^{1}

^{*}

^{2}

^{3}

^{4}

^{1}

^{1}

^{5}

^{1}

^{2}

^{3}

^{4}

^{5}

Edited by: Katrin Schroeder, Italian National Research Council (CNR), Italy

Reviewed by: Laurent Coppola, UMR 7093 Laboratoire d’Océanographie de Villefranche (LOV), France; Dimitris Velaoras, Institute of Oceanography, Greece

This article was submitted to Physical Oceanography, a section of the journal Frontiers in Marine Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The longest time series of CTD transects available in the Mallorca and Ibiza Channels (1996–2019) are presented. These hydrographic sections have a three-monthly periodicity and allow to resolve the seasonal cycle of water mass properties. They are organized in two closed boxes allowing the use of inverse models for the calculation of absolute geostrophic transports through the Channels. These long time series allow to establish the climatological distributions of potential temperature and salinity for each season of the year as well as other relevant statistical properties such as the variance and covariance functions. The results indicate that these distributions depart from normality making the median a better statistic than the mean value for the description of climatological fields. The salinity field shows a seasonal cycle in the upper layer indicating a higher influence of the Atlantic Water during summer, decreasing through the rest of the year. The Western Intermediate Water, which is mainly formed in the North-Western Mediterranean and the Balearic Sea, is observed preferentially in the Ibiza Channel during winter and spring. This water mass is better detected using a geometry-based method instead of the traditional criterion based on predefined temperature and salinity ranges. These water masses flow preferentially southwards through the Ibiza Channel, and northwards through the Mallorca Channel, although intrusions in the opposite directions are observed. Below, the Levantine Intermediate Water shows a similar behavior, but the mass transport analyses suggest that most of this water mass recirculates with the Balearic Current along the northern slope of the Islands. Although the depth of both Channels prevents the circulation of deep waters, a small fraction of the Western Mediterranean Deep Water could overflow the sills.

The Mediterranean Sea circulation is ultimately forced by its net evaporation and the net heat loss through its surface. As a result of these deficits, the Mediterranean receives a surface current of fresh Atlantic Water (AW) through the Strait of Gibraltar and exports to the Atlantic, saltier waters as a deep current. This deep current is composed of different types of Mediterranean Waters (MWs) formed by intermediate and deep convection and mixing processes in different areas of the Eastern and Western Mediterranean Sea (EMED and WMED, respectively). The upper layer of the WMED is comprised of AW with a variable degree of modification depending on its resident time within this basin. The MWs circulating in the WMED are originated from the WMED or the EMED. The water masses formed in the WMED are the Western Intermediate Water (WIW), the Western Mediterranean Deep Water (WMDW), and the Tyrrhenian Dense Water (TDW). WIW is mainly formed in the continental shelf of the Gulf of Lions and the Balearic Sea by winter intermediate convection (

Apart from the water volume that compensates for the net evaporation, and the fraction of AW that takes part in the formation of WIW and WMDW, the rest of this water mass flows out of the WMED through the Sicily Channel. In a similar way, all the intermediate and deep waters present in the WMED finally flow out through the Strait of Gibraltar (

Position of the stations monitored from 1996 to 2019 in the frame of the CANALES, CIRBAL and RADMED projects. These stations are distributed along four sections: Mallorca South (stations C1–C10), Ibiza South (C11–C21), Ibiza North (C21–C29) and Mallorca North (C30–C37). The Mallorca South and North sections form the Mallorca Channel triangle and the Ibiza South and North form the Ibiza Channel triangle. A scheme of the upper layer circulation in the Balearic Sea, inferred from the literature and this study is also included.

The southern part of the WMED cyclonic circuit is formed by the Algerian Current. This current is 30–50 km wide and 200–400 m deep and flows eastwards along the Algerian continental slope (

The Balearic Channels, which are located between the waters flowing through the Algerian basin and those in the Liguro-Provençal area, are consequently considered as a “choke point” for the north-south water, heat and salt exchanges within the WMED (

The first attempts to establish the properties of the water masses in the Channels and their associated transports, analyzed a reduced number of oceanographic campaigns, most of them during winter or spring (

Additional works have shown that the variability at short time scales could be as large as the variability at seasonal scale and consequently longer time series would be needed (

This study examines the longest time series of CTD seasonal sections in the Balearic Channels from 1996 to 2019. It could be considered as an extension of that by

The Instituto Español de Oceanografía (IEO, Spanish Institute for Oceanography) has monitored the oceanographic conditions in the Balearic Channels since 1996 to the present with a variable periodicity and under the umbrella of different projects. The first one was named CANALES (from the Spanish word for Channels) and lasted from 1996 to 1998. The second project, called CIRBAL (Circulation in the Balearic Channels), collected data from 1999 to 2006. Finally, in the frame of the RADMED project, the Balearic Channels have been monitored from 2007 to the present (

The sampling strategies and the collected variables have changed according to the different projects. Nevertheless, during all the oceanographic campaigns, a CTD vertical profile was collected at all the stations along the four sections within the Balearic Channels (

These four hydrographic sections were sampled during 71 campaigns over 1996–2009. ^{1} and under request in Sea Data Net.

This section and the next section (“Results”) are organized following the same structure (sub-sections) to better relate and understand each specific result to the corresponding methodology and objectives. First, the normality of the temperature and salinity distributions is examined, and the mean and median values as well as the dispersion of such distributions are estimated. Secondly, the temperature and salinity covariance functions are defined and the methods used for their estimations are presented. This sub-section aims at obtaining the parameters needed for the application of Optimal Statistical Interpolation. Thirdly, the water masses (AW, WIW, LIW, and WMDW) and the criteria used to define them are described. Finally the methodology corresponding to a box inverse model is presented.

The first objective of this work is to obtain the statistical properties of the temperature and salinity fields in the Balearic Channels, which have a strong variability at seasonal scale. For this reason, all the available campaigns were distributed into four seasonal groups: winter includes surveys from January to March, spring from April to June, summer from July to September, and autumn from October to December. The total number of surveys carried out during each season of the year were: 21 for winter, 24 for spring, 13 for summer and 13 for autumn.

Each campaign corresponding to a particular season and year shows different temperature and salinity values because of the natural variability of the sea and the ocean-atmosphere interaction. All the temperature and salinity data corresponding to the same season of the year and the same pressure level are distributed around a certain value. Using the usual terminology in descriptive statistics, such a value is named the central tendency of the distribution (

Histograms showing the salinity and potential temperature distribution for the four seasons of the year at the 50 dbar pressure level. A normal distribution was fitted to each distribution (solid line).

Besides the central tendency, the width of the distribution is a fundamental statistic since it provides the range of values that could be expected when a single measurement is obtained. Finally the mean value, the median and the standard deviation were estimated for the potential temperature and salinity for each of the four sections within the Balearic Channels and for each season of the year.

The covariance function of any observed variable informs about the spatial structure of such variable. Besides this, when interpolation is required and the variable is interpolated as a linear combination of the available observations, an optimal linear interpolation can be estimated if the covariance function of the variable and the noise to signal ratio are known (

Let’s consider _{i,t}_{i}_{i}, z_{i})

Being _{i}_{j}

The following objective was to find the analytical dependence of the covariance and correlation functions on the coordinates (_{i}, z_{i})_{j}, z_{j})

Where ^{2}_{x} are the parameters obtained from the fit of (4) to the data. ^{2}_{x} is the decaying distance for the covariance function (see also _{0} and _{x} are the parameters of the fit for the correlation function.

Notice that the fit for the correlation function assumes a _{0} value for

The parameters _{x}, _{0}, and

To find out the dependence of the covariance function on the vertical coordinate, the Eqs (2) and (3) were estimated for all pairs of points with the same _{i} and _{j} values. In this case, it cannot be assumed that the covariance only depends on the vertical distance between observations but also on the specific values of _{i} and _{j}. The vertical covariance was modeled as:

Considering the symmetry of the covariance matrix _{1}_{2}

the former equation for the covariance function could be expressed as:

The water masses which are mainly present in the Balearic Channels, are the Atlantic Water (AW), the Western Intermediate Water (WIW), the Levantine Intermediate Water (LIW), and the Western Mediterranean Deep Water (WMDW). Once the mean and median values had been calculated for each season and hydrographic section, the potential temperature, salinity, potential density and pressure levels corresponding to each water mass were estimated, in order to re-define the climatological properties of the main water masses in the Balearic Channels.

The strongest influence of AW is observed at the sea surface. Therefore, salinity, potential temperature and density for the upper 5 dbar of the water column were averaged for each season and hydrographic section. These values can be considered as indicators of the presence of this water mass at the area of study during the different seasons of the year.

The WIW has been traditionally considered as a cold water mass with potential temperature below 13°C and salinity values ranging between 37.7 and 38.3 (^{–3}. The minimum

The core of the LIW was identified as the absolute salinity maximum. Depth, potential temperature and salinity values at the position of such maximum were used to define the properties of this water mass.

Finally, WMDW is the densest water mass within the Balearic Channels. Therefore the maximum potential density was considered as the core of this water mass. In some shallow stations, the deepest levels were occupied by a mixing of LIW and WMDW and it would not be appropriate to consider these waters as WMDW. First it was considered the possibility of following ^{3}. Nevertheless, the analysis of the mean and median ^{3}. Notice that the depth of this maximum is not always the maximum depth of the station. In such cases, it simply indicates that the maximum density is reached somewhere above the bottom depth and that the potential density remained constant to the sea bottom. Also notice that for each campaign the maximum density reached at each station will be different depending on the recent history of deep convection and modification of WMDW (see for instance

Once the average distributions of potential temperature and salinity had been obtained, the circulation and the water mass transports associated to such distributions were estimated. Considering that the climatological

The box inverse problem method was developed by

The potential temperature and salinity values were assorted according to their season of the year and pressure level.

Hence, the median values were chosen to describe the climatological properties of water masses.

Median vertical profiles of salinity

Tables 1.1, 1.2, 1.3, and 1.4 show the climatological properties of AW, WIW, LIW, and WMDW for winter, spring, summer and autumn.

Table 1.1 | Winter | MS | MN | IS | IN |

AW | 37.81 | 37.92 | 37.93 | 37.98 | |

14.25 | 14.17 | 14.10 | 14.09 | ||

_{
θ} |
28.30 | 28.41 | 28.43 | 28.47 | |

0–5 | 0–5 | 0–5 | 0–5 | ||

WIW | 38.37 (*) | 38.32 (*) | 38.28 (38.08–38.26) | 38.26 (38.13–38.36) | |

13.23 (*) | 13.22 (*) | 13.16 (12.99–13.31) | 13.10 (13.05–13.40) | ||

_{θ} |
29.08 | 29.09 | 29.08 | 29.09 | |

416 | 437 | 435 | 447 | ||

WMDW | 38.49 | 38.49 | 38.49 | ||

12.93 | 12.96 | 12.93 | |||

_{θ} |
29.11 | 29.11 | 29.11 | ||

997 | 828 | 1068 | |||

AW | 37.67 | 37.81 | 37.73 | 37.78 | |

19.12 | 20.70 | 20.04 | 20.18 | ||

_{θ} |
27.03 | 26.71 | 26.83 | 26.83 | |

0–5 | 0–5 | 0–5 | 0–5 | ||

WIW | 38.31 (36.14–38.38) | 38.31 (38.18–38.36) | 38.29 (38.11–38.39) | 38.26 (38.13–38.41) | |

13.16 (13.09–13.42) | 13.08 (13.06–13.50) | 13.15 (12.88–13.41) | 13.04 (12.91–13.37) | ||

_{θ} |
28.93 | 28.94 | 28.91 | 28.92 | |

179 | 160 | 175 | 185 | ||

LIW | 38.51 | 38.52 | 38.51 | 38.53 | |

13.17 | 13.17 | 13.21 | 13.21 | ||

_{θ} |
29.08 | 29.09 | 29.08 | 29.09 | |

409 | 487 | 464 | 503 | ||

WMDW | 38.48 | 38.49 | |||

12.89 | 12.93 | ||||

_{θ} |
29.11 | 29.11 | |||

1277 | 986 | ||||

AW | 37.54 | 37.62 | 37.77 | 37.77 | |

25.26 | 24.87 | 24.90 | 24.75 | ||

_{θ} |
25.18 | 25.36 | 25.47 | 25.51 | |

0–5 | 0–5 | 0–5 | 0–5 | ||

WIW | 38.32 (36.18–38.36) | 38.35 (38.20–38.39) | 38.30 (38.18–38.49) | 38.27 (38.16–38.39) | |

13.21 (13.08–13.40) | 13.13 (13.09–13.45) | 13.14 (13.07–13.45) | 13.10 (13.04–13.50) | ||

_{θ} |
28.92 | 28.97 | 28.92 | 28.91 | |

182 | 211 | 172 | 189 | ||

LIW | 38.52 | 38.53 | 38.53 | 38.52 | |

13.17 | 13.18 | 13.24 | 13.18 | ||

_{θ} |
29.09 | 29.09 | 29.08 | 29.09 | |

472 | 479 | 418 | 512 | ||

WMDW | 38.48 | 38.49 | 38.49 | 38.49 | |

12.93 | 12.92 | 12.94 | 12.92 | ||

_{θ} |
29.11 | 29.12 | 29.11 | 29.12 | |

535 | 1152 | 797 | 1065 | ||

AW | 37.57 | 37.81 | 37.67 | 37.82 | |

21.19 | 20.93 | 21.11 | 21.23 | ||

_{θ} |
26.40 | 26.65 | 26.49 | 26.57 | |

0–5 | 0–5 | 0–5 | 0–5 | ||

WIW | S | 38.39 (36.18–38.30) | 38.47 (*) | 38.35 (38.18–38.29) | 38.44 (38.20–38.36) |

13.18 (13.00–13.44) | 13.19 (*) | 13.18 (13.18–13.48) | 13.19 (13.21–13.42) | ||

_{θ} |
28.99 | 29.05 | 28.95 | 29.02 | |

225 | 258 | 225 | 274 | ||

LIW | S | 38.51 | 38.53 | 38.53 | 38.53 |

13.17 | 13.20 | 13.20 | 13.20 | ||

_{θ} |
29.08 | 29.09 | 29.09 | 29.09 | |

394 | 405 | 523 | 531 | ||

WMDW | 38.48 | 38.49 | – | 38.49 | |

12.88 | 12.93 | – | 12.92 | ||

_{θ} |
29.12 | 29.11 | – | 29.11 | |

487 | 1167 | – | 1068 |

(^{2} is the variance for each depth level. (^{2} value estimated for each depth level. This depth dependence for the upper 100 m is modeled by means of the formula on the right at the top of the panels. Then a linear decrease of the variance is assumed from 100 to 400 m, and a constant value below this depth level.

The _{0} in the above formula accounts for the fact that the maximum variance is not always at the sea surface. All the parameters involved in the previous formula corresponding to the four seasons of the year and for both the salinity and potential temperature are presented in

Parameters for the analytical expressions for the covariance function for salinity and potential temperature in the Balearic Channels (see Eq. 11).

Salinity | σ_{0}^{2} |
z_{0} |
L_{z,1} |
L_{z,2} |
L_{x} |
γ | a | b*10^{–5} |
c*10^{–3} |

Winter | 0.054 | 10 | 48 | 53 | 50 | 0.12 | 0.0089 | 3.42 | 0.4 |

Spring | 0.045 | 10 | 43 | 46 | 60 | 0.16 | 0.0048 | 1.00 | 1.9 |

Summer | 0.045 | 1 | 43 | 38 | 52 | 0.15 | 0.0032 | 0.41 | 2.0 |

Autumn | 0.077 | 10 | 42 | 35 | 49 | 0.14 | 0.0078 | 1.65 | 2.8 |

_{0}^{2} |
_{0} |
_{z,1} |
_{z,2} |
_{x} |
^{–5} |
^{–3} |
|||

Winter | 0.51 | 1 | 87 | 53 | 54 | 0.08 | 0.037 | 15.4 | 6.2 |

Spring | 2.96 | 1 | 33 | 21 | 56 | 0.17 | 0.036 | 9.13 | 8.7 |

Summer | 1.33 | 20 | 28 | 21 | 45 | 0.10 | 0.025 | 4.67 | 11 |

Autumn | 5.75 | 1 | 34 | 18 | 56 | 0.09 | 0.074 | 34.2 | 5.1 |

_{1} and _{2} using (2) for some selected stations within the Mallorca South section and for the four seasons of the year. Constant covariance isolines take the form of ellipses and the covariance decreases as the semi-axis increases justifying the use of (7) and (8) to model the analytical form of this function. Nevertheless, this behavior was only observed for the upper 100 m of the water column.

Black lines indicate the salinity covariance estimated for pairs of points at fixed horizontal positions and depth levels z1 and z2 (horizontal axis). The gray lines are the least square fit using equations (7) and (8).

Once again to clarify these results, equation (10) shows the result of the fit for the salinity winter covariance at the upper 100 m:

Notice that the first two factors in (10) explain the depth dependence of the variance. The only difference with (9) is that in that case there was one single depth level, while in the present case the variance decreases with the average value of both depth levels. It was checked for all the seasons of the year and for both the salinity and potential temperature that the depth dependence obtained from the analysis on the vertical direction (Eqs 7, 8, and 10) and that inferred from the analysis on the horizontal coordinate were consistent. The third factor in (10) accounts for the vertical decay of the covariance with the vertical distance between pairs of points. The combination of the results obtained from the analysis on fixed depth levels (dependence on the horizontal distance) and the analysis for fixed horizontal positions (dependence on the vertical distance) allowed us to propose the following analytical form for the covariance function:

_{x} (the horizontal decaying distance of the covariance function) and

_{θ}

Same as

Same as

Same as

The ^{3} as previously considered and its depth range oscillates between 140 and 274 m.

As previously mentioned, the

The LIW also occupies the density range already considered in previous works (29.05–29.1). The salinity values at the core of this water mass are relatively constant throughout the year, ranging from 38.51 to 38.53. Its depth range is 394–531 m. Its potential temperature varies between 13.17 and 13.23° C. Finally, the WMDW was not always detected during all the seasons of the year and all the sections according to the specified criterion (potential density larger than 29.11 kg/m^{3}). The maximum density values reached 29.12 kg/m^{3}. The WMDW salinity values oscillate between 38.48 and 38.49 and the potential temperature values between 12.88 and 12.92°C (

The current velocity at the reference level (sea bottom) is estimated using the mass conservation for four layers defined by the potential density values: surface/28.8/29.05/29.1/bottom.

Cross section absolute geostrophic velocity (in cm/s) at the Ibiza South section for winter

Same as figure for the Mallorca South section. Winter

^{9} kg/s (approximately 1Sv) for the upper and the lower layers, for the four sections and the four seasons of the year. The upper layer is considered as the sum of the two upper layers used in the inverse model, that is, from the surface to the 28.8 kg/m^{3} surface, and from the 28.8 to the 29.05 kg/m^{3} surface. The lower layer is the sum of the two lower layers in the model, from 29.05 to 29.1 and from 29.1 to the bottom.

Transports in 10^{9} kg/s for the four sections analyzed in this work.

Layers: Surface-300 dbar. Transports in 10^{9} kg/s |
||||

Ibiza north | Ibiza south | Mallorca north | Mallorca south | |

Winter | −0.31 | −0.33 | 0.11 | 0.10 |

Spring | −0.22 | −0.18 | 0.00 | −0.05 |

Summer | −0.17 | −0.14 | 0.12 | 0.13 |

Autumn | −0.21 | −0.03 | 0.14 | 0.12 |

^{9} kg/s |
||||

Winter | −0.09 | −0.09 | 0.08 | 0.09 |

Spring | −0.06 | −0.07 | 0.02 | 0.03 |

Summer | −0.11 | −0.11 | 0.08 | 0.07 |

Autumn | −0.06 | −0.07 | −0.02 | −0.02 |

In the Ibiza Channel, the water mass transports are southwards in both layers and along the whole year, while in the Mallorca Channel, they are generally directed northwards, except at the upper layer of Mallorca South in spring, and at the deep layer of both Mallorca sections in autumn. Such transports are also higher in the Ibiza than in the Mallorca Channels. These results are in agreement with previous studies (

Schematic circulation in the upper layer (AW + WIW) during winter ^{9} kg/s, which approximately correspond to 1 Sverdrup. Net transports for the upper layer are expressed with gray numbers.

The mean values of any property, calculated from a long time series of data at different depth levels, are generally used to define the climatological values of such property. In the case of the hydrographic conditions in the Balearic Channels, we have shown that median values are more appropriate statistical estimates than mean values. As shown in ^{3} potential density range is lower with the median values than with the mean values (Ibiza South,

Another interesting feature arising from the analysis of the climatological values in the Balearic Channels is the existence of a clear seasonal cycle, not only for temperature, but also for salinity in the upper layer. The winter median temperature of the surface layer ranges between 14.09 and 14.25°C and the surface salinity ranges between 37.81 and 37.98 (

The salinity at the surface layer is minimum during summer when it ranges from 37.54 to 37.77 (

Another interesting result is that the presence of AW is higher in the Mallorca South section than in the Ibiza South one (

Below the surface layer, the salinity and temperature ranges are narrower than at surface, and make it difficult to establish the existence of any seasonal cycle. The traditional method based on fixed range values does not allow to detect such a cycle for the WIW. Applying the geometry-based method (

Considering the different sections, seasons of the year and methodologies, the depth of the WIW core could fluctuate between 101 and 274 m, whereas the depth of the LIW core would range between 394 and 531 m (

Below 300 m depth, the LIW occupies the layer between 394 and 531 m, with salinity and potential temperature values at its core that fluctuate between 38.51 and 38.54, and 13.16 and 13.24°C, respectively. A clear asymmetry between the Ibiza and Mallorca Channels is also highlighted. The lower layer flow goes to the south in the Ibiza Channel during the whole year, while it is directed to the north in the Mallorca Channel. This flow is mainly comprised of LIW and mixing waters of both LIW and WMDW. ^{3} are always present in the northern parts of the triangles of both channels, but only intermittently in the southern part of both channels. This result simply indicates that the WMDW mainly flows north-eastwards along the northern slope of the Balearic Islands since the topography of the Channels imposes a severe restriction to the flow of the densest waters which occupy deeper levels. Nevertheless it is important to remark that during some seasons of the year, waters as dense as 29.12 kg/m^{3} can flow through the channels.

Besides the analysis of climatological salinity and temperature fields and the associated mass transports, the variance and covariance of such fields provide information of paramount importance. The validation of numerical models is based on the comparison with available observations. Simulations run under climatological or perpetual atmospheric forcing should not only reproduce the long-term mean or medians values, but also the variance of the variables analyzed. This variance accounts for the inter-annual and decadal natural variability of the ocean-atmosphere system. Our results show that the standard deviation (square root of the variance) of the temperature exhibits a clear seasonal cycle in the upper 100 m of the water column with minimum values of 0.71 in winter and maximum values of 2.4°C in autumn. The winter minimum is associated to the vertical homogeneity of the upper water column. In autumn, the water column remains stratified and the stormy activity starts to be intense inducing a high variability in the temperature distribution of the upper layer. It should be taken into account that all the surveys corresponding to the same season are not conducted during the same date (

In summary, the analysis of the longest temperature and salinity time series in the Balearic Channels has allowed to describe the median distribution of these variables and the associated absolute geostrophic transports. The ranges that define the hydrographic properties of the different water masses within the Balearic Channels could be defined in a more accurate way than using a limited number of oceanographic surveys. Results from individual campaigns could strongly depart from this climatological situation as the short time scale variability could be of the same order of magnitude than the seasonal cycle of water masses and transports (

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: IBAMar data base (

MG-M and FM were involved in the monitoring design, the field work, and the data processing work. RB was involved in the data base management and data processing work. PV-B and AH-G were involved in the inverse box modeling. MV-Y was involved in data analysis and work redaction. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Supplementary Material for this article can be found online at: