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    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's 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.
    Publicationtype: Journal Article
      13
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    Development of statistical models for at-site probabilistic seasonal rainfall forecast
    (Wiley, 2012-11-30) ;
    A probabilistic seasonal rainfall forecasting system for the Bucharest-Filaret (Romania) station based on Generalized Additive Models in Location, Scale and Shape (GAMLSS) is proposed. First we develop statistical models to describe seasonal rainfall over the period 1926-2000, both considering the seasonal record as a continuous time series and accounting for seasonal changes, and by developing ad hoc models for each individual season. The Southern Oscillation Index (SOI), the North Atlantic Oscillation (NAO) and the seasonal rainfall for the previous year are included as possible covariates. Model selection is performed with respect to two penalty criteria [Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC)], each of them leading to different final model configurations in terms of predictors and their functional relation to the parameters of the probability distribution. Retrospective forecast, in which the parameters of the models are re-estimated every time new information becomes available, is performed on a yearly basis for the period 1986-2000. The quality of the forecasts is assessed in terms of several accuracy measures and by visual examination of the forecasts' probability distributions. The best forecasts are obtained for the winter season. While it is not possible to identify a single 'best' model according to all the forecast measures, we recommend using the model that considers the seasonal rainfall as a continuous time series and penalized with respect to AIC. © 2011 Royal Meteorological Society.
    Publicationtype: Journal Article
      5
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    Analyses of extreme flooding in Austria over the period 1951-2006
    (Wiley, 2012-06-30) ;
    Smith, James A.
    ;
    ;
    Ntelekos, Alexandros A.
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    Schwarz, Ulrich
    Analyses of extreme flooding in Austria is performed using daily discharge time series from 27 stations over the period 1951-2006. The main research questions revolve around: (1) temporal non-stationarities in the flood record, (2) upper tail and scaling properties of the flood peak records, and (3) relation between magnitude and frequency of flooding and the North Atlantic Oscillation (NAO). Two datasets are derived from the daily discharge time series: annual maximum daily discharge and peaks-over-threshold (POT) data. The validity of the stationarity assumption in the annual maximum discharge record is assessed by investigating the presence of abrupt and slowly varying changes using nonparametric tests. The time series are tested for abrupt changes both in the mean and variance of the flood peak distributions by means of the Pettitt test. The presence of monotonic trends is investigated by means of the Mann-Kendall and Spearman tests. Violations of the stationarity assumption are associated with abrupt rather than gradual changes. These step changes generally involve river regulation through construction of dams or other major engineering works. It is not possible to make conclusive statements about the presence of an anthropogenic climate change signal in the flood peak record. Similar conclusions are obtained when focussing on the frequency of POT floods. The Generalised Extreme Value distribution is used to study the upper tail and scaling properties of annual maximum daily discharge records. The location and scale parameters exhibit power-law behaviour as a function of drainage area. The shape parameters indicate that the flood peak distributions for Austria have a heavy tail. Non-stationary modelling of the annual maximum daily discharge and POT time series is used to explore the relation between flood magnitude and frequency and NAO. The results indicate that NAO is a significant covariate in explaining the magnitude and frequency of occurrence of flooding over a large part of Austria. © 2011 Royal Meteorological Society.
    Publicationtype: Journal Article
      2
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    Analyses of seasonal and annual maximum daily discharge records for central Europe
    (Elsevier, 2011-03-18) ;
    Smith, James A.
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    Ntelekos, Alexandros A.
    Annual and seasonal maximum daily discharge time series for 55 stations in central Europe (Germany, Switzerland, Czech Republic, and Slovakia) are used to examine flood frequency from a regional perspective. In this study we examine temporal nonstationarities in the flood peak records, and characterize upper tail and scaling properties of the flood peak distributions. There is a marked seasonality in the flood peak record, with a large fraction of annual maximum flood peaks occurring during the winter in the western part of the study domain, and during the summer in the southern portion of this region. The presence of abrupt and slowly varying changes in the flood time series is examined by means of non-parametric tests. Change-points in the mean and variance of the flood peak distributions are examined using the Pettitt test, while the presence of monotonic patterns is examined by means of Spearman and Mann-Kendall tests. Abrupt changes, rather than monotonic trends are responsible for violations of the stationarity assumption. These step changes can often be associated with anthropogenic effects, such as construction of dams and reservoirs and river training. Given the profound changes that these catchments have undergone, it is difficult to detect a possible climate change signal in the flood peak record. The estimates of the location, scale, and shape parameters of the Generalized Extreme Value distribution are used to examine the upper tail and scaling properties of the flood peak distributions. The location and scale parameters exhibit a power law behaviour when plotted as a function of drainage area, while the shape parameter decreases log-linearly for increasing catchment area. The findings of this study suggest that these records exhibit a heavy tail behaviour. © 2011 Elsevier B.V.
    Publicationtype: Journal Article
      5
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    On the stationarity of annual flood peaks in the continental United States during the 20th century
    (2009-08-13) ; ;
    Smith, James A.
    ;
    Annual peak discharge records from 50 stations in the continental United States with at least 100 years of record are used to investigate stationarity of flood peaks during the 20th century. We examine temporal trends in flood peaks and abrupt changes in the mean and/or variance of flood peak distributions. Change point analysis for detecting abrupt changes in flood distributions is performed using the nonparametric Pettitt test. Two nonparametric (Mann-Kendall and Spearman) tests and one parametric (Pearson) test are used to detect the presence of temporal trends. Generalized additive models for location, scale, and shape (GAMLSS) are also used to parametrically model the annual peak data, exploiting their flexibility to account for abrupt changes and temporal trends in the parameters of the distribution functions. Additionally, the presence of long-term persistence is investigated through estimation of the Hurst exponent, and an alternative interpretation of the results in terms of long-term persistence is provided. Many of the drainage basins represented in this study have been affected by regulation through systems of reservoirs, and all of the drainage basins have experienced significant land use changes during the 20th century. Despite the profound changes that have occurred to drainage basins throughout the continental United States and the recognition that elements of the hydrologic cycle are being altered by human-induced climate change, it is easier to proclaim the demise of stationarity of flood peaks than to prove it through analyses of annual flood peak data. Copyright 2009 by the American Geophysical Union.
    Publicationtype: Journal Article
      4
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    Flood frequency analysis for nonstationary annual peak records in an urban drainage basin
    (Elsevier, 2009-05-15) ;
    Smith, James A.
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    Bales, Jerad
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    Bates, Paul D.
    Flood frequency analysis in urban watersheds is complicated by nonstationarities of annual peak records associated with land use change and evolving urban stormwater infrastructure. In this study, a framework for flood frequency analysis is developed based on the Generalized Additive Models for Location, Scale and Shape parameters (GAMLSS), a tool for modeling time series under nonstationary conditions. GAMLSS is applied to annual maximum peak discharge records for Little Sugar Creek, a highly urbanized watershed which drains the urban core of Charlotte, North Carolina. It is shown that GAMLSS is able to describe the variability in the mean and variance of the annual maximum peak discharge by modeling the parameters of the selected parametric distribution as a smooth function of time via cubic splines. Flood frequency analyses for Little Sugar Creek (at a drainage area of 110 km²) show that the maximum flow with a 0.01-annual probability (corresponding to 100-year flood peak under stationary conditions) over the 83-year record has ranged from a minimum unit discharge of 2.1 m³ s⁻¹ km⁻² to a maximum of 5.1 m³ s⁻¹ km⁻². An alternative characterization can be made by examining the estimated return interval of the peak discharge that would have an annual exceedance probability of 0.01 under the assumption of stationarity (3.2 m³ s⁻¹ km⁻²). Under nonstationary conditions, alternative definitions of return period should be adapted. Under the GAMLSS model, the return interval of an annual peak discharge of 3.2 m³ s⁻¹ km⁻² ranges from a maximum value of more than 5000 years in 1957 to a minimum value of almost 8 years for the present time (2007). The GAMLSS framework is also used to examine the links between population trends and flood frequency, as well as trends in annual maximum rainfall. These analyses are used to examine evolving flood frequency over future decades.
    Publicationtype: Journal Article
      7
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    Item type:Publication,
    Modeling radar-rainfall estimation uncertainties using parametric and non-parametric approaches
    There are large uncertainties associated with radar estimates of rainfall, including systematic errors as well as the random effects from several sources. This study focuses on the modeling of the systematic error component, which can be described mathematically in terms of a conditional expectation function. The authors present two different approaches: non-parametric (kernel-based) and parametric (copula-based). A large sample (more than six years) of rain gauge measurements from a dense network located in south-west England is used as an approximation of the true ground rainfall. These data are complemented with rainfall estimates by a C-band weather radar located at Wardon Hill, which is about 40 km from the catchment. The authors compare the results obtained using the parametric and non-parametric schemes for four temporal scales of hydrologic interest (5 and 15 min, hourly and three-hourly) by means of several different performance indices and discuss the strengths and weaknesses of each approach.
    Publicationtype: Journal Article
      5