CC BY
12
УДК 551.46; 536.75
Dynamic Features of Frontal Zones Structure in the Ocean for Using in the Numerical Models Based on Satellite Data
Alexey V. Kartushinsky*
Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041,
Russia
Institute of Biophysics SB RAS, Akademgorodok, 50, Krasnoyarsk, 660036
Russia
Received 10.11.2010, received in revised form 10.11.2010, accepted 20.12.2010 Structural changes in the oceanic temperature frontal zones instead of TFZ, which are determined by the MSST satellite data, are related to the character of interactions between currents. Different intensities of interactions between currents cause either an increase or a decrease in SST gradients. In this work we discuss the reasons causing sharpening of SST gradients exhibited in spatial position of TFZs. Advection, turbulent diffusion, and solar radiation are the main factors for TFZs. The study areas for investigating TFZ dynamics are the North and the South Atlantic and the North and the South Pacific. Similarities in the structures of TFZs in different areas of the ocean have been determined. The 2D model is used to study the separate and concerted influence of advection, turbulence, and solar radiation on the formation of frontal zones. We present analytical and numerical estimates of changes in temperature gradients for the major frontal zones in the ocean and compare them with the satellite data. The variability of SST gradients has been quantified based on satellite, model, and analytical data. The obtained data on spatial and temporal scales of TFZs are indicative of the intensities of convergence and divergence of fluxes; these data are necessary for estimating vertical movement of the water mass as a component of the 3D models.
Keywords: modeling, sea surface temperature gradients, temperature frontal zones, advection, turbulent diffusion, solar radiation, convergence structures.
Introduction
At the present time there are numerous SST satellite data, which, after certain processing, can provide information on the position of temperature frontal zones in space [1-6]. An important feature of temperature frontal zones in the ocean is their variation. Reasons causing changes in the structure of frontal zones in space and time still remain to be understood, although attempts to investigate them have already been made [7-11]. In a number of experiments, the ship-board, buoy, and satellite data have been used concertedly [12-17]. Much consideration has been given to determination of SST anomalies, which is evident from numerous internet sources.
Major factors determining the dynamics of heat and mass transfer in the ocean can be identified by modeling. Recently, a large number of global and large-scale climatic models of ocean — atmosphere interaction have been developed [18-20]. However, the validity of the models is often restricted by local conditions of current circulations in different parts of the ocean and their interactions with the atmosphere [21,22], necessitating a more accurate adjustment of model parameters.
* kartalvas@rambler.ru © Siberian Federal University. All rights reserved
The temperature field in the ocean is formed under the impact of numerous factors, and its dynamics is a reflection of three-dimensional processes occurring on various scales in the ocean and the atmosphere. SST gradients are a derived characteristic of temperature, and, when used in calculations with the proper scale of SST gradient averaging, they yield mean weekly, mean monthly, mean seasonal, and mean yearly values of gradients in different parts of the ocean. This is the way to determine frontal zones, whose structure depends on intensity of advection, diffusion, and solar radiation [23].
Advection and diffusion, as dynamic processes, change the structure of frontal zones in different ways. Thus, we have also made numerical experiments to determine the intensities of separate physical factors when evaluating temporal variability of the frontal zones. We have evaluated the effect of solar heat radiation. Besides, it is necessary to determine the area of frontal zones for different time scales, which provides information on convergence and divergence. It has been reported that frontal zones and separate fronts influence the distribution of not only heat and salt but also living organisms, detritus, and nutrients [24].
3D models have been used before to investigate currents, thermohaline variations, and substance concentrations, yielding good results [25,26]. Local features of thermohaline fronts in different regions of the ocean have been not thoroughly investigated [27]. The main purpose of our work is to quantify parameters of SST gradients under the impact of separate physical factors: advection, turbulent diffusion, and solar radiation, using a 2D horizontal model, and some of the parameters — using a 1D vertical model.
1. Material and Methods
As initial data we use interpolated AVHRR data for the periods between 1982 and 1986 (mean monthly data) and between 1990 and 2000 (mean weekly data) [28]. We calculate SST gradients and investigate structural features of frontal zones by analytical method and numerical modeling.
To make a preliminary estimate of model parameters, it is necessary to analyze the heat transfer equation, which can conveniently be used in dimensionless form (Eq. 3). Using the similarity theory, we introduce characteristic values of variations in temperature, velocity components, and heat diffusion; characteristic horizontal scales and characteristic time and their dimensionless values (accented):
T = To • T ; u = uo • u ; v = vq • v ; Kt = Kt0 • KT; x = y = Lq • L ; t = to • t (1)
taking into account:
uo = vo = Vo; to = —0 (2)
Vo
we can write:
TqVq dT' VoTof 0T^ + dT_ \ = Kt0 To _,2,
L0 dt_ + Lq ^ dx_ + dy_ j LQ ' ( )
Then, for the 1°C characteristic temperature change, if V0=0.2 m/s, L0=18 km (spatial res-To Vo
olution of satellite data), ——=10-5, hence the characteristic time scale is t0=105 s. Thus,
Lo
advection, disregarding turbulence, can lead to temperature changes within 24 hours. If characteristic values of temperature change are estimated under the action of turbulence, at KTo=103
k t
m2/s, then —T<02 0 =5.5x10-5, hence, the characteristic time of temperature change will be about Lo
6 days.
In the ocean, the interaction of systems of currents, particularly jet streams, leads to a weakening of advection components and an increase in the contribution of turbulent diffusion. A significant contribution will be made by positive or negative radiation balance, as a background component. Besides, the contributions of advection parameters (components u,v) and turbulent diffusion components (KTx , KTy ) to the formation of frontal zones are different for different space-time scales. The current vector is an important parameter, too. Thus, based on numerical model experiments, it is necessary to find out the contributions of these factors to structural changes of frontal zones.
We use the initial data for MCSST fields to calculate SST horizontal gradients instead of GrS for the North and South Atlantic and for the North and South Pacific; then we average the gradients for a certain time scale. Thus, we obtain mean weekly, mean monthly, and mean seasonal gradient fields, which adequately show the position and structure of frontal zones.
To model the temperature frontal zones instead of TFZ, we used a 2D horizontal model based on the solution of the heat transfer equation, with the set scales of the computational grid related to the spatial resolution of satellite data [23]. The model is controlled by components of velocity with the proper vector, components of turbulence factor, solar heat, and the calculation period with an interval of 24 hours. As the initial data for the model we used mean weekly SST. Using the model, we calculate the model temperature field and model SST gradients instead of GrM. Accuracy of model calculations was checked by comparing them with satellite data. The major dynamic processes considered are heat advection and turbulent diffusion. To study the dynamics of the temperature vertical structure, we made numerical experiments on the 1D model, introducing the data on the surface radiation balance and the wind load, which influenced the vertical turbulent heat diffusion.
The main characteristics and model equations for the 1D model are presented in [29]. In the model we also considered the periodic function of the vertical water velocity directed upward and downward for a certain calculation period. Thus, based on the results of the 2D and 1D model calculations, we obtained quantitative parameters of SST and SST gradient variations showing the formation of the TFZ structures under the impact of different factors. We also studied the reasons of possible changes of these structures.
2. Results
The mean monthly and mean seasonal structures of some surface currents in the ocean are adequately presented as maps and animations at http://oceancurrents.rsmas.miami.edu/. There one can also find the main results of different authors investigating currents and factors that influence variability of currents and formation of thermohaline fronts.
In this work we try to answer the question: how do some factors influence the TFZ and separate fronts separately and concertedly? We studied the dynamic features of the frontal zones formed by currents, with the respective model areas:
(a) for the North Atlantic: Gulf Stream (GS) - Labrador Current (LC) - North Atlantic Current (NAC); the model square: 50°N-65°W; 35°N-65°W; 50°N-35°W; 35°N-35°W.
(b) for the South Atlantic there is an interacting system: Brazil Current (BC) - Malvinas (Falkland) Current (MFC) - the Antarctic Circumpolar Current (ACC) also known as the West Wind Drift; the model square: 40°S-70°W; 40°S-35°W; 60°S-70°W; 60°S-35°W.
(c) the system of North Pacific currents: Kuroshio - Oyashio (K-O); the model square: 50°N-135°E; 30°N-135°E; 50°N-180°E; 30°N—180°E.
(d) for the South Pacific: the region of South Equatorial Current (SEC), which can be considered
as the region of the El Nino - Southern Oscillation (ENSO); the model square: 10°N-150°W;
10°S-150°W; 10°N-75°W; 10°S-75°W. The area of the Antarctic Circumpolar Current
(ACC); the model square: 30°S-135°W; 60°S-135°W; 30°S-75°W; 60°S-75°W.
For the above regions we conducted numerical experiments on forming the SST field and calculation of SST gradients.
2.1. Analysis of the Structure of Frontal Zones in the North Atlantic
To model the structure of the frontal zone formed by the GS-LC-NAC interaction system, also called Subpolar Front (SF), we chose the summer and winter seasons of 1994. As reported at http://cru.uea.ac.uk/cru/data, in summer and winter the maximal cyclonic activity was registered in the area of Northern Atlantic Oscillations (NAO); NAO summer index was minimum, but NAO winter index was positive.
We calculated SST gradients for periods 1982-1986 and 1990-2000. For the subpolar front, the mean seasonal values of gradients are maximal in summer: 1.5-2.5 °C/km and minimal in winter: 0.05-0.1 °C/km. In spring, in the GS-LC-NAC system, the influence of LC on GS increases, the frontal zone widens, and by the beginning of summer, meandering occurs, weakening NAC. In autumn, the structure of the frontal zone is mainly influenced by GS, intensifying NAC by the beginning of winter; the front width narrows and gradients decrease.
Results of numerical experiments (Table 1) show that mean weekly TFZs are unstable and their structure is interrupted; the main factor is latitudinally directed advection; the turbulence component must also be higher than the meridional component. A more stable frontal zone is characteristic of mean monthly gradient fields; here the advection components must be an order of magnitude lower than the components for the calculation period of 10 days. For periods of 10 days and 30 days, total solar radiation produces a background effect on the TFZ structure, amounting to 10 kcal/cm2 month.
2.2. Analysis of the Structure of Frontal Zones in the South Atlantic
To model the structure of the frontal zone formed by the BC-MFC-ACC interaction system, we chose the summer and winter seasons of 1994. Here, in the Southwestern Atlantic Ocean (SWAO), the best pronounced fronts are the Subtropical Front (STF) — an MFC-BC interaction, the Subantarctic Front (SAF) — an MFC-ACC interaction, and the South Polar Front (SPF) formed by ACC. These interactions have been described by many authors [30-33].
We calculated mean monthly and mean seasonal gradients for 11 years, which showed that in the warm season (winter) the MFC - BC - ACC interaction leads to sharpening of STF and SAF. The fronts are structured as stable latitudinal zones 1500-2000 km long and up to 100 km wide. SPF is sharpened in summer as ACC intensifies. In spring-autumn this front is a stable zone about 500 km wide along the Antarctic coast. For STF and SAF the maximal winter gradients are 0.8-1.0 °C/km; in summer they are minimal — 0.1-0.2 °C/km. For SPF, seasonal cycles are less pronounced; the maximal gradients in autumn-winter are 0.4-0.6 °C/km and in summer 0.02-0.05 °C/km. The total solar radiation is up to 10 kcal/cm2 month.
2.3. Analysis of the Structure of Frontal Zones in the North Pacific
To model the structure of the frontal zones formed by the K-O interaction system, we chose the spring and autumn seasons of 1993. Here, in the Northwestern Pacific, a complex system of fronts is formed, which is related to the K-O interaction and the subsequent formation of the North Pacific Current (NPC). The structure of the fronts and their variability are strongly influenced by winds and eddies [1,11].
Table 1. Results of numerical experiments for different TFZs with control parameters of the
model (Variables are decoded in the text)
Model KTx , Kty , u, v, GrS, GrM, Characterization of the
period, days m2/s m2/s m2/s s 2 m °C/km °C/km TFZ structure
System GS-LC-NAC (SF)
10 (summer) 103 102 0.1 0.01 1.5-2.0 1.5-2.0 Narrow, ordered, with meanders
10 (winter) 102 102 -0.05 -0.05 0.1-0.15 0.1-0.5 Fuzzy, patchy, interrupted
30 (summer) 102 102 0.01 0.01 1.5-2.5 1.5-3.0 Wide, interrupted, with meanders
30 (winter) 103 102 -0.01 -0.005 0.05-0.1 0.5-1.0 Fuzzy, patchy, interrupted
System BC-MFC-ACC (STF, SAF)
30 (summer) 102 103 0.01 -0.05 0.1-0.2 0.2-0.4 Separate strips, patches, meanders
30 (winter) 103 103 0.5 0 0.8-1.0 0.6-0.8 Stable zones
System MFC-ACC (SPF)
30 (summer) 102 102 -0.05 -0.01 0.02-0.05 0.1-0.15 Stable zones
30 (winter) 102 103 0.01 -0.05 0.4-0.6 0.8-1.5 Fuzzy, in separate strips, with meanders
System K-O-NPC
10 (spring) 103 103 0.1 0.05 1.0-1.4 1.2-1.6 Separate strips, meanders
30 (autumn) 103 102 0.05 0.01 0.3-0.5 0.2-0.3 Separate strips, meanders
10 (winter) 103 103 0.1 0.01 0.2-0.3 0.3-0.5 Zone with separate fronts
30 (winter) 103 102 0.05 0.01 0.2-0.3 0.3-0.5 Fuzzy zone with separate fronts
System SEC-EN
10 (spring) 102 102 -0.01 0.001 0.4-0.6 0.3-0.5 Patchy, unordered
30 (spring) 10 10 -10-3 10-3 0.4-0.6 0.4-0.6 Patchy, unordered
90 (spring) 10 10 -10-3 10-3 0.3-0.5 0.4-0.6 Narrow meandering zone
30 (autumn) 102 102 -0.05 0.01 0.5-0.8 0.4-0.6 Narrow meandering zone
Our data show that in the spring of 1993 the maximal seasonal gradient GrS = 1.0—1.4 °C/km, the minimal seasonal gradient is 0.05-0.1 °C/km, and the mean seasonal gradient for 1990-2000 is 0.5 °C/km. In spring and autumn (March, April; October, November) several fronts about 1500-2000 km long and up to 100 km wide are formed ; they are parallel to each other and extend latitudinally from the coast of Japan. In winter their structure changes significantly and
a TFZ is formed. It is about 200 km wide, of a wave structure, extending to 180 °E, indicating the K-O-NPC interaction system.
2.4. Analysis of the Structure of Frontal Zones in the South Pacific
To model the structure of SST gradient fields in the central equatorial Pacific or area ENSO, we chose 1998, when South Oscillation Index (SOI) was maximal and maximal SST anomalies were observed [34]. To compare, we modeled the situation in early spring (February-March), when EN was weakly pronounced, and in summer, when the EN structure was stable. The spring mean weekly gradient fields were of patchy structure, but in autumn and summer we observed a pronounced meandering zone about 300 km wide, extending to 1500W. As the SEC-EN system meanders in space, we could not reveal any mean monthly and mean seasonal cycles, but we determined mean seasonal GrS values. Along the 0-degree line of latitude, from 90°W to 150°W, maximal GrS = 0.5-0.8 °C/km, the mean value for 11 years is 0.21 °C/km, and maximal values are 0.02-0.05 °C/km. The total solar radiation is 10 kcal/cm2 month for periods of 10 days and 1 kcal/cm2 month for 30 and 90 days. Results of model experiments are presented in Table 1. The model experiments and the obtained gradients and structure of the TFZ formed by ACC, also known as the West Wind Drift, correspond to the MFC-ACC system in the model parameters of velocity and diffusion components.
3. Summary and Discussion
Using numerical modeling, we obtained results of the joint action of advection and diffusion and radiation flux on the formation of the temperature field and frontal zones. So, this paper examines the fundamental physical processes controlling the structure of frontal zones based on the 2D horizontal numerical model.
To forecast heat transfer, our model involved latitudinal and meridional components of ad-vection velocity, latitudinal and meridional components of turbulence factor, and solar radiation intensity. The stratified structure of the TFZ suggests that interaction of currents gives rise to divergence and convergence zones [30]. In this case, the leading role is played by the advection component. If the frontal zone has a patchy or interrupted structure, the diffusion process is a determining factor. These conclusions are confirmed by the Peclet number (Pe) for the evolution of the gradient temperature field ( [26]):
= If <4)
Here Lf is the length of the temperature front. In this case, the Peclet number indicates how inertial processes are related to diffusion processes. If the current is characterized by large Pe values, variations in the temperature field and fronts are influenced by changes in the field of velocities. If Pe is small and tends to unity, variations in the temperature gradient field occur under the impact of turbulent diffusion. The data of Table 1 and characterization of the TFZ structure can be used to estimate transient states in the process of heat transfer self-organization.
We obtained the data on spatial and temporal boundaries of frontal zones and determined the position of surface water mass within the bounds of some frontal zones in the Atlantic and the Pacific. As we know the spatial and temporal boundaries of water mass distribution, we can make assumptions about convergence and divergence of fluxes. Hence, we can make a provisional conclusion about the vertical component of the velocity of water mass transfer, which is necessary for 3D modeling. To estimate this component, we used a 1D model. In our case, we analyze the data obtained from the numerical model. The vertical component of velocity is about 10-4-10-5
m/sec, when nonuniform surface temperatures can arise and, under the impact of advection, form gradient zones. However, a significant factor is the zone that can be convergence or divergence. Stability of convergence and divergence zones can be estimated from distribution of TFZs.
The vertical diffusion component increases under the influence of wind; at the wind velocity 10 m/sec it is about 10-3 m2/sec, which lessens the effect of the vertical velocity component in the convergence zone. The lower cold water cannot ascend to the surface and the surface front is weakened. On the contrary, the wind load in the divergence zone causes front sharpening. It is also important to take into account the direction of the wind with respect to the front, because advection can be weakened if the wind is perpendicular to the frontline. Besides, the wind can give rise to the generation of upwelling zones, with large surface gradients and the vortex structure of the temperature field. These conclusions are confirmed by [35-37] The main conclusion of this work is that different impact of dynamic factors forms different frontal zones in the ocean. For example, local features of jet streams and drifts are of great significance on a seasonal scale. From season to season, the TFZ structure changes as a result of impact of different factors. In one season advection is most important and diffusion plays a minor part. In transitional seasons (spring and autumn), factors act concertedly. Then, diffusion may become dominant while the action of diffusion subsides.
The work was supported by the grants of RFBR 02-05-64740, RDF REC-002 (Ministry of Education RF, US-CRDF), RFBR 06-05-90872-Mol_a. I am also grateful to E.L.Krasova for her help in the preparation of this paper.
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Динамические особенности структуры фронтальных зон в океане для использования в численных моделях, основанных на спутниковых данных
Алексей В. Картушинский
В 'работе представлено обсуждение основных причин, которые приводят к обострению градиентов, которые влияют на изменение пространственного положения ТФЗ. В данном случае адвекция, турбулентная диффузия и солнечная радиация рассматриваются как главные факторы при формировании температурных фронтальных зон. В работе исследуются особенности динамики ТФЗ для Северной и Южной Атлантики, Северной и Южной части Тихого океана. Определяются схожие структурные черты ТФЗ для различных районов океана. На горизонтальной двумерной пространственной модели изучается влияние на формирование температурных фронтальных зон процессов адвективного переноса, турбулентной диффузии и интенсивности солнечной радиации, которые рассчитываются совместно и по отдельности. Представлены аналитические и численные оценки изменения величины температурных градиентов для основных фронтальных зон в океане, которые сравниваются со спутниковыми данными.
Ключевые слова: моделирование, градиенты температуры поверхности океана, температурные фронтальные зоны, адвекция, турбулентная диффузия, солнечная радиация, конвергентные структуры.
