Wind Curl Research Articles

The Beaufort Gyre variation and its impacts on the Canada Basin in 2003–2012

The Beaufort Gyre (BG) was spun up in the last decade which is an important factor in regulating the variation of the upper ocean. The heat content and freshwater content of the upper ocean increased gradually in the Canada Basin, as did momentum input. Both the geostrophic wind curl and freshwater content could contribute to the spin-up of BG. However, even though there is no change of the wind field the increasing freshwater alone could result in the spin-up of BG. In this study we show that the Pacific Water is difficult to flow into the central basin as the BG spins up and the maximum temperature of the Pacific Summer Water (PSW) experienced a dramatic decrease inside the BG in 2005 and 2009 due to a change of flow pathway of PSW. The enhancement of Ekman Pumping (EP) contributed to the deepening of the Pacific Winter Water by piling up more freshwater. This change of water column dynamics has also contributed to the deepening ofthe Atlantic Water core after 2007. The EP decreased significantly in 2012 (indicating a spin down of BG) and the direction of Ekman transport turned to the north, which favoured the release of freshwater that had resided in the basin for years.

Connection of sea level variability between the tropical western Pacific and the southern Indian Ocean during recent two decades

Based on the merged satellite altimeter data and in-situ observations, as well as a diagnosis of linear baroclinic Rossby wave solutions, this study analyzed the rapidly rise of sea level/sea surface height (SSH) in the tropical Pacific and Indian Oceans during recent two decades. Results show that the sea level rise signals in the tropical west Pacific and the southeast Indian Ocean are closely linked to each other through the pathways of oceanic waveguide within the Indonesian Seas in the form of thermocline adjustment. The sea level changes in the southeast Indian Ocean are strongly influenced by the low-frequency westward-propagating waves originated in the tropical Pacific, whereas those in the southwest Indian Ocean respond mainly to the local wind forcing. Analyses of the lead-lag correlation further reveal the different origins of interannual and interdecadal variabilities in the tropical Pacific. The interannual wave signals are dominated by the wind variability along the equatorial Pacific, which is associated with the El Nino-Southern Oscillation; whereas the interdecadal signals are driven mainly by the wind curl off the equatorial Pacific, which is closely related to the Pacific Decadal Oscillation.

Three-dimensional properties of mesoscale eddies in the South China Sea based on eddy-resolving model output

Last decade has witnessed extensive studies on mesoscale oceanic eddies in the Southern China Sea (SCS), however most of these studies are focused on the surface eddies, and three-dimensional features of eddies are not well known except some individual eddies. We apply a three-dimensional eddy detection scheme to a 9-year (2000–2008) eddy-resolving numerical solution to acquire three-dimensional eddy data set in the SCS. The model solution is validated with observational data in terms of both seasonal and intra-seasonal scales. The statistical characteristics of eddies at the sea surface, such as eddy number, lifetime and radius, from the model are comparable with those derived from the satellite altimetry data. The vertical profiles of the physical features of eddies are exposed from the statistical analysis of the three-dimensional eddy data set. For examples, more cyclonic eddies (CEs) are generated than anticyclonic eddies (AEs) in the depth above about 350m and an opposite trend is presented below 350m. The lifetimes of CEs and AEs are statistically equal and no significant variation at different vertical levels. Eddies in the central SCS have the largest size than in other areas and their sizes decrease with the increase in water depth. The relative vorticity amplitude of eddies decreases with the increase in the depth. There are three different types of eddies: bowl-shaped with the largest size at the surface, lens-shaped with the largest size in the middle and cone-shaped with the largest size at the bottom. Most of eddies are bowl-shaped eddies. The three types of eddies have different effects on the temperature and salinity profiles. Eddy genesis mechanisms are discussed and categorized into three types in the SCS: surface wind curl input, current interaction with the bottom topography and Kuroshio intrusion.

Seasonal and interannual variability of the Black Sea eddies and its dependence on characteristics of the large-scale circulation

Mesoscale eddies in the Black Sea basin are investigated by automated eddy identification method (winding angle) using satellite altimetry data for 1992–2011. Seasonal and interannual eddy variability is strongly affected by the intensity of basin-scale circulation. Weakening of large-scale circulation in response to the decrease of the wind curl leads to the baroclinic instability of the Rim current and enhanced formation of mesoscale anticyclones. Increasing wind curl and circulation induce intensive formation of mesoscale cyclones. Intense developed large-scale circulation leads to the decrease in the number of both cyclonic and anticyclonic eddies. Eddies properties (orbital velocity, energy and lifetime) on the interannual time scales also depend on the intensity of the large-scale circulation. It was shown that the most powerful and long-lived anticyclones are generated in years with intense currents, right after the currents begin slowing down, which is related to the transfer of energy from large- to meso-spatial scales. Mechanisms of eddies formation and dissipation are discussed.

The formation of wind curl in the marine atmosphere boundary layer over the East China Sea Kuroshio in spring

Various data are used to investigate the characteristics of the surface wind field and rainfall on the East China Sea Kuroshio (ESK) in March and April, 2011. In March, the wind speed maximum shows over the ESK front (ESKF) in the 10 meter wind field, which agrees with the thermal wind effect. A wind curl center is generated on the warm flank of the ESKF. The winds are much weaker in April, so is the wind curl. A rainband exists over the ESKF in both the months. The Weather Research and Forecasting (WRF) model is used for further researches. The winds on the top of the marine atmosphere boundary layer (MABL) indicate that in March, a positive wind curl is generated in the whole MABL over the warm flank of the ESKF. The thermal wind effect forced by the strong SST gradient overlying the background wind leads to strong surface northeasterly winds on the ESKF, and a positive shearing vorticity is created over the warm flank of the ESKF to generate wind curl. In the smoothed sea surface temperature experiment, the presence of the ESKF is responsible for the strong northeast winds in the ESKF, and essential for the distribution of the rainfall centers in March, which confirms the mechanism above. The same simulation is made for April, 2011, and the responses from the MABL become weak. The low background wind speed weakens the effect of the thermal wind, thus no strong Ekman pumping is helpful for precipitation. There is no big difference in rainfall between the control run and the smooth SST run. Decomposition of the wind vector shows that local wind acceleration induced by the thermal wind effect along with the variations in wind direction is responsible for the pronounced wind curl/divergence over the ESKF.

Enhanced 2-h–8-day Oscillations Associated with Tropical Instability Waves

Abstract The westward South Equatorial Current (SEC) and eastward Equatorial Undercurrent (EUC) is a marginally stable current system due to the strong vertical shear. The existence of wavelike motions may locally reduce the Richardson number enough to trigger instabilities. Here, velocity measurements from the Tropical Atmosphere Ocean (TAO) array are used to examine the variability of oscillations within 0.125–12 cycles per day (cpd). It is found that the 0.125–12-cpd oscillations become more energetic in the presence of strong tropical instability waves (TIWs). The enhancement of shear variance is most pronounced around the EUC core (115 m), while prominent elevation of kinetic energy occurs around 85 m, where the EUC shear is strongest. Particularly, the energetic 0.125–12-cpd oscillations during strong TIW seasons do not cycle on a daily basis and are more evident during the southward phase of TIWs. The enhanced 0.125–12-cpd oscillations during strong TIW seasons can be ascribed neither to the changing background stratification nor to the vertical migration of EUC core at the corresponding time scales. Its strength is tightly correlated with the EUC shear and, to a lesser extent, the TIW shear. A partial correlation analysis suggests that the correlation to the TIW shear is mainly due to the association between EUC and TIW shear. The strength of the 0.125–12-cpd oscillations does not follow the variation of surface wind speed and wind curl, implying that they are not directly generated by surface wind forcing.

Process-based analysis of climate model ENSO simulations: Intermodel consistency and compensating errors

Systematic and compensating errors can lead to degraded predictive skill in climate models. Such errors may be identified by comparing different models in an analysis of individual physical processes. We examine model simulations of El Nino–Southern Oscillation (ENSO) in five Coupled Model Intercomparison Project (CMIP) models, using transfer functions to analyze nine processes critical to ENSO's dynamics. The input and output of these processes are identified and analyzed, some of which are motivated by the recharge oscillator theory. Several errors and compensating errors are identified. The east-west slope of the equatorial thermocline is found to respond to the central equatorial Pacific zonal wind stress as a damped driven harmonic oscillator in all models. This result is shown to be inconsistent with two different formulations of the recharge oscillator. East Pacific sea surface temperature (SST) responds consistently to changes in the thermocline depth in the eastern Pacific in the five CMIP models examined here. However, at time scales greater than 2 years, this consistent model response disagrees with observations, showing that the SST leads thermocline depth at long time scales. Compensating errors are present in the response of meridional transport of water away from the equator to SST: two different models show different response of the transport to off-equatorial wind curl and wind curl response to East Pacific SST. However, these two models show the same response of meridional transport to East Pacific SST. Identification of errors in specific physical processes can hopefully lead to model improvement by focusing model development efforts on these processes.

Phosphorus speciation and transformation along transects in the Benguela upwelling region

Transformation of phosphate (PO4) introduced by upwelling into the 20m surface layer was studied four times in turn along a transect perpendicular to the coast of Namibia from August 27th to September 15th 2011. [33P]PO4 uptake rates as well as the concentrations of inorganic nutrients (PO4, NO2/3), dissolved and particulate organic phosphorus, and particulate organic carbon and nitrogen were measured and the respective stoichiometry was determined. The fate and interactions of these components are described in relation to both the distance from the coast and a calculated “pseudoage” of the water masses to get knowledge about the phosphorus dynamics during surface transport and aging of upwelled water. PO4 decreased from 1.6μM in the upwelling cell near the coast to 0.4μM at remote stations. The decrease in PO4 was lower than that of nitrate, resulting in a lower N:P ratio seawards (from 12–16 to 5–9). PO4 depletion was reflected only partially in increasing DOP, but not in POP concentrations. Concentrations of POP, POC and PON decreased with the distance from the coast and with “pseudoage”, indicating that produced particulate matter is removed from the upper 20m layer. A mean PO4 turnover time of 57days, based on [33P]PO4 uptake measurements, suggested complete PO4 consumption within the transects and thus the need for an additional PO4 supply to sustain the gradient. Fast mineralisation of DOP could be one mechanism. Deduced from our bioassays, PO4 seemed to be transformed into DOP by heterotrophic bacteria which was mineralized back to PO4 within few days.Hence, our results support the hypothesis that the observed PO4 gradient in the 20m surface layer is not only due to input in the upwelling center and locomotion to the open ocean by Ekman transport combined with utilization by phyto- and bacterioplankton. PO4 has to be provided by remineralisation and input from deeper layers probably by wind curl driven mixing processes. However, most of the produced particulate organic matter seems to be transformed in the pelagial and enters the food web.

Interannual Bottom Pressure Signals in the Australian–Antarctic and Bellingshausen Basins

Abstract Analyses of large-scale (>750 km) ocean bottom pressure pb fields, derived from the Gravity Recovery and Climate Experiment (GRACE) and from an Estimating the Circulation & Climate of the Ocean (ECCO) state estimate, reveal enhanced interannual variability, partially connected to the Antarctic Oscillation, in regions of the Australian–Antarctic Basin and the Bellingshausen Basin, with pb magnitudes comparable to those of sea level and good correlation between the GRACE and ECCO pb series. Consistent with the theory of Gill and Niiler, the patterns of stronger pb variability are partly related to enhanced local wind curl forcing and weakened gradients in H/f, where H is ocean depth and f is the Coriolis parameter. Despite weaker H/f gradients, motions against them are sufficiently strong to play a role in balancing the local wind input. Topographic effects are as or more important than changes in f. Additionally, and contrary to the dominance of barotropic processes at subannual time scales, baroclinic effects are not negligible when balancing wind input at periods of a few years. Results highlight the emerging capability to accurately observe and estimate interannual changes in large-scale pb over the Southern Ocean, with implications for the interpretation of low-frequency variability in sea level in terms of steric height and heat content.

Daily composite wind fields from Oceansat-2 scatterometer

Oceansat-2 scatterometer (OSCAT) is an active microwave sensor, intended to provide ocean surface wind vectors over the global oceans. In the present work, an attempt has been made to generate daily composites of OSCAT Level-3 (L3) wind vectors using Data-Interpolating Variational Analysis (DIVA) method from ascending and descending passes over the Indian Ocean region. This could be useful for operational purposes and in generating value-added products like wind stress and curl of wind stress. The daily composite wind vectors of zonal (U) and meridional (V) components have been validated by comparing with Advanced Scatterometer (ASCAT) and wind from in situ buoys for the year 2012. Wind composites thus generated using DIVA are found to match well with in situ, and ASCAT wind products. Minor deviations are observed with respect to ASCAT wind, which could be attributed to the difference in interpolation techniques used for the two scatterometer products. Given that the repeat period of ASCAT is 5 days and that of OSCAT is only 2 days, OSCAT wind products could be conveniently used for real-time met-ocean studies.

Climate impacts of stochastic atmospheric perturbations on the ocean

An Interactive Ensemble (IE) platform was established based on a Standard Coupled (SC) climate model with seven atmosphere–land model realizations coupled to a single ocean model and a single sea ice model. The IE strategy reduces stochastic noise generated by atmospheric dynamics and therefore can be used to estimate the impact of atmospheric perturbations on the ocean. The atmospheric noise reduction shallows the mixed layer, modifies the oceanic upwelling/downwelling, and cools the surface. It is assumed that the deterministic part of the surface cooling is due to the reduced heat capacity of the mixed layer in high latitudes and the changed surface wind curl that causes upwelling/downwelling. The positive albedo feedback is responsible for the polar amplified changes. The weakening of meridional overturning circulation (MOC) further suppresses ocean heat transport to the Northern Hemisphere. The model results suggest that the irregular El Nino Southern Oscillation (ENSO) cycle partly arises from the stochastic perturbation in the atmosphere. Comparison between the IE and the SC simulations also indicates the overestimated atmospheric perturbations in the SC model.

Linear Wind-Forced Beta Plumes with Application to the Hawaiian Lee Countercurrent*

Abstract Two numerical ocean models are used to study the baroclinic response to forcing by localized wind stress curl (i.e., a wind-forced β plume, which is a circulation cell developing to the west of the source region and composed of a set of zonal jets) with implications for the Hawaiian Lee Countercurrent (HLCC): an idealized primitive equation model [Regional Ocean Modeling System (ROMS)], and a global, eddy-resolving, general circulation model [Ocean General Circulation Model for the Earth Simulator (OFES)]. In addition, theoretical ideas inferred from a linear continuously stratified model are used to interpret results. In ROMS, vertical mixing preferentially damps higher-order vertical modes. The damping thickens the plume to the west of the forcing region, weakening the near-surface zonal jets and generating deeper zonal currents. The zonal damping scale increases monotonically with the meridional forcing scale, indicating a dominant role of vertical viscosity over diffusion, a consequence of the small forcing scale. In the OFES run forced by NCEP reanalysis winds, the HLCC has a vertical structure consistent with that of idealized β plumes simulated by ROMS, once the contribution of the North Equatorial Current (NEC) has been removed. Without this filtering, a deep HLCC branch appears artificially separated from the surface branch by the large-scale intermediate-depth NEC. The surface HLCC in two different OFES runs exhibits sensitivity to the meridional wind curl scale that agrees with the dynamics of a β plume in the presence of vertical viscosity. The existence of a deep HLCC extension is also suggested by velocities of Argo floats.

The Response of the Surface Circulation of the Arabian Sea to Monsoonal Forcing

AbstractTwo decades of drifter and satellite data allow the authors to describe the seasonal evolution of the surface circulation of the Arabian Sea, which reverses annually with the Indian monsoon winds. This study finds several features that advance current understanding. Most significantly, northward flow appears along the length of the western boundary, together with a weak anticyclone at 6°N (a precursor to the Great Whirl) as early as March or April, one or two months before the southwest monsoon winds. This circulation is driven by planetary waves, which are initiated by wind curl forcing during the previous southwest monsoon, leading the authors to speculate that there is an oceanic mechanism through which one monsoon may precondition the next. Second, the authors find that the eastward South Equatorial Counter Current (SECC) is present year-round, fed by the northward East African Coastal Current (EACC). During the southwest monsoon the EACC overshoots the equator and splits, feeding both northward into the Somali Current and eastward into the SECC by looping back across the equator. This retroflection of the EACC is what was previously known as the southern gyre. At the surface, this circulation is obscured by strong, locally wind-driven, cross-equatorial transport. The semiannual variability of the SECC is governed by Ekman pumping over the equatorial gyre. Finally, there is broad, strong eastward flow at the mouth of the Gulf of Aden throughout the southwest monsoon, coincident with alongshore winds and a switch in sign of the wind stress curl along the axis of the atmospheric monsoon jet.

Leading Modes of the Upper-Ocean Temperature Interannual Variability along the Equatorial Atlantic Ocean in NCEP GODAS

Abstract In this work, the authors analyze the physical mechanisms of interannual variability of the upper-ocean temperature anomaly (OTA) in the equatorial Atlantic Ocean, using ocean reanalysis from the National Centers for Environmental Prediction (NCEP) Global Ocean Data Assimilation System. The variability of equatorial Atlantic OTA is dominated by two leading modes. The first mode is characterized by same-sign variation along the thermocline with pronounced amplitude in the central and eastern equatorial Atlantic. This mode represents the modulation of the overall thermocline depth at the equator generated by net heat convergence in the equatorial ocean, with heat content first accumulated mainly in the off-equatorial northwestern Atlantic in response to anomalous wind curl associated with Atlantic meridional mode. The second leading mode shows an opposite variation between the western and eastern Atlantic. This mode is mainly driven by the zonal wind stress fluctuation confined in the southwestern tropical and equatorial Atlantic and reflects the equatorial balanced response between the zonal slope of the equatorial thermocline depth and the atmospheric zonal wind variations with pronounced surface wind and ocean anomalies in the southwestern and equatorial ocean. The different characteristics of these two modes suggest that they may occur independently. In fact, evolution of the two leading modes is approximately in quadrature, and they may also occur in sequence on interannual time scales. The two leading mode-associated air–sea interaction processes suggest that the Atlantic meridional mode and zonal mode are statistically and physically connected in their evolution.

Mode water ventilation and subtropical countercurrent over the North Pacific in CMIP5 simulations and future projections

Seventeen coupled general circulation models from the Coupled Model Intercomparison Project Phase 5 (CMIP5) are analyzed to assess the dynamics and variability of the North Pacific Subtropical Countercurrent (STCC). Consistent with observations, the STCC is anchored by mode water to the north. For the present climate, the STCC tends to be stronger in models than in observations because of too strong a low potential vorticity signature of mode water. There are significant variations in mode water simulation among models, i.e., in volume and core layer density. The northeast slanted bands of sea surface height (SSH) anomalies associated with the STCC variability are caused by variability in mode water among models and the Hawaii islands are represented in some models, where the island‐induced wind curls drive the Hawaiian Lee Countercurrent (HLCC) located to the south of STCC. Projected future changes in STCC and mode water under the Representative Concentration Pathways (RCP) 4.5 scenario are also investigated. By combining the historical and RCP 4.5 runs, an empirical orthogonal function analysis for SSH over the central subtropical gyre (160°E–140°W, 15°–30°N) is performed. The dominant mode of SSH change in 17 CMIP5 models is characterized by the weakening of the STCC because of the reduced formation of mode water. The weakened mode water is closely related to the increased stratification of the upper ocean, the latter being one of the most robust changes as climate warms. Thus the weakened STCC and mode water are common to CMIP5 future climate projections.

A dipole wind curl pattern induced by Taiwan Island and its effect on upper stratification in the northeastern South China Sea

Using hydrographic data sampled during four successive late summer-early autumn cruises in 2004-2007, vertical stratification along transects in the lee of Taiwan Island was analyzed to investigate upper ocean responses to orographically induced dipole wind stress curl (WSC). Results indicate that mixed-layer depth (MLD) and its relationship with thermocline depth varied under different local wind forcings. Average MLD along the transects from the 2004 to 2007 cruises were 18.5, 30.7, 39.2 and 24.5 m, respectively. The MLD along the transects deepened remarkably and resulted in thermocline ventilation in 2005 and 2006, whereas ventilation did not occur in 2004 and 2007. Estimates indicate that frictional wind speed was the major factor in MLD variations. To a large degree, the combined effects of frictional wind speed and Ekman pumping are responsible for the spatial pattern of MLD during the cruises.

Generation and validation of analysed wind vectors over the global oceans

Daily and 12 hourly gridded analysed wind vectors (AWVs) over global ocean were generated using the simple spatial interpolation scheme of ‘box averaging’, with a horizontal resolution of 0.5° × 0.5°. For daily analysed winds, observations only from Oceansat-2 Scatterometer (OSCAT) were used. The 12 hourly AWVs were generated by combining the data from both OSCAT and Advanced Scatterometer (ASCAT). Apart from ocean wind vectors, an effort was made also to produce analysed wind stress, divergence and curl of wind stress. The daily and 12 hourly analysed winds were validated using in situ observations from 97 global moored buoys and data from European Centre for Medium Range Weather Forecasting analyses for a period of 9 months. The validation result shows a good agreement between AWV products and the buoy and model analysis data, yielding a standard deviation of around 2 m s−1 in wind speed and around 20° in wind direction.

Large‐scale coherence in New England lobster (Homarus americanus), settlement and associations with regional atmospheric conditions

AbstractTime series of American lobster (Homarus americanus) postlarval settlement from southern New England to Atlantic Canada exhibit many common features, and a cluster analysis indicates a block of regions extending from Massachusetts to Maine that have coherent interannual variations. The spatial scale of this block suggests that variability in settlement is related to large‐scale, rather than local, processes. We examined the association between settlement at six reference regions and monthly mean atmospheric conditions (temperature, geopotential height, westerly and southerly wind components, and wind curl) from the North American Regional Reanalysis. We first extracted the dominant modes of variability in monthly averaged geopotential height, temperature, and wind curl. The leading mode from September, which represents high geopotential height, warm temperatures, and negative wind curl throughout the study area, was strongly correlated with settlement at most of the regions. The third mode from August, which represents enhanced southwesterly winds, was correlated with settlement in Rhode Island. Correlations between local atmospheric conditions and lobster settlement confirm the principal component results. Settlement was correlated to varying degrees with geopotential height (positive), temperature (positive) and wind curl (negative) with lobster settlement at the northern sites, with temperature being a stronger indicator in the north and curl a stronger indicator in the south. Rhode Island settlement was strongly correlated with August westerly winds. The correlation between settlement and atmospheric conditions could improve our understanding of stock‐recruit relationships for lobster populations and provides one mechanism for how climate change could impact lobsters.

Exploring Mechanisms of Variability and Predictability of Atlantic Meridional Overturning Circulation in Two Coupled Climate Models

Abstract Multidecadal variability in the Atlantic meridional overturning circulation (AMOC) of the ocean is diagnosed in the NCAR Community Climate System Model, version 3 (CCSM3), and the GFDL Coupled Model (CM2.1). Common diagnostic approaches are applied to draw out similarities and differences between the two models. An index of AMOC variability is defined, and the manner in which key variables covary with it is determined. In both models the following is found. (i) AMOC variability is associated with upper-ocean (top 1 km) density anomalies (dominated by temperature) on the western margin of the basin in the region of the Mann eddy with a period of about 20 years. These anomalies modulate the trajectory and strength of the North Atlantic Current. The importance of the western margin is a direct consequence of the thermal wind relation and is independent of the mechanisms that create those density anomalies. (ii) Density anomalies in this key region are part of a larger-scale pattern that propagates around the subpolar gyre and acts as a “pacemaker” of AMOC variability. (iii) The observed variability is consistent with the primary driving mechanism being stochastic wind curl forcing, with Labrador Sea convection playing a secondary role. Also, “toy models” of delayed oscillator form are fitted to power spectra of key variables and are used to infer “quality factors” (Q-factors), which characterize the bandwidth relative to the center frequency and hence AMOC predictability horizons. The two models studied here have Q-factors of around 2, suggesting that prediction is possible out to about two cycles, which is likely larger than the real AMOC.

Impact of the Atmospheric Mean State on Tropical Instability Wave Activity

Abstract The features of simulated tropical instability waves (TIWs) in the Pacific Ocean are compared between atmospheric models of two different resolutions coupled with a uniform oceanic model. Results show that TIWs are more active in the high-resolution model, even though it includes atmospheric negative feedback. Such negative feedback is not identified in the low-resolution atmospheric model because of the absence of atmospheric responses. Comparison of the energetics between the two models shows that the large TIW activity in the higher-resolution model is due to the difference in barotropic energy sources near the surface. A high-resolution atmosphere results in a tighter intertropical convergence zone and associated stronger wind curl and shear. This causes a stronger surface current shear between the South Equatorial Current (SEC) and North Equatorial Counter Current (NECC), which is one of the main sources of TIW kinetic energy. These results indicate the important role of the atmospheric mean field on TIW activity and the advantage of using high-resolution models to represent coupling among multiscale phenomena.