Arya S.P.S. Introduction to Micrometeorology

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278 15 Agricultural and Forest Micrometeorology

15.5.1

TURBULENCE

INTENSITIES

AND VARIANCES

Limited observations of longitudinal turbulence intensity

i; =

a.l

suggest that, typically, t; = 0.4 in agronomic crops, 0.6 in temperate for-

ests

and

between

0.7 and 1.2 in tropical forests (Raupach and Thorn,

1981). In a gross sense,

increases with canopy density. The turbulence

intensity profiles broadly follow the

leaf

or plant area density profiles, but

are also influenced by mean wind speed and stability within the canopy.

The lateral and vertical turbulence intensities

(iu and i

)

are generally

proportional to

but

smaller than i

A comparison of turbulence intensity

profiles within rice

and

maize canopies shows that the profile is nearly

uniform in the former, with an approximately uniform

leaf

area density

distribution, while the profile in the maize canopy has a maximum near

the top of the

canopy

(see Uchijima, 1976). More recent measurements of

turbulence in a maize canopy also indicate increasing turbulence activity

with height.

For

example, Figure 15.10 shows the observed profiles of

normalized standard deviations of horizontal and vertical velocity compo-

nents.

15.5.2

TURBULENT

FLUXES

Direct measurements of turbulent fluxes of momentum, heat, and water

vapor are extremely difficult to make in plant canopies, and a few

at-

2.0

N 12

f--

0.8

0.4

(a)

CANOPY TOP

1--------

••-

...

P-

...

2.0

1.6

N 1.2

f--

0.8

0.4

(b)

f--------~

...-

,t!'.

.,.

...

,'"

....

...

2.0

1.6

-;; 1.2

0.8

0.4

(c)

-------~.-

..d

-',

. .

."..

.0.." 11

PINE FOREST

0.5

CT.,

(z)

(hal

Fig.lS.l0

Observed profiles of the normalized standard deviations of (a) longitudinal, (b)

lateral, and (e) vertical velocity fluctuations in a corn canopy. [After Wilson et al. Copyright

15.5 Turbulence in Plant Canopies 279

tempts have

been

made only recently. Figures 15.11 and 15.12 show some

eddy-correlation measurements of momentum and heat fluxes in a maize

canopy. In general, fluxes increase with height and reach their maximum

values somewhere

near

the top

the canopy. Their normalized profiles

also show some day-to-day variations.

More often, turbulent fluxes are estimated from the observed mean

profiles using gradient-transport hypotheses (e.g., eddy viscosity or mix-

ing length). This approach suffers from many conceptual and practical

limitations, however, and its validity has been seriously questioned by

micrometeorologists in recent years (see, e.g., Raupach and Thorn, 1981).

has been shown that vertical fluxes in plant canopies are not always

down the mean vertical gradients, as implied in simpler gradient-transport

hypotheses.

For

example, the vertical momentum flux

u'w'

may be driven

by the horizontal gradient of mean vertical velocity

(aw/ax) and/or by

buoyancy, and need not be uniquely related to

aU/az.

Even

when it can be

related to the latter through an eddy viscosity or a mixing-length relation-

2.0

1.6

..'1"

..•.

::.

f·

1.0

0.8

0.6

1.2"

0.8

0.4

0.2

1.0

0.5

O+------.-----t----JO

U'w' (z )

u'w'

(hal

Fig.15.11 Measured and calculated profiles of normalized shear stress in a corn canopy.

[After Wilson

permission.]

280 15 Agricultural and Forest Micrometeorology

(to~~~.~

A:A

•

1.0

2.0

...

""',,"

0.8

~oo

1.6I-

C\.~

.. 0.6

0'8

1.2

"$'.tP

NI.c°

<.!)

llJ

...

0.4

"'ct

0.8

•

0.4

0.2

1.0

0.5

w'8'

(z)

0'---------'--------'----'0

w,8,

)

Fig. 15.12 Daily normalized sensible heat flux profiles from eddy correlation measure-

ments in a corn canopy. Day:

e, 1; D, 2; D, 3;

4; [1], 5;

7; o, 8. [After Wilson et

ship, the prescription of K

or 1

is not straightforward. A number of

mutually contradictory

and l-« profiles have been proposed in the

literature and there is much confusion regarding the shapes of flux pro-

files.

There

are very few direct observations of fluxes and gradients in

canopy flows which support the gradient-transport

(K)

theories. On the

contrary, observations show strong evidence for countergradient fluxes.

Local-diffusion theories cannot cope with and predict such countergra-

dient fluxes. The main reasons for their failure in canopy flow are three-

dimensionality of the mean motion, nonlocal production of turbulence,

and the multiplicity of the scales of turbulence.

A far

better

method of estimating turbulent transports or fluxes from

measurements of mean wind, temperature, etc., inside canopies is based

on the integration of mean momentum and

other

conservation equations

15.5 Turbulence in Plant Canopies

281

(15.13)

U"W(z)

U"W(O)

uw (h

) -

uw (0)

with respect to height.

For

example, an integration of Eq. (15.10) yields

dAU

dAU2

in which the integrals

can

be numerically evaluated for the given (mea-

sured)

U profile, the

leaf

area density A(z), and the average drag coeffi-

cient

Ciz).

The flux uw(O) at the canopy floor can usually be neglected.

With this assumption, Eq. (15.13) is compared with the observed profile in

Fig. 15.11. The most uncertain parameter in this indirect estimation of

momentum flux is the canopy drag coefficient

Cd, which is known only for

certain idealized plant shapes such as a circular cylinder.

Similar relationships can be derived for sensible heat and water vapor

fluxes, using their appropriate conservation equations for the canopy

layer. Figures 15.13 and 15.14 show the observed profiles of soil and air

temperatures and

water

vapor pressure, together with the calculated pro-

files of sensible and latent heat fluxes in a grass canopy

= 0.17 m).

Radiative fluxes within this canopy for the same day were given in Fig.

15.3.

Note

that all the fluxes increase with height and attain their maxi-

mum values

just

above the canopy. During the late morning period the

sensible heat flux is negative in the shallow surface inversion layer that

gets destroyed later in the afternoon. This inversion in the lower part of

the canopy probably produces a build-up of water vapor in this region

during the morning period (see Fig. 15.14a). The decrease in vapor pres-

sure in early afternoon is a result of more vigorous turbulent mixing,

bringing in drier air from higher levels. The highest vapor pressure occurs

at the moist ground surface. The computed latent heat flux profiles in Fig.

15.14b indicate

that

the major source region is around z

= 0.10 m in

the morning and somewhat higher during the afternoon (Ripley and

Redman, 1976).

The calculated profiles of eddy diffusivities of heat and momentum

based on the above observations in a grass canopy during the morning

period are shown in Fig. 15.15. Within the canopy the estimated values of

and

are in close agreement, indicating the dominance of mechani-

cally generated turbulence in the canopy layer. Above the canopy (z

= 0.17 m), however,

values increase more rapidly with height than

values, which might be expected from increasing buoyancy effects on

turbulence. These are probably the most consistent estimates of eddy

diffusivities in a canopy flow, suggesting the usefulness and validity of

gradient-transport relations, at least in a thin grasslike canopy. The obser-

vation that

other

periods of the day did not show such a good agreement

cautions against any broad generalization of such results.

282 15 Agricultural and Forest Micrometeorology

0.20

0.15

0.10

0.05

....

Or--~~'t-----"*-==-----:::;lOJ-C----,/C---lH

-0.05

-0.10

-0.15

-0.20

(b)

VI'

....

"1,'

10'

if /

• : I

I /

;~/

, ' .i'

.I/./

0.25

0.20

....

0.15

0.10

0.05

-100

0 100

200

300

SENSIBLE HEAT FLUX (Wm

Fig. 15.13 Observed profiles of (a) temperature in the canopy and upper layer of soil and

(b) calculated profiles of sensible heat flux in a grass canopy at various times during a

summer day. [After Ripley and Redmann (1976).]

15,6

APPLICATIONS

A primary objective of the various micrometeorological studies involv-

ing plant canopies has

been

to better understand the processes of momen-

tum, heat,

and

mass exchanges between the atmosphere and the biologi-

cally active canopy. These exchanges influence the local weather as well

as the microclimate in which plants grow. A basic understanding of ex-

change mechanisms and subsequent development of practical methods of

parameterizing the same in terms of more easily and routinely measured

parameters is

e~sential

for many applications in meteorology, agriculture,

15.6 Applications

283

(0)

11.5

11.7

9.8

113

10.1

0.25

0.20

£.

0.15

0.10

0.05

...

ICl

0.25

020

0.15

0.10

0.05

oL..-_--L_--'-_--I.

L-_-'--

---I

100

150

200

LATENT HEAT FLUX (Wm-

Fig.15.14 Observed profiles of (a) water vapor pressure (in millibars) and (b) calculated

profiles of latent heat flux in a grass canopy at various times during a summer day. [After

Ripley and Redmann (1976).J

forestry, and hydrology. More specific applications of agricultural and

forest micrometeorology are as follows:

• Determining the mean wind, temperature, humidity, and carbon diox-

ide profiles in and above a plant

cover

• Determining the radiative and

other

energy fluxes in a plant cover

• Predicting the ground surface and soil temperatures and moisture

content

• Estimating evaporation and transpiration losses in plant canopies

284 15 Agricultural and Forest Micrometeorology

0301-

025

020

I-

0.02

0.01

EDDY DIFFUSIVITY (m

)

Fig.15.15 Vertical profiles of eddy diffusivity in a grass canopy calculated by the energy-

balance and momentum-balance methods.

Energy balance at 0957;

energy balance at

1154;

momentum balance at 0957-1154. [After Ripley and Redmann (1976).]

• Determining photosynthetic activity and carbon dioxide exchange be-

tween plants and the atmosphere

• Protection of vegetation from strong winds and extreme temperature

PROBLEMS

AND

EXERCISES

1. Explain the concept and physical significance of the zero-plane dis-

placement.

How

is it related to the height and structure of a plant

canopy?

2. (a)

Show

that

the aerodynamic resistance of a plant canopy in a stably

stratified surface layer is given by

k~*

[In(Z

do)

/3(z

d~)]

(b) Plot

as a function of the normalized height for the values of

u* = 0.25, 0.50, 0.75, and 1.0 m

sec!

in neutral conditions.

(c)

How

does atmospheric stability affect the aerodynamic resistance?

3. (a) Using the

Bear-Bouguer

law express the net all-wave radiation

)

as a function of height for a constant leafarea density canopy

of height

(b)

For

the same canopy, plot RN(z)IRN(h

as a function of z/h

for

different values of the extinction coefficient

a =

0.5,0.75,

and \.0.

Problems and Exercises

2~5

(c)

How

is the

net

longwave radiation

expected

to vary with height in

such a

canopy?

4. (a) Using

Eq.

(15.10) and the mixing-length relation for uw with a

constant

mixing length

l«,

derive the exponential wind profile [Eq.

(15.11)] for the canopy flow.

(b) Derive an expression for eddy viscosity

for the same flow.

as a function of z/h

for different values of the

parameter

n =

1,2,

3, and 4.

5. (a) Using the eddy viscosity relation for uw with a constant K

derive

the

canopy

wind profile

Eq.

(15.12).

(b)

Compare

the wind profiles given by Eqs. (15.11) and (15.12) for

= m = 3.

6. (a) Why do the fluxes

momentum, heat, and

water

vapor

generally

increase with height in a plant canopy?

(b) Derive an expression for the momentum flux profile in a uniform

plant

area

density canopy for the given exponential wind profile,

Eq.

(15.11).

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