Sinusoidal Fitting Research Articles

Removal of Co-Frequency Powerline Harmonics From Multichannel Surface NMR Data

Powerline harmonics are often the primary noise source in surface nuclear magnetic resonance (NMR) measurements. State-of-the-art techniques, such as notch filtering, Wiener filtering, and model-based subtraction, have been demonstrated to greatly mitigate powerline harmonic noise, but these approaches break down when one of the powerline harmonics has a frequency close to or coincident with the Larmor frequency $f_{L}$ , referred to as a co-frequency harmonic. We propose a hybrid scheme where model-based subtraction of powerline harmonics is coupled with data from a synchronous reference coil to specifically subtract the co-frequency harmonic component. In standard model-based subtraction of powerline harmonics, a sinusoidal model of all harmonic components is fit to the data and subtracted. In the new approach, the amplitude and phase of the co-frequency harmonic are determined by a sinusoidal model fit to the synchronous noise-only data recorded in a reference coil. From the reference coil co-frequency model, the co-frequency harmonic in the primary coil is estimated using relationships between the amplitude and phase of the co-frequency harmonic in the two coils established during noise-only segments. By utilizing data from the reference coil to model the co-frequency harmonic, accidental fitting of the surface NMR signal is avoided. We investigate the efficiency of the method using a synthetic surface NMR signal embedded in noise-only data recorded in Denmark. Our results demonstrate that the co-frequency powerline harmonic can be removed efficiently without distorting the surface NMR signal and the new method performs better than standard methods.

Dynamic measurement of first-order spatial derivatives of deformations by digital shearography

This paper presents a simple spatial phase shift shearography based on the Michelson interferometer. A novel digital shearography set-up with a large angle of view, which is based on a 4f system is demonstrated. In the system, the Michelson interferometer is used as a shearing device to generate a shearing distance by tilting a small angle in one of the two mirrors. In fact spherical wave fronts become plane after going through the first lens in 4f system. Tilting the mirror in the Michelson interferometer also generates spatial carrier frequency. Sinusoid fitting method is applied to evaluate the phase. This system can generate a phase map of shearography by using only a single image. The effects of shearing angle, the choice of algorithm and comparison result are discussed in detail. The theory and the application are presented.

Magnetic field geometry and chemical abundance distribution of the He-strong star CPD −57°3509

The magnetic field of CPD -57 3509 was recently detected in the framework of the BOB (B fields in OB stars) collaboration. We acquired low-resolution spectropolarimetric observations of CPD -57 3509 with FORS2 and high-resolution UVES observations randomly distributed over a few months to search for periodicity, to study the magnetic field geometry, and to determine the surface distribution of silicon and helium. We also obtained supplementary photometric observations at a timeline similar to the spectroscopic and spectropolarimetric observations. A period of 6.36d was detected in the measurements of the mean longitudinal magnetic field. A sinusoidal fit to our measurements allowed us to constrain the magnetic field geometry and estimate the dipole strength in the range of 3.9-4.5kG. Our application of the Doppler imaging technique revealed the presence of He I spots located around the magnetic poles, with a strong concentration at the positive pole and a weaker one around the negative pole. In contrast, high concentration Si III spots are located close to the magnetic equator. Further, our analysis of the spectral variability of CPD -57 3509 on short time scales indicates distinct changes in shape and position of line profiles possibly caused by the presence of beta Cep-like pulsations. A small periodic variability in line with the changes of the magnetic field strength is clearly seen in the photometric data.

Multi-dimensional and multi-temporal motion estimation of a beam surface during dynamic testing using low-frame rate digital cameras

The combination of digital close-range photogrammetric systems and image processing techniques has been employed in structural health monitoring applications for more than 10 years. The use of off-the-shelf entry level digital single-lens reflex cameras has lately become a suitable choice even for applications requiring sub-millimetre- level precision especially when the involved devices need to be inexpensive. The drawback of such low-cost cameras is in the trade-off between spatial resolution, frame rate, and burst rate—at the highest available spatial resolution, a high frame rate is either not possible or it has a low burst rate. This may be problematic when monitoring a structural component during a dynamic/fatigue test. In order to estimate specimen motion in such a situation, this paper proposes an innovative sinusoidal fitting based on a least squares adjustment. This method simultaneously processes multiple bursts of data in order to synthetically increase the sampling frequency of the system. The input data for the adjustment comes from a full surface modelling procedure based on a newly proposed generalized 3D polynomial. The experimental results include a beam deformation test performed in a structures laboratory. The new sinusoidal fitting method effectively increased the system temporal resolution three-fold, which improved the precision of the derived parameters with up to two orders of magnitude. The root mean square error of the residuals were as good as 26 μm, and the one of the estimated amplitudes from the photogrammetric system versus a set of laser transducers used as control was as small as 43 μm.

Search for exoplanets around pulsating stars of A–F type in Kepler short-cadence data and the case of KIC 8197761

We searched for extrasolar planets around pulsating stars by examining $\textit{Kepler}$ data for transit-like events hidden in the intrinsic variability. All Short Cadence observations for targets with 6000 K $< T_{\rm eff} <$ 8500 K were visually inspected for transit-like events following the removal of pulsational signals by sinusoidal fits. Clear transit-like events were detected in KIC 5613330 and KIC 8197761. KIC 5613330 is a confirmed exoplanet host (Kepler-635b), where the transit period determined here is consistent with the literature value. KIC 8197761 is a $\gamma$ Doradus - $\delta$ Scuti star exhibiting eclipses/transits occurring every 9.8686667(27) d, having durations of 8.37 h, and causing brightness drops $\frac{\Delta F}{F} = 0.00629(29)$. The star's pulsation spectrum contains several mode doublets and triplets, identified as $l = 1$, with a mean spacing of 0.001659(15) c/d, implying an internal rotation period of $301\pm3$ d. Trials to calculate the size of the light travel time effect (LTTE) from the pulsations to constrain the companion's mass ended inconclusive. Finding planets around $\gamma$ Doradus stars from the pulsational LTTE, therefore, is concluded to be unrealistic. Spectroscopic monitoring of KIC 8197761 revealed sinusoidal radial velocity variations with a semi-amplitude of $19.75 \pm 0.32$ km/s, while individual spectra present rotational broadening consistent with $v \sin i = 9\pm1$ km/s. This suggests that the stellar surface rotation is synchronized with the orbit, whereas the stellar core rotates $\sim$30 times slower. Combining the observed radial velocity variability with the transit photometry, constrains the companion's mass to be $\approx 0.28$ M$_{\odot}$, ruling out an exoplanet hypothesis.

Egg production curves and their prediction through mathematical models in a random-bred broiler breeder control population

Six mathematical models, namely, Logistic, MMF, Polynomial Fit, Rational Function, Sinusoidal Fit and Quadratic fit were selected and fitted to the weekly hen housed egg production from 19 to 52 weeks of age of two generations of a random-bred broiler breeder control line. The efficiency or reliability of the models was obtained by the coefficients of determination (R2) as per the Least

The New Sunspot-Number Index and Solar-Cycle Characteristics

We revisit several characteristics of the solar cycle using the new version of the sunspot-number index. Thus, we calculated several correlations, including the recent Solar Cycles 23 and 24 in the analysis. We applied two smoothing methods to the sunspot number: i) the usual 13-month running mean and ii) a 24-month Gaussian filter. Each of these methods contains two analyses: on the one hand, we consider all of the solar cycles available, and on the other hand, only those from Solar Cycle 10 onward. It can be seen that this new version improves or yields similar results for the correlations with respect to other works using the old version of the sunspot number, except for the amplitude–descending time effect and the linear fit of the secular trend. However, employing the same methodology in the analysis and considering the same solar cycles, it can be seen that the new sunspot number, in general, does not improve the correlations with respect to the old sunspot number and, moreover, the correlations obtained with the Gaussian filter generally are stronger than those with the 13-month running mean. Furthermore, from a sinusoidal fit to the solar-maximum amplitudes of the whole series, we have obtained a periodicity of the Gleissberg cycle equal to 97.7 years ( ${\approx}\,8.9$ solar cycles) for the 13-month running mean and 99.8 years ( ${\approx}\,9.1$ solar cycles) for the Gaussian filter. Lastly, the Waldmeier effect, the modified Waldmeier effect, the amplitude–period effect, the amplitude–minimum effect, and the even–odd effect are characteristics with high correlation coefficients and significance levels; the sinusoidal fit applied to the solar-maximum amplitudes yields a lower correlation coefficient value but a high significance level; and both the amplitude–descending-time effect and secular trend of the solar activity have weaker correlation coefficients and significance levels.

Principal component analysis based unsupervised feature extraction applied to budding yeast temporally periodic gene expression.

BackgroundThe recently proposed principal component analysis (PCA) based unsupervised feature extraction (FE) has successfully been applied to various bioinformatics problems ranging from biomarker identification to the screening of disease causing genes using gene expression/epigenetic profiles. However, the conditions required for its successful use and the mechanisms involved in how it outperforms other supervised methods is unknown, because PCA based unsupervised FE has only been applied to challenging (i.e. not well known) problems.ResultsIn this study, PCA based unsupervised FE was applied to an extensively studied organism, i.e., budding yeast. When applied to two gene expression profiles expected to be temporally periodic, yeast metabolic cycle (YMC) and yeast cell division cycle (YCDC), PCA based unsupervised FE outperformed simple but powerful conventional methods, with sinusoidal fitting with regards to several aspects: (i) feasible biological term enrichment without assuming periodicity for YMC; (ii) identification of periodic profiles whose period was half as long as the cell division cycle for YMC; and (iii) the identification of no more than 37 genes associated with the enrichment of biological terms related to cell division cycle for the integrated analysis of seven YCDC profiles, for which sinusoidal fittings failed. The explantation for differences between methods used and the necessary conditions required were determined by comparing PCA based unsupervised FE with fittings to various periodic (artificial, thus pre-defined) profiles. Furthermore, four popular unsupervised clustering algorithms applied to YMC were not as successful as PCA based unsupervised FE.ConclusionsPCA based unsupervised FE is a useful and effective unsupervised method to investigate YMC and YCDC. This study identified why the unsupervised method without pre-judged criteria outperformed supervised methods requiring human defined criteria.Electronic supplementary materialThe online version of this article (doi:10.1186/s13040-016-0101-9) contains supplementary material, which is available to authorized users.

STRUCTURAL 3D MONITORING USING A NEW SINUSOIDAL FITTING ADJUSTMENT

Digital photogrammetric systems combined with image processing techniques have been used for structural monitoring purposes for more than a decade. For applications requiring sub-millimetre level precision, the use of off-the-shelf DSLR cameras is a suitable choice, especially when the low cost of the involved sensors is a priority. The disadvantage in the use of entry level DSLRs is that there is a trade-off between frame rate and burst rate – a high frame rate is either not available or it cannot be sustained long enough. This problem must be overcome when monitoring a structural element undergoing a dynamic test, where a range of loads are cycled through multiple times a second. In order to estimate deflections during such a scenario, this paper proposes a new least-squares adjustment for sinusoidal fitting. The new technique is capable of processing multiple back-to-back bursts of data within the same adjustment, which synthetically increases the de-facto temporal resolution of the system. The paper describes a beam deformation test done in a structures laboratory. The experimental results were assessed in terms of both their precision and accuracy. The new method increased the effective sampling frequency three-fold, which improved the standard deviations of the estimated parameters with up to two orders of magnitude. A residual RMSE as low as 30 μm was attained, and likewise the RMSE of the computed amplitudes between the photogrammetric system and the control laser transducers was as small as 34 μm.

STRUCTURAL 3D MONITORING USING A NEW SINUSOIDAL FITTING ADJUSTMENT

Abstract. Digital photogrammetric systems combined with image processing techniques have been used for structural monitoring purposes for more than a decade. For applications requiring sub-millimetre level precision, the use of off-the-shelf DSLR cameras is a suitable choice, especially when the low cost of the involved sensors is a priority. The disadvantage in the use of entry level DSLRs is that there is a trade-off between frame rate and burst rate – a high frame rate is either not available or it cannot be sustained long enough. This problem must be overcome when monitoring a structural element undergoing a dynamic test, where a range of loads are cycled through multiple times a second. In order to estimate deflections during such a scenario, this paper proposes a new least-squares adjustment for sinusoidal fitting. The new technique is capable of processing multiple back-to-back bursts of data within the same adjustment, which synthetically increases the de-facto temporal resolution of the system. The paper describes a beam deformation test done in a structures laboratory. The experimental results were assessed in terms of both their precision and accuracy. The new method increased the effective sampling frequency three-fold, which improved the standard deviations of the estimated parameters with up to two orders of magnitude. A residual RMSE as low as 30 μm was attained, and likewise the RMSE of the computed amplitudes between the photogrammetric system and the control laser transducers was as small as 34 μm.

An integral model to calculate the growing degree-days and heat units, a spreadsheet application

The concept of heat units is used in several phenological studies like the prediction of sowing and harvesting dates, crop yield, length of plant stages, and maturity state. However, calculation of heat units as growing degree-days requires a summation process that is not easily performed like direct-substitution equations. The aim of this work was to develop a simple integral model to calculate the heat units as growing degree-days. The development involved two steps; the first step was applying a non-iterative sinusoidal fit to the discrete temperature data to get a fitting equation of each station in the two datasets, CLIMWAT 2 and FAOCLIM 2. The second step was to integrate each temperature equation to calculate the heat units, either by the average temperature or by both the minimum and maximum temperatures. The results showed that the sinusoidal model properly fits the temperature profiles in most of the studied stations (Most of the stations got the fit with R2>95% and 98.4% of the stations had <2°C root mean squared error). Additionally, the results showed no significant differences (in accuracy) between the developed integral model and the conventional summation methods of calculating the heat units, while the new model is faster and easier in application. Finally, it is recommended to use the new integral model with the fitted average temperature due to its accuracy and simplicity.

Angular momentum of the N2H+ cores in the Orion A cloud

Abstract We have analyzed the angular momentum of the molecular cloud cores in the Orion A giant molecular cloud observed in the N2H+J = 1–0 line with the Nobeyama 45 m radio telescope. We have measured the velocity gradient using position–velocity diagrams passing through core centers, and made sinusoidal fits against the position angle. Twenty-seven out of 34 N2H+ cores allowed us to measure the velocity gradient without serious confusion. The derived velocity gradient ranges from 0.5 to 7.8 km s−1 pc−1. We marginally found that the specific angular momentum J/M (against the core radius R) of the Orion N2H+ cores tends to be systematically larger than that of molecular cloud cores in cold dark clouds obtained by Goodman et al., in the J/M–R relation. The ratio β of rotational to gravitational energy is derived to be β = 10−2.3±0.7, and is similar to that obtained for cold dark cloud cores in a consistent definition. The large-scale rotation of the ∫-shaped filament of the Orion A giant molecular cloud does not likely govern the core rotation at smaller scales.

Analysis and Correction of Dynamic Geometric Misalignment for Nano-Scale Computed Tomography at BSRF.

Due to its high spatial resolution, synchrotron radiation x-ray nano-scale computed tomography (nano-CT) is sensitive to misalignments in scanning geometry, which occurs quite frequently because of mechanical errors in manufacturing and assembly or from thermal expansion during the time-consuming scanning. Misalignments degrade the imaging results by imposing artifacts on the nano-CT slices. In this paper, the geometric misalignment of the synchrotron radiation nano-CT has been analyzed by partial derivatives on the CT reconstruction algorithm and a correction method, based on cross correlation and least-square sinusoidal fitting, has been reported. This work comprises a numerical study of the method and its experimental verification using a dataset measured with the full-field transmission x-ray microscope nano-CT at the beamline 4W1A of the Beijing Synchrotron Radiation Facility. The numerical and experimental results have demonstrated the validity of the proposed approach. It can be applied for dynamic geometric misalignment and needs neither phantom nor additional correction scanning. We expect that this method will simplify the experimental operation of synchrotron radiation nano-CT.

The Global Network of Isotopes in Rivers (GNIR): integration of water isotopes in watershed observation and riverine research

Abstract. We introduce a new online global database of riverine water stable isotopes (Global Network of Isotopes in Rivers, GNIR) and evaluate its longer-term data holdings. Overall, 218 GNIR river stations were clustered into three different groups based on the seasonal variation in their isotopic composition, which was closely coupled to precipitation and snowmelt water runoff regimes. Sinusoidal fit functions revealed phases within each grouping and deviations from the sinusoidal functions revealed important river alterations or hydrological processes in these watersheds. The seasonal isotopic amplitude of δ18O in rivers averaged 2.5 ‰, and did not increase as a function of latitude, like it does for global precipitation. Low seasonal isotopic amplitudes in rivers suggest the prevalence of mixing and storage such as occurs via lakes, reservoirs, and groundwater. The application of a catchment-constrained regionalized cluster-based water isotope prediction model (CC-RCWIP) allowed for direct comparison between the expected isotopic compositions for the upstream catchment precipitation with the measured isotopic composition of river discharge at observation stations. The catchment-constrained model revealed a strong global isotopic correlation between average rainfall and river discharge (R2 = 0.88) and the study demonstrated that the seasonal isotopic composition and variation of river water can be predicted. Deviations in data from model-predicted values suggest there are important natural or anthropogenic catchment processes like evaporation, damming, and water storage in the upstream catchment.

An Algorithm for Surface Current Retrieval from X-band Marine Radar Images

In this paper, a novel current inversion algorithm from X-band marine radar images is proposed. The routine, for which deep water is assumed, begins with 3-D FFT of the radar image sequence, followed by the extraction of the dispersion shell from the 3-D image spectrum. Next, the dispersion shell is converted to a polar current shell (PCS) using a polar coordinate transformation. After removing outliers along each radial direction of the PCS, a robust sinusoidal curve fitting is applied to the data points along each circumferential direction of the PCS. The angle corresponding to the maximum of the estimated sinusoid function is determined to be the current direction, and the amplitude of this sinusoidal function is the current speed. For validation, the algorithm is tested against both simulated radar images and field data collected by a vertically-polarized X-band system and ground-truthed with measurements from an acoustic Doppler current profiler (ADCP). From the field data, it is observed that when the current speed is less than 0.5 m/s, the root mean square differences between the radar-derived and the ADCP-measured current speed and direction are 7.3 cm/s and 32.7°, respectively. The results indicate that the proposed procedure, unlike most existing current inversion schemes, is not susceptible to high current speeds and circumvents the need to consider aliasing. Meanwhile, the relatively low computational cost makes it an excellent choice in practical marine applications.

Numerical Determination of Equivalent Reflected Blast Parameters Acting on Circular Cross Sections

A number of experimenters observed that the blast shockwave loads experienced by circular cross sections were lower than the predicted loads. These observations revealed a gap in the understanding of the interaction between blasts and structures. The question of quantifying these reduced loads for purposes of analysis and design presented itself for investigation. This paper presents the numerical investigation of the blast reflection reduction due to diffraction around a circular cross section using the commercial software ANSYS Autodyn. The investigation focused on the effects of the cross section's diameter and the explosion's scaled distance on the reflected blast pressure and impulse. Nine numerical gauge points recorded pressure-time and impulse-time histories at regular radial intervals around the front quarter of the circular section. The model's results agreed with incident and reflected pressure and impulse design values. The results indicated that as the diameter of the section increased the peak reflected pressure and impulse at the point of incidence rapidly approached the design values. The results also indicated that both the pressure and the impulse varied sinusoidally between a maximum at the point of incidence and a minimum, approximately equal to the incident pressure and impulse, at the side of the section. Using a sinusoidal curve fit to obtain equivalent reflected pressure and impulse values showed that the actual pressure and impulse acting on a circular cross section were approximately half the recommended design values. The results supported the obvious advantages of designing circular members to resist blast loading. Simplified equations are proposed for calculating the equivalent pressure and impulse acting on circular sections from the standard design values.

ANALYSIS OF THE SOUTHERN PRE-CONTACT W UMA BINARY ZZ ERIDANI: A 34 YEAR PERIOD STUDY YIELDS A POSSIBLE LOW-MASS COMPANION

Complete Bessel BVRI light curves of ZZ Eridani [2MASS J04130109-1044545, HV 6280, NSVS 14888164 α(2000) = 04{sup h}13{sup m}1{sub ·}{sup s}10, δ(2000) = −10°44′54{sub ·}{sup ″}5 (ICRS), V = 13.9-14.4-15.0] are observed and analyzed. The system is a southern pre-contact W UMa binary. Its light curve has the appearance of an Algol (EA) light curve, however, it is made up of dwarf solar-type components with a period of only 0.4521 days. Our 34 year period study yields a sinusoidal fit or an increasing quadratic fit. The sinusoid may indicate that a third body is orbiting the close binary. The lower-limit mass of the third body is near that of the brown dwarf limit (0.095 M α). Also included is an improved ephemeris, a mass ratio search, and a simultaneous BVRI Wilson–Devinney solution.

Performance analysis of a photonic integrated interferometer circuit based on silicon-on-insulator

Small footprint photonic integrated interferometer based on silicon-on-insulator platform is reported. A passive interferometer comprising small footprint $$4\times 4$$ and $$2\times 2$$ multi-mode interference (MMI) couplers is designed and tested. The $$4\times 4 \,(2\times 2)$$ MMIs feature 0.16 dB (0.06 dB) excess loss, 0.22 dB (0.09 dB) power imbalance, and 1.7 $$^{\circ }$$ (0.12 $$^{\circ }$$ ) phase error. An efficient use of the small design area is accomplished by positioning the input and output ports of the passive interferometer along the same side of the chip with a separation of $$127\,\upmu \hbox {m}$$ between each other (pitch size). A passive-active interferometer terminated with Ge photodiodes has also been designed and tested. Sinusoidal fitting of the phase differences between output port number 1 and all other output ports are estimated to be under 2 $$^{\circ }$$ margin, i.e., $$90^{\circ }\pm 1^{\circ },180^{\circ }\pm 1^{\circ }$$ and $$270^{\circ }\pm 1^{\circ }$$ .

Measuring the polarization of a rapidly precessing deuteron beam

This paper describes a time-marking system that enables a measurement of the in-plane (horizontal) polarization of a 0.97-GeV/c deuteron beam circulating in the Cooler Synchrotron (COSY) at the Forschungszentrum J\"ulich. The clock time of each polarimeter event is used to unfold the 120-kHz spin precession and assign events to bins according to the direction of the horizontal polarization. After accumulation for one or more seconds, the down-up scattering asymmetry can be calculated for each direction and matched to a sinusoidal function whose magnitude is proportional to the horizontal polarization. This requires prior knowledge of the spin tune or polarization precession rate. An initial estimate is refined by re-sorting the events as the spin tune is adjusted across a narrow range and searching for the maximum polarization magnitude. The result is biased toward polarization values that are too large, in part because of statistical fluctuations but also because sinusoidal fits to even random data will produce sizeable magnitudes when the phase is left free to vary. An analysis procedure is described that matches the time dependence of the horizontal polarization to templates based on emittance-driven polarization loss while correcting for the positive bias. This information will be used to study ways to extend the horizontal polarization lifetime by correcting spin tune spread using ring sextupole fields and thereby to support the feasibility of searching for an intrinsic electric dipole moment using polarized beams in a storage ring. This paper is a combined effort of the Storage Ring EDM Collaboration and the JEDI Collaboration.

On the influence of cloud fraction diurnal cycle and sub-grid cloud optical thickness variability on all-sky direct aerosol radiative forcing

The objective of this study is to understand how cloud fraction diurnal cycle and sub-grid cloud optical thickness variability influence the all-sky direct aerosol radiative forcing (DARF). We focus on the southeast Atlantic region where transported smoke is often observed above low-level water clouds during burning seasons. We use the CALIOP observations to derive the optical properties of aerosols. We developed two diurnal cloud fraction variation models. One is based on sinusoidal fitting of MODIS observations from Terra and Aqua satellites. The other is based on high-temporal frequency diurnal cloud fraction observations from SEVIRI on board of geostationary satellite. Both models indicate a strong cloud fraction diurnal cycle over the southeast Atlantic region. Sensitivity studies indicate that using a constant cloud fraction corresponding to Aqua local equatorial crossing time (1:30PM) generally leads to an underestimated (less positive) diurnal mean DARF even if solar diurnal variation is considered. Using cloud fraction corresponding to Terra local equatorial crossing time (10:30AM) generally leads overestimation. The biases are a typically around 10–20%, but up to more than 50%.The influence of sub-grid cloud optical thickness variability on DARF is studied utilizing the cloud optical thickness histogram available in MODIS Level-3 daily data. Similar to previous studies, we found the above-cloud smoke in the southeast Atlantic region has a strong warming effect at the top of the atmosphere. However, because of the plane-parallel albedo bias the warming effect of above-cloud smoke could be significantly overestimated if the grid-mean, instead of the full histogram, of cloud optical thickness is used in the computation. This bias generally increases with increasing above-cloud aerosol optical thickness and sub-grid cloud optical thickness inhomogeneity. Our results suggest that the cloud diurnal cycle and sub-grid cloud variability are important factors to be accounted for in the studies of all-sky DARF.