Kaz Adamowski

Regional analysis of annual maximum and partial duration flood data by nonparametric and L-moment methods

Abstract The analysis of annual maximum (AM) flood series has revealed unimodal and multimodal probability density functions for floods in the Provinces of Ontario and Quebec, Canada. Based on density function shapes and the timing of floods, Ontario and Quebec have been divided into nine homogeneous regions reflecting similar flood generating mechanisms. A similar analysis of peak over threshold or partial duration (PD) data also revealed unimodality and bimodality linked to flood-generating mechanisms. These results point out deficiencies in currently used parametric approaches for both AM and PD series, since traditional regional flood frequency analysis procedures assume that all floods within a homogeneous region are generated by the same, often unimodal distribution. The analysis of AM and PD series using L-moments revealed that while the overall series did not appear to be unimodal, separate rainfall and snowmelt PD series extracted from the same data set could each be described by unimodal distributions. L-moment tests confirmed that separate rainfall and snowmelt PD series statistics are homogeneous but the overall series is heterogeneous. A regional relationship is developed using nonparametric analysis on the AM and PD flood series. Using the Geographic Information System methodology, mapping was performed for the site-specific L_coefficient of variation and the average snowpack depth. This analysis revealed an apparent correspondence between these variables.

A Monte Carlo comparison of parametric and nonparametric estimation of flood frequencies

Abstract The relationship of flood magnitude to frequency of occurrence can be estimated from observed annual flood data by the parametric method of fitting any of various theoretical distributions (e.g., Log-Pearson Type III) to the data, or by the nonparametric method, which does not require a distributional assumption. The fixed and variable kernel nonparametric methods are investigated in this paper, and are compared, using a Monte Carlo simulation technique. It is concluded that nonparametric methods are accurate, uniform, and particularly suitable for multimodal data. In addition, the variable kernel method provides more accurate estimates of the tail of a distribution.

Regional rainfall distribution for Canada

Abstract Current point rainfall frequency analysis techniques used in engineering design are outdated. In this study, data distribution and analytical techniques are reviewed, and a new method for regional analysis of rainfall is presented. The regional analysis is performed using data across Canada, and takes advantage of recently developed linear order statistics of L-moments. Numerical analysis of 320 stations showed that Canada may be considered as one homogeneous region with respect to L-skewness and L-kurtosis. However, the L-coefficient of variation shows regional variability that is related to the mean annual precipitation (MAP). A regional parent distribution is identified as the general extreme value (GEV), with parameters depending on MAP and storm duration. These findings differ from present methodology, whereby the Gumbel I distribution is used irrespective of storm duration.

Regional analysis of annual maxima precipitation using L-moments

Abstract Current precipitation frequency analysis used as a standard for urban runoff calculations are out of date. In this paper, the form of the distribution governing rainfall intensity of various durations in a regional context is investigated using the method of L -moments. The results indicate that the currently used Gumbel type I distribution is not generally valid for all the durations considered in this analysis. The form of the distribution is dependent on the duration of the event being considered.

Asymptotic variance of flood quantile in log Pearson Type III distribution with historical information

Maximum likelihood and censored sample theory are applied for flood frequency analysis purposes to the log Pearson Type III (LP3) distribution. The logarithmic likelihood functions are developed and solved in terms of fully specified floods, historical information, and parameters to be estimated. The asymptotic standard error of estimate of the T-year flood is obtained using the general equation for the variance of estimate of a function. The variances and covariances of the parameters are obtained through inversion of Fishers information matrix. Monte Carlo studies to verify the accuracy of the derived asymptotic expression for the standard errors of the 10, 50, 100, and 500 year floods, indicate that these are accurate for both Type I and Type II censored samples, while the bias is less than 2.5%. Subsequently, the Type II censored data were subjected to a random, multiplicative error. Results indicate that historical information contributes greatly to the accuracy of estimation of the quantiles even when the error of its measurement becomes excessive.

Detection of Trends in Low Flows across Canada

A study of trends and variability of low flow characteristics was conducted for the Reference Hydrometric Basin Network (RHBN). A seven-day low-flow index from 57 hydrometric stations was extracted and examined to detect trends and changes in the timing of summer and winter seven-day low-flows. A modified Mann-Kendall (MK) nonparametric trend test was applied to the time series at a 0.05 significance level. The variance of the S statistic was modified if the absolute value of serial correlation was significant at a 0.1 significance level. Numerical analysis indicated that northern Canada (stations located above latitude 60oN) experienced an increasing significant trend in seven-day low-flows. A significant downward trend dominated the Atlantic Provinces and southern British Columbia. No evidence of significant trends in the Prairies and eastern Ontario was found. Summer seven-day low-flow shifted to arrive earlier in the year in the Atlantic Provinces and southern Ontario; however, it arrived later in the year in western and northwestern Canada. In 88% of significant trends, winter seven-day low-flow shifted to arrive earlier. Although both winter and summer low flows experienced a shift towards earlier dates in the eastern part of the country, they were in opposite direction in western Canada where winter seven-day low-flows were arriving earlier whereas summer seven-day low-flows were arriving later in the year.

Regional flood frequency analysis using GIS, L-moment and geostatistical methods

Advances in space -time tools and techniques offer new possibilities to improve methods for exploratory data analysis and parameter estimation in regional flood frequency analysis (FFA). A general framework and methodological approach are proposed which integrate concepts and techniques of regional FFA, geostatistical theory and analytical geographical information systems (GIS) using data on climate, vegetation, geography and flood timing and magnitude statistics. Non-parametric methods are used to screen data and to delineate homogeneous regions. Simulations are used to identify discordant sites, diagnose each region using the signal-to-noise ratio and test regions for homogeneity based on L-moment ratios. Geostatistical measures of spatial autocorrelation are used to diagnose hierarchical spatial models for each L-moment ratio and to obtain map estimates of parameters using spatially explicit kriging techniques (analogous to regression). In addition to storing and displaying the spatio-temporal information accurately, the GIS is used to quantify spatial associations between dependent and independent variables and to diagnose homogeneous regions for further refinement using a simple spatial contrast measure. Analysis of data from central and eastern Canada (except the eastern parts of Newfoundland), encompassing a large area with significant random and systematic variability, demonstrates that: (i) map sets of L-mean and L-CV (coefficient of variation) for flood timing and magnitude can serve as indicators of climatic influences on the flood-generating mechanisms; (ii) models of spatial autocorrelation can be used to map point variables and their geostatistical spatial variance, which indicates whether maps are significant; and (iii) associations between L-CV and snow or vegetation could support improved mapping using co-kriging or geostatistical simulations. The mapbased method provides parameter values at ungauged sites and maps of spatial variance that could support decisions to add or remove gauges from a hydrometric network.

Stochastic analysis of Lake Superior elevations for computation of relative crustal movement

Abstract Using Lake Superior mean monthly elevations as recorded at five gauges around the lake, time series of elevations and differences in elevations between pairs of gauges were analysed for trends, periodicities and autoregressive components. It was found that the variance of the time series of elevations consisted of 4–12% linear trends, 35–44% periodicities in the mean, 0.23–0.66% periodicities in the variance, a 43–54% autoregressive component and a 5% random component. On the other hand, the time series of differences in lake elevations were found to consist of 30–52% linear trends, 5–35% periodicities in the mean and variance, up to a 30% autoregressive component and a random component of 21–31%. Rates of crustal movement were computed from the trends in gauge differences.

Annual maxima and partial duration flood series analysis by parametric and non-parametric methods

Annual maxima (AM) and partial duration (PD) flood series are modelled by parametric and non-parametric methods. In PD analysis the number of threshold exceedances is assumed to be Poisson distributed: the peak exceedances are described by the generalized Pareto (GP) and non-parametric (NP) distributions. The generalized extreme value (GEV) and non-parametric (NP) distributions are used to describe the AM series. L-moments are employed for parameter estimation for GEV and GP distributions. Analysis of data from the provinces of Quebec and Ontario, Canada, shows that both AM and PD series can be inferred as being unimodal and bimodal, both of which can be described by the NP method. Also, this method is found not to be sensitive to the choice of threshold level; however, it was also observed that parametric methods cannot detect biomodality, give different quantile estimates for AM and PD data and PD estimates are sensitive to the selection of threshold level. Therefore, the NP method is more advantageous than the parametric methods in flood frequency analysis for both AM and PD series.

Homogeneous region delineation based on annual flood generation mechanisms

Flood distributions can have unimodal or multimodal densities due to different flood generation mechanisms such as snowmelt and rainfall in the annual flood series. When applying nonparametric frequency analysis to annual flood data from the province of New Brunswick in Canada, unimodal, bimodal and heavy-tailed distribution shapes were found. By grouping basins with similarly-shaped densities on a geographical basis, homogeneous regions were delineated. Regional equations derived for a homogeneous region gave lower integral square errors than those of province-wide equations.