Rain Fields Research Articles

Tropical cyclone rainfall variability in coastal North Carolina derived from longleaf pine (Pinus palustris Mill.): AD 1771–2014

Records of tropical cyclone precipitation (TCP) in the USA typically begin in the mid-20th century and are insufficiently long to fully understand the natural range of TCP variability. In southeastern North Carolina, USA, we use longleaf pine (Pinus palustris Mill.) latewood chronologies from two study sites and a combined chronology as a proxy for TCP during AD 1771–2014 as the latewood growth period of June 1st–October 15th coincides with 93 % of annual TCP. We correlate latewood radial growth with TCP based on days when tropical cyclones tracked within a 223 km rain field, with the results (r = 0.71, p < 0.01) supporting the viability of this species to chronicle interannual variations in TCP for multiple centuries. Using annual latewood data during 1953–2014, we reconstruct TCP back to 1836 for the combined chronology. We creat three radial-growth groups (low, near-average, high) and find that corresponding TCP values are significantly different (p < 0.05) between groups. Low radial-growth values are a strong marker (91 % occurrence) of below-average TCP years and high radial-growth years are (73 % occurrence) also good indicators of above-average TCP years. Examination of the temporal occurrence of below- and above-average TCP years into the late 18th century indicate that a predominance of below-average TCP years occur from 1815 to 1876 that are unmatched in the historic record. The high fidelity between longleaf pine latewood growth and TCP coupled with the geographic distribution of the species throughout the southeastern USA where tropical cyclones are common suggest the utility of this species to help better understand the temporal variability of precipitation delivered via tropical cyclones.

Unfreezing Taylor’s Hypothesis for Precipitation

Abstract Since the seminal work of Zawadzki in the seventies, the so-called Taylor’s “frozen” hypothesis has been regularly used to study the statistical properties of rainfall patterns. This hypothesis yields a drastic simplification in terms of symmetry of the space–time structure—the large-scale advection velocity is the conversion factor used to link the time and space autocorrelation functions (ACFs) of the small-scale variability. This study revisits the frozen hypothesis with a geostatistical model. Using analytical developments and numerical simulations tuned on available case studies from the literature, the role of large- and small-scale rainfall kinematics on the properties of the space–time ACF and associated fluctuations is investigated. In particular, the merits and limits of the ACF signature classically used to test the frozen hypothesis are examined. The conclusion is twofold. Taylor’s hypothesis, understood as the quest for a space–time symmetry in rain field variability, remains important in hydrometeorology four decades after the pioneering work of Zawadzki. The frozen hypothesis, introduced for simplification purposes, appears difficult to check and too constraining. The methods proposed to check the hypothesis rely too directly on the use of the advection velocity as a space–time conversion factor instead of contemplating the ACF signature more globally. The model proposed that using two characteristic velocities instead of one appears more flexible to fit the ACF behaviors presented in the literature. This remains to be checked over a long-term high-resolution dataset.

A COMPARISON OF METHODS FOR THE APPROXIMATION AND ANALYSIS OF RAINFALL FIELDS IN ENVIRONMENTAL APPLICATIONS

Abstract. Digital environmental data are becoming commonplace and the amount of information they provide is huge, yet complex to process, due to the size, variety, and dynamic nature of the data captured by the available sensing devices. Making use of the data largely relies on the availability of efficient methods to extract meaningful information, and requires to process the environmental events at the speed data are acquired. This paper focuses on the evaluation of methods to approximate observed rain data, in real conditions of sparsity of the observations. The novelty stands in the selection of a particularly complex area, Liguria region, located in the north-west of Italy, where the orography and the closeness to the sea causes complex hydro-meteorological events. Approximation results are compared on a fine granularity in terms of cumulated rain interval used, gathered from two different rain gauge networks, with different characteristics and spatial distribution. Moreover, beside traditional cross-validation comparison, we provide a qualitative comparison based on the analysis of the number and location of maxima of the approximation. Rain maxima are indeed crucial features of rain fields needed for storm tracking, to support effective monitoring of meteorological events.

Prediction of annual joint rain fade on EHF networks by weighted rain field selection

AbstractWe present a computationally efficient method to predict joint rain fade on arbitrary networks of microwave links. Methods based on synthetic rain fields composed of a superposition of rain cells have been shown to produce useful predictions of joint fade, with low computational overhead. Other methods using rain fields derived from radar systems have much higher computational overhead but provide better predictions. The proposed method combines the best features of both methods by using a small number of measured rain fields to produce annual fade predictions. Rain fields are grouped into heavy rain and light rain groups by maximum rain rate. A small selection of rain fields from each group are downscaled and fade predictions generated by pseudointegration of specific attenuation. This paper presents a method to optimize the weights used to combine the heavy rain and light rain fade predictions to yield an estimate of the average annual distribution. The algorithm presented yields estimates of average annual fade distributions with an error small compared to year‐to‐year variation, using only 0.2% of the annual data set of rain fields.

Assessment of satellite rainfall products over the Andean plateau

Nine satellite rainfall estimations (SREs) were evaluated for the first time over the South American Andean plateau watershed by comparison with rain gauge data acquired between 2005 and 2007. The comparisons were carried out at the annual, monthly and daily time steps. All SREs reproduce the salient pattern of the annual rain field, with a marked north–south gradient and a lighter east–west gradient. However, the intensity of the gradient differs among SREs: it is well marked in the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis 3B42 (TMPA-3B42), Precipitation Estimation from remotely Sensed Information using Artificial Neural Networks (PERSIANN) and Global Satellite Mapping of Precipitation (GSMaP) products, and it is smoothed out in the Climate prediction center MORPHing (CMORPH) products. Another interesting difference among products is the contrast in rainfall amounts between the water surfaces (Lake Titicaca) and the surrounding land. Some products (TMPA-3B42, PERSIANN and GSMaP) show a contradictory rainfall deficit over Lake Titicaca, which may be due to the emissivity contrast between the lake and the surrounding lands and warm rain cloud processes. An analysis differentiating coastal Lake Titicaca from inland pixels confirmed this trend. The raw or Real Time (RT) products have strong biases over the study region. These biases are strongly positive for PERSIANN (above 90%), moderately positive for TMPA-3B42 (28%), strongly negative for CMORPH (−42%) and moderately negative for GSMaP (−18%). The biases are associated with a deformation of the rain rate frequency distribution: GSMaP underestimates the proportion of rainfall events for all rain rates; CMORPH overestimates the proportion of rain rates below 2mm day−1; and the other products tend to overestimate the proportion of moderate to high rain rates. These biases are greatly reduced by the gauge adjustment in the TMPA-3B42, PERSIANN and CMORPH products, whereas a negative bias becomes positive for GSMaP. TMPA-3B42 Adjusted (Adj) version 7 demonstrates the best overall agreement with gauges in terms of correlation, rain rate distribution and bias. However, PERSIANN-Adj's bias in the southern part of the domain is very low.

Correcting temporal sampling error in radar-rainfall: Effect of advection parameters and rain storm characteristics on the correction accuracy

Summary This study offers a method to correct for the radar temporal sampling error when determining radar-rainfall accumulations. The authors evaluate the correction effect with respect to multiple factors associated with storm advection, rainfall characteristics, and different rainfall accumulation time scales. The advection method presented in this study uses linear interpolation of static rain storm locations observed at two intermittent radar sampling times to correct for the missed rainfall accumulations. The advection correction is applied to the high space (0.5 km) and time (5-min) resolution radar-rainfall products provided by the Iowa Flood Center. We use the ground reference data from a high quality and high density rain gauge network distributed over the Turkey River basin in Iowa to evaluate the advection corrected rain fields. We base our evaluation on six rain events and examine the correction performance/improvement with respect to the advection discretization, spatial grid aggregation, rainfall basin coverage, and conditional average rainfall intensity. The results show that the 1-min advection discretization is sufficient to represent the observed distribution of storm velocities for the presented cases. Grid aggregation that is motivated by the need to expedite the computation may induce errors in estimating advection vectors. The authors found that while the advection correction tends to enhance the QPE accuracy for intense rain storms over small or isolated areas, it has little impact on the improvement of light rain estimation.

Analysis of the French insurance market exposure to floods: a stochastic model combining river overflow and surface runoff

Abstract. The analysis of flood exposure at a national scale for the French insurance market must combine the generation of a probabilistic event set of all possible (but which have not yet occurred) flood situations with hazard and damage modeling. In this study, hazard and damage models are calibrated on a 1995–2010 historical event set, both for hazard results (river flow, flooded areas) and loss estimations. Thus, uncertainties in the deterministic estimation of a single event loss are known before simulating a probabilistic event set. To take into account at least 90 % of the insured flood losses, the probabilistic event set must combine the river overflow (small and large catchments) with the surface runoff, due to heavy rainfall, on the slopes of the watershed. Indeed, internal studies of the CCR (Caisse Centrale de Reassurance) claim database have shown that approximately 45 % of the insured flood losses are located inside the floodplains and 45 % outside. Another 10 % is due to sea surge floods and groundwater rise. In this approach, two independent probabilistic methods are combined to create a single flood loss distribution: a generation of fictive river flows based on the historical records of the river gauge network and a generation of fictive rain fields on small catchments, calibrated on the 1958–2010 Météo-France rain database SAFRAN. All the events in the probabilistic event sets are simulated with the deterministic model. This hazard and damage distribution is used to simulate the flood losses at the national scale for an insurance company (Macif) and to generate flood areas associated with hazard return periods. The flood maps concern river overflow and surface water runoff. Validation of these maps is conducted by comparison with the address located claim data on a small catchment (downstream Argens).

Interpolation of daily rainfall networks using simulated radar fields for realistic hydrological modelling of spatial rain field ensembles

Given a record of daily rainfall over a network of gauges, this paper describes a method of linking the Gauge Wetness Ratio (GWR) on a given day to the joint distribution of the parameters of the anisotropic correlogram defining the spatial statistics of simulated radar-rainfall fields. We generate a large number of Gaussian random fields by sampling from the correlogram parameters conditioned on the GWR and then conditionally merge these fields to the gauge observations transformed into the Gaussian domain. Availability of such a tool allows better spatially distributed hydrological modelling, because good quality ensemble spatial information is required for such work, as it yields uncertainty of the fields so generated. To achieve these ends, correlograms of many Gaussianised daily accumulations of radar images were developed using the Fast Fourier Transform to generate their sample power spectra. Empirical correlograms were fitted using a 2D exponential distribution to yield the 3 key parameters of the correlogram: the range, the anisotropy ratio and the direction of the major axis. It was found that the range follows a Gamma distribution while the anisotropy parameters follow a Loglogistic one; a t5 copula was adequate to capture the bivariate negative dependence structure between the range and ratio. The Radar Wetted Area Ratio (RWAR) drives the parameters of the correlogram, and its link with GWR is modelled by a transition probability matrix. We take each of the generated Gaussian random fields and conditionally merge it with Gaussianised rainfall values at the gauge locations using Ordinary Kriging. The method produces realistic simulated radar images, on a grid chosen to suit the data, which match the gauge observations at their locations. Ensemble simulations of 1000 samples were used to derive the median and the inter-quartile range of the fields; these were found to narrow near the control gauge locations, as expected, emphasising the value of high density gauge networks. Ongoing research is looking towards integration of the presented methodology with a stochastic daily rainfall generator for useful spatial rainfall simulation over catchments with gauged records.

Impacts of Satellite-Based Rainfall Products on Predicting Spatial Patterns of Rift Valley Fever Vectors*

Abstract Spatiotemporal rainfall variability is a key parameter controlling the dynamics of mosquitoes/vector-borne diseases such as malaria, Rift Valley fever (RVF), or dengue. Impacts from rainfall heterogeneity at small scales (i.e., 1–10 km) on the risk of epidemics (i.e., host bite rate or number of bites per host and per night) must be thoroughly evaluated. A model with hydrological and entomological components for risk prediction of the RVF zoonosis is proposed. The model predicts the production of two mosquito species within a 45 km × 45 km area in the Ferlo region, Senegal. The three necessary steps include 1) best rainfall estimation on a small scale, 2) adequate forcing of a simple hydrological model leading to pond dynamics (ponds are the primary larvae breeding grounds), and 3) best estimate of mosquito life cycles obtained from the coupled entomological model. The sensitivity of the model to the spatiotemporal heterogeneity of rainfall is first tested using high-resolution rain fields from a weather radar. The need for high-resolution rain data is thus demonstrated. Several high-resolution satellite rainfall products are evaluated in the region of interest using a dense rain gauge network. Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis 3B42, version 6 (TMPA-3B42V6), and 3B42 in real time (TMPA-3B42RT); Global Satellite Mapping of Precipitation (GSMaP) in near–real time (GSMaP-NRT) and Moving Vector with Kalman version (GSMaP-MVK); African Rainfall Estimation Algorithm, version 2.0 (RFE 2.0); Climate Prediction Center (CPC) morphing technique (CMORPH); and Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) are tested and finally corrected using a probability matching method. The corrected products are then used as forcing to the coupled model over the 2003–10 period. The predicted number and size of ponds and their dynamics are greatly improved compared to the model forced only by a single gauge. A more realistic spatiotemporal distribution of the host bite rate of the RVF vectors is thus expected.

Conditions associated with large rain-field areas for tropical cyclones landfalling over Florida

To adequately warn the public about the potential for heavy rainfall, it is important to understand the conditions associated with large rain fields as tropical cyclones (TCs) move over land. This study examines rain-field areas during 29 landfalls over Florida utilizing data from the Tropical Rainfall Measuring Mission’s 3B42 product. A GIS was used to calculate the areas of regions delineated by 5 mm h−1 rain rates occurring within 48 h pre- or post-landfall. Thirteen conditions were evaluated, including intensity, motion, vertical wind shear, cause of demise, month, and time of day. After dividing observations into groups for each condition, Mann–Whitney U and Kruskal–Wallis tests determined that statistically significant differences existed among the groups for 11 conditions. The largest rain fields belonged to TCs that occurred in October or November, followed by those that were hurricanes and/or were intensifying at landfall. TCs nearing the end of an extratropical transition as well as those observed at 1100 Eastern Daylight Time also had relatively large areas of moderate-to-high rain rates. TCs meeting these conditions should be monitored closely as they move towards and over Florida due to their potential for widespread moderate-to-heavy rainfall, which may begin prior to the arrival of the fastest winds.

Stochastic convective rain‐field simulation using a high‐resolution synoptically conditioned weather generator (HiReS‐WG)

AbstractA new stochastic high‐resolution synoptically conditioned weather generator (HiReS‐WG) appropriate for climate regimes with a substantial proportion of convective rainfall is presented. The simulated rain fields are of high spatial (0.5 × 0.5 km2) and temporal (5 min) resolution and can be used for most hydrological applications. The WG is composed of four modules: the synoptic generator, the motion vector generator, the convective rain cell generator, and the low‐intensity rainfall generator. The HiReS‐WG was applied to a study region on the northwestern Israeli coastline in the Eastern Mediterranean, for which 12 year weather radar and synoptic data were extensively analyzed to derive probability distributions of convective rain cells and other rainfall properties for different synoptic classifications; these distributions were used as input to the HiReS‐WG. Simulated rainfall data for 300 years were evaluated for annual rain depth, season timing, wet‐/dry‐period durations, rain‐intensity distributions, and spatial correlations. In general, the WG well represented the above properties compared to radar and rain‐gauge observations from the studied region, with one limitation—an inability to reproduce the most extreme cases. The HiReS‐WG is a good tool to study catchments' hydrological responses to variations in rainfall, especially small‐size to medium‐size catchments, and it can also be linked to climate models to force the prevailing synoptic conditions.

Sector wise echoes study and climatology around Jaisalmer

The capability of Weather Radar to see through the thunder clouds and rain has made it a unique observation tool for remotely surveying the atmosphere. Pulsed radar technique has been applied with remarkable success to map the rain field of various duration and intensities along with movement of storms in real time within the effective detection range of radar. It is a very good tool for forecaster to provide better warning for impending storms and heavy rainfall over the area under radar surveillance and thereby losses due to storm can be minimized while their benefits can be continued like water resource management. In the present work attention has been focused on conducting a comprehensive study of frequencies of occurrence of echoes around Jaisalmer up to 200 km from radar site and the surrounding of it has divided into four equal sectors, i.e., sector-1 (NW, 270°-360° ) , sector-2 (NE, 0°-90°) , sector-3 (SE, 90°-180° ) and sector-4 (SW, 180°-270°). Total number of echoes under the study was 28918 for the period from 19th April, 1993 to 31st December, 2010. Total number of echoes analyzed in Sector-1, were 5441(18.8%), in sector-2, number of echoes analyzed were 9554(33.0%), in sector-3, number of echoes analyzed were 9479 (32.8%) and in sector-4, number of echoes analyzed were 4444(15.4%). Radar echoes to be classified month-wise and the lowest number of average echoes observed in the month of December was 0.4%, in the month of November 0.5%, in October and March 1.6% and in the month of January and February 2.0% .The highest number of annual average echoes observed in the month of July was 30.1% followed by August 24.6%, June 17.2%, May 8.3%, April 6.3% and September 5.8%. Height wise echoes analyzed and the highest number of echoes found for 3 km in all the four sectors were 29.0% and the lowest were for 16 km as 0.2%.

Low-Level ZDR Signatures in Supercell Forward Flanks: The Role of Size Sorting and Melting of Hail

Abstract The low levels of supercell forward flanks commonly exhibit distinct differential reflectivity (ZDR) signatures, including the low-ZDR hail signature and the high-ZDR “arc.” The ZDR arc has been previously associated with size sorting of raindrops in the presence of vertical wind shear; here this model is extended to include size sorting of hail. Idealized simulations of a supercell storm observed by the Norman, Oklahoma (KOUN), polarimetric radar on 1 June 2008 are performed using a multimoment bulk microphysics scheme, in which size sorting is allowed or disallowed for hydrometeor species. Several velocity–diameter relationships for the hail fall speed are considered, as well as fixed or variable bulk densities that span the graupel-to-hail spectrum. A T-matrix-based emulator is used to derive polarimetric fields from the hydrometeor state variables. Size sorting of hail is found to have a dominant impact on ZDR and can result in a ZDR arc from melting hail even when size sorting is disallowed in the rain field. The low-ZDR hail core only appears when size sorting is allowed for hail. The mean storm-relative wind in a deep layer is found to align closely with the gradient in mean mass diameter of both rain and hail, with a slight shift toward the storm-relative mean wind below the melting level in the case of rain. The best comparison with the observed 1 June 2008 supercell is obtained when both rain and hail are allowed to sort, and the bulk density and associated fall-speed curve for hail are predicted by the model microphysics.

On the Relationship Between the Spatial Correlation of Point Rain Rate and of Rain Attenuation on Earth-Space Radio Links

This contribution presents an analytical expression to predict the spatial correlation of the rain attenuation A impairing two Earth-space radio links in a site diversity configuration (ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> ) as a function of the spatial correlation of the rain precipitation affecting the area (ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> ), of the distance between the two stations d and of the electrical and geometrical characteristics of the links. Well-established properties of the rain field (i.e., quasi-ergodicity and spatial stationarity) are exploited in the derivation of the proposed analytical expression, whose accuracy is evaluated by means of an extensive set of rain field data collected by the NIMROD weather radar network in the UK. Results indicate a satisfactory prediction performance in the 10-50 GHz frequency range, with negligible dependence on the site separation distance d and on the electrical and geometrical characteristics of the system.

Space‐time variability of the rainfall over the western Mediterranean region: A statistical analysis

This study aims at better understanding the space‐time statistical properties of rain over a Mediterranean region. To this end we analyzed temporal, spatial, and spatio‐temporal spectra of rain field maps provided by an X‐band radar situated in the southeast part of France. The database extends from 2009 to 2012 and has a spatial and temporal resolution of 1 km2 and 5 min. The analysis highlights several scaling regimes, which are interpreted in terms of meteorological structures (convective cells, mesoscale structures, and midlatitude cyclones). The analysis of spectra per month confirms the dependency of the spectral signature to the underlying meteorological process. Nevertheless, our results also reveal that for a given range of scales (20–45 min in time and 7–20 km in space), spectral slope is monthly invariant. It means that rain behaves identically, in terms of scaling, whatever the mechanism that generated it (convection, front). Moreover, spectral analysis shows that the temporal decorrelation scale is 10 days, which can possibly be related to the longest lifetime of a meteorological phenomenon in the region (i.e., about 10 days). An approach to compute the scaling anisotropy between space and time is proposed. It reveals that, over two distinct ranges of scales (7–20 km/20–45 min and 20–70 km/45 min–3 h), the scaling anisotropic coefficient is equal to 2. It also reveals that the ratio of spectral slope of 2‐D angle averaged spatial spectrum versus 1‐D temporal spectrum is equal to 1 over these ranges of scales. It suggests a similarity in the second‐order properties (e.g., correlation) of temporal and spatial rain field. All these results are important to better understand rainfall statistical behavior and could also be used for the development of downscaling schemes and the validation of numerical weather models.

A Physically Based Identification of Vertical Profiles of Reflectivity from Volume Scan Radar Data

AbstractThe vertical profile of reflectivity (VPR) must be identified to correct estimations of rainfall rates by radar for the nonuniform beam filling associated with the vertical variation of radar reflectivity. A method for identifying VPRs from volumetric radar data is presented that takes into account the radar sampling. Physically based constraints on the vertical structure of rainfall are introduced with simple VPR models within a rainfall classification procedure defining more homogeneous precipitation patterns. The model parameters are identified in the framework of an extended Kalman filter to ensure their temporal consistency. The method is assessed using the dataset from a volume-scanning strategy for radar quantitative precipitation estimation designed in 2002 for the Bollène radar (France). The physical consistency of the retrieved VPR is evaluated. Positive results are obtained insofar as the physically based identified VPR (i) presents physically consistent shapes and characteristics considering beam effects, (ii) shows improved robustness in the difficult radar measurement context of the Cévennes–Vivarais region, and (iii) provides consistent physical insight into the rain field.

Experimental study on flutter stability of a long-span bridge subject to wind-rain actions

Based on the free vibration test method for extracting flutter derivatives, an experiment on flutter stability of a long-span bridge under simultaneous actions of wind and rain was carried out in a wind tunnel. A separated twin-box girder section model was employed as the specimen. The flutter derivatives and critical flutter wind speed of this girder subject to both wind and rain (with various rainfall intensities, wind speeds and attack angles) were obtained, then the flutter stability of the bridge influenced by rainfall was analyzed. Experimental results showed that the flutter derivatives of this bridge depend on the angles of attack of wind flow in the wind and rain fields. Also, rainfall has great effect on three flutter derivatives (H 2*, H 4* and A 4*) and has less effect on other three flutter derivatives (H 1*, H 3* and A 3*). With the increasing rainfall density, the critical flutter velocity first increases and then decreases. Low density of rainfall has the effect of increasing mass, stiffness and damping on bridge decks, and higher density of rainfall has the effect of random inhomogeneous impact on bridge decks.

Nowcasting of the Spatiotemporal Rain Field Evolution for Radio Propagation Studies

This paper presents a nowcasting method capable of short-term forecasting the spatiotemporal rain field evolution, based exclusively on the analysis of radar reflectivity data without any a priori assumption on its spatial structure. The method has been developed to be integrated into future foreseen propagation impairment mitigation techniques, which take advantage of the temporal and spatial variability of rain in order to improve significantly the capacity and performance of the next-generation radiocommunication networks, operating at frequencies above 10 GHz . The rain field database used for assessing the nowcasting method consisted of 746 radar images collected by the weather radar located at A Coruna (Northwest Spain) during 25 rain events. The proposed method is made up of three main parts: a procedure that estimates the rain field displacement between two consecutive weather radar images, an algorithm that makes predictions for the next rain field displacement, and an operation that shifts the rain field according to the forecast displacement. The forecast quality of the developed method has been assessed by means of six skill indices common in the literature. Results reveal that the nowcasting method achieves a reasonably good forecast skill.

Processes Influencing Rain-Field Growth and Decay after Tropical Cyclone Landfall in the United States

AbstractThis study measured rain-field sizes for tropical cyclones (TCs) after U.S. landfall and related changes in size to the diurnal cycle and extratropical transition (ET). For 45 TC landfalls, the spatial properties of the rain fields were calculated through an analysis of radar reflectivity returns within a geographic information system. Variables representing the conditions of the atmosphere and storm attributes were examined at three times and as changes over two time periods to account for lags between condition onset and change in raining-area sizes. Mann–Whitney U tests illustrated which of these variables had significantly different median values when the total raining area or high-reflectivity regions increased or decreased in areal extent over two 12-h periods after landfall. Results indicate that the diurnal cycle influenced changes in rain-field size. Rain-field growth occurred during the late morning and early afternoon, which is between the times for peak areal extent of oceanic- and land-based precipitation in the tropics. The rain fields of TCs completing an ET within 74 h of landfall increased in areal extent during the first 12 h after landfall and decayed during the second 12-h period as they neared the completion of ET. The availability of moisture, which was not related to either the diurnal cycle or processes associated with ET, was also important to rain-field growth or decay. In addition, it was discovered that, for the United States, landfall times have shifted from a peak before midnight during 1950–96 to after midnight during 1995–2008.

Analytical modeling of the hydrologic response under moving rainstorms: Storm–catchment interaction and resonance

Summary In this study, we propose a simple yet broad analytical framework for analyzing the hydrological response of a catchment under moving rainstorms; the method can be used as a tool to explore the main relevant features of the storm-catchment interactions. We analyze the response of the basin to an excess rain field (rain contributing to direct runoff), which is assumed to be variable in space and time; catchment response is supposed to be characterized by the time-invariant distribution of the travel time of water particles within the basin. We use the framework developed herein to investigate the conditions that enhance peak flow, leading to the so-called resonance effect, in terms of storm size, direction and velocity. Our results show how resonance conditions depend on the relative size of the rainstorm with respect to basin size. In particular, for storm sizes much smaller than the dimension of the catchment, a complete resonance effect occurs for infinite combinations of the direction and speed of the moving rainstorm. On the contrary, when storm size is much larger than the basin size, the flood peak tends to be independent on rainstorm movement. In the intermediate conditions a partial resonance effect emerges as a consequence of both the superposition of rainfall contributes in time and the increased flow response of the basin; the latter is a result of the larger rainfall volume injected over time. For illustration purposes, we present and discuss a case study based on the open-book idealized catchment.