Peter F. Rasmussen

Recent advances in flood frequency analysis

Research on flood frequency analysis has taken place with varying intensity over the last couple of decades. The eighties proved to be important years with many significant contributions, reviewed for instance by Greis [1983], Potter [1987], Kirby and Moss [1987], Cunnane [1987], NRC [1988], WMO [1989], and Bobee and Ashkar [1991]. Due to its large economical and environmental impact, flood frequency analysis remains a subject of great importance and interest, and the research on improved methods for obtaining reliable flood estimates has continued into the nineties, although with different emphasis. In the seventies and eighties much effort was spent on developing efficient at-site flood frequency procedures. New distributions and estimation methods were introduced in the hydrologic journals, some of them developed specifically for flood frequency analysis. It seems that this tendency has decelerated somewhat in the beginning of the nineties. Researchers are increasingly realizing that the lack of sufficiently long data series imposes an upper limit on the degree of sophistication that can reasonably be justified in at-site flood frequency analysis. It has been emphasized by many that instead of developing new methodologies for flood frequency analysis, effort should be spent on comparing existing ones and on looking for other sources of information [Potter, 1987; Bobee et al, 1993a]. Regionalization is probably the most viable avenue for improving flood estimates, and fortunately this seems to be the direction that the research in flood frequency analysis has taken in the nineties.

A recurrent neural networks approach using indices of low‐frequency climatic variability to forecast regional annual runoff

This paper evaluates the potential of using low-frequency climatic mode indices to forecast regional annual runoff in northern Quebec and the Labrador region. The impact of climatic trends in the forecast accuracy is investigated using a recurrent neural networks (RNN) approach, time-series of inflow to eight large hydropower systems in Quebec and Labrador, and indices of selected modes of climatic variability: El Nino-Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), Pacific-North American (PNA), Baffin Island-West Atlantic (BWA) and sea-level pressure (SLP) at Iceland. A wavelet analysis is used to show that the selected climatic patterns are related to annual runoff from 1950 to 1996 in northern Quebec. The forecast results indicate that the use of BWA, PNA and ENSO indices results in better forecast skill than the use of SLP or NAO. Overall, the use of the BWA index is found to provide the best forecast improvement (38% on average), whereas the use of PNA provides 28% of improvement on average. Using the SLP index improves the forecast accuracy by 4%, and the use of an ENSO indicator leads to an improvement of 6%. The NAO index used here is found to provide only a modest improvement.

Generalized probability weighted moments: Application to the generalized Pareto Distribution

Probability weighted moments (PWMs) are widely used in hydrology for estimating parameters of flood distributions. The classical PWM approach considers moments of the type E[XFj] (or, alternatively, E[X(1 − F)k]), where j (or k) takes values 0, 1, or 2 depending on the number of parameters to be estimated. The classical approach is here compared with an extended class of PWMs that does not restrict j or k to be small nonnegative integers. Estimation based on the extended class of PWMs is named the generalized method of PWMs to distinguish it from the classical procedure. To illustrate the method, we consider estimation of quantiles in the generalized Pareto distribution and demonstrate that substantial gain in estimation accuracy can be obtained by using generalized PWMs.

Bayesian Estimation of change points using the general linear model

Bayesian analysis is applied to the general linear model to develop a framework for studying different types of change in the mean value of time series and linear regressions. The output of the Bayesian analysis is the posterior distribution of change point location and amplitude. This information provides a rational and relatively objective basis for making decisions as to where to locate a change point. Several examples of hydrological applications are presented to demonstrate the utility of the methodology.

Use of the North American Regional Reanalysis for Hydrological Modelling in Manitoba

This study investigates the applicability of temperature and precipitation data from the North American Regional Reanalysis (NARR) for hydrological modelling of selected watersheds in northern Manitoba. For the specific region, it is found that NARR temperature and precipitation data are in much better agreement with observations than a popular global reanalysis data set. The hydrological model SLURP (Semi-distributed Land Use-based Runoff Processes) was set up and calibrated for three catchments (Burntwood, Taylor and Sapochi), using meteorological data from weather stations. When the calibrated models were run with temperature and precipitation data from NARR, runoff was underestimated by approximately 20%. The SLURP model was then recalibrated using the NARR temperature and precipitation data as input. This eliminated much of the bias and provided a goodness-of-fit that was only slightly inferior to simulations with observed weather data. This suggests that SLURP can be adequately calibrated with NARR data and used for modelling hydrological processes in northern Manitoba where weather stations are scarce.

Alternative PWM-estimators of the Gumbel distribution

Abstract Probability weighted moments (PWM) are widely used in hydrology for estimating parameters of statistical distributions, including the Gumbel distribution. The classical PWM-approach considers the moments β i = E [ XF i ] with i =0,1 for estimation of the Gumbel scale and location parameters. However, there is no reason why these probability weights ( F 0 and F 1 ) should provide the most efficient PWM-estimators of Gumbel parameters and quantiles. We explore an extended class of PWMs that does not impose arbitrary restrictions on the values of i . Estimation based on the extended class of PWMs is called the generalized method of probability weighted moments (GPWM) to distinguish it from the classical procedure. In fact, our investigation demonstrates that it may be advantage to use weight functions that are not of the form F i . We propose an alternative PWM-estimator of the Gumbel distribution that maintains the computational simplicity of the classical PWM method, but provides slightly more accurate quantile estimates in terms of mean square error of estimation. A simple empirical formula for the standard error of the proposed quantile estimator is presented.

Performance Evaluation of the Canadian Precipitation Analysis (CaPA)

AbstractThis paper presents an assessment of the operational system used by the Meteorological Service of Canada for producing near-real-time precipitation analyses over North America. The Canadian Precipitation Analysis (CaPA) system optimally combines available surface observations with numerical weather prediction (NWP) output in order to produce estimates of precipitation on a 15-km grid at each synoptic hour (0000, 0600, 1200, and 1800 UTC). The validation protocol used to assess the quality of the CaPA has demonstrated the usefulness of the system for producing reliable estimates of precipitation over Canada, even in areas with few or no weather stations. The CaPA is found to be better in autumn, spring, and winter than in summer. This is because of the difficulty in correctly producing convective precipitation in the NWP because of the low spatial resolution of the meteorological model. An investigation of the quality of the precipitation analyses in the 15 terrestrial ecozones of Canada indicates ...

A distribution function based bandwidth selection method for kernel quantile estimation

The key problem in nonparametric frequency analysis of flood and droughts is the estimation of the bandwidth parameter which defines the degree of smoothing. Most of the proposed bandwidth estimators have been based on the density function rather than the cumulative distribution function or the quantile that are the primary interest in frequency analysis. We propose a new bandwidth estimator derived from properties of quantile estimators. The estimator builds on work by Altman and Leger (1995). The estimator is compared to the well-known method of least squares cross-validation (LSCV) using synthetic data generated from various parametric distributions used in hydrologic frequency analysis. Simulations suggest that our estimator performs at least as well as, and in many cases better than, the method of LSCV. In particular, the use of the proposed plug-in estimator reduces bias in the estimation as compared to LSCV. When applied to data sets containing observations with identical values, typically the result of rounding or truncation, the LSCV and most other techniques generally underestimates the bandwidth. The proposed technique performs very well in such situations.

Regional estimation of flood quantiles: Parametric versus nonparametric regression models

A recent trend in regional frequency analysis is to consider floating regions where only basins that are sufficiently similar to the design site are considered for information transfer. Similarity is measured in some suitable metric of catchment characteristics. This paper discusses the analogy between this idea and nonparametric regression. Some of the techniques developed recently in the area of nonparametric regression are employed to develop improved regional flood estimators. The additive model used here to a large extent overcomes the curse of dimensionality often associated with nonparametric regression on multivariate predictor space. The application of the proposed methodology to selected areas of the United States suggests that there can be substantial gains over the traditional log linear models currently employed.

Assessing the impact of climate change on the frequency of floods in the Red River basin

The impact of climate change on the frequency distribution of spring floods in the Red River basin is investigated. Several major floods in the last couple of decades have caused major damages and inconvenience to people living in the Red River flood plain south of Winnipeg, and have raised the question of whether climate change is at least partly responsible for what appears to be more frequent occurrences of high spring runoff. To investigate whether this is the case, a regression model is used to associate spring peak flow at the US–Canada border with predictor variables that include antecedent precipitation in the previous fall (used as a proxy for soil moisture at freeze-up), winter snow accumulation and spring precipitation. Data from the Coupled Model Intercomparison Project – Phase 5 (CMIP5) are used to derive information about possible changes to the predictor variables in the future, and this information is then used to derive flood distributions for future climate conditions. While mean monthly precipitation during the winter months is expected to increase, winters are expected to be shorter in warmer climates and evaporation losses are expected to be higher, resulting in a net reduction in average snow pack accumulations. On the other hand, precipitation during the active snowmelt period is expected to increase. The average of future flood distributions obtained from an ensemble of 16 climate models is close to the distribution fitted to observed data, but there is considerable uncertainty surrounding the average, highlighting the difficulty in assessing changes in the frequency of extreme events.