1. Introduction
Since the 1960s expendable bathythermograph (XBT) probes, originally invented for military applications, have been widely used for collecting upper-ocean temperature profiles mainly by ships of opportunity. Because of its low price and simple operation, XBTs have become an important part of ocean observation systems since the 1970s.
The XBT probe has a slim body with a sensor (a thermistor) in the nose and twin wires dereeling from both the probe tail and a canister on board, and it is usually deployed from moving ships. As the probe touches the seawater and falls by a slightly decelerated motion, the water temperature is continuously sensed by the thermistor at a rate ranging from 10 to 20 Hz, which depends on the recording system used. The acquisition system stops recording data according to two criteria, either based on a preselected depth or until the probe completely dereels the wire from one of the two spools. Then, the wire breaks off and the probe is discarded. Different XBT models are available; the most used versions have a nominal terminal depth of 460 (T4/T6) and 760 m (T7/DB), but they can usually record data down to about 500 and 850 m, respectively. Because an XBT carries no pressure sensor, XBT depth is estimated from a depth–time mapping originally provided by the manufacturer (Lockheed Martin Sippican, hereafter Sippican) based on oversimplified assumptions about the probe motion. The elapsed time, beginning when the probe hits the seawater and the recording starts and ending at the moment when the first wire breaks, is the actual recorded parameter. The manufacturer’s fall-rate equation is z(t) = At − Bt2, where z(t) is depth at the elapsed time t and the coefficients are both positive and temperature independent.
Since the 1970s, when XBT measurements started to be compared with simultaneous temperature values recorded by other and usually more accurate and expensive instruments, such as salinity–temperature–depth (STD) or conductivity–temperature–depth (CTD), some discrepancies have become increasingly evident. For example, in a report describing several intercomparisons involving a total of about 2000 XBT profiles, Anderson (1980) pointed out several problems in XBT measurements yielding a general positive bias in measurements with XBT probes. Unfortunately, that paper, with its important but widely ignored list of troubles and errors in the XBT system, remained unknown until recent years.
In the 1980s and early 1990s some “cookbooks” and reports detailing the possible malfunctioning were prepared for the oceanographic community (see, e.g., Bailey et al. 1994). Several researchers reported the inadequacy of the manufacturer’s fall-rate equation in the description of the probe motion, both in the near-surface and the deeper layers, which possibly correlates with the seawater viscosity (e.g., Seaver and Kuleshov 1982; Heinmiller et al. 1983; Green 1984; Hanawa and Yoritaka 1987; Singer 1990; Hanawa and Yoshikawa 1991; Hallock and Teague 1992; Kezele and Friesen 1993). International meetings involving the manufacturers were also dedicated to analyzing problems in XBT measurements and eliminating the biases (e.g., IOC 1992). These studies indicated that XBT measurements contain systematic biases caused by diverse factors, with significant probe-to-probe, cruise-to-cruise, and time-to-time variability. In summary, the main part of the errors in the XBT measurements can be ascribed to inadequate fall-rate coefficients, pure temperature error, and start-up transient with an additional but hard-to-quantify component resulting from spikes and other random factors. Nevertheless, the most important efforts were focused on the fall-rate equation problem. Various techniques for computing the best fall-rate equation for a specific dataset were developed until the early 1990s, when, in collaboration with manufacturers, a task team sponsored by the Intergovernmental Oceanographic Commission (IOC) coordinated several XBT versus CTD comparisons in different oceanic regions. As a final result, a comprehensive report and a paper mainly dedicated to the problem of calculating the correct depth were released (Hanawa et al. 1994, 1995, hereafter H95). Only the structure of the manufacturer’s fall-rate equation was confirmed, but new constant-temperature independent fall-rate coefficients were calculated with a “temperature error free” technique for the most used XBT models manufactured by Sippican and TSK (the Japanese manufacturer). The use of these coefficients was strongly recommended by the IOC and accepted by the United Nations Educational, Scientific and Cultural Organization (UNESCO). As a consequence, it was recommended that the old profiles in the databases be converted to the new depth values.
Despite this improvement, discrepancies have still been found both in the H95 method and the H95 equation. Some reports showed that the H95 equation underestimated the actual fall-rate coefficients of the XBT probes (Boedecker 2001; Fang 2002). On the other hand, Thadathil et al. (2002) found that the old manufacturer’s fall-rate equation worked well in cold Antarctic waters, possibly because of viscosity changes, and they suggested that the fall-rate coefficients should depend on latitude (they admitted that the probe motion depended on water temperature). This correlation was confirmed for T5 probes manufactured by TSK (Kizu et al. 2005a), and for expendable conductivity–temperature–depth (XCTD) probes (Kizu et al. 2008). Subsequently, Reseghetti et al. (2007) proposed a different method to deal with the XBT measurements in regions of the Mediterranean with high temperature homogeneity because in those conditions the H95 technique would not work. On the other hand, the ad hoc method that was useful in the Mediterranean requires that some reference points in a profile must be visually determined, and it is slightly complicated to extend this procedure to all of the intercomparisons. These new coefficients also take into account the fall-rate differences between shallower (slower) and deeper (faster) probes. Table 1 shows a comparison between fall-rate coefficients suggested by manufacturers and reported publications.
In recent years, XBT measurements have attracted a renewed interest. Kizu and Hanawa (2002a,b) investigated several types of recording systems looking for the start-up transient, which is the source of the main error in the upper layer. Their results suggested that the depth of the transient differed for different types of recorders. Reseghetti et al. (2007) suggested a possible treatment of the transient by introducing an empirical time constant (ETC) value (implying a rescaling of the profile, with improvements in the upper and the thermocline regions), and they also calculated a method of fine tuning used to eliminate a probably intrinsic pure temperature error.
The existence of a globally time-dependent and systemic warm bias in XBT profiles came to light when various statistical methods were used to compare global datasets of XBT and CTD–Bottle–Argo (Bottle is a special device designed for taking deep water samples and measuring temperature at depth.) in the last 30 yr. In short,
Gouretski and Koltermann (2007) mainly concentrated on the overall biases in XBT measurements;
Wijffels et al. (2008) attributed all of the biases to errors in the fall-rate equation;
Levitus et al. (2009) focused on the pure temperature offset bias and instrumentation problems;
Ishii and Kimoto (2009) considered fall-rate error and estimated corrections through comparisons with nearby CTD and ocean station data; and
Gouretski and Reseghetti (2010) started from the manufacturer’s equation and considered both a time-dependent thermal bias and a stretching factor that was dependent on depth, time, and temperature.
The H95 method has been widely used to correct the XBT bias, but its equation is not so accurate when the temperature vertical gradient is weak. Moreover, it is still inadequate for modeling the start-up transient error and, more importantly, it cannot detect pure temperature errors, which are reasonably constant between consecutive depth measurements that are 0.7 m apart. In regards to the H95 method weaknesses, in section two, after a short discussion concerning the H95 method, this paper describes in detail a new technique using integrals to model temperature profiles that allows for a transient term and considers a pure temperature error. In section three, both the H95 and the new method are theoretically compared using statistical methods in which four types of errors had been randomly added to groups of data, as explained below, where all of these errors are quantified and simulated. In section four, two groups of actual XBT versus CTD intercomparisons from the Atlantic Ocean near Barbados and the western Mediterranean are analyzed, with both the methods and the results compared. The impact of the start-up transient is also tested. Moreover, the mean fall-rate coefficients for the correction of T7 and DB without collocated CTD are calculated. Section 5 concludes with the discussion of the feasibility and limitations of the new integral method.
2. Method
H95 compared the temperature gradient values extracted from an XBT profile with the corresponding ones from an almost simultaneous and collocated CTD profile. Because of its simplicity, the H95 method has been widely used, but it has some disadvantages. First, the inclusion of random errors and spikes in both XBT and CTD measurements would enlarge errors of temperature profiles and lead to poor gradient profiles. Moreover, the pure temperature error in temperature profiles might disappear because of the use of temperature gradients. Then, following the original text in the H95: “However, the new method does also occasionally fail to detect depth differences when the vertical temperature gradient is constant in a section of the profile larger than the search window, or when the XBT temperature profile has features not matched by the CTD profile” (Hanawa et al. 1995, p. 1431). That feature had been accurately shown by Kizu et al. (2005b) when computing the fall-rate equation of T5 probes using several groups of XBT and CTD data. In addition, because visual inspection and discretional selection is introduced, H95 must be considered a semiautomatic method. Finally, the start-up transient or any other depth-related errors are not taken into account.
Physically speaking, a raw XBT profile contains resistance measurements as a function of elapsed time. Then, resistances are converted into temperature values by applying the Steinhart–Hart equation with experimentally determined coefficients (e.g., Georgi et al. 1980). In the final step, a fall-rate equation specifies a mapping of the elapsed time to the depths, and the output of a XBT measurement is a depth–temperature profile. On the other hand, an accompanying CTD profile includes temperature and pressure data that are subsequently converted into depth values. If the fall-rate equation is affected by errors, an improper time-to-depth mapping can lead to dominating discrepancies between XBT and CTD profiles. In this context, our goal is to estimate an optimal mapping of the elapsed times to the depths for XBT profiles so that the discrepancies between the XBT and CTD measurements are minimized.
We assume that the mapping takes the form of a z(t) = At − Bt2 − transient, where t is the elapsed time and transient is a correction describing the up-to-now unpredictable phenomena occurring mainly in the near-surface layer, at the start up, with a deviation from the manufacturer’s equation. A similar structure of the fall-rate equation has been proposed in other papers (e.g., Heinmiller et al. 1983; Singer 1990), but the last term in the equation above was interpreted as an offset to give a better interpolation, and it was not calculated at the same time as the remaining fall-rate coefficients. This assumption could imply that the coefficients (A, B) are assumed to be constant (and temperature independent) over the whole water column. This is only partially true. The term transient could mask small variations of (A, B) values during the initial probe motion, and consequently the inadequacy of the (A, B) terms to describe the true probe motion with the required approximation.
The optimal values of the scale function f can be evaluated by assuming the partial derivatives to be 0 and solving the equations ∂f/∂A = 0, ∂f/∂B = 0, and ∂f/∂transient = 0. Unfortunately, the equation is too complex to compute the exact partial derivatives analytically. There are many approximation algorithms that can be used to solve the optimization problem, such as the genetic algorithm, simulated annealing, or artificial neural networks. In our paper, we simply adopt the “brute force” method of searching values for possible combinations of (A, B and transient), and then finding the optimal one. Although this method is not time efficient, detailed behaviors of the function, such as the uniqueness of the optimal values, can be obtained. As a drawback, analysis on a large number of XBT profiles would require more efficient methods.
The brute-force algorithm is described below.
a. Step 1: Filtering
Similar to the H95 method, two types of filters are applied to the raw data of both XBT and CTD in sequence: first a nonlinear median filter is used, and then a low-pass linear cosine Hanning filter without threshold logic.
b. Step 2: Calculation of values of f
For each pair of profiles from a XBT versus CTD comparison, the ranges and the steps of A, B and transient are the following:
5.800 m s−1 < A < 7.200 m s−1; step 0.002 m s−1;
0.000 m s−2 < B < 0.005 m s−2; step 0.000 02 m s−2; and
−5.0 m < transient < 15.0 m; step 0.3 m.
c. Step 3: Determination of new fall-rate equation
For each profile pair, the optimal combination of values of (A, B and transient) can be selected according to the minimal value of f. If there is a set of pairs, the mean values of optimal (A, B and transient) for each pair is adopted for the new fall-rate equation.
Figure 1 shows the matching principle of the new method. We mainly focus on a single time window. In each selected time window, the deviation of the temperature difference is zero when the XBT vertical temperature line is parallel to the corresponding CTD profile as in Fig. 1. The optimization problem specifies the XBT profile according to the coefficients A, B and transient to that parallel position (the dotted line in Fig. 1). In this way, the systematic temperature bias can be naturally ignored. In addition, the method is automatic given that visual inspection of the data has proved to be redundant.
3. Experiments with simulated data
a. Design
The purpose of the experiments using simulated XBT–CTD profiles is to test the performance of the proposed technique. In the H95 method, the start-up transient is not considered; therefore, in this section we assume that XBT measurements do not contain the start-up error, and we thus focus only on the four other main sources of errors in XBT data: wrong fall-rate equation, pure temperature error, spikes, and random errors.
One-hundred-forty profiles of the ENSEMBLES dataset (so-called EN3 data) CTD data (quality-controlled in situ ocean temperature and salinity profiles) from the oceanographic dataset World Ocean Database 2005 (WOD05; Boyer et al. 2006) of January 1980 have been extracted and regarded as true ocean profiles; these data were then labeled from 1 to 140. Vertical temperature profiles from different regions with various typical features of the equatorial seawater are shown in Fig. 2. To simulate the CTD observations, normally distributed 0 mean and 0.001°C standard deviation errors were added to these true temperature profiles, with 1-m-depth steps. The XBT observations are generated as follows:
(i) Adding the fall-rate error: It is assumed that the fall-rate equation ztrue(t) = 6.691t − 0.002 25t2 (proposed by H95) gives the true fall-rate coefficients of all these 140 profiles. To add the fall-rate error in simulated XBT observations, we assume the original manufacturer’s fall-rate coefficients to be wrong [zXBT(t) = 6.472t − 0.002 16t2]. Using the depth differences given by the two sets of fall-rate equations, we can shift the true profiles vertically to obtain fall-rate effects on simulated XBT observations. Usually, the sampling interval of XBT measurements is 0.1 s.
(ii) Adding the pure temperature error: Pure temperature error is defined as a linear function of the elapsed time, which refers to an approximate temperature correction of Reseghetti et al. (2007) in the form of Tbias = −0.029°C − 0.000 016t, which varies slowly with depth.
(iii) Adding spikes: Spikes caused by small-scale geophysical and instrumental noise are generated as random temperature variations in the range of 0.1°–0.2°C. Spikes were added randomly to 2% of the total measurements of the simulated XBT profiles.
(iv) Adding random error: The random error of XBT is regarded as having two components. For the first part, we added a normally distributed random number with 0 mean and 0.01°C standard deviation to each XBT temperature measurement in the whole profile. To take into account the possible bias in some incongruent segments, we added bias with values 0.00°, 0.01°, or 0.02°C to all profile segments. These values were randomly assigned, according to a probability distribution of 80%, 14%, and 6%, respectively. Each segment has a random time span less than 2 s.
b. Results
We have applied both methods separately to calculate the values of the A and B coefficients for each of the following groups:
(i) first group: only fall-rate equation errors,
(ii) second group, also pure temperature errors,
(iii) third group, fall-rate equation and random errors, and
(iv) fourth group, all four errors.
Figure 3 shows the distributions of these coefficients in the A–B plane, indicating that the new method performs better for two reasons. First, in all of the groups of experiments the mean values of the obtained A, B coefficients by the new method are closer to the original values than those from the H95 method. Moreover, the H95 method has a larger scattering (Fig. 3), which means that the results of the H95 method contain larger uncertainties. Finally, the new method estimates the fall-rate equation correctly (see Figs. 3a,b; when only fall-rate error is considered): the differences with respect to the true coefficients are small, within the range (−0.006, 0.006) m s−1 for A and (−0.000 15, 0.000 15) m s−2 for B, respectively. For comparison, results with H95 get a maximum error of 0.05 m s−1 for A and 0.0005 m s−2 for B.
On the other hand, Figs. 3c,d show that there are no significant differences between the results before and after the addition of the pure temperature error. This means that the pure temperature error exerts very little influence on the calculation of the coefficients by H95 (as expected because of the use of gradient profiles) and also by the new method.
When the random errors are added to the XBT–CTD measurements, with the new method, the distribution of the obtained fall-rate coefficients shows a larger variance. However, the errors are still less than 0.01 m s−1 for A and 0.000 25 m s−2 for B, and are better than the results of H95 (Figs. 3e,f).
When XBT profiles containing all of the possible errors are used as raw data, the estimated values using the new method disperses slightly in the A–B plane, but the results are better than those using H95 (Figs. 3g,h). Indeed, in the four trial tests described above, the mean values improve the individual estimations in both methods, but the new method yields better mean values than H95 does.
The H95 method also includes visual inspections to remove outliers, so we cannot be sure whether the depth difference profiles obtained by H95 are correct or whether they are due to the criteria of selection used by the operators. Thus, an additional experiment has been conducted to evaluate the impact of this process. We applied the H95 method to the above group 4 data, but without removing any XBT profiles or any extreme data from them using visual inspections. Figure 4 shows the depth differences (as function of depth), calculated by the H95 method with and without such a step. Without visual inspections and the removal of noncoherent points or entire XBT profiles, relatively large errors exist from the basis of the thermocline to the bottom, where the vertical temperature gradient is either zero or very small. In such conditions, the random errors and spikes can produce false gradients rather than the meaningful ones resulting from fall-rate equation error. Even after the eliminations of the noncoherent depth differences by visual inspections (see step 4 of H95 in detail), the uncertainties near the bottom still remain.
4. Actual XBT–CTD comparison experiments
The above detailed simulated experiments show the overall good performances of the new technique, but those procedures are based on simple assumptions, so they exclude unexpected error sources. A definitive test of the new method must use actual XBT versus CTD comparisons.
a. Datasets
A total of 122 XBT profiles from two groups of XBT versus CTD comparison experiments, which were independently carried out by two institutions in specific regions and periods, have been analyzed. The dataset is composed of the following:
Fifty-one Sippican T7 XBT probes were deployed in May 1990 by Hallock and Teague (1992) about 300 nm northeast of Barbados Island, in the Atlantic Ocean (Fig. 5a), which is an ideal region for XBT versus CTD comparisons because of alternating isothermal, isohaline layers and high-gradient “sheets.” The XBT depth was estimated by the manufacturer’s fall-rate equation. Within 2 h, three CTD casts were completed by using a Neil Brown, Mark III CTD system, which was calibrated before the cruise. During their descent, four T7 probes were launched using Sippican Mark-9 Launcher Acquisition Systems (for details, see Hallock and Teague 1992). They are available in the National Oceanographic Data Center’s (NODC’s) XBT quality tests references table.
Seventy-one Sippican DB probes from the western Mediterranean Sea were used (Fig. 5b). This group includes 27 profiles from comparisons carried out in 2003–04 (group 2.1), previously analyzed in Reseghetti et al. (2007), which are also available in the NODC database. The remaining profiles are from unpublished tests from 2008 to 2009 (group 2.2). All of the CTD profiles were recorded using a SeaBird 911 plus device, which was calibrated before and after each cruise. The only instrumental difference is the XBT recording system [a Mark (MK) 12 recorder for subset 2.1 and a MK21 recorder for subset 2.2]. The most evident feature of seawater in that region is the high temperature homogeneity, even with temperature inversions. All of the depths were calculated by the H95 fall-rate coefficients. The maximum difference between corresponding XBT and CTD profiles was 2 h in time and 0.15° both in latitude and longitude, but most profiles were recorded within 10 min and about 0.02° in geographical position.
Figures 6a,b show two typical sets of comparisons between simultaneous XBT and CTD profiles from the two groups, respectively. In group 1(Fig. 6a), temperature profiles decrease almost monotonically with depth, while in group 2 (Fig. 6b), the probes fall through a practically isothermal medium. Below 100-m depth and toward the bottom, seawater temperatures are constant within 1°C, with very small or null vertical temperature gradients, or even with temperature inversions. The different seawater properties between the two groups can lead to different fall-rate equation features resulting from viscosity effects.
To enhance different systematic errors in XBT profiles, we zoom in the typical profiles in Fig. 6. In Fig. 7, XBT profiles clearly show both a vertical depth offset and a temperature offset in comparison with the simultaneous CTDs.
First, because the depth error resulting from the improper fall-rate equation at the surface (0–50 m) is negligible, the depth discrepancies of the isothermal depth between XBT and CTD profiles at the surface clearly show a start-up transient error, as in Fig. 7a near 10 m and in Fig. 7c near 30 m. We also note the probe-to-probe difference of the transient term even when XBT probes are launched at the same time under the same conditions. The start-up transient error has been attributed to both the pure thermal transient, for example, a finite delay for the thermistor to adjust to the temperature of the surrounding water, and the dynamics of the XBT probe, such as launching conditions, entry angle, and mechanical effects. As shown in Gouretski and Reseghetti (2010), some tests in shallow water suggest that the manufacturer’s fall-rate equation overestimates the real depth of 1–3 m at about 30-m depth.
Second, in XBT measurements there is evidence of pure temperature errors. Figures 7b,d show that systematic temperature offsets occur especially in the regions with small vertical temperature gradients, where the impact of the fall-rate equation error on the temperature offset is reduced to a negligible level. It is also evident that most of the temperature differences are within the manufacturer’s tolerance of 0.2°C.
Furthermore, as presented in Fig. 6, the XBT profiles lie above the CTD profiles in group 1 and below CTD profiles in group 2. These features indicate that the actual fall rate of XBT is underestimated by the manufacturer’s equation for T7 but overestimated by the H95 equation for DB probes.
After visual inspection, some significantly bad profiles were eliminated, for example, XBT profiles with abnormal structures compared with the other profiles in the near region, or evidently erroneous and fake features. We also took in account the XBT profiles that had not achieved their terminal depths. After this inspection, all profiles in group 1 were labeled “good,” while nine profiles were eliminated in group 2. Then, both the H95 method and the new method were applied to the two groups.
b. Individual and overall XBT profile corrections
For each XBT profile, the individual coefficients (A, B, and transient) are computed using the new method. Then, the individual corrections are made according to the following procedure:
(i) the depth in each XBT profile is calculated using its own fall-rate coefficients;
(ii) a shift on the depth value according to its own transient value is applied to each profile; and
(iii) the temperature measurements are filtered by the median and the Hanning filter.
Following the application of this procedure, the mean temperature difference (a function of depth) between either the uncorrected (red line) or the corrected (blue line) XBT and the CTD profiles is shown in Fig. 8. Individual corrections significantly reduce the discrepancies of the temperature differences for profiles in both groups. In particular, in group 2, the corrections mainly work between 0 and 200 m, where the maximum temperature difference reduces from 0.3° to about 0.05°C. Additionally, the reason why the improvements are not so marked in the region below 300 m in group 2 is probably due to the low temperature gradient in this region. However, some small-scale uncertainties in the regions of relatively large gradients still remain (at about 0–200 and 450–650 m for group 1, 0–100 m for group 2.1, and 0–200 m for group 2.2).
The mean temperature differences peak at about 0.1°C for group 1, at about 0.05°C for group 2.1, and at about −0.05°C for group 2.2. These temperature offsets can be considered as pure temperature error. A linear regression of the temperature differences (as function of depth) can be easily introduced as ΔT = TXBT − TCTD = T2 × depth + T1, where T1 could be thought as the temperature error at surface (intrinsic thermal error) and T2 describes the variation with depth, probably including the pressure effect quoted by Roemmich and Cornuelle (1987).
The coefficients T1 and T2 have been calculated with the depth parameter ranging from 2 to 750 m for group 1, from 100 (at the basis of the upper thermocline) to 800 m for group 2.1, and from 200 to 800 m for group 2.2, because of great uncertainties in the upper ocean. The linear regression and the corresponding norm plot are shown in Fig. 9 for two groups. Both regressions confirm that systematic pure temperature offsets have an evident linear trend. Additionally, the amplitude of the oscillation of the residuals in group 1 (less than 0.1°C from 200 to 750 m) is much larger than those in group 2 (about 0.01°C from 200 to 800 m), while near the surface the oscillation gets much larger than in the deeper water in group 1. This phenomenon suggests that the systematic pure temperature error does exist and can be corrected by a linear function. Otherwise, the effect of the temperature gradient, random errors, and other unknown biases may induce a random-walk feature of the temperature differences, leading to difficulties in the estimation of the pure temperature error.
Equation (2.1) is in good agreement with the pure temperature correction for DB in Reseghetti et al. (2007) (ΔT = 0.000 014 × depth + 0.039), when the data we used are the same as those used by Reseghetti et al. (2007). Additionally, the significant contradiction of the pure temperature error between the two subsets suggests that different recording instruments could induce significantly different pure temperature errors.
After the application of this correction (in Figs. 8a–c, green line), the remaining temperature differences below the thermocline are mostly within the range from −0.05° to 0.05°C for group 1, and from −0.02° to 0.02°C for group 2. In this last region they seem to have a random or irregular fluctuation. On the other hand, some significant but small biases (less than 0.1°C) still remain both within the thermocline regions and at the 450–650-m depth, where the temperature gradients vary irregularly with depth. Indeed, this region deserves more detailed studies. In detail, for group 1, there is a small cold bias at the surface (about −0.1°C), which slightly increases with depth down to the basis of the thermocline (about 0.1°C). The results show that the specific corrections, namely, individual (A, B, and transient) correction and pure temperature correction, are effective and help to rebuild the structure of the individual XBT temperature profile very accurately, matching, and sometimes even improving, the manufacturer’s tolerance of 2% in depth values and 0.2°C in temperature.
At this point we proceeded with a visual inspection, which is not an essential part of this new method, because we wanted to double check that the depth differences between the corrected XBT profiles and CTD profiles were within the manufacturer’s tolerance. Only one profile from group 2.1 was eliminated, confirming the power of the new method and ensuring as accurate as possible mean values for the searched coefficients.
The individually corrected coefficients and their mean values are shown in Fig. 10 (for the A and B coefficients) and Fig. 11 (for transient). The distribution of the coefficients for group 1 appears to be more centered on their mean values than those in group 2, where a larger spread in B values appears. This is probably due to the high temperature homogeneity of the Mediterranean, which leads to a lack of useful information for estimating the corrected fall-rate coefficients, so the more important results lie mainly on the thermocline region; unfortunately, measurements in that region are not very accurate. Then, the final values of (A, B, and transient) are obtained by computing the mean value. In summary, the new fall-rate equations for the two groups are as follows:
- group 1, z(t) = 6.8458t − 0.002858t2 − transient
- group 2.1, z(t) = 6.6782t − 0.001 810t2 − transient
- group 2.2, z(t) = 6.6405t − 0.002 296t2 − transient
When the coefficients of Eq. (4.1) are compared with the values calculated by Reseghetti et al. (2007) for DB {z(t) = [(6.720 0.060) m s−1]t − [(0.002 35 ± 0.000 10) m s−2]t2 − (2.00 ± 0.70) m}, where the term 2 m represents the ETC correction (equivalent to the transient)}, the results show good agreement. The relatively high value of the standard deviation in Eqs. (4.1) and (4.2) could be a consequence of the high temperature homogeneity of Mediterranean seawater, but only the application of this method to several other profiles with similar characteristics could confirm such an interpretation.
The manufacturer states that T7 and DB probes have the same dimensions and the same motion in seawater, within probe-to-probe variability and the nominal uncertainty (2% in depth and 0.2°C in temperature). The present analysis seems to contradict this assumption, probably because of the unpredictable impact angle with the sea surface, variable impact speed, wake influence, variable seawater characteristics, and industrial standard probe variability. For example, the height of the launching position determines the probe entry speed and therefore the motion in the upper layer. As a consequence, the depth estimated by usual fall-rate equation is inaccurate in the near-surface layer, even within the nominal depth accuracy (5 m).
First we take account of the seawater properties in group 1, where temperature profiles show an almost monotonic decrease with depth; this means that the viscosity increases toward the bottom, where the probes should move more slowly than estimated by the fall-rate equation. On the other hand, in group 2, the probes fall through a practically isothermal medium where the variations of seawater temperature remain within 1°C down to the bottom. This implies that the viscosity should not vary in a significant way. The viscosity changes due to different seawater properties are considered to have an evident influence on the probe motion. Gouretski and Reseghetti (2010, p. 815) state that “According to Green (1984), the kinematic viscosity of sea water increases typically by about 50% between the near-surface layer and 750 m depth. In case of a fully turbulent flow around the probe, the hydrodynamic drag coefficient would exhibit an increase by less than 0.1% for a 5°C temperature change (and the corresponding fall speed decrease of about 0.05%).” Thus, viscosity changes in our new model will lead to significant fall-rate changes depending on the various geographic areas considered.
Second, recent works by Gouretski and Koltermann (2007), Wijffels et al. (2008), Levitus et al. (2009), Ishii and Kimoto (2009), and Gouretski and Reseghetti (2010) have suggested a time dependence of XBT biases. This could be one of the possible sources of the discrepancy between the coefficients of the fall-rate Eqs. (3), (4.1), and (4.2), but tests on more relevant data are needed to establish just how this takes place in order to determine more robust results for the accuracy of XBT measurements.
c. Impact of start-up transient error on H95
To validate the significance of the results described above, we performed XBT analysis with the H95 method, which does not include an estimation of the start-up transient. To check its influence, profiles from group 1 were processed under three alternative assumptions on start-up transient errors:
(i) no start-up transient error,
(ii) constant transient correction of 4.01 m (according to Hallock and Teague 1992), and
(iii) XBTs individual transient corrections (the individual values are shown in Fig. 11).
Then, we proceeded with the pure temperature error detection and removal [as described by Eqs. (1), (2.1), and (2.2)], and, finally, the corrected XBTs are compared with their simultaneous CTDs.
The temperature differences in these three cases are shown in the Fig. 12a. H95’s method cannot estimate the fall rate well when the start-up transient error is excluded. In the mixing layer and thermocline region (0–200 m), the maximum temperature differences are as large as 0.6°C, which is 3 times the manufacturer’s tolerance (0.2°C). The assumption that this discrepancy is mainly due to the transient term is reasonable: after the transient correction (pink or blue lines in Fig. 12a), the temperature differences in the thermocline region are strongly reduced. Furthermore, the individual corrections for the transient term perform better than the constant correction proposed in Hallock and Teague (1992). The advantage of using the individual start-up transient correction is more evident in the regions with either very low or high temperature gradient values. After this step, the results of the H95 method with the individual transient correction are compared with the corresponding results obtained by the new method (Fig. 12b). The results are similar, but a small discrepancy still remains, mainly in the region between the surface and 300-m depth.
As shown above, the start-up transient seems to play a very important role in estimating the XBT corrections. A small difference between an individual correction for each value and a constant transient correction valid for all data is considered acceptable. Thus, a constant correction seems to be a more practical and an easier way to estimate the transient term. Consequently, other trials have been introduced in section 4e to test the constant transient correction process.
The results of the same analysis on profiles from group 2 are shown in Fig. 13. There is a significant reduction of the calculated temperature differences between each corrected XBT and corresponding CTD profiles, mainly in the thermocline region (as for the group 1), but the performance in the deeper regions is even more satisfying. Furthermore, the temperature differences from using the H95 method strongly oscillate in deeper waters in both group 2.1 and 2.2, whereas in group 2.2, a slightly increased warm bias below the thermocline appears, independent of the individual transient corrections (red and blue lines in Fig. 13). The bias increases from about 0.00°C at 100-m depth to about 0.02°C near the bottom, even when pure temperature and transient errors are both corrected.
Figures 14 and 15 (for comparison, see Figs. 12 and 13) show the mean standard deviation of the temperature differences with a reduction of the uncertainties of temperature errors at each depth. Compared with the results obtained with H95 without transient correction, the advantages of the new method in the thermocline and the small gradient regions are evident (Fig. 14: 0–200 and 500–750 m; and Fig. 15: 0–700 m), while the improvements by H95 with individual transient corrections appear mainly in the upper-water layers (Fig. 14: 0–200 m). The figures show a similar trend for both groups when this new method is applied: the standard deviation decreases below the basis of the thermocline (200-m depth for group 1 and 100-m depth for both subsets in group 2), from about 0.04°–0.05° to about 0.01°–0.02°C. These smaller differences show that the individual corrections by the new method perform better than H95 mainly in the regions with either very low or very high temperature gradients.
d. XBT corrections using the overall fall-rate coefficients
To correct XBT profiles without simultaneous CTDs, we are forced to use precalculated fall-rate coefficients (A, B and transient). To examine how this may work, we compared elaborated datasets in which only the average values of fall-rate coefficients quoted in Eqs. (3), (4.1), and (4.2) were used. However, we were also constrained to use individually estimated transient values because the number of profiles in this research was not large enough to give statistically significant estimates of the transient value. We also applied the pure temperature corrections in their previously stated order [see Eqs. (1), (2.1), (2.2)].
The depth difference as a function of depth between corrected XBT and CTD profiles in group 1 is shown in Fig. 16, along with uncorrected profiles. The detection method adopted in this paper is the same as that in H95 (see H95, step 4). Before the corrections, mean depth differences variable from 0 to 25 m have been found within a depth range of 650 m, beyond the accuracy bar stated by the manufacturer (dotted black lines). The mean depth differences are about 4% (6.1% as a maximum value), which is well beyond the 2% nominal accuracy, and the maximum depth difference corresponds to about 40 m. This implies that the manufacturer’s fall-rate equation fails in estimating the depth of the T7 probes. On the other hand, there is almost no systematic bias after corrections, and most differences are within the stipulated bar in Fig. 16b, where the depth differences are dotted in blue. Three poor-quality profiles then discarded are also shown (light green, light blue, and pink dots in Fig. 16b). After these procedures, the maximum depth error becomes about 7–8 m at 650 m (about 1.1%).
Furthermore, the profiles of the mean temperature difference and the standard deviation after the application of the average (A, B) coefficients, pure temperature, and individual transient correction are shown in Figs. 17 and 18 (blue lines), and compared with original profiles without any corrections (red lines). There is a significant improvement: the mean temperature difference reduces to less than 0.1°C for both the groups. In detail, the disagreement in group 1 is larger where the larger temperature gradients occur (0–200 and 500–700 m), but decreases sharply otherwise, with a maximum difference of 0.03°C between 200 and 500 m. However, in group 2, the maximum temperature difference in the upper ocean (0–100 m) is about 0.1°C, with a steep decrease to less than 0.02°C below that depth. Additionally, the mean standard deviations are largely reduced for both groups. The main improvement appears in the mixed layer and thermocline region (from the surface down to 200 m, from 400 to 700 m for group 1, and down to 200 m for both subsets of group 2), and near the bottom.
e. XBT corrections using the mean value of the transient
The observed depth discrepancy of the isothermal depth between XBT and CTD profiles, usually ascribed to the transient effect, differs from probe to probe and from cruise to cruise; nevertheless, it is more convenient to use a constant-transient-correction term in the fall-rate equation when historical XBT profiles are corrected. Thus, in this section, the correction of a mean value of the transient is introduced and checked.
We applied the fall-rate equations with average (A, B and transient) coefficients [see Eqs. (3), (4.1), (4.2)] to the XBT profiles, and then the pure temperature corrections [see Eqs. (1), (2.1), (2.2)]. The corresponding depth–mean temperature differences between corrected XBT profiles and simultaneous CTD profiles and their standard deviations are presented for the two groups, respectively, in Fig. 17 and Fig. 18 (deep green lines). The use of the average transient can still improve the data as well as the individual corrections of the transient, though a little larger temperature differences and standard deviations occur mainly near the surface. This suggests that it is necessary in practice to apply a constant transient term to the fall-rate equation so as to obtain more reliable XBT profiles, but its value needs to be carefully estimated for different types of probe, water properties, and so on.
5. Summary and discussion
This paper proposes a method for calculating the coefficients of XBT fall-rate equations including the estimate of the start-up transient error: z(t) = At − Bt2 − transient. It uses properties over specific time windows of the integral temperature profile in each XBT trail profile rather than the differentials, as in H95; however, this procedure alone does not yield a correction for a pure temperature error that varies slightly with depth. A pure temperature correction can be then be applied when the coefficients (A, B and transient) are correctly calculated.
To check the robustness of the new method theoretical tests with simulated data and real XBT–CTD datasets were carried out, and results from two methods (H95 and new technique) were compared. According to the simulated experiments, the new method is more automatic and accurate both for the mean fall rate and for the scattering of coefficients A and B in the A–B plane when different types of error sources are taken in account.
Then, as a practical test, two groups of real ocean data are analyzed with the new method, and the values of the fall-rate coefficients (A, B, and transient) and the pure temperature error are obtained. In particular, we emphasize that the transient term is in substantial agreement with the results from a field test in a very shallow region aimed specifically at checking the XBT motion in the near-surface layer (Gouretski and Reseghetti 2010). There are several transient, ill-described, and even unknown factors influencing the entrance and the motion near the surface before the probe reaches its terminal speed. Indeed, H95 and the manufacturer’s fall-rate equations overestimate the probe speed and its depth in the surface layer, as shown by the results obtained using the new method in group 2.
This new method shows smaller temperature differences and standard deviations when compared with results from H95 even after the application of the individual transient correction. In the test using the transient correction as well, the new method shows a similar mean temperature difference profile in the water where temperature values changes continuously and even rapidly (e.g., group 1), but it has significantly better results when the temperature profiles have a null or small temperature gradient (e.g., group 2). This could be attributed to the general adequacy of the new method in analyzing highly homogeneous temperature profiles.
Furthermore, the validity of the mean fall-rate (A, B) as precalculated coefficients is checked and strengthened. The mean temperature difference and its standard deviation are respectively reduced to about 0.1° and 0.2°C for both groups, within the manufacturer’s tolerances, whereas the maximum difference in depth is at a level of 1.1% of the depth (group 1). This implies that the mean fall-rate equations [Eqs. (3), (4.1), (4.2)] can be applied to the XBT profiles near the locations of the experiments that we adopted in this paper (e.g., near Barbados and in the western Mediterranean). The transient term calculated here (about 1.99 m for group 2.1) is in good agreement with the results quoted in Reseghetti et al. (2007), after the conversion of that start-up transient (according to ETC = 0.3 s), in a depth value of about 1.8–2.0 m. A larger difference occurs with respect to the term quoted in Hallock and Teague (1992), where a constant value of 4.01 m is calculated to be compared with the 5.68-m correction obtained here. In summary, a better performance is observed mainly in the regions with an extreme temperature gradient (i.e., values near 0 or larger).
Additionally, the validity of the mean value of start-up transient as precalculated coefficients is also checked and strengthened. In fact, the application of the mean transient values in both groups of the profiles can significantly reduce the discrepancy between XBT and collocated and contemporaneous CTD profiles as well as the individual corrections, though it may lead to a little larger temperature differences and standard derivations, especially near the surface.
In all, these results show that the new method can lead to a possible way out of the problem of the XBT bias correction.
However, the following several questions are still unsolved and need to be further explored:
(i) According to our calculations, the function f in section 2 is continuous and stable, but within the bounded domain, more than one extreme value in some trail profiles has been found. We are striving to find a unique minimum value within the bounds of the variables. Many factors could contribute, such as the temperature features (as a function of depth), and random errors, spikes, other unexpected errors. It is usually assumed that this problem can be overcome by computing mean values based on a large number of comparisons.
(ii) In the thermocline regions, temperature values change rapidly with depth, but the new method seems to be able to detect small depth differences. This means that the results mainly depend on the comparatively large gradient regions, which can be regarded as decisive regions. Unfortunately, if the XBT measurements are bad in these regions, the results will contain this unpredictable uncertainty.
(iii) The transient term, which is represented in this paper as a constant term in the fall-rate equations [Eqs. (3), (4.1), (4.2)], should be thought of as a term somehow representing physical phenomena acting during the first seconds of the probe motion. The effect is that probes deviate from the motion predicted by the manufacturer’s equation and only subsequently do they adjust to a stable path below a certain depth that changes from probe to probe. Another possibility is that each probe falls in a specific and variable way, so that the transient term must differ from probe to probe, as a consequence its motion cannot be described by an equation with constant or only temperature-dependent fall-rate coefficients, but it would also include random factors. This could be linked to the mass loss ratio resulting from the wire dereeling, the angular momentum, and the spin rate. In addition, strong currents in seawater also have to be taken in account.
(iv) As previously indicated, viscosity is strongly suspected to have a strong influence on the probe motion, but no specific experimental tests checking its effects are available. Some useful information could be extracted from the XBT versus CTD comparison in sea regions having highly homogeneous water. The Mediterranean and the Arctic and Antarctic Oceans can offer the opportunity to compare the XBT probe motion in homogeneous waters at different temperature. Careful tests should be planned in order to accumulate statistical samples of probe data in order to extrapolate information allowing the modification of the structure of the presently accepted fall-rate equation, if necessary. Also, tests with undulating CTD (as a means of checking the effect of the speed ship on measurements) and launches from platforms with different heights should be useful.
For further research, because the correction of the historical XBT data without collocated CTD is an essential problem, the extension of our approach to all available profiles from the global ocean is suggested, in order to calculate a set of values for the (A, B and transient) coefficients from different probes, ocean regions, seasons, periods, cruises, and also pure temperature corrections. Additionally, the method may be also a proper way to further test the different results in different comparison with different recording systems, weather, and sea conditions.
Acknowledgments
The authors first thanks Shoichi Kizu (Tohoku University, Sendai, Japan) for his kind and useful comments. The authors also acknowledge Mireno Borghini (CNR-ISMAR, La Spezia, Italy) with the masters and crew of R/V Urania for their collaboration in recording XBT and CTD profiles in Mediterranean Sea, and Ruth Loewenstein for her help in the paper preparation. This research is supported by the Knowledge Innovation Program of Chinese Academy of Sciences (Grant KZCX1-YW-12-03), National Basic Research Program of China (Grant 2006CB403600), and China COPES project (Grant GYHY-200706005), and by the European SeaDataNet project (Grant RII3-026212) for one of the author (F.R.).
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Sketches of the principle of the new method.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
All of the originally vertical temperature profiles collected to simulate the XBT–CTD profiles.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
The distribution of the fall-rate coefficients in the A–B plane (dots); (left) results of H95 and (right) the new method. The simulated data are (a),(b) XBT profiles with fall-rate error; (c),(d) XBT–CTDs with fall-rate error and XBT pure temperature error; (e),(f) XBT–CTDs with fall-rate error and XBT CTD random errors; and (g),(h) XBT–CTDs with all of the error sources.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Depth differences calculated by the H95 method: all of the difference profiles without any processing (circle), and the profiles after eliminating the noncoherent points or profiles by visual inspections (dots).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
The geographical positions of (left) the T7 probes (group1) and (right) DB probes (group2). Different marks represent different datasets.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Typical set of XBT profiles (solid curves) and simultaneous CTD profiles (dashed curve) of temperature: (a) one CTD profile with four collocated T7 profiles from group 1, and (b) one CTD profile with two collocated DB profiles from group 2. The plots have different scales. The different characteristics of seawater column in those regions are well evident.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Illustration of the typical errors in XBT profiles, including the start-up transient and pure temperature errors, where the typical profiles in Fig. 6 are zoomed. The plots have different scales. Group 1: typical profiles are (a) near the surface and (b) from 480 to 570 m, and group 2: typical profiles are (c) near surface and (d) and from 300 to 600 m. CTD profiles (dashed curves) and collocated XBT profiles (solid lines) are shown.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Mean temperature differences for the two groups: (a) group 1, (b) group 2.1, and (c) group 2.2. The data processing are the manufacturer’s equations without any corrections (red), the individual fall-rate equations by the new method and the individual start-up transient corrections (blue), and the temperature correction that is applied based on the blue lines (deep green).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
The linear regression of the pure temperature errors, along with the corresponding norm plot of residuals, for (a) group 1, (b) group 2.1, and (c) group 2.2. The plots have different scales.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
The distribution of the individual fall-rate coefficients of the two groups (dot) and their mean values (cycle) for (a) group 1 and (b) group 2.1 (blue) and group 2.2 (pink). The plots have different scales.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
The distribution of the individual depth of start-up transient of the two groups (dot): group 1 (blue), group 2.1 (red), and group 2.2 (pink); the mean value of each group is shown (dashed line).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Mean temperature differences for T7 in group 1. The four sets of data corrections are the individual fall-rate coefficients using the H95 method, along with the corresponding pure temperature correction (red line), the individual fall-rate coefficients using the H95 method, along with the corresponding temperature correction’s individual start-up transients (blue line); the individual fall-rate coefficients by H95, along with the corresponding temperature corrections using the H95 method, and Hallock’s transient correction (4.01 m; pink line); and the individual fall-rate coefficients using the new method, along with the corresponding temperature correction’s individual transient corrections (green line). Comparison of (a) the first three sets of correction strategies and (b) the second and fourth strategies. The plots have different scales.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Mean temperature differences for DB in group 2. The used data corrections are the individual fall-rate coefficients using the H95 method, and the corresponding temperature correction (red line); the individual fall-rate coefficients using the H95 method, the corresponding temperature correction, and individual transients (blue line); the individual fall-rate coefficients using the new method, corresponding temperature correction’s individual transients (deep green line) for (a),(b) group 2.1 and (c),(d) group 2.2 from (a),(c) the upper ocean from 0 to 200 m and (b),(d) from 100 to 900 m. The plots have different scales.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Depth mean standard deviation of the temperature differences for T7 in group 1. Three types of corrections as stated in Fig. 13 are applied to the XBT profiles respectively (the colors are the same to those in Fig. 13): (a) the upper ocean from 0 to 300 m, and (b) from 300 to 750 m. The plots have different scales.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Depth mean standard deviation of the temperature differences for DB in group 2. Three types of corrections as stated in Fig. 13 are applied to the XBT profiles, respectively [the colors and (a)–(d) are defined as in Fig. 13]. The plots have different scales.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
The scattering of the depth error (blue dots) as a function of depth, and the mean value in each depth (red stars), with the nominal accuracy bar (dashed lines) for T7 in group 1.The used data are (a) original XBT profiles without any corrections, (b) XBT profiles with the corrections of Eq. (3) and Eq. (1) and individual transient correction. Light green, light blue, and pink dots are the result of three profiles that have not taken account of their poor results.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Mean temperature differences (solid lines) with their depth mean standard deviation (dashed lines) for T7 in group 1. The used data are original XBT profiles without any corrections (red); XBTs with corrections of Eq. (3), Eq. (1), and individual transient corrections (blue); and XBTs with corrections of Eq. (3), Eq. (1), and the mean transient corrections (deep green).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Mean temperature differences (solid lines) with their depth mean standard deviation (dashed lines) for DB in group 2. The data used are original XBT profiles without any corrections (red); XBTs with corrections of Eq. (4), Eq. (2), and individual transient corrections (blue); and XBTs with corrections of Eq. (4), Eq. (2), and the mean transient corrections (deep green) for (a),(b) group 2.1 and (c),(d) for group 2.2. (a),(c) The profiles in the upper ocean from 0 to 150 m, and (b),(d) from 100 to 900 m are stated. The plots have different scales.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO759.1
Different values for the coefficients of the fall-rate equation (T7 and DB).
