An application of network design procedures for redesigning ...

Hydrological Sciences - Journal - des Sciences Hydrologiques, 28, 2,6/1983

An application of network design procedures for redesigning Kizilirmak River basin raingauge network, Turkey UNAL §ORMAN* & GUVEN BALKAN Middle East Technical University, Engineering Department, Ankara,

Civil Turkey

ABSTRACT Recently developed rainfall network design techniques are discussed and compared. Present day hydrological studies require high levels of accuracy from collected data. Also, scientists need to know the degree of accuracy of the information they use. The existing rainfall network in the Kizilirmak basin must be redesigned in order to meet the required level of accuracy preset by rainfall data users. The three following techniques were applied: optimum interpolation procedure which is a flexible method; variance of mean areal rainfall; and the analysis of variance. The existing network of 52 gauges is redesigned so that the network will have an average root mean square error (rmse) of â 32 mm and the percentage of the area with rmse > 36 mm is limited to 10%. It is found that the proposed criteria are satisfied by a network of 53 gauges of which eight were newly established and seven of the existing ones removed.

Application des méthodes de planification des réseaux à la modernisation de système d'observations du bassin du Kizilirmak en Turquie RESUME Les techniques de planification récemment mises au point pour les réseaux de mesures pluviométriques ont été discutées et comparées. Les études hydrologiques nécessitent une précision de niveau élevé pour les données que l'on mesure. D'autre part, les scientifiques veulent connaître le degré de précision de l'information qu'ils utilisent. Le réseau pluviométrique doit être revu et modifié de manière à obtenir le degré de précision souhaitée par les utilisateurs des données pluviométriques. Les trois approches suivantes ont été utilisées: la méthode d'interpolation optimum dont l'avantage est la souplesse en vue de l'application aux réseaux pluviométriques; la méthode de variance de la hauteur pluviométrique moyenne spatiale l'analyse de variance. Une étude de rationalisation d'un réseau de 52 stations pluviométriques a été effectuée pour le bassin versant du Kizilirmak en Turquie. La rationalisation de ce réseau existant a été effectuée de telle façon que l'erreur moyenne quadratique (EMQ) soit S 32 mm et que le pourcentage de la surface ayant une EMQ > 36 mm

*Present address: UNITEK Ltd, Kavaklidere, Ankara, Turkey.

Architects

& Engineers,

P.K.

53, 233

234

Ûnal §orman & Gùven Balkan

soit intérieur à 10%. La conclusion est que les critères imposés sont valables pour un réseau rationalisé de 53 stations formée en ajoutant huit stations nouvelles et en supprimant sept stations existantes

INTRODUCTION Although the systematic measurement of rainfall has a long history, efforts to design and maintain networks of raingauges for the study of the areal and temporal variability of rainfall are recent. The density of a raingauge network, giving estimates of stated precision, depends on various factors which are directly related to the particular area under study and the purpose to which the data are to be* put. This paper examines three design approaches: optimum point interpolation procedure, variance of mean areal rainfall, and the analysis of variance. An application of these raingauge network design techniques is discussed with reference to the Kizilirmak River basin, with area 38 400 km 2 . The redesign of an existing rainfall network is possible in three ways: (a) The existing network is ignored and a completely new network is designed taking into account the correlation structure of the rainfall process. (b) The existing network is kept and new gauges are added. (c) Existing gauges are used where possible and any gaps are filled with new gauges. The first approach is very expensive because it requires a completely new network to be established. The third gives some control over the gauge numbers and allows reductions in the number of existing gauges. The Kizilirmak River basin was selected oecause a considerable number of stations exist which have a record length of more than 10 years; 45 gauges out of 52 have 12 years of data in common. The long term mean annual rainfall is calculated as 402 mm.

APPROACHES TO RAINFALL NETWORK DESIGN Studies on the systematic design of rainfall networks have been based on different design criteria. Eagleson (1967) and Osborn & Lane (1972) were interested in rainfall network density for flood forecasting and their studies were based on the resulting accuracy of the measured rainfall. Clarke & Edwards (1972) used the standard error of the mean areal rainfall as a criterion. Jones et al. (1978) and Gandin (1963) used the root mean square error of optimal interpolation as design criteria. Rodriguez-Iturbe & Mejia (1974a,b) have recently developed a technique for network design using the accuracy of the areal mean rainfall. This technique has been further developed by Bras & Colon (1978) who optimized the locations of the raingauges. Another approach in network design studies is the evaluation of networks in terms of the benefits and costs resulting from the use of the data obtained by these networks. Gandin & Kagan (1967) dealt with optimal design of meteorological networks for cost-benefit

Network design procedures for redesigning Kizilirmak basin

235

criteria, and in the literature there are several studies in which the optimum design of a raingauge network has been selected by maximizing the benefits. In this paper, the accuracy of predictions resulting from rainfall measurements is discussed as design techniques yielding the following basic items in network design problems: the number of data collection points; the locations of the points; and the duration for which rainfall records should be collected.

Network design for point interpolation

individual rainfall procedures

events

using

optimum

The interpolation methods can be separated into three groups: polynomial, weighted mean and optimum interpolation. In the interpolation method, weighting factors p^ can be calculated depending on the distance between interpolation points (o) and adjacent points (i) , and then be used in estimating the value of the given variable at the point of interest. In optimum interpolation, determined weighting factors make the mean square error of interpolation minimum. It should be noted that the time dimension is not directly taken into account in the interpolation procedure. The interpolation problem can be formulated in the form of linear weighting coefficients p^ of the known values of rainfall f^ at N observation points u^,..., u N , for determining the value f 0 at point u0 f_ = £ N ,p.f. O

(1)

1=1*1 1

It will be convenient to write the above equation in terms of deviations from the means: f' = 2 N

D

f'

(2)

where f ' = f - f , f ! = f . - f. , and p. are weighting factors. The unknowns in equation (2) are f and p ; mean square interpolation error of this equation can be written when gauges are sampled in space for individual events: mse = N" 1 I N

(f^

J 1

_ ZN

P i f!_)

2

(3)

l x

Equation (3) becomes dimensionless by dividing both sides by the variance of r; rainfall S provided that variances at different sites P are the same. e = 1 - 2 riPirQi + ^ j P i P j ^ j

(4)

where r J is the correlation coefficient between the interpolation point and point i; r^-j is the correlation coefficient between points i and j, and e is a measure of interpolation error. If the partial

236

Unal §orman & Gùven Balkan

derivative of equation (4) is taken with respect to p i , then the weighting factors p^ can be determined such that the measure of interpolation error (e) is a minimum (see equation (5)): 2

j=l p j r ij

= r

oi

36 mm. In this procedure, the gauge location and the number of gauges are considered to be the parameters in determining the optimum interpolation error. This procedure is quite good in estimating the areal mean rainfall when, as in this case, each year is considered as an individual event. The proposed network is built around 20 stations and 53 gauges which are sufficient to meet the specified accuracy criteria that < 10% of the area has rmse â 36 mm. Jones et al. (1978), and also the UK Wessex Case Study report presented by O'Connell et al. (1978) dealt with similar cases and concluded similar results using southwest England rainfall data. The methodology proposed by Rodriguez-Iturbe & Mejia (1974a,b) can be applied for two basic purposes. One is to estimate "the mean areal rainfall variance when each station is randomly distributed with equal chance of probabilities for various numbers of gauges with known values of point variance and variance reduction factors due to sampling in time and space. Secondly, for the existing raingauge network (such as for the Kizilirmak basin), the standard deviation of the mean areal annual rainfall can be estimated as 29.8 mm. In order to have a sound understanding for the second objective, one should compare the value with the mean areal rainfall to justify the network. An analysis of the variance approach provides the standard error of residuals which can be determined for the number of gauges and their record length. So, it gives an estimate of mean area rainfall. For the existing network of 52 gauges this value is computed to be 8.3 mm. The last two methodologies discussed can be used effectively for redesigning dense rainfall networks with long records until the required accuracy for long term mean areal rainfall is achieved with an acceptable number of gauges in the redesigned network. However, the optimum interpolation procedure does not consider explicitly the time dimension which plays a controlling and fundamental role in estimating long term mean areal rainfall.

REFERENCES Balkan, G. (1979) Rainfall network design approaches and applications.

246

Unal §orman & Guven Balkan

MSc Thesis, Civil Engineering Dept , Middle East Technical University, Ankara. Bras, R.L. & Colon, R. (1978) Time-averaged areal mean of precipitation: estimation and network design. Wat. Resour. Res. 14 (5), 878-888. Clarke, R.T. & Edwards, K.A. (1972) The applications of the analysis of variance to mean areal rainfall estimation. J. Hgdrol. 15, 97-112. Eagleson, P.S. (1967) Optimum density of rainfall networks. Wat. Resour. Res. 3 (4), 1021-1033. Gandin, L.S. (1963) Objective Analysis of Meteorological Fields. Leningrad. Gandin, L.S. & Kagan, R.L. (1967) The economic approach to the planning of a network of meteorological stations. Sov. Hydrol. Selected Pap. 6, 597-606. Jones, D.A. et al. (1978) Network design using optimal estimation procedures. AGU Chapman Conference on Design of Hydrologie Data Networks. Lenton, L.R. & Rodnguez-Iturbe, I. (1974) On the collection, the analysis and the synthesis of spatial rainfall data. MIT Report no. 194. O'Connell, P.E., Gurney, R.J., Jones, D.A., Miller, J.B., Nicholass, C.A. & Senior, M.R. (1978) Rationalization of the Wessex Water Authority raingauge network. Report no. 51, Institute of Hydrology, Wallingford, Oxon, UK. Osborn, H.B. & Lane, L.S. (1972) Optimum gauging of thunderstorm rainfall in southeastern Arizona. Wat. Resour. Res. 8 (1), 259-265. Rodrïguez-Iturbe, I. & Mejia, J.M. (1974a) The design of rainfall networks in time and space. Wat. Resour. Res. 10 (4), 713-728. Rodnguez-Iturbe, I. & Mejia, J.M. (1974b) On the transformation of point rainfall to areal rainfall. Wat. Resour. Res. 10 (4), 729-735. Received

15 May 1980;

revised

13 January

1983.