Feuille d`exercices

M1 SDE – MEC558 « Hydrologie continentale et ressources en eau »
Bloc Hydrologie quantitative – Séance 1
Feuille d’exercices
1. Introduction : water cycles on Earth
1.1 Exercice - Le cycle de l’eau global
-
-
Find the mean annual runoff to the oceans, RC, from the total annual discharge from land to oceans,
QC = 40.103 km3/an. To this end, compute the total land surface AC knowing that the mean Earth radius is
RE = 6,371 km, and that continents occupy about 30% of the total surface.
In practice, RC has to be estimated differently: how?
Deduce EC
Show that RC equals the mean moisture convergence over land
Show that the global means of evaporation and precipitation, EE and PE, are equal; what can you conclude
regarding the exchanged volumes of water between the land and ocean fractions of the Earth? Show how
it allows estimating EO from PO and RC
1.2 Exercice – Water resources
Compare the volume of water that is available per capita and per day, if consider either the stock of water in
rivers, or the flux of water through rivers. Use the values given in the lecture, and consider that the world’s
accounts 7 billion inhabitants. Compare the results to the needs of freshwater per inhabitant, using the value
of 1700m3/inhab/yr, which is the threshold below which a country is said to experience water stress.
1.3 Complément - Delineation of river basins
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A partir de cartes topographiques
A partir de modèles numériques de terrain (MNT) et systèmes d’information géographique (GIS)
o Calcul des pentes, directions d’écoulement, reconstitution des réseaux de drainage, corrections
o Exemple de MNT disponibles à différente résolution, en France et sur le globe
1.3 Exercice – Mean water balance of the Seine River basin
La station de mesure du débit la plus à l’aval du bassin de la Seine est à Poses, avec une superficie amont de
65 000 km². Le débit moyen interannuel (module) est QM = 538 m3/s, avec un régime pluvial. En moyenne,
les précipitations sont de 730 mm/an. Trouvez le runoff et l’évaporation moyens dans le bassin de la Seine.
1.4 Exercice – Residence times
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Calculate the residence times of water in the oceans, atmosphere, and rivers.
Discuss the case of groundwater.
Soil moisture (Exercise 1.1 in Brutsaert p9).
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2. Water in the atmosphere
2.1 Exercice - Express the relative humidity U as a function of the commonly measured variables qa, Ta, and
pa knowing an expression of es(T)
2.2 Exercice & Complément - How can we measure atmospheric humidity?
Dew point hygrometers
The dew point temperature of air can be determined by cooling a surface until water condenses on it and
measuring the temperature of the surface. When a surface is just cold enough to cause moisture to condense
from air onto it, the surface is at the dew point temperature of the air. When properly maintained, a cooled
mirror hygrometer is one of the most accurate methods of measuring atmospheric moisture in use today. The
disadvantage of this technique is that the instrument is usually complicated, costly, and requires main power
supply.
- How can we deduce ea from Td and Ta ?
- Charts can also be used, for instance to directly give the relative humidity U (Fig. 1a) : what is U when
Ta=30°C and Td=15°C ?
Psychrometers
The measure relies on the difference between Ta (also called the dry bulb temperature), and the wet bulb
temperature Tw, which is the temperature of adiabatic saturation, and can be measured as the temperature
of a moistened thermometer bulb that is let to evaporate until equilibrium in the studied air. The wet bulb is
colder than the one of the dry bulb except if air is saturated, and the larger the difference, the larger the
evaporation from the wet bulb, thus the smaller atmospheric humidity (for details, see Guyot, p 111-113):
ea = e(Tw) - γ (Ta -Tw), where γ is the psychrometric constant (γ = 0.67 hPa K-1).
«Psychrometers, if properly calibrated, maintained, and used, are not only the simplest and cheapest
humidity measuring instruments, they are among the most accurate. » (G.S. Campbell, Professor at
Washington State University, initial scientific counsel of Campbell Scientific and founder of Decagon)
- The so-called psychrometric chart (Fig1b) can be used to get U from Ta and Tw : what is U when Ta=30°C
and Tw =15°C ?
Infra-red hygrometers
They rely on the fact that water vapor emits infra-red radiation (this is the basis of the green-house effect).
2.3 Exercice - Effect of elevation on precipitation distribution and the water balance of a river basin: case
study of the Durance river basin
La Durance est un affluent du Rhône qui prend sa source dans le Massif des Ecrins, et dont le régime
hydrologique montre une forte composante nivale. Les précipitations augmentent avec l’altitude, au contraire
des températures.
- A la station hydrométrique de Serre-Ponçon, le débit moyen interannuel (module) est QM = 76 m3/s, pour
une surface contributive amont de 3588 km² (Haute Durance). Quelle est la valeur du runoff moyen
interannuel en mm/an ?
- Sachant les distributions des altitudes et des précipitations par bande d’altitude (Tableau 1), en déduire
l’évaporation annuelle, en moyenne sur le bassin et par bande d’altitude, en supposant le runoff uniforme
sur le bassin de la Haute Durance. Est-ce que la distribution vous parait raisonnable ?
2.4 Complément - Les filets à brouillard
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N° bande
1
2
3
4
5
6
7
8
9,61
13,3
20,5
29,2
22,2
4,42
0,56
0,08
min
782
1200 1600 2000 2400 2800 3200 3600
max
Précipitations
(mm/an)
1200 1600 2000 2400 2800 3200 3600 4080
Pmoy
810
%surface bande
Altitude (m)
Moy.
Arithm.
936
1078 1224 1355 1551 2309 2440
DeltaP/400m
126
142
146
131
196
758
132
DeltaP/100m
31
36
37
33
49
189
33
E
412
558
689
885
E/P (%)
38
46
51
57
Moy.
Pondérée
Evaporation (mm/an)
Tableau 1. Distribution des altitudes, précipitations et évaporation dans le bassin de la Haute Durance à
l’amont de Serre-Ponçon.
Figure 1. U=f(Ta,Td) on the left, U=(Ta,Tw) on the right.
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