Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change

Atmosphere–ocean general circulation models (AOGCMs) predict a weakening of the Atlantic meridional overturning circulation (AMOC) in response to anthropogenic forcing of climate, but there is a large model uncertainty in the magnitude of the predicted change. The weakening of the AMOC is generally understood to be the result of increased buoyancy input to the north Atlantic in a warmer climate, leading to reduced convection and deep water formation. Consistent with this idea, model analyses have shown empirical relationships between the AMOC and the meridional density gradient, but this link is not direct because the large-scale ocean circulation is essentially geostrophic, making currents and pressure gradients orthogonal. Analysis of the budget of kinetic energy (KE) instead of momentum has the advantage of excluding the dominant geostrophic balance. Diagnosis of the KE balance of the HadCM3 AOGCM and its low-resolution version FAMOUS shows that KE is supplied to the ocean by the wind and dissipated by viscous forces in the global mean of the steady-state control climate, and the circulation does work against the pressure-gradient force, mainly in the Southern Ocean. In the Atlantic Ocean, however, the pressure-gradient force does work on the circulation, especially in the high-latitude regions of deep water formation. During CO2-forced climate change, we demonstrate a very good temporal correlation between the AMOC strength and the rate of KE generation by the pressure-gradient force in 50–70°N of the Atlantic Ocean in each of nine contemporary AOGCMs, supporting a buoyancy-driven interpretation of AMOC changes. To account for this, we describe a conceptual model, which offers an explanation of why AOGCMs with stronger overturning in the control climate tend to have a larger weakening under CO2 increase

The relationship between the North American summer monsoon, the Rocky Mountains and the North Pacific subtropical anticyclone in HadAM3

In this study the relationship between the North American monsoon, the Californian sea surface temperature (SST) cold pool, the Rocky Mountains and the North Pacific subtropical anticyclone is investigated using the Hadley Centre's atmospheric climate model, HadAM3. In 1996 Hoskins hypothesized that heating in the North American monsoon might be important for the maintenance of the summertime North Pacific subtropical anticyclone, since the monsoon heating may induce descent to the north-west of the monsoon in the descending eastern flank of the subtropical anticyclone. This descent is further enhanced by radiative cooling and is associated with equatorward surface winds parallel to the western coast of North America. These equatorward winds induce oceanic upwelling of cold water and contribute to the formation of the Californian SST cold pool, which may feed back on the anticyclone by further suppressing convection and inducing descent. More recently, Rodwell and Hoskins also investigated the global summer monsoon–subtropical anticyclone relationship. They examined the role that mountains play in impeding the progress of the low-level mid-latitude westerlies, either deflecting the westerlies northwards where they ascend along the sloping mid-latitude isentropes or deflecting them southwards forcing them to descend along the isentropes. In particular, the introduction of the Rockies into a primitive-equation model adiabatically induces descent in the eastern descending flank of the North Pacific subtropical anticyclone. These hypothesized mechanisms have been investigated using HadAM3, focusing on the possible suppression of convection by the Californian SST cold pool, the response of the North Pacific subtropical anticyclone to the strength of the North American monsoon and the ‘blocking’ of the mid-latitude westerlies by the Rocky Mountains. The role of the Rockies is examined by integrating the model with modified orography for the Rocky Mountains. Changing the height of the Rockies alters the circulation in a way consistent with the mechanism outlined above. Higher Rocky mountains force the westerlies southwards, inducing descent in the eastern flank of the subtropical anticyclone as the air descends along the sloping isentropes. The relationship between the North American monsoon and the North Pacific subtropical anticyclone is investigated by suppressing the monsoon in HadAM3. The suppression of the monsoon is accomplished by increasing the surface albedo over Mexico, which induces anomalous ascent on the eastward flank of the subtropical anticyclone and anomalous polewards surface winds along the western coast of the North American continent, also providing support for the above hypothesis. The removal of the Californian SST cold pool, however, has a statistically insignificant effect on the model, suggesting that in this model the feedback of the SST cold pool on the eastern flank of the anticyclone is weak.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

New results on the thermodynamical properties of the climate system

In this paper the authors exploit two equivalent formulations of the average rate of material entropy production in the climate system to propose an approximate splitting between contributions due to vertical and eminently horizontal processes. This approach is based only on 2D radiative fields at the surface and at the top of atmosphere. Using 2D fields at the top of atmosphere alone, lower bounds to the rate of material entropy production and to the intensity of the Lorenz energy cycle are derived. By introducing a measure of the efficiency of the planetary system with respect to horizontal thermodynamic processes, it is possible to gain insight into a previous intuition on the possibility of defining a baroclinic heat engine extracting work from the meridional heat flux. The approximate formula of the material entropy production is verified and used for studying the global thermodynamic properties of climate models (CMs) included in the Program for Climate Model Diagnosis and Intercomparison (PCMDI)/phase 3 of the Coupled Model Intercomparison Project (CMIP3) dataset in preindustrial climate conditions. It is found that about 90% of the material entropy production is due to vertical processes such as convection, whereas the large-scale meridional heat transport contributes to only about 10% of the total. This suggests that the traditional two-box models used for providing a minimal representation of entropy production in planetary systems are not appropriate, whereas a basic—but conceptually correct—description can be framed in terms of a four-box model. The total material entropy production is typically 55 mW m−2 K−1, with discrepancies on the order of 5%, and CMs’ baroclinic efficiencies are clustered around 0.055. The lower bounds on the intensity of the Lorenz energy cycle featured by CMs are found to be around 1.0–1.5 W m−2, which implies that the derived inequality is rather stringent. When looking at the variability and covariability of the considered thermodynamic quantities, the agreement among CMs is worse, suggesting that the description of feedbacks is more uncertain. The contributions to material entropy production from vertical and horizontal processes are positively correlated, so that no compensation mechanism seems in place. Quite consistently among CMs, the variability of the efficiency of the system is a better proxy for variability of the entropy production due to horizontal processes than that of the large-scale heat flux. The possibility of providing constraints on the 3D dynamics of the fluid envelope based only on 2D observations of radiative fluxes seems promising for the observational study of planets and for testing numerical models.

Ensemble data assimilation in the presence of cloud

In numerical weather prediction (NWP) data assimilation (DA) methods are used to combine available observations with numerical model estimates. This is done by minimising measures of error on both observations and model estimates with more weight given to data that can be more trusted. For any DA method an estimate of the initial forecast error covariance matrix is required. For convective scale data assimilation, however, the properties of the error covariances are not well understood. An effective way to investigate covariance properties in the presence of convection is to use an ensemble-based method for which an estimate of the error covariance is readily available at each time step. In this work, we investigate the performance of the ensemble square root filter (EnSRF) in the presence of cloud growth applied to an idealised 1D convective column model of the atmosphere. We show that the EnSRF performs well in capturing cloud growth, but the ensemble does not cope well with discontinuities introduced into the system by parameterised rain. The state estimates lose accuracy, and more importantly the ensemble is unable to capture the spread (variance) of the estimates correctly. We also find, counter-intuitively, that by reducing the spatial frequency of observations and/or the accuracy of the observations, the ensemble is able to capture the states and their variability successfully across all regimes.

Rheology of milk foams produced by steam injection

Rheology of milk foams generated by steam injection was studied during the transient destabilization process using steady flow and dynamic oscillatory techniques: yield stress (τ_y) values were obtained from a stress ramp (0.2 to 25 Pa) and from strain amplitude sweep (0.001 to 3 at 1 Hz of frequency); elastic (G') and viscous (G") moduli were measured by frequency sweep (0.1 to 150 Hz at 0.05 of strain); and the apparent viscosity (η_a) was obtained from the flow curves generated from the stress ramp. The effect of plate roughness and the sweep time on τ_y was also assessed. Yield stress was found to increase with plate roughness whereas it decreased with the sweep time. The values of yield stress and moduli—G' and G"—increased during foam destabilization as a consequence of the changes in foam properties, especially the gas volume fraction, φ, and bubble size, R_32 (Sauter mean bubble radius). Thus, a relationship between τ_y, φ, R_32, and σ (surface tension) was established. The changes in the apparent viscosity, η, showed that the foams behaved like a shear thinning fluid beyond the yield point, fitting the modified Cross model with the relaxation time parameter (λ) also depending on the gas volume fraction. Overall, it was concluded that the viscoelastic behavior of the foam below the yield point and liquid-like behavior thereafter both vary during destabilization due to changes in the foam characteristics.

Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model

For data assimilation in numerical weather prediction, the initial forecast-error covariance matrix Pf is required. For variational assimilation it is particularly important to prescribe an accurate initial matrix Pf, since Pf is either static (in the 3D-Var case) or constant at the beginning of each assimilation window (in the 4D-Var case). At large scales the atmospheric flow is well approximated by hydrostatic balance and this balance is strongly enforced in the initial matrix Pf used in operational variational assimilation systems such as that of the Met Office. However, at convective scales this balance does not necessarily hold any more. Here we examine the extent to which hydrostatic balance is valid in the vertical forecast-error covariances for high-resolution models in order to determine whether there is a need to relax this balance constraint in convective-scale data assimilation. We use the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and a 1.5 km resolution version of the Unified Model for a case study characterized by the presence of convective activity. An ensemble of high-resolution forecasts valid up to three hours after the onset of convection is produced. We show that at 1.5 km resolution hydrostatic balance does not hold for forecast errors in regions of convection. This indicates that in the presence of convection hydrostatic balance should not be enforced in the covariance matrix used for variational data assimilation at this scale. The results show the need to investigate covariance models that may be better suited for convective-scale data assimilation. Finally, we give a measure of the balance present in the forecast perturbations as a function of the horizontal scale (from 3–90 km) using a set of diagnostics. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Effect of high-hydrostatic pressure and pH on the rheological properties of gum arabic

The effect on the viscoelastic behaviour, of pressure-treating hydrated gumarabic samples (800 MPa) at different pH values (2.8, 4.2 and 8.0) was investigated, using controlled stress rheometry. The treated samples were analysed for their complex (G∗), storage (G′) and loss (G″) moduli as a function of frequency, using dynamic oscillatory testing. Significant changes in the rheologicalproperties were observed in both the pressurised gum solutions and in those previously buffered at pH 2.8. The gum, at its natural pH (4.25) and at alkaline pH (8.0), was enhanced by pressure treatment, but only for the already “good” quality gum samples. High-pressure treatment had substantial effects on the frequency-dependence of the moduli of both the pressurised and the pressurised/pH-treated solutions, with the latter being more pronounced, suggesting differing structures or changes in the overall degree of interaction of the gum systems after pressure treatment.

Properties of singular vectors using convective available potential energy as final time norm

We study the feasibility of using the singular vector technique to create initial condition perturbations for short-range ensemble prediction systems (SREPS) focussing on predictability of severe local storms and in particular deep convection. For this a new final time semi-norm based on the convective available potential energy (CAPE) is introduced. We compare singular vectors using the CAPE-norm with SVs using the more common total energy (TE) norm for a 2-week summer period in 2007, which includes a case of mesoscale extreme rainfall in the south west of Finland. The CAPE singular vectors perturb the CAPE field by increasing the specific humidity and temperature of the parcel and increase the lapse rate above the parcel in the lower troposphere consistent with physical considerations. The CAPE-SVs are situated in the lower troposphere. This in contrast to TE-SVs with short optimization times which predominantly remain in the high troposphere. By examining the time evolution of the CAPE singular values we observe that the convective event in the south west of Finland is clearly associated with high CAPE singular values.

Evaluation of water and energy budgets in regional climate models applied over Europe

This study presents a model intercomparison of four regional climate models (RCMs) and one variable resolution atmospheric general circulation model (AGCM) applied over Europe with special focus on the hydrological cycle and the surface energy budget. The models simulated the 15 years from 1979 to 1993 by using quasi-observed boundary conditions derived from ECMWF re-analyses (ERA). The model intercomparison focuses on two large atchments representing two different climate conditions covering two areas of major research interest within Europe. The first is the Danube catchment which represents a continental climate dominated by advection from the surrounding land areas. It is used to analyse the common model error of a too dry and too warm simulation of the summertime climate of southeastern Europe. This summer warming and drying problem is seen in many RCMs, and to a less extent in GCMs. The second area is the Baltic Sea catchment which represents maritime climate dominated by advection from the ocean and from the Baltic Sea. This catchment is a research area of many studies within Europe and also covered by the BALTEX program. The observed data used are monthly mean surface air temperature, precipitation and river discharge. For all models, these are used to estimate mean monthly biases of all components of the hydrological cycle over land. In addition, the mean monthly deviations of the surface energy fluxes from ERA data are computed. Atmospheric moisture fluxes from ERA are compared with those of one model to provide an independent estimate of the convergence bias derived from the observed data. These help to add weight to some of the inferred estimates and explain some of the discrepancies between them. An evaluation of these biases and deviations suggests possible sources of error in each of the models. For the Danube catchment, systematic errors in the dynamics cause the prominent summer drying problem for three of the RCMs, while for the fourth RCM this is related to deficiencies in the land surface parametrization. The AGCM does not show this drying problem. For the Baltic Sea catchment, all models similarily overestimate the precipitation throughout the year except during the summer. This model deficit is probably caused by the internal model parametrizations, such as the large-scale condensation and the convection schemes.

Mechanisms linking volcanic aerosols to the Atlantic meridional overturning circulation

This study examines the sensitivity of the climate system to volcanic aerosol forcing in the third climate configuration of the Met Office Unified Model (HadCM3). The main test case was based on the 1880s when there were several volcanic eruptions, the well-known Krakatau being the largest. These eruptions increased atmospheric aerosol concentrations and induced a period of global cooling surface temperatures. In this study, an ensemble of HadCM3 has been integrated with the standard set of radiative forcings and aerosols from the Intergovernmental Panel on Climate Change Fourth Assessment Report simulations, from 1860 to present. A second ensemble removes the volcanic aerosols from 1880 to 1899. The all-forcings ensemble shows an attributable 1.2-Sv (1 Sv ≡ 106 m3 s−1) increase in the Atlantic meridional overturning circulation (AMOC) at 45°N—with a 0.04-PW increase in meridional heat transport at 40°N and increased northern Atlantic SSTs—starting around 1894, approximately 11 years after the first eruption, and lasting a further 10 years at least. The mechanisms responsible are traced to the Arctic, with suppression of the global water cycle (high-latitude precipitation), which leads to an increase in upper-level Arctic and Greenland Sea salinities. This then leads to increased convection in the Greenland–Iceland–Norwegian (GIN) Seas, enhanced Denmark Strait overflows, and AMOC changes with density anomalies traceable southward along the western Atlantic boundary. The authors investigate whether a similar response to the Pinatubo eruption in 1991 could still be ongoing, but do not find strong evidence.

Cloud-resolving model simulations with one- and two-way couplings via the weak temperature gradient approximation

A cloud-resolving model is modified to implement the weak temperature gradient approximation in order to simulate the interactions between tropical convection and the large-scale tropical circulation. The instantaneous domain-mean potential temperature is relaxed toward a reference profile obtained from a radiative–convective equilibrium simulation of the cloud-resolving model. For homogeneous surface conditions, the model state at equilibrium is a large-scale circulation with its descending branch in the simulated column. This is similar to the equilibrium state found in some other studies, but not all. For this model, the development of such a circulation is insensitive to the relaxation profile and the initial conditions. Two columns of the cloud-resolving model are fully coupled by relaxing the instantaneous domain-mean potential temperature in both columns toward each other. This configuration is energetically closed in contrast to the reference-column configuration. No mean large-scale circulation develops over homogeneous surface conditions, regardless of the relative area of the two columns. The sensitivity to nonuniform surface conditions is similar to that obtained in the reference-column configuration if the two simulated columns have very different areas, but it is markedly weaker for columns of comparable area. The weaker sensitivity can be understood as being a consequence of a formulation for which the energy budget is closed. The reference-column configuration has been used to study the convection in a local region under the influence of a large-scale circulation. The extension to a two-column configuration is proposed as a methodology for studying the influence on local convection of changes in remote convection.

Convective quasi–equilibrium

The concept of convective quasi–equilibrium (CQE) is a key ingredient in order to understand the role of deep moist convection in the atmosphere. It has been used as a guiding principle to develop almost all convective parameterizations and provides a basic theoretical framework for large–scale tropical dynamics. The CQE concept as originally proposed by Arakawa and Schubert [1974] is systematically reviewed from wider perspectives. Various interpretations and extensions of Arakawa and Schubert’s CQE are considered in terms of both a thermodynamic analogy and as a dynamical balance. The thermodynamic interpretations can be more emphatically embraced as a homeostasis. The dynamic balance interpretations can be best understood by analogy with the slow manifold. Various criticisms of CQE can be avoided by taking the dynamic balance interpretation. Possible limits of CQE are also discussed, including the importance of triggering in many convective situations, as well as the possible self–organized criticality of tropical convection. However, the most intriguing aspect of the CQE concept is that, in spite of many observational tests supporting and interpreting it in many different senses, it has 1never been established in a robust manner based on a systematic analysis of the cloud–work function budget by observations as was originally defined.

Drag produced by trapped lee waves and propagating mountain waves in a two-layer atmosphere

The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l_2/l_1 and of the corresponding dimensionless interface height l_1 H, for selected values of the dimensionless ridge width l_1 a and ratio of wind speeds in the two layers. When l_2/l_1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l_2/l_1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l_1 H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l_2/l_1 and slightly higher values of l_1 H than the propagating wave drag maxima. As l1a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l_2/l_1. These results are confirmed by numerical simulations for l_2/l_1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models.