Evaluation of GPROF V05 Precipitation Retrievals under Different Cloud Regimes

Precipitation retrievals from passive microwave satellite observations form the basis of many widely used precipitation products, but the performance of the retrievals depends on numerous factors such as surface type and precipitation variability. Previous evaluation efforts have identified bias dependence on precipitation regime, which may reflect the influence on retrievals of recurring factors. In this study, the concept of a regime-based evaluation of precipitation from the Goddard Profiling (GPROF) algorithm is extended to cloud regimes. Specifically, GPROF V05 precipitation retrievals under four different cloud regimes are evaluated against ground radars over the United States. GPROF is generally able to accurately retrieve the precipitation associated with both organized convection and less organized storms, which collectively produce a substantial fraction of global precipitation. However, precipitation from stratocumulus systems is underestimated over land and overestimated over water. Similarly, precipitation associated with trade cumulus environments is underestimated over land, while biases over water depend on the sensor’s channel configuration. By extending the evaluation to more sensors and suppressed environments, these results complement insights previously obtained from precipitation regimes, thus demonstrating the potential of cloud regimes in categorizing the global atmosphere into discrete systems.

Momentum Preserving Simulation of Cooperative Multi-Rotors with Flexible-Cable Suspended Payload

In this paper, a momentum-preserving integration scheme is implemented for the simulation of single and cooperative multi-rotors with a flexible-cable suspended payload by employing a Lie group based variational integrator (VI), which provides the preservation of the configuration manifold and geometrical constraints. Due to the desired properties of the implemented VI method, e.g. sypmlecticity, momentum preservation, and the exact fulfillment of the constraints, exponentially long-term numerical stability and good energy behavior are obtained for more accurate simulations of aforementioned systems. The effectiveness of Lie group VI method with the corresponding discrete systems are demonstrated by comparing the simulation results of two example scenarios for the single and cooperative systems in terms of the preserved quantities and constraints, where a conventional fixed-step Runge-Kutta 4 (RK4) and Variable-Step integrators are utilized for the simulation of continuous-time models. It is shown that the implemented VI method successfully performs the simulations with a long-time stable behavior by preserving invariants of the system and the geometrical constraints, whereas the simulation of continuous-time models by RK4 and Variable Step are incapable of satisfying these desired properties, which inherently results in divergent and unstable behavior in simulations.

Modeling of the criterion for predicting the loss of stability of discrete systems

The paper proposes a method for determining the estimated parameter of the stability state of discrete systems exposed to external influences. As a rule, the loss of stability of the first and second kind leads to a problematic operation process throughout the life cycle, or even the destruction of the system. Hence the requirements of a certain rigidity to the designed and operated systems in order to ensure their geometric immutability. At the same time, in practice, there are no naturally deformable systems from external influences. The paper sets and solves the problem of determining the stability parameter, with the help of which, even before the stage of loss of stability, it is possible to predict the future state of a discrete system, i.e. to predict whether it (the system) has sufficient internal properties to return to a stable position at any exit from the preliminary state of equilibrium due to the influence of external forces.

Some Possibilities of Modeling Colored Petri Nets

Petri nets are a mathematical apparatus for modelling dynamic discrete systems. Their feature is the ability to display parallelism, asynchrony and hierarchy. First was described by Karl Petri in 1962 [1,2,8]. The Petri net is a bipartite oriented graph consisting of two types of vertices - positions and transitions connected by arcs between each other; vertices of the same type cannot be directly connected. Positions can be placed by tags (markers) that can move around the network. [2] Petri Nets (PN) used for modelling real systems is sometimes referred to as Condition/Events nets. Places identify the conditions of the parts of the system (working, idling, queuing, and failing), and transitions describe the passage from one state to another (end of a task, failure, repair...). An event occurs (a transition fire) when all the conditions are satisfied (input places are marked) and give concession to the event. The occurrence of the event entirely or partially modifies the status of the conditions (marking). The number of tokens in a place can be used to identify the number of resources lying in the condition denoted by that place [1,2,8]. Coloured Petri nets (CPN) is a graphical oriented language for design, specification, simulation and verification of systems [3-6,9,15]. It is in particular well-suited for systems that consist of several processes which communicate and synchronize. Typical examples of application areas are communication protocols, distributed systems, automated production systems, workflow analysis and VLSI chips. In the Classical Petri Net, tokens do not differ; we can say that they are colourless. Unlike standard Petri nets in Colored Petri Net of a position can contain tokens of arbitrary complexity, such as lists, etc., that enables modelling to be more reliable. The article is devoted to the study of the possibilities of modelling Colored Petri nets. The article discusses the interrelation of languages of the Colored Petri nets and traditional formal languages. The Venn diagram, which the author has modified, shows the relationship between the languages of the Colored Petri nets and some traditional languages. The language class of the Colored Petri nets includes a whole class of Context-free languages and some other classes. The paper shows modelling the task synchronization Patil using Colored Petri net, which can't be modeled using well- known operations P and V or by classical Petri network, since the operations P and V and classical Petri networks have limited mathematical properties which do not allow to model the mechanisms in which the process should be synchronized with the optimal allocation of resources.

Dynamic Characteristics of Four Systems of Difference Equations with Higher Order

In this paper, we explore the global dynamical characteristics, boundedness, and rate of convergence of certain higher-order discrete systems of difference equations. More precisely, it is proved that for all involved respective parameters, discrete systems have a trivial fixed point. We have studied local and global dynamical characteristics at trivial fixed point and proved that trivial fixed point of the discrete systems is globally stable under respective definite parametric conditions. We have also studied boundedness and rate of convergence for under consideration discrete systems. Finally, theoretical results are confirmed numerically. Our findings in this paper are considerably extended and improve existing results in the literature.

Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology

Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology.

Simple dynamics in non-monotone Kolmogorov systems

In this paper we analyse the global dynamical behaviour of some classical models in the plane. Informally speaking we prove that the folkloric criteria based on the relative positions of the nullclines for Lotka–Volterra systems are also valid in a wide class of discrete systems. The method of proof consists of dividing the plane into suitable positively invariant regions and applying the theory of translation arcs in a subtle manner. Our approach allows us to extend several results of the theory of monotone systems to nonmonotone systems. Applications in models with weak Allee effect, population models for pioneer-climax species, and predator–prey systems are given.