Properties Of Extreme Rainfall Research Articles

Regional Ombrian Curves: Design Rainfall Estimation for a Spatially Diverse Rainfall Regime

Ombrian curves, i.e., curves linking rainfall intensity to return period and time scale, are well-established engineering tools crucial to the design against stormwaters and floods. Though the at-site construction of such curves is considered a standard hydrological task, it is a rather challenging one when large regions are of interest. Regional modeling of ombrian curves is particularly complex due to the need to account for spatial dependence together with the increased variability of rainfall extremes in space. We develop a framework for the parsimonious modeling of the extreme rainfall properties at any point in a given area. This is achieved by assuming a common ombrian model structure, except for a spatially varying scale parameter which is itself modeled by a spatial smoothing model for the 24 h average annual rainfall maxima that employs elevation as an additional explanatory variable. The fitting is performed on the pooled all-stations data using an advanced estimation procedure (K-moments) that allows both for reliable high-order moment estimation and simultaneous handling of space-dependence bias. The methodology is applied in the Thessaly region, a 13,700 km2 water district of Greece characterized by varying topography and hydrometeorological properties.

U.S. Hydrologic Design Standards Insufficient Due to Large Increases in Frequency of Rainfall Extremes

AbstractEvidence for intensifying rainfall extremes has not translated into “actionable” information needed by engineers and risk analysts, who are often concerned with very rare events such as “100‐year storms.” Low signal‐to‐noise associated with such events makes trend detection nearly impossible using conventional methods. We use a regional aggregation approach to boost this signal‐to‐noise, showing that such storms have increased in frequency over much of the conterminous United States since 1950, a period characterized by widespread hydrologic infrastructure development. Most of these increases can be attributed to secular climate change rather than climate variability, and we demonstrate potentially serious implications for the reliability of existing and planned hydrologic infrastructure and analyses. Though trends in rainfall extremes have not yet translated into observable increases in flood risks, these results nonetheless point to the need for prompt updating of hydrologic design standards, taking into consideration recent changes in extreme rainfall properties.

Characterizing and Modeling Seasonality in Extreme Rainfall

AbstractA comprehensive understanding of seasonality in extreme rainfall is essential for climate studies, flood prediction, and various hydrological applications such as scheduling season‐specific engineering works, intra‐annual management of reservoirs, seasonal flood risk mitigation, and stormwater management. To identify seasonality in extreme rainfall and quantify its impact in a theoretically consistent yet practically appealing manner, we investigate a data set of 27 daily rainfall records spanning at least 150 years. We aim to objectively identify periods within the year with distinct seasonal properties of extreme rainfall by employing the Akaike information criterion. Optimal partitioning of seasons is identified by minimizing the within‐season variability of extremes. The statistics of annual and seasonal extremes are evaluated by fitting a generalized extreme value distribution to the annual and seasonal block maxima series. The results indicate that seasonal properties of rainfall extremes mainly affect the average values of seasonal maxima and their variability, while the shape of their probability distribution and its tail do not substantially vary from season to season. Uncertainty in the estimation of the generalized extreme value parameters is quantified by employing three different estimation methods (maximum likelihood, method of moments, and least squares), and the opportunity for joint parameter estimation of seasonal and annual probability distributions of extremes is discussed. The effectiveness of the proposed scheme for seasonal characterization and modeling is highlighted when contrasted to results obtained from the conventional approach of using fixed climatological seasons.

Bivariate frequency analysis of rainfall intensity and duration for urban stormwater infrastructure design

This study presents a storm-event based bivariate frequency analysis approach to determine design rainfalls in which, the number, intensity and duration of actual rainstorm events were considered. To derive more realistic design storms, the occurrence probability of an individual rainstorm event was determined from the joint distribution of storm intensity and duration through a copula model. Hourly rainfall data were used at three climate stations respectively located in Singapore, South Korea and Canada. It was found that the proposed approach could give a more realistic description of rainfall characteristics of rainstorm events and design rainfalls. As results, the design rainfall quantities from actual rainstorm events at the three studied sites are consistently lower than those obtained from the conventional rainfall depth-duration-frequency (DDF) method, especially for short-duration storms (such as 1-h). It results from occurrence probabilities of each rainstorm event and a different angle for rainfall frequency analysis, and could offer an alternative way of describing extreme rainfall properties and potentially help improve the hydrologic design of stormwater management facilities in urban areas.

On the consideration of scaling properties of extreme rainfall in Madrid (Spain) for developing a generalized intensity-duration-frequency equation and assessing probable maximum precipitation estimates

The fractal behavior of extreme rainfall intensities registered between 1940 and 2012 by the Retiro Observatory of Madrid (Spain) has been examined, and a simple scaling regime ranging from 25 min to 3 days of duration has been identified. Thus, an intensity-duration-frequency (IDF) master equation of the location has been constructed in terms of the simple scaling formulation. The scaling behavior of probable maximum precipitation (PMP) for durations between 5 min and 24 h has also been verified. For the statistical estimation of the PMP, an envelope curve of the frequency factor (k m ) based on a total of 10,194 station-years of annual maximum rainfall from 258 stations in Spain has been developed. This curve could be useful to estimate suitable values of PMP at any point of the Iberian Peninsula from basic statistical parameters (mean and standard deviation) of its rainfall series.

Analyses of the temporal and spatial structures of heavy rainfall from a catalog of high-resolution radar rainfall fields

In this paper, we develop a storm catalog of heavy rainfall events for a region centered on the Milwaukee, Wisconsin WSR-88D (Weather Surveillance Radar — 1988 Doppler) radar. The study region includes portions of southern Wisconsin, northern Illinois and Lake Michigan. The long-term objective of this study is to develop rainfall frequency analysis methods based on a storm catalog of major rain events. The specific objectives of this study are to develop a long-term catalog of high-resolution radar rainfall fields and characterize key features of the space–time variability of rainfall. The research questions that underlie these objectives are: 1) What are the spatial heterogeneities of rainfall over the study region for major flood-producing storm systems? 2) What are the key elements of storm evolution that control the scale-dependent properties of extreme rainfall? The storm catalog contains a record of the 50 “largest” storm days during the 1996–2011 observation period. We show that mean rainfall for the 50 largest storm days exhibits pronounced spatial heterogeneity with a broad maximum in western Wisconsin and a minimum in the eastern portion of the study region over Lake Michigan. We also show that there is a narrow line of maximum mean rainfall extending from west to east along the Wisconsin–Illinois border. This feature is tied to a maximum in the probability of daily rainfall exceeding 100mm. There are characteristic elements to the storm life cycle of heavy rainfall days that relate to size, structure and evolution of heavy rainfall. Extreme rainfall is also linked with severe weather (tornados, large hail and damaging wind). The diurnal cycle of rainfall for heavy rain days is characterized by an early peak in the largest rainfall rates, an afternoon–evening peak in rain area exceeding 25mmh−1 and development of a large stratiform rain area during the night and early morning.

Critical Examination of Area Reduction Factors

AbstractArea reduction factors (ARFs), which are used to convert estimates of extreme point rainfall to estimates of extreme area-averaged rainfall, are central to conventional flood risk assessment. Errors in the estimation of ARFs can result in large errors in subsequent estimates of design rainfall and discharge. This paper presents a critical examination of commonly used ARFs, particularly those from the U.S. Weather Bureau TP-29, demonstrating that they do not adequately represent the true properties of extreme rainfall. This lack of representativeness is due mainly to formulations that mix rainfall observations from different storms and different storm types. Storm catalogs developed from a 10-year high-resolution radar rainfall data are used set to estimate storm-centered ARFs for Charlotte, North Carolina. Storms are classified as either tropical or nontropical to demonstrate that storm type strongly influences spatial rainfall structure. While there appears to be some relationship between ARF str...

Regional frequency analysis of extreme rainfalls using partial L moments method

An approach based on regional frequency analysis using L moments and LH moments are revisited in this study. Subsequently, an alternative regional frequency analysis using the partial L moments (PL moments) method is employed, and a new relationship for homogeneity analysis is developed. The results were then compared with those obtained using the method of L moments and LH moments of order two. The Selangor catchment, consisting of 37 sites and located on the west coast of Peninsular Malaysia, is chosen as a case study. PL moments for the generalized extreme value (GEV), generalized logistic (GLO), and generalized Pareto distributions were derived and used to develop the regional frequency analysis procedure. PL moment ratio diagram and Z test were employed in determining the best-fit distribution. Comparison between the three approaches showed that GLO and GEV distributions were identified as the suitable distributions for representing the statistical properties of extreme rainfall in Selangor. Monte Carlo simulation used for performance evaluation shows that the method of PL moments would outperform L and LH moments methods for estimation of large return period events.

Regional analysis of annual maximum rainfall using TL-moments method

Information related to distributions of rainfall amounts are of great importance for designs of water-related structures. One of the concerns of hydrologists and engineers is the probability distribution for modeling of regional data. In this study, a novel approach to regional frequency analysis using L-moments is revisited. Subsequently, an alternative regional frequency analysis using the TL-moments method is employed. The results from both methods were then compared. The analysis was based on daily annual maximum rainfall data from 40 stations in Selangor Malaysia. TL-moments for the generalized extreme value (GEV) and generalized logistic (GLO) distributions were derived and used to develop the regional frequency analysis procedure. TL-moment ratio diagram and Z-test were employed in determining the best-fit distribution. Comparison between the two approaches showed that the L-moments and TL-moments produced equivalent results. GLO and GEV distributions were identified as the most suitable distributions for representing the statistical properties of extreme rainfall in Selangor. Monte Carlo simulation was used for performance evaluation, and it showed that the method of TL-moments was more efficient for lower quantile estimation compared with the L-moments.

Downscaling transient climate change using a Neyman–Scott Rectangular Pulses stochastic rainfall model

Summary The future management of hydrological systems must be informed by climate change projections at relevant time horizons and at appropriate spatial scales. Furthermore, the robustness of such management decisions is dependent on both the uncertainty inherent in future climate change scenarios and the natural climate system. Addressing these needs, we present a new transient rainfall simulation methodology which combines dynamical and statistical downscaling techniques to produce transient (i.e. temporally non-stationary) climate change scenarios. This is used to generate a transient multi-model ensemble of simulated point-scale rainfall time series for 1997–2085 for the polluted Brevilles spring in Northern France. The recovery of this previously potable source may be affected by climatic changes and variability over the next few decades. The provision of locally-relevant transient climate change scenarios for use as input to hydrological models of both water quality and quantity will ultimately provide a valuable resource for planning and decision making. Observed rainfall from 1988–2006 was characterised in terms of a set of statistics for each calendar month: the daily mean, variance, probability dry, lag-1 autocorrelation and skew, and the monthly variance. The Neyman–Scott Rectangular Pulses (NSRP) stochastic rainfall model was fitted to these observed statistics and correctly simulated both monthly statistics and extreme rainfall properties. Multiplicative change factors which quantify the change in each statistic between the periods 1961–1990 and 2071-2100 were estimated for each month and for each of 13 Regional Climate Models (RCMs) from the PRUDENCE ensemble. To produce transient climate change scenarios, pattern scaling factors were estimated and interpolated from four time-slice integrations of two General Circulation Models which condition the RCMs, ECHAM4/OPYC and HadCM3. Applying both factors to the observed statistics provided projected transient rainfall statistics (PTRS) to which piece-wise smoothly varying transient rainfall model parameterizations were fitted. These fits provided good representations of the PTRS for each RCM. An ensemble of 100 continuous daily rainfall time series, with steadily varying stochastic properties which model these projections of transient climate change, was then simulated using a new transient NSRP simulation methodology for each RCM. Together the ensembles form a 1300 member transient multi-model ensemble of rainfall time series. The simulated transient ensemble properties were investigated, identifying RCMs giving rise to unusual behaviour. For the Brevilles, annual rainfall is projected to decrease until 2085 but the change is highly sensitive to General Circulation Model forcing; ECHAM4-driven RCMs project larger annual decreases than HadCM3/HadAM3H/P driven RCMs. All RCMs project an increase in winter rainfall and a larger summer decrease. An increase of ∼10% in the 10-year return period annual maximum rainfall is projected by 2085, however both strong increasing trends and a slight decreasing trend are found for individual RCMs. Compared with transient RCMs, the new methodology provides a number of advantages: reduced biases, point scale scenarios relevant for local-scale impact studies, improved representation of natural variability and improved representation of extremes.

DEVELOPMENT OF REGIONAL RAINFALL INTENSITY-DURATION-FREQUENCY CURVES BASED ON SCALING PROPERTIES

This study developed a regional Intensity?Duration?Frequency (IDF) relationship for ungauged locations based on the scaling theory. The scaling properties of extreme rainfall are examined to establish scaling relationship behaviors of statistical moments over different durations. The results show that a rainfall property in time does follow a simple scaling process. A scale invariance concept is explored for disaggregation (or downscaling) of rainfall intensity from low to high resolution and is applied to the derivation of scaling IDF curves. These curves are developed for ungauged sites based on scaling of the Extreme Value type 1 (EV1) or Gumbel probability distributions. The spatial distribution maps of three parameters: the scaling exponent and two statistical parameters are constructed. By using these maps, the IDF relationships are deduced from only daily rainfall with the scaling approach, which shows good agreements in comparison with the IDF curves obtained from traditional techniques.

Scaling model of a rainfall intensity‐duration‐frequency relationship

AbstractIntensity‐duration‐frequency (IDF) relationships are currently constructed based on an at‐site frequency analysis of rainfall data separately for different durations. These relationships are not accurate and reliable since they depend on many assumptions such as distribution selection for each duration; they require a large number of parameters, and are not time‐independent.In this study, scaling properties of extreme rainfall are examined to establish scaling behaviour of statistical non‐central moments over different durations. A scale invariance concept is explored for disaggregation (or downscaling) of rainfall intensity from low to high resolution and is applied to the derivation of scaling IDF curves. These curves are developed for gauged sites based on scaling of the generalized extreme value (GEV) and Gumbel probability distributions.Numerical analysis was performed on annual maximum rainfall series for the province of Ontario, for storm durations of 5, 10, 15, and 30 min (the typical time of concentration for small urban catchments) and 1, 2, 6, 12, and 24 h (the typical time of concentration for larger rural watersheds).Results show that rainfall does follow a simple scaling process. Estimates found from the scaling procedure are comparable to estimates obtained from traditional techniques; however, the scaled approach was more efficient and gives more accurate estimates compared with the observed rainfall total at all stations. Copyright © 2006 John Wiley & Sons, Ltd.

On the issue of trend and noise in the estimation of extreme rainfall properties

Up until today extreme rainfall properties are frequently applied in sewer design guidelines. Uncertainty in the estimation of such properties will hence directly influence the dimensions of sewers, structures and pumps. In this paper the issue of potential trend and noise in the estimation is investigated for 6 rain series ranging from 19 to 55 years in duration. Different to recent research that predicts a climate induced-increase in heavy precipitation no clear indication for such trend was found in the investigated historical rain series. Another important aspect is the length of the rain series that is required for the estimation of extreme rainfall properties and the associated uncertainty. The analysis indicates that at least a period of 10 years should be used for the estimation. But even so the possible deviation expressed in terms of the 90 percentile is in the order of 5 to 10% of the 'true value', defined as the value derived when the whole given series is used for the estimation.

Selection of regional historical rainfall time series as input to urban drainage simulations at ungauged locations

It has become established practice during the past 20 years to use high-resolution historical rainfall time series as input to hydrological model packages for detailed simulation of urban drainage systems. However, sufficiently long rain series are rarely available from the exact catchment in question and simulations are hence often based on available rain series from other locations. Extreme rainfall properties of importance to the performance of urban storm drainage systems vary significantly even in regions with only minor physiographic differences. Part of this variation can be explained by regional variations of the mean annual rainfall and the remaining statistical residue can be interpreted as statistical uncertainty. In Denmark, more than 75 high-resolution rain gauges are installed across a total area of 43,000 m. About 40 gauges had sufficiently long records to be included in a comprehensive national investigation where newly developed statistical regionalisation procedures were used to model the regional variation of extreme rainfalls. On this basis, a spreadsheet model was made available for estimation of extreme design rainfalls and the associated uncertainty at any location in the country. Statistics were furthermore computed to classify historical rainfall time series according to the developed regional model, and this makes it possible to assess the uncertainty related with using different historical rain series for simulations at ungauged locations. This research indicates that use of historical point rainfall data at ungauged locations introduces a significant uncertainty that is largely overlooked in today's practice. The engineering recommendation is to select historical rain series based on an evaluation of the local physiographic characteristics (e.g., the mean annual rainfall) and a (pre-defined) desired safety level of the simulations.

New estimates of future changes in extreme rainfall across the UK using regional climate model integrations. 2. Future estimates and use in impact studies

Under enhanced greenhouse conditions, climate models suggest an increase in rainfall intensities in the northern Hemisphere. Major flood events in the UK during autumn 2000 and central Europe in August 2002, have focussed attention on the dramatic impacts these changes may have on many sectors of society. In the companion paper [Fowler et al., J. Hydrol. (2004) this issue], we suggested that the HadRM3H model may be used with some confidence to estimate extreme rainfall distributions, showing good predictive skill in estimating statistical properties of extreme rainfall during the baseline period, 1961–1990. In this study, we use results from the future integration of HadRM3H (following the IPCC SRES scenario A2 for 2070–2100) to assess possible changes in extreme rainfall across the UK using two methods: regional frequency analysis and individual grid box analysis. Results indicate that for short duration events (1–2 days), event magnitude at a given return period will increase by 10% across the UK. For longer duration events (5–10 days), event magnitudes at given return periods show large increases in Scotland (up to +30%), with greater relative change at higher return periods (25–50 years). In the rest of the UK, there are small increases in the magnitude of more frequent events (up to +10%) but reductions at higher return periods (up to −20%). These results provide information to alter design storm depths to examine climate change impacts on various structures. The uncertainty bounds of the estimated changes and a ‘scaling’ methodology are additionally detailed. This allows the estimation of changes for the 2020s, 2050s and 2080s, and gives some confidence in the use of these estimates in impact studies.

Properties of extreme point rainfall III: Identification of spatial inter-site correlation structure

A general stochastic model that describes the observed variability of extreme rainfall properties estimated at different sites in a region is developed. The observed variability is divided into sampling variability and variability due to regional heterogeneity. A method for estimating the inter-site correlation structure of the at-site sampling errors based on partial duration series theory is developed, and geostatistical theory is introduced to estimate the spatial correlation structure of the true, but unknown, variables. On this basis the variance of the regional mean value can be determined and used in a regional design approach. The theory is applied to extreme values of rainfall depth and maximum 10 minutes intensity per rainfall event measured at 43 gauging stations in Denmark. Adding one design standard deviation to the regionally averaged T-year event estimates yields increased design values between 8 and 18%, depending on the return period and the rainfall characteristic considered. For small return periods this compares to results obtained from traditional non-parametric statistics, but for large return periods the suggested approach yields significantly lower and more accurate design values.