Periphery Theory and Its Application to Air Pollution Forecast

HONGXING CAO1, BAOSHAN NIU2, JIAN SONG3, HUI LIU3, XIUHUA CAI1

1Chinese Academy of Meteorological Sciences

CMA

Beijing, CHINA

2Shangshui Meteorological Station

Henan Meteorological Administration Province

Shangshui county, CHINA

3College of Sciences

Inner Mongolia University of Technology

Hohhot, CHINA

Abstract: — The periphery phenomena and periphery definition as well as periphery theory are introduced; The basic structure of

a periphery （jieke） of system is composed of both a wall, which defends system itself, and a gate ( or passage), through which

the exchange between the system and its environment is carried out. In order to describe the periphery mathematically, perimeter

set are presented. On the basis two indicant functions: security degree and subsist ratio are suggested. By using air pollution and

meteorological data, a case of air pollution forecast is exemplified in detail.

Keywords: —information, periphery theory, air pollution forecast, environment protect.

Received: April 11, 2024. Revised: September 3, 2024. Accepted: October 7, 2024. Published: November 6, 2024.

1. Introduction

One can easily find the periphery(jieke 界壳 in Chinese)

phenomena, for example, a hard shell of a turtle, an airplane

(Fig. 1), a castle, a watershed between two rivers, country or

region boundary, firewall in the internet etc. But a package of

goods, a coffin etc. are not a periphery, as they are out of

exchange. A gang syndicate has an almost closed periphery, its

members exchange less with other gang-organizations and

society. Periphery theory is just to study a kind of periphery

phenomena [1,2]; Nowadays periphery theory has been applied

to many fields [3,4,5]

At first the periphery phenomena and its definition as well

as periphery theory are briefed; herein perimeter set are

presented mathematically. By using the air pollution and the

meteorological data, a case of air pollution forecast is given as

an example.

Fig.1. Airplane

2. Periphery structure and Perimeter set

A periphery of system is undoubtedly a part of the system,

which situates on its boundary, and adjacent to environment. So

the periphery is an intermediary agent between the system and

its environment.

A kind of system boundary that plays a role in

•defending the existence of the system and

•exchanging between the system and its environment

is called as a periphery or jieke, There in after both periphery

and jieke will be used, depending on which is proper. The basic

structure of a periphery of system is composed of both a wall,

which defends system itself, and a gate (or passage), through

which the exchange between the system and its environment is

carried out (Fig. 2).

Fig.2. Schematic diagram of periphery

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The basic structure of a periphery of system is composed of

both a wall, which defends system itself, and a gate (or passage),

through which the exchange between the system and its

environment is carried out [6].

Suppose an periphery sub-unit in a system boundary (SB) is

u，which is a small part of system boundary, obviously there is

SB uU

Defense degree

()u



and its exchange degree

()u



the sub-unit are given, i.e.

( ), ( ) [0,1], ( ) ( ) 1u u u u

   

  

(1)

Besides, the state ζ of the sub-unit is surely considered,

the state change is related to the states of other parts of the

system and affects to defensiveness and exchange rate.

So it needs to define a perimeter set [6]. Let us have a

universe of discourse E. Let A be a subset of E. Then construct

the set

{ , ( ), ( ), ( ) | }

A u u u u u E

  

   

(2)

where

A A A A A

( ) [0,1], ( ) [0,1], ( ) [0,1], ( ) ( ) 1.u u u u u

    

    

will call the set A perimeter set with 3-logos. Suppose perimeter

set with n-elements, denote

1 1 1 1 2 2 2 2

( , , ) / ( , , ) / ( , , ) /

n n n n

A u u u

        

   L

(3)

“+” expresses another sub-unit following, not algebra

addition. Denote system state ζ∈ [0, 1], then the sub-unit u

of periphery is expressed as

( , , ) /zu

  



But for the sub-unit u of the system inner

( ,0,0) /zu





Because the sub-unit u of the system inner has not functions

of both defense and exchange, so μ=0

，

ν=0.

3. Indicant functions

For simplicity, first of all, ζ(u) is leaved out here. So it reads

{ , ( ), ( ) | }

A u u u u E



   

(4)

Suppose a perimeter set with n-elements, denote

1 1 1 2 2 2

( , ) / ( , ) / ( , ) /

n n n

A u u u

     

   L

(5)

“+” expresses another sub-unit following, not algebra

addition.

Two indicant functions: security degree and subsist ratio,

which belong to presentment function of the periphery. The sum

of defense degree is

, 1,2, ,

d i n



   L

The sum of exchange degree is

, 1,2, ,

e i n



   L

Mapping κ:｛x(μ,ν)u |u∈E｝→[0,1]

Formulates security degree of the periphery

κ=1/2+(d*－λe*)/2 κ∈[0，1]

(6)

where

   

* / , * / , * * 1, [0,1],d d d e e e d e d e



      

where λ is parameter relating to system state, environment and

defense degree. Security degree is periphery’s defense

capability taking account of exchange degree. Just be similar to

Chinese medicine theory and Chinese philosophy, the system

defense is regarded as pan-positive(Yang) but exchange as pan-

negative(yin). The system holds yin-yang equilibrium, then

maintains itself existence. Therefore several periphery methods

for forecast and evaluation are based on yin-yang equilibrium

principle.

Taking λ=1

If d*=0, e*=1, then κ=0;

If d*=1, e*=0, then κ=1;

If d*= e*, then κ=1/2.

Formulate subsist ratio of periphery

1, 0













(7)

where q is parameter with positive integer number. Subsist ratio

is relative exchange, i.e. proportion of exchange to defense.

Taking λ=1, q=2

If d*=0，e*=1, then φ=1;

If d*=e* then φ=1/2;

If d*→∞ or e*→0 φ→0.

If the defense is extra large or exchange is extra small, the

subsist ratio tends to zero, namely the system cannot be alive in

the case.

4. Air pollution forecast

Air pollutions are relative to a human live and the economic

activities as well as military operations. So the air pollution

forecast is important issue in the environment protect. Generally,

the air pollution forecasts are made by use of statistics and

numerical computation[7,8]. Herein a forecast method for the air

pollution is suggested based on periphery theory [9,10].

Firstly we selects some variables , which are correlative to

the air pollution by means of experience analysis. A concept of

departure pair and its calculation are suggested; The departure

pair will be developed to make the forecast for the city air

pollution. An example was made with the method, from this

availability for the city air pollution forecast is verified.

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A departure of variables x, e.g. temperature, humanity,

pollutant concentration etc. are defined

∆x = x− xp (8)

where xp is the mean or the median value of variable x.

∆x ≥ 0 called positive departure and denoted as x+

∆x < 0 called negative departure and denoted as x- .

TABLE 1 SIGN PROBABILITIES

Consider x+ as μ , x- as ν.

We apply (7) to make the forecast of air pollution, in (7)

taking q=2, λ=1; and

* / ( ), * / ( ); ,

d d d e e e d e d x e x



       

i = 1, 2,…,I，j = 1, 2,… ,J；I，J are number of the positive

departure and negative departure respectively.

Taking air pollution days from December 1999 to February

2002 (samples N=27) as predictand, and 5 atmospheric

circulation indexes as predictors, the forecast model has been set

up, then the test forecasts were made for March to May 2002,

denoted as 28, 29,30 sample.

5. Computing

The predictors are following:

1,x

meridian circulation index over Asia;

2,x

polar vortex index over Asia;

3,x

north latitude degree of western Pacific subtropical

high pressure;

4,x

index of Tibetan circulation;

5,x

Southern Oscillation index.

The data of the predictors and predictand can be obtained from

the open data in China. The predictand y are correlate with above

variables

with confidence level α=0.05. The departures were

calculated using the median value of variables, as it makes

almost the number of x+ to be equal to one of x-. All data are

standardized by use of extreme values difference to [0,1],

namely

When the correlation between y and

is positive, the

standardization is taken as

min

max min

zzz



When negative, take as

min

max min

zzz





where

min

and

max

are a minimum and a maximum of y or

series.

Instead of values of

x

and

x

we prefer to take the sign

probability p as μ, ν. p is calculated using

p =m/n

where m is the number of positive or negative (sign + or -) of y

departures, which coincide with that of

, namely, in same

sample the sign of the y departure have to same sign of the

According to the data the sign probabilities were calculated and

listed in Table 1.

As we know, the qualitative forecast is very important in the

climate prediction [11,12]. For example, in spring people want

to know the following summer will be rainy or dry, hot or cool.

This is a qualitative forecast. Besides present forecast technique

for climate is not high, an accurate quantitative forecast cannot

be made. So it demands to make the qualitative forecast.

Therefore it needs to develop the method of qualitative forecast.

Generally, the air pollution forecasts are made by use of

both numerical computing and statistics [13]. Up to now the

forecast accuracy is not satisfactory. A method based on the

periphery theory is described as follows. The method has

methodological meaning, it is to say, the periphery theory and

the perimeter set will be available to develop the air pollution

forecasts.

0.7857

0.3846

0.7143

0.4615

0.5294

0.7

0.4286

0.7692

0.8125

0.25

0.2143

0.6154

0.2857

0.5385

0.4706

0.3

0.5714

0.2308

0.1875

0.75

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Make the forecast of 28th case. Divide the + and - of 5

variables according to (8), then find out the corresponding

column in table 1, calculate

d = Σμ = 0.7857 + 0.7143 + 0.7 + 0.7692 + 0.8125 = 3.7817

e = Σν = 0.2143 + 0.2857 + 0.3 + 0.2308 + 0.1875 = 1.2183

d* = d/(d + e) = 3.7817/(3.7817 + 1.2183) = 3.7817/5.0 =

0.7563

e* = e/(d + e) = 1.2183/(3.7817 + 1.2183) = 1.2183/5.0 =

0.2437

φ+ = 1/[1 + (e*/d*)2 ] = 1/[1 + (0.2437/0.7563)2 ] = 0.9060

φ− =1/[1 + d*/e*)2 ] = 1/[1 + (0.7563/0.2437)2 ] = 0.0941

Here φ+, φ- represent the positive and negative total

contributions of the variables. Calculate the forecast indicator

F = φ+ − φ- = 0.906 − 0.0941 = 0.8119

F > 0 show the positive departure will appear, i.e. the

pollution days T will positive, namely the pollution days T

≥

14 d. , the observed is 25 d.

Similarly, for the 29th case, F>0，the pollution days T

≥

14d.,

the observed is 23 d.

Similarly, for the 30th case, F<0，the pollution days T<14d.,

the observed is 11d.

The forecasts for 3 cases are all correct. It demonstrates that

above forecast method can be used for qualitative forecast of the

air pollution.

Acknowledgment

The support of the National Natural Science Foundation of

China (Grant No. 42275052) are gratefully acknowledged.

Thanks to prof. Hongbo Zhang and Ms Jinyu Shen for their help.

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Funded by the National Natural Science Foundation

of China (Grant No. 42275052)

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Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

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Scientific Article or Scientific Article Itself

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that are relevant to the content of this article.

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DOI: 10.37394/232024.2024.4.13

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E-ISSN: 2944-9006

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