A New Method to Estimate the Systematical Biases of Expendable Bathythermograph

244 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

LIJING CHENG AND JIANG ZHU Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

FRANCO RESEGHETTI Italian National Agency for New Technologies, Energy and Sustainable Economic Development, Lerici, Italy

QINGPING LIU China University of Mining and Technology, Beijing, China

(Manuscript received 8 December 2009, in ﬁnal form 24 July 2010)

ABSTRACT

A new technique to estimate three major biases of XBT probes (improper fall rate, start-up transient, and pure temperature error) has been developed. Different from the well-known and standard ‘‘temperature error free’’ differential method, the new method analyses temperature profiles instead of vertical gradient temperature profiles. Consequently, it seems to be more noise resistant because it uses the integral property over the entire vertical profile instead of gradients. Its validity and robustness have been checked in two ways. In the first case, the new integral technique and the standard differential method have been applied to a set of simulated XBT profiles having a known fall-rate equation to which various combinations of pure temperature errors, random errors, and spikes have been added for the sake of this simulation. Results indicated that the single pure temperature error has little impact on the fall-rate coefficients for both methods, whereas with the added random error and spikes the simulation leads to better results with the new integral technique than with the standard differential method. In the second case, two sets of profiles from actual XBT versus CTD comparisons, collected near Barbados in 1990 and in the western Mediterranean (2003–04 and 2008–09), have been used. The individual fall-rate coefficients and start-up transient for each XBT profile, along with the overall pure temperature correction, have been calculated for the XBT profiles. To standardize procedures and to improve the terms of comparison, the individual start-up transient estimated by the integral method was also assigned and included in calculations with the differential method. The new integral method significantly reduces both the temperature difference between XBT and CTD profiles and the standard deviation. Finally, the validity of the mean fall-rate coefficients and the mean start-up transient, respectively, for DB and T7 probes as precalculated equations was verified. In this case, the temperature difference is reduced to less than 0.18C for both datasets, and it randomly distributes around the null value. In addition, the standard deviation on depth values is largely reduced, and the maximum depth error computed with the datasets near Barbados is within 1.1% of its real value. Results also indicate that the integral method has a good performance mainly when applied to profiles in regions with either a very large temperature gradient, at the thermocline or a very small one, toward the bottom.

1. Introduction of its low price and simple operation, XBTs have become an important part of ocean observation systems since the Since the 1960s expendable bathythermograph (XBT) 1970s. probes, originally invented for military applications, The XBT probe has a slim body with a sensor (a therm- have been widely used for collecting upper-ocean tem- istor) in the nose and twin wires dereeling from both the perature proﬁles mainly by ships of opportunity. Because probe tail and a canister on board, and it is usually deployed from moving ships. As the probe touches the seawater and Corresponding author address: Jiang Zhu, Institute of Atmospheric falls by a slightly decelerated motion, the water tempera- Physics, Chinese Academy of Sciences, Beijing 100029, China. ture is continuously sensed by the thermistor at a rate E-mail: [email protected] ranging from 10 to 20 Hz, which depends on the recording

DOI: 10.1175/2010JTECHO759.1

Ó 2011 American Meteorological Society Unauthenticated | Downloaded 09/25/21 03:47 PM UTC FEBRUARY 2011 C H E N G E T A L . 245 system used. The acquisition system stops recording data efforts were focused on the fall-rate equation problem. according to two criteria, either based on a preselected Various techniques for computing the best fall-rate equa- depth or until the probe completely dereels the wire from tion for a specific dataset were developed until the early one of the two spools. Then, the wire breaks off and the 1990s, when, in collaboration with manufacturers, a task probe is discarded. Different XBT models are available; team sponsored by the Intergovernmental Oceanographic the most used versions have a nominal terminal depth of Commission (IOC) coordinated several XBT versus CTD 460 (T4/T6) and 760 m (T7/DB), but they can usually re- comparisons in different oceanic regions. As a final result, cord data down to about 500 and 850 m, respectively. Be- a comprehensive report and a paper mainly dedicated to cause an XBT carries no pressure sensor, XBT depth is the problem of calculating the correct depth were released estimated from a depth–time mapping originally provided (Hanawa et al. 1994, 1995, hereafter H95). Only the by the manufacturer (Lockheed Martin Sippican, hereafter structure of the manufacturer’s fall-rate equation was con- Sippican) based on oversimplified assumptions about the firmed, but new constant-temperature independent fall- probe motion. The elapsed time, beginning when the probe rate coefficients were calculated with a ‘‘temperature error hits the seawater and the recording starts and ending at the free’’ technique for the most used XBT models manufac- moment when the first wire breaks, is the actual recorded tured by Sippican and TSK (the Japanese manufacturer). parameter. The manufacturer’s fall-rate equation is z(t) 5 The use of these coefficients was strongly recommended At 2 Bt 2,wherez(t) is depth at the elapsed time t and the by the IOC and accepted by the United Nations Educa- coefficients are both positive and temperature independent. tional, Scientific and Cultural Organization (UNESCO). Since the 1970s, when XBT measurements started to As a consequence, it was recommended that the old probe compared with simultaneous temperature values re- files in the databases be converted to the new depth values. corded by other and usually more accurate and expensive Despite this improvement, discrepancies have still been instruments, such as salinity–temperature–depth (STD) or found both in the H95 method and the H95 equation. conductivity–temperature–depth (CTD), some discrepan- Some reports showed that the H95 equation underes- cies have become increasingly evident. For example, in a timated the actual fall-rate coefficients of the XBT report describing several intercomparisons involving a total probes (Boedecker 2001; Fang 2002). On the other hand, of about 2000 XBT profiles, Anderson (1980) pointed out Thadathil et al. (2002) found that the old manufacturer’s several problems in XBT measurements yielding a general fall-rate equation worked well in cold Antarctic wa- positive bias in measurements with XBT probes. Unfortu- ters, possibly because of viscosity changes, and they nately, that paper, with its important but widely ignored list suggested that the fall-rate coefficients should depend on of troubles and errors in the XBT system, remained un- latitude (they admitted that the probe motion depended known until recent years. on water temperature). This correlation was confirmed for In the 1980s and early 1990s some ‘‘cookbooks’’ and T5 probes manufactured by TSK (Kizu et al. 2005a), and for reports detailing the possible malfunctioning were pre- expendable conductivity–temperature–depth (XCTD) pared for the oceanographic community (see, e.g., Bailey probes (Kizu et al. 2008). Subsequently, Reseghetti et al. et al. 1994). Several researchers reported the inadequacy (2007) proposed a different method to deal with the XBT of the manufacturer’s fall-rate equation in the descrip- measurements in regions of the Mediterranean with high tion of the probe motion, both in the near-surface and temperature homogeneity because in those conditions the the deeper layers, which possibly correlates with the sea- H95 technique would not work. On the other hand, the ad water viscosity (e.g., Seaver and Kuleshov 1982; Heinmiller hoc method that was useful in the Mediterranean requires et al. 1983; Green 1984; Hanawa and Yoritaka 1987; Singer that some reference points in a profile must be visually 1990; Hanawa and Yoshikawa 1991; Hallock and Teague determined, and it is slightly complicated to extend this 1992; Kezele and Friesen 1993). International meetings procedure to all of the intercomparisons. These new co- involving the manufacturers were also dedicated to an- efficients also take into account the fall-rate differences alyzing problems in XBT measurements and eliminating between shallower (slower) and deeper (faster) probes. the biases (e.g., IOC 1992). These studies indicated that Table 1 shows a comparison between fall-rate coefficients XBT measurements contain systematic biases caused by suggested by manufacturers and reported publications. diverse factors, with significant probe-to-probe, cruise- In recent years, XBT measurements have attracted to-cruise, and time-to-time variability. In summary, the a renewed interest. Kizu and Hanawa (2002a,b) in- main part of the errors in the XBT measurements can be vestigated several types of recording systems looking for ascribed to inadequate fall-rate coefficients, pure tem- the start-up transient, which is the source of the main perature error, and start-up transient with an additional error in the upper layer. Their results suggested that the but hard-to-quantify component resulting from spikes and depth of the transient differed for different types of re- other random factors. Nevertheless, the most important corders. Reseghetti et al. (2007) suggested a possible

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TABLE 1. Different values for the coefﬁcients of the fall-rate equation (T7 and DB).

Author Date Probe type Location A (m s21) B (1025 ms22) Max depth error (%) Sippican (manufacturer) 1965 T4/T6/T7/DB 6.472 216 2 H95 1995 T4/T6/T7 Global 6.691 225 H95 1995 T7/DB Global 6.701 238 Best fit T7/DB Hallock and Teague 1992 T7 Barbados 6.798 238 (1992) Reseghetti et al. (2007) 2007 DB Mediterranean 6.720 235 1.7 treatment of the transient by introducing an empirical intercomparisons from the Atlantic Ocean near Barbados time constant (ETC) value (implying a rescaling of the and the western Mediterranean are analyzed, with both profile, with improvements in the upper and the ther- the methods and the results compared. The impact of the mocline regions), and they also calculated a method of start-up transient is also tested. Moreover, the mean fall- fine tuning used to eliminate a probably intrinsic pure rate coefficients for the correction of T7 and DB without temperature error. collocated CTD are calculated. Section 5 concludes with The existence of a globally time-dependent and systemic the discussion of the feasibility and limitations of the new warm bias in XBT profiles came to light when various integral method. statistical methods were used to compare global datasets of XBT and CTD–Bottle–Argo (Bottle is a special device 2. Method designed for taking deep water samples and measuring H95 compared the temperature gradient values ex- temperature at depth.) in the last 30 yr. In short, tracted from an XBT profile with the corresponding ones from an almost simultaneous and collocated CTD profile. d Gouretski and Koltermann (2007) mainly concen- trated on the overall biases in XBT measurements; Because of its simplicity, the H95 method has been widely used, but it has some disadvantages. First, the inclusion of d Wijffels et al. (2008) attributed all of the biases to errors in the fall-rate equation; random errors and spikes in both XBT and CTD measurements would enlarge errors of temperature profiles and d Levitus et al. (2009) focused on the pure temperature offset bias and instrumentation problems; lead to poor gradient profiles. Moreover, the pure temperature error in temperature profiles might disappear be- d Ishii and Kimoto (2009) considered fall-rate error and estimated corrections through comparisons with nearby cause of the use of temperature gradients. Then, following CTD and ocean station data; and the original text in the H95: ‘‘However, the new method does also occasionally fail to detect depth differences when d Gouretski and Reseghetti (2010) started from the manufacturer’s equation and considered both a time- the vertical temperature gradient is constant in a section of dependent thermal bias and a stretching factor that the profile larger than the search window, or when the was dependent on depth, time, and temperature. XBT temperature profile has features not matched by the CTD profile’’ (Hanawa et al. 1995, p. 1431). That feature The H95 method has been widely used to correct the had been accurately shown by Kizu et al. (2005b) when XBT bias, but its equation is not so accurate when the computing the fall-rate equation of T5 probes using several temperature vertical gradient is weak. Moreover, it is still groups of XBT and CTD data. In addition, because visual inadequate for modeling the start-up transient error and, inspection and discretional selection is introduced, H95 more importantly, it cannot detect pure temperature er- must be considered a semiautomatic method. Finally, the rors, which are reasonably constant between consecutive start-up transient or any other depth-related errors are not depth measurements that are 0.7 m apart. In regards to taken into account. the H95 method weaknesses, in section two, after a short Physically speaking, a raw XBT profile contains resis- discussion concerning the H95 method, this paper de- tance measurements as a function of elapsed time. Then, scribes in detail a new technique using integrals to model resistances are converted into temperature values by ap- temperature profiles that allows for a transient term and plying the Steinhart–Hart equation with experimentally de- considers a pure temperature error. In section three, both termined coefficients (e.g., Georgi et al. 1980). In the final the H95 and the new method are theoretically compared step, a fall-rate equation specifies a mapping of the elapsed using statistical methods in which four types of errors had time to the depths, and the output of a XBT measurement been randomly added to groups of data, as explained be- is a depth–temperature profile. On the other hand, an ac- low, where all of these errors are quantified and simulated. companying CTD profile includes temperature and pres- In section four, two groups of actual XBT versus CTD sure data that are subsequently converted into depth values.

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If the fall-rate equation is affected by errors, an improper the equation above was interpreted as an offset to time-to-depth mapping can lead to dominating discrep- give a better interpolation, and it was not calculated at ancies between XBT and CTD profiles. In this context, our thesametimeastheremainingfall-ratecoefficients. goal is to estimate an optimal mapping of the elapsed times This assumption could imply that the coefficients (A, B) to the depths for XBT profiles so that the discrepancies are assumed to be constant (and temperature inde- between the XBT and CTD measurements are minimized. pendent) over the whole water column. This is only We assume that the mapping takes the form of a z(t) 5 partially true. The term transient could mask small vari- At 2 Bt2 2 transient, where t is the elapsed time and ations of (A, B) values during the initial probe motion, transient is a correction describing the up-to-now un- and consequently the inadequacy of the (A, B)terms predictable phenomena occurring mainly in the near- to describe the true probe motion with the required surface layer, at the start up, with a deviation from the approximation. manufacturer’s equation. A similar structure of the fall- The best estimator minimizes the vertical mean de- rate equation has been proposed in other papers (e.g., viation of the temperature differences between the XBT Heinmiller et al. 1983; Singer 1990), but the last term in and CTD profiles in the form of

0 1 ð 2 tm B T (t) T [Z(t)] C B XBT CTD , C 0 ð ð B t t C B mm C min[f (A, B, transient)] 5 minB dt dtC, B TXBT(t) TCTD[Z(t)] dt C B 0 ð 0 C @ tm A h dt i 0 where f(A, B, transient) is a 3D function. Then, a bounded a drawback, analysis on a large number of XBT profiles optimization problem has to be solved, where the vari- would require more efficient methods. ables A, B and the transient are all bounded, and tm is the The brute-force algorithm is described below. total acquisition time [the time at the terminal depth (see a. Step 1: Filtering Reseghetti et al. 2007)]. The definition of f enables the estimation to be free of a constant, time-independent pure Similar to the H95 method, two types of filters are temperature error, which could exist in the XBT profile. applied to the raw data of both XBT and CTD in se- The optimal values of the scale function f can be quence: first a nonlinear median filter is used, and then evaluated by assuming the partial derivatives to be 0 and a low-pass linear cosine Hanning filter without threshold solving the equations ›f/›A 5 0, ›f/›B 5 0, and ›f/ logic. ›transient 5 0. Unfortunately, the equation is too com- b. Step 2: Calculation of values of f plex to compute the exact partial derivatives analyti- cally. There are many approximation algorithms that At first, the function f is transformed to the form as can be used to solve the optimization problem, such as follows, by identifying some reference time windows the genetic algorithm, simulated annealing, or artificial (the selected dimension of the window is 2 s for 3 , t , neural networks. In our paper, we simply adopt the 35 s, and 4 s for 35 , t , tm 2 2 s). The initial value (3 s) ‘‘brute force’’ method of searching values for possible should be greater than the time the probe needs to reach combinations of (A, B and transient), and then finding a stable motion, without either bubbles or a helicoidal the optimal one. Although this method is not time effi- path, as quoted in Seaver and Kuleshov (1982), and di- cient, detailed behaviors of the function, such as the rectly recorded in a movie during tests in shallow waters uniqueness of the optimal values, can be obtained. As (Gouretski and Reseghetti 2010):

0 1 T (t) T [Z(t)] 2 XBTð CTD B t 1Wlength , C B W ð i ð C B ti1WLength T (t) T [Z(t)] dt ti1Wlength C B XBT CTD C min[f (A, B, transient)] 5 min t5t dt , Bå i ð C Bi51 t5t tm t5t C @ i h dt i i A o

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FIG. 1. Sketches of the principle of the new method. where Wlength is the length of the window and W is the number of the time window in each profile. In each time window, the systematic temperature error can be regarded as a constant offset. For each pair of profiles from a XBT versus CTD comparison, the ranges and the steps of A, B and tran- FIG. 2. All of the originally vertical temperature profiles collected sient are the following: to simulate the XBT–CTD profiles.

21 21 21 d 5.800 m s , A , 7.200 m s ; step 0.002 m s ; 22 22 22 technique. In the H95 method, the start-up transient is d 0.000 m s , B , 0.005 m s ; step 0.000 02 m s ; not considered; therefore, in this section we assume that and XBT measurements do not contain the start-up error, and d 25.0 m , transient , 15.0 m; step 0.3 m. we thus focus only on the four other main sources of errors in XBT data: wrong fall-rate equation, pure tem- c. Step 3: Determination of new fall-rate equation perature error, spikes, and random errors. For each profile pair, the optimal combination of One-hundred-forty profiles of the ENSEMBLES data- values of (A, B and transient) can be selected according set (so-called EN3 data) CTD data (quality-controlled in to the minimal value of f. If there is a set of pairs, the situ ocean temperature and salinity profiles) from the mean values of optimal (A, B and transient) for each oceanographic dataset World Ocean Database 2005 pair is adopted for the new fall-rate equation. (WOD05; Boyer et al. 2006) of January 1980 have been Figure1showsthematchingprincipleofthenew extracted and regarded as true ocean profiles; these data method. We mainly focus on a single time window. In each were then labeled from 1 to 140. Vertical temperature selected time window, the deviation of the temperature profiles from different regions with various typical features difference is zero when the XBT vertical temperature line of the equatorial seawater are shown in Fig. 2. To simulate is parallel to the corresponding CTD profile as in Fig. 1. the CTD observations, normally distributed 0 mean and The optimization problem specifies the XBT profile ac- 0.0018C standard deviation errors were added to these cording to the coefficients A, B and transient to that par- true temperature profiles, with 1-m-depth steps. The allel position (the dotted line in Fig. 1). In this way, the XBT observations are generated as follows: systematic temperature bias can be naturally ignored. In (i) Adding the fall-rate error: It is assumed that the addition, the method is automatic given that visual in- fall-rate equation z (t) 5 6.691t 2 0.002 25t2 spection of the data has proved to be redundant. true (proposed by H95) gives the true fall-rate coefficients of all these 140 profiles. To add the fall-rate 3. Experiments with simulated data error in simulated XBT observations, we assume the original manufacturer’s fall-rate coefficients to be a. Design 2 wrong [zXBT(t) 5 6.472t 2 0.002 16t ]. Using the The purpose of the experiments using simulated XBT– depth differences given by the two sets of fall-rate CTD profiles is to test the performance of the proposed equations, we can shift the true profiles vertically to

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obtain fall-rate effects on simulated XBT observa- On the other hand, Figs. 3c,d show that there are no tions. Usually, the sampling interval of XBT mea- significant differences between the results before and surements is 0.1 s. after the addition of the pure temperature error. This (ii) Adding the pure temperature error: Pure temper- means that the pure temperature error exerts very little ature error is defined as a linear function of the influence on the calculation of the coefficients by H95 elapsed time, which refers to an approximate tem- (as expected because of the use of gradient profiles) and perature correction of Reseghetti et al. (2007) in the also by the new method.

form of Tbias 520.0298C 2 0.000 016t, which varies When the random errors are added to the XBT–CTD slowly with depth. measurements, with the new method, the distribution of (iii) Adding spikes: Spikes caused by small-scale geo- the obtained fall-rate coefficients shows a larger vari- physical and instrumental noise are generated as ance. However, the errors are still less than 0.01 m s21 random temperature variations in the range of 0.18– for A and 0.000 25 m s22 for B, and are better than the 0.28C. Spikes were added randomly to 2% of the total results of H95 (Figs. 3e,f). measurements of the simulated XBT profiles. When XBT profiles containing all of the possible errors (iv) Adding random error: The random error of XBT is are used as raw data, the estimated values using the new regarded as having two components. For the first method disperses slightly in the A–B plane, but the results part, we added a normally distributed random are better than those using H95 (Figs. 3g,h). Indeed, in the number with 0 mean and 0.018C standard deviation four trial tests described above, the mean values improve to each XBT temperature measurement in the the individual estimations in both methods, but the new whole profile. To take into account the possible method yields better mean values than H95 does. bias in some incongruent segments, we added bias The H95 method also includes visual inspections to with values 0.008, 0.018, or 0.028C to all profile remove outliers, so we cannot be sure whether the depth segments. These values were randomly assigned, difference profiles obtained by H95 are correct or whether according to a probability distribution of 80%, they are due to the criteria of selection used by the oper- 14%, and 6%, respectively. Each segment has ators. Thus, an additional experiment has been conducted a random time span less than 2 s. 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 b. Results visual inspections. Figure 4 shows the depth differences We have applied both methods separately to calculate (as function of depth), calculated by the H95 method with the values of the A and B coefficients for each of the and without such a step. Without visual inspections and following groups: the removal of noncoherent points or entire XBT profiles, relatively large errors exist from the basis of the thermo- (i) first group: only fall-rate equation errors, cline to the bottom, where the vertical temperature gra- (ii) second group, also pure temperature errors, dient is either zero or very small. In such conditions, the (iii) third group, fall-rate equation and random errors, random errors and spikes can produce false gradients and rather than the meaningful ones resulting from fall-rate (iv) fourth group, all four errors. equation error. Even after the eliminations of the non- Figure 3 shows the distributions of these coefficients in coherent depth differences by visual inspections (see step the A–B plane, indicating that the new method performs 4 of H95 in detail), the uncertainties near the bottom still better for two reasons. First, in all of the groups of ex- remain. periments the mean values of the obtained A, B coefficients by the new method are closer to the original 4. Actual XBT–CTD comparison experiments values than those from the H95 method. Moreover, the H95 method has a larger scattering (Fig. 3), which means The above detailed simulated experiments show the that the results of the H95 method contain larger uncer- overall good performances of the new technique, but those tainties. Finally, the new method estimates the fall-rate procedures are based on simple assumptions, so they ex- equation correctly (see Figs. 3a,b; when only fall-rate clude unexpected error sources. A definitive test of the new error is considered): the differences with respect to the method must use actual XBT versus CTD comparisons. true coefficients are small, within the range (20.006, a. Datasets 0.006) m s21 for A and (20.000 15, 0.000 15) m s22 for B, respectively. For comparison, results with H95 get a max- A total of 122 XBT profiles from two groups of imum error of 0.05 m s21 for A and 0.0005 m s22 for B. XBT versus CTD comparison experiments, which were

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FIG. 3. 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.

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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. d 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 FIG. 4. Depth differences calculated by the H95 method: all of profiles were recorded using a SeaBird 911 plus device, the difference profiles without any processing (circle), and the which was calibrated before and after each cruise. The profiles after eliminating the noncoherent points or profiles by vi- only instrumental difference is the XBT recording sual inspections (dots). 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 tempera- independently carried out by two institutions in specific ture homogeneity, even with temperature inversions. regions and periods, have been analyzed. The dataset is All of the depths were calculated by the H95 fall-rate composed of the following: coefficients. The maximum difference between corre- d Fifty-one Sippican T7 XBT probes were deployed sponding XBT and CTD profiles was 2 h in time and in May 1990 by Hallock and Teague (1992) about 0.158 both in latitude and longitude, but most profiles 300 nm northeast of Barbados Island, in the Atlantic were recorded within 10 min and about 0.028 in geo- Ocean (Fig. 5a), which is an ideal region for XBT versus graphical position.

FIG. 5. The geographical positions of (left) the T7 probes (group1) and (right) DB probes (group2). Different marks represent different datasets.

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FIG. 6. 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.

Figures 6a,b show two typical sets of comparisons equation overestimates the real depth of 1–3 m at about between simultaneous XBT and CTD profiles from 30-m depth. the two groups, respectively. In group 1(Fig. 6a), tem- Second, in XBT measurements there is evidence of perature profiles decrease almost monotonically with pure temperature errors. Figures 7b,d show that sys- depth, while in group 2 (Fig. 6b), the probes fall through tematic temperature offsets occur especially in the re- a practically isothermal medium. Below 100-m depth and gions with small vertical temperature gradients, where toward the bottom, seawater temperatures are constant the impact of the fall-rate equation error on the tem- within 18C, with very small or null vertical temperature perature offset is reduced to a negligible level. It is also gradients, or even with temperature inversions. The dif- evident that most of the temperature differences are ferent seawater properties between the two groups can within the manufacturer’s tolerance of 0.28C. lead to different fall-rate equation features resulting from Furthermore, as presented in Fig. 6, the XBT profiles viscosity effects. lie above the CTD profiles in group 1 and below CTD To enhance different systematic errors in XBT pro- profiles in group 2. These features indicate that the ac- files, we zoom in the typical profiles in Fig. 6. In Fig. 7, tual fall rate of XBT is underestimated by the manu- XBT profiles clearly show both a vertical depth offset facturer’s equation for T7 but overestimated by the H95 and a temperature offset in comparison with the simul- equation for DB probes. taneous CTDs. After visual inspection, some significantly bad profiles First, because the depth error resulting from the im- were eliminated, for example, XBT profiles with abnormal proper fall-rate equation at the surface (0–50 m) is neg- structures compared with the other profiles in the near ligible, the depth discrepancies of the isothermal depth region, or evidently erroneous and fake features. We also between XBT and CTD profiles at the surface clearly took in account the XBT profiles that had not achieved show a start-up transient error, as in Fig. 7a near 10 m and their terminal depths. After this inspection, all profiles in in Fig. 7c near 30 m. We also note the probe-to-probe group 1 were labeled ‘‘good,’’ while nine profiles were difference of the transient term even when XBT probes eliminated in group 2. Then, both the H95 method and the are launched at the same time under the same conditions. new method were applied to the two groups. The start-up transient error has been attributed to both the pure thermal transient, for example, a finite delay for the b. Individual and overall XBT profile corrections thermistor to adjust to the temperature of the surrounding water, and the dynamics of the XBT probe, such as For each XBT profile, the individual coefficients (A, launching conditions, entry angle, and mechanical effects. B, and transient) are computed using the new method. As shown in Gouretski and Reseghetti (2010), some tests Then, the individual corrections are made according to in shallow water suggest that the manufacturer’s fall-rate the following procedure:

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FIG. 7. 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.

(i) the depth in each XBT profile is calculated using its line) XBT and the CTD profiles is shown in Fig. 8. In- own fall-rate coefficients; dividual corrections significantly reduce the discrep- (ii) a shift on the depth value according to its own ancies of the temperature differences for profiles in both transient value is applied to each profile; and groups. In particular, in group 2, the corrections mainly (iii) the temperature measurements are filtered by the work between 0 and 200 m, where the maximum tem- median and the Hanning filter. perature difference reduces from 0.38 to about 0.058C. Additionally, the reason why the improvements are not Following the application of this procedure, the mean so marked in the region below 300 m in group 2 is temperature difference (a function of depth) between probably due to the low temperature gradient in this either the uncorrected (red line) or the corrected (blue region. However, some small-scale uncertainties in the

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FIG. 8. 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).

regions of relatively large gradients still remain (at The linear regression and the corresponding norm plot about 0–200 and 450–650 m for group 1, 0–100 m for are shown in Fig. 9 for two groups. Both regressions group 2.1, and 0–200 m for group 2.2). conﬁrm that systematic pure temperature offsets have The mean temperature differences peak at about 0.18C an evident linear trend. Additionally, the amplitude of for group 1, at about 0.058C for group 2.1, and at about the oscillation of the residuals in group 1 (less than 20.058C for group 2.2. These temperature offsets can be 0.18C from 200 to 750 m) is much larger than those in considered as pure temperature error. A linear regression group 2 (about 0.018C from 200 to 800 m), while near of the temperature differences (as function of depth) can the surface the oscillation gets much larger than in the be easily introduced as DT 5 TXBT 2 TCTD 5 T2 3 depth 1 deeper water in group 1. This phenomenon suggests T1,whereT1 could be thought as the temperature error at that the systematic pure temperature error does exist surface (intrinsic thermal error) and T2 describes the var- and can be corrected by a linear function. Otherwise, iation with depth, probably including the pressure effect the effect of the temperature gradient, random errors, quoted by Roemmich and Cornuelle (1987). and other unknown biases may induce a random-walk

The coefﬁcients T1 and T2 have been calculated with feature of the temperature differences, leading to difﬁ- the depth parameter ranging from 2 to 750 m for group culties in the estimation of the pure temperature error. 1, from 100 (at the basis of the upper thermocline) to The linear regression processing along with the indi- 800 m for group 2.1, and from 200 to 800 m for group vidual corrections procedure is denoted as ‘‘pure tem- 2.2, because of great uncertainties in the upper ocean. perature detection procedure’’ hereafter. The results [see

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FIG. 9. 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.

Eqs. (1), (2.1), and (2.2) below] can be approximately (2007). Additionally, the significant contradiction of the regarded as the systematic pure temperature error: pure temperature error between the two subsets suggests that different recording instruments could induce group 1 (T7): DT 5 0.000 0275 3 depth significantly different pure temperature errors. 1 0.09578C, (1) After the application of this correction (in Figs. 8a–c, green line), the remaining temperature differences below group 2 subgroup 1 (DB): DT 5 0.000 015 87 the thermocline are mostly within the range from 20.058 to 0.058C for group 1, and from 20.028 to 0.028Cforgroup 3 depth 1 0.03788C, 2. In this last region they seem to have a random or ir- (2.1) regular fluctuation. On the other hand, some significant but small biases (less than 0.18C) still remain both within DT 5 group 2 subgroup 2 (DB): 0.000 017 21 the thermocline regions and at the 450–650-m depth, 3 depth 0.06188C. where the temperature gradients vary irregularly with (2.2) depth. Indeed, this region deserves more detailed studies. In detail, for group 1, there is a small cold bias at the sur- Equation (2.1) is in good agreement with the pure face (about 20.18C), which slightly increases with depth temperature correction for DB in Reseghetti et al. down to the basis of the thermocline (about 0.18C). The (2007) (DT 5 0.000 014 3 depth 1 0.039), when the data results show that the specific corrections, namely, individ- we used are the same as those used by Reseghetti et al. ual (A, B, and transient) correction and pure temperature

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FIG. 10. 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.

correction, are effective and help to rebuild the structure z(t) 5 [(6.678 6 0.096) m s1]t [(0.001 81 of the individual XBT temperature profile very accurately, 2 2 matching, and sometimes even improving, the manu- 6 0.001 56) m s ]t (1.99 6 1.34) m; (4.1) facturer’s tolerance of 2% in depth values and 0.28Cin group 2.2, z(t) 5 6.6405t 0.002 296t2 transient temperature. At this point we proceeded with a visual inspection, z(t) 5 [(6.641 6 0.157) m s1]t [(0.002 30 which is not an essential part of this new method, because we wanted to double check that the depth differ- 6 0.001 73) m s2]t2 (1.12 6 1.36) m. (4.2) ences between the corrected XBT profiles and CTD profiles were within the manufacturer’s tolerance. Only When the coefficients of Eq. (4.1) are compared with one profile from group 2.1 was eliminated, confirming the values calculated by Reseghetti et al. (2007) for DB 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) 5 6.8458t 0.002858t2 transient

z(t) 5 [(6.846 6 0.081) m s1]t [(0.002 86 IG 2 2 F . 11. The distribution of the individual depth of start-up 6 0.000 73) m s ]t (5.68 6 3.39) m; (3) 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 group 2.1, z(t) 5 6.6782t 0.001 810t2 transient (dashed line).

Unauthenticated | Downloaded 09/25/21 03:47 PM UTC FEBRUARY 2011 C H E N G E T A L . 257 fz(t) 5 [(6.720 0.060) m s21]t2 [(0.002 35 6 0.000 10) c. Impact of start-up transient error on H95 ms22]t2 2 (2.00 6 0.70) mg, where the term 2 m rep- resents the ETC correction (equivalent to the transient)g, To validate the significance of the results described the results show good agreement. The relatively high above, we performed XBT analysis with the H95 method, value of the standard deviation in Eqs. (4.1) and (4.2) which does not include an estimation of the start-up could be a consequence of the high temperature homo- transient. To check its influence, profiles from group 1 geneity of Mediterranean seawater, but only the applica- were processed under three alternative assumptions on tion of this method to several other profiles with similar start-up transient errors: characteristics could confirm such an interpretation. (i) no start-up transient error, The manufacturer states that T7 and DB probes have (ii) constant transient correction of 4.01 m (according the same dimensions and the same motion in seawater, to Hallock and Teague 1992), and within probe-to-probe variability and the nominal un- (iii) XBTs individual transient corrections (the in- certainty (2% in depth and 0.28C in temperature). The dividual values are shown in Fig. 11). present analysis seems to contradict this assumption, probably because of the unpredictable impact angle with Then, we proceeded with the pure temperature error the sea surface, variable impact speed, wake influence, detection and removal [as described by Eqs. (1), (2.1), variable seawater characteristics, and industrial stan- and (2.2)], and, finally, the corrected XBTs are com- dard probe variability. For example, the height of the pared with their simultaneous CTDs. launching position determines the probe entry speed The temperature differences in these three cases are and therefore the motion in the upper layer. As a con- shown in the Fig. 12a. H95’s method cannot estimate the sequence, the depth estimated by usual fall-rate equa- fall rate well when the start-up transient error is ex- tion is inaccurate in the near-surface layer, even within cluded. In the mixing layer and thermocline region the nominal depth accuracy (5 m). (0–200 m), the maximum temperature differences are as First we take account of the seawater properties in group large as 0.68C, which is 3 times the manufacturer’s tol- 1, where temperature profiles show an almost monotonic erance (0.28C). The assumption that this discrepancy is decrease with depth; this means that the viscosity increases mainly due to the transient term is reasonable: after the toward the bottom, where the probes should move more transient correction (pink or blue lines in Fig. 12a), the slowly than estimated by the fall-rate equation. On the temperature differences in the thermocline region are other hand, in group 2, the probes fall through a practically strongly reduced. Furthermore, the individual correc- isothermal medium where the variations of seawater tem- tions for the transient term perform better than the con- perature remain within 18C down to the bottom. This im- stant correction proposed in Hallock and Teague (1992). plies that the viscosity should not vary in a significant way. The advantage of using the individual start-up transient The viscosity changes due to different seawater properties correction is more evident in the regions with either very are considered to have an evident influence on the probe low or high temperature gradient values. After this step, motion. Gouretski and Reseghetti (2010, p. 815) state that the results of the H95 method with the individual transient ‘‘According to Green (1984), the kinematic viscosity of sea correction are compared with the corresponding results water increases typically by about 50% between the near- obtained by the new method (Fig. 12b). The results are surface layer and 750 m depth. In case of a fully turbulent similar, but a small discrepancy still remains, mainly in the flow around the probe, the hydrodynamic drag coefficient region between the surface and 300-m depth. would exhibit an increase by less than 0.1% for a 58C As shown above, the start-up transient seems to play temperature change (and the corresponding fall speed de- a very important role in estimating the XBT corrections. crease of about 0.05%).’’ Thus, viscosity changes in our A small difference between an individual correction for new model will lead to significant fall-rate changes de- each value and a constant transient correction valid for pending on the various geographic areas considered. all data is considered acceptable. Thus, a constant cor- Second, recent works by Gouretski and Koltermann rection seems to be a more practical and an easier way to (2007), Wijffels et al. (2008), Levitus et al. (2009), Ishii and estimate the transient term. Consequently, other trials Kimoto (2009), and Gouretski and Reseghetti (2010) have have been introduced in section 4e to test the constant suggested a time dependence of XBT biases. This could be transient correction process. one of the possible sources of the discrepancy between the The results of the same analysis on profiles from group coefficients of the fall-rate Eqs. (3), (4.1), and (4.2), but 2 are shown in Fig. 13. There is a significant reduction tests on more relevant data are needed to establish just of the calculated temperature differences between each how this takes place in order to determine more robust corrected XBT and corresponding CTD profiles, mainly results for the accuracy of XBT measurements. in the thermocline region (as for the group 1), but the

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FIG. 12. 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. performance in the deeper regions is even more satis- d. XBT corrections using the overall fall-rate fying. Furthermore, the temperature differences from coefficients using the H95 method strongly oscillate in deeper waters in both group 2.1 and 2.2, whereas in group 2.2, a slightly To correct XBT profiles without simultaneous CTDs, increased warm bias below the thermocline appears, we are forced to use precalculated fall-rate coefficients independent of the individual transient corrections (red (A, B and transient). To examine how this may work, we and blue lines in Fig. 13). The bias increases from about compared elaborated datasets in which only the average 0.008C at 100-m depth to about 0.028C near the bottom, values of fall-rate coefficients quoted in Eqs. (3), (4.1), even when pure temperature and transient errors are and (4.2) were used. However, we were also constrained both corrected. to use individually estimated transient values because Figures 14 and 15 (for comparison, see Figs. 12 and 13) the number of profiles in this research was not large show the mean standard deviation of the temperature enough to give statistically significant estimates of the differences with a reduction of the uncertainties of tem- transient value. We also applied the pure temperature perature errors at each depth. Compared with the results corrections in their previously stated order [see Eqs. (1), obtained with H95 without transient correction, the ad- (2.1), (2.2)]. vantages of the new method in the thermocline and the The depth difference as a function of depth between small gradient regions are evident (Fig. 14: 0–200 and corrected XBT and CTD profiles in group 1 is shown in 500–750 m; and Fig. 15: 0–700 m), while the improve- Fig. 16, along with uncorrected profiles. The detection ments by H95 with individual transient corrections ap- method adopted in this paper is the same as that in H95 pear mainly in the upper-water layers (Fig. 14: 0–200 m). (see H95, step 4). Before the corrections, mean depth The figures show a similar trend for both groups when differences variable from 0 to 25 m have been found this new method is applied: the standard deviation de- within a depth range of 650 m, beyond the accuracy bar creases below the basis of the thermocline (200-m depth stated by the manufacturer (dotted black lines). The for group 1 and 100-m depth for both subsets in group mean depth differences are about 4% (6.1% as a maxi- 2), from about 0.048–0.058 to about 0.018–0.028C. These mum value), which is well beyond the 2% nominal ac- smaller differences show that the individual corrections curacy, and the maximum depth difference corresponds by the new method perform better than H95 mainly in to about 40 m. This implies that the manufacturer’s fall- the regions with either very low or very high tempera- rate equation fails in estimating the depth of the T7 ture gradients. probes. On the other hand, there is almost no systematic

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FIG. 13. 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. bias after corrections, and most differences are within and individual transient correction are shown in Figs. 17 the stipulated bar in Fig. 16b, where the depth differ- and 18 (blue lines), and compared with original profiles ences are dotted in blue. Three poor-quality profiles without any corrections (red lines). There is a significant then discarded are also shown (light green, light blue, improvement: the mean temperature difference reduces and pink dots in Fig. 16b). After these procedures, the to less than 0.18C for both the groups. In detail, the maximum depth error becomes about 7–8 m at 650 m disagreement in group 1 is larger where the larger (about 1.1%). temperature gradients occur (0–200 and 500–700 m), Furthermore, the profiles of the mean temperature but decreases sharply otherwise, with a maximum dif- difference and the standard deviation after the applica- ference of 0.038C between 200 and 500 m. However, in tion of the average (A, B) coefficients, pure temperature, group 2, the maximum temperature difference in the

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FIG. 14. 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. upper ocean (0–100 m) is about 0.18C, with a steep de- transient term to the fall-rate equation so as to obtain crease to less than 0.028C below that depth. Addition- more reliable XBT profiles, but its value needs to be ally, the mean standard deviations are largely reduced carefully estimated for different types of probe, water for both groups. The main improvement appears in the properties, and so on. mixed layer and thermocline region (from the surface down to 200 m, from 400 to 700 m for group 1, and down 5. Summary and discussion to 200 m for both subsets of group 2), and near the bottom. This paper proposes a method for calculating the coefficients of XBT fall-rate equations including the e. XBT corrections using the mean value of the estimate of the start-up transient error: z(t) 5 At 2 transient Bt2 2 transient. It uses properties over specific time The observed depth discrepancy of the isothermal windows of the integral temperature profile in each depth between XBT and CTD profiles, usually ascribed XBT trail profile rather than the differentials, as in to the transient effect, differs from probe to probe and H95; however, this procedure alone does not yield a cor- from cruise to cruise; nevertheless, it is more convenient rection for a pure temperature error that varies slightly to use a constant-transient-correction term in the fall- with depth. A pure temperature correction can be then rate equation when historical XBT profiles are corrected. be applied when the coefficients (A, B and transient) are Thus, in this section, the correction of a mean value of correctly calculated. the transient is introduced and checked. To check the robustness of the new method theoreti- We applied the fall-rate equations with average (A, B cal tests with simulated data and real XBT–CTD data- and transient) coefficients [see Eqs. (3), (4.1), (4.2)] to sets were carried out, and results from two methods the XBT profiles, and then the pure temperature cor- (H95 and new technique) were compared. According to rections [see Eqs. (1), (2.1), (2.2)]. The corresponding the simulated experiments, the new method is more depth–mean temperature differences between corrected automatic and accurate both for the mean fall rate and XBT profiles and simultaneous CTD profiles and their for the scattering of coefficients A and B in the A–B standard deviations are presented for the two groups, plane when different types of error sources are taken in respectively, in Fig. 17 and Fig. 18 (deep green lines). account. The use of the average transient can still improve the Then, as a practical test, two groups of real ocean data data as well as the individual corrections of the transient, are analyzed with the new method, and the values of the though a little larger temperature differences and stan- fall-rate coefficients (A, B, and transient) and the pure dard deviations occur mainly near the surface. This sug- temperature error are obtained. In particular, we em- gests that it is necessary in practice to apply a constant phasize that the transient term is in substantial agreement

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FIG. 15. 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. with the results from a field test in a very shallow region the temperature profiles have a null or small temperature aimed specifically at checking the XBT motion in the gradient (e.g., group 2). This could be attributed to the near-surface layer (Gouretski and Reseghetti 2010). general adequacy of the new method in analyzing highly There are several transient, ill-described, and even un- homogeneous temperature profiles. known factors influencing the entrance and the motion Furthermore, the validity of the mean fall-rate (A, B) near the surface before the probe reaches its terminal as precalculated coefficients is checked and strength- speed. Indeed, H95 and the manufacturer’s fall-rate ened. The mean temperature difference and its standard equations overestimate the probe speed and its depth in deviation are respectively reduced to about 0.18 and the surface layer, as shown by the results obtained using 0.28C for both groups, within the manufacturer’s toler- the new method in group 2. ances, whereas the maximum difference in depth is at This new method shows smaller temperature differ- a level of 1.1% of the depth (group 1). This implies that ences and standard deviations when compared with re- the mean fall-rate equations [Eqs. (3), (4.1), (4.2)] can be sults from H95 even after the application of the individual applied to the XBT profiles near the locations of the transient correction. In the test using the transient cor- experiments that we adopted in this paper (e.g., near rection as well, the new method shows a similar mean Barbados and in the western Mediterranean). The tran- temperature difference profile in the water where tem- sient term calculated here (about 1.99 m for group 2.1) is perature values changes continuously and even rapidly in good agreement with the results quoted in Reseghetti (e.g., group 1), but it has significantly better results when et al. (2007), after the conversion of that start-up transient

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FIG. 16. 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.

(according to ETC 5 0.3 s), in a depth value of about by computing mean values based on a large num- 1.8–2.0 m. A larger difference occurs with respect to the ber of comparisons. term quoted in Hallock and Teague (1992), where (ii) In the thermocline regions, temperature values a constant value of 4.01 m is calculated to be compared change rapidly with depth, but the new method 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 FIG. 17. Mean temperature differences (solid lines) with their of the variables. Many factors could contribute, such depth mean standard deviation (dashed lines) for T7 in group 1. The used data are original XBT profiles without any corrections as the temperature features (as a function of depth), (red); XBTs with corrections of Eq. (3), Eq. (1), and individual and random errors, spikes, other unexpected errors. It transient corrections (blue); and XBTs with corrections of Eq. (3), is usually assumed that this problem can be overcome Eq. (1), and the mean transient corrections (deep green).

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FIG. 18. 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.

seems to be able to detect small depth differences. subsequently do they adjust to a stable path below This means that the results mainly depend on the a certain depth that changes from probe to probe. comparatively large gradient regions, which can be Another possibility is that each probe falls in regarded as decisive regions. Unfortunately, if the a specific and variable way, so that the transient XBT measurements are bad in these regions, the term must differ from probe to probe, as a conse- results will contain this unpredictable uncertainty. quence its motion cannot be described by an equa- (iii) The transient term, which is represented in this tion with constant or only temperature-dependent paper as a constant term in the fall-rate equations fall-rate coefficients, but it would also include [Eqs. (3), (4.1), (4.2)], should be thought of as random factors. This could be linked to the mass a term somehow representing physical phenomena loss ratio resulting from the wire dereeling, the acting during the first seconds of the probe motion. angular momentum, and the spin rate. In addition, The effect is that probes deviate from the motion strong currents in seawater also have to be taken in predicted by the manufacturer’s equation and only account.

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(iv) As previously indicated, viscosity is strongly sus- Boedecker, S., 2001: Comparison of CTD and XBT temperature pected to have a strong influence on the probe profiles. Naval Postgraduate School, 26 pp. [Available online motion, but no specific experimental tests checking at http://www.weather.nps.navy.mil/;psguest/OC3570/CDROM/ summer2001/Boedeker/report.pdf.] its effects are available. Some useful information Boyer, T. P., and Coauthors, 2006: World Ocean Database 2005. could be extracted from the XBT versus CTD NOAA Atlas NESDIS 60, 190 pp., DVDs. comparison in sea regions having highly homoge- Fang, C. L., 2002: XBT/CTD comparisons. Naval Postgraduate neous water. The Mediterranean and the Arctic School, Monterey Project Rep. for OC3570, 17 pp. [Available and Antarctic Oceans can offer the opportunity to online at http://www.weather.nps.navy.mil/;psguest/OC3570/ CDROM/summer2002/Fang/report.pdf.] compare the XBT probe motion in homogeneous Georgi, D. T., J. P. Dean, and J. A. Chase, 1980: Temperature waters at different temperature. Careful tests should calibration of Expendable Bathythermographs. Ocean Eng., 7, be planned in order to accumulate statistical sam- 491–499. ples of probe data in order to extrapolate informa- Gouretski, V. V., and K. P. Koltermann, 2007: How much is the tion allowing the modification of the structure of the ocean really warming? Geophys. Res. Lett., 34, L01610, doi: 10.1029/2006GL027834. presently accepted fall-rate equation, if necessary. ——, and F. Reseghetti, 2010: On depth and temperature biases in Also, tests with undulating CTD (as a means of bathythermograph data: Development of a new correction checking the effect of the speed ship on measure- scheme based on analysis of global ocean database. Deep-Sea ments) and launches from platforms with different Res., 57, 812–833. heights should be useful. Green, A. W., 1984: Bulk dynamics of the expendable bathythermograph XBT. Deep-Sea Res., 31, 415–426. For further research, because the correction of the Hallock, Z. R., and W. J. Teague, 1992: The fall-rate of the T7 historical XBT data without collocated CTD is an es- XBT. J. Atmos. Oceanic Technol., 9, 470–483. sential problem, the extension of our approach to all Hanawa, K., and H. Yoritaka, 1987: Detection of systematic errors in XBT data and their correction. J. Oceanogr. Soc. Japan, 43, available profiles from the global ocean is suggested, in 68–76. order to calculate a set of values for the (A, B and tran- ——, and H. Yoshikawa, 1991: Re-examination of the depth error sient) coefficients from different probes, ocean regions, in XBT data. J. Atmos. Oceanic Technol., 8, 422–429. seasons, periods, cruises, and also pure temperature cor- ——, P. Rual, R. Bailey, A. Sy, and M. Szabados, 1994: Calculation rections. Additionally, the method may be also a proper of new depth equations for expendable bathythermographs using a temperature-error-free method (application to Sippican/TSK way to further test the different results in different com- T7, T6 and T4 XBTs). Intergovernmental Oceanographic Com- parison with different recording systems, weather, and sea mission (IOC) Tech. Series 42, 51 pp. [Available online at http:// conditions. www.jodc.go.jp/info/ioc_doc/Technical/103567e.pdf.] ——, ——, ——, ——, and ——, 1995: A new depth-time equation Acknowledgments. The authors first thanks Shoichi for Sippican or TSK T7, T6 and T4 expendable bathythermographs (XBT). Deep-Sea Res. I, 42, 1423–1451. Kizu (Tohoku University, Sendai, Japan) for his kind Heinmiller, R. H., C. C. Ebbesmeyer, B. A. Taft, D. B. Olson, and and useful comments. The authors also acknowledge O. P. Nikitin, 1983: Systematic errors in expendable bathy- Mireno Borghini (CNR-ISMAR, La Spezia, Italy) with thermograph (XBT) profiles. Deep-Sea Res., 30, 1185–1196. the masters and crew of R/V Urania for their collabo- Intergovernmental Oceanographic Commission, 1992: Ad hoc ration in recording XBT and CTD profiles in Mediter- meeting of the IGOSS Task Team on quality control for au- tomated systems, Marion, Massachusetts, USA, 3-6 June 1991. ranean Sea, and Ruth Loewenstein for her help in the IOC Summary Rep. IOC/INF-888, 179 pp. [Available online paper preparation. This research is supported by the at http://unesdoc.unesco.org/images/0009/000978/097812eb. Knowledge Innovation Program of Chinese Academy of pdf.] Sciences (Grant KZCX1-YW-12-03), National Basic Ishii, M., and M. Kimoto, 2009: Reevaluation of historical ocean Research Program of China (Grant 2006CB403600), heat content variation with time-varying XBT and MBT depth and China COPES project (Grant GYHY-200706005), bias corrections. J. Oceanogr., 65, 287–299. Kezele, D., and G. Friesen, 1993: XBT test data comparison and and by the European SeaDataNet project (Grant RII3- analysis. Sea Technol., 34, 15–22. 026212) for one of the author (F.R.). Kizu, S., and K. Hanawa, 2002a: Start-up transient of XBT measurement by three types of Japanese recorder system. Deep- REFERENCES Sea Res. I, 49, 935–940. ——, and ——, 2002b: Recorder-dependent temperature error of Anderson, E. R., 1980: Expendable bathythermograph (XBT) ac- expendable bathythermograph. J. Oceanogr., 58, 469–476. curacy studies. Naval Ocean Systems Center Tech. Rep. 550, ——, S. Itoh, and T. Watanabe, 2005a: Inter-manufacturer differ- 201 pp. ence and temperature dependency of the fall rate of T-5 ex- Bailey, R., A. Gronell, H. Phillips, G. Meyers, and E. Tanner, 1994: pendable bathythermograph. J. Oceanogr., 61, 905–912. CSIRO cookbook for quality control of expendable bathy- ——, H. Yoritaka, and K. Hanawa, 2005b: A new fall-rate equation thermograph (XBT) data. 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