Insights gained from four component hydrograph separation

Many advances in rainfall–runoff modelling have been made in recent years by aiming to relate the gross rainfall input directly to the total streamflow (Beven 2001), rather than relating the effective rainfall to the storm runoff. This circumvents the initial problem posed (NERC 1975) of having to estimate rather poorly-defined storm runoff and baseflow components prior to unit hydrograph identification. Hydrograph separation is embraced within the procedure, with dominant quick and slow response components of modelled streamflow found as follow-on byproducts of the identification (Littlewood 2009).

The aim of this present paper is to apply these advances more fully to event-based models, in particular to the routing component. The parallel structure of fast and slow responses has been adopted, but each of these responses has been represented by a non-linear conceptual reservoir, thus avoiding the linear system constraint inherent in the linear transfer function model. The resulting four component hydrograph separation technique is examined to see what insights, both theoretical and practical, are gained into the hydrograph separation techniques of previous event-based models described in the literature:

• (i) General Separation (GS) model (Reed et al. 1975; Beven 1991)

• (ii) Flood Studies Report (FSR) model (NERC 1975)

• (iii) Revitalised Flood Hydrograph (ReFH) model (Kjeldsen 2007)

• (iv) Reservoir Inflow Sequence (RIS) model (Mandeville 2004).

These advances have only been partially reflected in recent versions of event-based models used to analyse a single observed storm hydrograph. For example, the ReFH rainfall–runoff model (Kjeldsen 2007) was introduced to supersede the then 32-year-old FSR model (NERC 1975). However it still involves an initial separation of the observed hydrograph into two components called the ‘direct runoff hydrograph’ and ‘baseflow’. A revised version of the unit hydrograph is used to relate the effective rainfall to this ‘direct storm runoff’. A linear conceptual reservoir is introduced to model the baseflow, which is an important improvement over the FSR technique. However, because a proportion of the shape of the output from the quick response component (the direct runoff hydrograph) is used to represent the format of the input to the slow response component, the overall routing structure of the ReFH model does not conform to that of a parallel linear transfer function, which is one of the foremost advances mentioned previously.

This paper does not directly address the major issue of comparing continuous simulation with event-based models. Both approaches have their own strengths and weaknesses. Rather than dismissing one or the other, it is felt there is merit in taking forward both approaches in parallel. Comparison between the results obtained from each separate approach serves to stimulate the advancement of the other. For example, in this paper adopting the routing structure of a parallel transfer function, used in certain leading continuous simulation models, and applying the concept to four event-based models, allows some useful insights about the latter to be gained.

In the alternative direction, there may well be cases where advances in event-based models could lead to some useful insights about corresponding continuous simulation models. For example, it appears feasible to identify the split between quickflow and slowflow contributions during pre-event and post-event recession periods using the RIS event-based model (Mandeville 2004). This method is based on examining the gradients abstracted from the observed streamflow data alone, without any additional supporting rainfall data. While some continuous simulation models, such as IHACRES, can accomplish the same task, they need both streamflow and corresponding rainfall as input data (Littlewood & Jakeman 1991).

There are two more areas on which this paper is not directly focused. First, it does not address the important task of identifying or predicting the volumes of effective rainfall which need to be routed through the parallel transfer function. However, identifying the correct storm runoff volumes in the first place, for quickflow and slowflow separately, is an integral consideration which these insights do address. Second, the paper does not seek to directly develop or justify any of the event-based models examined, or even the overall four component separation technique itself, as a stand-alone separation procedure. This paper concentrates on adopting the concept of the four component separation technique, and comparing it to the separation techniques used in four existing event-based models, to see what insights emerge, and whether the structures of those four models are amenable to any improvements.

By extending the pre-event quickflow recession curve, the quickflow hydrograph may be separated into two further subcomponents, as shown in Figure 2:

• QFP: the quickflow preceding runoff

• QFS: the quickflow storm runoff.

QFP is the quickflow hydrograph that would have occurred if the storm inflow had not taken place. QFS is the additional response due to the storm inflow; it is bounded by the extensions of the pre-event and post-event quickflow recession curves, that tend asymptotically to zero flow as values of time t become larger.

Similarly, by extending the pre-event slowflow recession curve, the slowflow hydrograph may be separated into two further subcomponents, as shown in Figure 3:

• SFP: the slowflow preceding runoff

• SFS: the slowflow storm runoff.

The resulting four subcomponents (QFP, QFS, SFP and SFS) form the basis of the so-called four component hydrograph separation technique.

In this section the observed storm hydrograph is first split into the two main components, the quickflow hydrograph (Figure 2) and the slowflow hydrograph (Figure 3). It is considered that these two quite different responses do physically exist and so can be identified, but the actual sources of water contributing to each component is still a matter of debate. These two components are then split into the subcomponents QFP, QFS, SFP and SFS. These four subcomponents are not thought to physically exist in general, except for the particular cases of QFP and SFP during the pre-event recession phase. Instead, they are put forward as concepts that will be employed to analyse the structures of some established event-based models.

The following three assumptions are adopted:

• (i) the pre-event and post-event quickflow recessions are formed of different portions of the same quickflow master recession curve;

• (ii) the pre-event and post-event slowflow recessions are formed of different portions of the same slowflow master recession curve;

• (iii) although the slowflow response is much more damped than that of quickflow, the inflow section of the slowflow hydrograph occurs during exactly the same period of time as the inflow section of the quickflow hydrograph, namely, starting a few ordinates prior to the time of minimum quickflow and finishing at the time ordinate of the inflection point on the quickflow hydrograph recession curve.

The method extends the pre-event observed recession until it eventually tends asymptotically to zero flow for higher values of time t. It relies on assuming that this extended recession represents the hydrograph that would have occurred if no storm inflow had happened. If this contribution is subtracted from the overall observed storm hydrograph, the remaining shape, as outlined by a solid line in Figure 5 and entitled the ‘storm runoff’, represents the contribution arising from the storm inflow alone.

This quantity represents the overall runoff response due to the storm inflow. In his 1991 review, Beven assumed that this volume was identical to just the quickflow storm runoff QFS alone, but Equation (1) demonstrates that it is actually a combination of both quickflow and slowflow. If this GS technique was adopted as an analysis method, it would consequently require an additional step to separate out the storm runoff into its constituent quickflow and slowflow subcomponents QFS and SFS, so the technique is incomplete.

Reed et al. (1975) had earlier applied this GS technique to individual storm events, dividing the observed hydrograph into ‘underlying flow’ and ‘runoff due to the storm’; the latter portion was not assumed to represent just quickflow. For an event occurring after a relatively dry spell, the underlying flow is approximated by the outflow from a linear conceptual reservoir. The runoff due to the storm is not assumed to cease at some arbitrary finite time ordinate, but is modelled by using a response function which possesses an infinitely long tail.

The authors even demonstrated how their technique can be applied to a sequence of multiple storm events. They claimed that continuous prediction with the model is, in principle, quite feasible, and in practice applied a computer program to examine the model response to a series of synthetic peaks.

Deficiencies in the FSR separation technique have been acknowledged for many years. In its defence, it should be repeated that the technique was originally established for undertaking systematic engineering hydrology applications under a tight schedule, at a moment in time prior to the rapid development of rainfall–runoff models over the last 40 years. It did not have the luxury of the generous time available under an applied research project. As such, it is a simplification of reality, specifying only two arbitrarily defined components of observed streamflow, prior to identification of the unit hydrograph for quick response runoff.

The IHACRES model is an example of a continuous simulation rainfall–runoff model that was first introduced in 1990 and which has since been refined and applied to many different sets of hydrometeorological data over the last 25 years (Littlewood 2008). That paper lists a number of general advantages that the IHACRES approach provides in comparison to the FSR separation technique, including:

• (i) low flows modelled;

• (ii) ability for continuous streamflow simulation;

• (iii) no prior hydrograph separation required;

• (iv) automatic hydrograph separation;

• (v) no smoothing of the unit hydrograph shape required.

In contrast, the aim of Figure 7 is more specific, namely, to illustrate in what way the separation lines used in the FSR technique are deficient and lead to unreliable components, and how they could possibly be improved. It highlights the problems caused by restricting the number of separated components to just two, and argues that the use of four subcomponents provides a much more flexible approach to dividing up the observed streamflow hydrograph.

One other point of interest concerns the extension of the pre-event observed recession curve. Figure 7 shows that this extension is composed of the flow formed by the combination of the subcomponents QFP and SFP. These, in turn, form the extensions of the pre-event recessions of the main quickflow and slowflow hydrograph components. During the analysis of observed storm events undertaken during the Flood Studies Report (NERC 1975), three different conceptual models were explored to provide a method to extend the pre-event observed hydrograph recession: a single linear reservoir, a non-linear reservoir and a set of two linear reservoirs in parallel. The third model was found to be best at matching the extended recessions. This result gives some credence to support the combined use of the two subcomponents QFP and SFP to represent the extension of the pre-event observed recession curve shown in Figure 7.

Note that, at the time ordinate at the end of the observed hydrograph post-event recession, before it is extended the total flow value is composed of four different flow contributions arising from the subcomponents SFP, SFS, QFP and QFS. This emphasises the complexity of trying to separate out the various different components, and may account for some of the myriad methods of hydrograph separation proposed in the past.

The four component hydrograph separation technique certainly supports the introduction of a conceptual reservoir to represent the slowflow component of the observed hydrograph. In this respect, the ReFH technique used to determine the direct runoff hydrograph has much greater justification than the FSR technique, which does not include such a conceptual reservoir; it is consequently a considerable improvement. Well before the development of the ReFH technique in 2007, the idea of a linear conceptual reservoir to represent the dominant slowflow response in continuous simulation models had been demonstrated for the IHACRES model by Littlewood & Jakeman (1991). Littlewood (2008) extended the range of this idea to the case of a single observed storm hydrograph by applying the IHACRES model to an event drawn from the river Lossie record at Torwinny in Scotland.

However, Figure 10 shows that there are important differences between the ReFH and four component separation techniques. The baseflow separation line adopted in the ReFH technique broadly follows the nonseparated flow line described in the previous section, rather than the lower down slowflow separation line (Figure 9). As the outflow from the ReFH linear conceptual reservoir closely resembles that from a slowflow system, it would seem more appropriate that it does not start from the first flow ordinate of the observed hydrograph, but rather from some smaller flow value instead, such as the initial ordinate of the SFP subcomponent. It should also preferably finish at a lower flow value than that of the observed post-event recession curve.

It appears that the ReFH technique assumes that the contributing flow from the QFP subcomponent is zero; under this scenario, the nonseparated flow and slowflow separation lines would coincide (Figure 9). While QFP may well be small, or even negligible, for summer storm events which occur after a long dry spell, it is suggested that this is not the case for the vast majority of storm events occurring during the remaining months of the year.

An analysis method involving gradients of the observed storm hydrograph is used to determine the slowflow hydrograph component for the pre-event and post-event recession periods, respectively. This method assumes that the slowflows during the pre-event recession period are constant, which is a reasonable approximation of the slowly decaying slowflow values actually occurring. Similarly, it assumes constant slowflow values during the post-event recession period, although normally this latter flow rate is found to be higher than that found during the pre-event recession period.

However, this particular analysis method, involving gradients of the observed storm hydrograph, is only valid for those periods during which the observed storm hydrograph is in recession; outside of these periods it cannot be employed. Therefore it is necessary to adopt a practical method, which has little theoretical justification, for interpolating the central portion of this slowflow hydrograph component. It can be seen from Figure 11 that the match between the estimated and theoretical slowflow hydrograph components is poor during this intervening period, and this is an area of the RIS technique that needs strengthening.

Although Equation (4) offers an exact theoretical solution, the RIS technique has also been found to be a viable practical procedure. It is currently being applied to observed hydrographs for groups of storm events drawn from seven catchments spread around the United Kingdom; for example, results for 25 events, recorded on the Western Cleddau river at Prendergast Mill in western Wales, are described in Mandeville (2004). For five of these events, it has been found in practice that there are some difficulties in obtaining a realistic inflow sequence I(t) when instability occurs near its maximum value, which highlights a second area of the RIS technique that needs strengthening.

The Recession Gradient Function m_r{Q(t)} has been developed to identify the master quickflow recession curve, for both pre-event and post-event periods, for a particular catchment. Each catchment will normally have a different version of m_r{Q(t)}, although sometimes it is found that the same example fits two catchments located far away from each other. If expressed in the form of a simple power law it will possess two parameters, as shown in Equation (3). The Recession Gradient Function may form a useful new catchment descriptor, which in the future could be related to catchment characteristics by suitable regression equations.

The question arises as to whether it is possible, in a practical case, to estimate the four flow subcomponents SFP, SFS, QFP and QFS, as shown in Figure 8, from relevant rainfall and streamflow data? A suitable procedure will now be described by considering the catchment No. 61001, the Western Cleddau river at Prendergast Mill, located in Wales, for which 25 storm events were available, the same data as those used in the Flood Studies Report (NERC 1975), with observed storm hydrographs recorded with hourly time intervals (Mandeville 2004).

The slowflow hydrograph encompasses the two subcomponents SFP and SFS. The first of these may be found by extending the initial constant value of pre-event slowflow all the way to the end time of the storm event. In the case of event No. 18, this value would be 0.061 mm.h⁻¹ (Table 1). In reality, it is likely that this SFP flow value would decay slightly during the course of the event, but a constant value provides a reasonable first approximation over the limited time period of the storm event. To determine the SFS subcomponent, the subcomponent SFP is simply subtracted from the slowflow hydrograph found earlier (Figure 13). Table 1 shows that the post-event slowflow has a value of 0.175 mm.h⁻¹. Therefore the maximum flow value of SFS, taken alone, is given by (0.175–0.061) = 0.114 mm.h⁻¹.

This procedure illustrates how the four subcomponents SFP, SFS, QFP and QFS can be estimated, even though they remain as concepts and cannot be assigned physical reality, except possibly for the values of SFP and QFP during the pre-event recession. The most important aspect of the procedure is that these estimates are ultimately based on values of both the observed streamflow and the gradient of observed streamflow for the particular event No. 18, as well as a Recession Gradient Function of quickflow based on the observed streamflows of the whole group of 25 events. No observed rainfall data are required to complete this process.

The four component hydrograph separation technique facilitates the definition of various important flows in terms of suitable combinations of the various subcomponents (Table 2). The terminology ‘underlying flow’ is adopted directly from the analysis presented in Reed et al. (1975), while that of ‘nonseparated flow’ is based more loosely on the term mentioned in NERC (1975). These suggested definitions may be more exact than those presented previously in the standard event-based models described earlier. For example, historically the use of the word ‘baseflow’ is sometimes ambivalent. More often than not it is used to represent the nonseparated flow, but occasionally it is used to suggest the underlying flow (see, for example, Figure 2.5 in Beven (2001)).

The two terms ‘slowflow hydrograph’ and ‘nonseparated flow’ have been discussed earlier and illustrated in Figure 9 in the section on new terminology. The interpretation of ‘underlying flow’ as the combination of the two subcomponents SFP and QFP seems intuitively sensible (Figure 4). These represent the slowflow and quickflow contributions that result from the size and time sequence of all storms that occurred prior to the start of the current storm. The form of SFP and QFP are not affected by the size or timing of the current storm input. Although SFP and QFP may exist as separate physical entities during the period of the observed hydrograph pre-event recession, after the start ordinate of the current storm they are represented only as concepts, because they do not actually occur in practice.

The four component separation technique serves to highlight the relative importance of the SFS subcomponent (Figure 4). Some traditional event-based two component separation techniques tend to downplay its significance, with the GS technique ignoring it altogether, and the FSR technique only partly incorporating it. In the present approach, SFS is considered to be a key component. It represents the slowflow contribution arising from the current storm.

In terms of runoff volume, because of the more slowly converging upper and lower limits of SFS as time t increases, it may play a more important role than QFS, with its more quickly converging limits (Figure 4). In some catchments the total runoff volume contributed by SFS may exceed that contributed by QFS. No relevant results from analysis of event-based models are readily available to support this supposition, but corresponding continuous simulation models compare the volumes of the slowflow hydrograph (SFP + SFS) with those of the quickflow hydrograph (QFP + QFS) (Figure 8). For example, Young & Beven (1994) fitted their bilinear power law model to the CI6 catchment at Llyn Briane in Wales, and their final fit showed that 33.4% of the effective rainfall passed through the fast transfer component of the parallel linear transfer function, to give the quickflow hydrograph, and 66.6% through the slow transfer function, to give the slowflow hydrograph.

Although the main contributor to the size of the observed hydrograph peak remains the quickflow storm runoff subcomponent QFS, Figure 4 shows that SFS adds a definite, but modest, contribution to this peak flow ordinate. One reason for this is that, although the slowflow response is much more damped than that of quickflow, there is no lag of the slowflow response compared to that of quickflow, as mentioned previously in the third assumption. The inflow to the slowflow conceptual reservoir starts a few ordinates prior to the time of minimum quickflow, and finishes at the time ordinate of the inflection point on the quickflow hydrograph recession curve.

This is in contrast to the FSR technique, where the average nonseparated flow was taken to represent the flow in the river before the event started and, to a lesser extent, the beginnings of the slow response from the event itself (NERC 1975). It was assumed that the slow response only started to occur some number of time intervals later than the start of the quickflow response, i.e., from the time ordinate corresponding to the peak of the observed storm hydrograph (Figure 6).

It was also assumed in the FSR procedure that the average nonseparated flow was broadly unvarying, and a constant value should be added to all ordinates of the design hydrograph, as in view of the almost trivial effect on the size of any design flood, nothing more complex could be justified (NERC 1975). However, the four component technique suggests that the size of SFS is dependent on the size of the current storm input, so it is variable, and if included in the nonseparated flow (Table 2) will no longer allow this latter function to be considered unvarying. Thus for a large design storm, the quickflow storm response QFS will be large, but SFS will also increase, to a more modest extent, so this latter increase needs to be incorporated into the final design hydrograph.

In contrast to the FSR technique, in the ReFH technique the baseflow contribution does directly increase for a larger direct runoff hydrograph because a proportion of the latter is taken as the inflow to the linear conceptual reservoir used to represent the baseflow routing structure.

During past discussions of event-based models, some confusion has arisen concerning the exact meaning of certain terms used, such as baseflow, nonseparated flow, and storm runoff. The same term may describe a different quantity for two separate models. The four component separation technique allows a suggested new terminology to be introduced, involving terms such as underlying flow, slowflow hydrograph, nonseparated flow and quickflow hydrograph. Each of these terms may then be defined exactly as a suitable combination of selected subcomponents.

The four component separation technique serves to highlight the relative importance of the slowflow storm runoff subcomponent SFS. This paper considers it a key component that has been either only partly incorporated or even ignored altogether in some previous event-based models. While SFS normally provides only a modest contribution to the peak flow value of the observed storm hydrograph, it may, in some catchments, make a major contribution to the overall runoff volume resulting from the current storm event. As the size of SFS depends partly on the size of the current storm, and SFS forms part of the nonseparated flow, the latter quantity cannot be assumed to be broadly unvarying, as proposed in NERC (1975), and consequently itself will increase for a larger storm event.

It is considered that under the four component separation technique the two main components identified, the quickflow and slowflow hydrographs, do physically exist, but the four subcomponents put forward exist only as concepts because they do not actually occur in practice. Despite this restriction, a procedure is outlined that demonstrates a way of estimating a time series of values for each of the four individual subcomponents, and is illustrated for a practical case study of a single historical event, observed on a catchment located in south-west Wales. The procedure described ultimately depends on only the streamflow data observed for a group of storm events occurring on the same catchment, and no corresponding rainfall data are required.