Multifractal detrended cross correlation analysis of Land-surface temperature anomalies and Soil radon concentration

Accepted Manuscript Multifractal detrended cross correlation analysis of Land-surface temperature anomalies and Soil radon concentration Alpa Kar, Sucharita Chatterjee, Dipak Ghosh

PII: DOI: Reference:

S0378-4371(19)30059-7 https://doi.org/10.1016/j.physa.2019.01.056 PHYSA 20487

To appear in:

Physica A

Received date : 28 August 2018 Revised date : 1 December 2018 Please cite this article as: A. Kar, S. Chatterjee and D. Ghosh, Multifractal detrended cross correlation analysis of Land-surface temperature anomalies and Soil radon concentration, Physica A (2019), https://doi.org/10.1016/j.physa.2019.01.056 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights:  

Cross correlation between land-surface temperature anomaly and soil radon emission. Multifractal detrended cross correlation analysis (MF-DXA) has been applied.



The value of the cross correlation coefficient (  X ) is  X = 0.012 ± 0.01.



The positive low value of  X clearly confirms the strong cross correlation.



The value of the spectral width ( WX ) suggests the multifractal nature of cross correlation.

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Manuscript Number: PHYSA-182184 Multifractal detrended cross correlation analysis of Land-surface temperature anomalies and Soil radon concentration Alpa Kar Biren Roy Research Laboratory, Jadavpur University, Kolkata-700032, India Sucharita Chatterjee Department of Physics, Bangabasi College, 19, Rajkumar Chakraborty Sarani, Kolkata-700009, India Email: [email protected] (Corresponding author) Dipak Ghosh UGC Emeritus Fellow (Former), Emeritus Professor, Department of Physics, Jadavpur University, Kolkata-700032, India Abstract: The phenomenon of increasing the temperature of the Earth’s atmosphere over the years is known as the Global warming. The Global warming has several adverse effects on our climate, our health and our communities. The resulting climate changes due to global warming produce significant changes in the weather patterns. It is also argued that the climate changes occurring due to global warming is responsible for the various geological hazards occurring in the world, like earthquakes, volcanic eruptions, tsunamis [Seismicity of the Earth and Associated Phenomena, Princeton University Press (1954), Geodynamics, Cambridge University Press, Cambridge (2002), Geophys. Research Letters 27 1323 (2000), Geophys. J. lnt. 125 415-430 (1996a), Geophys. J. lnt. 127 215-229 (1996b), Geophys. J. lnt. 130 365-382 (1997)]. McGuire in his book [Waking the Giant: How a changing climate triggers earthquakes, tsunamis and volcanoes, Oxford University Press (2012)] has explained in detail the interlink between the climate changes occurring due to global warming and the occurrence of geological disasters like earthquakes, volcanoes and tsunamis. Looking back to the past, when the climate changed naturally and our planet emerged from the ice age, the huge pressure exerted on the Earth’s crust suddenly disappeared causing the Earth’s crust to bounce back, the increased stress on the Earth’s crust activated earthquakes,

tremors and volcanic eruptions along the pre-existing fault lines. Currently, our planet, the Earth is still responding to the end of the last ice age some 20,000 or more years ago when the temperatures began to rise, huge masses of ice-sheets disappeared resulting from the melting of large masses of ice. Thus the rising temperature may be related to the anomalous emanation of soil radon-222 gas prior to an earthquake. The prime focus of this paper is to search for any cross correlation existing between the daily land-surface temperature anomalies and the soil radon concentration using a robust state of art method, Multifractal detrended cross correlation analysis (MF-DXA). The data sets for both the series used for the analysis are for a period from 2005 to 2014. The analysis shows that these two time series are not only cross correlated but having the cross correlation coefficient  X  0.012 ± 0.01, which clearly indicates a strong correlation between the soil radon-222 anomalies and the daily land-surface temperature anomalies.

PACS numbers: 05.45.Tp, 05.40.–a Keywords: Soil radon-222, temperature anomalies, multifractality, autocorrelation, cross correlation, long-range correlation. 1.Introduction: The climate of our planet, Earth has been changing over thousands of years. Climate changes can occur naturally or may be man-made. The main cause of the drastic climate changes could be attributed to the most serious problem of the present days, the global warming. The average temperature of the Earth’s atmosphere is incessantly increasing at its fastest rate over the past 50 years. The atmospheric gases known as greenhouse gases like carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O) fill our atmosphere, trap the longer wavelength infrared radiations and prevent them from escaping into the space, thereby warming our atmosphere. The increased concentration of atmospheric CO 2 either naturally or by man-made activities including the burning of fossil fuels, excessive growth of industries are mainly responsible for the phenomenon of global warming [1-3]. The global average atmospheric carbon dioxide concentration has reached above 400 ppm by 2016. Over the last century, the average global temperature has increased by more than about 1 0F or 0.70C. The global warming has several adverse effects on our climate, our health and our

communities. The climate changes due to global warming produce significant changes in the weather patterns. One important question that arises among the researchers and scientists is - ‘Can climate changes produce geological hazards like earthquakes ?’. Several scientists and geologists argues that climate changes due to global warming accelerates the melting of the glaciers producing sea level rise which not only intensifies the natural catastrophes like earthquakes, volcanic eruptions, tsunamis and landslides but can trigger such natural disasters [4-5]. McGuire in his book [4] has given a detailed description on the interconnections between the climate changes occurring due to global warming and the occurrence of the geological hazards like earthquakes, volcanoes and tsunamis. When the climate changed naturally in the past and the planet emerged from an ice age, large masses of ice sheets which covered large part of the Earth melted and retreated. The ice sheets were heavy and huge pressure was released on the Earth’s crust which caused the Earth to bounce back, the increasing stress on the Earth’s crust activated earthquakes, tremors and volcanic eruptions along the pre-existing fault lines. Currently, our planet is still responding to the end of the last ice age some 20,000 years or above ago when the temperatures began to rise, huge masses of icesheets disappeared resulting from melting of large ice-sheets. The warming of our planet due to human activities and industrialization may further lead to melting of more large ice masses and the natural processes, like earthquakes, volcanoes, and tsunamis might become more frequent and violent all across the world. There are several evidences that suggest that deglaciation (retreat of the glaciers) accelerates global rebound leading to a number of devastating earthquakes [6-18]. Gutenberg and Ritcher [6] first suggested that the post glacial rebound, as a result of the melting of the late-Paleistocene ice sheets [7] are the main cause of intraplate seismicity. Wu and Johnston [10] have also suggested that ice unloading due to melting of the ice triggers seismicity. On the basis of the recent investigations carried out by Wu and Hasegawa [11-12] and Wu [13] it has been concluded that the both tectonic forces and post glacial rebound stress are responsible for the seismic events, earthquakes in the seismic regions. Wu [14] investigated the relationship between postglacial rebound and intraplate earthquakes in the seismically active regions of Eastern Canada and Northern Europe. Chung [16] determined that the prime mechanism responsible of Greenland earthquakes of 1993 and 1997 has been deglaciation. A clear

spatial correlation has been observed between seismicity and deglaciated areas. The observations support the fact that postglacial rebound triggers earthquakes. Sauber and Molnia [17] observed that the tectonic strain is high in a region of south central Alaska where large glaciers are undergoing thinning. They also found an increase in the number of earthquakes and seismic rate with the melting of large masses of ice sheets. In a work by Brandes et al. [18] they have presented the first model that can explain both the occurrence of seismic events due to deglaciation and the historic earthquakes in northern Central Europe. According to them climate-induced melting of large ice sheets has been able to trigger fault reactivation and earthquakes. One of the most convincing pre-seismic geochemical signals is the anomalous radon emission. The study of radon gas (Rn-222) concentration as a pre-seismic geochemical signal has been proved to be very convincing and can be used as a reliable precursor of an earthquake. The anomalous emission of soil radon (222) gas has been observed just before the occurrence of some of the major earthquakes [19-43]. Radon (Rn) is the naturally occurring colourless, odourless, inert radioactive gas. It is produced naturally from the radioactive decay of radium, produced in the radioactive decay of uranium

238

U, found in

different amounts in the soils and rocks throughout the world. Three different isotopes of radon (Rn) are found to exist in nature. 222Rn which is a member of 238U series with half-life of 3.8 days, 220Rn which is a member of 232Th series with half-life of 54.5s and 219Rn which is a member of

235

U series with half-life of 3.92s. Radon itself is radioactive because it also

decays to element polonium by emitting an alpha particle. Among these

222

Rn has the

longest half-life and is the most important in the geophysical studies. Radon being a gas has high mobility and can easily leave the rocks and soils by escaping through the fractures in the rocks and the porous spaces in between the grains of the soils. The pioneering works related to the study on the occurrence of the anomalous changes in the concentration of radon has been performed by several researchers [19-43], to list a few. The tectonic deformations that take place before earthquakes alter the rock pressure and the fluid connective flows. The increased stress opens cracks and opens up various pathways through which the gas moves up to the surface. The stress-strain that develops within our Earth’s crust before an earthquake results in changes in gas transport and pushes the gas from deep within the earth to the surface [44-46], which leads to the anomalous changes in soil radon

emanation. The role of radon as an ‘earthquake precursor’ has been examined by several researchers [47-52]. The anomalous radon emission occurs a few days prior to the occurrence of the earthquakes. Ghosh et al. [47] studied the radon concentration in soil gas and the experiment was performed at Jadavpur University, Kolkata. Abnormal radon anomaly has been observed prior to the occurrence of earthquakes of magnitudes M≥4 for the period from November, 2005 to October, 2006 within the range of 1000 km from the measuring site. Radon anomalies occurred mostly within 7 to 14 days before the earthquakes, while for some of the earthquakes the precursor time is 2 or 18 days. Ghosh et al. [49] studied the time series of radon concentration (track/sq cm) over the period from September, 2007 to November, 2008 at site Matigara and at Jalpaiguri respectively, situated in active fault area in Himalayan foothills. They observed the distinct peaks showing the radon anomaly corresponding to seismic events. They found that the precursor time varies from 2 to 24 days. Deb and his co-workers [52] have studied the anomalous fluctuations of radon emission just before the recent earthquakes in Nepal and eastern India. They observed that for the most devastating Nepal earthquake of magnitude M7.8, the precursor time was of 5 days. For the earthquakes of magnitude M>6, the precursor time was 13 days and for the earthquakes of M>5 anomalous radon signal appeared 29 days before the event. Thus these studies support role of radon as an ‘earthquake precursor’. Several works on the study of the temperature and temperature anomalies have been reported [53-54]. However, in the studies related to climate changes, temperature anomaly is a more important parameter than absolute temperature and the researchers have shown a keen interest in studying the land-surface temperature anomalies [55-59]. The temperature anomaly means a departure from a reference value or long-term average. A positive anomaly signifies that the observed temperature is warmer than the reference value, while a negative anomaly corresponds to the fact that the observed temperature is cooler than the reference value. Thus it is evident that the rising temperature due to global warming may increase the melting of the glaciers which in turn will enhance the frequency of earthquakes in the coming future. Moreover, an anomalous emission of soil radon gas occurs prior to an approaching earthquake. So it may be expected that the rising temperature is related to the radon gas emission (precursor of seismicity). Very recently a work of Masih [5] reports a correlation between the rise in temperature due to global

warming and earthquake frequency using Pearson’s correlation coefficient and regression analysis based on a case study from Alaska. In view of this, we have attempted to study the correlation between the two time series, one is the daily land-surface temperature anomalies and the other is the time series of the concentration of the soil radon gas and both of which are intrinsically non-linear processes. Kantelhardt et al. [60] proposed Multifractal detrended fluctuation analysis (MF-DFA), a non-linear technique and has been proved to be very efficient in determining the multifractal scaling behaviour of various geophysical and earthquake related signals and in particular to the precursory seismic electric signals [61-73]. Later Detrended cross correlation analysis (DXA) proposed by Podobnik and Stanley has been used to study the cross correlations between different simultaneously recorded time series [74-82]. Zhou in 2008 [83] developed a new method, Multifractal detrended cross correlation analysis (MFDXA) which has been used extensively for a detailed analysis of the multifractal nature of the cross correlations between different variables from various fields [84-96]. In this paper we have studied the multifractal properties of the two individual time series using MF-DFA. We further applied MF-DXA to explore whether there is a positive correlation between the land-surface temperature anomalies and soil radon (Rn-222) emission. 2.Data and method: The data of the time series of earthquake related soil radon concentration for a long period of 10 years from 2005 to 2014 has been obtained from an experiment performed in Kolkata, India. The reason for selection of the Kolkata site for the experiment is that, we have developed a Radon monitoring station in Biren Roy Research Laboratory, at Jadavpur University long ago, and have been monitoring radon and have established with the radon data its importance as a precursor of earthquake as published in [47,52]. The details of the experiment has been published in [47,52] and is also given here. An experimental arrangement has been designed to measure the radon concentration. The concentration of radon was measured by employing CR-39 plate, which is a solid state nuclear track detector (SSNTD) capable of detecting the alpha particles of any energy value emitted from soil radon gas. The detector was provided by the Page Moulding Pershore Ltd., England. The

dimension of the CR-39 plate used was 1cm x 1cm and it was attached inside the bottom of a container and was covered with a semi-permeable membrane. The membrane was permeable to radon only. The container containing the detectors (SSNTDs) having height 4.7 cm, 6.3 cm diameter at the open end and 5.9 cm diameter at the closed end was placed 0.7m deep in the soil at the measuring site. The plates were removed at an interval of 48 hours and new plates were put at the same time. A 6N NaOH solution was used to etch the exposed plates at 7000C for 6 hours. The temperature of the solution was maintained uniform throughout the etching process. After being etched, the plates were washed under cold water for at least half an hour. The tracks formed in the plates due to the alpha particles were counted with the help of Carl-Zeiss Microscope with 10X ocular lens. The radon concentration (track/sq cm) was finally estimated for each plate. The variations of the soil radon concentration with time is shown in Fig.1. The temperature anomalies data includes the daily land-surface average temperature anomalies produced by the Berkeley Earth averaging method for a period from 2005 to 2014. The temperatures are in Celsius [Berkeleyearth.lbl.gov]. Fig.2 shows the variations of the daily land-surface temperature anomalies with time. The multifractal characterization of the cross correlation between the two series, the daily land-surface temperature anomalies data and the soil radon concentration data both for a period from 2005 to 2014 has been studied using Multifractal detrended cross correlation analysis (MF-DXA). In this section, the MF-DXA methodology has been discussed in details. Let x(i) for i=1……. N and y (i ) for i=1……. N be the two non-stationary time series of length

N . The mean of the above series are given by, x ave 

N

1 N

 x(i) , i 1

y ave 

1 N

N

 y(i) i 1

The integrated time series as obtained for the two data series are defined as, i

X (i )   [ x(k )  x ave ] for i  1,........., N k 1

(1)

i

Y (i )   [ y (k )  y ave ] for i  1,........., N

(2)

k 1

The integration reduces the noise existing in the experimental data. The time series was divided into N s non-overlapping bins (where s is the length of the bin and N s  int( N / s) ,

N is the length of the series). Since, N is often not a multiple of s , a short part of the series at one end will be left uncovered. To include this uncovered part the entire process is repeated starting from the other end. This is necessary to include the entire series in the analysis. Finally

2 N s bins are obtained. For each bin least square fit of the series has been

performed and covariance is evaluated, The covariance is, F ( s, ) 

1 s {Y [(  1)s  i]  y (i)}  X   1s  i  x i  s i 1

(3)

for each bin  , =1,…. N s and

F ( s, ) 

1 s {Y [ N  (  N s )s  i]  y (i)}  X N    N s s  i  x i  s i 1

(4)

for  = N s +1,….. , 2 N s where y (i) and x (i ) are the least square fitted value in the bin .

N in general is not a multiple of s , s is an integer. Fq (s ) is defined for s  m  2 only [60]. We have adopted the linear fit and m  1 . The least square linear fit has been performed. th The fluctuation functions Fq (s ) for both the time series are estimated. The q order

fluctuation function Fq (s ) obtained after averaging over the

  1 Fq ( s)   [ F ( s, )]    2 N s  1  2 Ns

q 2

2 N s bins is given as,

1 q

(5)

q is an index which can take all possible integer values except zero, because in that case the

factor 1/ q blows up. So, for q  0 Fq is estimated by a logarithmic averaging

procedure, instead of the normal averaging procedure,

 1 2 Ns  F0 ( s)  exp  ln[ F ( s, )] ~ s  ( 0)    4 N s  1

(6)

The entire procedure discussed is repeated by varying the values of s . Fq (s ) increases with increasing values of s . If the series under consideration is long-range power correlated, then the fluctuation functions Fq (s ) will exhibit a power law behaviour,

Fq (s)  s  ( q ) For, x = y, the method reduces to the standard MF-DFA. F( s , ) may appear negative. Then fluctuation functions may appear complex valued for different values of q , so the modulus are taken to eliminate the negative values. Oswiecimka et al. [97], introduced Multifractal cross correlation analysis (MFCCA) to deal with such negative values of cross covariances. The method MFCCA is a more natural generalization of DCCA than MF-DXA and at the same time there are less chances of losing information that are stored in the negative cross covariances. The log-log plots of Fq (s ) vs. s for each value of q were also analysed. The slopes of these plots give an estimation of values of the scaling exponents  (q ) . For a multifractal series log Fq ( s ) will depend linearly on log s , whereas in case of a monofractal series  (q ) would

have a single unique value for all values of q . The positive values of q signifies that the scaling exponents  (q ) displaying the scaling behaviour of the segments with large fluctuations, the reverse holds for the negative q values. When the value of  (q )  0.5 , it implies that there exists persistent long-range cross correlations, when  (q )  0.5 , it indicates the presence of anti-persistent correlations and  (q )  0.5 denotes the absence of cross correlations [98,99]. For both the time series possessing the same number of data,  (q ) is similar to the generalized Hurst exponent, h(q) . An empirical approximation for q  2 has been defined as,

 (q)  htemperatureanomaliesq  2  hRadonconcentrationq  2/ 2

(7)

The degree of multifractality for the cross correlated series can be obtained from the singularity spectrum. The singularity spectrum f ( ) is related to the scaling exponents,

 (q ) by,

   q  q ' q

(8)

f ( )  q   q +1

(9)

where  is the singularity strength and f ( ) is the dimension of subset series that is characterized by  . The singularity spectrum quantifies the long-range correlation property of a time-series [100]. The multifractal spectrum gives information about the relative importance of various fractal exponents in the series i.e., the width of the spectrum defines range of the exponents. A quantitative characterization of the spectra may be obtained by fitting it to a quadratic function [101] around the position of maximum  0 , f ( )  A(   0 ) 2  B(   0 )  C

(10)

where C is an additive constant C = f ( 0 ) = 1. B denotes the asymmetry of the spectrum.

B is zero for a symmetric spectrum. The width of the spectrum is obtained by extrapolating the fitted curve to zero. Width W of the spectrum is defined as, W = 1   2 with f (1 ) =

f ( 2 ) =0. The width of the multifractal spectrum is a measure of degree of multifractality [102]. For a monofractal series, h(q) is independent of q and a unique value of  and f ( ) are obtained, hence the width of the spectrum will be zero for a monofractal series.

The more the width, the more the multifractality of the spectrum. According to the autocorrelation function given by,

C ( )  [ x(i   )  x ][ x(i )  x ]  



(11)

Similarly the long-range cross correlation function is given by,

C X ( )  [ x(i   )  x ][ y(i)  y ]    X where  and 

X

(12)

are the autocorrelation and cross correlation coefficients respectively. The

Hurst exponent h(q) are related to autocorrelation coefficient [98,103], where   2  2h(q  2)

(13)

B. Podobnik et al. [74] have recently demonstrated the relation between cross correlation coefficient,  X and scaling exponent  (q ) , which is expressed as,

 X  2  2 (q  2)

(14)

 X has a value close to 1 in case of uncorrelated data, the lower the value of  X , the more is the correlation. The low values of  X indicate strong cross correlation i.e.,  X  1 .

The multifractality of a time series originates from two sources: (i) The multifractality due to the broad probability density function and (ii) The multifractality due to different long-range correlations for the small and large fluctuations. The analysis of the corresponding randomly shuffled series provides a clear understanding of the origin of multifractality of the time series. Now, if the multifractality is due to long-range correlations, then the shuffled series will exhibit a non-fractal scaling. On the other hand, if the original  (q ) dependence is not affected, i.e.  (q )   shuffled q  , the multifractality is then due to broad probability density. If both kinds of multifractality are present in a series, the shuffled series will display weaker multifractality than in case of the original series.

3.Results and Discussions: In this paper the time series of earthquake related soil radon concentration for a period of 10 years from 2005 to 2014 obtained from an experiment performed in Kolkata, India has been analysed. The temperature anomalies data includes the daily land-surface temperature anomalies for a period from 2005 to 2014. A multifractal cross correlation between the temperature anomalies data and soil radon concentration data has been performed applying MF-DXA methodology. The variations of the soil radon concentration with time is shown in Fig.1 and the Fig.2 shows the variations of the daily land-surface temperature anomalies with time. The individual time series of the land-surface temperature anomalies data and the soil radon concentration data were first transformed to obtain the integrated signals using Eq.(2). The integrated time series were divided into N S number of non-overlapping bins. The q

th

order fluctuation functions, Fq (s ) were obtained for q = -10 to +10 in steps of 1

including zero for all values of s . The values of s were chosen to lie in the range between 5 to N / 5 . The log-log plots of Fq (s ) vs. s for the individual and the cross correlated series for the q values ( q =-5,0,5) are displayed in Fig.3(a-c). log Fq ( s ) increases linearly with log s for different q values. The slopes of log Fq ( s ) vs. log s plots, Fig.3(c) give the values of the scaling exponents  (q ) for the cross correlated series. The slopes of log Fq ( s ) vs. log s plots

for the individual series, Fig.3(a,b) give the values of the Hurst exponents h(q) as derived from MF-DFA. The values of the scaling exponents  (q ) ( q =2) and Hurst exponents h(q) ( q =2) are shown in Table1. The graphs in Fig.4, reveal the fact that both the scaling exponents

 (q ) as well as the Hurst exponents h(q) decrease monotonically with increasing q values. The values of  (q ) and h(q) are large for q  0 and small for q  0 , such scaling behaviour clearly signifies different scaling for small and large fluctuations which confirms the multifractal scaling of the individual time series as well as the cross correlated series. The singularity spectrum for the individual and the cross correlated series were determined quantitatively. The values of  and f   were evaluated using Eq.(8) and Eq.(9). The graphs in Fig.5 show plots of the singularity spectrum ( f   vs.  ) for the individual time series and cross correlated series. The estimated widths of the spectra WR , WT and WX for the entire period from 2005 to 2014 for the two separate time series as well as for the cross correlated series are displayed in Table1. The shuffled random data for both the individual time series as well as for the cross correlated series were simultaneously studied to ascertain the source of multifractality of the time series. The values of WR and WT were also determined for the shuffled series and are listed in Table1. The variation of  (q ) and h(q) with q and f   with  for the original and the shuffled series are shown in Fig.4

and Fig.5. The width of the multifractal spectra for the shuffled series are smaller than those for the original series, which confirms the presence of multifractality of both the individual time series. Moreover, the non-zero positive finite value of WX for the cross correlation between the two time series firmly suggests that the cross correlation exhibits multifractality. The value of WX is listed in Table1. The multifractal width for the cross correlated series is lower than that of the individual time series. The cross correlated series shows a weaker multifractal behaviour than the individual series. The figures Fig.4 and Fig.5 represent the plots of  (q ) and h(q) vs. q and f   vs.  for the cross correlated series. The value of WX for the shuffled series was also determined and given in Table1 and it is smaller than that of the original series. Moreover, it has been observed that

Woriginal W shuffled in case of the individual series as well as the cross correlated series. This difference in the widths is a clear indication that the shuffled time series exhibit a weaker

multifractal behaviour in comparison to the original time series. This observation implies that the multifractal nature of the time series is due to both the long-range correlations and broad probability distribution, however, the influence of long-range correlations is dominant. According to Drożdż et al. [104] for a relatively short time series the shuffled series would exhibit traces of multifractality. However, as the number of data points increase the shuffled series shows strong monofractal behaviour. The autocorrelation coefficients  R and  T were estimated using Eq.(13). The values of  R and  T estimated for the original and shuffled series are listed in Table1. The values of  R and  T are small positive values for the original data series while those for shuffled random data were close to 1, which indicates that the shuffling process has destroyed the correlation. This noticeable difference in the values of autocorrelation coefficients between the original and shuffled series proves that both the individual time series are autocorrelated. The cross correlation coefficient  X for the cross correlation between the two series is estimated using Eq.(14) and is listed in Table1. The estimated value of  X  0.012 ± 0.01 for the original series. The sufficiently low value of  X clearly demonstrates the cross correlation between the daily land-surface temperature anomalies and the soil radon concentration. The value of  X as obtained for the shuffled series is  Xshuff  0.914 ± 0.02, which is very close to 1 as expected, the shuffling process actually destroys the correlation between the series. From a comparison of the values of  X for the original series and the shuffled series, it is confirmed that there exists significant cross correlation between the two series (the daily land-surface temperature anomalies and the soil radon concentration). It has been evidenced [47,49,50,52] that sudden change in the concentration of radon in soil gas indicates the approaching seismic events, like earthquakes. So the climate changes occurring due to global warming, may increase radon concentration by disturbing the tectonic activities, such as the changes in physico-chemical processes of the fluid reservoir under the earth and enhancing the strain within the Earth’s surface, thereby increasing the exhalation of radon and forecasting an impending earthquake. changes effectively produce changes in soil radon concentration.

So, the temperature

4.Conclusions: The objective of the present investigation was to explore whether there is any correlation between the earthquake activity and the climate variability (In this case Soil radon (Rn) concentration and daily land-surface temperature anomalies). In the introduction section, the genesis of studying this correlation has been elaborated in view of recent works by various authors in this area [6-18]. However, since both soil radon anomalies time series and global land-surface temperature anomalies time series are non-linear in character, the correlation can only be established by using a proper methodology. We have used in the present investigation a robust state of art method namely Multifractal detrended cross correlation analysis (MF-DXA). The soil radon anomaly as a precursor has been studied exhaustively in our works and other works [19-43,47-52]. The present study yields very interesting results which have been highlighted. i) The time series for the temperature anomalies and the soil radon concentration display multifractal characteristics. ii) The multifractal width for the soil radon concentration data is WR = 0.894 ± 0.03 and the temperature anomalies data is WT = 0.629 ± 0.02. This suggests that the two individual series exhibit different degrees of complexities. iii) The temperature anomalies data and the soil radon concentration data are cross correlated and the cross correlation is multifractal in nature with multifractal width, WX = 0.499 ± 0.02. iv) Further in multifractal cross correlation analysis we find that the value of the cross correlation coefficient (  X = 0.012 ± 0.01). As it has been discussed earlier, the lower the value of  X , the more is the cross correlation. Thus the low positive value of  X indicates a positive correlation between the soil radon anomalies and the land-surface temperature anomalies. Thus we may conclude that the present work provides a significant finding in favour of a positive correlation between the climate variability and seismicity.

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Table caption: [1] The values of hR , hT ,  , WR , WT , WX ,  R ,  T , 

X

for the original and the shuffled

series for the complete sets. Figure caption: [1] Plot of Soil Radon concentration (track/sq.cm) for a period from 2005 to 2014. [2] Plot of Land-surface temperature anomalies (0C) for a period from 2005 to 2014. [3a] Plot of log Fq ( s ) vs. log s for Soil Radon concentration data for the complete set. [3b] Plot of log Fq ( s ) vs. log s for Land-surface temperature anomalies data for the complete set. [3c] Plot of log Fq ( s ) vs. log s for the cross correlation for the complete set. [4] Plot of h(q) and  (q ) vs. q for the Soil Radon concentration data, Land-surface temperature anomalies data and cross correlation for the complete set for the original and the shuffled series. [5] Plot of

f ( ) vs.  for the Soil Radon concentration data, Land-surface temperature

anomalies data and cross correlation for the complete set for the original and the shuffled series.

Set

Parameters

Original Series

Shuffled Series

Complete sets

hR(q=2)

0.942 ± 0.02

0.437 ± 0.03

(2005-2014)

hT(q=2)

0.965 ± 0.03

0.517 ± 0.04

λ(q=2)

0.994 ± 0.02

0.543 ± 0.02

WR

0.894 ± 0.03

0.648 ± 0.04

WT

0.629 ± 0.02

0.398 ± 0.01

WX

0.499 ± 0.02

0.399 ± 0.02

γR

0.115 ± 0.01

1.126 ± 0.01

γT

0.069 ± 0.02

0.965 ± 0.01

γX

0.012 ± 0.01

0.914 ± 0.02

Soil Radon concentration (track/sq.cm)

Table1

1400 1200 1000 800 600 400 200 0

Time in Days (2005-2014)

Fig. 1

0

Land-surface Temperature anomalies ( C)

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0

Time in Days (2005-2014)

Fig. 2

10 9 8 7

log Fq

6 5 4 3

Soil Radon concentration (2005-2014) q=+5 q=0 q=-5

2 1 0 2.0

2.5

3.0

3.5

4.0

4.5

log s

Fig. 3(a)

5.0

5.5

6.0

6.5

2 1 0

log Fq

-1 -2 -3

Land-surface temperature anomalies (2005-2014) q=+5 q=0 q=-5

-4 -5 -6 2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

log s

Fig. 3(b)

5 4

log Fq

3 2 1 0

Cross correlations (2005-2014) q=+5 q=0 q=-5

-1 -2 2.0

2.5

3.0

3.5

4.0

4.5

log s

Fig. 3(c)

5.0

5.5

6.0

6.5

1.4 Soil Radon concentration Land-surface temperature anomalies Cross correlation Soil Radon concentration (shuff) Land-surface temperature anomalies (shuff) Cross correlation (shuff)

1.3 1.2 1.1

(q), h(q)

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 -10

-5

0

5

10

q

Fig. 4

1.0

0.8

f()

0.6

0.4

0.2 Soil Radon concentration Land-surface temperature anomalies Cross correlation Soil Radon concentration (shuff) Land-surface temperature anomalies (shuff) Cross correlation (shuff)

0.0

-0.2 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8



Fig. 5

0.9

1.0

1.1

1.2

1.3

1.4

1.5