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Emergence of global scaling behaviour in the coupled Earth-atmosphere interaction

View Article: PubMed Central - PubMed

ABSTRACT

Scale invariance property in the global geometry of Earth may lead to a coupled interactive behaviour between various components of the climate system. One of the most interesting correlations exists between spatial statistics of the global topography and the temperature on Earth. Here we show that the power-law behaviour observed in the Earth topography via different approaches, resembles a scaling law in the global spatial distribution of independent atmospheric parameters. We report on observation of scaling behaviour of such variables characterized by distinct universal exponents. More specifically, we find that the spatial power-law behaviour in the fluctuations of the near surface temperature over the lands on Earth, shares the same universal exponent as of the global Earth topography, indicative of the global persistent role of the static geometry of Earth to control the steady state of a dynamical atmospheric field. Such a universal feature can pave the way to the theoretical understanding of the chaotic nature of the atmosphere coupled to the Earth’s global topography.

No MeSH data available.


Related in: MedlinePlus

The plot of the variance of the near surface temperature fluctuations versus the length scale L over the lands (circles) and oceans (squares).The solid lines show the best power-law fit to data in the scaling region, capturing two distinct scaling regimes over lands and oceans described by two different scaling exponents 0.88(2) and 1.80(4) respectively.
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f6: The plot of the variance of the near surface temperature fluctuations versus the length scale L over the lands (circles) and oceans (squares).The solid lines show the best power-law fit to data in the scaling region, capturing two distinct scaling regimes over lands and oceans described by two different scaling exponents 0.88(2) and 1.80(4) respectively.

Mentions: Let us now highlight the different role played by water on Earth to assign the scaling behaviour to the topography and the near surface temperature. One should notice that the observed scaling law in the global Earth’s topography contains ‘indirect’ long-term erosive effects of water on the statistics of Earth’s bathymetry (i.e., the underwater equivalent to topography), while the global scaling behaviour in the temperature is ‘directly’ affected by the water which stabilizes and smoothens the temperature fluctuations in a wide range of length scales over the oceans. To further elucidate the relation between scaling exponents of topography and the near surface temperature, let us reexamine our computations for near surface temperature by separating the contributions coming from the topography over the lands and the water over the oceans (see Fig. 1 in the supplementary material for further illustration). As shown in Fig. 6, the variance of temperature over these two regions shows a distinct difference given by the exponent ~0.88(2) over the lands and ~1.80(4) over the oceans. Our analysis unravels an intriguing link between the scaling behaviour observed in the near surface temperature over the lands and the scaling law for the global Earth’s topography both described by the same exponent ~0.88. According to the fractional Brownian motion (fBm) model of self-affine interfaces, one can read the Hurst exponent H (0 ≤ H < 1) from 2Hland ~ 0.88 as Hland ~ 0.44 and since H < 0.5, it shows that the temperature fluctuation field as well as the global Earth topography, display anti-persistence characterized by negative long-range correlations, i.e., a trend at r = (x, y) is not likely to be followed by a similar trend at r + Δr.


Emergence of global scaling behaviour in the coupled Earth-atmosphere interaction
The plot of the variance of the near surface temperature fluctuations versus the length scale L over the lands (circles) and oceans (squares).The solid lines show the best power-law fit to data in the scaling region, capturing two distinct scaling regimes over lands and oceans described by two different scaling exponents 0.88(2) and 1.80(4) respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036056&req=5

f6: The plot of the variance of the near surface temperature fluctuations versus the length scale L over the lands (circles) and oceans (squares).The solid lines show the best power-law fit to data in the scaling region, capturing two distinct scaling regimes over lands and oceans described by two different scaling exponents 0.88(2) and 1.80(4) respectively.
Mentions: Let us now highlight the different role played by water on Earth to assign the scaling behaviour to the topography and the near surface temperature. One should notice that the observed scaling law in the global Earth’s topography contains ‘indirect’ long-term erosive effects of water on the statistics of Earth’s bathymetry (i.e., the underwater equivalent to topography), while the global scaling behaviour in the temperature is ‘directly’ affected by the water which stabilizes and smoothens the temperature fluctuations in a wide range of length scales over the oceans. To further elucidate the relation between scaling exponents of topography and the near surface temperature, let us reexamine our computations for near surface temperature by separating the contributions coming from the topography over the lands and the water over the oceans (see Fig. 1 in the supplementary material for further illustration). As shown in Fig. 6, the variance of temperature over these two regions shows a distinct difference given by the exponent ~0.88(2) over the lands and ~1.80(4) over the oceans. Our analysis unravels an intriguing link between the scaling behaviour observed in the near surface temperature over the lands and the scaling law for the global Earth’s topography both described by the same exponent ~0.88. According to the fractional Brownian motion (fBm) model of self-affine interfaces, one can read the Hurst exponent H (0 ≤ H < 1) from 2Hland ~ 0.88 as Hland ~ 0.44 and since H < 0.5, it shows that the temperature fluctuation field as well as the global Earth topography, display anti-persistence characterized by negative long-range correlations, i.e., a trend at r = (x, y) is not likely to be followed by a similar trend at r + Δr.

View Article: PubMed Central - PubMed

ABSTRACT

Scale invariance property in the global geometry of Earth may lead to a coupled interactive behaviour between various components of the climate system. One of the most interesting correlations exists between spatial statistics of the global topography and the temperature on Earth. Here we show that the power-law behaviour observed in the Earth topography via different approaches, resembles a scaling law in the global spatial distribution of independent atmospheric parameters. We report on observation of scaling behaviour of such variables characterized by distinct universal exponents. More specifically, we find that the spatial power-law behaviour in the fluctuations of the near surface temperature over the lands on Earth, shares the same universal exponent as of the global Earth topography, indicative of the global persistent role of the static geometry of Earth to control the steady state of a dynamical atmospheric field. Such a universal feature can pave the way to the theoretical understanding of the chaotic nature of the atmosphere coupled to the Earth&rsquo;s global topography.

No MeSH data available.


Related in: MedlinePlus