Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models

This paper seeks to illustrate the point that physical inconsistencies between thermodynamics and dynamics usually introduce nonconservative production/destruction terms in the local total energy balance equation in numerical ocean general circulation models (OGCMs). Such terms potentially give rise to undesirable forces and/or diabatic terms in the momentum and thermodynamic equations, respectively, which could explain some of the observed errors in simulated ocean currents and water masses. In this paper, a theoretical framework is developed to provide a practical method to determine such nonconservative terms, which is illustrated in the context of a relatively simple form of the hydrostatic Boussinesq primitive equation used in early versions of OGCMs, for which at least four main potential sources of energy nonconservation are identified; they arise from: (1) the “hanging” kinetic energy dissipation term; (2) assuming potential or conservative temperature to be a conservative quantity; (3) the interaction of the Boussinesq approximation with the parameterizations of turbulent mixing of temperature and salinity; (4) some adiabatic compressibility effects due to the Boussinesq approximation. In practice, OGCMs also possess spurious numerical energy sources and sinks, but they are not explicitly addressed here. Apart from (1), the identified nonconservative energy sources/sinks are not sign definite, allowing for possible widespread cancellation when integrated globally. Locally, however, these terms may be of the same order of magnitude as actual energy conversion terms thought to occur in the oceans. Although the actual impact of these nonconservative energy terms on the overall accuracy and physical realism of the oceans is difficult to ascertain, an important issue is whether they could impact on transient simulations, and on the transition toward different circulation regimes associated with a significant reorganization of the different energy reservoirs. Some possible solutions for improvement are examined. It is thus found that the term (2) can be substantially reduced by at least one order of magnitude by using conservative temperature instead of potential temperature. Using the anelastic approximation, however, which was initially thought as a possible way to greatly improve the accuracy of the energy budget, would only marginally reduce the term (4) with no impact on the terms (1), (2) and (3).

Assessing and understanding the impact of stratospheric dynamics and variability on the earth system

Advances in weather and climate research have demonstrated the role of the stratosphere in the Earth system across a wide range of temporal and spatial scales. Stratospheric ozone loss has been identified as a key driver of Southern Hemisphere tropospheric circulation trends, affecting ocean currents and carbon uptake, sea ice, and possibly even the Antarctic ice sheets. Stratospheric variability has also been shown to affect short term and seasonal forecasts, connecting the tropics and midlatitudes and guiding storm track dynamics. The two-way interactions between the stratosphere and the Earth system have motivated the World Climate Research Programme's (WCRP) Stratospheric Processes and Their Role in Climate (SPARC) DynVar activity to investigate the impact of stratospheric dynamics and variability on climate. This assessment will be made possible by two new multi-model datasets. First, roughly 10 models with a well resolved stratosphere are participating in the Coupled Model Intercomparison Project 5 (CMIP5), providing the first multi-model ensemble of climate simulations coupled from the stratopause to the sea floor. Second, the Stratosphere Historical Forecasting Project (SHFP) of WCRP's Climate Variability and predictability (CLIVAR) program is forming a multi-model set of seasonal hindcasts with stratosphere resolving models, revealing the impact of both stratospheric initial conditions and dynamics on intraseasonal prediction. The CMIP5 and SHFP model-data sets will offer an unprecedented opportunity to understand the role of the stratosphere in the natural and forced variability of the Earth system and to determine whether incorporating knowledge of the middle atmosphere improves seasonal forecasts and climate projections. Capsule New modeling efforts will provide unprecedented opportunities to harness our knowledge of the stratosphere to improve weather and climate prediction.

The link between the Barents Sea and ENSO events simulated by NEMO model

An analysis of observational data in the Barents Sea along a meridian at 33°30' E between 70°30' and 72°30' N has reported a negative correlation between El Niño/La Niña Southern Oscillation (ENSO) events and water temperature in the top 200 m: the temperature drops about 0.5 °C during warm ENSO events while during cold ENSO events the top 200 m layer of the Barents Sea is warmer. Results from 1 and 1/4-degree global NEMO models show a similar response for the whole Barents Sea. During the strong warm ENSO event in 1997–1998 an anomalous anticyclonic atmospheric circulation over the Barents Sea enhances heat loses, as well as substantially influencing the Barents Sea inflow from the North Atlantic, via changes in ocean currents. Under normal conditions along the Scandinavian peninsula there is a warm current entering the Barents Sea from the North Atlantic, however after the 1997–1998 event this current is weakened. During 1997–1998 the model annual mean temperature in the Barents Sea is decreased by about 0.8 °C, also resulting in a higher sea ice volume. In contrast during the cold ENSO events in 1999–2000 and 2007–2008, the model shows a lower sea ice volume, and higher annual mean temperatures in the upper layer of the Barents Sea of about 0.7 °C. An analysis of model data shows that the strength of the Atlantic inflow in the Barents Sea is the main cause of heat content variability, and is forced by changing pressure and winds in the North Atlantic. However, surface heat-exchange with the atmosphere provides the means by which the Barents sea heat budget relaxes to normal in the subsequent year after the ENSO events.

Foreword: International Space Science Institute (ISSI) workshop on the Earth’s cryosphere and sea level change

Rising sea level is perhaps the most severe consequence of climate warming, as much of the world’s population and infrastructure is located near current sea level (Lemke et al. 2007). A major rise of a metre or more would cause serious problems. Such possibilities have been suggested by Hansen and Sato (2011) who pointed out that sea level was several metres higher than now during the Holsteinian and Eemian interglacials (about 250,000 and 120,000 years ago, respectively), even though the global temperature was then only slightly higher than it is nowadays. It is consequently of the utmost importance to determine whether such a sea level rise could occur and, if so, how fast it might happen. Sea level undergoes considerable changes due to natural processes such as the wind, ocean currents and tidal motions. On longer time scales, the sea level is influenced by steric effects (sea water expansion caused by temperature and salinity changes of the ocean) and by eustatic effects caused by changes in ocean mass. Changes in the Earth’s cryosphere, such as the retreat or expansion of glaciers and land ice areas, have been the dominant cause of sea level change during the Earth’s recent history. During the glacial cycles of the last million years, the sea level varied by a large amount, of the order of 100 m. If the Earth’s cryosphere were to disappear completely, the sea level would rise by some 65 m. The scientific papers in the present volume address the different aspects of the Earth’s cryosphere and how the different changes in the cryosphere affect sea level change. It represents the outcome of the first workshop held within the new ISSI Earth Science Programme. The workshop took place from 22 to 26 March, 2010, in Bern, Switzerland, with the objective of providing an in-depth insight into the future of mountain glaciers and the large land ice areas of Antarctica and Greenland, which are exposed to natural and anthropogenic climate influences, and their effects on sea level change. The participants of the workshop are experts in different fields including meteorology, climatology, oceanography, glaciology and geodesy; they use advanced space-based observational studies and state-of-the-art numerical modelling.

Granular flow in the marginal ice zone

The region of sea ice near the edge of the sea ice pack is known as the marginal ice zone (MIZ), and its dynamics are complicated by ocean wave interaction with the ice cover, strong gradients in the atmosphere and ocean and variations in sea ice rheology. This paper focuses on the role of sea ice rheology in determining the dynamics of the MIZ. Here, sea ice is treated as a granular material with a composite rheology describing collisional ice floe interaction and plastic interaction. The collisional component of sea ice rheology depends upon the granular temperature, a measure of the kinetic energy of flow fluctuations. A simplified model of the MIZ is introduced consisting of the along and across momentum balance of the sea ice and the balance equation of fluctuation kinetic energy. The steady solution of these equations is found to leading order using elementary methods. This reveals a concentrated region of rapid ice flow parallel to the ice edge, which is in accordance with field observations, and previously called the ice jet. Previous explanations of the ice jet relied upon the existence of ocean currents beneath the ice cover. We show that an ice jet results as a natural consequence of the granular nature of sea ice.

Spatial and temporal variations of the seasonal sea level cycle in the northwest Pacific

The seasonal sea level variations observed from tide gauges over 1900-2013 and gridded satellite altimeter product AVISO over 1993-2013 in the northwest Pacific have been explored. The seasonal cycle is able to explain 60-90% of monthly sea level variance in the marginal seas, while it explains less than 20% of variance in the eddy-rich regions. The maximum annual and semi-annual sea level cycles (30cm and 6cm) are observed in the north of the East China Sea and the west of the South China Sea respectively. AVISO was found to underestimate the annual amplitude by 25% compared to tide gauge estimates along the coasts of China and Russia. The forcing for the seasonal sea level cycle was identified. The atmospheric pressure and the steric height produce 8-12cm of the annual cycle in the middle continental shelf and in the Kuroshio Current regions separately. The removal of the two attributors from total sea level permits to identify the sea level residuals that still show significant seasonality in the marginal seas. Both nearby wind stress and surface currents can explain well the long-term variability of the seasonal sea level cycle in the marginal seas and the tropics because of their influence on the sea level residuals. Interestingly, the surface currents are a better descriptor in the areas where the ocean currents are known to be strong. Here, they explain 50-90% of inter-annual variability due to the strong links between the steric height and the large-scale ocean currents.

ENSO and greenhouse warming

The El Niño/Southern Oscillation (ENSO) is the dominant climate phenomenon affecting extreme weather conditions worldwide. Its response to greenhouse warming has challenged scientists for decades, despite model agreement on projected changes in mean state. Recent studies have provided new insights into the elusive links between changes in ENSO and in the mean state of the Pacific climate. The projected slow-down in Walker circulation is expected to weaken equatorial Pacific Ocean currents, boosting the occurrences of eastward-propagating warm surface anomalies that characterize observed extreme El Niño events. Accelerated equatorial Pacific warming, particularly in the east, is expected to induce extreme rainfall in the eastern equatorial Pacific and extreme equatorward swings of the Pacific convergence zones, both of which are features of extreme El Niño. The frequency of extreme La Niña is also expected to increase in response to more extreme El Niños, an accelerated maritime continent warming and surface-intensified ocean warming. ENSO-related catastrophic weather events are thus likely to occur more frequently with unabated greenhouse-gas emissions. But model biases and recent observed strengthening of the Walker circulation highlight the need for further testing as new models, observations and insights become available.

Calculating the ocean's mean dynamic topography from a mean sea surface and a geoid

In principle the global mean geostrophic surface circulation of the ocean can be diagnosed by subtracting a geoid from a mean sea surface (MSS). However, because the resulting mean dynamic topography (MDT) is approximately two orders of magnitude smaller than either of the constituent surfaces, and because the geoid is most naturally expressed as a spectral model while the MSS is a gridded product, in practice complications arise. Two algorithms for combining MSS and satellite-derived geoid data to determine the ocean’s mean dynamic topography (MDT) are considered in this paper: a pointwise approach, whereby the gridded geoid height field is subtracted from the gridded MSS; and a spectral approach, whereby the spherical harmonic coefficients of the geoid are subtracted from an equivalent set of coefficients representing the MSS, from which the gridded MDT is then obtained. The essential difference is that with the latter approach the MSS is truncated, a form of filtering, just as with the geoid. This ensures that errors of omission resulting from the truncation of the geoid, which are small in comparison to the geoid but large in comparison to the MDT, are matched, and therefore negated, by similar errors of omission in the MSS. The MDTs produced by both methods require additional filtering. However, the spectral MDT requires less filtering to remove noise, and therefore it retains more oceanographic information than its pointwise equivalent. The spectral method also results in a more realistic MDT at coastlines. 1. Introduction An important challenge in oceanography is the accurate determination of the ocean’s time-mean dynamic topography (MDT). If this can be achieved with sufficient accuracy for combination with the timedependent component of the dynamic topography, obtainable from altimetric data, then the resulting sum (i.e., the absolute dynamic topography) will give an accurate picture of surface geostrophic currents and ocean transports.

Adjoint goal-based error norms for adaptive mesh ocean modelling

Flow in the world's oceans occurs at a wide range of spatial scales, from a fraction of a metre up to many thousands of kilometers. In particular, regions of intense flow are often highly localised, for example, western boundary currents, equatorial jets, overflows and convective plumes. Conventional numerical ocean models generally use static meshes. The use of dynamically-adaptive meshes has many potential advantages but needs to be guided by an error measure reflecting the underlying physics. A method of defining an error measure to guide an adaptive meshing algorithm for unstructured tetrahedral finite elements, utilizing an adjoint or goal-based method, is described here. This method is based upon a functional, encompassing important features of the flow structure. The sensitivity of this functional, with respect to the solution variables, is used as the basis from which an error measure is derived. This error measure acts to predict those areas of the domain where resolution should be changed. A barotropic wind driven gyre problem is used to demonstrate the capabilities of the method. The overall objective of this work is to develop robust error measures for use in an oceanographic context which will ensure areas of fine mesh resolution are used only where and when they are required. (c) 2006 Elsevier Ltd. All rights reserved.

On the steadiness of separating meandering currents

The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

A link between low-frequency mesoscale eddy variability around Madagascar and the large-scale Indian Ocean variability

A connection is shown to exist between the mesoscale eddy activity around Madagascar and the large-scale interannual variability in the Indian Ocean. We use the combined TOPEX/Poseidon-ERS sea surface height (SSH) data for the period 1993–2003. The SSH-fields in the Mozambique Channel and east of Madagascar exhibit a significant interannual oscillation. This is related to the arrival of large-scale anomalies that propagate westward along 10°–15°S in response to the Indian Ocean dipole (IOD) events. Positive (negative) SSH anomalies associated to a positive (negative) IOD phase induce a shift in the intensity and position of the tropical and subtropical gyres. A weakening (strengthening) results in the intensity of the South Equatorial Current and its branches along east Madagascar. In addition, the flow through the narrows of the Mozambique Channel around 17°S increases (decreases) during periods of a stronger and northward (southward) extension of the subtropical (tropical) gyre. Interaction between the currents in the narrows and southward propagating eddies from the northern Channel leads to interannual variability in the eddy kinetic energy of the central Channel in phase with the one in the SSH-field.

Observations of the inter-ocean exchange around South Africa

There is growing evidence that the interocean exchange south of Africa is an important link in the global overturning circulation of the ocean, the so‐called ocean conveyer belt. At this location, warm and salty Indian Ocean waters enter the South Atlantic and are pulled by currents that eventually reach the North Atlantic, where water cools and sinks. A major contributor to the exchange is the frequent shedding of ring eddies from the termination of the Agulhas Current south of the tip of Africa. This shedding is controlled by developments far upstream in the Indian Ocean, and variations in this ‘Agulhas Leakage’ can lead to changes in the rate and stability of the Atlantic overturning, with possible associated global climate variations [Weijer et al., 1999]. Regional climate variations in the tropical and subtropical Indian Ocean are known to affect the whole system of the Agulhas Current, including the interocean exchanges. This article reports on some of the seminal results of ongoing multinational, multidisciplinary projects that explore these issues.

How well do coupled models replicate ocean energetics relevant to ENSO?

Accurate replication of the processes associated with the energetics of the tropical ocean is necessary if coupled GCMs are to simulate the physics of ENSO correctly, including the transfer of energy from the winds to the ocean thermocline and energy dissipation during the ENSO cycle. Here, we analyze ocean energetics in coupled GCMs in terms of two integral parameters describing net energy loss in the system using the approach recently proposed by Brown and Fedorov (J Clim 23:1563–1580, 2010a) and Fedorov (J Clim 20:1108–1117, 2007). These parameters are (1) the efficiency c of the conversion of wind power into the buoyancy power that controls the rate of change of the available potential energy (APE) in the ocean and (2) the e-folding rate a that characterizes the damping of APE by turbulent diffusion and other processes. Estimating these two parameters for coupled models reveals potential deficiencies (and large differences) in how state-of-the-art coupled GCMs reproduce the ocean energetics as compared to ocean-only models and data assimilating models. The majority of the coupled models we analyzed show a lower efficiency (values of c in the range of 10–50% versus 50–60% for ocean-only simulations or reanalysis) and a relatively strong energy damping (values of a-1 in the range 0.4–1 years versus 0.9–1.2 years). These differences in the model energetics appear to reflect differences in the simulated thermal structure of the tropical ocean, the structure of ocean equatorial currents, and deficiencies in the way coupled models simulate ENSO.

Balanced Ocean-Data Assimilation near the Equator

The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.

An assessment of air-sea heat fluxes from ocean and coupled reanalyses

Sixteen monthly air–sea heat flux products from global ocean/coupled reanalyses are compared over 1993–2009 as part of the Ocean Reanalysis Intercomparison Project (ORA-IP). Objectives include assessing the global heat closure, the consistency of temporal variability, comparison with other flux products, and documenting errors against in situ flux measurements at a number of OceanSITES moorings. The ensemble of 16 ORA-IP flux estimates has a global positive bias over 1993–2009 of 4.2 ± 1.1 W m−2. Residual heat gain (i.e., surface flux + assimilation increments) is reduced to a small positive imbalance (typically, +1–2 W m−2). This compensation between surface fluxes and assimilation increments is concentrated in the upper 100 m. Implied steady meridional heat transports also improve by including assimilation sources, except near the equator. The ensemble spread in surface heat fluxes is dominated by turbulent fluxes (>40 W m−2 over the western boundary currents). The mean seasonal cycle is highly consistent, with variability between products mostly <10 W m−2. The interannual variability has consistent signal-to-noise ratio (~2) throughout the equatorial Pacific, reflecting ENSO variability. Comparisons at tropical buoy sites (10°S–15°N) over 2007–2009 showed too little ocean heat gain (i.e., flux into the ocean) in ORA-IP (up to 1/3 smaller than buoy measurements) primarily due to latent heat flux errors in ORA-IP. Comparisons with the Stratus buoy (20°S, 85°W) over a longer period, 2001–2009, also show the ORA-IP ensemble has 16 W m−2 smaller net heat gain, nearly all of which is due to too much latent cooling caused by differences in surface winds imposed in ORA-IP.