peak values that were used to scale the histograms for plotting.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
Comparison of the corrections derived from this work to those from Wijffels et al. (2008), Ishii and Kimoto (2009), and Gouretski and Reseghetti (2010). The shaded areas are the 99% confidence intervals of the corrections.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
Effect on the depth biases for the (left) Sippican T4 and (right) Sippican T7 of applying the corrections of Gouretski and Reseghetti (2010) to the XBT depth estimates. Solid black shows the modes of histograms of the ratio of the depth of the ocean from bathymetry to estimates from XBT data after application of the corrections. The dashed lines are the 99% confidence intervals. Gray circles show the result of applying the Gouretski and Reseghetti (2010) corrections after changing the offset parameter in their depth correction equation to align the recent years with the line of DBathy/DGR = 1.0 (dots). The modes of the histograms before application of the corrections are shown in gray.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
Variation with time of the relative proportions of Sippican T4, T7, and T10 XBTs. The colors represent different 4-yr periods, while the symbols show observations made in water shallower than the maximum depth of the XBT in all oceans (triangles); all oceans, any depth water (circles); Atlantic Ocean, all depths (squares); and Pacific Ocean, all depths (diamonds).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO773.1
The corrections and the 99% confidence ranges derived from the bootstrap analysis. The corrections are defined for the center of each year specified in the first column. To correct XBT depths obtained using the Hanawa et al. (1995) fall rate equation, they must be multiplied by the correction values.
