Sylvia R. Esterby

Review of methods for the detection and estimation of trends with emphasis on water quality applications

Methods for the detection and estimation of trends which are suitable for the type of data sets available from water quality and atmospheric deposition monitoring programmes are considered. Parametric and non-parametric methods which are based on the assumption of monotonic trend and which account for seasonality through blocking on season are described. The topics included are heterogeneity of trend, missing data, covariates, censored data, serial dependence and multivariate extensions. The basis for the non-parametric methods being the method of choice for current large data sets of short to moderate length is reviewed. A more general definition of trend as the component of gradual change over time is consistent with another group of methods and some examples are given. Spatial temporal data sets and longer temporal records are also briefly considered. A broad overview of the topic of trend analysis is given, with technicalities left to the references cited. The necessity of defining what is meant by trend in the context of the design and objectives of the programme is emphasized, as is the need to model the variability in the data more generally.

Inference about the Point of Change in a Regression Model

SUMMARY Consider a sequence of (n1 + n2) independent ordered pairs of observations for which the relationship between variables can be represented by a segmented polynomial regression model with unknown point of change n 1. The relative marginal likelihood function for n 1 is derived and the expressions for the relative conditional and maximum likelihood functions are given. Either of the first two likelihoods, which account for the uncertainty about the value of the other parameters, are to be preferred to the maximum likelihood function, with the relative marginal likelihood function being examined more extensively here. In the case where the segmented regression model can be represented by two polynomials of unknown degrees p and q, a procedure is described for estimating p and q. The use of these methods is illustrated using two observed sets of data and three artificially generated sets.

A Statistical Evaluation of Trends in the Water Quality of the Niagara River

Abstract Using water quality data collected at Niagara-on-the-Lake by the Water Quality Branch, Ontario Region, between 1975 and 1980, pH, alkalinity, total phosphorous, and nitrate concentrations are examined for changes over time. Moving averages, Spearmans rank correlation coefficient and regression methods, which model the seasonal cycle, are used. It appears that pH and alkalinity are decreasing, and nitrate increasing, but these changes do not occur for all months. Since river discharge did not change significantly in any month, the changes in pH, alkalinity, and nitrate are not due simply to changes in discharge. A change in total phosphorous concentrations over years was not detected.

Coliform concentrations in Lake Erie ― 1966 to 1970

Total coliform concentrations obtained from cruises of Lake Erie, conducted from the Canada Centre for Inland Waters between 1966 and 1970, have been analysed to determine the spatial and temporal distribution of total coliforms in the lake. Although year to year comparisons were made on a qualitative level due to the limitations in the data, some consistent seasonal features of the spatial distribution are evident. The location of zones of higher concentration have been attributed to proximity to large urban areas and lake currents. The contribution of fecal coliforms to the total coliform concentration has been examined with the conclusion that, at the low total coliform concentrations (⩽ 30 per 100 ml) observed in much of the lake, there is no relationship between the two concentrations but, over a broader range, fecal coliforms increase with total coliform concentrations and, at very high total coliform concentrations (⩾1000 per 100 ml), fecal coliforms are always present. The analysis demonstrates 1) the value of examining observed and fitted distributions to compare subsets of a large collection of data and 2) a clustering procedure which is generally applicable to data consisting of counts.

Compatibility of Sampling and Laboratory Procedures Evaluated for the 1985 Three-Ship Intercomparison Study on Lake Erie

Abstract To update the information concerning data intercomparability from Great Lakes monitoring programs, a three-ship laboratory comparison was conducted on the central basin (mid-lake) of Lake Erie in August 1985, in which eight water quality parameters were measured. Participating were ships operated by the U.S. Environmental Protection Agency, the Ohio State University, and Environment Canada. Two separate comparison studies were conducted, the first to identify that portion of variability due to analytical variability (AV), and the second to assess the overall variability (OV) in whole-ship operations, including water sampling procedures at two depths, epilimnion and hypolimnion. In general, differences in mean levels were due primarily to laboratory procedures, with significant differences occurring between at least one pair of laboratories for every parameter. For all parameters, except chloride and nitrate plus nitrite, these differences ranged from 30 to nearly 100 percent of the mean in the water layer with the lower concentration and from 12 to 95 percent in the layer with higher concentration. The results for some parameters were overly precise for one or more laboratories, which led to differences as small as 3 to 6 percent of the mean being significant (nitrate plus nitrite and chloride). However, large laboratory differences were observed for soluble reactive silica even though laboratory precision was high. These results are discussed in view of the quality assurance program of the EPA laboratory, the August 1985 monitoring of central basin stations by the three agencies, and the magnitude of changes in total phosphorus in Lake Erie over time. It is concluded that, although at least one laboratory exhibited precision better than that of the 1985 monitoring program, the differences between laboratories estimated from the intercomparison study are large enough to be of practical significance and thus careful consideration is necessary before combining results from monitoring programs of the different agencies.

Analysis of multiple depth profiles in sediment cores: an application to pollen and diatom data from lakes sensitive to acidification

The methods of clustering and ordination were compared with polynomial and segmented regression methods by application to the pollen and diatom profiles from two sediment cores obtained from lakes susceptible to acid precipitation. Clustering and ordination methods have previously been used to determine zones in sediment profiles, but regression methods which summarize the changes with depth in terms of one or more smooth curves, explicitly use the depth information. Plots of running means were also used to characterize profile shapes. The latter two methods provided a clearer understanding of the changes in diatom and pollen levels in the cores. For low diatom concentrations, non-parametric methods were used to test for a change in concentration with depth. Changes in dry weight of sediment, different bases for concentration and depth, and the effect of poor represententation of an extreme group on the pH spectrum were also considered. The regression procedures were shown to provide summaries useful for comparison of different species or of the same species in different cores. Finally, a summary is given of the similarity of the patterns in the depth profiles of eight pollen types and the non-rare diatom species in one core from each of Kejimkujik and Beaverskin Lakes, respectively.

Evaluating the Impact of Climate Change on Dynamics of House Insurance Claims

The adverse effects of climate change bring increasingly more alterations to all aspects of human life and welfare, and one of the sectors that is particularly affected by changing climate is the insurance sector. Indeed, the year 2013 brought a record number of claims and substantial losses due to weather-related damages, and in the USA and Canada alone, the extreme weather events cost the insurance industry more than 3 billion dollars. The objective of this paper is to provide statistical data-driven insight on the (non)linear relationship between weather-related house insurance claims and atmospheric variables and to predict future claim dynamics accounting for changes in extreme precipitation. In this paper we propose to employ a flexible Generalized Autoregressive Moving Average (GARMA) model for count time series of claims, develop a new method to compare tails of the observed and projected extreme precipitation, and evaluate the impact of climate change on a number of house insurance claims in the GARMA framework. We illustrate our approach by studying insurance dynamics in four Canadian cities.