The spread of disease through a physical-contact network and the spread of information about the disease on a communication network are two intimately related dynamical processes. We investigate the asymmetrical interplay between the two types of spreading dynamics, each occurring on its own layer, by focusing on the two fundamental quantities underlying any spreading process: epidemic threshold and the final infection ratio. We find that an epidemic outbreak on the contact layer can induce an outbreak on the communication layer and information spreading can effectively raise the epidemic threshold. When structural correlation exists between the two layers, the information threshold remains unchanged but the epidemic threshold can be enhanced, making the contact layer more resilient to epidemic outbreak. We develop a physical theory to understand the intricate interplay between the two types of spreading dynamics.

A systematic and intensive analysis is performed on 5 yr of reliable disdrometric data (over 20 000 one-minute drop size distributions, DSDs) to investigate the variability of DSDs in the Montreal, Quebec, Canada, area. The scale dependence (climatological scale, day to day, within a day, between physical processes, and within a physical process) of the DSD variability and its effect on rainfall intensity R estimation from radar reflectivity Z are explored in terms of bias and random errors. Detail error distributions are also provided. The use of a climatological R–Z relationship for rainfall—affected by all of the DSDs’ variability—leads on average to a random error of 41% in instantaneous rain-rate estimation. This error decreases with integration time, but the decrease becomes less pronounced for integration times longer than 2 h. Daily accumulations computed with the climatological R–Z relationship have a bias of 28% because of the day-to-day DSD variability. However, when daily R–Z relationships are used, a random error of 32% in instantaneous rain rate is still present because of the DSD variability within a day. This illustrates that most of the variability of DSDs has its origin within a storm or between storms within a day. Physical processes leading to the formation of DSDs are then classified according to the vertical structure of radar data as measured by a UHF profiler collocated with the disdrometer. The DSD variability among different physical processes is larger than the day-to-day variability. A bias of 41% in rain accumulations is due to the DSD variability between physical processes. Accurate rain-rate estimation (∼7%) can be achieved only after the proper underlying physical process is identified and the associated R–Z relationship is used.

Although precipitation has been measured for many centuries, precipitation measurements are still beset with significant inaccuracies. Solid precipitation is particularly difficult to measure accurately, and wintertime precipitation measurement biases between different observing networks or different regions can exceed 100 %. Using precipitation gauge results from the World Meteorological Organization Solid Precipitation Intercomparison Experiment (WMO-SPICE), errors in precipitation measurement caused by gauge uncertainty, spatial variability in precipitation, hydrometeor type, crystal habit, and wind were quantified. The methods used to calculate gauge catch efficiency and correct known biases are described. Adjustments, in the form of transfer functions that describe catch efficiency as a function of air temperature and wind speed, were derived using measurements from eight separate WMO-SPICE sites for both unshielded and single-Alter-shielded precipitation-weighing gauges. For the unshielded gauges, the average undercatch for all eight sites was 0.50 mm h−1 (34 %), and for the single-Alter-shielded gauges it was 0.35 mm h−1 (24 %). After adjustment, the mean bias for both the unshielded and single-Alter measurements was within 0.03 mm h−1 (2 %) of zero. The use of multiple sites to derive such adjustments makes these results unique and more broadly applicable to other sites with various climatic conditions. In addition, errors associated with the use of a single transfer function to correct gauge undercatch at multiple sites were estimated.

Normalization of drop size distributions (DSDs) is reexamined here. First, an extension of the scaling normalization that uses one moment of the DSD as a scaling parameter to a more general scaling normalization that uses two moments as scaling parameters of the normalization is presented. In addition, the proposed formulation includes all two-parameter normalizations recently introduced in the literature. Thus, a unified vision of the question of DSD normalization and a good model representation of DSDs are given. Data analysis of some convective and stratiform DSDs shows that, from the point of view of the compact representation of DSDs, the double-moment normalization is preferred. However, in terms of physical interpretation, the scaling exponent of the single-moment normalization clearly indicates two different rain regimes, whereas in the double-moment normalization the two populations are not readily separated. It is also shown that DSD analytical models (exponential, gamma, and generalize...

This paper explores the removal of normal ground echoes (GREs) and anomalous propagation (AP) in ground-based radars using a fuzzy logic approach. Membership functions and their weights are derived from the characteristics of radar echoes as a function of radar reflectivity. The dependence on echo intensity is shown to significantly improve the proper identification of GRE/AP. In addition, the proposed method has a better performance at lower elevation angles. The overall performance is comparable with that from a polarimetric approach and can thus be easily implemented in operational radars.

Errors in surface rainfall estimates that are caused by ignoring the vertical profile of reflectivity (VPR) and range effects have been assessed by simulating how fine-resolution 3D reflectivity measurements at close ranges are sampled by the radar at various ranges and heights. Uncorrected and corrected accumulations from 33 events of mainly stratiform precipitation, with a recognizable melting layer for over 250 h, have been generated using two basic procedures: (a) the “near range” or “inner” VPR and (b) the intensity-dependent “climatological” VPR. The root-mean-square (rms) error structure has been derived as a function of height and range, for accumulations ranging from 5 min to 2 h, for various brightband heights and verification areas. However, it is the errors along the lowest default height that are most relevant. The stratification of the results by the height of the bright band is essential to understand the influence of the bright band with range. The largest errors (>100% at near ranges without correction) are encountered with lower and stronger bright bands. After correction, errors of less than 20% can be achieved with method “a” but only over large verification areas (>100 km2), with long accumulation intervals (>45 min), with bright bands that are relatively high (>2.5 km), and for ranges within ∼130 km. The climatological correction yields errors that are roughly 2 times as large. The results with the inner VPR method can only be obtained by assuming conditions of spatial homogeneity in the VPR structure of the rainfall fields. Simulations of the VPR variability have indicated that larger errors are to be expected in real-time operations, particularly when measurements are made inside the bright band. The magnitude of these errors may approach those of a “realistic climatological” correction that incorporates some uncertainty in the brightband height.