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James A. Smith

Abstract

The principal process considered in this paper is the flux of raindrops through a volume of the atmosphere. This process is of fundamental importance for a wide variety of engineering and environmental problems, notably remote sensing of precipitation, infiltration of rainfall, soil erosion, atmospheric deposition of pollutants, and design of microwave communication systems. A marked point process model is developed in which the point process represents the arrival times of drops at the upper surface of a sample volume and the mark associated with a drop is its diameter. In the model, both the rate of occurrence of raindrops and the distribution of drop diameters vary randomly over time. Results that relate the drop-size distribution within the sample volume to the probability low of the drop-arrival process are presented. These results allow straightforward comparisons between temporal characterizations of drop-size distributions and spatial characterizations. Representations for derived processes such as rainfall rate and reflectivity are shown to be quite accurate using raindrop data from North Carolina.

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Brianne K. Smith and James A. Smith

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The authors identify the flashiest watersheds in the contiguous United States based on frequency of discharge peaks exceeding 1 m3 s−1 km−2. The entire digitized record of USGS instantaneous discharge data is used for all stream gauging stations with over 10 years of data. Using the 1 m3 s−1 km−2 threshold, the flashiest basins in the contiguous United States are located in urban areas along a swath of states from the south-central United States to the mid-Atlantic and in mountainous areas of the West Coast, especially the Pacific Northwest. The authors focus on small watersheds to identify the flashiest cities and states across the country and find Tulsa, Oklahoma; Baltimore, Maryland; and St. Louis, Missouri, to be the flashiest cities in the contiguous United States. Thunderstorms are major agents for peak-over-threshold flood events east of the Rocky Mountains, and tropical cyclones play a secondary role, especially in the Southeast. West Coast flood events are associated with winter storms. Flooding west of and within the Rockies is linked to steeply sloped terrain and compact watersheds. East of the Rockies, urban areas dominate flashy watersheds. The authors find that watersheds northeast (downwind) of city centers are flashier than other urban watersheds, consistent with the downwind maximum in rainfall found in many urban regions. They examine anomalous flood response in the Illinois–Missouri region; St. Louis is among the flashiest cities in the United States, while Chicago is among the least flashy. Their flashiness map is compared with other measures of flooding, including flood damage and National Weather Service flash flood reports.

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Marc Schleiss and James A. Smith

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Precipitation displays a remarkable variability in space and time. An important yet poorly documented aspect of this variability is intermittency. In this paper, a new way of quantifying intermittency based on the burstiness B and memory M of interamount times is proposed. The method is applied to a unique dataset of 325 high-resolution rain gauges in the United States and Europe. Results show that the MB diagram provides useful insight into local precipitation patterns and can be used to study intermittency over a wide range of temporal scales. It is found that precipitation tends to be more intermittent in warm and dry climates with the largest observed values in the southwest of the United States (i.e., California, Nevada, Arizona, and Texas). Low-to-moderate values are reported for the northeastern United States, the United Kingdom, the Netherlands, and Germany. In the second half of the paper, the new metrics are applied to daily rainfall data for 1954–2013 to investigate regional trends in intermittency due to climate variability and global warming. No evidence is found of a global shift in intermittency but a weak trend toward burstier precipitation patterns and longer dry spells in the south of Europe (i.e., Portugal, Spain, and Italy) and an opposite trend toward steadier and more correlated precipitation patterns in Norway, Sweden, and Finland is observed.

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Maofeng Liu and James A. Smith

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Hurricane Irene produced catastrophic rainfall and flooding in portions of the eastern United States from 27 to 29 August 2011. Like a number of tropical cyclones that have produced extreme flooding in the northeastern United States, Hurricane Irene was undergoing extratropical transition during the period of most intense rainfall. In this study the rainfall distribution of landfalling tropical cyclones is examined, principally through analyses of radar rainfall fields and high-resolution simulations using the Weather Research and Forecasting (WRF) Model. In addition to extratropical transition, the changing storm environment at landfall and orographic precipitation mechanisms can be important players in controlling the distribution of extreme rainfall. Rainfall distribution from landfalling tropical cyclones is examined from a Lagrangian perspective, focusing on times of landfall and extratropical transition, as well as interactions of the storm circulation with mountainous terrain. WRF simulations capture important features of rainfall distribution, including the pronounced change in rainfall distribution during extratropical transition. Synoptic-scale analyses show that a deep baroclinic zone developed and strengthened in the left-front quadrant of Irene, controlling rainfall distribution over the regions experiencing most severe flooding. Numerical experiments were performed with WRF to examine the role of mountainous terrain in altering rainfall distribution. Analyses of Hurricane Irene are placed in a larger context through analyses of Hurricane Hannah (2008) and Hurricane Sandy (2012).

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Yu Zhang and James A. Smith

Abstract

The hydrometeorological processes that control flash flooding are examined through analyses of space–time rainfall variability and flood response in the Milwaukee metropolitan region. The analyses focus on four flood events in the Menomonee River basin that occurred 21 June 1997, 2 July 1997, 6 August 1998, and 21 July 1999. The June 1997 and August 1998 flood events produced record flood peaks in the Menomonee River and its tributaries. Rainfall analyses, which are based on WSR-88D radar reflectivity observations and rainfall measurements from a dense network of rain gauges maintained by the city of Milwaukee, provide rainfall fields for each event at 1-km spatial resolution and 5-min timescale. The June 1997 and August 1998 storms exhibited striking contrasts in storm structure, evolution, and motion. Analyses of the structure and evolution of these storms are presented in conjunction with scaling analyses of the rainfall fields. The contrasting storm-scale properties of the June 1997 and August 1998 events resulted in sharp contrasts in extreme flood response between the two events. The regional flood response of the Menomonee River basin is examined in terms of space–time rainfall variability and heterogeneous land surface properties. Analyses are based on radar rainfall fields and 15-min discharge observations from stream gauging stations, with drainage area ranging from 47 to 319 km2 for the four flood events. Extreme flood response is examined in terms of flood peak magnitudes, peak response times, and event water balance. A distributed hydrologic model, which includes a Hortonian infiltration model and a network-based representation of hillslope and channel response, plays a central role in examining the regional flood response.

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Matthias Steiner and James A. Smith

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This study aims at assessing the potential of anomalous propagation conditions to occur, reviews past attempts to mitigate ground clutter contamination of radar data resulting from anomalous signal propagation, and presents a new algorithm for radar data quality control. Based on a 16-yr record of operational sounding data, the likelihood of atmospheric conditions to occur across the United States that potentially lead to anomalous propagation of radar signals is estimated. Anomalous signal propagation may lead to a significant contamination of radar data from ground echoes normally not seen by the radar, which could result in serious rainfall overestimates, if not recognized and treated appropriately. Many different approaches have been proposed to eliminate the problem of regular ground clutter close to the radar and temporary clutter resulting from anomalous signal propagation. None of the reported approaches, however, satisfactorily succeeds in the case of anomalous propagation ground returns embedded in precipitation echoes, a problem that remains a challenge today for radar data quality control. Taking strengths and weaknesses of past approaches into consideration, a new automated procedure has been developed that makes use of the three-dimensional reflectivity structure. In particular, the vertical extent of radar echoes, their spatial variability, and vertical gradient of intensity are evaluated by means of a decision tree. The new algorithm appears to work equally well in situations where anomalous propagation ground returns are either separated from or embedded within precipitation echoes. Moreover, sea clutter echoes are identified as not raining and successfully removed.

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Matthias Steiner and James A. Smith

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The relationships between radar reflectivity factor Z, rainfall rate R, and rainfall kinetic energy flux E were analyzed based on a multiyear raindrop spectra dataset recorded by a Joss–Waldvogel disdrometer in the Goodwin Creek research watershed in northern Mississippi. Particular attention was given to the climatological variability of the relationships and the uncertainty by which one rainfall parameter may be estimated from another. Substantial variability for the coefficients of a power-law relationship Y = A b X b between two rainfall parameters Y and X (where Y and X may stand for any paired combination of Z, R, and E) was found. The variability of the exponent b, however, was small enough to support approaches of climatologically fixed exponents to simplify radar rainfall estimation procedures. The multiplicative factor A b should typically be adjusted on a storm basis. The uncertainty of the estimation of one rainfall parameter from another, being a function of the difference in weighting of the drop size by the two parameters and the variability of raindrop spectra, was found to be approximately 50% for the Z–R relation, 40% for the E–R relation, and 25% for the Z–E relation. For extreme precipitation intensities (R ≥ 100 mm h−1), this drop spectra–based uncertainty reduced to approximately 20% for all three relationships. The results exhibited significant sensitivity to the choice of method applied to determine the relationship between two rainfall parameters. Appreciable sensitivity of the relationship between rainfall parameters (i.e., power-law coefficients and drop spectra–based uncertainty) to the number of raindrops registered per 1-min drop spectrum was also found.

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Matthias Steiner and James A. Smith

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Scale differences may introduce a bias when comparing, merging, or assimilating rainfall measurements because the dynamic range of values representing the underlying physical process strongly depends on the resolution of the data. The present study addresses this issue from the perspective of how well coarser-resolution radar-rainfall observations may be used for evaluation of hydrologic point processes occurring at the land surface, such as rainfall erosion, infiltration, ponding, and runoff. Conceptual and quantitative analyses reveal that scale differences may yield substantial biases. Even for perfect measurements, the overall bias is composed of two contributing factors: one related to a reduction of dynamic range of rain rates and the other related to a dependence of the relationship between observed radar reflectivity factor and retrieved rainfall rate on the scale of observation. The effects of scale differences are evaluated empirically from a perspective of averaging in time based on raindrop spectra observations. Averaging drop spectra over 5 min, on average over a large dataset, resulted in an underestimation of median and maximum rainfall rates of approximately 50% compared to the corresponding 1-min values. Overall, standard deviations of rain rates retrieved from 5-min-averaged radar reflectivity factors may easily be off a corresponding high-resolution (1 min) rainfall rate by a factor 2 or more. This magnitude is larger than the uncertainty resulting from limitations of the radar measurement precision. Scale-difference effects are thus important and should be considered when comparing, merging, or assimilating data from very different spatial and temporal scales. A similar challenge arises for downscaling schemes attempting to recover subgrid-scale features from coarse-resolution information.

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James A. Hansen and Leonard A. Smith

Abstract

Adaptive observation strategies in numerical weather prediction aim to improve forecasts by exploiting additional observations at locations that are themselves optimized with respect to the current state of the atmosphere. The role played by an inexact estimate of the current state of the atmosphere (i.e., error in the “analysis”) in restricting adaptive observation strategies is investigated; necessary conditions valid across a broad class of modeling strategies are identified for strategies based on linearized model dynamics to be productive. It is demonstrated that the assimilation scheme, or more precisely, the magnitude of the analysis error is crucial in limiting the applicability of dynamically based strategies. In short, strategies based on linearized dynamics require that analysis error is sufficiently small so that the model linearization about the analysis is relevant to linearized dynamics of the full system about the true system state. Inasmuch as the analysis error depends on the assimilation scheme, the level of observational error, the spatial distribution of observations, and model imperfection, so too will the preferred adaptive observation strategy. For analysis errors of sufficiently small magnitude, dynamically based selection schemes will outperform those based only upon uncertainty estimates;it is in this limit that singular vector-based adaptive observation strategies will be productive. A test to evaluate the relevance of this limit is demonstrated.

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Leonard A. Smith and James A. Hansen

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Uncertainty in the initial condition is one of the factors that limits the utility of single-model-run predictions of even deterministic nonlinear systems. In practice, an ensemble of initial conditions is often used to generate forecasts with the dual aims of 1) estimating the reliability of the forecasts and 2) estimating the probability distribution of the future state of the system. Current rank histogram ensemble verification techniques can only evaluate scalars drawn from ensembles and associated verification; a new method is presented that allows verification in high-dimensional spaces, including those of the verifications for 106 dimensional numerical weather prediction forecasts.

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