## 1. Introduction

*z*

_{xbt}using a fall-rate equation (FRE): where the

*a*and

*b*coefficients are empirical constants related to the physics of the probe descent.

This FRE results from a simple dynamical model of the descent of the XBT with the net buoyant force being balanced by hydrodynamic drag proportional to the square of the probe speed (Green 1984; Hallock and Teague 1992). The linear term *bt* in (1) results from this balance when the acceleration of the probe *d*^{2}*z*/*dt*^{2} is neglected. As a result, the fall speed is virtually equal to the terminal velocity, a reasonable assumption for depths larger than 10 m. The *b* coefficient represents the value of this terminal velocity and is, to first order, determined by the drag coefficient and the mass of the probe in the water. The deceleration term −*at*^{2} accounts for the both the reduction of probe mass as the wire pays out and the increasing drag with depth, where the latter is more important. The depth dependence of the fall rate due to changes in seawater density is one order of magnitude smaller than the temperature dependence of the drag or the mass loss due to wire payout (Green 1984).

The bulk of XBT temperature profiles are collected using probes manufactured by Sippican, Inc. (now Lockheed Martin Sippican, hereafter Sippican). Even though these coefficients are based on physical parameters of the probe (Green 1984), they are empirically determined by the manufacturer with standard values for *b* = 6.472 m s^{−1} and *a* = 216 × 10^{−5} m s^{−2}. The processes involved in the descent of an XBT probe are certainly more complex than the first-order dynamics implied in Eq. (1). As a result, the determination of the XBT depth is the most important source of error in XBT temperature profiles, with reported values of 17 m (McDowell 1977; Seaver and Kuleshov 1982) and 19 m (Fedorov et al. 1978) at 750-m depths. Systematic errors in the computed XBT depths have been identified since the mid-1970s: Comparison studies between simultaneous XBTs and onductivity–temperature–depth (CTD) casts found a small positive bias above the thermocline and a much larger negative bias for depths below (Fedorov et al. 1978; Flierl and Robinson 1977; McDowell 1977; Seaver and Kuleshov 1982). Evidence of surface offsets associated with initial transients has also been found (e.g., Singer 1990), pointing at the limitations of the FRE (1) in the determination of XBT depths. Nonetheless, XBT temperature profiles have been shown to be accurate enough to characterize mesoscale phenomena (Seaver and Kuleshov 1982; Flierl and Robinson 1977).

*f*

_{H95}= 1.0336 was recommended to correct this bias and later applied to the Sippican original FRE as follows:

Recent studies suggest time-varying biases between XBT and CTD observations that are consistent with changes in the *b* coefficient, that is, the probe’s terminal velocity (Gouretski and Koltermann 2007; Wijffels et al. 2008; Ishii and Kimoto 2009). The time-varying errors found by these studies represent up to 10% changes in the *b* coefficient of the FRE, leading to commensurate changes in *z*_{xbt}. The implied changes in the FRE exceed the 2% error specified by Sippican and are likely to be responsible for spurious decadal signals in global mean heat storage time series (Wijffels et al. 2008; Levitus et al. 2009).

Starting in 2000, the rapidly expanding Argo array (Gould et al. 2004) provides global and highly quality controlled ocean temperature and salinity data with CTD accuracy. Nonetheless, XBT profiles make up to 25% of the current global temperature profile observations during the period of study. Therefore, assessing and correcting this bias is key to monitoring changes of global ocean heat content. Moreover, systematic biases between observing systems with disparate quality capabilities, such as Argo and XBTs, can also introduce spurious climatic signals in heat storage as the ratio of the number of observations collected with each platform changes (e.g., Willis et al. 2009). Argo and CTD profiles also have uncertainties in the determination of pressure/depth. For instance, profiles from Argo floats are often corrected for drifts in the pressure sensor (http://www.argo.ucsd.edu/Acpres_drift_apex.html). Most of the Argo pressure drifts are less than 2 dbar, with very rare cases as large as 10 dbar. These large drifts are unlikely to have a global impact compared with the hypothesized XBT bias, which, if detected, should exhibit a global extent. Moreover, the magnitude of the hypothesized XBT bias, about 20 m at 700-m depth (e.g., Wijffels et al. 2008, their Fig. 6), is substantially larger than the Argo drifts in addition to having very different depth dependence. Ideally, XBT data should be evaluated against CTD data in order to obtain an absolute correction (e.g., Hanawa et al. 1995). However, the sparse coverage provided by CTDs during the 2000–07 period does not permit a global comparison. For these reasons, in this study we evaluate XBTs relative to Argo data. This should be kept in mind if the correction derived here is applied to XBT data.

Most intercomparisons have focused on localized concurrent CTD and XBT casts, which have limited temporal and spatial scope. On the other hand, very few studies have analyzed the spatial dependence of these errors (e.g., Schmid 2005; Wijffels et al. 2008). In this study we use temperature profiles obtained from XBT and Argo combined with satellite altimetry observations to investigate the spatial dependence of potential XBT errors globally. Simultaneously, a methodology is developed to estimate the uncertainty of these errors. This methodology takes advantage of the high correlation between satellite altimeter sea height observations and the thermal structure of the upper ocean to reduce uncertainty associated with sampling by in situ observations. This methodology is shown to produce statistically significant (1*σ*) estimates of the XBT bias over relatively short periods compared with conventional climatologies, thus becoming a viable procedure to correct future XBT observations on an operational basis. Furthermore, in this study we characterize the spatial extent of this bias^{1} and provide more evidence for an FRE problem.

## 2. Data

Temperature profiles obtained from XBTs, profiling floats, and CTD casts are used in this study. The XBT data are obtained from the Global Temperature–Salinity Profile Program (GTSPP; http://www.nodc.noaa.gov/GTSPP). The profiling float data are available from the GTSPP and from the Argo Global Data Assembly Centers (GDACs; http://www.usgodae.org/argo/argo.html and http://www.coriolis.eu.org/cdc/argo.htm). CTD data are also obtained from the GTSPP. Temperature profiles in the GTSPP and GDACs are typically quality controlled with different standards. All profiles analyzed here, including XBTs, are quality controlled following an additional procedure based on the standard procedures that are approved by the international Argo data management team consisting of removal of duplicates, spike detection, pressure increasing test, and a vertical gradient test (Schmid 2005). In addition, the profiles were compared with climatology (Conkright et al. 2002). For the Argo data, only pressure and temperature values with quality control flags equal to 1 are used, in addition to “adjusted” fields when available. Since 50% of the Argo profiles collected during 2000–07 are available in delayed mode, real-time profiles were used to complete the Argo data. After the additional quality control and duplicate removal are performed, the majority (85%) of the non-XBT profiles used in our study are profiling floats obtained from the Argo GDACs. The remaining profiles are profiling float profiles obtained from the GTSPP (5%) and CTDs (10%). Approximately 120 000 XBT temperature profiles and 380 000 Argo and CTD temperature profiles that passed the quality control were included in this study.

All XBT-derived profiles analyzed here correspond to “deep” XBTs, such as Sippican models T7 and Deep Blue. These XBTs are designed to reach depths of about 750 m and represent the bulk of the XBT observations since 2000. Profiles shorter than 550 m were not considered, to avoid including *shallow* XBTs (Sippican models T4 and T6), which have different FRE coefficients. The transition from the original Sippican coefficients to the H95 correction has resulted in profiles submitted to the GTSPP with the original FRE during a period after the H95 correction was recommended (Wijffels et al. 2008). Some profiles were submitted to the GTSPP without any information on the coefficients used in the FRE. However, from 2000 to 2007 virtually all profiles include information indicating the FRE coefficients, with the majority including the H95 correction. In this study, we only consider XBT profiles with FRE coefficients unambiguously indicated in the profile. The H95 correction was applied whenever the metadata unambiguously indicated that it was not applied in the data submitted to the GTSPP. About 20% of the XBT profiles required this adjustment. No profiles with ambiguous FRE coefficients were found for the period of study. As a result, all XBT profiles considered in this study have the H95 FRE coefficients applied. A pressure offset has been recently found in a group of Argo profiling floats. All temperature profiles obtained by floats with this problem have not been considered in this study, following the recommendation of the Argo project (http://www-argo.ucsd.edu/Acpres_offset2.html).

Altimetry-derived sea surface height observations are used in this study for two reasons: first, to avoid potential biases in climatological estimates of isotherm depth that arise from the relatively inhomogeneous sampling inherent to in situ hydrography; second, to reduce the uncertainty of the climatological estimates of isotherm depth in regions where the thermal structure of the upper ocean is correlated with the sea surface height. The altimetry data used here are the delayed-mode optimally interpolated gridded sea height anomaly (SHA) fields produced by Archiving, Validation and Interpretation of Satellite Oceanographic data (AVISO) according to the methodology of Le Traon et al. (1998), with spatial resolution of 0.25° and temporal resolution of 1 week. The altimetric observations used to produce these gridded fields were obtained from two or three satellites throughout the period from January 2000 to December 2007. The AVISO SHA fields are anomalies computed with respect to the 1993–99 mean from the direct altimetry observations. Therefore, the time-mean field for the 2000–07 period is not necessarily zero. To apply our methodology we removed the time-mean SHA corresponding to the 2000–07 period on every grid point. This simplifies the interpretation of the isotherm depth estimates obtained from our methodology as climatological mean estimates.

## 3. Methods

The methodology to identify and quantify biases between XBT and Argo observations presented here consists of the following steps:

- The climatological isotherm depths and their uncertainty are estimated from H95-corrected XBTs and from Argo profiles separately. Because of the short duration of the Argo dataset, correlations with altimetry-derived SHA fields are used to reduce the uncertainty of the isotherm depth estimates.
- The geographical distribution of the differences between XBT-minus-Argo isotherm depths is analyzed. Systematic biases between the two observing systems are expected to affect the mean climatological estimates. Only differences with nonoverlapping 1
*σ*confidence intervals are considered. - The depth dependence of the XBT-minus-Argo differences is analyzed to confirm a problem in the XBT FRE. The depth-dependent biases in the XBTs are estimated globally, and in different regions, to infer other potential sources of error than the FRE.

Potential biases in the XBT observations are explored here by comparing estimates of the mean-climatological isotherm depth derived from XBTs with estimates derived from Argo profiling floats and CTDs. Throughout the analysis, Argo and CTD observations are collectively referred to as Argo because of the prevalence of this platform during the period of study. Unlike XBTs, Argo and CTD casts measure the pressure at each temperature observation directly. Thus, the depth of these temperature profiles is determined with higher accuracy than the XBT FRE. For Argo and CTD profiles the pressure is converted into depth following a methodology that accounts for the variation of gravity with latitude and depth, and the effect of pressure on density (Saunders 1981). This methodology neglects the small influence of salinity and temperature on density with an error less than 0.25 m, which is at least one order of magnitude smaller than the hypothesized biases in the FRE equation we seek to identify and quantify. For these reasons, in this study we evaluate the depth of isotherms derived from XBT data relative to Argo data, since the latter are expected to have smaller systematic biases.

Several studies have shown that observations of sea surface height are strongly correlated with the thermal structure of the upper ocean (Goni et al. 1996; Gilson et al. 1998; Mayer et al. 2001; Willis et al. 2004). Based in this virtually ubiquitous relationship, we propose a methodology that combines altimetry-derived SHA fields with in situ temperature profiles to produce climatologies capable of quantifying potential biases in the XBT observations. The depths of the 5°–28°C isotherms, every 1°C, are estimated for each XBT and Argo temperature profile. The SHA fields are interpolated into the location and day of the temperature profiles using a Gaussian filter in space and linear interpolation in time. The pairs of interpolated SHA values and in situ isotherm depths are binned into 3° × 3° bins globally, with XBT and Argo profiles separately. On each 3° × 3° bin, the isotherm depth values are linearly regressed on the interpolated SHA estimating a correlation coefficient, regression gain, and a *y* intercept.

Results for the depth of the 10° and 20°C isotherms are highlighted because these isotherms lie in thermocline waters in subtropical and equatorial oceans, respectively. The spatial distribution of the correlation coefficients obtained for the depth of the 10°C isotherm (*h*_{10}) are similar between estimates using Argo (Fig. 1a) and XBT (Fig. 1b) observations. High correlations (*r* > 0.6) are found in regions where this isotherm is within thermocline waters, such as in the subtropical gyres, with the exception of the South Atlantic subtropical gyre, where observations are scarce. The correlation coefficients obtained for the depth of the 20°C isotherm (*h*_{20}) show high values in the equatorial oceans for both Argo (Fig. 1c) and XBT (Fig. 1d) observations. The correlation coefficients between the Argo-derived isotherm depth and altimetry-derived SHA are statistically significant over most of the global ocean, with a 67% confidence level (1*σ*) based on a chi-squared distribution. The correlation coefficients between XBT-derived isotherm depth and altimetry-derived SHA are statistically significant (1*σ*) over regions covered by XBT transects, where the density of observations is largest. We assume that all observations are independent in the estimation of the statistical uncertainty. This is a reasonable assumption for the Argo profiles, which could show some correlation between successive 10-day profiles but are generally decoupled between casts in the Ekman layer. In contrast, multiple XBT casts sampling one single mesoscale feature are more common along high-density transects (Roemmich and Gilson 2001). In these cases, the uncertainty of the correlations will be underestimated. However, the conclusions presented are robust because our estimation of the depth-dependent XBT error is performed using estimates of isotherm depth resulting from regions with very high correlations (*r* > 0.8) with the SHA fields. We tested the robustness of our results by considering the case of three XBTs sampling the same eddy, resulting in a factor of

*y*intercept are obtained by least squares fitting of a straight line to the pairs of interpolated SHA values

*η*′ and the in situ isotherm depth observations

*h*on each 3° × 3° bin: where

*ĥ*is the isotherm depth estimated by this statistical model for each altimetry-derived

*η*′ value, ɛ

^{−1}is the regression gain, and

*h̃*is the

*y*intercept. For each isotherm, the regression slope ɛ

^{−1}is related to the reduced gravity of a two-layer model, thus representing a measure of the local stratification. Conversely, since the time-mean value of

*η*′ at each location is zero, the

*y*intercept,

*h̃*, represents the time-mean isotherm depth predicted by this statistical two-layer model. We refer to

*h̃*as pseudoclimatology to distinguish it from the climatology obtained from averaging the Argo or XBT observations directly: The pseudoclimatologies

*h̃*obtained from (3) weight the in situ observations with the satellite-derived

*η*′ fields in a least squares sense. This procedure avoids biases due to inhomogeneous sampling and reduces the statistical uncertainty of the pseudoclimatologies. In the following subsections we discuss these two key features of the methodology that allow identification and estimation of potential biases in the XBT observations.

### a. Reduced sampling bias

Throughout this study we compare the parameters obtained from the regression (3) between the satellite-derived *η*′ and *h* obtained from each platform. Any statistical significant difference between the regression parameters may be indicative of problems in either or both platforms. Argo floats have high accuracy in depth and temperature but may have spatial and temporal sampling problems inherent to a Lagrangian observing platform. XBTs are also prone to sampling problems; however, the most important source of error is in the determination of depth, which is much larger than the error in the temperature sensor. As discussed in the introduction, there is evidence suggesting that XBTs suffer from systematic biases associated with changes in the terminal velocity. In regions of high correlations, the methodology proposed here reduces the sampling bias using high-resolution SHA fields, allowing us to identify other systematic errors, such as those associated with the FRE. Thus, discrepancies in the regression parameters will point to problems related to XBT depth estimates.

*h̃*and

*h*

*r*and mean SHA

*η*

*σ*and

_{h}*σ*are the standard deviation of the

_{η}*h*and

*η*′ observations, respectively. Note that while the time-mean

*η*′ is zero, the mean

*η*′ corresponding to the in situ observations

*η*

*η*′ values and isotherms deeper than the background flow, the

*h*

*rσ*/

_{h}*σ*

_{η}*η*

*η*

*h̃*estimate will be lower than

*h*

For example, 82 Argo and 36 XBT quality-controlled observations are analyzed in a 3° × 3° bin centered at 4°S, 169°W. The mean depths of the 20°C isotherm estimated from Argo and XBTs are *h*_{20} = 179.4 ± 1.3 and *h*_{20} = 182.9 ± 2.4, respectively, where the uncertainty is given by the standard error of the sample. The 1*σ* confidence intervals overlap; therefore, the two estimates are statistically indistinguishable with a 67% probability. A scatterplot of the observed isotherm depths from each platform and their corresponding *η*′ values (Fig. 2a), suggests that 66 out of 82 Argo observations were collected over positive *η*′ values. In other words, most of the Argo observations were collected over anticyclonic features; therefore, the *h**η*′ values. However, the *h*

This apparent contradiction may be elucidated with the analysis of the results from the linear regression. The correlation coefficients are 0.6 and 0.5 for Argo and XBT, respectively. The regression gains obtained from each platform are statistically indistinguishable within 1*σ* confidence levels. On the other hand, the *y* intercepts or pseudoclimatology estimates are statistically distinct within 1*σ* confidence levels, with Argo and XBT values of *h̃*_{20} = 172.1 ± 1.4 and *h̃*_{20} = 181.2 ± 2.1, respectively. These estimates suggest that XBTs overestimate the depth of the 20°C isotherm by about 10 m. This difference between the estimates is statistically significant based on the 1*σ* confidence intervals of the *y* intercept resulting from the linear regressions, *h̃*.

The previous example illustrates how, in regions of high correlations, this methodology takes advantage of the homogenous sampling of satellite altimetry to correct biases in the estimates of isotherm depth. On the other hand, when the sampling is homogeneous and in the absence of systematic biases, *h**h̃* converge to the same value. Thus, in regions with high density of observations, the *h**h̃* estimates are expected to converge. For instance, in the 3° × 3° bin centered at 25°S, 175°E the number of XBT and Argo observations is large, and the in situ observations are evenly distributed between positive and negative *η*′ values (Fig. 2b). This example shows how the climatological estimates converge when the sampling is homogeneous in each platform. This is shown by the overlapping between the *h**h̃* estimates obtained from each platform, respectively (Fig. 2b). However, the *h**h̃* estimates show a difference of about 30 m between Argo and XBT, which cannot be explained as a sampling bias and could result from biases in either observing platform.

### b. Reduced statistical uncertainty

*h*

*h̃*. According to the least squares method (e.g., Lawson and Hanson 1974) the standard error of

*h̃*is related to the standard error of the climatological isotherm depth

*h*

*r*: where

*S*( ) represents the standard error estimator,

*η*

*η*′ observations, and

*σ*is their standard deviation. This equation shows that the statistical uncertainty of the

_{η}*h̃*estimates is reduced in the limit of

*η*

*r*

^{2})

*η*

*h̃*is reduced with respect to the climatological isotherm depth

*h*

*σ*is large. To conclude, in the limit of no correlation between

_{h}*h*and

*η*′,

*h̃*converges to

*h*

## 4. Results

Global maps of *h̃* are estimated for isotherms from 5° to 28°C (every 1°C) for XBT and Argo observations separately. In this section we describe the spatial features of the pseudoclimatologies and the differences between XBT and Argo estimates, focusing on the 10° and 20°C isotherms. The estimates of *h̃*_{10} obtained from XBTs and Argo show similar spatial patterns consistent with large-scale ocean features, such as gyres, currents, and fronts (Fig. 3). For example, the pseudoclimatologies capture the deepening of the 10°C isotherm toward the centers of subtropical gyres. The largest values of *h̃*_{10} are found in the North Atlantic, where the thermocline is deeper compared with other basins. Frontal regions, such as the Gulf Stream and the North Atlantic Current can also be identified from these fields. The XBT- and Argo-derived estimates of *h̃*_{20} also show similar spatial patterns (Fig. 4). Both XBT and Argo estimates capture the location of the subtropical gyres in the Pacific and South Atlantic and the east–west gradient of the depth of the 20°C isotherm in the equatorial oceans as well. The Argo-derived *h̃* estimates are statistically significant over most of the global ocean. The XBT-derived *h̃* are statistically significant in most regions, with the exception of subpolar oceans, the northeastern tropical Pacific, and the South Atlantic subtropical gyre, where the density of observations is low.

Subtle differences are identified between the XBT- and Argo-derived pseudoclimatologies for the 10° and 20°C isotherm depth. For instance, the pseudoclimatological 20°C isotherm is deeper in the center of the North Pacific subtropical gyre in the XBT-derived estimates (Fig. 4). These differences are revealed when the respective climatologies are subtracted (Fig. 5). A large fraction of the observed regions of the ocean show differences that are not statistically significant, especially in the Atlantic and Indian Oceans. In regions where the difference can be estimated with 1*σ* confidence, the differences between the estimates are mostly positive. This suggests a systematic depth bias in the XBTs compared with the Argo estimates, as Argo floats are assumed not to have systematic bias because of their higher accuracy in measuring depths. The differences are considered statistically significant when the 1*σ* confidence intervals of the XBT and Argo estimates do not overlap. The confidence intervals are obtained from the standard error of the *h̃* estimator, the amplitude of which is given by (6). The differences between estimates are not significant over large regions, such as the North Pacific and North Atlantic subtropical gyres. This could be related to larger variability in these regions and highlights the difficulty in identifying biases from the highly energetic mesoscale field. Nonetheless, the number of bins where the implied differences are statistically significant greatly exceeds the spatial coverage of previous studies (e.g., Hanawa et al. 1995; Gouretski and Koltermann 2007; Wijffels et al. 2008).

Differences in the values of ɛ^{−1}, a parameter related to the stratification, are also possible but possibly restricted to higher-order problems in the XBT FRE. Our analysis shows very few bins with statistically significant differences in the correlation gain (Fig. 6). This is consistent with an FRE problem, since this type of error should not introduce changes in the stratification. However, other systematic errors, such a temperature bias, should not introduce biases in the estimation of the stratification as well.

Furthermore, the differences between the XBT-minus-Argo isotherm depths are larger for the 10°C isotherm (Fig. 5a) compared with the 20°C isotherm (Fig. 5b). Differences increasing with depth could be linked with a depth-dependent bias between the two observing platforms. Globally, this depth dependence is clearly observed for all isotherms when the XBT-minus-Argo differences are analyzed as a function of isotherm depth (Fig. 7). Most of the statistically significant differences are positive (red dots in Fig. 7), indicating that XBT-derived pseudoclimatologies are deeper than the Argo-derived estimates. The differences that are not statistically significant (gray dots in Fig. 7) fall inside the 2% error bounds specified by Sippican (dash–dotted line in Fig. 7). These XBT-minus-Argo differences (Fig. 7) correspond to pseudoclimatology estimates obtained from regressions with correlation coefficients larger than 0.8 and that do not differ by more 0.1 between XBT and Argo. The depth-dependent bias implied by the XBT-minus-Argo differences is independent of the correlations between isotherm depth and SHA; however, the differences between pseudoclimatologies from these high correlations show reduced scatter.

*h*are adjusted using a least squares best-fit line with no offset at the ocean surface: or, with an offset at the surface,

The slope of these straight lines (solid and dashed lines in Fig. 7, respectively) represents an estimate of a depth-dependent error expressed as a percentage of the depth. For instance, (7) indicates that XBTs overestimate the depths of the isotherms with respect to Argo depths by (3.0 ± 0.2)% in the global ocean. The offset in (8) indicates that XBTs overestimate the isotherm depths by (4.7 ± 1.3) m plus (2.0 ± 0.4)% of the Argo depths. The uncertainty in the coefficients corresponds to the 1*σ* confidence intervals obtained from the least squares fit. The implications of these results for detecting problems in the FRE are discussed in the following section. The slope and offset for the least squares lines show values ranging from 0.1% to 3.7% and from 0.1 to 11.4 m, respectively, in different ocean basins and depending on the type of equation used to fit the differences (Table 1; Fig. 8). Both lines fall outside the 2% error envelope specified by Sippican in all ocean basins (dash–dotted line in Figs. 7 and 8).

## 5. Discussion

*z*

_{H95}is the H95-corrected XBT depth, and

*z*

_{Argo}is considered here to be the true depth. This depth-dependent error allows correction of

*z*

_{H95}as follows: The global correction factor (1 +

*γ*

_{1})

^{−1}of 0.97 in (10) is approximately the inverse of the stretching factor

*f*

_{H95}= 1.0336, implemented after the H95 study. This strongly suggests that the H95 correction could have introduced the bias during the 2000–07 period.

The conclusion presented above is consistent with the analysis of Wijffels et al. (2008), which showed that, since 2000, XBTs have been falling with a terminal velocity close to the original Sippican values. Their comparison of CTD and XBT data showed that the H95 study was done at a time when the terminal velocity (represented by the *b* coefficient in the FRE) was faster than at any other time. This return of the terminal velocity values back to the original Sippican values has been independently confirmed by field intercomparisons (D. Snowden 2008, personal communication). Our study not only confirms the value of the FRE bias but also provides evidence of its global extent, since we identify approximately the same error in the H95-corrected XBT depths in all ocean basins, with the exception of the North Pacific (Table 1). The apparent global extent of the bias points to problems in the XBT instruments rather than the influence of regional differences in ocean conditions, such as the effect of temperature on the hydrodynamic drag.

*γ*

_{2}and offset

*δ*

_{2}obtained from the least squares fit allows correction of

*z*

_{H95}as follows: The values obtained for the

*γ*

_{2}and

*δ*

_{2}coefficients show more disparity between the different ocean basins (Table 1) compared with the

*γ*

_{1}coefficient in correction (10). Overall, the values of the

*δ*

_{2}offset are consistent with values reported by previous studies of 3.7 m (Bailey et al. 1989), 4.2 m (Singer 1990), 2–10 m (Kizu and Hanawa 2002), 2 m (Reseghetti et al. 2007), and 4.5 m (D. Snowden 2008, personal communication).

Surface offsets have received a great deal of attention and have been attributed to a wide range of transients resulting from the thermistor response, the recording system, or the hydrodynamics of the descent of the probe (Green 1984; Roemmich and Cornuelle 1987; Hallock and Teague 1992; Kizu and Hanawa 2002; Reseghetti et al. 2007). Sippican recommends launching XBTs from a height *H* of about 2.5 m to ensure that the entry speed is *gH*^{−1}, equal to the terminal speed, and thus avoid hydrodynamical transients. In other words, the FRE assumes that the probe starts the descent with the terminal velocity implied by the *b* coefficient. The entry speed is expected to be much larger for XBTs launched from cargo ships, because they are typically dropped from the stern or the bridge, which are several meters above the ocean surface. An initial velocity larger than the terminal velocity represents a faster *b* coefficient during the initial descent and results in a negative offset at the surface. In contrast, the *positive* 4.7-m offset suggested by our analysis is consistent with a probe descending with an initial velocity closer to zero (Hallock and Teague 1992, Table 1) and thus is unlikely to result from hydrodynamic transients.

A positive offset could also result from the finite time response of the temperature sensor to sudden changes in temperature, which typically occur when the probe enters the ocean and when it crosses the base of the mixed layer (e.g., Roemmich and Cornuelle 1987; Kizu and Hanawa 2002; Reseghetti et al. 2007). Different recording systems are used in the different ocean basins, thus explaining why we find different values. However, a comparison of the different acquisition systems (SEAS2000, Devil, Sippican) indicates that they exhibit approximately the same offset (D. Snowden 2008, personal communication). In contrast, our analysis shows that considering a surface offset in the least squares fit of the XBT-minus-Argo differences leads to less robust estimates of depth error *γ* and surface offset *δ* (Table 1, columns 3 and 4). Briefly stated, the only robust bias detected from our analysis is a 3% depth-dependent error, with no evidence for a robust surface offset. Addressing this problem is important because this surface offset could introduce biases of up to 10% when estimating the depth of shallow mixed layers, becoming an important source of error. More research is needed to determine its origin, and whether it is introduced when the probe enters the ocean or when the probe crosses the mixed layer.

## 6. Conclusions

A methodology is proposed to estimate climatologies of isotherm depths using a combination of in situ and satellite observations. The methodology allows the estimation of climatologies for relatively short periods, reducing sampling problems by using correlations with satellite-derived SHA fields. Comparison of XBT and Argo climatologies obtained using this methodology represents an important advantage compared with the analysis of nearby XBT–CTD pairs, which is difficult to perform on a global scale, and that has been the main methodology for identifying and characterizing XBT errors up to date. Moreover, this methodology overcomes limitations in comparing XBTs with in situ hydrography directly, which requires very large amounts of data to be able to detect these small biases, which can be obscured by the highly energetic mesoscale field. The methodology presented here avoids these limitations by taking advantage of the high temporal and spatial resolution of satellite altimetry observations.

Comparison of XBT and Argo estimates of isotherm depth suggests a depth-dependent bias in XBT observations in all regions of the World Ocean, which confirms the global extent of a depth-dependent error in the XBTs reported in previous studies (Gouretski and Koltermann 2007; Wijffels et al. 2008). Moreover, our results show that this error can be identified with 1*σ* statistical significance despite the inhomogeneous sampling of the eddy variability by Argo and XBTs. The 3% depth error identified here is also suggestive of a time-dependent bias in the XBTs, since it appears that the H95 correction is no longer appropriate for current XBTs. This indicates that the original FRE coefficients specified by Sippican would be adequate for the 2000–07 period. Although the source of the time-dependent FRE bias remains unclear, the global extent of the implied bias points to problems in the instrumentation, such as changes in the terminal velocity of the XBTs, which are likely to result from variations in the drag characteristics of the probes. The robust global extent of the bias points to problems in the XBT instruments rather than the influence of regional differences in ocean conditions. While there are several potential sources of near-surface errors due to transients in the descent of the probe, our study shows that surface offsets are different among ocean basins and thus unable to be explained by a systematic problem in the XBT FRE. According to our results, returning to the original FRE coefficients is the only correction that seems to be robust. This correction could bring the XBT dataset to consistency with Argo during the 2000–07 period.

XBTs remain the second most important source of upper-ocean thermal data and the most important source of temperature along transects. The FRE coefficients need to be monitored on a continuous basis to identify future changes in the terminal velocity of the XBT, which may avoid introducing spurious decadal signals in global heat storage. The methodology presented here is especially well suited for this purpose because it allows the comparison of XBT and Argo data over relatively short periods. High-density transects, which are run 4 times per year, could provide the number of observations to perform this type of analysis over 1- or 2-yr periods. Additionally, these transects must coincide with regions of high density of Argo observations, such as the North Pacific or the North Atlantic.

Argo data were collected and made freely available by Argo (a pilot program of the Global Ocean Observing System) and contributing national programs (http://www.argo.net/). The altimeter products were produced by Ssalto/Duacs and distributed by AVISO, with support from CNES. We thank all the scientists, technicians, and crewmembers of ships of opportunity that contribute to the collection of XBT and Argo observations around the world. We thank Claudia Schmid for providing the quality-controlled CTD, Argo, and XBT profiles. This research was carried out in part under the auspices of CIMAS, a join institute of the University of Miami and NOAA (Cooperative Agreement NA17RJ1226). We are grateful to Molly Baringer, Ann Thresher, Viktor Gouretski, Robert Molinari, Joshua Willis, and two anonymous reviewers for insightful comments that helped improved the study. The NOAA Climate Program Office funded this work.

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Corrections to the fall-rate equation obtained from least squares fitting of the XBT-minus-Argo differences as a function of depth obtained in this study. The uncertainty in the coefficients corresponds to the 1*σ* confidence intervals obtained from the least squares fit.

^{1}

The term bias and error are used indistinguishably throughout this paper to refer to those errors that are systematic.