Temporal relations of column water vapor and tropical precipitation

Empirical studies using satellite data and radiosondes have shown that precipitation increases with column water vapor (CWV) in the tropics, and that this increase is much steeper above some critical CWV value. Here, eight years of 1-min-resolution microwave radiometer and optical gauge data at Nauru Island are analyzed to better understand the relationships among CWV, column liquid water (CLW), and precipitation at small time scales. CWV is found to have large autocorrelation times compared with CLW and precipitation. Before precipitation events, CWV increases on both a synoptic-scale time period and a subsequent shorter time period consistent with mesoscale convective activity; the latter period is associated with the highest CWV levels. Probabilities of precipitation increase greatly with CWV. Given initial high CWV, this increased probability of precipitation persists at least 10–12 h. Even in periods of high CWV, however, probabilities of initial precipitation in a 5-min period remain low enough that there tends to be a lag before the start of the next precipitation event. This is consistent with precipitation occurring stochastically within environments containing high CWV, with the latter being established by a combination of synoptic-scale and mesoscale forcing.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Holocene settlement shifts and paleoenvironments on the Central Iranian Plateau: investigating linked systems

For thousands of years, humans have inhabited locations that are highly vulnerable to the impacts of climate change, earthquakes, and floods. In order to investigate the extent to which Holocene environmental changes may have impacted on cultural evolution, we present new geologic, geomorphic, and chronologic data from the Qazvin Plain in northwest Iran that provides a backdrop of natural environmental changes for the simultaneous cultural dynamics observed on the Central Iranian Plateau. Well-resolved archaeological data from the neighbouring settlements of Zagheh (7170—6300 yr BP), Ghabristan (6215—4950 yr BP) and Sagzabad (4050—2350 yr BP) indicate that Holocene occupation of the Hajiarab alluvial fan was interrupted by a 900 year settlement hiatus. Multiproxy climate data from nearby lakes in northwest Iran suggest a transition from arid early-Holocene conditions to more humid middle-Holocene conditions from c. 7550 to 6750 yr BP, coinciding with the settlement of Zagheh, and a peak in aridity at c. 4550 yr BP during the settlement hiatus. Palaeoseismic investigations indicate that large active fault systems in close proximity to the tell sites incurred a series of large (MW ~7.1) earthquakes with return periods of ~500—1000 years during human occupation of the tells. Mapping and optically stimulated luminescence (OSL) chronology of the alluvial sequences reveals changes in depositional style from coarse-grained unconfined sheet flow deposits to proximal channel flow and distally prograding alluvial deposits sometime after c. 8830 yr BP, possibly reflecting an increase in moisture following the early-Holocene arid phase. The coincidence of major climate changes, earthquake activity, and varying sedimentation styles with changing patterns of human occupation on the Hajiarab fan indicate links between environmental and anthropogenic systems. However, temporal coincidence does not necessitate a fundamental causative dependency.