Auswahl der wissenschaftlichen Literatur zum Thema „Rain Interarrival Times Modeling“

The paper refers to a study on droughts in a small Portuguese Atlantic island, namely Madeira. The study aimed at addressing the problem of dependent drought events and at developing a copula-based bivariate cumulative distribution function for coupling drought duration and magnitude. The droughts were identified based on the Standardized Precipitation Index (SPI) computed at three and six-month timescales at 41 rain gauges distributed over the island and with rainfall data from January 1937 to December 2016. To remove the spurious and short duration-dependent droughts a moving average filter (MA) was used. The run theory was applied to the smoothed SPI series to extract the drought duration, magnitude, and interarrival time for each drought category. The smoothed series were also used to identify homogeneous regions based on principal components analysis (PCA). The study showed that MA is necessary for an improved probabilistic interpretation of drought analysis in Madeira. It also showed that despite the small area of the island, three distinct regions with different drought temporal patterns can be identified. The copulas approach proved that the return period of droughts events can differ significantly depending on the way the relationship between drought duration and magnitude is accounted for.

An N-system with different units submitted to shock and wear is studied. The shocks cause damage and, eventually, simultaneous failures of several units. The units can also fail due to internal failures. At random times, the system is inspected, and the down units are simultaneously replaced by identical ones. The arrival of shocks is governed by a Markovian arrival process. The operational times and the interarrival times between inspections follow phase-type distributions. The generator of the multidimensional Markov process modeling the system is constructed. This is performed introducing indicator functions for the different transition rates among the units using the algorithm of Kronecker. This is a general Markov process that can be applied for modeling different reliability systems depending on the structure of the units and how the systems operate. The general model is applied to the study of k-out-of-N systems, calculating the main performance measures. A practical example is presented showing the approximation of the model to a system with units following different Weibull distributions.

Abstract. The modeling of the occurrence of a rainfall dry spell and wet spell (ds and ws, respectively) can be jointly conveyed using interarrival times (its). While the modeling has the advantage of requiring a single fitting for the description of all rainfall time characteristics (including wet and dry chains, an extension of the concept of spells), the assumption of the independence and identical distribution of the renewal times it implicitly imposes a memoryless property on the derived ws, which may not be true in some cases. In this study, two different methods for the modeling of rainfall time characteristics at the station scale have been applied: (i) a direct method (DM) that fits the discrete Lerch distribution to it records and that then derives ws and ds (as well as the corresponding chains) from the it distribution and (ii) an indirect method (IM) that fits the Lerch distribution to the ws and ds records separately, relaxing the assumptions of the renewal process. The results of this application over six stations in Europe, characterized by a wide range of rainfall regimes, highlight how the geometric distribution does not always reasonably reproduce the ws frequencies, even when its are modeled well by the Lerch distribution. Improved performances are obtained with the IM thanks to the relaxation of the assumption of the independence and identical distribution of the renewal times. A further improvement of the fittings is obtained when the datasets are separated into two periods, suggesting that the inferences may benefit from accounting for the local seasonality.

Modeling large-scale flood inundation requires weeks of calculations using complex fluid software. The state-of-the-art in operational hydraulic modeling does not currently allow flood real-time forecasting fields. Data driven models have small computational costs and fast computation times and may be useful to overcome this problem. In this paper, we propose a new modeling approach based on a coupled of Hydrodynamics finite element model and Multi-headed Deep convolutional neural network (MH-CNN) with rain precipitations as input to forecast rapidly the water depth reached in large floodplain with few hours-ahead. For this purpose, one first builds a database containing different simulations of the physical model according to several rain precipitation scenarios (historic and synthetic). The multi-headed convolutional neural network is then trained using the constructed database to predict water depths. The pre-trained model is applied successfully to simulate the real July 2014 flood inundation in an 870 km2 area of La Nive watershed in the south west of France. Because rain precipitation forecast data is more accessible than discharge one, this approach offers great potential for real-time flood modelling for ungauged large-scale territories, which represent a large part of floodplain in the world.

Abstract The scaling and distributional properties of precipitation interamount times (IATs) are investigated using 10 years of high-resolution rain gauge observations from the U.S. Climate Reference Network. Results show that IATs above 200 mm tend to be approximately uncorrelated and normally distributed. As one moves toward smaller scales, autocorrelation and skewness increase and distributions progressively evolve into Weibull, Gamma, lognormal, and Pareto. This procession is interpreted as a sign of increasing complexity from large to small scales in a system composed of many interacting components. It shows that, as one approaches finer scales, IATs take over more of the characteristics of power-law distributions and (multi)fractals. Regression analysis on the log moments reveals that IATs generally exhibit better scaling, that is, smaller departures from multifractality, than precipitation amounts over the same range of scales. The improvement is attributed to the fact that IATs, unlike rainfall rates, always remain positive, no matter how small the scale. In particular, the scaling is shown to be more resilient to dry periods within rain events. Nevertheless, most analyzed IAT time series still exhibited a breakpoint at about 20 mm (7 days), corresponding to the average lifetime of a low pressure system at midlatitudes. Additional breakpoints in IATs at smaller and larger time scales are possible, but could not be determined unambiguously. The results highlight the potential of IATs as a new and promising tool for the stochastic modeling, simulation, and downscaling of precipitation.

Our research group at the Florida State University has been using a multianalysis/multimodel approach on real time for the short-range prediction of heavy rains over the tropical belt. The methodology for the construction of the superensemble forecasts follows our recent publications on this topic. Recent improvements in multianalysis/multimodel superensemble forecasts of precipitation have led to much higher skills compared to the member models. This suggested that some useful guidance for regional floods arising from heavy rains might be possible from this approach. These are 1 to 5 day forecasts where the equitable threat scores for rainfall totals in excess of 25 mm/day have been two to three times better for the superensemble compared to the best member model. This study includes forecasts using multimodels from a number of global operational centers and a multianalysis component, which is based on the FSU global spectral model that utilizes TRMM and SSM/I data sets and a number of rain rate algorithms. The differences in the analyses arise from the use of these different rain rate algorithms within physical initialization, which in turn, produces distinct differences among divergence, heating, moisture, and rain rate descriptions. A total of 11 models, of which 5 represent global operational models and 6 represent multianalysis forecasts from the FSU model initialized by different rain rate algorithms, are embedded in the multianalysis/multimodel system studied here. The TRMM and the SSM/I rainfall data sets derived from microwave instruments are key to these marked improvements of rainfall forecasts. The statistical biases of the models are determined from a multiple linear regression of these forecasts against a ‘best’ rainfall analysis field, which is based on a TRMM and SSM/I data set that utilizes rain rate algorithms recently developed at NASA Goddard. We also display a sequence of computations that illustrate a “walk-through” of a heavy rain episode. This study specifically deals with recent flood episodes over India, Bangladesh, the United States of America, Mozambique/Madagascar and the Philippines. These results compare the performance of the superensemble against the best and lowest performing model, the ensemble mean and the control experiment (that does not use any TRMM or SSM/I data sets). Overall these results show great promise over the current best models.

California is increasingly experiencing drought conditions that restrict irrigation deliveries to perennial nut crops such as almonds and pistachios. During drought, poorer quality groundwater is often used to maintain these crops, but this use often results in secondary salinization that requires skilled management. Process-based models can help improve management guidelines under these challenging circumstances. The main objective of this work was to assess seasonal soil salinity and root water uptake as a function of irrigation water salinity and annual rain amounts. The manuscript presents a comparison of three-year experimental and numerically simulated root zone salinities in and below the root zone of almond and pistachio drip-irrigated orchards at multiple locations in the San Joaquin Valley (SJV), California, with different meteorological characteristics. The HYDRUS-1D numerical model was calibrated and validated using field measurements of soil water contents and soil solute bulk electrical conductivities at four root zone depths and measured soil hydraulic conductivities. The remaining soil hydraulic parameters were estimated inversely. Observations and simulations showed that the effects of rain on root zone salinity were higher in fields with initially low salinities than in fields with high salinities. The maximum reduction in simulated root water uptake (7%) occurred in response to initially high soil salinity conditions and saline irrigation water. The minimum reduction in simulated water uptake (2.5%) occurred in response to initially low soil salinity conditions and a wet rain year. Simulated water uptake reductions and leaching fractions varied at early and late times of the growing season, depending on irrigation water salinity. Root water uptake reduction was highly correlated with the cumulative effects of using saline waters in prior years, more than salt leaching during a particular season, even when rain was sufficient to leach salts during a wet year.

Abstract Cloud-scale models apply two drastically different methods to represent condensation of water vapor to form and grow cloud droplets. Maintenance of water saturation inside liquid clouds is assumed in the computationally efficient saturation adjustment approach used in most bulk microphysics schemes. When super- or subsaturations are allowed, condensation/evaporation can be calculated using the predicted saturation ratio and (either predicted or prescribed) mean droplet radius and concentration. The study investigates differences between simulations of deep unorganized convection applying a saturation adjustment condensation scheme (SADJ) and a scheme with supersaturation prediction (SPRE). A double-moment microphysics scheme with CCN activation parameterized as a function of the local vertical velocity is applied to compare cloud fields simulated applying SPRE and SADJ. Clean CCN conditions are assumed to demonstrate upper limits of the SPRE and SADJ difference. Microphysical piggybacking is used to extract the impacts with confidence. Results show a significant impact on deep convection dynamics, with SADJ featuring more cloud buoyancy and thus stronger updrafts. This leads to around a 3% increase of the surface rain accumulation in SADJ. Upper-tropospheric anvil cloud fractions are much larger in SPRE than in SADJ because of the higher ice concentrations and thus longer residence times of anvil particles in SPRE, as demonstrated by sensitivity tests. Higher ice concentrations in SPRE come from significantly larger ice supersaturations in strong convective updrafts that feature water supersaturations of several percent.

Abstract. Climate change affects precipitation phase, which can propagate into changes in streamflow timing and magnitude. This study examines how the spatial and temporal distribution of rainfall and snowmelt affects discharge in rain–snow transition zones. These zones experience large year-to-year variations in precipitation phase, cover a significant area of mountain catchments globally, and might extend to higher elevations under future climate change. We used observations from 11 weather stations and snow depths measured from one aerial lidar survey to force a spatially distributed snowpack model (iSnobal/Automated Water Supply Model) in a semiarid, 1.8 km2 headwater catchment. We focused on surface water input (SWI; the summation of rainfall and snowmelt on the soil) for 4 years with contrasting climatological conditions (wet, dry, rainy, and snowy) and compared simulated SWI to measured discharge. A strong spatial agreement between snow depth from the lidar survey and model (r2 = 0.88) was observed, with a median Nash–Sutcliffe efficiency (NSE) of 0.65 for simulated and measured snow depths at snow depth stations for all modeled years (0.75 for normalized snow depths). The spatial pattern of SWI was consistent between the 4 years, with north-facing slopes producing 1.09–1.25 times more SWI than south-facing slopes, and snowdrifts producing up to 6 times more SWI than the catchment average. Annual discharge in the catchment was not significantly correlated with the fraction of precipitation falling as snow; instead, it was correlated with the magnitude of precipitation and spring snow and rain. Stream cessation depended on total and spring precipitation, as well as on the melt-out date of the snowdrifts. These results highlight the importance of the heterogeneity of SWI at the rain–snow transition zone for streamflow generation and cessation, and emphasize the need for spatially distributed modeling or monitoring of both snowpack and rainfall dynamics.

L'analyse des données de précipitations et la modélisation des nombreuses variables associées sont essentielles dans des domaines tels que l'agriculture, l'écologie et l'ingénierie, et reposent sur des archives historiques en raison de la complexité des systèmes hydrologiques. Les séries de précipitations quotidiennes obtenues à partir de réseaux de pluviomètres sont parmi les plus utilisées. Un modèle fiable et flexible pour un site unique est crucial pour développer des modèles multi-sites plus complexes tenant compte des corrélations spatiales observées dans un réseau dense de stations. Compte tenu de l'intérêt croissant pour l'étude des cycles de pluie et de sécheresse, les modèles discrets en deux parties, qui séparent l'occurrence des précipitations de leur quantification, sont des outils utiles pour décrire les précipitations quotidiennes à une station. Dans ce contexte, nous examinons d'abord la modélisation des temps d'inter-arrivée des précipitations à l'aide de la famille Hurwitz-Lerch-Zeta et de deux autres distributions associées, jamais utilisées dans ce cadre. Basée sur les relations entre les temps d'inter-arrivée et d'autres variables temporelles, une méthodologie pour leur modélisation et analyse empirique est détaillée. Cette procédure, ainsi que la performance d'ajustement des distributions susmentionnées, est démontrée sur un ensemble de données couvrant divers régimes de précipitations.La modélisation fiable des variables de précipitations est également cruciale pour aborder le changement climatique. Un point de départ pour détecter ces changements est la modélisation multivariée des variables de précipitations, car des changements dans leurs inter-relations peuvent refléter des altérations climatiques régionales. Les copules sont bien connues et appréciées pour leur flexibilité, mais elles perdent leur efficacité avec les vecteurs aléatoires discrets, compromettant leur unicité et entraînant des incohérences qui minent les procédures inférentielles typiques des cas continus. Récemment, Gery Geenens a proposé une nouvelle approche fondée sur des idées historiques liées à l'analyse des tableaux de contingence. Ses idées théoriques, combinées à la procédure d'ajustement proportionnel itératif, ouvrent la voie à de nouveaux modèles (semi-paramétriques ou paramétriques) pour des vecteurs aléatoires discrets bivariés à support fini. Pour cela, nous démontrons une décomposition de type Sklar d'une fonction de masse de probabilité discrète bivariée entre ses marges et une fonction de masse de probabilité copule, sur laquelle reposent les modèles mentionnés. Les procédures d'inférence et d'ajustement sont étudiées théoriquement et empiriquement.L'impact des précipitations sur les masses d'eau et les surfaces terrestres est aussi important que leur modélisation. Par exemple, déterminer le temps nécessaire pour que les précipitations fassent dépasser les niveaux des rivières au-delà d'un seuil de crue est essentiel pour la prévision et la gestion des inondations. Plus généralement, il est souvent crucial de déterminer le moment où certains seuils hydrologiques sont franchis par une quantité hydrologique donnée. Lorsque cette valeur est modélisée par un processus stochastique, le problème se reformule en termes de temps de passage initial. Dans ce contexte, le calcul pratique de la densité de probabilité et de la fonction de distribution du temps de passage initial est délicat. Nous proposons une méthode d'approximation basée sur une expansion en série. Les résultats théoriques sont accompagnés de discussions sur les aspects computationnels. Des expériences numériques étendues sont menées pour le mouvement brownien géométrique et le processus de Cox-Ingersoll-Ross
Analysis of rainfall data and subsequent modeling of the many variables concerning rainfall is fundamental to many areas such as agricultural, ecological and engineering disciplines and, due to the complexity of the underlying hydrological system, it relies heavily on historical records. Daily rainfall series obtained from rain gauge networks are arguably the most used. A reliable and flexible single site model is the fundamental starting point of any more complex multi-site model taking into account the spatial correlations arising when observing a dense network of stations. Given the ever-growing interest in analysing the alternance between period of continuous rainfall and periods of drought, two-part discrete time models accounting separately for rainfall occurrence and rainfall amount processes are an useful tool to describe the behaviour of daily rainfall at a single station. In this context, we initially investigate the modeling of daily rainfall interarrival times through a family of discrete probability distributions known as the Hurwitz-Lerch-Zeta family, along with two other distributions which are deeply related to the latter and have never been considered with this aim. Building up on the relationships between the interarrival times and certain other temporal variables, a methodology for their modeling and empirical analysis is detailed. The latter procedure and the fitting performance of the aforementioned distributions is shown on a dataset composed of a variety of rainfall regimes.Moreover, being able to provide reliable modeling of rainfall related variables is essential in the well known issue of climate change. A starting point in detecting change is the multivariate modeling of rainfall variables, as a perceivable shift in the inter-relationships between these could reflect climate changes in a region. In this context, copulas are well known and valued for their flexibility. However, they lose their charm when dealing with discrete random vectors. In this case, the uniqueness of the copula is compromised, leading to inconsistencies which basically break down the theoretical underpinnings of the inferential procedures commonly used in the continuous case. Recently, Gery Geenens made a compelling case for a new approach, grounding its beliefs in historical ideas regarding the statistical analysis of contingency tables. The theoretical insights he gives, coupled with a computational tool known as iterative proportional fitting procedure, open up the path to our development of novel (semi-parametric or parametric) models for finitely supported bivariate discrete random vectors. With this aim, we prove a sklar-like decomposition of a bivariate discrete probability mass function between its margins and a copula probability mass function, on which the previously mentioned models hinge upon. Related inferential and goodness of fit procedures are investigated, both theoretically and empirically.Of the same significance as modeling the behavior of rainfall is its impact on water bodies and land surfaces. For istance, understanding the time it takes for rainfall to cause river levels to exceed a flood stage is of paramount importance for flood prediction and management. More in general, it is often crucial to determine the time at which certain hydrological thresholds are crossed by some hydrological quantity. When the latter's value in time is modelled by a stochastic process, the problem mentioned above can be restated in terms of the well known first passage time problem. In this context, a practical closed form computation of the first passage time probability density and distribution function is a delicate issue. Regarding this, we propose an approximation method based on a series expansion. Theoretical results are accompanied by discussions on the computational aspects. Extensive numerical experiments are carried out for the geometric Brownian motion and the Cox-Ingersoll-Ross process

Each pipeline river crossing is a unique project and depends on the local environmental conditions. Sediment movement or erosion of the river bed can, for example, originate free spans superior to those for which the pipeline was designed to resist. A thorough understanding of the sediment dynamics is necessary in order to guarantee the integrity of the pipeline from damages caused by variation of the river bed. PETROBRAS designed and installed two gas pipelines in Negro River, state of Amazonia, Brazil. The new pipelines will have a total length of 383 km through the rain forest, 10 km of which was laid along the river bed and a second branch crossing the river over 5 km. In order to guarantee the structural safety of the pipeline, characterization of river hydraulics and bed dynamics was carried out with acquisition of environmental data, numerical modeling and surveying. Current and flow measurements with ADCPs, hydrodynamic and morphological modeling were carried out. Multibeam, side scan sonar and SBP surveys at different times were compared in order to assess large scale changes in the river bed and presence of bed forms. Hydraulic characterization of the Negro River indicated relatively low bed mobility in comparison to the Amazon River, for example. Finally, parametric calculations for onset of scour, length and depth of scour holes and related time scale, as well as bottom velocities over the hydrological cycle were used to obtain parameters for engineering design (route stability, free span analysis, etc.), protection requirements and survey periodicity for monitoring of free span development along the pipeline.

Abstract The demand of affordable, renewable electric energy is still increasing. Wind energy is seen as one of the most promising resources for future electric energy supply. To reduce the cost of wind energy the dimensions of wind energy turbines are still increasing. This leads to higher power output due to the larger rotor diameters, but also due to the higher wind speeds above the boundary layer. This increase in rotor diameter is achieved at the expense of much higher structural loads especially in the rotor blade root. These loads consist of bending moments, that are mainly caused by gravity, wind shear, gusts and the tower influence to the blade. A reduction of these root bending moments would allow a further increase of the rotor diameter, a longer lifetime or a lighter design and therefore be advantageous for the turbine. Load reduction can be achieved by using a trailing edge flap at the outer region of the blade, comparable to control surfaces of aircraft. This trailing edge is capable of moving several times per blade revolution and allows the manipulation of the flow to alleviate changes in the aerodynamic loading. In contrast to aircraft, sealing against environmental media, such as rain, dust, insects and so on is much more important to allow a high lifetime and low maintenance effort. Therefore, a flexible and gapless morphing trailing edge has been designed within the SmartBlades projects at the German Aerospace Center (DLR) for the mentioned purpose. Based on this design, a demonstrator was built, which was tested in a wind tunnel and on a rotational test site for its performance. The paper will present the approach beginning with some design and modeling considerations of the flexible trailing edge and the demonstrator, which was used for testing. Main focus of the paper is the presentation of results obtained from a wind tunnel experiment at Oldenburg University and the rotational experiment at the field research site of the Technical University in Denmark (DTU). In these experiments, the effectiveness of the trailing edge flap could be demonstrated in the wind tunnel as well as in free field. Based on pressure taps and force sensors, the change in the lift of the airfoil due to the deflection of the flexible trailing edge was measured and the resulting polars are shown in this paper. Furthermore, the result of different simple control strategies for the trailing edge in terms of load reduction at the rotating test rig will be presented.