Comparison of Type I Error Rates of Siegel-Tukey and Savage Tests among Non-Parametric Tests

This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.

Investigation into Recent Temperature and Rainfall Trends in Mali Using Mann-Kendall Trend Test: Case Study of Bamako

Rainfall and temperature variability analysis is important for researchers and policy formulators in making critical decisions on water availability and use in communities. The Western Sahel, which comprises Mali is considered as one of the vulnerable regions to climate change, and also encountered the challenges of climatic shocks such as flood and drought. This research therefore sought to investigate climate change effects on hydrological events and trends in Sahelian rainfall intensity using Bamako (Mali) as a case study from 1991 to 2020, as limited data availability did not allow an extended period of study. Monthly observed data provided by MALI-METEO was used to validate daily rainfalls data from African Rainfall Climatology Version 2 (ARC2) satellite-based rainfall product on monthly basis. The validated model performance used Nash-Sutcliffe Efficiency (NSE) and Percent Bias (PBAIS) and gave results of 0.904 and 1.0506 respectively. Trends in annual maximum temperatures and rainfalls were analyzed using Mann-Kendall trend test. The result indicated that the trend in annual maximum rainfalls was decreasing, while annual total rainfall was increasing but not significant at 5% significance level. The rate of increase in annual total rainfalls was 0.475 mm/year according to the observed annual rainfall series and decreased to 0.68 mm/year in annual maximum. The analysis further found that annual maximum temperatures were increasing at the rate of 0.03°C/year at 5% significance level. To provide more accurate climate predictions, it is recommended that further studies on rainfall and temperature with data sets spanning 60 - 90 years be carried out.

A method to predict rockburst using temporal trend test and its application

Rockbursts have become a significant hazard in underground mining,underscoring the need for a robust early warning model to ensure safety management.This study presents a novel approach for rockburst prediction,integrating the Mann-Kendall trend test(MKT)and multi-indices fusion to enable real-time and quantitative assessment of rockburst hazards.The methodology employed in this study involves the development of a comprehensive precursory index library for rockbursts.The MKT is then applied to analyze the real-time trend of each index,with adherence to rockburst characterization laws serving as the warning criterion.By employing a confusion matrix,the warning effectiveness of each index is assessed,enabling index preference determination.Ultimately,the integrated rockburst hazard index Q is derived through data fusion.The results demonstrate that the proposed model achieves a warning effectiveness of 0.563 for Q,surpassing the performance of any individual index.Moreover,the model’s adaptability and scalability are enhanced through periodic updates driven by actual field monitoring data,making it suitable for complex underground working environments.By providing an efficient and accurate basis for decision-making,the proposed model holds great potential for the prevention and control of rockbursts.It offers a valuable tool for enhancing safety measures in underground mining operations.

Detecting Global Vegetation Changes Using Mann-Kendal(MK) Trend Test for 1982–2015 Time Period

Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understand the trends of vegetation cover, this research examined the spatial-temporal trends of global vegetation by employing the normalized difference vegetation index(NDVI) from the Advanced Very High Resolution Radiometer(AVHRR) Global Inventory Modeling and Mapping Studies(GIMMS) time series(1982–2015). Ten samples were selected to test the temporal trend of NDVI, and the results show that in arid and semi-arid regions, NDVI showed a deceasing trend, while it showed a growing trend in other regions. Mann-Kendal(MK) trend test results indicate that 83.37% of NDVI pixels exhibited positive trends and that only 16.63% showed negative trends(P < 0.05) during the period from 1982 to 2015. The increasing NDVI trends primarily occurred in tree-covered regions because of forest growth and re-growth and also because of vegetation succession after a forest disturbance. The increasing trend of the NDVI in cropland regions was primarily because of the increasing cropland area and the improvement in planting techniques. This research describes the spatial vegetation trends at a global scale over the past 30+ years, especially for different land cover types.

Analysis of Trends in Drought with the Non-Parametric Approach in Vietnam: A Case Study in Ninh Thuan Province

A quantitative study was used in the study of the tendency to change drought indicators in Vietnam through the Ninh Thuan province case study. The research data are temperature and precipitation data of 11 stations from 1986 to 2016 inside and outside Ninh Thuan province. To do the research, the author uses a non-parametric analysis method and the drought index calculation method. Specifically, with the non-parametric method, the author uses the analysis, Mann-Kendall (MK) and Theil-Sen (Sen’s slope), and to analyze drought, the author uses the Standardized Precipitation Index (SPI) and the Moisture Index (MI). Two Softwares calculated in this study are ProUCL 5.1 and MAKENSEN 1.0 by the US Environmental Protection Agency and Finnish Meteorological Institute. The calculation results show that meteorological drought will decrease in the future with areas such as Phan Rang, Song Pha, Quan The, Ba Thap tend to increase very clearly, while Tam My and Nhi Ha tend to increase very clearly short. With the agricultural drought, the average MI results increased 0.013 per year, of which Song Pha station tended to increase the highest with 0.03 per year and lower with Nhi Ha with 0.001 per year. The forecast results also show that by the end of the 21st century, the SPI tends to decrease with SPI 1 being −0.68, SPI 3 being −0.40, SPI 6 being −0.25, SPI 12 is 0.42. Along with that is the forecast that the MI index will increase 0.013 per year to 2035, the MI index is 0.93, in 2050 it is 1.13, in 2075 it will be 1.46, and by 2100 it is 1.79. Research results will be used in policymaking, environmental resources management agencies, and researchers to develop and study solutions to adapt and mitigate drought in the context of variable climate change.

Spatiotemporal changes in sunshine duration and its influential factors in Chongqing,China from 1961 to 2020

The surface solar radiation in most parts of the world has undergone a phenomenon known as global dimming and brightening,characterized by an initial decrease followed by an increase.As a result,the sunshine duration(SD)has decreased in the past 60 years.Against the backdrop of global dimming and brightening,SD has decreased to varying degrees in many regions of China.Using the observed data of SD,cloud amount(total cloud amount and low cloud amount,abbreviated as TCA and LCA),precipitation,and relative humidity(RH)from 34 meteorological stations in Chongqing during the period of 1961-2020,along with a digital elevation model(DEM)with a resolution of 90 m,this study analyzed the spatiotemporal variations and influencing factors of SD.The analysis employed methods such as linear regression,Mann-Kendall test,wavelet transformation,and DEM-based possible SD distributed model.The results showed that the annual SD in Chongqing has significantly decreased over the last 60 years,with a decreasing interannual trend rate(ITR)of 40.4 h/10a.Except for no obvious trend in spring,SD decreased significantly in summer,autumn and winter at the ITR of 21.1 h/10a,8.5 h/10a and 7.5 h/10a,respectively.An abrupt decrease in the annual SD was found in 1979.The difference before and after the abrupt decrease was 177.7 h.The difference before and after the abrupt decrease was 177.7 h.The annual SD possessed the oscillation period of 11a.The spatial heterogeneity of the mean annual SD during the last 60 years was obvious.The distribution of SD in Chongqing is high in the northeast and low in the southeast.In addition,about 73%of the total area in Chongqing showed a significant and very significant decreasing trend.The regions with significant changes are mainly concentrated in the regions with altitudes of 200~1000 m.The increasing LCA was the main cause of the decrease of the annual SD in the regions with 200-400 m altitude decreased the most and changed the most.Increasing LCA is the primary cause of the reduction in annual SD,showing a strong negative correlation coefficient of-0.7292.In Chongqing,PM2.5 concentration showed a significant decrease trend in annual,spring,autumn and winter during 2000-2020,but the significant correlation between PM2.5 concentration and SD was only in autumn and reached an extremely significant level.

Surface air temperature change in the Wuyi Mountains,southeast China

Detecting changes in surface air temperature in mid-and low-altitude mountainous regions is essential for a comprehensive understanding of warming trend with altitude.We use daily surface air temperature data from 64 meteorological stations in Wuyi Mountains and its adjacent regions to analyze the spatio-temporal patterns of temperature change.The results show that Wuyi Mountains have experienced significant warming from 1961 to 2018.The warming trend of the mean temperature is 0.20℃/decade,the maximum temperature is 0.17℃/decade,and the minimum temperature is 0.26℃/decade.In 1961-1990,more than 63%of the stations showed a decreasing trend in annual mean temperature,mainly because the maximum temperature decreased during this period.However,in 1971-2000,1981-2010 and 1991-2018,the maximum,minimum and mean temperatures increased.The fastest increasing trend of mean temperature occurred in the southeastern coastal plains,the quickest increasing trend of maximum temperature occurred in the northwestern mountainous region,and the increase of minimum temperature occurred faster in the southeastern coastal and northwestern mountainous regions than that in the central area.Meanwhile,this study suggests that elevation does not affect warming in the Wuyi Mountains.These results are beneficial for understanding climate change in humid subtropical middle and low mountains.

Evaluation of Rainfall Tendency for the Twentieth Century over Indira Sagar Region in Central India

The study investigates long-term changes in annual and seasonal rainfall patterns in the Indira Sagar Region of Madhya Pradesh, India, from 1901 to 2010. Agriculture sustainability, food supply, natural resource development, and hydropower system reliability in the region rely heavily on monsoon rainfall. Monthly rainfall data from three stations (East Nimar, Barwani, and West Nimar) were analyzed. Initially, the pre-whitening method was applied to eliminate serial correlation effects from the rainfall data series. Subsequently, statistical trends in annual and seasonal rainfall were assessed using both parametric (student-t test) and non-parametric tests [Mann-Kendall, Sen’s slope estimator, and Cumulative Sum (CUSUM)]. The magnitude of the rainfall trend was determined using Theil-Sen’s slope estimator. Spatial analysis of the Mann-Kendall test on an annual basis revealed a statistically insignificant decreasing trend for Barwani and East Nimar and an increasing trend for West Nimar. On a seasonal basis, the monsoon season contributes a significant percentage (88.33%) to the total annual rainfall. The CUSUM test results indicated a shift change detection in annual rainfall data for Barwani in 1997, while shifts were observed in West and East Nimar stations in 1929. These findings offer valuable insights into regional rainfall behavior, aiding in the planning and management of water resources and ecological systems.

Parameters Estimation of a Bivariate Generalized Poisson Distribution with Applications to Metabolic Syndrome Data

Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.

Assessment of the Spatio-Temporal Trends of Annual Extreme Temperature Indices over Tanzania during the Period of 1982-2022

Extreme weather and climatic phenomena, such as heatwaves, cold waves, floods and droughts, are expected to become more common and have a significant impact on ecosystems, biodiversity, and society. Devastating disasters are mostly caused by record-breaking extreme events, which are becoming more frequent throughout the world, including Tanzania. A clear global signal of an increase in warm days and nights and a decrease in cold days and nights has been observed. The present study assessed the trends of annual extreme temperature indices during the period of 1982 to 2022 from 29 meteorological stations in which the daily minimum and maximum data were obtained from NASA/POWER. The Mann-Kendall and Sen slope estimator were employed for trend analysis calculation over the study area. The analyzed data have indicated for the most parts, the country has an increase in warm days and nights, extreme warm days and nights and a decrease in cold days and nights, extreme cold days and nights. It has been disclosed that the number of warm nights and days is on the rise, with the number of warm nights trending significantly faster than the number of warm days. The percentile-based extreme temperature indices exhibited more noticeable changes than the absolute extreme temperature indices. Specifically, 66% and 97% of stations demonstrated positive increasing trends in warm days (TX90p) and nights (TN90p), respectively. Conversely, the cold indices demonstrated 41% and 97% negative decreasing trends in TX10p and TN10p, respectively. The results are seemingly consistent with the observed temperature extreme trends in various parts of the world as indicated in IPCC reports.

Wavelet Analysis and Nonparametric Test for Climate Change in Tarim River Basin of Xinjiang During 1959-2006

Using wavelet analysis,regression analysis and the Mann-Kendall test,this paper analyzed time-series(1959-2006) weather data from 23 meteorological stations in an attempt to characterize the climate change in the Tarim River Basin of Xinjiang Uygur Autonomous Region,China.Major findings are as follows:1) In the 48-year study period,average annual temperature,annual precipitation and average annual relative humidity all presented nonlinear trends.2) At the 16-year time scale,all three climate indices unanimously showed a rather flat before 1964 and a detectable pickup thereafter.At the 8-year time scale,an S-shaped nonlinear and uprising trend was revealed with slight fluctuations in the entire process for all three indices.Incidentally,they all showed similar pattern of a slight increase before 1980 and a noticeable up-swing afterwards.The 4-year time scale provided a highly fluctuating pattern of periodical oscillations and spiral increases.3) Average annual relative humidity presented a negative correlation with average annual temperature and a positive correlation with annual precipitation at each time scale,which revealed a close dynamic relationship among them at the confidence level of 0.001.4) The Mann-Kendall test at the 0.05 confidence level demonstrated that the climate warming trend,as represented by the rising average annual temperature,was remarkable,but the climate wetting trend,as indicated by the rising annual precipitation and average annual relative humidity,was not obvious.

Hydrological Mann-Kendal Multivariate Trends Analysis in the Upper Yangtze River Basin

Hydrological events should be described through several correlated variables, so multivariate HFA has gained popularity and become an active research field during recent years. However, at present multivariate HFA mainly focuses directly on fitting the frequency distribution without confirming whether the assumptions are satisfied. Neglecting testing these assumptions could get severely wrong frequency distribution. This paper uses multivariate Mann-Kendal testing to detect the multivariate trends of annual flood peak and annual maximum 15 day volume for four control hydrological stations in the?Upper Yangtze River Basin. Results indicate that multivariate test could detect the trends of joint variables, whereas univariate tests can only detect the univariate trends. Therefore, it is recommended to jointly apply univariate and multivariate trend tests to capture all the existing trends.

Response of runoff to climate change in the area of runoff yield in upstream Shiyang River Basin,Northwest China:A case study of the Xiying River

The objective of this study was to analyze the response of runoff in the area of runoff yield of the upstream Shiyang River basin to climate change and to promote sustainable development of regional water resources and ecological environment.As the biggest tributary of the Shiyang River,Xiying River is the only hydrological station(Jiutiaoling) that has provincial natural river and can achieve long time series monitoring data in the basin.The data obtained from this station is representative of natural conditions because it has little human activites.This study built a regression model through identifying the characteristics of runoff and climate change by using Mann-Kendall nonparametric statistical test,cumulative anomaly,and correlation analysis.The results show that the average annual runoff is 320.6 million m3/a with the coefficient of variation of 0.18 and shows slightly decrease during 1956-2020.It has a significant positive correlation the average annual precipitation(P<0.01).Runoff is sensitive to climate change,and the climate has becoming warm and wet and annual runoff has entering wet period from 2003.Compared to the earlier period(1955-2000),the increases of average annual temperature,precipitation and runoff in recent two decades were 15%,9.3%,and 7.8%,respectively.Runoff in the Shiyang River is affected by temperature and precipitation among climate factors,and the simulation results of the runoff-climate response model(R=0.0052P-0.1589T+2.373) indicate that higher temperature leads to a weakening of the ecological regulation of surface runoff in the flow-producing area.

Comparative Analysis of Climatic Change Trend and Change-Point Analysis for Long-Term Daily Rainfall Annual Maximum Time Series Data in Four Gauging Stations in Niger Delta

The aim of this study is to establish the prevailing conditions of changing climatic trends and change point dates in four selected meteorological stations of Uyo, Benin, Port Harcourt, and Warri in the Niger Delta region of Nigeria. Using daily or 24-hourly annual maximum series (AMS) data with the Indian Meteorological Department (IMD) and the modified Chowdury Indian Meteorological Department (MCIMD) models were adopted to downscale the time series data. Mann-Kendall (MK) trend and Sen’s Slope Estimator (SSE) test showed a statistically significant trend for Uyo and Benin, while Port Harcourt and Warri showed mild trends. The Sen’s Slope magnitude and variation rate were 21.6, 10.8, 6.00 and 4.4 mm/decade, respectively. The trend change-point analysis showed the initial rainfall change-point dates as 2002, 2005, 1988, and 2000 for Uyo, Benin, Port Harcourt, and Warri, respectively. These prove positive changing climatic conditions for rainfall in the study area. Erosion and flood control facilities analysis and design in the Niger Delta will require the application of Non-stationary IDF modelling.

石油污染场地浅层地下水监测式自然衰减效果评价

监测式自然衰减(Monitored Natural Attenuation,简称MNA)能够有效地修复石油污染场地,降低土壤及地下水中污染物的浓度,已经成为国内外的研究热点。文章采用统计学方法、Mann-Kendall test和溶质通量计算法,分析并计算场地地下水中总石油烃(TPH)浓度,评价石油污染场地地下水监测式自然衰减的效果。结果显示:石油污染场地中的TPH浓度呈现降低的趋势。污染晕内,不同位置的衰减率不同,污染晕内部更容易发生自然衰减作用;污染晕边缘的衰减作用则较小。MNA的衰减率为0.00876~0.10095 mg/(L·d);MNA的修复周期为1.3~10.6 a。

Temperature Variation and Mutation Analysis over the Past 59 Years in Shenyang

In this paper,based on the observation data of air temperature during 1951-2009 in Shenyang,the interannual and interdecadal variation of annual average temperature,maximum and minimum temperature in Shenyang were conducted the statistical analysis by means of linear trend estimation and mutation detection by using Mann-Kendall method.As was demonstrated in the results,the annual average temperature,maximum and minimum temperature in Shenyang showed an upward trend,whose linear tendency rate was 0.231,0.181 and 0.218 respectively.The increment trend of annual average temperature,maximum and minimum temperature was extremely clear.The increase in minimum temperature was more significant than that in mean temperature and maximum temperature.The abrupt change point of annual mean temperature in Shenyang appeared in 1981;the abrupt change point of annual mean maximum temperature appeared in 1994;the annual mean minimum temperature underwent mutation in 1978.

Analysis on the Climate Change Characteristics in Zhumadian in Recent 50 Years

By means of linear function and Mann-Kendall test method,the climate change characteristics of temperature and precipitation from Zhumadian meteorological station in recent 50 years were analyzed.The results revealed that annual mean temperature and extreme temperature showed increase trend,especially minimum temperature,and there was a slight increase in annual precipitation.Temperature increase was more obvious in spring than that in autumn and winter,while there was a decrease of temperature in summer.Meanwhile,precipitation went down in spring and autumn,particular in autumn,while the increase of summer precipitation was most obvious.Mann-Kendall test showed that temperature in Zhumadian had obvious increase trend in recent 50 years,while there was abrupt change in temperature in the late 1990s and fluctuation change in annual precipitation.

Streamflow trends and hydrological response to climatic change in Tarim headwater basin

This paper has studied the change of streamflow and the impact of climatic variability conditions on regional hydrological cycle in the headwater of the Tarim River Basin. This study investigates possible causes of observed trends in streamflow in an environment which is highly variable in terms of atmospheric conditions, and where snow and ice melt play an important role in the natural hydrological regime. The discharge trends of three head streams have a significant increase trend from 1957 to 2002 with the Mann-Kendall test. Complex time-frequency distributions in the streamflow regime are demonstrated especially by Morlet wavelet analysis over 40 years. The purpose is to ascertain the nature of climatic factors spatial and temporal distribution, involved the use of EOF （Empirical Orthogonal Function） to compare the dominant temperature, precipitation and evaporation patterns from normally climatic records over the Tarim＇s headwater basin. It shows that the first principal component was dominated since the 1990s for temperature and precipitation, which identifies the significant ascending trend of spatial and temporal pattern characteristics under the condition of the global warming. An exponential correlation is highlighted between surface air temperature and mean river discharge monthly, so the regional runoff increases by 10%-16% when surface air temperature rises by 1 ℃. Results suggest that headwater basins are the most vulnerable environments from the point of view of climate change, because their watershed properties promote runoff feeding by glacier and snow melt water and their fundamental vulnerability to temperature changes affects rainfall, snowfall, and glacier and ice melt.

Spatial and temporal variability of daily precipitation in Haihe River basin, 1958-2007

The seasonal variability and spatial distribution of precipitation are the main cause of flood and drought events. The study of spatial distribution and temporal trend of precipitation in river basins has been paid more and more attention. However, in China, the precipitation data are measured by weather stations （WS） of China Meteorological Administration and hydrological rain gauges （RG） of national and local hydrology bureau. The WS data usually have long record with fewer stations, while the RG data usually have short record with more stations. The consistency and correlation of these two data sets have not been well understood. In this paper, the precipitation data from 30 weather stations for 1958-2007 and 248 rain gauges for 1995-2004 in the Haihe River basin are examined and compared using linear regression, 5-year moving average, Mann-Kendall trend analysis, Kolmogorov-Smirnov test, Z test and F test methods. The results show that the annual precipitation from both WS and RG records are normally distributed with minor difference in the mean value and variance. It is statistically feasible to extend the precipitation of RG by WS data sets. Using the extended precipitation data, the detailed spatial distribution of the annual and seasonal precipitation amounts as well as their temporal trends are calculated and mapped. The various distribution maps produced in the study show that for the whole basin the precipitation of 1958-2007 has been decreasing except for spring season. The decline trend is significant in summer, and this trend is stronger after the 1980s. The annual and seasonal precipitation amounts and changing trends are different in different regions and seasons. The precipitation is decreasing from south to north, from coastal zone to inland area.

Trend in pan evaporation and its attribution over the past 50 years in China

Trends in pan evaporation are widely relevant to the hydrological community as indicators of hydrological and climate change. Pan evaporation has been decreasing in the past few decades over many large areas with differing climates globally. This study analyzes pan evaporation data from 671 stations in China over the past 50 years in order to reveal the trends of it and the corresponding trend attribution. Mann-Kendall test shows a significant declining trend in pan evaporation for most stations, with an average decrease of 17.2 mm/10a in China as a whole, the rate of decline was the steepest in the humid region （29.7 mm/10a）, and was 17.6 mm/10a and 5.5 mm/10a in the semi-humid/semi-arid region and arid region, respectively. Complete correlation coefficients of pan evaporation with 7 climate factors were computed, and decreases in diurnal temperature range （DTR）, SD （sunshine duration） and wind speed were found to be the main attributing factors in the pan evaporation declines. Decrease in DTR and SD may relate to the increase of clouds and aerosol as well as the other pollutants, and decrease in wind speed to weakening of the Asian winter and summer monsoons under global climate warming.