scholarly journals The cold regions’ temperature nonlinear prediction method basing on phase space reconstruction and Volterra filter

2019 ◽  
Vol 49 (6) ◽  
pp. 733-740
Author(s):  
XianFeng HE ◽  
ZiLi WANG ◽  
Qi HE ◽  
BaoSen ZHANG
Author(s):  
Huug van den Dool

How many degrees of freedom are evident in a physical process represented by f(s, t)? In some form questions about “degrees of freedom” (d.o.f.) are common in mathematics, physics, statistics, and geophysics. This would mean, for instance, in how many independent directions a weight suspended from the ceiling could move. Dofs are important for three reasons that will become apparent in the remaining chapters. First, dofs are critically important in understanding why natural analogues can (or cannot) be applied as a forecast method in a particular problem (Chapter 7). Secondly, understanding dofs leads to ideas about truncating data sets efficiently, which is very important for just about any empirical prediction method (Chapters 7 and 8). Lastly, the number of dofs retained is one aspect that has a bearing on how nonlinear prediction methods can be (Chapter 10). In view of Chapter 5 one might think that the total number of orthogonal directions required to reproduce a data set is the dof. However, this is impractical as the dimension would increase (to infinity) with ever denser and slightly imperfect observations. Rather we need a measure that takes into account the amount of variance represented by each orthogonal direction, because some directions are more important than others. This allows truncation in EOF space without lowering the “effective” dof very much. We here think schematically of the total atmospheric or oceanic variance about the mean state as being made up by N equal additive variance processes. N can be thought of as the dimension of a phase space in which the atmospheric state at one moment in time is a point. This point moves around over time in the N-dimensional phase space. The climatology is the origin of the phase space. The trajectory of a sequence of atmospheric states is thus a complicated Lissajous figure in N dimensions, where, importantly, the range of the excursions in each of the N dimensions is the same in the long run. The phase space is a hypersphere with an equal probability radius in all N directions.


2013 ◽  
Vol 10 (11) ◽  
pp. 14331-14354 ◽  
Author(s):  
N. H. Adenan ◽  
M. S. M. Noorani

Abstract. The estimation of river flow is significantly related to the impact of urban hydrology, as this could provide information to solve important problems, such as flooding downstream. The nonlinear prediction method has been employed for analysis of four years of daily river flow data for the Langat River at Kajang, Malaysia, which is located in a downstream area. The nonlinear prediction method involves two steps; namely, the reconstruction of phase space and prediction. The reconstruction of phase space involves reconstruction from a single variable to the m-dimensional phase space in which the dimension m is based on optimal values from two methods: the correlation dimension method (Model I) and false nearest neighbour(s) (Model II). The selection of an appropriate method for selecting a combination of preliminary parameters, such as m, is important to provide an accurate prediction. From our investigation, we gather that via manipulation of the appropriate parameters for the reconstruction of the phase space, Model II provides better prediction results. In particular, we have used Model II together with the local linear prediction method to achieve the prediction results for the downstream area with a high correlation coefficient. In summary, the results show that Langat River in Kajang is chaotic, and, therefore, predictable using the nonlinear prediction method. Thus, the analysis and prediction of river flow in this area can provide river flow information to the proper authorities for the construction of flood control, particularly for the downstream area.


2018 ◽  
Vol 27 (6) ◽  
pp. 1221-1228 ◽  
Author(s):  
Jingjing Li ◽  
Qijin Zhang ◽  
Yumei Zhang ◽  
Xiaojun Wu ◽  
Xiaoming Wang ◽  
...  

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