NG43A-01 INVITED
Extreme events in precipitation: Universal features and clustering
It is well known that precipitation, in contrast to temperature and river flow, is characterized by the absence of linear long-term correlations. Here we study the statistics of the return intervals between events above a threshold Q, for a large number of precipitation records from all over the globe. We find the surprisng results that the pdfs PQ(r) of the return intervals, when plotted in scaled form (RQPQ versus r/RQ, where RQ is the return period at threshold Q) show a data collapse for all thresholds and records considered, such that one functional form which can be fitted to a generalized gamma function, describes all records. In addition, the return intervals are weakly long-term correlated, which leads to a weak clustering of the extreme events. We compare these intriguing features with the results from a multiplicative random cascade model.
NG43A-02 INVITED
Multifractal Precipitation Extreme-Event Behavior Evaluated From the Radar-Pixel Scale up: Is the Scaling Consistent With the Smallest Resolvable Scales?
Intensity-duration-area-frequency (IDAF) functions for precipitation (combining classical IDF curves and area reduction factors) are a concise way to represent the hydro-meteorologically most useful information contained in the joined probability distribution functions of the rainfall process. Several studies have determined the expressions of IDAF functions for multifractal fields, and a parameterization thereof has been performed for the smallest resolvable scales of rainfall (drop-by-drop count). The importance of performing the same parameterization exercise from the radar-pixel scale up, resides in several expected results: (a) The identification of whether radar-pixel scaling is part of the same underlying multiplicative cascade found at the smallest resolvable scales (no scaling break within this domain of scales); (b) The deduction of a theoretically-based scaling expression, covering rainfall scales that are relevant for hydrologic model inputs: and (c) Determining the existence of a unique spectral shift exponent between rain gauge and radar measurements, corresponding to a fractional integration of the rainfall field, performed at the smallest scales, which would constitute an indication in favor of a unique underlying multifractal cascade at all considered scales.
NG43A-03
Regionalization of scaling properties of heavy rainfall for short durations.
The region of study, Cévennes-Vivarais in the South-East of France, is prone to severe rainfall and floods with serious consequences. Therefore, a relatively dense rainfall survey has been developed since the middle of the last century by means of hourly and daily rain gauges, and enhanced during the last 20 years in densifying the rain gauge network and implementing a radar network. It is well known that understanding, forecasting and assessing forecasts of heavy rainfall events necessitate to manage with point and spatialized rainfall data with different temporal resolutions. Moreover, it has been shown (Ramos et al., 2005, J. of Hydrology, V. 315) that storm severity from a socio-economical point of view depends both on the rainfall intensity and on the spatial and temporal scales at which it is assessed (return periods at given temporal and spatial scales). The need to compare storm severity from different data sets (raingauges, radar, model outputs) motivates our investigations of scale relationships in rainfall fields of the Cévennes-Vivarais region. Hourly rainfall series of raingauges support the evidence that the probability density functions of the most intense rainfall rates behave as power-laws. However, a careful determination of the power-law parameters is needed to avoid idiosyncratic parameter values of point rainfall in rainfall fields. Following Goldstein et al., 2004 (Eur. Phys. J. B, V. 41), the lower cut-off of the distribution has been been determined by an objective statistical method based on the Kolmogorov-Smirnov test. The maximum likelihood estimator has been implemented has it gives unbiased estimates of the power-law exponent compared to the classical least square fitting. Even though, the terrain elevation of the region is complex, well-defined spatial structures at the hourly and daily time scales have been found. These results are in good agreement with heavy rainfall features determined by classical extreme rainfall analysis. However, they support the evidence that rainfall distributions have hyperbolic tails in the Cévennes-Vivarais region which are not adapted to the independent-maxima extraction method. Hyperbolic distribution tails are compatible with stable distributions, which constitute the statistical basement to deal with scale invariances. An area where the hyperbolic behavior of distribution tails is obvious, has been delineated. In this area, the power-law exponent seems to be constant for accumulation periods ranging from to 2 to 24 hours.
NG43A-04
Universal Multifractal Parameters Applied to the Characterization and Simulation of Rainfall Events in the Peruvian High Plateau
The atmosphere is probably the most studied highly non-linear dynamic system. The analytical tools employed for characterizing, scaling and modeling atmospheric events such as rainfall have remained virtually unchanged for the last 25 years, notwithstanding the fast developments in both theory and analytical tools to characterize and model scale invariant features. We review these developments concentrating on multifractals, a theory deemed to provide the appropriate conceptual framework for scaling nonlinear dynamic systems. Five-year daily rain gauge data from ten meteorological stations spread throughout the Peruvian high plateau were used to obtain a quantitative characterization of the events. The three universal multifractal exponents were calculated using the double trace moment technique. These three parameters, α multifractality index; C1, codimension index; and H, smoothing index, totally characterized the rainfall fields and clearly showed the presence of space-time singularities in the rainfall events. The α and C1 values were used to estimate the Levy distribution for each station data. This distribution is characterized for its stability.. Rainfall events were simulated with the universal multifractal parameters calculated for each meteorological station. The general results of the analysis showed that the multifractal parameters were very sensitive to the time and spatial behaviors for the different series analyzed. These parameters also characterized well the rainfall fields and their simulations appropriately described the rainfall data trends.
NG43A-05
Path-Average Rainfall Estimation From Optical Extinction Measurements Using a Large- Aperture Scintillometer
We employ a Scintec BLS900 near infrared (880 nm) large aperture boundary layer scintillometer as path average rain gauge. The instrument was installed over a path of 2.4 km in Benin as part of the AMMA CATCH (African Monsoon Multidisciplinary Analysis) intensive observation period during 2006 and 2007. Measurements of the one minute average and variance of the received signal intensity from two transmitter disks of 462 LEDs each, operating at a pulse repetition rate of 5 Hz (i.e. 300 samples per minute), were collected for a few rainfall events that occurred during the dry season and several events during the wet season. Using estimates of the signal base level just before the start of the rain events, the optical extinction coefficient was estimated from the path integrated signal attenuation for each minute. The corresponding one minute path average rain rates were computed using a power law relation between the optical extinction coefficient and rain rate obtained from measurements of raindrop size spectra with an optical spectropluviometer. The estimated rain rates are compared to measurements from nearby rain gauges. Our results demonstrate the potential of optical extinction measurements from large aperture boundary layer scintillometers to obtain estimates of rainfall variability at high temporal resolution for hydrologically relevant spatial scales.