Anna Deluca

Universality of rain event size distributions

We compare rain event size distributions derived from measurements in climatically different regions, which we find to be well approximated by power laws of similar exponents over broad ranges. Differences can be seen in the large-scale cutoffs of the distributions. Event duration distributions suggest that the scale-free aspects are related to the absence of characteristic scales in the meteorological mesoscale.

Fitting and Goodness-of-Fit Test of Non-Truncated and Truncated Power-Law Distributions

Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.

Data-driven prediction of thresholded time series of rainfall and self-organized criticality models

We study the occurrence of events, subject to threshold, in a representative self-organized criticality (SOC) sandpile model and in high-resolution rainfall data. The predictability in both systems is analyzed by means of a decision variable sensitive to event clustering, and the quality of the predictions is evaluated by the receiver operating characteristic (ROC) method. In the case of the SOC sandpile model, the scaling of quiet-time distributions with increasing threshold leads to increased predictability of extreme events. A scaling theory allows us to understand all the details of the prediction procedure and to extrapolate the shape of the ROC curves for the most extreme events. For rainfall data, the quiet-time distributions do not scale for high thresholds, which means that the corresponding ROC curves cannot be straightforwardly related to those for lower thresholds. In this way, ROC curves are useful for highlighting differences in predictability of extreme events between toy models and real-world phenomena.

The perils of thresholding

The thresholding of time series of activity or intensity is frequently used to define and differentiate events. This is either implicit, for example due to resolution limits, or explicit, in order to filter certain small scale physics from the supposed true asymptotic events. Thresholding the birth–death process, however, introduces a scaling region into the event size distribution, which is characterized by an exponent that is unrelated to the actual asymptote and is rather an artefact of thresholding. As a result, numerical fits of simulation data produce a range of exponents, with the true asymptote visible only in the tail of the distribution. This tail is increasingly difficult to sample as the threshold is increased. In the present case, the exponents and the spurious nature of the scaling region can be determined analytically, thus demonstrating the way in which thresholding conceals the true asymptote. The analysis also suggests a procedure for detecting the influence of the threshold by means of a data collapse involving the threshold-imposed scale.

Testing universality in critical exponents: The case of rainfall

One of the key clues to consider rainfall as a self-organized critical phenomenon is the existence of power-law distributions for rain-event sizes. We have studied the problem of universality in the exponents of these distributions by means of a suitable statistic whose distribution is inferred by several variations of a permutational test. In contrast to more common approaches, our procedure does not suffer from the difficulties of multiple testing and does not require the precise knowledge of the uncertainties associated to the power-law exponents. When applied to seven sites monitored by the Atmospheric Radiation Measurement Program the tests lead to the rejection of the universality hypothesis, despite the fact that the exponents are rather close to each other. We discuss the reasons of the rejection.

Scientific challenges of convective-scale numerical weather prediction

CapsuleNumerical weather prediction (NWP) models are increasing in resolution and becoming capable of explicitly representing individual convective storms. Is this increase in resolution leading to better forecasts? Unfortunately, we do not have sufficient theoretical understanding about this weather regime to make full use of these NWPs.

Testing Universality and Goodness-of-Fit Test of Power-Law Distributions

Power-law distributions contain precious information about a large variety of physical processes [10]. Although there are sound theoretical grounds for these distributions, the empirical evidence giving support to power laws has been traditionally weak.

Criticality on Rainfall: Statistical Observational Constraints for the Onset of Strong Convection Modelling

A better understanding of convection is crucial for reducing the intrinsic errors present in climate models [4]. Many atmospheric processes related to precipitation have large scale correlations in time and space, which are the result of the coupling between several non-linear mechanisms with different temporal and spatial characteristic scales. Despite the diversity of individual rain events, a recent array of statistical measures presents surprising statistical regularities giving support to the hypothesis that atmospheric convection and precipitation may be a real-world example of Self-Organised Criticality (SOC) [2, 16].