Fractional properties of geophysical field variability on the example of hydrochemical parameters

Abstract

Abstract. Using the properties of compound Poisson process and its fractional generalizations, statistical models of geophysical fields variability are considered on an example of hydrochemical parameters system. These models are universal to describe objects of different nature and allow us to explain various pulsing regime. Manifestations of non-conservatism in hydrochemical parameters system and the advantages of the system approach in the description of geophysical fields variability are discussed.Universal character and wide use of power laws in nature are associated with the fundamental summation of identically distributed random variables and the law of large numbers. We can list many examples of power law characterizing complicated systems of heterogeneous elements in different areas of natural sciences (astrophysics, seismology, turbulence theory etc.) including the same relations describing sea water chemical parameters system [1,2]. The elements of this system are interacting between each other (directly and indirectly) and with the elements of other systems represented by hydrophysical fields and hydrobiology objects. All these interactions create a great diversity of variability factors affecting the chemical system behavior. Fig. 1 represents the dependencies of standards σ on time average concentrationsρ of 16 chemical parameters measured at 13 points of diurnal observations in Amur Bay of the Sea of Japan (for initial data see [3]). Two regions are notable in the concentration range of 10 −4 − 3.3 × 10 4 mg/kg, they are: withρ< 10 2 mg/kg for non-conservative parameters and withρ>10 2 mg/kg for conservative ones. All the data of non-conservative parameters (dissolved oxygen, nutrients, carbonic parameters) are approximated by a unified power law regression with the exponent γ = 0.68 ± 0.02. The conservative parameter data (salinity and components of major salt composition) are approximated by a series of separate parallel regressions with γ = 1, each of which refers to a separate observation point.It is obvious that for each concentration region there is a own set of peculiar basic factors of variability. In the parameters system under consideration, the fluctuation regime change corresponds to the boundary concentration ofρ=10 2 mg/kg. In this paper, we consider how and what factors determine the behavior of a hydrochemical system.Before we turn to the discussion of a statistical model of hydrochemical parameters system behavior, we shall adduce some analogies. For example, a flow of seismic events may be considered