Extreme precipitation time trends in Ontario, 1960–2010

The impact of climate change on the behaviour of intensity–duration–frequency curves is critical to the estimation of design storms, and thus to the safe design of drainage infrastructure. The present study develops a regional time trend methodology that detects the impact of climate change on extreme precipitation from 1960 to 2010. The regional time trend linear regression method is fitted to different durations of annual maximum precipitation intensities derived from multiple sites in Ontario, Canada. The results show the relationship between climate change and increased extreme precipitation in this province. The regional trend analysis demonstrates, under nonstationary conditions arising from climate change, that the intensity of extreme precipitation increased decennially between 1.25% for the 30‐min storm and 1.82% for the 24‐h storm. A comparison of the results with a regional Mann–Kendall test validates the found regional time‐trend results. The results are employed to extrapolate the intensity–duration–frequency curves temporally and spatially for future decades across the province. The results of the regional time trend assessment help with the establishment of new safety margins for infrastructure design in Ontario. Copyright © 2016 John Wiley & Sons, Ltd.     

Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity

This paper proposes an approach to estimating the uncertainty related to EPA Storm Water Management Model model parameters, percentage routed (P_R) and saturated hydraulic conductivity (K_sat), which are used to calculate stormwater runoff volumes. The methodology proposed in this paper addresses uncertainty through the development of probability distributions for urban hydrologic parameters through extensive calibration to observed flow data in the Philadelphia collection system. The established probability distributions are then applied to the Philadelphia Southeast district model through a Monte Carlo approach to estimate the uncertainty in prediction of combined sewer overflow volumes as related to hydrologic model parameter estimation. Understanding urban hydrology is critical to defining urban water resource problems. A variety of land use types within Philadelphia coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils. The complexity of urban hydrology can make model parameter estimation and defining model uncertainty a difficult task. The development of probability distributions for hydrologic parameters applied through Monte Carlo simulations provided a significant improvement in estimating model uncertainty over traditional model sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

On robustness of large quantile estimates to largest elements of the observation series

The robustness of large quantile estimates of largest elements in a small sample by the methods of moments (MOM), L‐moments (LMM) and maximum likelihood (MLM) was evaluated and compared. Bias (B) and mean square error (MSE) were used to measure the estimation methods performance. Quantiles were estimated by eight two‐parameter probability distributions with the variation coefficient being the shape parameter. The effect of dropping largest elements of the series on large quantile values was assessed for various variation coefficient (C_V)/sample size (n) ‘combinations’ with n = 30 as the basic value. To that end, both the Monte Carlo sampling experiments and an asymptotic approach consisting in distribution truncation were applied. In general, both sampling and asymptotic approaches point to MLM as the most robust method of the three considered, with respect to bias of large quantiles. Comparing the performance of two other methods, the MOM estimates were found to be more robust for small and moderate hydrological samples drawn from distributions with zero lower‐bound than were the LMM estimates. Extending the evaluation to outliers, it was shown that all the above findings remain valid. However, using the MSE variation as a measure of performance, the LMM was found to be the best for most distribution/variation coefficient combinations, whereas MOM was found to be the worst. Moreover, removal of the largest sample element need not result in a loss of estimation efficiency. The gain in accuracy is observed for the heavy‐tailed and log‐normal distributions, being particularly distinctive for LMM. In practice, while dealing with a single sample deprived of its largest element, one should choose the estimation method giving the lowest MSE of large quantiles. For n = 30 and several distribution/variation coefficient combinations, the MLM outperformed the two other methods in this respect and its supremacy grew with sample size, while MOM was usually the worst. Copyright © 2006 John Wiley & Sons, Ltd.     

Changing river temperatures in northern Germany: trends and drivers of change

Climate change is one of the main drivers of river warming worldwide. However, the response of river temperature to climate change differs with the hydrology and landscape properties, making it difficult to generalize the strength and the direction, of river temperature trends across large spatial scales and various river types. Additionally, there is a lack of long‐term and large‐scale trend studies in Europe as well as globally. In this study, we investigated the long‐term (25 years; 132 sites) and the short‐term (10 years; 475 sites) river temperature trends, patterns and underlying drivers within the period 1985–2010 in seven river basins of Germany. The majority of the sites underwent significant river warming during 1985–2010 (mean warming trend: 0.03 °C year^?1, SE = 0.003), with a faster warming observed during individual decades (1985–1995 and 2000–2010) within this period. Seasonal analyses showed that, while rivers warmed in all seasons, the fastest warming had occurred during summer. Among all the considered hydro‐climatological variables, air temperature change, which is a response to climate forcing, was the main driver of river temperature change because it had the strongest correlation with river temperature, irrespective of the period. Hydrological variables, such as average flow and baseflow, had a considerable influence on river temperature variability rather than on the overall trend direction. However, decreasing flow probably assisted in a faster river temperature increase in summer and in rivers in NE basins (such as the Elbe basin). The North Atlantic Oscillation Index had a greater significant influence on the winter river temperature variability than on the overall variability. Landscape and basin variables, such as altitude, ecoregion and catchment area, induced spatially variable river temperature trends via affecting the thermal sensitivity of rivers, with the rivers in large catchments and in lowland areas being most sensitive. Copyright © 2016 John Wiley & Sons, Ltd.     

Spatial variations in throughfall in a Moso bamboo forest: sampling design for the estimates of stand‐scale throughfall

We investigated the spatial and seasonal variations in throughfall (Tf) in relation to spatial and seasonal variations in canopy structure and gross rainfall (Rf) and assessed the impacts of the variations in Tf on stand‐scale Tf estimates. We observed the canopy structure expressed as the leaf area index (LAI) once a month and Tf once a week in 25 grids placed in a Moso bamboo (Phyllostachys pubescens) forest for 1 year. The mean LAI and spatial variation in LAI did have some seasonal variations. The spatial variations in Tf reduced with increasing Rf, and the relationship between the spatial variation and the Rf held throughout the year. These results indicate that the seasonal change in LAI had little impact on spatial variations in Tf, and that Rf is a critical factor determining the spatial variations in Tf at the study site. We evaluated potential errors in stand‐scale Tf estimates on the basis of measured Tf data using Monte Carlo sampling. The results showed that the error decreases greatly with increasing sample size when the sample size was less than ～8, whereas it was near stable when the sample size was 8 or more, regardless of Rf. A sample size of eight results in less than 10% error for Tf estimates based on Student's t‐value analysis and would be satisfactory for interception loss estimates when considering errors included in Rf data. Copyright © 2009 John Wiley & Sons, Ltd.     

Variability and trends in runoff in the rivers of British Columbia's Coast and Insular Mountains

This study examines the 1914–2015 runoff trends and variability for 136 rivers draining British Columbia's Coast and Insular Mountains. Rivers are partitioned into eastward and westward flowing rivers based on flow direction from the Coast Mountains. Thus, eastward and westward runoff trends and influence of topography on runoff are explored. Our findings indicate that rivers flowing eastward to the Nechako and Chilcotin plateaus contribute the lowest annual runoff compared to westward rivers where runoff is high. Low interannual runoff variability is evident in westward rivers and their alpine watersheds, whereas eastward rivers exhibit high interannual runoff variability. On Vancouver Island, some of the rivers with the highest annual runoff exhibit high interannual variability. A significant (p < .05) negative correlation exists between mean annual runoff (R_m) and latitude, gauged area, mean elevation, and its corresponding coefficient of variation. However, a significant positive correlation was found between the glacierized area of mountainous regions and R_m. The mean coefficient of variation in annual runoff is significantly negatively correlated with latitude and glacierized area, but significantly positively correlated with longitude. Annual and seasonal runoff trend analyses of each river were performed for an early (1936–2015), a middle (1966–2015), and a late (1986–2015) period using the Mann–Kendall test. Trend analyses revealed a shift towards more positive detectable (signal‐to‐noise ratio > 1) trends in annual and seasonal runoff from the middle to the late period across the study domain. Most positive detectable seasonal runoff trends in the middle period occur in spring in glacierized westward rivers located >1,200 m, whereas in the late period, they all occur in fall and are regionally coherent around Vancouver Island and south coastal BC. Rivers draining eastward exhibit more positive trends over 1986–2015 compared to westward rivers. This study provides crucial information on the hydrology of mountain watersheds across British Columbia's coast in response to Pacific Decadal Oscillation phase changes, the elevational amplification of regional climate change, and their influences on precipitation and glacier retreat.     

Lake ice and temperature trends for Ontario and Manitoba: 2001 to 2014

Lakes are a prominent geographic feature in northern landscapes and play an important role in understanding regional climate systems. In order to better model changes within climate systems, it is important to study lake ice processes. Although the availability of records for lake ice through ground measurements has declined in recent years, the increased use of remote sensing provides an alternative to this. Using a preclassified snow and ice remote sensing product with a 500‐m resolution, based on images from the Moderate Resolution Imaging Spectroradiometer (MODIS/MOD10A1), and the use of measured and reanalysis temperature data, this study evaluated lake ice phenology dates in connection to recent trends in temperature and 0 °C isotherms within Ontario and Manitoba between 2001 and 2014. Temperature trends indicated both regional warming and cooling, with significant cooling observed in Southern Ontario (p < .05) and significant warming in Southern Manitoba (p < .1) during the fall. Spatial analysis of the trends in the lake ice data showed significant clustering of significant trends in ice on dates (p < .01). When analysing the trends in ice phenology in connection to the trends in temperature, it was found that 70% of lakes experienced a change in the ice on date with the expected change in temperature and 85% of lakes for ice off date. When shifting ice on and ice off dates are investigated in relation to 0 °C isotherms, it was seen that 80% of ice on dates and 100% of ice off dates shifted in sync with the isotherm dates. This demonstrates that the ice phenology of lakes in Ontario and Manitoba, Canada, is responding to short‐term variability in temperature. The MODIS product could be used to investigate ice phenology on a large scale and contribute towards expanding existing records of ice phenology. Establishing long‐term ice records could be a valuable asset for other research ranging from water balance studies to the response of lake biota under changing climate.     

POD-based Monte Carlo approach for the solution of regional scale groundwater flow driven by randomly distributed recharge

We present a methodology conducive to the application of a Galerkin model order reduction technique, Proper Orthogonal Decomposition (POD), to solve a groundwater flow problem driven by spatially distributed stochastic forcing terms. Typical applications of POD to reducing time-dependent deterministic partial differential equations (PDEs) involve solving the governing PDE at some observation times (termed snapshots), which are then used in the order reduction of the problem. Here, the application of POD to solve the stochastic flow problem relies on selecting the snapshots in the probability space of the random quantity of interest. This allows casting a standard Monte Carlo (MC) solution of the groundwater flow field into a Reduced Order Monte Carlo (ROMC) framework. We explore the robustness of the ROMC methodology by way of a set of numerical examples involving two-dimensional steady-state groundwater flow taking place within an aquifer of uniform hydraulic properties and subject to a randomly distributed recharge. We analyze the impact of (i) the number of snapshots selected from the hydraulic heads probability space, (ii) the associated number of principal components, and (iii) the key geostatistical parameters describing the heterogeneity of the distributed recharge on the performance of the method. We find that our ROMC scheme can improve significantly the computational efficiency of a standard MC framework while keeping the same degree of accuracy in providing the leading statistical moments (i.e. mean and covariance) as well as the sample probability density of the state variable of interest.     

Analysis of trends in annual streamflow to the Arctic Ocean

There is increasing interest in the magnitude of the flow of freshwater to the Arctic Ocean due to its impacts on the biogeophysical and socio‐economic systems in the north and its influence on global climate. This study examines freshwater flow based on a dataset of 72 rivers that either directly or indirectly contribute flow to the Arctic Ocean or reflect the hydrologic regime of areas contributing flow to the Arctic Ocean. Annual streamflow for the 72 rivers is categorized as to the nature and location of the contribution to the Arctic Ocean, and composite series of annual flows are determined for each category for the period 1975 to 2015. A trend analysis is then conducted for the annual discharge series assembled for each category. The results reveal a general increase in freshwater flow to the Arctic Ocean with this increase being more prominent from the Eurasian rivers than from the North American rivers. A comparison with trends obtained from an earlier study ending in 2000 indicates similar trend response from the Eurasian rivers, but dramatic differences from some of the North American rivers. A total annual discharge increase of 8.7 km³/y/y is found, with an annual discharge increase of 5.8 km³/y/y observed for the rivers directly flowing to the Arctic Ocean. The influence of annual or seasonal climate oscillation indices on annual discharge series is also assessed. Several river categories are found to have significant correlations with the Arctic Oscillation, the North Atlantic Oscillation, or the Pacific Decadal Oscillation. However, no significant association with climate indices is found for the river categories leading to the largest freshwater contribution to the Arctic Ocean.     

Multivariate nonparametric resampling scheme for generation of daily weather variables

A nonparametric resampling technique for generating daily weather variables at a site is presented. The method samples the original data with replacement while smoothing the empirical conditional distribution function. The technique can be thought of as a smoothed conditional Bootstrap and is equivalent to simulation from a kernel density estimate of the multivariate conditional probability density function. This improves on the classical Bootstrap technique by generating values that have not occurred exactly in the original sample and by alleviating the reproduction of fine spurious details in the data. Precipitation is generated from the nonparametric wet/dry spell model as described in Lall et al. [1995]. A vector of other variables (solar radiation, maximum temperature, minimum temperature, average dew point temperature, and average wind speed) is then simulated by conditioning on the vector of these variables on the preceding day and the precipitation amount on the day of interest. An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, USA, is provided.     

An approach for the determination of precipitation input for worst-case flood modelling

ABSTRACT

There is a lack of suitable methods for creating precipitation scenarios that can be used to realistically estimate peak discharges with very low probabilities. On the one hand, existing methods are methodically questionable when it comes to physical system boundaries. On the other hand, the spatio-temporal representativeness of precipitation patterns as system input is limited. In response, this paper proposes a method of deriving spatio-temporal precipitation patterns and presents a step towards making methodically correct estimations of infrequent floods by using a worst-case approach. A Monte Carlo approach allows for the generation of a wide range of different spatio-temporal distributions of an extreme precipitation event that can be tested with a rainfall–runoff model that generates a hydrograph for each of these distributions. Out of these numerous hydrographs and their corresponding peak discharges, the physically plausible spatio-temporal distributions that lead to the highest peak discharges are identified and can eventually be used for further investigations.

Editor A. Castellarin; Associate editor E. Volpi     

Snow hydrology signatures for model identification within a limits‐of‐acceptability approach

Discharge simulation from snow‐dominated catchments seems to be an easy task. Any spatially explicit precipitation–runoff model coupled to a temperature‐index snow model generally yields simulations that mimic well the observed daily discharges. The robustness of such models is, however, questionable: in the presence of strong annual discharge cycles, small model residuals do not guarantee high explanatory power of the underlying model. This paper proposes a methodology for snow hydrological model identification within a limits‐of‐acceptability framework, where acceptable model simulations are the ones that reproduce a set of signatures within an a priori specified range. The signatures proposed here namely include the relationship between the air temperature regime and the discharge regime, a new snow hydrology signature that can be readily transferred to other Alpine settings. The discriminatory power of all analysed signatures is assessed with a new measure of their discriminatory power in the model prediction domain. The value of the proposed snow hydrology signatures and of the limits‐of‐acceptability approach is demonstrated for the Dischma river in Switzerland, whose discharge shows a strong temporal variability of hydrologic forcing conditions over the last 30 years. The signature‐based model identification for this case study leads to the surprising conclusion that the observed discharge data contains a multi‐year period that cannot be reproduced with the model at hand. This model‐data mismatch might well result from a yet to be identified problem with the discharge observations, which would have been difficult to detect in a classical residual‐based model identification approach. Overall, the detailed results for this case study underline the robustness of the limits‐of‐acceptability approach in the presence of error‐prone observations if it is applied in combination with relatively robust signatures. Future work will show whether snow hydrology signatures and their limits‐of‐acceptability can be regionalized to ungauged catchments, which would make this model selection approach particularly powerful for Alpine environments. Copyright © 2016 John Wiley & Sons, Ltd.     

Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. II. Development of LH-moments parameters for the generalized Pareto and generalized logistic distributions

As part II of a sequence of two papers, previously developed L-moments by Hosking (1990), and the LH-moments by Wang (1997) are further investigated. The LH-moments (L to L₄) are used to develop the regional parameters of the generalized extreme value distribution, generalized Pareto (GPA) distribution and the generalized logistic (GLO) distributions. These respective probability distribution functions (PDFs) are evaluated in terms of their performances. Flood peaks by the corresponding PDFs are compared with those generated by Monte Carlo simulation of randomized data, considering the respective LH-moments. The influence of the LH-moments on estimated PDFs are studied by evaluating the relative bias (RBIAS) in quantile estimation due to variability of the k parameter. Karkhe watershed located in western Iran was used as a case study area. Part I of this study identified the study area as regions A and B. The minimum calculated relative root mean square error (RRMSE) and RBIAS between simulated flood peaks and flood peaks by the corresponding PDFs were used in PDF selection, considering the respective LH-moments. The boxplots of the RRMSE tests identified the L₃ level of the GPA distribution as the suitable PDF for sample sizes 20 and 80; for region A. Similar results were found for the RBIAS test. As for region B, the boxplots of the RRMSE tests indicated similar results for the three PDFs. However, the boxplots of the RBIAS tests identified the L₄ level of the GLO most suitable for sample sizes 20 and 80. Relative efficiencies of the LH-moments were investigated, measured as RRMSE ratios of L-moments over the respective LH-moments. For the most parts the findings of this part of the study were similar to those of part I.     

Image analysis and circular statistics for shape-fabric analysis: applications to lithified ignimbrites

 Computer-assisted image analysis can be successfully used to derive quantitative textural data on pyroclastic rock samples. This method provides a large number of different measurements such as grain size, particle shape and 2D orientation of particle main axes (directional- or shape-fabric) automatically and in a relatively short time. Orientation data reduction requires specific statistical tests, mainly devoted to defining the kind of particle distribution pattern, the possible occurrence of preferred particle orientation, the confidence interval of the mean direction and the degree of randomness with respect to pre-assigned theoretical frequency distributions. Data obtained from image analysis of seven lithified ignimbrite samples from the Vulsini Volcanic District (Central Italy) are used to test different statistics and to provide insight about directional fabrics. First, the possible occurrence of a significant deviation from a theoretical circular uniform distribution was evaluated by using the Rayleigh and Tukey χ ² tests. Then, the Kuiper test was performed to evaluate whether or not the observation fits with a unimodal, Von Mises-like theoretical frequency distribution. Finally, the confidence interval of mean direction was calculated. With the exception of one sample (FPD10), which showed a well-developed bimodality, all the analysed samples display significant anisotropic and unimodal distributions. The minimum number of measurements necessary to obtain reasonable variabilities of the calculated statistics and mean directions was evaluated by repeating random collections of the measured particles at increments of 100 particles for each sample. Although the observed variabilities depend largely on the pattern of distribution and an absolute minimum number cannot be stated, approximately 1500–2000 measurements are required in order to get meaningful mean directions for the analysed samples. Received: 9 April 1996 / Accepted: 26 December 1996     

Analyses of trends and causes for variations in runoff and sediment load of the Yellow River

Due to the impacts of globe climate change and human activities, dramatic variations in runoff and sediment load were observed for the Yellow River. Analyses of nearly 65 years' data measured at main hydrologic-stations on the Yellow River from 1950 to 2014 indicated that, except for the Tangnaihai station in the head region, sharp downward trends existed in both the annual runoff and annual sedi-ment load according to the Mann–Kendal trend test;and their abrupt changes occurred in 1986 and in 1980, respectively, according to the rank sum test. Factors affecting the changes in the runoff and sediment load were very complicated. Results indicated that the reducing precipitation and the increasing water consumption were the main causes for the runoff decline, while the impoundment of the Longyangxia Reservoir and its combined operation with the Liujiaxia Reservoir exerted a direct bearing on the abrupt change in the annual runoff. In addition to the sediment load decrease associated with the runoff reduction, the reduced storm intensity, the conducted soil erosion control, and the constructed dam buildings all played an important role in the trends and abrupt changes of sediment load decline.     

Estimation of Tsunami Hazard in New Zealand due to South American Earthquakes

We develop a probabilistic model for estimating the tsunami hazard along the coast of New Zealand due to plate-interface earthquakes along the South American subduction zone. To do this we develop statistical and physical models for several stages in the process of tsunami generation and propagation, and develop a method for combining these models to produce hazard estimates using a Monte-Carlo technique. This process is largely analogous to that used for seismic hazard modelling, but is distinguished from it by the use of a physical model to represent the tsunami propagation, as opposed to the use of empirical attenuation models for probabilistic seismic hazard analysis.     

The use of multivariate statistics to elucidate patterns of floodplain sedimentation at different spatial scales

Floodplains are depositional features of riverine landscapes that display complex sedimentation patterns that are amenable to multi‐scale approaches. We examined sedimentation in the Lower Balonne floodplain, Queensland, Australia, at three different spatial scales: the channel (10³ km), floodplain process zone (10 km) and geomorphic unit (10² m) scales, and compared scale‐related patterns evident from stratigraphy with those evident from quantitative multivariate analysis. Three stratigraphic sequences were found in the Lower Balonne floodplain: generally fining upward, episodic fining upward, and mud‐dominated. Stratigraphical analysis revealed the detailed character of sedimentary sequences embedded within the scale patterns derived from multivariate analysis. Multivariate statistical analyses of a range of textural and geochemical data revealed different patterns of floodplain sedimentation at each scale. At the channel scale, sediment texture and geochemistry were more heterogeneous in the Culgoa River than in Briarie Creek. At the floodplain process zone scale clear patterns of sediment texture and geochemistry were observed along the upper, mid and lower floodplain process zones of Briarie Creek, but not along the Culgoa River. At the geomorphic unit scale, clear patterns of sediment texture and geochemistry were observed among the bank, buried channel and flat floodplain units of the Culgoa River, but were not as clear in Briarie Creek. Recognition of rivers as hierarchically organized systems is an emerging paradigm in river science. Our study supports this paradigm by demonstrating that different sedimentation patterns occur at different scales to reveal a hierarchically organized floodplain environment. Copyright © 2006 John Wiley & Sons, Ltd.     

A faster simulation method for the stochastic response of hysteretic structures subject to earthquakes

A semi-analytical forward-difference Monte Carlo simulation procedure is proposed for the determination of the lower order statistical moments and the joint probability density function of the stochastic response of hysteretic non-linear multi-degree-of-freedom structural systems subject to nonstationary gaussian white noise excitation, as an alternative to conventional direct simulation methods. The method generalizes the so-called Ermak-Allen algorithm developed for simulation applications in molecular dynamics to structural hysteretic systems. The proposed simulation procedure rely on an assumption of local gaussianity during each time step. This assumption is tantamount to various linearizations of the equations of motion. The procedure then applies an analytical convolution of the excitation process, hereby reducing the generation of stochastic processes and numerical integration to the generation of random vectors only. Such a treatment offers higher rates of convergence, faster speed and higher accuracy. The procedure has been compared to the direct Monte Carlo simulation procedure, which uses a fourth-order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process. The considered system was a multi-dimenensional hysteretic shear frame, where the constitutive equation of the hysteretic shear forces are described by a bilinear hysteretic model. The comparisons show that significant savings in computer time and accuracy can be achieved.