Abstract
Geographic Information System (GIS) is an information technology that is readily applied as a decision aid for a variety of water resource applications. System dynamics as a method of computer simulation of dynamic systems is based on the basic concept of stock with incoming and outgoing flows. In most real-world problems the change in the level of the basin is considered to be the result of summation of incoming and outgoing flows over a certain period of time, taking into account the initial level of the basin. This makes system dynamics an appropriate tool for modelling the behaviour of water basins. A digital terrain model consists of a digital elevation model and a digital model of the situation. For the needs of system dynamics modelling in this case-study only the digital elevation model (DEM) is used. GIS product - DEM -usage in system dynamics models advances simulation-based analysis and decision making for local and regional operational forecasting. The task of the article is to formulate both necessary and sufficient requirements for DEM usage in effective forecasting of water basin behaviour with system dynamics model. Within the proposed approach simple system dynamics models of a basin are developed and verified. These models include incoming and outgoing flow models in form of time-series and basin level DEMbased model. The incoming flow is defined with a hydrograph. The water regime of the basin is determined by its geometrical properties. The outgoing flow is formed at the exit from the basin. The models are formalized as a set of first-order difference equations, which are solved sequentially after constant time steps. The solutions provide simulation progress over time. The concept of constant time step is associated with the periodicity of observations of the natural water objects. The basin level function of the volume makes it possible to develop the system dynamics model of the basin suitable for simulation of the level changes in the basin. The developed system dynamics models are used for experimentation with various scenarios of the behaviour of the system under investigation and for forecasting the consequences of changes in parameters or structure of the system. The requirements for DEM usage in system dynamics models are formulated. The application of system dynamics with incorporated DEMbased basin models makes it possible to analyse the behaviour of the investigated basins and to obtain operational forecasts of the situation for various scenarios. Further research is outlined on the accuracy of simulation results depending on the complexity increase in the simulated object for closer similarity to real reservoirs.
Highlights
Copulas have become popular in the finance and insurance community in the past years, where modeling and estimating the dependence structure between several univariate time series are of great interest; see Frees and Valdez (1998) [1] and Embrechts et al (2002) [2] for review.A copula function is a multivariate distribution function with standard uniform marginals
The research studies the estimation of a semiparametric stationary Markov models based on a Frank copula density function
Described techniques allow us to estimate the parameters of the Frank copula, which has a better fit compared to previously selected regression models
Summary
Copulas have become popular in the finance and insurance community in the past years, where modeling and estimating the dependence structure between several univariate time series are of great interest; see Frees and Valdez (1998) [1] and Embrechts et al (2002) [2] for review. A copula function is a multivariate distribution function with standard uniform marginals. It is useful to represent copulas as joint distribution functions of standard uniform random variables:. The outcome of uniform random variables falls into the interval [0, 1]; the domain of a copula must be the N-dimensional unit cube. Because the mapping represents a probability, the range of the copula must be the unit interval. The expression above indicates how the simple product of two marginal distributions will fail to properly measure the joint distribution of two asset prices unless they are independent and the dependence information captured by the copula density [4], c(F1 (u), F2 (v)) , is normalized to unity
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