Gallacher, Kelly Marie
(2016)
Using river network structure to improve estimation of common temporal patterns.
PhD thesis, University of Glasgow.
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Abstract
Statistical models for data collected over space are widely available and commonly used.
These models however usually assume relationships between observations depend on
Euclidean distance between monitoring sites whose location is determined using two dimensional coordinates, and that relationships are not direction dependent. One example
where 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 as
important as the location in two dimensional space since it can be expected that spatial
patterns will depend on the direction of water flow and distance between monitoring
sites measured along the river network. Euclidean distance therefore might no longer
be the most appropriate distance metric to consider. This is further complicated where
it might be necessary to consider both Euclidean distance and distance along the river
network if the observed variable is influenced by the land in which the river network is
embedded.
The Environment Agency (EA), established in 1996, is the government agency responsible
for monitoring and improving the water quality in rivers situated in England (and
Wales until 2013). A key responsibility of the EA is to ensure that efforts are made to
improve and maintain water quality standards in compliance with EU regulations such
as the Water Framework Directive (WFD, European Parliament (2000)) and Nitrates
Directive (European Parliament, 1991). Environmental monitoring is costly and in many
regions 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 much
information as possible from existing or reduced monitoring networks. One way to do
this is to identify common temporal patterns shared by many monitoring sites so that
redundancy in the monitoring network could be reduced by removing noninformative
sites exhibiting the same temporal patterns. In the case of river water quality, information
about the shape of the river network, such as flow direction and connectivity of
monitoring sites, could be incorporated into statistical techniques to improve statistical
power and provide efficient inference without the increased cost of collecting more
data. Reducing the volume of data required to estimate temporal trends would improve
efficiency and provide cost savings to regulatory agencies.
The overall aim of this thesis is to investigate how information about the spatial structure
of river networks can be used to augment and improve the specfic trends obtained
when using a variety of statistical techniques to estimate temporal trends in water quality
data. Novel studies are designed to investigate the effect of accounting for river
network structure within existing statistical techniques and, where necessary, statistical
methodology is developed to show how this might be achieved. Chapter 1 provides an
introduction to water quality monitoring and a description of several statistical methods
that might be used for this. A discussion of statistical problems commonly encountered
when modelling spatiotemporal data is also included. Following this, Chapter 2 applies
a dimension reduction technique to investigate temporal trends and seasonal patterns
shared among catchment areas in England and Wales. A novel comparison method
is also developed to identify differences in the shape of temporal trends and seasonal
patterns estimated using several different statistical methods, each of which incorporate
spatial information in different ways. None of the statistical methods compared in
Chapter 2 specifically account for features of spatial structure found in river networks:
direction of water flow, relative influence of upstream monitoring sites on downstream
sites, and stream distance. Chapter 3 therefore provides a detailed investigation and
comparison of spatial covariance models that can be used to model spatial relationships
found in river networks to standard spatial covariance models. Further investigation
of the spatial covariance function is presented in Chapter 4 where a simulation study
is used to assess how predictions from statistical models based on river network spatial
covariance functions are affected by reducing the size of the monitoring network.
A study is also developed to compare the predictive performance of statistical models
based on a river network spatial covariance function to models based on spatial covariate
information, but assuming spatial independence of monitoring sites. Chapters 3
and 4 therefore address the aim of assessing the improvement in information extracted
from 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 a
novel statistical method where estimated common temporal patterns are adjusted for
known spatial structure, identified in Chapters 3 and 4. Adjusting for known structure
in the data means that spatial and temporal patterns independent of the river network
structure can be more clearly identified since they are no longer confounded with known
structure. 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 structure
in an appropriate form.
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