Barry Saltzman

A Survey of Statistical-Dynamical Models of the Terrestrial Climate

Publisher Summary This chapter discusses statistical dynamic models and explains how these models stem from the most general statements of the hydro thermodynamic laws and fit into a hierarchy of increasing complexity and simulation capability. The chapter discusses the physical foundation and reviews the development of an important group of models known as statistical-dynamical models. It also presents a review of the fundamental equations (namely, continuity equations, the equations of motion, the thermodynamical energy equation, and constitutive equations) that are the basis of both the explicit- and statistical-dynamical climate models. Climatic averaging is also discussed. The chapter then discusses the vertically integrated, thermodynamic models and describes its foundations and applications. It illustrates equations for the axially symmetric and asymmetric mean states, symmetric (zonal) models, asymmetric (nonzonal) models, and the complete time average state. Finally, the chapter explains modeling the evolution of climate, its general concepts and studies of forced climatic change, studies of free climatic change, and climatic prediction.

The Late Quaternary Glaciations as the Response of a Three-Component Feedback System to Earth-Orbital Forcing

Abstract A climatic feedback system previously described, consisting of three prognostic nonlinear equations governing the mass of ice sheets ζ, the mass of marine and continental marginal ice χ, and the mean ocean temperature θ is forced by a representation of the effects of external earth-orbital variations. With reasonable amplitudes for the eccentricity, obliquity, and precession forcing, the free oscillatory solutions of major period near 100 kyr can be modified in a way that substantially agrees with the δ18O-derived observations of ice mass evolution. In particular, a proper structure, variance spectrum, and “phase lock” of the major variations are obtained over the last 400 kyr. An analysis of the sensitivity of these results to variations in the model parameters and to random perturbations shows that the solution is robust for small changes in all but a few of the equation coefficients. Concomitant variability in the marine ice mass, ocean temperature and net radiation at the top of the atmospher...

Decadal‐to‐centennial‐scale climate variability: Insights into the rise and fall of the Great Salt Lake

We demonstrate connections between decadal and secular global climatic variations, and historical variations in the volume of the Great Salt Lake. The decadal variations correspond to a low-frequency shifting of storm tracks which influence winter precipitation and explain nearly 18% of the interannual and longer-term variance in the record of monthly volume change. The secular trend accounts for a more modest approximately 1.5% of the variance.

The Mid-Quaternary Climatic Transition as the Free Response of a Three-Variable Dynamical Model

Abstract A simplified version of a previously described dynamical model governing global ice mass, atmospheric carbon dioxide, and mean ocean temperature (that may also be a proxy for some other CO2–controlling oceanic variable, e.g., nutrient supply) is shown to possess solutions, in a realistic parameter range, that can replicate the main features of the climatic variations implied by the full, two million years, Quarternary δ18O record. These variations include a major “transition” between a low-ice (δ18O, low variance mode before roughly 900 kyr BP to a high-ice (near 100 kyr period) variance mode after that time to the present. The model contains only three free parameters in this simplified form. No external earth-orbital forcing is prescribed; i.e., the model represents only internal dynamics. From the previous studies it seems clear that additional variance representing such features as the “rapid” deglaciation and the phase of the major Quaternary oscillation can be largely explained with no more...

Carbon dioxide and the δ18O record of late-Quaternary climatic change: a global model

A dynamical model for the late-Quaternary global variations of δ18O, mean ocean surface tempeature τ, ice mass I, deep ocean temperature θ, and atmospheric carbon dioxide concentration μ, is constructed. This model consists of two diagnostic equations (for δ18O and τ), and three prognostic equations (for I, θ, and μ) of a form studied extensively in previous articles. The carbon dioxide equation includes forcing by a representation of the Milankovitch earth-orbital radiation effects, and contains a basic instability that drives a free oscillation of period near 100,000 years. The system is constrained to conserve mass and energy, contain physically plausible feedbacks including a system time constant no greater than 10.000 years, and be robust (i. e., structurally stable in the presence of expected noise levels and uncertainties in values of coefficients). Within the limits of these constraints, coefficients are chosen such that (i) the solution gives a good fit to the observed SPECMAP δ18O variations, and (ii) the ice mass variations are qualitatively similar to the δ18O variations. The predicted long term variations of sea surface temperature and atmospheric carbon dioxide are in reasonably good agreement with the limited observational evidence available for these quantities, while the predicted variations of deep ocean temperature remain to be verified when paleoclimatic estimates of this quantity become available. The relative contributions of ice mass changes and surface water temperature changes to the variations of δ18O at any time are given by the model.

A model of the internal feedback system involved in late quaternary climatic variations

Abstract Because of the small net rates of energy flow involved in very long-term changes in ice mass (10−1 W m−2) it will be impossible to proceed in a purely deductive manner to develop a theory for these changes. An inductive approach will be necessary-perhaps beg formulated in terms of multi-component stochastic-dynamical systems of equations governing the variables and feedbacks thought to be relevant from qualitative physical reasoning (e.g., “conceptual models”). The output of such models should be required to conform as closely as possible to all lines of observational evidence on climatic change, have a predictive quality in the search for new observational evidence, and satisfy the general conservation laws and all the results of physical measurement of the fast response (high energy flux) processes that generally lead to diagnostic relationships. A prototype of such an inductive model is described. This model is formulated as a nonlinear dynamical system governing three components: continental ...

Sensitivity of equilibrium surface temperature of CCM3 to systematic changes in atmospheric CO2

We have redone our computations of the equilibrium response of surface temperature to atmospheric CO2 concentrations using the latest version of the NCAR Community Climate Model (version 3 rather than version 1). Eight GCM simulations with CO2 concentrations varying from 180 to 3000 ppmv were conducted with CCM3 compared to six CO2 concentrations with CCM1. A preliminary examination of the CCM3 simulations showed the same basic non-linear behaviour of temperature to CO2 concentrations obtained previously with CCM1. The magnitude of the sensitivities, however, were much lower in the new CCM3 runs than in the older CCM1 runs. Four possible reasons for the reduced sensitivity in CCM3 are discussed.

Glacial meltwater cooling of the Gulf of Mexico - GCM implications for Holocene and present-day climates

An atmospheric general circulation model, the NCAR CCM, has been used to investigate the possible effects that reduced Gulf of Mexico sea surface temperatures (SST) could have on regional and hemispheric climates. δ18O records and terrestrial evidence indicate at least two major glacial meltwater discharges into the Gulf of Mexico subsequent to the last glacial maximum. It is probable that these discharges reduced Gulf of Mexico SST. We have conducted three numerical experiments, with imposed gulf-wide SST coolings of 3°C, 6°C, and 12°C, and find in all three experiments significant reductions in the North Atlantic storm-track intensity, along with a strong decrease in transient eddy water vapor transport out of the Gulf of Mexico. Surface pressures are higher over the North Atlantic, indicating a reduction of the climatological Icelandic low. The region is generally cooler and drier, with a reduction in precipitation that agrees well with evidence from Greenland ice cores. Other statistically significant changes occur across the Northern Hemisphere, but vary between the three experiments. In particular, warmer, wetter conditions are found over Europe for both the 6°C and 12°C SST reductions, but cooler conditions are found for the 3°C reduction. This indicates a dependence, in both the sign and magnitude of the model response, on the magnitude of the imposed SST anomaly. The results suggest that the present-day North Atlantic storm track is dependent on warm Gulf of Mexico SST for much of its intensity. They also suggest that meltwater-induced coolings may help account, in part, for some of the climatic oscillations that occurred during the last glacial/interglacial transition.

Climatic Systems Analysis

Publisher Summary This chapter presents a discussion on analysis of climatic system. Fundamental physical equations that provide the deterministic basis for such an analysis of the climatic system are illustrated. Some systematics of the averaging process for climatic variability based on the discussion is also explained. A simple two-component climatic feedback system is formulated containing some speculative elements that can serve as a prototype illustrating the application of the above sequence of steps in a dynamical systems analysis. Physical considerations are discussed that are relevant in forming climate models in general, focusing on the consequences of the disparate “time constants” of the various domains of the climate system, and the integral mass and energy constraints on the system. Results from studies of atmospheric equilibration to its lower boundary state are presented, leading up to the presentation of a special two-component system for longer term variability that serves as a prototype for the application of the systems analysis approach.

A first-order global model of late Cenozoic climatic change II. Further analysis based on a simplification of CO2 dynamics

A model developed recently for the long-term variations of global ice mass, carbon dioxide, and mean ocean temperature through the late Cenozoic is simplified by hypothesizing a new equation for the CO2 variations containing one less adjustable parameter, but retaining the essential physical content of the previous equation (including nonlinearity and the potential for instability). By assuming plausible time constants for the glacial ice mass and global mean ocean temperature, and setting the values of six adjustable parameters (rate constants), a solution for the last 5 My is obtained displaying many of the features observed over this period, including the transition to the near-100 ky major ice-age oscillations of the late Pleistocene. In obtaining this solution it is also assumed that variations in tectonic forcing lead to a reduction of the equilibrium CO2 concentration (perhaps due to increased weathering of rapidly uplifted mountain ranges over this period). As a consequence of this CO2 reduction, the model dynamical system can bifurcate to a free oscillatory ice-age regime that is under the “pacemaker” influence of earthorbital (Milankovitch) forcing. Expanded discussions are given of the surface temperature variations accompanying the evolution of ice, CO2, and ocean temperature, and of the bifurcation properties of the model from both mathematical and physical viewpoints.