Pressure, temperature, and conductivity measurements and associated time information are reported by Sea-Wing gliders. In addition, a Global Positioning System (GPS) fix and time stamp is obtained when the glider starts to dive or reaches the sea surface from underwater. A precise duration calculation often applies the UNIX epoch, which is the number of seconds that have elapsed since 1 January 1970 (midnight UTC/GMT). Therefore, all the date and time information for both CTD measurements and GPS fixes are converted into the UNIX epoch time before processing.

Because sea water salinity is computed from the conductivity, temperature, and pressure measured by a GPCTD sensor on the Sea-Wing glider, it is necessary to detect and exclude abnormal conductivity induced by the behavior of the glider or biofouling on the CTD sensor. When a glider starts to dive or ends its ascending profile, the CTD sensor mounted may be exposed to the air and record abnormal conductivity data. Three QC tests are conducted to detect erroneous conductivity measurements.

(1) Global range test

The global range test is conducted to detect erroneous conductivity values out of the range of the measurement range of the conductivity sensor; i.e., 0−6 S/m. If any conductivity value fails this test, the conductivity value and its corresponding temperature value are flagged as bad data (“4”) and excluded from the further calculation of salinity.

(2) Spike test

Prior to the spike test, the descent and ascent phases of a glider cycle are split into a downcast and upcast. The spike test does not consider differences in pressure but assumes a sampling that adequately reproduces changes in conductivity with pressure. The conductivity value $C\left( i \right)$ is flagged as bad if not previously flagged and

where $C$ is the conductivity and i is the start-to-end array index of the profile, K = 0.15 S/m (Z(i) < 500×10⁴ Pa) or K = 0.02 S/m (Z(i) ≥ 500 ×10⁴ Pa), and Z is the pressure.

(3) Running standard-deviation test

The running standard-deviation algorithm is taken from the United States IOOS Glider DAC QC manual. The values of the running average (Cave(i)) and standard deviation (Cstd(i)) over nine consecutive points (if not previously flagged as bad) are computed for each i = 4 to N − 3 (where N is the total number of points in a profile). The preceding and succeeding points are not used in the calculation if the time interval between adjacent points is greater than 30 s or the depth interval is greater than 5×10⁴ Pa. For the first (last) four points of the time series, the average and standard deviation are computed as for the fifth (N−4th) value.

A conductivity value should be flagged as bad if not previously flagged and both $\left| {C\left( i \right) - Cave\left( k \right)} \right| > 2.2 \times Cstd\left( i \right)$ and $| C $$\left( i \right) -Cave\left( k \right) | > 0.001$ S/m (the assumed approximate minimum resolution of the GPCTD conductivity measurement).

A thermal lag correction should be applied prior to the QC of the glider observations. A Matlab script from the SOCIB Glider toolbox is employed for the thermal lag correction of Sea-Wing gliders installed with a GPCTD sensor. This script adopts the approach developed by Lueck and Picklo (1990). They expressed the conductivity correction (${C_T}$) as

where $n$ is the sample index, $T$ is the temperature, and $\gamma $ is the sensitivity of conductivity to temperature given by the manufacturer. The coefficients $a$ and $b$ are given as

where ${f_n}$ is the Nyquist sampling frequency and $\alpha $ and $\tau $ are respectively the amplitude of the error and time constant. Both $\alpha $ and $\tau $ depend on the flow speed through the conductivity cell. On the basis of conventional CTD methodology, in which the flow speed is constant because it is controlled manually in a CTD operation, Morison et al. (1994) suggested $\alpha $ and $\tau $ be expressed as

where $V$ is the average velocity (having units of m/s) through the conductivity cell. Considering the variable speed of the glider, Garau et al. (2011) gave the above two equations as

where the subscripts $o\;{\rm{and}}\;s$ respectively indicate the offsets and slopes. The determination of the parameters ${\alpha _o},{a_s},{\tau _o},{\rm{and}}\;{\tau _s}$ is critical in the thermal lag correction. On the basis of the hypothesis that the downcast and upcast CTD profiles measure the same water mass (assuming a low horizontal advection), Garau et al. (2011) proposed a practical method of determining those parameters by minimizing an objective function that measures the area between two T–S curves from the sequent downcast and upcast of a glider. After correction of the thermal lag, salinity is calculated from conductivity, temperature, and pressure measurements using state equations (UNESCO, 1981).

Conductivity is a strong function of temperature as mentioned above, and an increasing mismatch between the temperature in the conductivity cell and ambient water therefore leads to a remarkable salinity error. To illustrate the thermal lag effect in different water columns, we selected three profiles (downcast and upcast) recorded by GPCTD sensors on two Sea-Wing gliders (Fig. 3). The downcast and upcast of each profile were observed within 3 km spatially and 4 h temporally. Figures 3a−c presents observations obtained by Glider 1000J003 operating in the SCS on 5 July 2016 under conditions of a relatively weak thermocline (the average temperature gradient was 0.09°C/m between 20×10⁴ and 80×10⁴ Pa) and shallow mixed layer depth (MLD) of ~20×10⁴ Pa. No thermal lag effect is evident, and the salinity difference between the downcast and upcast is only ~0.05 between 60×10⁴ and 180×10⁴ Pa. Figures 3d−f presents observations obtained by the same glider except that the profile was observed in the northern SCS on 8 May 2015. In this case, the thermocline is stronger with an average temperature gradient of about 0.13°C/m in the range of 20×10⁴−80×10⁴ Pa. A salinity difference between the downcast and upcast is evident above a depth of 200×10⁴ Pa, with the difference being a maximum of ~0.35 around a depth of 50×10⁴ Pa (Fig. 3e). The salinities from the downcast are higher than those from the upcast between 30×10⁴ and 200×10⁴ Pa. This appreciable salinity difference is obviously induced by the thermal lag effect and larger temperature gradients when the glider crosses the thermocline. Using the Matlab script from the SOCIB Glider toolbox, the thermal lag was corrected with an initial guess for $\alpha $ and $\tau $ of 0.067 7 and 11.143 1, respectively. Here, an estimated constant flow rate of ~0.486 7 m/s ($V$) from reported Sea-Bird GPCTD specifications is applied. The correction effect is evident for the downcast around depths of 40×10⁴ to 160×10⁴ Pa in the water column, where the salinities are corrected by as much as about −0.3 (Fig. 3e), which is equivalent to the result reported by Garau et al. (2011). In the case of a relatively weak thermocline (Fig. 3a), the thermal lag correction for the downcast is much smaller than that in the case of the strong thermocline, with the maximum correction being only about −0.05 at a depth of 70×10⁴ Pa. The last case is that of Glider 1000K003 located east of the Luzon Strait (near 19.28°N and 122.58°E) on 10 October 2016 (Figs 3g−i). The temperature gradient is only 0.04°C/m between 20×10⁴ and 80×10⁴ Pa while the MLD is thick (~80×10⁴ Pa). The thermal lag effect is almost negligible, such that the downcast and upcast salinities coincide well. The thermal lag correction across a weak thermocline is also negligible in this case.

Statistically, below the mixed layer, the downcast salinities after thermal lag correction are lower than the raw salinities directly computed from the reported conductivities (Fig. 4). In particular, the amplitude of the correction can be larger than 0.1 at water depths of 50×10⁴ −60×10⁴ Pa with strong temperature gradients. In contrast, the upcast salinities after thermal lag correction are generally higher than the raw salinities throughout the water column, but the amplitude of the correction across a strong temperature gradient is much smaller than that for the downcast. The reason why the thermal lag effect is more remarkable for the downcast is not clear and requires further investigation.

Because the underwater glider has a mission schematic and CTD sensor similar to those of the Argo profiling float, the real-time QC tests being applied to Argo can also be adopted for gliders; e.g., the United States IOOS Glider data assembly center (DAC) has developed QC tests referring to Argo (U.S. Integrated Ocean Observing System, 2016). In the real-time QC of Argo CTD data, about 16 tests are automatically conducted by computers, including tests for the profile location, date and time, drifting speed, density inversion, stuck values, global/regional range, deepest pressure, spikes, and gradients of temperature and salinity profiles (Wong et al., 2019). It is worth noting that a climatological test strongly recommended by the glider community has not yet been adopted in Argo real-time QC, probably because delayed-mode QC methods (Wong et al., 2003; Böhme and Send, 2005; Owens and Wong, 2009) have been adopted to calibrate Argo salinity profiles using a global high quality and high-resolution hydrographic data set. However, in our work, when we develop a real-time QC tool for Sea-Wing gliders, a climatological test is considered together with Argo-equivalent QC tests.

(1) Date test

The date test requires that the Julian day (JULD) of a glider downcast/upcast profile be later than 1 January 2010 and earlier than the current date of the check (in UTC time). If JULD denotes the number of days that have elapsed since 1 January 1970, then the date of a glider profile fails the test when JULD < 14 610 or JULD > UTC date of the test. The date of the profile is flagged as bad data (“4”) and none of the data from the profile are used.

(2) Position test

First, the observation latitude and longitude of a glider profile should be between −90° and 90° and between −180° and 180° respectively. If either the latitude or longitude fails this test, the profile position is flagged as bad data and none of the data from the profile are used.

Second, the profile position should be located in an ocean. We make use of the global 5-min bathymetry data set (ETOPO5/TerrainBase), which can be downloaded from http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NGDC/.ETOPO5/datasetdatafiles.html. If a position cannot be located in an ocean, the profile is flagged as bad data.

(3) Pressure test

All pressure measurements in seawater should be larger than 0 Pa. If any pressure fails this test, the pressure and its corresponding temperature and salinity are flagged as bad data. In addition, if we know the preprogrammed maximum profiling depth (DEEPEST_PRES) of an underwater glider, a deepest-pressure test can be conducted as no pressure measurement of a profile should be greater than 1.1 × DEEPEST_PRES.

(4) Global range test

A gross filter is applied to observations of temperature and salinity. The ranges need to accommodate all expected extremes that may occur in the oceans; i.e., temperatures in the range of −2.5 to 40.0°C and salinity in the range of 0 to 41.

(5) Stuck profile test

The stuck profile test looks for measurements of temperature and salinity in a profile being identical. Each point in a profile is flagged as bad if the difference between the minimum and maximum values on the profile is less than the resolution of the CTD sensor; i.e., max(T(i)) − min(T(i)) < 0.001°C and max(S(i)) − min(S(i)) < 0.001, where T and S are respectively the temperature and salinity, and i is the start-to-end array index of the profile.

(6) Spike test

The spike test uses the same algorithm as that used for conductivity; i.e., Eq. (1).

For temperature (T(i)):

temp_flag(i) = 4 if not previously flagged and

where K = 6°C (Z(i) < 500×10⁴ Pa) or K = 2°C (Z(i) ≥ 500×10⁴ Pa) and Z is the pressure.

For salinity (S(i)):

salt_flag(i) = 4 if not previously flagged and

where K = 1.0 (Z(i) < 500×10⁴ Pa) or K = 0.5 (Z(i) ≥ 500×10⁴ Pa).

(7) Gradient test

The gradient test is failed when the difference between vertically adjacent measurements is too great. The test does not consider differences in pressure but assumes a sampling that adequately reproduces changes in temperature and salinity with pressure. The algorithm from the United States IOOS Glider DAC QC manual (U.S. Integrated Ocean Observing System, 2016) is adopted here.

For temperature:

temp_flag(i) = 4 and temp_flag(i+1) = 4 if not previously flagged and

where K = 2°C/10⁴ Pa (Z(i+1) ≤ 5×10⁴ Pa), K = 8°C/10⁴ Pa (5×10⁴ Pa < Z(i+1) ≤ 500×10⁴ Pa), K = 2°C/10⁴ Pa (Z(i+1) > 500×10⁴ Pa).

For salinity:

salt_flag(i) = 4 and salt_flag(i+1) = 4 if not previously flagged and

where K = 0.3/10⁴ Pa (Z(i+1) ≤ 5×10⁴ Pa), K = 1.7/×10⁴ Pa (5×10⁴ Pa < Z(i+1) ≤ 500×10⁴ Pa), K = 0.15/10⁴ Pa (Z(i+1) > 500×10⁴ Pa).

(8) Running standard-deviation test

The running standard-deviation test employs the same algorithm as that used for conductivity in Section 3.2.

For temperature:

temp_flag(i) = 4 if not previously flagged and both $\left| {T\left( i \right) - Tave\left( k \right)} \right| > 2.2 \times Tstd\left( i \right)$ and $\left| {T\left( i \right) - Tave\left( k \right)} \right| > 0.001$ (temperature resolution of the GPCTD).

For salinity:

salt_flag(i) = 4 if not previously flagged and both $| S\left( i \right) -$$ Save\left( k \right)| > 2.2 \times Sstd\left( i \right)$ and $\left| {S\left( i \right) - Save\left( k \right)} \right| > 0.001$ (salinity resolution of the GPCTD).

(9) Racape’s spike test

A new spike test is based on the method presented by Racape et al. (2018) at the 19^th meeting of the Argo data management team (San Diego, U.S.A., December 2018) and is expected to be applied to Argo real-time QC in the future. In the method, a five-point moving median is suggested and computed along the entire profile (while the median value is computed if there are fewer than five points). If the difference between the observed value and its associated moving median is greater than a given standard deviation, the value is flagged as bad data (“4”). The thresholds of the temperature and salinity standard deviations depend on depth and have spatiotemporal variability. One can compute a global-ocean monthly temperature and salinity standard deviation climatology using the WOA or other datasets. We here use thresholds similar to those given by Racape et al. (2018) as shown in Table 1. Figure 5 shows an example of the test for a given salinity profile. Two successive salinity anomalies around a depth of 500×10⁴ Pa and three at depths between 700×10⁴ and 800×10⁴ Pa are defined manually prior to testing. Results show that Racape’s spike test screened the former two successive anomalies successfully but failed to screen the latter three successive anomalies. The new spike test is thus limited and can detect no more than two successive spikes efficiently.

(10) Density inversion test

Before the density inversion test, the potential density is computed using the Matlab seawater toolbox (http://www.cmar.csiro.au/datacentre/ext_docs/seawater.htm). From top to bottom, if the potential density calculated at the greater pressure Z(i+1) is less than that calculated at the lesser pressure Z(i) by more than 0.03 kg/m³, both the temperature and salinity values at Z(i) and Z(i+1) are flagged as bad data.

(11) Vertical velocity test

Figure 2 shows that the vertical speed of a Sea-Wing glider is no lower than 0.1 m/s on average. We define 0.03 m/s as the threshold of vertical velocity, and any pressure, temperature, and salinity measurements excluding data shallower than 10×10⁴ Pa and 10×10⁴ Pa shallower than the maximum profiling depth should be flagged as bad data if the calculated vertical velocity is less than 0.03 m/s. This test ensures that observations made by a Sea-Wing glider are obtained during a period of good behavior and pitch change of the glider.

(12) Climatological test

A climatological test is strongly recommended for the real-time QC of gliders because a sensor on a glider may drift several months after the glider’s deployment. This sensor drift usually results in a systematic error in the temperature or salinity profile that is difficult to detect in Argo-equivalent QC tests. A good climatology data set can be used to visually inspect the quality of temperature and salinity profiles and detect potential sensor drift. We here choose the historical hydrographic data set maintained by the Coriolis data center (IFREMER) as the climatology data set that we will apply in the glider climatological test. Each shipboard CTD profile contained in the data set has been visually checked by the operator at the Coriolis data center. The data set (named the DMQC_Argo CTD dataset) is not publicly available and can only be used in Argo delayed-mode QC. In addition, considering the many gaps, especially in the Southern Ocean (Fig. 6), we downloaded the WOA2018 climatology (Garcia et al., 2019) as an alternative to the DMQC_Argo CTD dataset. However, a global climatology data set usually has many profiles, which reduces the search speed when we conduct a climatological test for profiles one by one. We therefore separated both the DMQC_Argo CTD and WOA18 data sets into many small boxes (10° × 10°), which is expected to accelerate our data search.

The temperature/salinity mean and standard deviation are calculated as functions of the standard depth for the DMQC_Argo CTD data set using all the temperature/salinity profiles in each box, whereas existing standard deviations in the WOA18 are directly used. In the climatological test for our glider, according to the GPS fix of a downcast/upcast profile, a corresponding box is searched for either from the DMQC_Argo CTD or WOA18. Both the temperature and salinity standard-deviation profiles are linearly interpolated to the glider’s vertical level. The glider-observed profile and mean climatological profile are then compared. If the difference between the two profiles is larger than n_std × Qstd(i), then the corresponding value should be flagged as doubtable (‘3’), where Qstd(i) is the temperature or salinity standard deviation from the DMQC_Argo_CTD or WOA18 that we have interpolated to the glider’s level and n_std is the multiple factor of the standard deviation that gives the threshold. A robust choice of n_std is expected to accommodate seasonal and long-term ocean variability on a basin scale. The selection of n_std should therefore be made cautiously, which requires the local QC operator to know the regional ocean variability. According to the United States Navy’s standard monthly ocean temperature and salinity climatology (GDEM), n_std = 5 was previously used for the United States IOOS Glider DAC, but there were too many cases in which this test was failed even though the temperature and salinity were apparently good (U.S. Integrated Ocean Observing System, 2016). In our work, a larger threshold in the range of 6 to 8 is recommended.

Figure 7 presents an example of the climatological test using temperature and salinity profiles obtained from an Argo profiling float (WMO number: 2902581; cycle number: 93). We did not use data from Sea-Wing gliders because we have not found a profile from the existing glider data set that both contains sensor drift and has good shape. It is clearly seen that the salinity profile of the 93^th cycle has a systematic offset against the other profiles (Fig. 7a), which is probably due to biofouling or other technical problems. The entire temperature profile falls into the climatological standard-deviation envelop with n_std = 6 (Fig. 7c), while part of the salinity data fails the test between 400×10⁴ and 2 000×10⁴ Pa, suggesting that the salinity data from this float contain a positive sensor drift or offset.

After correcting for thermal lag and conducting the 12 proposed real-time QC tests, the data are clearer and more consistent between downcast and upcast profiles than the raw data. However, mismatches between the downcast and upcast profiles, especially across the thermocline, are not completely eliminated (Fig. 8). The corrected temperature data in the downcast profile tend to be lower than those in the upcast profile. Conversely, the corrected salinity data in the downcast profile are higher than those in the upcast profile. A simple average taken between the downcast and upcast profiles thus seems to be more reasonable if we consider that the two profiles should measure the same water mass. Meanwhile, even large spikes should have been removed by the two spike tests in Section 3.4 and yet small hooks are found in both the temperature and salinity profiles (not shown). To remove these hooks, a moving (five-point) mean filter is strongly suggested before averaging. Afterward, both the corrected downcast and upcast temperature/salinity profiles are first linearly interpolated to the same vertical levels. The two interpolated profiles are then averaged into one single profile. The effect of the moving mean filter and averaging is seen in Fig. 8 (blue lines). In order to illustrate the amplitude of the salinity difference between post-processed and corresponding corrected downcast/upcast profiles, we selected all observations (1 566 profiles in total) from three gliders (1000J001−003) that operated in the SCS. It can be seen from Fig. 9 that the mean salinity differences between post-processed and corrected downcast are almost within ±0.1. The most notable differences are found at depths of 40×10⁴−60×10⁴ Pa(with the maximum standard deviation being as high as 0.08 for Glider 1000J002), where temperature gradients are strongest. These differences are negligible below 150×10⁴ Pa. The upcast profiles have the similar post-processed−corrected salinity differences as the downcast profiles but show an inverse distribution in vertical (not shown)