Prediction of flow duration curves in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 143

precipitation

total flow

0.17 - 0.21
0.22 - 0.25
0.26 - 0.27
0.28 - 0.30

0.31 - 0.33
0.34 - 0.36
0.37 - 0.40
0.41 - 0.50

0.01 - 0.12
0.13 - 0.23
0.24 - 0.36
0.37 - 0.50

0.51 - 0.77
0.78 - 1.22
1.23 - 2.7
2.80 - 4.

slow flow

fast flow

0.02 - 0.0
0.10 - 0.14
0.15 - 0.18
0.1 - 0.23

0.24 - 0.2
0.30 - 0.35
0.36 - 0.47
0.48 - 0.70

0.03 - 0.27
0.28 - 0.53
0.54 - 0.83
0.84 - 1.24

1.25 - 1.88
1.8 - 2.87
2.88 - 4.44
4.45 - 7.57

Figure 7.9. Regional distribution of the shape parameter κ of the FDCs for 197 catchments across the continental USA.
From Cheng et al.( 2012 ).

parameter mixed gamma distribution to scaled daily total
runoff (scaled by mean daily runoff), which is given by:

Sauquet and Catalogne ( 2011 ) assessed hydrological
similarity through two simple indicators: the concavity
index (IC) and the seasonality ratio (SR). The concavity
index is calculated as IC

α ¼

, q 0 ¼

Q 99 ) and
measures the contrast between low flow and high flow
regimes, representing the shape of the dimensionless
FDC. Figure 7.10 represents the spatial distribution of
the IC in France: values close to 1 are observed where
large aquifers (e.g., in northern France) and storage in
snowpacks (e.g., in mountainous areas) moderate the
variability of daily runoff. Values close to 0 are found
in catchments exposed to contrasting climate (e.g., small
catchments in the Mediterranean area experiencing hot
and dry summers and intense short rainy events in
autumn) and also to catchments with no storage capacity
(e.g., founded on impermeable substrata) resulting in
severe low flow and quick runoff response to precipitation
events. The seasonality ratio is the ratio of summer
and winter median runoff. SR

(Q 10 − Q 99 )/(Q 1 −

f ð q, κ , θ , αÞ¼ ð 7 : 1 Þ

ð −αÞ ð κ , θÞ , >

1 g q, q 0

where is the probability of zero runoff, i.e., the number of

zero runoff days divided by the total length of runoff
records; g( ) represents the probability distribution function
of the gamma distribution; and

α

are parameters of
the gamma distribution, satisfying the condition that
κ θ ¼

κ and θ

1 =ð 1 −αÞ . This means that two of the three param-

eters and the mean daily runoff will be sufficient

to characterise the duration curves. Cheng et al.( 2012 )
found that the statistical model parameters showed inter-
esting regional patterns. For example, Figure 7.9 presents
the regional patterns of the shape parameter

α , κ and θ

across the
continental USA. In each case these patterns also reveal
how the shapes of the duration curves change from pre-
cipitation to fast flow, slow flow and total runoff, raising
questions about the role of climate, catchment properties
and the resulting process interactions.

κ

1 applies to catchments
with nearly uniform runoff throughout the year, often
when significant groundwater contributions filter out sea-
sonal climatic variability. Catchments influenced by