scholarly journals Study of Unbiased Plotting Position Formulae for the Generalized Extreme Value (GEV) Distribution

2021 ◽  
Vol 6 (4) ◽  
pp. 94-99
Author(s):  
Itolima Ologhadien
Keyword(s):  
Distribution Model ◽  
Hydraulic Structures ◽  
Accurate Estimation ◽  
Gev Distribution ◽  
Pearson Type ◽  
Type 3 ◽  
Best Fit ◽  
River Niger ◽  
Annual Maximum Series

The determination of appropriate quantile relations between the magnitude of extreme events and the corresponding exceedance probabilities is a prerequisite for optimum design of hydraulic structures. Various plotting position formulae have been proposed for estimating the exceedance probabilities or recurrence in. In this study, eight plotting position formulae recommended for GEV distribution were used for estimating the exceedance probabilities of annual maximum series of River Niger at Baro, Kouroussa and Shintaku hydrological stations. The performance measures of PPCC, RRMSE, PBIAS, MAE and NSE were calculated by applying their individual equations to each pair of observed AMS, arranged in ascending order, and exceedance probabilities calculated using each plotting positions. The result of the study show that Weibull was the best plotting position formula, seconded by Beard and thirdly, In – na and Ngugen. This study underscores the necessity to accurately size water infrastructure. In a recent paper, the author found GEV distribution the best – fit probability distribution model in Nigeria. Thus, the need to develop indepth understanding and accurate estimation of exceedance probabilities and return periods using the GEV distribution. Furthermore, this paper recommends similar studies to be conducted for Pearson Type 3(PR3) and Log Pearson Type 3 (LP3) distributions.

scholarly journals Best-Fit Probability Distribution Model for Rainfall Frequency Analysis of Three Cities in South Eastern Nigeria

2017 ◽  
Vol 1 (1) ◽  
pp. 34-42 ◽  
Author(s):  
A. I. Agbonaye ◽  
O. C. Izinyon
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Distribution Model ◽  
Hydraulic Structures ◽  
Annual Maximum ◽  
Rainfall Frequency ◽  
Pearson Type ◽  
Rainfall Frequency Analysis ◽  
Best Fit ◽  
Annual Maximum Series

Rainfall frequency analysis is the estimation of how often rainfall of specified magnitude will occur. Such analyses are helpful in defining policies relating to water resources management. It serves as the source of data for flood hazard mitigation and the design of hydraulic structures aimed at reducing losses due to floods action. In this study rainfall frequency analysis for three (3) cities in South Eastern Nigeria were carried out using annual maximum series of daily rainfall data for the stations. The objective of the study was to select the probability distribution model from among six commonly used probability distribution models namely: Generalized Extreme value distribution (GEV), Extreme value type I distribution (EVI), Generalized Pareto distribution (GPA), Pearson Type III (PIII), log Normal (LN) and Log Pearson Type III (LP111) distributions. These distributions were applied to annual maximum series of daily precipitation data at each station using the parameters of the distributions estimated by the method of moments. The best fit probability distribution model at each location was selected based on the results of seven goodness of fit tests entry: root mean square error (RMSE), relative root mean square error (RRMSE), mean absolute deviation index (MADI) and probability plot correlation coefficient (PPCC), Maximum Absolute Error (MAE), Chi square test and D- Index and a scoring and ranking scheme. Our results indicate that the best fit probability distribution model at all study locations is GEV and this was used to forecast rainfall return values for the stations for return periods of between 5years and 500years. The values obtained are useful for planning, design and management of hydraulic structures for flood mitigation and prevention of flood damage at the location.

scholarly journals Evaluation of Plotting Position Formulae for Pearson Type 3 Distribution in Three Hydrological Stations on the Niger River

2021 ◽  
pp. 117-128
Author(s):  
Itolima Ologhadien
Keyword(s):  
Goodness Of Fit ◽  
Absolute Error ◽  
Distribution Model ◽  
Pearson Type ◽  
Simulated Series ◽  
The Individual ◽  
Individual Scores ◽  
Type 3 ◽  
River Niger ◽  
Relative Root

In this study, eight unbiased plotting position formulae recommended for Pearson Type 3 distribution were evaluated by comparing the simulated series of each formula with the annual maximum series (AMS) of River Niger at Baro, Koroussa and Shintaku hydrological stations, each having data length of 51years, 53 years and 58 years respectively. The parameters of Pearson Type 3 distribution were computed by the method of moments with corrections for skewness. While the fitting of Pearson Type 3 distribution proceeds with the development of flood – return period (Q-T) relationship, followed by application of the derived Q- T relation to compute simulated discharges for comparison with AMS of the study stations. The plotting position formulae were evaluated on the basis of optimum values of the statistically goodness-of-fit of probability plot correlation coefficient (PPCC), relative root mean square error (RRMSE), percent bias (PBIAS), mean absolute error (MAE) and Nash-sutcliffe efficiency (NSE), across the stations. The plotting position formulae were ranked on scale of 1 to 8. Thus a plotting formula that best simulates the empirical observations using the goodness-of-measures was scored “1” and so on. The individual scores per plotting position were summed across the gof tests to obtain the total score.    The study show that Chegodayev is the best plotting position formula for Baro, Weibull is the best plotting position Formula for Kourassou and Shintaku hydrological stations. The overall performances of the eight plotting position formulae across the hydrological stations show that weibull distribution is the overall best having scored 27, seconded by Chegodayev with 30 and thirdly, Beard with 38. The Pearson Type 3 distribution had been found one of the best probability distribution model of flood flow in Nigeria and this study was conducted to gain in-depth knowledge of the distribution. Finally, this study recommends extension of the studies to Log-Pearson Type 3 distribution.

scholarly journals Flood Flow Probability Distribution Model Selection on Niger/Benue River Basins in Nigeria

2021 ◽  
pp. 76-94
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
River Basins ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Distribution Model ◽  
Distribution Models ◽  
Type Iii ◽  
Pearson Type ◽  
Best Fit

Flood frequency analysis is a crucial component of flood risk management which seeks to establish a quantile relationship between peak discharges and their exceedance (or non-exceedance) probabilities, for planning, design and management of infrastructure in river basins. This paper evaluates the performance of five probability distribution models using the method of moments for parameter estimation, with five GoF-tests and Q-Q plots for selection of best –fit- distribution. The probability distributions models employed are; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value( GEV). The five statistical goodness – of – fit tests, namely; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR) were used to identify the most suitable distribution models. The study was conducted using annual maximum series of nine gauge stations in both Benue and Niger River Basins in Nigeria. The study reveals that GEV was the best – fit distribution in six gauging stations, LP3 was best – fit distribution in two gauging stations, and PR3 is best- fit distribution in one gauging station. This study has provided a significant contribution to knowledge in the choice of distribution models for predicting extreme hydrological events for design of water infrastructure in Nigeria. It is recommended that GEV, PR3 and LP3 should be considered in the development of regional flood frequency using the existing hydrological map of Nigeria.

scholarly journals Determination of Environmental Factors for the Implementation of the Exploitability Index in Industrial Aggregate Mining Using Multi-Criteria Analysis

2021 ◽  
Vol 10 (4) ◽  
pp. 196
Author(s):  
Julio Manuel de Luis-Ruiz ◽  
Benito Ramiro Salas-Menocal ◽  
Gema Fernández-Maroto ◽  
Rubén Pérez-Álvarez ◽  
Raúl Pereda-García
Keyword(s):  
Environmental Factors ◽  
Environmental Factor ◽  
Human Life ◽  
Accurate Estimation ◽  
Analytic Hierarchy ◽  
Main Components ◽  
Hierarchy Process ◽  
Made In

The quality of human life is linked to the exploitation of mining resources. The Exploitability Index (EI) assesses the actual possibilities to enable a mine according to several factors. The environment is one of the most constraining ones, but its analysis is made in a shallow way. This research is focused on its determination, according to a new preliminary methodology that sets the main components of the environmental impact related to the development of an exploitation of industrial minerals and its weighting according to the Analytic Hierarchy Process (AHP). It is applied to the case of the ophitic outcrops in Cantabria (Spain). Twelve components are proposed and weighted with the AHP and an algorithm that allows for assigning a normalized value for the environmental factor to each deposit. Geographic Information Systems (GISs) are applied, allowing us to map a large number of components of the environmental factors. This provides a much more accurate estimation of the environmental factor, with respect to reality, and improves the traditional methodology in a substantial way. It can be established as a methodology for mining spaces planning, but it is suitable for other contexts, and it raises developing the environmental analysis before selecting the outcrop to be exploited.

scholarly journals Reactor rate modulation oscillation analysis with two detectors in Double Chooz

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
T. Abrahão ◽  
◽  
H. Almazan ◽  
J. C. dos Anjos ◽  
S. Appel ◽  
...  
Keyword(s):  
Reactor Power ◽  
Background Model ◽  
Fast Neutrons ◽  
Mixing Angle ◽  
Oscillation Analysis ◽  
Central Value ◽  
Double Chooz ◽  
Model Independent ◽  
Best Fit

Abstract A θ13 oscillation analysis based on the observed antineutrino rates at the Double Chooz far and near detectors for different reactor power conditions is presented. This approach provides a so far unique simultaneous determination of θ13 and the total background rates without relying on any assumptions on the specific background contributions. The analysis comprises 865 days of data collected in both detectors with at least one reactor in operation. The oscillation results are enhanced by the use of 24.06 days (12.74 days) of reactor-off data in the far (near) detector. The analysis considers the $$ {\overline{\nu}}_e $$ ν ¯ e interactions up to a visible energy of 8.5 MeV, using the events at higher energies to build a cosmogenic background model considering fast-neutrons interactions and 9Li decays. The background-model-independent determination of the mixing angle yields sin2(2θ13) = 0.094 ± 0.017, being the best-fit total background rates fully consistent with the cosmogenic background model. A second oscillation analysis is also performed constraining the total background rates to the cosmogenic background estimates. While the central value is not significantly modified due to the consistency between the reactor-off data and the background estimates, the addition of the background model reduces the uncertainty on θ13 to 0.015. Along with the oscillation results, the normalization of the anti-neutrino rate is measured with a precision of 0.86%, reducing the 1.43% uncertainty associated to the expectation.

Determination of the Discharge Coefficient of a Thin-Walled Orifice Used in Hydrostatic Bearings

2005 ◽  
Vol 127 (3) ◽  
pp. 679-684 ◽  
Author(s):  
S. Charles ◽  
O. Bonneau ◽  
J. Fre^ne
Keyword(s):  
Discharge Coefficient ◽  
Ad Hoc ◽  
Thrust Bearing ◽  
Accurate Estimation ◽  
Hydrostatic Bearing ◽  
Hydrostatic Bearings ◽  
Flow Through ◽  
Thin Walled ◽  
Experimental Bench

The characteristics of hydrostatic bearings can be influenced by the compensating device they use, for example, a thin-walled orifice (diaphragm). The flow through the orifice is given by a law where an ad hoc discharge coefficient appears, and, in order to guarantee the characteristics of the hydrostatic bearing, this coefficient must be calibrated. The aim of this work is to provide an accurate estimation of the discharge coefficient under specific conditions. Therefore an experimental bench was designed and a numerical model was carried out. The results obtained then by the experimental and theoretical approach were compared with the values given by the literature. Finally, the influence of the discharge coefficient on the behavior of a thrust bearing is examined.

Flood estimation for ungauged catchments in the Philippines using multiple archival data records

2021 ◽  
Author(s):  
Trevor Hoey ◽  
Pamela Tolentino ◽  
Esmael Guardian ◽  
Richard Williams ◽  
Richard Boothroyd ◽  
...  
Keyword(s):  
Catchment Area ◽  
Daily Rainfall ◽  
The Philippines ◽  
Data Availability ◽  
Estimation Methods ◽  
Annual Maximum ◽  
Ungauged Catchments ◽  
Pearson Type ◽  
Flood Estimation ◽  
Best Fit

<p>Assessment of flood and drought risks, and changes to these risks under climate change, is a critical issue worldwide. Statistical methods are commonly used in data-rich regions to estimate the magnitudes of river floods of specified return period at ungauged sites. However, data availability can be a major constraint on reliable estimation of flood and drought magnitudes, particularly in the Global South. Statistical flood and drought magnitude estimation methods rely on the availability of sufficiently long data records from sites that are representative of the hydrological region of interest. In the Philippines, although over 1000 locations have been identified where flow records have been collected at some time, very few records exist of over 20 years duration and only a limited number of sites are currently being gauged. We collated data from three archival sources: (1) Division of Irrigation, Surface Water Supply (SWS) (1908-22; 257 sites in total); (2) Japan International Cooperation Agency (JICA) (1955-91; 90 sites); and, (3) Bureau of Research and Standards (BRS) (1957-2018; 181 sites). From these data sets, 176 contained sufficiently long and high quality records to be analysed. Series of annual maximum floods were fit using L-moments with Weibull, Log-Pearson Type III and Generalised Logistic Distributions, the best-fit of these being used to estimate 2-, 10- and 100-year flood events, Q<sub>2</sub>, Q<sub>10</sub> and Q<sub>100</sub>. Predictive equations were developed using catchment area, several measures of annual and extreme precipitation, catchment geometry and land-use. Analysis took place nationally, and also for groups of hydrologically similar regions, based on similar flood growth curve shapes, across the Philippines. Overall, the best fit equations use a combination of two predictor variables, catchment area and the median annual maximum daily rainfall. The national equations have R<sup>2</sup> of 0.55-0.65, being higher for shorter return periods, and regional groupings R<sup>2</sup> are 0.60-0.77 for Q<sub>10</sub>. These coefficients of determination, R<sup>2</sup>, are lower than in some comprehensive studies worldwide reflecting in part the short individual flow records. Standard errors of residuals for the equations are between 0.19 and 0.51 (log<sub>10</sub> units), which lead to significant uncertainty in flood estimation for water resource and flood risk management purposes. Improving the predictions requires further analysis of hydrograph shape across the different climate types, defined by seasonal rainfall distributions, in the Philippines and between catchments of different size. The results here represent the most comprehensive study to date of flood magnitudes in the Philippines and are being incorporated into guidance for river managers alongside new assessments of river channel change across the country. The analysis illustrates the potential, and the limitations, for combining information from multiple data sources and short individual records to generate reliable estimates of flow extremes.</p>

Exploring the use of gpr and satellite-based snow data for snowmelt runoff predictions

2021 ◽  
Author(s):  
Ilaria Clemenzi ◽  
David Gustafsson ◽  
Jie Zhang ◽  
Björn Norell ◽  
Wolf Marchand ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Spatial Distribution ◽  
Data Assimilation ◽  
Snow Water Equivalent ◽  
Distribution Model ◽  
Accurate Estimation ◽  
Snowmelt Runoff ◽  
Snow Water ◽  
Snow Distribution ◽  
The Impact

<p>Snow in the mountains is the result of the interplay between meteorological conditions, e.g., precipitation, wind and solar radiation, and landscape features, e.g., vegetation and topography. For this reason, it is highly variable in time and space. It represents an important water storage for several sectors of the society including tourism, ecology and hydropower. The estimation of the amount of snow stored in winter and available in the form of snowmelt runoff can be strategic for their sustainability. In the hydropower sector, for example, the occurrence of higher snow and snowmelt runoff volumes at the end of the spring and in the early summer compared to the estimated one can substantially impact reservoir regulation with energy and economical losses. An accurate estimation of the snow volumes and their spatial and temporal distribution is thus essential for spring flood runoff prediction. Despite the increasing effort in the development of new acquisition techniques, the availability of extensive and representative snow and density measurements for snow water equivalent estimations is still limited. Hydrological models in combination with data assimilation of ground or remote sensing observations is a way to overcome these limitations. However, the impact of using different types of snow observations on snowmelt runoff predictions is, little understood. In this study we investigated the potential of assimilating in situ and remote sensing snow observations to improve snow water equivalent estimates and snowmelt runoff predictions. We modelled the seasonal snow water equivalent distribution in the Lake Överuman catchment, Northern Sweden, which is used for hydropower production. Simulations were performed using the semi-distributed hydrological model HYPE for the snow seasons 2017-2020. For this purpose, a snowfall distribution model based on wind-shelter factors was included to represent snow spatial distribution within model units. The units consist of 2.5x2.5 km<sup>2</sup> grid cells, which were further divided into hydrological response units based on elevation, vegetation and aspect. The impact on the estimation of the total catchment mean snow water equivalent and snowmelt runoff volume were evaluated using for data assimilation, gpr-based snow water equivalent data acquired along survey lines in the catchment in the early spring of the four years, snow water equivalent data obtained by a machine learning algorithm and satellite-based fractional snow cover data. Results show that the wind-shelter based snow distribution model was able to represent a similar spatial distribution as the gpr survey lines, when assessed on the catchment level. Deviations in the model performance within and between specific gpr survey lines indicate issues with the spatial distribution of input precipitation, and/or need to include explicit representation of snow drift between model units. The explicit snow distribution model also improved runoff simulations, and the ability of the model to improve forecast through data assimilation.</p>

Variation in the respiratory quotient of birds and implications for indirect calorimetry using measurements of carbon dioxide production

1995 ◽  
Vol 198 (1) ◽  
pp. 213-219 ◽  
Author(s):  
G Walsberg ◽  
B Wolf
Keyword(s):  
Carbon Dioxide ◽  
Power Consumption ◽  
Indirect Calorimetry ◽  
Respiratory Quotient ◽  
Current Knowledge ◽  
Bird Species ◽  
Passer Domesticus ◽  
Carbon Dioxide Production ◽  
Accurate Estimation

Determination of animal power consumption by indirect calorimetry relies upon accurate estimation of the thermal equivalent of oxygen consumed or carbon dioxide produced. This estimate is typically based upon measurement or assumption of the respiratory quotient (RQ), the ratio of CO2 produced to O2 consumed. This ratio is used to indicate the mixture of lipids, carbohydrates and proteins in the metabolic substrate. In this analysis, we report the RQ for two bird species, Passer domesticus and Auriparus flaviceps, under several dietary and fasting regimes. RQ commonly differed substantially from those typically assumed in studies of energy metabolism and often included values below those explainable by current knowledge. Errors that could result from these unexpected RQ values can be large and could present the primary limit to the accuracy of power consumption estimates based upon measurement of carbon dioxide production.

scholarly journals A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

2016 ◽  
Vol 11 (1) ◽  
pp. 432-440 ◽  
Author(s):  
M. T. Amin ◽  
M. Rizwan ◽  
A. A. Alazba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Future Research ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Northern Regions ◽  
Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

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