H41A-01
Validation of ground-based radar rain-rate estimates using flow measurements: the role of scale behavior
Validation is an essential step in the use of radar data for rainfall-rate estimation. However, the different scales of measurement between radar pixels and rain gauges, combined with the intrinsic space-time variability of the process, creates a non-trivial problem in the attempt of performing the validation, a fact that has been mentioned repeatedly in recent literature. In the present work, we therefore attempt a validation from ground-based radar precipitation estimates at various scales, involving a combination of rain gauge scale and an integral river-flow scale. We are using ground-based radar rain-rate estimates from the years 2002 to 2004, over an area located at the Mexico-USA border, around 30N-100W, besides rain-gauge and river-flow measurements from a hydrometric station during the same period. The results of the comparison are used to validate a scaling model of precipitation space-time variability, which in turn gives us an estimate of the expected averaging errors of estimations.
H41A-02
Design Flood Estimation in the Presence of Nonstationarity: Overcoming the Limitations of Traditional Flood Frequency Analysis
Issues arising from climate change and long-term climate variability have become the focus of much recent research. Traditional flood frequency analysis assumes stationarity, and cannot account for the non-stationarity in flood frequency distributions caused by long-term climate variability and human-induced climatic or land use change. In this paper, we will specifically discuss their impacts of climate variability and change on flood frequencies. The analysis of the flood frequencies are investigated in semiarid-temperate and tropical landscapes in Australia, using the derived flood frequency approach. These approaches are driven by rainfall event sequences generated by a stochastic rainfall model coupled with a rainfall-runoff model that captured the water balance variability at a multiplicity of time scales ranging from event to seasonal, inter-annual and multi- decadal time scales. The study demonstrates that the multi-annual, multi-decadal trends and long term climate shifts have a significant impact upon the flood frequencies. On the basis of these results a new variation to traditional flood frequency estimation procedures, based on flood risk assessment, is proposed as a potential solution to overcome the limitations of the traditional flood frequency analysis.
H41A-03
Flow Rate Estimation via Inverse Flood Routing and Spectral Error Control
Flow rate gauging stations along river channels are located at topographical constrictions where a hydraulic control is likely to exist. Dams are also located at topographic constrictions and, particularly in developing countries, the operation of flow rate gauging stations is discontinued once a dam has been built at the same or nearly the same site where the station was located. Thereafter, to keep the flow rate record up to date, the dam reservoir is used as a measurement device; i.e., inflow rates are estimated by employing the observed time evolution of the reservoir water levels and solving the continuity equation in an inverse fashion, a procedure known as "inverse flood routing". The inverse numerical solution of such equation entails dividing stored volume differences in a given time interval by the time step. Numerical procedures such as the popular trapezoidal rule, perform very poorly in the solution of the inverse problem. This is due to the fact that small errors in water levels are amplified when stored volumes are estimated, and amplified once again when stored volume differences are divided by small time steps. A theoretical analysis of the problem is presented and the performance of the trapezoidal rule (Crank-Nicolson), the second order Adams-Bashforth scheme, and the central difference scheme, is evaluated. By employing an analytical solution of the reservoir flood routing problem and an error propagation analysis, it is shown that the third scheme outperforms the other two, since it is the only one that does not propagate the error in a given time level to succeeding time levels. Now, some times the use of the central difference scheme is not enough to counteract the influence of errors in water levels, since these may contain a large level of high frequency components. Hence, water level and stored volume spectra are estimated, in order to identify spurious Fourier components, which may be eliminated via filtering. The application of the combined central difference-spectral error control methodology to various rivers and dams in Mexico produces excellent results.
H41A-04 INVITED
Bivariate estimation of dam design floods
Design floods for dams and reservoirs are often estimated on the basis of flood frequency analysis. This method consists of fitting a theoretical extreme-value probability distribution to the maximum annual flow rate data collected at a streamflow gauging station, thus enabling the hydrologist to estimate, via extrapolation, the flow rate or peak discharge corresponding to a given design return period. It is often the case that medium- to large-sized dams are designed by using return periods of up to 10,000 years. Even though fewer dams are under construction nowadays than in the past, it is also necessary to revise design flood from time to time, as new data become available, especially when retrofitting plans are underway. A design flood is fully characterized by a hydrograph, which is routed through the reservoir in order to determine its flood control capacity and the spillway design discharge. Nevertheless, flood frequency analyses often rely upon the estimation of probability distributions associated with peak discharges only. The determination of the design hydrograph is usually made through arbitrary procedures, such as assuming that its form is the same as the one corresponding to the hydrograph of the largest recorded flood. The simplest characterization of a hydrograph must involve, at least, its most important characteristics, namely: peak discharge, time to peak and volume. However, the authors of this paper have performed a sensitivity analysis that shows that the two most important parameters in characterizing a hydrograph, in terms of the response of a reservoir are the peak discharge and the runoff volume. Furthermore, experience demonstrates that the response of some reservoirs may be more sensitive to the flood runoff volume than to its peak discharge. Thus it is highly desirable to address the problem of characterizing the whole design hydrograph in a probabilistic framework. On the basis of these results, a new approach for estimating the design flood of dams and reservoirs has been developed. The method is based on the use of the bivariate extreme-value distribution of peak discharge and volume. Thus, an expression for the joint return period of these two parameters is derived. It is shown that an infinite number of pairs of peak discharge and volume possess a given joint return period. Hence, in order to determine the design flood hydrograph, a nonlinear optimization problem is posed. The solution of this problem represents the combination of values of peak discharge and volume that produces the worst effect on the reservoir for a given joint return period. The worst effect is obtained by choosing the combination of peak discharge and volume that produces the highest level of the water surface and, by correspondence, the highest flow through the spillway. The methodology was applied to the revision of several dams in Mexico finding that some of them are not as safe as it was supposed.
H41A-05 INVITED
Bayesian Combination of Regional and Local Information Using Some Common Distributions in Hydrology
The main challenge in flood frequency analysis is to find relevant and sufficient information to fit a local distribution with an acceptable precision to the variable of interest. This precision impacts the cost and reliability of hydraulic structures as well as the safety of downstream communities. If the site of interest has been monitored for a sufficiently long period (more than 30-40 years), at-site frequency analysis can be used to estimate flood quantiles with a fair precision. Otherwise, regional estimation may be used to mitigate the lack of data, but local information is then ignored. The authors propose a Bayesian method in this paper that uses both sources of information for even more precise quantile estimation. The proposed method uses the classical log- linear regression as regional model and assumes that the local flood peaks are GEV, Gamma, Weibull, Log- Normal or exponentially distributed. The method works even with a single local observation besides relaxing the hypothesis of normality of the quantiles probability distribution that is used in the empirical Bayes approach. A thorough performance assessment was made with the GEV distribution and it was shown that a) when the regional model is unbiased, the proposed method gives better estimation of the GEV quantiles and parameters than the local, regional and empirical Bayes estimators; b) even when the regional model displays a severe relative bias when estimating the quantiles, the proposed method still gives the best estimation of the GEV shape parameter and outperforms the other approaches on higher quantiles provided that the relative bias is the same for all quantiles; c) the gain in performance with the new approach is considerable for sites with very short records. Theoretical developments and some preliminary results are presented for the other distributions. Keywords: regionalization, probability distribution, linear regression, empirical Bayesian method, flood frequency analysis, combination.
H41A-06 INVITED
Scaling and Extremes in precipitation and streamflow
The hydrologic cycle begins with precipitation input followed by topography modulated runoff leading to streamflow distributed over river networks. Each of these parts of the cycle involve spatial structures varying over planetary down to millimetric scales; in time, the precipitation and streamflow are strongly variable from climatological scales down to less than a second. In the last 25 years much progress has been made in understanding scaling processes which generically generate variability over huge ranges. Scaling processes have nonlinear dynamical mechanisms which repeat scale after scale from large to small scales leading to non- classical multifractal resolution dependencies. This means that the statistical properties vary systematically in strong, power law ways with the resolution, that classical geostatistics - which assume strong regularity and homogeneity assumptions - do no apply. We can now broadly understand hydrological variability as a consequence of scale invariant dynamics - although as we discuss - the notion of scale invariance must be suitably generalized to take into account the strong (spatial and space-time) anisotropies of the processes. These nonclassical scaling "cascade" processes have the particularity that the variability builds up scale by scale so that at any given scale the variability is precisely the consequence of the huge dynamical range of the phenomena. Due to the existence of stable, attractive multifractal processes, in the limit of a large number of interacting processes or scales, only three "universal" parameters are generally important. These generic features of scaling imply that at a given finite scale, the variability due to the effects of the larger scales is enough to give rise to long-tailed lognormal and log-Levy distributions. However if we also take into account the "hidden" subgrid variability, then we find that the extremes are even stronger; they are generically power laws, "fat-tailed". In this way, cascades provide a nonclassical route to Self-Organized Criticality. We illustrate these ideas on both precipitation data from the recent HYDROP stereophotography experiment which directly determined the size and position of drops and - at the other scale extreme - the planetary TRMM (Tropical Rainfall Monitoring Mission) satellite radar data from 5 - 20,000km scales. We then review recent analyses of streamflow showing how the mean flow information - coupled with universal multifractal parametrizations with power law tails - can be used to estimate return times for extreme flood events.
H41A-07
Space-time Scaling of Radar Precipitation
Radar measurements offer a space-time detailed image of precipitation. Spatial and temporal scaling properties of these datasets are compared to those obtained from point observations. A dataset of 2 years radar observations in South-West Germany is used for this purpose. The influence of random measurement errors, spatially dependent support of the radar measurements and the temporal representativity of the measurements is investigated to explain the differences of the results.