Alan Seed

A simple scaling model for extreme rainfall

The simple scaling hypothesis is applied to the intensity-duration-frequency (IDF) description of rainfall. It is shown that the cumulative distribution function for the annual maximum series of mean rainfall intensity has a simple scaling property over the range 30 min to 24 hours and in some instances to 48 hours. This behavior is demonstrated through an examination of the scaling properties of the moments and the scaling of the parameters of an extreme value distribution fitted to the data. A simple analytical formula for the IDF relationship is proposed, which embodies the scaling behavior. Once the scaling parameter has been obtained for a gauge or set of gauges in a region, this formula enables the calculation of rainfall amounts, of a chosen return period and duration shorter than a day, directly from the information obtained from the analysis of daily data.

A space and time model for design storm rainfall

Realistic rainfields that represent storms with a known return period are required as input to design calculations for hydrological projects that cover a wide range of hydrological scales. The current standard practice is to assume either that the storm is uniform in time and space or that it varies in some very simple manner. Multiaffine models of rainfall, based on the concept of a multiplicative cascade, provide the possibility of generating a stochastic series of space and time rainfall that reproduces the observed behavior. The spatial distribution of a field of instantaneous rain rates is modeled using the multiplicative cascade approach. The temporal development of the cascade weights at each level in the cascade is modeled with a simple autoregressive ARMA(1,1) model where the parameters vary in a systematic manner with scale. The model is verified using rain fields produced by a monsoonal depression that passed over a weather radar at Darwin, Australia. Radar data for the event were used to estimate the model parameters. The model was able to reproduce the observed temporal and spatial correlation functions over a range of scales, and the probability distributions over a range of scales, for both the instantaneous and the hourly accumulations.

Sydney 2000 Forecast Demonstration Project: Convective Storm Nowcasting

Abstract Five of the nowcasting systems that were available during the Sydney 2000 Forecast Demonstration Project (FDP) were selected for evaluation. These systems, from the United States, the United Kingdom, and Australia, had the capability to nowcast the location and, with one exception, the intensity of convective storms. Six of the most significant convective storm cases from the 3-month FDP were selected for evaluating the performance of these state-of-the-art nowcasting systems, which extrapolated storms using a variety of methods, including cell and area tracking, model winds, and sounding winds. Three of the systems had the ability to forecast the initiation and growth of storms. Nowcasts for 30 and 60 min were evaluated, and it was found that even for such short time periods the skill of the extrapolation-only systems was often very low. Extrapolation techniques that allowed for differential motion performed slightly better, since high-impact storms often have motions different than surrounding ...

The Nowcasting of Precipitation during Sydney 2000: An Appraisal of the QPF Algorithms

Abstract Statistical and case study–oriented comparisons of the quantitative precipitation nowcasting (QPN) schemes demonstrated during the first World Weather Research Programme (WWRP) Forecast Demonstration Project (FDP), held in Sydney, Australia, during 2000, served to confirm many of the earlier reported findings regarding QPN algorithm design and performance. With a few notable exceptions, nowcasting algorithms based upon the linear extrapolation of observed precipitation motion (Lagrangian persistence) were generally superior to more sophisticated, nonlinear nowcasting methods. Centroid trackers [Thunderstorm Identification, Tracking, Analysis and Nowcasting System (TITAN)] and pattern matching extrapolators using multiple vectors (Auto-nowcaster and Nimrod) were most reliable in convective scenarios. During widespread, stratiform rain events, the pattern matching extrapolators were superior to centroid trackers and wind advection techniques (Gandolf, Nimrod). There is some limited case study and s...

Radar rainfall error variance and its impact on radar rainfall calibration

Abstract The high degree of uncertainty in radar rainfall estimation is caused by the variability in the vertical profile of reflectivity, the errors in measurements of radar reflectivity, conversion of reflectivity to rainfall rate, and the error of using point rain gauge rainfall in representing mean-areal rainfall of a radar grid size in the radar rainfall calibration. Presented here is an approach that explicitly takes into account the variations in reliability of radar rainfall estimates associated with range from the radar in calibrating of Z – R relationship. The reliability of radar rainfall estimates is calculated from the proposed climatological variance of radar rainfall error model that accounts for rainfall intensity, nature of rainfall event and number of pulses averaged in obtaining a reflectivity pixel value. Modifications to the parametric and probability matching methods (PMM) are proposed to account for the reliability of the radar rainfall estimates at the gauge locations. Six months of reflectivity-rain gauge data from the Kurnell radar in Sydney, Australia are used to test the model. The result shows the improvements in accuracy of radar measurements of rainfall by incorporating the reliability of radar rainfall estimates in the PMM are about 10% and 5% compared with the conventional PMM and parametric Z – R relationship method, respectively.

An Integrated Approach to Error Correction for Real-Time Radar-Rainfall Estimation

Abstract A procedure for estimating radar rainfall in real time consists of three main steps: 1) the measurement of reflectivity and removal of known sources of errors, 2) the conversion of the reflectivity to a rainfall rate (Z–R conversion), and 3) the adjustment of the mean field bias as assessed using a rain gauge network. Error correction is associated with the first two steps and incorporates removing erroneous measurements and correcting biases in the Z–R conversion. This paper investigates the relative importance of error correction and the mean field bias–adjustment processes. In addition to the correction for ground clutter, the bright band, and hail, the two error correction strategies considered here are 1) a scale transformation function to remove range-dependent bias in measured reflectivity resulting from an increase in observation volume with range, and 2) the classification of storm types to account for the variation in Z–R relationships for convective and stratiform rainfall. The mean fi...

A Stochastic Model of Radar Measurement Errors in Rainfall Accumulations at Catchment Scale

Abstract The accuracy of rainfall data is critical for hydrology, as errors in rainfall estimation will affect the quality of hydrological predictions. In hydrology, it is the accuracy of the rainfall measurement at spatial and temporal scales that drive catchment response that is important. Random sampling errors are the residual errors that remain in radar rainfall measurements after systematic biases have been removed. This paper quantifies radar rainfall sampling errors at catchment scale by developing and applying a stochastic space–time model. Random errors caused by temporal and spatial sampling, random variations in the vertical profile of reflectivity, and variations in the reflectivity–rainfall intensity (Z–R) relationship have been included in the model. The stochastic radar rainfall error model is applied in a numerical experiment to quantify sampling errors in radar rainfall accumulations for periods between 10 min and 1 day across catchment areas of between 1 and 1024 km2. Spatial and tempor...

The Sydney 2000 World Weather Research Programme Forecast Demonstration Project: Overview and Current Status

The first World Weather Research Programme (WWRP) Forecast Demonstration Project (FDP), with a focus on nowcasting, was conducted in Sydney, Australia, from 4 September to 21 November 2000 during a period associated with the Sydney 2000 Olympic Games. Through international collaboration, nine nowcasting systems from the United States, United Kingdom, Canada, and Australia were deployed at the Sydney Office of the Bureau of Meteorology (BOM) to demonstrate the capability of modern forecast systems and to quantify the associated benefits in the delivery of a real-time nowcast service. On-going verification and impact studies supported by international committees assisted by the WWRP formed an integral part of this project. A description is given of the project, including component systems, the weather, and initial outcomes. Initial results show that the nowcasting systems tested were transferable and able to provide valuable information enhancing BOM nowcasts. The project provided for unprecedented intercha...

Sampling errors in radar estimates of rainfall

The relatively slow rate of application of radar rainfall to operational hydrology is partially due to concerns about the measurement errors. The errors that result in a bias in the field mean have been studied extensively and can to some extent be treated, but errors that manifest themselves as more or less white noise become important when considering what scale is appropriate for spatially distributed hydrological modeling. This paper evaluates the errors that arise in radar estimates of rainfall as a result of temporal sampling, spatial averaging, measuring the field at some distance above the ground, and recording the reflectivity data with a limited radiometric resolution. By far the most significant source of error was found to be due to measuring the field at some height above the ground. The mean standard difference in rainfall rate between fields separated by 1 km in height at 1 km spatial resolution was found to be of the order of 100% of the mean rainfall rate. When the spatial resolution is reduced to 5 km the mean standard difference between the fields with the same 1 km vertical separation fell to about 50% of the mean rainfall rate. Temporal sampling was found to be quite sensitive to the intermittency of the rain field being sampled. The mean standard error caused by 2-min sampling for 10-min accumulations decreased from 14% for scattered rainfall to 8% for widespread rainfall.

Multiaffine random field model of rainfall

A new method for the statistical description and simulation of two-dimensional rainfall radar images is proposed. It is based on the theory of multiaffine random fields and the bounded lognormal cascade model. The model has three free parameters, which are shown to provide a parsimonious and robust statistical description of rainfall images. The parameters retrieved from the analysis of the real rainfall data by fitting the one- and two-point statistics are used for simulation. The simulated rainfall fields are in good statistical and visual agreement with their real counterparts.