Data analysis

2.2.7.1. Hydrograph separation

A tracer-based mass balance hydrograph separation was performed following the procedures detailed by Christophersen and Hooper (1992), Hooper (2003) and Sklash and Farvolden (1979). The number and nature of components required to explain most of the variation in the composition of stream water collected at the catchment outflow were determined by performing a principal component analysis (PCA) and an end-member mixing analysis (EMMA). As a factor analysis, the PCA allows to explain discrete levels of the variation in the chemistry and isotopic abundance of runoff, concurrent with a reduction in dimensionality of the dataset (Abdi and Williams, 2010; Christophersen and Hooper, 1992).

The EMMA is a systematic approach applied to identify the most likely components (i.e. end-members) of runoff (Christophersen et al., 1990; Hooper et al., 1990; Hooper, 2003). The potential end-members were throughfall, groundwater, and soil water at several depths at the hillslope, toeslope, and riparian areas of the catchment (see Table 2.4). Soil water was separated into distinct end-members on the basis of landscape elements and layering of the soil in terms of saturated hydraulic conductivity (Table 2.1). Precipitation was not considered a potential end-member as opposed to throughfall, since the catchment is covered at ~100%

by a forest canopy.

Prior to these analyses, the conservative nature and linear mixing of the measured natural tracers were assessed. Bivariate plots of all tracer pairs of stream water were generated and linear correlation was assessed. A residual analysis of tracer values was performed following Hooper (2003). A tracer was considered to be conservative and to linearly mix if it was linearly correlated with at least one other tracer (r² > 0.5, p < 0.01; following Barthold et

Chapter 2 − A Sudden Shift in Runoff Generation Processes at a Forested Catchment

45 al., 2011), the residuals between the destandardized orthogonal projections of the values and the measured values plotted against the latter displayed a random pattern, and the relative root-mean-square error (RRMSE; Taylor, 1997) of the plot was relatively low (≤ 15%). The degree of randomness of the pattern and the RRMSE of the residuals plotted against the measured values in one- and multi-dimensional subspaces were also assessed in relation to the dimensionality of the mixing subspace. Only conservative tracers which linearly mixed were used for further analyses.

A PCA was performed on the correlation matrix of the tracer values of stream water.

The number of principal components (i.e. eigenvectors) to retain was selected by applying the rule of one, which states that only principal components with eigenvalues ≥ 1 should be retained (Preisendorfer et al., 1981). The dimensionality of the resulting mixing subspace (i.e.

U-space) corresponded to the number of principal components retained. An EMMA was initiated by standardizing the median and quartiles of the tracer values of potential end-members to stream water values. The standardized values were then projected into the mixing subspace defined by the orthogonal projections of stream water values. For m principal components retained, the minimum number of end-members required to explain most of the variation in the composition of stream water is m+1 and, for n tracers used, the maximum number of end-members is n+1. A subset of end-members was selected on the basis of four criteria outlined by Ali et al. (2010). The subset should comprise end-members which have distinct tracer values for at least one tracer, which have a lower temporal variability in tracer values than stream water, and of which the orthogonal projections bound the projections of stream water values while being as close as possible. The differences between the projected and the measured values of the selected end-members should also be < 15%, which indicates a good fit in the mixing subspace. By assessing the fulfillment of these criteria by different combinations of end-members and their ability to circumscribe the projections of stream water values, further subsets of end-members were selected and used in the mixing model.

The subset for which the mixing model could best reproduce the measured values was finally identified, and consisted of the most likely end-members of runoff.

In order to estimate the relative contributions (i.e. proportions, %) of the most likely end-members to runoff, mixing equations based on the mass balance approach (Eqs. (1) – (3)) were solved by the use of matrix operations (Eqs. (4) – (6)). This approach was adapted from its initial use for a two-component hydrograph separation (Pinder and Jones, 1969; Sklash and Farvolden, 1979) to account for multi-component contributions to runoff (Christophersen et

al., 1990; Hooper et al., 1990). An assessment of the data regarding the assumptions underlying the hydrograph separation technique (Buttle, 1994; Inamdar, 2011) was realized and taken into account for the interpretation of the results (refer to section 2.4.2). In the case of two principal components retained, three tracers used and four end-members identified, the following equations were solved:

where RC is the relative contribution of an end-member to runoff; T is the value of a tracer;

subscripts denote end-members and superscripts denote tracers; and T_st is the tracer value of stream water. The ability of the mixing model to reproduce the measured stream water tracer values was then assessed by analyzing the residuals between the predicted and the measured values. The negative fractions of relative contributions associated with projections of stream water values exceeding the mixing subspace set by the identified end-members were forced to null, as outlined by Ali et al. (2010). Daily mean values of relative contribution were calculated.

Chapter 2 − A Sudden Shift in Runoff Generation Processes at a Forested Catchment

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2.2.7.2. Individual rainfall events

Individual rainfall events were identified following the criteria (1) that events induced an increase in discharge greater than the maximum diurnal variation in discharge at low-flow conditions, and (2) a minimum inter-event time (MIT) of 6 hours. It was observed that the peak in discharge induced by an event always occurred during the event or within 6 hours of its end. The MIT was set as a compromise between the duration of the variation in discharge and the intra-event variability in precipitation intensity.

2.2.7.3. Recession analysis and runoff coefficient

In order to calculate the total runoff of individual rainfall events shortly followed by subsequent events, a recession analysis of the hydrograph was performed following Tallaksen (1995). An initial analysis of the data revealed that recession rates greatly varied within a few hours and that more than half of the recession periods were shorter than 2 days. These facts and the will to examine runoff responses to individual events prompted our choice of hourly discharge values over daily values, and of the individual segments procedure. A total of seven segments with recession rates following the Dupuit-Boussinesq exponential equation were extracted (Eq. (2a) in Tallaksen, 1995). Constants were derived, which for the respective segments were almost equal for all events except for the third segment, for which two constants were derived (one from the two most important events in terms of precipitation and one from the rest of events). The runoff coefficient of each individual rainfall event was then calculated by dividing total runoff from the start of the event to when discharge on the receding limb was measured or calculated as equal to its initial value, by total precipitation of the event (following WMO, 2009).