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

Weight Discrimination: A Multidisciplinary Analysis

Protection against obesity discrimination is extremely limited under the Americans with Disabilities Act (ADA). No obese plaintiff has won using the actual disability theory, but a few have won under the perceived disability theory. Weight-related appearance standards are legal. We estimate weight-based wage penalties for young men and women. We find that mildly obese (20% over standard weight) white women experience greater wage penalties than black men experience for weight that is 100% over standard weight. Men do not experience wage penalties until their weight exceeds standard weight by over 100 lb. A gender-plus analysis under Title VII is more appropriate than the ADA for addressing the weight-based wage penalties that women experience

Implications of climate variability for the detection of multiple equilibria and for rapid transitions in the atmosphere-vegetation system

Paleoclimatic records indicate a decline of vegetation cover in the Western Sahara at the end of the African Humid Period (about 5,500 years before present). Modelling studies have shown that this phenomenon may be interpreted as a critical transition that results from a bifurcation in the atmosphere-vegetation system. However, the stability properties of this system are closely linked to climate variability and depend on the climate model and the methods of analysis. By coupling the Planet Simulator (PlaSim), an atmosphere model of intermediate complexity, with the simple dynamic vegetation model VECODE, we assess previous methods for the detection of multiple equilibria, and demonstrate their limitations. In particular, a stability diagram can yield misleading results because of spatial interactions, and the system's steady state and its dependency on initial conditions are affected by atmospheric variability and nonlinearities. In addition, we analyse the implications of climate variability for the abruptness of a vegetation decline. We find that a vegetation collapse can happen at different locations at different times. These collapses are possible despite large and uncorrelated climate variability. Because of the nonlinear relation between vegetation dynamics and precipitation the green state is initially stabilised by the high variability. When precipitation falls below a critical threshold, the desert state is stabilised as variability is then also decreased. © 2011 The Author(s)

Thermodynamics of climate change: generalized sensitivities

Using a recent theoretical approach, we study how global warming impacts the thermodynamics of the climate system by performing experiments with a simplified yet Earth-like climate model. The intensity of the Lorenz energy cycle, the Carnot efficiency, the material entropy production, and the degree of irreversibility of the system change monotonically with the CO2 concentration. Moreover, these quantities feature an approximately linear behaviour with respect to the logarithm of the CO2 concentration in a relatively wide range. These generalized sensitivities suggest that the climate becomes less efficient, more irreversible, and features higher entropy production as it becomes warmer, with changes in the latent heat fluxes playing a predominant role. These results may be of help for explaining recent findings obtained with state of the art climate models regarding how increases in CO2 concentration impact the vertical stratification of the tropical and extratropical atmosphere and the position of the storm tracks

El Niño-related summer precipitation anomalies in Southeast Asia modulated by the Atlantic multidecadal oscillation

AbstractHow the Atlantic Multidecadal Oscillation (AMO) affects El Niño-related signals in Southeast Asia is investigated in this study on a subseasonal scale. Based on observational and reanalysis data, as well as numerical model simulations, El Niño-related precipitation anomalies are analyzed for AMO positive and negative phases, which reveals a time-dependent modulation of the AMO: (i) In May?June, the AMO influences the precipitation in Southern China (SC) and the Indochina peninsula (ICP) by modulating the El Niño-related air-sea interaction over the western North Pacific (WNP). During negative AMO phases, cold sea surface temperature anomalies (SSTAs) over the WNP favor the maintaining of the WNP anomalous anticyclone (WNPAC). The associated southerly (westerly) anomalies on the northwest (southwest) flank of the WNPAC enhance (reduce) the climatological moisture transport to SC (the ICP) and result in wetter (drier) than normal conditions. In contrast, during positive AMO phases, weak SSTAs over the WNP lead to limited influence of El Niño on precipitation in Southeast Asia. (ii) In July?August, the teleconnection impact from the North Atlantic is more manifest than that in May?June. During positive AMO phases, the warmer than normal North Atlantic favors anomalous wave trains, which propagate along the ?great circle route? and result in positive pressure anomalies over SC, consequently suppressing precipitation in SC and the ICP. During negative AMO phases, the anomalous wave trains tend to propagate eastward from Europe to Northeast Asia along the summer Asian jet, exerting limited influence on Southeast Asia

Thermodynamic analysis of snowball Earth hysteresis experiment: Efficiency, entropy production and irreversibility

We present an extensive thermodynamic analysis of a hysteresis experiment performed on a simplified yet Earth-like climate model. We slowly vary the solar constant by 20% around the present value and detect that for a large range of values of the solar constant the realization of snowball or of regular climate conditions depends on the history of the system. Using recent results on the global climate thermodynamics, we show that the two regimes feature radically different properties. The efficiency of the climate machine monotonically increases with decreasing solar constant in present climate conditions, whereas the opposite takes place in snowball conditions. Instead, entropy production is monotonically increasing with the solar constant in both branches of climate conditions, and its value is about four times larger in the warm branch than in the corresponding cold state. Finally, the degree of irreversibility of the system, measured as the fraction of excess entropy production due to irreversible heat transport processes, is much higher in the warm climate conditions, with an explosive growth in the upper range of the considered values of solar constants. Whereas in the cold climate regime a dominating role is played by changes in the meridional albedo contrast, in the warm climate regime changes in the intensity of latent heat fluxes are crucial for determining the observed properties. This substantiates the importance of addressing correctly the variations of the hydrological cycle in a changing climate. An interpretation of the climate transitions at the tipping points based upon macro-scale thermodynamic properties is also proposed. Our results support the adoption of a new generation of diagnostic tools based on the second law of thermodynamics for auditing climate models and outline a set of parametrizations to be used in conceptual and intermediate-complexity models or for the reconstruction of the past climate conditions. Copyright © 2010 Royal Meteorological Societ

Interdecadal variability of winter precipitation in Southeast China

Interdecadal variability of observed winter precipitation in Southeast China (1961–2010) is characterized by the first empirical orthogonal function of the three-monthly Standardized Precipitation Index (SPI) subjected to a 9-year running mean. For interdecadal time scales the dominating spatial modes represent monopole features involving the Arctic Oscillation (AO) and the sea surface temperature (SST) anomalies. Dynamic composite analysis (based on NCEP/NCAR reanalyzes) reveals the following results: (1) Interdecadal SPI-variations show a trend from a dryer state in the 1970s via an increase during the 1980s towards stabilization on wetter conditions commencing with the 1990s. (2) Increasing wetness in Southeast China is attributed to an abnormal anticyclone over south Japan, with northward transport of warm and humid air from the tropical Pacific to South China. (3) In mid-to-high latitudes the weakened southward flow of polar airmasses induces low-level warming over Eurasia due to stronger AO by warmer zonal temperature advection. This indicates that AO is attributed to the Southeast China precipitation increase influenced by circulation anomalies over the mid-to-high latitudes. (4) The abnormal moisture transport along the southwestern boundary of the abnormal anticyclone over south Japan is related to anomalous south-easterlies modulated by the SST anomalies over Western Pacific Ocean; a positive (negative) SST anomaly will strengthen (weaken) warm and humid air transport, leading to abundant (reduced) precipitation in Southeast China. That is both AO and SST anomalies determine the nonlinear trend observed in winter precipitation over Southeast China

Diagnosing the entropy budget of a climate model

A general circulation model (GCM) of intermediate complexity (Planet Simulator) is subjected to an analysis of the entropy budget and its sensitivity. The entropy production is computed directly based on temperature and temperature tendencies and estimated indirectly based on boundary fluxes. For indirect estimates, the model shows reasonably good agreement with observations. The direct computation indicates deficits of the indirect measures, as they, for example, overestimate the material entropy production (that is, the production by turbulent fluxes). Sensitivity analyses of entropy production are provided, which, depending on changing parameters, hint to a possible applicability of maximum entropy production (MEP) under the constrained dynamics of a complex GC