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Mapping mean annual and monthly river discharges
geostatistical developments for incorporating
river network dependencies Eric
SAUQUET Cemagref, Hydrology-Hydraulics Research
Unit, Lyon
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How to adapt kriging for mapping runoff
characteristics ?

• Streamflow data
• are affected by scale effect (the size of the
  gauged basin)
• are organised by the river network with
  upstream-downstream dependencies (overlapping
  drainage area)
• are measured at one point, not representative of
  the basins

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River flow time series observed at N gauging
stations
DEM and river network
Runoff characteristics q for N sub-basins
Heterogeneity
q f(x,y,z,) err q-q
q
Kriging applied to

Map of q
Map of err
Map of q
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Application

• Variable under study qa runoff generated by
  portion of gauged basins and weight
  coefficients related to EOF analysis
• Stations with strong karstic influences ( )
  are excluded
• River network deriving from 1 by 1 km Digital
  Elevation Model is considered
• Elevation is supposed to be the most
  influencing factor for spatial variability
• France is divided into ten regions and
• empirical formulas incorporating
• elevation are derived for each of them to
  test homogeneity
• Target partition is composed by 6000 elementary
  areas

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Application to mean annual runoff
Linear regression qa aH b err qa - (aHb)
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Application to mean annual runoff
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Mapping monthly pattern
A temporal disaggregation of the mean annual
runoff is suggested to ensure consistency with
the map of qa.
? T and S are given by EOF analysis
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The temporal amplitude functions T
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Interpolating the weight coefficients S
f(A,t)S1(A)T1(t)S2(A)T2(t)
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Estimating runoff along the river network
River flows are deduced from runoff value
estimated for each cell DA by aggregation along
the river network
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Maps of monthly discharges
January
July
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Conclusions
A technique based on objective methods specially
adapted to account for the related drainage basin
supporting areas and the hierarchy in the
discharge data imposed by the structure of the
river network was presented To interpolate the
twelve mean monthly discharges, a method keeping
the auto-correlation between successive terms is
used. The developed procedures ensure consistency
in space and in time the continuity equation is
fulfilled by aggregation along the water path and
the temporal redistribution of annual values
ensures monthly estimates coherent with the
intra-annual water cycle and with the annual
values of discharge The next steps should
involve - assessing the uncertainty in the
procedure (cross-validation) - comparing with
other methods - testing other explanatory
variable (climate indices, land-use
descriptors) - testing the benefits of using
homogeneous regions