The importance of Environmental Conservation– Lake Biwa’s Case –Yasuaki WATANABE
Kochi University of Technology
ABSTRACT:The problem of environmental pollution is rampant around the globe with the passage of time. Here, wetake up water pollution seen at Lake Biwa located in Shiga Prefecture in Japan. A few decades has passed
since the water pollution of the lake became a topic. Many people who live in Kyoto and Osaka areas
highly depend on their water in the lake. If we take contaminated water and fish periodically, our heath will
be destroyed gradually. The serious problem is that some materials which cause cancer are included. Thus,
we must show some prescription to provide for the safe water and maintain the fishing volume in the lake.
Basically, this analysis is based on the models of liner first order differential equations made up by theauthor. At first, we show the mechanism how this kind of pollution occurs. Generally speaking, manycauses are considered including contaminated materials discharged by houses and factories, etc. adjacent tothe lake. Time series analysis is taken into consideration to indicate the pollution mechanism. Secondly, weshow the decline of fishing volume in the lake. Intuitively, we can imagine the negative correlation between
water pollution and fishing volume. Namely, if the water pollution be serious, the fishing volume would
decline. Furthermore, we refer to the metamorphosis of ecosystem in the lake. Thirdly, we show the statusquo of the lake and how administrative sides tackle this problem. Fortunately, the water pollution of thelake is diminishing and fishing volume is increasing due to the efforts of the parties concerned. However, it
seems there needs more improvement to reach the satisfactory level. Finally, we show a future perspective
to resolve this problem smoothly by indicating the concrete examples.
Key Words : Environmental pollution, Environmental Conservation, Differential Equation
with since a considerable amount of water has to be
1. INTRODUCTION

cleaned. How long will this take? For example, howlong would it take to clean up the Lake Biwa? The

Industrialized nations are now facing the problems

main cleanup mechanism is the natural process ofof water pollution.

gradually replacing the water in the lake, provided

Once pollution of a river is stooped, it will rapidlyof course that the pollution has not caused

clean itself provided the pollution has not caused

irreversible damage and already perished the lake.

extreme damage. Lakes are not quite so easy to deal

Figure 1. shows a map of lake Biwa.

Figure 1.

e∫r / Vdtis,

d rt / Ve Pβ = e rt / V Pα r / V ……...………….
dt= e rt / V ; that()(3)
Integrating both sides and evaluating at t = 0and t gives()

e rt / V Pβ (t ) − Pβ (0 ) = ∫ e rt / V Pα r / V dt , i.e.
t0(Source : © Lake Biwa Museum. ALL RIGHTS RESERVED.)Pβ (t ) = e − rt / V Pβ (0 ) + e − rt / V (r / V )∫ e rt / V Pα dtt0…………………………………………...… (4)2. ModelWe can determine the effect of various

The basic idea behind the model is to regard
the flow in the lakes as a perfect mixing
problem, ignoring biological action,
sedimentation, etc. The following assumptions
are made.
1. Rainfall and evaporation balance eachother.
2. When water enters the lake, perfect mixing
occurs, so that pollutants are uniformly
distributed.
3. Pollutants are only removed from the lakeby outflow.
By these assumptions, the net change in total
pollutants during the time interval

δ t is δ t (VPβ ) = (Pα − Pβ )(rδ t ) ……...…….(1)anti-pollution schemes by using (4).
The fastest possible cleanup will occur if all thepollution inflow ceases.
Namely, Pα = 0 , so that Pβ (t ) = e − rt / V Pβ (0 )giving⎛ P (0) ⎞t = τIn⎜ β ⎟(Qτ = V / r ) ..........................(5)⎜ P (t ) ⎟⎝ β ⎠where τ = V / r is Rainey’s value. The model isapparently a very simplified one, but this model
can be used to find out how long it would taketo reduce pollution to a given percentage of its
present level.
While, when we consider the fishing volume of
the lake Biwa, we must think about the model

where V is the volume of the lake, Pβ is thepollution concentration in the lake, Pα is thepollution concentration in the inflow to the lake,r is the rate of flow.
Thus, dividing by δ t and letting δ t → 0 , weobtain the differential equation

dPβdt(P − P )r …………………….…… (2)=αβVThis is a linear first order differential equation
with integrating factorof fishing populations. If there is no harvesting,the number in this group would decline due tovarious other reasons. We will suppose that thetotal number declines in an exponential manner,
i.e. n(t ) = n0e− ct − Pα (t )r………..…………….(6)where n0 is a total number of initial group ofyoung fish and c is a constant.

Thus, n(t ) is the number of fish whichsurvive to age t years when there is noharvesting. We can surmise that the size of each

Evaluating this integral gives

individual fish increases with the passage ofy = y ( f , Pα , m ) ………………………………

time. And the total weight of the fish population…………..…(10)is increasing even though the total number isThat is, the yield is a function of the controls,decreasing. We can also incorporate into thef the fishing effort, Pα the pollution

model the effect of fishing. Fish which are tooconcentration in the inflow to the lake andyoung to be caught can be avoided by using am the minimum size caught. The following

certain minimum mesh size for the nets. So, weFigure 3. shows the number of fish surviving tocan suppose that fish no younger than m years

age t years.

old are caught. The effect of fishing can beFigure 3.

modeled by supposing that the decline rate isincreased from c + Pα r to c + Pα r + f , wheren0

Decaying at ratec + Pα r

f is some measure of the fishing effort. So,n = n0 e − cm− Pα (m )r (Q t = m) ………………...(7)Decaying at rate c + Pα r + f
Number ; n(t)andn(t ) = n0 e − cm e − (c + f )(t − m )− Pα (t − m )r (Q t ≥ m ) ……
…………………………………………(8)∞mm(mtAge

3. Status quo of the lake Biwa

This yield is now given by∞

0The lake Biwa is a freshwater lake and the)y = ∫ ω (t ) fn(t )dt = ∫ ω∞ 1 − e −λt fn0 e −cm e −(c + f )(t −m )− Pα (t −m )r dt
3largest lake in Japan. But, the rank is 129th inthe world. The area is 670 square kilometer.

………………………………………………(9)The circumference is about 235 kilometer.

Where the predicted growth in fish size is given

There is a bridge on the narrowest part of the()by ω = ω∞ 1 − e −λt and the factor

lake. The bridge divides the lake into two parts.

f represents the proportion of the fish alive at

quality of water in Lake Biwa used to be criticalage t which are caught.

conditions. The south of Lake Biwa occurred

The predicted growth in fish size is illustrated

plankton frequently as compared with the northin Figure 2.

of Lake Biwa. Concerning the COD (Chemical3

That is, the north and south of Lake Biwa. The

Oxygen Demand), the figure of south of Lake
Biwa is worse than the north of Lake Biwa.
There were three stages in the pollution of Lake

Figure 2

ω∞ ……………………………
Fish weight ; ωBiwa. The bad smell of mold occurred at thefirst stage in 1969. The red tide of fresh wateroccurred at the second stage in 1977. The
Microcystis aeruginosa occurred massively at
the third stage in 1987. There are 460 rivers

Timetflowed through Lake Biwa. Householdwastewater, factory wastewater, chemical

fishing volume to the original level. Because

fertilizer of agricultural lands and golf courses,

the cleanup level and fishing volume have aand agrochemicals are flowed in through thepositive correlation from the past examples.

water of rivers. It is often said that at least

In addition, global warming is now worsening

nineteen years is needed to replace all the water

rapidly. This trend spurs the deterioration ofin Lake Biwa. If we want to know the time tocleanup of Lake Biwa. Because the snowfall isreduce pollution to a target level, we canuseful to accelerate the pace of replacement of

measure the time by applying for equation (5).

the polluted water in the Lake. Recently, theFor example, if we plug into the actual value

volume of snowfall is decreasing year by yearin equation (5), We can get

due to the affection of global warming.

⎛ P (0) ⎞∴ t = τIn⎜ β ⎟ = 1.31( year )⎜ P (t ) ⎟⎝ β ⎠Sweetfish(Q P (0) = 2.8, P (t ) = 3.0,τ = 19)
ββ

CarpCrucianMinnow

Figure 4.

So, the wastewater in Lake Biwa flows in Yodoriver at Osaka and this wastewater is used forabout 14 million people in Kyoto, Osaka andKobe area. Thus, a water filtering plant treats
drinking water with a large amount of chlorine.
However, this water contains high density
carcinogen such as trihalomethane. The densityof carcinogen in Osaka is much higher thanTokyo and Nagoya areas. Recently, it seems

4. Conclusionthat the water in Osaka is improved thanks toWe examine the relationship between pollution

highly sophisticated water filtering plant.

and fishing volume at Lake Biwa from theOn the other hand, historical fishing volume isperspective of environmental conservation in thisexhibited in Figure 4.. We can see that fishingpaper. And we notice that once the water wasvolume is decreasing with the passage of time.

polluted, it will take a long time to recover theApparently, sweetfish increased around 1990,

cleanup water again. Furthermore, if thebut declined again after that. And we can also

pollution level becomes lower with efforts,conjecture the reason of declining the fishingfishing volume would increase gradually withvolume from Figure 3.. Namely, one of thesome time lag. We can not see a noteworthy

major factors of declining the fishing volume

improvement now in Lake Biwa. So, we mustlies in the pollution of Lake Biwa. We must

utilize the latest technology to clean up the waternote that there is a time lag between pollutionin Lake Biwa in order to reduce the level of COD.

inflow cease and cleanup of Lake Biwa. Then,

Because if the level of COD will increase year

even if we stop the pollution inflow to the Lakeby year, the environments of Lake Biwa will notBiwa, it will take much more time to recover its

be suitable for the life of fish, etc. The increase

of COD is highly correlated with the chemicalmaterials which are not dissolved in the water.
This chemical materials are derived from theartificial materials. As for the lake Biwa, weshould oblige each house to install seweragesystems and to use soap instead of synthetic
detergent. Concerning the factories and businessoffices, they are controlled by the Water
Pollution Control Law under the surveillance ofShiga prefecture.
Finally, we would highly anticipate and support
for the continuous efforts of Shiga prefecturesuch as environmental education and social
awareness to keep the water clean forever.
REFERENCE
Aqua Biwa’s website documents of Lake Biwa
Development Integrated Operation andMaintenance Office.URL:
http://www.aquabiwa.jp
Burghes D.N. and M.S. Borrie., 1981.
Modelling with Differential Equations, Ellis
Horwood Limited,168p. (book)
Shiga Prefecture Fisheries Department
Statistical Annual Report,2007.URL:http://pref.shiga.jp