13 solar radiation

Riccardo Rigon

Il S

ole

, F. L

elon

g, 2

00

8, V

al d

i Se

lla

Solar Radiation Physics and Geometry

for hydrologists

Monday, December 10, 12

When you see the Sun rise,

do you not see a round disc of fire

somewhat like a guinea?

Oh no, no! I see an innumerable

company of heavenly host

crying

“Glory, glory, glory is the Lord God

Almighty.”

W. Blake

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2


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Educational Goals

• To recognise that the water cycle is powered by solar energy

• To present the ways in which radiation is produced, received by the

Earth, transmitted by the atmosphere, reflected, absorbed, and reemitted

by the Earth’s surface

• To gain knowledge of the spatial and temporal variation of the

radiation distribution on the Earth

• To introduce the concepts necessary to better understand the elements

of the energy balance needed in remote-sensing applications, the snow

balance, and evapotranspiration

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3

Introduction


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The Sun is the origin of the water cycle

2

4

The Sun


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The Sun is mainly composed of hydrogen. The rest is prevalently He4.

Hydrogen is the fuel for the nuclear fusion that takes place inside the Sun and

produces helium. However, the He4 contained in the Sun for the most part

originates from previous stellar lives.

Composition of the Sun

3

5

The Sun


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Sun Fact Sheet

The Sun is a G2 type star, one of the hundred billion stars of this type in our

galaxy (one of the hundred billion galaxies in the known universe).

Diameter: 1,390,000 km (the Earth: 12,742 km or 100 times smaller)

Mass: 1.1989 x 1030 kg (333,000 times the mass of the Earth)

Temperature: 5800 K (at the surface) 15,600,000 K (at the core)

The Sun contains 99.8% of the total mass of the Solar System (Jupiter

contains nearly all the rest).

Chemical composition:

Hydrogen 92.1%

Helium 7.8%

Other elements: 0.1%

4

6

The Sun


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The Sun and the planets to scale

5

7

The Sun


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The Sun’s energy is created in the core by fusing hydrogen into helium. This

energy is irradiated through the radiative layer, then transmitted by convection

through the convective layer, and, finally, radiated through the photosphere,

which is the part of the Sun that we see.

The internal structure of the Sun

6

8

The Sun


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9

The Sun

Provide a relatively constant rate of radiation energy that in few minutes

from the cromosphere arrives to the Earth.

Det

ail

of

a P

elli

zza

da

Volp

edo P

ain

tin

g


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Solar Spots

Solar spots appear as dark spots on the surface of the Sun and they have a temperature of 3,700 K (to be compared to the 5,800 K of the surrounding photosphere). A solar spot can last for may days, the most persistent lasting for many weeks.

7

10

The Sun

Radiation flux is regular up to a point. In reality it manifests variations.


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An image of the sun in X-ray

band, taken by the Yohkoh solar

observatory satellite, which

shows changes in emissions of

the solar corona from a

maximum in 1991 (left) to a

minimum in 1995 (right).

Variability of the Emissions

8

11

The Sun


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Solar radiation is subject to

fluctuations, some of which are

localised in restricted areas, while

others are more global and follow

an 11-year cycle.

Every 11 years the sun goes from

a limited number of solar spots

and flares to a maximum, and

vice versa. During this cycle the

Sun’s magnetic poles switch

orientation . The last solar

minimum was in 2006.


8

12

The Sun


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The graph shows the solar spot cycle over the last 400 years. It should be

noted that before 1700 there was a period in which very few solar spots were

observed. This period coincides with the Little Ice Age, which is why there are

suggestions that there is a connection between solar spot activity and the

climate on Earth. The most evident cycle has a period of 11 years. But there

is a second cycle which seems to have a period of 55-57 years.


9

13

The Sun


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R = ✏ � T 4

Every body with a temperature different than T=0 K emits radiation as a function

of its temperature according to the Stefan-Boltzmann law

The Stefan-Boltzmann law

10

14

The Sun


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Radiation

emitted

R = ✏ � T 4




10

14

The Sun


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Radiation

emitted

emissivity

R = ✏ � T 4




10

14

The Sun


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Radiation

emitted

emissivityStefan-Boltzmann constant

R = ✏ � T 4




10

14

The Sun


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Radiation

emitted

emissivityStefan-Boltzmann constant

absolute temperatureR = ✏ � T 4




10

14

The Sun


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RSun = ✏ � T 4 = 1 ⇤ 5.67 ⇤ 10�8 ⇤ 60004 ⇡ 25.12 ⇤ 109J m�2 s�1

The physics of Radiation

On the basis of the temperature of the Sun photosphere (~6000 K), and the

Stephan-Boltzmann law, the total energy emitted by the Sun is

11

15

The Sun


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The Sun is practically a blackbody. The difference between a true blackbody

and the Sun is due to the fact that the corona and the chromosphere

selectively absorb certain wavelengths.

The Sun is nearly a “blackbody”!

12

16

The Sun


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The area below the curves is given by the Stefan-Boltzmann law. The curves

themselves are given by Planck’s law.

The Sun is nearly a “blackbody”!

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17

The Sun


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The complete electromagnetic spectrum

The spectrum of solar radiation stretches far beyond the visible band where,

however, nearly half the available energy is concentrated

Figu

re 2

.9

C.B

. A

gee

16

18

The Sun


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Planck’s Law

•Planck’s law is the general law for electromagnetic emission from the

surface of a blackbody*:

W� =2⇡c2h��5

ech

�KT � 1[Wm�2µm�1]

14

19

The Sun

* Stefan-Boltzmann law is just the integration of Plank’s law over wavelengths


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The energy irradiated by the Sun passes through an imaginary disc with diameter

the same as the Earth’s. The energy flow is maximum at that point on the Earth

where the radiation is perpendicular.

From Sun to Earth

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20

From Sun To Earth


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T h e S u n i r r a d i a t e s

approximately at the solar

constant rate, which is, on

the average, on the top of

the atmosphere,

Solar radiation

http://en.wikipedia.org/wiki/Solar_constant

Froli

ch, 1

98

5

19

21

From Sun To Earth




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In its orbit around the Sun, the Earth keeps its north-south rotational axis

unvaried, causing a different angle between the Sun’s rays and the surface of the

Earth.

Astronomical variability of radiation

22

Copying with Earth surface


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Seasons

The Earth is 5 million kilometers closer to the Sun during the northern winter: a clear indication that temperature is controlled more by orientation than by distance.

Figure 3.1

23

From Sun To Earth


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The Earth’s orbit around the Sun is an ellipse. The shape of the ellipse is

determined by its eccentricity, which varies in time, changing the distances of

the aphelion and perihelion

Corrections to the solar constant

http://www.ascensionrecta.com/

20

24

From Sun To Earth




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Precession of the polar axis

The axis of rotation moves with a slow period, executing a complete precession every 26,000 years.

Polar stars behave like this for only a very short period

25

From Sun To Earth


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Astronomical influences

Orbit angle

Orbit change

Orbit shape

26

From Sun To Earth


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Therefore the solar contant must be corrected

(e.g. Corripio, 2002):

Solar radiation in hydrological models

27

S�

From Sun To Earth


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N is the day of the year (in 1, ..., 365)

where:

Solar radiation in hydrological models

28

Therefore the solar contant must be corrected

(e.g. Corripio, 2002):S�

From Sun To Earth


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Radiation intensity

Solar intensity governs seasonal climatic changes and the local climatic niches

which are linked to the apparent height of the Sun.

29



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Insolation and latitude

Incoming solar radiation is not evenly distributed across all lines of latitude, creating a heating imbalance.

Figu

re 3

.7

30



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Radiative imbalance

31



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decreases towards the poles and it is reduced in areas where clouds

form frequently

For example, the complete energy balance is greater at the equator but the

greatest amount of insolation is in the subtropical deserts

Average annual radiation is

< 80 W/m2 in the cloudy parts of the arctic and the antarctic

>280 W/m2 in the subtropical deserts

Radiation received from the Sun

50



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From a subjective point of view, the Sun varies its height in the sky seasonally.

This is the subject of interest in the study of the geometry of radiation.

The geometry of radiation

33



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Calculations of the incident radiation onto the surface of the Earth need to

take account of the geometry of the interaction between the Sun’s rays and

the surface of the Earth, which is curved and therefore variably

exposed with respect to the direction of the Sun in function of latitude,

time of day (longitude) and, naturally, day of the year. Moreover the

Earth rotation is inclined with respect to its orbit around the Sun , and

this causes seasons to happen.

To sum up

34



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To calculate the aforementioned

quantities it is usual to use a

topocentric coordinate system,

that is, with the origin in the

geographic position of the

observer, which is right-handed

and positioned on the plane

tangent to the Earth’s surface in

the considered point.

N.B. - A coordinate system located at the

centre of the Earth id called geocentric.

Nau

tic

Alm

anac

Off

ice,

19

74

35



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The X-axis is, therefore, tangent

to the earth and positive in a

West-East direction. The Y-axis

is tangent in the North-South

direction and is directed towards

the South. The Z-axis lies on the

segment joining the centre of the

Earth with the point being

considered on the surface.

It is assumed that the Sun lies in

the ZY plane at the solar noon.

Nau

tic

Alm

anac

Off

ice,

19

74

36



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Solar Vector

The solar vector can be expressed as a

function of the angles that have been

defined. The resulting trigonometric

expression is:

Therefore, to determine the position of

the Sun one needs to know the latitude,

t h e h o u r a n g l e , a n d t h e s o l a r

declination.

⌥s =

�

⇤� sin⇥ cos �

sin⇤ cos ⇥ cos � � cos ⇤ cos �cos⇤ cos ⇥ cos � + sin⇤ sin �

⇥

⌅

37


X

Y

Z


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Hour angle

The hour ang le can be eas i l y

calculated as:

⇥ = �

�t

12� 1

⇥

if t is the solar hour

38



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Solar declination

The solar declination is a function of the day of the year (and the era). It

requires complex calculations that take account of the precession movements

of the Earth. There are, however, various approximations. The one that is

presented here is due to Bourges, 1985:

where is the day of the year

39


Is the angular height of Sun from the horizon at equator at noon*

*http://en.wikipedia.org/wiki/Declination


http://en.wikipedia.org/wiki/Declination

http://en.wikipedia.org/wiki/Declination

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X

Y

Z

40

Projection on a plane at a certain latitude

is the solar vector

⌥s =

�



⇥

⌅

If is the vertical unit row-vector

corresponding to the Z axis:

and



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41

Projection on a plane at a certain latitude

with the symbols explained above

Then the projection of the solar

irradiation on the plane YX is reduced by

the factor where:

or:


X

Y

Z


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42

To sum up:

Was:

Is now:

The solar constant can be modified as follows.



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Atmosphere is a gray body

• The blackbody is an ideal object that absorb all the radiative energy it receives

• Real objects (bodies, “gray bodies”) are not capable of absorbing all radiation.

• To understand the difference between a blackbody and a gray body we need to

analyse the interactions between a surface and the electromagnetic radiation

incident onto it.

43

Absorption and transmission of short wave radiation


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Atmospheric absorption

44

Radiation passes quite freely through the Earth’s atmosphere and it warms

the surfaces of seas and oceans. A portion of between 45% and 50% of the

incident radiation onto the Earth reaches the ground



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Shortwave Radiation budget

The solar radiation penetrates the

atmosphere, and it is transferred

towards the ground, after being

reflected and scattered.

45



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Radiation reflected






45



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Radiation transmitted

Radiation reflected






45



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the incoming radiation equals

the reflected one plus

the absorbed plus

the transmitted

46


S� It should not be forgot that

the radiation budget is an

energy budget, for which



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the incoming radiation equals

the reflected one plus

the absorbed plus

the transmitted

46


S� It should not be forgot that

the radiation budget is an

energy budget, for which

Radiation

absorbed



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47

S�

This budget can be apply to any slice of the atmosphere




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47

S�

Corrected Solar constant





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47

S�


Solar radiation

reflected back to space





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47

S�

Transmitted

radiation


Solar radiation






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47

S�

Energy absorbed by atmosphere

Transmitted

radiation


Solar radiation






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• is the reflection coefficient, said atmospheric reflectivity (albedo)

• is the transmission coefficient, said atmospheric transmissivity

• is the absorption coefficient, said atmospheric absorptivity

Coefficients

The following coefficients can also be defined

48



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Energy conservation:

Which is, indeed, valid for reflectivity, transmissivity and absorptivity of any other body

implies that reflectivity, transmissivity and absorptivity sum to one:

49




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50

S�




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We just forget for a moment this. It will be splitted into two parts:

one depending on diffuse radiation and

another on cloud cover

50

S�




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51

S�




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Atmosphere is pretty transparent: which means that we can, as a first approximation, neglect it (atmosphere is heated from below)

51

S�




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In any case let’s concentrate on

the transmitted radiation

This can be decomposed into two parts:

direct and diffuse solar radiation

52


S�



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Evidently, for simmetry

is also composed by reflected and diffuse solar radiation

53


S�



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5

Diffuse radiation comes from scattering

Incident solar radiation strikes gas molecules, dust particles, and

pollutants, ice, cloud drops and the radiation is scattered. Scattering

causes diffused radiation.

Two types of light diffusion can be distinguished:

Mie scattering

Rayleigh scattering



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Rayleigh Scattering

•The impact of radiation with air molecules smaller than λ/π causes

scattering (Rayleigh scattering) the entity of which depends on the frequency of the incident wave according to a λ-4 type relation.

•In the atmosphere, the wavelengths corresponding to blue are scattered more readily than others.

incident radiation

diffuse radiation

transmitted radiation

55



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•When in the atmosphere there are particles with dimensions greater than 2 λ/π

(gases, smoke particles, aerosols, etc.) there is a scattering phenomenon that does not depend on the wavelength, λ, of the incident wave (Mie scattering).

•This phenomenon can be observed, for example, in the presence of clouds.

Mie Scattering

56

incident radiation

diffuse radiation

transmitted radiation



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Diffused Light

Scattering selectively eliminates the shorter visible wavelengths, leaving the longer wavelengths to pass. When the Sun is on the horizon, the distance travelled by a ray within the atmosphere is five or six times greater than when the Sun is at the Zenith and the blue light has practically been completely eliminated.

57



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Tilt of the Earth’s axisand atmospheric effects

The tilt of the earth’s axis and atmospheric effects together affect the amount of radiation that reaches the ground.

58



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59

One way to take into account of absorption

Would be to run a full model of atmospheric transmission (e.g. Liou, 2002).

However hydrologists prefer to use parameterizations, and the

concept of atmospheric transmissivity.



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Solar radiation transmitted to the ground under clear sky conditions

Finally:

Cor

rip

io, 2

00

2

60

S�



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Finally:

Fraction of direct solar radiation included between the considered

wavelengths

Cor

rip

io, 2

00

2

60

S�



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Finally:


wavelengths

Transmittance of the atmosphere

Cor

rip

io, 2

00

2

60

S�



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Finally:


wavelengths

Transmittance of the atmosphere

Correction due to elevation of the site

Cor

rip

io, 2

00

2

60

S�



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We do not enter in the details of how

and

are determined. Please look, for instance, at Formetta et al., 2012


61

S�



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Transmitted direct radiation at the surface after clouds correction

Hydrologists (and not only them) treat the

influence of clouds separately

It is assumed that the effects of

clouds is an attenuation of the

transmitted solar radiation

62

Considering Clouds


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Transmitted direct radiation at the surface before clouds correction

Transmitted direct radiation at the surface after clouds correction



It is assumed that the effects of

clouds is an attenuation of the

transmitted solar radiation

62

Considering Clouds


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An analogous formulation holds for diffuse radiation:

63

Considering Clouds


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Correction coefficient for diffuse radiation



An analogous formulation holds for diffuse radiation:

63

Considering Clouds


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Estimation of the reduction coefficients(decomposition model)

These reduction coefficients can be

determined when we have ground

measurements of total radiation,

diffuse plus direct:

64

Considering Clouds


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Measured total radiation at the ground station i


These reduction coefficients can be

determined when we have ground

measurements of total radiation,

diffuse plus direct:

64

Considering Clouds


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These assumption that is often

made is that, the diffuse solar

radiation measured at the station is

proportional to the total radiation:

65

Considering Clouds


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reduction coefficient for diffuse radiation


These assumption that is often

made is that, the diffuse solar

radiation measured at the station is

proportional to the total radiation:

65

Considering Clouds


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Therefore when substituting this

diffuse radiation expression in the

total radiation equation of previous

slides, it results at stations:

66

Considering Clouds


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And, for the direct radiation, at

stations:

67

Considering Clouds


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The key factor is the to determine the above coefficient, on which the

procedure followed so far has moved all the unknown.

Its estimation pass through various parameterizations:

Among the most known:

•Erbs et al., 1982

•Reindl et al. 1990

•Boland et al. 2001

please find the details in Formetta et al., 2012

68

Considering Clouds


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One more issue

With the help of the parameterizations above, the correction facotrs are

determined for the stations. Which are a few points in a rugged terrain.

Fig. 7. River Piave area, (Italy).

35

How do you solve the problem to transport it everywhere ?

69

Considering Clouds


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We need to use some interpolation

technique

Like Kriging* or the Inverse distance weighting method** which is not

the matter of the present slides.

* Goovaerts, 1997

**Shepard, 196870

Considering Clouds


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Finally the residual radiation hits the terrain

The terrain is not a plane

but it is inclined. Therefore,

besides correcting radiation

for latitude, longitude and

hour, it is necessary to

account for slope and

aspect

71

Hitting the terrain


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In the presence of topographic surfaces

In the northern hemisphere, slopes that face South receive a greater insolation

and, therefore, the water in the soil evaporates more quickly or the snow melts

faster. Slopes with differing aspects are often characterized by different species

and densities of plants and trees. 72

Hitting the terrain


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Projection of radiation onto an inclined surface

Aft

er C

orr

ipio

, 20

03

First we calculate the normal to the surface 73

Hitting the terrain


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⇧nu =1

|⇧nu|

�

⇧⇧⇧⇧⇤

1/2 (z(i,j) � z(i+1,j) + z(i,j+1) � z(i+1,j+1))

1/2 (z(i,j) + z(i+1,j) � z(i,j+1) � z(i+1,j+1))

l2

⇥

⌃⌃⌃⌃⌅

where z are the elevations of the four points used and l2 is the are of the

cell - of side l.


Unit normal vector:

74

Aft

er C

orr

ipio

, 20

03

Hitting the terrain


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Aft

er C

orr

ipio

, 20

03

75

Representation of the vector normal to the surface of Mount Bianco

Hitting the terrain


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Aft

er C

orr

ipio

, 20

03


And we compare with the solar vector, indicating the direction of the Sun 76

Hitting the terrain


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77

⌥s =

�



⇥

⌅


Where all the quantities were already defined previously

Hitting the terrain


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Aft

er C

orr

ipio

, 20

03


78Then we calculate the angle between the sun vector and the normal

s

Hitting the terrain


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We can define then the angle

of solar incidence

Aft

er C

orr

ipio

, 20

03


79

s

Hitting the terrain


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Angle of solar incidence

cos �s = ⌅s · ⌅nu

⇧nu =1

|⇧nu|

�

⇧⇧⇧⇧⇤

1/2 (z(i,j) � z(i+1,j) + z(i,j+1) � z(i+1,j+1))

1/2 (z(i,j) + z(i+1,j) � z(i,j+1) � z(i+1,j+1))

l2

⇥

⌃⌃⌃⌃⌅

⌥s =

�



⇥

⌅

80

Hitting the terrain


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�s = cos�1 nu.z

Aspect (from the North anti-clockwise)


Slope

The above angles needs to be compared with those of the terrain:

81

Hitting the terrain


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82


Remarkably the form of formula for the incident radiation is the same that for a flat surface when the projection angle is accounted:

Hitting the terrain


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Therefore, for the direct shortwave radiation:

Cor

rip

io, 2

00

2

83

S�

as, it was before

Hitting the terrain


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84

However, it is not just matter of light but also of shadows

Hitting the terrain


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Incident radiationTopographic effects: shading

85

More schematically

shadow

light

Hitting the terrain


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86

More schematically

Hitting the terrain


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86

More schematically

shadow

Hitting the terrain


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86

More schematically

light

shadow

Hitting the terrain


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Incident radiationD

etai

ls i

n C

orr

ipio

, 20

03

87

Therefore the direct solar radiation must be corrected to include shading

Hitting the terrain


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What about diffuse radiation ?Topographic effects: angle of view

88

Hitting the terrain


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sky view factor


88

Hitting the terrain


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sky view factor

diffuse radiation due to

Rayleigh scattering


88

Hitting the terrain


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sky view factor


Rayleigh scattering


aerosols


88

Hitting the terrain


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sky view factor


Rayleigh scattering


aerosols

diffuse radiation due

multiple scattering


88

Hitting the terrain


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Incident radiationTopographic effects: angle of view

89

Any point in a rugged landscape see just a part of the sky sphere. Its fraction

says which portion of the sky contribute to diffuse shortwave radiation.

Hitting the terrain


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Incident radiationTopographic effects: angle of view

90

Different points view a different sky

Hitting the terrain


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91

The sum

Hitting the terrain


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Aft

er C

orr

ipio

, 20

03

92

Now it really hits the terrainand, in part, it is reflected away

Hitting the terrain


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Aft

er C

orr

ipio

, 20

03

93Insolation received by Mont Blanc at Spring Equinox

Finally a map

Hitting the terrain


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Typical albedo values

94

http://en.wikipedia.org/wiki/Albedo

Albedo




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Typical albedo values

95


Albedo




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51

The percentage of radiation that is reflected (reflectance) depends on

wavelength of the radiation, and on the geometry, nature, and structure

of the surface under investigation.

Spectral Signature (or Response)

96

Spectral response


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•In the case of solar radiation, the spectral signature is defined as the reflectance of the surface in function of the wavelength.

97

Spectral response


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98

•Every type of surface can be statistically characterised by a spectral signature.

Spectral response


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•The spectral signature of a specific element of a territory will

vary due to the variability of local environmental factors.

•Given a certain type of ground cover, static elements, such as

slope and exposition, and dynamic elements, such as surface

ground humidity, the phenological state of the vegetation, the

atmospheric transparence, etc., will cause variations in the

spectral signature curve.

Factors

99

Spectral response


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Radiation that hits the terrain, heats it.

Or causes changes of phase

water to vapor

ice to water

100

Spectral response


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101

Or is used for photosynthesis

or other chemical reactions

Spectral response


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102

Earth “is” a gray body

Having a temperature emits radiation

A. A

dam

s -

Par

t of

the

snak

e ri

ver

pic

ture

Long wave radiation


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Gray Bodies

• Plank’s Law for gray bodies:

• The Stefan-Boltzmann equation for gray bodies:

W� = ✏�2⇡c2h��5

ech

�KT � 1[Wcm�2µm�1]

W = ✏�T 4[Wcm�2]

103

where ε is the average emissivity calculated over the entire electromagnetic

spectrum.

Long wave radiation


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Gray Bodies

The behavior of a real (gray) body is related to that of a black body by means of the quantity ελ, known as the emission coefficient or emissivity, which is defined as:

Kirchhoff (1860) demonstrated that a good “radiator” is also a good “absorber”, that is to say:

✏� =W�(real body)W�(black body)

↵ = ✏ ⇢ + ⌧ + ✏ = 1

104

Long wave radiation


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Comparison of blackbody and gray body

105

In reality emissivity depends, at least, on wavelength. Earth should be probably defined a selective radiator

Long wave radiation


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See the Earth as gray body

a n d g i v e n t h a t t h e

temperature of the Earth’s

surface is, on average,

about 288 K, it obviously

e m i t s a s p e c t r u m o f

radiation in the infrared

band.

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Long wave radiation


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Radiation emitted by the Sun and the Earth

Yochanan Kushnir

107

Long wave radiation


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See the Earth as gray body

a n d g i v e n t h a t t h e

temperature of the Earth’s

surface is, on average,

about 288 K, it obviously

e m i t s a s p e c t r u m o f

radiation in the infrared

band.

A t m o s p h e r e i s n o t

anymore transparent to at

these wavelengths.

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Long wave radiation


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The atmosphere is warmed from below

Therefore the temperature is higher at ground level than it is at higher altitudes.

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Long wave radiation


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Greenhouse Effect

In the absence of atmospheric absorption the average temperature of the Earth’s surface would be about -170C.

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Long wave radiation


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Instead the average temperature is about 15 0C

Greenhouse Effect

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Long wave radiation


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Radiative heating

is completed by convective heat transfer, and by water vapor fluxes (latent and

sensible heat).

112But this you can see better on the energy budget slides.

Long wave radiation


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But now concentrate on the surroundings of a point

113

Aft

er H

elb

ig, 2

00

9

Any point being at a certain temperature emits long wave radiation

which must be accounted for

Long wave radiation


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114

The atmosphere emits infrared itself

bacause of its temperature

Long wave radiation


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Long-wave radiation is given by the

balance of incident radiation from

the atmosphere and the radiation

emitted by the ground. Both values

are calculated with the Stefan-

Boltzmann law.

115

All the contributions

Long wave radiation


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Longwave (infrared) raditationTopographic effects: angle of view

116

Long wave radiation


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Longwave radiation coming from sky


116

Long wave radiation


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Longwave radiation coming from surrounding



116

Long wave radiation


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Longwave radiation coming from surrounding

Radiation losses

by the area under exam



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Long wave radiation


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Long-wave radiation

The first component should be

calculated by integrating the formula

over the entire atmosphere, but,

given how complex this process is,

typically an empirical formula is

used that uses the value of air

temperature as measured near

ground level (2m) and a value of the

atmospheric emissivity based on

specific humidity, temperature, and

cloudiness. The second component,

on the other hand, is function of the

s u r f a c e t e m p e r a t u r e a n d i t s

emissivity.

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The real process:

The hydrological parameterisation:

Long-wave radiation

118

Long wave radiation


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The real process:


Long-wave radiation

118

Long wave radiation

Global emissivity of the atmosphere


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The real process:


Long-wave radiation

118

Long wave radiation

Global emissivity of the atmosphere

Temperature at 2 m from ground


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€

εatm = εBrutsaert (1− N6) + 0.979N 4 Brutsaert (1975) + Pirazzini et al. (2000)

€

εatm = εBrutsaert (1+ 0.26N)

€

εatm = εIdso(1− N6) + 0.979N 4

€

εatm = εIdso,corr(1− N6) + 0.979N 4

Brutsaert (1975) + Jacobs (1978)

Idso (1981) + Pirazzini et al. (2000)

Hodges et al. (1983) + Pirazzini et al. (2000)

Parameterisation of Long-wave radiation

119

Long wave radiation

where N is the fraction of sky covered by clouds


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120

Net Radiation

The sum of longwave and shortwave ratio

is called net radiation


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121

1Thank you for your attention !

G.U

lric

i -

20

00

?


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Table of symbols

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123

Table of symbols


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124

Table of symbols


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125


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126
