Fig. 2: Quantifying the transition to clustering. | npj Climate and Atmospheric Science

Fig. 2: Quantifying the transition to clustering.

From: Diurnal self-aggregation

Fig. 2

a Clustering coefficient \({\mathcal{C}}(l)\) at different box sizes l for A2a. Curves range from day one (red) to seven (green). The pattern of rain events is regular, as \({\mathcal{C}}(l)\,<\,1\) throughout. Note the double-logarithmic axis scaling. b Analogous to a, but for A3.5. c Analogous to a, but for A5a. In b and c, at small scales (l ~10 km) or early times (t < 2 d), rain events are regularly distributed (\({\mathcal{C}}(l)\,<\,1\)), whereas at larger scales (l ~ 180 km) and later times (t ≥ 3d) events are clustered (\({\mathcal{C}}(l)\,>\,1\)). d Maximum of \({\mathcal{C}}(l)\) versus time for different simulations (see: legend and Table 1). Note the general increase for large Ta (A3.5, A5: upward-pointing triangles) but flat behaviour for small Ta (A2: downward-pointing triangles). e Scales of clustering, i.e., the position l at which the maxima in \({\mathcal{C}}(l)\) occur in A3.5 and A5. The grey shaded area marks the standard error of lmax, averaged over all times t ≥ 3d. f Autocorrelation c(τ) for τ = 1 and τ = 2 shows increasing c(τ) with scale l for both A2 and A5. Several points for A2 are not shown due to lack of statistical significance at the 1% confidence level. Each data point represents an average over all possible correlations for the experiment at hand: that is, for c(2), the pairs (1, 3), (2, 4), etc. were used.

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