Lomb-Scargle Periodogram Research Articles

ClinCirc identifies alterations of the circadian peripheral oscillator in critical care patients.

BackgroundAssessing circadian rhythmicity from infrequently sampled data is challenging; however, these types of data are often encountered when measuring circadian transcripts in hospitalized patients.MethodsWe present ClinCirc. This method combines 2 existing mathematical methods (Lomb-Scargle periodogram and cosinor) sequentially and is designed to measure circadian oscillations from infrequently sampled clinical data. The accuracy of this method was compared against 9 other methods using simulated and frequently sampled biological data. ClinCirc was then evaluated in 13 intensive care unit (ICU) patients as well as in a separate cohort of 29 kidney-transplant recipients. Finally, the consequences of circadian alterations were investigated in a retrospective cohort of 726 kidney-transplant recipients.ResultsClinCirc had comparable performance to existing methods for analyzing simulated data or clock transcript expression of healthy volunteers. It had improved accuracy compared with the cosinor method in evaluating circadian parameters in PER2:luc cell lines. In ICU patients, it was the only method investigated to suggest that loss of circadian oscillations in the peripheral oscillator was associated with inflammation, a feature widely reported in animal models. Additionally, ClinCirc was able to detect other circadian alterations, including a phase shift following kidney transplantation that was associated with the administration of glucocorticoids. This phase shift could explain why a significant complication of kidney transplantation (delayed graft dysfunction) oscillates according to the time of day kidney transplantation is performed.ConclusionClinCirc analysis of the peripheral oscillator reveals important clinical associations in hospitalized patients.FundingUK Research and Innovation (UKRI), National Institute of Health Research (NIHR), Engineering and Physical Sciences Research Council (EPSRC), National Institute on Academic Anaesthesia (NIAA), Asthma+Lung UK, Kidneys for Life.

Radio and γ-Ray Variability in Blazar S5 0716+714: A Year-like Quasi-periodic Oscillation in the Radio Light Curve

The nearly 33 yr long-term radio light curve obtained with the Metsähovi Radio Observatory 14 m telescope at 37 GHz and the recent 12.7 yr γ-ray light curve of the blazar S5 0716+714 at 0.1–300 GeV from the Fermi Large Area Telescope (Fermi-LAT) were analyzed by using the Lomb–Scargle periodogram and the weighted wavelet Z-transform techniques. In the radio light curve, we discovered a possible quasi-periodic oscillation (QPO) signal of about 352 ± 23 days at a confidence level of ∼3σ. We recalculated the periodicity and its significance in a chosen time range that has higher variability and denser sampling, and then found that the significance had increased to a confidence level of 99.996% (∼4.1σ). This QPO component was further confirmed by fitting a linear autoregressive integrated moving average model to the selected radio light curve. A possible QPO of 960 ± 80 days at a 99.35% level (∼2.7σ) was found in the γ-ray light curve, which generally agrees with the earlier QPO claims of S5 0716+714. This paper discusses possible mechanisms for this potential year-like QPO. One possibility is a pure geometrical scenario with blobs moving helically inside the jet. Another is a supermassive binary black hole involving a gravitational wave-driven regime. In the latter scenario, we derived a milliparsec separation in the binary system that undergoes coalescence within a century due to the emission of low-frequency gravitational waves.

ON SIMILARITIES BETWEEN DEFORMATION PROCESSES PRECEDING ICE SHOCKS AND TECTONIC EARTHQUAKES

The instrumental monitoring reveals an autowave nature of ice deformation behavior prior to ice shocks. A few minutes or the first tens of minutes before the shock, this process shows an increase in the amplitude of oscillations, often with a multi-fold reduction in their period. An autowave dynamics of ice deformations is due to self-organization of a structurally heterogeneous ice environment under critical conditions. The self-organization ability of the deformation process is confirmed by the results of ice deformation time series processing by the structural function curvature analysis method (SFCAM) and by the Lomb-Scargle periodogram method. The results of seismic monitoring of ice showed that autowave processes are characterized by constant frequency of 0.1 Hz. Taking into account the ice deformation and microseismic fluctuation features preceding the ice shocks, spectral analysis was performed on the data of deformation and seismicity monitoring at the Buguldeika geodynamic polygon before the Kudara earthquake. According to the results, 14 hours before the earthquake the seismogram recorded a gradual increase in auto-oscillation amplitudes in the frequency range from 0.01 to 0.1 Hz. The maximum amplitude increase is 19.5 against the background.

Quasi-periodic behaviour in the radio and γ-ray light curves of blazar PKS 1510–089

Abstract We explore the possible quasi-periodic oscillations (QPOs) of the blazar PKS 1510–089, utilizing the ∼38-year Metsähovi flux density observations at 37 GHz and over ten-year Fermi-LAT observations in the 0.1–300 GeV energy range. Both the flux distributions of the radio and γ-ray light curves suggest a log-normal distribution, and power spectral densities (PSDs) of both light curves can be well represented by a bending power-law model. Comparing the results from the Weighted Wavelet Z-transform and Lomb-Scargle Periodogram approaches, a quasi period of 1330 ± 55 days at a 99.80% (>3σ) significance against the red noise background is observed in the radio light curve, whereas no similar modulation is seen in the γ-ray light curve. We briefly discuss the research actuality of blazar QPO phenomena and explain the observed radio QPO as the result of Keplerian motion in a supermassive binary black hole system and periodic modulation induced by the Lense-Thirring precession of the innermost portions of the accretion disk.

A New Algorithm for Measuring Vegetation Growth Using GNSS Interferometric Reflectometry

The use of global navigation satellite system interferometric reflectometry (GNSS-IR) to measure vegetation growth status has become a rapidly growing technique in remote sensing. GNSS signals reflected by the soil surface affect the accuracy of vegetation growth status (vegetation cover density) measurement, and the influence of soil moisture (SM) varies. This study establishes a calibration model that can reduce the influence of SM and snow layer on reflectivity. We used a direct-reflected signal amplitude ratio and GNSS-IR altimeter based on the Lomb–Scargle Periodogram to calculate the reflectivity of vegetation and snow layer depth. GNSS data from plate boundary observation were used to verify the validity of our model. The results show that reflectivity correlates better with vegetation growth status after calibrating the influence of the SM and snow layer. Moreover, the correlation increased by nearly 0.14. This study analyzed the influence of the snow layer and found that it had a noticeable effect on vegetation growth status measurement when the snow depth was over 30 cm. Furthermore, a fusion method is proposed to improve the accuracy of vegetation growth status measurement by combining the reflectivity and normalized microwave reflection index (NMRI). The experimental results show that better performance can be obtained compared to the single observation of the reflectivity and NMRI, and the best correlation between the measured and in situ normalized difference vegetation index is over 0.91, and the root mean square error decreases to 0.1893.

High-Precision ZTD Model of Altitude-Related Correction

Zenith tropospheric delay (ZTD) is one of the main error sources in space geodesy. The existing regional or global models, such as Global Pressure and Temperature 3 (GPT3), Global Tropospheric model, Global Hopfield, and Shanghai Astronomical observatory tropospheric delay model models, have good performance. However, the precision of these models is relatively low in regions with a large height difference, which becomes the focus of this article. A high-precision ZTD model considering the height effect on tropospheric delay is proposed, and China is selected as study area due to its large height difference, which is called the high-precision ZTD model for China (CHZ). The initial ZTD value is calculated on the basis of the GPT3 model, and the periodic terms of ZTD residual between the global navigation satellite system (GNSS) and GPT3 model, such as annual, semiannual, and seasonal periods, are determined by the Lomb–Scargle periodogram method in different subareas of China. The relationship between the ZTD periodic residual term and the height of the GNSS station is further analyzed at different seasons, and linear ZTD periodic residual models are obtained. A total of 164 GNSS stations derived from the Crustal Movement Observation Network of China and 87 radiosonde stations are selected to validate the proposed CHZ model, and hourly ZTD data derived from GNSS are used to establish the CHZ model. Statistical result shows that the averaged root mean square and Bias of the CHZ model are 21.12 and −2.51 mm, respectively, in the whole of China. In addition, the application of CHZ model in precision point positioning (PPP) show that the convergence time is improved by 34%, 15%, and 35%, respectively, in N, E, and U components when compared to GPT3-based PPP.

Detection of Quasiperiodic Oscillations in the Blazar S4 0954+658 with TESS

We report the detection of several quasiperiodicities around 0.6–2.5 days in the optical emission of the blazar S4 0954+658. The source was observed by the Transiting Exoplanet Survey Satellite in six sectors and it showed these features in all but one of them, with a quasiperiodic oscillation of 1.52 days apparently present in portions of four of them. We used the generalized Lomb–Scargle periodogram method to search for significant signals and we confirmed them using a weighted wavelet transform for time–frequency domain analyses. We discuss several possible explanations for these rapid quasiperiodic variations and suggest that an origin in the innermost part of the accretion disk is most likely. Within this framework, we provide estimates for the mass of the black hole at the core of this blazar.

KOBEsim: A Bayesian observing strategy algorithm for planet detection in radial velocity blind-search surveys

Context. Ground-based observing time is precious in the era of exoplanet follow-up and characterization, especially in high-precision radial velocity instruments. Blind-search radial velocity surveys thus require a dedicated observational strategy in order to optimize the observing time, which is particularly crucial for the detection of small rocky worlds at large orbital periods. Aims. We developed an algorithm with the purpose of improving the efficiency of radial velocity observations in the context of exoplanet searches, and we applied it to the K-dwarfs Orbited By habitable Exoplanets experiment. Our aim is to accelerate exoplanet confirmations or, alternatively, reject false signals as early as possible in order to save telescope time and increase the efficiency of both blind-search surveys and follow-up of transiting candidates. Methods. Once a minimum initial number of radial velocity datapoints is reached in such a way that a periodicity starts to emerge according to generalized Lomb-Scargle periodograms, that period is targeted with the proposed algorithm, named KOBEsim. The algorithm selects the next observing date that maximizes the Bayesian evidence for this periodicity in comparison with a model with no Keplerian orbits. Results. By means of simulated data, we proved that the algorithm accelerates the exoplanet detection, needing 29-33% fewer observations and a 41–47% smaller time span of the full dataset for low-mass planets (mp < 10 M⊕) in comparison with a conventional monotonic cadence strategy. For 20 M⊕ planets we found a 16% enhancement in the number of datapoints. We also tested KOBEsim with real data for a particular KOBE target and for the confirmed planet HD 102365 b. These two tests demonstrate that the strategy is capable of speeding up the detection by up to a factor of 2 (i.e., reducing both the time span and number of observations by half).

Research on a 3.7-year Quasi-periodic Oscillation for FSRQ J0351-1153

From the Owens Valley Radio Observatory 40 m radio telescope, we have collected the light curves of the 15 GHz radio band for FSRQ J0153-1153, spanning from 2009 February to 2018 February. The Lomb–Scargle Periodogram method and the Weighted Wavelet Z-transform method are employed to search for the quasi-periodic oscillation (QPO) signal of these data, and the simulation method for the light curve is utilized to estimate the significance level of this QPO signal; thus through these techniques, the QPO signal of 3.7 ± 0.5 yr with a significance level of 3.68σ is revealed for the first time. It is most likely an explanation for the QPO signal that a binary black hole system gives rise to a Newtonian-driven the precession of jet. Based on this assumption, we find that the mass of the secondary black hole in this system may be larger than the mass of the primary black hole; and we estimate the intrinsic QPO of jet precession and the QPO of companion star orbit.

Multi- GNSS reflectometry performance evaluation for coastal sea level monitoring: A case study in Antarctic Peninsula

Antarctica is a continent that crucial for studying climate change and its progression across time, as well as analyzing and forecasting local and global change. In this environment, due to the challenges caused by sea-level rise, storm surges, and tsunamis, sustainability is a critical concern, particularly for coastal regions. As a result, the long-term observations that will be conducted in Antarctica are critical for monitoring the adverse impacts of climate change. In recent years, many monitoring approaches, both space, and ground-based are performed to monitor sea/ice level trends in space-based scientific investigations conducted in and around the region. In the study, based on one year of observations from the Palmer GNSS Station, the GNSS Reflectometry technique was used to measure the sea level on the Antarctic Peninsula (PALM). GNSS Station observations were analyzed with a Lomb-Scargle periodogram to monitor sea-level changes, and results were validated with data from a co-located tide gauge (TG). The results show that the correlation between GNSS-R sea-level changes and tidal sea-level changes is found as 0.91.

First discovery of quasi-periodic oscillations in the dwarf nova HS 2325+8205 based on TESS photometry

ABSTRACT HS 2325+8205 is a long-period eclipsing dwarf nova with an orbital period above the period gap (Porb > 3 h) and is reported to be a Z Cam-type dwarf nova. We study the light variation and the quasi-periodic oscillations (QPOs) of HS 2325+8205 based on the photometry of theTransiting Exoplanet Survey Satellite (TESS). Using a continuous wavelet transform, a Lomb–Scargle periodogram (LSP), and sine fitting methods, we find for the first time that there is a QPO of ∼2160 s in the long outburst top light curves of HS 2325+8205. Moreover, we find that the oscillation intensity of the QPOs of HS 2325+8205 is related to the orbital phase, and the intensity in orbital phases 0.5–0.9 is stronger than in orbital phases 0.1–0.5. Therefore, the relationship between the oscillation intensity of QPOs and the orbital phase may become a topic of research into the origin of QPOs. In addition, we use the LSP to correct the orbital period of HS 2325+8205 to 0.19433475(6) d.

Meta-analysis of Photometric and Asteroseismic Measurements of Stellar Rotation Periods: The Lomb–Scargle Periodogram, Autocorrelation Function, and Wavelet and Rotational Splitting Analysis for 92 Kepler Asteroseismic Targets

We perform intensity variability analyses (photometric analyses: the Lomb–Scargle periodogram, autocorrelation, and wavelet) and asteroseismic analysis of 92 Kepler solar-like main-sequence stars to understand the reliability of the measured stellar rotation periods. We focus on the 70 stars without reported stellar companions, and classify them into four groups according to the quarter-to-quarter variance of the Lomb–Scargle period and the precision of the asteroseismic period. We present detailed individual comparison among photometric and asteroseismic constraints for these stars. We find that most of our targets exhibit significant quarter-to-quarter variances in the photometric periods, suggesting that the photometrically estimated period should be regarded as a simplified characterization of the true stellar rotation period, especially under the presence of the latitudinal differential rotation. On the other hand, there are a fraction of stars with a relatively small quarter-to-quarter variance in the photometric periods, most of which have consistent values for asteroseismically and photometrically estimated rotation periods. We also identify over 10 stars whose photometric and asteroseismic periods significantly disagree, which would be potentially interesting targets for further individual investigations.

Spatiotemporal Analysis of Southeast Asian Lower Atmosphere using Historical Radiosonde Data

This study utilized historical radiosonde data from 37 selected WMO stations to analyze the physical properties of Southeast Asian lower atmosphere in both spatial and temporal regimes. The proposed analysis method includes the estimation of static atmospheric parameters and their correlations, the trend analysis from the parameters’ time series, and the extraction of annual and interannual variations from the detrended parameters’ time series. The vertical structure analysis of temperature and pressure “profiles” (i.e., temperature and pressure as functions of altitude at a given time) shows that their residuals from the isentropic atmosphere are altitude-dependent and predictable. The correlation analysis between estimated parameters shows that the heat capacity ratio is a function of the environmental lapse rate, which can be used in the parameterization of the atmospheric model. The molar mass of the Southeast Asian lower atmosphere was also estimated from the parameterization to be 29.65 g/mol, slightly higher than that of the average value of dry air at 28.97 g/mol. The spatial analysis of their average values indicates that the Southeast Asian lower atmosphere can be zonally classified into the Northern Equatorial Subregion (NES) and Central Equatorial Subregion (CES), where their boundary is located between the latitude of 5° N to 10° N. The trend analysis of each parameter’s time series suggests that the Southeast Asian lower atmosphere is a transient system manipulated by climate oscillations and climate change. Their equilibrium values can be estimated using linear regression analysis. The results from the Lomb-Scargle periodogram analysis also suggest that the annual variation originated from the Brewer-Dobson Circulation (BDC) and the interannual variation was manipulated by climate oscillations such as the Quasi-biennial Oscillation (QBO). This knowledge can be used to adjust the isentropic model to suit applications requiring accurate approximation, parameterize the model without sacrificing accuracy, and study the effect of climate oscillations and climate change on the Southeast Asian lower atmosphere. HIGHLIGHTS Time series of Southeast Asian lower atmosphere’s physical parameters were estimated from historical radiosonde data Southeast Asian lower atmosphere can be classified into Northern and Central Equatorial Subregions based on physical parameters Southeast Asian lower atmosphere is a transient system manipulated by climate oscillations and climate change GRAPHICAL ABSTRACT

Decadal Continuous Meteor-Radar Estimation of the Mesopause Gravity Wave Momentum Fluxes over Mohe: Capability Evaluation and Interannual Variation

In the present work, the momentum fluxes of gravity wave (GW) around the mesopause are estimated, using the decadal continuous observations by meteor radar at Mohe (53.5°N, 122.3°E). Applying the Hocking’s (2005) approach with the modified-composite-day (MCD) analysis, the GW momentum fluxes of short-periods (less than 2 h) are estimated month by month. As the first step, several experiments are designed to evaluate the accuracy and uncertainty in the estimation. The results show that Mohe meteor radar has the ability to give reasonable estimations on the GW momentum fluxes at a height of 82–94 km, in which errors are generally less than 5 m2/s2. The uncertainty induced by different angular information of the detected meteor in each month achieves ~2 m2/s2. It is inferred that the variability of the GW momentum fluxes over 2 m2/s2 can be distinguished in the observation. The interannual variation of the estimated GW momentum fluxes show a significant enhancement in 2012, and a depression in 2013, with a fluctuation over ±10 m2/s2 at 82 km. However, no obvious quasi-biennial oscillation (QBO) -like signal has been found in the Lomb–Scargle periodogram.

Coastal High-Temporal Sea-Surface Altimetry Using the Posterior Error Estimations of Ionosphere-Free PPP and Information Fusion for Multi-GNSS Retrievals

Ocean tidal variation is a key parameter for ensuring coastal safety, monitoring marine climate, and maintaining elevation datum. Recently, the ground-based global navigation satellite system reflectometry (GNSS-R) technique has been applied for regional tidal measurements, which is somewhat restricted in terms of temporal and spatial resolutions. A convenient method to improve temporal resolution of measurements is to combine multi-GNSS observations. This paper proposes a new sea-surface altimetry method using the posterior errors (PE) of dual-frequency carrier-phase signals derived from the ionosphere-free Precise Point Positioning (IF-PPP). Considering that the number of initial retrievals is obviously unsuitable for minute-level tidal measurements, both the time sliding window based on the Lomb–Scargle periodogram and a weighted cubic spline smoothing function are significant processing steps for estimating the reflector heights between the sea surface and antenna center. Measurements from two coastal GNSS stations with different tidal amplitudes are used to test the proposed method and compare it with the tide gauge and the signal-to-noise ratio (SNR) methods, respectively. The experimental results show that the multi-GNSS PE combination method can be used to estimate a minute-level sea level time series, and its root-mean-squared errors (RMSE) are about 12.5 cm. In terms of correlation, for all results, the corresponding coefficients exceed 0.97. Moreover, this combined PE method demonstrates a significant advantage in increasing temporal resolution, which is beneficial for application on high-frequency sea-level monitoring.

Assessment of long-term structural movements in a historic cliffside construction through Lomb-Scargle spectral analysis of unevenly spaced time records: the Punta Begoña Galleries (Getxo, Spain)

Long-term monitoring of structural movements in historic buildings and heritage sites allows assessing their stability and recognizing damages that require intervention. The Punta Begoña Galleries, built in the earlier part of the twentieth century, present pioneering techniques in the use of reinforced concrete in building construction. They stand directly over a coastal cliff, and their recovery requires first to guarantee their stability, while maintaining their historic and patrimonial values. Thus, with the goal of analyzing their global stability, as well as the extent of the observed damages, we implemented a motion monitoring network that includes three boreholes for extensometric control, an inclinometer, and five crack gauges (crackmeters). This monitoring was complemented with the recording of hydrometeorological variables at the surface and in four piezometers. The spectral analysis of the signals of movements was performed by introducing the use of the Lomb-Scargle (LS) periodogram, which is particularly well-suited for the analysis of unevenly spaced time series. This analysis allowed us to differentiate the reversible seasonal elastic components of the records and to recognize the irreversible long-term plastic displacements, which highlight the sectors with active instability. In our case, the identified damages are related to two local problems of building support. Even though the irreversible component of the displacement after seasonal sinusoidal detrending is small (with maximums up to 0.12 mm/year), it does imply a dynamic plastic deformation, which calls for the need to adopt structural stabilization measures.

Evidence of Quasi-periodic Oscillation in the Optical Band of the Blazar 1ES 1959+650

We analyzed the optical monitoring data in the R band of TeV blazar 1ES 1959+650 from 2002 to 2018, and provided evidence of a quasi-periodic oscillation in this object. The light curve shows a stable and persistent periodicity at ∼540 days, detected by the Lomb–Scargle periodogram, Jurkevich and weighted wavelet z-transform techniques. The red noise power spectrum was estimated using the PSRESP method, and this period was found to be at >3σ significance level. There are also two possible periodicities at ∼268 and ∼1100 days detected by all three methods. However, their significance levels are relatively low, and thus these two periods cannot be verified by the present data. We discuss several possible physical models that could explain the periodic variability in this object.

Revisit the periodicity of SGR J1935+2154 bursts with updated sample

ABSTRACT Since FRB 200428 has been found to be associated with an X-ray burst from the Galactic magnetar SGR J1935+2154, it is interesting to explore whether the magnetar bursts also follow the similar active periodic behaviour as some repeating FRBs. Previous studies show that there is possible period of about 230 days in SGR J1935+2154 bursts. Here, we collected an updated burst sample from SGR J1935+2154, including all bursts reported by Fermi/GBM and GECAM till 2022 January. We also developed a targeted search pipeline to reveal more bursts from SGR J1935+2154 in the Fermi/GBM data from 2008 August to 2014 December (i.e. before the first burst detected by Swift/BAT). With this burst sample, we re-analysed the possible periodicity of SGR J1935+2154 bursts using the Period Folding and Lomb–Scargle Periodogram methods. Our results show that the periodicity ∼238 days reported in literature is probably fake and the observation effects may introduce false periods (i.e. 55 days) according to simulation tests. We find that, for the current burst sample, the most probable period is 126.88 ± 2.05 days, which could be interpreted as the precession of the magnetar. However, we note that the whole burst history is very complicated and difficult to be perfectly accommodated with any period reported thus far, therefore more monitoring observations of SGR J1935+2154 are required to test any periodicity hypothesis.

A study of the magnetic activity and variability of GJ 436

ABSTRACT We present a magnetic activity study of GJ 436 using spectroscopic data from HARPS, spanning over 14 yr, and additional data from NARVAL, falling within the HARPS observations. We study the Ca ii H&K, He i D3, Na i doublet, H α, and Ca ii IRT triplets lines and explore linear correlations between them. Using the full HARPS data set, we found indices H α versus Ca ii H&K & H α versus He i to correlate positively. From the NARVAL data set, covering one observing epoch, we found Ca ii IRT3 versus Ca ii IRT2 & Ca ii IRT3 versus H α index to correlate negatively. We investigate long and short-term periodicity in these index variations, using the Generalized Lomb–Scargle periodogram. For Ca ii H&K, Na i and H α indices, we detect long-term periods of 2470.7 d (∼ 6.8 yr), 1861.6 d (∼ 5.1 yr), and 2160.9 d (∼ 5.9 yr) respectively, consistent with GJ 436’s photometric cycle of ∼ 7.4 yr. Applying the ‘Pooled Variance’ technique to H α & Na i indices, we found ∼ 2500 d to be the period of an activity cycle mechanism, in good agreement with the detected 2470.7 d period. For Ca ii H&K and H α indices, we detect short-term periods of $39.47^{+0.11}_{-0.15}$ d and $40.46^{+0.44}_{-0.52}$ d, respectively, identified as the stellar rotation period. The stellar rotation is detected after pre-whitening the long-term periodicity. It is detected as well in the analysis of individual observing epochs.

On the time lag between solar wind dynamic parameters and solar activity UV proxies

The solar activity displays variability and periodic behaviours over a wide range of timescales, with the presence of a most prominent cycle with a mean length of 11 years. Such variability is transported within the heliosphere by solar wind, radiation and other processes, affecting the properties of the interplanetary medium. The presence of solar activity–related periodicities is well visible in different solar wind and geomagnetic indices, although their time lags with respect to the solar cycle lead to hysteresis cycles. Here, we investigate the time lag behaviour between a physical proxy of the solar activity, the Ca II K index, and two solar wind parameters (speed and dynamic pressure), studying how their pairwise relative lags vary over almost five solar cycles. We find that the lag between Ca II K index and solar wind speed is not constant over the whole time interval investigated, with values ranging from 6 years to ∼1 year (average 3.2 years). A similar behaviour is found also for the solar wind dynamic pressure. Then, by using a Lomb-Scargle periodogram analysis we obtain a 10.21-year mean periodicity for the speed and 10.30-year for the dynamic pressure. We speculate that the different periodicities of the solar wind parameters with respect to the solar 11-year cycle may be related to the overall observed temporal evolution of the time lags. Finally, by accounting for them, we obtain empirical relations that link the amplitude of the Ca II K index to the two solar wind parameters.