1. Introduction
The changing ocean heat content is a key climate metric because it reflects the imbalance in Earth’s energy budget associated with global warming (Hansen et al. 2011; Church et al. 2011). Whereas natural fluctuations such as volcanic eruptions, internal modes (e.g., El Niño–Southern Oscillation), or variations in solar forcing cause variations on decadal or shorter time scales, the changes on multidecadal time scales in global ocean heat content (GOHC) likely express the competition between the two anthropogenic climate forcings: warming by long-lived greenhouse gases and cooling by tropospheric aerosols (Hansen et al. 2005). GOHC change is also nearly linearly proportional to thermal expansion of the oceans, which composes a large portion of sea level rise over the past 50 years (Domingues et al. 2008; Church et al. 2011) and dominates its spatial pattern (Johnson and Wijffels 2011; Church et al. 2011). In the historical databases of upper-ocean temperature used to estimate GOHC, such as the World Ocean Database 2009 (WOD09), expendable bathythermograph (XBT) data compose some 18% of available ocean temperature data and 56% of the data between 1967 and 2001 (pre-Argo era).
There have been several manufacturers of XBTs since the mid-1960s but the majority of probes have been supplied by Sippican, Inc. (now known as Lockheed Martin Sippican, Inc.), with a significant contribution from the Japanese manufacturer Tsurumi-Seiki Co., Ltd. (TSK; Fig. 1). Smaller numbers of probes have been manufactured by the Sparton of Canada company and the Plessey company (probes were manufactured in Ilford, Essex, United Kingdom, by Plessey Marine under license from Sippican). Prior to 1990, 68% of XBT profiles in the WOD09 have no probe type information as compared with 35% from 1990 to the present.
The total number of XBT profiles by year, split by probe type and manufacturer, in the WOD09. Sippican T4/T6 includes casts marked as Sippican T4, Sippican T6, unknown T4 (non-Japanese), and unknown T6 (non-Japanese). Sippican T7/DB includes casts marked as Sippican T7, Sippican DB, unknown T7 (non-Japanese), and unknown DB (non-Japanese). TSK T6 includes casts marked as TSK T6 and unknown T6 (Japanese). TSK T7/DB includes casts marked as TSK T7, TSK DB, unknown T7 (Japanese), and unknown DB (Japanese). Sippican shallow includes casts marked T10, T11, Sparton XBT-1–Sparton XBT-4, Sparton XBT-6, Sparton XBT-10, and unknown XBT type with maximum depth ≤ 550 m (non-Japanese). Sippican deep includes casts marked Fast Deep, Sparton XBT-7, Sparton XBT-7DB, Sparton XBT-20, Sparton XBT-20DB, and unknown XBT type with maximum depth > 550 m (non-Japanese). TSK shallow is unknown XBT type with maximum depth ≤ 550 m (Japanese). TSK deep is unknown XBT type with maximum depth > 550 m (Japanese). Other includes T5s, air-drop XBTs, submarine launch XBTs, and National Academy of Sciences of Ukraine Marine Hydrophysical Institute XBTs.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
The manufacturer’s product catalogues specify an accuracy of ±2% or 4.6 m in depth (whichever is greater) and ±0.2°C in temperature, both of which were assumed to be random errors and thus greatly reduced by the massive averaging to produce GOHC estimates. However, a significant time-varying warm bias in the historical XBT database was discovered by Gouretski and Koltermann (2007, hereinafter GK), and they showed that it had a great impact on the time trajectory of GOHC from the 1950s to the present.
The GK paper spurred several subsequent studies aimed at deducing the cause of the bias—depth error or temperature bias (a thermistor error) or both. Many studies have used comparisons of broadscale buddies (XBT profiles within 1 month and 100 km or so of a more accurate CTD or Nansen cast profile) to deduce a time-variable bias (GK; Ishii and Kimoto 2009, hereinafter IK09; Gouretski and Reseghetti 2010, hereinafter GR10; Levitus et al. 2009, hereinafter L09; Wijffels et al. 2008, hereinafter W08; Hamon et al. 2012, hereinafter H12), modeling the bias as a depth error only (IK09; W08), a temperature bias (L09), or a combination (GR10; H12). This broadscale approach requires massive averaging (tens of thousands of profiles; IK09) to extract a bias estimate because of mesoscale spatial and temporal variability. Separation of depth versus pure temperature bias can be done with the broadscale approach, but only with large uncertainty (GR10). All past studies do, however, agree that XBTs [after Sippican T4/T6/T7/Deep Blue (DB) and TSK T7/T6 are corrected to a Hanawa et al. (1995, hereinafter H95) fall rate] were more strongly warm biased from around 1975 to 1985, with the bias reducing in the late 1980s/early 1990s and then increasing again to the present. Lyman et al. (2010) note that differences in XBT bias corrections remain a major source of differences between year-to-year estimates of GOHC over the past 15 years.
Here, we take a new approach to defining the time-evolving bias in XBT data by assembling and analyzing a large number of contemporaneous side-by-side profiles measured by XBTs and CTDs or bottle casts. Because these profile pairs measure the same ocean vertical structure, we can more clearly separate out the two sources of error in XBT measurements—the error in depth versus a pure temperature bias. There have been many previous reports of the collection and analysis of side-by-side XBT–CTD pair data (e.g., Heinmiller et al. 1983; Hanawa and Yoritaka 1987; Seaver and Kuleshov 1982; Hallock and Teague 1992; Singer 1990; Thadathil et al. 2002; Reseghetti et al. 2007; Kizu et al. 2011; DiNezio and Goni 2011), which appear to show diverging views of the depth and thermal errors. Unfortunately, it is common for such studies to be based on a limited number of pairs, usually collected at one point in time and one location. A further complication is that different analysis methods were used in these studies as well as different probe types and acquisitions systems. It is of great importance to recognize that, even with side-by-side pairs, deduced differences are subject to random noise from the behavior of the probe’s motion (which can be affected by sea state) and normal manufacturing tolerances, which also vary among manufacturers (Kizu et al. 2011). Thus, the small but climatically significant biases can only be deduced in a statistically meaningful way from ensembles of many pairs, as recommended in the appendix. This information is vital when interpreting reports in the literature, which may be based on too few pairs and thus be dominated by random noise.
Our work here is novel in that 1) we have been able to assemble a large number of side-by-side pairs back to 1967, some of which have been used in earlier studies, and 2) we use a single, consistent approach to the analysis. In this way, we aim to generate the clearest view to date of the time-varying depth and temperature bias in historical XBT data. The comprehensive past analysis of H95 assembled 285 “good” pairs from 1987 to 1992, as compared with this study with 4115 pairs from 1967 to 2011.
We begin by describing the data preparation and the methods used to analyze the data in section 2. Section 3 focuses on Sippican T4/T6 and T7/DB probe–type results and discusses the characteristics of the XBT depth bias and the remaining temperature bias after depth correction, discusses the effects of water temperature and recorder type on fall rate and temperature bias, compares the results of the two methods of analysis, compares the corrections proposed with previous works; and applies the corrections to global ocean heat content calculations. We finish with some conclusions and comments on XBT depth and temperature biases in section 4.
2. Data description and methods
Hanawa and Yoritaka (1987) describe a “temperature-error free” method of determining depth errors in the XBT depth–time equation, using side-by-side XBT and CTD profiles, in which features of the vertical temperature gradient are matched. This method was subsequently developed by Hanawa and Yasuda (1992) and further modified by H95. H95 determined a new depth–time equation for Sippican and TSK T7, T6, and T4 XBT probes, using pairs from the late 1980s and the early 1990s. We base our method of determining depth errors on the method of Hanawa and Yoritaka (1987) and apply it to the analysis of pairs with finely resolved temperature gradients (high-vertical-resolution data; section 2d). To improve coverage of the early years of XBT data, we incorporate inflection-point and standard-depth XBT data with bottle/reversing-thermometer data (designated as low-vertical-resolution data). A different method of using the temperature gradients to determine depth errors in these low-resolution pairs is described in section 2e.
To collect enough XBT–CTD pairs to perform a statistically valid analysis, data were collated from several sources, including the XBT quality-tests reference table on the National Oceanographic Data Center (NODC) website (http://www.nodc.noaa.gov/OC5/XBT_BIAS/xbt_bibliography.html), the World Ocean Database (WOD09), and the archives at the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Marine and Atmospheric Research (CMAR), with additional datasets kindly made available from the National Oceanic and Atmospheric Administration Atlantic Oceanographic and Meteorological Laboratory (AOML) and the Bundesamt für Seeschifffahrt und Hydrographie (BSH; Germany). The details of each dataset used in the analysis are shown in Table 1, and a count of probe types by latitude is in Table 2. The locations and times of deployments are shown in Fig. 2. We were able to collect a total of 4115 pairs that span from 1967 to 2011. Of these, 2096 are high-resolution pairs (0.6–1-m depth intervals in the XBT and 1- or 2-m depth intervals in CTD) and 2019 are low-resolution pairs (>1-m depth intervals in XBT and >2-m depth intervals in CTD or bottle). Of the total, 3624 pairs have Sippican probe types, 397 are of TSK type, and 94 are of Sparton type. During the mid-1980s, digital recorders became available (Emery et al. 1986), and high-resolution data are more abundant in the pairs database from the mid-1980s to the present. The majority of low-resolution data dates from the period before 1985, which we call the analog era.
Summary of datasets used in the analysis. Here, R/V is Research Vessel, NOAAS is National Oceanographic and Atmospheric Administration Ship, USCGC is U.S. Coast Guard Cutter, HMAS is Her Majesty’s Australian Ship, and CLS is Collecte Localisation Satellites.
Summary of the number of pairs by probe type (Sippican, TSK, and Sparton) and 2.5°C temperature bin in the pairs database.
(a) Location of XBT/CTD pairs (see Tables 1 and 2 for full details of datasets). Crosses refer to high-resolution pairs, and dots refer to low-resolution pairs. (b) Temporal distribution by probe type of pairs analyzed in this study.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
The datasets (summarized in Tables 1 and 2) can be broadly classified into three groups: 1) known XBT–CTD pair studies that have been found from the literature and have good metadata, 2) pairs from cruises that are not in the scientific literature but have been found by careful searching and have good metadata, and 3) isolated pairs that were found in the WOD09 that were not part of any known bias study. These may or may not have good metadata, as detailed in the following section.
a. Metadata
Until the late 1980s, the manufacturer fall-rate equation (FRE) was used to determine depth. In 1989 work began to develop a revised equation (IOC 1992). Fall-rate errors were identified during the 1970s (Flierl and Robinson 1977; Fedorov et al. 1978), but it was not until the mid-1990s that a working group was formed to determine a new depth–time equation for Sippican and TSK T7, T6, and T4 XBTs (H95). Since the H95 publication, a mix of both old and new fall-rate equations have been used to calculate depth, and this information has not always been included in the associated metadata. TSK recording software changed to the H95 fall rate in January 1996 (G. Ferguson, US TSK, 2005, personal communication) and the H95 fall rate became the default choice in Sippican software in September 1996 (J. Hannon, Lockheed Martin Sippican, 1999, personal communication). It was of vital importance that reported fall rates be accurate in this study to avoid errors in the final depth-error estimations, and much time was spent verifying metadata records. From about 1985 to 1990, digital high-resolution records became more common and metadata recording improved in the global ocean temperature database. Since then, it has generally become easier to determine which FRE was used for high-resolution data, but it is not always the case for low-resolution data. The FRE recommended by H95 was applied to XBT data in the pairs database, and all results are relative to the H95 FRE.
Particular attention was paid to the XBT probe-type information. Where probe type was not included in the metadata, an alternative method of assigning a probe type was required. For the known XBT–CTD pair studies (group 1), the information was in the literature. For studies not included in the literature (group 2), where possible, information found from other cruises on that ship in the same year (usually from voyage reports) was combined with the maximum depth of the profile. In the WOD09 dataset (group 3), where most pairs were isolated, the probe type was determined from the country that submitted the dataset, the maximum depth of the profile, and the year of deployment. The premise of this decision is based on the sales territories (current as of August 2010) of TSK (sold in Japan, Taiwan, China, and South Korea) and Sippican (all other countries), the maximum depth of each probe type, and the start year of manufacture for each probe type (Table 3). A total of 711 XBT profiles in the database have a probe type selected from this process.
Summary of probe types, date to market, and depth cutoffs used for assigning probe types to “unknowns.” Percentage estimates in WOD09 includes probes flagged as unknowns after assigning probe types using the method described in section 2j.
Recorder type was also available for many of the pairs, and, by using the same method outlined above, the datasets from groups 1 and 2 had recorder types assigned if the information was not included in the metadata. There are a total of 2519 XBT profiles with recorder type included.
In some cases, the serial number of probes was included with the metadata or in log sheets. For this study, the serial number information was not assessed, as only 805 pairs contained this information. However, where the date of manufacture of the probe was available, it was used in place of the deployment date.
b. Quality control
All data were translated into a Network Common Data Form (netCDF) format that can be read by “Mquest,” a quality control program that was developed by A. Thresher at CMAR (available online at http://www.marine.csiro.au/~gronell/Mquest/index.htm). Using this program, each XBT profile was subjected to expert manual quality control procedures according to Bailey et al. (1994). The most common quality control used included removal of the surface measurements to 3 m (for high-resolution data); interpolation over spikes; and flagging of data as “bad” below wire leakages, insulation penetrations, wire breakages, and “hit bottom” signals. The quality control step is necessary to remove false warm biases in the XBT data (in the case of wire leakages, insulation penetrations, and wire breakages) and to improve the depth-error analysis process (all quality issues can affect the analysis described in sections 2d and 2e). Data deeper than data points flagged as bad were not included in the analysis, and analysis was completed to the full depth of good data available. Spikes were removed from CTD data if required. CTD and bottle data were not quality controlled any further. It was assumed that the agency responsible for the data collection followed good quality control procedures and processed the data appropriately. Also assumed is that XBT equipment was used in accordance with manufacturer specifications.
c. Pair identification method
Each quality-controlled dataset was individually checked for valid CTD and XBT data pairs. Because of inaccuracies in the time and location metadata, we could not rely on temporal and spatial proximity alone to determine whether a profile pair was truly contemporaneous. So, for each cruise dataset, an initial pair selection box was defined on the basis of a time and distance range to give “possible” pairs. After the analysis of depth errors and temperature bias, pairs with lower depth correlations had to pass a visual examination for shared temperature finescale to be included in the database. More than 90% of XBTs included in the final database were located within 45 min and 3 km of their CTD or bottle pairs. Corrections to time and location metadata were made if possible, but some pairs that passed visual inspection and are clearly pairs still contain time and/or location errors.
d. Analysis of high-resolution pairs
This analysis consisted of seven steps. In the first step, for each candidate pair, the XBT and CTD data were interpolated onto a common 1-m depth grid after using a zero-phase forward and reverse digital filter (“filtfilt” in the MATLAB proprietary software program) to match resolved vertical scales in the profiles. In the second step, vertical temperature gradients dT/dz were then calculated for the CTD and XBT profiles. In step 3, we then performed a cross correlation (using “xcorr” in MATLAB) of the XBT and CTD dT/dz to find the depth error or lag at every 10 m for the XBT profile. The depth-error determination process was mostly automated, but several variables were adjusted to suit each dataset. These variables included correlation bin range, extent of filtering, and several variables used to maintain a smooth path of depth-error selection (where correlation was at a maximum) through the depth of the profile.
In step 4, candidate pairs with more than 50% of their depth lags above a correlation ratio of 0.8 were automatically retained. The remaining pairs and pairs with highly homogenized temperature profiles were reviewed manually and were excluded from the dataset if they did not clearly share vertical finescale features. Figure 3 shows an example of a pair taken from the Aurora Australis cruise in 2010. This is a particularly good example of the automated correlation analysis. Then, in step 5, for each pair we fit a linear equation Δz = αz + β, where Δz is the depth error and z is the 10-m depth grid from step 3. Coefficients β and α were found using the “robustfit” routine in MATLAB, which employs iteratively reweighted least squares with a bisquare weighting function.
An example of a well-matched pair. (a) Raw XBT (red) and CTD (blue) data. (b) Temperature gradients dT/dz with depth of the XBT and CTD data. (c) The correlation R between the XBT and CTD gradients at 10-m intervals, the correlation chosen by the automated software (black line), and the depth-error linear model fit (red line).
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
For step 6, using the above coefficients, we depth corrected each XBT profile and then determined the remaining temperature bias for each depth. A major result is that, after depth correction, the remaining pure temperature bias is depth independent for the high-resolution data (Fig. 4). The T7/DB high-resolution profiles have a positive bias of ~0.05°C (1743 pairs from all years). The T4/T6 high-resolution profiles have a temperature bias of ~0.03°C (108 pairs from all years). To examine the time dependence of this pure temperature bias, for each pair we formed the vertical median of the differences between the XBT temperature TXBT and CTD temperature TCTD at each depth: ΔT(°C) = median(TXBT − TCTD). This ΔT term will hereafter refer to the temperature bias that remains in XBTs after depth correction.
The variation of median ΔT with depth for high- and low-resolution Sippican probe types. Dotted lines show 2 times the standard error. The manufacturers specify an accuracy of ±0.2°C.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
In step 7, outliers that are greater than the mean ± 3 standard deviations for each probe type in 3-yr nonoverlapping bins were removed for the α, β, and ΔT results. Also eliminated from the ΔT results (but retained in the α and β results) were three voyages [Research Vessel (R/V) Franklin in 1987 and 1986 and Hakuho Maru in 1987], where known large systematic temperature offsets existed in the data. The dataset from the U.S. Naval Ship (USNS) Bartlett in 1990 [used in the study by Hallock and Teague (1992)] was removed from the depth-error results because the results were inconsistent with the majority of the pairs from that period. Temperature bias results for the USNS Bartlett dataset were retained.
e. Analysis of low-resolution pairs
The low-resolution pair data required a different method of analysis from the high-resolution pairs because of the lack of resolved vertical finescale precluding use of poor dT/dz correlations to find Δz. To proceed, we assumed a key result from our high-resolution analysis applies to the low-resolution data—that the temperature bias is almost constant with depth (Fig. 4). We estimated an initial temperature difference for each pair, calculated the depth error (α and β), corrected for this depth error, and then recalculated the remaining temperature bias (ΔT).
This process involved six steps. In step 1, for each pair, the profile (XBT or CTD) with the most data points was selected as the depth grid. The other profile was interpolated onto the depths of this profile. In step 2, vertical temperature gradients dT/dz were then calculated for the CTD and XBT profiles. In the third step, using the assumption of depth-independent temperature bias (as discussed above), an initial temperature difference was calculated: ΔTi = median[TCTD(z) − TXBT(z)], where ΔTi is the initial temperature difference and TCTD(z) and TXBT(z) are temperatures at selected depths from thermostads (where the temperature gradient dT/dz < ±0.0025°C m−1 after H12). If no thermostads are present in the profile, then ΔTi is determined from surface measurements (from > 3 m to < 15 m). The higher-resolution profile (XBT or CTD) of the pair is used to find the thermostads.
In step 4, by removing ΔTi from the XBT profile we were able to calculate the depth error by dividing the remaining XBT temperature offset by the CTD temperature gradient dT/dzCTD: Δz(m) = [(TXBT − TCTD) − ΔTi]/(dT/dzCTD), where Δz is a depth error at each depth and TXBT and TCTD are temperatures at every depth of the profile. Depth errors Δz of greater than ±60 m and areas of low gradient dT/dzCTD < ±0.0025°C m−1 were excluded from further analysis because they are dominated by noise. As for the high-resolution data, a linear depth-error model was fitted to Δz to find the α and β terms. Then, each XBT profile was corrected for its individual depth error using its α and β terms.
The pure temperature bias was then determined in step 5 after depth correction in the same manner as for the high-resolution pairs: ΔT (°C) = median(TXBT − TCTD), and is the remaining temperature bias after depth correction. In step 6, outliers that are greater than the mean ± 3 standard deviations for each probe type in 3-yr nonoverlapping bins were removed for the α, β, and ΔT results. Also eliminated from the temperature bias results (but retained in the α and β results) was one dataset from 1980 (R/V Oceanographer) for which it was clear that there were large temperature offsets in the data.
We tested the above approach to the low-resolution profiles by using it on several high-resolution datasets containing a total of 322 pairs. A two-tailed Student’s t test showed that both methods give statistically similar results at a significance level of 99% for all three bias parameters.
f. Statistical grouping of probe types
We have grouped similar probe types in this study—Sippican T7 with DB and Sippican T4 with T6. The physical differences between T7 and DB and between T4 and T6 probes are in the amount of wire on the ship-end spool. T7 and DB have identical probe structures, (J. Hannon, Lockheed Martin Sippican, 1999, personal communication), and the original Sippican FRE for all four probe types is the same (Sippican 1991, p. 4-3). To ensure that grouping the probes for analysis was statistically valid, we compared the α term between 1980 and 1990 for both high- and low-resolution pairs. It was found that the medians of the T7 and DB probe types and of the T4 and T6 probe types were not different at the 95% confidence level. Therefore, Sippican T7 and DB probe types are grouped together for analysis (a total of 2404 pairs), as are Sippican T4 and T6 probe types (a total of 773 pairs). TSK produces T6 and T7 probe types, and there are 306 and 84 pairs, respectively, in the database.
g. Validation of the temperature-gradients method using an independent method
To validate the methods described above that use temperature gradients (TG method), we used the independent method of Cheng et al. (2011, hereinafter the CH method) and applied it to the same quality-controlled pairs database that was used in the TG method. The form of the FRE was given by the manufacturer as z = at − bt2, where z is depth in meters, t is time in seconds, a is a constant describing the initial probe velocity (m s−1), and b is a constant describing the probe deceleration rate (m s−2). For this analysis, we have determined a and b as described by the manufacturer’s equation, as well as with a depth-offset term c. The modified form of the depth equation therefore becomes z = at − bt2 − c. The benefits of including the offset term are discussed in section 2h.
To directly compare the a/b/c results from the CH method with the α and β terms derived from the TG method, we used the following method to convert a/b/c to an equivalent α and β term: z1 = 6.691t − 0.002 25t2 and z2 = ait − bit2 − ci, where t is time in seconds; z1 is the depth derived from H95 coefficients; ai, bi, and ci are each pair’s terms derived from the CH method, and z2 is the depth calculated from the CH results. The polynomial curve-fitting routine “polyfit” in MATLAB is then used to determine an equivalent α by performing a least squares fit to the depth error (z2 − z1): α = polyfit(z1, z2 − z1, 1). The β term from the TG method is compared directly to the c term in the CH method.
h. Comment on inclusion of the offset term in the depth-correction models
In the TG method and the CH method, we have included an offset term (β in the TG method and c in the CH method). The true XBT fall rate is different for each probe and can vary considerably near the surface. Variables that affect the fall rate include the way the probe enters the water (sideways, upside down, or nose first), wave state, the height above the water at launch, the rate of unspooling of the wire, and small variations in the structure of the probe (Green 1984; GR10). By including a β value in the TG model and the c term in the CH model, we can account for small changes in fall rate near the surface. To test the effectiveness of the β and the c terms, we corrected the XBTs in every high-resolution Sippican T7 and DB pair using both methods with and without the offset term (Fig. 5). The mean depth error remaining after correction when the offset term is included is less than ±1 m over all depths for both methods. When the offset term is not included, the mean depth-error residual from the TG method is greater than 1 m in the top 500 m. In the TG method and CH method, the residual depth error is lowest when the offset term is included. The residual temperature bias is depth independent when the offset term is included—particularly in the top 100 m. Including the offset term is a simple method of accounting for variations in fall rates near the surface and results in lower residual depth errors and depth-independent temperature errors. For these reasons, we have included the offset terms in the results for both methods.
Comparison of (left) residual depth and (right) temperature errors after correction of high-resolution Sippican T7/DB XBTs using the TG method with and without an offset term and the CH method with and without an offset term.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
3. Results and discussion
The presence of a temperature bias in XBT data, separate from depth errors, has been well documented (e.g., Wright and Szabados 1989; Reverdin et al. 2009; Heinmiller et al. 1983; Seaver and Kuleshov 1982; Budéus and Krause 1993; Reseghetti et al. 2007; GR10; Gouretski 2012, hereinafter G12) and is summarized well in GR10. Across our database, there is clearly a significant reduction in the temperature bias after depth correction (Fig. 6). Prior to depth correction, the raw temperature bias across all depths for high-resolution data forms a broad distribution, and there is a mean warm temperature bias of ~0.08°C. After each pair is individually depth corrected, the peak narrows and the temperature bias reduces to ~0.05°C. The effect of depth correction on the spread of the bias distribution for low-resolution pairs is less marked. The median ΔT is similar to the high-resolution results (~0.07°C before depth correction and ~0.04°C after depth correction). In the following sections, we will examine the characteristics of both the depth errors and the remaining temperature bias after depth correction, focusing on Sippican types because these are the most abundant in the database.
The effect of depth correction on the temperature bias: a histogram of the ΔT before (dotted) and after (solid) depth correction for high-resolution (red) and low-resolution (blue) pairs of all probe types combined.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
a. Characteristics of the depth bias
During the early, low-resolution period (1969–93 shown in Fig. 7), the H95 FRE for Sippican T4/T6 probes feature little or no depth bias, with the exception from the mid-1970s to the early 1980s, during which a clear positive depth bias is apparent. The positive depth bias in these probe types during this time period has been identified by other authors (IK09; W08; GR10; Good 2011, hereinafter GD11). From the H95 period (late 1980s and on), high-resolution Sippican T7/DB data become more common and the depth bias for these probe types is clearly changing, from no bias in the early 1990s to ~15 m at 700-m depth in the last 2011 time bin. The shape of the depth bias in both high- and low-resolution data types lends itself nicely to a first-order slope α and offset β fit for each independent grouping. The first ~50 m of the depth bias in many of the bins is different, and the linear fit does not allow for this shape, but including the β term does account for some of the surface variation.
The evolution of depth errors for low-resolution Sippican T4/T6 (1969–93; green dots) and high-resolution Sippican T7/DB (1987–2011; black dots) probes in 3-yr nonoverlapping bins. Dots are the depth errors for all of the results. Heavy black lines are the median for all results. Shaded red area is 2 standard errors.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
To look at the evolution of the α term (slope) over time, the data for Sippican probes were binned into nonoverlapping time bins, each with a minimum of 30 pairs per bin (Fig. 8; values presented in Tables 4 and 5). With one keeping in mind that the depths have been corrected to the H95 equation, Sippican T4/T6 probe types show a time-varying fall rate, slower in the late 1970s. From the mid-1980s to mid-1990s, α returns to zero, equivalent to the H95 fall rate. Sippican T7/DB probe types have little depth error during the period from the mid-1970s to the 1980s in this pairs database, which disagrees with results from global analyses (GD11; W08; IK09). The depth error deduced in global buddy analyses also includes the effect of the temperature bias, which, when unaccounted for, will give a larger apparent depth error relative to the TG method. A review of early papers that compare Sippican T7 XBT and CTD pairs (Flierl and Robinson 1977; Fedorov et al. 1978; Seaver and Kuleshov 1982; Heinmiller et al. 1983) indicates that there was a negative depth error in the manufacturer’s FRE (around −15 m at 750 m, or −2%) of a similar magnitude to that found by H95 (around −22 m at 750 m, or −3%) and a positive temperature offset of 0.19° for T4 and 0.13°C for T7 XBTs in the analog data collected at the time (1973–80). Most of the data discussed in these papers are included in our dataset, and we find a similar result: that is, after correction to H95, there is little depth error in Sippican T7/DB prior to 1990. After 1985, the α of the depth error for Sippican T4/T6 probe types is close to zero until the late 1990s, when the number of pairs becomes small and the α estimate covers ~15 years. For the more recent Sippican T7/DB probe types, the α of the depth error is clearly increasing after 1985, with our nonoverlapping bins showing a very consistent, statistically stable result. A similar slowing of fall rate (2.1% slower than H95) was found by Kizu et al. (2011) for recent Sippican T7 probes and by DiNezio and Goni (2011) for Sippican T7 and Deep Blue probes.
Depth slope error α for (a) Sippican T4/T6 probes and (b) Sippican T7/DB probes in nonoverlapping time bins with a minimum of 30 pairs per bin. The manufacturer’s tolerance limits (±2%) are shown. The error bars are 2 standard errors. Shading of the error bars indicates how many pairs are included in the time bin, and the width of the shaded areas indicates the time coverage. The original 1965 Sippican equivalent fall rate (0.0336 m m−1) is included as the dotted line and is marked as S65. Label H95 indicates the H95 equivalent fall rate.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
Corrections derived from the TG and CH methods using the pairs database for Sippican T4/T6 probe types. Median values for all pairs are included at the bottom. The α and b values and their associated 2σ values should be multiplied by 10−3; the ΔT values and their associated 2σ values should be multiplied by 10−2; and the β, a, and c values and their associated 2σ values need no multiplier.
The TSK pairs in the database are concentrated from the mid-1970s to the mid-1990s. A complete estimate of fall-rate error over the entire time period cannot be made from these data, but the fall-rate correction for the time periods available is given in Tables 6 and 7. Other probe types were not sufficient in number to provide correction estimates.
The β term (surface depth offset) for Sippican has a broad distribution (Fig. 9a), with a positive median of ~2 m for Sippican probe types and ~0 m for TSK probe types. The median offsets for each probe type are given in Tables 4–7. The β term appears to increase slightly over time (Figs. 9b,c) but clearly is positive in nearly all years for the more numerous Sippican T7/DB pairs (Fig. 9c).
(a) Distribution of the β term from the depth-error analysis for Sippican and TSK probes. (b) The β term plotted in nonoverlapping time bins with a minimum of 30 pairs per bin for Sippican T4/T6 probes. (c) As in (b), but for Sippican T7/DB probes. The error bars are 2 standard errors, shading of the error bars indicates how many pairs are included in the time bin, and the width of the shaded areas indicates the time coverage.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
b. Influence of water temperature on fall rate
Does water temperature influence the fall rate of the XBT? Previously, Thadathil et al. (2002) presented depth errors (when using the Sippican manufacturer FRE) of approximately −25 m at 350 m for low latitudes and +3 m at 350 m for high latitudes and argued for a slower fall rate in cooler, higher-latitude waters. However, this conclusion was drawn from fewer than 10 pairs, most of which were not close enough in space and time and did not have enough finescale matches for inclusion in our analysis. Kizu et al. (2011) used some well-matched side-by-side pairs to elegantly show that temperature may have an influence on initial fall rate. With our large pairs database, we also attempted to define the effect of water temperature on fall rate. We looked at our most abundant and best-quality results—the high-resolution Sippican T7/DB results (1665 pairs), which span the years 1985–2011. The distribution of these pairs (Fig. 10a) indicates that any test of fall-rate changes with temperature will be biased by year-to-year fall-rate variations, particularly since α increases between 2000 and 2005 (Fig. 8b). To separate out the effects of fall rate over time from the fall rate with water temperature, we grouped the α results into 1985–2000 and 2005–11 groups, because these periods have some pairs in water of less than 7.5°C (0–700-m mean temperature; Fig. 10a) and have minimal changes in α within the time period (Fig. 8b). We then binned α into 2.5°C nonoverlapping bins (0–100-m mean temperature; Fig. 10b). In the 1985–2000 group, no trend of decreasing fall rate with decreasing temperature in the range 0°–25°C is apparent. In both groupings, there is little change in α with temperature and the error bars overlap, indicating no significant difference between each bin. The impact of the year of manufacture on fall rates is much greater than the effect of water column temperature; the 2005–11 grouping shows a significantly slower fall rate than the 1985–2000 grouping, as also seen in Fig. 8b.
(a) Number of high-resolution Sippican T7/DB pairs per year for each 2.5°C temperature bin. Pairs are binned based on the mean CTD temperature from 0 to 700 m. (b) Slope α of the depth error for high-resolution Sippican T7/DB probes plotted by mean CTD temperature from 0 to 700 m. (c) Offset β of the depth error for high-resolution Sippican T7/DB probes plotted by mean temperature from 0 to 700 m. The error bars are 2 standard errors, shading of the error bars indicates how many pairs are included in the temperature bin, and the width of the shaded areas indicates the time coverage.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
We also binned the β term of the fall rate by temperature after splitting the data into two time groups: 1985–93 and 1993–2000 (Fig. 10c). No trend in β with water column temperature is apparent in either grouping.
Since the basic probe structure is similar between the major probe types, similar effects of temperature on fall rate for Sippican T4/T6 and TKS T6 and T7 probe types could be expected. From our results, we can conclude that water temperatures in the range 0°–25°C do not significantly affect the offset β part of the fall-rate error. The α part of the fall-rate error appears to be affected more by temporal changes in fall rate than by water temperature. H12 found a much larger decrease in fall rate with decreasing water temperature in their broadscale analysis of ~8 m at 100-m depth and 0°C (equivalent to 0.08 m m−1, as compared with ~0.02 m m−1 at 0°C in our analysis). In the 10°–25°C range, they found a depth error from −0.01 to 0.03 m m−1. These differences may be due to the different analysis methods (broadscale vs pairs), the fact that we have highly quality-controlled data (all leakage, wire breaks, and spikes are removed, thus removing false warm data), or that we have accounted for yearly fall-rate biases prior to assessing the effect of water temperature on fall rate.
c. Influence of recorder type on fall rate
The effect of recorder type on fall rate can also be investigated using the pairs database. Five recorder types were included in the analysis (strip chart, Sippican MK-9, Sippican MK-12, Sippican MK-21, and Devil) for a total of 1796 pairs (Fig. 11a). Only results from Sippican T7 and DB probe types are investigated.
(a) Distribution of recorder types used for Sippican T7/DB probe types in the pairs database; (b) α, (c) β, and (d) ΔT for each recorder type used for Sippican T7/DB probes in the pairs database. The error bars are 2 standard errors. Here, SC denotes strip chart, M9 is the Sippican MK-9, M12 is the Sippican MK-12, M21 is the Sippican MK-21, and Dvl denotes Devil.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
It is difficult to separate the effect of changes in α with time (Fig. 8) from changes in α with recorder type. By choosing time periods with minimal changes in α, we can examine the effect of recorder type on α. When the results for all time periods are viewed (Fig. 11b), we get a false impression that there is variation in α with recorder type. When all data are included, a Student’s t test indicates that the mean α between strip-chart and all other recorder types is significantly different at the 95% confidence interval; MK-9 is significantly different from MK-21 and Devil and MK-12 is significantly different from MK-21 and Devil. However, when the data are grouped from 2005 to 2011 and from 1985 to 2000, the Student’s t test shows no significant difference between mean α of each recorder type in each of the two time periods at the 95% confidence interval. We conclude that the fall rate appears to be independent of recorder type but is dependent upon the probe’s manufacture date.
Interpreting the changes in β with recorder type (Fig. 11c) is more difficult, since, when referring to Fig. 9c, we see that there is a small increase in β during 1985–2000; however, after 2005, there is significant difference between the last time bin and the previous two. The Student’s t test shows significant difference at the 99% confidence interval between the strip-chart/MK-9 and MK-12/MK-21/Devil systems when all data are included. When separated into the two time periods, the mean β of MK-12 is significantly different from MK-9 and MK-21 systems during the 1985–2000 period and the MK-12 system is significantly different from the MK-21 and Devil systems after 2005. Despite these t-test results, it is difficult to conclude that the β term is dependent on recorder type, as the dependence is not consistent across the two time groups. The variation in temperature bias (ΔT; Fig. 11d) with recorder type is discussed in section 3e.
d. Characteristics of the temperature bias after depth correction
Although depth correction reduces the temperature bias ΔT in the XBT profiles, it does not completely remove it, regardless of probe type (Fig. 12a). Sippican probe types show a positive ΔT of ~0.05°C, with TSK probe types having a lower ΔT (Fig. 12b). The cause of the different ΔT in Sippican and TSK probes could be the differences in wire coating [see Kizu et al. (2011) for TSK and Sippican structural differences]. Sippican and TSK are known to have different wire-coating techniques, with TSK having a thicker coating that is thought to result in a lower rate of wire insulation leakage failures than is seen for Sippican probe types. Wire and thermistor leakage failures give a false increase in temperature (Anderson 1980; Bailey et al. 1994), which is enhanced in colder temperatures and by increasing the amount of wire in the water (Anderson 1980; Reseghetti et al. 2007). The data in the pairs database are quality controlled, but small leakages undetected by manual quality control may be the cause of a higher temperature bias in the deeper probe types (Fig. 4).
(a) Temperature bias after depth correction ΔT for each probe type, plotted by year. Filled circles are high-resolution pairs, and open circles are low-resolution pairs. If known, year of manufacture of the probe is used; otherwise, deployment date is used. (b) The distribution of ΔT after depth correction for each probe-type grouping used in the TG method.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
In Sippican probes, ΔT is clearly time varying (Fig. 13). From 1966 to 1980, the median ΔT (0.095°C) is higher than that observed for the post-1980 period (0.041°C) for T4/T6 probes. Similarly, for T7/DB probes, the bias is higher before 1985 (0.11°C) than after 1985 (0.043°C). The majority of the data in the pre-1985 pairs is of low resolution and is likely to have been collected on analog recorders, whereas after 1985 the pairs are mostly high-resolution, digitally recorded data. The Sippican analog system used from 1966 to the mid-1980s split the temperature error between the probe and the recording system. With the introduction of the digital recording system, the temperature errors due to recording were removed and the temperature error was halved (Stegen et al. 1975). Heinmiller et al. (1983) found that large temperature offsets (0.05°–0.31°C) in the analog systems used in the early years need to be removed before depth corrections are applied and that they may not apply to profiles recorded electronically because of the higher accuracy in the electronic recording systems. Our results clearly show the remaining ΔT after depth correction is lower in the age of the digital recording system, in agreement with these studies.
The ΔT plotted by year for (a) Sippican T4/T6 probes and (b) Sippican T7/DB probes. The error bars are 2 standard errors, and shading of the error bars indicates how many pairs are included in the time bin. The manufacturer accuracy is ±0.2°C.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
e. Influence of recording system on temperature bias
Is it possible that the recording system is the source of temperature bias ΔT? The early strip-chart recorder types have a significantly higher ΔT (Fig. 11d) than the later digital recording systems when all data were tested with a Student’s t test at the 95% confidence interval. Similarly, MK-12 systems are significantly different from the other recorder types at the 95% confidence interval with all data included. Grouping the data into 1985–2000 years and post-2005 years gives similar results to the group with all data included, with the exception of the MK-21 data in the 1985–2000 group. These results indicate that the ΔT is highest in the early strip-chart systems and is lowest in MK-12 systems and that the MK-9, MK-21, and Devil systems have a very similar ΔT. Grouping of the data by time period results in little difference, indicating a robust relationship between temperature bias and recorder type. A similar result was found by Kizu and Hanawa (2002b), who found that recorder type had an effect on the start-up transient measurements, and by Kizu and Hanawa (2002a), who found that temperature errors varied with recorder type.
f. Influence of water temperature on temperature bias
In an attempt to confirm previous studies (Reverdin et al. 2009; Zanasca 1994; IOC 1989, work by A. Sy therein, pp. 185–192.) in which a temperature bias that varies with temperature has been found in XBTs, we used the high-resolution Sippican T7/DB and all resolutions of Sippican T4/T6 results and avoided interferences from time variations by using only the data from 1993 to 2005 (T7/DB) and from 1982 to 1993 (T4/T6), because the ΔT over this time period is reasonably consistent (Fig. 13). We binned the pairs into groups containing a minimum of 30 pairs, based on the mean surface temperature (Figs. 14a,b). An increase in ΔT with increasing surface water temperature is apparent for Sippican T7/DB probe types. Some similarities exist with the data from Reverdin et al. (2009), who show a small trend of increasing ΔT with increasing surface temperature. There is no conclusive trend in the T4/T6 pairs, possibly because of the low numbers available (Fig. 14b). To further investigate the reason for the increase in ΔT with surface temperature, we compared the ΔT at each 1-m interpolated depth with the CTD temperature at that depth by binning the data into 2.5°C bins (Figs. 14c,d). A similar trend of increasing ΔT with water temperature is observed in both T7/DB and T4/T6 types. These results indicate a temperature effect on the thermistor response and show that it is reproducible in both sets of Sippican probe types. GR10 present results from bath calibrations performed by A. Sy (IOC 1989) and Zanasca (1994), which show a similar small trend upward (slopes of ~0.002–0.009).
The ΔT binned by temperature for Sippican probes. (a) High-resolution profiles for Sippican T7/DB from 1993 to 2005 binned by CTD surface temperature (blue line) and results from Reverdin et al. (2009; black dots) in which surface temperature bias is estimated from differences between XBT and ship intake, CTD, or XCTD. (b) As in (a), but for Sippican T4/T6 from 1982 to 1993 (all resolutions). (c) High-resolution Sippican T7/DB pairs from 1993 to 2005 binned by CTD temperatures from the entire profile. (d) As in (c), but for Sippican T4/T6 from 1982 to 1993 (all resolutions). The error bars are 2 standard errors, and shading of the error bars indicates how many pairs [in (a) and (b)] or temperature/ΔT data points [in (c) and (d)] are included in the temperature bin.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
If we correct the temperature bias for the trend, does it have an effect on the ΔT over time? To investigate this question, we applied the linear correction for ΔT based on water temperature separately for high- and low-resolution profiles and saw that it had negligible effect on the majority of the ΔT error. However, there were two periods (2003–04 and 2011) for which there was a significant difference. These two periods have data collected in the coldest water (Fig. 10a). Given the differences in these two bins, we conclude that the influence of water temperature on temperature bias is largest in very cold waters but can be disregarded when applying corrections to the historical database. More pairs in cold waters should be collected and examined.
g. Comparison with an independent method
To verify our results, we compared the TG results above with the CH analysis method directly where the a and b terms determined using the CH method were converted to an equivalent slope as described in section 2g. The α estimates for Sippican T4/T6 and T7/DB probe types from both methods agree very well (Figs. 15a,d). Both methods give similar trends over time, with a slower fall rate from the mid-1970s to the early 1980s for T4/T6 types and a slowing over time since 1990 for T7/DB types. The offset terms (β and c) for both analysis methods can be compared directly and give a similar offset range (~0–2 m) but have some variation in results (Figs. 15b,e). Temperature bias after depth correction ΔT over time is similar for both methods; a larger ΔT exists in the early years for Sippican T4/T6 and T7/DB probe types and reduces in the post-1985, digital era. The strong agreement between the two methods used to separate depth and temperature errors shows the robustness of the results.
Comparison of results from the TG and CH methods of analysis. The FRE coefficients calculated in the CH method are converted to equivalent slope and offset values as described in section 2g. Shown are results for Sippican (top) T4/T6 and (bottom) T7/DB probes for (a),(d) α, (b),(e) β, and (c),(f) ΔT.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
h. How to apply the corrections to historical data
For both the TG and CH methods, we first assign probe types to “unknowns” based on the deploying country, depth maximum, and start date of manufacture for each probe type (Table 3). TSK probe types are assigned to probes deployed by Japan, Taiwan, Korea, Thailand, and China. All other countries are designated as Sippican types. Next, all depths are recalculated using the H95 coefficients. To obtain the corrected depth using the TG method, we use zc = zh(1 − α) − β, where zc is the corrected depth, zh is the XBT depth obtained using the H95 FRE, and α and β are supplied in Tables 4–7 for each year. To correct the depth using the CH method, time t is calculated using: t = (ah/2bh) − [(ah/2bh)2 − zh/bh)]0.5, where ah = 6.691, bh = 0.002 25, and zh = H95 XBT depth. Then, zc = at − bt2 − c, where a, b, and c are supplied in Tables 4–6 for each year. For both TG and CH methods, the ΔT (Tables 4–7) should then be subtracted from the XBT temperatures for the corresponding year: Tc = Txbt − ΔT, where Tc is corrected temperature and Txbt is original XBT temperature.
Corrections are not provided for probe types other than Sippican T4/T6 and T7/DB and TSK T6 and T7. Not all years are covered for these types. Section 2j describes an application of the corrections and handling of different probe types.
i. Application of other correction methods to the pairs database
Several other correction schemes for XBT data have been proposed previously (IK09; W08; GR10; GD11; G12; H12), and we compare these schemes with ours presented as a correction factor (Fig. 16). To obtain the correction factor cf, we used cf = mean(zc/zh), where zc are the corrected depths obtained using each correction scheme and zh are the depths using the H95 FRE. The depths used were from 0 to 460 m for T4/T6 probes and from 0 to 760 m for T7/DB probes. The correction schemes were applied based on descriptions given online (http://www.nodc.noaa.gov/OC5/XBT_BIAS/xbt_bias.html). The IK09 new corrections in conjunction with version-6.12 analysis of ocean temperature and salinity were applied.
Comparison of correction schemes for Sippican (top) T4/T6 and (bottom) T7/DB probe types for (a),(c) equivalent correction factors and (b),(d) diagnosed temperature bias over time. Correction schemes are from authors as listed in the text. Label G12 SX refers to the shallow XBT correction in G12. Labels H12 high and H12 low refer to the high and low temperature schemes in H12, respectively. Label H95 is the H95 equivalent fall rate, and S65 is the Sippican 1965 equivalent fall rate.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
Sippican T4/T6 probe types dominate the database until the mid-1980s (Fig. 1), and the recommended corrections during this time vary but all have a peak from the mid-1970s to the early 1980s (Fig. 16a). The TG and CH methods have a much smaller correction during this time. During the period around 1990, about one-half of the schemes agree very well with the H95 FRE (equivalent to 1 in Fig. 16a), but the schemes diagnosed using bathymetry (GD11; G12) have a bigger correction. The corrections recommended for Sippican T7/DB probe types all tend to agree during the data-rich period from ~1985 on, with the exception of H12. Prior to this, there is little agreement, but most have a peak from the mid-1970s to the early 1980s.
Temperature biases diagnosed by H12, GR10, and G12 for Sippican T4/T6 probe types are similar to those determined using the TG and CH methods, with a higher bias in the pre-1985 years. The T7/DB temperature bias from G12 and H12 in the data-rich post-1990 period is somewhat higher than GR10 and the TG and CH methods.
Because we have such a large number of XBT and CTD side-by-side pairs, it provides us with an excellent opportunity to apply corrections proposed by other authors to assess their effectiveness. Therefore, we applied the corrections presented using the TG and CH methods (Tables 4 and 5) and those proposed by several other authors (IK09; W08; GR10; GD11; G12; H12; L09) to the pairs database. Corrections from IK09, GR10, G12, L09, H12, and W08 were applied based on the most recent methods and tables available online (http://www.nodc.noaa.gov/OC5/XBT_BIAS/xbt_bias.html). In some schemes, corrections were not available beyond the publication date, and in these cases the last correction available was used to correct the later years.
To assess the depth corrections, only high-resolution pairs were used. Each recommended correction was applied to the raw XBT data, and the TG method was used to calculate the residual depth errors. There were 107 high-resolution Sippican T4/T6 pairs assessed for depth errors (Fig. 17a). Prior to correction, the mean depth error (XBT − CTD) is ~5 m at 450-m depth. All correction schemes reduce the positive depth bias, but GD11, G12, and W08 overcorrect to approximately −5 m at 450-m depth, and H12 provides the smallest correction in the more recent data (bottom panel on right). There were significantly more Sippican T7/DB high-resolution pairs available for assessment of depth errors (1613 pairs). The mean depth error before correction was ~8 m at 750-m depth (Fig. 17b). The GR10 and W08 schemes overcorrect the depth, with a residual of approximately −5 m at 750-m depth. With the exception of H12, the remaining schemes do well at removing the depth bias, with a median of less than ±3 m of error remaining at 750 m. The H12 scheme increases the depth error after 1995, particularly at depth (bottom panel on right). The application of the H12 method is based on the deepest depth of the XBT probe and disregards probe type, which could result in poor results for probes that do not reach their full depth. The CH method, which has the extra fitted term in the FRE, appears to do the best on average but has some large negative errors at depth remaining in the first three time bins. All schemes (with the exception of H12) tend to overcorrect at depth from ~1985 to 1995.
Comparison of mean residual depth errors (XBT − CTD) in the high-resolution pairs after depth corrections from the TG, CH, GR10, GD11, W08, G12, > and H12 methods are applied. Temperature corrections from the TG, CH, GR10, G12, and H12 methods are not applied. Shown are results for Sippican (a) T4/T6 and (b) T7/DB probe types. The “raw” label indicates uncorrected data.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
We looked also at the residual temperature bias (XBT − CTD) after all depth and temperature corrections were applied to all resolutions in the database (2137 Sippican T7/DB and 723 Sippican T4/T6). For the TG, CH, GR10, H12, and G12 methods, the temperature bias corrections recommended were applied after depth correction. The L09 method is a temperature-only correction, and this was also included for comparison.
Uncorrected Sippican T4/T6 (Fig. 18a) have a mean residual temperature bias of ~0.1°C over the depth range. The G12 corrections remove the surface temperature bias but overcorrect at depth to between −0.2° and −0.1°C, whereas the GD11 corrections, which have a method of deriving corrections that is similar to that of G12 and have no temperature bias correction, similarly overcorrect at depth but undercorrect at the surface. The GR10 corrections overcorrect to approximately −0.1°C. The W08 and L09 correction methods both overcorrect to approximately −0.05°C, and some of the W08 overcorrection may be due to the last year of these corrections (2005) being applied into later years. The TG, CH, H12, and IK09 methods do well at depth, but the top 200 m of TG, H12, and IK09 have a positive residual temperature bias.
Comparison of temperature residuals (XBT − CTD) in the pairs database after depth corrections from the TG, CH, GR10, GD11, W08, G12, IK09, and H12 methods are applied. Temperature bias corrections from the TG, CH, GR10, L09, G12 and H12 methods are applied. Shown are results for Sippican (a) T4/T6 and (b) T7/DB probe types. “Raw” = uncorrected data.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
The Sippican T7/DB uncorrected data have a positive temperature bias of ~0.1°C (Fig. 18b). All correction schemes reduce this bias, with the GR10, G12, and W08 schemes overcorrecting to approximately −0.05°C. The IK09 and H12 corrections do not quite remove all of the warm temperature bias, particularly in the latter time bins. L09 performs well below 200 m but overcorrects above this depth. A warm temperature bias remains in the surface layers in all schemes. The results from the TG method and the CH method give the least temperature residual over all depths.
That the corrections outlined in this study perform better is not surprising because they were derived from the same controlled pairs dataset used to compare studies whereas the other published schemes are based on broad-scale buddies from the global databases. A key consideration in going forward is, How representative of the global XBT archive is the pairs database? Besides being highly quality controlled and relatively metadata rich, our database was largely derived from research institutions that tended to adopt digital systems earlier than the navies, operational agencies, and fishing fleets who collected much of the data in the global archives. Given that one key result is that historical thermal biases were larger in the past than at present and that recorder type appears to be a key driver of this change, a simple application of our results to the global archive might not be appropriate, and a more nuanced approach using intelligent guesses at recorder type appears to be warranted.
j. Calculation of global heat content after correction
Despite the caveats discussed above, it is still instructive to explore the impact of our corrections on one calculation of GOHC. Ocean temperatures from the World Ocean Database were used to calculate an initial GOHC anomaly (the mean field used for the anomaly calculations was a profiling-float-only climatology). The corrections were then applied to the XBT data as described in section 2h. Approximate percentages of each probe type in the WOD are included in Table 3. TSK corrections were used for TSK DB types. Where a correction was not available for a particular year, T4/T6 corrections were used for T7/DB probes and vice versa for Sippican types; the equivalent Sippican correction was used for TSK types. In addition, the Sippican T4/T6 corrections were applied to all T10 and T11 types and to unknown types with terminal depth of less than 550 m. Sippican T7/DB corrections were applied to Sippican Fast Deep and to unknown types with terminal depth greater than 550 m and less than 1005 m. Any probes with depths greater than 1005 m were not corrected. No correction was applied to Sippican T5, and TSK T5s were corrected after Kizu et al. (2005). Sparton XBTs had equivalent Sippican corrections applied. XBT data from 1996 to the present, which do not have depth-equation information, are not included in the GOHC calculation.
Corrections for mechanical bathythermograph data were derived from L09, and finally the GOHC was recalculated (Fig. 19). Also included is the GOHC calculated after the corrections from L09, who use median differences between XBT and CTD/ocean surface (bottle) data in a large global dataset.
GOHC calculations with and without corrections derived from the TG and CH methods. Also included are calculations from L09.
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
Removal of the depth and temperature biases in Sippican and TSK probe types significantly reduces the GOHC calculation for the period from 1970 to the late-1980s. A reduction from the 1990s to the present time is also clear but to a lesser extent than for the earlier time period. The 1970–80 period is dominated by shallow (<500 m) Sippican probe types (Fig. 1), which we have found require a large depth correction and an additional ~0.1°C temperature bias correction. The post-1985 period is dominated by deeper Sippican T7 and DB types (Fig. 1), and these require a smaller correction for depth bias and temperature bias, resulting in a smaller reduction in GOHC.
4. Conclusions
A time-varying fall rate clearly exists even when the H95 fall rate is applied to XBT data, but the variation is within manufacturer specifications. The errors in fall rate are easier to determine in high-resolution profile pairs. The Sippican T4/T6 probe types have a slower fall rate than that of H95 from the mid-1970s to the early 1980s. The Sippican T7/DB probe types show no significant difference from the H95 fall rate from the mid-1970s to 1995, but after 1995 the fall rate slows. We consider this to be statistically significant, as the time bins are independent of each other and the statistical uncertainty is small.
We have a limited number of TSK probe types in the pairs database, and it is difficult to derive a fall-rate correction for these data. Others (Kizu et al. 2011) have shown that recent TSK T7 probes fall more quickly than Sippican T7 by 3%–4%, and the addition of more TSK pairs to this database may help to define the differences between the two.
Our results also show unambiguously that there is a constant temperature bias (but within manufacturer specifications) in most Sippican XBTs after depth correction (~0.05°C database wide) and that this bias is constant with depth for all Sippican probe types. This bias accounts for at least one-half of the thermal error diagnosed in the XBT archive. The temperature bias after depth correction before 1985 is significantly higher than that of the post-1985 era, accounting for some of the larger biases seen in archived data between 1975 and 1985. This larger historical bias appears to be attributed to the strip-chart recorder types used during the early history of XBTs, as the pure temperature biases were found to be clearly related to recorder types in this study.
There is no effect of water temperature on the α term of the fall-rate error in the 0°–25°C range. The effects of water temperature on fall rate found in this study are significantly smaller than the effect of temporal changes, but further investigations into the effects of temperature on fall rate, such as computational models (Stark et al. 2011; Abraham et al. 2012) and collection of XBT/CTD pair data, are recommended. Water temperature does not have an effect on the offset term β of the depth error. In our simple slope/offset model of depth bias, the offset term appears to compensate for an acceleration over the upper 100 m or so. This conclusion suggests that a different parametric model of the depth bias (and thus FRE) is worth pursuing in future studies.
Water temperature and ΔT are also related in Sippican probes, suggesting that the water temperature affects the response of the thermistor, resulting in a negative temperature bias in temperatures of lower than 0°C and up to 0.06°C in waters of 25°C.
Two very different analysis methods of the depth error in the pairs database were investigated and were found to give similar results, indicating that the results are robust to analysis method. In comparing our depth corrections with those in the literature based on the global archive, we find a smaller correction in the early time history when compared with other schemes. All schemes agree well in the data-rich, post-1985 years for Sippican T7/DB probe types. Application of all correction schemes to the pairs database revealed that several schemes overcorrected the depths while others did very well at removing the majority of the depth error and temperature bias.
GOHC estimates were reduced when the corrections recommended in the TG method and when using the CH method were applied. There is a significant reduction in GOHC from the 1970s to the mid-1980s, during which period larger corrections to Sippican T4/T6 probe types were applied.
We suggest that application of our time-dependent bias estimates on the global database be undertaken with caution, because a key result is that the pure thermal bias is substantial and changes in time and is very likely based on recorder type. It is unlikely that the changeover in acquisition systems in the research-agency-sourced pairs database analyzed here parallels that in the global archives. Thus, a more nuanced approach may be warranted in determining which corrections to apply to historical XBT profiles.
The pairs collected for this study will be made publicly available online through the NODC XBT bias Internet site (http://www.nodc.noaa.gov/OC5/XBT_BIAS/xbt_bibliography.html), and we encourage other institutions to add to this database to allow an open study of the XBT biases. We recommend that XBT/CTD side-by-side comparisons be undertaken routinely, especially when there are changes in the technology, probe design, or manufacture, to ensure that we have a high-quality record of fall rates and that the results of these future studies be added to the current database. It is also vital that comparisons collect 30–40 pairs to overcome the natural random error in the system (see the appendix).
Acknowledgments
We acknowledge the help of Esmee van Wijk (CSIRO) in undertaking pairs comparisons on the Aurora Australis that contributed to the pairs database. We also acknowledge the assistance of Sabine Huettl-Kabus and Birgit Klein of BSH and Gustavo Goni of AOML for supplying pair data for this study. We gratefully acknowledge the assistance of JMA and JODC with identification of duplicate Japanese data.
APPENDIX
Error Estimates for Future XBT/CTD Pair Studies
Even in side-by-side analysis, XBT data are noisy and variable. A key question is, How many pairs are required to deduce a certain size bias? To determine accurate estimates of the errors involved (especially for ensembles of small numbers of pairs), a bootstrap analysis of our large pairs dataset was undertaken. The results of this bootstrap analysis are used throughout this study to estimate the standard error for results for which there were less than 50 pairs.
Ensembles of each parameter (α, β, and ΔT) were formed by grouping the data by resolution and probe type. A bootstrap analysis was performed on each group by randomly selecting n pairs (from 1 to the maximum number available), followed by calculation of the median of the result, and then repeating this process 500 times. The standard deviation of the medians of the 500 “pseudo” datasets was calculated for each n (Fig. A1; Table A1). The equivalent depth error at 800 m (Table A1) for a comparison in which only five pairs are used to determine a depth error is ±4.41 m for data collected on a single cruise. A much smaller error is achieved with 35 pairs (±1.70 m at 800 m). For future XBT bias studies, we recommend a minimum of 30–40 high-resolution pairs be analyzed before presenting fall rate or temperature bias estimate. If the pairs are not collected in a single cruise, then the experimental design should aim to minimize probe batch-to-batch variability and variability in the systems used. Collection of pair data over multiple cruises results in a higher standard error (Table A1). We recommend following the procedures outlined by Sy and Wright (2000) for collection of XBT/CTD pairs.
Output from bootstrap analysis of high- and low-resolution pairs from the cruises with the most pairs for (left) α and (right) ΔT. The thin solid lines indicate four single cruises, and the dotted lines are a median value of these four cruises. The thick solid lines show the standard error to expect when collecting pairs over multiple cruises (MC).
Citation: Journal of Atmospheric and Oceanic Technology 30, 6; 10.1175/JTECH-D-12-00127.1
One standard error as calculated from the bootstrap analysis of high-resolution pairs.
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