Linear Detrending Research Articles

Steadystate: A MATLAB-based routine for determining steady-state friction conditions in the framework of rate-and-state friction analysis

Reliable determination of rate-and-state friction (RSF) parameters depends on achieving steady-state (SS) friction conditions before and after experimental velocity-stepping friction tests. This operation, through nonlinear least squares fitting, is commonly preceded by the removal of any overall slip weakening/hardening after friction velocity steps (VSs) through a sufficiently large window of slip displacement at SS ( = linear detrend). However, to date, the identification of SS and thus the correct linear detrend is dependent on the user, which potentially results in differing RSF outputs from the same data set. Here, we demonstrate that large errors in the determination of the fitted RSF parameters can result if SS conditions are not reached before and after VSs. Such errors can be particularly relevant for materials characterized by long evolution of frictional resistance with slip, such as clay-rich gouge layers, in which identifying SS after VSs is not always obvious. To this end, we propose a methodology to accurately and consistently identify where SS is achieved after VSs. This methodology is coded into a new MATLAB-based routine, steadystate. We show the key features of the methodology, as well as how to use steadystate and read its output. We also illustrate the broad applicability of the approach to friction data with different noise levels and sampling frequencies referenced to slip velocity, by reviewing observations from synthetic data sets and specific examples of experiments from different laboratories involving various sheared materials.

The Death of Vulcan: NEID Reveals That the Planet Candidate Orbiting HD 26965 Is Stellar Activity* * HD 26965 is also known as 40 Eridani A, which is the host star of the planet Vulcan in the Star Trek universe.

We revisit the long-studied radial velocity (RV) target HD 26965 using recent observations from the NASA-NSF “NEID” precision Doppler facility. Leveraging a suite of classical activity indicators, combined with line-by-line RV analyses, we demonstrate that the claimed 45-day signal previously identified as a planet candidate is most likely an activity-induced signal. Correlating the bulk (spectrally averaged) RV with canonical line activity indicators confirms a multiday “lag” between the observed activity indicator time series and the measured RV. When accounting for this lag, we show that much of the observed RV signal can be removed by a linear detrending of the data. Investigating activity at the line-by-line level, we find a depth-dependent correlation between individual line RVs and the bulk RVs, further indicative of periodic suppression of convective blueshift causing the observed RV variability, rather than an orbiting planet. We conclude that the combined evidence of the activity correlations and depth dependence is consistent with an RV signature dominated by a rotationally modulated activity signal at a period of ∼42 days. We hypothesize that this activity signature is due to a combination of spots and convective blueshift suppression. The tools applied in our analysis are broadly applicable to other stars and could help paint a more comprehensive picture of the manifestations of stellar activity in future Doppler RV surveys.

Scoring Six Detrending Methods on Timing, Lead-Lag Relations, and Cycle Periods: An Empirical Study of US and UK Recessions 1977–2020

AbstractThis study evaluates six commonly used detrending methods and discuss how detrending may change the timing of events, the identification of lead-lag relations between GDP and employment, and the identification of cycle periods. The detrending methods examined includes linear detrending, polynomial detrending, the first-order differencing, locally weighted scatterplot smoothing (LOESS), Hodrick–Prescott filter, and the Hamilton filter. We apply the detrending methods to the United States and United Kingdom gross domestic product (GDP) from 1977 to 2020. We find that for the GDP series the first-order differencing score best on all three criteria, however, it also shows more false recessions than the other detrending methods. A linear, a polynomial, and a LOESS trend all scored well. The three methods miss-specified the timing of the recessions with less than one quarter and all three gave results that would comply with stylized facts in macroeconomics. The Hodrick–Prescott (HP) filter and Hamilton filter did not achieve high scores on one or two of the criteria and scored worst on average performance.

Impacts of Extreme-High-Temperature Events on Vegetation in North China

Understanding the response of vegetation to temperature extremes is crucial for investigating vegetation growth and guiding ecosystem conservation. North China is a vital hub for China’s economy and food supplies, and its vegetation is highly vulnerable to complex heatwaves. In this study, based on remote sensing data, i.e., the normalized difference vegetation index (NDVI), spatio-temporal variations in vegetation and extreme high temperatures are investigated by using the methods of trend analysis, linear detrending, Pearson correlation and ridge regression. The impacts of extreme-high-temperature events on different vegetation types in North China from 1982 to 2015 are explored on multiple time scales. The results indicate that the NDVI in North China exhibits an overall increasing trend on both annual and monthly scales, with the highest values for forest vegetation and the fastest growth trend for cropland. Meanwhile, extreme-high-temperature events in North China also display an increasing trend. Before detrending, the correlations between the NDVI and certain extreme-high-temperature indices are not significant, while significant negative correlations are observed after detrending. On an annual scale, the NDVI is negatively correlated with extreme temperature indices, except for the number of warm nights, whereas, on a monthly scale, these negative correlations are only found from June to September. Grassland vegetation shows relatively strong correlations with all extreme temperature indices, while forests show nonsignificant correlations with the indices. This study offers new insight into vegetation dynamic variations and their responses to climate in North China.

Linear versus Quadratic Detrending in Analyzing Simultaneous Changes in DC-EEG and Transcutaneous pCO2.

Physiological direct current (DC) potential shifts in electroencephalography (EEG) can be masked by artifacts such as slow electrode drifts. To reduce the influence of these artifacts, linear detrending has been proposed as a pre-processing step. We considered quadratic detrending, which has hardly been addressed for ultralow frequency components in EEG. We compared the performance of linear and quadratic detrending in simultaneously acquired DC-EEG and transcutaneous partial pressure of carbon dioxide during two activation methods: hyperventilation (HV) and apnea (AP). Quadratic detrending performed significantly better than linear detrending in HV, while for AP, our analysis was inconclusive with no statistical significance. We conclude that quadratic detrending should be considered for DC-EEG preprocessing.

Использование методов детрендирования для интеллектуальной обработки данных мониторинга строительных процессов

Data processing of monitoring systems of various processes at the stage of construction and operation of buildings requires the development of special tools that belong to the field of artificial intelligence. The trend removal method is one of the ways to preprocess data collected from various sensors and IoT devices that monitor the state of buildings, structures and soil masses during construction and operation. This article analyzes how different approaches to detrending time series affect the performance and accuracy of algorithms for CI computational intelligence models. The analysis compares three approaches: linear detrending, non-linear detrending, and first-order differentiation.
 Five representative methods are used as CI models: DENFIS dynamic evolving fuzzy neural network, GP Gaussian process, MLP multilayer perceptron, OP-ELM optimally trimmed extremal learning machine, and SVM support vector machine. There are three main conclusions from the experiments performed on the four datasets: 1) detrending does not improve overall performance, 2) the empirical mode decomposition method provides better performance than linear detrending, and 3) first-order differentiation in some cases can be effective and in some cases counterproductive for series with common patterns.

Sources of anisotropy in the Reynolds stress tensor in the stable boundary layer

AbstractData collected by 12 sonic anemometers over the Plaine Morte Glacier (Swiss Alps) during the Snow Horizontal Arrays Turbulence Study are used to investigate sources of anisotropy in the Reynolds stress tensor for stable boundary layers. A coarse‐graining approach is applied to evaluate transfers of kinetic energy across scales, and internal gravity waves (IGWs) are detected with a suitable criterion. Both approaches are combined with a classification of anisotropy based on the barycentric map of 1 min Reynolds stress tensors. A wind‐speed threshold is found that discriminates between regimes with a different dominant topology of the Reynolds stress tensor. One‐component and isotropic states are frequent for low wind speed and strong stratification, whereas two‐component axisymmetric states dominate the high wind speed regime with strong vertical shear. Results suggest that the presence of IGWs is mostly responsible for one‐component states, and additionally influences the relative amount of kinetic and potential energy in the perturbation field. To provide supporting evidence, a complementary analysis of a clean IGW detected during a field campaign in Dumosa (Australia) is presented. This case study highlights how waves contribute to drive the Reynolds stress tensor towards the one‐component limit. Cases are shown where a linear detrending procedure may be effective in filtering out waves and avoid their spurious contributions in turbulence statistics.

A New Model for Isolating the Marine Heatwave Changes under Warming Scenarios

Abstract Marine heatwaves (MHWs) exert devastating impacts on ecosystems. Understanding their responses to anthropogenic forcing has attracted rapidly growing scientific interest. Given the disparate adaptation capacity and mobility among marine species, it is crucial to disentangle changes of MHWs related to the rising mean temperature from those to the changing temperature variability. It has been suggested that the latter’s effects could be isolated by replacing a fixed baseline with a moving one for calculating the climatological mean and percentile metrics in MHW analysis. In this study, the effects of a moving baseline on MHW statistics (annual MHW days and cumulative intensity) changes in a warming climate are systematically evaluated based on simulations from simple stochastic climate models and a set of coupled general circulation models in the Community Earth System Model Large Ensemble project. On the one hand, a moving baseline does not necessarily remove the influences of rising mean temperature on MHW changes and will artificially cause negative trends in MHW statistics when the ocean exhibits an accelerated warming rate as in the RCP8.5 scenario. On the other hand, it always underestimates the effects of changing temperature variability on MHW changes. We propose a new model that adopts a “partial” moving baseline combined with a local linear detrending to isolate MHW changes caused by changing temperature variability. Significance Statement A new model is proposed to isolate marine heatwave changes caused by changing temperature variability from those by rising mean temperature under greenhouse warming.

Impact of filtering methods on ultrafine particles turbulent fluxes by eddy covariance

In the present work, a comparison between Linear Detrending (LDT) and a Recursive Digital Filter (RDF) in removing the low-frequency contribution to the vertical turbulent fluxes was performed. The two methods were applied in order to obtain a correct evaluation of ultrafine particles, sensible heat and momentum turbulent fluxes. Exchange velocity was also evaluated separating the positive cases (the so called deposition velocity Vd) from negative cases (named emission velocity Ve). The low-frequency time scales (τc) required by the RDF were obtained by means of an ogive analysis of turbulent fluxes for different atmospheric stability conditions (i.e. unstable, stable and neutral). RDF was applied also with a constant low-frequency time scale (RDF300, τc = 300s). The stationarity test proposed by Mahrt (1998 - MST98) has been applied to momentum, kinematic temperature and particle number fluxes before and after applying LDT and RDF methods, in order to investigate the impact of filtering criteria on stationarity of time series. Results emphasised that there were no significant differences in stationary cases for different filtering procedures. The comparison analysis on the main turbulent variables highlighted that wider discrepancies occurred between LDT and RDF300, showing on average an increase in turbulent number particles flux obtained through RDF methods, especially in unstable atmospheric conditions. On the other hand, a mean decrease for momentum and sensible heat fluxes was observed. Filtering procedures led to a slight increase of exchange velocity, although an underestimation occurred for emission and deposition velocities when considered separately.

An RGB‐D framework for capturing soft‐sediment microtopography

Abstract Capturing sediment topography is one component in understanding how large animals in soft sediment ecosystems affect ecosystem processing. Traditional approaches for sampling soft‐sediment systems are too invasive and destructive for the fragile sediment structures. In contrast, non‐invasive approaches, such as LIDAR and monocular structure‐from‐motion (SfM) systems, can be expensive and cumbersome for data processing. We developed a low cost and practical framework for measuring morphological characteristics of soft sediment topography at the millimetre scale. Using an RGB‐D (red, green, blue and depth) device and a semi‐opaque container, the sediment surface can be imaged rapidly while operating in outdoor environments. The RGB‐D device imaged 0.3 m2 intertidal sediment surfaces, creating depth imagery over seven sites and 82 surfaces. First, using simulated surface data, we formulated and tested four variations of a geometrical detrending model to extract and measure the undulating surface microtopography. We then computed nine morphological characteristics, including arithmetic mean roughness, mean sediment peaks and rugosity, for the detrending models. We then used the two best performing models, linear and quadratic detrending models, to compare extracted morphological characteristics from the field data. We found a strong correlation between the models for extracted surface measures and similar extracted sediment trends. The results showed that RGB‐D real‐time imaging is a promising rapid scanning tool for collecting field data in intertidal regions and can be expanded to other fragile sediment surfaces outside the marine environment. The low costs and real‐time feedback makes it an attractive data collection tool for environments where data collection is challenging.

Regional Signatures of Forced North Atlantic SST Variability: A Limited Role for Aerosols and Greenhouse Gases

AbstractPrior studies that argue external forcings drive Atlantic Multidecadal Variability (AMV) use linear detrending to remove the global warming trend from North Atlantic sea surface temperatures (SSTs). The linear detrending method, however, aliases residual nonlinear, global‐scale warming, affecting the interpretation of results. Here we revisit the role of external forcing in AMV using large climate model ensembles, examining the influences of greenhouse gases (GHGs) and industrial aerosols—the two dominant 20th‐century external forcing agents—on North Atlantic SSTs separately from their respective global response. Our approach shows that GHGs have little to no influence unique to the North Atlantic, while industrial aerosols exert only modest influences as part of a broader loading over the Northern Hemisphere. We demonstrate that a prominent role for external forcings on AMV is an artifact of the linear detrending method that disappears when their global responses common to the World Ocean are correctly accounted for.

Short-term forecasting of monthly water consumption in hyper-arid climate using recurrent neural networks

Freshwater supply is a major challenge in regions with limited water resources and extremely arid climatic conditions. The objective of this study is to model the monthly water demand in Kuwait using the nonlinear autoregressive with exogenous input (NARX) neural network approach. The country lacks conventional surface water resources and is characterized by extremely arid climate. In addition, it has one of the fastest growing populations. In this study, linear detrending is performed on the water consumption time series for the period from January 1993 to December 2018 to eliminate the influence of population growth before application to the NARX model. Monthly temperature data are selected as exogenous input to the NARX model, because they are strongly associated with the water consumption data. Correlation analyses are performed to determine the input and feedback delays of the NARX model. The results demonstrate that the recurrent NARX model is efficient and robust for forecasting the short-term water demand, with a Nash-Sutcliffe (NS) coefficient of 0.837 in the validation period. Seasonal model assessment shows that the model performs best during the critical summer season. The NARX-based recurrent model is established as a powerful and promising tool for predicting urban water demand. Thus, it can efficiently aid the development of resilient water supply plans.

Effect of de-trending climatic parameters on temporal changes of reference evapotranspiration in the eastern Himalayan region of Sikkim, India

AbstractReference Evapotranspiration (ET0) is an essential factor in irrigation scheduling, climate change studies, and drought assessment. The study's main objective was to identify the influences of detrending input climatic parameters (CPs) on ET0 using linear and nonlinear approaches throughout 1980–2015 in Gangtok, East Sikkim, India. The benchmark values of ET0 were calculated using the global standard FAO56 Penman–Montieth equation. The ET0-related CPs included for the analysis are maximum temperature (Tmax), minimum temperature (Tmin), maximum relative humidity (RHmax), minimum relative humidity (RHmin), and sunshine duration (SSH). The linear and nonlinear trends in various CPs affect ET0 change. Linearly detrended series was obtained by linear regression method whereas, nonlinearly detrended series was obtained using the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise method. Twenty-three scenarios, including the original scenario, 11 scenarios in Group 1 (CPs de-trended linearly), and 11 scenarios in Group 2 (CPs de-trended nonlinearly) were generated. Influences of Tmax and SSH were more substantial than the influences of other CPs for both Group 1 and Group 2. The SSH masked the weak influence of other CPs. The effects of the trends in CPs, especially of SSH and Tmax, were clearly shown. The ET0 values decreased significantly during 1980–2015; however, no significant decreasing trend was observed in the case of SSH, during the same period. The nonlinear detrending gave closer results to the benchmark values as compared to linear detrending because of non-monotone variations of the ET0 and CPs. Therefore, the results from nonlinear detrending were more plausible as compared to linear detrending. The diminishing trend of ET0 prompted an overall alleviation of the dry spell, hence there would be a somewhat lower risk of water use in the study region.

Fling-Step Recovering from Near-Source Waveforms Database

We present an upgraded processing scheme (eBASCO, extended BASeline COrrection) to remove the baseline of strong-motion records by means of a piece-wise linear detrending of the velocity time history. Differently from standard processing schemes, eBASCO does not apply any filtering to remove the low-frequency content of the signal. This approach preserves both the long-period near-source ground-motion, featured by one-side pulse in the velocity trace, and the offset at the end of the displacement trace (fling-step). The software is suitable for a rapid identification of fling-containing waveforms within large strong-motion datasets. The ground displacement of about 600 three-component near-source waveforms has been recovered with the aim of (1) extensively testing the eBASCO capability to capture the long-period content of near-source records, and (2) compiling a qualified strong-motion flat-file useful to calibrate attenuation models for peak ground displacement (PGD), 5% damped displacement response spectra (DS), and permanent displacement amplitude (PD). The results provide a more accurate estimate of ground motions that can be adopted for different engineering purposes, such as performance-based seismic design of structures.

Wind effects on soil thermal properties measured by the dual‐probe heat pulse method

AbstractWhen a dual‐probe heat pulse (DPHP) sensor is installed in soil near the soil–atmosphere interface, the basic assumptions of the infinite line heat source (ILS) model and its improvement, the infinite line heat source model with an adiabatic boundary condition (ILS‐ABC) might not be satisfied because of wind. This study aims to explore the effects of wind on DPHP measurements and to compare the performance of the ILS and ILS‐ABC models at different values of wind velocity (υ) and burial depth (d). Our study shows that the results of laboratory experiments, COMSOL simulations, and field experiments are consistent with each other. For dry sand with d ≤ 4 mm, the effects of wind is non‐negligible at υ ≥ 3.5 m s−1 and the DPHP method does not provide accurate estimations whether the ILS model or the ILS‐ABC model is used. Field experiments are prone to large background temperature fluctuations, which can cause a commonly used linear detrending method to perform poorly. In general, at υ < 2.7 m s−1 in field and d = 5 mm, the ILS‐ABC model provides more accurate estimations with relative errors of <15% in thermal conductivity and relative errors of <9% in heat capacity.

Scaling of Peak Ground Displacement with Seismic Moment above the Mexican Subduction Thrust

AbstractWe use accelerograms, seismograms, and data from sparse continuous Global Positioning System (GPS) and campaign-mode GPS stations, deployed along the Pacific coast of Mexico, to study scaling of horizontal peak ground displacement (PGD) with seismic moment (M0) in the epicentral zone above the Mexican subduction thrust. The thrust interface is located at a depth of ∼25 km below the coast. We select recordings with (S–P) time ≤5.9 s (R≤46 km) and reduce the amplitudes to (S–P) time of 3.2 s (R = 25 km). The dataset consists of 58 events and covers a M0 range of 1013–1021 N·m. We find that the double integration of accelerograms, using piecewise linear detrending schemes, leads to sufficiently accurate estimation of PGD to study the scaling relation. The sparse data for great earthquakes are complemented with theoretical static displacement computed using the model of Okada (1992). For earthquakes with M0≤1.26×1018 N·m (Mw≤6.0) the point-source, far-field approximation holds, and the PGD data follows theoretically expected M02/3 scaling. For great earthquakes (M0>1.26×1021 N·m; Mw>8.0), static offset (which is approximately equivalent to PGD) scales as M01/3. About two-thirds of the observed PGD data fall within a factor of 0.67 and 1.5 of the relation given above. The relationship may be useful in earthquake engineering as well as for rapid estimation of magnitude for early tsunami alert.

Dynamic Error Correction for Magnetic Property Measurement

In this paper, we present an efficient technique to compensate the dynamic offset error in the voltamperometric method, for the subhertz characterization of hysteretic magnetic materials. The integration of the output voltage at the secondary winding inherently tends to cumulate the residual offset voltage that is not constant over long experiments as often supposed. Slight variations of the residual offset voltage due to multiple effects make simple linear detrend techniques ineffective and limit the achievable accuracy up to make useless the obtained data. We first use custom signals to identify the thermal and electrical dynamic models of the measurement setup, and further we remove the model-based expected trends. The results confirm the effectiveness of the proposed method for error compensation, with accuracy improvements up to 40 dB.

Response of lower Yellow River bank breachings to La Niña events since 924 CE

The El Niño/Southern Oscillation (ENSO) is the dominant mode of inter-annual climate variability, strongly affecting summer precipitation and streamflow of large rivers. So far, no effort has been made to relate ENSO events with alluvial river stability. Based on the historical document of the lower Yellow River (LYR) and the data of previously reconstructed ENSO variability, the present study aims to establish the relation between the LYR's artificial levee breaching events (LBEs) and the ENSO events from 924 CE to 1938, and thereby reveal how river instability responds to climate change in millennial scale, for a better understanding of the coupling relation between the climate, hydrology and river channel changes. From 924 CE to 1938, there are 303 La Niña influenced years (ENSO variability < −0.5), of which 172 (56.8%) are related to the occurrence of LBE. We divided the reconstructed ENSO variability into 9 classes and calculated the LBE frequency for each class. We found that the LBE frequency is negatively correlated with class average value of ENSO variability, significant at p < 0.05. By relating the 21 major course shifting events (CSEs) of the LYR (924 CE to 1938) to the occurrence of La Niña influenced years, we found that 13 (61.9%) were influenced by La Niña. The decadal LBE frequency (Fb) and decadal average of ENSO amplitude show anti-phase variations since 1100 CE, with r = −0.356 (n = 82, p = 0.0010) after a linear detrending treatment. Through the control on summer rainfall and therefore on floods in the Yellow River, La Niña events influence the occurrence of the LBEs and CSEs in the LYR.

Fling Effects from Near‐Source Strong‐Motion Records: Insights from the 2016 Mw 6.5 Norcia, Central Italy, Earthquake

We propose a semiautomatic processing scheme (extended BASeline Correction [eBASCO]) for recovering the tectonic fling from near-source records. The method, based on a piecewise linear detrend of the strong-motion (SM) recordings, is applied to reconstruct the ground displacement field of the 30 October 2016 M w 6.5 earthquake in central Italy. The robustness of the results is checked against geodetic measurements, remote sensing data, ground-motion simulations, and existing empirical models for fling amplitude. The outcomes of eBASCO are analyzed with the goal of testing its capability to preserve long-period content in near-source SM recordings affected by tectonic fling, different from standard processing schemes based on bandpass filtering. Comparison of peak ground displacements, peak ground velocities, and spectral displacements shows that long-period ground motion recorded over and in proximity of the fault can be underestimated by standard processing. Spectral displacement ordinates can diverge up to the 25% for periods longer than 5 s when an appropriate baseline correction is made.

The step-like evolution of Arctic open water

September open water fraction in the Arctic is analyzed using the satellite era record of ice concentration (1979–2017). Evidence is presented that three breakpoints (shifts in the mean) occurred in the Pacific sector, with higher amounts of open water starting in 1989, 2002, and 2007. Breakpoints in the Atlantic sector record of open water are evident in 1971 in longer records, and around 2000 and 2011. Multiple breakpoints are also evident in the Canadian and Russian halves. Statistical models that use detected breakpoints of the Pacific and Atlantic sectors, as well as models with breakpoints in the Canadian and Russian halves and the Arctic as a whole, outperform linear trend models in fitting the data. From a physical standpoint, the results support the thesis that Arctic sea ice may have critical points beyond which a return to the previous state is less likely. From an analysis standpoint, the findings imply that de-meaning the data using the breakpoint means is less likely to cause spurious signals than employing a linear detrend.