Approche fonctionnelle

Dans cette section, nous allons nous placer du point de vue décrit au Chapitre 1, et étudier quelles peuvent être les conséquences des différents processus décrits précédemment sur la transformation pluie-débit. Pour cela, nous prendrons comme illustration sept bassins versants situés eux aussi en Seine-Maritime (cf. Figure 3.9) :

• six d’entre eux sont situés sur la craie : l’Andelle, le Cailly, le Commerce, le Durdent, la Ganzéville et l’Yères. Ils sont tous influencés par la nappe de la Craie ;

• le septième est situé dans le pays de Bray, région correspondant à un anticlinal érodé où des niveaux plus anciens et imperméables ont été mis à jour (marnes du Crétacé inférieur et calcaires du Jurassique supérieur). Ce bassin ne subissant que très peu, voire pas du tout, d’influences souterraines, nous le prendrons comme bassin « témoin ».

1La porosité efficace de l’air est égale à 1, si l’on ose dire !

2Mentionnons dès à présent qu’il existe de nombreuses méthodes d’estimation de la recharge, basées sur le suivi de profils d’humidité, de température, de concentration de divers isotopes, etc. mais que la question de leurs incertitudes et de leur représentativité spatiale est encore plus problématique que dans le cas de la pluie.

La Sein e

Craie Marnes

Séries carbonatées Argiles / Sables Alluvions

Ganzéville

Commerce

Cailly

Andelle

Epte Yères

Durdent

j3

c2 c1 j3

c2

c1 10 km

Faille de Lillebonne

FIG. 3.9: Localisation de six bassins versants influencés par la nappe de la Craie (Andelle, Cailly, Com-merce, Durdent, Ganzéville et Yères) et d’un septième bassin témoin situé sur un substratum imperméable (Epte). En haut : carte géologique simplifiée ; En bas : carte piézométrique moyenne, isopièzes 5 m (source :http ://www.sidesa.fr/Upload/medias/nappecraie.jpg).

3.3.1 Influences sur le bilan interannuel

L’indicateur le plus simple pour détecter d’éventuelles contributions souterraines au débit des bassins versants est le rapportyentre le moduleQ_m(i.e., le débit annuel moyen calculé sur un grand nombre d’années), exprimé en mm, et la pluie annuelle moyenneP_ms’abattant sur le bassin topographique. Si ce rapport est élevé, par exemple proche ou supérieur à 1, ce sera l’indication que la pluie seule ne peut pas expliquer le débit : à moins qu’il ne s’agisse d’erreurs de mesure, une contribution souterraine nette apparaît nécesssaire. À l’inverse, si le bassin écoule une très faible part de la pluie, on suspectera une perte nette vers l’hydrosystème souterrain.

Nous pouvons préciser un petit peu plus avant ce que nous entendons par « faible » et « fort » en faisant intervenir une autre grandeur interannuelle,E_m, l’ETP de bassin. À supposer que le bassin soit conservatif, le débit écoulé se situe entre deux comportements extrêmes :

• à une extrémité, l’évapotranspiration réelle ne représente qu’une toute petite fraction de l’ETP et en conséquence le débit écoulé est égal à la pluie :Qm≃Pm, soity=^Q_Pm^m =1,

• à l’autre extrémite, l’évapotranspiration réelle atteint le taux potentiel E_m, la quantité d’eau restant pour l’écoulement étant alorsQ_m≃P_m−E_m.

En notantx=^P_E^m_m nous obtenons donc l’encadrement suivant pour le rendementydes pluies sous l’hypothèse de conservativité (Mouelhi, 2006) :

1−1

x ≤y≤1 (3.4)

Cette méthode de représentation adimensionnelle du bilan interannuel sera abondamment employée au Chapitre 5. Les erreurs de mesures et les variations de stock mises à part, nous pouvons d’ores et déjà dire qu’à chaque fois que la valeur de y sera située nettement en dehors de cet intervalle, une influence souterraine est certaine (apport si y >1, perte si y<1−¹_x, aux problèmes de mesure près), la réciproque n’étant pas systématique.

Le Tableau 3.1 résume le bilan annuel moyen pour les sept bassins versants décrits précé-demment.

Bassin versant P_m(mm) E_m(mm) Q_m(mm) y 1−¹_x

Andelle 903 631 357 0.40 0.30

Cailly 923 635 415 0.45 0.31

Commerce 978 647 97 0.10 0.34

Durdent 950 639 372 0.39 0.33

Ganzéville 969 644 298 0.31 0.34

Yères 918 627 322 0.35 0.32

Epte 899 631 244 0.27 0.30

TAB. 3.1: Termes du bilan annuel moyen pour les sept bassins de la Figure 3.9.

Pour des conditions climatiques très similaires, nous pouvons constater une grande disparité du rendement des pluies y sur ces sept bassins. L’Andelle et le Cailly ont un rendement nettement supérieur à celui de l’Epte, qui indique très certainement un apport net de la nappe à ces deux rivières. À l’inverse, le Commerce (perché sur une bonne partie de son cours) a un rendement très faible¹, inférieur à 10%, ce qui est même moins que la différence entre la pluie et l’évapotranspiration potentielle (i.e.,y≪1−¹_x).

3.3.2 Influences sur la dynamique

Les échanges entre système de surface et système souterrain dépendent des états de chacun des deux systèmes et ne sont donc pas stationnaires, comme nous l’avons déjà noté au paragraphe 3.2.1. En conséquence, le fait que le débit spécifique moyen du Commerce soit deux fois et demi plus faible que celui de l’Epte ne signifie pas que l’hydrogramme du Commerce soit simplement une homothétie de celui de l’Epte.

Pour montrer cela, nous avons tracé sur la Figure 3.10 les hydrogrammes au pas de temps horaire pour l’Epte et pour la Ganzéville, qui ont un module et un rendement assez similaires (244 mm, 27% et 298 mm, 31% respectivement). Ces valeurs annuelles moyennes masquent la dynamique des échanges entre la nappe de la Craie et la Ganzéville : les étiages de la rivière sont massivement soutenus par l’aquifère, tandis que ses crues sont très atténuées par l’infiltration et la recharge. Il en résulte une variance des débits bien plus faible pour la Ganzéville que pour l’Epte.

Nous pouvons synthétiser ces différences de dynamique au moyen d’un graphique quantile-quantile (QQ-plot), représenté Figure 3.11, dont le principe est le suivant :

• on construit la courbe des débits horaires classés pour chaque bassin,

1Pour être exact, le Commerce détient le record du plus petit module sur tout l’échantillon français. Ceci tient entre autres au fait qu’il est localisé sur la faille de Lillebonne (faille Fécamp-Rouen), qui crée une condition aux limites du type (4) de la Figure 3.5 (page 57).

Q (mm/h)

FIG. 3.10: Hydrogrammes horaires de l’Epte et de la Ganzéville sur deux années hydrologiques (1999–

2000). Les débits sont exprimés en mm/h (débits spécifiques).

• on échantillonne cette courbe pour l’Epte en n valeurs de fréquences {f₁,...,fn}, ce qui nous donnenvaleurs de débit {q₁,...,qn}=X (série d’abscisses),

• pour chacun des six autres bassins, on trouve les quantiles de mêmes fréquences {f₁,...,f_n} ce qui nous fournit six séries d’ordonnéesY_i,

• on trace les six séries de points définies par (X,Y_i).

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FIG. 3.11: Graphique quantile-quantile des débits horaires, avec comme référence les débits de l’Epte.

Les échelles sont logarithmiques et les droites en pointillés indiquent des rapports de 2 successifs.

On observe ainsi quantitativement ce que nous avons décrit plus haut :

• À l’étiage (gauche du graphique), les bassins de la Craie ont un débit spécifique systémati-quement supérieur à celui de l’Epte, même le Commerce. Malgré tout, ces débits d’étiage sont très variables d’un bassin à l’autre (de 0.005 mm/h pour le Commerce à 0.03 mm/h pour le Cailly en étiage extrême),

• En crue, les débits sur les bassins de la Craie sont nettement inférieurs à ceux de l’Epte, même ceux du Cailly (les surfaces étant suffisamment proches pour ne pas influencer notablement le temps de réaction). De plus, contrairement aux étiages, il semble y avoir un comportement convergent des six bassins de la Craie, les débits de pointe étant compris entre la moitié et le quart des débits de même fréquence sur l’Epte¹.

Ces conclusions sont principalement valables en domaine de nappe continue. En domaine karstique, les transferts, qui sont beaucoup plus rapides et représentent des volumes beau-coup plus importants, jouent souvent systématiquement dans le même sens en crue et à l’étiage. Ainsi les principales résurgences (Fontaine de Vaucluse, Touvre, Loue, etc.) sont-elles continuement alimentées par des pertes de surface ; ces bassins de surface voient quant à eux leur débit réduit en crue comme à l’étiage (il n’est pas rare que certains cours d’eau disparaissent intégralement dans le karst en été).

Dans tous les cas, les échanges surface–souterrain affectent non seulement le débit moyen annuel mais également la dynamique des bassins versants. En outre, ils peuvent affecter toute la gamme des débits, jusqu’aux crues, et pas uniquement les débits d’étiage : cela montre qu’il n’est pas du tout absurde de travailler à un pas de temps fin (horaire) pour l’étude des bassins influencés par les eaux souterraines.