Using river network structure to improve estimation of common temporal patterns

HA Statistics

Gallacher, Kelly Marie ; EPSRC DTA ; Scott, Marian

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: river networks, connected network, flow direction, principal components analysis, common patterns, water quality.;   

Others  :  http://theses.gla.ac.uk/7208/1/2016gallacherKphd.pdf

来源: University of Glasgow

【 摘 要 】

Statistical models for data collected over space are widely available and commonly used.These models however usually assume relationships between observations depend onEuclidean distance between monitoring sites whose location is determined using two dimensional coordinates, and that relationships are not direction dependent. One examplewhere these assumptions fail is when data are collected on river networks. In this situation,the location of monitoring sites along a river network relative to other sites is asimportant as the location in two dimensional space since it can be expected that spatialpatterns will depend on the direction of water flow and distance between monitoringsites measured along the river network. Euclidean distance therefore might no longerbe the most appropriate distance metric to consider. This is further complicated whereit might be necessary to consider both Euclidean distance and distance along the rivernetwork if the observed variable is influenced by the land in which the river network isembedded.The Environment Agency (EA), established in 1996, is the government agency responsiblefor monitoring and improving the water quality in rivers situated in England (andWales until 2013). A key responsibility of the EA is to ensure that efforts are made toimprove and maintain water quality standards in compliance with EU regulations suchas the Water Framework Directive (WFD, European Parliament (2000)) and NitratesDirective (European Parliament, 1991). Environmental monitoring is costly and in manyregions of the world funding for environmental monitoring is decreasing (Ferreyra et al.,2002). It is therefore important to develop statistical methods that can extract as muchinformation as possible from existing or reduced monitoring networks. One way to dothis is to identify common temporal patterns shared by many monitoring sites so thatredundancy in the monitoring network could be reduced by removing non-informativesites exhibiting the same temporal patterns. In the case of river water quality, informationabout the shape of the river network, such as flow direction and connectivity ofmonitoring sites, could be incorporated into statistical techniques to improve statisticalpower and provide efficient inference without the increased cost of collecting moredata. Reducing the volume of data required to estimate temporal trends would improveefficiency and provide cost savings to regulatory agencies.The overall aim of this thesis is to investigate how information about the spatial structureof river networks can be used to augment and improve the specfic trends obtainedwhen using a variety of statistical techniques to estimate temporal trends in water qualitydata. Novel studies are designed to investigate the effect of accounting for rivernetwork structure within existing statistical techniques and, where necessary, statisticalmethodology is developed to show how this might be achieved. Chapter 1 provides anintroduction to water quality monitoring and a description of several statistical methodsthat might be used for this. A discussion of statistical problems commonly encounteredwhen modelling spatiotemporal data is also included. Following this, Chapter 2 appliesa dimension reduction technique to investigate temporal trends and seasonal patternsshared among catchment areas in England and Wales. A novel comparison methodis also developed to identify differences in the shape of temporal trends and seasonalpatterns estimated using several different statistical methods, each of which incorporatespatial information in different ways. None of the statistical methods compared inChapter 2 specifically account for features of spatial structure found in river networks:direction of water flow, relative influence of upstream monitoring sites on downstreamsites, and stream distance. Chapter 3 therefore provides a detailed investigation andcomparison of spatial covariance models that can be used to model spatial relationshipsfound in river networks to standard spatial covariance models. Further investigationof the spatial covariance function is presented in Chapter 4 where a simulation studyis used to assess how predictions from statistical models based on river network spatialcovariance functions are affected by reducing the size of the monitoring network.A study is also developed to compare the predictive performance of statistical modelsbased on a river network spatial covariance function to models based on spatial covariateinformation, but assuming spatial independence of monitoring sites. Chapters 3and 4 therefore address the aim of assessing the improvement in information extractedfrom statistical models after the inclusion of information about river network structure.Following this, Chapter 5 combines the ideas of Chapters 2, 3 and 4 and proposes anovel statistical method where estimated common temporal patterns are adjusted forknown spatial structure, identified in Chapters 3 and 4. Adjusting for known structurein the data means that spatial and temporal patterns independent of the river networkstructure can be more clearly identified since they are no longer confounded with knownstructure.The final chapter of this thesis provides a summary of the statistical methods investigated and developed within this thesis, identifies some limitations of the work carried out and suggests opportunities for future research. An Appendix provides details of many of the data processing steps required to obtain information about the river network structurein an appropriate form.