Academic literature on the topic 'Hershfield Method:'

Abstract. Probable maximum precipitation (PMP) estimation is one of the most important components for designing hydraulic structures. The aim of this study was the estimation of 24 h PMP (PMP24) using statistical and hydro-meteorological (physical) approaches in the humid climate of the Qareh-Su basin, which is located in the northern part of Iran. Firstly, for the statistical estimate of PMP, the equations of empirical curves of the Hershfield method were extracted and the Hershfield standard and modified methods were written in Java programming language, as a user-friendly and multi-platform application called the PMP Calculator. Secondly, a hydro-meteorological approach, which is called the convergence model, was used to calculate PMP24. The results of both approaches were evaluated based on statistical criteria, such as the mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), mean absolute percentage error (MAPE), correlation coefficient (r), and coefficient of determination (R2). The maximum values of PMP24 for the Hershfield standard and modified methods were estimated to be 448 and 201 mm, respectively, while the PMP obtained by the physical approach was 143 mm. Comparison of PMP24 values with the maximum 24 h precipitation demonstrated that based on performance criteria including the MAE, MSE, RMSE, MAPE, r, and R2, the physical approach performed better than the statistical approach and it provided the most reliable estimates for PMP. Also, the accuracy of the Hershfield modified method was better than the standard method using modified Km values, and the standard method gives excessively large PMP for construction costs.

The article discusses two statistical methods to estimate PMP values, the Hershfield and the NERC methods. Neither method offers any explanation why the PMP values can be calculated by the use of unbounded statistical distributions, but both methods include the use of envelope curves that are not independent of the region. Bounded data that fits an unbounded distribution must deviate from the distribution for high return periods and tend to a limiting value, and then there exists, a limiting reduced variate that can be used to find the PMP value. When the distribution is EV1, the limiting reduced variate can be defined by a mapping transformation, or by cutting off the distribution. It is shown that when Hershfield or NERC methods are used, the limiting reduced variate is included in the PMP values and can be separated from regional parameters. It is suggested that the limiting reduced variate, that depends solely on return period, may more easily be transferred between regions than the other parameters. This may be a great help in finding PMP values in regions where observations are not extensive enough to define limiting return periods with necessary certainty. A case study with data from Iceland demonstrates, that using the limiting reduced variate, similarities emerge in the Icelandic data and the NERC PMP that justify the acceptance of the NERC method.

The meteorological stations in Iceland are rather few compared to the size of the country, and their service time is short compared to other developed countries. Investigations of individual 24-hour station PMP values computed by the Hershfield and NERC methods show trends that are important for the application of PMP values in engineering design. The results fall into two series, one with high PMP values and the other with lower values. The low values originate from station groups situated in areas with mildly sloping terrain and here the results compare fully with what should be expected from experience from other countries. The other series shows results that do not compare as well with previously published results. Their general characteristics is that PMP values calculated hy the Hershfield method are of the order 80% higher than the corresponding results obtained by the NERC method. The results of this high series do not check against results obtained from meteorological models. It is noteworthy, that all the stations of the low series belong to station groups where the terrain is gently sloping, i.e. average terrain slopes less than 1.4%, while in the high series all the stations belong to station groups where the terrain slopes steeply from a highland plateau down to sea level. It is concluded that the generalized estimates of PMP values needed in engineering design could be obtained.

The purpose of this study was to analyze the effect of spillway width on flow elevation at the weir crest based on the flood discharge design for the Probable Maximum Flood (PMF) return period using flood routing hydrologically at the Cacaban Dam (Indonesia). The rainfall Probable Maximum Precipitation (PMP) design uses the Hershfield Equation. The design of the flood discharge analysis of QPMF used the Nakayasu Synthetic Unit Hydrograph (HSS). Flood routing uses the hydrologic routing method. The Cacaban Dam is located in Jati Village, Kedung Banteng District, Tegal Regency, Central Java Province, Indonesia. The results of the research data analysis showed that increased spillway crest widths led to decreased flow evaluation at the spillway crest, and increased outflow discharge. Thus, if a large storage volume of the reservoir is intended, then the width of the spillway crest must be reduced. Otherwise, the width of the spillway crest must be increased. In terms of flood control in the Tegal Regency, it's better to make the crest of the spillway smaller. Doi: 10.28991/CEJ-2022-08-04-08 Full Text: PDF

Abstract Probable Maximum Flood (PMF) used in the design of hydrological structures reliabilities and safety which its value is obtained from the Probable Maximum Precipitation (PMP). The objectives of this study are to estimate PMP and PMF value in Upper Citarum Watershed and understand the impact from different PMP value to PMF value with two scenarios those are Scenario A and B. Scenario A will calculate the PMP value from each Global Satellite Mapping of Precipitation (GSMaP) rainfall data grid and Scenario B calculate the PMP value from the mean area rainfall. PMP value will be obtained by the statistical Hershfield method, and the PMF will be obtained by employed the PMP value as the input data in Gridded Surface Subsurface Hydrologic Analysis (GSSHA) hydrologic model. Model simulation results for PMF hydrographs from both scenarios show that spatial distribution of rainfall in the Upper Citarum watershed will affect the calculated discharge and whether Scenario A or B can be applied in the study area for PMP duration equal or higher than 72 hours. PMF peak discharge for Scenario A is averagely 13,12% larger than Scenario B.

The variability of extremely heavy precipitation events with duration of 120 min occurring in the area of Cracow, southern Poland was assessed. The analysis was performed using time series of maximum annual precipitation events with durations t = 5, 10, 15, 30, 60, and 120 min, recorded at the Botanical Garden station at the Jagiellonian University in the period of 1906–1990. The periodicity of precipitation was analyzed using the autocorrelation function and Fourier spectral density analysis. The Probable Maximum Precipitation (PMP) was calculated by Hershfield’s statistical method. The analysis of the autocorrelation function of sequences and the Fourier spectral density revealed a clear periodicity of the maximum precipitation. For precipitation with t = 60 min, the maximum values occur every 9 years, but also shorter periods (3-year) may be observed. The PMP values calculated for Cracow differ significantly from the values calculated using the probability distribution, as well as from the ones observed and they increase with increasing precipitation duration. The differences between the PMP and probable as well as observed precipitation tend to decrease with increasing duration of precipitation.

Extensive hydrological analysis is carried out to estimate floods for the Batu Dam, a hydropower dam located in the urban area upstream of Kuala Lumpur, Malaysia. The study demonstrates the operational state and reliability of the dam structure based on hydrologic assessment of the dam. The surrounding area is affected by heavy rainfall and climate change every year, which increases the probability of flooding and threatens a dense population downstream of the dam. This study evaluates the adequacy of dam spillways by considering the latest Probable Maximum Precipitation (PMP) and Probable Maximum Flood (PMF) values of the concerned dams. In this study, the PMP estimations are applied using comparison of both statistical method by Hershfield and National Hydraulic Research Institute of Malaysia (NAHRIM) Envelope Curve as input for PMF establishments. Since the PMF is derived from the PMP values, the highest design flood standard can be applied to any dam, ensuring inflow into the reservoirs and limiting the risk of dam structural failure. Hydrologic modeling using HEC-HMS provides PMF values for the Batu dam. Based on the results, Batu Dam is found to have 200.6 m3/s spillway discharge capacities. Under PMF conditions, the Batu dam will not face overtopping since the peak outflow of the reservoir level is still below the crest level of the dam.

The probable maximum precipitation (PMP) is the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographical location at a certain time of the year. PMP is very important to be considered for the design of river regulating structures i.e Dams and Barrages to overcome any possible chance of overtopping failure as well as for public safety and hazards downstream of any of these structures. Especially if these structures located in the upstream of the of the populated town or city than the failure could damage severely such areas. As such the PMP convention is always a requirement as primary design dam/reservoir criteria when public safety is of concern. The PMP is used to derive Probable Maximum Flood (PMF), which further used in hydraulic modeling to check the impact assessments for such occasions. This paper focuses on estimation of PMP for Linau River Basin in Sarawak using statistical method proposed by World Meteorological Organization (WMO), which is described in its operational manual. Long Lidam and Long Laku are located in Linau River Basin but Long Laku has long discontinuity in the data set thus the rainfall series at Long Lidam is further used for PMP estimation. The missing data was in-filled using Belaga rain gauge station as Long Lidam rainfall has good correlation with Belaga rainfall data. Hershfield statistical method has been adopted to estimate the 24-hour duration PMP. The Probable Maximum Precipitation for 24-hour duration storm is estimated as 691 mm for the Linau River Basin.

Extreme rainfall and floods have increased in frequency and severity in recent years, due to climate change and urbanization. Consequently, interest in estimating the probable maximum precipitation (PMP) has been burgeoning. The World Meteorological Organization (WMO) recommends two types of methods for calculating the PMP: hydrometeorological and statistical methods. This study proposes a modified Hershfield’s nomograph method and assesses the changes in PMP values based on the two representative concentration pathway (RCP4.5 and RCP8.5) scenarios in South Korea. To achieve the intended objective, five techniques were employed to compute statistical PMPs (SPMPs). Moreover, the most suitable statistical method was selected by comparing the calculated SPMP with the hydrometeorological PMP (HPMP), by applying statistical criteria. Accordingly, SPMPs from the five methods were compared with the HPMPs for the historical period of 2020 and the future period of 2100 for RCP 4.5 and 8.5 scenarios, respectively. The results confirmed that the SPMPs from the modified Hershfield’s nomograph showed the smallest MAE (mean absolute error), MAPE (mean absolute percentage error), and RMSE (root mean square error), which are the best results compared with the HPMP with an average SPMP/HPMP ratio of 0.988 for the 2020 historical period. In addition, Hershfield’s method with varying KM exhibits the worst results for both RCP scenarios, with SPMP/HPMP ratios of 0.377 for RCP4.5 and 0.304 for RCP8.5, respectively. On the contrary, the modified Hershfield’s nomograph was the most appropriate method for estimating the future SPMPs: the average ratios were 0.878 and 0.726 for the 2100 future period under the RCP 4.5 and 8.5 scenarios, respectively, in South Korea.

Estimates of design flood are necessary at locations of hydrologic structures (e.g., flood control dams, barrages) in studies related to their planning, design and risk assessment. In situations, where failure of hydrologic structures could have catastrophic consequences on environment and mankind owing to the presence of thickly populated areas and/or nuclear facilities downstream, the design flood estimate is considered to be the probable maximum flood (PMF). The PMF could be estimated by convoluting probable maximum precipitation (PMP) for catchment contributing flow to the target location with Unit hydrograph (UH) of the catchment. For the purpose of convoluting PMP with UH, their effective durations should be the same. Geomorphological Instantaneous Unit Hydrograph (GIUH) could form the basis to arrive at UH of any required effective duration. There is ambiguity in GIUH constructed for gauged locations, as parameters of GIUH are sensitive to (i) scale of map and support/threshold area for initiation of the first order streams, and (ii) the position of outlet of catchment. To address this, recently a strategy based on the hypothesis of self-similarity of stream networks was proposed by Moussa (2009) to estimate GIUH parameters and the resulting GIUH is referred to as equivalent GIUH (E-GIUH). Previous studies on the self-similarity hypothesis were confined to a few French catchments, and did not examine digital elevation model (DEM) based uncertainty. In this perspective, hypothesis of self-similarity‖ was tested on 200 catchments in four Indian river basins (Mahanadi, Godavari, Krishna and Cauvery) having wide range in their areas (19 km2 to 3,00,870 km2) by using the Shuttle Radar Topography Mission (SRTM) DEM data. Results indicated that the self-similarity hypothesis is valid for all the 200 catchments. Parameters required to construct E-GIUH for each of the catchments are provided. In addition, investigations were carried out on 42 gauges in two river basins (Mahanadi and Cauvery) to examine (i) validity of the hypothesis of "self-similarity" with change in DEM source, and (ii) the effect of DEM source (30m resolution Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and 90m resolution SRTM) on morphometric properties of the channel networks, equivalent H-S ratios and the corresponding equivalent GIUH constructed for the catchments. The results indicated that the hypothesis of "self-similarity" was valid for all the 42 catchments irrespective of the DEM source considered for the analysis. Further, SRTM DEM was found to be reliable (when compared to ASTER DEM) for extracting morphometric descriptors for the catchments. Overall the results indicated that uncertainty associated with DEM source cannot be ignored in hydrological studies involving E-GIUHs. To account for spatial variability in extreme rainfall, catchment of a target location (e.g., dam) is often delineated into sub-catchments, many of which could be ungauged. There is dearth of studies to predict E-GIUH for ungauged catchments. To address this, entropy based regionalization approach is proposed which utilizes catchment geomorphological descriptors suggested by Moussa (2008a). Effectiveness of the approach was evaluated by application to 55 catchments of reasonable size (< 5200 km2) in four Indian river basins (Mahanadi, Godavari, Krishna and Cauvery). The analysis yielded three regions, which were shown to be effective in arriving at E-GIUH for ungauged locations through leave-one-out cross-validation experiment. The PMP estimates necessary to arrive at PMF could be determined based on various approaches. Douglas and Barros (2003) proposed multifractal approach (MA) which is deemed to be effective as it considers both physics and statistics of the rainfall process, in contrast to the conventional approaches which are based either on statistical concepts or physical aspects. Their study was confined to eastern United States, and the MA has seldom been used elsewhere possibly due to its theoretical complexity. Investigations were carried out on Mahanadi and Godavari river basins to examine if PMP estimates corresponding to 1-day to 5-day durations obtained using this approach are consistent with estimates obtained using two commonly used approaches [Hershfield method (HM) and Storm Model approach (SMA)]. The SMA is based on physical aspects responsible for causing the storm event at target location, whereas HM is based on statistical concepts. For investigation, 0.5˚ resolution gridded rainfall data was considered, and PMP estimates obtained at grid scale were considered to prepare PMP maps for the basins and to arrive at PMP estimates for catchments in each of the basins. The results indicated that HM and SMA underestimate PMP (relative to MA) for larger durations (>3 days), as storm events whose accumulated rainfall forms the basis to arrive at PMP estimates are less likely to be uninterrupted. Further, among HM and SMA, PMP estimates based on the former method are found to be higher than those based on the latter method for majority of grids over all the durations. In addition, fractal maximum precipitation (FMP) and design PMP (DPMP) maps corresponding to various durations (and return periods) were prepared by applying multifractal approach to 0.25˚ gridded daily rainfall data (3890 grid points) covering the entire India (excluding high altitude Himalayan region). Results indicated that FMP/DPMP estimates cannot be obtained for 651 grid points using the approach. Majority of those 651 grid points are located in north-west (Rajasthan and Punjab states) and north-east of the country, and some parts of Maharashtra and Tamil Nadu states. In addition, a new cluster analysis based regionalization procedure is proposed to address issues associated with construction of envelope curve in Hershfield method, which helps in averting overestimation of PMP for majority of gauges (sites) in the study area. As engineering designs of large-scale hydrological structures are conventionally based on PMF derived from PMP, reduction in PMF estimates is likely to have economic implications. The procedure involves delineation of the study area into zones (regions) on the basis of extreme rainfall characteristics. Those zones are suggested to be considered as the basis for construction of envelope curve and estimation of PMP by Hershfield method. Application of the proposed procedure to India yielded 20 homogeneous PMP zones when regionalization was performed using global K-means (GKM) clustering algorithm for both 1-day and 2-day durations. When the analysis was repeated by considering global fuzzy c-means (GFCM) clustering algorithm, the procedure yielded 17 homogeneous PMP zones. Envelope curve constructed for each of the zones (resulting from GKM and GFCM cluster analysis) was considered as the basis to estimate PMP for each of the 0.25˚ resolution grid points in the zone. The following inferences were drawn from comparison of the PMP estimates with those obtained for the grid points by considering (a) a single envelope curve for the entire India, (b) two envelope curves (one prepared for grid points which are towards north of 20˚ latitude and another prepared for grid points towards south of the latitude) as considered by Rakhecha et al. (1992) and Rakhecha and Soman (1994). (i) PMP estimates obtained based on single/two envelope curve(s) for the entire India are significantly higher than estimates obtained using GKM- and GFCM-based zones (regions),(ii)The differences in GKM and GFCM zone-based PMP estimates appear marginal across India, except for south-eastern part of Rajasthan, Jharkhand and Maharashtra states (in the case of 1-day PMP) and north-eastern part of India (in the case of 2-day PMP), (iii) The differences in PMP estimates obtained based on single/two envelope curve(s) appear (a) marginal for most part of the country in the case of 1-day PMP, but (b) significant for northern part of the country in the case of 2-day PMP (owing to higher values for estimates obtained by fitting a single envelope curve for the entire India) Additional investigations were carried out by fitting river basin specific envelop curves to estimate 1-day and 2-day PMP for each of the 0.25˚ resolution grid points in four river basins (Mahanadi, Godavari, Krishna, Cauvery). Those PMP estimates were found to be generally lower than the corresponding estimates obtained based on single/two envelope curve(s) for the entire India. The river basin based 1-day PMP estimates were significantly lower in the case of Cauvery and Mahanadi river basins. Further it was noted that GKM- and GFCM-based 1-day PMP estimates could be higher/equal/lower than the corresponding PMP estimates obtained based on single/two envelope curve(s) for the entire India or river basin-based region. The GKM- and GFCM-based 2-day PMP estimates for grid points in the river basins are lower than (i) PMP estimates obtained based on single/two envelope curve(s) for the entire India in the case of all the river basins, (ii) river basin-based PMP estimates for Mahanadi, Krishna and Godavari basins, but higher than those for Cauvery river basin. As regions delineated using cluster analysis are based on attributes affecting/depicting rainfall, PMP estimates based on those regions could be considered reliable. On the other hand, river basin constitutes a geographical area demarcated based solely on area draining streamflow on land surface which has no effect on PMP, while other regions (India-, 20˚ latitude-based regions) that formed the basis for PMP estimation are based on political boundary which has no influence on PMP. The utility of E-GIUH and PMP estimates in arriving at probable maximum flood (PMF) for catchment of Hirakud dam in Mahanadi river basin (India) is demonstrated. Further, the sensitivity of PMF estimate to PMP estimates obtained by using Hershfield method, storm model approach and multifractal approach was examined for 1-day and 2-day durations. This involved (i) delineation of catchment of Hirakud dam into sub-catchments of reasonable size (< 5200 km2), (ii) construction of E-GIUH for the sub-catchments (using the proposed entropy based regionalization approach in the case of ungauged sub-catchments), (iii) derivation of 1-day and 2-day unit hydrographs for each of the sub-catchments from its E-GIUH, (iv) determination of 1-day and 2-day PMP estimates for each of the sub-catchments, (v) convoluting PMP estimate with unit hydrograph of corresponding effective duration to arrive at PMF for the sub-catchment, and (vi) routing the PMFs of the sub-catchments through the channel network in catchment of Hirakud dam to arrive at PMF at the dam location.

Dam failure due to extreme runoff events can cause major impact to human lives and property. In order to protect the life and property downstream of Kenyir catchment in Malaysia, this research aimed to estimate Probable Maximum Flood (PMF) using the Hydrological Model HEC-HMS version 4.8 accompanied with the Geographic Information System (ArcGIS). The methods adopted herein includes the collection of historical meteorological data and process it using Hershfield’s statistics for generating the Probable Maximum Precipitation (PMP). Results indicate that there are very good and good matching for both of calibration and validation respectively between the predicted and observed values. whereby for calibration, NSE and PBIAS of 0.873 and -1.76% are obtained while NSE and PBIAS of 0.679 and -8.78% are obtained for validation. Moreover, the simulated reservoir pool elevations are closely correlated to the observed pool elevations during both storm events. Although slight differences are observed from the comparison, it can be concluded that the differences are considered acceptable as the general trend is similar for those simulations. Furthermore, the developed hydrologic model is reliable and applicable for the Kenyir Hydrological Watershed.