Zero-dimensional Climate Model Research Articles

The impact of Snowball Earth glaciation on ocean water [formula omitted] values

It has been long recognized that glacial episodes can affect the δ18O value of ocean water, where preferential storage of 16O in ice changes the 18O/16O ratio of the ocean. However, these effects are generally thought of as transient, as Cenozoic glaciation has had neither the magnitude or duration to cause long-term change with ocean water buffered to values close to 0±2‰ VSMOW by tectonic processes. The Snowball Earth glaciations of the Cryogenian have the potential to cause much larger changes in ocean water δ18O values due to their increased ice volume and long duration relative to Cenozoic glaciation, but these effects have not been previously investigated.Here, I use a numerical box model to investigate ocean water δ18O values over the Proterozoic and Phanerozoic. The model simulates various temperature and tectonics dependant fluxes of 18O, while also incorporating a zero-dimensional climate model and ice volume component to model glacial cycles. Monte Carlo simulations of the Sturtian and Marinoan glaciations reveal that these had the potential to alter ocean water δ18O values for hundreds of millions of years after the termination of glaciation, providing a mechanism for secular change in the δ18O value of ocean water. This occurs as a very large volume of ice (presumably, but not necessarily 18O depleted) is sequestered from the ocean, causing the ocean to become enriched enough in 18O for exchange at mid-ocean ridges to remove 18O from the ocean and slowly change the overall ocean water δ18O value. If Snowball Earth ice volumes were as large as proposed (∼28-32% of ocean volume), present day values of ice δ18O would cause significant secular change in ocean water δ18O extending into the Phanerozoic. An additional finding of this work is that the duration of the Sturtian glaciation required a very low CO2 degassing rate on the order of ∼2 Tmol/year, significantly less than that estimated from most other mass balance approaches for the Phanerozoic.

Sensitivity and Feedback Loops of a Zero-Dimensional Climate Model in the Context of the Weather and Earth’s Climate Control

Anthropogenic climate change requires the development of methods to prevent global warming. One of the possible geoengineering ways to stabilize climate is a manipulation of the solar radiation influx by forming artificial aerosol clouds in the stratosphere. The effectiveness of such activities is usually estimated on the basis of numerical modeling outside of the optimal control theory, without the formulation of the objective functional. In this paper, a zero-dimensional energy-balance climate model is discussed, and its basic properties are analyzed that are important from the viewpoint of the development of optimal control systems for climate and weather. On the basis of the model we evaluated the effects of intentional manipulations of the solar radiation influx on the global mean surface temperature. Since the obtained estimates are consistent with the results of previous studies, the present model can be considered as a basis for developing physically sound and technically feasible methods of optimal climate and weather control.

Solar Radiation Simulation by Using Zero-dimensional Climate Model

Solar Radiation Simulation by Using Zero-dimensional Climate Model

Stochastic resonance in climatic change

An amplification of random perturbations by the interaction of non-linearities internal to the climatic system with external, orbital forcing is found. This stochastic resonance is investigated in a highly simplified, zero-dimensional climate model. It is conceivable that this new type of resonance might play a role in explaining the 10 5 year peak in the power spectra of paleoclimatic records. DOI: 10.1111/j.2153-3490.1982.tb01787.x

Comments on “Delayed Albedo Effects in a Zero-Dimensional Climate Model”

Comments on “Delayed Albedo Effects in a Zero-Dimensional Climate Model”

Delayed Albedo Effects in a Zero-Dimensional Climate Model

Abstract A globally averaged radiative energy-balance model incorporating a time-delayed albedo has been investigated. The parameterization of the albedo in terms of the average global temperature is furthermore not monotonic since it incorporates a “link.” This irregularity is assumed to occur for a temperature range wherein the general circulation states of the atmosphere are associated with a high degree of cloud cover, i.e., a large albedo. The fundamental stability properties of the governing delay-differential equation have been resolved using analytical techniques. Numerical investigations have revealed that this simple model does justice to many of the qualitative features generally associated with more complex one-dimensional climate models. Hence it is capable of demonstrating auto-oscillatory behavior as well as a sequence of period-doubling bifurcations towards chaos.

Stochastic resonance in climatic change

An amplification of random perturbations by the interaction of non-linearities internal to the climatic system with external, orbital forcing is found. This stochastic resonance is investigated in a highly simplified, zero-dimensional climate model. It is conceivable that this new type of resonance might play a role in explaining the 10 5 year peak in the power spectra of paleoclimatic records. DOI: 10.1111/j.2153-3490.1982.tb01787.x

Stochastic resonance in climatic change

An amplification of random perturbations by the interaction of non-linearities internal to the climatic system with external, orbital forcing is found. This stochastic resonance is investigated in a highly simplified, zero-dimensional climate model. It is conceivable that this new type of resonance might play a role in explaining the 105 year peak in the power spectra of paleoclimatic records.

Stochastic aspects of climatic transitions-response to a periodic forcing

The time-dependent properties of the Fokker–Planck equation corresponding to a zero-dimensional climate model, showing bistable behavior and subject to a weak external periodic forcing are analyzed. Conditions under which the response is amplified are found analytically. In this way the possibility of transitions between climatic states is established. The results are illustrated by the 100,000-yr periodicity of the eccentricity of the earth's orbit, in connection with glaciation cycles. DOI: 10.1111/j.2153-3490.1982.tb01786.x

Convergence Rate and Stability of Ocean-Atmosphere Coupling Schemes with a Zero-Dimensional Climate Model

Abstract A zero-dimensional climate model is considered with three thermal reservoirs, i.e., the atmosphere, the surface mixed layer and the intermediate water of the ocean. Realistic values are adopted for the rates of heat transfer between those reservoirs. If heat is added suddenly to the atmosphere, the atmospheric temperature increases a small amount in a few days. Thereafter, the atmosphere and mixed layer increase in temperature. About one-half the mixed-layer response occurs on a time scale of two years and the rest on a time scale of about 100 years. Numerical solution of atmosphere-ocean general circulation models may require asynchronous coupling strategies to link the two models. A semi-implicit approach is considered which generalizes previously suggested schemes. Its convergence and stability are examined by application to the zero-dimensional climate model. It may be unstable if it is made too explicit. On the other hand, the fully implicit approach greatly slows down the response of the mi...