Pre-whitening Approach Research Articles

Combined use of graphical and statistical approaches for rainfall trend analysis in the Mae Klong River Basin, Thailand

AbstractThe main purpose of this paper was to investigate the monthly, seasonal, and annual rainfall variability in the Mae Klong River Basin in Thailand using the Mann–Kendall (MK) test, Sen's slope method, Spearman's Rho (SR) test, and the innovative trend analysis (ITA) method. The monthly rainfall data of eight stations for the period 1971–2015 were used for trend analysis. Datasets with significant serial correlation were corrected by the trend-free pre-whitening (TFPW) approach for statistical methods. The MK test showed increasing rainfall trends for five out of eight stations in the dry season while 50% of stations indicated increasing trends in the wet season. On an annual scale, 75% of the stations exhibited increasing rainfall trends. The results of the SR test were in line with the MK test for seasonal and annual rainfall. The ITA method showed comparable findings with those of the statistical methods. For the entire basin, trend analysis found increasing rainfall on both seasonal and annual scales by all the tests. The findings of this study could benefit water supply and management, drought monitoring, agricultural production activities, and socioeconomic development in the Mae Klong River Basin in the future.

Variance correction principal component analysis—gross error detection with serially correlated data

Process industries have complex measurement systems set up to measure process variables for control, dynamic optimization, online diagnostics, and real-time monitoring. Errors in measured process data are typically classified as random or fixed (gross) errors. Data reconciliation (DR) addresses random errors, whereas gross error detection and reconstruction (GEDR) addresses gross errors. In most GEDR techniques, data collected from sources are considered independently and identically distributed (i.i.d.). Most GEDR approaches consider data acquired from sources to be dispersed independently and identically (i.i.d.). Data acquired from multiple sources do not have to be independent in industrial manufacturing practice. They may have serial correlation due to control loops, process dynamics, feedback networks, etc. This paper proposes a new technique, variance correction (VC) principal component analysis (VCPCA) based measurement test, to identify gross errors in serially correlated data. The proposed technique uses a VC approach to estimate the variance of serially correlated data and a PCA-based estimator to calculate the residuals. The advantages of the proposed technique are assessed by comparing its performance with other existing methods like VC and pre-whitening approaches. The results demonstrated the superior performance of VCPCA and produced 99% success in all simulation trials in identifying gross errors and only 1% false identification.

Trend Detection in the Presence of Positive and Negative Serial Correlation: A Comparison of Block Maxima and Peaks‐Over‐threshold Data

AbstractSerial correlation in a hydrometeorological time series can have deleterious effects on trend detection tests. To account for significant autocorrelation detected in datasets, various techniques have been developed over time, each having their own assumptions and accuracy. Furthermore, the existence of positive or negative serial correlation has dissimilar effects on these statistical techniques. This research compares the power and Type I error rates of various well‐known and several newer techniques to account for positive and negative serial correlation in combination with the Mann‐Kendall nonparametric trend test. The study additionally explores the application of these techniques in the presence of higher order dependence structures. Through a case study of southern Ontario watersheds, it is determined that the block maxima series (BMS) data are more likely to have significant negative lag‐1 serial correlation. Peaks‐over‐threshold (POT) data are more likely to be serially correlated and this autocorrelation is more likely to be positive. It is determined that in the case of positively serially correlated AR(1) data, block bootstrap (BBS), Hamed and Rao (1998), variance correction (VCCF1), Yue and Wang (2004), variance correction (VCCF2), and sieve bootstrap (SBS) are the most robust. Alternatively, in the case of negative AR(1) autocorrelation, the corrected trend‐free prewhitening approach (CTFPW), modified trend‐free prewhitening (MTFPW), bias corrected prewhitening (BCPW), and VCCF1 are recommended. In the presence of higher order dependence structures, VCCF1 (with all significant lags included) and VCCF2 (with all lags included) should be applied cautiously. Lastly, an assessment of the causality of the serial correlation is provided.

Assessing the significance of directed and multivariate measures of linear dependence between time series

Inferring linear dependence between time series is central to our understanding of natural and artificial systems. Unfortunately, the hypothesis tests that are used to determine statistically significant directed or multivariate relationships from time-series data often yield spurious associations (Type I errors) or omit causal relationships (Type II errors). This is due to the autocorrelation present in the analysed time series -- a property that is ubiquitous across diverse applications, from brain dynamics to climate change. Here we show that, for limited data, this issue cannot be mediated by fitting a time-series model alone (e.g., in Granger causality or prewhitening approaches), and instead that the degrees of freedom in statistical tests should be altered to account for the effective sample size induced by cross-correlations in the observations. This insight enabled us to derive modified hypothesis tests for any multivariate correlation-based measures of linear dependence between covariance-stationary time series, including Granger causality and mutual information with Gaussian marginals. We use both numerical simulations (generated by autoregressive models and digital filtering) as well as recorded fMRI-neuroimaging data to show that our tests are unbiased for a variety of stationary time series. Our experiments demonstrate that the commonly used $F$- and $\chi^2$-tests can induce significant false-positive rates of up to $100\%$ for both measures, with and without prewhitening of the signals. These findings suggest that many dependencies reported in the scientific literature may have been, and may continue to be, spuriously reported or missed if modified hypothesis tests are not used when analysing time series.

Influence of non-stationarity and auto-correlation of climatic records on spatio-temporal trend and seasonality analysis in a region with prevailing arid and semi-arid climate, Iran

Trend and stationarity analysis of climatic variables are essential for understanding climate variability and provide useful information about the vulnerability and future changes, especially in arid and semi-arid regions. In this study, various climatic zones of Iran were investigated to assess the relationship between the trend and the stationarity of the climatic variables. The Mann-Kendall test was considered to identify the trend, while the trend free pre-whitening approach was applied for eliminating serial correlation from the time-series. Meanwhile, time series stationarity was tested by Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests. The results indicated an increasing trend for mean air temperature series at most of the stations over various climatic zones, however, after eliminating the serial correlation factor, this increasing trend changes to an insignificant decreasing trend at a 95% confidence level. The seasonal mean air temperature trend suggested a significant increase in the majority of the stations. The mean air temperature increased more in northwest towards central parts of Iran that mostly located in arid and semiarid climatic zones. Precipitation trend reveals an insignificant downward trend in most of the series over various climatic zones; furthermore, most of the stations follow a decreasing trend for seasonal precipitation. Furthermore, spatial patterns of trend and seasonality of precipitation and mean air temperature showed that the northwest parts of Iran and margin areas of the Caspian Sea are more vulnerable to the changing climate with respect to the precipitation shortfalls and warming. Stationarity analysis indicated that the stationarity of climatic series influences on their trend; so that, the series which have significant trends are not static. The findings of this investigation can help planners and policy-makers in various fields related to climatic issues, implementing better management and planning strategies to adapt to climate change and variability over Iran.

Complexity of Forces Driving Trend of Reference Evapotranspiration and Signals of Climate Change

Understanding the trends of reference evapotranspiration (ETo) and its influential meteorological variables due to climate change is required for studying the hydrological cycle, vegetation restoration, and regional agricultural production. Although several studies have evaluated these trends, they suffer from a number of drawbacks: (1) they used data series of less than 50 years; (2) they evaluated the individual impact of a few climatic variables on ETo, and thus could not represent the interactive effects of all forces driving trends of ETo; (3) they mostly studied trends of ETo and meteorological variables in similar climate regions; (4) they often did not eliminate the impact of serial correlations on the trends of ETo and meteorological variables; and finally (5) they did not study the extremum values of meteorological variables and ETo. This study overcame the abovementioned shortcomings by (1) analyzing the 50-year (1961–2010) annual trends of ETo and 12 meteorological variables from 18 study sites in contrasting climate types in Iran, (2) removing the effect of serial correlations on the trends analysis via the trend-free pre-whitening approach, (3) determining the most important meteorological variables that control the variations of ETo, and (4) evaluating the coincidence of annual extremum values of meteorological variables and ETo. The results showed that ETo and several meteorological variables (namely wind speed, vapor pressure deficit, cloudy days, minimum relative humidity, and mean, maximum and minimum air temperature) had significant trends at the confidence level of 95% in more than 50% of the study sites. These significant trends were indicative of climate change in many regions of Iran. It was also found that the wind speed (WS) had the most significant influence on the trend of ETo in most of the study sites, especially in the years with extremum values of ETo. In 83.3% of the study sites (i.e., all arid, Mediterranean and humid regions and 66.7% of semiarid regions), both ETo and WS reached their extremum values in the same year. The significant changes in ETo due to WS and other meteorological variables have made it necessary to optimize cropping patterns in Iran.

Trends in the Magnitude and Frequency of Extreme Rainfall Regimes in Florida

Trends in the extreme rainfall regimes were analyzed at 24 stations of Florida for four analysis periods: 1950–2010, 1960–2010, 1970–2010, and 1980–2010. A trend-free pre-whitening approach was utilized to correct data for autocorrelations. Non-parametric Mann-Kendall test and Theil-Sen approach were employed to detect and estimate trends in the magnitude of annual maximum rainfalls and in the number of annual above-threshold events (i.e., frequency). A bootstrap resampling approach was used to account for cross-correlations across sites and evaluate the global significance of trends at the 10% level (p-value ≤ 0.10). Dominant locally significant (p-value ≤ 0.10) increasing trends were found in the magnitudes of 1–12 h extreme rainfalls for the longest period, and in 6 h to 7 day rainfalls for the shortest period. The trends in 2–12 h rainfalls were also globally significant (i.e., exceeded the trends that could occur by chance). In contrast, globally significant decreasing trends were noted in the annual number of 1–3 h, 1–6 h, and 3–6 h extreme rainfalls during 1950–2010, 1960–2010, and 1980–2010, respectively. Trends in the number of 1–7 day extreme rainfalls were mixed, lacking global significance. Our findings would guide stormwater management in tropical/subtropical environments of Florida and around the world.

Integrated nested Laplace approximation method for hierarchical Bayesian inference of spatial model with application to functional magnetic resonance imaging data

Analysis of functional magnetic resonance imaging (fMRI) data plays a crucial role in medical statistics. Many developed approaches have relied on the voxel-wise general linear model (GLM). Despite the popularity of classical GLM, this procedure has some drawbacks in modeling complex structure of fMRI data. Bayesian approaches have largely dealt with this issue. Due to the computational cost of Bayesian approach such as Monte Carlo Markov Chain (MCMC), approximate Bayesian methods including variational Bayes (VB) and Integrated Nested Laplacian Approximation (INLA) have been proposed. In this study, we use INLA for inferences of spatial hierarchical model. Moreover, temporal correlations of time series is addressed by pre-whitening approach. To detect regions of activation, we apply joint posterior distributions as opposed to marginal distributions. The joint posterior probability map (PPM) is computed based on excursions set theory, and multiple comparisons problem is properly corrected. The performance of the proposed Bayesian approach is evaluated via simulation studies and a real task fMRI dataset. The results are compared with VB and classical GLM. The Bayesian approach based on joint PPM leads to more precise results by controlling false positive rate. The posterior mean from INLA fairly agree with the posterior mean from VB, however VB underestimates posterior variance.

Observed trends in temperature and rainfall in Bangladesh using pre-whitening approach

Abstract Understanding the trend of temperature and rainfall is of prime importance for climate change related research. This research aims to identify the trends of temperature and rainfall for the last 50 years (1966–2015) for Bangladesh. To detect the trends, the non-parametric Mann–Kendall test in combination with a trend-free pre-whitening approach for correcting the time series to eliminate the influence of serial correlation has been used whereas the Sen's slope method is used for identification of the trend value. Maximum, minimum, and mean monthly temperatures have been analyzed to identify the monthly, seasonal and annual trend. Four seasons are distinct in Bangladesh, namely, pre-monsoon, monsoon, post-monsoon and winter. In case of rainfall, mean monthly rainfall, 1-day maximum rainfall and consecutive 3-day maximum rainfall are analyzed in a similar fashion. For maximum, minimum and mean monthly temperature, the majority of the stations show an increasing trend for all three indices. Monsoon season observes highest increasing trend of 0.015 °C/yr for mean monthly temperature whereas the winter season shows the negative trend of −0.002 °C/yr. On an annual basis, the trend is increasing with a value of 0.008 °C/yr or 0.4 °C in 50 years having significance level, p .10. The trend of mean rainfall for annual basis shows an increasing trend of 5.675 mm/yr. The trend in one day and consecutive three-day maximum rainfall depicts that the trend is increasing in few places whereas in other places the trend is decreasing with no significant change. The research concludes that the climate of Bangladesh is getting cooler and drier for winter, on the other hand, warmer and wetter for the rest of the year.

Analysis of changes in thermal growing season indices (tGSI) and their relations with some selected atmospheric teleconnection patterns (ATPs) over the northwest of Iran.

The daily minimum air temperature data from 18 stations located in the northwest of Iran during the period 1986-2015 was used to analyse the inter-annual variations and trends of thermal growing season indices (tGSI) and their relations with different atmospheric teleconnection patterns (ATPs). To analyze the changes in tGSI, tGSS (thermal growing season start), tGSE (thermal growing season end), and tGSL, the time period between tGSS and tGSE were considered. Using non-parametric Mann-Kendall and Spearman tests, the existence of a significant trend for time series of the tGSI and the correlation between ATPs and tGSI was evaluated. For eliminating the effect of serial correlation on test results, the trend-free pre-whitening approach was applied. Furthermore, residual bootstrap method was used to estimate the standard deviation of the Spearman correlation coefficient between tGSI and ATPs. The climate-based results showed the maximum tGSL increase (13.3daysperdecade) for SA-C-M climate. For SH-K-W climate, the maximum significant trends for tGSS and tGSE were 9.6 (earlier start) and 10.8 (delay) days per decade, respectively. In general, in all statistically significant cases, the main cause of the extended tGSL was both earlier tGSS and delayed tGSE. In regional scale, it was found that the most effective teleconnection pattern on tGSS and tGSE are MEI (positive correlation), occurring during late winter and spring, and PDO index (negative correlation) in the summer, respectively. Moreover, the tGSL demonstrated the highest correlation (negative) with PDO with 1-month delay. The findings highlight that the inter-annual variations of tGSI in northwest of Iran can be attributed to the influence of certain atmospheric teleconnection patterns such as MEI, PDO, NAO, AO, EA, and AMO.

Investigating light curve modulation via kernel smoothing

Context.Recent studies have revealed a hitherto unknown complexity of Cepheid pulsations by discovering irregular modulated variability using photometry, radial velocities, and interferometry.Aims.We aim to perform a statistically rigorous search and characterization of such phenomena in continuous time, applying it to 53 classical Cepheids from the OGLE-III catalog.Methods.We have used local kernel regression to search for both period and amplitude modulations simultaneously in continuous time and to investigate their detectability. We determined confidence intervals using parametric and non-parametric bootstrap sampling to estimate significance, and investigated multi-periodicity using a modified pre-whitening approach that relies on time-dependent light curve parameters.Results.We find a wide variety of period and amplitude modulations and confirm that first overtone pulsators are less stable than fundamental mode Cepheids. Significant temporal variations in period are more frequently detected than those in amplitude. We find a range of modulation intensities, suggesting that both amplitude and period modulations are ubiquitous among Cepheids. Over the 12-year baseline offered by OGLE-III, we find that period changes are often nonlinear, sometimes cyclic, suggesting physical origins beyond secular evolution. Our method detects modulations (period and amplitude) more efficiently than conventional methods that are reliant on certain features in the Fourier spectrum, and pre-whitens time series more accurately than using constant light curve parameters, removing spurious secondary peaks effectively.Conclusions.Period and amplitude modulations appear to be ubiquitous among Cepheids. Current detectability is limited by observational cadence and photometric precision: detection of amplitude modulation below 3 mmag requires space-based facilities. Recent and ongoing space missions (K2, BRITE, MOST, CoRoT) as well as upcoming ones (TESS, PLATO) will significantly improve detectability of fast modulations, such as cycle-to-cycle variations, by providing high-cadence high-precision photometry. High-quality long-term ground-based photometric time series will remain crucial to study longer-term modulations and to disentangle random fluctuations from secular evolution.

Optimisation of cropping pattern considering stomatal response to elevated CO<sub align="right">2 emission and climate change

The current article seeks to explore the function of elevated CO2 emission on the variations of reference evapotranspiration (ET0) for optimising cropping pattern in 18 Iranian regions. Accordingly, meteorological data and agricultural information were collected since 1961 to 2010 and 2002 to 2013, respectively. A trend-free pre-whitening (TFPW) approach was applied to modify Mann-Kendall test to determine the ET0 trend based on the Food and Agriculture Organization of the United Nation (FAO)-Penman-Monteith (FPM) method. Then, the function of stomatal response was investigated as an assimilation coefficient to adjust the ET0 since 2050 to 2100. In the next step, the anomalies of the ET0 were calculated in both monthly and annual scales with respect to the significant trends of the meteorological parameters and stomatal response via three different schemes. Finally, to optimise cropping pattern, two indicators namely total virtual water (TVW) and unit blue water value (UBWV) were employed.

Optimisation of cropping pattern considering stomatal response to elevated CO<sub align="right">2 emission and climate change

The current article seeks to explore the function of elevated CO2 emission on the variations of reference evapotranspiration (ET0) for optimising cropping pattern in 18 Iranian regions. Accordingly, meteorological data and agricultural information were collected since 1961 to 2010 and 2002 to 2013, respectively. A trend-free pre-whitening (TFPW) approach was applied to modify Mann-Kendall test to determine the ET0 trend based on the Food and Agriculture Organization of the United Nation (FAO)-Penman-Monteith (FPM) method. Then, the function of stomatal response was investigated as an assimilation coefficient to adjust the ET0 since 2050 to 2100. In the next step, the anomalies of the ET0 were calculated in both monthly and annual scales with respect to the significant trends of the meteorological parameters and stomatal response via three different schemes. Finally, to optimise cropping pattern, two indicators namely total virtual water (TVW) and unit blue water value (UBWV) were employed.

Multivariate time series modeling of selected childhood diseases in Akwa Ibom State

This paper is focused on modeling the five most prevalent childhood diseases in Akwa Ibom State using a multivariate approach to time series. An aggregate of 78,839 reported cases of malaria, upper respiratory tract infection (URTI), Pneumonia, anaemia and tetanus were extracted from five randomly selected hospitals in the State from 1997 to 2011. The monthly Cumulative clinical cases of aforesaid childhood diseases constitute vector time series. Pre-whitening approach was employed to determine whether the components of vector series are interrelated so that each series can be predicted on the bases of lagged values of itself and others. This process revealed that except tetanus; malaria, URTI, Pneumonia and anaemia series are interrelated. Hence, the four interrelated time series were considered in the multivariate analysis. Order selection criteria were employed to determine the order of the vector autoregressive (VAR) model to be fitted to these series. It was discovered that VAR(1) model fitted well. Diagnostic checks were applied to ascertain the adequacy of the model and VAR(1) model was found appropriate. Forecasts were generated. The model revealed that upper respiratory tract infection, pneumonia and anaemia are linked to or caused by malaria.

Spatio-Temporal Analysis of Regional Trends and Shift Changes of Autocorrelated Temperature Series in Urmia Lake Basin

Recently, the Urmia Lake located in northwestern Iran which is the second largest hyper saline in the world suffers from the significant fluctuations of water level and surface area. The current study tries to investigate the spatiotemporal trends of mean (Tmean), maximum (Tmax) and minimum (Tmin) temperatures of monthly, seasonal and annual time-series. To do so, the data of 15 temperature gauge stations within the Urmia Lake basin, for the period 1972–2011 was employed. The pre-whitening approach was applied to remove the effects of serial correlation in the air temperature series based on the Mann-Kendall (MK) test. The results of Ljung-Box test showed positive serial correlation in the Tmean and Tmax series for all of the stations at the 0.05 significance level. In the monthly series, the significant warming trends in the Tmean series were more perceptible than the same ones in Tmax series; however, Tmax trend was found more than Tmin series. The Mann–Whitney (MW) test detected a significance upward shift changes in the annual Tmean, Tmax and Tmin series of about 86, 73 and 80 % of the stations, respectively. The average magnitude of significant warming trends in annual Tmean, Tmax and Tmin series were (+) 0.58 °C, (+) 0.52 °C and (+) 0.69 °C per decade, respectively. Furthermore, the interpolation maps showed that warming trends in the east and west of Urmia Lake were more than southern area. Therefore, the results showed that the basin has suffered from increasing trends in the Tmean, Tmax and Tmin over the recent decades. Finally, significant changes were found in 1980s and 1990s based on the Mann-Kendall ranks and change point tests. In this study, it is interesting that the period of significant changes in warming trends were close to the beginning of decreasing water level of the Lake.

Rotation, differential rotation, and gyrochronology of activeKeplerstars

The high-precision photometry from the CoRoT and Kepler satellites has led to measurements of surface rotation periods for tens of thousands of stars. Our main goal is to derive ages of thousands of field stars using consistent rotation period measurements in different gyrochronology relations. Multiple rotation periods are interpreted as surface differential rotation (DR). We re-analyze the sample of 24,124 Kepler stars from Reinhold et al. (2013) using different approaches based on the Lomb-Scargle periodogram. Each quarter (Q1-Q14) is treated individually using a prewhitening approach. Additionally, the full time series, and different segments thereof are analyzed. For more than 18,500 stars our results are consistent with the rotation periods from McQuillan et al. (2014). Thereof, more than 12,300 stars show multiple significant peaks, which we interpret as DR. Gyrochronology ages between 100 Myr and 10 Gyr were derived for more than 17,000 stars using different gyrochronology relations. We find a bimodal age distribution for Teff between 3200-4700 K. The derived ages reveal an empirical activity-age relation using photometric variability as stellar activity proxy. Additionally, we found 1079 stars with extremely stable (mostly short) periods. Half of these periods may be associated with rotation stabilized by non-eclipsing companions, the other half might be due to pulsations. The derived gyrochronology ages are well constrained since more than 93.0 % of the stars seem to be younger than the Sun where calibration is most reliable. Explaining the bimodality in the age distribution is challenging, and limits accurate stellar age predictions. The existence of cool stars with almost constant rotation period over more than three years of observation might be explained by synchronization with stellar companions, or a dynamo mechanism keeping the spot configurations extremely stable.

Temperature and Precipitation Variability and Its Effects on Streamflow in the Upstream Regions of the Lancang–Mekong and Nu–Salween Rivers

Abstract Hydrological regimes of alpine rivers are highly sensitive to climate variability/change. Temperature and precipitation variability and its effects on streamflow in the upstream regions of the Lancang–Mekong River (LMR) and Nu–Salween River (NSR) are examined in this study based on long-term observational data from 16 meteorological stations and 2 hydrological stations between the 1950s and 2010. This study employs the Mann–Kendall nonparametric test, together with the trend-free prewhitening (TFPW) approach to test trends and the Breaks For Additive Season and Trend (BFAST) method to detect abrupt changes in the hydrometeorological time series. The relations between air temperature, precipitation, and streamflow trends are assessed using random forest regression. The results show significant climate warming and related prevalent positive precipitation trends both at the annual and seasonal scale. A substantial precipitation increase paralleling climate warming, especially in spring, was also observed. However, no consistent abrupt change in meteorological time series was found. The increasing trends of streamflow with climate warming are seen both for the outlets of the LMR and NSR upstream regions, with the abrupt changes occurring in the mid-1960s and the late 1990s, respectively. The relation of streamflow to annual and wet season precipitation is pronounced, especially for the upstream region of the LMR with a percent variance explained of more than 65%. However, the relatively minor linkage of streamflow to air temperature and dry season precipitation may be confounded by the climate warming–driven changes in snowpack, permafrost, glacier, and evapotranspiration. These results could provide further a reference for the regional water resources management under climate change scenarios.

Evolution of low flows in Czechia revisited

Abstract. Although a nationwide study focusing on the evolution of low flows in Czechia was conducted in the past, a need for the revision of the results has arisen. By means of the trend analysis, which specifically considers the presence of significant serial correlation at the first lag, the former study highlighted areas where 7-day low flows increase or decrease. However, taking into account only the lag-one autoregressive process might still have led to the detection of so-called pseudo-trends because, besides short-term persistence, also long-term persistence may adversely influence the variance of the test statistic when the independence among data is required. Therefore, one should carefully investigate the presence of persistence in time series. Before the trend analysis itself, the authors' previous studies aimed at the discrimination between short memory processes and long memory processes employing jointly the Phillips–Perron test and the Kwiatkowski–Phillips–Schmidt–Shin test. This analysis was accompanied by the Hurst exponent estimation. Here, the subsequent identification of trends is carried out using three modifications of the Mann–Kendall test that allow different kinds of persistence. These include the Bayley–Hammersley–Matalas–Langbein–Lettenmaier equivalent sample size approach, the trend-free pre-whitening approach and a block bootstrap with automatic selection of the block length, which was applied for the first time in hydrology. The general results are similar to those presented in the former study on trends. Nevertheless, the divergent minimum discharges evolution in the western part of Czechia is now much clear. Moreover, no significant increasing trend in series incorporating Julian days was found.

Wet-dry runoff correlation in Western Route of South-to-North Water Diversion Project, China

The Western Route of the South-to-North Water Diversion Project is an important trans-basin diversion project to transfer water from the upstream Yangtze River and its tributaries (water-exporting area), to the upstream of the Yellow River (water-importing area). The long-term hydrological data from 14 stream gauging stations in the Western Route area and techniques including the pre-whitening approach, non-parametric test, Bayes, law, variance analysis extrapolation, and Wavelet Analysis are applied to identify the streamflow characteristics and trends, streamflow time series cross-correlations, wetness-dryness encountering probability, and periodicities that occurred over the last 50 years. The results show that the water-exporting area, water-importing area, and the stretch downstream of the water-exporting have synchronization in high–low flow relationship, whereas they display non-synchronization in long-term evolution. This corresponds to the complicated and variable climate of the plateau region. There is no obvious increasing or decreasing trend in runoff at any gauging station. The best hydrological compensation probability for rivers where water is diverted is about 25% to 10%, and those rivers influenced significantly by diversion are the Jinsha and Yalong rivers. Proper planning and design of compensation reservoirs for the water-exporting area and stretch downstream of the water-exporting area can increase the hydrological compensation possibility from water-exporting area to the water-importing area, and reduce the impact on the stretch of river downstream of the water-exporting area.

Precipitation Trends over Time Using Mann-Kendall and Spearman’s rho Tests in Swat River Basin, Pakistan

Accurately predicting precipitation trends is vital in the economic development of a country. This research investigated precipitation variability across 15 stations in the Swat River basin, Pakistan, over a 51-year study period (1961–2011). Nonparametric Mann-Kendall (MK) and Spearman’s rho (SR) statistical tests were used to detect trends in monthly, seasonal, and annual precipitation, and the trend-free prewhitening approach was applied to eliminate serial correlation in the precipitation time series. The results highlighted a mix of positive (increasing) and negative (decreasing) trends in monthly, seasonal, and annual precipitation. One station in particular, the Saidu Sharif station, showed the maximum number of significant monthly precipitation events, followed by Abazai, Khairabad, and Malakand. On the seasonal time scale, precipitation trends changed from the summer to the autumn season. The Saidu Sharif station revealed the highest positive trend (7.48 mm/year) in annual precipitation. In the entire Swat River basin, statistically insignificant trends were found in the subbasins for the annual precipitation series; however, the Lower Swat subbasin showed the maximum quantitative increase in the precipitation at a rate of 2.18 mm/year. The performance of the MK and SR tests was consistent at the verified significance level.