Objective mapping of Argo data in the Weddell Gyre

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availability, primarily along the Prime Meridian. The aim of this paper is to provide a dataset of the upper water column properties of the entire Weddell Gyre. Objective mapping was applied to Argo float data in order to produce spatially gridded, time composite maps of temperature and salinity for fixed pressure levels ranging from 50 to 2000 dbar, as well as temperature, salinity and pressure at the level of the subsurface temperature maximum. While the data are currently too limited to incorporate time into the gridded structure, the data are extensive enough to produce maps of the entire region across three time composite periods (2002-2005, 2006-2009 and 2010-2013), which can be used to determine how representative conclusions drawn from data collected along general RV transect lines are on a gyre scale perspective. The 15 work presented here represents the technical prerequisite in addressing climatological research questions in forthcoming studies. These data sets are available in netCDF format at doi:10.1594/PANGAEA.842876.

Introduction
The Weddell Gyre provides an important link between the upper ocean and the ocean 20 interior through the formation of Weddell Sea Deep Water (WSDW) and Weddell Sea Bottom Water (WSBW). WSDW in particular contributes significantly to Antarctic Bottom Water; a prominent water mass present throughout much of the abyssal global ocean (Orsi et al., 1999;Johnson, 2008). As such, the Weddell Gyre acts as a buffer through its role in transferring heat into the deep ocean; potentially playing a key role 1987; Fahrbach et al., 1994Fahrbach et al., , 1995Fahrbach et al., , 2011. A schematic showing the basic Weddell Gyre circulation overlying a map of the bathymetry is shown in Fig. 1.
It has been well documented that the global ocean is warming (Lyman et al., 2010;Levitus et al., 2012;Abraham et al., 2013). Furthermore, observations show a warming trend in the upper parts of the CDW (Boning et al., 2008;Gille, 2008) as well as 15 in AABW within the Atlantic Ocean (Purkey and Johnson, 2013;Couldrey et al., 2013;Azaneu et al., 2013). Within the Weddell Gyre, a general increase in potential temperature of the WSDW and WSBW from the 1980s until 2008 has been observed, along with a warming of the entire water column over 24 years . It therefore stands to reason that the key water mass that links the above mentioned 20 water masses may also be warming. However, WDW is renowned for being subject to significant variation from year to year (Robertson et al., 2002;Fahrbach et al., 2011), complicating the issue as to whether or not long-term change is occurring.
To date, the literature focusing on Weddell Gyre hydrography has been largely based on observations from repeat hydrographic sections -primarily collected during various -influencing the relatively high frequency fluctuations of observed WDW properties.
In addition to repeat hydrographic sections and moorings throughout the Weddell Gyre, Argo floats have been deployed in the region since 2000. Argo is a global array of over 3500 free-drifting profiling floats that measure the temperature and salinity of the upper 2000 m of the ocean, allowing for continuous monitoring of the global upper 10 ocean. While in the major ocean basins the data are abundant enough to provide a relatively uniform distribution of data throughout, the deployment of Argo floats at high latitudes has been considerably more limited, especially prior to 2007. This is due to the risk of damage to floats resulting from the seasonal presence of sea ice; preventing the float from surfacing or converging around the float while it is at the surface transmit- 15 ting data to satellite, thus crushing and damaging the float. A sea-ice sensing algorithm was introduced to floats after 2007  whereby floats would "sense" the likelihood of sea-ice at the surface, and may subsequently temporarily abort mission to surface, storing the hydrographic data until the next opportunity to surface arises. The location of the float at (1) the last profile prior to entering the sea-ice zone, and (2) the 20 first profile upon exiting the sea-ice zone, are linearly interpolated in order to provide a rough guess of the float location for the profiles that took place under the sea-ice. Such profiles can be seen in particular in Fig. 2d. There are symbols distributed along straight lines; these represent the linearly interpolated location estimates of stored profile stations while the float is under ice. 25 There are now over 10 years of Argo float data available for the entire Weddell Gyre region, spanning from December 2001 to present, which can be used to determine the spatial variation of upper water column properties throughout the gyre. However, due to the irregular nature of the free-drifting profiling float, both in a spatial and temporal ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre K context, there are significant challenges regarding the utilization of these data in the creation of statistically robust gridded datasets. One common method in dealing with profile data is the application of objective mapping; an adapted form of kriging first developed in application to oceanography by Bretherton et al. (1976), though a similar method was previously applied in a meteorological context (Gandin, 1965). The tech- 5 nique is based on the Gauss-Markov Theorem and provides a point-wise estimate of the interpolated field; this estimate is linear and unbiased and is based on the minimization of the expected interpolation error (i.e. is optimal in the least squares sense; Gandin, 1965;McIntosh, 1990). The method also provides a map of error variance which takes into account the spatial distribution of the data used. 10 The objective mapping method has been implemented for a number of studies. Wong et al. (2003) and Böhme and Send (2005) have applied the method in a twostage procedure in order to calibrate float profile salinity data, while Rabe et al. (2011) mapped Arctic observation data in order to determine changes in freshwater content. On a global scale, objective mapping has been used to provide monthly hydrographic 15 fields for the World Ocean Atlas (Chang et al., 2009) and to determine warming of the global upper ocean (Lyman et al., 2010;Lyman and Johnson, 2008). The dynamic nature of the major ocean basins and the relatively sensitive salinity investigations require temporally and spatially dense data in order to apply objective mapping at suitable spatial and temporal correlation length scales. The studies described above were feasible 20 as there is a significantly higher volume of data available for the lower and intermediate latitudes of the ocean than at high latitudes. However, the limited volume of data at high latitudes is such that when objective mapping has been applied to float data on a global scale, regions south of ∼ 50-60 • S are poorly represented in the mapping process and are typically the primary cause of discrepancies (e.g. Roemmich and Gilson, 2009;von 25 Schuckmann and Le Traon, 2011;Chang et al., 2009). The aim of this paper is to provide a spatially gridded dataset of the upper water column properties with particular focus on the entire Weddell Gyre. We describe the method followed in order to objectively map the irregular Argo float profile data 513 ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre onto regularly gridded fields, excluding regions beyond the Weddell Gyre boundaries. Associated mapping errors are also provided. While spatially gridded, the resulting mapped fields represent time composites of three separate time periods (2002-2005, 2006-2009 and 2010-2013), since the data are currently too limited to incorporate both a spatial and temporal averaging scheme.  an ice-sensing algorithm that allows floats to abort the present mission to surface if the presence of sea-ice is predicted at the surface Fig. 3). The majority of profiles have a vertical limit of 2000 dbar, although there are more than 1500 profiles that are limited to 1000 dbar (about 75 % of these profiles are actually located north of the gyre boundary and most likely occur due to the complex bottom bathymetry of the 20 region. Some of these "shallow" profiles within close proximity to Maud Rise may also be explained by bottom bathymetry). Data are filtered according to their corresponding quality flags; only those with a quality flag of 1 are used, which indicates that the data have passed all quality control tests and that the "adjusted value is statistically consistent" (for more information about the quality control procedure of Argo floats, refer 25 to the quality control manual at www.argodatamgt.org). Additionally, any data points 514 ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre with increasing sensor drift. Delayed mode processing subjects all float profiles to detailed scrutiny, by comparison with historical data (Owens and Wong, 2009), providing corrected adjusted values while assigning each value with a quality flag. Conservative Temperature, Absolute Salinity and potential density are determined from the in-situ temperature, practical salinity and pressure variables in the profile data, 10 in accordance with TEOS-10 (IOC et al., 2010). Conservative Temperature is more representative of the "heat content" of seawater in comparison to potential temperature (McDougall and Barker, 2011). The profile data are linearly interpolated onto 41 dbar levels, ranging from 50 to 2000 dbar. The pressure levels used are shown in Table 1. Objective mapping is applied to the entire dataset spanning from December 2001 to 15 March 2013, as well as to 3 sub-sets, where the data are split according to the follow-

Sub-surface temperature maximum
In addition to the temperature and salinity maps of the 41 standardized pressure levels to which the profile data are interpolated, maps of temperature, salinity and pressure are also determined at the level of the sub-surface temperature maximum. Examples of typical Temperature-Pressure profiles from Argo float data within the Weddell Gyre are 25 shown in Fig. 5. The sub-surface temperature maxima are clearly marked. There are two reasons for providing the sub-surface temperature maximum. Firstly, it represents the core of incoming Circumpolar Deep Water, which is the main source water feeding 515 the core of warm water from the Antarctic Circumpolar Current meets the relatively cold subsurface water of the Weddell Gyre . Thus, the sub-surface temperature maximum is used to aptly define the latitude at which the meridional temperature gradients are the highest -which is the definition of the northern boundary of the Weddell Gyre in this study. The sub-surface temperature maximum is determined by taking the sum of the z scores of temperature and pressure. The z score assigns "scores" to data points based on their deviation from the mean. Using z scores instead of the standard deviations (from which the z scores are calculated) allows for the direct consideration of standard deviations from two different variables; here we seek the warmest temperature at the deepest depth, in order to ensure the sub-surface temper-15 ature maximum is selected rather than, for example, the summer surface water. The index of the sum of z scores with the smallest magnitude then represents the level of the sub-surface temperature minimum (i.e. the coldest water at the shallowest depth). The maximum sub-surface temperature can then be determined as the maximum temperature below the minimum. This method finds the deepest temperature maximum, 20 thus taking into account seasonal surface warming.

Approach to objective mapping
Objective mapping was applied to Argo float data in order to produce spatially gridded fields of temperature and salinity for the upper ocean in the Weddell Gyre region. One requirement of objective mapping is to have knowledge of the mean field, x , which, 25 due to the irregular nature of the Argo array, presents a challenge and is the very motivation for objective mapping in the first place. Many studies involve the decomposition of measured fields into large and small scale components, where the subsequent large-516 ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre  Böhme and Send (2005) and Chang et al. (2009). Other studies provide an estimate of the mean (first guess) field using model output data, or climatology fields, such as in Hadfield et al. (2007). For the examples listed above, the mapping method is applied in regions where the hydrography is highly variable, and data are spatially and temporally abundant. Thus, the small-scale signal 10 is essential in resolving small-scale features in both a spatial and temporal context. By comparison, hydrography in the sub-surface Weddell Gyre is relatively invariant, and the volume of available data is considerably smaller, rendering such high-resolution mapped field variables unfeasible. There is always a compromise regarding the degree of detail achievable in a spatial context vs. a time context. In this study, the aim is to 15 provide a broad outlook on the properties across the entire Weddell Gyre. Therefore a slightly different approach is chosen here. Firstly, rather than incorporate a temporal separation factor into the equation which assigns a weight to each data point, which would lead to a spatially and temporally regular gridded dataset, the data is split into sub-sets of time periods, so that the resulting maps represent spatially gridded time 20 composites of the field variables for these time periods. This is due to the sparsity of the dataset. Secondly, the mapping process is implemented in a two-step procedure, allowing for a step-by-step improvement of the mean field estimate. In the first stage, the first guess field (in other words, the expected true value of the variable at the grid point location) is the zonal mean, calculated from all floats binned within the ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre separation, which gives extra weight to close-by data in regions where the data are abundant. In regions of sparse data density, the objective estimate reverts back to the mean guess field and the corresponding mapping error is large. This 2-stage method reduces the possibility for errors by providing an improved estimate of the first guess field, which leads to a general reduction in the magnitude of the signal variance, s 2 , 5 by which the covariance matrices are scaled by. The error variance is calculated from the second stage of the mapping only.

Objective mapping
For each pressure surface, the corresponding temperature and salinity data are extracted from the vertically linearly interpolated float profiles (for further details refer 10 to Sect. 2.1). Thus, only vertically interpolated data at the pressure surface to be mapped to are included in the mapping. The extracted data points are objectively mapped onto a regular 1 This results in grid cells of approximately 110 km × 110 km at 65 • S; roughly the central axis of the gyre. For each grid point, N representative profiles (x) are selected for the mapping procedure (for details 15 regarding the selection procedure, refer to Sect. 2.5). The objective estimate of the variable, X g1 , at the grid point g is given by Eq. (1a) for stage 1 and Eq. (1b) for stage 2. The zonal mean, x z , is the first guess field in stage 1 while the objective estimate from stage 1 becomes the first guess field used in stage 2. The term ω denotes the weighting matrix (Wong et al., 2003).
Each profile x is weighted by the horizontal distance D and the fractional distance F in potential vorticity: (1) between the grid point location g and the profile location i , and (2) between the neighbouring N profile locations, i and j . Thus, the profiles are 25 not just weighted according to their distance to the grid point, but also to neighbouring 518 ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre profiles. As such, where three profiles may have the same distance to a grid point, the profile furthest apart from the neighbouring profiles will be assigned the largest weight (for example, refer to Fig. 6). The fractional distance F (Eq. 2) accounts for the cross-isobath separation between two locations. This reflects the influence of potential vorticity, and thus bathymetry (Fig. 7) and the Coriolis force (and therefore change in 5 latitude); potential vorticity strongly influences the flow patterns of water masses, which is accounted for by (Böhme and Send, 2005):  The decay scales determined by the distances D and F and their associated length scales are applied in the form of covariance functions in order to determine the weight matrix, ω (Eq. 3). The data-grid covariance (C dg ; Eq. 4) is a function of the distances between the grid point g and the profile location i while the data-data covariance (C dd ; Eq. 5) is a function of the distance between the N neighbouring profiles, i and j . Thus, 20 for every grid point, while C dg is a 1 × N vector, C dd is a N × N matrix. The covariance of the data is assumed to be Gaussian, following Böhme and Send (2005).
The covariance functions are scaled by the signal variance, s 2 (Eq. 6), which measures the squared deviations of the data from the mean field. N is the number of profiles 5 used to estimate the value at the grid point. The mean field X , is the zonal mean in the first mapping stage while the objective estimate from stage 1 becomes the mean field in the second mapping stage. A random noise signal (i.e. the noise variance), η 2 (Eq. 7), is added to the diagonal of the data-data covariance function, where x n is the variable of the profile with the smallest distance to the profile location i . This term 10 accounts for the variations between nearby data. In addition to providing an estimate of the field at locations where there are no data, objective mapping also provides an error variance of the objective estimate. This is taken from the second stage of the mapping: where the superscript T signifies the transpose of the vector C dg .

Choosing appropriate length scales (L, F ) and selecting N surrounding data points to a grid point
In stage 1 of the mapping, the length scales are L = 1000 km and φ = 0.5 while in the second mapping stage, in order to give extra weight to nearby data points, L = 500 km and φ = 0.25. Thus, a factor of 4 in the difference f /H is equivalent to a 500 km horizontal separation on the separation parameter; the decay scale used in the covariance functions (Hadfield et al., 2007). The performance of the objective mapping is sensitive to the length scales used in the correlation function. For a successful and accurate mapping of the field of variables, the applied length scales need to be larger than the 5 minimum distance between data points. Otherwise, the mapped estimate will revert to the mean first guess field used in the mapping, and the resulting mapping error will be large. In order to establish suitable length scales for the mapping, the percentage of grid points with at least 40 data points within certain distances are calculated, in a similar manner to Hadfield et al. (2007). The results are shown in Fig. 8. The mini- This value rapidly decreases for distances less than 500 km. Therefore, 1000 km is used for the large length scale in the first mapping stage and 500 km is the small length scale L used in the second mapping stage. If a temporal separation factor were to be incorporated into the decay scale for the second stage of 20 the mapping, the length scales would have to increase accordingly. The number of data points (N) used in the calculation of the field estimate was set to 40. The decay scale of the data-grid covariance function (D to the data with the large length scales of stage 1 (L = 1000 km and F = 0.5), and all corresponding data points where the decay scale was larger than 1 were filtered 25 out (i.e. only data within the e-folding scale of the covariance function were selected; D 2 ig /L 2 +F 2 ig /φ 2 < 1). Where more than 40 profiles were available within the decay scale limit, data were sub-selected by the shortest possible distance to the grid point (i.e. smallest decay scale values). At first, the mapping process was carried out for the sub-surface temperature maximum. The resulting field of conservative temperature was used to determine the northern boundary of the gyre: for each longitudinal bin, the latitude where the sub-surface temperature is more than 2 • C is masked. Following this, the latitude at which the meridional sub-surface temperature gradient is largest is defined as the position of the Wed-5 dell Front. All grid cells north of this latitude are masked in the following objective mapping processes. The mapping process is then carried out for 41 pressure surfaces, ranging from 50 to 2000 dbar.

Masking grid cells of high error variances
In addition to the mapped variables and associated mapping errors, error masks are 10 also provided corresponding to the mapping errors of conservative temperature and absolute salinity. Where a grid cell mapping error passes the masking criteria, the grid cell is represented by the number 1; all other grid cells are represented by the fill value NaN. The method of defining the masking criteria is outlined as follows. Separate histograms of temperature and salinity mapping errors are created, where the 15 grid cells are binned according to their error variances and a subsequent percentage of grid cells within each error variance bin are determined. A sample histogram (of conservative temperature at 800 dbar of the entire 11 year time composite) is shown in Fig. 9. The masking error criterion at 95 % is about 0.01 • C; all grid cells with an error variance that exceeds this value are masked and shown as slightly transparent 20 in the maps presented in Sect. 3. The masking criterion is defined by the error value which is not exceeded by 95 % of the grid cells. Any grid cell where the corresponding mapping error is larger than the masking criterion is masked (by a 1 in the masking array). This is carried out separately for each vertical level of mapped variables. There are two masks -the "temperature mask" is based on the masking criterion from the 25 temperature mapping error alone, whereas the salinity mask is based on the condition that if either temperature or salinity mapping errors exceed the corresponding masking criteria, the respective grid cell is masked (again with a 1 in the masking array). layer over the contour maps (see Sect. 3). For pressure at the level of the subsurface temperature maximum, the temperature mask is applied instead of a mask based on the pressure error map. This is because the subsurface temperature field is relatively stable, whereas the pressure is more dynamic. This is discussed further in Sect. 4.2.

10
The following section describes the format of the dataset resulting from applying objective mapping to Argo float data and provides some examples of the subsequent mapped fields of data. The pressure and conservative temperature at the level of the sub-surface temperature maximum is presented for the entire 11 year time composite. Additionally, the mapped fields of conservative temperature and absolute salinity 15 at 800 dbar are shown, along with the corresponding error variances, for the entire 11 year time composite and the three time period subsets (2002-2005, 2006-2009 and 2010-2013).

Data format: gridded fields of upper Weddell Gyre water properties
The time composite data sets of mapped field variables are provided as netCDF files; 20 one file for each available time period. The filenames and corresponding variables provided in each netCDF file are listed in Tables 2 and 3 respectively. Mapped fields of conservative temperature ( • C), absolute salinity (g kg −1 ) and potential density (kg m −3 ) are provided for 41 vertical pressure levels (listed in Table 1). Additionally, the three variables listed above, as well as pressure (dbar) at the level of the subsurface temper- detailed in the attributes of each variable, and are also detailed throughout this paper.

Sub-surface conservative temperature maximum
A typical feature in the hydrography of polar regions is the presence of a sub-surface temperature maximum, as displayed in Fig Sect. 2.6). This occurs for all contour maps presented in this paper. The boundary of the gyre to the north is clear as a sharp transition between warmer temperatures above 2 • C to the north and cooler temperatures of the gyre below 1 • C to the south. southern limb of the gyre. A double gyre structure is also suggested, where the secondary gyre occurs in the north-east sector, splitting from the main gyre at about 5 • W. The associated mapping error is relatively small, with the largest errors occurring at the gyre boundary, particularly in regions of complex bathymetry. The error is small within the gyre, even in regions of especially sparse data density (with the exception of 45-5 55 • W, 64-72 • S, where no profile floats are located within the region). This is because the temperature field is relatively stable, which results in a small signal variance field. The field of pressure at the sub-surface temperature maximum, Pr (Θmax) , Fig. 11, is less stable in comparison to Θ (Θmax) , which is why the error (Fig. 11c) is larger, again at the gyre periphery as well as along the Antarctic coast. There is also a considerable deepening of the sub-surface temperature maximum at about 65 • S, just east of the Prime Meridian, from about 200 m in the surrounding region to roughly 400 m, which occurs directly over Maud Rise (note the mapping error is relatively small in this region). The sub-surface temperature maximum is shallowest within the gyre centre, and deepest towards the gyre peripheries, demonstrating the domed structure associated with the 15 cyclonicity of the gyre. The mean meridional sub-surface temperature, Θ (Θmax) along the Prime Meridian (as extracted from the corresponding objectively mapped gridded data set) is given in Fig. 12a along with the resultant meridional temperature gradient in Fig. 12b. The large dots show the latitude at which the gradient is largest, which occurs at 56 • S (note: 20 the gradient is negative due to the south-north direction). This is the latitude used to define the northern boundary at the Prime Meridian, which corresponds with the northern boundary used in the long-term analysis of properties at the Prime Meridian in Fahrbach et al. (2011). All grid points north of this latitude are masked from the mapping process for the subsequent isobaric mapped surfaces.  Figure 14 shows the same but for absolute salinity, S A . The temperature field shows the structure of the gyre, where relatively warm water from the north enters the gyre in the southern limb (south of 60 • S) at about 30 • E and gradually cools as it circulates in a clockwise direction throughout the gyre. There is a gradual transition from relatively warm water in the south east sector of the gyre, to cooler water 5 in the western southern limb of the gyre, to even cooler water in the northern limb of the gyre. The coolest water at 800 dbar occurs in the east within the northern limb of the gyre. The cyclonic-gyre signal is less clear in the absolute salinity field (Fig. 14b).
Regardless, there is a gradual freshening from the southern limb to the northern limb of the gyre, consistent with the cooling spatial trend. Again, the associated mapping 10 errors are small, in particular in the centre of the gyre, and larger in regions of complex bathymetry at the gyre boundaries. Figure 15a-c shows the mapped conservative temperature fields at 800 dbar for data sub-sampled to the time periods 2002-2005, 2006-2009 and 2010-2013 respectively, while Fig. 15d-f shows the corresponding mapping errors. The temperature fields rep-15 resent the gyre structure with the water cooling as it transitions from the southern limb to the northern limb in a clockwise direction. While the northern boundary appears to be relatively stable, with minimal change across the three time periods, the region where warm water enters from the east varies with each time period. The warmest signal that extends furthest into the gyre (about 1 • C) occurs in 2006-2009 (Fig. 15b). 20 However, the error associated with this region ( Fig. 15e; about 10-30 • E, 62-68 • S) is relatively large, due to a considerable data gap that can be seen in Fig. 2c. There is also a large data gap and associated mapping error for 2010-2013 ( Fig. 2d and Fig. 15f respectively). Figure 16 shows the same as Fig. 15 but for absolute salinity. Again the freshest signal occurs in the northern limb. The southern limb appears to be saltier in 25 the first time period (2002)(2003)(2004)(2005), particularly in comparison to the second time period (2006)(2007)(2008)(2009). The errors in Fig. 16d

Discussion
The following Section assesses the performance of the objective mapping method (outlined in Sect. 2) in providing gridded fields of water column properties of the upper 2000 m of the entire Weddell Gyre. Certain decisions regarding the mapping method are discussed and potential implications are highlighted. Additionally, the mapping er-5 rors are carefully considered in terms of the likely causes of large error variances in certain regions. Lastly, in place of a regular grid, the profiles were objectively mapped to the locations of the profiles themselves in order to directly gauge the performance of the mapping process, by assessing the difference between the original data and the mapped product.

Objective mapping performance
Argo float data were objectively interpolated in order to provide gridded fields of water column properties of the upper 2000 m of the Weddell Gyre. By comparing the scatter-grams of the original data (e.g. Fig. 13a) to the corresponding mapped products (e.g. Fig. 13b), it is clear that the objective mapping method performs generally 15 well in producing regularly gridded fields of (i) temperature at the sub-surface temperature maximum (Fig. 10b), and (ii) of temperature and salinity at 800 dbar (e.g. Fig. 13b and Fig. 14b respectively). In addition, the associated mapping errors are relatively small throughout (e.g. Fig. 13c); less than 0.01 • C across the majority of the Weddell Gyre in Fig. 15d-f. The discernable general hydrographic features of Figs. 10-16 are 20 also to be expected; the cyclonicity of the gyre is demonstrated by the relatively cool gyre interior (e.g. Fig. 13b). Furthermore, shoaling of the sub-surface temperature maximum occurs at the centre (Fig. 11b), exhibiting the dome-like structure of the gyre as discussed by Orsi et al. (1993) and Fahrbach et al. (2011). By assessing the spatial variability of temperature across the three time periods in Fig. 15a- variability of the incoming source water, Circumpolar Deep Water, which is influenced by the variability of the Antarctic Circumpolar Current and possibly wind forcing of the Weddell Gyre Cisewski et al., 2011). Additionally, the influence of Maud Rise leads to increased spatial variability in the region; such as a deepening of the sub-surface temperature maximum in Fig. 11b and a regional cooling at 800 dbar 5 across all three time periods in Fig. 15 (although the cooling is so slight during the first time period (2002)(2003)(2004)(2005) that the contour levels in Fig. 15a fail to resolve the localised cooling). The cooling and freshening over Maud Rise at 800 dbar (Figs. 13b and 14b respectively), along with the deepening of a cooler temperature maximum, represents trapped water in a Taylor Column and shows agreement with Bersch et al. (1992), 10 Muench et al. (2001) and Leach et al. (2011). The factors discussed above could explain the variability of Warm Deep Water along the Prime Meridian as observed and discussed by Fahrbach et al. (2011). However, considerable data gaps within the eastern sector of the southern limb, especially for the latter two time periods (e.g. Fig. 2c and d), render it challenging to draw concrete observations for this region. The impor- 15 tance of establishing efforts to monitor this region is becoming increasingly recognized, due to the potential contribution of incoming deep water masses from further east on the export of Antarctic Bottom Water to the lower limb of the global oceanic overturning circulation (Meredith et al., 2000(Meredith et al., , 2014Jullion et al., 2014). There appears to be two main influences determining the magnitude of the map-20 ping error variances throughout the Weddell Gyre. The mapping error is typically large in regions of sparse data coverage (e.g. in the south-west corner of the Weddell Sea in Fig. 10c), which is especially prominent in the first time period, as shown by the large masked area in Fig. 15a (the masked areas are semi-transparent and mark regions where the mapping error is larger than 0.007 • C; see Sect. 2.6 for an expla-25 nation of the error masks). However, there are also regions of dense data coverage where the mapping errors are also relatively large (e.g. at about 60 • S, west of 45 • W, in Fig. 13c). In particular, the north-west corner of the gyre has relatively high mapping errors throughout all maps. This is due to the dynamic nature of the region. The Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | bathymetry is complex due to the presence of submerged ridges and trenches. It is also at the very periphery of the gyre where complex interaction with the Antarctic Circumpolar Current takes place (e.g. Klatt et al., 2005;Fahrbach et al., 2004Fahrbach et al., , 2011Cisewski et al., 2011). Thus, the objective mapping is poorly representative of these highly variable, complex regions. One way to improve the objective estimate of these 5 regions is to incorporate more suitable correlation length scales as well as a temporal separation factor into the decay scale in Eqs. (4) and (5), such as in Böhme and Send (2005). The correlation length scales would need to match the scale of the true field in order to adequately map these regions. Since these regions typically only occur at the very periphery of the gyre, and due to data sparsity throughout the relatively invariant 10 inner gyre, the correlation length scales are chosen to represent the large scale field of the entire gyre, as opposed to a small-scale, temporally scaled field of a smaller area of the gyre (since the mapping would be restricted to regions where there are enough data to perform the interpolation). Additionally, the incorporation of a temporal separation factor would require an increase in the correlation length scales in Eqs. (4) 15 and (5), in order to provide an adequate number of data points which exist within the efolding scale (D 2 ig /L 2 + F 2 ig /φ 2 < 1, see Sect. 2.5). 1000 km, the horizontal length scale for the first mapping stage, incorporates about 9 • in the Meridional direction. Since the gyre generally spans about 10-15 • in the Meridional direction, a larger length scale would draw on data from outside the gyre, thus reducing the quality of the mapping. 20 In order to reduce the correlation length scales as is sensibly possible in obtaining a gyre-scale view of the Weddell Gyre hydrography, while at the same time assessing variability in a temporal context, a compromise is reached by way of creating temporal composites of three time periods. Regardless, the mapping errors are relatively large in regions of sparse data coverage within the gyre across all three time periods. This is 25 most prevalent in the first time period, 2002-2005, where the mapping error (Fig. 15d) across the west and north-west sector of the gyre is masked out in Fig. 15a Fig. 2b. There are also areas of limited data coverage in the time period 2006) and in the time period 2010-March 2013 (Fig. 2d), both at about 20 • E, south of 60 • S, which lead to maximum mapping errors of 0.035 and 0.06 • C in Fig. 15e and f respectively. Thus, while steps were made to optimise the quality of the objective mapping based on the limited data available (e.g. Fig. 8), it is important to 5 assess the corresponding mapping errors when interpreting the gridded fields of data, particularly the sub-sets of the three time periods, especially due to regions of limited data availability. Furthermore, across all maps, the region of most prevalent mapping errors occurs at the northern boundary of the gyre. Where the meridional gradients of the sub-surface temperature maximum are largest defines the northern boundary of the gyre, which coincides with these regions of relatively large mapping errors. Therefore it is important to acknowledge that the definition used for the northern boundary in this study is sensitive to the associated mapping error variances in Fig. 10c. Mapping errors vary according to the corresponding pressure level. Figure 17a and b shows the vertical variation of the error mask limits (based on the 95 % error value, 15 i.e. 95 % of grid points have a smaller error than the 95 % limit; for an explanation of the error masks, see Sect. 2.6) for conservative temperature and absolute salinity respectively. While the error limits are relatively invariant below 400 dbar, there is a considerable change in shallower waters. With the exception of the time period 2002-2005, where the error limit monotonically increases in magnitude from about 200 to 50 dbar 20 for temperature, and from about 400 to less than 200 dbar for salinity, the remaining time periods show a peak in error limit at about 120-180 dbar and a relatively small minimum at about 70 dbar for temperature. Regarding salinity, the error limit more or less increases with decreasing pressure, although a peak maximum (minimum) error occurs at about 100 (70) dbar for the time period 2010-2013, and 180 (100) dbar for 25 the entire time period. This coincides with the region of Winter Water, where the peak in the error limit for temperature occurs at the approximate depth of the lower boundary (e.g. see Fig. 3 in Behrendt et al., 2011). Thus seasonal signals may have led to ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre the increase of the mapping errors in the shallower mapped surfaces, which should be taken into account when interpreting the mapped surfaces above 200 dbar. In addition to regions of dynamic hydrography and regions of low data density, a further potential factor influencing the mapped data output is linked to the selection process of N representative profiles for each grid point objective estimate. Many studies 5 incorporate a decision process whereby one third of the profiles are randomly selected from within the e-folding scale of the covariance function in Eqs. (4) and (5); (i.e. D 2 ig /L 2 + F 2 ig /φ 2 < 1), one third are selected with the smallest distance within the large correlation length scales, and the remaining third of profiles are selected with the shortest spatial and temporal separation distances (e.g. Rabe et al., 2011;Böhme and Send, 2005). This was done in order to remove potential bias by selecting nearby profiles, such as, for example, those from along repeat hydrographic sections, which are closely spaced in both distance and time. In this study, only data within the e-folding scale of stage 1 are selected, in accordance with the studies above. Where there are more than N(N = 40) profiles available, the N profiles with the smallest spatial sepa- 15 rations are simply selected. This is justified because the only data utilized comes from Argo floats, which are independent of repeat-ocean transects. Furthermore, it is a necessary compensation due to limited data availability (and thus the necessity of large correlation scales). Another source of error which must be taken into consideration concerns the winter 20 profiles that have become available since 2007, when a "sea-ice sensing" algorithm allowed for the survival of floats in regions of sea-ice cover . While these floats provide profiles that would otherwise be unavailable due to sea-ice, an important assumption has been made regarding the corresponding "under-ice" profile positions. The position of these profiles is estimated by linear interpolation between the 25 last known position of the float before it enters the sea-ice zone, and the first known position of the float upon exiting the sea-ice zone. Thus, the positions of these floats are clearly incorrect. Examples of such profiles can be seen in Fig. 2d: there are profiles that are distributed along straight lines, particularly in the south west sector of the gyre. 8,2015 Objective mapping of Argo data in the Weddell Gyre It is therefore a priority to improve the position estimates of such floats. However, such profiles within the gyre interior do not appear to increase the mapping error of the mapped surfaces, reflective of the stable, relatively invariant gyre interior. The regions where these profiles may increase the mapping error are along the Antarctic coastline where complex bathymetry, lack of available profiles, and interaction between the flow 5 of the incoming Circumpolar Deep Water and the cold, westward Antarctic coastal current also play a role in increasing the mapping error.

Mapping the sub-surface temperature maximum: two approaches compared
When mapping to the level of the sub-surface temperature maximum, there are two 10 approaches one can make. One approach is to extract the corresponding pressure, temperature and salinity values at the sub-surface temperature maximum for every float profile in the dataset and map each variable independently. This is the approach outlined in Sect. 2.2. Another approach is to extract the pressure of the sub-surface temperature maximum for each float profile and apply objective mapping to the pres- 15 sure variable alone in order to determine a regular gridded dataset of pressure at the level of the sub-surface temperature maximum. For each grid point, one then selects the N closest profiles, from which the temperature and salinity values are extracted at the pressure level provided by the mapped field previously determined. Thus, the resulting mapped fields of temperature and salinity are dependent on the mapped pres-20 sure of the sub-surface temperature maximum rather than the individual profiles themselves. Both approaches were investigated and compared for the entire time period from 2002 to March 2013. The resulting mapped field of temperature and the corresponding mapping error are shown in Fig. 10b and c respectively for the first approach, and in Fig. 18a and b respectively for the second approach. The mapped temperature 25 fields for the two approaches are similar. The differences between the two temperature maps is less than 0.2 • C throughout the Weddell Gyre, with the exception of regions at the gyre periphery where the differences can be as high as 0.4 • C (Fig. 19) Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | approach typically yields warmer values than the second approach throughout most of the region (hence the map in Fig. 19 is largely negative (blue), as it shows temperature from approach 2 w.r.t temperature from approach 1). The second approach leads to slightly larger mapping errors, in particular along the Antarctic coastline. Thus, the first approach, where the temperature, salinity and pressure of the sub-surface temperature 5 maximum are independently mapped, is the approach followed in this study. Pressure at the level of the sub-surface temperature maximum has the largest corresponding mapping errors of all mapped surfaces, despite the relatively small errors in the mapping of conservative temperature at the sub-surface temperature maximum. This is because it is subjective to allocate a specific point at which the temperature has 10 reached its maximum in many of the profiles. Although a statistical method is employed here (see Sect. 2.2), the processes that influence the position of the temperature maximum are too complex for the method to be extremely accurate, and the number of profiles are too numerous to identify each peak manually. Some profiles do not have a pronounced sub-surface temperature maximum. The peak temperature then occurs 15 with a small vertical gradient, so a small change in temperature could shift the peak temperature by 100s of meters. Thus, while the mapping of the sub-surface temperature maximum is relatively successful, caution needs to be made when considering the pressure at the level of the sub-surface temperature maximum. It is primarily for this reason that the second approach described above was not used in the mapping 20 process.

Objective Mapping to float profile locations
In addition to objectively mapping Argo float data to a grid to create a spatially regular field of data variables, the profile data were also objectively mapped to the locations of the profiles themselves, in order to assess the performance of the objective mapping 25 procedure. It is important to note that the resulting maps should not precisely match the profile data, due to the assumption of noise in the dataset ( η 2 ; Eq. 7). While the objective mapping was carried out at the level of the sub-surface temperature maxi-533 ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | mum as well as at 800 dbar, only the latter is presented here. Figure 20a shows the original profile data of conservative temperature at 800 dbar for the entire time period 2002-2013. Figure 20b shows the objectively mapped field estimate, mapped to the profile locations, while Fig. 20c shows the difference, where the mapped profile data has been subtracted from the original data (i.e. Fig. 20a minus Fig. 20b). The mapping 5 process performs well particularly within the gyre centre, where the differences for the profile locations within the gyre are less than ±0.2 • C. The differences are larger north of the gyre (mostly north of 60 • S), especially in the bathymetrically complex region west of 15 • W (i.e. approaching Drakes Passage). This is outside of the Weddell Gyre region, yet may influence the accuracy of the northern boundary of the gyre. Taking 10 into account all data points shown in Fig. 20c, 87 % of the data points have differences between the original data and the mapped data that are within ±0.2 • C (Fig. 21a). Furthermore, by considering only profiles within the gyre itself (using the northern boundary definition described in Sect. 2.2), 89 % of the mapped data points differ from the original data points by ±0.2 • C (Fig. 21b). Regarding sub-surface temperature maxi-15 mum (Fig. 22), 82 % (84 %) of the mapped data points differ to the original data by utmost ±0.2 • C for the entire data set (for only those profiles within the Weddell Gyre). Lastly, for pressure at the sub-surface temperature maximum, 77 % of the mapped data points differ from the original data points by ±100 m (Fig. 23a); this value increases to 84 % when considering just those profiles within the Weddell Gyre (Fig. 23b). Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | maps of conservative temperature and absolute salinity are provided at 41 standardized pressure levels ranging from 50 to 2000 dbar. The corresponding mapping errors are also provided. The resulting mapped fields provide a more complete as well as more detailed view of the pertinent features of the Weddell Gyre, such as the doming of the gyre centre owing to its cyclonic rotation and the associated relatively cool gyre 5 interior, than existed before. The relatively warm incoming source water at the eastern sector of the southern limb is also visible, along with the variability of water properties owing to bathymetric features such as Maud Rise. The mapping errors corresponding to the mapped field variables are relatively small, with the exception of regions where the bathymetry is complex, or where data coverage is limited. The mapping errors vary 10 with pressure, where the overall largest mapping errors coincide with the region of Winter Water, particularly within the vicinity of its lower boundary (about 120-180 dbar). In order to gauge the performance of the mapping procedure, objective mapping was also applied to the location of the float profiles themselves. The objective mapping successfully represents the Weddell Gyre in its entirety, whereby 89 % of mapped profiles within 15 the Weddell Gyre differ from the original profile values (for temperature at 800 dbar) by less than 0.2 • C. Caution should be taken in consideration of the increased error variances at the gyre periphery, in regions of limited data coverage, and due to the fact that all mapped fields are spatially gridded temporal composites. The work presented here provides the prerequisite technical component of investigations into the variabil-20 ity of Weddell Gyre water mass properties, providing further insight to the role of the Weddell Gyre in a changing climate.
ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre  , Ocean Sci., 7, 783-791, doi:10.5194/os-7-783-2011, 2011. Wong, A. P. S., Johnson, G. C., andOwens, W. B.: Delayed-mode calibration of autonomous ctd profiling float salinity data by θ-s climatology, J. Atmos. Ocean. Tech., 20, 308-318, doi:10.1175/1520-0426(2003  ESSDD 8,2015 Objective mapping of Argo data in the Weddell Gyre    Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Figure 6. In objective mapping, the profile data are weighted based on their distance D to the grid point g, as well their distance to neighbouring profiles. Thus, while profiles x 1 , x 2 and x 3 are all equally distanced from the grid point g, x 2 and x 3 are more closely spaced to each other than they are to x 1 . Thus, the weight of x 1 would be equivalent to the sum of weights for x 2 and x 3 (i.e. W (x 1 ) = W (x 2 ) + W (x 3 )). 8,2015 Objective mapping of Argo data in the Weddell Gyre