Intra- and inter-annual subsurface hydrologichydrographic variations in the vicinity of the Tropic of Cancer (Mazatlán, Mexico).
David Serrano and Arnoldo Valle-Levinson* *Corresponding author (Si estás de acuerdo)
Abstract…
1. INTRODUCTION
Sea temperature is one of the most relevant oceanographic parameters associated with climate and weather systems. Salinity, together with temperature and pressure, determine the density of sea water; changes in density over time and space are responsible for important movements in the ocean. Sea surface temperature (SST) is widely used in studies of atmospheric and oceanic problems, including the environmental management of oceans and fisheries. Subsurface temperature has a complex and variable vertical structure that is associated with atmospheric forcing, ocean turbulence, advective processes, internal waves and changes in sea surface level, among other things. Changes in the mixed layer depth, in the thermocline and in the depth of a specific isotherm are usually analyzed to describe the spatiotemporal variations of subsurface seawater temperature. Variations in sea surface height are also related to vertical fluctuations of the thermocline. Despite their relevance to climate studies, in situ oceanographic observations are not sufficient to fully characterize the kinematics and thermal states of the oceans.
Seasonal, inter-seasonal and longer time-scale variations in sea temperature and salinity
(surface and subsurface) have been described and analyzed in different regions of the world. In the South China Sea, Zhou and Gao (2002) investigated the intraseasonal variability of the subsurface temperature; they concluded that the intraseasonal variability of subsurface temperature is determined by the vertical displacement of the thermocline, which produces subsurface temperature variations of large amplitude. In addition, Ishii et al. (2003) determined that dynamic height anomalies estimated from temperature and climatological salinity were highly correlated with sea level height observations in the tropical Pacific. Moreover, based on conductivity-temperature-depth
(CTD) measurements from the western Pacific Ocean (along 165º E ) for the 1993–
1998 period, Maes and Behringer (2000) showed that altimetry observations such as those from the TOPEX/Poseidon satellite are representative of thermal and haline variability, and that altimetry signals may be projected downward into the upper oceanic layers. In the North Atlantic, Hughes et al. (2009) used time series of SST and sea subsurface temperature to demonstrate that variations in surface temperature are reflected in sea subsurface conditions; they concluded that surface temperature in situ may or may not have a close relationship with subsurface temperature; therefore, it is important to consider the local hydrography using SST data as an approximation of subsurface conditions.
In the Gulf of California, several studies reported relevant information on the subject; for example, in an ecological study, Carballo and Nava (2007) described the sea surface temperature of the Bay of Mazatlán for the period 2001-2003, and determined that temperature varies over a wide range along the seasonal cycle, reaching 12 °C (January-
August 2001). In Bahía Concepción, a bay on the west coast of the Gulf of California,
López-Cortés et al. (2003) found that subsurface water temperature in the bay for the year 1998 was affected by El Niño, recording higher temperatures compared to the years 1997 and 1999, along with a 2 to 3 month delay of the stratification period. In a subsequent study conducted in 2005 in the same bay, Cheng et al. (2010) studied the variations of water temperature along a seasonal cycle, and found that the temperature in the water column remained almost homogeneous during the winter, whereas in the summer it was stratified; they also determined that the advection of cold water from the
Gulf of California has an important role in the thermal structure of the water column.
Moreover, to analyze the spatiotemporal variation of the subsurface thermal structure of the ocean, several authors have used time series analysis, empirical orthogonal functions, the estimation of the heat fluxes at the ocean-atmosphere interface, as well as the estimation of sea level surface variations with respect to fluctuations in time and space of the thermocline. For example, in the Canary and Iberian Basins of the North
Atlantic, Müller and Siedler (1992) used an array of 22 subsurface moorings to determine that the vertical structure of the water column can be well approximated by the barotropic and first-order baroclinic dynamical modes as well as with an empirical orthogonal function. Along the Atlantic Ocean, at about 26ºN, Szuts et al. (2012) found that subsurface fluctuations in the center of the basin are large and were well described by a first baroclinic mode; they also found that these signals have long periods and were accurately described by sea surface height. In the South China Sea, Liu et al. (2001) determined that at three oceanographic stations the amplitudes of the time series of the depth of the 22 ºC isotherm were two orders of magnitude greater than the sea surface height. They also concluded that the first baroclinic mode, represented by the ratio between sea surface height and thermocline depth anomaly, is dynamically important in the central South China Sea. In the Tropical Pacific Ocean, Smith and Chelliah (1995) used harmonic analysis to show that, in general, subsurface temperature variations are much larger than surface variations, and that most of the subsurface variations are associated with changes in the depth of the thermocline. Finally, Cheng et al. (2010) determined the horizontal heat advection in Conception Bay by calculating the difference between the rate of change of heat content in the water column and the net surface heat flux. Similarly, Castro et al. (1994) estimated the horizontal heat advection along the Gulf of California by integrating the difference between the rate of change of heat content at a depth of 400 m and the net surface heat flux.
The present study was conducted over four years of water column observations in the vicinity of Mazatlán, Sinaloa, (Fig. 1), located in the Mexican Pacific coast, at the mouth of the Gulf of California. The main objectives of this study were to analyze changes of temperature, salinity and density in time and space, and to determine the role of sea surface height fluctuations in the thermocline, as well as the role of the water masses and advective processes that are reflected in the heat content of the water column. Section 2 briefly describes the area of study and data collection methods.
Section 3 describes the changes in time and space of temperature and salinity in the water column from the surface to 127 m depth; it also describes and identifies the most important harmonics of the time series, as well as the dominant modes of variability in temperature and salinity. The relationship between the sea surface height and the isotherm of 18 °C is also addressed in this section, as well as the heat content in the water column and the net heat flux. Finally, the discussion and the conclusions are presented in sections 4 and 5 respectively.
2. STUDY AREA AND DATA COLLECTION
Mazatlán Bay is in northwestern Mexico in the coastal state of Sinaloa, located at 23°
12’ N and 106º 25’ W in the southeastern Gulf of California (Fig. 1). This region is influenced by the water masses of the Gulf of California, by Subtropical Subsurface water, Tropical Surface water and California Current water (Castro et al., 2000;
Hendrickx and Serrano, 2010). The tide in the bay is mixed, mainly semidiurnal, with a form number F = 0.575. The maximum air temperature can reach 40 ºC (August-
September) and the minimum temperature 15 °C (January-February; data from the weather station at the Mazatlán Airport). The region is under the influence of tropical cyclones from May to November; winds from the northwest have been recorded at the entrance of the Gulf of California, from December to March, reaching magnitudes of 12 m s-1 (Douglas et al., 1993).
Hydrographic data were obtained from 49 oceanographic surveys carried out from
August 2005 to August 2009. Water temperature and salinity were measured by CTD
(SEABIRD-9) at one station located at 23º 05’ N and 106º 36’ W, approximately 20 km of coastline (Fig. 1). The samplings were carried out on the boat Miztli of ICMyL
(UNAM). The sampling interval was about a month; the station depth was 127 m; the vertical sampling frequency was 2 Hz; the temperature and salinity were interpolated for every meter depth and all the samples were collected between 9 and 11 a.m. The data were analyzed every meter depth (127 time series constructed from 49 surveys of the water column performed with the CTD). The time series were constructed using piecewise cubic Hermite interpolation, with Δt = 5 days; the interpolation generated
matrices of 127 rows by 292 columns of temperature, salinity and t . In order to relate the surface changes of sea level with the subsurface temperature structure, we used a regional time series (23º N 106º 30’ W) of sea surface height (SSH) from September
2005 to September 2009 constructed with readings from the TOPEX/Poseidon satellite
(http://coastwatch.pfeg.noaa.gov/erddap/griddap/erdTAssh1day.html). In order to assess the horizontal heat advection, we calculated the difference between the rate of change of heat content in the water column and the net surface heat flux (Castro et al., 1994;
Cheng et al., 2010). To approximate the net heat flux of the area of study, we used daily meteorological data from the Mazatlán Airport (23º 10’ N and 106º 16’ W) from August
2005 to August 2009. (http://www.wunderground.com/global/stations/76459.html). In addition, the time series of sea surface temperature was constructed using data from
NOAA (http://coastwatch.pfeg.noaa.gov/erddap/griddap/erdAAssta1day.html). The heat content (HC, in J m-2) of the water column was calculated in accordance with Cheng et
H HC C (T T )dz. al. (2010), ps s s ref 0
Where C ps is the specific heat of seawater, s is water density, Ts is water temperature,
Tref is a reference temperature arbitrarily set to zero ºC, and H is the depth of the water
column (127 m); C ps was calculated in agreement with Millero et al. (1973).
-2 The net heat flux at the surface Qn (W m ) was calculated as the sum of:
Qn Qt Qs Ql .
Where Qn is the net heat flux, or the difference between heat gains and losses across the
air-sea interface, Qt is the net radiation flux calculated as the difference between the net downward flux of solar radiation and the net upward flux of long-wave radiation from
the ocean (Gill, 1982), Qs is the sensible heat flux due to air-sea temperature
differences, and Ql is the latent heat flux due to water vapor transport.
The sensible and latent heat fluxes were estimated using the standard bulk formulae from the tropical ocean global atmosphere/coupled ocean atmosphere response experiment (Fairall et al., 1996)
Qs aCpaChU (Ta SST). and
Ql a LeCeU (qa qs ). Where a is the air density, C pa is the specific heat of the air, Ch is the sensible heat
transfer coefficient (Stanton number), U is the wind speed, Ta is the air temperature, Le
is the latent heat of evaporation of seawater, Ce is the latent heat transfer coefficient,
qa is the specific humidity at air temperature, and qs is the specific humidity at sea surface. Moreover, we used Fourier analysis to estimate the amplitude and phase of the six main
harmonics of the temperature and salinity fields. Power spectra were calculated for
the time series of temperature and salinity at depths of 1, 30, 60, 90 and 120 m. In
addition, the relative influence of conservative temperature () and absolute
salinity (S) on the stratification of the water column and on the double diffusive
convection was calculated using the TEOS-10 (Thermodynamic Equation of
Seawater-2010), in which the Turner angle (Tu) is defined as:
1 S 1 Tu tan , where is the coefficient of thermal S
expansion, 1 is the haline contraction coefficient and is the S
density of seawater; represents the vertical gradient. Finally, with the purpose of
identifying the water masses in the water column, a TS-diagram was constructed
using data from the 49 surveys.
3. RESULTS
3.1. Temperature, salinity and t
Figure 2a shows the time series of temperature for a four year period (2005-2009) from the surface to 127 m depth. Four cycles are evident in the time series. The maximum surface temperature of 31.47 °C was recorded in August 2009 and the minimum temperature of 12.25 °C in January 2009 at 127 m depth. At the surface, the minimum temperature was 18.32 ºC, recorded in December 2007. The average surface temperature throughout the observation period was 26 °C. Subsurface (50-80 m depth) intrusions of cold water without apparent external thermal forcing (atmospheric heat fluxes) were recorded between September 2006 and February 2007, as well as between
August 2008 and February 2009. The isotherm of 18 °C can be regarded as the lower limit of the thermocline ( T z < -0.08 ºC m-1).
The time series of salinity shows four seasonal cycles that are still evident in the first 40 m depth (Figure 2b). Highest salinities were recorded in May and June between 40 m and the surface, with a maximum of 35.35 g kg-1. The lowest salinities occurred between July and November (the wet or tropical season). The minimum value was
31.08 gr kg-1, recorded at the surface in October 2008. The variance of salinity over time decreased with increasing depth, with 0.393, 0.041, 0.023, 0.008 and 0.003 g kg-1 for 1,
30, 60, 90 and 120 m, respectively. The fact that the highest temperatures coincided with the lowest salinities suggested that these relatively warm and fresh waters were associated with river plumes advected from shore. This is the first time that freshwater influence is reported in this part of the entrance to the Gulf of California.
Figure 2c shows the phase diagram (depth vs time) of t during four years. The
distribution of t was similar to the temperature distribution. Four seasonal cycles are evident. Values less than 20 kg m-3 were recorded between September and October
2008. The greatest t fluctuations were recorded between September 2006 and
February 2007, and between August 2008 and February 2009, from 40 to 60 m depth
(corresponding to fluctuations in temperature). The vertical lines in 2a, 2b and 2c, with depths between 35 and 105 m, indicate the presence of the water mass of the California
Current; this water mass was not recorded between the months of February and July over the four years of study.
Moreover, 95.0% of the Turner angles calculated according to You (2002) (Figure 2d) were between 90° and 0° (0º < Tu < 90º); only 5.0% were between 0° and -90º (-90 < Tu < 0º). In addition, 43.0% of the Tu were between 0° and 45°, while 1.5% were between 0º and -45º, indicating that the water column was doubly stable, i.e., the water column was stratified and stable with respect to temperature and salinity; 52.0% of the
Tu were between 45° and 90°, indicating that the double diffusion process caused by salt fingers may have occurred. Finally, 3.5% of the Tu were between -90º and -45º, indicating that double-diffusion convection (DDC) is a possible occurrence.
The TS diagram shown in Fig. 3 indicates the water masses found in the water column during the study. The main water masses indicated by the diagram are: Tropical Surface water and Subtropical Subsurface water, a few observations of California Current water and Gulf of California water. The greatest stratification occurred between July and
October, while a relatively weak stratification occurred between the months of
December and March.
The relatively warm and cold spells during the observation period were determined in the water column based on the anomaly of the average temperature profile (Fig. 4a).
The four periods of cold sea surface temperatures lasted between 195 and 150 days in the winters of 2005-2006 and 2008-2009, respectively. The mean duration of the four cold periods was 176 days. The three warm periods lasted between 205 and 179 days in the summers of 2006 and 2007, respectively. The mean duration of the warm periods was 189 days. Moreover, the dates at which the periods of warm surface temperatures began were: 05-18-06, 05-22-07, 05-31-08 and 05-01-09, while the dates at which the cold periods started were: 11-04-05, 12-09-06, 11-17-07 and 12-20-08.
The duration of the warm and cold periods was not the same throughout the water column. For example, the first warm period at 80 m lasted for 270 days, with two cool periods lasting approximately one month each (Fig. 4a). The second warm period at 80 m lasted for 70 days. The third period was similar from the surface to ~100 m. Nevertheless, in this third period, a cooling period was observed between 60 and 80 m, with a duration of ~1 month. At the bottom (127 m), this third warm period lasted for 80 days. In addition, the largest positive anomalies (Fig. 4a) were recorded between 30 and
60 m depth, with values of 8 ºC. The largest negative anomalies were observed between
60 m and the surface, reaching values of -6 ºC.
Figure 4b shows the vertical temperature gradient T z . The isoline of 0.08 ºC m-1 was chosen as the lower limit for determining the zone of the biggest changes in vertical temperature (base of the thermocline). Thermal stratification was observed at different depths throughout the four years. Stratification even reached the bottom during three warm periods: June-September 2006, July-August 2008 and June-August 2009. During the second warm period, the isoline of 0.08 ºC m-1 did not reach the bottom, as it was located at 100 m depth during September-October 2007. Values greater than 0.4 °C m-1 were recorded between 10 and 50 m depth, at the transition from warm to cold to warm periods. Figure 4c shows the differences in temperature over time for any depth z
-1 T t |z . Absolute values > 0.25 °C day were recorded from the surface to 80 m depth during warm-cold-warm transitions. These values were apparently associated with the advection of warm or cold water. Figure 4d shows the average annual temperature field of the four years of logs.
3.2. Power spectral density and harmonic analysis (HA)
The power spectra of temperature and salinity for the depths of 1, 30, 60, 90 and 120 m are shown in Figure 5a and 5b, respectively. Temperature: a peak was found at between 0.5 and 1 cycles per year (CPY) in the five spectra, although the amplitude of the peak decreased with depth. A peak near the frequency 2 CPY was evident in the five spectra, but its relative amplitude increased with depth, reaching almost the same amplitude as the signal at 1 CPY at 120 m depth. Peaks with frequencies between 3 and
4 CPY were observed for depths of 30, 90 and 120 m. Salinity: Two peaks are evident in the five spectra; the highest energy peak was located around a frequency of 1 CPY; the second most important was the peak at the frequency of 2 CPY. Two other peaks were seen between the frequencies of 3 and 4 CPY, at the depths of 1, 30, 90 and 120 m.
The variation in temperature and salinity of the water column in Mazatlán Bay is represented as the sum of the quadrennial, biennial, annual, biannual, 4-monthly and 3- monthly harmonics for each meter of the water column using the following equation:
6
(T(t),S(t))z (T,S)0z AizCos2 izt iz z , (1) i1
where (T,S)0z is the average temperature (salinity) at depth z ; Aiz , iz , iz are the amplitude, frequency and phase of the harmonics mentioned above. The amplitude is defined as A a2 b2 and Tan1b a , where a and b were calculated iz iz iz iz iz iz iz iz using the discrete Fourier transform (Jenkins and Watts, 1969; Bendat and Piersol,
1986). The amplitudes, phases and percent variance of the six harmonics from surface to 127 m depth are shown in Figure 6 (temperature) and Figure 7 (salinity).
3.2.1. HA Temperature
The annual harmonic was the most important from the surface to 120 m depth Fig. 6a.
The maximum amplitude of 5.2 ºC appeared at 22 m; below this depth, the annual amplitude decreased almost linearly to a value of 0.53 °C at 127 m. The second most important harmonic was the biennial, with a maximum amplitude of 2.3 °C at 36 m depth; this harmonic increased by 1.1 °C from the surface to 36 m; below the maximum amplitude, the biennial harmonic decreased steadily to a value of 0.24 ºC at 117 m. The semiannual harmonic was third in importance, with a maximum amplitude of 2.1 °C at
40 m (slightly lower than the amplitude of the biennial harmonic); the absolute minimum was observed at a depth of 7 m with a value of 0.14 ºC; below this depth, the amplitude increased to a maximum and then decreased almost linearly to 0.56 °C at 127 m; the semiannual harmonic was relatively more important than the biennial harmonic below 50 m. The quadrennial harmonic was fourth, with a maximum amplitude of 0.88
°C at 38 m depth; this amplitude was 17.0% of the amplitude of the annual harmonic at
22 m depth. The 4-monthly harmonic was fifth in importance, with a maximum amplitude of 0.54 °C at 9 m. Finally, the maximum amplitude of the 3-monthly harmonic was 0.21 ºC at 22 m depth.
Figure 6b shows the phase profiles in degrees of the six harmonics. The quadrennial profile showed the highest variation, with a range of 60° (~8 months). For the quadrennial harmonic, the phase range was less than 11.25° (1.5 months) from the surface to 25 m. For the biennial harmonic, the phase decreased almost linearly from the surface to 110 m; the phase difference between the surface and this depth was 38º (2.5 months). The phase interval for the annual harmonic is lower than 42° (1.4 months).
The phase ranges for semiannual, 4-monthly and 3-monthly harmonics was broader compared with longer harmonics. For the biannual harmonic, the phase difference between the surface and 25 m was 114° (1.9 months); however, the difference between the surface and 127 m was 180° (~ 3 months). The phase interval for the quarterly harmonic was 175° (1.95 months), with pronounced changes between 20 m and 40 m, and between 90 m and 100 m. Finally, the phase interval for the 3-monthly harmonic was the biggest with 211°, equivalent to 1.75 months; the major phase changes occurred between 25 m and 90 m. Figure 6c shows the percentage of variability contributed by the temperature harmonics.
The annual harmonic contributed most of the temperature variation throughout the water column; the percentage of the biannual harmonic was slightly greater below 120 m. Moreover, the quadrennial cycle remained almost constant with a contribution of
10.0%, while the biennial cycle contributed between 10% and 20.0%. The 4-monthly and 3-monthly harmonics contributed 10.0% in the best case, remaining throughout most of the water column below 5.0%.
3.2.2. HA Salinity
Figure 7a shows the amplitudes of the salinity harmonics. The annual harmonic was the most important throughout most of the water column, with a maximum amplitude at the surface of 0.46 g kg-1; it was overtaken by the quadrennial harmonic around 124 m depth. It is noteworthy that the greatest amplitude was recorded near the surface for all harmonics and that the variance decreased with depth.
Figure 7b shows the phase profiles in degrees for salinity. The phase interval for the annual harmonic was 62° (~ 2 months), and this was the smallest interval of salinity for any harmonics. The phase interval for the quadrennial harmonic was 258º (~ 34 months), and this harmonic showed the greatest interval (195°) between the surface and
40 m; the phase interval for the biennial harmonic was 101º (~ 7 months) and for the biannual harmonic 110° (~ 2 months); lastly, the phase interval for the 4-monthly and 3- monthly harmonics was 210° and 325°, respectively. Figure 7c shows the percentage of the variance of salinity harmonics. The annual harmonic contributed the largest percentage of variability throughout most of the water column; it was overtaken by the quadrennial harmonic at 124 m depth, and was equaled by the biennial harmonic at 127 m. The biannual, biennial and quadrennial harmonics contributed between 10.0% and 20.0% of the variability. The percentage of variance of salinity for the 4-monthly and 3- monthly harmonics did not exceed 11.0%.
A representation of the temperature and salinity signals, from surface to 127 m depth, is shown in Figures 8a and 8c using equation 1, respectively. The root-mean-square error
(RMSE) was calculated at each depth to determine the validity of the approximation given by eq. 1. Temperature (Fig. 8b): the RMSE for the surface was ~1 °C, increasing up to its maximum of ~2 °C at 46 m depth. Below 46 m, the RMSE progressively decreased until reaching an absolute minimum of 0.48 °C at 127 m. RMSE values > 1
°C were found from the surface down to 88 m, indicating greatest variability induced by other mechanisms not included in the 6 harmonics analyzed. Salinity (Fig. 8d): The absolute maximum of RMSE was found on the surface with ~ 0.4 g kg-1; above 20 m, the RMSE was between 0.12 and 0.4 g kg-1; below 20 m, the RMSE decreased progressively, with values between 0.12 and 0.034 g kg-1; two peaks were recorded at
53 and 65 m, with values of 0.124 and 0.11 g kg-1, respectively. However, in general, the RMSE decreased with depth.
3.3. Empirical orthogonal functions (EOFs)
The spatial and temporal patterns of temperature and salinity data from the surveys were determined using empirical orthogonal functions (EOFs) (Fig. 9).
Temperature: the first two modes explained 96.0% of the variance, while the contribution of the other modes was negligible. The first EOF explained 90.0% of the total variance and was associated with the warming or cooling of the entire water column. There were evident fluctuations in the principal component 1 (PC1, Fig. 9a, thick line) between September 2006 and February 2007, and between August 2008 and
February 2009. The value of the contribution of each EOF mode to the temperature variance was the product of the EOF modes and their corresponding PC. Because the first EOF1 (Fig. 9c, thick line) mode was negative, the PC1 represented heating when it was negative and cooling when it was positive. The PC1 (Fig. 9a, thick line) represented noticeable seasonal changes throughout the four years (cold periods were positive).
According to EOF1, the greatest temperature variation occurred between the surface and
63 m (reaching a maximum at 31 m) and was associated with thermocline variability.
Below 63 m, the variance decreased almost linearly. The periodogram of PC1 (not shown) indicated that the most energetic frequencies were 1, 0.5 and 2 CPY; however, the 1 CPY peak was one order of magnitude greater than the 0.5 CPY peak. The maximum variations of EOF1 were of 4.3 °C at the surface, and 6.2 °C at 31 m. The second EOF mode explained 6.3% of the variability. The EOF2 was negative from the surface down to 32 m, and became positive below this depth (Fig. 9c, thin line). EOF2 represented heating above 32 m when PC2 was negative. The most energetic frequencies for EOF2 were of 1 and 2 CPY; the ratio between the amplitudes of these two frequencies was 0.94. There was no clear seasonal signal in this mode (Fig. 9a, thin line). The maximum variance was seen at the surface, with ~3 °C, and remained almost constant up to 7 m; below 7 m, the variance decreased to zero at 32 m. A relative maximum was recorded at 60 m.
Salinity: the first two modes explained 90.0% of the variance, while each of the other modes explained less than 3.0%. The first EOF represented 74.0% of the total variance and this was associated with periods of drought and rain. Because the first EOF1 (Fig.
9d, thick line) mode was negative, the PC1 represented a period of drought when it was negative and the rainy season when it was positive. The PC1 showed noticeable seasonal changes (Fig. 9b, thick line). According to EOF1, the greatest salinity variation occurred at the surface, and the variance decreased exponentially with increasing depth
(Fig. 9d, thick line). The periodogram of the PC1 (not shown) indicated that the most energetic frequencies were of 1, 0.5 and 2 CPY; however, the peak at 1 CPY was two and five times higher than the peaks at 0.5 and 2 CPY, respectively. The maximum variations of EOF1 were of 1.92 g kg-1 at the surface. The second EOF mode explained
16.0% of the variance. The EOF2 was positive from the surface to 14 m, and became negative below this depth (Fig. 9d, thin line); the EOF2 represented an increase in salinity above 14 m, when PC2 was positive (Fig. 9b, thin line). The most energetic frequencies for EOF2 were 1 and 0.25 CPY, with similar amplitudes. The maximum variance for this mode was found at the surface, with ~0.65 g kg-1; the variance decreased to zero at 14 m. A relative maximum was recorded at 40 m.
3.4. Thermocline depth and sea surface height
The depth of the thermocline, as is represented by the depth of a selected isotherm, can be regarded as a measure of the volume of water in the upper-layer. The variations of the thermocline depth can be related to variations in sea surface height (SSH) and vice versa: variations in sea surface height can be related to variations in thermocline depth.
In this study, we determined that the 18 ºC isotherm (IT18) represented the thermocline depth. This isotherm was present in both cold and warm periods and could be considered as the lower limit of the thermocline (Fig. 2a). The IT18 was located at between 19 m in winter and 113 m in summer (Fig. 10a). Significant changes in the location of the IT18 between September 2006 and February 2007, and between July
2008 and February 2009, were recorded after the IT18 was at the maximum depth for the corresponding seasonal cycle. Warm water on the surface was recorded on January
2006 and October 2008, causing the IT18 to descend. However, on October 2006, the
IT18 rose without an apparent decrease in the surface temperature. In addition, in
January 2007 the thermocline moved up without apparent surface cooling. Similar upwelling fluctuations of the IT18 were recorded on September and December of 2008. Moreover, removing the seasonal cycle from the time series of the IT18 before calculating the periodogram (not shown) showed that the most energetic frequencies were those of between 2 and 4 CPY. The IT18 (Fig. 10a) was strongly correlated
(correlation coefficient = 0.99) to the PC1 (Fig. 9a).
The time series of SSH and IT18 (Fig. 10a) showed a clear seasonal cycle. The range of
SSH was 0.42 m, and the range of the IT18 was 95 m. Oscillations with periods shorter than the annual cycle were evident in both series. The oscillations of SSH had a negative phase with the IT18, as expected. These oscillations were recorded more clearly after the IT18 reached its seasonal maximum depth between September 2006 and February 2007, and between August 2008 and February 2009. These oscillations were of 0.11 m for SSH and 27 m for IT18. Without the seasonal cycle of both series
(Fig, 10b), their correlation coefficients during the two periods mentioned above were
-0.62 and -0.53, respectively.
3.5. Net surface heat flux and heat content
The heat content of the water column, the net heat flux and the difference between the
HC rate of change of heat content and the net heat flux (removing average) are all t shown in Fig. 11a, 11b and 11c, respectively. The daily net heat flux was smoothed with a 15-point running mean to remove synoptic variability. The seasonal cycle is noticeable in the time series of heat content and net heat flux. The net heat flux increased from winter to summer, showing a seasonal heat transfer from the atmosphere to the ocean. The net heat flux was responsible for the warming of the region and contributed to the development of the summer stratification of the water column.
Moreover, there was a lag of approximately 3 months occurred between the net heat flux and heat content of the water column. A decrease in the net heat flux was recorded between June and July 2008, while further fluctuations occurred during the four years of this study, with amplitudes that did not exceed 60 W m-2 and periods of between 1 and 2 months. Regarding heat content, three remarkable decreases were registered at
September 2006, January 2007 and September 2008. The heat content showed, as expected, that the water column was gaining heat from the winter to the summer.
Moreover, the distinct peaks (relative maximum and minimum) shown in Fig. 11c are related to advection processes. The relative minimums are associated with the advection of cooler water from its surroundings. The relative maximums in the same figure are related to the advection of water with higher temperature than its surroundings, or to an external heat forcing.
A qualitative approximation of heat advection (A) can be obtained by integrating the vertical temperature anomaly with respect to an average year, i.e.,
1 z A (ATF AAT )dz, z127 0
Where ATF is the annual temperature field at the depth z, and AAT is the mean annual temperature field (Fig. 11d).
4. DISCUSSION
According to the 49 tempesrature and salinity profiles measured between august 2005 and August 2009, the presence of four complete seasonal cycles is clear; the seasonality of the temperature of the water column is related to solar radiation and the net heat flux.
Cheng et al. (2010) showed that the temperature of the water column in Bahía
Concepción (26° 48’ N and 111° 51’ W) is related to seasonal atmospheric heat fluxes as well as to cold water intrusions forced by wind-driven upwelling. Likewise, the temperature profiles allowed us to determine basic but important oceanographic parameters such as the depth of the thermocline, represented by the depth of a selected isotherm. In addition, the seasonal cycle of salinity was determined for the dry and rainy seasons.
High surface temperatures in the region are due to the geographical location and the influence of tropical water masses; southward (20° 30’ N and 105° 30’ W, in Bahía de
Banderas) water masses, with temperatures ≥ 26 °C, intruded in the area 218 days a year during the period of this study (nomad3.ncep.nooaa.gov/cgi-bin/pdisp-sst.h?). However, at the same latitude of Mazatlán but at a different location on the coast of Baja
California Sur (Pacific Ocean), the temperature of the sea surface was ≥ 26 °C for 124 days each year. Furthermore, on the coast of Mazatlán the beginning of the warm period occurs on average on the 140th day of the year, with a standard deviation of ± 13 days
(during May). The cold period begins on average at day 331 of the year, with a standard deviation of ± 20 days (between November and December).
The largest positive differences with respect to the average temperature at the depth z, between 30 and 60 m, were recorded when the IT18 was deeper and when the highest surface temperatures were recorded. The largest negative differences were recorded between 60 m and the surface, when the IT18 was shallower and the surface temperature recorded its seasonal relative minimum. This indicated that the largest temperature variations were recorded between 30 and 60 m depth during the study period. Smith and Chelliah (1995) concluded that, in general, subsurface temperature variations in the tropical Pacific were much larger than surface variations, and that these variations are associated with changes in the depth of the thermocline.
Differences equal to 0 °C day-1 (Figure 4c) are related to the relative maximum and minimum temperatures in the water column with respect to time. The isoline of 0 °C day-1 was not always present on the same date throughout the water column, indicating a slight lag in the heating and cooling processes; furthermore, the phase of the annual harmonic presented a range of 42 ° (1.4 months) in the water column. Similarly, Beron-
Vera and Ripa (2000) reported a lag of less than one month between the surface temperature and the temperature at 200 m depth in the southern Gulf of California.
Differences greater than 0.25 °C day-1 are related to the transition between heating and cooling (inflection points of the isotherms). On the other hand, differences smaller than
-6 °C (compared to the average annual temperature) were recorded in the winter of
2007-2008, indicating an anomalously cold winter with temperatures below 19 °C at the surface. These low temperatures were associated with La Niña, which was documented by McClatchie et al. (2008) who reported temperature anomalies of below -1 °C in the
SST of this area, with respect to the average temperature of the period 1950-1979.
Moreover, from October 2007 to March 2008, the Oceanic Niño Index was between
-1.1 and -1.5 for the Niño 3.4 region
(http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml
).
Salinities ≥ 35 g kg-1 are due to the advection of Gulf of California water, with
and , as reported by Hendrickx and Serrano (2010) and Castro 12 T 30 23 t 26 et al. (2000) for this region of the Gulf of California. Moreover, Beron-Vera and Ripa
(2000), using historical temperature and salinity data recorded along the Gulf of
California, determined that the greatest variability in salinity occurred at the surface, decreasing with increasing depth until reaching a minimum around 200 m. The TS diagram and the decrease in the range of salinity with depth reported in this study reaffirms that assertion. Moreover, the Turner angle for this region is between 45° and 60° according to You (2002). In the present study, the average value was 42°, relatively close to that reported in the climatological atlas of the Turner angle.
Furthermore, the DDC for this area can be considered anomalous, because the DDC in the Pacific occurs in high latitudes (You, 2002). The biggest DDC event in this study was related to the high rainfall recorded between July and November 2008. A decrease of surface salinity occurred in this interval due to the precipitation, generating a salinity gradient with depth. In addition, the temperature showed a slight increase with depth of about 0.2 °C in the first 10 m. A similar behavior of temperature and salinity occurred in the DDC event registered between October and November 2005. DDC events, with increases of salinity with depth, were reported in fjords of the Chilean Patagonia, associated with an almost constant temperature profile near the surface (Pérez-Santos et al., 2013).
The decrease in the heat content of the water column in October 2006 and January 2007 is explained by the horizontal advection of cold water. The lifting of isotherms and isopycnals during these months was due to the advection of California Current water, which is ~ 1.0% higher in density compared to the surrounding waters (± 15 days).
Cheng et al. (2010) argued that the fluctuations of the thermocline in Bahía Concepción are correlated with advective processes of cold water, which is reflected in the minimum relative heat content. The other intrusions of California Current water did not significantly disturb the isotherms and isopycnals because the surrounding water was
~0.3% lower in density; in addition, the advection volume was lower compared to the advection that occurred in October 2006 and January 2007 (indicated by vertical lines).
Salinities below 34.5 g kg-1 between September 2006 and February 2007 concealed the advection of California Current water. However, in November 2005, December 2007, November 2008 and August 2009, the advection was evident, reflected by the decrease in salinity.
The noticeable decrease in net heat flux occurred between July and August 2008, caused a decrease in the heat content of the water column; however, this is not the factor that causes the IT18 to subside. Cheng et al. (2010) emphasized that the fluctuations of the thermocline are not correlated with the net heat flux, and that atmospheric heat fluxes only affect the first 5 m of the water column. The sinking of IT18 in September 2008 was caused by high temperatures and heavy rainfall. Rainfall was concentrated over a period of 80 days, accompanied by runoff, causing a decrease in density for the first meters (z <20 m). Rainfall exceeded the annual average by more than 300 mm, according to García-Páez and Cruz-Medina (2009).
Moreover, the lag between the heat content of the water column and the net heat flux is explained by the lag that exists between the maximum temperature reached by the atmosphere and the maximum temperature reached by the ocean (~3 months later); due to the different heat capacity of the two fluids. Higher temperatures are recorded in the atmosphere for ~3 months (in a seasonal cycle); the air undergoes significant changes in temperature every 24 hours (throughout the day and night), but the net change during these three months did not exceed 1.5 °C (according to the time series of temperature from the airport station). The high relative humidity, higher than 80.0%, prevents that atmosphere from significantly gaining or losing heat. In June, the sea surface temperature has not yet reached its peak and continues to rise until reaching its maximum three months afterwards.
According to harmonic analysis, a simulation of the water column temperature (with a maximum error of 15.0% at 55 m depth) is feasible based on the annual, biennial, biannual, quadrennial, 4-monthly and 3-monthly harmonics. These harmonics explained 46, 20, 19, 8, 5 and 2.0% of the variance respectively. Harmonics with a period ≥ 1 year contributed 74.0% of the variance, harmonics with a period ≤ 6 months contributed
26.0% of the variance; however, the contribution of the biannual harmonic is remarkable. Smith and Chelliah (1995) determined that within 10° N-S the biannual harmonic contributes only a fraction of the variance contributed by the annual harmonic; however, in this study, conducted at ~21’ from the Tropic of Cancer, the semiannual harmonic contributed 19.0% of the total variance and is 41% of the annual harmonic. Szuts et al. (2012) established that the relative balance between important dynamic processes is dissimilar for different latitudes, and associated this lack similarity with the presence of Kelvin and planetary waves.
The biannual harmonic represents a double heating process during the year, which is more noticeable below 50 m. The first temperature increase is due to the conduction of heat from the upper to the lower layers of the water column during the period of heating of the surface by solar radiation. The second increase in temperature occurs because the subsurface layers between 25 and 40 m provide heat to the lower layers during the superficial cold period, which contributes to homogenize the water column. The relaxation of the thermocline, which involves the attenuation produced by a physical barrier during the cold period, facilitates the exchange of physical and chemical properties between layers. Moreover, the biennial harmonic is related to El Niño; Smith and Chelliah (1995) determined that in the Tropical Pacific Ocean, the variance of temperature and salinity is dominated by Southern Oscillation variations, which have timescales of 2-10 yrs. In this study, the biennial harmonic above 50 m was the second most important.
The phase of the six harmonics was not constant throughout the water column; the harmonics that showed minor changes were the low frequency ones, which corresponded to the annual, biennial and quadrennial periods. The low frequency harmonics were associated with the barotropic mode. Major phase changes occurred in high frequency harmonics, which corresponded to the biannual, 4-monthly and 3- monthly periods. The biannual harmonic was associated with a strong water column stratification, in particular with a thermal structure consisting of two layers, corresponding to the first baroclinic mode. The harmonics with a phase difference in the water column between 90° and 270° (T/4 and 3T/4), in a range Δz, were associated with the baroclinic modes.
The fluctuations that occurred after the IT18 reached its maximum depth (October 2006 and January 2007--produced by the advection of California Current water-- and
September and December 2008) had periods of ~3 months, and can thus be related to the 3-monthly harmonic. These fluctuations occurred when the thermal gradient was relatively weak, allowing surface disturbances to be amplified at the interface; disturbances at the interface were in turn reflected at the surface.
The relatively high values of RMSD (greater than 1 °C between the surface and 88 m depth) showed that this fringe zone was very dynamic throughout the seasonal cycle and during the four years of records. It should be noted that the IT18 remained in this fringe zone ~ 89.0% of the time of this study. Liu et al. (2001) determined that small amplitude fluctuations in the SSH, caused by the geostrophic vorticity, produced large amplitude fluctuations in the thermocline. Moreover, Beron-Vera and Ripa (2000) calculated that about 80.0% of the total variation of heat content in the water column is concentrated within the upper 200 m in the southern region of the Gulf of California.
These results show how complicated it is to model the temperature changes over time in the water column; however, the results presented in this work are a good approximation. With respect to temperature EOFs, the first two modes explained 96.5% of the variability; the first EOF represented 90.2% of the total variance. EOFs describe the variability of a data set in terms of orthogonal functions and statistical modes; however, a direct relationship with the dynamics of a system has not been reported. Considering that EOFs describe the variance of a time series with a few modes, it can be said that the first PC1 of the matrix of time-temperature-depth used in this study is related to the
IT18 located in the thermocline. Smith and Chelliah (1995) showed a sharp thermocline in the Tropical Pacific Ocean, with a 20 °C isotherm and the largest standard deviation around the center of the thermocline; they also determined that most subsurface variations are associated with changes in the depth of the thermocline. The relationship between the IT18 and PC1 is confirmed by the correlation coefficient ~1. Finally, the three most energetic frequencies of the PC1 were also the main frequencies obtained through HA.
Based on the phase difference of the semiannual harmonic of temperature, on the vertical structure of EOF2 and the high values of the thermal gradient (| T z | > 0.08
ºC m-1), it can be considered that between August 2005 and August 2009, the study area was composed of two layers. The similarity between IT18 and SSH and their correlation coefficient (eliminating low frequencies) confirm this assertion. The relations between sea level and thermocline depth in the tropical ocean will depend on how much the ocean resembles a two-layer system. Variations in the gradient of the thermocline will adversely affect these relations; an ideal two-layer system has only one internal oscillation mode, namely, the first baroclinic mode (Rebert et al., 1985). Moreover, in the same work, the authors concluded that the correlation between sea level and the depth of the 20 °C isotherm breaks down at latitudes between 15° and 20°; they argued that the isotherm is deeper in this region than in the equatorial band, and that the thermocline is weaker. Nevertheless, Liu et al. (2001) found acceptable correlation coefficients between these variables in the Central South China Sea (between 12° 58.5’
N and 18° 05.9’ N). Furthermore, this work was carried out in the vicinity of the Tropic of Cancer and reported good correlation coefficients between IT18 and SSH.
The raising of the IT18, produced by the advection of the California Current water, was reflected in the decreased amplitude of the SSH. Considering that the water column is stratified into two layers, the ratio between the SSH and the thermocline depth anomaly
can be interpreted as g'H 2 / gH (Gill 1982), where H and H 2 are the total depth and the depth of the second layer at rest, while g and g' are normal and reduced gravity respectively. Based on the density profiles from this study, a typical ratio would be
1/250, meaning that a perturbation in the thermocline with an amplitude of 25 m would represent about 10 cm at the surface. This consideration is in agreement with our results.
Similarly, Liu et al. (2001) reported ratios of 1/437, 1/170 and 1/240 between the SSH and the 22 °C isotherm depth in the Central South China Sea. In addition, subsurface oscillations are more noticeable (high amplitude) in the second half of the year, which is explained because relatively large values of N2 (the square of the Brunt-Väisälä frequency) are distributed in a wide strip of the water column, dissipating the tension produced by a considerable change in density (pycnocline). Likewise, to convert the integrated temperature fluctuations into vertical displacements, Konyaev et al. (1995) and Plata and Filonov (2007) proposed the following equation:
(t) T (t1) T (t2 )/ dT / dz , where dT / dz (Tsup Tinf ) / z is the mean vertical temperature gradient. When applying this equation to the fluctuations that occurred in
September 2008, with a difference in temperature of 6.5 °C between peak and valley and dT / dz 0.18 °C m-1, the resulting displacement is 36 m; the actual recorded displacement was 38 m. (t) is inversely proportional to the mean vertical temperature gradient; thus, if the average temperature gradient decreases, the vertical displacement increases. Finally, the quantitative approximation of heat advection could be improved by taking measurements over longer periods of time.
SUMARY or CONCLUSION… (Si lo consideras necesario)
Acknowledgments DS is grateful to the Unidad Académica Mazatlán of Instituto de Ciencias del Mar y Limnología (ICMyL) of UNAM and too at Evlin Ramírez Félix for the facilities provided for this study. Also thank to Michel Hendrickx for the support with the CTD and José Salgado Barragán, Juan Toto Fiscal, Raquel Briseño Dueñas and Eva Visauta Girbau for their support and collaborative to carry out hydrological records. Our thanks also to Gustavo Rodríguez for their thoughtful comments for improving the manuscript.
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Zhou, F.X., Gao, R.Z. (2002). Intraseasonal variability of the subsurface temperature observed in the South China Sea. Chin. Sci. Bull. 47: 337-342. Figure 1. Study area. Figure 2. (a) Temperature (° C) and 18° isotherm thick line. (b) Salinity (g kg-1). (c) σ-t (kg m-3). (d) Turner angle. Average profiles of temperature, salinity and σ-t are shown to the left right of their respective figure. Figure 3. T-S Diagram. (I) Tropical Surface Water; (II) Gulf of California Water; (III) California Current Water; (IV) Subtropical Subsurface Water. Figure 4. (a) Temperature anomalies relative to the series-long mean profile. (b) T z (°C m- 1). (c) T t (°C day-1). (d) Yearly average of temperature; the black line represents the 18 °C isotherm. Figure 5. Spectra of temperature (a) and salinity (b) for 1 m, 30 m, 60 m, 90 m and 120 m depth. Figure 6. (a) Amplitude of the harmonics of temperature. (b) Phase six harmonics. (c) Percentage contribution of each harmonic to the depth z. Amplitudes and phases both used in equation 1. Figure 7. (a) Amplitude of the harmonics of salinity. (b) Phase six harmonics. (c) Percentage contribution of each harmonic to the depth z. Amplitudes and phases both used in equation 1. Figure 8. (a) Simulation of temperature field using six harmonics (equation 1). (b) Root-mean- square deviation (RMSD), between temperature records and harmonic reconstruction (equation 1). (c) Same as (a) to salinity. (d) Same as (b) to salinity. Figure 9. EFO’sEOF’s. (a) Show the first and the second principal components (temperature). Thick line PC1, thin line PC2. (b) Same as (a) to salinity. (c) Shows the first two EOF modes (temperature). Thick line EFO1, thin line EFO2. (d) Same as (c) to salinity. Figure 10. 18 °C Isotherm (solid line) and SSH (dashed line). (a) Original Series. (b) Series removing the seasonal cycle. Figure 11. (a) Heat content (per unit horizontal area). (b) Net heat flux. (c) Integration the difference between the rate of change of heat content and the net heat flux (removing average). (d) Vertical integration of the temperature anomaly for 2006, 2007 and 2008.