Space Time

Riccardo RigonRiccardo Rigon

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Monday, March 11, 13

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R. Rigon

River Networks

Monday, March 11, 13

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R. Rigon

River Networks

Monday, March 11, 13

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R. Rigon

River Networks

Monday, March 11, 13

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R. Rigon

River Networks

Monday, March 11, 13

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R. Rigon

River Networks

Monday, March 11, 13

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R. Rigon

Scales and patterns

Monday, March 11, 13

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R. Rigon

Scales and patterns

Monday, March 11, 13

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R. Rigon

Scales and patterns

Monday, March 11, 13

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F. S

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R. Rigon

Scales and patterns

Monday, March 11, 13

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F. S

eraf

in, 2

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1

R. Rigon

Scales and patterns

Monday, March 11, 13

12

F. S

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in, 2

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1

R. Rigon

Scales and patterns

Monday, March 11, 13

13

F. S

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1

R. Rigon

Scales and patterns

Monday, March 11, 13

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R. Rigon

Function and Form

Monday, March 11, 13

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R. Rigon

Function and Form

Monday, March 11, 13

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Sub

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R. Rigon

Hillslopes

Monday, March 11, 13

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Pix

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R. Rigon

Smaller scales

Monday, March 11, 13

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R. Rigon

Smaller scales

Monday, March 11, 13

Mass and energy

Riccardo Rigon

Bru

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Monday, March 11, 13

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Budgets

First you chose a control

volume

The budget represent

the variation of the given

quantity in the control

volume , for a given

time interval.

This is the algebraic sum

of what enters minus what

left the volume.

Depending on the budget type,

you have also to account for

chemical transformations,

including phase changes.

The water and energy budget

R. Rigon

Monday, March 11, 13

21

The water budget

Surface

Vadose zone

Water tables

R. Rigon

The water and energy budget

Monday, March 11, 13

22

In the previous slides surface runoff, flow in

soils, and groundawater fluxes were still

missing.

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

23

Eapotranspiration is also missing. This is the

sum of evaporation from surface waters,

evaporation from soils, and transpiration from

plants (grass, bushes, trees).

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

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The water budget in a soil volume

Groundwater runoff

R. Rigon

The water and energy budget

Monday, March 11, 13

24

The water budget in a soil volume

V a r i a t i o n o f t h e v o l u m e o f w a t e r within the volume of soil

Groundwater runoff

R. Rigon

The water and energy budget

Monday, March 11, 13

24

The water budget in a soil volume

V a r i a t i o n o f t h e v o l u m e o f w a t e r within the volume of soil I n t en s i t y o f

precipitation

Groundwater runoff

R. Rigon

The water and energy budget

Monday, March 11, 13

24

The water budget in a soil volume

V a r i a t i o n o f t h e v o l u m e o f w a t e r within the volume of soil I n t en s i t y o f

precipitation

Evapotranspiration

Groundwater runoff

R. Rigon

The water and energy budget

Monday, March 11, 13

24

The water budget in a soil volume

V a r i a t i o n o f t h e v o l u m e o f w a t e r within the volume of soil I n t en s i t y o f

precipitation

Evapotranspiration

Surface runoff

Groundwater runoff

R. Rigon

The water and energy budget

Monday, March 11, 13

24

The water budget in a soil volume

V a r i a t i o n o f t h e v o l u m e o f w a t e r within the volume of soil I n t en s i t y o f

precipitation

Evapotranspiration

Surface runoff

Groundwater runoff

Runoff in the soil

R. Rigon

The water and energy budget

Monday, March 11, 13

24

The water budget in a soil volume

V a r i a t i o n o f t h e v o l u m e o f w a t e r within the volume of soil I n t en s i t y o f

precipitation

Evapotranspiration

Surface runoff

Groundwater runoff

Runoff in the soil

Time step

R. Rigon

The water and energy budget

Monday, March 11, 13

25

The control volume does not need to

be a simple form: a basins, for

instance, is a typical control volume.

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

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Examples

Control volume

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

27

Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

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Qg

Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

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Qg

Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

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Qg

Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

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Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

29

Il bilancio di massaAltri esempi

R. Rigon

The water and energy budget

Monday, March 11, 13

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Il bilancio di massaAltri esempi

R. Rigon

The water and energy budget

Monday, March 11, 13

29

Il bilancio di massaAltri esempi

R. Rigon

The water and energy budget

Monday, March 11, 13

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Il bilancio di massaAltri esempi

R. Rigon

The water and energy budget

Monday, March 11, 13

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Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

30

Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

30

Examples

The water budget

R. Rigon

The water and energy budget

Monday, March 11, 13

31

Lateraladvection ofvapour andwater

S u r f a c e runoff

subsurface runoff

The mass balance for a volume of atmosphere above the soil

R. Rigon

The water and energy budget

Monday, March 11, 13

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Variation of water and vapour in the layer of atmosphere considered

Lateraladvection ofvapour andwater

S u r f a c e runoff

subsurface runoff

The mass balance for a volume of atmosphere above the soil

R. Rigon

The water and energy budget

Monday, March 11, 13

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Variation of water and vapour in the layer of atmosphere considered

Intensity of net evaporation

Lateraladvection ofvapour andwater

S u r f a c e runoff

subsurface runoff

The mass balance for a volume of atmosphere above the soil

R. Rigon

The water and energy budget

Monday, March 11, 13

32

The Energy budget

The first group of term in the

energy budget is the radiation

budget.

It includes short wave radiation

from the Sun; and long wave

radiation: from atmosphere and

clouds to the atmosphere.

Il bilancio di massa ed energia

R. Rigon

Monday, March 11, 13

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Precipitation too enters in the

budget, which, for instance, can

contribute to snowmelt.

Heat flux towards the Earth center

depends on the depth of the control

volume, and can be either positive

or negative.

The Energy budget

R. Rigon

The water and energy budget

Monday, March 11, 13

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Il bilancio di energia

Finally we have also

evapotraspiration, and

heat exchanges by

convention from surface

and atmosphere.

R. Rigon

The water and energy budget

Monday, March 11, 13

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Il bilancio di energia

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

R. Rigon

The water and energy budget

Monday, March 11, 13

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The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

Timeinterval

R. Rigon

The water and energy budget

Monday, March 11, 13

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The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

Variation of energy stored in the soil

Timeinterval

R. Rigon

The water and energy budget

Monday, March 11, 13

36

The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

Variation of energy stored in the soil

Net short-wave radiation

Timeinterval

R. Rigon

The water and energy budget

Monday, March 11, 13

36

The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

Variation of energy stored in the soil

Net short-wave radiation

Net long-wave radiation

Timeinterval

R. Rigon

The water and energy budget

Monday, March 11, 13

36

The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

Variation of energy stored in the soil

Net short-wave radiation

Net long-wave radiation

Release of heat by convection / conduction to the atmosphere

Timeinterval

R. Rigon

The water and energy budget

Monday, March 11, 13

36

The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

Variation of energy stored in the soil

Net short-wave radiation

Net long-wave radiation

Release of heat by convection / conduction to the atmosphere

Heat content of evapotranspiration

Timeinterval

R. Rigon

The water and energy budget

Monday, March 11, 13

36

The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

Variation of energy stored in the soil

Net short-wave radiation

Net long-wave radiation

Release of heat by convection / conduction to the atmosphere

Heat content of evapotranspiration

Timeinterval

Release of heat by convection / conduction to ground below

R. Rigon

The water and energy budget

Monday, March 11, 13

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The energy balance

�E = (Rsw n �Rlw n �H � �e ET n �G)�t

E n t h a l p y o f vaporisation (or l a t e n t h e a t o f vaporisation)

Evapotranspiration

R. Rigon

The water and energy budget

Monday, March 11, 13