Nonlinear variability of the climatic system from singular and power spectra of Late Quaternary records

Stable-isotope records from seven marine cores and one ice core provide invaluable information on the intricate behavior of the climatic system over time scales of 104 to 105 years. These records, in conjunction with a simple coupled climate model, help us understand major mechanisms of paleoclimatic variability. The time intervals covered by the records include the last glacial-interglacial cycle. In spite of the difference in the nature of the records, common features are revealed by advanced spectral-analysis tools. The dominant features are the presence of orbital frequencies, on the one hand, and a low number of internal degrees of freedom, on the other. The climatic system appears therefore to act on the Quaternary time scales considered as a forced nonlinear oscillator. The internal mechanisms giving rise to the aperiodic oscillations include ice-albedo feedback, precipitation-temperature feedback, and interactions between the ice sheets and the bedrock.     

Mass-Weighted Symplectic Forms for the N-Body Problem

Mass-weighted symplectic forms provide a unified framework for the treatment of both finite and vanishingly small masses in the N-body problem. These forms are introduced, compared to previous approaches, and their properties are discussed. Applications to symplectic mappings, the definition of action-angle variables for the Kepler problem, and Hamiltonian perturbation theory are outlined This revised version was published online in July 2006 with corrections to the Cover Date.     

Error evolution in the dynamics of an ocean general circulation model

The problem of error propagation is considered for spatially uncorrelated errors of the barotropic stream function in an oceanic general circulation model (OGCM). Such errors typically occur when altimetric data from satellites are assimilated into ocean models. It is shown that the error decays at first due to the dissipation of the smallest scales in the error field. The error then grows exponentially before it saturates at the value corresponding to the difference between independent realizations. A simple analytic formula for the error behavior is derived; it matches the numerical results documented for the present primitive-equation ocean model, and other models in the literature.     

Interannual and interdecadal variability in United States surface-air temperatures, 1910-87

Monthly mean surface-air temperatures at 870 sites in the contiguous United States were analyzed for interannual and interdecadal variability over the time interval 1910-87. The temperatures were analyzed spatially by empirical-orthogonal-function analysis and temporally by singularspectrum analysis (SSA). The dominant modes of spatio-temporal variability are trends and nonperiodic variations with time scales longer than 15 years, decadal-scale oscillations with periods of roughly 7 and 10 years, and interannual oscillations of 2.2 and 3.3 years. Together, these modes contribute about 18% of the slower-than-annual United States temperature variance. Two leading components roughly capture the mean hemispheric temperature trend and represent a long-term warming, largest in the southwest, accompanied by cooling of the domain's southeastern quadrant. The extremes of the 2.2-year interannual oscillation characterize temperature differences between the Northeastern and Southwestern States, whereas the 3.3-year cycle is present mostly in the Western States. The 7- to 10-year oscillations are much less regular and persistent than the interannual oscillations and characterize temperature differences between the western and interior sectors of the United States. These continental- or regional-scale temperature variations may be related to climatic variations with similar periodicities, either global or centered in other regions; such variations include quasi-biennial oscillations over the tropical Pacific or North Atlantic and quasi-triennial oscillations of North Pacific sea-surface temperatures.The U.S. Government right to retain a non-exclusive, royalty-free licence in and to any copyright is acknowledged.     

Atmospheric radiative equilibria. Part II: bimodal solutions for atmospheric optical properties

 A simple theoretical model of atmospheric radiative equilibrium is solved analytically to help understand the energetics of maintaining Earth's tropical and subtropical climate. The model climate is constrained by energy balance between shortwave (SW) and longwave (LW) radiative fluxes. Given a complete set of SW and LW optical properties in each atmospheric layer, the model yields a unique equilibrium-temperature profile. In contrast, if the atmospheric temperature profile and SW properties are prescribed, the model yields essentially two distinct LW transmissivity profiles. This bimodality is due to a nonlinear competition between the ascending and descending energy fluxes, as well as to their local conversion to sensible heat in the atmosphere. Idealized slab models that are often used to describe the greenhouse effect are shown to be a special case of our model when this nonlinearity is suppressed. In this special case, only one solution for LW transmissivity is possible. Our model's bimodality in LW transmissivity for given SW fluxes and temperature profile may help explain certain features of Earth's climate: at low latitudes the temperature profiles are fairly homogeneous, while the humidity profiles exhibit a bimodal distribution; one mode is associated with regions of moist-and-ascending, the other with dry-and-subsiding air. The model's analytical results show good agreement with the European Centre for Medium-Range Weather Forecasts' reanalysis data. Sensitivity analysis of the temperature profile with respect to LW transmissivity changes leads to an assessment of the low-latitude climate's sensitivity to the “runaway greenhouse” effect. Received: 7 December 1999 / Accepted: 19 February 2001     

Atmospheric radiative equilibria in a simple column model

 An analytic radiative-equilibrium model is formulated where both short- and longwave radiation are treated as two-stream (down- and upward) fluxes. An equilibrium state is defined in the model by the vertical temperature profile. The sensitivity of any such state to the model atmosphere’s optical properties is formulated analytically. As an example, this general formulation is applied to a single-column 11-layer model, and the model’s optical parameters are obtained from a detailed radiative parametrization of a general circulation model. The resulting simple column model is then used to study changes in the Earth-atmosphere system’s radiative equilibrium and, in particular, to infer the role of greenhouse trace gases, water vapor and aerosols in modifying the vertical temperature profile. Multiple equilibria appear when a positive surface-albedo feedback is introduced, and their stability is studied. The vertical structure of the radiative fluxes (both short- and longwave) is substantially modified as the temperature profile changes from one equilibrium to another. These equilibria and their stability are compared to those that appear in energy-balance models, which heretofore have ignored the details of the vertical temperature and radiation profiles. Received: 22 December 1995/Accepted: 17 January 1997     

Impact of the modulated annual cycle and intraseasonal oscillation on daily-to-interannual rainfall variability across monsoonal India

Variability of the Indian summer monsoon is decomposed into an interannually modulated annual cycle (MAC) and a northward-propagating, intraseasonal (30–60-day) oscillation (ISO). To achieve this decomposition, we apply multi-channel singular spectrum analysis (M-SSA) simultaneously to unfiltered daily fields of observed outgoing long-wave radiation (OLR) and to reanalyzed 925-hPa winds over the Indian region, from 1975 to 2008. The MAC is essentially given by the year-to-year changes in the annual and semi-annual components; it displays a slow northward migration of OLR anomalies coupled with an alternation between the northeast winter and southwest summer monsoons. The impact of these oscillatory modes on rainfall is then analyzed using a 1-degree gridded daily data set, focusing on Monsoonal India (north of 17°N and west of 90°E) during the months of June to September. Daily rainfall variability is partitioned into three states using a Hidden Markov Model. Two of these states are shown to agree well with previous classifications of “active” and “break” phases of the monsoon, while the third state exhibits a dipolar east–west pattern with abundant rainfall east of about 77°E and low rainfall to the west. Occurrence of the three rainfall states is found to be an asymmetric function of both the MAC and ISO components. On average, monsoon active phases are favored by large positive anomalies of MAC, and breaks by negative ones. ISO impact is decisive when the MAC is near neutral values during the onset and withdrawal phases of the monsoon. Active monsoon spells are found to require a synergy between the MAC and ISO, while the east–west rainfall dipole is less sensitive to interactions between the two. The driest years, defined from spatially averaged June–September rainfall anomalies, are found to be mostly a result of breaks occurring during the onset and withdrawal stages of the monsoon, e.g., mid-June to mid-July, and during September. These breaks are in turn associated with anomalously late MAC onset or early MAC withdrawal, often together with a large-amplitude, negative ISO event. The occurrence of breaks during the core of the monsoon—from late July to late August—is restricted to a few years when MAC was exceptionally weak, such as 1987 or 2002. Wet years are shown to be mostly associated with more frequent active spells and a stronger MAC than usual, especially at the end of the monsoon season. Taken together, our results suggest that monthly and seasonal precipitation?predictability is higher in the early and late stages of the summer monsoon season.