1. Introduction
Investigations of regional and global change in the heat content of the ocean can be affected by biases in instrumentation as well as changes in the observing system (Gouretski and Koltermann 2007, hereafter GK07; Willis et al. 2009). One of the main components of the observing system for subsurface temperatures in the open ocean for the period of 1970–2001 was the expendable bathythermograph (XBT; Fig. 1). GK07 demonstrate that XBT temperatures are systematically higher, on the order of 0.1°C, than those measured with conductivity–temperature–depth (CTD) instruments and bottle samples. Moreover, GK07 show that this warm bias has changed over time and also varies with depth. Wijffels et al. (2008), Levitus et al. (2009), Ishii and Kimoto (2009), and Gouretski and Reseghetti (2010) have all provided statistical corrections on a global scale for the XBT temperature bias. Note that although it is referred to as a temperature bias here, the main cause seems to be actually a fall-rate equation (FRE), which leads to a depth under- or overcalculation. Hanawa et al. (1995, hereafter H95) provided the first generally adopted modified fall-rate-equation coefficients (FRECs), which improved upon the original Sippican FRECs, but the H95 FRECs are static in time and space. Thadathil et al. (2002) showed that XBTs dropped in cold Antarctic waters may have a different fall rate with a speed lower than XBTs dropped in other geographic areas, confirming conclusions proposed in unpublished cruise reports (Wisotzki and Fahrbach 1991; Turner 1992). Thus, while statistical corrections may be appropriate on a global scale, they may not be appropriate for some regions. The physical motivation of this variability could be due to the influence of temperature on viscosity, which is a fundamental parameter determining the characteristics of the probe motion, as earlier noted by Seaver and Kuleshov (1982), and recently by Kizu et al. (2005, 2008, hereafter K08) for XBT and expendable CTD (XCTD) probes, respectively.
Under the Indian XBT program supported by the Ministry of Earth Sciences, Government of India, XBTs are deployed onboard ships of opportunity along selected shipping lanes in the seas around India. In the Bay of Bengal (IX-14) XBT data are collected at near-monthly and/or bimonthly intervals along Chennai, India–Port Blair, India, Port Blair–Kolkata, India, and Chennai–Singapore transects, thus giving rise to a now-20-yr time series of regular temperature observations. Fewer opportunities in the Arabian Sea have resulted in 8 yr (1992–99, with intermittent cruises in 2002 and 2007) of time series data along Mumbai, India–Mauritius (IX-8), and fortnightly XBT deployments in the southeastern Arabian Sea during 2002, continuing to the present. Prior to the advent of profiling float technology, there are very few subsurface measurements in this area, making these XBTs an important time series dataset.
2. Data and method
a. Data
To examine the possibility of quantifying and correcting XBT and XCTD biases for waters west and east of India, the National Institute of Oceanography undertook, between October 2008 and August 2009, four special cruises onboard research ships—two in the southeastern Arabian Sea and two in the Bay of Bengal (Fig. 2)—during which XBTs and XCTDs were dropped nearly simultaneously with CTD casts. Near simultaneous refers to times within 15 min of the start time of the CTD cast. Logistical information about the four cruises is listed in Table 1. Henceforth, each cruise will be referred to with the designation given in column 1 of this table. Temperature profiles for all of the casts used in this work are shown in Fig. 3. The Arabian Sea and the Bay of Bengal are two areas of the ocean that have distinct temperature–salinity structures. Both basins have very warm temperatures resulting from the insolation typical in tropical latitudes. The four cruises have very similar temperature structures, with small differences in near-surface temperatures and differences in the depth of the mixed layer and gradients of the thermocline. Temperatures below 300-m depth decrease gradually in either basin for each of the two cruises in the basin, with temperatures ∼1°C cooler in the Bay of Bengal than in the Arabian Sea.
b. Instrumentation
For each side-by-side test, the CTD was assumed to have the correct temperature and pressure readings. A SE
XCTD data were collected using a Tsurumi Seiki Company Limited (TSK; Japan) MK130 data acquisition system and XCTD-3 probes [measuring temperature with an accuracy (±0.02°C), terminal depth (1000 m), and depth resolution (0.203 m)], and a LM-3A handheld launcher manufactured by Lockheed Martin Sippican (United States). K08 is the only previously published work on the XCTD-3 FRE. These probes are different than previous XCTD models because they were manufactured to work at higher ship speeds, and as a result are less stable (see K08 for details). The T-7 XBT probes manufactured by Lockheed Martin Sippican (nominal temperature accuracy of ±0.15°C and depth resolution of 0.65 m) were also deployed.
Depths for both XBTs and XCTDs were calculated from a parabolic FRE z = at − bt2, where a is the initial velocity (m s−1), b is the probe acceleration (m s−2), and t is time (s), the elapsed time since the probe hits seawater. The XCTD depths were calculated initially using the TSK-supplied FRECs a = 5.07958 m s−1 and b = 7.2 × 10−4 m s−2. XBT depths were calculated initially using the H95 FRECs with a = 6.691 m s−1 and b = 2.25 × 10−3 m s−2. The error in depth on the obtained values indicated by manufacturers is 2% of the depth values, but not less than 5 m. This means that all depth values down to 250-m depth do have an “intrinsic” 5-m uncertainty, making fine analyses difficult in the near-surface layer and the upper thermocline. After depth calculation, depths were interpolated to 1-m increments. The method outlined in H95 for obtaining the XBT FRECs was used as a basis for the present method, so a quick description of H95 will be provided here before a description of the present method.
c. H95 method
CTD data and XBT data of near-simultaneous drops are interpolated to 1-m increments. The CTD depth–temperature pairs are considered to have the correct values. Vertical temperature gradients between each 1-m-depth increment are calculated. Gradients are used instead of full temperatures to eliminate any effect of systematic thermal bias so as to concentrate only on FRE errors. Time is back calculated from FRE, giving a time–depth–temperature gradient triplet. Starting at the 100-m XBT depth–temperature gradient pair, a 50-m-wide vertical section of the XBT depth–temperature gradient set is moved vertically up 50 m and down 30 m through each 1-m increment of the CTD data. At each 1-m increment, the difference between the XBT temperature gradient and the CTD temperature gradient is calculated. These differences are summed for the entire 50-m section. There are a maximum of 80 such summations. The CTD depth at which the summation is minimal is recorded as the true depth for the XBT drop, matched with the original time from the triplet. This process is repeated for each 50th XBT time–depth–temperature gradient triplet (100th, 150th, 200th, 250th, etc., to the bottom of XBT drop). For a 760-m XBT drop, this should result in 13 time–depth points. A least squares fit to this line gives the best pair (a, b) of values for FRECs. A similar method has been used for XCTD data (Johnson 1995; K08).
The H95 method is sensitive to quality control of the XBT, XCTD, and CTD data. Removal of one or two minimum summed time–depth pairs can significantly affect the calculated FRECs. On AS08, winch problems resulted in the CTD only reaching a maximum of 406-m depth. For this cruise, after quality control, the H95 method resulted in only four or five points with which to linearly regress to new FRECs for some XBTs. Because of this, a modified H95 method was used.
d. Modification to H95 method
We preserve the H95 method of comparing temperature gradients between XBT and CTD instead of full temperature values. However, we eliminate the need for linear regression between a possibly sparse set of time–depth pairs by summing all of the differences between XBT and CTD gradients over the vertical profile from 100 to 700 m (or to the end of the CTD profile if it does not extend to the deeper depth) for all sets of probable initial velocities and decelerations. The sets used were 6.00–7.15 m s−1 for initial velocities (a), and 0.00–4.00 × 10−3 m s−2 for the deceleration (b), both exceeding the range of published FRECs. Each initial velocity at increments of 0.01 m s−1 in this range is tested with each deceleration in its range at 0.01 × 10−3 m s−2 increments. The CTD has 1-m-incremented depth–temperature gradient pairs. The XBT data are interpolated to 1-m increments and time is back calculated. For each initial velocity pair and deceleration, depth is calculated and then interpolated back to 1-m increments from which 1-m temperature gradients are calculated. The XBT and CTD gradients are then subtracted and the absolute values are summed. This sum is then divided by the number of depth–gradient pairs that were summed to give an average gradient difference for each (a, b) pair. The minimal mean gradient difference is indicative of the best-fit (a, b) pair because it represents the minimum error in the XBT profile compared with the CTD profile. The same procedure was used to compare XCTD and CTD side-by-side pairs, except an initial velocity (a) range of 4.80–5.50 m s−1 and decelerations of 0.0–2.0 × 10−3 m s−2 (b) were used, reflecting the different characteristics of the XCTDs drop through the water column. Because the XCTD can reach deeper than 1000 m, the depth interval of 100–1000 m was used for the summation of gradient differences. The time is back calculated for XCTDs using the TSK-provided FRE. In many cases, the very end of the XBT or XCTD cast deviates from the CTD cast temperature gradients in a manner suggesting some inconsistency in the XBT–XCTD data, probably resulting from a wire-stretching process immediately before the end of the wire spool. In some cases, the variability in the 100–200-m depth range caused large differences in the XBT–XCTD and CTD temperature gradients. Both of these discrepancies near the top and bottom of the cast resulted in less-than-optimal FREC fit over the entire profile. Thus, the above procedure was repeated using the depth interval of 200–600 m for XBTs and 200–900 m for XCTDs (or the bottom of CTD casts, if shallower). The better fit between the results of the two depth intervals, based on minimum mean gradient differences, was used for the final FREC selection.
e. Thermal bias calculation
Once the FRECs have been selected, the new FRE is applied to the XBT (XCTD) time–temperature pair, and the XBT (XCTD) depths are again interpolated to 1-m increments. Assuming that the FRE has corrected any depth bias, any systematic thermal bias can now be estimated simply by subtracting the full temperature values of each instrument at each 1-m increment and taking the average difference as the thermal bias. This procedure is performed only on the depth interval over which the new FRECs were estimated.
f. Additional adjustment
Depth changes resulting from the deceleration coefficient are smaller in magnitude and harder to accurately track using side-by-side tests than changes resulting from different initial velocities (Figs. 4a,b). To better estimate the deceleration, additional tests, using the best-fitting 1% of the FRECs based on minimal mean gradient differences are applied. An FRE with an inappropriate deceleration coefficient often shows a distinct slope in the temperature (or depth) difference between the XBT (XCTD) and CTD. Within the small vertical scale (1–3 m) variability, the slowly increasing discrepancy between XBT and CTD temperature, represented by the linearly fit slope in the difference, is the most distinct residual feature found after applying a best-fit initial velocity with an incorrect deceleration coefficient. We take the FRECs that produced the minimum 1% of the gradient difference means and calculate the slope of the linearly regressed curve of the difference between CTD and XBT (XCTD) temperatures using each of these FRECs. The slope of the line that is closest to 0.0 represents the best estimate of the deceleration, and hence the FRECs that give the best-fit FRE. Finally, the thermal bias is expected to be small; Reseghetti et al. (2007) give an estimated value of <0.05°C. Gouretski and Reseghetti (2010) give statistical estimates of between 0.0° and 0.04°C from 1990 to 2002, and slightly higher since 2002, which is possibly due to a decrease in CTD data for statistical comparison. The fluctuations in the small-scale (1–3 m) vertical structure will, in some cases, result in coefficient choices with two very similar mean gradient differences—one with a resultant high thermal bias and one with a resultant lower thermal bias. In these cases, given that thermal bias has been shown to be small, the FRECs resulting in the lower thermal bias are chosen. It should be noted that this may result in a small underestimation of thermal bias. Thus, from the minimum 1% of gradient difference means, now ordered in terms of minimum slope, the first case with the minimum thermal bias is chosen for the final set of FRECs. That is, if more than one of the minimal 1% of the gradient difference means had the same minimal thermal bias (which is very likely because the XBT temperature readings are recorded to two decimal places by the provided software), then the case with the minimum slope is chosen. It was found that XBTs whose minimal thermal bias was >0.10°C had poor fits to the CTD data, regardless of the FRE (or thermal bias) used. These cases were not included in the final statistics (see Table 1c). Only 5 of the 57 XBT–CTD comparisons were disqualified using these criteria, and 1 of 40 XCTDs, excluding the second cast comparisons for AS09.
3. Results
a. Cast-to-cast CTD differences
Before comparing XBT (XCTD) temperature profiles with CTD temperature profiles, it is important to take a look briefly at the CTD profiles themselves. On AS09, the CTD was lowered twice in succession. The consecutive CTD casts have start times within 45 min to 1 h 15 min of each other. Figure 5 shows the difference in the temperature profiles between each set of consecutive casts. Because nothing was changed on the CTD package and the winch lowered the CTD at the same speed each time, the differences between the consecutive CTD drops are mainly due to the change of position resulting from the ship drift and the alteration of the temperature structure of the water column resulting from internal waves and other processes. Temperature differences between consecutive CTDs are of the same order as the temperature differences between CTDs and XBTs (XCTDs). This adds to the difficulty of estimating the FRECs of the XBT (XCTD) with the comparison with a near-concurrent CTD cast. XBTs and XCTDs were dropped within 15 min of the start time of the CTD cast (the first CTD cast in the case of AS09).
b. Example with individual XBT case from the Bay of Bengal
Figures 6a,b show full XBT–CTD temperature (as opposed to gradient) and depth differences, respectively, for a side-by-side XBT–CTD test from BB08 both before and after correction. In the top 50 m the XBT is slightly warmer than the CTD using H95’s FRE (gray line, Fig. 6a), but through the rest of the water column to the end of the XBT cast at 760-m depth, the XBT temperatures are cooler than those from the CTD. The differences are large from 75- to 200-m depth, around 0.3°C with high-frequency variability, but they decrease to about 0.05°C below 200 m. Figure 6b shows the temperature for the XBT at slightly deeper depths in the upper 50 m relative to the CTD, at shallower depths from there to the end of the XBT profile, with the difference increasing slowly with depth to about 8-m difference at the end of the XBT profile. A linear fit to the depth difference is given to illustrate the increasing difference with depth associated with ill-fitting FRE without the high-variability noise and other factors. While there is high-frequency variability in the differences, the linear fit shows a steadily increasing difference in the depth of the same temperature value, which is indicative of an FRE that is either too low in initial velocity or too high in its deceleration coefficient, or both. The linear fit to the corrected FRE depth difference still has a small slope representing residual depth errors.
Figure 7 shows the results of using different FREC (a, b) pairs on the mean gradient difference between instruments, which is essentially a measure of the error in the XBT temperature profile for each set of FRECs. The striking feature of Fig. 7 is that there is a relatively small range of initial velocities represented by the blue–magenta end of the color spectrum, but a large range of decelerations, covering nearly the whole range being tested. This is due to the relative effect of initial velocity changes and deceleration changes on the calculated depths (Figs. 4a,b). The new best-fit FRE is applied and the thermal bias is calculated and subtracted from the XBT temperatures.
c. Bay of Bengal XCTD example
Figure 8 shows the set of gradient difference means for the XCTD dropped near simultaneously with the same CTD from the above XBT example. The blue and magenta areas are wider along the initial velocity axis and there is not as strong a linear relation between initial velocity and deceleration within the minimal magenta area as for the XBT case. The temperature and depth differences (Figs. 9a,b) show a changing relationship between the CTD and XCTD with depth, whereas the XBT exhibited a more steady relationship of increasing depth difference with depth. The calculated FRECs (a = 5.09 m s−1, b = 0.58 × 10−3 m s−2) are not very different from the manufacturer’s FRECs (a = 5.08 m s−1, b = 0.72 × 10−3 m s−2); however, the newly calculated FRECs improve the relationship between the CTD and XCTD temperatures. The XCTD records temperatures for a greater distance vertically in the water column than the XBT, so even a small adjustment to the FRE can have a significant effect as depths approach 1000 m.
d. Arabian Sea examples
Figures 10a,b show the results of the method for an XBT from AS09. The XBT bias from the AS09 example is opposite in sign to that of the example from BB08. Figures 11a,b present results from the AS09 XCTD test using the same CTD as for the XBT example. The corrected XCTD profile correlates very well with the near-simultaneous CTD. The newly calculated FRECs are very different from the manufacturer FRECs, with 7.6% higher initial velocity and 166% higher deceleration. Some 200 s after deployment, the newly calculated initial velocity would give a depth that is 77 m greater than the manufacturer’s initial velocity, while the deceleration would result in a 48-m shallower depth than the manufacturers’ deceleration. The XCTD biases are of the same sign for the AS09 and BB08 examples, but the AS09 example has a much larger bias.
e. Multiple XBT drops
The AS09 cruise provides a chance to compare multiple XBT drops to the same CTD cast to give some idea of the consistency of the XBT–CTD comparison. Figures 12a–d show the set of gradient difference means between XBT and CTD for each set of (a, b) coefficients for four XBTs dropped while a single CTD cast was being performed. The four figures show distinct but different minimum areas of the difference mean. The final calculated a and b coefficients are shown for each case, along with Sippican and H95 values for comparison. The XBTs are all dropped within 15 min of the start of the CTD cast, and they all complete their measurements while the CTD is still making its measurements. This minimizes, but does not eliminate, the effects of natural variability. Another possible reason for the different FRECs calculated in the same test is XBT probe-to-probe variability. Kizu et al. (2005) and Reseghetti et al. (2007) have verified a probe-to-probe variability in dimensions with slight differences in weight, wire characteristics, diameter of the central hole in the nose, and shape of terminal fins. The XBT manufacturer (Sippican) states that the difference in weight in water still remains within 2 g and, even combined with other differences, the variability induced on the motion and the measurement does not exceed the quoted tolerance in depth and temperature (Sippican 2009, personal communication). Despite this, and maybe because of an unknown influence of launching and external conditions, the observed range of probe-to-probe variability in the temperature measurements and individual FRECs was larger than expected.
Figures 13a–d show the difference means for the same four XBTs as in Figs. 12a–d, but versus the second CTD cast, which occurred 33–45 min after the four XBT drops; thus, they are not concurrent, but they are within a very small space–time window. The FRECs for these four tests are similar to those from the four tests versus the first CTD cast. However, the area covered by the blue–magenta color spectrum is wider with respect to the initial velocity. The range of difference sums for each of the eight panels in Figs. 12 and 13 (see color bars) shows the relative range of errors of each XBT versus each CTD, with those versus the second CTD cast showing significantly higher errors. Natural variability is occurring in time and space, which adds to the uncertainty of calculating a new FRE. This shows the importance of dropping the XBTs as close as possible to the time when the CTD cast is being carried out while performing studies such as the one described here.
f. Mean FRECs
Tables 2a,b summarize mean calculated FRECs and thermal biases for XBTs and XCTDs for each cruise, but each cruise requires a detailed comment. Figures 14a–d show the FRE initial velocity–deceleration pairs for each cruise with the ellipse representing the 95% confidence interval (two standard deviations from the mean) for the coefficients. The figure is arranged in chronological order, but the cruises will be discussed basin by basin. Figure 14c shows initial velocity–deceleration pairs calculated for each XBT–CTD comparison from the AS09 cruise. There is a large spread of points on this graph with the pairs mainly oriented, with lower initial velocities being paired with lower decelerations and vice versa, consistent with the results of H95. This large spread results in a mean initial velocity (6.68 m s−1) that is nearly identical to that of H95 and a deceleration (1.89 × 10−3 m s−2) that is lower than that of H95, with a large standard deviation. Noting the importance of temporal proximity in XBT drops and CTD casts, using only the XBT–CTD pairs from the first cast of the CTD, the FRECs become slightly smaller [with an initial velocity of 6.65 ± 0.16 m s−1 and a deceleration of 1.71 × 10−3 ±(1.18 × 10−3) m s−2]. The uncertainty, represented by the standard deviation, in both the initial velocity and the deceleration translates to significant depth uncertainties (see Figs. 4a,b) resulting from the large probe-to-probe variability. There is a small positive mean thermal bias of (0.01° ± 0.02°C) using all of the XBT–CTD pairs and (0.00° ± 0.03°C) using the first CTD pair only.
Figure 14b shows the initial velocity–deceleration pairs for the AS08 cruise. The mean initial velocity (6.56 m s−1) and the mean deceleration (1.32 × 10−3 m s−2) are smaller than H95, and substantially so, with a large standard deviation for deceleration. The calculated thermal bias is (−0.01° ± 0.04°C). Optimally, it would be good to have one resultant FRE for the Arabian Sea. However, the mean calculated FRECs for the two Arabian Sea cruises are quite different. To see if the cutoff of the AS08 comparison at 400 m due to CTD problems has a significant bearing on the difference in the FRECs for AS08 and AS09; the AS09 FREs were calculated using depth–temperature pairs only down to 400 m. The resultant FRECs a = (6.67 ± 0.18 m s−1), b = (2.15 ± 1.49 m s−2) for AS09 show that the depth limitation of the AS08 cruise is probably not the reason for the large difference in FRECs for the two Arabian Sea cruises. AS08 and AS09 used XBTs from the same manufactured batch (as did cruise BB09, Table 1b) so batch-to-batch variability should not be a factor. In addition to the temperature and salinity differences outlined previously between AS08 and AS09, the currents during the two cruises were also very different. During April, in response to the commencement of southwesterlies, alongshore ocean surface currents in the Arabian Sea are directed equatorward giving rise to an offshore Ekman drift producing coastal upwelling. These currents are strongest during July–August with a mean velocity of about 30 cm s−1 (Shetye 1984). However, this coastal current reverses its direction and starts flowing poleward during November to January with weaker velocities (15 cm s−1) during December. Strong currents can have an effect on XBTs, straining and even breaking their copper wire (Beaty et al. 1981), but the main effect could be a change in the XBT spin rate value, with unpredictable variations of the motion (Cunningham 2000). Without current measurements for each cruise, the relative effects of currents on the XBT drops from each cruise are not known.
The set of XBT–CTD comparisons in the Bay of Bengal for cruise BB08 are shown in Fig. 14a. The mean initial velocity (6.79 ms−1) and the mean deceleration (2.54 × 10−3 m s−2) are higher than H95. The calculated mean thermal bias is (0.01° ± 0.02°C). Figure 14d gives the results for BB09. The pattern of probe-by-probe scatter with lower initial velocities coupled with lower decelerations is present in this cruise, as in the other three cruises. The initial velocity (6.59 m s−1) is significantly lower than the initial velocity of BB08, as is the deceleration (1.85 × 10−3 m s−2). BB08 covered a wider geographic area of the Bay of Bengal and occurred after the southwest monsoon. BB09 covered only the lower salinity waters of the central and northern Bay of Bengal and occurred near the end of the southwest monsoon. This would suggest that different environmental conditions may have been a factor in the different FREs. However, the results for the XCTDs for the two cruises (see below) make this assumption harder to justify. XBTs from BB08 and BB09 came from different manufacture batches (Table 1b), which may be a factor in the differences in FRE between cruises. The XBTs from BB08 came from the same batch as the two Arabian Sea cruises, but the FRECs for BB08 are much higher than for either Arabian Sea cruise.
Figures 15a–d show the full set of initial velocities and decelerations for XCTD probes for the BB08, AS08, AS09, and BB09 cruises, respectively, along with ellipses representing the 95% confidence interval (two standard deviations) for each cruises FRECs. Like the XBTs, the XCTD mean FRECs for the Arabian Sea are quite different between the two cruises. The BB09 XCTD mean FRECs are very close to those calculated for cruise BB08 XCTDs. AS09 has higher (a, b) coefficients than the Bay of Bengal cruises, while AS08 has lower FRECs. All of the calculated XCTD FRECs are higher than the manufacturer’s coefficients. K08 calculate (a, b) coefficients of the XCTD FRE lower than those given by the manufacturer for two cruises in the North Pacific. The difference in the results of K08 and the present results may be due to regional environmental differences. The Arabian Sea and Bay of Bengal water temperatures are warmer than for either cruise used in K08. K08 calculates a temperature dependency of the XCTD FRE based on the two cruises using the temperature at 500-m depth (T500). If this temperature-dependent FRE is applied to the cruises in the present study, the maximum resultant FRECs (for the Arabian Sea) are a = 5.024 m s−1, b = 0.540 × 10−3 m s−2, based on a T500 = 10.77°C. These coefficients are much lower than the presently calculated (a, b) coefficients. Interestingly, if the temperature in the mixed layer (TML = 30.72°C) is used, the temperature-dependent coefficients become a = 5.184 m s−1, b = 0.910 × 10−3 m s−2, so it may be that the XCTD has a temperature dependence that can explain some of the difference between the Arabian Sea cruises, the Bay of Bengal cruises, and the North Pacific cruises of K08. Additional work needs to be done to better quantify such temperature dependence. Because both XBTs and XCTDs function in the same manner, with wire unspooling during their drop through the water column, it would be expected that environmental variables, including temperature, would affect both instrument’s FRE in a similar manner. The XBT FRECs for BB08 and BB09 are quite different, while the XCTD FRECs for the same cruises are nearly identical. This seems to point to probe-to-probe differences between the XBTs on the Bay of Bengal cruises as a larger factor than environmental variability as a source of the difference in the XBT FRECs for the two cruises. A possible significant difference is that XBTs used in the present work were manufactured by Sippican, whereas the XCTDs were manufactured by TSK. The variability in the dimensions of the probes manufactured by TSK was (statistically) smaller than that in the Sippican probes in a small sample of analyzed probes. This could be a physical basis in part supporting the more pronounced random behavior of the XBT probes (Sippican) than XCTD (TSK). It could also be the larger external dimensions and heavier weight of the XCTD probes that make them more stable and less prone to probe-to-probe variability.
g. Comparison with terminal velocity model
Gouretski and Reseghetti (2010) try to explain what occurs in the near-surface layer and usually describe the startup as having transient effects. In such a region, the XBT motion seems to be different from the description resulting from the standard FRE. The speed of XBT probes in the top 20–30 m is slightly slower than that calculated by both Sippican and H95 FREs; after that they accelerate to a terminal velocity before assuming the characteristics represented by either the Sippican or H95 FRE. Another factor they take into account is the interaction among the different components of the XBT system (i.e., the recorder and thermistor) and the ambient environment (i.e., differences in conditions between instrument storage area and air/seawater temperature, humidity, etc.) creating problems such as thermal shock of the probe and affecting the thermal response of the thermistor. The XBT manufacturer states than XBT probes need a short time [∼(2–3) s], before they assume the terminal speed and the right spin rate, for example, the motion conditions as described by the standard FRE (Sippican 2009, personal communication). Recent field tests in a very shallow area (with a depth range from 15 to 27 m) confirm that depth calculated using H95 FRE overestimates the actual depth by about 1.0–1.5 m at the bottom (Gouretski and Reseghetti 2010; F. Reseghetti et al., unpublished manuscript). This difference is well within the depth error provided by the manufacturer (5 m), but it reveals that some other phenomena occur in the first few seconds deviation from the simple description adopted by the standard FRE. A video also shows that immediately after an XBT hits seawater, the probe has both a helical motion, and a reduced spin rate. This could explain how the depth difference in Fig. 6b switches sign around 50-m depth.
To verify the idea of Gouretski and Reseghetti (2010), a terminal velocity model for calculating a new FRE was tested on the AS09 cruise dataset (using a comparison with the first CTD only). In this model, the first 3 s of the drop are assumed to cover the top 18 m (as opposed to ∼20 m for the H95 FRE), and then an FRE is fit from this point, assuming terminal velocity has been reached. The 2-m difference from H95 is an overestimate, but a reasonable one given the 1-m increments of the XBT data. The calculated mean terminal velocity and deceleration for AS09 for the terminal velocity case are a = (6.75 ± 0.17 m s−1) and b = (2.69 ± 1.22 m s−2), and the thermal bias is (0.00° ± 0.3°C). This is higher than the initial velocity model for both (a, b). Figure 16 shows the depth difference between the initial velocity model and the terminal velocity model at each depth of the initial velocity model. For this case, the depth difference is always between −1 and +2 m down to 700-m depth. On a probe-by-probe basis for AS09, there was not much difference in the mean of the gradient differences between the initial velocity and terminal velocity cases, with sometimes one and sometimes the other giving the better result. For this study, results from the initial velocity model are reported with the understanding that improved application of the terminal velocity case may give improved results in future studies.
h. Comparison of results with previous tests in the Arabian Sea
There have been no previous XBT–CTD comparisons in the Bay of Bengal. Thadathil et al. (1998) found a set of FRECs for the Arabian Sea and equatorial Indian Ocean based on one cruise in 1994 and two cruises in 1996 in the Arabian Sea and one cruise in 1997 for the equatorial Indian Ocean. They did not give cruise-specific mean FRECs; instead, they aggregated all of the data from the Arabian Sea cruises along with data from the equatorial Indian Ocean, and their values (a = 6.694 m s−1, b = 2.22 m s−2) are nearly coincident with the H95 FRECs. However, their Fig. 5 shows a similar (a, b) coefficient scatter diagram as in Figs. 14a–d of the present work and the same type of probe-to-probe and cruise to cruise variability as shown in Figs. 14a–d. The Thadathil et al. (1998) aggregated results are closer to the calculated values of FRECs for AS09 than AS08.
i. Test of new mean FREs
The results summarized in Table 2 present further challenges and questions. The present dataset with four cruises worth of XBT comparisons with near-concurrent CTDs show large enough cruise-to-cruise (and probe to probe) variability that a revised set of basin-specific FRECs for either the Bay of Bengal or the Arabian Sea cannot be confidently proposed. The results for XCTDs are encouraging for the Bay of Bengal but not the Arabian Sea.
Two questions that can be addressed with the present dataset are as follows: 1) Can a cruise-specific set of FRECs be calculated despite the exhibited probe-to-probe variations? 2) In the absence of a reliable set of recalculated FRECs, are the errors inherent in using the H95 coefficients small enough to use XBT data for climate studies? If the answer to 1) is affirmative, then it would be beneficial to continue side-by-side tests in the Arabian Sea and the Bay of Bengal until a large enough dataset exists to reliably calculate revised FRECs, which is the aggregation technique used in H95 originally. Regardless of the answer to 1), 2) is an important question for the immediate use of the long Bay of Bengal and Arabian Sea XBT time series. To find the answers to these questions, we look at average temperature anomalies at standard depths in the water column for each of the mean FRECs in Table 2. Temperature anomalies, the difference between observed temperature and a reference mean temperature, are used to remove the seasonal cycle to investigate interannual changes in the temperature structure of an area over time, and are also used to calculate regional and global integrals of heat content change (see Levitus et al. 2009, e.g.). Aggregating the XBT data into mean temperature anomalies can have the effect of removing much of the probe-to-probe variability (though not environmental variability), providing a more accurate comparison than the individual profiles. The temperature anomalies are calculated here by subtracting the median temperature for the depth interval around 16 standard depths from the surface to 700 m from the standard level temperature value from appropriate geographic location from the World Ocean Atlas 2005 (WOA05; Locarnini et al. 2006) climatological mean monthly temperature fields at 1° resolution. Anomalies based on WOA05 are used to calculate heat content anomalies in Levitus et al. (2009) and it is thus of interest to see how XBT FRE errors and corrections affect these anomalies. Table 3 gives the 16 standard depth levels and the depth interval around each standard depth from which the median was calculated. Figures 17a–d show the mean temperature anomaly at the 16 standard depths from the surface to 700 m from all XBT data using the H95 FRE (solid black line with diamonds), the FRE with the newly calculated FRECs (dashed black line with circles), and all CTD data (gray line with crosses). Looking first at Fig. 17c (AS09), the H95 FRE-calculated anomalies generally result in an overestimate of water column warming for AS09 for positive temperature anomalies, and an underestimate for negative temperature anomalies; the new FRE lessens, but does not eliminate, this bias. The AS08 cruise (Fig. 17b) measures a different temperature anomaly structure in the upper 200 m than the AS09 cruise, and all three AS08 temperature anomaly curves show a large temperature anomaly around 100-m depth of the opposite sign to the temperature anomaly found in AS09 in the following April. In the AS08 case, the H95 FRE XBT anomalies are ∼0.5°C smaller than CTD anomalies from 50 to 125. Deeper down the differences are smaller but still significant, ∼0.2°C at the 200-m level. The recalculated FRE temperature anomalies show considerable improvement over the H95 FRE temperature anomalies in comparison with the CTD temperature anomalies. As with AS09, AS08 has a positive temperature bias. However, in the case of AS08, the agreement with CTD temperature anomalies at many depths is significantly improved by applying the new FRE. At the last depth for the CTDs for this cruise (400 m), there is a relatively high anomaly that is not seen in the mean XBT anomalies or in the mean XCTD anomalies. The slightly anomalous temperatures may be due to problems associated with the winch on this cruise.
In the Bay of Bengal, BB08 (Fig. 17a), the mean XBT temperature anomalies XBT FRE calculated with the new FRECs correlate more closely with the composite temperature anomalies from CTD casts than do the temperature anomalies from the H95 FRE case, except at the last standard level at 700 m. Even here, all three mean temperature anomalies are within 0.1°C of each other. Unlike AS08 and AS09, the bias in the temperature anomaly for BB08 is cooler, and the bias is eliminated when applying the new FRE.
For cruise BB09 (Fig. 17d) at all levels, the adjusted FRE temperature anomalies are nearly indistinguishable from the CTD temperature anomalies, and both are lower than the H95 FRE temperature anomalies by ∼0.05°C below 200-m depth. The bias with the H95 FRE is always positive for BB09, like the Arabian Sea cruises, but unlike BB08. The improvement in the agreement of mean temperature anomalies with adjusted FRE for the Bay of Bengal cruises is much better than for the Arabian Sea cruises. This may be due to the relatively high velocity and variable currents in the area of the Arabian Sea cruises, which make it more difficult to model the FRE. This cannot be verified for AS08 and AS09 because of the lack of current measurements.
The difference between the CTD and XCTD anomalies are shown in Figs. 18a–d. The newly calculated XCTD FREs bring the XCTD temperature anomalies significantly closer to the CTD temperature anomalies. In all cases the manufacturer’s FRE produces a cool bias. This includes BB08, the lone cruise with a cool XBT bias.
4. Discussion
Side-by-side XBT and XCTD drops with CTDs on two cruises in the Arabian Sea and two cruises in the Bay of Bengal during 2008 and 2009 reveal the difficulty of assigning definitive and unique FREs and thermal biases to XBT data in these regions. Probe-to-probe and cruise-to-cruise variability are significant. The standard deviations for the initial velocity and deceleration coefficients calculated for each cruise are large enough to account for the depth error incurred when using the H95 FRE for XBTs and the original TSK FRE for the XCTDs. Initial velocity is the main driver in FRE variation, but changes resulting from using different deceleration coefficients can be significant when attempting to get accuracy sufficient for climate study purposes, such as integrating heat content in the upper ocean. Decelerations are correspondingly hard to accurately calculate with the present technique despite steps designed to do just that. Thermal bias seems very small for the XBTs, consistent with the findings of Reseghetti et al. (2007), but they may be underestimated because of the nature of the technique. Given the small thermal bias and the large standard deviation, it is not practical to attempt to assign a mean thermal bias to all XBT drops. Gouretski and Reseghetti (2010) propose a description of the motion in the near-surface layer as resulting from an accelerated motion to a terminal velocity and a lag resulting from the whole XBT system. The use of a pure FRE with acceleration down to 18-m depth (the terminal velocity case) does not give better matches between XBT and CTD profiles in the four cruises in the present study. Newly calculated FRECs for each of the four cruises, using the older model of initial velocity from the surface, reveal a large spread of values for both initial velocity and deceleration coefficients for XBTs. No definitive recalculated FRE can be suggested for the Arabian Sea or the Bay of Bengal. For XCTDs, the FRECs calculated for the cruises in the Bay of Bengal are very similar and suggest that a new FRE, with higher initial velocity (5.18 m s−1) and the same or slightly higher deceleration than the original TSK FRE, should be used. For the Arabian Sea the FRECs calculated for each cruise are different, possibly resulting from variations in the currents in the area, and no new FRE can be proposed.
Tests of the H95 FRECs and new FRECs for each cruise show that the H95 XBT FRECs result in significant errors (>0.2°C) between the 75- and 200-m levels, with most errors <0.1°C below 200 m. Temperature anomalies with the new FRE for each cruise show much better agreement with CTD temperature anomalies than similar anomalies using the H95 FRE at all levels, or little change, as is the case with AS09. The tests with the XBT probes show that further side-by-side tests in both the Arabian Sea and the Bay of Bengal can be beneficial in aggregating enough data to eventually average out probe-to-probe variability and propose new FREs that will substantially improve climate studies, such as integrated ocean heat content change. In the meantime, individual cruise-corrected XBT FRE from side-by-side test cruises can be used to do smaller-scale climate studies with the full set of XBTs from these cruises. For the full set of the Bay of Bengal and Arabian Sea XBT cruises, the data can be used for climate studies with the H95 FRE with the understanding of the errors inherent in using this FRE shown here for the different depth levels. However, it must be kept in mind during studies with these XBT time series, that XBT probe-to-probe variability is high, and even the sign of the XBT bias for a given cruise cannot be assumed. Recent tests by Sippican (personal communication, 2010) show that recently produced Sippican Deep Blue XBTs have a fall rate that is modeled correctly by the H95 FRE, while older probes have a slightly slower fall rate. Thus, it may be that there will be no need for FRE corrections for XBT drops going forward. However, it remains to be seen if these results hold for all XBTs manufactured in the future, or for all ocean conditions.
For XCTDs, application of the new FREs for each cruise results in the definite improvement for all cruises. More study is necessary to modify the temperature dependence of the XCTD-3 FRE as given in K08. Given the temperature structure of the Arabian Sea and Bay of Bengal and the lower probe-to-probe variability in the XCTD as compared with the XBT, the FREs calculated for the Bay of Bengal can be used to remove the cool bias in the XCTD data for this region.
Acknowledgments
We would like to acknowledge the help of Pr. Shoichi Kizu, Tohoku Univeristy, and LM Sippican for sharing their research and knowledge regarding XBT and XCTD fall rates. We would also like to acknowledge our colleagues Syd Levitus and Ricardo Locarnini and three anonymous reviewers for their helpful comments on the manuscript. The data were collected under the ongoing long-term observational program supported by the Ministry of Earth Sciences through INCOIS.
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Percent of global 1° ocean squares with adequate coverage using all instrument types (solid line) and using all instrument types except XBTs (dashed line). A 1° square is considered to have adequate coverage if there are at least three 1° squares with at least one temperature profile within a 440-km radius of the center of the 1° square. Criteria are as used for the climatologies in Levitus et al. (2009).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Locations of side-by-side XBT–XCTD–CTD comparison test sites in the Arabian Sea and Bay of Bengal, 2008/09. Cruises are BB08 (circles), AS08 (stars), AS09 (open squares), and BB09 (diamonds).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
The CTD temperature profiles from comparison tests for BB08 (green), AS08 (red), AS09 (blue), and BB09 (magenta).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
(a) Calculated depth difference using depth calculated with different initial velocities vs depth calculated using initial velocity from H95, (6.69 m s−1). Deceleration rate in all cases are equal to H95 (2.25 × 10−3 m s−2). The case using the H95 initial velocity (solid gray line) and the case using the initial velocity from the original Sippican equation (6.472 m s−1; dashed gray line) are shown. Initial velocities starting at 6.40 m s−1 and incremented by 0.1 m s−1 intervals to 7.00 m s−1 are shown (black lines). Values of initial velocity (m s−1) are shown under or to the side of the associated black line. (b) Calculated depth difference using depth calculated with different deceleration rates vs depth calculated using the deceleration rate from H95 (2.25 × 10−3 m s−2). The initial velocity in all of the cases is the same as H95 (6.691 m s−1). The case using H95 deceleration (solid gray line), the case using the Sippican original equation deceleration (2.16 × 10−3 m s−2; dashed gray line), and decelerations starting at 4.00 × 10−3 m s−2, decrementing by 0.50 × 10−3 m s−2 down to 0.0 m s−2 (black lines) are shown. Values of deceleration (10−3 m s−2) are shown under or to the side of the associated black line.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Temperature difference (°C) as a function of depth between the first CTD cast at each station and the second CTD cast at each station from AS09 (nine CTD pairs).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Difference in (a) temperature at same depth and (b) depth of same temperature between XBT and concurrent CTD dropped in the Bay of Bengal from the Sagar Kanya on 18 Oct 2008 at 14°N, 91°E (BB08) using H95 FRE (gray), newly calculated FRE [z = (6.80 m s−1)t − (2.62 × 10−3 m s−2)t2] (solid black), and newly calculated FRE with thermal bias (0.01°C) removed (dotted black). Additionally, (a) has CTD temperature profile to show the vertical temperature gradient.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Mean of differences of vertical temperature gradients at each 1-m interval between XBT drop and concurrent CTD drop in the Bay of Bengal from the Sagar Kanya on 18 October 2008 at 14°N, 91°E (BB08) for each initial velocity (incremented at 0.01 m s−1 intervals from 6.00 to 7.00 m s−1) and each deceleration (incremented at 0.01 × 10−3 m s−2 intervals from 0.00 to 3.90 × 10−3 m s−2). Best-fit FRECs minimize this mean difference (blue and magenta shading). S: Sippican FRECs, H95: H95 FRECs, N: newly calculated FRECs.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
As in Fig. 7, but for XCTD drops for velocity intervals from 4.80 to 5.50 m s−1) and deceleration intervals from 0.00 to 2.00 × 10−3 m s−2). TSK: TSK FRECs.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
As in Fig. 6, but for XCTDs using TSK manufacturer FRE (gray), newly calculated FRE [z = (5.09 m s−1)t − (0.58 × 10−3 m s−2)t2] (black). Thermal bias was 0.0°C for this case.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
As in Fig. 6, but in the Arabian Sea from the Sagar Purvi on 2 Apr 2009 at 10°N, 75.23°E (AS09) using newly calculated FRE [z = (6.50 m s−1)t − (1.18 × 10−3 m s−2)t2] (solid black) and newly calculated FRE with thermal bias (0.02°C) removed (dotted black).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
As in Fig. 10, but for XCTDs and newly calculated FRE [z = (5.46 m s−1)t − (1.92 × 10−3 m s−2)t2] (black). Thermal bias was 0.0°C for this case.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Mean of differences of temperature gradients at 1-m increments between XBT and first CTD cast from the Sagar Purvi on 2 Apr 2009 at 10°N, 76.25°E (AS09) in the Arabian Sea for each initial velocity (incremented at 0.01 m s−1 intervals from 6.00 to 7.00 m s−1) and each deceleration (incremented at 0.01 × 10−3 m s−2 intervals from 0.00 to 3.90 ×10−3 m s−2) for (a) XBT-1 [newly calculated FRE z = (6.64 m s−1)t − (2.35 × 10−3 ms−2)t2 and 0.00°C thermal bias], (b) XBT-2 [newly calculated FRE z = (6.79 m s−1)t − (1.75 × 10−3 ms−2)t2 and 0.04°C thermal bias], (c) XBT-3 [newly calculated FRE z = (6.71 m s−1)t − (2.20 × 10−3 m s−2)t2 and 0.0°C thermal bias], and (d) XBT-4 [newly calculated FRE z = (6.64 m s−1)t − (2.01 × 10−3 m s−2)t2 and 0.0°C thermal bias]. S: Sippican FRECs, H95: H95 FRECs, and N: newly calculated FRECs.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
As in Fig. 12, but for the second CTD cast for (a) XBT-1 [newly calculated FRE z = (6.66 m s−1)t − (1.94 × 10−3 m s−2)t2 and 0.00°C thermal bias], (b) XBT-2 [newly calculated FRE z = (6.85 m s−1)t − (1.62 × 10−3 m s−2)t2 and 0.07°C thermal bias], (c) XBT-3 [newly calculated FRE z = (6.80 m s−1)t − (1.25 × 10−3 m s−2)t2 and 0.04°C thermal bias], and (d) XBT-4 [newly calculated FRE z = (6.76 m s−1)t − (2.69 × 10−3 m s−2)t2 and 0.01°C thermal bias]. D: depth (m), S: Sippican FRECs, H95: H95 FRECs, N: newly calculated FRECs.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Recalculated FRECs for all XBT–CTD pairs for (a) BB08, (b) AS08, (c) AS09 (values in box are FRECs from comparison with first CTD casts only), and (d) BB09. Ellipses enclose 95% confidence interval (two standard deviations from mean). For AS09 (closed circles), XBT vs first CTD cast (solid ellipse), XBTD vs CTD cast (open circles), and all XBT–CTD pairs (dashed ellipse) are shown.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
As in Fig. 14, but for XCTD–CTD pairs.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Difference between initial velocity model depth and terminal velocity model depth for the AS09 cruise mean FRECs (from first CTD cast comparisons only). The y-axis depths are calculated from the initial velocity case where initial velocity is 6.65 m s−1 and mean deceleration is 1.71 × 10−3 m s−2. For the terminal velocity case, initial velocity is 6.75 m s−1 and mean deceleration is 2.69 × 10−3 m s−2.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
Mean temperature anomalies (vs WOA05 monthly climatologies) for all XBTs from the cruise using H95 FRECs (solid black with diamonds), for all CTDs from the cruise (gray with crosses), and for all XBTs from the cruise using mean cruise FRECs (dashed black with circles): (a) BB08, (b) AS08, (c) AS09 (FRECs from comparison with first CTD casts only), and (d) BB09.
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
As in Fig. 17, but for XCTDs and TSK original FRECs (solid black with diamonds).
Citation: Journal of Atmospheric and Oceanic Technology 28, 2; 10.1175/2010JTECHO784.1
General cruise and CTD details for four cruises included in this study.
XBT–XCTD instrument details for four cruises included in this study.
Simultaneous CTD–XBT–XCTD drops from four cruises included in this study. XBT–CTD and XCTD–CTD pairs not used were discarded because of thermal bias >0.10°C. Numbers in parentheses are compared with the first CTD cast only.
Recalculated XBT mean FRECs and temperature biases for each cruise. First row gives H95 values for comparison. AS091+2 uses XBT comparisons with both the first and second CTD cast. AS091 uses comparisons with the first CTD cast only.
Recalculated XCTD mean FRECs and temperature biases for each cruise. First row gives default TSK values for comparison. AS091+2 uses XCTD comparisons with both first and second CTD cast. AS091 uses comparisons with first CTD cast only.
Standard depths and depth intervals used to calculate temperature anomalies. The intervals include all depths ≥ the first depth shown in column 3, and < second depth shown in column 3.
