Which distribution is used with rates frequencies and flows

The Log-Pearson Type III distribution tells you the likely values of discharges to expect in the river at various recurrence intervals based on the available historical record. This is helpful when designing structures in or near the river that may be affected by floods. It is also helpful when designing structures to protect against the largest expected event.

For this reason, it is customary to perform the flood frequency analysis using the instantaneous peak discharge data. However, the Log-Pearson Type III distribution can be constructed using the maximum values for mean daily discharge data.

A tutorial and example is supplied for both instantaneous and mean daily data. Data Manipulation. Analysis Techniques. Example Applications. What is it? How is it calculated? The Log-Pearson Type III distribution is calculated using the general equation: where x is the flood discharge value of some specified probability, is the average of the log x discharge values, K is a frequency factor, and is the standard deviation of the log x values.

Tutorial Example. This website was developed by Oregon State University's Civil, Construction, and Environmental Engineering Department with support from the state water institutes program of the U. Flood frequency analysis is a technique used by hydrologists to predict flow values corresponding to specific return periods or probabilities along a river.

The application of statistical frequency curves to floods was first introduced by Gumbel. Using annual peak flow data that is available for a number of years, flood frequency analysis is used to calculate statistical information such as mean, standard deviation and skewness which is further used to create frequency distribution graphs. The best frequency distribution is chosen from the existing statistical distributions such as Gumbel, Normal, Log-normal, Exponential, Weibull, Pearson and Log-Pearson.

After choosing the probability distribution that best fits the annual maxima data, flood frequency curves are plotted. These graphs are then used to estimate the design flow values corresponding to specific return periods which can be used for hydrologic planning purposes. Flood frequency plays a vital role in providing estimates of recurrence of floods which is used in designing structures such as dams, bridges, culverts, levees, highways, sewage disposal plants, waterworks and industrial buildings.

In order to evaluate the optimum design specification for hydraulic structures, and to prevent over-designing or under designing, it is imperative to apply statistical tools to create flood frequency estimates. These estimates are useful in providing a measurement parameter to analyze the damage corresponding to specific flows during floods.

Along with hydraulic design, flood frequency estimates are also useful in flood insurance and flood zoning activities. This depends on the probability distribution function applied to the non-zero flow values. Indeed, negative values obtained for in Equation 9 mean that, for the given return period T and fraction k , the probability of observing the flow value, x , is zero for the river under consideration. For the commonly used return periods, the fractions of non-zero values, k , that would be greater are given in Table 3.

The best-fit probability distribution function was determined for each D -day low flow sequence of streamflow gauging stations in the Meric-Ergene, Gediz, Ceyhan and Seyhan basins after being properly checked with statistical tests.

Table 4 shows the percentage of probability distribution functions for each D -day low flow sequence with the highest underlined in bold. It is seen that mostly the LN3 distribution conformed to low flows in the Meric-Ergene, Gediz and Ceyhan basins as it has the highest percentage for most of the D -day low flow sequences. G2 has been the best twice for the day low flow sequence in Meric-Ergene, and the day low flow sequence in Gediz and one of the best two probability distribution functions once for the day low flow sequence in Gediz.

Also W3 has been the best twice for 1-day low flow in Meric-Ergene and 7-day low flow in Ceyhan. It has also been one of the two best probability distribution functions for day low flow in Ceyhan. LN2 and G3 have never been the best in this analysis although each has either been the second best or shared the second-best place in some cases.

For example, LN2 is the second best for day low flow in Meric-Ergene, and G3 is one of the three second-best probability distribution functions for day low flow in Gediz.

In the past, Bulu et al. W2 and exponential distributions were found suitable for the Aegean Region in the study by Duran With use of recent flow observations in this study, W3 but mainly LN3 appeared to be more suitable for low flows of the mentioned basins; namely Meric-Ergene and Gediz. From this comparison, it becomes inevitable to stress that a higher number of parameters in the probability distribution functions are more advantageous for better fitting the D -day low-flow sequences compared with probability distribution functions with a lower number of parameters.

Once the best-fit probability distribution of the D -day low flow sequence is determined, the D -day low flow discharge corresponding to any given return period can be calculated.

It should be emphasized that the analysis in this study is station-based. Therefore, the low flow-duration-frequency curves were obtained on a gauging station basis. The low flow-duration-frequency curves are useful tools for many purposes but particularly for practicing engineers. An engineer can get any low-flow design discharge from the low flow-duration-frequency curves. In estimating low flows for a given return period, zero D -day low flows were considered through the total probability theorem as explained above.

One streamflow gauging station per hydrological basin was selected to demonstrate the suitability of the fitted probability distributions Figure 2. No matter what probability distribution function was found to be the best for any D -day low flow sequence of individual gauging stations, LN3 was applied to all D -day low flows of all stations in the Meric-Ergene, Gediz and Ceyhan basins while W3 was used for the Seyhan Basin.

Parameters of the selected probability distribution functions LN3 and W3 were determined for each of the streamflow gauging stations and used in calculating the D -day low flows in every individual gauging station for return periods of 2, 5, 10, 25, 50 and years. It is important to notice that for a threshold of zero flow, lower frequency low flows cannot be calculated by the probability distribution function due to the constraint in Equation For example, the non-zero fraction of low flows allows one to calculate the year return period 1-day low flow in station D01A of Meric-Ergene Basin.

Indeed, for higher return periods such as 25, 50 and years, the D -day low flow is simply taken to be zero. One more point worth mentioning is that no zero D -day low flow was observed in the Seyhan Basin. The general behavior of the low flow-duration-frequency curves in basins other than Seyhan looks similar. A family of upward curves was obtained in Seyhan Basin while families of downward curves were observed for the other three basins. A quick reasoning for this could be that the W3 probability distribution function was found the best-fit for the D -day low flow sequences in Seyhan Basin and LN3 for the other three.

The reason for obtaining a different probability distribution function for Seyhan Basin can be linked to the non-intermittent character of stream gauges taken from this particular basin. The D -day low flow sequences of Meric-Ergene, Gediz and Ceyhan basins have, however, zero values whose number increases with decreasing D.

Low flow frequency analysis is a commonly used analytical tool to assess low flow characteristics of streams. Different D -day low flows are considered in this study for streamflow gauging stations from four hydrological basins located in different geographical regions in Turkey.

The 2- and 3-parameter probability distribution functions commonly used for low flow frequency analysis are applied to fit the D -day low flow sequences of every gauging station. In total, 2, station-year up-to-date daily streamflow data from 99 gauging stations on intermittent and non-intermittent rivers are used. It is found that the 3-parameter Log-Normal LN3 probability distribution function fits quite well to most of the D -day low flows in Meric-Ergene, Gediz and Ceyhan basins in the northwestern, western and southern parts of Turkey, respectively.

The 3-parameter Weibull W3 distribution fits best to the majority of the low flow sequences in Seyhan Basin in the south of the country. Gauging stations of the former basins have zero low-flows, demonstrating their intermittent character, while the latter basin is characterized by non-intermittent gauging stations. The frequency analysis takes into account the zero-flow fraction in the low-flow sequences.

It is important that zero-flows are considered in the low flow-duration-frequency curves used for calculating the design low-flow discharges in intermittent rivers. Impact Factor 1. CiteScore 1. This paper is Open Access via a Subscribe to Open model. Individuals can help sustain this model by contributing the cost of what would have been author fees.

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Article Navigation. Research Article March 02 Frequency analysis of low flows in intermittent and non-intermittent rivers from hydrological basins in Turkey Ebru Eris ; Ebru Eris. E-mail: ebru. This Site. Google Scholar. Hafzullah Aksoy ; Hafzullah Aksoy. Bihrat Onoz ; Bihrat Onoz. Mahmut Cetin ; Mahmut Cetin. Bulent Selek ; Bulent Selek. Hakan Aksu ; Hakan Aksu. Musa Esit ; Musa Esit. Isilsu Yildirim Isilsu Yildirim.