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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.


The plot of the height variances within the boxes that are randomly chosen on Earth topography (green squares for the square (L × L) and blue circles for the rectangle (2L × L) box sizes).The solid line shows the best power-law fit. Due to the higher number of data points within a rectangular region of size L, rather than a square one, we see a wider scaling interval with higher statistics for rectangular regions. That’s why in our next computations, we only report on averages over rectangular regions.
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f3: The plot of the height variances within the boxes that are randomly chosen on Earth topography (green squares for the square (L × L) and blue circles for the rectangle (2L × L) box sizes).The solid line shows the best power-law fit. Due to the higher number of data points within a rectangular region of size L, rather than a square one, we see a wider scaling interval with higher statistics for rectangular regions. That’s why in our next computations, we only report on averages over rectangular regions.

Mentions: First, different areas with equal scale (2L × L) are randomly chosen on the Earth’s surface (Fig. 2). Then, the variance of heights is averaged over the whole ensemble of areas with scale L. The same approach is repeated over all the possible scales Lmin ≤ L ≤ Lmax, where Lmin denotes for the smallest rectangular scale containing reasonable number of data points (83 km in our case). Lmax equals the upper limit which covers the entire data set on Earth. Finally, the power-law fit to the graph of variances versus the scales, shows the scaling exponent in the data-set [The rectangular region of size 2L × L is chosen only to cover the whole data set at the largest scale, our results, however, do not change if we choose a square region of size L × L (Fig. 3)].


Emergence of global scaling behaviour in the coupled Earth-atmosphere interaction
The plot of the height variances within the boxes that are randomly chosen on Earth topography (green squares for the square (L × L) and blue circles for the rectangle (2L × L) box sizes).The solid line shows the best power-law fit. Due to the higher number of data points within a rectangular region of size L, rather than a square one, we see a wider scaling interval with higher statistics for rectangular regions. That’s why in our next computations, we only report on averages over rectangular regions.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: The plot of the height variances within the boxes that are randomly chosen on Earth topography (green squares for the square (L × L) and blue circles for the rectangle (2L × L) box sizes).The solid line shows the best power-law fit. Due to the higher number of data points within a rectangular region of size L, rather than a square one, we see a wider scaling interval with higher statistics for rectangular regions. That’s why in our next computations, we only report on averages over rectangular regions.
Mentions: First, different areas with equal scale (2L × L) are randomly chosen on the Earth’s surface (Fig. 2). Then, the variance of heights is averaged over the whole ensemble of areas with scale L. The same approach is repeated over all the possible scales Lmin ≤ L ≤ Lmax, where Lmin denotes for the smallest rectangular scale containing reasonable number of data points (83 km in our case). Lmax equals the upper limit which covers the entire data set on Earth. Finally, the power-law fit to the graph of variances versus the scales, shows the scaling exponent in the data-set [The rectangular region of size 2L × L is chosen only to cover the whole data set at the largest scale, our results, however, do not change if we choose a square region of size L × L (Fig. 3)].

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.