Network optimization: A simple approach applying GIS and MLR

z. Heport no.38 January 1991 lÎ~tji(·

T

U

Delft

Delft University of Technology

A Simple Approach Applying GIS

and MLR

Communications of the Sanita ry Engineering & Water Management Division

N.StavridesfT.H.M. Rientjes/J.C. van Dam

Fa c ult y of Civil Engineering

Sanitary Engineering& Water Management Div ision HydrologySectio n

R'fp

C-I

a simple approach applying

Geografica

l

Information Systems

&

Multiple Linear Regression

Technische

Uni

versite.it

Delft

Faculteit CiTG

Bibliotheek CivieleTechniek

Stevinweg 1 2628 eN

Delf

t

WmG-C:l.

9'

_:l&

January 1991

TUDelft

N. Stavrides, T.H.M. Rientjes, J.C. van Dam

DELFT UNIVERSJTY OF TECHNOLOGY

F"acultyof Civil Engineering

Sonltary Engineering and Water Ltanogement Divlslon

The collection of information (data) of a specific kind, in space and/or time is of major importance to the hydrologist. On regional scale, measurements of precipitation at several locations provide information of the input of a river catchment system.

The study area with dimensions of 60

*

55.4 km2, comprises 16 precipitation stations establishing a network. In general one can say that many experiments have been performed on gauged regions and many suggestions have been made relating the desired accuracy with the distance between the stations and the density of the network with the relief (WMO) , the local climatic conditions and the estimation of the study flood for a desired return periode

Also i t is proved that the increase of the network density is not always the best solution (even though one might not be so interested in the increase of costs). So the real problem is not only quantitative but qualitative as weIl and therefore more complex.

This study dealt with the optimization of the existing network applying a mathematical- and a digital technique in combination with operational aspects. Although the influence of the individual approaches is difficult to quantify, conclusions which can be drawn are very satisfying; 2 stations can be abolished, 2 stations need to be re-equipped, for 3 stations the observer needs to be reconsidered. Also possible locations for new stations are distinguished.

For composing the optimum network and rainfall-runoff relation ships additional research with more sophisticated digital techniques are requested.

page ACJCNOWLEDGEMENTS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 2

OF THE STUDY AREA •• 1. INTRODUCTION.

1.1. PREFACE.

1.2. AVAILABLE DATA . . • • • • • . . . • • 1.3. LOCATION AND CHARACTERISTICS

• • • • • • • • 3 · .3 • .4 • .4 2. THE CLIMATE . . . • . . . . • . . . • • . • . . • • • . . . . • . . . 10 3. OBJECTIVES 12 ..15 . .15 . . . 16 • ••• 18 PRECIPITATION DATA •••..••••.•...•.... ERRORS RELATING TO PRECIPITATION MEASUREKENTS .. REPRESENTATION OF THE QUALITY OF MEASUREKENTS .. PRECIPITATION DATA OF STUDY AREA • • . . . • . . . . ACCURACY OF 4.1. 4.2. 4.3. 4. 5. MULTIPLE LINEAR REGRESSION •• 5.1. "STATE OF THE ART". 5.2. DATA ANALYSIS •••••• . 19 . 19 • •. 22 6. GEOGRAPHICAL INFORMATION SYSTEKS... ••••••. .25

6.1. GENERAL DESCRIPTION... . ..•••. 25

6.2. GIS IN THE STUDY AREA... . . . • . . . • . . . . • . • . • 26

6.2.1. Packages applied... . ..••...26

6.2.2. Applications of GIS... . ...••••.26

6.2.3. The Kriging technique. ••••••••••. • •••••31 6.2.4. Kriging of annual precipitation figures •••••• 33 7. EXISTING SITUATION . . . • • . • • • • . . . • • • . . • . . • . . . . • . . . • . • • . 36 8. NETWORK OPTIMIZATION ••••••••••••••••••••.••••••••.•••..•• 37 9. CONCLUSIONS • . • . . . . • . • • • . . • • • • • • • • . • . . • • • . . . • . . . • . . . 39 LIST OF FIGURES 40 LIST OF TABLE8 41 REFERENCE8 •••••••••••••••••••••••••••••••••••••••••••••• 54

Directorate

in Greece,

to prepare

ACKNOWLEDGEHENTS

This study was possible due to the very kind support and

assistance of several persons . From this position we would

like to thank;

1. The Director of Hydro-electric Development

(DAYE) of he Public Power corporation (PPC)

Mr. Evangelos Kolonias, for his permission

this study.

2. The former head of the Hydrology Sector/DAYE of PPC,

Mr. K. Nikolaidis, for his agreement for obtaining data

from the archive of the Hydrology sector.

3. The Hydrological inspector of Hydrology sector/DAYE of

PPC, Mr. Dimitris Papachristou for the given operational

information of the network.

4. The staff of the Hydrology section of Delft University of Technology.

5. Dr. Ir. J.W. van der Made of the Tidal Water Division of

"Rijkswaterstaat" , for his introductory explanation of

the mathematical theory related to network optimization.

6. Ing. H.J.M. Oosterwijk of the Tidal Water Division of

"Rijkswaterstaat" for his kind cooperation in applying

the Multiple Linear Regression program.

7. Ir. W. van Deursen of the Geography Dpt. of the

University of Utrecht for his advises related to the

1. INTRODUCTION

1.1. PREFACE

After a proposal made by Prof.dr.ir. J.C. van Dam, Head of the Hydrology section of the Delft University of Technology, concerning an integrated study in network optimization, an attempt has been made in the field, within the framework of the European Community Programme on co-operation between Universities and Industry regarding Training in the Field of Technology (COMETT). ~clY ~re~~__,~

A Greek region as shown in Fig. 1 has been selected as study area. In this region seventeen precipitation stations are operated by the

PPC as part of their

hydrological network. For this study fourteen stations have been selected.

In order to improve the existing situation, some recently developed techniques, combined with a mathematical one, have been applied.

Fig. 1.: Loco. tton mep Techniques applied for the optimization are:

mathematical technique (Multiple Linear Regression, MLR) digital technique (Geographical Information Systems, GIS). For the mathematical approach a MLR computer program has been applied. This program is currently applied by the Division of Tidal Waters of the Public Works Department (Rijkswaterstaat) for water level forecasting and water temperature estimation for tidal estuary in the Netherlands • In future the program will be applied for wave heights estimation.

For the GIS application the following software packages have been applied:

- GEOSTATi a geo-statistical package developed by the University of Utrecht, Department of Geography

- PCMAP •• i a GIS made by the State Ohio University

- SURFER4i a presentation package from Golden Software Inc.

U.S.A.

Both of the above mentioned techniques will be combined with the knowledge and practical view of operation of the network. The final result of this study will be a proposal for optimization of the network.

1.2. AVAlLABLE DATA

- A photogrammetric map, of a scale 1:200.000, of the "study area" as shown in Fig. 2.

- For the period 1971-1982 daily precipitation data of the fourteen stations (Pournia, Pades, Distrato, Vovoussa, Papingo, Kipoi, Elatochori, M. Perister i , Spilaio, Kipourghio, Fourka, Scamneli, Moni Vella, Mazi). For the period 1986-1990 daily precipitation data of three stations

(Laista, Zitsa and Chrisovitsa).

1.3. LOCATION AND CHARACTERISTICS OP TBE STUDY AREA

The study area is situated in the northern - northwestern part of Greece, between 39°42' - 40°12' lat. N and 20°38' - 21°19'

long. E. The area belon~s to the Epirus District and has dimensions of 60

*

55.4 km

The basin of the Aoos river is included in this area as weIl as large areas of the river basins : Voidomatis and Sarantaporos and smaller areas of the river basins: Kalamas, Arachthos and Aliakmon.

The study area has been selected for the present study because of:

- The quality of precipitation data which is rather good due to:

*

the sufficient number of stations in operation.

*

their distribution in space as shown in Fig. 3.

*

their distribution in elevation as shown in Fig. 4.

*

the good quality of instruments as shown in Table 1.

*

only very few precipitation data are missing.

- The relief of the study area which makes GIS application interesting as shown in Fig. 5.

By applying these data the mathematical and statistica I approaches of optimizing the network will become conscientious. Also stations with non-reliable data can be distinguished. Because of the heterogeneity of the study area the effectiveness of GIS can be demonstrated clearly. Especially the suitability of locations of existing and possible new precipitation stations in relation to topography can be analyzed. This is shown in Fig. 6.

The selected period and the selected stations are shown in table 2.

• Ro.ingo.uge

-

-

-7 iJuMber of sta. tions

..

_I ; 7 l 6 -'_: 5 ~_, I 4

-i

i 3 -.J i_, 2 -.: i 1 J

before op t tr-izct ion

a.fter opttnrzo tion elev ct ien in Meter i

I

I

I

!

I

I

..

i

_I

Fig. 4. : Classification of the stations according to their elevation before and after optimization

.

I

~

0"

-

-

-

-

_I'~

~

=

to 14 <?Xlstlng sto. trens

15 to 40 possible new stations

\0 I • 32 \1/"'-!

'"

o.al.. _ _

1

Fig. 6.: and 8. M. peristerl 9. spucto . 10. klpoyglo 15. paraskevl 16. zu z u ll 17. konrt so 18. elefthero 19. SMlxl 20. neo.poll 21. o.g Mlno.s 22. tsepelovo 23. vrisochorl 24. totstc 25. elafotopos 26. nspro.geli 27. negades 28. leptokaria 29. f!aburarl 30. grevenltr 31. Milia 32. zrt so 33. c s f ako 34. ohpo t ano 35. kr-te 36. Itea 37. chr-ys sovrt s c 38. Metsovo 39. perivoll 40. s o.ncr-mc

2. THE CLl:MATE

Greece bel6ngs to the subtropical climatic zone. Due to climatic differences within the country four regions can be defined:

a) highlands b) continental

c) marine - along the Ionian Sea d) marine - around the Aegean Sea.

The study area belongs to the a) region and is very close to the so called "Short-winter zone". This zone is known for several features as described below.

Rainfall during the summer is not frequent. During autumn and in early winter, cyclonic rains (from southward moving frontal zones) are reinforced by movements of convective fronts on the shore. Due to air-mass movements from the sea, which is at this time of the year warmer than the land, convective fronts carry showers. The inter-action between the cyclonic ra ins and the convective fronts cause a precipitation high in the month december. The daily and annual ranges of temperatures are relatively small.

Due to the altitude (500-2500 m.), mountains cause climates different from those of the adj acent lowlands. Mountainous climates may differ not only with altitude but also with the . mountain slope direction (orographic effects). An inherent effect of the increase in altitude is noticed by a decrease in pressure and temperature. This causes a decrease in absolute humidity and an increase in solar radiation.

All these differences are directly reflected in changes of vegetation with altitude, which is also seen in the study area.

b a

Precipitation, while generally showing an increase with

altitude, shows approximately the same seasonal distribution

in the study area. Differences in precipitation due to

altitude are not clear as shown in Fig. 8. The two stations

which are situated in the same mountain area have a difference of altitude of 454 m. preclpltQ tlon In MM. 350 300 250 200 150 100 :so o D N D J r M A M J

HDN1' VELLA nattonna. 13

ELACHDTDRI stQtlon na. 7

J A S

tiMe In Month

Fig. 8.: 24 Year average monthly variation of precipitation

at Moni Vella st.nr (13) and at Elatochori st. nr. (7)

The difference of altitude is 454 m.

For the stations in the study area the seasonal precipitation distribution ranges are:

winter spring summer autumn 24% - 45% 20% - 40% 8% - 20% 26% - 38%

Most of the winter precipitation in the study area occurs as

snow. The average annual number of days with snow for places

at high altitude (>1000 m.) is 30, for places at intermediate

altitude (500 - 800 m.) this is 10. For hail the figures are 3

and 1 days respectively.

In the present study the effect of high mountain ranges being an obstacle to some air-mass movements, will be examined.

3. OBJECT:IVES

The estimation of precipitation is a continuing goal in

meteorological research and a continuing need in hydrology.

This since modelling studies depend greatly on these data and more specific, the accuracy of these data.

A measurements of a rainfall depth in a gauge is only useful

to the extent that i t represents the actual rainfall in the

surrounding region . When estimating precipitation at a

regional scale, precipitation measurements from a network are

only useful to the extent that, within a certain accuracy, an

estimate of precipitation at any place and any time in the

network area can be made.

The basic problem for all networks is to establish a network

that provides its users sufficient information against minimum

costs. In relation to an existing network this leads to the

subject of network optimization, including the choices of: - sampling variables:

- instrumentation •.. :

- sampling locations:

- frequencies .

- duration :

(which features are to be measured) (with what to measure)

(where to measure) (how often to measure) (for how long to measure)

For the existence of any hydrological network, the measuring

equipment instalIed, the implementation of a data processing

system and the organization of a Measurement Service are very

important. These aspects of network operation will not be

discussed here since they are out of the scope of this report.

This study is restricted to the accuracy of the collected

data, the density of the network and the distribution of

stations in space and elevation.

Raingauge networks are commonly dense in populated areas as

lowlands, they are sparse in rural areas and rare in upper

reaches of most basins of the world.

The rather dense precipitation network of the PPC (1 station

per 150 km2_{) is of major hydrological importance for}

hydro-electric development. The network is primarily established and

operated for planning in water resources development.

Collected data however is also being used for management and in some cases for research.

The requirements of data for such a diverse kind of use are: - Planning •• :. Extensive data on a long time basis, in order

to determine the magnitude and the natural variability of the phenomena.

- Management: Less extensive data as "planning" needs but they must be very near to "real time" for daily management and for forecasting.

- Research .• : Intensive data of very high precision. within the limitations of an Electricity Company, like the PPC is, research can be considered as being a secondary task.

long 'tIMe

5!rle5

( PLANNING

MANAGEMENT ".

Fig. 9.: Requirements for data

since in general the values of *) costs, *) interpolation errors and *) information losses (which can be seen as the "damage" to the society because of unsafe or non economical constructions), are based on subjective and/or political considerations such as:

- the number and distribution of the stations in space and elevation

- the guar~ntee of good operational conditions (location, observer, instrument, data interpretation, etc)

- the representativeness of stations in relation to the prevailing wind direction

- the frequency of the hydrological inspections (the accessibility of a station plays an important role) •

the real optimal network will not be achieved.

The network which is going to be "very close" to the optimal one is based on the information gained from the former and the present network. The present network is generally a derivative from a historically grown initial network. Also a network configuration can change since objectives can change.

In other words the operation of a network is a perpetual dynamic procedure in order to achieve an optimal network.

For network optimization a required fixed minimum period of

network operation is not known. It is however accepted that at

least twenty years of data is needed to give an reliable

impression of the network operation. After an evaluation of

the network operation adjustments to the network should be

made based on:

a) the hydrological information obtained from the past b) changes in social and economie aspects

c) modification of the scope of the network

A general problem of all networks is to investigate the

accuracy of collected data and to optimize its operation.

Although this is known as one of the most complex facets of

hydrological engineering i t is one of the goals of this study. The main goal however is to optimize the present network based on the results obtained by the MLR and GIS techniques and the operational aspects as weIl.

In our case study the present precipitation network embody's the 14 stations as revealed in chapter 1.

4. ACCURACY OF PRECIPITATION DATA

This chapter deals with errors relating to precipitation

measurements, the representation of the quality of measured

data and the available precipitation data of the network in

the study area.

4.1. ERRORS RELATING TO PRECIPITATION MEASUREKENTS

According to the World Meteorological organisation (WMO) a

network can be defined as follows. "The aim of a network is to

provide a density and distribution of stations in a region

such that, by interpolation between data sets at different

stations, i t will be possible to determine with sufficient

accuracy for practical purposes, the characteristics of the

basic hydrological and meteorological elements anywhere in the

region." (WMO, 1981)

Taking this definition into accourrt : i t implies that i t is

possible to measure and calculate at any place of interest,

any phenomena (iee. precipitation) with suff icient accuracy.

It is also known that the accuracy of data is strongly related to errors of measurements and not to mistakes in measurements.

This brings us to the point of possible errors of

precipitation measurements. These errors mainly occur due to:

1. The location of the precipitation station (obstacles:

trees, houses or other constructions nearby).

2. The surrounding area of the station in relation to the

topographic relief and the type of precipitation

(orientation of slopes, direct ion of prevailing wind in

relation to rain and snow etc.).

3. Instrument errors, inadequate design and construct ion of

the instrument might cause insplash or outsplash. 4. Observation and processing errors.

All the above mentioned errors of measurements can be

systematic or at random ones.

For optimising the existing network the assumption that all

stations belong to the same network has to be made. This

however implies that:

- Precipitation can be estimated within a certain accuracy at any place and any time in the network area.

- the 'true' depth Y_t

- the measured depth Ym - the calculated depth Yc:

4.2. REPRESENTATION OF TBE gUALITY OF MEASOREMENTS

When speaking about a measurement of precipitation, this measurement is expressed as a precipitation depth. In this regard several depth values can be distinguished;

value expressing the most probable state of an element, and represen-tative of a certain site

a depth obtained by measurement a depth obtained by using the relation: _{yc=f(x, •.. xm)}

where x, .•. xm = measured depth at the network stations Considering differences between these depth the following errors can be defined;

er;

_{= Ym - Yt} (error of measurement)

tJ.Yc = Yc - Yt (error of estimate) (4.1) tJ.Yd = Ym - Yc (error of difference =

measurement-estimate)

When n is the number of stations I:1Yd can also be expressed as:

n

à Y_{d -} Y_{m -} (a + Ebi Xm)

i-l (4.2)

The MLR technique in (4.2) will be discussed in par. 5.1. from the equations (4.1) i t follows that:

= (4.3)

Assuming independenee between errors of measurement tJ.Ymand those of estimatel:1Yc it follows from (4.3) that

or (4.4) varày -n ~ (àYd - ï1Yd) 2 ~-1 n (4.5)

(4.6) This is also known as the unexplained variance of measurement

(a2_by) and can be presented as:

~

_ I

Rall stations

I

*

0 2 Ay

IR

_{mai n stationJ} y where: (v.d. Made, 1986)

=

=

=

I

~in stations

I

a2_Y

I

Ra ll stations

I

the variance of the precipitation at the station P.

the determinant of the correlation matrix between the precipitation depths at all stations i.e. at the main stations and at the station P.

the determinant of the correlation matrix between the precipitation depths at the main stations only.

The unexplained variance of measurement (a2_by) can be defined as the variance of the differences (residuals) between the measured values Ym and the "calculated" ones Yc.

Recommencing this theory, the best thing to do is to compare the results with reality. This means that at every station having sufficient data, measured data (Ym) can be compared with "calculated" data (Yc) which have to be generated using a MLR technique.

For the detection of the standard error of measurement the following procedures can be used based on:

1. Observations at the same station at different times (different instruments and different observers).

2. Comparison of the observations at the station under consideration with the observations at a station nearby. 3. Comparison of the observations at the station under

consideration wi th the observations at several stations in the same area at different distances.

(v.d.Made, 1988) The last procedure (3.) is of great importance for network optimization. This procedure is one of the subj ects of this study.

5. MULTIPLE LINEAR REGRESSION

For the assessment of hydrological data at places between stations several methods can be used, based on:

1. mathematical interpolation (i.e. linear interpolation) 2. interpolation based on statistical considerations (i. e.

optimum interpolation)

3. physical model. (v.d.Made, 1988)

All these methods might be combined with an adaptive mechanism, i.e. Kalman filter, in order to obtain the best results. In the case of interpolating precipitation figures these mechanisms are still in an experimental phase.

This chapter deals with the Multiple Linear Regression (MLR) technique for interpolation.

5.1. "STATE OF THE ART"

A method applied in this case study is based on the MLR theory. The existence of a correlation structure between precipitation data at various sites (stations) in the study area is assumed. This however is also subj ect of the case study. If: Yj i y ._J,l. Xlc,i a, b1 ' b2, bic k n

The calculated value of precipitation at check point j (station in or out of operation).

The instant time of the observations. The measured value of precipitation, at checkpoint j at instant time i. The measured value of precipitation at station k at instant time unit i. The partial regression coefficients. the number of network stations.

Number of available observations at checkpoint j. then; y._J,1

=

a + b_{1 X 1 1} + b_{2 X 2 1} + + _{bic xlc 1} + b₁ , + b₂ , + + bic , Y·2J,

=

a x1 2, X 2,2 xlc , 2 (5.1) Yj,n

=

a + b₁ x1, n + b2 x2,n +

Summarizing the n equations; n :E y .. = • J,1 1=1 and n na + b, :E x, i + i=l ' n b_{2 •}:Ex_2,1· + · · · + 1=1 n bic :E x_lc • • ,1 1=1 (5.2) n n n n I: y . . :E

x,

.

I: x₂ . I: x_lc • • J,1 • ,1 • ,1 • ,1 1=1 1=1 1=1 1=1 = a + b, + b₂ +

...

+ bic n n n n or: b, b₂

-

_bic

-Yj = a + x, + x2 +

...

+ xlc where: (5.3) (5.4)

Yj'

x"

x

_{2 '} • • • ,

x

_{lc :} average value of Yj'

xp x

_{2 '} ••• ,

x

_lc

From the equations (5.1) and (5.4) the deviations from the

mean values ean be ealeulated:

(5.5)

For def ining the regression eoeff ieients a, b, , b₂ • • • bic the

least squares method will be used.

If:

n 2

S =_•:E [y_J,..₁ - (a + b, x, . + b₂ x_{2 .} + ••. + bic x_lc 1·) ]

11 , 1 ,

1=1

then the following equations have to be solved:

(5.6)

as

aa

=

0,

as

= 0,

as

=

0, ••• ,

as

= 0 (5.7)

For k independent variables (preeipitation stations) there are

for eaeh station k + 1 regression eoeffieients whieh ean be

ealeulated from k + 1 equations.

:E { y_j,i

=

a + b, x, ,l' + b_{2 X2} 1· + :E { Yj, i = a + b, x" i + b₂ x_2:i +

*

1

*

x,

,1

.

= 0

=

0 :E { y. ._{J ,1}

=

a + b, x,_{, 1 , 1}. + b₂ x_{2 .} + ••• + bic x_{lc, 1 , 1}' }

*

x_lc '

=

0

(5.8)

or:

n n n n 1: y .. = na + b, 1: x, . + b₂ 1: X₂ . +

..

.

+ b k 1: Xk . • J ,1 • ,1 • ,1 • ,1 1.=1 1.=1 1.=1 1.=1 n n n 2 n n 1: x, . y .. = a 1: x, . + b, 1: x, . + b₂ 1: X₂ . X, . +

...

+ b_{k 1: Xk . x',i} • ,1 J ,1 • ,1 • ,1 • ,1 ,1 • ,1 1.=1 1.=1 1.=1 1.=1 1.=1 n n n n 2 n I: x₂ . _Yj,i = a _{I: X} 2 i + b, I: x, . X2,i + b2 I: X2 . +

.

.

.

+ bk I: Xk . X2,i • ,1 • ,1 • ,1 . ,1 1.=1 i=l ' 1.=1 1.=1 1.=1 n n n n n 1: Xk . y .. = a _{1: Xk .} + b, 1: x, . Xk,i + b₂ 1: X₂ . _Xk . ₊

...

₊ b_{k 1: Xk .} • ,1 J ,1 • ,1 _{• ,1} • ,1 ,1 • ,1 1.=1 1.=1 1.=1 1.=1 1.=1 (5.9)

Assuming that n > k, then the former set (5.9) can be written as:

n

1:x, ._,1

I:x, ._,12

1:x,_,1.

~X2 i • • • • • • • •

I:X2' iX, i_{, ,} ••• 1:xk ._I:xk,1_,1.X, ._,1

*

a b, I:y . . J,1 I:x,_,IJ,1.y. .

=

1:xk·,1 1:x,. Xk ., 1 , 1 1:X2,1.Xk .,1 1:xk,1.2 1:Xk,IJ,1.y.. n in which 1:••• means: I: ••• i=l (5.10)

Solving these k + 1 equations (5.9) we get the values of the

coefficients a, b" b₂ ••• b_{k •} Expressing b, and b₂ gives:

=

I:x,_{, I J , 1}. y. . I:x_{2, I J , 1}. y. . 1:X k, I J , 1. y.. 1:x,_,1.2 1:x, . X2 .,1 ,1 1:x, . Xk .,1 ,1 I:x,_,1.2 1:x, . x 2 .,1 ,1 I:x2 . x,_{,12 ,1}. I:X2 .,1 1:x2 . _Xk . ,1 ,1 1:X2_,12. x, ._,1 1:X2 .,1 1:x2 . x k·,1 ,1 I:x,_{, I J , 1}. y. . 1:x₂ . y .. , I J , 1 I:xk_,1. x, ._,1 I:xk . x 2 .,1 ,1 1:X k,1.2 1:xk . x, .,1 ,1 1:X_k . x₂ . ,1 ,1 1:x k,1.2 I:xk_,1. x,_,1. 1:xk . x 2 .,1 ,1

..

.

..

..

.

.

.

...

...

.

...

.

.

= 1:x,_,1. _{x k .,1} 1:x, .2_,1 1:x, . x 2 .,1 ,1 1:x, . x k .,1 ,1 1:x_k . y .. , I J , 1 1:x2 . x, .,12 ,1 1:x2 .,1 1:x2 . x k .,1 ,1 1:x k,1.2 1:xk· x, .,1 ,1 I:xk . x 2 .,1 .1

ë.

...

x

I

Cl 16 c

]

:l

....

_lil 0 C Cl 0 ₁₆ :l :.:l "0 ...0 > VI c _{ë i} Cl 14 .... e I E

....

0

_!

12

I

..

5 7 9 11 '13

nUMber of sta. tiens ta.ken In t o o.ccount

J4 c J2 0 > JD ë. x ₂₈ al c :l 26 .... L1 c C .tl :2 ~4 ::l C -a 1) _{22 1} >

x

ë

::L

0

....

E 0 5 nUMbE'r of I I i

I

I

I

.:

I i I I r.> 7 lOl 11 13

s:ta. tiens tc.ken iflto c.cccunt

.: 12 0 > ë. x 11 al c :J

....

L, 0 C .~ 10 IJ ₀ ::l ë ....

_"

> ë ti 9 'Ë ....0 1 i i I I lil-5 7 9 11 13

nUi"lber of stations tc.ken In;;o c ccourrt of mean, variances stations Fig. 10. : Relationships unexplained precipitation interpolation maximum with the taken into and minimum number of account for

...

14Q0

j

Cl

....

_Cl 11 E I .E i_i c 1200

1

2 12 0 :;; c 8 > 1000

~

7 CIl ₄ G: _:5 i 5 9 El j 6 BOa I I I 60a

1

1J 14 4QO ~

"

1J 15 17 19 21 2J 25 27 29 J1 33

highellt unexplcinad vorionce for the individu a! stotions

Fig. 11.: The highest standard error for the

So, there is an optimum number of station to be found and to be taken into account.

After this the following cases can be distinguished:

1)

2)

The value of the mean unexplained variance sufficiently low for the operational scope of network.

The value of the mean unexplained variance is accepted from the operational scope of the network.

is the not

Ad 1) The network optimization consists minor modifications relating to location, instruments, observers etc.

Ad 2) This case demands for major modifications to the network, more stations have to be installed in order to increase the network density.

The best locations for new stations are at places were the value of the unexplained variance is very high. GIS can help to point out these locations.

After the application of MLR several conclusions for the existing network can be drawn:

1) station number 11 must be abolished

2) station number 4 has to abolished or modif ied because of the high value of unexplained variance

3) several stations need to be modified in order to reduce the mean value of unexplained variance which is almost 25% of the overall mean of decade values.

6. GEOGRAPHICAL INFORMATION SYSTEMS

6.1. GENERAL DESCRIPTION

Geographical information systems (GIS) are (still) rapidly developed computer aided systems for interpolation, analyzing and representation of spatial distributed data in thematic maps. Results can be presented on a color screen or a hard copy device. Thematic maps can be represented in vectorized files or gridded raster files.

- vectorized files: These files can contain point entities, line entities and area entities represented in polygons. - Gridded raster files: These files contain information

represented as a numeric value on every (regularly spaced) gridded raster point.

For the practical implementation in GIS the main differences between the two files are:

- Vectorized files; a) good graphical presentation is possible

b) data file sizes are of manageable size c) spatia1 ana1ysis app1ications are

limited

- Gridded raster files; a) limited graphical presentation b) large data files

c) the files allow easy quantitative spatia1 ana1ysis

One could say that geographical data describe objects from the real word in a digitized numerical form. Objects are transformed in files in terms of;

- their position with respect to a known coordinate system - their attributes that are unrelated to position

- their spatial inter-relations with each other (topological relations), which describe how they are linked together or how one can travel between them. (Burrough, 1986)

In hydrology GIS have been applied for defining; - catchment boundaries

- runoff patterns - ridges and streams - orographic effects - erosion susceptibility

- land suitability for irrigation. Other potential applications can bei

- defining drought sensitive areas

- decision support for reservoir planning. Although this is a very

application in hydrology , impression of GIS. brief overview hopefully i t of GIS gives and its a first

6.2. GIS IN THE STUDY AREA 6.2.1. Packages applied

For this study three different packages have been applied;

1) GEOSTAT: A geostatistical package with limited possibi-lities for GIS data manipulation and analysis. 2) PCMAP •• : A GIS package with the basic data manipulation

and analysis possibilities.

3) SURFER4: A two and three dimensional presentation

program for plotter devices but with limited

interpolation possibilities.

In Table 20 one can see that all three packages have their

specific applications but also their specific limitations. In

genera I the applied systems support each other, although in

practice working with three different packages was experienced

as very inconvenient (i.e. different file formats, different

presentations on screen, different legends, hard disk set-up

etc. )

6.2.2. Applications of GIS.

In the study area GIS have been applied as following; 1. preparation of a Digital Elevation Model (DEM) 2. defining shaded places

3. defining watersheds and drainage patterns

4. interpolation of isohyetal and unexplained varianee maps.

All four applications will be described below.

1. preparatioD of a DEK.

For formatting a Digital Elevation Model (DEM), the elevation

contour lines (interval 200 m.) of the photogrammetric map

(Fig. 2) have been manually digitized. This resulted in a data

base file holding about 13.000 data points. As interpolation

technique a second order inverse distance method has been

applied based on the following equation (surfer,1989):

t

Zi . d2 ~-1 i Z -n 1

~-d2

~-1 i

in which: Z.••. : interpolated grid value

Zi .•• : value of a data point di ..• : distance to a data point n •••. : Number of Z elements

Applying this formula one can see that interpolated grid values depend on the positions of the grid point and the data points and also the Z values of the data points. A weighting factor is defined in such a way that the influence of one data point on another declines with an increase of distance to the grid point. The greater the weighting power, the faster the decline in influence and the less effect points further out will have on the interpolation. A disadvantage of this empirical formula is the biased interpolation. An estimation and moreover a minimization of the error in interpolation is not possible.

The DEM has been interpolated with a second order inverse di stance formula applying an at random search for the ten nearest data points. The grid size applied is 400

*

400 m, This resulted in a 138 row by 150 column raster file enclosing 20700 data points. Per grid point this gives the ratio of 13000/20700 ::= 0.63 data point per grid point which can be considered as being rather high. The interpolation of this raster file took an 20287 AT about 36 hours. Although the grid size is fairly large for GIS applications i t supported the aim of this study (i.e. the optimization of a precipitation network) •

2. D tininq shaded places.

The second application of GIS deals with the DEM which has been applied for a viewing angle simulation program. Azimuth as weIl as zenith angles were user defined in the program.

For the planning of water resources development and for management purposes representative precipitation data should be applied. In mountainous areas precipitation measurements can be effected by orographic effects . In case the natural precipitation angel is smaller then the actual slope side of a mountain, precipitation stations positioned at the slope side don't represent regional precipitation; the regional precipitation pattern will become differentiated. This is what we call a "shaded place". Therefore precipitation stations positioned at a shaded place should be reconsidered for continuation.

Also possible new locations for precipitation stations can be selected applying shaded maps. Fig. 11 gives an example of a 3 dimensional elevation map of the area. In Table 21 the results of the shaded maps are presented. The zenith angle was set to 45°, for the azimuth angle 8 rotations ranging from 0° to 315° with a constant increase of 45° have been applied.

For the optimization of the existing network one can see that station nr. 11 is shaded from most viewing angles including the prevailing wind direct ion . Therefore the continuation of observation should be reconsidered. For the planning of new precipitation stations 25 new locations have been selected, based on the presence of population and the accessibility. Locations suitable for installing a precipitation station are also shown in Table 21.

The final proposal for optimization depends greatly on the GIS results in the mentioned tabIe.

3. Defininq watersheds and drainaqe patterns.

Applieations of GIS in river basin main studies in the study area are:

- finding the watershed at every point of interest (number of upstream elements, shape, area, ete.)

- drawing the water divide for every watershed and

surrounding watersheds

- draw the drainage pattern, greater than speeified desired

size.

Besides this several other applieations of GIS in the study

area can be very efficient;

- vegetation in the eatehment area (type, loeation, area,

ete)

- rainfall-runoff relationships (an approximative estimation

of the runoff eoeffieient)

- groundwater studies (soil eharacteristies, interpolation

between boreholes, piezometrie levels, etc) - geologieal eonditions

- flood foreeasting - hydrologie design - flood routing.

These possible applieations ean be part of an extended

research program relating to the study area.

A few of the above mentioned GIS applications are presented

in:

- Fig. 12: A three dimensional presentation of the study area. - Fig. 13: The Aoos river watershed at Konitsa.

- Fig. 14: The Aoos river eatehment, drainage pattern (threshold values 10, 50 and 100).

4. Interpolation of isohyet and unexplained varianee map.

The fourth applieation of GIS is the interpolation of

isohyetal and unexplained varianee maps. As optimal

geostatistieal interpolation method for spatial data the

Kriging teehnique has been applied.

The theory of Kriging ineluding its limitations and its

applieations in the study area will be deseribed in par.

3D ELEVATION

.-"

MAP

+

= Location and number of precipitation station viewing angle

~~

O~ ~

O~ ~

~~

t~

~ Sl"'~ ° 0_o o;.s.~ ~ Q? 0 0 C'~ • 00 ~ ~ o A \ ~:pO ,cs ~::po ~ ~:P <f:'0 ":J0cs ... <::-~:p ~CjftJ b<.0cs ?$ot?;-C> ~:P <,;,ocs

°

elevation zones 0 500 1000 1500 2000

~

X 500 m 1000 m 1500 m 2000 m 2500 m N \0

Fig. 12.: A three dimensional presentation of the st.udy

o - 500 m

500 - 1000 m

---100 0 - 1500 m

---1500 - 20 0 0 m

-2000 - 25 0 0 m

-SCALE1 cm. - 857 1 dato unit,

~E""?~c~=.=r ::J + = Locatio n and number of

precipitation statian

ELEVATION OF STUDY AREA

+ ++++: 8oundory of Aoos rfver wote rshed elevatian zanes

5000 ,10 0 0 0

,

o o o .,., o o o o o o o o

...

o o o .,., ..., o o o o ..., o o o .,., "" o o o o "" ~b~~~'--.lLJ-LLL-J:_ o 0 0 0 0 o 0 0 0 0 o 0 0 0 0 U1 0 L() 0 L() N I") n -q- v distance in m o 0 o 0 o 0 o .,.,

Fig. 13: The Aoos river watershed.

50 '00

Fig. 14: Drainage patterns of the Aoos river catchment (threshold values tv = 10, 50 and 100).

In the study case a threshold value tv = 100 means that every grid point shown in the drainage pattern has at least 100 upstream elements. In our case one element is 0,4

*

0,4 km2, so 100 elements represent an area of 16 km2.

6.2.3. The Kriging technique

The Kriging technique is based on the regionalized variabIe

theory which assumes that the spatial variation of any

variabIe can be expressed as the sum of three major

componentsj

a) a structural component, associated with a constant mean value or a constant trend

b) a random, spatially correlated component

c) a random noise or residual error term that is independent of location.

In a formula this theory can be expressed as:

Z(x)

=

m(x) + e'(x) +e"

in which:

(6.3)

m(x) = a determinist ic function describing the structural

component of Z at x

e' (x)

=

is the term denoting the stochastic, locally

varying, spatially dependent residuals from m(x)

e"

=

a spatially independent Gaussian noise term having

zero mean and variance a2 _{(Burrough, 1986)}

For larger sampling areas m(x) equals the mean value of the

sampling area. The average or expected difference between two

p~aces x and x+h separated by a di stance vector h, expressed

as the lag, will be zero. One could say that sampling areas

are homogeneous.

This represented in a formulaj

E[Z(x)-Z(x+h)]

=

0 (6.4)

The variance of differences depends now only on the di stance

between sites expressed in h. In other words the spatial

random component e'(x) has zero mean and (isotropic) variation

defined byj

E[{Z(X)-Z(x+h)}2] = E[{e'(x)-e'(x+h)}2]

=

2a(h)

(6.5)

The per observation variance between pairs is half the value

thus 2a(h) (Yates, 1948). This is called the semi-variance and

is a measure of similarity, on average, between points a

di stance hapart. The graph of 2a(h) versus h is called a

semi-variogram.

For compiling a semi-variogram from sample data the following formula is appliedj 1 n Z (h) = I:{Z(x.)-Z (X_i+ h)}2 2n i=l (Burrough, 1986) (6.6)

Fig. 15.: Semi-variogram

Important characteristics of the semi-variogram are:

(6.7)

h û C + Co

I

I

I

I

I

_ _ _ _ _ _ _ _ --1

I

- - - = " " ' . . , . -n Z(xo)= 1: aj.Z(x j) i=l Co

c

The intercept, also called the 'nugget' variance. According to formula (6.6) at di stance h=O the semi-variance should be zero. A positive value of Co is known

as the spatial uncorrelated noise el! due to variation in measuring errors and in spatial variation within the lag distance h.

Is called the ' s i l l ' . The sill value represents the range of variance due to spatial dependence in the data. Also i t defines the distance a.

Distance at which data become spatially independent.

cr(h)

r

a :

C

Semi-variograms cannot be described by one general mathematical formula since sampled entities differ often by nature. Appropriate formulas can be based on a linear fit, an exponential fit, a spherical fit, a gaussian fit or even a mathematical formula taking anisotropy into account.

An optimum fit will be achieved by iterative changing lag distances for a chosen model in order to optimize the compilation of the semi-variogram expressed in Co' C and a. This is known as the most difficult part of the Kriging technique. An understanding of the features of the data points is hereby a necessity.

The minimumvariance of Z(x_o) is obtained when:

For interpolation weights have to be defined for the data points to optimize the influence of every data point incorporated in interpolation. The fitted semi-variogram will be used to determine the weights _{Lj • The weights should be} chosen in such a way that the estimated Z(x_o) is unbiased and that the estimation variance a2 is less than any other linear

• • e

n

I:L.. a(x-,x.) + J.'

=

a(xl-,x_o) for i

=

1,2, •..• ,n

• I I J )=1 n with I: L.

=

1 • I 1.=1 (6.8) in which: J.' = a (xi' x.) = a(xi'x_o) =

a Lagrange papameter required minimization

the semi-variance of Z between the points

the semi-variance of Z between the point xi and the unvisited point X_o

for the sampling sampling and n 0'2e

=.

I:L_{i •}a(Xj 'X_O) + JoL )=1 (6.9) to all geostatistical concerning the annual the 1800 mm isohyet When mapping the estimation variance a2

e information on the

reliability of interpolation can be visualized. 6.2.4. Kriging of annual precipitation figures The isotropy of the magnitude is assumed.

Fig. 16 shows an isohyetal map interpolated with averaged 2 year (1976-77 and 1978-79) annual precipitation data of the 14 stations. Although the isohyetal map may look comprehensive, limitations of the Kriging technique show up when taking the natura I features of the area into account.

station nr. 9 is situated on the east site of the mountain range Pindos and i t is "protected" against the prevailing wind direction. This effect is clearly expressed in the isohyet pattern as shown in Fig. 16.

Also reconsidering the physics of convective rainstorms, a gradual change of isohyets is expected when looking in the direction of station nr. 4.

The Kriging method is limited to interpolations only, i t means that the highest values of the magnitude under consideration, will appear only at input points.

Although this limitation is inherent interpolation techniques, the question precipitation in the centre part of remains unanswered.

In the south-western part of the area the influence of the mount Mitsikeli range (elev. 1810 m) does not appear on the isohyetal map. Obviously this happens due to a shortage of precipitation stations in that area. To judge the actual interpolation reliability cross validations as weIl as the application of other interpolation techniques should be applied on a more excessive data base.

Therefore more precipitation stations in this area are a necessity.

A fina1 conc1usion of the app1ication of the Kriging technique in mountainous areas is that, a1though trivia1 to say, the app1ication is 1imited to those areas with a sufficient amount of precipitation stations to describe orographic effects. Or in other words, comparing the interpolation results with expected resu1ts based on physical features, places can be pointed out where supp1ementary hydro1ogica1 information is needed.

The same technique has been app1ied for the unexp1ained varianee of every station. The iso-unexp1ained varianee 1ines are shown in Fig. 17.

It is c1ear that new stations must be placed there where: 1. The isohyeta1 density is very high and

2. The va1ue of unexp1ained varianee exceeds a user specified va1ue.

SCAI.E 1 cm. - 8571 data unIt.

... '

1319

+Location and 2 year annual precipitation of station 20000 2'000 45000 40000 1'000 30000 of35000 o 0 o 0

§

~ 8

§

o o o ~ 8 8 o

§

o 55000_-r--.,.--.,.--r----,-...,--,r--.,...-r=~-T_~55000 45000 10000 50000 40000 E35000 .f:30000 ~2'000 C 220000 G') ~1'000 o o 5iI

Fig. 16 . Isohyetal ma p of the study area.

o 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 o 0 ~ 0 0 ~ 0 ~ 0 ~ o ~ ~ n n v ~ ~ ~ 55000

l

i

-

J

-r-t-: ~"-,---.----r-l55000 50000 JIJ

I

15 0 0 0 0

::::

@)

';

~-W

~

:::::

.~::::

_~

p

"

? ~"

~

::::

25000

(

,~

(

®

)

I

/

''1

C)

~

~~

250 0 0 ~20000 ~~ 1.8

j

20000 U 15 0 0 0

U

15 0 0 0

'::::

~

8

,

J

:::'

o 0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0 0 0 0 0 0 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ N C'I ,..., " , v ... LO lf) distance in m 34

+ Locoti on and unexp la ined

vari anc e of pre cipitation st a t i on

SCALE1 cm. - 85 71 data units

...

~==-=

7. EXISTING SITUATION

In the study area 17 precipitation stations are operated by PPC. There are a few more which are not presented here for several reasons:

- they don't have adequate data for the selected period - they are operated by other state institutions

- they are situated at the edges of the study area

From the above mentioned stations, 14 stations have been selected because of their time of operation, which covers the selected period 1971 - 1982 as shown in Table 2.

Studying the existing network situation from hydrological point of view, the following, specific operational information should be taken into account:

- station nr. 4 (Vovoussa): For several reasons there is no good contact between the hydrological inspectors and the observer. Also the location of the station is not very suitable, i t is situated in a river valley.

- station nr. 5 (Papingo) : It is situated in a touristic village. During the touristic season the inhabitants (the observer included) are very busy. Observations therefore cannot be normal and regular ones.

- station number 7 (Elatochori): In the period under consideration hydrological inspections have not been taken place regularly.

- The stations nr. 9 and nr. 10 (Spilaio and Kipourghio): Both stations are situated at the eastern part of the mountain range Pindos which from the geographical and hydrological point of view as weIl, divides the study area into two separate regions.

- station nr. 11 (Fourka): It is located at the highest elevation of all the stations (1350 m). More than 50% of its precipitation occurs as snow. These measurements are much more difficult and less accurate than measurements of rainfall. Also the accessibility to the station is problematic for hydrological inspectors since the location cannot be reached by car.

- station nr. 13 (Moni Vella): It is situated very close to a former monastery. At the same place a second station has been instalIed which belongs to another state institution. This station is equipped with instruments of a different type. The observer being the only person who lives there all year through is responsible for both stations. It is known that he does not execute the observations for both stations properly. From 1988 onwards the PPC station is operated at a new place 2.5 km apart from the previous location.

- The direction of the prevailing wind is southwest , but sometimes storms are coming from west or south directions.

8. NETWORK OPTIMIZATION

In order to gain insight in the combined results of the MLR and GIS approaches Table 21 has been prepared. The existing situation (instruments, elevation, slope direction, locations, observer, accessibility, inspection) is presented in the table as weIl.

Studying this table not only improvements to the network operation can be made but also real optimization based on objective arguments is possible. This optimization can be achieved by:

- The abolishment of stations for which i t is expected that they do not be long to the network due to location and/or bad correlation with other stations.

- The installation of new stations at suitable locations for specified tasks (e.g. in order to reduce the unexplained varianee).

- changing instruments for more appropriate ones.

For every station of the existing network a review of the results obtained will be given in a numerical order.

1. station nr.1 (pournia): MLR results showed an acceptable unexplained variance (12.5 mm). The west slope direction is not effected by orography. Operational conditions are very good.

2. station nr.2 (Pades) : The MLR results were sufficient. GIS results showed that the slope direct ion is not favourable. Operational conditions however are good.

3. station nr.3 (Distrato): Considering all the results this station is probably the best station of the network. It requires no modification.

4. station nr.4 (Vovoussa): MLR results showed a high unexplained variance of 20 mm for the 10-day totals. This is explainable when combining the MLR results with the operational condition which are not very good. This station is situated at a location on a river side in a deep valley. It would be preferabIe to move i t to a southwest slope on an elevation at least 250 m. higher. Also the observer should be reconsidered (more inspections) .

5. station nr. 5 (Papingo): MLR and GIS results were satisfying. To improve however the accuracy of the measurements i t is necessary to equip this station with a raingauge recorders (tipping bucket type).

6. station nr.6 (Kipi) : MLR results showed a high unexplained variance ranging between 20.5 and 17.4 mmo In contradiction to MLR results the GIS results were very good. Therefore operational conditions i.e. the location should be improved.

7. station nr. 7 (Elatochori): It is clear what caused the rather high value of unexplained variance (e.g. ± 18 mm.) Partly i t can be explained due to the use of a raingauge. The replacement with a raingage recorder (tipping bucket type) is necessary.

unexplained

result are

very good

installing unexplained

8. station nr.8 (M.peristeri): According to table 21 this is

one of the best stations. GIS results were very good, MLR results were satisfying although a decrease of the unex-plained variance is expected by changing the observer if possible.

9. station nr.9 (Spilaio): MLR results and operational

conditions are very good. Although GIS results are bad

this station should be continued. An additional station

in this region, situated at a south-west slope can be

considered for management purposes.

station nr.10 (Kipourgio): This station has a very low

unexplained variance. Operational conditions are very

good. GIS results could not be obtained since the station was out of the digitized study are. The station does not need any modification.

station nr .11 (Fourka): It is obvious that this station

does not belong to the network, mainly because of the

very high unexplained variance, orientation of slope in

relation to prevailing wind, difficulties in

accessibi-l ity etc. It is advisable to abolish the station or to

re-install i t at a more appropriate location. In case of

maintaining the station only local meteorological

information can be collected.

station nr.12 (Scamneli): MLR and GIS results were good.

An improvement to the operation of the station can be

made by changing the operational conditions (observer and location).

station nr.13{Moni vella): The MLR showed an

variance ranging from 16.7 to 17.9 mmo GIS

very good. The operational conditions are

although by changing the observer or by

automatic instruments i t is excepted that the variance will decrease.

station nr.14 (Mazi): This station has a very low

unexplained variance, this probably due to the

-me a s u r e me nt s with a raingauge recorder.

12. 10.

13.

14. 11.

If i t is possible from the point of view of the operational

conditions new stations have to be installed at the following places as presented in Fig. 6.

nr. 15 (Agia Paraskevi) and nr. 16 (Zouzouli): These

locations will supply hydrological information of the

area near station nr.11. after its abolishment.

nr. 24 (Laista) and nr. 39 (Perivoli): At these places

the density of the isohyetal and unexplained variance

lines are very high. In order to be sure of a rapid

change of precipitation with distance and/or to

express the phenomenon, i t is necessary to have more

stations in this area.

nr. 26 (Asprangeloi) , nr. 33 (Asfaka) , nr. 34

(Dipotamo), nr. 35 (Kria): The demand for adequate data

of the area near to mount Mitsikeli is obvious

according to the isohyetal pattern since the influence of this mountain did not appear.

nr. 40 (Samarina): This village is situated at a high

elevation. In order to study more clearly the influence

of elevation to the unexplained variance the

installation of an instrument suitable for accurate

9. CONCLOSIONS

Accurate measurements of precipitation is a continueing goal

in hydrology. For measuring precipitation on a regional scale

a weIl designed and operated system, called network, is

necessary.

Network design is strongly related with conveniences and

costs, ignoring the required accuracy and sometimes the

topographic conditions as weIl. Therefore the network

operation should be evaluated based on sufficient adequate

measurements in order to realize an optimization.

Real optimization will be achieved by operating more or less

the optimum number of stations which are very weIl equipped

and established at representative locations and which provide sufficient data of good quality suitable for defined tasks. Many different factors play an important role for the design

of the optimum network. Mathematical relations, like MLR, can

be used for testing the accuracy of existing data but cannot account for the extent of coherence between phenomena in time

and place. From the other side GIS is going to be a very

powerful tooI for hydrologists. Using this, they are able to

observe and to study very accurately, all the hydrological,

topographical, social and geological features of the area of

interest (i.e. direction of slopes, geological structures,

population distribution, drainage pattern, accessibility,

roads, vegetation etc.).

General conclusion which can be drawn are:

- The calculation of unexplained variances using a MLR

technique has proven to be very good for defining the

quality of a network. Also the quality of individual

stations can be defined very clearly. The selected period

(i.e. in this case 10-day totals) is depended upon the size

of the area, the relief, the desired accuracy, the

instrumentation and the local conditions.

The application of a GIS including pure data manipulation

options as weIl as geo-statistical options proved to be

very functional for network optimization.

The present case of study proves very weIl the validity of

the combination of a pure mathematical analysis (MLR) with

the physical one (GIS) and both with the reality. The optimization of the network can be achieved by:

- The abolishment of stations nr. 4 and 11. Both stations

have very high unexplained variances due to bad operational conditions.

- The replacement of the observer for the stations nr. 6, 13

and 14 depending on possibilities.

- The re-equipment of the stations 5 and 7 with a raingauge recorder in order to improve the accuracy of measurements.

- Installing additional stations at places were orographic

effects are not expressed in the isohyetal map. The

locations nr 24, 26, 33, 34 and 39 should therefore be

LIST OP pIGCRES

page

Fig. 1.: Location map 3

Fig. 2.: Photogrammetric map of the study area •.•••..••••.... 5 Fig. 3.: Existing precipitation network 6 Fig. 4.: Classification of the stations according

to their elevation before and after

optimization 7

Climatic region in Greece ••..•••••••.••....••.•••.. 10 Locations of existing precipitation stations

and examined locations for possible new stations •... 9 Topographic map of the study area •••••••...••.••.... S Fig. 5. :

Fig. 6. :

Fig. 7. :

Fig. 8. : 24 Year average monthly variation of precipitation at Moni Vella and at

Elatochori 11

Fig. 9.: Requirements for data .••...•.•...••. 13 Fig.10.: Relationships of mean, maximum and minimum

unexplained variances with the number of

precipitation stations taken into account for

interpolation 23

Fig.11.: The highest standard error for the individual

stations in relation to the elevation •••...•.•••.•. 23 Fig.12.: A three dimensional presentation of the area .•••..• 29 Fig.13.: The Aoos river watershed ...•....•••...•.••.••••.. 30 Fig.14.: Drainage patterns of the Aoos river catchment

(threshold values tv

=

10, 50 and 100) ...•...•••. 30

Fig.15.: Semi-variogram 32

Fig.16.: Isohyet map of the study area ...•••...•.•• 35 Fig.17.: Iso-unexplained variance map of the study area ..••• 35

Precipitation station elevation longitude latitude instrwnents

no. name in meter

1 Pournia 950 20° 51' 40° 08' R, S 2 Pades 1170 20° 55' 40° 03' RR ,

-

S 3 Distrato 950 21° 01' 40° 02' R, S 4 Vovoussa 1000 21° 03' 39° 56' RR ,

-

S 5 Papingo 900 20° 44' 39° 58' R, S 6 Kipoi 790 20° 48' 39° 52' RR ,

-

S 7 Elatochori 1014 20° 59' 39° 52' R, S 8 Micro Peristeri 1040 21° 05' 39° 45' RR , R, S 9 Spilaio 900 21° 17' 40° 00' R, S 10 Kipourghio 868 21° 22' 39° 57' R, S 11 Fourka 1350 20° 56' 40° 10' R, S 12 Skamneli 1180 20° 51' 39° 55' RR ,

-

S 13 Moni Vella 560 20° 36' 39° 51' R 14 Mazi 475 20° 40' 40° 02' RR , R, S ---

---

--- --- ---

---15 Mazaraki (*) 420 20° 37' 39° 49' R, S 16 Limni (*) 600 20° 32' 39° 55' RR ,

-

S 17 Laista (*) 1100 20° 57' 39° 58' R, S Legend: R

=

RR

=

S

₌

(*)

=

raingage raingage recorder snow sampler

station not selected for the present study Table 1: stations in operation in the study area.

station 1971 selected period 1981

no. name 1960

---

1971

,

1981---1990 1 Pournia 71 81 --- 90 2 Pades 67

---

71 81 --- 90 3 Distrato 71 81 --- 90 4 Vovoussa 67

---

71 81 --- 90 5 Papingo 71 81

---

90 6 Kipoi 67

---

71 81 --- 90 7 Elatochori 63

---

71 81

---

90 8 Micro Peristeri 60

---

71 81 --- 90 9 Spilaio 64 --- 71 81 --- 90 10 Kipourghio 62

---

71 81 --- 90 11 Fourka 73 81 --- 90 12 Skamneli 73 81 --- 90 13 Moni Vella 72 -81

---

88 . 14 Mazi 73 81 --- 90 ----

---

---15 Mazaraki (*) 80--81 --- 90 16 Limni (*) 80--81

---

90 17 Laista (*) 80--81 --- 90

Legend: (*)

=

station not selected for the present study

---~ station number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 year 71/72 1223 1298 1239 1438 1613 1574 1426 1127 774 976 **** **** **** **** 72/73 1020 1141 **** 1376 1495 1485 1472 1258 1011 856 **** **** **** **** 73/74 1117 1038 875 1333 1160 1360 **** 1260 992 921 1623 1778 1097 **** 74/75 954 1033 **** 1173 963 1142 1211 1037 754 839 1616 1221 994 729 75/76 944 887 885 1123 1049 1408 1234 1253 847 789 1419 1293 970 852 76/77 1158 1125 1153 1515 926 1516 1583 1298 664 611 1190 1635 1373 1098 77/78 1362 1358 1201 1689 1023 1697 **** 1527 902 863 1940 1872 **** 1192 78/79 1401 1383 1316 1942 1282 1829 2097 1690 916 903 1447 2122 1515 1185 79/80 1218 1243 1154 1525 1114 1473 1582 1397 1203 1019 1616 1801 1379 1018 80/81 1479 1435 1396 1656 1250 1789 1741 1579 954 965 1981 2045 **** 1315 81/82 1175 1274 1083 1450 1090 1435 1625 1398 **** 961 1445 1713 1139 1052

Legend: ****

=

discontinued year Table 3.: Annual precipitation values

.---~ nr. of station a N b

K-

1 2 3 4 5 6 7 1 *** 0.88 148 0.80 307 0.67 193 0.21 918 0.74 60 0.60 225 *** 11 0.82 9 0.77 11 0.80 11 0.03 11 0.74 9 0.75 2 *** 0.92 164 0.62 273 0.42 662 0.67 177 0.54 351 *** 9 0.82 11 0.74 11 0.11 11 0.64 9 0.69 ~ 3 *** 1.07 291 0.44 661 0.91 509 1.21 201 *** 9 0.66 9 0.14 9 0.80 7 0.60

...

4 *** 0.15 954 1.00 -47 0.91 39.4 *** 11 0.02 11 0.76 9 0.97

-5 *** 0.35 635 0.23 835 *** 11 0.11 9 0.06

-6 *** 0.67 469 *** 9 0.75 -7 *** *** Legend: a N b R2

the regression coefficient number of observations intercept

the square of the correlation coefficient

..---~ nr. of station a N b

+

8 9 10 11 12 13 14 1 0.73 196 0.25 964 0.22 616 0.38 600 0.58 205 0.66 332 0.99 162 11 0.67 10 0.04 11 0.12 9 0.26 9 0.90 7 0.80 8 0.90 2 0.61 379 0.24 973 0.29 531 0.36 620 0.52 292 0.65 353 0.86 300 11 0.48 10 0.04 11 0.20 9 0.24 9 0.73 7 0.65 8 0.75 3 0.60 695 0 1188 0.28 895 . 0.57 933 1.09 539 1.14 5 1.05 6 9 0.35 8 0.00 9 0.03 8 0.15 8 0.61 6 0.88 7 0.91 4 1.03 77 0.3 1203 .37 1144 .22 1130 0.77 164 1.20 -15 1.21 229 11 0.75 10 0.03 11 0.03 9 0.04 9 0.82 7 0.87 8 0.73 5 0 1231 0.29 922 0.24 600 0.16 835 0.29 584 0.24 790 0.39 670 11 0 10 0.03 11 0.22 9 0.11 9 0.56 7 0.18 8 0.34 6 0.86 346 .16 1372 .27 1273 .27 1078 0.61 447 0.82 444 1.11 358 11 0.69 10 0.01 11 0.02 9 0.09 9 0.69 7 0.69 8 0.86 7 0.68 267 0.14 666 0.11 699 .05 1439 1.07 -13 0.61 276 1. 29 242 9 0.76 8 0.05 9 0.06 7 0 7 0.90 6 0.77 7 0.69 8 *** .49 897 36 1028 .24 995 .59 363 .74 435 .97 369 *** 10 0.13 11 0.04 9 0.09 9 0.83 7 0.62 8 0.80 9 *** 0.92 91 0.70 964 0.92 885 0.28 970 0.20 671 *** 10 0.47 8 0.18 8 0.21 6 0.05 7 0.06 . . -10 *** 0.26 455 0.16 597 0 859 0.13 732 *** 9 0.31 9 0.17 7 0 8 0.03

-11 *** .30 1068 0 1758 0.55 991 *** 9 0.13 7 0.09 8 0.15

-12 *** 1.20 190 1.58 37 *** 7 0.67 8 0.85 -13 *** 1.18 59 *** 6 0.76 -14 *** ***

Legend: the regression coefficient

number of observations intercept

the square of the correlation coefficient

10-day totals of precipitation in mmo 1911 - 1982

year okt. nov. dec. jan. feb. march april may j~ july aug. sept.

11112 3 1 19 29 33 48 8 52 1 14 1 35 82 23 3 1 58 41 69 3 5 19 8 28 0 129 3 166 29 1 35 2 3 52 31 45 12/13 122 3 8 11 12 36 23 2 14 8 12 4 14 16 0 10 121 55 42 29 18 0 1 29 81 36 20 19 43 29 32 0 1 6 21 12 13114 25 59 121 35 106 34 16 16 0 0 0 21 21 0 84 10 61 4 121 25 19 1 4 11 56 23 41 10 18 9 14 2 4 14 29 47 74/75 97 119 5 19 0 1 29 17 2 7 37 1 5 0 24 8 39 36 30 22 18 9 0 1 158 62 4 6 1 66 21 10 24 11 13 0 75/16 44 3 3 4 10 9 21 1 16 28 10 10 163 58 58 1 23 9 23 14 11 0 3 14 1 29 0 11 0 51 19 21 20 24 21 0 16/71 5 11 202 0 32 13 12 15 11 2 5 23 75 120 31 85 80 35 36 21 2 0 0 39 41 40 53 11 2 3 4 5 2 0 34 52 71/18 20 31 16 11 38 33 143 81 24 0 0 51 24 71 6 38 64 32 35 18 0 2 2 69 0 118 29 111 36 55 10 11 5 0 0 47 18/19 4 0 31 162 13 14 105 6 24 4 0 13 5 0 68 86 88 32 75 33 10 18 35 24 81 12 60 80 0 75 26 38 20 2 29 8 19/80 36 18 5 108 42 35 23 32 46 6 0 6 38 116 46 18 8 22 8 93 15 0 18 0 39 11 51 41 0 94 46 11 0 2 0 52 80/81 1 16 184 33 35 34 13 101 4 0 0 15 204 95 11 54 104 12 35 22 0 6 24 4 54 69 59 18 16 0 33 21 0 9 22 21 81182 26 18 54 48 6 29 48 13 31 2 58 14 8 28 181 0 0 49 21 5 8 4 6 1 156 25 87 0 51 6 64 25 0 19 9 57

Table 5. Precipitation data of station 1

10-day totals of precipitation in mmo 1911 - 1982

year okt. nov. dec. jan. feb. march april may j~ july aug. sept.

71112 5 2 113 53 29 92 7 89 1 12 4 12 71 33 8 11 59 14 111 2 2 40 25 23 0 145 5 119 51 6 28 8 0 14 13 21 12/13 96 3 20 31 11 32 16 1 15 11 16 3 108 21 0 54 115 61 29 31 52 1 1 54 105 21 26 36 30 31 42 0 2 6 10 18 13114 35 54 112 46 96 43 16 10 0 0 0 11 24 0 84 13 65 3 101 18 23 1 3 10 28 15 33 5 6 2 15 8 3 10 20 60 14/75 59 88 11 12 0 1 39 10 9 26 45 0 85 2 20 3 63 23 33 30 21 16 0 1 159 62 0 10 3 11 21 22 63 9 6 0 75116 33 4 5 6 3 5 12 10 18 20 0 34 131 100 90 0 27 15 20 20 26 39 3 14 2 30 1 44 0 50 24 50 13 10 20 2 16/71 4 82 219 1 19 9 13 22 24 0 2 50 19 104 23 12 18 21 36 11 2 0 0 26 53 43 35 20 2 3 1 12 0 0 21 42 71/18 15 21 69 11 40 20 111 75 49 0 0 48 20 10 1 92 82 26 10 18 0 1 2 58 0 138 21 120 33 52 12 39 4 0 0 23 18/19 6 0 62 139 65 8 120 16 20 6 0 15 5 0 14 42 89 31 61 21 11 9 31 9 64 92 41 129 0 41 19 18 26 0 32 9 19/80 38 30 0 135 33 56 8 29 56 10 3 10 30 118 41 32 13 24 0 16 8 0 29 0 61 20 69 34 0 83 31 33 0 1 3 51 80/81 11 13 185 35 49 26 5 10 32 0 0 21 207 91 11 19 66 42 34 16 5 2 29 3 41 80 89 6 27 1 9 24 0 3 28 23 81182 44 30 95 44 2 10 40 11 32 3 18 10 1 36 169 0 0 67 18 6 0 4 22 10 161 49 95 0 10 16 55 58 0 0 6 86