A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

Dynamics of the lower stratospheric circulation response to ENSO

A robust feature of the observed response to El Nin˜o–Southern Oscillation (ENSO) is an altered circulation in the lower stratosphere. When sea surface temperatures (SSTs) in the tropical Pacific are warmer there is enhanced upwelling and cooling in the tropical lower stratosphere and downwelling and warming in the midlatitudes, while the opposite is true of cooler SSTs. The midlatitude lower stratospheric response to ENSO is larger in the Southern Hemisphere (SH) than in the Northern Hemisphere (NH). In this study the dynamical version of the Canadian Middle Atmosphere Model (CMAM) is used to simulate 25 realizations of the atmospheric response to the 1982/83 El Nin˜o and the 1973/74 La Nin˜ a. This version ofCMAMis a comprehensive high-top general circulation model that does not include interactive chemistry. The observed lower stratospheric response to ENSO is well reproduced by the simulations, allowing them to be used to investigate the mechanisms involved. Both the observed and simulated responses maximize in December–March and so this study focuses on understanding the mechanisms involved in that season. The response in tropical upwelling is predominantly driven by anomalous transient synoptic-scale wave drag in the SH subtropical lower stratosphere, which is also responsible for the compensating SH midlatitude response. This altered wave drag stems from an altered upward flux of wave activity from the troposphere into the lower stratosphere between 208 and 408S. The altered flux of wave activity can be divided into two distinct components. In the Pacific, the acceleration of the zonal wind in the subtropics from the warmer tropical SSTs results in a region between the midlatitude and subtropical jets where there is an enhanced source of low phase speed eddies. At other longitudes, an equatorward shift of the midlatitude jet from the extratropical tropospheric response to El Nin˜o results in an enhanced source of waves of higher phase speeds in the subtropics. The altered resolved wave drag is only apparent in the SH and the difference between the two hemispheres can be related to the difference in the climatological jet structures in this season and the projection of the wind anomalies associated with ENSO onto those structures.

Four-dimensional data assimilation and balanced dynamics

The problem of spurious excitation of gravity waves in the context of four-dimensional data assimilation is investigated using a simple model of balanced dynamics. The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode, and can be initialized such that the model evolves on a so-called slow manifold, where the fast motion is suppressed. Identical twin assimilation experiments are performed, comparing the extended and ensemble Kalman filters (EKF and EnKF, respectively). The EKF uses a tangent linear model (TLM) to estimate the evolution of forecast error statistics in time, whereas the EnKF uses the statistics of an ensemble of nonlinear model integrations. Specifically, the case is examined where the true state is balanced, but observation errors project onto all degrees of freedom, including the fast modes. It is shown that the EKF and EnKF will assimilate observations in a balanced way only if certain assumptions hold, and that, outside of ideal cases (i.e., with very frequent observations), dynamical balance can easily be lost in the assimilation. For the EKF, the repeated adjustment of the covariances by the assimilation of observations can easily unbalance the TLM, and destroy the assumptions on which balanced assimilation rests. It is shown that an important factor is the choice of initial forecast error covariance matrix. A balance-constrained EKF is described and compared to the standard EKF, and shown to offer significant improvement for observation frequencies where balance in the standard EKF is lost. The EnKF is advantageous in that balance in the error covariances relies only on a balanced forecast ensemble, and that the analysis step is an ensemble-mean operation. Numerical experiments show that the EnKF may be preferable to the EKF in terms of balance, though its validity is limited by ensemble size. It is also found that overobserving can lead to a more unbalanced forecast ensemble and thus to an unbalanced analysis.

Zonal-mean dynamics of extended recoveries from stratospheric sudden warmings

The recovery of the Arctic polar vortex following stratospheric sudden warmings is found to take upward of 3 months in a particular subset of cases, termed here polar-night jet oscillation (PJO) events. The anomalous zonal-mean circulation above the pole during this recovery is characterized by a persistently warm lower stratosphere, and above this a cold midstratosphere and anomalously high stratopause, which descends as the event unfolds. Composites of these events in the Canadian Middle Atmosphere Model show the persistence of the lower-stratospheric anomaly is a result of strongly suppressed wave driving and weak radiative cooling at these heights. The upper-stratospheric and lower-mesospheric anomalies are driven immediately following the warming by anomalous planetary-scale eddies, following which, anomalous parameterized nonorographic and orographic gravity waves play an important role. These details are found to be robust for PJO events (as opposed to sudden warmings in general) in that many details of individual PJO events match the composite mean. Azonal-mean quasigeostrophic model on the sphere is shown to reproduce the response to the thermal and mechanical forcings produced during a PJO event. The former is well approximated by Newtonian cooling. The response can thus be considered as a transient approach to the steady-state, downward control limit. In this context, the time scale of the lower-stratospheric anomaly is determined by the transient, radiative response to the extended absence of wave driving. The extent to which the dynamics of the wave-driven descent of the stratopause can be considered analogous to the descending phases of the quasi-biennial oscillation (QBO) is also discussed.

Hamiltonian geophysical fluid dynamics

Hamiltonian dynamics describes the evolution of conservative physical systems. Originally developed as a generalization of Newtonian mechanics, describing gravitationally driven motion from the simple pendulum to celestial mechanics, it also applies to such diverse areas of physics as quantum mechanics, quantum field theory, statistical mechanics, electromagnetism, and optics – in short, to any physical system for which dissipation is negligible. Dynamical meteorology consists of the fundamental laws of physics, including Newton’s second law. For many purposes, diabatic and viscous processes can be neglected and the equations are then conservative. (For example, in idealized modeling studies, dissipation is often only present for numerical reasons and is kept as small as possible.) In such cases dynamical meteorology obeys Hamiltonian dynamics. Even when nonconservative processes are not negligible, it often turns out that separate analysis of the conservative dynamics, which fully describes the nonlinear interactions, is essential for an understanding of the complete system, and the Hamiltonian description can play a useful role in this respect. Energy budgets and momentum transfer by waves are but two examples.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

Interactions between different convection modes can be investigated using an energy–cycle description under a framework of mass–flux parameterization. The present paper systematically investigates this system by taking a limit of two modes: shallow and deep convection. Shallow convection destabilizes itself as well as the other convective modes by moistening and cooling the environment, whereas deep convection stabilizes itself as well as the other modes by drying and warming the environment. As a result, shallow convection leads to a runaway growth process in its stand–alone mode, whereas deep convection simply damps out. Interaction between these two convective modes becomes a rich problem, even when it is limited to the case with no large–scale forcing, because of these opposing tendencies. Only if the two modes are coupled at a proper level can a self–sustaining system arise, exhibiting a periodic cycle. The present study establishes the conditions for self–sustaining periodic solutions. It carefully documents the behaviour of the two mode system in order to facilitate the interpretation of global model behaviours when this energy–cycle is implemented as a closure into a convection parameterization in future.

Exploring the climatic impact of the continental vegetation on the Mezosoic atmospheric CO2 and climate history

In this contribution, we continue our exploration of the factors defining the Mesozoic climatic history. We improve the Earth system model GEOCLIM designed for long term climate and geochemical reconstructions by adding the explicit calculation of the biome dynamics using the LPJ model. The coupled GEOCLIM-LPJ model thus allows the simultaneous calculation of the climate with a 2-D spatial resolution, the coeval atmospheric CO2, and the continental biome distribution. We found that accounting for the climatic role of the continental vegetation dynamics (albedo change, water cycle and surface roughness modulations) strongly affects the reconstructed geological climate. Indeed the calculated partial pressure of atmospheric CO2 over the Mesozoic is twice the value calculated when assuming a uniform constant vegetation. This increase in CO2 is triggered by a global cooling of the continents, itself triggered by a general increase in continental albedo owing to the development of desertic surfaces. This cooling reduces the CO2 consumption through silicate weathering, and hence results in a compensating increase in the atmospheric CO2 pressure. This study demonstrates that the impact of land plants on climate and hence on atmospheric CO2 is as important as their geochemical effect through the enhancement of chemical weathering of the continental surface. Our GEOCLIM-LPJ simulations also define a climatic baseline for the Mesozoic, around which exceptionally cool and warm events can be identified.

Impact of atmospheric forcing on Antarctic continental shelf water masses

The Antarctic continental shelf seas feature a bimodal distribution of water mass temperature, with the Amundsen and Bellingshausen Seas flooded by Circumpolar Deep Water that is several degrees Celsius warmer than the cold shelf waters prevalent in the Weddell and Ross Seas. This bimodal distribution could be caused by differences in atmospheric forcing, ocean dynamics, ocean and ice feedbacks, or some combination of these factors. In this study, a highly simplified coupled sea ice–mixed layer model is developed to investigate the physical processes controlling this situation. Under regional atmospheric forcings and parameter choices the 10-yr simulations demonstrate a complete destratification of the Weddell Sea water column in winter, forming cold, relatively saline shelf waters, while the Amundsen Sea winter mixed layer remains shallower, allowing a layer of deep warm water to persist. Applying the Weddell atmospheric forcing to the Amundsen Sea model destratifies the water column after two years, and applying the Amundsen forcing to the Weddell Sea model results in a shallower steady-state winter mixed layer that no longer destratifies the water column. This suggests that the regional difference in atmospheric forcings alone is sufficient to account for the bimodal distribution in Antarctic shelf-sea temperatures. The model prediction of mixed layer depth is most sensitive to the air temperature forcing, but a switch in all forcings is required to prevent destratification of the Weddell Sea water column.

Northern Hemisphere atmospheric blocking as simulated by 15 atmospheric general circulation models in the period 1979-1988

As a part of the Atmospheric Model Intercomparison Project (AMIP), the behaviour of 15 general circulation models has been analysed in order to diagnose and compare the ability of the different models in simulating Northern Hemisphere midlatitude atmospheric blocking. In accordance with the established AMIP procedure, the 10-year model integrations were performed using prescribed, time-evolving monthly mean observed SSTs spanning the period January 1979–December 1988. Atmospheric observational data (ECMWF analyses) over the same period have been also used to verify the models results. The models involved in this comparison represent a wide spectrum of model complexity, with different horizontal and vertical resolution, numerical techniques and physical parametrizations, and exhibit large differences in blocking behaviour. Nevertheless, a few common features can be found, such as the general tendency to underestimate both blocking frequency and the average duration of blocks. The problem of the possible relationship between model blocking and model systematic errors has also been assessed, although without resorting to ad-hoc numerical experimentation it is impossible to relate with certainty particular model deficiencies in representing blocking to precise parts of the model formulation.

Upland streamwater nitrate dynamics across decadal to sub-daily timescales: a case study of Plynlimon, Wales

Streamwater nitrate dynamics in the River Hafren, Plynlimon, mid-Wales were investigated over decadal to sub-daily timescales using a range of statistical techniques. Long-term data were derived from weekly grab samples (1984–2010) and high-frequency data from 7-hourly samples (2007–2009) both measured at two sites: a headwater stream draining moorland and a downstream site below plantation forest. This study is one of the first to analyse upland streamwater nitrate dynamics across such a wide range of timescales and report on the principal mechanisms identified. The data analysis provided no clear evidence that the long-term decline in streamwater nitrate concentrations was related to a decline in atmospheric deposition alone, because nitrogen deposition first increased and then decreased during the study period. Increased streamwater temperature and denitrification may also have contributed to the decline in stream nitrate concentrations, the former through increased N uptake rates and the latter resultant from increased dissolved organic carbon concentrations. Strong seasonal cycles, with concentration minimums in the summer, were driven by seasonal flow minimums and seasonal biological activity enhancing nitrate uptake. Complex diurnal dynamics were observed, with seasonal changes in phase and amplitude of the cycling, and the diurnal dynamics were variable along the river. At the moorland site, a regular daily cycle, with minimum concentrations in the early afternoon, corresponding with peak air temperatures, indicated the importance of instream biological processing. At the downstream site, the diurnal dynamics were a composite signal, resultant from advection, dispersion and nitrate processing in the soils of the lower catchment. The diurnal streamwater nitrate dynamics were also affected by drought conditions. Enhanced diurnal cycling in Spring 2007 was attributed to increased nitrate availability in the post-drought period as well as low flow rates and high temperatures over this period. The combination of high-frequency short-term measurements and long-term monitoring provides a powerful tool for increasing understanding of the controls of element fluxes and concentrations in surface waters.

The impact of sea ice dynamics on the Arctic climate system

Five paired global climate model experiments, one with an ice pack that only responds thermodynamically (TI) and one including sea-ice dynamics (DI), were used to investigate the sensitivity of Arctic climates to sea-ice motion. The sequence of experiments includes situations in which the Arctic was both considerably colder (Glacial Inception, ca 115,000 years ago) and considerably warmer (3 × CO2) than today. Sea-ice motion produces cooler anomalies year-round than simulations without ice dynamics, resulting in reduced Arctic warming in warm scenarios and increased Arctic cooling in cold scenarios. These changes reflect changes in atmospheric circulation patterns: the DI simulations favor outflow of Arctic air and sea ice into the North Atlantic by promoting cyclonic circulation centered over northern Eurasia, whereas the TI simulations favor southerly inflow of much warmer air from the North Atlantic by promoting cyclonic circulation centered over Greenland. The differences between the paired simulations are sufficiently large to produce different vegetation cover over >19% of the land area north of 55°N, resulting in changes in land-surface characteristics large enough to have an additional impact on climate. Comparison of the DI and TI experiments for the mid-Holocene (6000 years ago) with paleovegetation reconstructions suggests the incorporation of sea-ice dynamics yields a more realistic simulation of high-latitude climates. The spatial pattern of sea-ice anomalies in the warmer-than-modern DI experiments strongly resembles the observed Arctic Ocean sea-ice dipole structure in recent decades, consistent with the idea that greenhouse warming is already impacting the high-northern latitudes.

The role of soil microbes in the global carbon cycle: tracking the below-ground microbial processing of plant-derived carbon for manipulating carbon dynamics in agricultural systems.

It is well known that atmospheric concentrations of carbon dioxide (CO2) (and other greenhouse gases) have increased markedly as a result of human activity since the industrial revolution. It is perhaps less appreciated that natural and managed soils are an important source and sink for atmospheric CO2 and that, primarily as a result of the activities of soil microorganisms, there is a soil-derived respiratory flux of CO2 to the atmosphere that overshadows by tenfold the annual CO2 flux from fossil fuel emissions. Therefore small changes in the soil carbon cycle could have large impacts on atmospheric CO2 concentrations. Here we discuss the role of soil microbes in the global carbon cycle and review the main methods that have been used to identify the microorganisms responsible for the processing of plant photosynthetic carbon inputs to soil. We discuss whether application of these techniques can provide the information required to underpin the management of agro-ecosystems for carbon sequestration and increased agricultural sustainability. We conclude that, although crucial in enabling the identification of plant-derived carbon-utilising microbes, current technologies lack the high-throughput ability to quantitatively apportion carbon use by phylogentic groups and its use efficiency and destination within the microbial metabolome. It is this information that is required to inform rational manipulation of the plant–soil system to favour organisms or physiologies most important for promoting soil carbon storage in agricultural soil.