Storm Splitting Research Articles

Intensification and Changing Spatial Extent of Heavy Rainfall in Urban Areas

AbstractUrban areas have been shown to impact rainfall by altering both its intensity and spatial structure at sub‐hourly and sub‐kilometer scales. However, there is currently no clear understanding of the precise pattern of change and the mechanisms that drive these changes. Since the hydrological response in urban areas is highly sensitive to such rainfall properties, understanding these changes is critical to improving our ability to assess urban flood risk. We use 7 years of high‐resolution weather radar data (4‐ or 5‐min and 1 km) to analyze changes in patterns of rainfall intensity, spatial structure, and storm evolution across eight urban areas within Europe and the United States. The use of the same methodology across the different cities enables a consistent comparison among them. We track convective rainfall events using a storm tracking algorithm and assess changes in rainfall properties in the upwind, center, and downwind regions of each city. We also investigate changes in the frequency of storm initiations, terminations, splitting, and merging. Our results show that urban areas act to intensify rainfall—mostly over them, but sometimes on their peripheries. Overall, larger cities tend to show the largest rainfall enhancements. Our findings highlight that rainfall spatial structure is altered over the urban core; usually resulting in more spatially concentrated rainfall. We also observe increased storm initiations over most cities and increased storm splitting over one. Given that demographic projections show that future urban population will increase, our results point toward an increased future flood risk in growing cities.

Synoptic, dynamical and microphysical properties for splitting and non-splitting hailstorms

Understanding storm splitting is of great importance for improving severe weather prediction and risk management. To further understand the mechanisms that cause hailstorm splitting, synoptic, dynamical and microphysical properties for a splitting hailstorm occurred on 19 June 2017 and a non-splitting hailstorm on 16 July 2014 in Beijing in the middle latitudes are investigated and compared based on synoptic maps, radar and sounding observations, as well as a three-dimensional cloud model with hail-bin microphysics. The results indicate that both hailstorms occurred under conditions with quite similar synoptic patterns, a tilting westerly trough at 500 hPa and a cold vertex at 700 hPa, and a clockwise-curved hodograph. However, the intensities of the westerly trough and low-level vertical wind shear were much stronger for the splitting hailstorm case than those for the non-splitting hailstorm case, so that the interactions between dynamical and microphysical processes in the splitting storm are also much stronger. It is found that for the splitting storm case the strong low-level vertical wind shear can cause large asymmetric pressure perturbation, pressure gradient forces and selective development in the storm and induce an obvious main updraft core splitting in the developing stage. The descending of high graupel/hail loading in the stable tropopause and lower stratospheric layer can excite strong downward propagating gravity waves (GWs) that induce a rapid storm splitting in the mature and decaying stages. In contrast, for the non-splitting storm, the relevant processes in the developing stage and the GWs excited by the descending of graupel/hail in the mature and decaying stages are too weak to cause an obvious splitting in the storm.

Storm splitting process and the associated mechanisms for a long-lived hailstorm

Storm splitting poses a great challenge in storm tracking and forecasting. However, most of previous studies have focused on the effect of warm rain microphysics on storm splitting, that of ice microphysics, especially hail microphysics on hailstorm splitting remain unknown. The storm splitting and associated mechanisms for a long-lived severe hailstorm occurred on 19 June 2017 in Beijing are investigated in this study based on radar observations and simulated results from a three-dimensional cloud model with hail-bin microphysics. The results show that the hailstorm experienced twice splitting. Both right-moving and left-moving cells strengthened in the first splitting, while only the right-moving cell strengthened in the secondary splitting. It is found that the clockwise-curved hodograph environment initially creates asymmetric negative pressure perturbations at the low levels. With the development of the storm, the negative pressure perturbations are strengthened, lifted, and evolved as vertically clockwise- or anticlockwise-rotating low-pressure centers, which significantly enhance both upward and outward pressure gradient forces at the levels where the low-pressure centers are located, and selectively induce the updraft development on the flanks of the storm, resulting in the low-level upward-curved updraft splitting structure. In the mature and decaying stage of the storm, strong downward propagating gravity waves excited by high graupel/hail loading through buoyancy oscillations are found to have a critical role in the subsequent rapid updraft splitting prior to the graupel/hail-induced downdraft. Both the gravity waves and graupel/hail-induced downdraft have important roles in the hailstorm splitting rather than rain-induced downdraft as proposed in previous studies.

The Evolution of Hail Production in Simulated Supercell Storms

AbstractHailstorms pose a significant socioeconomic risk, necessitating detailed assessments of how the hail threat changes throughout their lifetimes. Hail production involves the favorable juxtaposition of ingredients, but how storm evolution affects these ingredients is unknown, limiting understanding of how hail production evolves. Unfortunately, neither surface hail reports nor radar-based swath estimates have adequate resolution or details needed to assess evolving hail production. Instead, we use a novel approach of coupling a detailed hail trajectory model to idealized convective storm simulations to better understand storm evolution’s influence on hail production. Hail production varies substantially throughout storms’ mature phases: maximum sizes vary by a factor of two, and the concentration of severe hail more than fivefold during 45-60-min periods. This variability arises from changes in updraft properties, which come from (i) changes in low-level convergence, and (ii) internal storm dynamics, including anticyclonic vortex shedding/storm splitting, and the response of the updraft’s airflow and supercooled liquid water content to these events. Hodograph shape strongly affects such behaviors. Straighter hodographs lead to more prolific hail production through wider updrafts and weaker mesocyclones, and a periodicity in hail size metrics associated with anticyclonic vortex shedding and/or storm splitting. In contrast, a curved hodograph (favorable for tornadoes) led to a storm with a stronger but more compact updraft, which occasionally produced giant (10-cm) hail, but that was a less-prolific severe hail producer overall. Unless storms are adequately sampled throughout their lifecycles, snapshots from ground reports will insufficiently resolve the true nature of hail production.

Understanding the dependence of storm splitting on numerical models: Comparing UM and WRF

AbstractThis article performs a systematic study to understand the dependence of the splitting of an initially axisymmetric storm on the various components of the Unified Model (UM) and Weather Research and Forecasting model (WRF). The models are adapted to keep their differences at a minimum. Results at km‐scale grid resolution show that the models differ significantly even under a controlled environment with no surface and radiative forcing. The initial storm in UM splits into two within the first hour. WRF also produces two separate updraughts, but it does not split entirely because of a secondary downdraught that falls just ahead of the original updraught. The cold pool from this downdraught converges with the oncoming winds at lower levels to generate a ring of updraughts connecting the two. UM also shows a similar secondary downdraught, but it is relatively weak. Experiments with the successive reduction in complexity of the microphysics scheme show that the models start to differ with the inclusion of rain processes. Sensitivity experiments with the magnitude of turbulent mixing length do not impact this aspect of model behaviour. Resolution sensitivity experiments show that the storm does not split in UM for a horizontal resolution of O(100 m), whereas WRF behaves consistently across all the resolutions. Through further analyses, we argue that the formal accuracy of the model dynamical core has no control in deciding whether the initial storm will undergo a split or not.

Solving the storm split-merge problem—A combined storm identification, tracking algorithm

Many storm identification and tracking algorithms based on radar data have been designed and widely used in weather forecasting. However, most of these algorithms have concentrated on storm cells. As a convective storm splits (merges), many storm cells will be generated (disappeared) within close proximity to each other resulting in errors in storm tracking and analysis of storm evolution. To resolve this, a new combined storm identification tracking algorithm (referred as CSIT) is devised after detailed testing of various existing convective storm identification and tracking methods. The connected neighborhoods labeling and a lower radar reflectivity threshold(30dBz) is used in CSIT, which ensures that newly formed storms can be detected. Moreover, with a lower reflectivity threshold, merger of convective cells is regarded as one convective storm, thus reducing the occurrence of storm split-merge. In terms of storm tracking, five tracking algorithms with different storm motion estimation, search radius calculation, and matching principles are designed and quantitatively evaluated using the contingency table approach and objective method. The best-performing algorithm that considers different situations of storm splitting and merging is selected to devise CSIT and the optimal thresholds for two parameters in the algorithm (i.e. maximum matching distance and search radius adjust factor) is determined through a series of sensitivity tests and objective evaluation using six years of warm season (JJA) radar data from 2012 to 2017. The devised storm identification and tracking algorithm has the potential to be applied to other data, such as cloud top brightness temperature from satellites, lightning frequency and other model output variables. The objective evaluation method does not rely on manual tracking results and thus can be used to improve and adapt automatic tracking algorithms for different situations (different storm types, regions etc).

Tropical convection: the effects of ambient vertical and horizontal vorticity

AbstractWe present a series of idealized numerical model experiments to investigate aspects of deep convection in tropical depressions, including the effects of boundary‐layer wind structure on storm structure, especially on vertical vorticity production and updraught splitting, and the combined effects of horizontal and vertical shear on vertical vorticity production, with and without background rotation.In warm‐cored disturbances such as tropical depressions, the vertical shear and horizontal vorticity change sign at some level near the top of the boundary layer so that, unlike in the typical middle‐latitude ‘supercell’ storm, the tilting of horizontal vorticity by a convective updraught leads not only to dipole patterns of vertical vorticity, but to a reversal also in sign of the updraught rotation with height. This finding has implications for understanding the merger of convectively induced vorticity anomalies during vortex evolution. Ambient cyclonic horizontal shear and/or cyclonic vertical vorticity favour amplification of the cyclonically rotating gyre of the dipole.Consistent with an earlier study, storm splitting occurs in environments with pure horizontal shear as well as pure vertical shear, but the morphology of splitting is different. In both situations, splitting is found to require a relatively unstable sounding and relatively strong wind shear.

Comments on “A Comparison of Tropical and Midlatitude Thunderstorm Evolution in Response to Wind Shear”

In a recent paper, Wissmeier and Goler (2009, hereafter WG09) presented the results of a numerical experiment meant to examine the different potential for convective storm splitting in the tropics versus the midlatitudes. WG09 found that simulated storms in tropical environments were less likely to undergo classical supercellular splitting because the storms’ outflow quickly spread out and cut the storms off from their source of inflow before the splitting process could occur. The main conclusion reached by WG09 is that higher vertical wind shear values are necessary for storm splitting to occur in the tropics than in the midlatitudes because the comparatively large vertical wind shear weakens and delays the convective outflow produced by storms. These are thought-provoking results and conclusions, but they hinge on some questionable assumptions and choices in the experimental design. The purpose of the present comment is to document and discuss several aspects of the study that bias WG09’s results and diminish the generality of their conclusions.

Simulation of a supercell storm in clean and dirty atmosphere using weather research and forecast model with spectral bin microphysics

The development of supercell storms was simulated using a 2‐km‐resolution weather research and forecast (WRF) model with spectral (bin) microphysics (WRF‐SBM) and a recent version of the Thompson bulk‐parameterization scheme. The simulations were performed in clean, semipolluted, and dirty air under two values of relative humidity, conditionally referred to as low and high humidity. Both SBM and the Thompson scheme simulated the development of supercell storm with storm splitting. Both SBM and the Thompson scheme demonstrated that an increase in relative humidity by ∼10% invigorates convection and increases precipitation by factor of 2, i.e., to much larger extent than can be achieved by variations of the aerosol concentration. At the same time the storms simulated by the schemes are quite different. The maximum updrafts in the Thompson scheme are about 65 m/s, and the left‐moving storm prevails. The SBM predicts 35 m/s maximum updrafts, and the right‐moving storm prevails in the SBM simulations. While the bulk scheme predicts decrease in precipitation in clean air at both low and high humidity, the SBM indicates decrease precipitation in polluted air under low humidity and increase in precipitation under high humidity. The SBM scheme shows a substantial effect of aerosols on spatial distribution of precipitation, especially in the low‐humidity case. The sensitivity of the Thompson scheme to aerosols turns out to be much less than that of SBM. The difference in the results (vertical velocities, microphysical cloud structure, and precipitation) obtained by different schemes is much larger than the changes caused by variation of the aerosol concentration within each scheme. However, the average amount of precipitation in the Thompson scheme in each simulation was about twice that of the corresponding SBM simulation. The possible reasons for such difference are discussed. A scheme for classifying aerosol effects on precipitation from clouds and cloud systems is also discussed.

A Comparison of Tropical and Midlatitude Thunderstorm Evolution in Response to Wind Shear

Abstract The influence of vertical wind shear on storm development within a tropical environment is studied with the aid of two numerical models and compared with that in simulations of midlatitude storms. The simulations show that larger wind shears are required in a tropical environment than in a midlatitude environment for a storm of given updraft velocity to split. This finding is supported by the experience of forecasters at the Australian Bureau of Meteorology Regional Forecasting Centre in Darwin that the operational storm forecasting tools developed for midlatitude storms overforecast supercells within the tropics. That tropical storms require higher shears to split can be attributed either to the larger gust front speed or to the earlier gust front occurrence compared to those in the midlatitudes. A fast gust front cuts off the storm from the warm moist inflow and the updraft has little or no time to split. In the cases where the midtropospheric relative humidity is larger in the tropics or comparable with that in the midlatitudes, the total liquid water and ice content within the deeper tropical storms is larger than in the midlatitude storms, causing a stronger downdraft. In other words, the main contribution to the negative buoyancy of the downdraft is the water loading rather than the evaporative cooling. When a tropical storm is simulated in an environment with smaller midtropospheric relative humidity than in the midlatitudes, the amount of liquid water and ice within the storm is comparable to that within the midlatitude storm. Intense evaporation within the tropical storm then leads to a stronger negative buoyancy than in the midlatitude storm, causing a stronger downdraft and thus an earlier or a faster-spreading gust front. At higher shears in the tropics, entrainment reduces the storm depth and thus water loading, resulting in a delayed gust front initiation and/or reduction of the gust front speed, which then allows storm splitting to occur.

Storm Identification and Tracking Algorithm for Modeling of Rainfall Fields Using 1-h NEXRAD Rainfall Data in Texas

A method to identify and track rainfall structures using 1-h accumulated NEXt generation RADar (NEXRAD) rainfall data is presented and used to analyze the dynamics of storm features over an area in Texas. Storm features are identified from a Gaussian mixture model using the expectation maximization algorithm. The method assigns NEXRAD pixels to storm features, simultaneously producing a smooth fitted function to the rainfall intensity distribution. Once the storm features are identified, they are tracked using inverse cost functions and using the fact that continuous features overlap each other from frame to frame in the accumulated data. The inverse cost functions also account for storm feature merging, splitting, birth, and death. Application of this storm identification and tracking algorithm for Brazos County (1,500 km2 ) in southeastern Texas distinguishes several characteristics of the storm feature dynamics. From September through April, storm features are predominantly of a frontal nature, with st...

The impact of the choice of the entire drop size distribution function on Cumulonimbus characteristics

The study compares two different ways to represent the size distributions of cloud droplets and raindrops in bulk microphysical schemes in the scope of cloud-resolving mesoscale modeling of cumulonimbus clouds. A unified Khrgian-Mazin size distribution for the entire liquid water is systematically compared to a widely applied approach using a Marshall-Palmer size distribution for rain and a fitted monodisperse distribution for cloud droplets. The impact of the distribution function on cloud microphysics, precipitation characteristics, cloud appearance and dynamics of one simulated cumulonimbus case is investigated. The agreement of the model values with typical observed cloud characteristics is discussed. The results of our study reveal that there are considerable differences between the two approaches, both with respect to the microphysical production terms and with respect to the cloud appearance while the differences are less pronounced in cloud dynamics. An important result is that the Khrgian-Mazin size distribution leads to more cumulative rain compared to the one composed of a monodisperse and a Marshall-Palmer distribution. There is observational evidence that a storm splitting, hail field characteristics and cumulative total precipitations are simulated more accurately by the Khrgian-Mazin distribution function.

The influence of merging and individual storm splitting on mesoscale convective system formation

The aim of present study is to simulate the formation of mesoscale convective system (MCS) through splitting and merging of two single convective storms that is characteristic for mountainous regions by help of cloud-resolving mesoscale model. Features of simulated storms are as follows: they are aligned along leading flow at different stages of life cycle under sharp-sheared condition. The storm in upwind direction (denoted as primary) is initialized earlier as it is a common feature in reality. Formation of MCS passes by several phases as follows: - Primary storm moves faster along leading flow direction than secondary one that is initialized later. Both storms split into right- and left-moving storms in such a manner that primary storm splits at first; - Boundaries of cold air outflows associated by single storms collide. At their intersection air is forced lifted upward, possibly forming a new convection; - As a result the merging process produces the MCS in which the single storms are distributed along curved line. Above results encourage modelers to use more frequently the cloud-resolving models in simulations of great variety of MCS.

Photographic Documentation and Environmental Analysis of an Intense, Anticyclonic Supercell on the Colorado Plains

Abstract Anticyclonic left-moving supercells are observed each year in the United States, emanating both discretely and from storm splitting processes. Such thunderstorms often produce severe hail and wind gusts and, on rare occasion, tornadoes. The body of documentary literature on this subset of supercells is relatively scant compared with right-moving storms, and this is especially true regarding visual characteristics and conceptual models. Here a characteristic example of the anticyclonic supercell is presented using an intense and well-defined specimen that passed over Aroya, Colorado, on 15 June 2002. Photographic and radar documentation is provided in original and mirrored forms, for aid in conceptualizing the left-moving supercell and associated structures and processes. A summary overview is presented of the environment, development, evolution, and effects of this remotely located but noteworthy event.

Observations of a Severe Left Moving Thunderstorm

Abstract Observations have shown that right moving thunderstorms are favored in environments characterized by clockwise-turning hodographs. There are, however, a few observational and numerical studies of long-lived, left moving storms within environments characterized by clockwise-turning hodographs. For example, a documented left mover that occurred on 26 May 1992, near Coldspring, Texas, with a mesoanticyclone and hail spike (also called a three-body scattering signature) produced severe weather. Although a few cases have been documented, left moving thunderstorms have received less study than right moving cells. The long-lived, severe thunderstorm of 17 May 1996 is presented to improve documentation of left moving thunderstorms. The storm occurred over eastern Nebraska and will be referred to as the York County storm. This left mover resulted from storm splitting and moved to the west of a surface cold front. The relatively isolated storm subsequently split approximately 1 h later, yielding a new righ...

The Structure and Evolution of a Numerically Simulated High-Precipitation Supercell Thunderstorm

The structure and evolution of a high-precipitation (HP) supercell thunderstorm is investigated using a threedimensional, nonhydrostatic, cloud-scale numerical model (TASS). The model is initialized with a sounding taken from a mesoscale modeling study of the environment that produced the 28 November 1988 Raleigh tornadic thunderstorm. TASS produces a long-lived convective system that compares favorably with the observed Raleigh tornadic thunderstorm. The simulated storm evolves from a multicell-type storm to a multiple-updraft supercell storm. The storm complex resembles a hybrid multicell-supercell thunderstorm and is consistent with the conceptual model of cool season strong dynamic HP supercells that are characterized by shallow mesocyclones. The origin of rotation in this type of storm is often in the lowest levels. Interactions between various cells in the simulated convective system are responsible for the transition to a supercellular structure. An intense low-level updraft core forms on the southwest flank of the simulated storm and moves over a region that is rich in vertical vorticity. The stretching of this preexisting vertical vorticity in the storm’s lowest levels is the most important vertical vorticity production mechanism during the initial stages of the main updraft’s development. Interactions with an extensive cold pool created by the storm complex are also important in producing vertical vorticity as the main updraft grows. Overall, the development of vorticity associated with the main updraft appears similar to nonsupercellular tornadic storms. However, classic supercell signatures are seen early in the simulation associated with other updrafts (e.g., formation of vortex couplet due to tilting of ambient horizontal vorticity, storm splitting, etc.) and are deemed important. In the storm’s supercell stage, rotation is sustained in the lowest levels of the storm despite large amounts of precipitation located near and within the main mesocyclone. Pulsating downdrafts periodically invigorate the storm and the gust front never occludes, thus allowing the main updraft to persist for a prolonged period of time. The storm’s intensity is also maintained by frequent updraft mergers.

A Supercell Thunderstorm with Hook Echo in the San Joaquin Valley, California

This study documents a damaging supercell thunderstorm that occurred in California's San Joaquin Valley on 5 March 1994. The storm formed in a “cold sector” environment similar to that documented for several other recent Sacramento Valley severe thunderstorm events. Analyses of hourly subsynoptic surface and radar data suggested that two thunderstorms with divergent paths developed from an initial echo that had formed just east of the San Francisco Bay region. The southern storm became severe as it ingested warmer, moister boundary layer air in the south-central San Joaquin Valley. A well-developed hook echo with a 63-dBZ core was observed by a privately owned 5-cm radar as the storm passed through the Fresno area. Buoyancy parameters and hodograph characteristics were obtained both for estimated conditions for Fresno [on the basis of a modified morning Oakland (OAK) sounding] and for the actual storm environment (on the basis of a radiosonde launched from Lemoore Naval Air Station at about the time of the storm's passage through the Fresno area). Both the estimated and actual hodographs essentially were straight and suggested storm splitting. Although the actual CAPE was similar to that which was estimated, the observed magnitude of the low-level shear was considerably greater than the estimate. The bulk Richardson number for the observed conditions (BRN = 21) was well within the range observed for supercells elsewhere in the country. Both the estimated and observed 0–3-km storm-relative helicities were in the range observed for mesocyclone development. Forecasters familiar with the relation of buoyancy, shear, and hodograph characteristics to the development of severe storms could have made useful inferences about the potential for severe weather in the Central Valley on the basis of simple modification of the morning OAK sounding.

TOGA-COARE集中観測期間中のパプアニューギニア、マヌス島における雲群の構造に関するドップラーレーダー観測

Three distinct mesoscale convective systems (MCSs), composing a tropical cloud cluster, observed on January 18-19, 1993 were investigated. This event was observed by two Doppler radars on Manus Island (2°S, 147°E), Papua New Guinea, during the TOGA-COARE TOP. The cloud cluster was formed within the radar range, and extended to a diameter of about 200km. The environmental wind was weak, but a strong vertical shear existed at the middle level (3-8km).The first characteristic MCS moved faster than the environmental wind, and thus is referred to as a fast-moving convective system (FMCS). The orientation of this FMCS was nearly perpendicular to the direction of the dominant vertical shear. Behind the convective cell of the FMCS, an anvil echo extended to upper levels. The front inflow had two branching sub-flows in front of the convective cell with a strong downdraft. The lower level outflow from the downdraft also branched out to southward and northward flows. The branching inflow and outflow were associated with symmetrically-arranged strong convergence regions. These features were similar to a structure produced by the storm splitting, and is recognized as a squall line system with a three-dimensional structure. The second MCS was composed of individual convective cells, moving at a slower speed than the first system. This slow-moving convective system (SMCS) was associated with the south-easterly inflow at lower levels, and extended in a line parallel to the vertical shear direction from north to south. The last system was a stratiform-looking echo system marked by an obvious bright band at the melting level. This system brought more precipitation than the other MCSs. In the echo system, a vortex with a diameter of 20km was found at the middle layer (4-6km). In the middle layer, some vertical circulations were also found, and vertical circulations with a maximum velocity of 5ms-1 were found in the upper layer (>6km). These circulations seemed to cause the heavy precipitation.

Positive Ground Flashes Produced by Low-Precipitation Thunderstorms in Oklahoma on 26 April 1984

Abstract A group of thunderstorms developed in western Oklahoma during the afternoon of 26 April 1984. Two of these storms initially exhibited characteristics of low-precipitation (LP) thunderstorms. Lightning ground flashes produced by these storms were mostly positive. These storms split, with one right-moving component evolving into a tornadic supercell. Ground flashes produced by the supercell, however, were predominantly negative. The highest rate of positive ground flashes (1.5 min−1) occurred during LP storm splitting and merging, when about 84% of ground flashes were positive. The maximum total ground-strike rate was 3.4 min−1and occurred during the tornadic supercell phase and when all but one of 136 ground flashes were negative. Analysis of lightning ground-strike and radar reflectivity data reveals a concentration of positive ground flashes in areas of maximum reflectivity within the LP storms; furthermore, the concentration of positive flashes appeared during storm split. After storm splitting...

A Numerical Study of Storm Splitting that Leads to Long-Lived Storms

Abstract We have used a three-dimensional cloud model to investigate the splitting of an initially isolated storm in a one-directional east-west shear. The simulated evolution of storm splitting in some cases follows all four stages suggested by Achtemeier (1969) after analysis of radar data, including the development of two self-sustaining storm. One of these storms moves to the right of the mean wind vector and the other to the left. In the right-moving storm the updraft rotates cyclonically and the downdraft anticyclonically, forming a vortex pair, as depicted in the schematic model of Fankhauser (1971). The vortex pair structure is also similar to that observed with Doppler radar and analyzed by Ray (1976). The downdraft-induced gust front interacts with the low-level environmental wind to produce the convergence necessary to sustain the storm. This convergence extends to the south and west of the storm, and if enough low-level moisture is available a flanking line develops. The distribution of rainwa...