Solar Magnetic Activity Research Articles

What drives the solar magnetic cycle?

Solar magnetic activities show an about 11-year cycle period with the variations of the amplitudes. The increasing technological advancement induces the stronger influence of the solar magnetic cycle on humans. The magnetic cycle is believed to be caused by a magnetohydrodynamic (MHD) dynamo process in the solar interior, where the flows and the magnetic fields interact in the strongly turbulent convective zone. The intrinsic features of the solar interior, e.g., the stratification, the turbulence and the nonlinearities, make the global MHD simulations of solar convection with the realistic parameters of the Sun extremely hard. The past substantial progress in understanding the solar magnetic cycle benefitted from the simplified models, e.g., the axisymmetric kinematic ones. The mean field electrodynamics and the helioseismology laid the foundation of the progress. Under the effects of the large-scale flows, the poloidal and the toroidal components of the magnetic field sustain each other, which persists the cycle variations of the solar magnetic field. The key ingredients in the dynamo process include the mechanism and the location of the toroidal field generation, the mechanism and the location of the poloidal field generation, the rising of toroidal field to form the sunspots with tilts and the mechanism for the equatorward migration of the sunspots. So far, only the generation of the toroidal field by differential rotations is less controversial. The current dynamo models usually do not include the toroidal flux tube emergence, which was investigated as a separated topic. As the workhorse to understand the solar cycle during the past decade, the Babcock-Leighton (BL) type flux transport dynamos is a popular paradigm for explaining the cyclic nature of solar magnetic activity. They were even used to predict future solar cycles by assimilating observed surface flows and fields into the models. Recently the flux transport dynamos faces some challenges, such as the depth variation of the equatorward flow, the strong turbulent diffusivity, and so on. But the BL mechanism which is due to the decay of the tilt sunspot groups on the solar surface to regenerate the poloidal field, is most probably at the heart of the solar cycle. The further understanding of the solar magnetic cycle will benefit from the constraints of the solar historical data, the helioseismology, the different magnetic cycles of different types of stars, and the global MHD numerical simulations. These fields will be developed in parallel with the kinematic dynamo and fertilize each other. The three dimensional Babcock-Leighton type dynamo models coupled with the toroidal flux tube emergence is expected to be the workhorse of the next generation of solar dynamo.

A Parameter Leveraging Method for Unsupervised Big Data Modelling

Increasingly sophisticated methods and tools are needed for tracking the dynamics and detecting inherent structures in modern day highly voluminous multi-faceted. Data scientists have long realized that tackling global challenges such as climate change, terrorism and food security cannot be contained within the frameworks and models of conventional data analysis. For example, separating noise from meaningful data in even a low-dimensional data with heavy tails and/or overlaps is quite challenging and standard non-linear approaches do not always succeed. Tracking the dynamics of multi-faceted data involving complex systems is tantamount to tracking agent-based complex systems with many interacting agents. Dimensional-reduction methods are commonly used to try and capture structures inherent in data but they do not generally lead to optimal solutions mainly because their optimisation functions and theoretical methods typically rely on special structures. We propose a parameter leveraging method for unsupervised big data modelling. The method searches for structures in data and creates a series of sub-structures which are subsequently merged or split. The strategy is to present the algorithm with a set of periodic data as one complex system. It then uses the patterns in the sub-structures to determine the overall behaviour of the complex system. Applications on solar magnetic activity cycles and seismic data show that the proposed method out-performs conventional unsupervised methods. We illustrate how the method can be extended to supervised modelling.

Sun, Ocean, Nuclear Bombs, and Fossil Fuels: Radiocarbon Variations and Implications for High-Resolution Dating

Radiocarbon, or 14C, is a radiometric dating method ideally suited for providing a chronological framework in archaeology and geosciences for timescales spanning the last 50,000 years. 14C is easily detectable in most common natural organic materials and has a half-life (5,730±40 years) relevant to these timescales. 14C produced from large-scale detonations of nuclear bombs between the 1950s and the early 1960s can be used for dating modern organic materials formed after the 1950s. Often these studies demand high-resolution chronology to resolve ages within a few decades to less than a few years. Despite developments in modern, high-precision 14C analytical methods, the applicability of 14C in high-resolution chronology is limited by short-term variations in atmospheric 14C in the past. This article reviews the roles of the principal natural drivers (e.g., solar magnetic activity and ocean circulation) and the anthropogenic perturbations (e.g., fossil fuel CO2 and 14C from nuclear and thermonuclear bombs) that are responsible for short-term 14C variations in the environment. Methods and challenges of high-resolution 14C dating are discussed.

Multiple dynamo modes as a mechanism for long-term solar activity variations

Solar magnetic activity shows both smooth secular changes, such as the Grand Modern Maximum, and quite abrupt drops that are denoted as Grand Minima. Direct numerical simulations (DNS) of convection driven dynamos offer one way of examining the mechanisms behind these events. In this work, we analyze a solution of a solar-like DNS that has been evolved for roughly 80 magnetic cycles of 4.9 years, during which epochs of irregular behavior are detected. The emphasis of our analysis is to find physical causes for such behavior. The DNS employed is a semi-global (wedge) magnetoconvection model. For data analysis we use Ensemble Empirical Mode Decomposition (EEMD) and phase dispersion ($D^2$) methods. A special property of the DNS is the existence of multiple dynamo modes at different depths and latitudes. The dominant mode is solar-like. This mode is accompanied by a higher frequency mode near the surface and a low-frequency mode in the bottom of the convection zone. The overall behavior of the dynamo solution is very complex exhibiting variable cycle lengths, epochs of disturbed and even ceased surface activity, and strong short-term hemispherical asymmetries. Surprisingly, the most prominent suppressed surface activity epoch is actually a global magnetic energy maximum. We interpret the overall irregular behavior to be due to the interplay of the different dynamo modes showing different equatorial symmetries, especially the smoother part of the irregular variations being related to the variations of the mode strengths, evolving with different and variable cycle lengths. The abrupt low activity epoch in the dominant dynamo mode near the surface is related to a strong maximum of the bottom toroidal field strength, which causes abrupt disturbances especially in the differential rotation profile via the suppression of the Reynolds stresses.

The HERMES solar atlas and the spectroscopic analysis of the seismic solar analogue KIC 3241581

Solar-analog stars provide an excellent opportunity to study the Sun's evolution, i.e. the changes with time in stellar structure, activity, or rotation for solar-like stars. The unparalleled photometric data from the NASA space telescope Kepler allows us to study and characterise solar-like stars through asteroseismology. We aim to spectroscopically investigate the fundamental parameter and chromospheric activity of solar analogues and twins, based on observations obtained with the HERMES spectrograph and combine them with asteroseismology. Therefore, we need to build a solar atlas for the spectrograph, to provide accurate calibrations of the spectroscopically determined abundances of solar and late type stars observed with this instrument and thus perform differential spectral comparisons. We acquire high-resolution and high signal-to-noise spectroscopy to construct three solar reference spectra by observing the reflected light of Vesta and Victoria asteroids and Europa (100<S/N<450) with the \Hermes spectrograph. We then observe the Kepler solar analog KIC3241581 (S/N~170). We constructed three solar spectrum atlases from 385 to 900 nm obtained with the Hermes spectrograph from observations of two bright asteroids and Europa. A comparison between our solar spectra atlas to the Kurucz and HARPS solar spectrum shows an excellent agreement. KIC3241581 was found to be a long-periodic binary system. The fundamental parameter for the stellar primary component are Teff=5689+/-11K, logg=4.385+/-0.005, [Fe/H]=+0.22+/-0.01, being in agreement with the published global seismic values confirming its status of solar analogue. KIC 3241581 is a metal rich solar analogue with a solar-like activity level in a binary system of unknown period. The chromospheric activity level is compatible to the solar magnetic activity.

Variations of the Position of Perturbation Layer of Solar Frequency Shifts

The variation of solar p-mode oscillation frequency with the solar magnetic activity is called the frequency shift, which is considered to be caused by a perturbation in a thin layer near the solar surface. A method for predicting the frequency shift by the magnetic activity index and the solar model had been developed previously. In this method, the frequency shift depends on the intensity of magnetic activity and the position of the perturbing source. The intensity of magnetic activity is considered to be proportional to the magnetic activity index. And the position of the perturbing source was assumed to be fixed previously. This paper has studied the variation of the position of perturbing source. By using the observed p-mode oscillation frequency and Ca II index of the Sun, it is found that the position of perturbing source may be varied with the solar magnetic activity. In the solar maximum year, the position of perturbing source is deeper, but it is shallower in the solar minimum year.

ENSEMBLE EMPIRICAL MODE DECOMPOSITION OF THE MAGNETIC FIELD OF THE SUN AS A STAR

ABSTRACT The ensemble empirical mode decomposition (EEMD) analysis is utilized to extract the intrinsic mode functions (IMFs) of the solar mean magnetic field (SMMF) observed at the Wilcox Solar Observatory of Stanford University from 1975 to 2014, and then we analyze the periods of these IMFs as well as the relation of IMFs (SMMF) with some solar activity indices. The two special rotation cycles of 26.6 and 28.5 days should be derived from different magnetic flux elements in the SMMF. The rotation cycle of the weak magnetic flux element in the SMMF is 26.6 days, while the rotation cycle of the strong magnetic flux element in the SMMF is 28.5 days. The two rotation periods of the structure of the interplanetary magnetic field near the ecliptic plane are essentially related to weak and strong magnetic flux elements in the SMMF, respectively. The rotation cycle of weak magnetic flux in the SMMF did not vary over the last 40 years because the weak magnetic flux element derived from the weak magnetic activity on the full disk is not influenced by latitudinal migration. Neither the internal rotation of the Sun nor the solar magnetic activity on the disk (including the solar polar fields) causes the annual variation of SMMF. The variation of SMMF at timescales of a solar cycle is more related to weak magnetic activity on the full solar disk.

SYSTEMATIC REGULARITY OF HEMISPHERIC SUNSPOT AREAS OVER THE PAST 140 YEARS

ABSTRACT Solar magnetic activity varies with time in the two hemispheres in different ways. The hemispheric interconnection of solar activity phenomena provides an important clue to understanding the dynamical behavior of solar dynamo actions. In this paper, several analysis approaches are proposed to analyze the systematic regularity of hemispheric asynchronism and amplitude asymmetry of long-term sunspot areas during solar cycles 9–24. It is found that, (1) both the hemispheric asynchronism and the amplitude asymmetry of sunspot areas are prevalent behaviors and are not anomalous, but the hemispheric asynchronism exhibits a much more regular behavior than the amplitude asymmetry; (2) the phase-leading hemisphere returns back to the identical hemisphere every 8 solar cycles, and the secular periodic pattern of hemispheric phase differences follows 3 (south leading) + 5 (north leading) solar cycles, which probably corresponds to the Gleissberg cycle; and (3) the pronounced periodicities of (absolute and normalized) asymmetry indices and lines of synchronization (LOSs) are not identical: the significant periodic oscillations are 80.65 ± 6.31, 20.91 ± 0.40, and 13.45 ± 0.16 years for the LOS values, and 51.34 ± 2.48, 8.83/8.69 ± 0.07, and 3.77 ± 0.02 years for the (absolute and normalized) asymmetry indices. The analysis results improve our knowledge on the hemispheric interrelation of solar magnetic activity and may provide valuable constraints for solar dynamo models.

An empirical model of heliospheric cosmic ray modulation on long-term time scale

Galactic Cosmic Rays (GCRs) entering the heliosphere are subject to modulation processes due to variable solar magnetic activity. Finding a relationship between cosmic-ray variations and the heliospheric parameters is important for reconstruction of solar activity in the past. Here, we develop a semi-empirical model describing the heliospheric modulation of GCRs in terms of heliospheric parameters such as the open solar magnetic flux, the tilt angle of the heliospheric current sheet and the polarity of the large scale solar magnetic field. Our model is fitted using annual data obtained for the period 1976–2013, which includes the very weak solar minimum during 2008–2010. The model shows a good agreement with the data, and therefore, can be used for reconstructions of the modulation potential at different levels of solar activity. The model’s validity is also tested using the cosmogenic radionuclides 14 C and 10 Be stored in terrestrial archives. The tilt angle used to fit the parameters in our semi-empirical modulation model is reconstructed by a mathematical model described here.

Dynamical systems for modeling the evolution of the magnetic field of stars and Earth

The cycles of solar magnetic activity are connected with a solar dynamo that operates in the convective zone. Solar dynamo mechanism is based on the combined action of the differential rotation and the alpha-effect. Application of these concepts allows us to get an oscillating solution as a wave of the toroidal field propagating from middle latitudes to the equator. We investigated the dynamo model with the meridional circulation by the low-mode approach. This approach is based on an assumption that the solar magnetic field can be described by non-linear dynamical systems with a relatively small number of parameters. Such non-linear dynamical systems are based on the equations of dynamo models. With this method dynamical systems have been built for media which contains the meridional flow and thickness of the convection zone of the star. It was shown the possibility of coexistence of quiasi-biennial and 22-year cycle. We obtained the different regimes (oscillations, vacillations, dynamo-bursts) depending on the value of the dynamo-number, the meridional circulation, and thickness of the convection zone. We discuss the features of these regimes and compare them with the observed features of evolution of the solar and geo magnetic fields. We built theoretical paleomagnetic time scale and butterfly-diagrams for the helicity and toroidal magnetic field for different regimes.

COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

ABSTRACT The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.

On the Current Solar Magnetic Activity in the Light of Its Behaviour During the Holocene

Solar modulation potential (SMP) reconstructions based on cosmogenic nuclide records reflect changes in the open solar magnetic field and can therefore help us obtain information on the behaviour of the open solar magnetic field over the Holocene period. We aim at comparing the Sun's large-scale magnetic field behaviour over the last three solar cycles with variations in the SMP reconstruction through the Holocene epoch. To achieve these objectives, we use the IntCal13 $^{14}$C data to investigate distinct patterns in the occurrences of grand minima and maxima during the Holocene period. We then check whether these patterns might mimic the recent solar magnetic activity by investigating the evolution of the energy in the Sun's large-scale dipolar magnetic field using the Wilcox Solar Observatory data. The cosmogenic radionuclide data analysis shows that $\sim$71\% of grand maxima during the period from 6600 BC to 1650 AD were followed by a grand minimum. The occurrence characteristics of grand maxima and minima are consistent with the scenario in which the dynamical non-linearity induced by the Lorentz force leads the Sun to act as a relaxation oscillator. This finding implies that the probability for these events to occur is non-uniformly distributed in time, as there is a memory in their driving mechanism, which can be identified via the back reaction of the Lorentz force.

WHAT CAUSES THE INTER-SOLAR-CYCLE VARIATION OF TOTAL SOLAR IRRADIANCE?

The Physikalisch Meteorologisches Observatorium Davos total solar irradiance (TSI), Active Cavity Radiometer Irradiance Monitoring TSI, and Royal Meteorological Institute of Belgium TSI are three typical TSI composites. Magnetic Plage Strength Index (MPSI) and Mount Wilson Sunspot Index (MWSI) should indicate the weak and strong magnetic field activity on the solar full disk, respectively. Cross-correlation (CC) analysis of MWSI with three TSI composites shows that TSI should be weakly correlated with MWSI, and not be in phase with MWSI at timescales of solar cycles. The wavelet coherence (WTC) and partial wavelet coherence (PWC) of TSI with MWSI indicate that the inter-solar-cycle variation of TSI is also not related to solar strong magnetic field activity, which is represented by MWSI. However, CC analysis of MPSI with three TSI composites indicates that TSI should be moderately correlated and accurately in phase with MPSI at timescales of solar cycles, and that the statistical. significance. test indicates that the correlation coefficient of three TSI composites with MPSI is statistically significantly higher than that of three TSI composites with MWSI. Furthermore, the cross wavelet transform (XWT) and WTC of TSI with MPSI show that the TSI is highly related and actually in phase with MPSI at a timescale of a solar cycle as well. Consequently, the CC analysis, XWT, and WTC indicate that the solar weak magnetic activity on the full disk, which is represented by MPSI, dominates the inter-solar-cycle variation of TSI.

Using the Sun to estimate Earth-like planets detection capabilities

Stellar activity induced by active structures (eg, spots, faculae) is known to strongly impact the radial velocity time series. It then limits the detection of small planetary RV signals (eg, an Earth-mass planet in the habitable zone of a solar-like star). In previous papers, we studied the detectability of such planets around the Sun seen as an edge-on star. For that purpose, we computed the RV and photometric variations induced by solar magnetic activity, using all active structures observed over one entire cycle. Our goal is to perform similar studies on stars with different physical and geometrical properties. As a first step, we focus on Sun-like stars seen with various inclinations, and on estimating detection capabilities with forthcoming instruments. To do so, we first parameterize the solar active structures with the most realistic pattern so as to obtain results consistent with the observed ones. We simulate the growth, evolution and decay of solar spots, faculae and network, using parameters and empiric laws derived from solar observations and literature. We generate the corresponding structure lists over a full solar cycle. We then build the resulting spectra and deduce the RV and photometric variations for a `Sun' seen with various inclinations. The produced RV signal takes into account the photometric contribution of structures as well as the attenuation of the convective blueshift. The comparison between our simulated activity pattern and the observed one validates our model. We show that the inclination of the stellar rotation axis has a significant impact on the time series. RV long-term amplitudes as well as short-term jitters are significantly reduced when going from edge-on to pole-on configurations. Assuming spin-orbit alignment, the optimal configuration for planet detection is an inclined star (i~45{\deg}).

UV solar irradiance in observations and the NRLSSI and SATIRE‐S models

AbstractTotal solar irradiance and UV spectral solar irradiance has been monitored since 1978 through a succession of space missions. This is accompanied by the development of models aimed at replicating solar irradiance by relating the variability to solar magnetic activity. The Naval Research Laboratory Solar Spectral Irradiance (NRLSSI) and Spectral And Total Irradiance REconstruction for the Satellite era (SATIRE‐S) models provide the most comprehensive reconstructions of total and spectral solar irradiance over the period of satellite observation currently available. There is persistent controversy between the various measurements and models in terms of the wavelength dependence of the variation over the solar cycle, with repercussions on our understanding of the influence of UV solar irradiance variability on the stratosphere. We review the measurement and modeling of UV solar irradiance variability over the period of satellite observation. The SATIRE‐S reconstruction is consistent with spectral solar irradiance observations where they are reliable. It is also supported by an independent, empirical reconstruction of UV spectral solar irradiance based on Upper Atmosphere Research Satellite/Solar Ultraviolet Spectral Irradiance Monitor measurements from an earlier study. The weaker solar cycle variability produced by NRLSSI between 300 and 400 nm is not evident in any available record. We show that although the method employed to construct NRLSSI is principally sound, reconstructed solar cycle variability is detrimentally affected by the uncertainty in the SSI observations it draws upon in the derivation. Based on our findings, we recommend, when choosing between the two models, the use of SATIRE‐S for climate studies.

Two-dimensional model for an αΩ-dynamo with meridional circulation and an associated Hamilton–Jacobi equation

A two-dimensional model for an αΩ-dynamo is constructed, taking into account meridional flows. A Hamilton–Jacobi equation for the resulting system of magnetic-field generation equatons is constructed using an asymptotic method analogous to the WKB method. This equation makes it possible to analytically study the influence of meridional flows on the duration of the solar magnetic-activity cycle and the evolution of magnetic waves.

THE CAUSE OF THE WEAK SOLAR CYCLE 24

The ongoing 11-year cycle of solar activity is considerably less vigorous than the three cycles before. It was preceded by a very deep activity minimum with a low polar magnetic flux, the source of the toroidal field responsible for solar magnetic activity in the subsequent cycle. Simulation of the evolution of the solar surface field shows that the weak polar fields and thus the weakness of the present cycle 24 are mainly caused by a number of bigger bipolar regions emerging at low latitudes with a `wrong' (i.e., opposite to the majority for this cycle) orientation of their magnetic polarities in the North-South direction, which impaired the growth of the polar field. These regions had a particularly strong effect since they emerged within $\pm10^\circ$ latitude from the solar equator.

Deciphering solar magnetic activity: on grand minima in solar activity

The Sun provides the energy necessary to sustain our existence. While the Sun provides for us, it is also capable of taking away. The weather and climatic scales of solar evolution and the Sun-Earth connection are not well understood. There has been tremendous progress in the century since the discovery of solar magnetism - magnetism that ultimately drives the electromagnetic, particulate and eruptive forcing of our planetary system. There is contemporary evidence of a decrease in solar magnetism, perhaps even indicators of a significant downward trend, over recent decades. Are we entering a minimum in solar activity that is deeper and longer than a typical solar minimum, a minimum? How could we tell if we are? What is a grand minimum and how does the Sun recover? These are very pertinent questions for modern civilization. In this paper we present a hypothetical demonstration of entry and exit from grand minimum conditions based on a recent analysis of solar features over the past 20 years and their possible connection to the origins of the 11(-ish) year solar activity cycle.

LOOKING FOR GRANULATION AND PERIODICITY IMPRINTS IN THE SUNSPOT TIME SERIES

The sunspot activity is the end result of the cyclic destruction and regeneration of magnetic fields by the dynamo action. We propose a new method to analyze the daily sunspot areas data recorded since 1874. By computing the power spectral density of daily data series using the Mexican hat wavelet, we found a power spectrum with a well-defined shape, characterized by three features. The first term is the 22 yr solar magnetic cycle, estimated in our work to be of 18.43 yr. The second term is related to the daily volatility of sunspots. This term is most likely produced by the turbulent motions linked to the solar granulation. The last term corresponds to a periodic source associated with the solar magnetic activity, for which the maximum of power spectral density occurs at 22.67 days. This value is part of the 22-27 day periodicity region that shows an above-average intensity in the power spectra. The origin of this 22.67 day periodic process is not clearly identified, and there is a possibility that it can be produced by convective flows inside the star. The study clearly shows a north-south asymmetry. The 18.43 yr periodical source is correlated between the two hemispheres, but the 22.67 day one is not correlated. It is shown that towards the large timescales an excess occurs in the northern hemisphere, especially near the previous two periodic sources. To further investigate the 22.67 day periodicity we made a Lomb-Scargle spectral analysis. The study suggests that this periodicity is distinct from others found nearby.

Day‐to‐day variability and solar preconditioning of thermospheric temperature over Millstone Hill

AbstractWe use a continuous 30 day incoherent scatter radar experiment at Millstone Hill in October 2002 to examine day‐to‐day thermospheric variability in exospheric temperature Tex. Solar flux and magnetic activity influences as the main driving factors for day‐to‐day variability are investigated quantitatively. Solar ultraviolet flux levels are based on the TIMED/SEE space weather product, allowing for analysis of ultraviolet flux‐Tex correlation. Tex is most sensitive to solar EUV flux with approximately a 2 day delay at wavelengths of 27–34 nm (including 30.4 nm). In particularly, a 20–60 h time delay occurs in Tex response to EUV flux at 27–34 nm band, with shorter delays in the morning and longer delays in the afternoon and at night. The 1 ∼ 2 day delayed Tex response to solar ultraviolet flux and associated thermospheric solar preconditioning (“memory”) are most significant in the daily mean for the 27–34 nm band, in the diurnal and semidiurnal amplitudes for the soft X‐ray flux at 0.1–7 nm, and in the diurnal amplitude for longer wavelengths. An empirical model driven only by EUV flux at 27–34 nm from 2 days in advance reproduces 90% of the observed variability in the Tex daily mean. With a 2 day time delay, solar X‐ray flux at 0.1–7 nm is correlated positively with Tex diurnal amplitude and negatively with Tex semidiurnal amplitude. Finally, magnetic activity control, as represented by the Dst index, is weaker during the day and stronger at night and is important for the semidiurnal amplitude but not important for the daily mean.