Lakshmi H. Kantha

A Quasi-equilibrium Turbulent Energy Model for Geophysical Flows

Abstract The Mellor-Yamada hierarchy of turbulent closure models is reexamined to show that the elimination of a slight inconsistency in their analysis leads to a quasi-equilibrium model that is somewhat simpler than their level 2½ model. Also the need to impose realizability conditions restricting the dependence of exchange coefficients on shearing rates is eliminated. The model is therefore more robust while the principal advantage of the level 2½ model, namely the solution of a prognostic equation for turbulent kinetic energy is retained. Its performance is shown to be not much different from that of level 2½.

An improved mixed layer model for geophysical applications

An improved mixed layer model, based on second-moment closure of turbulence and suitable for application to oceanic and atmospheric mixed layers, is described. The model is tested against observational data from different locations in the global oceans, including high latitudes and tropics. The model belongs to the Mellor-Yamada hierarchy but incorporates recent findings from research on large eddy simulations and second-moment closure. The modified expansion of Galperin, Kantha, Hassid and Rosati (1988) that leads to a much simpler and more robust quasi-equilibrium turbulence model is employed instead of the original Mellor and Yamada (1974) model. Findings from ongoing research at the National Center for Atmospheric Research on large eddy simulations of the atmospheric boundary layer are utilized to improve parameterizations of pressure covariance terms in the second-moment closure. Shortwave solar radiation penetration is given careful treatment in the model so that the model is applicable to investigations of biological and photochemical processes in the upper ocean. But by far the major improvement is in the inclusion of the shear instability-induced mixing in the strongly stratified region below the oceanic mixed layer that leads to a more realistic and reliable mixed layer model that is suitable for application to a variety of geophysical mixed layers and circulation problems. The model appears to predict the mixing in the upper ocean well on a variety of time scales, from event scale storm-induced deepening and diurnal scale variability to seasonal time scales. With proper attention to the heat and salt balances in the upper ocean, it should be possible to use it for simulations of interannual variability as well. While the model validation has been primarily against oceanic mixed layer data sets, it is believed that the improvements can be readily incorporated into a model of the atmospheric boundary layer as well.

Numerical Simulations of Air-Sea Interaction under High Wind Conditions Using a Coupled Model: A Study of Hurricane Development

Abstract In this study, a coupled atmosphere–ocean wave modeling system is used to simulate air–sea interaction under high wind conditions. This coupled modeling system is made of three well-tested model components: The Pennsylvania State University–National Center for Atmospheric Research regional atmospheric Mesoscale Model, the University of Colorado version of the Princeton Ocean Model, and the ocean surface gravity wave model developed by the Wave Model Development and Implementation Group. The ocean model is initialized using a 9-month spinup simulation forced by 6-hourly wind stresses and with assimilation of satellite sea surface temperature (SST) and altimetric data into the model. The wave model is initialized using a zero wave state. The scenario in which the study is carried out is the intensification of a simulated hurricane passing over the Gulf of Mexico. The focus of the study is to evaluate the impact of sea spray, mixing in the upper ocean, warm-core oceanic eddies shed by the Gulf Loop ...

On the effect of surface gravity waves on mixing in the oceanic mixed layer

Abstract We apply a one-dimensional mixed layer model, based on second moment closure of turbulence, to study the effects of surface gravity waves on mixing in the oceanic mixed layer. The turbulent kinetic energy injected near the surface by breaking waves, and the kinetic energy input from Langmuir circulations that may exist in the presence of surface gravity waves, are both parameterized and included in the turbulence model. As expected, the wave breaking elevates both the turbulent kinetic energy and its dissipation rate in the upper few meters, well above the classical values expected from similarity theory for shear layers adjacent to a boundary. While there is a significant impact on mixed layer properties near the surface, wave breaking-induced turbulence decays rapidly with distance from the surface and hence the overall effects on the mixed layer are small. On the other hand, the energy input to turbulence from Langmuir cells elevates the turbulent kinetic energy and mixing throughout the mixed layer, and is therefore more effective in deepening the mixed layer. While the changes in sea surface temperature (SST) brought about by the inclusion of Langmuir cells are rather small on diurnal time scales, they can be appreciable over seasonal time scales. Nevertheless, these SST changes are well within the uncertainties in the modeled SST resulting from an imperfect knowledge of the air–sea fluxes used to drive the mixed layer models.

The Behavior of the Bulk – Skin Sea Surface Temperature Difference under Varying Wind Speed and Heat Flux

Abstract The observed and predicted response of the bulk – skin sea surface temperature difference (δT) to changes in the wind speed and net heat flux is analyzed. Observations of δT from the northern Atlantic and tropical Pacific Oceans demonstrate that the wind speed affects δT through the net heat flux and turbulent mixing. Increased winds typically increase the net heat flux, which increases the size of δT. At the same time, increased winds cause enhanced mixing, which decreases the size of δT. To predict the net change to δT, both effects must be properly modeled. The theoretical development of existing models for δT is traced and compared. All the models can be similarly derived from surface renewal theory with their differences resulting only from the corresponding definition of the dissipation rate. The differences are manifested in the predicted dependence of δT on the wind speed. The predicted δT values and wind speed dependencies are evaluated with the available δT observations to determine the...

Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides: 1. Model description and results

In this first part of a two-part paper we present results from a high-resolution, data-assimilative, fully nonlinear barotropic tidal model of the global oceans that excludes the Arctic. The model assimilates, in waters deeper than 1000 m, altimetric tides derived from the analysis of 2 years of TOPEX altimetric data. It also assimilates tide gage data from coastal tide gages. The model domain includes that covered by the altimeter and extends to the Antarctic. In the first part we present tidal results for the primary semidiurnal (M2, S2, N2, and K2) and diurnal (K1, O1, P1, and Q1) constituents. The second part deals with applications (Kantha, et al., this issue). The model results are compared with observational data from pelagic gages. These comparisons show that overall in the open ocean, in deep waters away from the margins of the primary basins, the model performance is comparable to other tidal models derived using TOPEX data, except for M2 and S2. However, one advantage of this model compared with those based solely on the analysis of altimetric data is that the altimetry-derived tides are subjected to dynamical constraints by the model. This results in reduction of subtidal variability often folded into tidal signals by TOPEX data analysis. It is also shown that in shallow waters along the margins, especially in east Asian marginal seas, the model differs substantially from these other models. In addition to sea surface heights, we also present dynamically consistent barotropic currents in the form of tidal ellipses for M2 and K1 constituents. Since the goal of this research is a global tidal model uniformly valid in both deep and shallow waters, we finally present tidal elevations and currents on two well-known shallow water areas, the northwest European shelf and the northeast American shelf, and a semienclosed western Pacific marginal sea, the Bering Sea. The model results are compared with independent observations and, where possible, with results from other numerical models. The results highlight the importance of bottom topography; on the northwest European shelf, where accurate bottom topography was included in the model, the results are much better than on the northeast American shelf, where the Digital Bathymetric Data Base 5 (DBDB5) topographic database has significant errors. Results from the Bering Sea, where the topography is more accurate than the DBDB5, compare well with known tides in the region.

Global baroclinic tides

An approximate estimate of the energy in the first mode M2 baroclinic tide has been made from satellite observations. Results based on TOPEX/POSEIDON (T/P) precision altimetry indicate that the internal tide patterns are similar to those expected from mid-ocean topographic features in the global oceans. Both the orthotide and harmonic analyses indicate that the total energy in global M2 baroclinic tide is approximately 50 PJ. For a variety of reasons, M2 is the only component that can be obtained reliably from altimetric measurements. Even then, the energy value may be an underestimate and the energy flux, the dissipation rate, cannot be deduced from altimetry. Since it is the tidal currents flowing over mid-ocean topographic features that are responsible for generating internal tides, a model calibrated by M2 observations is a plausible alternative. Currents from a high resolution (15°) barotropic tidal model have therefore been used to obtain an estimate of both the energy and the dissipation rate in M2, S2 and K1 baroclinic tides. A simple model of baroclinic tide generation has been used, and the unknown constant in this model has been selected to yield a total energy of 50 PJ in the first mode M2 baroclinic tide. Based on this calibration, the total energy is 8 PJ in S2 first mode baroclinic tide and 15 PJ in K1. The total in all first mode baroclinic tides is 90 PJ, about 16% of the total energy (580 PJ) in barotropic tides. The model results also suggest that about 360 GW of tidal energy are dissipated in M2 baroclinic tides alone, and 520 GW are dissipated in all first mode baroclinic tides. The latter value is approximately 15% of the power input into barotropic ocean tides (3490 GW) by the lunisolar tidal forces. We have preferred to be conservative and hence these are likely to be underestimates, especially since the altimetric tracks do not often intersect mid-ocean topographic features at optimum angles. While these values are very much within the range of earlier estimates in literature, they should be regarded as still uncertain to perhaps a factor of two (the dissipation rate could be anywhere from 400 GW to 800 GW, the most likely value being about 600 GW). The small signal to noise ratio involved in altimetric measurements of the surface manifestation of internal tides, and potential contamination by mesoscale signals are serious problems. In situ measurements at least a few locations underneath altimetric tracks are essential for confirmation and/or refinement of these preliminary estimates. Hopefully, these very first estimates of the energy and dissipation rate in global baroclinic tides, though rather crude, will serve as a catalyst for a better estimation in the future, since internal tides are likely to be a prominent source of mixing in the deep oceans and important to thermocline maintenance.

A real‐time oceanographic nowcast/forecast system for the Mediterranean Sea

We describe here a nowcast/forecast system for the entire Mediterranean Sea, designed for real-time forecasts and closely resembling operational numerical weather prediction systems. The core of the system is a high-resolution (10 km) three-dimensional primitive equation-based, sigma-coordinate numerical circulation model, assimilating remotely sensed multi-channel sea surface temperature and in situ expendable bathythermograph/conductivity-temperature-depth observational data, using an optimal-interpolational scheme. We present results for 1993 and 1994 from this data-assimilation model, focusing principally on the mesoscale features prevalent in the western and eastern Mediterranean Sea. We show that the model exhibits considerable skill in simulating both the permanent and transient mesoscale features in the Mediterranean. In particular, hitherto less well-known and less well-studied circulation features in the Adriatic and Aegean Seas are carefully examined and presented. Particular care is given to discussing the circulation in the entire Mediterranean, with particular attention to flows through various straits and their variability.

On the heat and mass transfer from an ascending magma

The maximum heat transfer possible from a sphere of magma ascending through a viscous lithosphere is estimated using a Nusselt number formulation. An upper bound is found for the Nusselt number by using the characteristics of a potential flow which, it is argued, is similar in the limit to a non-isothermal Stokes-flow in which the fluid (wall rock) viscosity is sensitive to temperature. A set of cooling curves are calculated for a magma ascending at a constant velocity beneath an island arc. If the magma is to arrive at the surface without solidifying its ascent velocity must be greater than about 5.8 × 10−3 cm s−1, for a magma radius of 1 km, and greater than about 2.7 × 10−5 cm s−1, for a magma radius of 6 km. If the magma begins its ascent crystal free it will generally become superheated over most of its ascent. Using essentially the same formulation as for heat transfer the mass transfer to or from a spherical body of magma ascending at these velocities is given approximately by ΔC ⋍ ΔW/10, where ΔC is the change in weight percent of a component in the magma during ascent and ΔW is the compositional contrast of that component between the magma and its wall rock.

Time to replace the Saffir-Simpson hurricane scale?

The 2005 hurricane season set many new records, including the most named storms (26) and the most hurricanes in a season (14). Of the four hurricanes that made landfall in the U.S., three (Katrina, Rita, and Wilma) reached Category 5, struck the Gulf Coast, and inflicted severe damage and loss of life. Hurricane Wilma had an observed sealevel center pressure of 882 millibar (mbar) at its peak and is the strongest hurricane ever recorded in the Atlantic Ocean. Katrina damaged vast areas along the Mississippi coast, flooded large parts of New Orleans, and is the most destructive hurricane on record