scholarly journals Universal Power Law for Relationship between Rainfall Kinetic Energy and Rainfall Intensity

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Seung Sook Shin ◽  
Sang Deog Park ◽  
Byoung Koo Choi
Keyword(s):  
Kinetic Energy ◽  
Power Law ◽  
Rainfall Intensity ◽  
Mathematical Expression ◽  
Power Laws ◽  
Relative Difference ◽  
Universal Power Law ◽  
Average Rainfall ◽  
Independent Variable ◽  
Logarithmic Functions

Rainfall kinetic energy has been linked to linear, exponential, logarithmic, and power-law functions using rainfall intensity as an independent variable. The power law is the most suitable mathematical expression used to relate rainfall kinetic energy and rainfall intensity. In evaluating the rainfall kinetic energy, the empirical power laws have shown a larger deviation than other functions. In this study, universal power law between rainfall kinetic energy and rainfall intensity was proposed based on the rainfall power theory under an ideal assumption that drop-size is uniformly distributed in constant rainfall intensity. An exponent of the proposed power law was 11/9 and coefficient was estimated at 10.3 from the empirical equations of the existing power-law relation. The rainfall kinetic energy calculated by universal power law showed >95% concordance rate in comparison to the average values calculated from exponential and logarithmic functions used in soil erosion model such as USLE, RUSLE, EUROSEM, and SEMMA and <5% relative difference as compared to the average rainfall kinetic energies calculated by other empirical functions. Therefore, it is expected that power law of ideal assumption may be utilized as a universal power law in evaluating rainfall kinetic energy.

Estimating Errors in Sizing LID Device and Overflow Prediction Using the Intensity-Duration-Frequency Method

Water ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1853
Author(s):  
Tang ◽  
Xu ◽  
Jia ◽  
Luo ◽  
Shao
Keyword(s):  
Rainfall Intensity ◽  
Relative Difference ◽  
Absolute Difference ◽  
Storm Event ◽  
Process Data ◽  
Frequency Method ◽  
Average Rainfall ◽  
Standard Deviations ◽  
Intensity Duration Frequency ◽  
Design Depth

Low impact development (LID) devices or green infrastructures have been advocated for urban stormwater management worldwide. Currently, the design and evaluation of LID devices adopt the Intensity-Duration-Frequency (IDF) method, which employs the average rainfall intensity. However, due to variations of rainfall intensity during a storm event, using average rainfall intensity may generate certain errors when designing a LID device. This paper presents an analytical study to calculate the magnitude of such errors with respect to LID device design and associated device performance evaluation. The normal distribution rainfall (NDR) with different standard deviations was employed to represent realistic rainfall processes. Compared with NDR method, the error in sizing the LID device was determined using the IDF method. Moreover, the overflow difference calculated using the IDF method was evaluated. We employed a programmed hydrological model to simulate different design scenarios. Using storm data from 31 regions with different climatic conditions in continental China, the results showed that different rainfall distributions (as represented by standard deviations (σ) of 5, 3, and 2) have little influence on the design depth of LID devices in most regions. The relative difference in design depth using IDF method was less than 1.00% in humid areas, −0.61% to 3.97% in semi-humid areas, and the significant error was 46.13% in arid areas. The maximum absolute difference in design depth resulting from the IDF method was 2.8 cm. For a LID device designed for storms with a 2-year recurrence interval, when meeting for the 5-year storm, the relative differences in calculated overflow volume using IDF method ranged from 19.8% to 95.3%, while those for the 20-year storm ranged from 7.4% to 40.5%. The average relative difference of the estimated overflow volume was 29.9% under a 5-year storm, and 12.0% under a 20-year storm. The relative difference in calculated overflow volumes using IDF method showed a decreasing tendency from northwest to southeast. Findings from this study suggest that the existing IDF method is adequate for use in sizing LID devices when the design storm is not usually very intense. However, accurate rainfall process data are required to estimate the overflow volume under large storms.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals Maximal modularity and the optimal size of parliaments

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Luca Gamberi ◽  
Yanik-Pascal Förster ◽  
Evan Tzanis ◽  
Alessia Annibale ◽  
Pierpaolo Vivo
Keyword(s):  
Power Law ◽  
Real World ◽  
Empirical Data ◽  
Random Network ◽  
Functional Relation ◽  
Optimal Size ◽  
Real World Data ◽  
Universal Power Law ◽  
The Empirical Analysis ◽  
Democratic Country

AbstractAn important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent equal to 1/3, between the size of an elected parliament and the country’s population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. In this work, we analyse this intriguing regularity using tools from complex networks theory. We model the population of a democratic country as a random network, drawn from a growth model, where each node is assigned a constituency membership sampled from an available set of size D. We calculate analytically the modularity of the population and find that its functional relation with the number of constituencies is strongly non-monotonic, exhibiting a maximum that depends on the population size. The criterion of maximal modularity allows us to predict that the number of representatives should scale as a power-law in the size of the population, a finding that is qualitatively confirmed by the empirical analysis of real-world data.

Effect of Adsorbed Water and Temperature on the Universal Power Law Behavior of Lepidocrocite-Type Alkali Titanate Ceramics

2021 ◽  
Author(s):  
Saichon Sriphan ◽  
Phieraya Pulphol ◽  
Thitirat Charoonsuk ◽  
Tosapol Maluangnont ◽  
Naratip Vittayakorn
Keyword(s):  
Power Law ◽  
Adsorbed Water ◽  
Universal Power Law ◽  
Titanate Ceramics

scholarly journals Power Laws in Economics: An Introduction

2016 ◽  
Vol 30 (1) ◽  
pp. 185-206 ◽  
Author(s):  
Xavier Gabaix
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Power Laws ◽  
Economic Fluctuations ◽  
Formal Definition ◽  
Empirical Power

Many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. However a series of power laws in economics do count as true and nontrivial quantitative laws—and they are not only established empirically, but also understood theoretically. I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock market. I summarize some of the theoretical explanations that have been proposed. I suggest that power laws help us explain many economic phenomena, including aggregate economic fluctuations. I hope to clarify why power laws are so special, and to demonstrate their utility. In conclusion, I list some power-law-related economic enigmas that demand further exploration. A formal definition may be useful.

Rainfall intensity–kinetic energy relationships: a critical literature appraisal

2002 ◽  
Vol 261 (1-4) ◽  
pp. 1-23 ◽  
Author(s):  
A.I.J.M van Dijk ◽  
L.A Bruijnzeel ◽  
C.J Rosewell
Keyword(s):  
Kinetic Energy ◽  
Rainfall Intensity ◽  
Energy Relationships ◽  
Critical Literature

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

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