Computation of Average Run Length for Residual-Based T^2 Control Chart for Multivariate Autocorrelated Processes

The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.

On-line Recognition of Abnormal Patterns in Bivariate Autocorrelated Process Using Random Forest

It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time.Meanwhile,the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics.This goes against the statistical I.I.D assumption in using the multivariate control charts,which may lead to the performance of multivariate control charts collapse soon.Meanwhile,the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation,and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities.This study proposed a pattern recognition model using Random Forest(RF)as pattern model to detect and identify the abnormalities in bivariate autocorrelated process.The simulation experiment results demonstrate that the model is superior on recognition accuracy(RA)(97.96%)to back propagation neural networks(BPNN)(95.69%),probability neural networks(PNN)(94.31%),and support vector machine(SVM)(97.16%).When experimenting with simulated dynamic process data flow,the model also achieved better average running length(ARL)and standard deviation of ARL(SRL)than those of the four comparative approaches in most cases of mean shift magnitude.Therefore,we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process.Although bivariate autocorrelated process is focused in this study,the proposed model can be extended to multivariate autocorrelated process control.

A Simulation Study on the Performances of Classical Var and Sims-Zha Bayesian Var Models in the Presence of Autocorrelated Errors

It is well known that a high degree of positive dependency among the errors generally leads to 1) serious underestimation of standard errors for regression coefficients;2) prediction intervals that are excessively wide. This paper set out to study the performances of classical VAR and Sims-Zha Bayesian VAR models in the presence of autocorrelated errors. Autocorrelation levels of (-0.99, -0.95, -0.9, -0.85, -0.8, 0.8, 0.85, 0.9, 0.95, 0.99) were considered for short term (T = 8, 16);medium term (T = 32, 64) and long term (T = 128, 256). The results from 10,000 simulation revealed that BVAR model with loose prior is suitable for negative autocorrelations and BVAR model with tight prior is suitable for positive autocorrelations in the short term. While for medium term, the BVAR model with loose prior is suitable for the autocorrelation levels considered except in few cases. Lastly, for long term, the classical VAR is suitable for all the autocorrelation levels considered except in some cases where the BVAR models are preferred. This work therefore concludes that the performance of the classical VAR and Sims-Zha Bayesian VAR varies in terms of the autocorrelation levels and the time series lengths.

On the Performances of Classical VAR and Sims-Zha Bayesian VAR Models in the Presence of Collinearity and Autocorrelated Error Terms

In time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR models with quadratic decay on bivariate time series data jointly influenced by collinearity and autocorrelation. We simulate bivariate time series data for different collinearity levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) and autocorrelation levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) for time series length of 8, 16, 32, 64, 128, 256 respectively. The results from 10,000 simulations reveal that the models performance varies with the collinearity and autocorrelation levels, and with the time series lengths. In addition, the results reveal that the BVAR4 model is a viable model for forecasting. Therefore, we recommend that the levels of collinearity and autocorrelation, and the time series length should be considered in using an appropriate model for forecasting.

Influence of Human Activity Intensity on Habitat Quality in Hainan Tropical Rainforest National Park,China

Due to long-term human activity interference,the Hainan Tropical Rainforest National Park(HTRNP)of China has experienced ecological problems such as habitat fragmentation and biodiversity loss,and with the expanding scope and intensity of human activity impact,the regional ecological security is facing serious challenges.A scientific assessment of the interrelationship between human activity intensity and habitat quality in the HTRNP is a prerequisite for achieving effective management of ecological disturbances caused by human activities and can also provide scientific strategies for the sustainable development of the region.Based on the land use change data in 2000,2010,and 2020,the spatial and temporal variations and the relationship between habitat quality(HQ)and human activity intensity(HAI)in the HTRNP were explored using the integrated valuation of ecosystem services and trade-offs(InVEST)model.System dynamics and land use simulation models were also combined to conduct multi-scenario simulations of their relationships.The results showed that during 2000–2020,the habitat quality of the HTRNP improved,the intensity of human activities decreased each year,and there was a negative correlation between the two.Second,the system dynamic model could be well coupled with the land use simulation model by combining socio-economic and natural factors.The simulation scenarios of the coupling model showed that the harmonious development(HD)scenario is effective in curbing the increasing trend of human activity intensity and decreasing trend of habitat quality,with a weaker trade-off between the two compared with the baseline development(BD)and investment priority oriented(IPO)scenarios.To maintain the authenticity and integrity of the HTRNP,effective measures such as ecological corridor construction,ecological restoration,and the implementation of ecological compensation policies need to be strengthened.

A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration,without requiring a specific form of the incident pulse function.A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form.The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals,which are not captured by the classical local model.To assess the performance of the global model compared to the classic local model,we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum(FWHMs).When the incident pulse waveform is Lorentzian with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 399.9 fs,while the classic local model predicts an FWHM of 331.4 fs.The difference between the two models is 68.6 fs,corresponding to an error of 17.2%.Similarly,for a sech-type incident pulse with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 343.9 fs,while the local model predicts an FWHM of 308.8 fs.The difference between the two models is 35.1 fs,with an error of 10.2%.We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs,200 fs and 500 fs.The differences between the global and local models are 17.1 fs,68.6 fs and 86.0 fs,respectively,with errors approximately around 17%.These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

Enhancing transboundary natural tourism resources governance:unveiling the spatial pattern and its influencing factors

Tourism resources that span provincial boundaries in China play a pivotal role in regional development,yet effective governance poses persistent challenges.This study addresses this issue by constructing a comprehensive database of transboundary natural tourism resources(TNTR)through amalgamation of diverse data sources.Utilizing the Getis-Ord Gi^(*),kernel density estimation,and geographical detectors,we scrutinize the spatial patterns of TNTR,focusing on both named and unnamed entities,while exploring the influencing factors.Our findings reveal 7883 identified TNTR in China,with mountain tourism resources emerging as the predominant type.Among provinces,Hunan boasts the highest count,while Shanghai exhibits the lowest.Southern China demonstrates a pronounced clustering trend in TNTR distribution,with the spatial arrangement of biological landscapes appearing more random compared to geological and water landscapes.Western China,characterized by intricate terrain,exhibits fewer TNTR,concurrently unveiling a significant presence of unnamed natural tourism resources.Crucially,administrative segmentation influences TNTR development,generating disparities in regional goals,developmental stages and intensities,and management approaches.In response to these variations,we advocate for strengthening the naming of the unnamed transboundary tourism resources,constructing a geographic database of TNTR for government and establishing a collaborative management mechanism based on TNTR database.Our research contributes to elucidating the intricate landscape of TNTR,offering insights for tailored governance strategies in the realm of cross-provincial tourism resource management.

A Probing Model of Secret Key Generation Based on Channel Autocorrelation Function

Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,there is a lack of research on the optimization of the probing process.This study investigates how to optimize correlated parameters to maximize the SKG rate(SKGR)in the time-division duplex(TDD)mode.First,we build a probing model which includes the effects of transmitting power,the probing period,and the dimension of sample vectors.Based on the model,the analytical expression of the SKGR is given.Next,we formulate an optimization problem for maximizing the SKGR and give an algorithm to solve it.We conclude the SKGR monotonically increases as the transmitting power increases.Relevant mathematical proofs are given in this study.From the simulation results,increasing appropriately the probing period and the dimension of the sample vector could increase the SKGR dramatically compared to a yardstick,which indicates the importance of optimizing the parameters related to the channel probing phase.

Study on the Spatiotemporal Pattern Evolution and Influencing Factors of Population Aging in Henan Province

This study utilized census data from Henan Province for the years 2000,2010,and 2020 to investigate the spatiotemporal evolution of population aging,defined by the proportion of the population aged 65 and above.Employing spatial analysis techniques such as spatial autocorrelation and the standard deviation ellipse,the research mapped out the progression and distribution of aging demographics.Furthermore,the study delved into the influencing factors of aging using an optimal parameters-based geographical detector.Results indicate a deepening degree of population aging in Henan Province,transitioning from an adult type to an old type structure.There is a marked positive spatial correlation among counties,with high-value aging areas initially decreasing,then increasing,and notably spreading from the central to the central and southern regions of the province.The center of gravity for population aging,specifically around Changge City and Xuchang City,exhibits a trajectory moving southeast before shifting northwest.Factor detection reveals that in 2000,2010,and 2020,the elderly dependency ratio predominantly influences the aging trend,with explanatory powers of 88.4%,87.9%,and 90.9%,respectively.Interaction analysis indicates that the interaction between the old-child ratio and the elderly dependency ratio has a strong explanatory power for the aging patterns in Henan Province,reaching 97.3%,97.0%,and 97.4%,respectively.

Spatial Analysis of the Aging Population and Socio-economic Factors of China:Global and Local Perspectives

Population aging has become an inevitable trend and exerted profound influences on socio-economic development in China.In this study,we utilized data from national population census and statistical yearbooks in 2010 and 2020 to explore spatio-temporal patterns of aging population and its coupling correlations with socio-economic factors from both global and local perspectives.The results from Local Indicators of Spatial Association(LISA)uncover notable spatial disparities in aging population rates,with higher rates concentrated in the eastern regions and lower rates in the western areas of the Chinese mainland.The results from the global correlation analysis with the changes in aging population rates show significant positive correlations with government interventions and industrial structures,but negatively correlated with economic development,social consumption,and medical facilities.From a local perspective,a Geographically Weighted(GW)correlation analysis is employed to uncover local correlations between aging trends and socio-economic factors.The insights gained from this technique not only underscore the complexity and diversity of economic implications stemming from population aging,but also provide invaluable guidance for crafting region-specific economic policies tailored to various stages of population aging.

Evaluation of COVID-19 Cases and Vaccinations in the State of Georgia, United States: A Spatial Perspective

This study evaluates the distribution of COVID-19 cases and mass vaccination campaigns from January 2020 to April 2023. There are over 235,000 COVID-19 cases and over 733,000 vaccinations across the 159 counties in the state of Georgia. Data on COVID-19 was acquired from usafact.org while the vaccination records were obtained from COVID-19 vaccination tracker. The spatial patterns across the counties were analyzed using spatial statistical techniques which include both global and local spatial autocorrelation. The study further evaluates the effect of vaccination and selected socio-economic predictors on COVID-19 cases across the study area. The result of hotspot analysis reveals that the epicenters of COVID-19 are distributed across Cobb, Fulton, Gwinnett, and DeKalb counties. It was also affirmed that the vaccination records followed the same pattern as COVID-19 cases’ epicenters. The result of the spatial error model performed well and accounted for a considerable percentage of the regression with an adjusted R squared of 0.68, Akaike Information Criterion (AIC) 387.682 and Breusch-Pagan of 9.8091. ESDA was employed to select the main explanatory variables. The selected variables include vaccination, population density, percentage of people that do not have health insurance, black race, Hispanic and these variables accounted for 68% of the number of COVID-19 cases in the state of Georgia during the study period. The study concludes that both COVID-19 cases and vaccinated individuals have spatial peculiarities across counties in Georgia state. Lastly, socio-economic variables and vaccination are very important to reduce the vulnerability of individuals to COVID-19 disease.

Spatial Morphology Evolution Characteristics Analysis of the Resident Population Distribution in Henan, China

The population spatial distribution pattern and its evolving pattern play an important role in regional allocation of social resources and production factors, formulation of regional development plans, construction of a better life society, and promotion of regional economic development. Based on the resident population statistics data of Henan province from 2006 to 2021, with county as the basic study unit, the paper studies the spatial morphology characteristics and its evolution patterns of resident population distribution, by using spatial analysis methods such as population distribution center, standard deviation ellipse, and spatial auto correlation analysis. The results show that: the resident population spatial distribution shows unbalanced state, the population agglomeration areas mainly distribute in the northeast part and north part, where the resident population growth rate is significantly higher than other regions, over time, this trend is gradually becoming significant. The resident population distribution has a trend of centripetal concentration, with the degree and trend of centripetal gradually strengthening. The resident population distribution has obvious directional characteristics, but the significance is not high, the weighted resident population average center is approximately located at (4.13740˚N, 113.8935˚E), and the azimuth of the distribution axis is approximately 11.19˚. The population distribution has obvious agglomeration characteristics, with the built-up areas of Zhengzhou and Luoyang as their centers, where have a significant siphon effect on the surrounding population. The southern and southwestern regions in the province form a relatively stable belt area of Low-Low agglomeration areas.

PROCESS CAPABILITY ANALYSIS AND ESTIMATION SCHEME FOR AUTOCORRELATED DATA

Autocorrelation is prevalent in continuous production processes, such as the processes in the chemical and pharmaceutical industries. With the development of measurement technology and data acquisition technology, sampling frequency is getting higher and the existence of autocorrelation cannot be ignored. This paper analyzes five estimation schemes of process capability for autocorrelated data. Comparisons among these schemes are discussed for small sample and large sample. In conclusion, this paper gives a procedure of process capability analysis for autocorrelated data.

Is there regional convergence between Morocco and its OECD partner countries in terms of well-being?

Morocco wants its 12 regions to play the role as the main lever of its public policies to initiate harmonized spatial multidimensional development. In the context of this goal and Morocco’s openness over the past two decades to bilateral and multilateral cooperation in an effort toward regional integration, this article studies the convergence of 389 regions in 36 countries(Morocco and 35 of its partner member countries in the Organization for Economic Co-operation and Development(OECD)) between 2000 and 2019 in terms of well-being. To this end, we considered the territorial dimension of β-convergence models for well-being and its four domains(economic, social, environmental, and governance). Then, we adapted the absolute β-convergence model by taking into account the existence of spatial heterogeneity according to five specifications of spatial models. Thus, apart from environmental domain, we found that β-convergence of regions is significant for well-being and three of its domains(economic, social, and governance). These convergences are made by a spatially autocorrelated error model(SEM). However, the speed and period of convergence are relatively low for social domain, partly explaining the very exacerbated tensions at the territorial level. The fastest convergence was achieved in governance domain, followed by economic domain. This suggests that emerging countries must pay particular attention to national public action in favor of social cohesion at the territorial level. The lack of convergence in environmental domain calls for common actions for all countries at the supranational level to protect the commons at the territorial level.

2011-2020年我国医学生分布的区域差异及动态演进

目的研究我国医学生分布的集聚水平、空间分布特征和时空演变趋势,为宏观调控医学高等院校区域均衡发展提供依据。方法运用集聚度、空间自相关模型和核密度估计法分析医学生空间分布情况和发展趋势。结果2011—2020年,我国医学生集聚水平在观察末期升至7.478,涨幅15.43%,呈现“东高西低、南高北低”的空间分布格局。各省份间呈空间正相关性,形成稳定的“高高集聚、低低集聚”的空间分布特征。医学生分布的绝对差异在中部地区趋于缓和,在东、西部地区持续扩大,总体呈多极化演化特征。结论我国医学生分布的集聚水平稳步上升且存在不均衡现象,已形成稳定的聚集区域并存在低流动性。建议构建区域医学高等教育协同发展机制,以促进医学院校资源的优质均衡发展。

Temporal and spatial responses of ecological resilience to climate change and human activities in the economic belt on the northern slope of the Tianshan Mountains, China

In the Anthropocene era,human activities have become increasingly complex and diversified.The natural ecosystems need higher ecological resilience to ensure regional sustainable development due to rapid urbanization and industrialization as well as other intensified human activities,especially in arid and semi-arid areas.In the study,we chose the economic belt on the northern slope of the Tianshan Mountains(EBNSTM)in Xinjiang Uygur Autonomous Region of China as a case study.By collecting geographic data and statistical data from 2010 and 2020,we constructed an ecological resilience assessment model based on the ecosystem habitat quality(EHQ),ecosystem landscape stability(ELS),and ecosystem service value(ESV).Further,we analyzed the temporal and spatial variation characteristics of ecological resilience in the EBNSTM from 2010 to 2020 by spatial autocorrelation analysis,and explored its responses to climate change and human activities using the geographically weighted regression(GWR)model.The results showed that the ecological resilience of the EBNSTM was at a low level and increased from 0.2732 to 0.2773 during 2010–2020.The spatial autocorrelation analysis of ecological resilience exhibited a spatial heterogeneity characteristic of"high in the western region and low in the eastern region",and the spatial clustering trend was enhanced during the study period.Desert,Gobi and rapidly urbanized areas showed low level of ecological resilience,and oasis and mountain areas exhibited high level of ecological resilience.Climate factors had an important impact on ecological resilience.Specifically,average annual temperature and annual precipitation were the key climate factors that improved ecological resilience,while average annual evapotranspiration was the main factor that blocked ecological resilience.Among the human activity factors,the distance from the main road showed a negative correlation with ecological resilience.Both night light index and PM2.5 concentration were negatively correlated with ecological resilience in the areas with better ecological conditions,whereas in the areas with poorer ecological conditions,the correlations were positive.The research findings could provide a scientific reference for protecting the ecological environment and promoting the harmony and stability of the human-land relationship in arid and semi-arid areas.

Assessment of China’s forest fi re occurrence with deep learning, geographic information and multisource data

Considerable economic losses and ecological damage can be caused by forest fi res,and compared to suppression,prevention is a much smarter strategy.Accordingly,this study focuses on developing a novel framework to assess forest fi re risks and policy decisions on forest fi re management in China.This framework integrated deep learning algorithms,geographic information,and multisource data.Compared to conventional approaches,our framework featured timesaving,easy implementation,and importantly,the use of deep learning that vividly integrates various factors from the environment and human activities.Information on 96,594 forest fi re points from 2001 to 2019 was collected on Moderate Resolution Imaging Spectroradiometer(MODIS)fi re hotspots from 2001 to 2019 from NASA’s Fire Information Resource Management System.The information was classifi ed into factors such as topography,climate,vegetation,and society.The prediction of forest fi re risk was generated using a fully connected network model,and spatial autocorrelation used to analyze the spatial aggregation correlation of active fi re hotspots in the whole area of China.The results show that high accuracy prediction of fi re risks was achieved(accuracy 87.4%,positive predictive value 87.1%,sensitivity 88.9%,area under curve(AUC)94.1%).Based on this,it was found that Chinese forest fi re risk shows signifi cant autocorrelation and agglomeration both in seasons and regions.For example,forest fi re risk usually raises dramatically in spring and winter,and decreases in autumn and summer.Compared to the national average,Yunnan Province,Guangdong Province,and the Greater Hinggan Mountains region of Heilongjiang Province have higher fi re risks.In contrast,a large region in central China has been recognized as having a long-term,low risk of forest fi res.All forest risks in each region were recorded into the database and could contribute to the forest fi re prevention.The successful assessment of forest fi re risks in this study provides a comprehensive knowledge of fi re risks in China over the last 20 years.Deep learning showed its advantage in integrating multiple factors in predicting forest fi re risks.This technical framework is expected to be a feasible evaluation tool for the occurrence of forest fi res in China.

Observation 20-s periodic signals on Mars from InSight,Sols 800-1,000

Seismometers of the InSight probe(Interior Exploration using Seismic Investigation,Geodesy and Heat Transport)currently operating on Mars have recorded not only seismic events but also high-frequency non-seismic periodic signals that appear to have been induced by variations in the Martian environment and the hardware.Here,we report an observation of a long-period signal with a dominant period of~20 s from Martian solar days(Sol)800 to Sol 1,000.This 20-s signal is detected mostly at quiet nighttime—from22:00 to 04:00 LMST(Local Mean Solar Time)—at the InSight landing site.The measurement of the particle motion suggests that this linearly polarized signal focuses on the horizontal plane with an angle of~30°from the north.By examining the temporal variation of the signal’s amplitude and polarization angle and its times of occurrence in relation to the planet’s atmospheric data,we suggest that this20-s signal may be relevant to wind and temperature variations on Mars.Furthermore,we study the possible influence of this 20-s signal on the noise autocorrelation and find that the stacked autocorrelograms can be quite different when the 20-s signal is present.

Image-Based Ultrasound Speed Estimation: Phantom and Human Liver Studies

Purpose: A novel image-based method for speed of sound (SoS) estimation is proposed and experimentally validated on a tissue-mimicking ultrasound phantom and normal human liver in vivo using linear and curved array transducers. Methods: When the beamforming SoS settings are adjusted to match the real tissue’s SoS, the ultrasound image at regions of interest will be in focus and the image quality will be optimal. Based on this principle, both a tissue-mimicking ultrasound phantom and normal human liver in vivo were used in this study. Ultrasound image was acquired using different SoS settings in beamforming channels ranging from 1420 m/sec to 1600 m/sec. Two regions of interest (ROIs) were selected. One was in a fully developed speckle region, while the other contained specular reflectors. We evaluated the image quality of these two ROIs in images acquired at different SoS settings in beamforming channels by using the normalized autocorrelation function (ACF) of the image data. The values of the normalized ACF at a specific lag as a function of the SoS setting were computed. Subsequently, the soft tissue’s SoS was determined from the SoS setting at the minimum value of the normalized ACF. Results: The value of the ACF as a function of the SoS setting can be computed for phantom and human liver images. SoS in soft tissue can be determined from the SoS setting at the minimum value of the normalized ACF. The estimation results show that the SoS of the tissue-mimicking phantom is 1460 m/sec, which is consistent with the phantom manufacturer’s specification, and the SoS of the normal human liver is 1540 m/sec, which is within the range of the SoS in a healthy human liver in vivo. Conclusion: Soft tissue’s SoS can be determined by analyzing the normalized ACF of ultrasound images. The method is based on searching for a minimum of the normalized ACF of ultrasound image data with a specific lag among different SoS settings in beamforming channels.

The Classification to Stationary Process of Tidal Motion Observed at the Time of Kuroshio’s Meandering

The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion.