scholarly journals Probabilistic analysis of the controls on groundwater depth using Copula Functions

2020 ◽  
Vol 51 (3) ◽  
pp. 406-422 ◽  
Author(s):  
Yifei Bai ◽  
Yi Wang ◽  
Yaning Chen ◽  
Leyuan Zhang
Keyword(s):  
Water Table ◽  
Joint Distribution ◽  
Time Series Data ◽  
Groundwater Resources ◽  
Distribution Functions ◽  
Groundwater Depth ◽  
Irrigation District ◽  
Series Data ◽  
Copula Functions ◽  
Groundwater Exploitation

Abstract Groundwater is an essential water resource in the Yarkant River Basin Irrigation District, which is the largest oasis in Xinjiang, China. This study used a novel approach to analyze the relationship between groundwater depth and three driving factors by developing Copula Functions from monthly time series data collected from 16 monitoring wells. More specifically, marginal distribution and joint distribution functions were established, and the conditional probabilities for three data ranges were calculated using both two- and three-dimensional Copula Functions. The developed statistical models showed that groundwater exploitation, runoff, and surface water irrigation significantly affected groundwater depth. The most significant effect on water table declines was associated with groundwater exploitation and lagged 1-month behind the groundwater withdrawals. The amount of runoff and irrigation were both inversely related to water table depth due to groundwater recharge. Frank Copula Functions were found to produce the best fit to the joint distribution of the variables and were used herein, allowing for the establishment of a detailed probability distribution of the change in groundwater depth under the combined effect of multiple controlling factors. The results provided key insights into how irrigation and groundwater withdrawals can be adjusted to effectively manage groundwater resources.

scholarly journals The Response of Groundwater Level to Climate Change and Human Activities in Baotou City, China

Water ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 1078
Author(s):  
Yingjie Cui ◽  
Zilong Liao ◽  
Yongfu Wei ◽  
Xiaomin Xu ◽  
Yifan Song ◽  
...  
Keyword(s):  
Climate Change ◽  
Human Activities ◽  
Groundwater Resources ◽  
Reduction Rate ◽  
Northern China ◽  
Groundwater Depth ◽  
Wavelet Coherence ◽  
Confined Water ◽  
Groundwater Exploitation ◽  
Decrease Rate

The response mechanism of groundwater to climate change and human activities in cities within arid and semi-arid regions, such as the Urban Planning Area of Baotou City (UPABC), northern China, is a complicated problem to understand. We analyzed the climate change relationships, including precipitation and temperature, and analyzed changes in human activities, such as groundwater consumption, and then statistically analyzed the main factors affecting groundwater depth. Furthermore, cross-wavelet and wavelet coherence methods were used to analyze the response relationship and hysteresis of groundwater depth to precipitation to better understand the groundwater depth response law. The results showed that the annual precipitation in the UPABC reduction rate was 3.3 mm/10 yr, and the annual average temperature increase rate was 0.43 °C/10 yr, from 1981 to 2017. The unconfined water decrease rate was 0.50 m/yr, and the confined water decrease rate was 0.7 m/yr. The unconfined and confined water depths were affected by precipitation and groundwater exploitation, respectively, with correlation coefficients of 0.58 and 0.57, respectively. The hysteresis of groundwater depth to precipitation was about 9–14 months. However, changes in groundwater depth, especially confined water depth, were greatly affected by groundwater exploitation. This reflected the imbalance in consumption and recharges in the UPABC, highlighting the long-term risk in areas relying on access to this resource. Therefore, arid inland zones of northern China, such as the UPABC, should pay more attention to the rational development of groundwater and strengthen the management and protection of groundwater resources.

scholarly journals Comments on Copula Functions and Their Relationship to Probability Density Functions

2020 ◽  
pp. 1115-1122
Author(s):  
Ahmed AL-Adilee ◽  
Ola Hassan
Keyword(s):  
Probability Density ◽  
Statistical Inference ◽  
Joint Distribution ◽  
Probability Density Functions ◽  
Distribution Functions ◽  
Density Functions ◽  
Copula Functions ◽  
Statistical Inferences ◽  
Dependence Structures

Copulas are very efficient functions in the field of statistics and specially in statistical inference. They are fundamental tools in the study of dependence structures and deriving their properties. These reasons motivated us to examine and show  various types of copula functions and their families. Also, we separately explain each method that is used to construct each copula in detail with different examples. There are various outcomes that show the copulas and their densities with respect to the joint distribution functions. The aim is to make copulas available to new researchers and readers who are interested in the modern phenomenon of statistical inferences.

scholarly journals Modelling the Cumulative Number of COVID-19 Cases

2021 ◽  
Vol 02 (02) ◽  
pp. 1-1
Author(s):  
Mieczysław Szyszkowicz ◽  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Series Data ◽  
Cumulative Number ◽  
Daily Time Series ◽  
Non Linear ◽  
The Usa ◽  
Daily Time

Each country has its own characteristics of COVID-19 infection trajectory and epidemic waves. Differences in government-implemented restrictions and social regulations result in variability of the virus transmissions and spread dynamics. This in turn results in various shapes of the growth function used to represent and describe the propagation of infection. Statistical methods are applied to fit non-linear functions to represent daily time-series data of the cumulative numbers of COVID-19 cases. The aim of this work is to fit various statistical models to the cumulative number of COVID-19 cases. Also to overview various types of the existed numerical methodologies. The data (since December 31, 2019) are available for almost each country in the world. As the examples, we used daily time-series data of the cumulative number of COVID-19 cases in Poland, Italy, Canada, and the USA. Non-linear approximations are applied to represent these time series data. The fitted functions allow us to investigate the dynamics of the pandemic. The constructed approximations are compositions of a few nonlinear functions, which describe the growth process of the COVID-19 infection trajectories. Two Gompertz functions and cumulative distribution functions (cdf) were estimated for the data of Poland and Italy (using the cdf for the normal distribution) and for the data of Canada and the USA (using the cdf for the gamma distribution). An analytical (parametric) functions representation of the number of COVID-19 cumulative cases is a useful tool to study the propagation of epidemics.

scholarly journals A simple integer-valued bilinear time series model

2006 ◽  
Vol 38 (2) ◽  
pp. 559-578 ◽  
Author(s):  
P. Doukhan ◽  
A. Latour ◽  
D. Oraichi
Keyword(s):  
Time Series ◽  
Method Of Moments ◽  
Joint Distribution ◽  
Time Series Data ◽  
Stationary Process ◽  
Existence Condition ◽  
Series Data ◽  
Bilinear Model ◽  
Numerical Examples ◽  
Strictly Stationary Process

In this paper, we extend the integer-valued model class to give a nonnegative integer-valued bilinear process, denoted by INBL(p,q,m,n), similar to the real-valued bilinear model. We demonstrate the existence of this strictly stationary process and give an existence condition for it. The estimation problem is discussed in the context of a particular simple case. The method of moments is applied and the asymptotic joint distribution of the estimators is given: it turns out to be a normal distribution. We present numerical examples and applications of the model to real time series data on meningitis and Escherichia coli infections.

scholarly journals Quantification of Groundwater Exploitation and Assessment of Water Quality Risk Perception in the Dar Es Salaam Quaternary Aquifer, Tanzania

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2552
Author(s):  
Kassim Mussa ◽  
Ibrahimu Mjemah ◽  
Kristine Walraevens
Keyword(s):  
Water Quality ◽  
Risk Perception ◽  
Time Series Data ◽  
Household Survey ◽  
Dar Es Salaam ◽  
Series Data ◽  
Groundwater Exploitation ◽  
Quaternary Aquifer ◽  
Quality Risk ◽  
Household Heads

This study quantified groundwater exploitation and assessed water quality risk perception in the Dar es Salaam quaternary aquifer through a socio-economic survey. Annual total groundwater exploitation was estimated, using the daily per capita consumption of groundwater derived from the household survey. A logistic regression analysis was performed to ascertain the influence of sex, marital status, education level, employment, income, and cost of water on groundwater quality risk perception. It was revealed that most residents of Dar es Salaam use groundwater as a main source of water supply. The results of this study further showed that 78% consider groundwater as a reliable source. Averting strategies for insufficient quantity of groundwater consist of minimizing less necessary water uses, while for poor quality, buying bottled water and water treatment by boiling and using chemicals. The chance for water quality risk perception is 0.205 times greater for married than unmarried household heads, and it is 623 times higher for employed versus unemployed household heads. To get an overall view of the importance of groundwater for domestic needs in Dar es Salaam it is imperative to combine a time series data of groundwater and surface water exploitation.

scholarly journals Dealing with drought in irrigated agriculture through insurance schemes: an application to an irrigation district in Southern Spain

2015 ◽  
Vol 13 (4) ◽  
pp. e0106 ◽  
Author(s):  
Jorge Ruiz ◽  
María Bielza ◽  
Alberto Garrido ◽  
Ana Iglesias
Keyword(s):  
Time Series Data ◽  
Hydrological Drought ◽  
Southern Spain ◽  
Irrigation District ◽  
Series Data ◽  
Irrigated Agriculture ◽  
Small Scale ◽  
Drought Risk ◽  
Insurance Premiums ◽  
Drought Insurance

<p class="Abstract">Hydrological drought is expected to have an increasing impact on both crop and fruit yields in arid and semi-arid regions. Some existing crop insurance schemes provide coverage against water deficits in rain-fed agriculture. The Prevented Planting Program in the USA covers against drought for irrigated agriculture. However, drought insurance for irrigated agriculture is still a challenge for companies and institutions because of the complexity of the design and implementation of this type of insurance. Few studies have attempted to evaluate the risk of loss due to irrigation water scarcity using both stand-alone production functions and crop simulation models. This paper’s contributions are that it evaluates the suitability of AquaCrop for calculating drought insurance premiums for irrigated agriculture and that it discusses contract conditions and insurance design for hydrological drought risk coverage as part of a traditional insurance product, with on-field loss assessment in combination with a trigger index. This method was applied to an irrigation district in southern Spain. Our insurance premium calculation showed that it is feasible to apply this method provided that its data requirements are met, such as a large enough set of reliable small-scale yield and irrigation time series data, especially soil data, to calibrate AquaCrop. The choice of a trigger index should not be underestimated because it proved to have a decisive influence on insurance premiums and indemnities. Our discussion of the contract conditions shows that hydrological drought insurance must comply with a series of constraints in order to avoid moral hazard and basis risk.</p>

scholarly journals A simple integer-valued bilinear time series model

2006 ◽  
Vol 38 (02) ◽  
pp. 559-578 ◽  
Author(s):  
P. Doukhan ◽  
A. Latour ◽  
D. Oraichi
Keyword(s):  
Time Series ◽  
Method Of Moments ◽  
Joint Distribution ◽  
Time Series Data ◽  
Stationary Process ◽  
Existence Condition ◽  
Series Data ◽  
Bilinear Model ◽  
Numerical Examples ◽  
Strictly Stationary Process

In this paper, we extend the integer-valued model class to give a nonnegative integer-valued bilinear process, denoted by INBL(p,q,m,n), similar to the real-valued bilinear model. We demonstrate the existence of this strictly stationary process and give an existence condition for it. The estimation problem is discussed in the context of a particular simple case. The method of moments is applied and the asymptotic joint distribution of the estimators is given: it turns out to be a normal distribution. We present numerical examples and applications of the model to real time series data on meningitis and Escherichia coli infections.

A method of estimating sequential average unsaturated zone travel times from precipitation and water table level time series data

2017 ◽  
Vol 554 ◽  
pp. 570-581 ◽  
Author(s):  
Jina Jeong ◽  
Eungyu Park ◽  
Weon Shik Han ◽  
Kue-Young Kim ◽  
Junho Oh ◽  
...  
Keyword(s):  
Time Series ◽  
Water Table ◽  
Unsaturated Zone ◽  
Time Series Data ◽  
Series Data ◽  
Travel Times ◽  
Water Table Level
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