scholarly journals Probability Models and Statistical Tests for Extreme Precipitation Based on Generalized Negative Binomial Distributions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 604 ◽  
Author(s):  
Victor Korolev ◽  
Andrey Gorshenin
Keyword(s):  
Negative Binomial ◽  
Daily Precipitation ◽  
Global Climate ◽  
Statistical Tests ◽  
Real Data ◽  
Total Precipitation ◽  
Climate Trends ◽  
Probability Models ◽  
Precipitation Volume ◽  
Precipitation Total

Mathematical models are proposed for statistical regularities of maximum daily precipitation within a wet period and total precipitation volume per wet period. The proposed models are based on the generalized negative binomial (GNB) distribution of the duration of a wet period. The GNB distribution is a mixed Poisson distribution, the mixing distribution being generalized gamma (GG). The GNB distribution demonstrates excellent fit with real data of durations of wet periods measured in days. By means of limit theorems for statistics constructed from samples with random sizes having the GNB distribution, asymptotic approximations are proposed for the distributions of maximum daily precipitation volume within a wet period and total precipitation volume for a wet period. It is shown that the exponent power parameter in the mixing GG distribution matches slow global climate trends. The bounds for the accuracy of the proposed approximations are presented. Several tests for daily precipitation, total precipitation volume and precipitation intensities to be abnormally extremal are proposed and compared to the traditional PoT-method. The results of the application of this test to real data are presented.

scholarly journals Statistical Tests for Extreme Precipitation Volumes

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 648 ◽  
Author(s):  
Victor Korolev ◽  
Andrey Gorshenin ◽  
Konstatin Belyaev
Keyword(s):  
Extreme Precipitation ◽  
Negative Binomial ◽  
Daily Precipitation ◽  
Statistical Tests ◽  
Real Data ◽  
Total Precipitation ◽  
The Novel ◽  
The Real ◽  
Precipitation Volume

The analysis of the real observations of precipitation based on the novel statistical approach using the negative binomial distribution as a model for describing the random duration of a wet period is considered and discussed. The study shows that this distribution fits very well to the real observations and generalized standard methods used in meteorology to detect an extreme volume of precipitation. It also provides a theoretical base for the determination of asymptotic approximations to the distributions of the maximum daily precipitation volume within a wet period, as well as the total precipitation volume over a wet period. The paper demonstrates that the relation of the unique precipitation volume, having the gamma distribution, divided by the total precipitation volume taken over the wet period is given by the Snedecor–Fisher or beta distributions. It allows us to construct statistical tests to determine the extreme precipitations. Within this approach, it is possible to introduce the notions of relatively and absolutely extreme precipitation volumes. An alternative method to determine an extreme daily precipitation volume based on a certain quantile of the tempered Snedecor–Fisher distribution is also suggested. The results of the application of these methods to real data are presented.

scholarly journals Parameterization of the COM-Poisson Distribution through the Mean Using Spectral Algorithms for Solving Nonlinear Equations

2019 ◽  
pp. 701-712
Author(s):  
Isaac Adeola Adeniyi ◽  
Dolapo Abidemi Shobanke ◽  
Helen Olaronke Edogbanya
Keyword(s):  
Poisson Distribution ◽  
Nonlinear Equations ◽  
Negative Binomial ◽  
Likelihood Function ◽  
Real Life ◽  
Location Parameter ◽  
Real Data ◽  
Probability Models ◽  
Spectral Algorithm ◽  
The Mean

The Poisson regression is popularly used to model count data. However, real data often do not satisfy the assumption of equality of the mean and variance which is an important property of the Poisson distribution. The Poisson – Gamma (Negative binomial) distribution and the recent Conway-Maxwell-Poisson (COM-Poisson) distributions are some of the proposed models for over- and under-dispersion respectively. Nevertheless, the parameterization of the COM-Poisson distribution still remains a major challenge in practice as the location parameter of the original COM-Poisson distribution rarely represents the mean of the distribution. As a result, this paper proposes a new parameterization of the COM-Poisson distribution via the central location (mean) so that more easily-interpretable models and results can be obtained.  The parameterization involves solving nonlinear equations which do not have analytical solutions. The nonlinear equations are solved using the efficient and fast derivative free spectral algorithm. Implementation of the parameterization in R (R Core Team, 2018) is used to present useful numerical results concerning the relationship between the mean of the COM-Poisson distribution and the location parameter in the original COM-Poisson parameterization. The proposed technique is further used to fit COM-Poisson probability models to real life datasets. It was found that obtaining estimates via this parameterization makes the estimation easier and faster compared to directly maximizing the likelihood function of the standard COM-Poisson distribution.

scholarly journals Climatic trends of temperatures and precipitation in Brazilian localities

2020 ◽  
Vol 42 ◽  
pp. e44359
Author(s):  
Júlio César Penereiro
Keyword(s):  
Industrial Development ◽  
Global Climate ◽  
Statistical Tests ◽  
Maximum Temperature ◽  
Climate Trends ◽  
Air Temperatures ◽  
Annual Time Series ◽  
Statistical Trends ◽  
Increasing Trends ◽  
Annual Time

In recent decades, scientific and academic researchers around the world have been concerned with the assessment of regional and global climate trends.  Under the hypothesis of the presence of climate change in Brazil, the aim of this work was to verify annual climate trends of maximum and minimum air temperatures and precipitation in 243 localities over all the Brazilian political regions. The data were obtained from National Institute of Meteorology. In this work there were identified and analysed trends in annual time series distributed between in 1961 and 2017. The detections and analyses were performed by the application of the statistical tests of Mann-Kendall and the Pettitt to evaluate the presence of statistical trends. The statistical results and the trend distributions maps show that, from all the studied localities, for maximum temperature indicate increasing trends in 35% of the series, decreasing trends in 1 and no trends in 64%. The minimum temperature showed increasing trends in 30% of the analysed series, decreasing in 8% and no trends in 63%. The precipitation, showed increasing trends in 6% of the studied series, decreasing in 4 and no trends in 91%. The observed climate trends can be related to anthropological activities like urban spraw, industrial development and increasing population density.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

scholarly journals Quantifying the Northward Spread of Ticks (Ixodida) as Climate Warms in Northern Russia

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 233
Author(s):  
Leonid N. Vladimirov ◽  
Grigory N. Machakhtyrov ◽  
Varvara A. Machakhtyrova ◽  
Albertus S. Louw ◽  
Netrananda Sahu ◽  
...  
Keyword(s):  
Negative Binomial ◽  
Global Climate ◽  
Indigenous Communities ◽  
Tick Bite ◽  
Negative Binomial Regression Model ◽  
Tick Abundance ◽  
Climate Parameters ◽  
Average Annual Temperature ◽  
The Republic ◽  
Northern Russia

Climate change is affecting human health worldwide. In particular, changes to local and global climate parameters influence vector and water-borne diseases like malaria, dengue fever, and tick-borne encephalitis. The Republic of Sakha in northern Russia is no exception. Long-term trends of increasing annual temperatures and thawing permafrost have corresponded with the northward range expansion of tick-species in the Republic. Indigenous communities living in these remote areas may be severely affected by human and livestock diseases introduced by disease vectors like ticks. To better understand the risk of vector-borne diseases in Sakha, we aimed to describe the increase and spatial spread of tick-bite cases in the Republic. Between 2000 and 2018, the frequency of tick bite cases increased 40-fold. At the start of the period, only isolated cases were reported in southern districts, but by 2018, tick bites had been reported in 21 districts in the Republic. This trend coincides with a noticeable increase in the average annual temperature in the region since the 2000s by an average of 1 °C. Maps illustrate the northward spread of tick-bite cases. A negative binomial regression model was used to correlate the increase in cases with a number of climate parameters. Tick bite case frequency per district was significantly explained by average annual temperature, average temperature in the coldest month of the year, the observation year, as well as Selyaninov’s hydrothermal coefficient. These findings contribute to the growing literature that describe the relationship between tick abundance and spread in Northern Latitudes and changes in temperatures and moisture. Future studies might use these and similar results to map and identify areas at risk of infestation by ticks, as climates continue to change in Sakha.

An Indirect Method for Estimating the Weight of Glaze on Wires

1955 ◽  
Vol 36 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Robert W. Lenhard
Keyword(s):  
Indirect Method ◽  
Daily Precipitation ◽  
Meteorological Data ◽  
Power Lines ◽  
Daily Maximum ◽  
Third Order ◽  
Precipitation Total ◽  
Climatological Station ◽  
Temperature Variable ◽  
The Relationship

The relationship between the weight of glaze on power lines and common meteorological variables is examined. The icing data used are those collected by the Pennsylvania Electric Association; the meteorological data are those available in third-order climatological station records. A graphical correlation between ice weight, daily precipitation total and a derived temperature variable is obtained. In addition, the regression of ice weight on daily precipitation is explored and the probability of occurrence of daily maximum and minimum temperatures associated with glaze storms is given. These two relations are suggested as alternative estimating tools.

scholarly journals Historical Spatial and Temporal Climate Trends in Southern Ontario, Canada

2017 ◽  
Vol 56 (10) ◽  
pp. 2767-2787 ◽  
Author(s):  
Hussein Wazneh ◽  
M. Altaf Arain ◽  
Paulin Coulibaly
Keyword(s):  
Climate Models ◽  
Global Climate ◽  
Global Climate Models ◽  
Climate Indices ◽  
Total Precipitation ◽  
Southern Ontario ◽  
Temperature And Precipitation ◽  
Annual Total ◽  
Precipitation Indices ◽  
Temperature Indices

AbstractSpatial and temporal trends in historical temperature and precipitation extreme events were evaluated for southern Ontario, Canada. A number of climate indices were computed using observed and regional and global climate datasets for the area of study over the 1951–2013 period. A decrease in the frequency of cold temperature extremes and an increase in the frequency of warm temperature extremes was observed in the region. Overall, the numbers of extremely cold days decreased and hot nights increased. Nighttime warming was greater than daytime warming. The annual total precipitation and the frequency of extreme precipitation also increased. Spatially, for the precipitation indices, no significant trends were observed for annual total precipitation and extremely wet days in the southwest and the central part of Ontario. For temperature indices, cool days and warm night have significant trends in more than 90% of the study area. In general, the spatial variability of precipitation indices is much higher than that of temperature indices. In terms of comparisons between observed and simulated data, results showed large differences for both temperature and precipitation indices. For this region, the regional climate model was able to reproduce historical observed trends in climate indices very well as compared with global climate models. The statistical bias-correction method generally improved the ability of the global climate models to accurately simulate observed trends in climate indices.

scholarly journals Disaggregative Invariance of Daily Precipitation

1997 ◽  
Vol 36 (6) ◽  
pp. 721-734 ◽  
Author(s):  
Roman Krzysztofowicz ◽  
Thomas A. Pomroy
Keyword(s):  
Empirical Evidence ◽  
Diurnal Cycle ◽  
Daily Precipitation ◽  
Precipitation Amount ◽  
Total Precipitation ◽  
Stochastic Independence ◽  
Precipitation Forecasting ◽  
Precipitation Timing ◽  
Temporal Disaggregation ◽  
Precipitation Records

Abstract Disaggregative invariance refers to stochastic independence between the total precipitation amount and its temporal disaggregation. This property is investigated herein for areal average and point precipitation amounts accumulated over a 24-h period and disaggregated into four 6-h subperiods. Statistical analyses of precipitation records from 1948 to 1993 offer convincing empirical evidence against the disaggregative invariance and in favor of the conditional disaggregative invariance, which arises when the total amount and its temporal disaggregation are conditioned on the timing of precipitation within the diurnal cycle. The property of conditional disaggregative invariance allows the modeler or the forecaster to decompose the problem of quantitative precipitation forecasting into three tasks: (i) forecasting the precipitation timing; (ii) forecasting the total amount, conditional on timing; and (iii) forecasting the temporal disaggregation, conditional on timing. Tasks (ii) and (iii) can be performed independently of one another, and this offers a formidable advantage for applications.

Improved trend-aware post-processing of GCM seasonal precipitation forecasts

2021 ◽  
Keyword(s):  
Climate Models ◽  
Global Climate ◽  
Processing Method ◽  
Global Climate Models ◽  
Seasonal Precipitation ◽  
Seasonal Temperature ◽  
Post Processing ◽  
Climate Trends ◽  
Climate Forecasting ◽  
New Formulation

Abstract Climate trends have been observed over the recent decades in many parts of the world, but current global climate models (GCMs) for seasonal climate forecasting often fail to capture these trends. As a result, model forecasts may be biased above or below the trendline. In our previous research, we developed a trend-aware forecast post-processing method to overcome this problem. The method was demonstrated to be effective for embedding observed trends into seasonal temperature forecasts. In this study, we further develop the method for post-processing GCM seasonal precipitation forecasts. We introduce new formulation and evaluation features to cater for special characteristics of precipitation amounts, such as having a zero lower bound and highly positive skewness. We apply the improved method to calibrate ECMWF SEAS5 forecasts of seasonal precipitation for Australia. Our evaluation shows that the calibrated forecasts reproduce observed trends over the hindcast period of 36 years. In some regions where observed trends are statistically significant, forecast skill is greatly improved by embedding trends into the forecasts. In most regions, the calibrated forecasts outperform the raw forecasts in terms of bias, skill, and reliability. Wider applications of the new trend-aware post-processing method are expected to boost user confidence in seasonal precipitation forecasts.

scholarly journals Temporal and Spatial Variations of Precipitation Change from Southeast to Northwest China during the Period 1961–2017

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2622
Author(s):  
Zhu Li ◽  
Honghu Liu
Keyword(s):  
Daily Precipitation ◽  
Global Climate ◽  
Heavy Rain ◽  
Northwest China ◽  
Annual Rainfall ◽  
Trend Test ◽  
Spatiotemporal Variations ◽  
Light Rain ◽  
Daily Precipitation Data ◽  
Northwest Region

Global climate change is significant, and the spatiotemporal variations of precipitation associated with it are pronounced. Based on the daily precipitation data from 10 weather stations located from southeast to northwest across China from 1961–2017, the Mann–Kendall trend test was generally applied to analyze the spatiotemporal variations of precipitation. The factors influencing the precipitation changes were investigated. The results revealed that (1) the annual, summer, and winter rainfall amount (RA) exhibited increasing rates of 16.36, 12.31, and 2.49 mm/10 year, respectively. The change rates of annual rainfall days (RD) were 2.68 day/10 year in the northwest region and −1.88 day/10 year in the southeast. The annual and seasonal daily precipitation on rainy days (RP) exhibited an increasing trend. (2) All of the RA, RD, and RP values initially increased, then decreased, and then slightly increased from Southeast to Northwest China. These results proved that the RA increased with the increase of light rain in Northwest China and heavy rain in Southeast China. In addition, changes in the monsoon have altered the rate at which RA, RD, and RP vary with distance from the sea. These findings may help to provide suggestions for the rational spatial utilization of water resources in China.

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