2006/1 PAGES 10 – 18 RECEIVED 18. 2. 2006 ACCEPTED 15. 4. 2006

S. KOHNOVÁ, L. GAÁL, J. SZOLGAY, Associate Prof. Silvia Kohnová, PhD. Prof. Ján Szolgay, PhD. Associate Prof. Kamila Hlavčová, PhD. K. HLAVČOVÁ Department of Land and Water Resources Management Faculty of Civil Engineering, SUT Bratislava Radlinského 11, 813 68 Bratislava REGIONAL ESTIMATION Tel: 02/59274623,02/5974499 E-mail:[email protected] [email protected] OF DESIGN 10-DAY [email protected]

Mgr. Ladislav Gaál PRECIPITATION TOTALS IN Czek Hydrometeorological Institute Libuš Na Šabatce 17 THE UPPER HRON REGION 143 06 Praha 4 – Komořany, ČR [email protected]

ABSTRACT KEY WORDS

In the paper 10-day maximum precipitation totals from 23 rain gauges from the period • extreme precipitation, 1961 to 2000 in the upper Hron River basin in were analysed. A combined • L-moments, method, based on statistical criteria and on the evaluation of evaporation and runoff • regional frequency analysis, conditions during long precipitation events, has been used for the selection of the 10- • 10-day maximum precipitation totals. day precipitation totals. N-year values of the 10-day annual maximum precipitation totals were estimated separately in the summer and winter seasons using a methodology developed by Hosking and Wallis (1997). The regional distribution function was selected using a L-moments diagram. Finally, a comparison of the resulting N-year maximum precipitation totals estimated from these regional distributions with the at–site analyses was performed.

INTRODUCTION or heavy rainstorms. In Great Britain, the Flood Studies Report (NERC, 1975) and subsequently the Flood Estimation Handbook An essential part of flood risk assessment in engineering hydrology (FEH, 1999) were broad studies lasting for decades on the methods is the issue of intensive and long-lasting precipitation events. Such of estimating extraordinary flood events, which also included several-day precipitation events can, under special synoptical methods for estimating design precipitation for durations of hour circumstances, bring extraordinary precipitation amounts to to 8 days at any location in Great Britain. The German KOSTRA watersheds, which can result in severe floods and cause damage project (Malitz, 1999; Bartels, et al. 1997), the Italian VAPI project to human property and human lives as well. Examples of such (Ferrari, 1994), the HIRDS system of New Zealand (Thompson, natural disasters have also been observed in the very recent past 2002) and the Australian guide to rainfall and runoff (Pilgrim, 1987) in Central Europe, including flood events in Slovakia, the Czech are other examples of such complex national studies on flood or Republic, Austria and Germany (July 1997; August, 2002). The precipitation risk assessment. reliable estimation of such intensive, several-day precipitation totals A new perspective on design rainfall estimating has recently been therefore plays a key role in flood risk assessment, and particular developed by the National Weather Service (NWS) at National attention has been paid to this issue for decades worldwide. Oceanic and Atmospheric Administration (NOAA) in the United In most of the national meteorological offices of the world, there States: the NOAA Atlas Vols. 1 and 2 (Bonnin, et al.; 2004a, 2004b) has been an intensive effort to develop complex statistical methods are exclusively available via the Precipitation Frequency Data in order to cope better with natural hazards such as flash floods Server through the internet (http://dipper.nws.noaa.gov/hdsc/pfds)

10 20065 SLOVAK UNIVERSITY OF TECHNOLOGY

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- they no longer exist in the form of a classic, hard-copy handbook. precipitation analyses have been carried out, for example, in the NOAA Atlas 14, Vol. 1 (Bonnin, et al.; 2004a) contains precipitation United States (Schaeffer, 1990; Guttman, 1993; Sveinsson, et al., frequency estimates for the semi-arid areas in the south-west of 2002), Canada (Pilon, et al., 1991; Adamowski, et al., 1996) and the U.S., while NOAA Atlas 14, Vol. 2 (Bonnin, et al.; 2004b) South Africa (Smithers and Schulze, 2001). Fowler and Kilsby focuses on the Ohio River basin and the 14 surrounding states in (2003) concentrated on regional analysis of extreme precipitation the northeastern parts of the U.S. Thanks to the convenience of the for a duration of 1 to 10 days in the United Kingdom: the authors Internet, precipitation frequency estimates for 5-minute through examined changes in the shape of regional growth curves in the 60-day durations at average recurrence intervals of 2 years through last decades of the 20th century. Gellens (2002) investigated k-day 1000 years can be easily achieved for any location of interest among precipitation totals (k = 1… up to 30) for Belgium, while the whole the states featured in the analysis. Similar work has been undertaken territory of the country was treated as a single region for all the for the state of Alabama (not included in the aforementioned combinations of the 11 durations and 3 seasons (calendar year, warm studies) by Durrans and Kirby (2004). The Alabama Rainfall and cold hydrological half-year) analyzed. In the Czech Republic, Atlas is an internet-based server for providing design information the regional frequency analysis of several-day precipitation totals on the characteristics of extreme precipitation, which include has been processed recently: Kyselý, et al. (2004) presented methods intensity-duration-frequency (IDF) curves and 24-hr design storm and principles for the delineation of homogeneous groups for annual hyetographs. maximum precipitation totals of 1, 3, 5 and 7 day durations. The most promising methodology for estimating design rainfall In Slovakia, 2-day and 5-day precipitation totals were analysed in recent decades has turned out to be the so-called index flood in the upper Hron Region in Stehlová, et al. (2001) and Jurčová, methodology in combination with L-moments. An index value et al. (2002). Gaál and Lapin (2002) analyzed k-day precipitation approach assumes that the region is homogeneous, i.e., the frequency totals in a 100-year series from Hurbanovo. In Lapin, et al. (2003), distributions of the observations from all the sites in the region are an at-site analysis of 1-, 2-, and 5-day precipitation totals and identical, apart from a site-specific scaling factor (i.e., Hosking and a subsequent geostatistical regionalization was undertaken for 557 Wallis, 1997). In other words, an estimate of an amount of rainfall sites in Slovakia. with a given return period for a selected site is obtained by the In the past, only daily maximum precipitation totals were usually product of the index value from this site (usually, the average value evaluated in Slovakia (Šamaj et al., 1985). As the previous examples of the sample) and the desired quantile of the regional growth curve illustrate, it is necessary to deal with rainfalls of various durations. that is common for all of the sites in the region. Issues involving testing new methodologies used for rainfall L-moments represent a unique tool within the field of design value frequency analysis and acquiring experience concerning their estimation. L-moments are statistical characteristics analogous to applicability under the various physical/geographic conditions of conventional (product) moments – they can describe any statistical Slovakia are also of interest. The number of new types of acceptable properties of the probability distributions (such as the location, probability distribution functions and parameter estimation methods scale, skewness, kurtosis or others). However, they are computed implies that the use of a single distribution function (for instance, from a linear combination of the ascending ordered data sample. the almost exclusively used Gumbel or the 3-parameter Pearson The superiority of L-moments over conventional moments has distributions – Šamaj, et al., 1985) may not be appropriate in the been proved in a number of studies (Sankarasubramanian and future. Srinivasan, 1999; Peel, et al., 2001). For example, L-moments do In this paper, problems of selecting 10-day precipitation totals not have sample size related boundaries and are less sensitive to are discussed and a case study on fitting the appropriate regional the presence of extraordinary values (’’outliers’’) in the data sample distribution functions to 10-day maximum precipitation values in as conventional moments (Hosking, 1990). Vogel and Fenessey the upper Hron region is presented. (1993) proved the advantage of using L-moments ratio diagrams in the identification of a parent statistical distribution from which the data sample might have originated. A detailed overview of the METHODOLOGY FOR THE SELECTION OF regional frequency analysis based on L-moments can be found in 10-DAY MAXIMUM PRECIPITATION TOTALS the handbook of Hosking and Wallis (1997). Several examples of the successful adoption of the aforementioned In previous studies (e.g., Stehlová, et al., 2001; Jurčová, et al., methods can be found in the various regions of the world; however, 2002), the selection of k-day precipitation totals (k = 2, and 5 days) most of the studies are devoted to an analysis either of short was based on the requirement of recording daily precipitation duration rainstorms or to 1-day precipitation totals. Such regional totals higher than 0.0 mm for each day of the selected k-day

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period. However, when calculating k-day precipitation totals for sample L-Cv ratios. The properties of the simulated homogeneous k higher than 6 days from several locations in Slovakia we came pooling group are compared to the sample L-Cv ratios as to the conclusion, that, especially in the lowlands, the number of such continuous events dramatically decreases with increasing k (Kohnová, et al., 2005). (1) A possible explanation for this fact is that long lasting precipitation

events are usually caused by cyclonic synoptic situations with where µV is the mean of the simulated V1 values, and σV is the a mean duration of about 6 days. That means that in the case of standard deviation of the simulated V1 values. For the sample and 10-day precipitation events, probably two consecutive synoptic simulated pooling groups, respectively, V1 is calculated as situations divided by a one-day or two day ”dry gap” in precipitation may be connected. The effects of these gaps are more pronounced in the lowlands and less in the mountains. Therefore, a revision of the selection criterion used in our previous (2) studies has been implemented in this study. Accordingly, in the process of selecting of 10-day precipitation totals, no more than two

(separate or consecutive) ”dry days” (i.e. days with 0 mm or 0.0 mm where N is the number of sites, ni is the record length at the site i, precipitation) were allowed during the selected 10-day period. t(i) is the sample L-Cv at site i, and tR is the regional average sample In the cold season (CS) the 2-day evapotranspiration total is usually L-Cv.

lower than 1 mm, so (especially in the case of maximum events) Two other analogous tests H2 and H3 are based on L-skewness t3 and these gaps do not play any important role in the selection of 10- L-kurtosis t4, respectively. day precipitation totals. In the warm season (WS) dry day gaps Following Hosking and Wallis, pooling groups were classified

in precipitation could be connected with sunny and quite warm as acceptably homogeneous if Hj < 1 (j = 1, 2, 3), possibly weather, causing two-day evapotranspiration to rise even well above homogeneous if 1 ≤ Hj < 2 and heterogeneous if Hj ≥ 2 (Hosking 10 mm. Moreover, the preceding precipitation may have caused and Wallis, 1997). runoff from the catchment. In such a case we believe, that the next In order to select the appropriate regional frequency distribution precipitation event could not be connected to the previous rainy function for a particular pooling group, the ZDIST goodness-of-fit test days. Therefore, if a 10-day precipitation event was interrupted by and L-moment ratio diagrams were used. The goodness-of-fit test two consecutive dry days in the WS, attention had to be paid to described by Hosking and Wallis (1997) is based on a comparison potential evapotranspiration and runoff during these two days so between the sample L-Ck and population L-Ck for different additional analysis was introduced in order to identify events with distributions. The test statistic is ZDIST and is given as: a small (negligible) decrease in the catchment´s saturation during the two consecutive dry day precipitation gap. For details, see Kohnová, et al. (2005). (3)

DIST where DIST refers to a candidate distribution, τ4 is the population R REGIONAL ESTIMATION OF DESIGN 10-DAY L-Ck of the selected distribution, τ4 is the regional average sample PRECIPITATION TOTALS L-Ck, B4 is the bias of the regional average sample L-Ck, and σ4 is the standard deviation of the regional average sample L-Ck (for In order to be able to apply a regional method for estimating design a detailed description, see Hosking and Wallis, 1997). 10-day precipitation totals, we first had to identify a homogenous pooling group. Hosking and Wallis (1997) proposed to test the homogeneity of pooled sites by a measure based on L-moment INPUT DATA ratios which compares the between-site variation in sample L-Cv (coefficient of a variation) values with the expected variation for Ten-day maximum annual precipitation totals were analysed a homogeneous pooling group. This method fits a four-parameter separately in two seasons during the year – the warm season kappa distribution to the regional average L-Cv ratios. The estimated (covering the season from April to September), and the cold season kappa distribution is used to generate 500 homogeneous pooling for the remaining part of the year (from October of the previous year groups with population parameters equal to the regional average to March of the current year). This selection was primarily based on

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CHOPOK

JASENIE

KRÍŽNA JARABÁ MOTYCKY M. P. DUMBIEROM HELPA STARÉ HORY TELGART BENUŠ ŠUMIAC D. HARMANEC ULANKA BRUSNO S. LUPCA C. BALOG P. POLHORA B. BYSTRICA LUBIETOVÁ

MOLCA

LOM N. RIMAVICOU

Figure 1. The site map of the analysed precipitation stations in the upper Hron region

Table 1 The list of analysed precipitation stations. Elevation Length of Station Station code Observation period (m a.s.l.) observation (years) Chopok 21 080 2008 1961-2000 40 Telgárt 33 020 901 1951-2000 50 Pohorelá 33 060 764 1961-2000 40 33 080 695 1961-2000 40 Polomka 33 120 586 1961-2000 40 Beňuš 33 140 542 1961-2000 40 Pohronská Polhora 33 160 618 1961-2000 40 Brezno 33 200 490 1961-2000 40 Čierny Balog – Krám 33 240 530 1961-2000 40 Mýto pod Ďumbierom 34 040 634 1961-2000 40 Jasenie na Kyslej 34 060 705 1961-2000 40 Jasenie 34 070 492 1961-2000 40 Brusno 34 080 406 1961-2000 40 Ľubietová 34 100 477 1961-2000 40 Slovenská Ľupča 34 120 372 1951-2000 50 Môlča 34 140 459 1961-2000 40 Dolný Harmanec 34 160 481 1961-2000 40 Motyčky 34 180 688 1961-2000 40 Krížna 34 200 1570 1961-2000 40 Staré Hory 34 220 483 1961-2000 40 Banská Bystrica - Uľanka 34 240 398 1961-2000 40 Banská Bystrica 34 260 427 1961-2000 40 54 120 1018 1961-2000 40

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the similarity of the physical conditions for precipitation occurrence Table 2 The values of the Hosking-Wallis heterogeneity test for the in the region (Lapin et al., 2002). whole upper Hron region (23 stations). Twenty three precipitation stations in the upper Hron basin to the Maximum 10-day precipitation totals gauging station Banská Bystrica were selected. The observation Hj values period ranged from 1961 to 2000, however, two stations had Warm season Cold season longer observation periods from 1951 to 2000. The list of stations H1 -1.03 -1.91

is presented in Table 1. Ten-day annual maximum values in each H2 -0.95 -0.69 season were used in the statistical analysis, and were selected using H3 -1.17 -0.98 the methodology described in this paper.

flood frequency based on L-moments. By applying this methodology RESULTS OF REGIONAL ESTIMATION OF we have tested the homogeneity of the whole upper Hron region as DESIGN 10-DAY PRECIPITATION TOTALS a single pooling group. We used Hosking and Wallis’ heterogeneity test

(Hosking and Wallis, 1997). The Hj (j = 1, 2, 3) values of the test for One possible way recommended for obtaining a single type of the cold and warm seasons are presented in Table 2. According to the distribution function for a whole region is to use the method of regional test, the whole region was found to be homogenous.

Figure 2 A comparison of the design values by applying at site and regional estimations for N = 2, 5, 10, 20, 50 and 100 years at the Brezno station (warm season). (Legend of the distribution functions: LP3: logPearson III, AE: General Extreme Value, GPA: General Pareto, GLO: General Logistic, MM - method of moments, LM - L-moments, R-LM - regional estimation using L-moments, MLM - maximum likelihood method, PWM – probably weighted moments)

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Figure 3 A comparison of the design values by applying at site and regional estimations for N = 2, 5, 10, 20, 50 and 100 years at the Brezno station (cold season). (Legend of the distribution functions: P3: Pearson III, WB3: Weibul, MM - method of moments, LM - L-moments, R-LM - regional estimation using L-moments, MLM - maximum likelihood method)

Using the RFFA Matlab tool created by Gaál (unpublished), which the warm season and the P3 (3-parameter Pearson) distribution for is based on the original Fortran routines for regional frequency the cold season. analysis devised by Hosking (2000), the values of the L-Cs, and the L-Ck at all the stations were estimated; subsequently, an L- moment ratio diagram was used to compare the L-skewness and COMPARISON OF THE RESULTS L-kurtosis relations of the different distributions and data samples. An L-moment ratio diagram gives a visual indication of which The results of the at site and regional estimated design values of the distribution may be expected to provide a good fit for a data sample 10-day maximum precipitation totals in the stations of the upper or samples. The L-moment ratios for all the analysed stations for Hron region were summarised in tables and figures. the cold and warm seasons were presented in a previous study In Figs. 2 and 3 a comparison of the design values by applying dealing with local estimation of 10-day maximum precipitation at site and regional estimations for N = 2, 5, 10, 20, 50 and 100 totals (Kohnová, et al. (2005)). Due to the location of the regional years at the Brezno station is presented. We can see that the values L-moment ratios, the following distribution functions were selected of the regional estimation are close to the at site estimation and as regional ones: the GLO (Generalised Logistic) distribution for comparable in the cold season. In the warm season the regional

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Table 3 Values of N-year 1-, 2-, 5- and 10-day maximum precipitation cold season. When we compare the 100-year values of 5- and totals at the Brezno station in the cold and warm seasons in [mm]. 10-day maximum precipitation totals, they achieve higher values in the cold season. It is also important to stress that the 100-year T [years] Cold values of the 10-day maximum precipitation totals are two to 100/ season 2 10 20 50 three times higher than the estimated values of 100-year values 100regional of 1-day maximum precipitation totals at the same station. This 10-day fact should be taken into consideration in the practical application 52.2 98 115 138 154/154.3 prec. of design values of k-day maximum precipitation totals, e.g., 5-day prec. 44.8 77.2 91.8 112.9 130.8/117.0 when designing engineering structures. By comparing the 100- year regional estimations with the highest 100-year local values, 2-day prec. 35.1 57.9 66.7 77.9 86.5/103.9 we can observe that they are very close in most cases. Regional 1-day prec. 25.5 41.5 46.0 55.4 61.4/61.0 100-year values are the highest estimations in the majority of the stations, but according to the selected distribution function, T [years] they can also result in lower estimates by comparing them with Warm 100/ the local estimation, as can be observed at the Brezno station in season 2 10 20 50 100regional the cold season by its 5-day 100-year maximum precipitation totals and in the warm season by its 1-day 100-year maximum 10-day 73.3 106 114 122 131/148.1 precipitation totals. prec. 5-day prec. 53.7 89.9 102 117.1 127.9/133.1 2-day prec. 50.4 66.8 74.6 86.1 95.8/99.9 CONCLUSIONS 1-day prec. 39.3 59.4 67.4 78.1 86.3/77.1 In this study seasonal 10-day maximum precipitation totals in the upper Hron region were analysed. Precipitation data from 23 and local estimated values are comparable to N= 20 years; with the stations were used, with the longest observations from 1951 to 2000. higher return periods (50-year and 100-year), the regional value The 10-day maximum precipitation totals were divided into two overestimates the at site estimations of more than 20 mm at this seasons - the cold and warm seasons. station. The L-moment method based on Hosking and Wallis’ approach To test the consistency of the design values for engineering (1997) was applied for the regional estimation of seasonal 10-day calculations, we have also compared the values of N-year 10-day design precipitation totals. L-moment ratio diagrams were used maximum precipitation totals with 1-, 2- and 5-day maximum for choosing the appropriate regional distribution function. The precipitation totals in the cold and warm seasons, which were at-site and regional design value estimates of the 10-day maximum estimated in previous studies, e.g. Hasbach (2001), Jurčová (2002) precipitation totals in all the stations were compared. Finally, the and Stehlová, et al. (2001). The results for the Brezno station consistency of these values was tested by using the example of the are presented in Table 3. The distribution functions which gave Brezno station, where the values of the N-year 10-day maximum the highest at site value of the 100-year maximum precipitation precipitation totals with the N-year 1-, 2- and 5-day maximum total from the ”best” selected distributions for 1, 2, 5, or 10-day precipitation totals in the cold and warm season were compared. maximum precipitation totals were selected for this comparison. In the table the highest local estimated 100-year value is also Acknowledgement compared with the regional estimations of the 100-year maximum precipitation totals. This work was supported by the Science and Technology Assistance We can observe that the 100-year values of 1-day maximum Agency under Contract No. APVT-20-003204 and the Slovak Grant precipitation totals, which are caused mostly by extreme Agency under VEGA Project Nos. 1/2032/05 and 2/5056/25. The convective rainfall, were higher in the warm season than in the support is gratefully acknowledged.

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