Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models

Discrete multiplicative random cascade (MRC) models were extensively studied and applied to disaggregate rainfall data, thanks to their formal simplicity and the small number of involved parameters. Focusing on temporal disaggregation, the rationale of these models is based on multiplying the value assumed by a physical attribute (e.g., rainfall intensity) at a given time scale <I>L</I>, by a suitable number <I>b</I> of random weights, to obtain <I>b</I> attribute values corresponding to statistically plausible observations at a smaller <I>L/b</I> time resolution. In the original formulation of the MRC models, the random weights were assumed to be independent and identically distributed. However, for several studies this hypothesis did not appear to be realistic for the observed rainfall series as the distribution of the weights was shown to depend on the space-time scale and rainfall intensity. Since these findings contrast with the scale invariance assumption behind the MRC models and impact on the applicability of these models, it is worth studying their nature. This study explores the possible presence of dependence of the parameters of two discrete MRC models on rainfall intensity and time scale, by analyzing point rainfall series with 5-min time resolution. Taking into account a discrete microcanonical (MC) model based on beta distribution and a discrete canonical beta-logstable (BLS), the analysis points out that the relations between the parameters and rainfall intensity across the time scales are detectable and can be modeled by a set of simple functions accounting for the parameter-rainfall intensity relationship, and another set describing the link between the parameters and the time scale. Therefore, MC and BLS models were modified to explicitly account for these relationships and compared with the continuous in scale universal multifractal (CUM) model, which is used as a physically based benchmark model. Monte Carlo simulations point out that the dependence of MC and BLS parameters on rainfall intensity and cascade scales can be recognized also in CUM series, meaning that these relations cannot be considered as a definitive sign of departure from multifractality. Even though the modified MC model is not properly a scaling model (parameters depend on rainfall intensity and scale), it reproduces the empirical traces of the moments and moment exponent function as effective as the CUM model. Moreover, the MC model is able to reproduce some rainfall properties of hydrological interest, such as the distribution of event rainfall amount, wet/dry spell length, and the autocorrelation function, better than its competitors owing to its strong, albeit unrealistic, conservative nature. Therefore, even though the CUM model represents the most parsimonious and the only physically/theoretically consistent model, results provided by MC model motivate, to some extent, the interest recognized in the literature for this type of discrete models

Multivariate linear parametric models applied to daily rainfall time series

International audienceThe aim of this paper is to test the Multivariate Linear Parametric Models applied to daily rainfall series. These simple models allow to generate synthetic series preserving both the time correlation (autocorrelation) and the space correlation (crosscorrelation). To have synthetic daily series, in such a way realistic and usable, it is necessary the application of a corrective procedure, removing negative values and enforcing the no-rain probability. The following study compares some linear models each other and points out the roles of autoregressive (AR) and moving average (MA) components as well as parameter orders and mixed parameters

Spatial And Temporal Modeling Of Radar Rainfall Uncertainties

It is widely acknowledged that radar-based estimates of rainfall are affected by uncertainties (e.g., mis-calibration, beam blockage, anomalous propagation, and ground clutter) which are both systematic and random in nature. Improving the characterization of these errors would yield better understanding and interpretations of results from studies in which these estimates are used as inputs (e.g., hydrologic modeling) or initial conditions (e.g., rainfall forecasting). Building on earlier efforts, the authors apply a data-driven multiplicative model in which the relationship between true rainfall and radar rainfall can be described in terms of the product of a systematic and random component. The systematic component accounts for conditional biases. The conditional bias is approximated by a power-law function. The random component, which represents the random fluctuations remaining after correcting for systematic uncertainties, is characterized in terms of its probability distribution as well as its spatial and temporal dependencies. The space-time dependencies are computed using the non-parametric Kendall\u27s τ measure. For the first time, the authors present a methodology based on conditional copulas to generate ensembles of random error fields with the prescribed marginal probability distribution and spatio-temporal dependencies. The methodology is illustrated using data from Clear Creek, which is a densely instrumented experimental watershed in eastern Iowa. Results are based on three years of radar data from the Davenport Weather Surveillance Radar 88 Doppler (WSR-88D) radar that were processed through the Hydro-NEXRAD system. The spatial and temporal resolutions are 0.5. km and hourly, respectively, and the radar data are complemented by rainfall measurements from 11 rain gages, located within the catchment, which are used to approximate true ground rainfall. © 2013 Elsevier B.V

Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series

Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in determining the Hurst index of time series.Comment: 6 pages (including 3 figures) + 3 supplementary figure

Effects of growth rate, size, and light availability on tree survival across life stages: a demographic analysis accounting for missing values and small sample sizes.

The data set supporting the results of this article is available in the Dryad repository, http://dx.doi.org/10.5061/dryad.6f4qs. Moustakas, A. and Evans, M. R. (2015) Effects of growth rate, size, and light availability on tree survival across life stages: a demographic analysis accounting for missing values.Plant survival is a key factor in forest dynamics and survival probabilities often vary across life stages. Studies specifically aimed at assessing tree survival are unusual and so data initially designed for other purposes often need to be used; such data are more likely to contain errors than data collected for this specific purpose