Examining geological controls on baseflow index (BFI) using regression analysis: An illustration from the Thames Basin, UK
Introduction
Hydrological characteristics of catchments, such as baseflow, or measures of high and low stream flow, may be estimated using a variety of physical descriptors (Nash, 1960, Hall, 1968, Nathan and McMahon, 1990a, Nathan and McMahon, 1992). These descriptors include physiographic and climatological parameters and may involve geologically or hydrogeologically related parameters. A hydrogeological characteristic of catchments that has been the focus of a number of studies, particularly in the context of modelling ungauged catchments, is baseflow index (BFI). BFI is the long-term ratio of baseflow to total stream flow and thus represents the slow or delayed contribution to river flow and may be influenced to a significant extent by catchment geology. However, to date the relationship between catchment geology and BFI has not been quantified in a systematic manner. Even though there is a tacit assumption that the underlying geology influences baseflow, previous studies that estimate BFI typically simplify the effect of catchment geology to a parameter that represents the fractional area of aquifers in a catchment (Nathan et al., 1996, Sefton and Howarth, 1998, Mwakalila et al., 2002, Mwakalila, 2003, Abebe and Foerch, 2006, Santhi et al., 2008). Some studies have adopted a slightly more refined approach to include a number of discrete geologies as physical catchment descriptors (Nathan and McMahon, 1990b, Lacey and Grayson, 1998, Mazvimavi et al., 2005), and, rather than use the areas of aquifers or different lithologies as catchment descriptors, Haberlandt et al. (2001) used the physical properties of the aquifers (effective porosity and saturated hydraulic conductivity). However, because, in addition to geological parameters, all these studies use non-geological parameters to estimate baseflow or BFI they cannot provide specific insights into the relationships between the geological characteristics of catchments and baseflow or BFI. The motivation for this study is to examine geological controls on BFI independent of other catchment factors.
A streamflow hydrograph describes the variation in the rate of flow of a stream with time and consists of four basic elements: direct surface runoff, interflow, groundwater flow or baseflow (Nash, 1960, Hall, 1968, Nathan and McMahon, 1990a, Eckhardt, 2008), and channel precipitation. In most hydrograph analyses, interflow and channel precipitation are grouped with direct runoff (unless there is a need to explicitly treat them independently) and the total runoff hydrograph is made up of the sum of surface runoff and discharge from saturated groundwater storage or baseflow (Nathan and McMahon, 1990a, Viessman and Lewis, 2002). The baseflow component of the hydrograph represents longer-term (weeks to months) changes in the regional groundwater head and flow system and typically varies in response to relatively long seasonal changes in saturated groundwater head driven by seasonal changes in factors such as evapotranspiration (Wittenburg and Silvapalan, 1999). BFI is defined as the difference in area under the baseflow hydrograph and total runoff hydrographs obtained by baseflow or hydrograph separation (Institute of Hydrology, 1980). There are a variety of graphical or manual methods of baseflow separation. For example, Viessman and Lewis (2002) describe five methods and Eckhardt (2008) has recently compared seven different automated methods. In each case the separation methods are designed to separate the fast component of flow from the slower baseflow component by identifying the onset of rising limbs in the total stream hydrograph and the end of direct surface runoff towards the end of a local peak in the total stream hydrograph. Regardless of the details of the method used, and as Eckhardt (2008) notes, since the true values of the baseflow index are always unknown it is not possible to identify which of the methods provides the ‘best’ estimate of BFI.
Geological information, along with other variables, has been correlated with BFI using a range of approaches including: multiple linear regression techniques (Nathan et al., 1996, Lacey and Grayson, 1998, Mwakalila et al., 2002, Mazvimavi et al., 2005, Abebe and Foerch, 2006), neural network methods (Mazvimavi et al., 2005), and regional landscape mapping (Santhi et al., 2008). The fractional area of aquifers, or in some cases specific lithologies, typically shows some correlation with BFI. Lacey and Grayson, 1998 demonstrated that there was a strong relationship between combined geology–vegetation groups and BFI, but suggested that the groups also represented other factors such as climatic history, recharge capacity and transmissivity. Mazvimavi et al. (2005) found that geology was not a significant predictor of BFI in their study area, but concluded that this was due to groundwater in certain formations in their study area (several catchments in Tanzania) being relatively deep and disconnected from surface streams.
Soil data has also been used extensively in studies of baseflow and BFI in ungauged catchments as a surrogate for the underlying geology. The Institute of Hydrology low flow study developed the ‘hydrology of soil types’ (HOST) classification to estimate flow duration and flow frequency parameters (Gustard et al., 1992, Boorman et al., 1995). It consists of a grouping of soil associations into classes based on physical properties of soils and on their hydrogeological setting. Multivariate regression of soil type data against BFI data for representative catchments in the United Kingdom produced continuous BFI catchment characteristics scaled on continuous soil parameters, referred to as BFIHOST (Gustard et al., 1992, Boorman et al., 1995). The BFIHOST methodology and data have been used successfully in a number of studies (Boorman et al., 1995, Sefton and Howarth, 1998, Dunn and Lilly, 2001, Lee et al., 2005, Marechal and Holman, 2005, Young, 2006).
The present study uses a similar approach to BFIHOST, in that geological associations are grouped into classes, based on lithological or hydrogeological characteristics, which are then correlated with observed BFI. However, unlike the previous studies, including BFIHOST, where the aim was to build robust predictive models using sometimes very limited information, the central task of the present study is to quantify as fully as possible the relationship between geological or hydrogeological characteristics of an area and observed BFI independent of any other factors. This is possible in the Thames Basin because high quality geological mapping and river flow data are available. In this study, linear regression models have been used to quantify geological controls on BFI by correlating detailed 1:50,000 scale geological mapping with BFI values for catchments with diverse geological and aquifer characteristics at the basin scale (∼10,000 km2). There are two complementary aims for the work described in this paper. The first aim is to investigate if physically meaningful relationships between lithological characteristics of catchments and BFI can be quantified at the basin scale using regression methods. The second aim is to show how a geologically-based model of BFI can be used to produce continuous BFI catchment characteristics in a similar manner to BFIHOST. The models have been applied to the Thames Basin, UK, as a case-study. The approach, however, is not basin specific and the methodology description and discussion include generic observations related to the application of regression modelling to the quantification of geological controls on baseflow regardless of basin hydrology or geology.
Section snippets
Study area
The Thames Basin, defined by the catchment of the River Thames and its tributaries, is situated in the south east of the United Kingdom (Fig. 1a). For the purposes of this study the Thames Basin is defined by the Environment Agency’s Thames River Basin District (Environment Agency, 2007). The source of the River Thames is in the Costwolds in Gloucestershire. The length of the river down to Teddington Lock, in west London, is approximately 235 km, and the area of the Basin is about 16,100 km2.
Model methodology
Three least squares regression models are described in this paper. Two related step-wise multiple linear regression models, Models 1a and 1b, have been developed to quantify the relative influence of the fractional areas of lithostratigraphic classes on observed BFIs. A third model, Model 2, has been developed to investigate whether regression models based on an alternative hydrogeologically-based classification scheme can be used to produce continuous characteristics, similar to BFIHOST, that
Results
Table 3a, Table 3b, Table 3c show the results for the regression models, Model 1a, 1b and 2, respectively. Fig. 4 shows modelled values of BFI plotted against observed BFI for the 44 calibration catchments for Models 1a, 1b and 2. It also shows the distribution of residuals for Models 1a, 1b and 2 as a function of the modelled values of BFI.
Geological controls on BFI
By regressing fractional areas of discrete lithologies within catchments onto BFI and by demonstrating that the resulting regression models have some physical meaning, this study has shown that BFI can be considered as an integrated expression of the fractional areas of discrete lithologies within catchments. This can be done because only geological factors were considered during model calibration enabling the role of geology to be quantified independent of other factors. However, it has
Summary
Despite a common assumption that underlying geology in catchments influences baseflow, to date the relationship between catchment geology and BFI has not been quantified in a systematic manner. In this study, relationships between lithological characteristics of catchments and BFI are quantified at the basin scale by multiple linear regression methods using the Thames Basin, UK, as a case-study. Multiple linear regression methods have been used before to relate catchment parameters to BFI,
Acknowledgements
The authors would like to thank Milly Lewis and Mike Cheetham for help with the lithological classification used in the study and Jenny Cunningham for help with spatial data analysis. This paper is published with the permission of the Executive Director of the British Geological Survey (Natural Environment Research Council).
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