A Markov modulated Poisson process model for rainfall increments

The problems encountered when using traditional rectangular pulse hierarchical point processmodels for fine temporal resolution and the growing number of available tip-time records suggest that rainfall increments from tipping-bucket gauges be modelled directly. Poisson processes are used with an arrival rate modulated by a Markov chain in Continuous time. The paper shows how, by using two or three states for this chain, much of the structure of the rainfall intensity distribution and the wet/dry sequences can be represented for time-scales as small as 5 minutes.

Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Uniqueness and extinction properties of generalised Markov branching processes

This paper focuses on the basic problems regarding uniqueness and extinction properties for generalised Markov branching processes. The uniqueness criterion is firstly established and a differential–integral equation satisfied by the transition functions of such processes is derived. The extinction probability is then obtained. A closed form is presented for both the mean extinction time and the conditional mean extinction time. It turns out that these important quantities are closely related to the elementary gamma function.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

Probabilistic approach in weighted Markov branching processes

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

A regime shift in the North Sea circa 1988 linked to changes in the North Sea horse mackerel fishery

After 1987, Phytoplankton Colour (a visual estimate of chlorophyll) measured on samples taken by the continuous plankton recorder (CPR) in the North Sea increased substantially, both in level and seasonal extent, compared to earlier years since 1946. Many species of phytoplankton and zooplankton showed marked changes in abundance at about the same time. These events coincided with a large increase in catches of the western stock of the horse mackerel (Trachurus trachurus L.) in the northern North Sea reflecting a northerly expansion of the stock along the shelf edge from the Bay of Biscay to the North Sea after 1987. Using a 3D hydrodynamic model, with input from measured wind parameters, monthly transport of oceanic water into the North Sea has been calculated for the period 1976–1994, integrated for a section from Orkney to Shetland to Norway. A substantial increase in oceanic inflow occurred in the winter months, December to March, from 1988. Higher sea surface temperatures were also measured after 1987 especially in spring and summer months. These biological and physical events may be a response to observed changes in pressure distribution over the North Atlantic. From 1988 onwards, the North Atlantic Oscillation (NAO) index, the pressure difference between Iceland and the Azores, increased to the highest positive level observed in this century. Positive NAO anomalies are associated with stronger and more southerly tracks of the westerly winds and higher temperatures in western Europe. These changing wind distributions may have led to an increase in the northerly advection of water along the western edge of the European shelf and may have assisted the migration of the horse mackerel. This study is possibly a unique demonstration of a correlation between three different trophic levels of a marine ecosystem and hydrographic and atmospheric events at decadal and regional scales. The results emphasise the importance of maintaining into the future long term programmes such as the CPR.

Regime shifts in marine ecosystems: detection prediction and management

Regime shifts are abrupt changes between contrasting, persistent states of any complex system. The potential for their prediction in the ocean and possible management depends upon the characteristics of the regime shifts: their drivers (from anthropogenic to natural), scale (from the local to the basin) and potential for management action (from adaptation to mitigation). We present a conceptual framework that will enhance our ability to detect, predict and manage regime shifts in the ocean, illustrating our approach with three well-documented examples: the North Pacific, the North Sea and Caribbean coral reefs. We conclude that the ability to adapt to, or manage, regime shifts depends upon their uniqueness, our understanding of their causes and linkages among ecosystem components and our observational capabilities.

The Mediterranean Sea Regime Shift at the End of the 1980s, and Intriguing Parallelisms with Other European Basins

Regime shifts are abrupt changes encompassing a multitude of physical properties and ecosystem variables, which lead to new regime conditions. Recent investigations focus on the changes in ecosystem diversity and functioning associated to such shifts. Of particular interest, because of the implication on climate drivers, are shifts that occur synchronously in separated basins. In this work we analyze and review long-term records of Mediterranean ecological and hydro-climate variables and find that all point to a synchronous change in the late 1980s. A quantitative synthesis of the literature (including observed oceanic data, models and satellite analyses) shows that these years mark a major change in Mediterranean hydrographic properties, surface circulation, and deep water convection (the Eastern Mediterranean Transient). We provide novel analyses that link local, regional and basin scale hydrological properties with two major indicators of large scale climate, the North Atlantic Oscillation index and the Northern Hemisphere Temperature index, suggesting that the Mediterranean shift is part of a large scale change in the Northern Hemisphere. We provide a simplified scheme of the different effects of climate vs. temperature on pelagic ecosystems.