Vol. 5 No. 4 Advances in Atmospheric Sciences Nov. 1988

SEVERAL PROPERTIES OF METEOROLOGICAL

KNOWLEDGE USED FOR EXPERT SYSTEM

Dai Honghua ( ~ ' ~ )

Institute of Atmospheric Physics, Academia Sinica, Beijing

Received August 24, 1987

ABSTRACT

This paper describes seven important, specific properties of meteorological knowledge from the view of KP (Knowledge Processing) and ES (Expert System). It also discusses the viewpoint of knowledge motion and the evolution-transition theory. These specific properties are very important for MKP (Me- teorological KP)and building MES (Meteorological ES).

I. INTRODUCTION

A M E S is a computer software system which solves difficult meteorological problems

that can only be solved by experienced meteorologists. In order to develop such systems for

automatic weather forecasting, meteorological knowledge must be mastered and understood

by the system. How can a system master and understand knowledge, especially meteorolo-

gical knowledge? First of all, some specific properties of MK (Meteorological Knowledge)

must be known. It is most important for MK P and building a MES.

With the advances of atmospheric scientific research, more and more meteorological knowledge is being acquired. It is impossible for a forecaster to utilize all the useful know-

ledge in his/her work, partly because of the complexity of MK and the large amount of MK and the relative data. Furthermore, it is also vex'3, difficult for a forecaster to distinguish which knowledge-cell is most useful, and which part is more useful for forecasting in some definite periods or some definite regions. For this reason, it is necessary for us to deal with meteorological knowledge processing and to develop the meteorological expert system. To do this, we must study the specific properties of MK to find out how we can do it

well. The scientific research of meteorological knowledge has shown that the following seven

specific properties of meteorological knowledge are very important for MKP and developing

MES from the viewpoint of KP.

II. THE MOTIVE PROPERTY OF METEOROLOGICAL KNOWLEDGE AND METEOROLOGICAL KNOWLEDGE K AS A FUNCTION OF TIME t AND PROBLEM P~P~"~

It is well known that everything is in motion, with no exception of meteorological

knowledge. It is also in incessant motion, development and change, from simple to com-

plex, and from less correct to more correct. Let us take a meteorological knowledge-cell

a as an example. Assume that a is a natural law. It is always true that at first the a

was not discovered and we did not know it at all, and then some phenomena related to

516 Advances in Atmospheric Sciences Vol. 5

were discovered. If and only if some kind of processes of cognition and practice act upon it, can the knowledge-cell be acquired. What is in this processing is a in motion. From this point, we find that meteorological knowledge changes with time t and different MK must be found to solve different problems, i. e., MK is also dependent on problems, so we consider that MK is a function of time 3 and problem pC~ p(m). That is

K = K ( 3 , p ) , ( 1 ) and the problem also depends on the time 3, so

K = K ( t , p ( 3 ) ) . (1 ' ) Generally, original meteorological knowledge always starts from some kind of weather forecasting experience k0 or from other scientific branches, such as, physics, fluid mechanics, and so on, and we also denote it k0. Now, we assume that k0 is produced at time 30, and the intelligence action ~b of human beings also acts upon k0 continuously, and so a knowledge sequence

/0,t~,3~, ... . . . ,t~, ... . . . ( 2 ) k o , k l , k 2 , . . . . . . , k . , . . . . . .

is produced with the lapse of time and deepening of understanding. Experience is raised to knowledge, general knowledge is raised to universal truth. Universal truth approaches absolute truth incessantly, but it never reaches absolute truth. In equation (1), we fixed problem p, and let 3 vary. Fig. 1 shows the variation of K ( 3 , p ) .

Absolute truth

z f / I i !

O l to t l . . . t , /

k(t .P.)

- - t

Fig. I. Production of MK and its development and variation.

That is to say, we may constantly improve the accuracy of weather forecasting, but never reach such a level, i. e. absolute correctness. This inference always holds true for human beings or for machines. This is because although the understanding of human beings or machines incessantly deepens, MK increases constantly. On the other hand, everything develops and varies constantly, new problems and new contradictions never stop occurring. Therefore, the procedures for understanding the laws of atmospheric motion are never li-

mited. From the view of problem solving, knowledge is also a function of problem; for a

series of problems, the corresponding knowledge for solving problems may be produced.

That is

p.. p o , p , , p 2 , . . . . . . , p~ , . . . . . . ( 3 )

No. 4 Properties of MK for expert system ,517

K : ho,k l ,kz , ...... , k , , ...... From the view of understanding procedure, understanding knowledge for solving problems

always follows understanding the problem itself for some period, as shown in Fig. 2 and Fig. 3. With elapsing of time, more k(t) may approach the p( t ) , i.e, there exists such a trend

limllk(t) ~ p ( t ) ll=O, ( 4 )

where ' ~ ' means to measure the difference between two non-numerical items.

let-

Fig. 2. Illustration of motion of MK and its development.

understanding

Fig. 3. Illustration of development and variation of p(t) and g ( t ) .

III. PROPERTY OF INCOMPLETE UNDERSTANDING

So far, the law of atmospheric motion has not yet been recognized completely, neither has the origin of some weather phenomena. There have been a great number of natural laws to further research and understanding. Some forecasting knowledge is not completely reliable and some accidental phenomena may occur in practice, and so on. This may be due to the incompleteness and limitations of understanding. It is necessary for us to consider the abilities of alternating known knowledge, and understanding and exploring unknown knowledge in MKP and building MES.

IV. THE REFINABLE PROPERTY

For all MK, the property of incomplete understanding determines less exactitude and in turn determines the probability of refinement to meteorological knowledge. We may get the distribution curve of the practical rate of meteorological knowledge in some processing, as shown in Fig. 4.

Now assume M to be a meteorological knowledge field, P a problem space defined upon M , k E K tm~ a knowledge-cell which is used to solve problem p e p cr~, a the confi- dence of k, and ~ the clearity of problem p, thus, the practicability C of the knowledge- cell k to the problem p may be formally defined as:

c= -IIk-p[I (5)

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C = 0 means that the knowledge-cell k is not suitable completely to problem p, whereas C = 1 means that the k is well suitable to solving problem p.

Thus, in a MES, for a given problem-set p,m~ and forecasting knowledge-set K (m, and according to real efficiency for the application of MES and requirement of problem solving, we give a threshold o r, then we can get the knowledge set

K ; " = {kl ( ~ (k) ~>or) } ( 6 ) and

-K~'~' = {k[ (~, (k) <or) }. ( 7 )

~o(k)

!

d

I

ka Po kb X

Fig. 4. Distribution of MK practicability.

We use the new forecasting knowledge s e t / ( 7 "~ to replace the old one K v"~ in the knowl- edge-base in MES, in using this K~ "), the accuracy for new forecasting knowledge set K~ m~ may be better within sight than that of using K(mL Meanwhile, the new knowledge may be supplied by human beings, such as meteorological experts, and machine learning and ma- chine exploration systems. Repeating the aboVe-mentioned refinement procedure, some excellent results may be obtained. The procedure may be operated automatically by the machine.

V. COMPLEXITY AND INTERWOVEN MULTI-PROCESSING

In meteorological knowledge processing, numerical processing may mingle with non- numerical processing and computations with inferences. A wide range of relations, pro- perties, procedures and processings, which cannot be described completely by general ma- thematics, require MES processing abilities to deal with various processings and describe corresponding interwoven relations, such as temperature increasing procedure; real weather record data retrieval; processing of various isopleth, producing condition; time; existing place; producing procedure; relation and influence between low-vortex, trough, ridge, shear-line, front and subtropical high p~essure; recall of history facts; processing of various special factors; interpolation and smoothing for lacking data, depicting universal character- istics and general law, and so on.

VL LIMITATIONS

A great deal of weather forecasting knowledge is relevant only to some definite ranges;

No. 4 Properties of MK tbr expert system $19

that is to say, a few MK have their specific background and suitable field. Why does the limitation occur? This results from the properties of incomplete understanding and motion.

The limitation of MK is shown in two important aspects: the first is time limitation. a MK-cell is correct in time A, but may be wrong in time B. Conversely, a MK-cell is wrong' in time A, but may be right in time B. For example, it may be correct for some forecasting knowledge in Meiyu season, but it may be incorrect in winter. This is the typical limitation of time. The second is regional limitation. A MK-cell is practical in area A, but may be unpractical in area B; on the contrary, a forecasting knowledge cell is not pragmatic in region A, but it may be pragmatic in region B. For example, the weather forecasting knowledge which is practical in Guangzhou, China, may not be practical in

Harbin.

VII. PROPERTY OF VARIOUS FORMS TO MK

Weather forecasting knowledge is not only in great amounts, but also in various forms. Some are described only literally. For instance, if the trough-line passes through Enshi, then there is no heavy rainfall in Changsha, Hunan Province. We call this kind of knowledge literal form weather forecasting knowledge. Some forecasting knowledge is always with some kind of targets, and we call it target form knowledge, e.g., if the wind direction in Huang- shan and Lushan shifts to south-east, and the wind speed is greater than or equal to 8 m/s, then precipitation will occur in Jiangsu Province after 12-24 hours.

Some are in the form of figures or pictures. This kind of knowledge may be shown as synoptic charts, satellite cloud pictures and so on. The general form is that,

if G, Then G1. (8 or

If G, Then R. (9 where G, G1 are figures/pictures, R the result. This kind of knowledge is very

popular in routine practical forecasting. Almost all observatories use this kind of knowledge

to make weather forecasts. Another important kind of weather forecasting knowledge takes the numerical form.

it is particularly important in numerical weather forecasting, e.g.,

9.8 ( AH v g = ~ f - - \ An-n )p, (10)

~ , = ~ + f , f = 2Dsin q~ (11) and equations

duo + 1 (V,Vo-V~ctgO)=- 1 0 p +2v~f2cosO+De dt r pr O0

1 8P dV~dt + rl (vrv ~ + roy, c t gO) = ~ sin0o~, - 2v0Dcos 0 - 2v,s sin 0 + D x

dv~ 1 (v,~o+v~)_ 1 Op -9+2vxDsinO+D~. dt r p Or

There are also other forms of knowledge which will not be dealt with here.

VIII. PROPERTY OF EVOLUTION AND TRANSITION

Almost all predicting knowledge is related to some kind of meteorological data and has

(12)

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its definite acting relations in itself. Therefore, any predicting rule may be expressed as,

P : D )R , (13) where D is an evoluted component-list, P is an evoluting operating-list, and R is repre- sentative of a kind of result. The meteorological data may be expressed as a function

d = d ( x , y , l , t , e ) (14)

in the 5-dimensional data space, or expressed as

d = d ( x , y , z , t , e ) , (15) where, x , y , z , t , e represent the coordinates of x-axis, y-axis, z-axis, time and meteoro- logical element, respectively. 1 is layer, and e may take the discrete values as follows:

T �9 Temperature

H : Height

D : Wind direction J

e = . f : Wind speed (16)

m. Humidity

] P : Pressure

[' R= Precipitation.

Moreover, we can process Eq. (14) as following 4-variable functions

d = d ( s , l , t , e ) , (17)

where: sC S(") ,S c") is a set of meteorological station numbers. Now, we make overlaying processing upon (17); first, let

e ( s ) (18) be the value of e element at station s , e C E (m) and s C S ('''), and let

e . ~ = e ( s l , s 2 , . . . , sn) = Ee ( s l ) , e ( s2) , . . - , e (sn) ] (19) s i~ S (m) ( 1 - ~ i ~ n ) ,

let

el(s) (20) be the e element value of l layer at station s , l ~ L (m) ; similarly, let

el. ~ = el ( s l , s2, . . . , sn) = Eel ( s l ) , el (s2) , . . . , el (sn) 3. (21) s~C S (m) ( l ~ i ~ n )

Furthermore, let

elt(s) (22) be the value of clement e at station s; layer l; time t , t C T ('n), correspondingly, let

ett(~) = e l t ( s l , s2,... , sn) = [ e l t ( s l ) ,ell (s2) ,.. . ,elt (sn) ] (23) s~C S (~) ( l ~ i ~ n )

We call e , l , t , the processing operators, or specifically, evoluting operators, and these are all of the first level processing or the pre-processing in meteorological knowledge processing. Thus, we have transformed the meteorological data processing into evolution processing by using some special operators.

According to this idea, we can also process forecasting knowledge as mentioned above. So we get the following theorem, THEOREM: The predicting rule (13) may also be represented by:

r ~b._l ...... ~. ~ r (24) This is just the evolution transition formula.

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IX. CONCLUSIONS

From these fundamental principles we have designed a special language MKL (Meteo- rological Knowledge Language), which has been used in the WMES (Wuhan Meteorological Expert System) system as described in the article (Dai, 1987). And the procedure using forecasting knowledge may be treated as acting the operators which the knowledge means upon data, evoluting the states, verifying the knowledge and transmitting it into results.

There are also some additional specific properties of meteorological knowledge, but what is mentioned above is most important in automatic processing of meteorological know- ledge and building a Meteorological Expert System.

REFERENCES

Dai Honghua, 1987, An expert system for predicting heavy rain, Advances in Atmospheric Sciences, 4: No. 4 496--505.

Dai Honghua, 1986, Foundations to meteorological expert system, 1:2 (in Chinese), Inst. of Atmospheric physics, Academia Sinica.

Dai Honghua, 1985, On meteorological expert system, China Meteorology, 1:2:3:4 (in Chinese).