Testing reliability of the spatial Hurst exponent method for detecting a change point

Abstract

The reliability of using abrupt changes in the spatial Hurst exponent for identifying temporal points of abrupt change in climate dynamics is explored. If a spatio-temporal dynamical system undergoes an abrupt change at a particular time, the time series of spatial Hurst exponent obtained from the data of any variable of the system should also show an abrupt change at that time. As expected, spatial Hurst exponents for each of the two variables of a model spatio-temporal system – a globally coupled map lattice based on the Burgers' chaotic map – showed abrupt change at the same time that a parameter of the system was changed. This method was applied for the identification of change points in climate dynamics using the NCEP/NCAR data on air temperature, pressure and relative humidity variables. Different abrupt change points in spatial Hurst exponents were detected for the data of these different variables. That suggests, for a dynamical system, change point detected using the two-dimensional detrended fluctuation analysis method on a single variable alone is insufficient to comment about the abrupt change in the system dynamics and should be based on multiple variables of the dynamical system. HIGHLIGHTS In a non-linear dynamical system, the spatio-temporal images of one variable also contain information about the interaction of this variable with other coupled variables of the system.; When a parameter of the dynamical system changes abruptly, the spatial distribution of all the coupled variables should show an abrupt change simultaneously.; It is found that the 2D-DFA method successfully detected abrupt change points in each variable of GCML based on Burgers' chaotic map at the same time as a system parameter was changed.; The 2D-DFA method detected different abrupt change points in the time series of the spatial Hurst for the NCEP/NCAR data of three different variables.; This study suggests, for a dynamical system, change point detected using 2D-DFA method on a single variable alone is insufficient to comment about the abrupt change in the system dynamics and should be based on multiple variables of the dynamical system.;

Keywords

• burgers’ chaotic map
• change point detection
• globally coupled map lattice
• hurst exponent
• two-dimensional detrended fluctuation analysis