scholarly journals New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Jescica Spannenberg ◽  
Abdon Atangana ◽  
P.D. Vermeulen
Keyword(s):  
Groundwater Recharge ◽  
Memory Effect ◽  
Real World ◽  
Numerical Solutions ◽  
Estimation Methods ◽  
Adequate Model ◽  
Space And Time ◽  
Non Linear ◽  
Recharge Estimation ◽  
Geological Formations

AbstractFractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

Comparison of groundwater recharge estimation methods for the semi-arid Nyamandhlovu area, Zimbabwe

2009 ◽  
Vol 17 (6) ◽  
pp. 1427-1441 ◽  
Author(s):  
Tenant Sibanda ◽  
Johannes C. Nonner ◽  
Stefan Uhlenbrook
Keyword(s):  
Groundwater Recharge ◽  
Estimation Methods ◽  
Recharge Estimation ◽  
Semi Arid

scholarly journals The State-of-the-Art Estimation of Groundwater Recharge and Water Balance with a Special Emphasis on India: A Critical Review

2021 ◽  
Vol 14 (1) ◽  
pp. 340
Author(s):  
Pazhuparambil Jayarajan Sajil Kumar ◽  
Michael Schneider ◽  
Lakshmanan Elango
Keyword(s):  
Water Balance ◽  
Groundwater Recharge ◽  
State Of The Art ◽  
Climatic Conditions ◽  
Estimation Methods ◽  
Sustainable Water Management ◽  
Factors Affecting ◽  
Aquifer Systems ◽  
Recharge Estimation ◽  
Water Level Measurements

Groundwater recharge estimation is essential for sustainable water management and water supply schemes. In this paper, we review groundwater recharge estimation techniques and identify the appropriate methods by considering India’s hydrological and climatic conditions. Significant components of recharge, factors affecting groundwater recharge, aquifer systems of India, and historical groundwater recharge estimation practices are reviewed. Currently used recharge estimation methods are assessed based on case studies. The most popular estimation methods are studied and compared based on their application in various regions. It is observed that the accuracy of the recharge estimates is largely influenced by false assumptions, the possibility of erroneous measurements, a potential lack of reliable data, and a variety of problems associated with parameter estimation. The suitability of different methods for a region is found to depend on time and space considerations, the objective of the study, hydrogeological condition, and availability of data. In Indian conditions, it is suggested to use water table fluctuation and water balance methods for the recharge estimation, provided that accurate water level measurements are assured.

scholarly journals Higher-order temporal network effects through triplet evolution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Qing Yao ◽  
Bingsheng Chen ◽  
Tim S. Evans ◽  
Kim Christensen
Keyword(s):  
Real World ◽  
Link Prediction ◽  
Higher Order ◽  
Prediction Algorithm ◽  
Interaction Patterns ◽  
Temporal Networks ◽  
World Systems ◽  
Order Interaction ◽  
Space And Time ◽  
Pairwise Interactions

AbstractWe study the evolution of networks through ‘triplets’—three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm’s performance on four temporal networks, comparing our approach against ten other link prediction methods. Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.

Improving the External Validity of Conjoint Analysis: The Essential Role of Profile Distribution

2021 ◽  
pp. 1-27 ◽  
Author(s):  
Brandon de la Cuesta ◽  
Naoki Egami ◽  
Kosuke Imai
Keyword(s):  
Conjoint Analysis ◽  
Real World ◽  
External Validity ◽  
Causal Effect ◽  
The Other ◽  
Estimation Methods ◽  
Social Scientists ◽  
Actual Distribution ◽  
Open Source Software Package ◽  
Profile Distribution

Abstract Conjoint analysis has become popular among social scientists for measuring multidimensional preferences. When analyzing such experiments, researchers often focus on the average marginal component effect (AMCE), which represents the causal effect of a single profile attribute while averaging over the remaining attributes. What has been overlooked, however, is the fact that the AMCE critically relies upon the distribution of the other attributes used for the averaging. Although most experiments employ the uniform distribution, which equally weights each profile, both the actual distribution of profiles in the real world and the distribution of theoretical interest are often far from uniform. This mismatch can severely compromise the external validity of conjoint analysis. We empirically demonstrate that estimates of the AMCE can be substantially different when averaging over the target profile distribution instead of uniform. We propose new experimental designs and estimation methods that incorporate substantive knowledge about the profile distribution. We illustrate our methodology through two empirical applications, one using a real-world distribution and the other based on a counterfactual distribution motivated by a theoretical consideration. The proposed methodology is implemented through an open-source software package.

scholarly journals Groundwater recharge estimation in arid hardrock-alluvium aquifers using combined water-table fluctuation and groundwater balance approaches

2017 ◽  
Vol 31 (19) ◽  
pp. 3437-3451 ◽  
Author(s):  
Azizallah Izady ◽  
Osman A.E. Abdalla ◽  
Ata Joodavi ◽  
Akbar Karimi ◽  
Mingjie Chen ◽  
...  
Keyword(s):  
Groundwater Recharge ◽  
Water Table ◽  
Groundwater Balance ◽  
Water Table Fluctuation ◽  
Recharge Estimation

scholarly journals Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 760 ◽  
Author(s):  
Johan Anderson ◽  
Sara Moradi ◽  
Tariq Rafiq
Keyword(s):  
Anomalous Diffusion ◽  
Transport Coefficient ◽  
Numerical Solutions ◽  
Distribution Functions ◽  
Space Distribution ◽  
Non Linear ◽  
Non Local ◽  
Local Transport ◽  
Fokker Planck Equations ◽  
Fokker Planck

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

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