scholarly journals Effects of the prewhitening method, the time granularity and the time segmentation on the Mann-Kendall trend detection and the associated Sen's slope

2020 ◽  
Author(s):  
Martine Collaud Coen ◽  
Elisabeth Andrews ◽  
Alesssandro Bigi ◽  
Gonzague Romanens ◽  
Giovanni Martucci ◽  
...  
Keyword(s):  
Time Series ◽  
Trend Analysis ◽  
Statistical Significance ◽  
Parametric Method ◽  
Kendall Test ◽  
Trend Detection ◽  
Temporal Segmentation ◽  
Sen’S Slope ◽  
Power Of The Test ◽  
Mann Kendall Test

Abstract. The most widely used non-parametric method for trend analysis is the Mann-Kendall test associated with the Sen's slope. The Mann-Kendall test requires serially uncorrelated time series, whereas most of the atmospheric processes exhibit positive autocorrelation. Several prewhitening methods have been designed to overcome the presence of lag-1 autocorrelation. These include a prewhitening, a detrending and/or a correction for the detrended slope and the original variance of the time series. The choice of which prewhitening method and temporal segmentation to apply has consequences for the statistical significance, the value of the slope and of the confidence limits. Here, the effects of various prewhitening methods are analyzed for seven time series comprising in-situ aerosol measurements (scattering coefficient, absorption coefficient, number concentration and aerosol optical depth), Raman Lidar water vapor mixing ratio and the tropopause and zero degree levels measured by radio-sounding. These time series are characterized by a broad variety of distributions, ranges and lag-1 autocorrelation values and vary in length between 10 and 60 years. A common way to work around the autocorrelation problem is to decrease it by averaging the data over longer time intervals than in the original time series. Thus, the second focus of this study is evaluation of the effect of time granularity on long-term trend analysis. Finally, a new algorithm involving three prewhitening methods is proposed in order to maximize the power of the test, to minimize the amount of erroneous detected trends in the absence of a real trend and to ensure the best slope estimate for the considered length of the time series.

scholarly journals Effects of the prewhitening method, the time granularity, and the time segmentation on the Mann–Kendall trend detection and the associated Sen's slope

2020 ◽  
Vol 13 (12) ◽  
pp. 6945-6964
Author(s):  
Martine Collaud Coen ◽  
Elisabeth Andrews ◽  
Alessandro Bigi ◽  
Giovanni Martucci ◽  
Gonzague Romanens ◽  
...  
Keyword(s):  
Time Series ◽  
Trend Analysis ◽  
Statistical Significance ◽  
Parametric Method ◽  
Kendall Test ◽  
Trend Detection ◽  
Temporal Segmentation ◽  
Sen’S Slope ◽  
Power Of The Test ◽  
Original Time

Abstract. The Mann–Kendall test associated with the Sen's slope is a very widely used non-parametric method for trend analysis. It requires serially uncorrelated time series, yet most of the atmospheric processes exhibit positive autocorrelation. Several prewhitening methods have therefore been designed to overcome the presence of lag-1 autocorrelation. These include a prewhitening, a detrending and/or a correction of the detrended slope and the original variance of the time series. The choice of which prewhitening method and temporal segmentation to apply has consequences for the statistical significance, the value of the slope and of the confidence limits. Here, the effects of various prewhitening methods are analyzed for seven time series comprising in situ aerosol measurements (scattering coefficient, absorption coefficient, number concentration and aerosol optical depth), Raman lidar water vapor mixing ratio, as well as tropopause and zero-degree temperature levels measured by radio-sounding. These time series are characterized by a broad variety of distributions, ranges and lag-1 autocorrelation values and vary in length between 10 and 60 years. A common way to work around the autocorrelation problem is to decrease it by averaging the data over longer time intervals than in the original time series. Thus, the second focus of this study evaluates the effect of time granularity on long-term trend analysis. Finally, a new algorithm involving three prewhitening methods is proposed in order to maximize the power of the test, to minimize the number of erroneous detected trends in the absence of a real trend and to ensure the best slope estimate for the considered length of the time series.

Precipitation Trend Analysis by Mann-Kendall Test: A Case of Tianchang County Anhui Province, China

2013 ◽  
Vol 864-867 ◽  
pp. 2218-2223 ◽  
Author(s):  
Elsie Akwei ◽  
Bao Hong Lu ◽  
Han Wen Zhang
Keyword(s):  
Climate Change ◽  
Time Series ◽  
Trend Analysis ◽  
Null Hypothesis ◽  
Kendall Test ◽  
Anhui Province ◽  
Significant Trend ◽  
Precipitation Data ◽  
Precipitation Time Series ◽  
Mann Kendall Test

The purpose of this research is to study the temporal variability of precipitation time series of Tianchang County in Anhui Province, China to aid in the understanding of the state of the hydrology of the catchment. Trend analysis of one of the main component of the water balance of a catchment and a climate variable, precipitation was conducted with the aim of detecting a possible trend in the precipitation time series of Tianchang County, the non-parametric Mann-Kendall test was applied to precipitation series from 1951-2010 of Tianchang County. It was performed using Trend (version 1.0.2) to identify the significant positive or negative trends in the precipitation data if any. The 59 years period of precipitation data for the different towns in whole area showed, on the whole, some significant trend at an alpha level of 0.01 and 0.05 when grouped into the four seasons present in the area. The trend analysis revealed an overall upward and significant trend in five towns namely Datong, Xinjie, Shiliang, Qinlan and Tongcheng with downward statistically non-significant trend in the other ten areas .Using hypothesis testing, the null hypothesis states that there is no trend and alternative state there is a trend. From the results we reject the null hypothesis within the level of confidence 0.05 and 0.01. The rising rate of precipitation in some months and decreasing in others signifies an overall random pattern in the time series. This result is a part contribution to the effect of Climate change on hydrology and indicates that there is still room for research on the impact of climate change to ensure sustainable development in future.

scholarly journals Can innovative trend analysis identify trend change points?

2020 ◽  
Vol 1 (3) ◽  
pp. 6-15
Author(s):  
Sadık Alashan
Keyword(s):  
Time Series ◽  
Trend Analysis ◽  
Statistical Significance ◽  
Bootstrap Method ◽  
Change Points ◽  
Trend Detection ◽  
Significance Level ◽  
Related Data ◽  
Innovative Trend Analysis ◽  
June July

Trends in temperature series are the main cause of climate change. Because solar energy directs hydro-meteorological events and increasing variations in this resource change the balance between events such as evaporation, wind, and rainfall. There are many methods for calculating trends in a time series such as Mann-Kendall, Sen's slope estimator, Spearman's rho, linear regression and the new Sen innovative trend analysis (ITA). In addition, Mann-Kendall's variant, the sequential Mann Kendall, has been developed to identify trend change points; however, it is sensitive to related data as specified by some researchers. Şen_ITA is a new trend detection method and does not require independent and normally distributed time series, but has never been used to detect trend change points. In the literature, multiple, half-time and multi-durations ITA methods are used to calculate partial trends in a time series without identifying trend change points. In this study, trend change points are detected using the Şen_ITA method and named ITA_TCP. This approach may allow researchers to identify trend change points in a time series. Diyarbakır (Turkey) is selected as a study area, and ITA_TCP has detected trends and trends change points in monthly average temperatures. Although ITA detects only a significant upward trend in August, given the 95% statistical significance level, ITA_TCP shows three upward trends in June, July and August, and a decreasing trend in September. Critical trend slope values are obtained using the bootstrap method, which does not require the normal distribution assumption.

scholarly journals Can innovative trend analysis identify trend change points?

2020 ◽  
Vol 1 (3) ◽  
pp. 6-15
Author(s):  
Sadık Alashan
Keyword(s):  
Time Series ◽  
Trend Analysis ◽  
Statistical Significance ◽  
Bootstrap Method ◽  
Change Points ◽  
Trend Detection ◽  
Significance Level ◽  
Related Data ◽  
Innovative Trend Analysis ◽  
June July

Trends in temperature series are the main cause of climate change. Because solar energy directs hydro-meteorological events and increasing variations in this resource change the balance between events such as evaporation, wind, and rainfall. There are many methods for calculating trends in a time series such as Mann-Kendall, Sen's slope estimator, Spearman's rho, linear regression and the new Sen innovative trend analysis (ITA). In addition, Mann-Kendall's variant, the sequential Mann Kendall, has been developed to identify trend change points; however, it is sensitive to related data as specified by some researchers. Şen_ITA is a new trend detection method and does not require independent and normally distributed time series, but has never been used to detect trend change points. In the literature, multiple, half-time and multi-durations ITA methods are used to calculate partial trends in a time series without identifying trend change points. In this study, trend change points are detected using the Şen_ITA method and named ITA_TCP. This approach may allow researchers to identify trend change points in a time series. Diyarbakır (Turkey) is selected as a study area, and ITA_TCP has detected trends and trends change points in monthly average temperatures. Although ITA detects only a significant upward trend in August, given the 95% statistical significance level, ITA_TCP shows three upward trends in June, July and August, and a decreasing trend in September. Critical trend slope values are obtained using the bootstrap method, which does not require the normal distribution assumption.

A simulation study of trend detection methods for integrated ecosystem assessment

2019 ◽  
Vol 76 (7) ◽  
pp. 2060-2069 ◽  
Author(s):  
Sean Hardison ◽  
Charles T Perretti ◽  
Geret S DePiper ◽  
Andrew Beet
Keyword(s):  
Time Series ◽  
Generalized Least Squares ◽  
Kendall Test ◽  
Trend Detection ◽  
Detection Methods ◽  
Times Series ◽  
Model Selection Approach ◽  
Mann Kendall Test ◽  
Ecosystem Level ◽  
Rejection Rates

Abstract The identification of trends in ecosystem indicators has become a core component of ecosystem approaches to resource management, although oftentimes assumptions of statistical models are not properly accounted for in the reporting process. To explore the limitations of trend analysis of short times series, we applied three common methods of trend detection, including a generalized least squares model selection approach, the Mann–Kendall test, and Mann–Kendall test with trend-free pre-whitening to simulated time series of varying trend and autocorrelation strengths. Our results suggest that the ability to detect trends in time series is hampered by the influence of autocorrelated residuals in short series lengths. While it is known that tests designed to account for autocorrelation will approach nominal rejection rates as series lengths increase, the results of this study indicate biased rejection rates in the presence of even weak autocorrelation for series lengths often encountered in indicators developed for ecosystem-level reporting (N = 10, 20, 30). This work has broad implications for ecosystem-level reporting, where indicator time series are often limited in length, maintain a variety of error structures, and are typically assessed using a single statistical method applied uniformly across all time series.

scholarly journals Time Series Modelling of Monthly Temperature and Reference Evapotranspiration for Navsari (Gujarat), India

2019 ◽  
pp. 1-13
Author(s):  
D. K. Dwivedi ◽  
P. K. Shrivastava
Keyword(s):  
Time Series ◽  
Reference Evapotranspiration ◽  
Kendall Test ◽  
Trend Detection ◽  
Positive Trend ◽  
Monthly Temperature ◽  
Mean Temperature ◽  
Time Series Modelling ◽  
Mann Kendall Test ◽  
Past Data

Time series modelling has been proved its usefulness in various fields including meteorology, hydrology and agriculture. It utilizes past data and extracts useful information from them to build up a model which could simulate various processes. The prior knowledge of evapotranspiration could help in estimating the amount of water required by the crops that is useful for optimizing design of irrigation systems. In this study, the time series modelling of monthly temperature and reference evapotranspiration has been carried out utilizing past data of 35 years (1983-2017) to assist decision makers related to agriculture and meteorology. 30 years (1983-2012) of temperature and evapotranspiration data were used for training and remaining 5 years of data (2013-2017) were used for validation. The monthly evapotranspiration was estimated using Penman-Monteith FAO-56 method. Mann-Kendall test was used at 5% significant level for identifying trend component in mean temperature. The time series of temperature and evapotranspiration was made stationary for modelling the stochastic components using ARIMA (Autoregressive Integrated Moving Average) model. In order to check the normality of residuals, the Portmantaeu test was applied. The time series models for temperature and evapotranspiration which were validated for 5 years (2013-2017) and further deployed for forecasting of 5 years (2018-2022). It was found that for modelling temperature and reference evapotranspiration for Navsari, seasonal ARIMA (1,0,0)(0,1,1)12 and seasonal ARIMA (1,0,1)(1,1,2)12 were found to be appropriate models respectively. Mann Kendall test used for trend detection in monthly mean temperature revealed that October and November months had significant positive trend. Negative trend was observed only in the month of June.

scholarly journals Trend analysis of seasonal rainfall and temperature pattern in Damota Gale districts of Wolaita Zone, Ethiopia

2021 ◽  
Author(s):  
Elias Bojago ◽  
Dalga YaYa
Keyword(s):  
Trend Analysis ◽  
Meteorological Data ◽  
Statistical Significance ◽  
Kendall Test ◽  
Maximum Temperature ◽  
Temperature Pattern ◽  
Positive Trend ◽  
Annual Minimum Temperature ◽  
Increasing Trend ◽  
Mann Kendall Test

Abstract This paper investigated the recent trends of precipitation and temperature on Damota Gale districts of Wolaita Zone. This study used the observed historical meteorological data from 1987 to 2019 to analyze the trends. The magnitude of the variability or fluctuations of the factors varies according to locations. Hence, examining the spatiotemporal dynamics of meteorological variables in the context of changing climate, particularly in countries where rain-fed agriculture is predominant, is vital to assess climate-induced changes and suggest feasible adaptation strategies. Both rainfall and temperature data for a period of 1987 to 2019 were analyzed in this study. Statistical trend analysis techniques namely Mann–Kendall test and Sen's slope estimator were used to examine and analyze the problems. The long-term trend of rainfall and temperature was evaluated by linear regression and Mann–Kendall test. The temperature was shown a positive trend for both annual and seasonal periods and had a statistical significance of 95%. This study concluded that there was a declining rainfall in the three seasons; spring, summer and winter but in autumn it shows increasing trends and rapid warming, especially in the last 32 years. The detailed analysis of the data for 32 years indicate that the annual maximum temperature and annual minimum temperature have shown an increasing trend, whereas the Damota Gale seasonal maximum and minimum temperatures have shown an increasing trend. The findings of this study will serve as a reference for climate researchers, policy and decision-makers.

scholarly journals Probability and Trend Analysis of Monthly Rainfall in Haryana

2019 ◽  
Vol 34 (02) ◽  
Author(s):  
Mohit Nain ◽  
B. K. Hooda
Keyword(s):  
Trend Analysis ◽  
Monsoon Rainfall ◽  
Kendall Test ◽  
Rain Gauge ◽  
Monthly Rainfall ◽  
Annual Rainfall ◽  
Sen’S Slope Estimator ◽  
Sen’S Slope ◽  
Mann Kendall Test ◽  
Slope Estimator

Study on rainfall pattern of a region over a number of years is very useful for crop planning and irrigations scheduling. The present study deals with the probability and trend analysis of monthly rainfall in selected rain gauge stations scattered over the entire state of Haryana. Probabilities for drought, normal and abnormal events for monthly rainfall have been worked out using monthly rainfall data for 42 years (1970-2011), covering 27 rain gauge stations in the state of Haryana. Analysis indicated that drought months are more probable than normal months while normal months are more probable than abnormal months. The monotonic trend direction and magnitude of change in rainfall over time have been examined using the Mann-Kendall test and Sen’s slope estimator tests. Using the Mann-Kendall test and Sen’s slope estimator, the significant decrease in annual rainfall was noticed at Ballabgarh and Thanesar, While in monsoon rainfall, a significant decrease was noticed at Thanesar and Narnaul. But Sirsa is the only district which shows a significant increase in annual and monsoon rainfall. In probability analysis the highest per cent of normal, draughts and abnormal months was observed for Ambala, Hassanpur and Dujana respectively.

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