In this example, a step-by-step procedure is used to derive and compare streamflow deficit characteristics from rivers in two contrasting river-flow regimes. The calculations were programmed in C++ and the
resulting time series of deficit characteristics were imported into Excel spreadsheets and plotted. Data from the Drammenselv at Fiskum (Norway) and the Arroyo Seco at Soledad (United States) are used to demonstrate the procedure in the example below.
Figure 8.3 Illustration of threshold levels: fixed threshold (top); monthly varying threshold (middle); daily varying threshold (bottom) (modified from Stahl, 2001; reproduced with the author’s permission)
daily hydrograph period of record Q90 seasonal Q90 daily hydrograph montly varying Q90 daily hydrograph daily varying Q90 daily hydrograph period of record Q90 seasonal Q90 daily hydrograph montly varying Q90 daily hydrograph daily varying Q90 daily hydrograph period of record Q90 seasonal Q90 daily hydrograph montly varying Q90 daily hydrograph daily varying Q90
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(a) Data: Drammenselva at Fiskum has a cold climate with no distinct dry season. Annual precipitation is between 800 and 850 mm. Winter precipitation falls as snow and there is a distinct snowmelt peak dis- charge in the spring. A second streamflow peak often occurs in the autumn, caused by rain. The river is perennial and the 30-year period from 1976 to 2005 is analysed. To be able to distinguish between summer deficits caused by a lack of precipitation and high evaporation losses, and winter deficits caused by precipitation being stored as snow, only the summer season (15 May – 15 October) is studied. Arroyo Seco at Soledad has a temperate climate with dry summers and wet winters. The annual pre- cipitation is about the same as at Fiskum. However, the river is intermittent, that is, it has periods with zero flow and Q90 is zero. The complete 30-year period from 1968 to 1997 is studied and the whole year is analysed since temperatures never fall below zero;
(b) Parameter determination:
(i) Threshold selection: A sequence of deficit events is obtained from the streamflow hydro- graph by considering periods with flow below a certain threshold, Q0. The threshold level is obtained as an exceedance percentile from the FDC. In this example, to be able to compare the deficit characteristics from these two con- trasting river-flow regimes, the same percentile, Q70, is used as the threshold for both stations; (ii) Dependent and minor deficits: To reduce the
problem of dependent and minor deficits, the MA procedure has been used with a filter width of 7 days;
(c) Calculation: The following deficit characteristics are calculated:
(i) The start date, defined as the first day below the threshold;
(ii) The end date, defined as the last day below the threshold;
(iii) The deficit volume (1 000 m³), defined as the sum of the daily deficit flows multiplied by the duration in days;
(iv) The deficit duration (days): A histogram of the deficit durations is shown in Figure 8.4. It can be seen that the two rivers have different de- ficit characteristics. The total number of deficit events at Fiskum is 59, on average almost two per year. Short-duration deficits dominate, with the average being 22 days. The most
severe deficit occurred in 1976 and lasted 90 days (from 6 July to 3 October). At Soledad, the deficits are fewer (38 in total) and last longer, with an average of 168 days. The sample is split into two. Except for one deficit lasting 42 days, there is one sample of less than 25 days and another with durations of more than 70 days. The longest deficit occurred in 1991/1992 with a duration of 245 days (from 2 June to 1 February); It should be noted that, because only summer deficits are studied at Fiskum, the maximum deficit duration is from 15 May to 15 October, that is, 154 days. Multi-year deficits cannot occur. In this ex- ample, none of the deficits starts prior to 15 May, but two deficits end on 15 October. 8.4 Definitions of low-flow and deficit character-
istics: National standards in Germany Some countries have developed national standards for deriving low-flow and deficit characteristics. One example is Germany, where the German Association for Water, Wastewater and Waste (DWA, formerly DVWK) has issued recommendations for statistical low-flow analysis and defined the following low-flow and deficit indices (DVWK, 1983, 1992):
NMxQ: Lowest arithmetic mean of n consecutive daily values of flow within the time period ZA during the reference period BZ (in m3/s). With BZ = ZA equal to one year, this is the annual mini- ma of the n-day flow, AM(n-day) (Chapter 5). MaxD: Longest period of non-exceedance of a
threshold Q0 within the time period ZA during the reference period BZ (in days). With BZ = ZA equal to one year, this is the annual maxi- mum deficit duration.
SumD: Sum of all periods of non-exceedance of a threshold Q0 within the time period ZA during the reference period BZ (in days). With BZ = ZA equal to one year, this is the sum of the deficit durations of all the deficit events within one year.
MaxV: Maximum deficit volume between the threshold, Q0, and the hydrograph Q(t) within the time pe- riod ZA during the reference period BZ (in mm or hm3). With BZ = ZA equal to one year, this is the annual maximum deficit volume.
75 0 2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30 40 50 60 70 80 90 100 110 120 > 120
Drought duration (days)
C
ou
nt
s
Fiskum Arroyo Seco
Figure 8.4 Histogram of drought duration for the Drammenselv at Fiskum (Norway) and the Arroyo Seco at Soledad (United States); selection criteria: threshold level Q70 and MA(7)
SumV: Sum of all deficit volumes between the threshold, Q0, and the hydrograph Q(t) within the time period ZA during the reference period BZ (in mm or hm3). With BZ = ZA equal to one year, this is the sum of the deficit volumes of all the deficit events within one year. BZ is a reference period that depends on the low-flow regime of the river under consideration; in a pluvial flow regime, the water year from 1 April to 31 March is used. ZA is the time period under consideration, for
instance, the summer half-year, the water year, or the growth season. An illustration is given in Figure 8.5. Practical studies define the threshold, Q0, by referring to flow minima that are either ecologically required or required by water resources management, reservoir operation and navigation. Regional comparisons are usually based on the mean low-flow. These definitions of low flow and deficit characteristics and the resulting statistics are used in Germany, Hungary and the Czech Republic. 0 50 100 150 200 01 /0 1/ 19 65 01 /0 2/ 19 65 01 /0 3/ 19 65 01 /0 4/ 19 65 01 /0 5/ 19 65 01 /0 6/ 19 65 01 /0 7/ 19 65 01 /0 8/ 19 65 01 /0 9/ 19 65 01 /1 0/ 19 65 01 /1 1/ 19 65 01 /1 2/ 19 65 01 /0 1/ 19 66 01 /0 2/ 19 66 01 /0 3/ 19 66 01 /0 4/ 19 66 01 /0 5/ 19 66 01 /0 6/ 19 66 01 /0 7/ 19 66 01 /0 8/ 19 66 01 /0 9/ 19 66 01 /1 0/ 19 66 01 /1 1/ 19 66 01 /1 2/ 19 66 Fl ow [ m ³/s ] Flow Threshold BZ = 1 year 1 2 3 Figure 8.5 An illustration of deficit indices (BZ and ZA equal the water year). The 1965/66 year has three low flow events below a
threshold of Q0 = 30 m3/s.
The annual maximum duration (MaxD) and deficit volume (MaxV) are determined from event number 3. SumD and SumV are the sums of all three events.
76 stReamFloW DeFICIt
References
Deutscher Verband für Wasserwirtschaft und
Kulturbau (DVWK), 1983: Niedrigwasseranalyse, Teil I: Statistische Untersuchung des Niedrigwas- ser-Abflusses. DVWK – Regeln 120, Hamburg and Berlin.
— , 1992. Niedrigwasseranalyse, Teil II: Statistische Untersuchung des Niedrigwasser-Abflusses. Re-
geln zur Wasserwirtschaft Nr. 121, Hamburg and Berlin.
Dingman, S.L., 2002: Physical Hydrology. Second edition, Prentice Hall, New Jersey, United States. Fleig, A., L.M. Tallaksen, H. Hisdal and S. Demuth, 2006: A global evaluation of streamflow drought
characteristics. Hydrology and Earth System Sciences, 10: 535–552.
Hisdal, H., B. Clausen, A. Gustard, E. Peters and L.M. Tallaksen, 2004: Event definitions and
indices. In: Hydrological Drought – Processes and Estimation Methods for Streamflow and Ground- water (L.M. Tallaksen and H.A.J. van Lanen, eds). Developments in Water Science, 48, Elsevier Science B.V., Amsterdam: 139–198.
Stahl, K., 2001: Hydrological drought – A study across Europe. PhD thesis, Freiburger Schriften zur
Hydrologie, Band 15, Institute of Hydrology, Uni- versity of Freiburg, Freiburg, Germany.
Tallaksen, L.M., H. Madsen and B. Clausen, 1997: On the definition and modelling of streamflow
drought duration and deficit volume. Hydrological Sciences Journal, 42(1): 15–33.
77 estImatIng loW FloWs at ungaugeD sItes