Spatial-temporal rainfall simulation using generalized linear models

We consider the problem of simulating sequences of daily rainfall at a network of sites in such a way as to reproduce a variety of properties realistically over a range of spatial scales. The properties of interest will vary between applications but typically will include some measures of "extreme'' rainfall in addition to means, variances, proportions of wet days, and autocorrelation structure. Our approach is to fit a generalized linear model (GLM) to rain gauge data and, with appropriate incorporation of intersite dependence structure, to use the GLM to generate simulated sequences. We illustrate the methodology using a data set from southern England and show that the GLM is able to reproduce many properties at spatial scales ranging from a single site to 2000 km 2 ( the limit of the available data)

Assessment of apparent nonstationarity in time series of annual inflow, daily precipitation, and atmospheric circulation indices: A case study from southwest Western Australia

The southwest region of Western Australia has experienced a sustained sequence of low annual inflows to major water supply dams over the past 30 years. Until recently, the dominant interpretation of this phenomenon has been predicated on the existence of one or more sharp breaks (change or jump points), with inflows fluctuating around relatively constant levels between them. This paper revisits this interpretation. To understand the mechanisms behind the changes, we also analyze daily precipitation series at multiple sites in the vicinity and time series for several indices of regional atmospheric circulation that may be considered as drivers of regional precipitation. We focus on the winter half-year for the region (May to October) as up to 80% of annual precipitation occurs during this "season". We find that the decline in the annual inflow is in fact more consistent with a smooth declining trend than with a sequence of sharp breaks, the decline is associated with decreases both in the frequency of daily precipitation occurrence and in wet-day amounts, and the decline in regional precipitation is strongly associated with a marked decrease in moisture content in the lower troposphere, an increase in regionally averaged sea level pressure in the first half of the season, and intraseasonal changes in the regional north-south sea level pressure gradient. Overall, our approach provides an integrated understanding of the linkages between declining dam inflows, declining precipitation, and changes in regional atmospheric circulation that favor drier conditions

Empirical fragility curves: The effect of uncertainty in ground motion intensity

Empirical fragility curves derived from large post-disaster databases with data aggregated at municipality-level, commonly make the assumption that the ground motion intensity level is known and is determined at the centroid of each municipality from a ground motion prediction equation. A flexible Bayesian framework is applied here to the 1980 Irpinia database to explore whether more complex statistical models that account for sources of uncertainty in the intensity can significantly change the shape of the fragility curves. Through this framework the effect of explicitly modelling the uncertainty in the intensity, the spatial correlation of its intra-event component and the uncertainty due to the scatter of the buildings in the municipality are investigated. The analyses showed that the results did not change substantively with increased model complexity or the choice of prior. Nonetheless, informed decisions should be based on the defensible modelling of the significant variability in the data between municipalities

Analysis of rainfall variability using generalized linear models: A case study from the west of Ireland

In the early 1990s a cluster of extreme flood events occurred in the south Galway region of western Ireland, and this led to speculation of changing rainfall patterns in the area. In this paper we illustrate the use of generalized linear models (GLMs) to test for such changes and quantify their structure. GLMs, long established in the statistical literature, provide a flexible and rigorous formal framework within which to distinguish between possible climate change scenarios and are able to deal with high levels of variability, such as those typically associated with daily rainfall sequences. The study indicates that the GLM approach provides a powerful tool for interpreting historical rainfall records

Quantifying Sources of Uncertainty in Projections of Future Climate

A simple statistical model is used to partition uncertainty from different sources, in projections of future climate from multimodel ensembles. Three major sources of uncertainty are considered: the choice of climate model, the choice of emissions scenario, and the internal variability of the modeled climate system. The relative contributions of these sources are quantified for mid- and late-twenty-first-century climate projections, using data from 23 coupled atmosphere–ocean general circulation models obtained from phase 3 of the Coupled Model Intercomparison Project (CMIP3). Similar investigations have been carried out recently by other authors but within a statistical framework for which the unbalanced nature of the data and the small number (three) of scenarios involved are potentially problematic. Here, a Bayesian analysis is used to overcome these difficulties. Global and regional analyses of surface air temperature and precipitation are performed. It is found that the relative contributions to uncertainty depend on the climate variable considered, as well as the region and time horizon. As expected, the uncertainty due to the choice of emissions scenario becomes more important toward the end of the twenty-first century. However, for midcentury temperature, model internal variability makes a large contribution in high-latitude regions. For midcentury precipitation, model internal variability is even more important and this persists in some regions into the late century. Implications for the design of climate model experiments are discussed

Inference with the Whittle Likelihood: A Tractable Approach Using Estimating Functions

The theoretical properties of the Whittle likelihood have been studied extensively for many different types of process. In applications however, the utility of the approach is limited by the fact that the asymptotic sampling distribution of the estimator typically depends on third-order and fourth-order properties of the process that may be difficult to obtain. In this article, we show how the methodology can be embedded in the standard framework of estimating functions, which allows the asymptotic distribution to be estimated empirically without calculating higher-order spectra. We also demonstrate that some aspects of the inference, such as the calculation of confidence regions for the entire parameter vector, can be inaccurate but that a small adjustment, designed for application in situations where a mis-specified likelihood is used for inference, can lead to marked improvements

Lightning prediction for Australia using multivariate analyses of large-scale atmospheric variables

Lightning is a natural hazard that can lead to the ignition of wildfires, disruption and damage to power and telecommunication infrastructures, human and livestock injuries and fatalities, and disruption to airport activities. This paper examines the ability of six statistical and machine-learning classification techniques to distinguish between non-lightning and lightning days at the coarse spatial and temporal scales of current general circulation models and reanalyses. The classification techniques considered were: a combination of principal component analysis and logistic regression; classification and regression trees; random forests; linear discriminant analysis; quadratic discriminant analysis; and logistic regression. Lightning flash count observations at six locations across Australia for the period 2004 to 2013 were used, together with atmospheric variables from the ERA-Interim reanalysis. Ten-fold cross validation was used to evaluate classification performance. It was found that logistic regression was superior to the other classifiers considered, and that its prediction skill is much better than climatology. The sets of atmospheric variables included in the final logistic regression models were primarily composed of spatial mean measures of instability and lifting potential, and atmospheric water content. However, the memberships of these sets varied between climatic zones

Classification of Australian Thunderstorms using Multivariate Analyses of Large-Scale Atmospheric Variables

Lightning accompanied by inconsequential rainfall (i.e., “dry” lightning) is the primary natural ignition source for wildfires globally. This paper presents a machine-learning and statistical-classification analysis of dry and “wet” thunderstorm days in relation to associated atmospheric conditions. The study is based on daily data for lightning-flash count and precipitation from ground-based sensors and gauges and a comprehensive set of atmospheric variables that are based on ERA-Interim for the period from 2004 to 2013 at six locations in Australia. These locations represent a wide range of climatic zones (temperate, subtropical, and tropical). Quadratic surface representations and low-dimensional summary statistics were used to characterize the main features of the atmospheric fields. Four prediction skill scores were considered, and 10-fold cross validation was used to evaluate the performance of each classifier. The results were compared with those obtained by adopting the approach used in an earlier study for the U.S. Pacific Northwest. It was found that both approaches have prediction skill when tested against independent data, that mean atmospheric field quantities proved to be the most influential variables in determining dry-lightning activity, and that no single classifier or set of atmospheric variables proved to be consistently superior to its counterpart for the six sites examined here

Estimating trends and seasonality in Australian monthly lightning flash counts

We present the results of a statistical analysis of lightning characteristics in mainland Australia for the period from approximately 1988 to 2012, based on monthly lightning flash count (LFC) series obtained from a network of 19 Comité Internationale des Grands Réseaux Electriques, 500 Hz peak transmission filter circuit sensors. The temporal structures of the series are examined in terms of detecting and characterizing seasonal cycles, long-term trends, and changes in seasonality over time. A generalized additive modeling approach is used to ensure that the estimated structures are determined by the data, rather than by the constraints of any assumed mathematical form for the trends and seasonal cycle. Results indicate strong seasonality at all sites, the presence of long-term trends at 16 sites, and interactions between trend and seasonality (corresponding to changes in seasonality over time) at 13 sites. The most systematic change corresponds to a progressive deepening of the seasonal cycle (i.e., an ongoing decline in winter lightning flash counts) and is most noticeable across southern Australia (south of 30°S). These results are consistent with previous analyses that have detected decreasing atmospheric instability during the austral winter since the mid-1970s. This is associated with increasing mean sea level pressure and declining rainfall

A generalized regression model of arsenic variations in the shallow groundwater of Bangladesh

Localized studies of arsenic (As) in Bangladesh have reached disparate conclusions regarding the impact of irrigation-induced recharge on As concentrations in shallow (≤50 m below ground level) groundwater. We construct generalized regression models (GRMs) to describe observed spatial variations in As concentrations in shallow groundwater both (i) nationally, and (ii) regionally within Holocene deposits where As concentrations in groundwater are generally high (>10 μg L). At these scales, the GRMs reveal statistically significant inverse associations between observed As concentrations and two covariates: (1) hydraulic conductivity of the shallow aquifer and (2) net increase in mean recharge between predeveloped and developed groundwater-fed irrigation periods. Further, the GRMs show that the spatial variation of groundwater As concentrations is well explained by not only surface geology but also statistical interactions (i.e., combined effects) between surface geology and mean groundwater recharge, thickness of surficial silt and clay, and well depth. Net increases in recharge result from intensive groundwater abstraction for irrigation, which induces additional recharge where it is enabled by a permeable surface geology. Collectively, these statistical associations indicate that irrigation-induced recharge serves to flush mobile As from shallow groundwater