An application of the weighted horizontal magnetic gradient to solar compact and eruptive events

We propose to apply the weighted horizontal magnetic gradient (${\mathit{WG}}_M$), introduced in Korsós et al., 2015, for analysing the pre-flare and pre-CME behaviour and evolution of Active Regions (ARs) using the SDO/HMI-Debrecen Data catalogue. To demonstrate the power of investigative capabilities of the ${\mathit{WG}}_M$ method, in terms of flare and CME eruptions, we studied two typical ARs, namely, AR 12158 and AR 12192. The choice of ARs represent canonical cases. AR 12158 produced an X1.6 flare with fast “halo” CME ($v_{\mathit{linear}}$ = 1267 $\text{km}{\text{s}}^{-1}$) while in AR 12192 there occurred a range of powerful X-class eruptions, i.e. X1.1, X1.6, X3.1, X1.0, X2.0 and X2.0-class energetic flares, interestingly, none with an accompanying CME. The value itself and temporal variation of ${\mathit{WG}}_M$ is found to possess potentially important diagnostic information about the intensity of the expected flare class. Furthermore, we have also estimated the flare onset time from the relationship of duration of converging and diverging motions of the area-weighted barycenters of two subgroups of opposite magnetic polarities. This test turns out not only to provide information about the intensity of the expected flare-class and the flare onset time but may also indicate whether a flare will occur with/without fast CME. We have also found that, in the case when the negative polarity barycenter has moved around and the positive one “remained” at the same coordinates preceding eruption, the flare occurred with fast “halo” CME. Otherwise, when both the negative and the positive polarity barycenters have moved around, the AR produced flares without CME. If these properties found for the movement of the barycenters are generic pre-cursors of CME eruption (or lack of it), identifying them may serve as an excellent pre-condition for refining the forecast of the lift-off of CMEs.     

Detailed analysis of dynamic evolution of three Active Regions at the photospheric level before flare and CME occurrence

We present a combined analysis of the applications of the weighted horizontal magnetic gradient (denoted as ${\mathit{WG}}_M$ in Korsós et al. (2015)) method and the magnetic helicity tool (Berger and Field, 1984) employed for three active regions (ARs), namely NOAA AR 11261, AR 11283 and AR 11429. We analysed the time series of photospheric data from the Solar Dynamics Observatory taken between August 2011 and March 2012. During this period the three ARs produced a series of flares (eight M- and six X-class) and coronal mass ejections (CMEs). AR 11261 had four M-class flares and one of them was accompanied by a fast CME. AR 11283 had similar activities with two M- and two X-class flares, but only with a slow CME. Finally, AR 11429 was the most powerful of the three ARs as it hosted five compact and large solar flare and CME eruptions. For applying the ${\mathit{WG}}_M$ method we employed the Debrecen sunspot data catalogue, and, for estimating the magnetic helicity at photospheric level we used the Space-weather HMI Active Region Patches (SHARP’s) vector magnetograms from SDO/HMI (Solar Dynamics Observatory/Helioseismic and Magnetic Imager). We followed the evolution of the components of the ${\mathit{WG}}_M$ and the magnetic helicity before the flare and CME occurrences. We found a unique and mutually shared behaviour, called the U-shaped pattern, of the weighted distance component of ${\mathit{WG}}_M$ and of the shearing component of the helicity flux before the flare and CME eruptions. This common pattern is associated with the decreasing-receding phases yet reported only known to be a necessary feature prior to solar flare eruption(s) but found now at the same time in the evolution of the shearing helicity flux. This result leads to the conclusions that (i) the shearing motion of photospheric magnetic field may be a key driver for solar eruption in addition to the flux emerging process, and that (ii) the found decreasing-approaching pattern in the evolution of shearing helicity flux may be another precursor indicator for improving the forecasting of solar eruptions.     

Solar EUV flux variation and flare brightenings

On 2010 February 8, the Extreme ultraviolet (EUV) flux variation in 195 Å and flare brightening has been examined in different sizes of active regions by using SOHO/EIT, MDI and Hα$\alpha$ observational data. These three active regions represent a large active region with a sunspot group, a moderate active region without a sunspot and a small region with weak plage in Hα$\alpha$ band respectively. Our study shows that the main full disk EUV flux comes from active regions, especially from large active regions. The sudden increases of EUV flux are corresponding to the EUV flare brightenings. For the large active region, the local EUV 195 Å flux peaks are well correlated to that of the GOES X-ray flux. The EUV 195 Å flux peaking time of M-class flares delay GOES X-ray flux a few minutes. For the moderate active region, the local EUV 195 Å flux is not well correlated to GOES X-ray flux. The EUV 195 Å flare brightenings in the moderate active region appeared in the duration of sudden increase of its own local EUV flux. For the small active region, the local EUV 195  Å flux varied almost independently of the GOES X-ray flux. Our study suggests that for an active region its local EUV 195 Å flux is more closely correlated to the EUV flare brightening than the full disk GOES X-ray flux.     

Power-law spectra of energetic electrons in solar flares from the maximum entropy and dimensional considerations

The maximum entropy formalism and dimensional analysis are used to derive a power-law spectrum of accelerated electrons in impulsive solar flares, where the particles can contain a significant fraction of the total flare energy. Entropy considerations are used to derive a power-law spectrum for a particle distribution characterised by its order of magnitude of energy. The derivation extends an earlier one-dimensional argument to the case of an isotropic three-dimensional particle distribution. Dimensional arguments employ the idea that the spectrum should reflect a balance between the processes of energy input into the corona and energy dissipation in solar flares. The governing parameters are suggested on theoretical grounds and shown to be consistent with solar flare observations. The flare electron flux, differential in the non-relativistic electron kinetic energy E, is predicted to scale as $E^{-3}$. This scaling is in agreement with RHESSI measurements of the hard X-ray flux that is generated by deka-keV electrons, accelerated in intense solar flares.     

Multi-wavelength study of the short term TeV flaring activity from the blazar Mrk 501 observed in June 2014

In this work, we study the short term flaring activity from the high synchrotron peaked blazar Mrk 501 detected by the FACT and H.E.S.S. telescopes in the energy range 2–20 TeV during June 23–24, 2014 (MJD 56831.86–56831.94). We revisit this major TeV flare of the source in the context of near simultaneous multi-wavelength observations of $\gamma$–rays in MeV-GeV regime with Fermi-LAT, soft X-rays in 0.3–10 keV range with Swift-XRT, hard X-rays in 10–20 keV and 15–50 keV bands with MAXI and Swift-BAT respectively, UV-Optical with Swift-UVOT and 15 GHz radio with OVRO telescope. We have performed a detailed temporal and spectral analysis of the data from Fermi-LAT, Swift-XRT and Swift-UVOT during the period June 15–30, 2014 (MJD 56823–56838). Near simultaneous archival data available from Swift-BAT, MAXI and OVRO telescope along with the V-band optical polarization measurements from SPOL observatory are also used in the study of giant TeV flare of Mrk 501 detected by the FACT and H.E.S.S. telescopes. No significant change in the multi-wavelength emission from radio to high energy $\gamma$–rays during the TeV flaring activity of Mrk 501 is observed except variation in soft X-rays. The varying soft X-ray emission is found to be correlated with the $\gamma$–ray emission at TeV energies during the flaring activity of the source. The soft X-ray photon spectral index is observed to be anti-correlated with the integral flux showing harder-when-brighter behavior. An average value of 4.5$\%$ for V-band optical polarization is obtained during the above period whereas the corresponding electric vector position angle changes significantly. We have used the minimum variability timescale from the H.E.S.S. observations to estimate the Doppler factor of the emission region which is found to be consistent with the previous studies of the source.     

Kelvin–Helmholtz instability in a twisting solar polar coronal hole jet observed by SDO/AIA

We investigate the conditions under which the fluting ($m=2$), $m=3$, and $m=12$ magnetohydrodynamic (MHD) modes in a uniformly twisted flux tube moving along its axis become unstable in order to model the Kelvin–Helmholtz (KH) instability in a twisting solar coronal hole jet near the northern pole of the Sun. We employed the dispersion relations of MHD modes derived from the linearized MHD equations. We assumed real wavenumbers and complex angular wave frequencies, namely complex wave phse velocities. The dispersion relations were solved numerically at fixed input parameters (taken from observational data) and varying degrees of torsion of the internal magnetic field. It is shown that the stability of the modes depends upon five parameters: the density contrast between the flux tube and its environment, the ratio of the external and internal axial magnetic fields, the twist of the magnetic field lines inside the tube, the ratio of transverse and axial jet’s velocities, and the value of the Alfvén Mach number (the ratio of the tube axial velocity to Alfvén speed inside the flux tube). Using a twisting jet of 2010 August 21 by SDO/AIA and other observations of coronal jets we set the parameters of our theoretical model and have obtained that in a twisted magnetic flux tube of radius of $9.8$ Mm, at a density contrast of $0.474$ and fixed Alfvén Mach number of $?0.76$, for the three MHD modes there exist instability windows whose width crucially depends upon the internal magnetic field twist. It is found that for the considered modes an azimuthal magnetic field of $1.3$–$1.4$ G (computed at the tube boundary) makes the width of the instability windows equal to zero, that is, it suppress the KH instability onset. On the other hand, the times for developing KH instability of the $m=12$ MHD mode at instability wavelengths between 15 and 12 Mm turn out to be in the range of $1.9$–$4.7$ min that is in agreement with the growth rates estimated from the temporal evolution of the observed unstable jet’s blobs in their initial stage.     

Multi-instrument observations of large-scale atmospheric gravity waves/traveling ionospheric disturbances associated with enhanced auroral activity over Svalbard

This study reports on observations of large-scale atmospheric gravity waves/traveling ionospheric disturbances (AGWs/TIDs) using Global Positioning System (GPS) total electron content (TEC) and Fabry–Perot Interferometer’s (FPI’s) intensity of oxygen red line emission at 630?nm measurements over Svalbard on the night of 6 January 2014. TEC large-scale TIDs have primary periods ranging between 29 and 65?min and propagate at a mean horizontal velocity of $～$749–761?m/s with azimuth of $～$345–347$°$ (which corresponds to poleward propagation direction). On the other hand, FPI large-scale AGWs have larger periods of $～$42–142?min. These large-scale AGWs/TIDs were linked to enhanced auroral activity identified from co-located all-sky camera and IMAGE magnetometers. Similar periods, speed and poleward propagation were found for the all-sky camera ($～$60–97?min and $～$823?m/s) and the IMAGE magnetometers ($～$32–53?min and $～$708?m/s) observations. Joule heating or/and particle precipitation as a result of auroral energy injection were identified as likely generation mechanisms for these disturbances.     

Kink mode m = 1 in magnetic tube with discontinuous magnetic field

In this paper, we study conditions of realization and stability of kink modes with azimuthal wave numbers $m=\pm 1$ in cylindrical plasma flex with twisted magnetic field and homogeneous current along its axis. We assume permanent axial magnetic field both inside and outside the flex, surrounded by currentless plasma. Azimuthal magnetic field decreases inversely proportional to the distance from the boundary beyond the flex. We derived dispersion equations for stable and unstable modes in approximation of “thin” plasma flex. The analysis of equations has been provided for the case of discontinuous axial magnetic field on flex’s boundary. Conditions of propagation of wave modes have been defined. It was shown, that unstable modes can be implemented in certain interval of longitudinal wavenumbers. Results can be applied for the interpretation of solar magnetic tubes behavior, using measurements, provided by spacecrafts.     

First solar observations with ALMA

The Atacama Large Millimeter-Submillimeter Array (ALMA) has opened a new window for studying the Sun via high-resolution high-sensitivity imaging at millimeter wavelengths. In this contribution I review the capabilities of the instrument for solar observing and describe the extensive effort taken to bring the possibility of solar observing with ALMA to the scientific community. The first solar ALMA observations were carried out during 2014 and 2015 in two ALMA bands, Band 3 ($\lambda =3$?mm) and Band 6 ($\lambda =1.3$?mm), in single-dish and interferometric modes, using single pointing and mosaicing observing techniques, with spatial resolution up to $～$2″ and $～$1″ in the two bands, respectively. I overview several recently published studies which made use of the first solar ALMA observations, describe current status of solar observing with ALMA and briefly discuss the future capabilities of the instrument.     

A combination method using evolutionary algorithms in initial orbit determination for too short arc

With the combination of two evolutionary algorithms EDA and DE, a new method of initial orbit determination for satellites based on ground-based too-short-arc is established. Compared with other algorithms, the proposed method focuses on the most densely populated region in the solution space rather than the individual with best fitness value. Both the global information and local information are well fused in the search of optimum. In the method $(a,e,M)$ are treated as variables of the optimization, and the optimization procedure is carried out as a two-stage hierarchical optimization problem which has three variables for each stage. Kernel density estimation is applied to build the probability distribution model without any assumptions of the specified distribution, accompanied by handling semi-major axis and eccentricity as a pair of dependent variables in the construction of the probability for the correlation between them in the practice. Numerical experiments with real ground-based observations show that the proposed method is applicable to too-short-arc with even 3?s, and the result of bias in several kilometers can be achieved with $5^{″}$ error added to angular measurements.     

An attempt to inverse the ionospheric sporadic-E layer critical frequency based on the COSMIC radio occultation data

Ionospheric sporadic E layer refers to localized thin irregularity with enhanced plasma density appearing in the height range of ionospheric E layer (～90–130?km). The much higher electron density in the sporadic E layer than the background ionosphere would cause sudden TEC enhancement in the occultation TEC profile. A wavelet decomposition and reconstruction method is applied to extract the TEC fluctuation in this paper, and then $S_{\text{max}}$ index is defined to represent the intensity of the sudden TEC enhancement. $S_{\text{max}}$ index is compared with sporadic E critical frequency ($\mathit{foEs}$) observed by the ionosonde. The results show a well linear correlation between them with mean correlation coefficient about 0.7. Thus, an empirical linear model is established to inverse the $\mathit{foEs}$. The monthly/hourly mean values and global distribution of sporadic E intensity and occurrence ratio are calculated using this method based on the COSMIC occultation data from 2007 to 2011. The statistical analysis results indicate that it is feasible to inverse the $\mathit{foEs}$ based on the occultation TEC profile data and the inversion results can be applied to the long-term global variations of sporadic E investigations.     

Delayed outburst of H 1743–322 in 2003 and relation with its other outbursts

The Galactic transient black hole candidate H 1743–322 exhibited a long duration outburst in 2003 after more than two and a half decades of inactivity. The 2003 event was extensively studied in multi-wavelength bands by many groups. The striking feature is that the total energy released is extremely high as compared to that in tens of outbursts which followed. In this paper, we look at this event and study both the spectral and temporal properties of the source using two component advective flow (TCAF) paradigm. We extract accretion flow parameters for each observation from spectral properties of the decay phase and determine the mass of the black hole. We computed the energy released during all the known outbursts since 2003 and showed that on an average, the energy release in an outburst is proportional to the duration of the quiescent state just prior to it, with the exception of the 2004 outburst. A constant rate of supply of matter from the companion cannot explain the energy release in 2004 outburst. However, if the energy release of 2003 is incomplete and the leftover is released in 2004, then the companion’s rate of matter supply can be constant since 1977 till date. We believe that erratic behaviour of viscosity at the accumulation radius $X_p$ of matter as well as location the $X_p$ itself, rather than the random variation of mass transfer rate from the companion, could be responsible for non-uniformity in outburst pattern. We discuss several factors on which the waiting time and duration of the next outburst could depend.     

The dynamic chromosphere: Pushing the boundaries of observations and models

The interface between the bright solar surface and the million-degree corona continues to hold the key to many unsolved problems in solar physics. Advances in instrumentation now allow us to observe the dynamic structures of the solar chromosphere down to less than $0_{.}^{″}1$ with cadences of just a few seconds and in multiple polarisation states. Such observational progress has been matched by the ever-increasing sophistication of numerical models, which have become necessary to interpret the complex observations. With an emphasis on the quiet Sun, I will review recent progress in the observation and modelling of the chromosphere. Models have come a long way from 1D static atmospheres, but their predictions still fail to reproduce several key observed features. Nevertheless, they have given us invaluable insight into the physical processes that energise the atmosphere. With more physics being added to models, the gap between predictions and observations is narrowing. With the next generation of solar observatories just around the corner, the big question is: will they close the gap?     

Effects of space weather on the ionosphere and LEO satellites’ orbital trajectory in equatorial,low and middle latitude

We study the effects of space weather on the ionosphere and low Earth orbit (LEO) satellites’ orbital trajectory in equatorial, low- and mid-latitude (EQL, LLT and MLT) regions during (and around) the notable storms of October/November, 2003. We briefly review space weather effects on the thermosphere and ionosphere to demonstrate that such effects are also latitude-dependent and well established. Following the review we simulate the trend in variation of satellite’s orbital radius (r), mean height (h) and orbit decay rate (ODR) during 15 October–14 November 2003 in EQL, LLT and MLT. Nominal atmospheric drag on LEO satellite is usually enhanced by space weather or solar-induced variations in thermospheric temperature and density profile. To separate nominal orbit decay from solar-induced accelerated orbit decay, we compute $r\text{,}h$ and ODR in three regimes viz. (i) excluding solar indices (or effect), where $r=r_0\text{,}h=h_0$ and $\mathit{ODR}={\mathit{ODR}}_0$ (ii) with mean value of solar indices for the interval, where $r=r_m\text{,}h=h_m$ and $\mathit{ODR}={\mathit{ODR}}_m$ and (iii) with actual daily values of solar indices for the interval ($r\text{,}h$ and ODR). For a typical LEO satellite at h?=?450?km, we show that the total decay in r during the period is about 4.20?km, 3.90?km and 3.20?km in EQL, LLT and MLT respectively; the respective nominal decay ($r_0$) is 0.40?km, 0.34?km and 0.22?km, while solar-induced orbital decay ($r_m$) is about 3.80?km, 3.55?km and 2.95?km. h also varied in like manner. The respective nominal ${\mathit{ODR}}_0$ is about 13.5?m/day, 11.2?m/day and 7.2?m/day, while solar-induced ${\mathit{ODR}}_m$ is about 124.3?m/day, 116.9?m/day and 97.3?m/day. We also show that severe geomagnetic storms can increase ODR by up to 117% (from daily mean value). However, the extent of space weather effects on LEO Satellite’s trajectory significantly depends on the ballistic co-efficient and orbit of the satellite, and phase of solar cycles, intensity and duration of driving (or influencing) solar event.     

Velocity shear Kelvin-Helmholtz instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In this paper parallel flow velocity shear Kelvin-Helmholtz instability has been studied in two different extended regions of the inner magnetosphere of Saturn. The method of the characteristic solution and kinetic approach has been used in the mathematical calculation of dispersion relation and growth rate of K-H waves. Effect of magnetic field (B), inhomogeneity (P/a), velocity shear scale length ($A_i$), temperature anisotropy ($T_{\perp }/T_{||}$), electric field (E), ratio of electron to ion temperature ($T_e/T_i$), density gradient (${\epsilon }_n{\rho }_i$) and angle of propagation ($\theta$) on the dimensionless growth rate of K-H waves in the inner magnetosphere of Saturn has been observed with respect to $k_{\perp }{\rho }_i$. Calculations of this theoretical analysis have been done taking the data from the Cassini in the inner magnetosphere of Saturn in the two extended regions of Rs ～4.60–4.01 and Rs ～4.82–5.0. In our study velocity shear, temperature anisotropy and magnitude of the electric field are observed to be the major sources of free energy for the K-H instability in both the regions considered. The inhomogeneity of electric field, electron-ion temperature ratio, and density gradient have been observed playing stabilizing effect on K-H instability. This study also indicates the effect of the vicinity of icy moon Enceladus on the growth of K-H instability.     

Study the behavior of the ionospheric frequencies at Karachi during three consecutive solar minima of cycle 21, 22 & 23 and their comparison with IRI-2016

The behavior of critical frequencies of ionospheric E and F2 layers (foE & foF2) along with minimum ionospheric frequency (fmin) is studied for solar minima of cycle 21 (1986), 22 (1996) and 23 (2008) over Karachi (24.95$°$N, 67.13$°$E), Pakistan. The station is located at the crest of equatorial ionization anomaly region. Beside seasonal differences, pronounced change in the values of frequencies is noted from one solar minimum to another solar minimum. A strong and direct correlation of foF2 with Smoothed Sunspot Number (SSN) and F10.7?cm solar flux is observed. In the minimum of cycle 23, reduction in foF2 is noted due to reduction of solar EUV as compared to other minima. Also disappearance of semi-annual variations in foF2 is noted in cycle 23 minimum. Unexpectedly higher values of foE and fmin are observed in minimum of cycle 23 as compared to other minima. It is difficult to explain this unusual behavior of fmin and foE along with disappearance of semi-annual variation in foF2. It is possible that during very low solar activity, thermospheric conditions are changed which in turn altered the ionosphere. Further investigation of atmosphere-ionosphere coupling is required to understand this complex behavior. On comparison of observed values with IRI-2016, higher deviations are observed in foE before noon hours while in case of foF2, large deviations are noted during daytime. The absence of foF2 semi-annual variation in cycle 23 is not reproduced by IRI-2016. It is suggested that IRI-2016 need some modification for extremely low solar activity condition.     

Physical characterization of the deep-space debris WT1190F: A testbed for advanced SSA techniques

We report on extensive ${\mathit{BVR}}_c{I}_c$ photometry and low-resolution ($\lambda /\mathrm{\Delta }\lambda ～250$) spectroscopy of the deep-space debris WT1190F, which impacted Earth offshore from Sri Lanka, on 2015 November 13. In spite of its likely artificial origin (as a relic of some past lunar mission), the case offered important points of discussion for its suggestive connection with the envisaged scenario for a (potentially far more dangerous) natural impactor, like an asteroid or a comet.Our observations indicate for WT1190F an absolute magnitude $R_c={32.45}_{\pm 0.31}$, with a flat dependence of reflectance on the phase angle, such as ${\mathit{dR}}_c/d?～{0.007}_{\pm 2}$?mag?deg^?1. The detected short-timescale variability suggests that the body was likely spinning with a period twice the nominal figure of $P_{\mathrm{flash}}={1.4547}_{\pm 0.0005}\mathrm{s}$, as from the observed lightcurve. In the ${\mathit{BVR}}_c{I}_c$ color domain, WT1190F closely resembled the Planck deep-space probe. This match, together with a depressed reflectance around 4000 and 8500 Å may be suggestive of a “grey” (aluminized) surface texture.The spinning pattern remained in place also along the object fiery entry in the atmosphere, a feature that may have partly shielded the body along its fireball phase perhaps leading a large fraction of its mass to survive intact, now lying underwater along a tight ($～1\times 80$?km) strip of sea, at a depth of 1500?m or less.Under the assumption of Lambertian scatter, an inferred size of ${216}_{\pm 30}/\sqrt{\alpha /0.1}$?cm is obtained for WT1190F. By accounting for non-gravitational dynamical perturbations, the Area-to-Mass ratio of the body was in the range $(0.006?\mathit{AMR}?0.011)$?m²?kg^?1.Both these figures resulted compatible with the two prevailing candidates to WT1190F’s identity, namely the Athena II Trans-Lunar Injection Stage of the Lunar Prospector mission, and the ascent stage of the Apollo 10 lunar module, callsign “Snoopy”. Both candidates have been analyzed in some detail here through accurate 3D CAD design mockup modelling and BRDF reflectance rendering to derive the inherent photometric properties to be compared with the observations.     

Effects of dust polarity and nonextensive electrons on the dust-ion acoustic solitons and double layers in earth atmosphere

Propagation of dustion acoustic solitary waves (DIASWs) and double layers is discussed in earth atmosphere, using the Sagdeev potential method. The best model for distribution function of electrons in earth atmosphere is found by fitting available data on different distribution functions. The nonextensive function with parameter $q=0.58$ provides the best fit on observations. Thus we analyze the propagation of localized waves in an unmagnetized plasma containing nonextensive electrons, inertial ions, and negatively/positively charged stationary dust. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the sign (and the value) of dust polarity. Characters of propagated waves are described using the presented model.     

The influence of the spatial and temporal collocation windows on the comparisons of the ionospheric characteristic parameters derived from COSMIC radio occultation and digisondes

GPS radio occultation (RO) ionospheric products obtained by Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) mission during the year of 2014 and the observations from 3 digisonde stations which are located at different latitudes are used to study the influence of different time and space collocation windows on the comparisons of the ionospheric characteristic parameters (ICPs), including the peak density and peak height, derived from the two techniques. The results show that the correlation coefficients (CC) and the standard deviation of the absolute biases (SDAB) between the ICPs derived from the two techniques vary distinctly under different spatial and time collocation windows. Generally, the CC (SDAB) of the ICPs decrease (increase) as the size of the collocation window increases in time dimension or in space dimension. The rate of change of the statistic parameters with the increase in the size of the collocation window in time dimension and space dimension is analyzed for each digisonde station. It is found that within the collocation window of $\left(60\mathrm{m}\mathrm{i}\mathrm{n},{20}^{°},{20}^{°}\right)$, the influence of the increase of $1^{°}$ in the space window on the statistical comparison is much more significant than that of the increase of 1?min in the time window, and it is suggested that there can be appropriate relaxation on the time window within the threshold of 60?min to get a balance between the quality of the comparison results and the number of the matched pairs. In addition, it is found that the same variations in the longitude window and in the latitude window may have different influences on the comparison results when the horizontal gradients in electron density are distinctly different along different directions at the digisonde station, and strict space collocation window is preferred when comparing the observations from COSMIC RO with those from the digisonde station in such cases.