8. Streamflow deficit
8.1 Introduction
Streamflow deficits (Hisdal and others, 2004) are pe- riods when the river is below a specific threshold that defines a drought or critical deficit. There are two main methods to select and characterize deficits, namely the threshold-level method and the sequent peak algorithm initially used for reservoir storage-yield analysis. In this chapter, only the threshold-level method is described. This method is used for providing estimates of the fre-
quency of low-flow periods and for designing and opera- ting regulating reservoirs where reservoir releases are made to support downstream abstractions. Examples of water use include those related to hydropower, public water supply and irrigation.
Figure 8.1 shows the definition of the timing, durations and volumes of deficits below a threshold discharge in a river. Streamflow deficits can also be characterized by intensity and spatial extent. The threshold-level method was initially named the “method of crossing theory” and is also referred to as “run sum analysis” because it generally studies runs below or above a given threshold. A detailed discussion of the method applied to a global
dataset is given in Fleig and others (2006).
Figure 8.1 Definition of deficit characteristics (modified from Hisdal and others, 2004; reproduced with Elsevier’s permission) Time (days) Fl ow (m 3/s) d1 d2 d3 d4 v2 Qmin v3 v4 v1 Q0
8.2 Definition and derivation
The threshold level Q0 is also referred to as the trunca- tion level and is used to define whether the flow in a river is in deficit (Figure 8.1). The deficit starts when the flow goes below the threshold and ends as soon as the flow returns above the threshold. Thus, the beginning and the end of a deficit period can be defined. In addition, the following deficit characteristics can be defined: (a) The duration, which is the period of time where
the flow is below the threshold level and is also referred to as drought duration, low-flow spell or run length (di, Figure 8.1);
(b) The volume or severity, which is also referred to as drought volume or run sum (vi, Figure 8.1);
(c) The intensity, which is also referred to as deficit or drought magnitude, mi, is the ratio between deficit volume and deficit duration;
(d) The minimum flow of each deficit event (Qmin in Figure 8.1);
(e) The time of occurrence, for example, the star- ting date, the mean of the onset and termination, or the date of the minimum flow.
Based on the time series of the deficit characteristics, it is possible to derive indices, such as the average deficit duration or average deficit volume.
Time resolution
Whether to analyse annual, monthly or daily dischar- ge depends on the hydrological regime under study, the data available and the specific problem to be solved. In temperate climates a year might include severe short-duration deficits followed by periods of high flow, and therefore daily flow series would be required to identify deficit periods.
Deficits may last for several years in arid and semi- arid regimes, and monthly data may be sufficient. Different time resolutions might lead to different re- sults regarding the selection of deficit periods.
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The threshold-level method was originally based on analysing sequential time series with a time resolution of one month or longer. Daily data is now more com- monly used. However, the use of daily data introduces the problems of dependency between deficits and minor deficits. During prolonged dry periods, the flow may exceed the threshold level for a short period of time, dividing a large deficit into a number of minor periods that are mutually dependent (Figure 8.2). This is inap- propriate for extreme value modelling, which requires independent events. It is therefore recommended that pooling procedures be applied to define an independent sequence of deficits. A large number of minor events may also introduce bias in the extreme value modelling, and a procedure to remove such events may be required. Pooling procedures include the moving average pro- cedure (MA), the inter-event time (IT) and the inter- event time and volume criterion (IC). The MA pro- cedure simply smoothes the time series applying a moving average filter. This is demonstrated in Figure 8.2, where a 10-day averaging interval has been used. A study by Fleig and others (2006) found that the MA
procedure is applicable to both quickly and slowly res- ponding streams. The averaging interval can easily be optimized, and a filter width of around 7 days is appro- priate for many hydrological regimes. An additional advantage of the MA pooling method is that it reduces the problem of minor deficits. A drawback is that the method modifies the discharge series and might introdu- ce dependency between the deficit events, particularly for long moving averages.
The IT method pools mutually dependent deficits with characteristics (di, vi) and (di+1, vi+1) if they occur less than a predefined number of days, tmin, apart. The pooled duration and deficit volume can be defined as:
dpool = di + di+1 (8.1(a))
vpool = vi + vi+1 (8.1(b))
Fleig and others (2006) used the IT method and con- cluded thattmin = 5 days can be applied for perennial as well as intermittent streams if the stream is not very flashy when the method tends to pool too many events. Tallaksen and others (1997) suggest the IC method, where two events are pooled if: (a) they occur less than a predefined number of days, tmin, apart (the inter-event time, τi, is less thantmin) and; (b) the ratio between the inter-event excess volume, si, and the preceding deficit volume, vi, is less than a critical ratio, pi. The pooled deficit is then pooled with the next one if the require- ments of (a) and (b) are fulfilled, and so on. The pooled deficit characteristics can be calculated as follows:
dpool = di + di+1 + τi (8.2(a))
vpool = vi + vi+1 – si (8.2(b))
The method was tested on two rivers with contrasting flow regimes and it was found that the optimal values of the pooling criteria were tmin = 5 days and pi = 0.1. When the IT or IC method is used, minor deficits have
to be excluded in an additional step by excluding de- ficits if the deficit volume or duration is smaller than predefined values. 1.0 1.5 2.0 2.5 Dischar ge (m 3/s)
May Jun Jul Aug Sep
Dependent droughts s1 τ2 s2 Minor droughts τi
siExcess durationExsess volume
Oct Nov Q MA (10-day) 3.0 Qz Figure 8.2 Illustration of pooling mutually dependent deficits and removal of minor deficits by an MA(10-day) filter (modified from Fleig and others, 2006; repro- duced with the authors’ permission)
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