New Approaches to Hydrological Prediction in Data-sparse Regions (Proc. of Symposium HS.2 at the Joint IAHS & IAH Convention, Hyderabad, India, September 2009). IAHS Publ. 333, 2009.

Copyright © 2009 IAHS Press

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Robust and flexible hydroinformatics to account for rainfall space–time variability in a data-sparse region SAMEH CHARGUI1,2,3, CHRISTOPHE CUDENNEC2,3,4, MOHAMED SLIMANI1, JEAN-CHRISTOPHE POUGET5 & JALEL AOUISSI1,2,3

1 INAT, Lab. STE, 1082 Tunis, Tunisia chargui_sameh@yahoo.fr, cudennec@agrocampus-ouest.fr

2 Agrocampus Ouest, UMR1069, Soil Agro and hydroSystem, F-35000 Rennes, France 3 INRA, UMR1069, Soil Agro and hydroSystem, F-35000 Rennes, France 4 IRD, UMR G-EAU, 1004 Tunis, Tunisia 5 IRD, UMR G-EAU, Quito, Equator

Abstract Rainfall is a major meteorological factor in water assessment in semi-arid basins. For mesoscale basins, the rainfall space–time variability is high and has a major influence on hydrological dynamics. A geomorphology-based rainfall–runoff approach is developed to account for rainfall space–time variability in a robust and flexible manner, according to changing available raingauging configurations. The approach is based on a two-step hydroinformatics protocol, firstly to analyse geomorphometry, and secondly to account for and benefit from available rainfall data. Key words rainfall–runoff; geomorphology-based transfer function; rainfall space–time variability; isochrone INTRODUCTION In semi-arid regions, variability of rainfall inputs is high at different time and space scales. Thus, intense and highly variable hydrometeorological events, which generate both potential resource and hazards, are of major interest. However, raingauge networks are rarely dense and stable enough to observe space–time variability and structures precisely, and to feed rainfall–runoff modelling accurately. A robust and flexible method is proposed to account for the available event space–time variability of rainfall in a rainfall–runoff model. The transfer function used is a geo-morphology-based unit hydrograph, with an explicit territorial significance which allows enrichment of the convolution through accounting for a variability matrix. This variability matrix can be built differently depending on the available raingauge network. This allows it to be adapted to evolving network configurations, even in data-sparse contexts, such as through historical changes, breakdown episodes, designed optimization schemes or local changes of design storm events following climatic changes. Such a robust and flexible hydro-geomorphology-based modelling approach is enabled by a dedicated two-step informatics protocol and is illustrated with a Tunisian basin. ILLUSTRATIVE BASIN This approach is illustrated with the Skhira basin (192 km2; Fig. 1), part of the major central-Tunisian Merguellil basin (Cudennec et al., 2005, 2006a, 2007; Lacombe et al., 2008). The semi-arid region is characterized by strong rainfall variability (Kingumbi et al., 2005; Jebari et al., 2007; Slimani et al., 2007): the rainfall gradient is globally north–south; the role of topography is major; Atlantic and Mediterranean influences are combined with strong seasonal effects; and rainfall is episodic with major storm seasons at the beginning of autumn (September, October) and at the end of winter and beginning of spring (February–May). MODELLING PRINCIPLES Modelling is based on two steps, the former dealing with the geomorphological analysis of the basin and the deduction of the rainfall–runoff transfer function, and the latter dealing with the enriched convolution through the accounting for rainfall space–time variability.

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Fig. 1 The Skhira basin: location, river network and raingauges (from Cudennec et al., 2005).

Geomorphology-based transfer function

Geomorphology-based rainfall–runoff transfer functions were proposed, either from hierarchy-based considerations, or from whole-basin functions (Rodriguez-Iturbe & Rinaldo, 1997; Cudennec et al., 2004; Cudennec, 2007). The explicit observable geomorphometric basis of such approaches is of major interest for hydrological modelling in data-sparse contexts where heavy calibration cannot be implemented. Moreover, the conceptualisation of water transfers can be adjusted according to available data and knowledge on flows, allowing development of methods for assessing design floods (e.g. Nasri et al., 2004; Rodriguez et al., 2005), or for transposing discharges between outlets (Boudhraâ et al., 2006). A robust approach consists in observing the geomorphometry of water paths down to the outlet from sampling the basin area and to assess the experimental probability density function of the length L run by water, pdf(L). Transforming this into a probability density function of water travel times pdf(t), through the simple application of an average velocity, is a simplifying hypothesis which is supported by the literature (Naden, 1992; Beven & Wood, 1993; Blöschl & Sivapalan, 1995; Robinson et al., 1995; Yang et al., 2002; Giannoni et al., 2003). Furthermore, pdf(t) can be used as a transfer function of the unit hydro-graph type through the following convolution:

( ) ( ) ( )τττ

pdf1Δ 1

⋅+−= ∑=

ttR

tStQ (1)

where S is the surface of the basin, Δt the time step, Q(t) the discharge at the outlet at time t; and ( )tR the average net rainfall over the basin at time t.

Accounting for the rainfall space–time variability

Cudennec et al. (2005) proposed the following enrichment of the convolution in terms of the accounting for the net rainfall space–time variability:

Hadada

Fictitious Kesra

Skhira

Abdessadek Morra

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( ) ( ) ( )τττ

τ pdf1Δ

),max(

1

+−= ∑=

tRt

StQtK

(2)

where ( )tRτ is the average net rainfall over the isochrone area τ at time t, which can be turned into:

( ) ( ) ( ) ( )τττΔ τ

τ

pdf.1.1),max(

0

+−+−= ∑=

tVtRt

StQtK

(3)

where ( ) ( ) ( )jRjRjV /ττ = is a variability factor which forms a hydrologically significant space–time variability matrix when τ ranges over the whole basin up to the ultimate isochrone area K and j over the whole event duration. Cudennec et al. (2005) implemented this method by using image processing (Fig. 2). Firstly a series of net rainfall field raster images is generated by interpolation – linear interpolation was used since sparse data do not justify more elaborate methods – between available raingauge measurements for each time t, with time step Δt . Then a crossed analysis of the rainfall field raster images series and the vector map of the basin isochrone areas allows to assess Rτ(j) and thus to build the variability matrix. Results appear to be encouraging (Fig. 3) and the following alternate matrix approach was developed both to gain calculation time and space, and to allow flexibility in terms of accounting for raingauge networks.

Fig. 2 Vector and raster data management and crossing. (a) Isochrone vector map of the Skhira basin. (b) Overlapping of the interpolated rainfall field raster image with the isochrone vector layer. Example of 10 May 1996, 20:39–20:44 (Cudennec et al., 2005).

OPERATIONALITY AND FLEXIBILITY Matrix implementation Given a configuration of n available raingauges Gi, building the rainfall space–time variability matrix Vτ(j), to be introduced in the convolution, through a linear interpolation of net rainfall depth can be achieved as follows. For each raingauge Gi, a matrix of geometric distance di is built for each raster element (x,y) of the whole basin, based on the same raster discretization scheme than the geomorphological analysis. For each raingauge Gi, a matrix of weight is deduced through the application of the following expression for each raster element (x,y):

∑

∑

=

=

−

−

= n

jj

i

n

jj

ixy

dn

dd

1

1

)1(α (4)

(a) (b)

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0

10

20

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40

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80

18:00 20:24 22:48 1:12 3:36

Flow

(m3/

s)

0

2

4

6

8

10

Rai

nfal

l (m

m /

5 m

in)

Observation Enriched ReferenceAbdessadek Hadada Skhira

0

100

200

300

400

500

18:15 19:15 20:15 21:15 22:15 23:15 0:15 1:15 2:15

Flow

(m3/

s)

0

4

8

12

16

20

Rai

nfal

l (m

m /

5 m

in)

Observation Enriched ReferenceAbdessadek Hadada Skhira

Fig. 3 Observed and simulated hydrographs, without (reference) and with accounting for the rainfall space–time variability, based on rainfall data observed at Skhira, Hadada and Abdessadek raingauges. (a) 10 May 1996 event. (b) 9 September 1997 event (Cudennec et al., 2005).

Then a combination of these n weight matrices and of the isochrone matrix allows to assess the matrix of the weight of each raingauge Gi for each isochrone area τ, i

τα . At each time t, rainfall over the isochrone area τ, Rτ(t) is then assessed as the following linear combination of rainfall observed by the raingauges of the available configuration:

( ) ( )tRtRn

j

jj∑=

=1

ττ α (5)

Parallel to this, the average rainfall over the whole basin )(tR is obtained by the linear combination, equivalent to the Thiessen averaging method:

( ) ( )tRtRn

j

jj∑=

=1β (6)

where ∑=

=K

jj

1

)(pdf.τ

τ ταβ is the global weight of raingauge Gi over the basin, itself deduced from

its weights over isochrone areas τ (K being the last existing one) combined with their density distribution as observed from the geomorphological analysis. Hydro-geomorpho-informatics

The first step is led with the HydroStruct software application (Fig. 4), which is dedicated to combined spatial, topological and scaling analysis of morphometry of river networks, in the frame of the OdefiX java framework (Cudennec et al., 2006a,b; Pouget et al., 2006). Vector data of river networks and basins boundaries, however they are obtained, are analysed through both tree formalisation and spatial sampling. Results are extracted as global, classified and scaled statistics; and in terms of spatial distribution through raster images. Raster images of scaled geometric variables can be combined to assess and explore further structural evidences, and be linked with territorial maps of hydrological parameters and/or socio-anthropic properties. Sub-basins and populations of basins can be easily analysed, by crossing, filtering and merging vector, raster and tree data (Cudennec & Fouad, 2005; Cudennec et al., 2006a). Furthermore, a major prospect is the crossing of hydro-geomorphometric results with spatio-temporal variables of different kinds. The matrix approach presented here is such a development based on the particular geomorphetric interpretation of the basin rainfall–runoff spatial structure. The matrix approach was implemented in the frame of Matlab™ software.

(a) (b)

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Fig. 4 HydroStruct software user interface.

433570.75 438570.75 443570.75 448570.75 455870.75

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X(m)

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X(m)

Y(m)

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Fig. 5 Geometric characterisation raster mapping of the Skhira (outlet) raingauge as regards the basin: (a) distance from the gauge; (b) gauge weight in a three-gauges (Skhira, Kesra and Morra) configuration; and (c) gauge weight in a two-gauges (Skhira and Morra) configuration.

(a) (b)

(c)

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Adaptive and proactive flexibility

Recent rainfall events are mostly observed by two or three recording raingauges only: Skhira, Morra and Kesra gauges, at the outlet, outside of the basin and inside of the basin, respectively (Fig. 1). Figure 5 displays the raster map of the geometric distance from the Skhira gauge, and the maps of its weight for the three-gauges and the two-gauges (with Morra) configurations. For a given basin, and the corresponding set of existing and historical raingauges, all the operational configurations can be considered in terms of weight mapping. For any recorded or real-time event, using the pre-defined set of weight maps corresponding to effectively operational configuration – and even further, switching between configurations in case of a sudden breakdown – is an important aspect in terms of adaptative flexibility. The approach also provides a synthetic view of the hydro-geomorphological vision offered by a raingauging configuration, thanks for instance to multi-gauge weight/isochrone graphs (Fig. 6). Furthermore, this flexibility can be used in a proactive way, especially in terms of network optimisation based on the search for the best locations to implement new raingauges, in terms of the best hydro-geomorphological added value. As an example of such a perspective, Fig. 6 displays the hydro-geomorphological vision with a fictitious gauge (see Fig. 1 for location), instead of the actual Morra raingauge.

00.10.20.30.40.50.60.70.80.9

1 11 21 31Isochrone

Wei

ght

Skhira Morra

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

1 11 21 31Isochrone

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ght

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ght

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1 11 21 31Isochrone

Wei

ght

Skhira FictitiousKesra

Fig. 6 Weight of raingauges along the Skhira basin isochrone areas for different configurations.

CONCLUSION

The proposed geomorphology-based rainfall–runoff accounting for rainfall space–time variability is promising. Its potential is especially interesting in data-sparse regions where the geo-morphology-based approach can be applied in a robust and adaptable manner, and where the accounting for rainfall variability is much flexible. The two-step hydro-geomorpho-informatics protocol is a major assessment, rending the method robustness and flexibility fully operational. Rainfall–runoff improvement is obvious, in coherence with the results of Cudennec et al. (2005). However, the easy-to-use and adaptable hydro-geomorpho-informatics protocol opens new major perspectives in terms of switching between various raingauges configurations, both through

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history and towards network improvement scenarios. Finally, the major perspective consists of feeding the approach, for a given raingauge configuration, with design storms expressed in terms of net rainfall series for each raingauge. Developing such design storms, and further performing the whole rainfall–runoff modelling, for events of diverse rainfall variability and associated intensity and frequency, will be a major step for hydrological engineering in data-sparse basins and areas. REFERENCES Beven, K. & Wood, E. F. (1993) Flow routing and the hydrological response of channel networks. In: Channel Network

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