Length Of Data Series Research Articles

Modeling Riverbed Elevation and Bedload Tracer Transport Resting Times Using Fractional Laplace Motion

AbstractRiverbed elevations play a crucial role in sediment transport and flow resistance, making it essential to understand and quantify their effects. This knowledge is vital for various fields, including river engineering and stream ecology. Previous observations have revealed that fluctuations in the bed surface can exhibit both multifractal and monofractal behaviors. Specifically, the probability distribution function (PDF) of elevation increments may transition from Laplace (two‐sided exponential) to Gaussian with increasing scales or consistently remain Gaussian, respectively. These differences at the finest timescale lead to distinct patterns of bedload particle exchange with the bed surface, thereby influencing particle resting times and streamwise transport. In this paper, we utilize the fractional Laplace motion (FLM) model to analyze riverbed elevation series, demonstrating its capability to capture both mono‐ and multi‐fractal behaviors. Our focus is on studying the resting time distribution of bedload particles during downstream transport, with the FLM model primarily parameterized based on the Laplace distribution of increments PDF at the finest timescale. Resting times are extracted from the bed elevation series by identifying pairs of adjacent deposition and entrainment events at the same elevation. We demonstrate that in cases of insufficient data series length, the FLM model robustly estimates the tail exponent of the resting time distribution. Notably, the tail of the exceedance probability distribution of resting times is much heavier for experimental measurements displaying Laplace increments PDF at the finest scale, compared to previous studies observing Gaussian PDF for bed elevation.

Effect of Data and Gap Characteristics on the Nonlinear Calculation of Motion During Locomotor Activities.

This study investigated how data series length and gaps in human kinematic data impact the accuracy of Lyapunov exponents (LyE) calculations with and without cubic spline interpolation. Kinematic time series were manipulated to create various data series lengths (28% and 100% of original) and gap durations (0.05-0.20s). Longer gaps generally resulted in significantly higher LyE% error values in each plane in noninterpolated data. During cubic spline interpolation, only the 0.20-second gap in frontal plane data resulted in a significantly higher LyE% error. Data series length did not significantly affect LyE% error in noninterpolated data. During cubic spline interpolation, sagittal plane LyE% errors were significantly higher at shorter versus longer data series lengths. These findings suggest that not interpolating gaps in data could lead to erroneously high LyE values and mischaracterization of movement variability. When applying cubic spline, a long gap length (0.20s) in the frontal plane or a short sagittal plane data series length (1000 data points) could also lead to erroneously high LyE values and mischaracterization of movement variability. These insights emphasize the necessity of detailed reporting on gap durations, data series lengths, and interpolation techniques when characterizing human movement variability using LyE values.

The Effect of Training Data Series Length on the Performance of the Tank Model for Transforming Rainfall into Runoff Data Series

The Tank model by Sugawara is included in the lumped model category. As with other types of lumped models, the effectiveness of the application of the Tank model is largely determined by the parameter optimization method applied and the quantity of training data involved in the calibration process. This article proposes the Tank-DE model to transform rain data series into discharge in a watershed. The Tank-DE model is built from a combination of a simulation equation system based on the Tank model and a multi-parameter optimization equation system based on the Differential evolution (DE) Algorithm. This article also examines the sensitivity analysis of the model to study the effect of the length of the training data series involved in the calibration process on the predictive discharge quality generated by the Tank-DE model. Thus, the minimum length of the training data series can be recommended, related to the application of the model. The results of the analysis show that the Tank-DE model can present the relationship between rainfall data series and daily period discharge very well. The results of the sensitivity analysis show that there is an indication that the longer the training data series, the more quantitatively positive impact on the performance of the model. The calibration process involving a training data set for 1 year produces a very good value of the coefficient of determination (r2 = 0.94), but the indicator decreases drastically at the validation stage. The calibration process involving a relatively long training data series produces a more consistent value of the coefficient of determination. This indicates that the Tank-DE model can be an alternative solution to solve the problem of scarcity of discharge data series which is a classic problem in water resource development activities.

Optimization of sizing of annual water storage reservoirs considering return period association

An increasing concern among water resources managers is the search for ways to improve reservoir sizing techniques. A simple technical and scientifically based technique is the sequent peak method, which has been widely disseminated, but presents limitations with respect to the length of the available data series. The objective of this study was to propose modifications to the sequent peak method to overcome the limitations related to the impossibility of associating the reservoir storage capacity with return periods different from the length of the data series. Storage capacities were estimated for every year, considering gauge stations located in the Urucuia River Basin, based on the sequent peak method. In order to associate such capacities with a frequency factor (return period), the Gumbel distribution was applied to the estimated storage values. This association with return periods which differ from the number of years in the data series showed great applicability

Quantifying false positives in simulated events using partial interval recording and momentary time sampling with dual‐criteria methods

The dual‐criteria (DC) and conservative dual‐criteria (CDC) methods allow clinicians and researchers to quantify the occurrence of false‐positive outcomes within single‐case experimental designs. The purpose of the current study was to use these DC and CDC methods to measure the incidence of false positives with simulated data collected via discontinuous interval methods (i.e., momentary time sampling, partial‐interval recording) as a function of data series length. We generated event data to create 316,800 unique simulated data series for analysis. In Experiment 1, we evaluated how changes in relevant parameters (i.e., interval sizes, event durations, IRT‐to‐event‐run ratios) produced false positives with momentary time sampling procedures. We also assessed the degree that the CDC method produced fewer false positives than the DC method with simulated interval data. In Experiment 2, we used similar procedures to quantify the occurrence of false positives with partial‐interval recording data. We successfully replicated outcomes from previous research in the current study, though such results only highlight the generality of the procedures relating to false positive (and not false negative) outcomes. That is, these results indicate MTS and PIR may adequately control for false positives, but our conclusions are limited by a lack of data on power.

Analysis of extreme flow uncertainty impact on size of flood hazard zones for the Wronki gauge station in the Warta river

In this paper, the impact of maximum flow uncertainty on flood hazard zone is analyzed. Two factors are taken into account: (1) the method for determination of maximum flows and (2) the limited length of the data series available for calculations. The importance of this problem is a consequence of the implementation of the EU Flood Directive in all EU member states. The factors mentioned seem to be among the most important elements responsible for potential uncertainty and inaccuracy of the developed flood hazard maps. Two methods are analyzed, namely the quantiles method and the maximum likelihood method. The maximum flows are estimated for the Wronki gauge station located in the reach of the Warta river. This simple river system is located in the central part of Poland. The length of the available data is 44 years. Hence, the series of the lengths 40, 30 and 20 years are tested and compared with reference calculations for 44 years. The hydrodynamic model HEC-RAS is used to calculate water surface profiles in steady state flow. The Python scripting language is applied for automation of HEC-RAS calculations and processing of final results in the form of inundation maps. The number of trials for each factor is not huge to keep the presented methodology useful in practice. The chosen measure of uncertainty is the range of variability for maximum flow values as well as inundation areas. The estimated values stressed the great importance of the factors analyzed for the uncertainty of the maximum flows as well as inundation areas. The impact of the data series length on the maximum flows is straightforward; a shorter data series gives a wider range of variability. However, the dependencies between other factors are more complex. Hence, the application of methodology based on the simulation and GIS data processing for assessment of this problem seems to be quite a good approach.

Low frequency variability and sensitivity of the Atlantic meridional overturning circulation in selected IPCC climate models

Abstract The structure of main modes of the decadal and multidecadal variability of the Atlantic meridional overturning circulation (AMOC) is analyzed for the climate models INM-CM5 (INM RAS), CCSM4 (NCAR), MPI-LR and MPI-MR (MPI). It is shown that oscillations with characteristic periods of 25–35 and 50–70 years are recognized in the models, and the corresponding spatial structures are variations of the intensity and position of the AMOC. Relations connecting changes of thermohaline circulation with external impacts on the system are constructed for the above models. The analysis of stability of calculations relative to the length of data series used for calculations is performed. The optimal impacts leading to the greatest response of the AMOC and influence functions causing its response along the leading modes of low-frequency variability are constructed. The optimal impacts have the form of density anomalies localized in the North Atlantic, and the structures of the corresponding responses are dominated by leading low-frequency modes of variability. The structure of optimal impacts varies greatly from model to model.

When does more mean worse? Accuracy of judgmental forecasting is nonlinearly related to length of data series

When people make forecasts from series of data, how does their accuracy depend on the length of the series? Previous research has produced highly conflicting findings: some work shows accuracy increases with more data; other research shows that it decreases. In two experiments, we found an inverted U-shaped relation between forecast error and series length for various series containing different patterns and noise levels: error decreased as the length of the series increased from five through 20 to 40 items but also decreased as the series length decreased from five through two to one item. We argue that, with short series, people use a simple heuristic approach to forecasting (e.g., the naïve forecast). With longer series, they extract patterns from the series and extrapolate from them to produce their forecasts. Use of heuristics is poorer but extraction of patterns is better when there are more items in the series. For series of intermediate length, neither type of strategy operates well, thereby producing the inverted U-shaped relation that we observed. Implications for unaided judgmental forecasting and for forecasting based on a combination of judgmental and statistical methods are discussed.

A distribution-free ordinal classification of floods based on moments

ABSTRACTClassification of floods is often based on return periods of their peaks estimated from probability distributions and hence depends on assumptions. The choice of an appropriate distribution function and parameter estimation are often connected with high uncertainties. In addition, limited length of data series and the stochastic characteristic of the occurrence of extreme events add further uncertainty. Here, a distribution-free classification approach is proposed based on statistical moments. By using robust estimators the sampling effects are reduced and time series of different lengths can be analysed together. With a developed optimization procedure, locally and regionally consistent flood categories can be defined. In application, it is shown that the resulting flood categories can be used to assess the spatial extent of extreme floods and their coincidences. Moreover, groups of gauges, where simultaneous events belong to the same classes, are indicators for homogeneous groups of gauges in regionalization.

Application of linear mean-square estimation in ocean engineering

The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method’s overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations (adjacent to the concerning sea area) and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.

Effect of calibration data series length on performance and optimal parameters of hydrological model

In order to assess the effects of calibration data series length on the performance and optimal parameter values of a hydrological model in ungauged or data-limited catchments (data are non-continuous and fragmental in some catchments), we used non-continuous calibration periods for more independent streamflow data for SIMHYD (simple hydrology) model calibration. Nash-Sutcliffe efficiency and percentage water balance error were used as performance measures. The particle swarm optimization (PSO) method was used to calibrate the rainfall-runoff models. Different lengths of data series ranging from one year to ten years, randomly sampled, were used to study the impact of calibration data series length. Fifty-five relatively unimpaired catchments located all over Australia with daily precipitation, potential evapotranspiration, and streamflow data were tested to obtain more general conclusions. The results show that longer calibration data series do not necessarily result in better model performance. In general, eight years of data are sufficient to obtain steady estimates of model performance and parameters for the SIMHYD model. It is also shown that most humid catchments require fewer calibration data to obtain a good performance and stable parameter values. The model performs better in humid and semi-humid catchments than in arid catchments. Our results may have useful and interesting implications for the efficiency of using limited observation data for hydrological model calibration in different climates.

Mapping trends of large and medium size carnivores of conservation interest in Romania

We analysed yearly estimates of population size data during 2001-2012 for five carnivores species of conservation interest ( Ursus arctos, Canis lupus, Lynx lynx, Felis silvestris and Canis aureus ). Population size estimations were done by the game management authorities and integrated by the competent authorities on the Ministry of Environment and Climate Change. Trends in data were detected using non-parametric Mann-Kendall test. This test was chosen considering the short length of data series and its usefulness for non-normal distributed data. The trend was tested at three spatial scales: game management units (n=1565), biogeographical region (n=5) and national. Trends depicted for each game management unit were plotted using ArcGIS, resulting species trend distribution maps. For the studied period increasing population trends were observed for Ursus arctos, Canis lupus, Canis aureus and Lynx lynx , while for Felis silvestris there was no trend recorded. Such an analysis in especially useful for conservation proposes, game management and reporting obligations under article 17 of the EC Habitat Directive, using population trend as a proxy for population dynamics. We conclude that the status of the five carnivore species is favourable during the study period.

APPLICATION OF ARIDITY INDEX IN ESTIMATION OF DATA ADJUSTMENT PARAMETERS IN THE XINANJIANG MODEL

Based on the sensitivity analysis at annual, monthly and daily scales, parameters of the Xinanjiang model could be divided into three groups and optimized independly without considering the effects from other groups. This paper focuses on the optimization of data adjustment parameters, Cp and Cep, which are sensitive at annual scale. The concept of aridity index is introduced into the optimization process, and proposed a relationship describing Cp and Cep as a function of annual runoff coefficient and pan aridity index. Three different methods are developed to estimate the value ofCp andCep in ideal condition and actual practice respectively. The results show that, compared with optimizing Cp and Cep independly, the method considering the relationship of runoff coefficient and pan aridity index will narrow the parameter space, and keep the same accuracy. The effectivity of method using the simple linear relationship will depend on the length of data series and correlation between annual runoff coefficient and pan aridity index.

Applications of the MVWG Multivariable Stochastic Weather Generator

Weather generators (WG) became significant modules of crop models and decision support systems in the past decade. Using a large meteorological database from North America; two basic problems, related to the applicability of WGs in case of short or lacking data series, were investigated in the framework of the Multivariable weather generator (MVWG). First, the minimum data series length, required for adequate parameterization of the WG, was determined. Our results suggest that 15 years of observed data are enough for adequate parameterization of the MVWG. We then investigated a possibility of spatial interpolation of WG parameters using the outputs of the WG for sites with no meteorological observations. Coupled with the presented interpolation technique, MVWG was able to generate realistic weather data for sites with no measurements situated in climatically and geographically homogeneous regions.

Hubungan Panjang Seri Data Historik Terhadap Kualitas Data Hasil Prediksi Pada Penerapan Model Rantai Markov Untuk Peramalan Aliran Sungai

Markov Chain Model is a stochastic model for forecasting the river flow which in his analysis always involves a long series of historical data. In most studies the method is still highly theoretical and not fully applicable significantly due to the limited data in the field.This study is an attempt to optimize the application of Markov Chain Model for its functionality extensively to extrapolate data streams. The scope of this research is basically conducted a study on the relationship between the length of the historical flow data series with data quality prediction results. By knowing these characteristics, the error correction of analysis results can be expected due to data limitations, so that the Markov Chain Model can be widely applied to optimization of waterworks operations.Results for the Konto River and River showed that the prediction of flow Kwayangan next year with Markov chain models tend to give better results than the results of forecasting by conventional methods are widely applied. Markov model is good enough to predict the river flow has low flow fluctuations, but for a river flow fluctuated sharply less than satisfactory results. The length of data series ranges from 15 to 20 of the optimal inputs to produce a minimum error rate prediction. Accuracy of prediction result is not determined by the length of the input data series, but is determined by the nature of statistical data. Value of lag-1 correlation coefficient are large and small skewness coefficient of the historical data tends to give a satisfactory prediction results.Key words: river flow, data, prediktion, markov model.

Shannon and Renyi Entropies to Classify Effects of Mild Traumatic Brain Injury on Postural Sway

BackgroundMild Traumatic Brain Injury (mTBI) has been identified as a major public and military health concern both in the United States and worldwide. Characterizing the effects of mTBI on postural sway could be an important tool for assessing recovery from the injury.Methodology/Principal FindingsWe assess postural sway by motion of the center of pressure (COP). Methods for data reduction include calculation of area of COP and fractal analysis of COP motion time courses. We found that fractal scaling appears applicable to sway power above about 0.5 Hz, thus fractal characterization is only quantifying the secondary effects (a small fraction of total power) in the sway time series, and is not effective in quantifying long-term effects of mTBI on postural sway. We also found that the area of COP sensitively depends on the length of data series over which the COP is obtained. These weaknesses motivated us to use instead Shannon and Renyi entropies to assess postural instability following mTBI. These entropy measures have a number of appealing properties, including capacity for determination of the optimal length of the time series for analysis and a new interpretation of the area of COP.ConclusionsEntropy analysis can readily detect postural instability in athletes at least 10 days post-concussion so that it appears promising as a sensitive measure of effects of mTBI on postural sway.AvailabilityThe programs for analyses may be obtained from the authors.

Long-term trends in the temperature of the mesosphere/lower thermosphere region: 2. Solar response

Understanding trends in any atmospheric quantity typically requires the ability to distinguish between naturally occurring processes that result in trends, such as the 11 year solar cycle, and potential anthropogenic secular trends that occur simultaneously. After the review of mesospheric and lower thermospheric temperature response to solar activity by Beig et al. (2008), a few new results along with some modified results by revisiting the older data sets have been reported recently. Main improvement is due to the length of data series and amount of data which have been accounted in recent years. This article summarizes the progress made in the field of temperature variability due to changing solar activity as reported recently. Recent investigations revealed that the solar signal becomes stronger with increasing latitude in the mesosphere. Temperature response to solar activity at the lower part of mesopause region is around a few degrees per 100 solar flux units (sfu), which becomes stronger (4-5 K/100 sfu) in the upper part of this region in both hemispheres. The overall global picture indicates that the solar signal in the mesopause region temperature in the Northern Hemisphere is relatively stronger in recent time in a majority of locations compared to results reported in earlier reviews.

Analysis of extreme hydrological Events on THE danube using the Peak Over Threshold method

Analysis of extreme hydrological Events on THE danube using the Peak Over Threshold methodThe Peak Over Threshold Method (POT) was used as an alternative technique to the traditional analysis of annual discharge maxima of the Danube River. The POT method was applied to a time-series of daily discharge values covering a period of 60 years (1931-1990) at the following gauge stations: Achleiten, Kienstock, Wien, Bratislava and Nagymaros. The first part of the paper presents the use of the POT method and how it was applied to daily discharges. All mean daily discharges exceeding a defined threshold were considered in the POT analysis. Based on the POT waves independence criteria the maximum daily discharge data were selected. Two theoretical log-normal (LN) and Log-Pearson III (LP3) distributions were used to calculate the probability of exceeding annual maximum discharges. Performance of the POT method was compared to the theoretical distributions (LN, LP3). The influence of the data series length on the estimation of theN-year discharges by POT method was carried out too. Therefore, with regard to later regulations along the Danube channel bank the 40, 20 and 10-year time data series were chosen in early of the 60-year period and second analysed time data series were selected from the end of the 60-year period. Our results suggest that the POT method can provide adequate and comparable estimates ofN-year discharges for more stations with short temporal coverage.

Statistical precision and sensitivity of measures of dynamic gait stability

Recently, two methods for quantifying a system's dynamic stability have been applied to human locomotion: local stability (quantified by finite time maximum Lyapunov exponents, λS-stride and λL-stride) and orbital stability (quantified as maximum Floquet multipliers, MaxFm). Thus far, however, it has remained unclear how many data points are required to obtain precise estimates of these measures during walking, and to what extent these estimates are sensitive to changes in walking behaviour.To resolve these issues, we collected long data series of healthy subjects (n=9) walking on a treadmill in three conditions (normal walking at 0.83m/s (3km/h) and 1.38m/s (5km/h), and walking at 1.38m/s (5km/h) while performing a Stroop dual task). Data series from 0.83 and 1.38m/s trials were submitted to a bootstrap procedure and paired t-tests for samples of different data series lengths were performed between 0.83 and 1.38m/s and between 1.38m/s with and without Stroop task.Longer data series led to more precise estimates for λS-stride, λL-stride, and MaxFm. All variables showed an effect of data series length. Thus, when estimating and comparing these variables across conditions, data series covering an equal number of strides should be analysed. λS-stride, λL-stride, and MaxFm were sensitive to the change in walking speed while only λS-stride and MaxFm were sensitive enough to capture the modulations of walking induced by the Stroop task. Still, these modulations could only be detected when using a substantial number of strides (>150).

Métodos de variável instrumental fuzzy para identificação de sistemas

Este artigo apresenta uma proposta teórica de métodos de variável instrumental fuzzy para identificação de sistemas não-lineares no tempo discreto e estimação paramétrica em ambientes ruidosos a partir do conceito de variável instrumental fuzzy. A análise teórica é apresentada a partir de uma formulação adequada associada ao modelo fuzzy Takagi-Sugeno. A complexidade do algoritmo é baixa e as propriedades estatísticas mostram que o erro assintótico das estimações paramétricas tende a zero quando o conjunto de dados aumenta.