Hydrological Sciences - Journal - des Sciences Hydrologiques, 34,2, 4/1989

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1 Hydrological Sciences - Journal - des Sciences Hydrologiques, 34,2, 4/1989 Predicting the mean annual flood and flood quantiles for ungauged catchments in Greece MRI MLMIKOU & JOHN GORDIOS Department of Water Resources and Maritime Engineering, School of Civil Engineering, Technical University of thens, Greece. bstract The spatial variation of the mean annual flood of both mean daily and instantaneous extremes and of the parameters of the Extreme Value Type 1 (EV1) distribution for catchments in the northwest and west regions of Greece are significantly explained in terms of physiographic and climatological characteristics of the catchments by using multiple regression techniques. The catchment characteristics used in the study are the following: drainage area, mean annual areal precipitation, stream frequency, main stream slope and length, intensity of the one-day rainfall of five-year return period, and a soil type index. The EV1 distribution has been found to describe adequately the annual frequency distributions of the daily and of the standardised by-their-mean-value daily extremes of the catchments. Based on the regional models for the parameters of the distribution, annual flood frequency curves, and thus flood quantiles of the assumed distribution, can be derived. The developed regional models are successfully used in predicting with satisfactory accuracy the mean annual floods and flood quantiles, needed in hydrological design, for ungauged catchments within the region studied. Les prévision de la crue moyenne annuelle et les quantiles de la crue pour des bassins non-observés en Grèce. Résumé Les variations de la crue moyenne annuelle et des paramètres de la distribution EV1 pour des bassins du Nord- Ouest de la Grèce sont expliquée en fonction des caractéristiques géomorphologiques des bassins i.e. aire du bassin, précipitation moyenne annuelle du bassin, la densité de drainage, la pente et longueur du cours principal, l'intensité de la pluie journalière pour une période de retour de cinq ans et l'index du type du sol. Les modèles régionaux résultant de l'étude prédisent avec une précision satisfaisante les crues moyennes annuelles et les quantiles qui sont nécessaires pour les calculs hydrologiques des ingénieurs pour les bassins nonobservés de la région étudiée. Open for discussion until 1 October

2 Maria Mimikou & John Gordios 170 INTRODUCTION One of the most frequent and important practical tasks for hydrologists is the estimation of future flood conditions at a site for structural designs, water supply plans, flood plain regulations, hydropower development, to name only a few examples from the variety of river engineering works. The method of estimation employed depends upon the quantity and quality of the available data and the nature and the economic life of the project. Data-intensive methods used in flood frequency analysis include statistical techniques which attempt to fit probability distributions for at-site estimation of flood quantiles (discharges with specified probabilities of exceedance), and simulation techniques which use rainfall-runoff models to generate synthetic flood flows from rainfall series. Régionalisation techniques for estimating flood quantiles at gauged sites have been intensively used as well in the flood frequency literature (Kuczera, 1982; Potter, 1987). ll these methods require significant amounts of reliable flood flow data, either to provide adequate sample sizes for the statistical and the regional approach, or to calibrate adequately the basin rainfall-runoff response for the simulation approach. The main problem in hydrological design arises when flood quantile estimates or design flood hydrographs with specified probabilities of exceedance are needed at sites where no or limited streamflow data are available, a situation which is very common in practice. In such cases two techniques are in common use in estimating flood quantiles: regional prediction from catchment characteristics using linear regression (Stedinger & Tasker, 1985) or the combination of regional flood estimation with limited at-site historic flood information (Wall et al, 1987), and rainfall-runoff modelling involving stochastic modelling of rainfall (Bras et al, 1985). nother item of flood information which is usually needed in hydrological design, especially for small projects, is the mean annual flood Q, the mean of the annual maximum flood flow series (the series formed by the highest - daily or instantaneous - discharge to occur in each year of record). Q is an index of the potential magnitude of flood flows. Division by Q has been widely used to standardise flood data from different basins (NERC, 1975). In this paper an attempt is made to predict both the mean annual flood of mean daily and of instantaneous extremes, and the flood quantiles for catchments in the hydrologically homogeneous region of northwestern and western Greece (Mimikou, 1984). The major rivers of the country are concentrated in those regions of the country (Mimikou & Kaemaki, 1985) as is the main interest for water resources development. Regional prediction models have been developed which take as inputs physiographic and climatological characteristics of the catchments. Conclusions have been drawn for the prediction accuracy of the proposed models and for the relative performance of the Greek regional models compared with other models developed for the same purpose in different climatic regimes. Finally, the limitations of the models and the validity of the assumptions made are discussed.

3 DT USED 171 Predicting meanfloodsfor ungauged catchments in Greece Data from 11 gauged stations of the five major rivers (liakmon, cheloos, rachthos, oos and Kalamas) in northwestern and western Greece have been used in the calibration of the regional models. The data of the stations used in this study include all the available observed flood information from the region, and represent the recorded flooding experience in that region. The annual maximum daily discharges (mean daily values) and the instantaneous peak discharges have been estimated from the flow records of the stream gauge stations, which belong to the Public Power Corporation (PPC). ll stations are equipped with permanent installations for measuring flows with current meters and with staff gauge recorders and have limited but accurate and reliable flood data, giving a total of 186 station-years for the daily flood data and of 166 station-years for the instantaneous data. The latter are less than the former mainly because of operational problems in some stations, e.g. the operation of the staff gauge recorders was sometimes temporarily interrupted at the time of the peak of flash floods. This situation is common and frequent in hydrometric stations in Greek mountainous catchments. The general location of the river catchments is shown in Fig. 1. The physiographic and climatological characteristics of the catchments and their units which have been used in the development of the regional models are the following: the drainage area (km 2 ); the mean annual areal precipitation P (mm); the stream frequency SF (ju nct i ns km" 2, measured by counting channel junctions on the 1: map of each catchment and dividing by the drainage area); the slope S (m km" 1 ) and the length L (km) of the main river course from the divide of the basin to the measuring station; the intensity of the 1-day rainfall of 5-year return period M51D (mm hr" 1 ); and a soil type index SO. The soil index is based on the soil map (1: scale) which has been prepared for the region of the study, where seven classes of soil have been distinguished in accordance to their "winter rain acceptance potential". Weights R i (i = 1...7) were assigned to each soil class indicating their runoff potential. The soil index SO for a catchment is estimated by measuring the fraction S { (i = 1...7) of the catchment within each soil class (by overlaying the soil map with a catchment map at the same scale), and adopting a weighted mean of these soil fractions as follows: ll catchment physiographic characteristics have been estimated from maps by taking into consideration the instructions given in the Guide to the Flood Studies Report (Institute of Hydrology, 1978). The climatological characteristics P and M51D have been taken from previous hydrological studies of the PPC of Greece. The catchment characteristics and their units used in the study are given in Table 1. In the separated last two rows of Table 1, the characteristics of two test catchments, the Gogos

4 Maria Mimikou & John Gordios 172 Fig. 1 General location of the catchments. catchment of the rachthos River and the Sykia catchment of the cheloos River, are given. The data for these two catchments were used for verification purposes. The independence of the catchment characteristics was checked by testing the significance of their interrelationships. Drainage area and main stream length were found to be significantly interrelated as were mean annual precipitation and 5-year 1-day precipitation. For this reason, such related catchment characteristics were not used together in the regression equations, with the exception of the prediction equations for some of the parameters of the EV1 distribution, where the significance of the partial contribution of drainage area, along with that of main stream length, was clear.

5 173 Predicting mean floods for ungauged catchments in Greece Table 1 Physiographic and climatological characteristics of the catchments Station River (km 2 ) P (mm) SF (junct. km' 2 ) S (m km' 1 ) L (km) M51D (mm h ) SO Venetikos Siatista Ilarion Tsimovo Plaka na Mesohora vlaki Vovousa Konitsa Kioteki liakmon liakmon liakmon rachthos rachthos rachthos cheloos cheloos oos oos Kalamas Gogos Sykia rachthos cheloos THE MEN NNUL FLOOD The mean annual flood Q is determined as the mean of the annual maximum flow series of a catchment. In the present study, Q is estimated for both the mean daily and for the instantaneous extremes of the records. The daily extremes have been used as well as instantaneous peaks because, as noted above, in Greece the number of data readily available for the former variable is usually higher than for the latter. Q provides useful preliminary information concerning the flood regime of a catchment because it indicates the general magnitude of flood flows. It is a usual practice to standardise flood data from different basins by dividing by the at-site estimate of Q (NERC, 1975). The dependence of Q on the physical nature and the climatic regime of a catchment has long been recognized by many researchers (Biswas & Fleming, 1966; Nash & Shaw, 1966; NERC, 1975; Institute of Hydrology, 1978; creman, 1985). Regional regression models have been derived with a varying degree of complexity, from very simple models (i.e. the rational method) to more complicated ones, like the ones developed in England and Scotland (NERC, 1975; creman, 1985). In this study, an attempt is made to develop regional models for predicting the mean annual flood of daily and of instantaneous extremes which will be applicable to Greek Mediterranean basins. The developed models are compared to those calibrated in England and Scotland and their differences discussed in order to draw conclusions on the influence of climate. The regional models The arithmetic means of both the daily and the instantaneous series of annual extremes have been used as estimates of the mean annual floods Q d and Q { (both in m 3 s" 1 ) respectively for all catchments. Since the analysed

6 Maria Mimikou & John Gordios 174 series of extremes do not include outliers, the arithmetic mean is believed to be a good estimator of the mean annual flood (Institute of Hydrology, 1978). Multiple regression techniques have been used in the development of regional relationships between the physiographic and climatological characteristics (independent variables) given in Table 1, and the mean annual floods Q d and Q i (dependent variables) of the catchments used in the calibration phase. The multiple regression analysis was performed according to standard statistical texts (Haan, 1977). logarithmic transformation was used for both dependent and independent variables, since this improved the linear association between them. s measures of the association of the variables, the coefficient of determination ^(0 5 r 2 i 1), the standard error of the regression SE, and the prediction error PE, were used. The standard error SE is defined as the square root of the ratio of the residual (actual minus estimated values) sum of squares of the dependent variable to the degrees of freedom (n - p), with n the number of observations (equal here to 11) and p the number of independent variables (pin) increased by one in order to account for the constant of the regression equation. Both r 2 and SE were adjusted for loss of degrees of freedom, in order to remove the bias. The prediction error PE is defined as follows: PE = n l X? =1 (^ - Y^[Y t \ x 100 W where Y i is the value of Q d S>t?, estimated fjpm the jlata for the catchment i (i = 1, 2,..., n = 11) and Y i is the value Q d or ) (. estimated from the regression equations. The best estimated exponential regression equations for both variables are as follows: for the daily flood flows: h d = x lu" 8 W12 P 2311 S 0M2 (^0.216 (SO)3.266 r 2 = 0.754, SE = 0.176, PE = 21.06% for the instantaneous flood flows: Qi = x 10" 4 (SFf S5 (M51D) 1 ' 805 (SO) 3278 S 2U r 2 = 0.897, SE = 0.155, PE = 17.81% Using L instead of in both equations (2) and (3), M51D instead of P in equation (2) and P instead of M51D in equation (3) decreased the r 2 values of the equations. The exponents in equations (2) and (3) are positive, which means that the mean annual floods are increasing functions of the physiographic and the climatological characteristics. The independent variables in equations (2) and (3) are arranged in decreasing order of significance of their contribution, tested by a t-test. The

7 175 Predicting mean floods for ungauged catchments in Greece relative significance of the independent variables in the case of Q d is completely different from that for Q r Nevertheless, for both variables, two morphological and one climatological characteristics appear to provide the most significant contributions. For the daily data, drainage area, mean areal precipitation and stream slope play the most significant roles. The contribution provided by stream frequency in the first place and by drainage area and 5-year 1-day rainfall intensity in the subsequent places, appear to be the most significant for the instantaneous data. The appearance of SF as the most important variable with positive exponent can be explained by the fact that a dense river network helps significantly to produce a simultaneous drainage from the various parts of a basin, resulting thus in high peaks during flood events. nother important observation is that the climatological characteristic displaying the strongest association with the instantaneous flows is the extreme rainfall intensity M5VD and not the mean areal value P, whereas the opposite is true of the daily flows. This fact can be explained by the "event" character of the instantaneous flows and of the M51D whereas P, expressing the average flood potential of the catchment, is expected to affect significantly the mean daily flood flows. n analysis of the variance of the mean annual floods Q d and Q i explained by each of the basin characteristics used in equations (2) and (3), respectively, is shown in Table 2. For each dependent variable the Table 2 nalysis of variance Dependent variables Independent ' variables (cumulative % of variance explained) 2, 2/ Original l/a ^ Original u Dimensionless Dimensionless l/a u 36.9 SF 59.5 L SF 67.5 SF 97.6 P SO 65.4 P 67.8 L 70.3 S 97.6 S 73.7 M51D S 75.7 S 75.1 L 28.3 SF 74.6 SO 86.9 P 76.2 SF SO 75.4 S 89.7 S 77.2 SO 78.4 P 85.7 SO 99.1 SF 78.1 SO 85.9 P 99.2 contributing basin characteristics are arranged in a horizontal series and in decreasing order of significance. number is assigned to each point of the ordered series of characteristics indicating the cumulative percentage of the variance of the respective dependent variable explained by the regional regression containing the characteristics from the beginning of the series up to that point. The regional models calibrated in Britain for predicting the mean annual instantaneous peak flood are as follows: (a) The average country-wide equation proposed by the Natural Environment

8 Maria Mimikou & John Gordios 176 Research Council (NERC, 1975) uses data from England and Scotland, but it is rather biased towards the English basins from which the majority of data came. The equation takes the following form: tr C - 94 (RSMD) tm (SF) 0210 (SO) 1230 S - m (LKE + l)" (4) (b) where the constant C varies from for East nglia to for the southwest of England. The equation proposed by creman (1985) for Scotland is as follows: Q. = /t a843 P 1 ' 085 (SF) - 1S7 (SO) 1J5 (10QLOCH + IV (5) The variables of equations (4) and (5) which have not been used in the Greek equation are: RSMD (in mm) defined as the depth of the M51D (in mm) minus the effective mean soil moisture deficit SMDBR (in mm), and the term LKE (fraction of the basin draining through a lake or reservoir), which is replaced by the term LOCH in the Scottish model (fraction of the basin covered by lakes or reservoirs). RSMD has not been used in the present study, because it is believed that the intensity of the M51D event is more closely related to the peak flow producing mechanism than the effective rainfall depth (Mimikou, 1984). Furthermore, reliable estimates of the effective soil moisture deficit are very difficult to obtain. For this reason SMDBR has not been used herein. term for the lakes has not been used either, since this is a negligible factor in the Greek basins. By taking into consideration the above mentioned differences in the usage of the independent variables, the form of the Greek model in equation (3) is closer to the English model in equation (4) than to the Scottish model in equation (5). Testing the models' performance and their prediction accuracy The prediction errors PE(%), as estimated by equation (1), for the proposed regional models in equations (2) and (3) are 21% and 18% and the standard errors SE axe and 0.155, respectively. The errors are within the order of magnitude of errors estimated by other researchers (creman, 1985), even though the number of Greek gauged sample basins is very limited. In order to further test the performance and the prediction accuracy of the models in equations (2) and (3), two additional gauged test catchments within the region are used, the Sykia catchment of the cheloos river and the Gogos catchment of the rachthos river, whose characteristics are given in Table 1. The former catchment has a very limited number of years of data, only seven years, whereas 16 years of data are available for the latter catchment. The mean annual floods estimated from the observed data and the regionally estimated mean annual floods for the test catchments along with the corresponding Pis-values are given in Table 3. The average error for equation (2) is estimated equal to 24%, whereas for equation (3), it is 19%. These values can be accepted as satisfactory compared with the prediction errors

9 177 Predicting meanfloodsfor ungauged catchments in Greece Table 3 Errors in predicting mean annual floods Test Estimated from Predicted PE% PE% Catchment observed data 2 j 2- QJ Q; for equation (2) for equation (3) Gogos Sykia verage error: obtained during the calibration of the regional models. FLOOD FREQUENCY NLYSIS - ESTIMTION OF FLOOD QUNTILES The flood frequency analysis was performed by using the annual maximum daily discharges of the 11 calibration catchments. The usage of the daily extremes instead of the instantaneous extremes in the flood frequency analysis is justified because in several of the stations studied the number of data available for the latter variable is insufficient for a reliable statistical analysis (Gumbel, 1958). This is due to operational problems of the staff gauge recorders, explained earlier. Since this situation is very frequently met in Greek catchments, the flood frequency prediction models developed herein are widely applicable. Parameterisation of the flood frequency distributions Two of the most widely applicable statistical distributions of extremes, the Gumbel or Type 1 Extreme Value distribution (EV1) and the log Pearson Type III have been fitted to the annual flood flows of the catchments. The X goodness-of-fit (Kottegoda, 1980) has shown that the data fit the EV1 distribution at the 10% confidence level for all catchments, whereas the data of the majority of the catchments do not fit the log Pearson type III at the same confidence level. It is to be noted that because of the limited flood data available at all sites the selection of any distribution on the basis of a goodness-of-fit test and its extrapolation to return periods of 1000 years may involve serious errors. The attempt made herein is to test the appropriateness of a simple and widely applicable flood distribution for the entire region studied, based on the available data only. Thus, it can be assumed that all sites have an identical annual flood flow frequency distribution, the EV1 distribution, except for scale. The latter becomes regionally compatible by standardising all samples by the mean value, i.e. by the mean annual flood Q d, of each sample. Even though it is known (Stedinger, 1983) that the

10 Maria Mimikou & John Gordios 178 distribution of the dimensionless flood data can have substantially smaller coefficients of skewness and kurtosis than exhibited by the distribution of the original data, an attempt has been made to fit the constant-skew-evl distribution on the dimensionless flood flows as well. The hypothesis that the assumed distribution describes adequately the frequency distribution of the dimensionless flood flows was acceptable at the 5% confidence level for all the catchments studied. This is an acceptable level of adequacy for the purposes of this study, in a region with limited site data (Kuczera, 1982). The fact that a single distribution can describe adequately the annual frequency distributions of both the original and the dimensionless flood data allows a regional analysis of the parameters of the distributions and a comparison of the latter's regional predictability in dimensionless and in original form. Based on the regional models for the parameters, one can derive estimated annual flood frequency distributions and flood quantités at other locations by assuming that the annual flood flows at the sites of interest within the region fit the EV1 distribution. The latter has been shown to be a reasonable approximation for the region studied, even though such an assumption cannot be entirely true (Stedinger, 1983). The EV1 distribution has been fitted on the daily extremes Q d (original distribution) and on the latter standardised by the mean annual flood Q d fq d (dimensionless distribution) by using the Weibull plotting position for the return period T given by T = (N + l)/m, where N is the sample size and m is the rank commencing with the largest value. The EV1 is defined by its distribution function (Gumbel, 1958), as follows: F(x) = exp{- exp[(x - u)a]} (6) where x stands for Q d (m 3 sec" 1 ) and for Q d fq d alternatively and a,u are the parameters of the distribution. For a given return period T, the T-year event x(t) is obtained from equation (6) after the incorporation of T, which is related to the probability F(x) = 1-1/T, as follows: x(t) = u - ln{ln(t) - ln(t- l)}la (7) The distribution in equation (7) plots as a straight line on Gumbel probability paper with a double exponential scale for T. The parameter Va is the scale parameter and u is the location parameter, indicating, in units of discharge, the most probable flood (Kottegoda, 1980). In order to obtain estimates of the parameters Ha and u of equation (7) the method-of-moments fitting procedure has been followed, where the population mean \L and the standard deviation 0 of the variable x axe, estimated by the sample mean x and the sample standard deviation s respectively, as follows: 1/a = &y6/n = (8) û = n - y/a = x (9) where 7 = is Euler's constant. The arithmetic mean of the

11 179 Predicting mean floods for ungauged catchments in Greece dimensionless flood flows is equal to unity, whereas their standard deviation is the coefficient of variation Cv = six of the original flood flows (Stedinger, 1983). Thus, the expressions for the dimensionless parameters become as follows: lia = CV (10) û = CV (11) The coefficient of variation Cv is a dimensionless measure of the at-site dispersion of the flood flows. Its site-to-site variation, often used in regional flood frequency analyses to model spatial heterogeneity (Potter, 1987), is examined in this paper along with the regional behaviour of the dimensionless frequency parameters. The regional models From equations (8), (9), (10) and (11) it becomes apparent that the analysis can be conducted either in terms of the pairs of the parameters of the distribution or in terms of the statistical characteristics x~, s and Cv of the daily extreme discharges. It was decided to describe explicitly the regional behaviour of each distribution's parameter separately, because the conclusions drawn are directly related to the flood frequency characteristics of the assumed distribution. The spatial variation of the original and of the dimensionless parameters 1/2 and «(dependent variables) of the 11 calibration catchments were explained in terms of the physiographic and the climatological characteristics (independent variables) of the catchments, as given in Table 1. The multiple regression procedure followed in developing the best regional relationships, and the statistical tests used, are the same as the ones described previously in analysing the mean annual floods. The best estimated exponential regression equations for the parameters are given in the following equations: Original parameters (in m 3 s" 1 ): Va = x 10 5 L 1 ' 951 (SO) ^-0.732^ (SF) r 2 = 0.781, SE = 0.196, PE = 21.53% (12) U = x lo" 8^1-000 P S 0M9 (SF) 0325 (SO) 2 ' 739 r 2 = 0.784, SE = 0.165, PE = 20.27% ( 3) Dimensionless parameters: 1/3 = (SF)- 0 ' 424 L a640 5 a F a799 (SO)" (14)

12 Maria Mimikou & John Gordios 180 r 2 = 0.859, SE = 0.080, PE = 9.89% Û = (SFf- m S' L m (SOf m P 0237 (15) r 2 = 0.992, SE = 0.014, PE = 1.72% The catchment characteristics in equations (12) to (15) are arranged in decreasing order of significance of their contribution. The rainfall intensity M5W is missing from the equations, since the regressions became worse when the M51D intensity was used instead of the mean precipitation P. The other interrelated pair of catchment characteristics, i.e. the stream length L and the drainage area, are used together for the original 1/3 and for the dimensionless lia and û because of the significant partial contribution of the drainage area, in addition to the very significant role of the stream length. Comparing the corresponding r 2 values and the error SE and PE values between the original and the dimensionless models in equations (12) to (15), one can see that the latter explain better the spatial variation of the dependent variables and exhibit smaller error values than the former. Thus, the regional predictability of the parameters of the EV1 distribution is improved when they are estimated from the dimensionless models (after multiplication by the mean annual flood Q d of the catchment) instead of using the original models directly. The location parameter û of the original distribution is directly related to and primarily affected by the arithmetic mean of the daily extremes, as shown by equation (9). Thus, this parameter is expected to be affected by the catchment characteristics which have been found to explain significantly the spatial variation of the mean annual flood Q d. This is clearly shown by comparing equations (2) and (13). The signs of the exponents in the regression equations for the original and the dimensionless lia indicate that these parameters increase with increasing stream length and slope, while they decrease with increasing stream frequency, drainage area, precipitation and runoff coefficient of the catchment. The same influence of catchment characteristics is exercised on the statistical characteristics which are related to the parameters 1/8 namely on the at-site and the regional mean standard deviations and coefficients of variation of the flood flows. Exactly the opposite to the influence of the catchment characteristics previously described is exercised on the dimensionless parameter w, which is a decreasing function of 1/2, according to equations (10) and (11). The analysis of variance for each of the dependent variables in equations (12) to (15) explained by each of the basin characteristics was performed by following the previously described procedure and is given in Table 2, along with the corresponding analysis for the mean annual floods. Prediction of flood quantiles for ungauged catchments The performance of the regional models in equations (12) to (15) in predicting flood quantiles was tested by utilizing the data of the Gogos test

13 181 Predicting meanfloodsfor ungauged catchments in Greece catchment of the rachthos river. The regionally derived flood quantiles Q(T) for given values of T, were directly estimated from equation (7), when the regional models in equations (12) and (13) were used in estimating the parameters of the distribution. The usage of equations ^(14) and (15) required additionally the estimation of the mean annual flood ) rf of the catchment of interest by utilizing the regional model in equation (2). Then the dimensionless flood quantiles QJQJT) (estimated ratio of the daily extreme Q d for a return period T divided by the estimated mean annual flood Q d ) were estimated from equation (7) and transformed to flood quantiles in discharge units as follows: Q(T)=[Q d lb d (T)]b d (16) Both procedures were followed in estimating flood quantiles Q{T) for T = 10, 50, 100 and 1000 years. The data-based flood quantiles Q(T) have been estimated by fitting the EV1 distribution to the observed annual maximum daily discharges, following the previously described fitting procedure. The x 2 goodness-of-fit test showed the adequacy of the EV1 distribution at the 10% confidence level. comparison between the values predicted from the regional models and those estimated directly from the data is given in Table 4. The average prediction error for all flood quantiles estimated by using the Table 4 Errors in predictingfloodquantiles Return period T (y) Q(T) estimated from observed data (m 3 *- 1 ) Predicted original distribution? -7 Q(T) dimensionless distribution (m 3 i 2 ) PE% original distribution PE% dimensionless distribution verage error: first procedure with the original data was 37%, larger than the error obtained by the other procedure, applicable to the dimensionless data, which was 12%. In Fig. 2, a graphical presentation on Gumbel paper of the performance of both procedures is given, comparing the EV1 distribution fitted to the observed data and the two regionally derived EV1 distributions. On the same Figure the extreme control band of the distribution at the 95.4% probability level is given (Gumbel, 1958, p. 218). From Fig. 2 and from Table 4 one can see that the dimensionless procedure has better prediction accuracy and gives a predicted distribution closer than the one fitted on the observed data. Nevertheless, it is difficult to draw general conclusions and to evaluate the accuracy of the regional methods by using data at only one site, with a lot of questions concerning the at-site estimation of flood quantiles from limited

14 Maria Mimikou & John Gordios 182 RETURN PERIOD T (years) PROPBILITY F(X)=P(X«)i) Fig. 2 t-site estimated vs regionally derived frequency distribution. observed data. Further research is needed on this subject. The regional models developed could be successfully used in predicting flood quantiles needed in hydrological design for ungauged catchments within the region studied and without any available historic flood information. The assumption that the missing annual flood flows at the sites of interest fit the EV1 distribution is considered to be a reasonable approximation justified by the hydrological experience from the region and by the wide applicability of the EV1 distribution in analysing annual extremes (Phien, 1987). The models, as for all regional models, cannot take into account future changes in the catchments and cannot be safely applied outside the region of the study. CONCLUSIONS The conclusions drawn from this research are the following: (a) The spatial variation of the mean annual flood of mean daily extremes and of instantaneous extremes and of the parameters of the EV1 distribution for catchments in the northwest and west region of Greece can be significantly explained in terms of physiographic and climatological characteristics of the catchments by using multiple regression techniques. The EV1 distribution has been found to describe adequately the annual

15 183 Predicting meanfloodsfor ungauged catchments in Greece frequency distributions both of the daily extremes and of the daily extremes standardised by their mean value of the catchments. (b) For the mean annual (daily) flood, drainage area, annual mean areal precipitation and stream slope play the most signifcant roles in the regression. The contributions provided by stream frequency, drainage area and 1-day 5-year rainfall intensity appear to be the most significant for the mean annual (instantaneous) flood. The regional models developed predict the mean annual floods for ungauged catchments of the region with satisfactory accuracy. (c) The mean annual (instantaneous) flood prediction model in Greece uses different extreme rainfall characteristic from the models developed in England and Scotland and neglects the effect of lakes. The form of the Greek model is closer to the English model than to the Scottish one. (d) The location parameter û of the original EV1 distribution, indicating the most probable flood, shows the same influence of the catchment characteristics and the mean annual (daily) flood. (e) The original and the dimensionless lia and the statistical characteristics related to these parameters, namely the at-site and the regional mean standard deviations and coefficients of variation of the flood flows, increase with increasing stream length and slope, while they decrease with increasing stream frequency, drainage area, precipitation and runoff coefficient of the catchment. Exactly the opposite is exercised on the dimensionless parameter u, since «is a decreasing function of 1/3. (f) The flood quantile regional prediction procedure, which is based on the dimensionless distribution, applied to one test catchment was found to give estimates closer to the ones at-site obtained from the observed flood data than the other prediction procedure developed for the original distribution. Nevertheless, general conclusions cannot be drawn at this stage, because it is difficult to evaluate the accuracy of the regional methods by using data at only one site with doubtful at-site estimation of flood quantiles from limited observed data. Further research is needed on this subject. (g) The regional models developed were successfully used in predicting flood quantiles, needed in hydrological design, for ungauged catchments within the region studied. The assumption that the missing annual flood flows at the sites of interest fit the EV1 distribution is considered to be a reasonable approximation justified by hydrological experience from the region and by the wide applicability of the EV1 distribution. cknowledgements The authors wish to thank the Public Power Corporation of Greece for providing the data used in the study. REFERENCES creman, M. C. (1985) Predicting the mean annual flood from basin characteristics in Scotland. Hydrol. Sci. J. 30(1,3),

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