Radar rainfall estimation for flash flood forecasting in small urban watersheds

Radar rainfall estimation for flash flood forecasting in small, urban catchments is examined through analyses of radar, rain gage and discharge observations from the 14.3 km² Dead Run drainage basin in Baltimore County, Maryland. The flash flood forecasting problem pushes the envelope of rainfall estimation to time and space scales that are commensurate with the scales at which the fundamental governing laws of land surface processes are derived. Analyses of radar rainfall estimates are based on volume scan WSR-88D reflectivity observations for 36 storms during the period 2003–2005. Gage-radar analyses show large spatial variability of storm total rainfall over the 14.3 km² basin for flash flood producing storms. The ability to capture the detailed spatial variation of rainfall for flash flood producing storms by WSR-88D rainfall estimates varies markedly from event to event. As spatial scale decreases from the 14.3 km² scale of the Dead Run watershed to 1 km² (and the characteristic time scale of flash flood producing rainfall decreases from 1 h to 15 min) the predictability of flash flood response from WSR-88D rainfall estimates decreases sharply. Storm to storm variability of multiplicative bias in storm total rainfall estimates is a dominant element of the error structure of radar rainfall estimates, and it varies systematically over the warm season and with flood magnitude. Analyses of the 7 July 2004 and 28 June 2005 storms illustrate microphysical and dynamical controls on radar estimation error for extreme flash flood producing storms.     

Empirically-based modeling of spatial sampling uncertainties associated with rainfall measurements by rain gauges

In the quantitative evaluation of radar-rainfall products (maps), rain gauge data are generally used as a good approximation of the true ground rainfall. However, rain gauges provide accurate measurements for a specific location, while radar estimates represent areal averages. Because these sampling discrepancies could introduce noise into the comparisons between these two sensors, they need to be accounted for. In this study, the spatial sampling error is defined as the ratio between the measurements by a single rain gauge and the true areal rainfall, defined as the value obtained by averaging the measurements by an adequate number of gauges within a pixel. Using a non-parametric scheme, the authors characterize its full statistical distribution for several spatial (4, 16 and 36 km²) and temporal (15 min and hourly) scales.     

Rainfall stochastic modeling for runoff forecasting

Rainfall fields estimation over a catchment area is an important stage in many hydrological applications. In this context, weather radars have several advantages because a single-site can scan a vast area with very high temporal and spatial resolution. The construction of weather radar systems with dual polarization capability allowed progress on radar rainfall estimation and its hydro-meteorological applications. For these applications of radar data it is necessary to remove the ground clutter contamination with an algorithm based on the backscattering signal variance of the differential reflectivity. The calibration of the GDSTM model (Gaussian Displacements Spatial-Temporal Model), a cluster stochastic generation model in continuous space and time, is herewith presented. In this model, storms arrive in a Poisson process in time with cells occurring in each storm that cluster in space and time. The model is calibrated, using data collected by the weather radar Polar 55C located in Rome, inside a square area of 132 × 132 km², with the radar at the centre. The GDSTM is fitted to sequences of radar images with a time interval between the PPIs scans of 5 min. A generalized method of moment procedure is used for parameter estimation. For the validation of the ability of the model to reproduce internal structure of rain event, a geo-morphological rainfall-runoff model, based on width function (WFIUH), was calibrated using simulated and observed data. Several rainfall fields are generated with the stochastic model and later they are used as input of the WFIUH model so that the forecast discharges can be compared to the observed ones.     

Analysis and modeling of spatial correlation structure in small-scale rainfall in Central Oklahoma

Spatial correlation structure in small-scale rainfall is analyzed based on a dense cluster of raingauges in Central Oklahoma. This cluster, called the EVAC PicoNet, consists of 53 gauges installed in 25 measurement stations covering an area of about 3 km by 3 km. Two raingauges are placed in 24 stations and five in the central station. Three aspects of the estimated spatial correlation functions are discussed: dependence on time-scale ranging from 1 min to 24 h, inter-storm variability, and dependence on rainfall intensity. The results show a regular dependence of the correlogram parameters on the averaging time-scale, large differences of the correlograms in the individual storms, and the dominance of storms with high spatial variability on the average large sample characteristics. The authors also demonstrate and discuss the ambiguities in correlation estimates conditioned on rainfall intensities. The findings of this study have implications for raingauge network design, rainfall modeling, and conclusive evaluation of radar and satellite estimates of rainfall.     

Influence of rainfall and soil properties spatial aggregation on extreme flash flood response modelling: An evaluation based on the Sesia river basin,North Western Italy

High resolution radar rainfall fields and a distributed hydrologic model are used to evaluate the sensitivity of flood and flash flood simulations to spatial aggregation of rainfall and soil properties at catchment scales ranging from 75 to 983 km². Hydrologic modeling is based on a Hortonian infiltration model and a network-based representation of hillslope and channel flow. The investigation focuses on three extreme flood and flash flood events occurred on the Sesia river basin, North Western Italy, which are analysed by using four aggregation lengths ranging from 1 to 16 km. The influence of rainfall spatial aggregation is examined by using the flow distance as a spatial coordinate, hence emphasising the role of river network in the averaging of space–time rainfall. The effects of reduced and distorted rainfall spatial variability on peak discharge have been found particularly severe for the flash flood events, with peak errors up to 35% for rainfall aggregation of 16 km and at 983 km² catchment size. Effects are particularly remarkable when significant structured rainfall variability combines with relatively important infiltration volumes due to dry initial conditions, as this emphasises the non-linear character of the rainfall–runoff relationship. In general, these results confirm that the correct estimate of rainfall volume is not enough for the accurate reproduction of flash flood events characterised by large and structured rainfall spatial variability, even at catchment scales around 250 km². However, accurate rainfall volume estimation may suffice for less spatially variable flood events. Increasing the soil properties aggregation length exerts similar effects on peak discharge errors as increasing the rainfall aggregation length, for the cases considered here and after rescaling to preserve the rainfall volume. Moreover, peak discharge errors are roughly proportional to runoff volume errors, which indicates that the shape of the flood wave is influenced in a limited way by modifying the detail of the soil property spatial representation. Conversely, rainfall aggregation may exert a pronounced influence on the discharge peak by reshaping the spatial organisation of the runoff volumes and without a comparable impact on the runoff volumes.     

Microwave link rainfall estimation: Effects of link length and frequency,temporal sampling,power resolution,and wet antenna attenuation

Issues associated with microwave link rainfall estimation such as the effects of spatial and temporal variation in rain, the nonlinearity of R–k$R''–''k$ relations, temporal sampling, power resolution, and wet antenna attenuation are investigated using more than 1.5 years of data from a high-resolution X-band weather radar. Microwave link signals are generated for different link frequencies and lengths from these radar data, so that retrieved path-averaged rainfall intensities can be compared to true path-averaged values. Results of these simulations can be linked to the space–time structure of rain. A frequency-dependent relation between the rainfall intensity at an antenna and the attenuation caused by its wetting is derived using microwave link and rain gauge data. It is shown that if the correct temporal sampling strategy is chosen, the effects of the degradation of power resolution and of wet antenna attenuation (if a correction is applied) are minor (i.e., MBE and bias-corrected RMSE are >−20% and <20% of the mean rainfall intensity, respectively) for link frequencies and lengths above ∼20 GHz and ∼2 km, respectively.     

A cascade approach to continuous rainfall data generation at point locations

High-resolution temporal rainfall data sequences serve as inputs for a range of applications in planning, design and management of small (especially urban) water resources systems, including continuous flow simulation and evaluation of alternate policies for environmental impact assessment. However, such data are often not available, since their measurements are costly and time-consuming. One alternative to obtain high-resolution data is to try to derive them from available low-resolution information through a disaggregation procedure. This study evaluates a random cascade approach for generation of high-resolution rainfall data at a point location. The approach is based on the concept of scaling in rainfall, or, relating the properties associated with the rainfall process at one temporal scale to a finer-resolution scale. The procedure involves two steps: (1) identification of the presence of scaling behavior in the rainfall process; and (2) generation of synthetic data possessing same/similar scaling properties of the observed rainfall data. The scaling identification is made using a statistical moment scaling function, and the log–Poisson distribution is assumed to generate the synthetic rainfall data. The effectiveness of the approach is tested on the rainfall data observed at the Sydney Observatory Hill, Sydney, Australia. Rainfall data corresponding to four different successively doubled resolutions (daily, 12, 6, and 3 h) are studied, and disaggregation of data is attempted only between these successively doubled resolutions. The results indicate the presence of multi-scaling behavior in the rainfall data. The synthetic data generated using the log–Poisson distribution are found to exhibit scaling behaviors that match very well with that for the observed data. However, the results also indicate that fitting the scaling function alone does not necessarily mean reproducing the broader attributes that characterize the data. This observation clearly points out the extreme caution needed in the application of the existing methods for identification of scaling in rainfall, especially since such methods are also prevalent in studies of the emerging satellite observations and thus in the broader spectrum of hydrologic modeling.     

Assessment on the function of reservoirs for flood control during typhoon seasons based on a distributed hydrological model

A grid‐based distributed hydrological model, PDTank model, is used to simulate hydrological processes in the upper Tone River catchment. The Tone River catchment often suffers from heavy rainfall events during the typhoon seasons. The reservoirs located in the catchment play an important role in flood regulation. Through the coupling of the PDTank model and a reservoir module that combines the storage function and operation function, the PDTank model is used for flood forecasting in this study. By comparing the hydrographs simulated using gauging and radar rainfall data, it is found that the spatial variability of rainfall is an important factor for flood simulation and the accuracy of the hydrographs simulated using radar rainfall data is slightly improved. The simulation of the typhoon flood event numbered No. 9 shows that the reservoirs in the catchment attenuate the peak flood discharge by 423·3 m³/s and validates the potential applicability of the distributed hydrological model on the assessment of function of reservoirs for flood control during typhoon seasons. Copyright © 2011 John Wiley & Sons, Ltd.     

Investigation of the scale-dependent variability of radar-rainfall and rain gauge error covariance

There is a significant spatial sampling mismatch between radar and rain gauge data. The use of rain gauge data to estimate radar-rainfall error variance requires partitioning of the variance of the radar and rain gauge difference to account for the sampling mismatch. A key assumption in the literature pertaining to the error variance separation method used to partition the variance is that the covariance between radar-rainfall error and the error of rain gauges in representing radar sampling domain is negligible. Our study presents the results of an extensive test of this assumption. The test is based on empirical data and covers temporal scales ranging from 0.25 to 24 h and spatial scales ranging from 1 to 32 km. We used a two-year data set from two high quality and high density rain gauge networks in Oklahoma and excluded the winter months. The results obtained using a resampling procedure show that covariance can be considerable at large scales due to the significant variability. As the variability of the covariance rapidly increases with larger spatial and shorter temporal scales, applications of the error variance separation method at those scales require more caution. The variability of the covariance and one of its constituting variables, the variance ratio of radar and gauge errors, shows simple scaling behavior well characterized by a power-law.     

Rainfall spatial variability observed by X-band weather radar and its implication for the accuracy of rainfall estimates

The main objective of this paper is to estimate the error in the rainfall derived from a polarimetric X-band radar, by comparison with the corresponding estimate of a rain gauge network. However the present analysis also considers the errors inherent to rain gauge, in particular instrumental and representativeness errors. A special emphasis is addressed to the spatial variability of the rainfall in order to appreciate the representativeness error of the rain gauge with respect to the 1 km square average, typical of the radar derived estimate. For this purpose the spatial correlation function of the rainfall is analyzed.     

Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions

Abstract

Given that radar-based rainfall has been broadly applied in hydrological studies, quantitative modelling of its uncertainty is critically important, as the error of input rainfall is the main source of error in hydrological modelling. Using an ensemble of rainfall estimates is an elegant solution to characterize the uncertainty of radar-based rainfall and its spatial and temporal variability. This paper has fully formulated an ensemble generator for radar precipitation estimation based on the copula method. Each ensemble member is a probable realization that represents the unknown true rainfall field based on the distribution of radar rainfall (RR) error and its spatial error structure. An uncertainty model consisting of a deterministic component and a random error factor is presented based on the distribution of gauge rainfall conditioned on the radar rainfall (GR|RR). Two kinds of copulas (elliptical and Archimedean copulas) are introduced to generate random errors, which are imposed by the deterministic component. The elliptical copulas (e.g. Gaussian and t-copula) generate the random errors based on the multivariate distribution, typically of decomposition of the error correlation matrix using the LU decomposition algorithm. The Archimedean copulas (e.g. Clayton and Gumbel) utilize the conditional dependence between different radar pixels to obtain random errors. Based on those, a case application is carried out in the Brue catchment located in southwest England. The results show that the simulated uncertainty bands of rainfall encompass most of the reference raingauge measurements with good agreement between the simulated and observed spatial dependences. This indicates that the proposed scheme is a statistically reliable method in ensemble radar rainfall generation and is a useful tool for describing radar rainfall uncertainty.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Distributed hydrological modelling using weather radar in gauged and ungauged basins

Distributed hydrological modelling using space–time estimates of rainfall from weather radar provides a natural approach to area-wide flood forecasting and warning at any location, whether gauged or ungauged. However, radar estimates of rainfall may lack consistent, quantitative accuracy. Also, the formulation of hydrological models in distributed form may be problematic due to process complexity and scaling issues. Here, the aim is to first explore ways of improving radar rainfall accuracy through combination with raingauge network data via integrated multiquadric methods. When the resulting gridded rainfall estimates are employed as input to hydrological models, the simulated river flows show marked improvements when compared to using radar data alone. Secondly, simple forms of physical–conceptual distributed hydrological model are considered, capable of exploiting spatial datasets on topography and, where necessary, land-cover, soil and geology properties. The simplest Grid-to-Grid model uses only digital terrain data to delineate flow pathways and to control runoff production, the latter by invoking a probability-distributed relation linking terrain slope to soil absorption capacity. Model performance is assessed over nested river basins in northwest England, employing a lumped model as a reference. When the distributed model is used with the gridded radar-based rainfall estimators, it shows particular benefits for forecasting at ungauged locations.     

Ability of a dual polarized X-band radar to estimate rainfall

The aim of this study is to assess rainfall estimates by a dual polarized X-band radar. This study was part of the European project FRAMEA (Flood forecasting using Radar in Alpine and Mediterranean Areas). Two radars were set up near the small town of Collobrières in South Eastern France. The first radar was a dual polarized X-band radar (Hydrix^®) associated with a ZPHI^® algorithm while the second one was an S-band radar (Météo France). We compared radar rainfall data with measurements obtained by two rain gauge networks (Météo France and Cemagref). During the experiments from February 2006 to June 2007, four significant rainfall events occurred. The accuracy of the rain rate obtained with both S-band and X-band radars decreased significantly beyond 60 km, in particular for the X-band radar. At closer ranges, such as 30–60 km from the radars, the X-band and the S-band radar retrievals showed similar performance with Nash criteria around 0.80 for the X-band radar and 0.75 for the S-band radar. Furthermore, the X-band radar did not require calibration on rainfall records, which tends to make it a useful method to assess rainfall in areas without a rain gauge network.     

Dissecting the effect of rainfall variability on the statistical structure of peak flows

This study examines the role of rainfall variability on the spatial scaling structure of peak flows using the Whitewater River basin in Kansas as an illustration. Specifically, we investigate the effect of rainfall on the scatter, the scale break and the power law (peak flows vs. upstream areas) regression exponent. We illustrate why considering individual hydrographs at the outlet of a basin can lead to misleading interpretations of the effects of rainfall variability. We begin with the simple scenario of a basin receiving spatially uniform rainfall of varying intensities and durations and subsequently investigate the role of storm advection velocity, storm variability characterized by variance, spatial correlation and intermittency. Finally, we use a realistic space–time rainfall field obtained from a popular rainfall model that combines the aforementioned features. For each of these scenarios, we employ a recent formulation of flow velocity for a network of channels, assume idealized conditions of runoff generation and flow dynamics and calculate peak flow scaling exponents, which are then compared to the scaling exponent of the width function maxima. Our results show that the peak flow scaling exponent is always larger than the width function scaling exponent. The simulation scenarios are used to identify the smaller scale basins, whose response is dominated by the rainfall variability and the larger scale basins, which are driven by rainfall volume, river network aggregation and flow dynamics. The rainfall variability has a greater impact on peak flows at smaller scales. The effect of rainfall variability is reduced for larger scale basins as the river network aggregates and smoothes out the storm variability. The results obtained from simple scenarios are used to make rigorous interpretations of the peak flow scaling structure that is obtained from rainfall generated with the space–time rainfall model and realistic rainfall fields derived from NEXRAD radar data.     

Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data

The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.     

Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data

The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.     

Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes

Diverse linear and nonlinear statistical parameters of rainfall under aggregation in time and the kind of temporal memory are investigated. Data sets from the Andes of Colombia at different resolutions (15 min and 1-h), and record lengths (21 months and 8-40 years) are used. A mixture of two timescales is found in the autocorrelation and autoinformation functions, with short-term memory holding for time lags less than 15-30 min, and long-term memory onwards. Consistently, rainfall variance exhibits different temporal scaling regimes separated at 15-30 min and 24 h. Tests for the Hurst effect evidence the frailty of the R/S approach in discerning the kind of memory in high resolution rainfall, whereas rigorous statistical tests for short-memory processes do reject the existence of the Hurst effect.Rainfall information entropy grows as a power law of aggregation time, S(T) ∼ T^β with 〈β〉 = 0.51, up to a timescale, T_MaxEnt (70-202 h), at which entropy saturates, with β = 0 onwards. Maximum entropy is reached through a dynamic Generalized Pareto distribution, consistently with the maximum information-entropy principle for heavy-tailed random variables, and with its asymptotically infinitely divisible property. The dynamics towards the limit distribution is quantified. Tsallis q-entropies also exhibit power laws with T, such that S_q(T) ∼ T^β(q), with β(q) ? 0 for q ? 0, and β(q) ? 0.5 for q ? 1. No clear patterns are found in the geographic distribution within and among the statistical parameters studied, confirming the strong variability of tropical Andean rainfall.     

Improving NWP through radar rainfall-driven land surface parameters: A case study on convective precipitation forecasting

In this study we investigate the effect of forcing the land surface scheme of an atmospheric mesoscale model with radar rainfall data instead of the model-generated rainfall fields. The goal is to provide improved surface conditions for the atmospheric model in order to achieve accurate simulations of the mesoscale circulations that can significantly affect the timing, distribution and intensity of convective precipitation. The performance of the approach is evaluated in a set of numerical experiments on the basis of a 2-day-long mesoscale convective system that occurred over the US Great Plains in July 2004. The experimental design includes multiple runs covering a variety of forcing periods. Continuous data integration was initially used to investigate the sensitivity of the model’s performance in varying soil state conditions, while shorter time windows prior to the storm event were utilized to assess the effectiveness of the procedure for improving convective precipitation forecasting. Results indicate that continuous integration of radar rainfall data brings the simulated precipitation fields closer to the observed ones, as compared to the control simulation. The precipitation forecasts (up to 48 h) appear improved also in the cases of shorter integration periods (24 and 36 h), making this technique potentially useful for operational settings of weather forecasting systems. A physical interpretation of the results is provided on the basis of surface moisture and energy exchange.     

Estimation of tail dependence coefficient in rainfall accumulation fields

Extreme rainfall events are of particular importance due to their severe impacts on the economy, the environment and the society. Characterization and quantification of extremes and their spatial dependence structure may lead to a better understanding of extreme events. An important concept in statistical modeling is the tail dependence coefficient (TDC) that describes the degree of association between concurrent rainfall extremes at different locations. Accurate knowledge of the spatial characteristics of the TDC can help improve on the existing models of the occurrence probability of extreme storms. In this study, efficient estimation of the TDC in rainfall is investigated using a dense network of rain gauges located in south Louisiana, USA. The inter-gauge distances in this network range from about 1 km to 9 km. Four different nonparametric TDC estimators are implemented on samples of the rain gauge data and their advantages and disadvantages are discussed. Three averaging time-scales are considered: 1 h, 2 h and 3 h. The results indicate that a significant tail dependency may exist that cannot be ignored for realistic modeling of multivariate rainfall fields. Presence of a strong dependence among extremes contradicts with the assumption of joint normality, commonly used in hydrologic applications.     

Estimation of rainfall from infrared‐microwave satellite data for basin‐scale hydrologic modelling

The infrared‐microwave rainfall algorithm (IMRA) was developed for retrieving spatial rainfall from infrared (IR) brightness temperatures (TBs) of satellite sensors to provide supplementary information to the rainfall field, and to decrease the traditional dependency on limited rain gauge data that are point measurements. In IMRA, a SLOPE technique (ST) was developed for discriminating rain/no‐rain pixels through IR image cloud‐top temperature gradient, and 243K as the IR threshold temperature for minimum detectable rainfall rate. IMRA also allows for the adjustment of rainfall derived from IR‐TB using microwave (MW) TBs. In this study, IMRA rainfall estimates were assessed on hourly and daily basis for different spatial scales (4, 12, 20, and 100 km) using NCEP stage IV gauge‐adjusted radar rainfall data, and daily rain gauge data. IMRA was assessed in terms of the accuracy of the rainfall estimates and the basin streamflow simulated by the hydrologic model, Sacramento soil moisture accounting (SAC‐SMA), driven by the rainfall data. The results show that the ST option of IMRA gave accurate satellite rainfall estimates for both light and heavy rainfall systems while the Hessian technique only gave accurate estimates for the convective systems. At daily time step, there was no improvement in IR‐satellite rainfall estimates adjusted with MW TBs. The basin‐scale streamflow simulated by SAC‐SMA driven by satellite rainfall data was marginally better than when SAC‐SMA was driven by rain gauge data, and was similar to the case using radar data, reflecting the potential applications of satellite rainfall in basin‐scale hydrologic modelling. Copyright © 2010 John Wiley & Sons, Ltd.