Arya S.P.S. Introduction to Micrometeorology

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(14.13)

258 14 Nonhomogeneous Boundary Layers

(a)

Fig. 14.20 Schematics of air flow

over

a two-dimensional ridge with an elevated inver-

sion upwind. (a) Low wind speed with

Uo/N(h - H)

I, flow separation on lee slope. (b)

High wind speed with

Uo/N(h -

= I, no flow separation on lee slope, hydraulic jump

downwind. [After

Hunt

and Simpson (1982).]

stratification that the parcel must overcome, i.e.,

pUij(H

)

= g

z)(

~~)

This integral equation, first suggested by Sheppard (1956), can be used for

any approach flow and topographical arrangement. In practice, it must be

solved for H, iteratively, because the unknown appears as the lower limit

of integration.

For

the particular case of a stratified approach flow with a

constant density gradient, Eq. (14.13) reduces to the simpler formula

= H(1 - F)

(14.14)

which was suggested by

Hunt

and Snyder (1980) on

other

theoretical and

experimental bases.

14.8 Applications 259

Laboratory

experiments and a few observations of smoke plumes im-

pinging on hillsides have confirmed the validity and usefulness of the

dividing streamline concept (see, e.g.,

Snyder

et al., 1985). These also

indicate that Eq. (14.13) provides only a necessary (but not the sufficient)

condition for the fluid above

to go

over

rather than around a hill.

can

still pass

around

the sides

and

take a

path

requiring less potential energy

to overcome than that given by Eq. (14.13). Experiments also indicate

that

the lateral

aspect

ratio (W/H) of the hill is relatively unimportant, but

the stratification

and

shear

in the approach flow, upwind slope of the hill,

and obliqueness of the flow to an elongated hill are all important in deter-

mining the flow

over

and around the hill.

In the

case

of strongly stratified

1) flow approaching normal to a

very long (nearly two-dimensional) ridge, there is a distinct possibility of

upstream blocking of the fluid, because very little

can

over

the ridge. A

region

nearly stagnant fluid occurs below the dividing streamline and

far away from the edges where it

can

go around the ridge. Such a flow field

may not acquire a steady state, because the upwind edge of the blocked

flow propagates farther upstream as a density front and certain columnar

disturbance modes

and

gravity waves generated near the ridge can also

propagate upstream. Topographically blocked flows have important im-

plications for local

weather

and

for dispersion of pollutants from upwind

sources.

14.8 APPLICATIONS

Spatial variations of surface roughness, temperature, wetness, and ele-

vation frequently

cause

nonhomogeneous atmospheric boundary layers

developing

over

these surface inhomogeneities. A basic understanding of

horizontal

and

vertical variations of mean flow, thermodynamic variables,

and turbulent exchanges in nonhomogeneous boundary layers is essential

in micrometeorology and its applications in

other

disciplines and human

activities. Specifically, the following applications may be listed for the

material

covered

in this chapter:

• Determining the development of modified internal boundary layers

following step changes in surface roughness

and

temperature

• Determining the fetch required for air flow adjustment to the new

surface following a discontinuity in surface elevation or

other

proper-

ties

• Selecting an appropriate site and height for locating meteorological or

micrometeorological instruments for representative observations for

the local terrain

260 14 Nonhomogeneous Boundary Layers

• Determining wind and air mass modifications under situations of cold

or warm air advection

over

a warmer or colder surface

• Estimating urban influences on surface energy balance and surface

and air temperatures

• Determining possible modifications of mean flow, turbulence, and the

PBL

height

over

an urban

area

• Estimating transport and diffusion of pollutants in the urban boundary

layer and the urban plume

• Estimating pollutant dispersion around hills and buildings

• Estimating wind loads on buildings and knowing the wind environ-

ment

around buildings

• Siting and designing wind-power generators in hilly terrain

•

Other

wind-engineering applications in urban architecture and plan-

ning

PROBLEMS

AND

EXERCISES

1. A 1500-m thick near-neutral atmospheric boundary layer encounters a

sudden change in

the

surface roughness in going from land (zo = 0.1 m)

to a large lake

(zo = 0.0001 m) of the same surface temperature. The

observed wind speed at a 10-m height in the approach flow is 10 m

sec-I.

Assuming

that

the overall

PBL

thickness (h = 1500m) and the

surface layer thickness

= 150 m) remain unchanged

over

the lake,

calculate

and

plot the following parameters, using Eqs. (14.1) and

(14.3), with

ai = 0.4 for the internal boundary layer:

(a) The

IBL

height as a function of distance, and the distances where it

reaches the top of the approach flow surface layer and the PBL

(b)

The

friction velocity

and

wind speed at a 10-m height

over

the lake

as functions of distance from the shore

Repeat

the calculations in Problem 1for the case of an onshore neutral

boundary layer flow with the same wind speed (10 m sec-I) and depth

(1500 m)

over

the lake, and compare the results for the two cases.

3. Calculate

and

graphically compare the development of thermal internal

boundary layers in the following two situations, using Eqs. (l4.8c) and

(l4.8d), respectively, with

a4 = 1.7 and as = 1.0.

(a) A stably stratified boundary layer flow with

a0/az = 0.02 K m

over

land advecting

over

lOoC

warmer sea. Assume a typical

value of the drag coefficient

(u*/Um)Z = 0.002 for the free

convective marine

boundary

layer.

(b) An unstable warm continental boundary layer capped by an inver-

Problems and Exercises

261

sion with aT/az = 0.08 K

advecting

over

a 10°C colder sea

surface. Assume a typical drag coefficient of 0.5 x

1O~3

for the

stably stratified IBL.

4. (a) What are the leading causes of an urban heat island?

(b) If the population of a midwestern United States city has increased

from 100,000 to 1,000,000 in the past 20 yr, estimate the expected

change in its maximum heat-island intensity and the annual rate of

urban warming

over

that period.

5. (a) Give physical reasons for the urban mixed-layer dome phenome-

non and list conditions underwhich it might be enhanced and those

in which it would be suppressed.

(b) Calculate

and

compare the nocturnal urban mixed-layer height at

the city center, where the near-surface temperature is 15°C, with

that

at a suburban location of near-surface temperature l2°C, when

the upwind rural sounding indicates a temperature gradient of

0.02°C m

over

a deep-surface inversion layer and a near-surface

temperature

9°C.

6. (a)

What

are the causes and consequences of boundary layer separa-

tion from hills and buildings?

(b) In

what

respects do the cavity and near-wake flow regions behind

an isolated square-shaped building differ from those behind a cylin-

drical building?

7. (a) Why is the length of a recirculating cavity region behind a long

ridge much larger than that behind an axisymmetrical hill of the

same height and slope?

(b) In

what

respects does a three-dimensional hill wake differ from a

building wake?

8. (a)

Show

that, for constant density-gradient uniform or shear flow,

Eq. (14.13) reduces to Eq. (14.14).

(b) Calculate the dividing streamline height for a constant gradient

shear

flow with auo/az = 0.1 sec

a0/az = 0.05 K m

and

= 280 K, approaching a 200-m-high axisymmetric hill. What are

the implications of this to flow

over

and around the hill?

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Chapter 15

Agricultural and Forest

Micrometeorology

15.1 FLUX-PROFILE RELATIONS ABOVE PLANT CANOPIES

In this final

chapter

we discuss the particular applications of microme-

teorological principles

and

methods to vegetative surfaces, such as agri-

cultural crops, grasslands, and forests. Here, the micrometeorologist is

interested in the atmospheric environment, both above and within the

plant canopies, as well as in the complex interactions between vegetation

and its environment. First, we discuss the vertical profiles of mean wind,

temperature, specific humidity, etc., and their relationships to the vertical

fluxes of momentum, heat,

water

vapor, etc., above plant canopies.

The semiempirical flux-profile relations developed in Chapters 10-12

should, in principle, apply to any homogeneous surface layer, well above

the tops of roughness elements

(z >

h«

zo).

should be kept in mind,

however,

that

for any tall vegetation the apparent reference level for

measuring heights

must

be shifted above the true ground level by an

amount

equal to the zero-plane displacement

(do),

which is related to the

mean height

)

of roughness elements and roughness density. Also, for

flexible plant canopies,

and do may not have fixed ratios to h

but may

vary with wind speed. Physically, one

can

argue that for a vegetative

canopy acting as a sink of momentum and a source or sink of heat, water

vapor, CO

etc.,

the effective source or sink height must lie between 0

and

For

exchange processes in the atmospheric boundary layer well

above the canopy, it is found convenient to consider the canopy as an

area

source or sink of infinitesimal thickness located at an effective height

doabove the ground level, and to consider it an effective reference plane.

Then, the zero-plane displacement does not appear explicitly in theoreti-

calor

semiempirical flux-profile relations, such as those given in Chapters

10-12.

In most experimental situations and practical applications, how-

ever, the ground level is the most convenient reference plane for measur-

ing heights.

is also the appropriate reference plane for representing

263

264 15 Agricultural and Forest Micrometeorology

mean

and

turbulent

quantities within

the

canopy

layer.

For

these

reasons,

in this

chapter,

we will

use

the

height z

above

the

local ground level

and

account

for

the

zero-plane

displacement,

wherever

appropriate

(e.g., in

above-canopy

flux-profile relations).

Applying

the

Monin-Obukhov

similarity relations to

the

fully devel-

oped

(horizontally

homogeneous)

above-canopy

surface layer,

the

mean

wind

speed

(U),

the

potential

temperature

(0),

and

the

specific humidity

(Q), profiles

can

represented

= i

[In(Z

do)

do)]

0;*

= i

[In(Z

~odo)

do)]

(15.1)

where

and

are

the

values at Z =

+ zo,

and

()*

and

q* are

the

scaling

parameters,

each

representing

the

ratio

the

appropriate

vertical

flux (in kinematic units) to

the

friction velocity u; [see, e.g.,

Eq.

(12.12)].

The

M-O

similarity functions

and

are

presumably

equal,

but

may

differ from

the

momentum

function

~m,

especially in unstable

and

free

convective

conditions.

The

empirical forms

these

functions

have

al-

ready

been

discussed

Chapters

and

12.

The

gradient

and

bulk

parameterizations

the

vertical fluxes of mo-

mentum,

heat,

etc.,

in an idealized (constant-flux, horizontally homoge-

neous,

quasistationary)

surface

layer

have

also

been

discussed in Chap-

ters

and

12.

These

can

be applied to

the

above-canopy

surface layer,

especially in

the

height range O.lh > Z > 1.5h

The

range

validity of

the

surface

layer

similarity relations

becomes

narrower

for taller canopies

and

for

shallow

boundary

layers.

may

disappear

completely

when

the

PBL

thickness

is less

than

10-15

times

the

vegetation height, a distinct

possibility

over

mature

forest canopies.

TRANSFER

COEFFICIENTS

AND

RESISTANCES

The

flux

parameterizations

that

employ

the

drag coefficient

and

other

transfer

coefficients

are

commonly

used

in micrometeorology

and

its ap-

plications to

air-sea

interaction,

air

pollution, hydrology, large-scale at-

mospheric

modeling,

etc.

these,

the

various fluxes

are

linearly related

the

products

wind

speed

and

the

difference

between

the

values of

15.1 Flux-Profile Relations above Plant Canopies 265

variables at some reference height in the surface layer and at the surface

itself.

For

example

'To

= pC

DU2

U(0

Eo = pCwU(Qo - Q)

(15.2)

in which the drag coefficient

(CD) and other transfer coefficients can be

prescribed as functions of the surface roughness (more appropriately,

zlzo)

and stability parameters (ziL or

RiB),

as discussed in Chapter 11. On

the basis of Reynolds analogy (similarity

transfer mechanisms of heat,

water

vapor, etc.), one expects that C

= C

Another

commonly used approach or method of parameterizing the

vertical fluxes in terms of the difference in mean property values at two

heights is the

"aerodynamic

resistance"

approach, which is based on the

analogy to electrical resistance and

Ohm's

law:

potential difference

current

= I . I .

ectnca

resistance

The analogous relations for turbulent fluxes are

'To

prM1U

= pcprfi1(00 -

Eo =

prv.}(Qo

- Q)

(15.3)

in which

rM,

rH,

etc.,

are the aerodynamic or aerial resistances to the

transfer

momentum, heat, etc.

Note

that a flux will increase as the

appropriate aerodynamic resistance decreases.

The resistance approach is more frequently used in micrometeorologi-

cal applications in agriculture and forestry. This is largely because of the

simple additive property of resistances in series, which can be used to

express the total aerodynamic resistance in terms of resistances of its

components (bare soil surface, leaves, branches, and stems of plants). A

disadvantage is that, unlike the dimensionless transfer coefficients, aero-

dynamic resistances are dimensional properties, having dimensions of the

inverse of velocity, which depend not only on the canopy structure, but

also on the wind speed at the appropriate height and atmospheric stabil-

ity. Also, in practice, it is

not

easy to determine and specify the compo-

nent resistances for estimating the overall canopy resistance. A compari-

son of

Eqs.

(15.2) and (15.3) clearly shows that the bulk transfer method is

266 15 Agricultural and Forest Micrometeorology

clearly superior to the aerodynamic resistance method, but the two sets of

coefficients are interrelated as

rw'

= UC

(15.4)

Thus, for a given canopy, aerial resistances are inversely related to wind

speed and are

not

unique properties of canopy and the surface.

15.2

RADIATION

BALANCE WITHIN PLANT CANOPIES

Solar or shortwave radiation is the main source of energy for the vege-

tation. Longwave radiation is also a major component of energy balance

in daytime and the primary component at nighttime. In plant canopies

radiation has important thermal and photosynthetic effects; it also plays a

major role in plant growth and development processes. The visible part of

the shortwave radiation (0.38-0.71

fLm) is called the photosynthetically

active radiation (PAR).

Radiative transfer in a plant canopy is a very complicated problem for

which no satisfactory general solution has been found. There are signifi-

cant

amounts of internal radiative absorption, reflection, transmission,

and emission within the canopy elements. Complications also arise from

the large variability

and

inhomogeneity of the canopy architecture, as well

as of individual plants.

The

canopy architecture also determines, to a

large extent, the turbulent exchanges of momentum, heat, water vapor,

etc., within the canopy and is discussed briefly in the following

section.

15.2.1

CANOPY

ARCHITECTURE

The size and shape of canopy elements, as well as their distributions in

space

and

time, determine the physical characteristics of the canopy

structure. A detailed description

a nonhomogeneous or nonuniform

plant canopy in a complex terrain would necessarily involve many param-

eters. A commonly accepted simplification is made by assuming that the

plant stand is horizontally uniform and its average characteristics may

vary only with height above the ground.

The simplest characteristic of the canopy structure is its average height

or thickness

Along with the

area

density of the plants, h

determines

the roughness

parameter

and the effective heights of the sources or sinks

of momentum, heat, moisture, etc. Another widely used characteristic of

the canopy architecture is the cumulative

leaf

area

index (LA!), defined as

the

area

of the

upper

sides of leaves within a vertical cylinder of unit

15.2 Radiation Balance within Plant Canopies 267

cross-section and height

The leafarea index is a dimensionless param-

eter

which is related to the foliage

area

density function A(z) as (Ross,

1975)

= 0 A(z)

(15.5)

Here,

A(z) is a local characteristic of the canopy architecture which repre-

sents the one-sided

leaf

area

per

unit volume

the canopy at the height z.

A more convenient dimensionless local characteristic is the local cumula-

tive

leaf

area

index

LAI(Z)

= z A(z) dz

(15.6)

which represents the leaf

area

per

unit horizontal

area

of the canopy

above the height

Note

that

LAl(O)

= L

In most

crop

and grass canopies leaves are the most active and domi-

nant elements of interaction with the atmosphere, and the fractional

area

represented by plant stems and branches can be neglected. Exceptions

are certain forest canopies in which woody elements may not be ignored.

Particularly for a deciduous forest in late fall and winter, the woody-

element silhouette

area

index

), which can be defined in a manner

similar to

is an important architectural characteristic. The sum of the

two indices is called the plant

area

index

(15.7)

Both the leaf

area

density and the leafarea index are found to vary over

a wide range for

the

various crops and forests.

For

a particular crop, they

also depend on the density of plants and their stage of growth.

For

illus-

tration purposes, Figs. 15.1 and 15.2 show their observed distributions in

a deciduous forest canopy in summer months.

Note

that for this particular

canopy,

= 4.9, W

= 0.6, and

PAl

= 5.5. Observations of the same

parameters for

other

forest and crop canopies are reviewed in Monteith

(1975, 1976).

The

orientation

leaves is characterized by the mean leaf inclination

angle from the horizontal. One

can

also measure the cumulative fre-

quency distribution

the inclination angle. The foliage

many plant

stands are more or less uniformly oriented,

but

some may display a nar-

row range

inclination angles around the horizontal, vertical, or some-

where in between (these are called panophile, erectophile, and plagiophile

canopies). A useful inclination index of the foliage is defined by Ross

(1975). This index also depends on plant species and has a height and

seasonal dependency.