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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

Abstract

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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Leonard A. Smith
and
James A. Hansen

Abstract

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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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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A. Allen Bradley
and
James A. Smith

Abstract

Convective storms are commonplace in the southern plains of the United States. Occasionally, convective storms produce extreme rainfall accumulations, causing streams and rivers to flood. In this paper, we examine the hydrometeorological environment associated with these extreme rainstorms. Datasets used include hourly precipitation data from more than 200 stations, upper-air data, and daily weather maps.

The seasonal distribution of extreme rainstorms in the southern plains has pronounced peaks in late spring and early fall. Moisture availability and convective instability are higher than climatological averages during spring and fall extreme rainstorms, but nearer their averages during summer extreme rainstorms. Although high levels of moisture and convective instability are most common in the summer, the dynamic forcings that can initiate and focus convection are weak. It appears that late spring and early fall are the most likely times for extreme rainstorms because anomalously high levels of moisture and convective instability often encounter strong dynamic forcings.

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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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Mary Lynn Baeck
and
James A. Smith

Abstract

Storms that produce extreme flooding present a special challenge for the WSR-88D rainfall algorithms. The authors assess the utility of weather radar in the investigation of extreme rain-producing storms through both climatological analyses of long-term radar datasets and case studies of storm events. Climatological analyses are presented for long records of WSR-88D volume scan reflectivity observations, for hourly radar rainfall accumulations products (WSR-88D and WSR-57D), and for radar–rain gauge intercomparisons. These analyses provide a context for interpreting case study assessments of WSR-88D rainfall estimates. Case studies are presented of five storms that produced extreme floods in the United States. Events include 1) the orographically enhanced Rapidan storm in the Blue Ridge region of Virginia, which resulted in more than 600 mm of rain during a 6-h period on 27 June 1995; 2) the southeast Texas storms of 16–17 October 1994 in which approximately 750 mm of rain fell during a 6-h time period; 3) the Dallas, Texas, hailstorm of 5 May 1995, which resulted in 16 flash flood deaths during a period of several hours and property damage exceeding $1 billion; 4) the Chicago, Illinois, storms of 17 July 1996 during which the 24-h rainfall record for Illinois was shattered; and 5) Hurricane Fran, which resulted in unprecedented flooding in North Carolina and Virginia during September of 1996. For each event, analyses revolve around volume scan WSR-88D reflectivity observations. The climatological analysis presented, in conjunction with the case studies analyzed, illustrate the significance of 1) brightband contamination, 2) tilt selection, 3) hail, 4) radar calibration, and 5) ZR relationships for quantitative rainfall estimates by the WSR-88D.

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James A. Smith
and
Witold F. Krajewski

Abstract

In this paper procedures are developed for estimating the mean field bias of radar rainfall estimates. Mean field bias is modeled as a random process that varies not only from storm to storm but also over the course of a storm. State estimates of mean field bias are based on hourly raingage data and hourly accumulations of radar rainfall estimates. The procedures are developed for the precipitation processing systems used with products of the Next Generation Weather Radar (NEXRAD) system. To implement the state estimation procedures, parameters of the bias model must be specified. Likelihood-based procedures are developed for estimating these parameters. A simulation experiment is carried out to assess performance of the parameter estimation procedure. Convergence of parameter estimators is rapid for the cases studied, with data from approximately 25 storms providing parameter estimates of acceptable accuracy. The state estimation procedures are applied to radar and raingage data from the 27 May 1987 storm, which was centered near the NSSL radar in Norman, Oklahoma. The results highlight dependence of the state estimation problem on the parameter estimation problem.

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Matthias Steiner
and
James A. Smith

Abstract

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

Abstract

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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