The target EQ of this paper is the famous 1995 Kobe EQ that happened at 5 h 46 m (JST, local time (LT)) on January 17, 1995, having its epicenter at the geographical coordinates (34˚35.9’N, 135˚02.1’E), as shown in Figure 1 , with a magnitude $M=7.3$, and with a depth of 16 km. We have plotted a few AMeDAS meteorological stations (black boxes) close to the EQ epicenter together with the fault regions (Rokko/Awaji island faults) possibly related with this EQ.

Figure 2 illustrates the temporal evolutions of the geomagnetic activity (Dst and Kp indices) and the solar radiation flux at the wavelength of 10.7 cm (f10.7) during the period of 1 May, 1994 through 31 May, 1995 (over one year) including the day of the EQ. We think that unlike the ionosphere, the meteorological parameters studied in this paper are likely to be much less influenced by solar-geomagnetic conditions and perturbations. As seen from the plot of Dst ( Figure 2 )

some geomagnetic disturbances with Dst below –50 nT are only noticed in October and November, 1994, but the geomagnetic activity after the beginning of December, 1994 till the day of the EQ, which is very important for the short-term EQ prediction, was extremely quiet, because Dst is less than –20 nT. Further, the solar radiation flux (F10.7) as an indicator of overall solar activity levels was also found to be less than 100. Taking into account the quiet solar-terrestrial conditions just before the EQ, we are ready to investigate short-term EQ precursors within the short-term EQ prediction span of one month before and two weeks after the EQ.

JMA has established an AMeDAS since 1975, and it has been in operation very regularly. Four meteorological parameters are being measured at each station: 1) precipitation (or rainfall) (in units of 0.5 mm), 2) air temperature (in units of 0.1˚C) and air relative humidity (in %), 3) sunshine duration, and 4) wind direction/speed, and this AMeDAS network includes as many as 1300 stations all over Japan, so the stations are located, on average, with an interval of 17 km.

We have studied the following two meteorological quantities proposed in Haya-kawa et al. (2022) [34] and Schekotov et al. (2023) [51] . The fundamental idea may be that radon (Rn) rises to the Earth’s surface more intensely along seismic faults or volcanic fumaroles during the EQ preparation phase, and the subsequent air ionization leads to a decrease in the air humidity and an increase in its temperature [51] . So, the first quantity of our interest is the simple ratio of temperature, T (in ˚C) to humidity (relative humidity), Hum (in %), i.e., T/Hum, because of our expectation of an enhanced seismogenic effect of increasing T and decreasing Hum. The second quantity is ACP (atmospheric chemical potential) which is given by the following equation [2] :

$ACP\left(\text{in}\text{eV}\right)=5.8\times {10}^{-10}{\left(20T+5463\right)}^2\ln \left(100/Hum\right)$ (1)

Here we indicate the reason why we call this the chemical potential. Because at the moment of water molecule condensation/evaporation or attachment/detachment to the ions, the latent heat release/absorption is equal to the chemical potential [5] . This ACP value is supposed to yield an increase during the process of air ionization by any agents including galactic cosmic rays etc., one of them being by the exhalation of radon (Rn) and charged aerosols which is known to be released during the pre-EQ enhancement as reported by several workers (e.g., [52] - [56] ).

We have analyzed the data from some other AMeDAS of stations near the EQ epicenter in the western part of Japan: Kobe (34˚41'N, 135˚12'E), Osaka (34˚41'N, 135˚31'E), Sumoto (34˚19'N, 134˚51'E), and Himeji (34˚54'N, 134˚40'E) as indicated by black boxes in Figure 1 and we have confirmed the presence of the same anomalous day at all of these stations. So, in the following, we will present again the results only for one particular station of Kobe from [41] as a representative example.

The basic quantities of T and Hum only around midnight are used, and we choose LT = 01 h because daytime is strongly influenced by strong solar radiation and we think that the time period around midnight is considered to be most suitable for our analysis by excluding this solar effect.

We will first repeat the statistical results from [41] . Figure 3(a) is the temporal evolution of the detrended daily value of $T/Hum$ (i.e., $\delta \left(T/Hum\right)=\left(T/Hum\right)-m$ (where $m$ is the running mean during the previous 30 days), and the standard deviation of σ is also estimated during the previous 30 days, as followed by Hayakawa et al. (2022) [34] . Each vertical black bar indicates the current value for each day and the abscissa indicates the date. The day of EQ (17 January, 1995) is indicated by a vertical red line. When there is no vertical bar on a particular day, it means that the current value is below the means value of m. There are plotted three curves in the figure; the bottom green curve refers to $m+\sigma$, the orange curve to $m+2\sigma$, and the red curve to $m+3\sigma$. The period of presentation in Figure 3 is a time window of about one month before and a few weeks after an EQ as short-time EQ prediction window. Now we will try to identify any anomalous variations by using the confidence bounds with $m$ and $\sigma$. In our previous works it has been taken a criterion of $m+2\sigma$, as it is usually done when dealing with different physical parameters (e.g., [3] ), but in this paper we adopt a much more severe criterion of $m+3\sigma$ as used conventionally in the field of astrophysics. Figure 3(a) indicates that we can notice a single and a very remarkable peak exceeding $m+3\sigma$ only on 10 January, 1995, just one week before the EQ. Other weather effects (such as storm, fog, etc) could not influence this anomaly.

Now we move on to Figure 3(b) for the plot of detrended $ACP$, i.e. $\delta \left(ACP\right)$. Quite similarly as in Figure 3(a) , we can identify the same anomaly on the same day in Figure 3(b) . Its anomalous value is not exceeding this criterion of $m+3\sigma$, but stands out well above $m+2\sigma$. This peak is again the only one within the short-term EQ prediction window.

Finally, we can conclude that the significant peaks in the two parameters, as seen in Figure 3(a) and Figure 3(b) , both appear on 10 January, 1995, just one week before the EQ. Hence, it is highly likely that an anomaly on 10 January, 1995 is a possible precursor to the EQ. Further, we will apply a critical analysis to the same meteorological quantities, $T/Hum$ and $ACP$, in order to identify whether the above presented peaks are due to the criticality or the causality relationship with this EQ.

The NT time series analysis method has initially been applied to the ultra-low frequency (≤1 Hz) seismic electric signals (SES) [57] - [59] , and has been shown to be optimal for enhancing the signals in the time-frequency space [60] . The full theoretical details of this method can be found in the monograph by Varotsos et al. [42] (and references therein), while the application of NT analysis to various seismo-EM signals has been presented in detail in [46] . Also, recent studies using the NT time series method to other observable quantities of LAIC have shown the existence of critical dynamics before EQs [46] - [48] . In what follows, we will briefly present the key notions of this method and the process of applying it to our meteorological data.

Initially, for a number of $N$ events, we determine the NT of the k-th (in order of occurrence) event as ${\chi }_k=k/N$, which is actually the order of occurrence normalized in the interval (0, 1]. Next, we determine the “energy” of each event in NT, which is symbolized as $Q_k$ for the k-th event. At this point we have to mention that $Q_k$ corresponds to different kinds of quantities, depending on the time series under analysis. For example, in the case of seismic events $Q_k$ is the seismic energy released (seismic moment), while for the dichotomous SES signals $Q_k$ corresponds to the SES pulse duration [59] . On the other hand, in the case of the fracto-electromagnetic emission signals in the MHz band, which are non-dichotomous signals, $Q_k$ denotes the energy of each event by using consecutive amplitude values above a noise threshold as described in [44] .

Then, we study the resulting time series $\left({\chi }_k,Q_k\right)$. The approach of a dynamical system to criticality is identified by means of the variance ${\kappa }_1=\langle {\chi }^2\rangle -{\langle \chi \rangle }^2$ of NT, where $\langle f\left(\chi \right)\rangle ={\displaystyle {\sum }_{k=1}^N{p}_{k}f\left({\chi }_k\right)}$, where $p_k=Q_k/{\displaystyle {\sum }_{n=1}^N{Q}_n}$ is the normalized energy released during the k-th event. Hence, the quantity ${\kappa }_1$ can be written as ${\kappa }_1={\displaystyle {\sum }_{k=1}^N{p}_k{\chi }_k^2}-{\left({\displaystyle {\sum }_{k=1}^N{p}_k{\chi }_k}\right)}^2$. Moreover, the entropy in NT is defined as $S_{nt}={\displaystyle {\sum }_{k=1}^N{p}_k{\chi }_k\ln {\chi }_k}-\left({\displaystyle {\sum }_{k=1}^N{p}_k{\chi }_k}\right)\ln \left({\displaystyle {\sum }_{k=1}^N{p}_k{\chi }_k}\right)$ [61] . The entropy in NT is a dynamic entropy, depending on the order of the events [60] . Also, $S_{nt-}$, the entropy under time reversal, i.e., by reversing the order of the considered events (which of course changes the natural time used for the calculations), is also studied [61] .

In many dynamical systems studied by the NT analysis method, it has been found that the value of ${\kappa }_1$ is a measure to quantify the extent of the organization of the system at the onset of the critical stage [41] . The criticality is reached when (a) ${\kappa }_1$ takes the value ${\kappa }_1=0.07$, and (b) at the same time both the entropy in NT and the entropy under time reversal satisfy the following condition $S_{nt},S_{nt-}<S_u=\left(\ln 2/2\right)-1/4$ [42] [62] , where $S_u$ is the entropy of the uniform distribution in NT [41] [62] .

In the special case of NT analysis of foreshock seismicity [57] [59] [61] [63] , we study the evolution of the quantities ${\kappa }_1,S_{nt},S_{nt-}$, and $\langle D\rangle$ over time, where $\langle D\rangle$ is the “average” distance between the normalized power spectra $\text{Π}\left(\tilde{\omega }\right)={\left|{\displaystyle {\sum }_{k=1}^N{p}_k\exp \left(j\tilde{\omega }{\chi }_k\right)}\right|}^2$ ( $\tilde{\omega }$ stands for the angular frequency in NT) of the evolving seismicity and the theoretical estimation of $\text{Π}\left(\tilde{\omega }\right)$ for ${\kappa }_1=0.07$, ${\Pi }_{critical}\left(\tilde{\omega }\right)\approx 1-{\kappa }_1{\tilde{\omega }}^2$. Moreover, an “event” for the NT analysis of seismicity is considered to be any data point of the original seismicity time series (time series of magnitudes of EQs) that surpasses a magnitude threshold, $M_{Thres}$.

The analysis starts with an appropriate low threshold and taking into account only an adequate number of, first in the order of occurrence, events. Next, the subsequent events, in their original order, are one-by-one taken into account. For each additional event that is taken into account, the quantity ${\chi }_k$ is rescaled within the interval (0, 1] and all ${\kappa }_1,S_{nt},S_{nt-}$, and $\langle D\rangle$ are re-calculated. This way, a temporal evolution of these quantities is obtained. The described procedure is repeated for several, increasing, values of $M_{Thres}$ for each studied geographic area, and everything is repeated for different overlapping areas.

The seismicity is considered to be in a true critical state, a “true coincidence” is achieved, as soon as (a) ${\kappa }_1$ takes the value ${\kappa }_1=0.07$, (b) at the same time for both the entropy in NT and the entropy under time reversal satisfy the condition $S_{nt},S_{nt-}<S_u$, and three additional conditions are satisfied: (c) The “average” distance $\langle D\rangle$ should be smaller than 10⁻², i.e., $\langle D\rangle =\left|\Pi \left(\tilde{\omega }\right)-{\Pi }_{critical}\left(\tilde{\omega }\right)\right|<{10}^{-2}$ (this is a practical criterion for signaling the achievement of spectral coincidence) [42] ; (d) the parameter ${\kappa }_1$ should approach the value ${\kappa }_1=0.070$ “by descending from above”, i.e., before the main event the parameter ${\kappa }_1$ should gradually decrease until it reaches the critical value 0.070 (this rule was found empirically) [42] [57] ; (e) the above-mentioned conditions (a)-(d) should continue to be satisfied even if the considered $M_{Thres}$ or the area within which the seismicity is studied are changed (within reasonable limits).

The use of the magnitude threshold excepts some of the weaker EQ events (those events that their magnitude is $<M_{Thres}$) from the NT analysis. However, the usage of the magnitude threshold is valid for the reason that some recorded magnitudes are not considered reliable due to the seismographic network. On the other hand, the application of various $M_{Thres}$ values are useful in determining the time range within which criticality is reached. This is because, in some cases, it is found that more than one time-points may satisfy the rest of the NT critical state conditions (a)-(d), and criterion (e) is the one that finally reveals the true time of criticality.

For the application of NT analysis to the meteorological quantities analyzed in this study, we follow the paradigm of the NT analysis of seismicity. Specifically, in the case of the atmospheric chemical potential (ACP) the necessary threshold values are defined in terms of ACP values and the “energy” $Q_k$ values are daily ACP values exceeding the considered threshold. Similarly, in the case of the temperature over humidity ( $T/Hum$), the positive detrended daily values $\delta \left(T/Hum\right)$ are used to define the necessary threshold values and the “energy” $Q_k$. The detrended daily values are calculated by subtracting the running mean of $T/Hum$ (see Section 4.2 and Figure 3(a) ) from the $T/Hum$ daily values, in order to remove $T/Hum$ seasonal variation.

In this section we present the results obtained by the application of the NT analysis method to the daily-valued time series of ACP ( Figure 4 ) and $\delta \left(T/Hum\right)$ ( Figure 5 ). We have applied the NT method to the above-mentioned meteorological quantities as explained in Section 5.1. Specifically, for each one of the aforementioned meteorological quantities, we consider as an event any daily value of the meteorological quantity under analysis, that is higher than a certain threshold; that is, we exclude values which are weaker than the specific threshold. Then, the “energy” $Q_k$ of the k-th revealed event is considered to be equal to the corresponding daily value of the analyzed meteorological quantity. Finally, the NT analysis is applied to the time series of the revealed events of each meteorological quantity, as in the case of the pre-EQ seismic activity (see [45] [46] ).

Figure 4 presents the NT analysis results for the ACP time series over a time period of three months from 17 November 1994 to 17 February 1995 (two months before and one month after the occurrence of the 1995 Kobe EQ). As can be seen from Figure 4 , the NT criticality criteria were satisfied during the time period 23-30 December 1994, since during that time interval, simultaneously, ${\kappa }_1$ approaches the value ${\kappa }_1=0.070$ “ by descending from above”, $S_{nt},S_{nt-}<S_u$ and $\langle D\rangle <{10}^{-2}$ for all four presented $AC{P}_{Th}$ threshold values (see also Subsection 5.1). The magenta patches in Figure 4 show the time intervals during which the approach to criticality was found for each $AC{P}_{Th}$, while their intersection reveals that “true coincidence”, i.e., true critical state (see Subsection 5.1), was achieved during the time period 23-30 December 1994. This means that critical dynamics are embedded in the ACP time series for a time period of 7 days, ~3 weeks before the 1995 Kobe EQ (from 25 days up to 18 days before the EQ occurrence on17 January 1995).

For the $\delta \left(T/Hum\right)$ quantity, the NT analysis results are portrayed in Figure 5 . Similarly, for this meteorological quantity, the NT criticality criteria were satisfied on 27 December 1994, also ~ 3 weeks before the 1995 Kobe EQ. As already mentioned in Subsection 5.1, for the NT analysis of $\delta \left(T/Hum\right)$ only the positive values of the $\delta \left(T/Hum\right)$ time series were considered as events. Due to

that, the number of $\delta \left(T/Hum\right)$ events during the time period used for the ACP case was quite low for NT analysis. Consequently, in order to increase the number of $\delta \left(T/Hum\right)$ events taken into account, the NT analysis of $\delta \left(T/Hum\right)$ has been performed for a longer time period than in the ACP case, namely from 17 October 1994 to 17 February 1995 (three months before and one month after the occurrence of the 1995 Kobe EQ).