Terrestrial Hydrometeorology (Shuttleworth/Terrestrial Hydrometeorology) || Example Questions and Answers

Introduction

This chapter gives example questions based on the text, together with example

answers. The purpose is to allow students opportunity to gain greater insight and

experience in applying their understanding. Some questions seek numerical

answers while others provide opportunity to express opinions. In the latter case,

example opinions are given in the answers, but these are not necessarily unique

and students are encouraged to propose alternative or additional opinions and to

discuss these with their instructor. In these questions the time within a day is given

in local time expressed in military-time format, i.e., 6:00 AM is written as 06:00

and 3:15 PM as 15:15.

Example questions

Question 1 (Uses understanding and equations from Chapters 2 and 3.)

At 14:00 on June 25 just above the ground near the desert floor about 60 miles west

of Tucson, at an altitude of 3700 ft, the temperature and pressure of the air are

114°F and 29.8 inches (of mercury), respectively, and the relative humidity is 25%.

(a) What are the air temperature in °C and K, the air pressure in mb and in

kPa, the saturated vapor pressure at air temperature in kPa, the vapor

pressure in kPa, the specific humidity in kg kg−1 and Ra, the gas constant,

for the moist air in J kg−1 K?

26 Example Questions and Answers

Terrestrial Hydrometeorology, First Edition. W. James Shuttleworth.

© 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.

Shuttleworth_c26.indd 404Shuttleworth_c26.indd 404 11/3/2011 6:37:21 PM11/3/2011 6:37:21 PM

Example Questions and Answers 405

(b) A hydrometeorologist is making measurements at 7080 ft at the nearby Kitt

Peak Observatory. Neglecting any small changes in specific humidity

between the desert floor and the top of Kitt Peak (and hence in the gas

constant for moist air) and assuming the lapse rate in the lower atmosphere

is that of the US Standard Atmosphere, estimate what she measures for the

air temperature in K and the air pressure in kPa.

(c) She decides to boil water to make coffee. Water boils when its saturated

vapor pressure equals air pressure. Calculate the temperature in °C at which

she finds her water boils. (Hint: compare with the calculation of dew point.)

Assume parcels of air that are warmed by the surface are 5°C warmer than the

surrounding ambient air but have the same vapor pressure.

(d) At what temperature will these parcels saturate? Assuming the air parcels

rise and cool at the adiabatic lapse rate, at what height above the desert floor

will they saturate? At approximately what height do the warmed parcels

lose relative buoyancy? Was there convective cloud on this day? Why?

(Assume 0°C = 273.15 K; 1 inch = 2.54 cm; 1013.3 mb = 30.006 inches of mercury;

cp = 1010 J kg−1 K−1; and the gas constant for moist air R

a = 286.5(1+0.61q) J kg−1 K−1).

Question 2 (Uses understanding and equations from Chapters 2 and 5.)

Assume that at the top of the atmosphere the instantaneous incoming flux of solar

radiation, Stop, can be computed in W m−2 from:

( ). .cos( ) . . sin sin cos cos costopo r o rS S d S d= = +q f d f d w (26.1)

where So is the solar constant ( = 1367 W m−2) ; d

r is eccentricity factor of the

Earth’s orbit (no units); f is the latitude of the site in radians; d is the solar

declination in radians; and w is the hour angle in radians. This equation is implicit

in Equations (5.14) and (5.15). When Equation (26.1) computes a negative value

for Stop the Sun is below the horizon and the true value is zero. The variables dr and

d are functions of the day of the year, and w is a function of the hour, t, within the

day in local time. (Definitions of dr, d and w are given in Chapter 5). Equation

(5.16), which is called the Brunt Equation, is normally used to estimate the all-day

average solar radiation reaching the ground from the all-day average value at the

top of the atmosphere. However, for the purpose of this question the Brunt

Equation is also assumed to apply when calculating Sgrnd, the instantaneous flux of

solar radiation reaching the ground, hence Sgrnd is given by:

Sgrnd=[as+(1-c).b

s]Stop (26.2)



where c is the fractional cloud cover and as and b

s empirical constants here assumed

equal to their typical all-day average values, i.e., as = 0.25 and b

s = 0.5.

Develop a spreadsheet to make the calculations in sections 2(a) to 2(e) below

and sections (g) and (h) then reduce to applying this spreadsheet in different

conditions. The spreadsheet should set the value of Stop to zero for hours when

Equation (26.1) gives a negative value and the Sun is below the horizon. Set up the

spreadsheet to also calculate the daily average values of solar, net solar, net

longwave and net radiation.

On July 13 at an arid site 32.5°N of the equator the measured all-day average

values of air temperature and relative humidity are 71.6 °F and 50 %, respectively.

(a) What are the equivalent all-day average values of air temperature in K, the

saturated vapor pressure in kPa, and the vapor pressure in kPa on this day.

(b) Assuming the cloud factor c = 0.7 all day, estimate the all-day average net

longwave radiation in W m−2 (giving results of intermediate calculations) at

this arid site and recalling that the Stefan-Boltzmann constant is 5.67 × 10−8

W m−2 K−4.

(c) Still assuming the cloud factor c = 0.7 all day, now estimate the all-day

average net longwave radiation in W m−2 (giving results of intermediate

calculations) had this been assumed to be a humid site.

(d) Still assuming the cloud factor c = 0.7 all day and also that the albedo at this

site is equal to 0.23 and is constant through the day and that the net

longwave radiation flux is also constant all day. At hourly intervals between

05:00 and 23.30 hours, calculate and plot the incoming solar radiation, net

solar radiation, and the net radiation fluxes assuming first that this is an

arid site, and second, a humid site.

(e) Calculate the all-day average values of the incoming solar radiation, net

solar radiation and net radiation assuming first that this is an arid site, and

second, a humid site.

You have now created a spreadsheet which you can use to make estimates of solar,

net solar, longwave and net radiation at any latitude, for any day of the year, in dif-

ferent cloud cover conditions and for different types of land cover, as characterized

by their albedo. Using this spreadsheet make the following investigations. You will

need to make appropriate selections for albedo from Table 5.1.

(f) Explore the effect of seasonality by making calculations and plotting graphs

for a humid grassland site near Saskatoon, Canada at 55°N on January 15

when the air temperature is 33°F, and on July 15 when the air temperature

is 90°F. For simplicity, assume c = 0.6 all day and the relative humidity is

80% on both days.

(g) Explore the effect of deforestation on the surface radiation balance by

making calculations and plotting graphs for a humid site near Manaus,

Brazil on March 23 with forest cover and pasture cover. Assume a

temperature of 90°F, a relative humidity of 85%, and a cloud cover of 70%.



Question 3 (Uses understanding and equations from Chapters 1, 4, 6, and 7.)

A farmer has a copy of Terrestrial Hydrometeorology and therefore has

wide-ranging knowledge of the subject. He has a field that is currently bare soil

near Casa Grande, Arizona which is 32.5°N of the equator. This is the arid site for

which you calculated values of net radiation in 2(d). He recently irrigated the field

prior to planting and the sandy soil is close to saturated. He decides to measure the

evaporation loss from the field but he only has three thermometers and a set of tall

stepladders with which to do so. He installs one thermometer in the soil to measure

the temperature very close to the surface of the soil. He wraps the mercury bulb of

a second thermometer in a small piece of cloth that he is careful to keep moist so

that it measures wet bulb temperature. The third thermometer he uses as a dry

bulb thermometer to measure air temperature.

Starting at midnight on July 13 he measures the wet bulb and dry bulb

temperature 0.5 m above the ground and then quickly runs up the stepladder and

makes the same measurements at 3.0 m from the ground. Every 5 minutes he

repeats this operation throughout the next 24 hours. In his spare time he monitors

the thermometer in the soil and notices that the minimum temperature of 20°C

occurs at 01:00 and the maximum temperature of 24°C occurs at 13:00. He also

monitors the sky and decides that the fractional cloud cover is 0.7 and fairly

constant all day. He computes the hourly-average values of wet and dry bulb

temperature at the top and bottom of the stepladder given in Table 26.1.

Having read Chapter 6 in Terrestrial Hydrometeorology, the farmer realizes that if

he assumes the soil is uniform with depth and the diurnal cycle in soil surface

Table 26.1 Values of hourly average dry and wet bulb temperatures measured by the farmer in question 3.

Bottom Top Bottom Top

Time (hour)

Dry bulb (°C)

Wet bulb (°C)

Dry bulb (°C)

Wet bulb (°C)

Time (hour)

Dry bulb (°C)

Wet bulb (°C)

Dry bulb (°C)

Wet bulb (°C)

0.5 16.786 11.714 15.654 11.177 12.5 33.139 21.096 28.347 16.7031.5 14.337 11.026 14.609 11.117 13.5 34.790 21.547 29.391 17.0432.5 12.482 10.157 14.069 10.948 14.5 34.820 21.365 29.932 17.0933.5 9.963 9.146 14.068 10.948 15.5 34.600 20.918 29.931 16.8884.5 8.838 8.482 14.609 11.052 16.5 33.255 20.360 29.391 16.7335.5 13.222 10.473 15.653 11.563 17.5 30.856 18.978 28.346 16.2826.5 17.093 13.081 17.130 11.996 18.5 27.105 17.012 26.870 15.7697.5 20.394 15.325 18.938 12.808 19.5 25.255 15.567 25.061 15.1258.5 23.451 17.181 20.956 13.978 20.5 24.786 15.274 23.043 14.3949.5 26.654 18.610 23.044 14.851 21.5 22.795 14.562 20.955 13.44510.5 29.122 19.718 25.062 15.733 22.5 20.439 13.644 18.938 12.68511.5 31.598 20.625 26.870 16.306 23.5 18.632 12.692 17.129 11.870



temperature is sinusoidal, and if he chooses the form of the sinusoidal wave to agree

with the timing and magnitude of the minimum and maximum soil temperatures

that he measured and also selects values of soil properties appropriate for the moist

sandy soil, he can calculate the soil heat flux at any time during the day.

(a) What were the values of the mean soil surface temperature, and the

amplitude and the time slip of the cycle in soil surface temperature that he

selected?

(b) What were the values of soil thermal conductivity, ks, and thermal

diffusivity, αs, that he selected, what was the value of damping depth, D, for

the daily time period (expressed in seconds) that he calculated. Which

equation from Terrestrial Hydrometeorology did he use to calculate the

instantaneous surface soil heat flux?

The farmer assumes that the psychrometric constant is 0.0667 kPa K−1 when

applying the wet-bulb equation and when calculating the Bowen ratio. For

simplicity he also assumes that the difference in virtual potential temperature is

equal to the difference in measured air temperature between the two levels. (This

is a common assumption when calculating Bowen ratio). In the course of his

calculations he found that the all-day average air temperature and vapor pressure

at the bottom level were the same as those you calculated and used in question

2(a). Using these values with the day of the year and latitude of the site he was able

to calculate the same estimates of net radiation for this arid site that you calculated

in question 2(d). You can therefore adopt those values of hourly net radiation for

use in this question.

(c) Develop a spreadsheet to tabulate the values of vapor pressure at the bot-

tom level, vapor pressure at the top level, Bowen ratio, net radiation [copied

from 2(e)], soil heat flux, available energy, latent heat flux and sensible heat

flux at hourly intervals between 0.5 and 23.5 hours.

(d) Plot the calculated net radiation, soil heat flux, available energy, latent heat

flux and sensible heat flux as a function of time through the day.

(e) What were the all-day average values of the Bowen ratio and Evaporative

Fraction at his site on this day?

(f) Suppose the farmer had chosen to neglect soil heat flux in his calculation of

available energy. Without recalculating all the rates, can you suggest

whether he would have overestimated or underestimated the all-day

average evaporative fraction and explain why?

Question 4 (Uses understanding from Chapters 1, 2, and 8.)

(a) Shuttleworth says, ‘As an annual-average, the value is about 1.2 m. However

we, as land dwellers, see only about 10% of this, and we lose almost two-

thirds back to the atmosphere. We keep an even smaller proportion



in Arizona.’ In your opinion, what is Shuttleworth talking about? The

annual-average of what is about 1.2 m? How do we lose two-thirds back to

the atmosphere? Approximately what proportion do we keep in Arizona?

(b) Shuttleworth says, ‘These two components of these models have jargon

names and are run alternately. The first applies the conservation laws while

the second, by representing relevant processes, changes the divergence

terms in these laws prior to their next application.’ In your opinion, what

components of what models is he talking about and what are their jargon

names. Which ‘laws’ does he refer to? Can you suggest some of the relevant

processes that change the divergence terms in these laws?

(c) Shuttleworth says, ‘Of course, if all the continents were constrained to be in

the tropics then, as a global average, the proportion of the Sun’s radiant

energy reflected at the Earth’s surface would vary less between summer and

winter.’ In your opinion, what is at least one reason why Shuttleworth might

be correct?

(d) Shuttleworth says, ‘Most of the time the temperature gradient in the lower

atmosphere is less than the dry adiabatic lapse rate. Water vapor is also

strongly concentrated at the bottom of the atmosphere. Presumably, the

same processes are responsible for both of these phenomena.’ In your

opinion, could Shuttleworth’s presumption be correct? What process or

processes might simultaneously reduce the actual lapse rate below the

adiabatic rate and also reduce the vapor content of the atmosphere at levels

well above the ground?

(e) Shuttleworth says, ‘These models are used in three main ways, each with a

different objective. However, in fact, one application was a by-product of

the original model application. “Initiation” is a keyword in all of these

applications.’ In your opinion, now what is Shuttleworth talking about?

What models? What are the three different objectives? Can you suggest

why he puts emphasis on model initiation?

(f) Shuttleworth says, ‘The specific heat is 4 times bigger and the density is

nearly 1000 times bigger. If this wasn’t true, we might have http://www.

weather.gov/ but we probably would not have http://www.cpc.ncep.noaa.

gov/’ In your opinion, what has a specific heat and density respectively 4

and 1000 times bigger than what? If this were not the case, can you explain

why in your opinion this might mean that http://www.cpc.ncep.noaa.gov/

would not be needed but http://www.weather.gov/ likely still would be?

(g) Shuttleworth says, ‘One important potential consequence of ‘greenhouse

warming’ is that it will enhance the hydrological cycle. It is interesting that

non-linearity in the basic relationship that would cause this enhancement

tends to compensate for the projected warming being twice as large at the

poles than at the equator.’ In your opinion, what does Shuttleworth mean

by this? Can you suggest what basic relationship might allow greenhouse

warming to enhance the hydrological cycle? Why might this relationship

be more effective at the equator, thus compensating for the potentially

enhanced warming at the poles?



Question 5 (Uses understanding from Chapter 9.)

The planet Malleable is fascinating. In many respects it is identical to the Earth. It

has identical dimensions and is located in a solar system identical to ours. It rotates

around an identical sun, in an identical orbit, and its solar declination changes

seasonally as does the Earth’s. Moreover, on average, the relative area of oceans and

continents is the same as that on Earth. The planet is the adopted home to an

advanced civilization that can manipulate the location of the continents on

Malleable’s surface. When it was settled, the ‘Founding Fathers’ of Malleable chose

to distribute these continents as shown in Fig. 26.1.

The planet Malleable is governed by a single planetary government. It is election

year and three main parties are seeking election. They are as follows.

The Reduce Warm Deserts (RWD) Party, whose platform is to redefine the

continents so as to reduce the non-productive continental areas that are deserts

on planet Malleable.

The Reduce Tropical Storms (RTS) Party, whose platform is to redefine the conti-

nents so as to reduce the ‘seed areas’ for tropical storms on planet Malleable.

The Maximize Monsoons (MM) Party, the central theme of whose platform is to

enhance seasonal precipitation in subtropical regions and thus allow the

production of additional seasonal crops on planet Malleable.

Each political party has devised a banner that expresses their ideas symbolically by

approximately representing the new continental distributions they are respectively

suggesting. As the most effective printer on Malleable, you have been awarded the

Current continental arrangement

Banner A

Banner B

Banner C

Figure 26.1 Current

continental arrangement on

planet Malleable and the three

banners used by three political

parties in the election.



contract to print these banners. Unfortunately the three party symbols have

arrived at your printing works without you knowing which symbol belongs to

which party. On the basis of your understanding derived from Terrestrial

Hydrometeorology, you must choose the most appropriate symbol for each party’s

banner. These symbols are also shown in Fig. 26.1.

(a) In your opinion, which banner (A, B, or C) most likely represents the

continental distribution advocated by the RWD Party and briefly explain

what you think is the basis for them suggesting this particular continental

distribution.

(b) In your opinion, which banner (A, B, or C) most likely represents the

continental distribution advocated by the RTS Party and briefly explain


distribution.

(c) In your opinion, which banner (A, B, or C) most likely represents the

continental distribution advocated by the MM Party and briefly explain


distribution.

Late in the election campaign, a fourth party, the Reduce El Niño (REN) Party,

emerges. Their objective is to seek to reduce the severity of fluctuations in climate

associated with building unstable ‘warm pools’ in Malleable’s tropical oceans.

Their hope is to gain a share of power by forming a coalition with one of the other

parties after the election. They see most opportunity of making a deal with either

the RWD or the RTS parties and have opened secret discussions with these two

parties before the election.

(d) In your opinion, how might the RWD Party be arguing for the support of

the REN Party after the election?

(e) In your opinion, how might the RTS Party be arguing for the support of the

REN Party after the election?

Question 6 (Uses understanding from Chapters 9, 10 and 11.)

Briefly answer the following.

(a) In your opinion, what is the fundamental cause of the difference between

the thermal structure of the oceans and the atmosphere? What is your

opinion on the consequence of the above phenomenon on the vertical

structure of the oceans, and say how this changes with latitude and

season.

(b) A student said, ‘Ocean currents tend to go north on the eastern sides of

continents, and south on the western side of continents’. In your opinion, is

the student correct? Why?



(c) In your opinion, why do ocean currents tend to behave this way?

(d) Discuss the statement, ‘The geographical distribution of land masses

influences the effect of ocean circulation on tropical Sea Surface

Temperature’ in the context of the Atlantic Ocean, and give your opinion

on any consequences on the relative frequency of tropical storms in Cuba

and in northeast Brazil.

(e) A student said, ‘The hydroclimatic mechanism which most influences the

food supply of half the world’s population is related to difference in the way

surface radiation is shared for continents and oceans.’ In your opinion,

what did she mean?

(f) For clouds to occur in the atmosphere a mechanism which gives rising air

and therefore cooling air is required. In your opinion, what are two other

requirements and which of them is most likely to be the limiting

requirement?

(g) If a parcel of air is moister than its surroundings but it has the same

temperature and pressure, in your opinion will it tend to rise or will it tend

to fall? Briefly explain why.

(h) In convective conditions parcels of air are heated and start to rise because

they are warmer and lighter. As soon as a parcel rises the air cools. In your

opinion why does this cooling not necessarily stop the air parcel rising to

the cloud condensation level?

(i) Once the cloud condensation level is reached, cloud formation begins. Give

your opinion on what effect the condensation process will have on the

buoyancy of the parcel of air and its further ascent in the cloud.

(j) In a particular mid-latitude cloud, the air temperature is -25°C. In your

opinion, which phases of water (solid, liquid or vapor) are likely to be

present in the cloud, and what is likely to be the most important physical

mechanism giving ice particle growth in the cloud.

Question 7 (Uses understanding from Chapters 12, 13 and 14.)

(a) Draw a diagram of what in your opinion is the ideal site and mounting for

a rain gauge. It should show its relation to surrounding objects and to the

ground. Give a brief explanation of why you consider your design to be

good. Discuss this design with your instructor.

(b) Obtain values of mean monthly precipitation for a site that interests you

(e.g., your home town, state, or country). Compute the Seasonality Index

from these data using the formulae given in your class notes (or an

alternative measure of seasonality if you prefer; there are alternative

measures.) Comment on what this index implies about the seasonality of

the precipitation climate that you choose.

(c) Using the same data you used in question 7(b), draw a ‘pie’ diagram to

illustrate the seasonal behavior of the rainfall showing the percentage

contributions to the annual rainfall in each month.



(d) During a storm the chart from a siphon rain gauge produced the (simu-

lated) form illustrated in Fig. 26.2. This was digitized to give the numerical

time sequence in Table 26.2. Plot the mass curve for this particular storm

and, on the basis of this mass curve, speculate as to whether the chart was

most likely to be for a frontal or convective storm and explain your

reasoning.

(e) The July rainfall amounts in Tanzania over the period 1931–1960 are given

in Table 13.1. Calculate the mean value and estimate the median value of

the July rainfall in Tanzania between 1931 and 1960. If you find they differ,

say why.

10

8

6

4

2

00 20 40 60

Time (minutes)

80 100 120

Rai

nfal

l (m

m)Figure 26.2 A (simulated) chart

of precipitation for a storm

measured using a siphon rain

gauge. Note that once the

chamber reaches a storage that is

equivalent to 10 mm of rainfall,

the chamber is siphoned empty

and then continues to refill as the

storm proceeds.

Table 26.2 Digitized form of a chart measured using a siphon rain gauge illustrated in

Figure 12.2 and used in question 7(d).

Time (minutes)

Gauge reading (mm)

Time (minutes)

Gauge reading (mm)

Time (minutes)

Gauge reading (mm)

0.00 2.62 31.40 10.00 60.00 7.495.00 5.25 31.40 0.00 65.00 9.27

10.00 7.76 35.00 9.48 68.69 10.0011.85 10.00 35.19 10.00 68.69 0.0011.85 0.00 35.19 0.00 70.00 0.2615.00 3.82 39.02 10.00 75.00 1.2118.38 10.00 39.02 0.00 80.00 1.8218.38 0.00 40.00 2.50 85.00 2.5520.00 2.97 43.14 10.00 90.00 2.6823.45 10.00 43.14 0.00 95.00 3.3223.45 0.00 45.00 4.02 100.00 3.8625.00 3.16 48.70 10.00 105.00 4.8327.60 10.00 48.70 0.00 110.00 5.9627.60 0.00 50.00 2.11 115.00 6.2930.00 6.30 55.00 4.52 120.00 6.72



(f) Compute and plot the time variations in the 7-year running mean for July

Tanzanian rainfall data between 1934 and 1957.

(g) Compute and plot the mass curve for July Tanzanian rainfall data between

1931 and 1960.

(h) Compute and plot the cumulative deviation for July Tanzanian rainfall data

between 1931 and 1960.

(i) A farmer owns the field illustrated in Fig. 26.3 which is 6 km by 4 km. He

has access to the data from three rain gauges which are located at P1, P

2, and

P3 in this diagram. In April these three gauges measure 16, 8, and 7 mm of

rainfall, respectively, in May they measure 26, 34, and 43 mm of rainfall,

respectively, and in June they measure 51, 44, and 37 mm of rainfall,

respectively. He decides to estimate the area-average rainfall for his field by

using the Reciprocal-Distance-Squared to estimate rainfall estimates at the

center of each square kilometer of his field (i.e., at the points shown), and

then averaging these values. What were the area-average precipitation

values he calculated for April, May, and June?

Question 8 (Uses understanding and equations from Chapters 16, 17, and 18.)

(a) Starting from Equation (16.46), i.e., the basic equation for conservation of

water vapor in the atmosphere, by analogy with the derivation given in

Chapter 17 for vertical velocity in your class notes or otherwise, derive

2−2

−2

4

4

(Distance in km)

6 8

2

P1

P2

P3

(−1.0, −1.5)

(2.5, 5.0)

(7.0, 2.5)

Field

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

(Dis

tanc

e in

km

)

Figure 26.3 The field for which

area-average precipitation is to

be calculated, and the three rain

gauge positions P1, P2, and P3 at

which the gauges are located

from which calculations are to be

made in question 7(i).



Equation (26.3), the prognostic equation describing for water vapor

fluctuations in the atmosphere:

( ) ( ) ( )

2

' ' ' ' ' '

qq

a a

Sq q q q Eu v w qt x y z

u q v q w qx y z

∂ ∂ ∂ ∂+ + + = + + ∇

∂ ∂ ∂ ∂⎛ ⎞∂ ∂ ∂

− + +⎜ ⎟∂ ∂ ∂⎝ ⎠

ur r

(26.3)

explaining each step in the derivation as you do so.

The prognostic equations describing the conservation of mean potential tem-

perature has a similar form, thus:

( ) ( ) ( )

2

' ' ' ' ' '

n

a p a p

R Eu v wt x y z c c

u v wx y z

θ

∇∂θ ∂θ ∂θ ∂θ+ + + = − − + υ ∇ θ

∂ ∂ ∂ ∂⎛ ⎞∂ θ ∂ θ ∂ θ

− + +⎜ ⎟∂ ∂ ∂⎝ ⎠

r r

(26.4)

Give the terms that become negligible in Equations (26.3) and (26.4) when the

following assumptions are made.

(b) There is no mechanism for creating water vapor chemically in the

atmosphere.

(c) There is no phase change between water vapor and liquid/solid water.

(d) There is no horizontal or vertical change in the net radiation flux in the

ABL.

(e) Molecular diffusion can be neglected.

(f) There is no ascent or subsidence (i.e. no persistent rising or sinking of the

air).

(g) There is no horizontal divergence of turbulent fluxes.

(h) There is no horizontal advection of humidity or potential temperature.

(i) After making all of the above simplifying assumptions, write down the

(much simpler) versions of Equations (26.3) and (26.4) which then apply.

Figure 26.4 sketches the simplified average height dependence of the sensible heat

flux H(z) and the moisture flux E(z) through the daytime atmospheric boundary

layer over uniform terrain in cloudless conditions when there is no subsidence. It

labels five levels different levels (i), (ii), (iii), (iv), and (v). You are only allowed to

choose between the following three options for changes in air temperature – be

warmer, be cooler, or change little; and you are only allowed to choose between the

following three options for changes in atmospheric humidity – be wetter, be drier,

or change little. On the basis of the answer to question (i), say how the temperature

and humidity will change over the next few minutes at the levels given below.



(j) How will the temperature and humidity change at level (i)?

(k) How will the temperature and humidity change at level (ii)?

(l) How will the temperature and humidity change at level (iii)?

(m) How will the temperature and humidity change at level (iv)?

(n) How will the temperature and humidity change at level (v)?

Question 9 (Uses understanding and equations from Chapters 2, 21, 22 and 24.)

The molecular diffusion coefficients are υ = 1.33 × 10−5 (1+0.007T) m2 s−1,

DH = 1.89 × 10−5 (1+0.007T) m2 s−1, D

V = 2.12 × 10−5 (1+0.007T) m2 s−1, and D

C =

1.29 × 10−5 (1+0.007T) m2 s−1, see Chapter 21.

Assume that the aerodynamic interactions of the leaves on deciduous trees can

be approximated by those of a circular flat plate with a diameter of 5 cm while

those of evergreen conifers can be represented by the aerodynamic interactions of

cylinders of diameter 2.5 mm. The boundary-layer resistance to heat transfer per

unit surface area of each vegetation element (i.e., leaf or needle) is estimated by

Equation (21.9). The in-canopy wind speed, U, is 0.5 m s−1 and the in-canopy

temperature is 20°C. By first calculating the Reynolds number from Re = (Ud)/n,

where d is a characteristic dimension of the leaf or needle (in this case the

diameter), and then by selecting the relevant empirical equation for the Nusselt

number, Nu, from Table (21.1), use Equation (21.9) to estimate the boundary-

layer resistance per unit area for heat transfer for:

(a) individual deciduous leaves

(b) individual coniferous needles

Assume the transfer from individual vegetative elements is always by forced con-

vection so that the relative transfer resistances for other exchanges is determined

Mixed layer

Surface layer

Entrainment layer

Free atmosphere(v)

(iv)

(iii)

(ii)

(i)

H(z) E(z)

Figure 26.4 The simplified

average height dependence of the

sensible heat flux H(z) and the

moisture flux E(z) through the

daytime atmospheric boundary

layer over uniform terrain in

cloudless conditions when there

is no subsidence.



only by their relative diffusion coefficients, see Equations (21.10) and (21.11).

From the answer to Question 9(b), estimate the boundary-layer resistance for:

(c) vapor transfer for coniferous needles;

(d) carbon dioxide transfer for coniferous needles.

(e) Equations (22.2), (22.3) and (22.4), approximately describe how the zero

plane displacement, d, and aerodynamic roughness length, zo, of a vegeta-

tion stand vary relative to the crop height, h, as a function of the leaf area

index, LAI, for a canopy with maximum vegetation density approximately

halfway through canopy depth. Assuming the aerodynamic roughness

length for bare soil, z0’, can be neglected, plot the values of (d/h) and (z

o/h)

as a function of leaf area index in the range LAI = 0 to 5 and comment on

why these two ratios vary with LAI in this way. Calculate the values of (d/h)

and (zo/h) when LAI = 4 for use in 9(f).

(f) Assume the aerodynamic resistance for latent and sensible heat transfer

to a vegetation stand in neutral conditions, ra, is given by Equation (22.9).

If both wind speed and vapor pressure deficit are measured 2 m above

the top of a 10 cm high grass stand, at 2 m above the top of a 1 m high

cereal crop stand, and at 2 m above the top of a 30 m high forest stand,

and all these stands have LAI = 4, plot the aerodynamic resistance of

these three vegetation stands as a function of wind speed from 0.25 m s−1

to 8 m s−1.

(g) Some SVAT represent the behavior of the surface resistance using the

Jarvis-Stewart model. Assume the surface conductance for the forest stand

considered in (f) is given by Equation (24.1) with g0 = 40 mm s−1 and g

M = 1

(i.e., there is no soil moisture stress); and with gR, g

D , and g

T , given

by Equations (24.2), (24.3) and (24.4), and (24.5), with KR = 200 W m−2,

KD

1 = –0.307 kPa−1, KD

2 = 0.019 kPa−2, TL =273 K, T

0 = 293 K, and T

H = 313 K.

Plot the variation in the individual stress functions gR, g

D , and g

T over the

solar radiation ranges 0–1000 Wm−2, VPD range 0–4 kPa, and temperature

range 0–40°C, respectively. If any stress function is calculated to be less

than zero, it should be set to zero. (Hint: do your calculations look plausible

in comparison with Fig. 24.5?)

In the following, assume the meteorological data given in Table 26.3 were measured

2 m above the top of the 30 m high forest and that it is acceptable to use the

aerodynamic resistance ra calculated in 9(f) and the formulae for surface

conductance specified in 9(g) to calculate the surface resistance rs (= g

s−1).

(h) Plot the variation through the day of the individual stress functions gR, g

D ,

and gT , and also the total stress function, i.e., the product (g

R g

D g

T g

M).

(i) Using the Penman-Monteith equation (Equation 21.33) and the surface

energy balance, plot the variation through the day of available energy,

latent heat and sensible heat fluxes.



Table 26.3 Meteorological data measured 2 m above the 30 m high forest for use in question 9(h) and 9(i).

Time (hour) Wind speed (m s−1)

Solar radiation (W m−2)

Available energy (W m−2) Temperature (°C)

Vapor pressure deficit (kPa)

0.5 1.39 0 17 26.74 0.561.5 1.11 0 1 26.13 0.482.5 1.30 0 9 25.47 0.413.5 1.36 0 −2 25.08 0.334.5 0.70 0 2 24.83 0.285.5 0.87 0 0 24.32 0.206.5 1.84 0 2 23.72 0.117.5 1.34 84 7 24.74 0.248.5 0.36 333 30 26.02 0.429.5 0.77 602 412 27.56 0.69

10.5 1.46 832 564 28.89 0.9311.5 2.36 965 697 30.00 1.2512.5 1.75 981 638 30.93 1.5713.5 3.16 1075 755 31.75 1.9714.5 2.77 994 618 32.11 2.0515.5 2.68 732 374 32.03 2.0916.5 2.85 617 321 32.66 2.3317.5 1.90 346 131 32.48 2.2918.5 1.97 85 26 31.75 2.0819.5 0.88 0 −3 30.39 1.7220.5 1.18 0 −16 28.72 1.1221.5 0.98 0 −9 27.71 0.9022.5 2.42 0 −2 27.58 0.9223.5 1.90 0 16 27.36 0.91

Question 10 (Uses understanding and equations from Chapters 2, 5, and 23.)

Create spreadsheets to make the calculations that are demonstrated in Tables 23.1,

23.2, 23.3 23.4 using the data for three sites in Australia given in Table 26.4. Then

create a spreadsheet to make calculations of crop evaporation in a table similar to

Table 23.6 but in this case for Alfalfa, Cotton and Sugar Cane. In this way you will

create a spreadsheet that you can use to give daily estimates of evaporation

wherever relevant data are available.

Example Answers

Answer 1

(a) Near the desert floor where the altitude is 3700 ft, or 1128 m, air tempera-

ture is 45.56°C, or 318.71 K, air pressure is 1006 mb, or 100.6 kPa, saturated



vapor pressure is 9.86 kPa [from Equation (2.17)], vapor pressure is 2.46

kPa [from Equation( 2.19)], specific humidity is 0.0152 kg kg−1 [from

Equation (2.9], and the gas constant for moist air is 289.2 J kg−1 K [from the

equation given in the question].

(b) At Kitt Peak where the altitude is 7080 ft, or 2158 m, air temperature is

312.01 K assuming the local lapse rate is 0.0065 Km−1, and air pressure is

90.1 kPa [from Equation (3.13)].

(c) From Equation (2.21), at the ambient air pressure on Kitt Peak water boils

at 96.5°C.

(d) The warmed parcels of air near the desert floor have a temperature of

50.56°C or 323.7 K, and their vapor pressure is still 2.46 kPa. They will

saturate at a dew point temperature of 20.85°C [from Equation (2.21)], or

at 294.0 K. If the ascending parcels cool at the adiabatic lapse rate of

0.00968 Km−1, they would need to reach a height of 3068 m above the

desert floor before their temperature falls from 323.71 K to 294.0 K and

they saturate. The warmed air parcels will lose buoyancy at a height h at

which their temperature has fallen such that it is equal to that of the

surrounding air, i.e., when (323.7 – 0.0097h) = (318.17 – 0.0065h), thus at

about 1500 m above the desert floor. Consequently there is unlikely to be

any convective cloud on this day because the warmed air parcels lose

buoyancy at ∼1500 m above the desert floor before they can saturate at

about 3000 m.

Table 26.4 Site characteristics and meteorological variables for the three Australian

sites considered in question 10.

Variable Units Site 1 Site 2 Site 3

Maximum air temperature (°C) 29.10 35.00 23.00Minimum air temperature (°C) 17.90 21.40 11.50Dry bulb temperature (°C) 24.00 n/a n/aWet bulb temperature (°C) 19.00 n/a n/aRelative humidity (%) n/a 39 n/aDew point (°C) n/a n/a 11.00Wind measurement height (m) 10.00 10.00 2.00Wind speed (m s−1) 5.60 4.70 3.70Day of year (none) 40 46 52Latitude (deg) −19.62 −15.78 −33.13Cloud fraction (none) 0.40 0.10 n/aNumber of bright sunshine hours (hours) n/a n/a 4.000Elevation (m) 12 44 30Assigned site humidity (none) Humid Arid HumidMeasured pan evaporation (mm) 7.6 11.2 4.9Selected value for Albedo (none) 0.23 0.23 0.23Albedo of open water (none) 0.08 0.08 0.08



Answer 2

(a) At this site on this day, the all-day average air temperature is 22°C, or

295.13 K, the saturated vapor pressure is 2.644 kPa, and the vapor pressure

is 1.322 kPa.

(b) When calculating net longwave radiation, the effective emissivity e’ = 0.194

[from Equation (5.23)] and assuming c = 0.7 all through the day, for an arid

site the empirical cloud factor f = 0.37 [from Equation (5..25)]. The esti-

mated all-day average net longwave radiation is therefore –28 W m−2 [from

Equation (5..22)].

(c) Were this a humid site the empirical cloud factor, f, would then be 0.533

[from Equation (5..24)] and the estimated all-day average net longwave

radiation would be -41 W m−2 [from Equation (5..22)].

(d) July 12 is Day Of Year 193, hence the eccentricity factor dl = 0.968 [from

Equation (5.5)] and the solar declination δ = 0.385 radians [from Equation

(5.8)]. The latitude of the site is 32.5°N, which is +0.567 radians, and the

hour angle, w, can be calculated in radians from the time of day, t, in hours

[using Equation (5.10)], with t running in hourly increments from 0.5 to

23.5. Consequently, the solar radiation at the top of the atmosphere, Stop, can

be calculated [from Equation (26.1)] and solar radiation at the ground, Sgrnd,

calculated [from Equation (26.2)]. Values of net solar radiation can then

be calculated for each value of t by allowing for the albedo of 0.23 [by

comparison with Equation (5.18)]. Values of net radiation can then be cal-

culated for each value of t by adding the relevant values of longwave radiation

for arid and humid conditions calculated in sections (b) and (c), respectively.

The resulting values of solar radiation, net solar radiation, and net radiation

for an arid and a humid site are given in Table 26.5 and plotted in Fig. 26.5.

(e) The required all-day average values are 190 W m−2 for (incoming) solar

radiation, 146 W m−2 for net solar radiation, 118 W m−2 for net radiation at

this arid site, and 105 W m−2 for net radiation were it assumed to be a

humid site.

(f) The required all-day average fluxes and plots of the diurnal variation in

solar, net solar, and net radiation for the Saskatoon site with fresh snow

cover on January 15 and grassland cover on July 15 are given in Fig. 26.6.

(g) The required all-day average fluxes and plots of the diurnal variation in

solar, net solar, and net radiation for the Manaus site on March 23 with for-

est and pastureland cover given in Fig. 26.7.

Answer 3

(a) The mean soil surface temperature, Tm

, is (24+20)/2 = 22°C, the amplitude

of the daily cycle, Ta, is (24–20)/2 = 2°C, and the time slip, t

o, which gives a

minimum 01.00 am and a maximum at 13.00 in Equation (6.11) is (7 ×

60 × 60) = 25,200 seconds.



(b) For saturated sandy soil the thermal conductivity, ks, is 2.20 W m−2 K−1 and

the thermal diffusivity, αs, is 0.74 × 10−6 m2 s−1. The damping depth, D, for

the daily time period P = (24 × 60 × 60) = 86,400 seconds is 0.143 m [from

Equation (6.13)]. The farmer used Equation (6.14) to estimate the instanta-

neous surface soil heat flux.

(c) The vapor pressure at the bottom level, vapor pressure at top level, Bowen

ratio, net radiation, soil heat flux, available energy, latent heat flux and sen-

sible heat flux are tabulated in Table 26.6.

(d) The net radiation, soil heat flux, available energy, latent heat flux and the sen-

sible heat flux are plotted as a function of time through the day in Fig. 26.8.

60 12Time (hrs)

18 24

Solar

Net (arid)Net (humid)

600

500

400

300

200

100

0

−100

Ene

rgy

flux

(W m

−2)

Figure 26.5 The diurnal cycle

of (incoming) solar radiation, net

solar radiation, longwave

radiation, and net radiation

calculated in 2(d) assuming it is

an arid and a humid site.

Table 26.5 Values of (incoming) solar radiation, net solar radiation, longwave radiation, and net radiation calculated in 2(d)

assuming it is both an arid and a humid site.

Hour (local)

Solar (W m−2)

Net solar (W m−2)

Net (arid) (W m−2)

Net (humid) (W m−2)

Hour (local)

Solar (W m−2)

Net solar (W m−2)

Net (arid) (W m−2)

Net (humid) (W m−2)

0.5 0 0 −28 −41 12.5 517 398 369 3571.5 0 0 −28 −41 13.5 489 376 348 3352.5 0 0 −28 −41 14.5 435 335 306 2943.5 0 0 −28 −41 15.5 358 276 248 2354.5 0 0 −28 −41 16.5 265 204 176 1635.5 53 41 12 0 17.5 161 124 95 836.5 161 124 95 83 18.5 53 41 12 07.5 265 204 176 163 19.5 0 0 −28 −418.5 358 276 248 235 20.5 0 0 −28 −419.5 435 335 306 294 21.5 0 0 −28 −41

10.5 489 376 348 335 22.5 0 0 −28 −4111.5 517 398 369 357 23.5 0 0 −28 −41



All-day average values

30

6

−46

−40

Solar (W m−2)

Net solar (W m−2)

Longwave (W m−2)

Net (W m−2)


208

160

−19

141

Solar (W m−2)

Net solar (W m−2)

Longwave (W m−2)

Net (W m−2)

200

150

100

50

0

−50

−100

0 6 12

Time (hrs)

18 24Ene

rgy

flux

(W m

−2)

Solar

Net solar

Net

Saskatoon Jan 15 (fresh snow)

−100

0

100

200

300

400

500

600

Time (hrs)

0 6 12 18 24

Solar

Net solar

Net

Saskatoon Jan 15 (grassland)

Ene

rgy

flux

(W m

−2)

Figure 26.6 Diurnal variation

in all-day average radiation

fluxes calculated in 2(f).

(e) The all-day average values of the Bowen ratio and Evaporative Fraction at

his site are calculated from the all-day average values of latent and sensible

(not by averaging the hourly average values) and are 0.486 and 0.673,

respectively.




175

154

−15

139

Solar (W m−2)

Net Solar (W m−2)

Longwave (W m−2)

Net (W m−2)


175

135

−15

120

Solar (W m−2)

Net solar (W m−2)

Longwave (W m−2)

Net (W m−2)

600

500

400

300

200

0

100

−1000 6 12

Time (hrs)18 24

En

erg

y fl

ux

(W m

-2) Solar

Net solar

Net

Manaus March 23 (forest)

−100

0

100

200

300

400

500

600

Time (hrs)

0 6 12 18 24

Solar

Net solar

Net

Manaus March 23 (pasture)

En

erg

y fl

ux

(W m

-2)

Figure 26.7 Diurnal variation

in all-day average radiation

fluxes calculated in 2(g).

(f) Had the farmer neglected soil heat flux he would have estimated greater

available energy during the day when evaporation is the dominant flux,

and less at night when sensible heat is the dominant flux. The net effect

would have been to overestimate the all-day average evaporation flux.


424 Example Questions and AnswersTable 26.6 The vapor pressure at the bottom level, vapor pressure at top level, Bowen ratio, net radiation, soil heat flux,

available energy, latent heat flux and sensible heat flux at hourly intervals calculated in 3(c).

Vapor pressure

Time (hour)

Bottom (k Pa)

Top (k Pa)

Bowen ratio

Net radiation (W m−2)

Soil heat (W m−2)

Available energy (W m−2)

Latent heat (W m−2)

Sensible heat (W m−2)

0.5 1.036 1.028 9.129 −28 −35 6 1 61.5 1.093 1.088 −4.402 −28 −27 −2 1 −32.5 1.084 1.098 7.579 −28 −17 −12 −1 −103.5 1.104 1.098 −52.074 −28 −6 −23 0 −234.5 1.084 1.078 −72.617 −28 6 −34 0 −355.5 1.083 1.088 29.388 12 17 −5 0 −46.5 1.236 1.058 −0.014 95 27 69 70 −17.5 1.400 1.068 0.292 176 35 141 109 328.5 1.538 1.128 0.406 248 40 207 147 609.5 1.604 1.140 0.519 306 43 263 173 90

10.5 1.666 1.162 0.538 348 43 305 198 10711.5 1.693 1.146 0.577 369 40 329 209 12012.5 1.693 1.122 0.559 369 35 335 215 12013.5 1.683 1.116 0.635 348 27 321 197 12514.5 1.640 1.089 0.592 306 17 290 182 10815.5 1.557 1.051 0.615 248 6 242 150 9216.5 1.526 1.057 0.550 176 −6 181 117 6417.5 1.398 1.043 0.472 95 −17 112 76 3618.5 1.262 1.048 0.073 12 −27 39 36 319.5 1.119 1.054 0.196 −28 −35 6 5 120.5 1.098 1.060 3.070 −28 −40 12 3 921.5 1.106 1.039 1.822 −28 −43 15 5 1022.5 1.106 1.048 1.714 −28 −43 15 5 923.5 1.070 1.038 3.170 −28 −40 12 3 9

400

350

300

250

200

150

100

50

0

−50

−100

0 6 12 18 24

Net

Soil

Available

Latent

Sensible

Ene

rgy

flux

(W m

−2)

Figure 26.8 The net radiation,

soil heat flux, available energy,

latent heat flux and the sensible

heat flux calculated in 3(d)

plotted as a function of time

through the day.



Answer 4

(a) Shuttleworth is speaking about the annual average evaporation from the

oceanic surfaces of the globe which is about 1.2 m per year. Around 90% of

this water falls back to the ocean while 10% moves and falls over land. When

averaged over all continental surfaces, about 65% of the precipitation falling

over land re-evaporates back to the atmosphere but in semi-arid areas the

proportion is higher. In Arizona, for instance, around 95% re-evaporates.

(b) Shuttleworth is talking about General Circulation models (GCMs). The

two components of these models he is referring to are the dynamics and the

physics. The dynamics applies conservation laws to calculate the fields of

atmospheric variables such as temperature, humidity and wind speed using

prescribed values for the divergence terms in these laws, see Chapters 16

and 17. The physics re-calculates the values of the divergence terms using

the (now modified) fields of atmospheric variables. Some of the processes

represented in the physics include radiation absorption, convection, and

precipitation processes in the atmosphere, and boundary layer and surface

exchange processes

(c) If all the Earth’s continents were clustered at the equator the seasonality of

the global average surface reflection coefficient for solar radiation, i.e. the

global average albedo, might well be less because, being on average warmer

than at present, they would presumably experience less snowfall. The

change in albedo associated with seasonal variations in snow and ice cover

is large because the albedo of fresh snow is around 80% while that for most

natural surfaces is around 20%. Alternative reasons for reduced seasonality

in global albedo include the possibility of reduced seasonal changes in the

vigor of the vegetation covering the continents.

(d) Shuttleworth is referring to the fact that the processes giving rise to

precipitation above, but comparatively close to the Earth’s surface, release

water vapor from the atmosphere and return it to the ground as precipitation,

which at the same time releases latent heat in the atmosphere. On average,

they therefore have the dual effect of reducing the lapse rate in the atmospheric

boundary layer so it is less than the adiabatic lapse rate while simultaneously

ensuring that atmospheric water vapor largely remains fairly near the surface.

(e) Presumably Shuttleworth is talking about GCMs again, because GCMs

have three main applications, namely (i) weather forecasting, (ii) climate

forecasting, and (iii) the synthesis of model-calculated fields of atmos-

pheric and surface variables across the entire globe as a by-product of

application (i). Weather forecasting seeks to predict actual weather a few

days ahead from well-defined initial conditions that may become the data

product (iii). In the case of (ii), initiation is less important because in this

application it is not actual weather but rather the statistics of weather (i.e.,

climate) that is the objective.

(f) Shuttleworth is respectively referring to the specific heat and density of

water relative to that of air. This difference means that the water in oceans



absorbs and releases energy more slowly than air and this is the fundamental

basis for the seasonal predictions that are the focus of interest of the Climate

Prediction Center whose website is at http://www.cpc.noaa.gov. Even if

seasonal predictions were not possible, presumably short-term prediction

would still be possible, and weather forecast centers such as the National

Weather Service at http://www.cpc.noaa.gov would still exist.

(g) ‘Greenhouse warming’ is predicted to increase near-surface air tempera-

tures. Since 70% of the Earth is covered with ocean, this likely will increase

surface evaporation rates because the saturated vapor pressure is a strong

function of temperature. Putting more water into the air as water vapor will

likely enhance the Earth’s overall hydrologic cycle by increasing the moisture

available for release by precipitation processes. At first sight, the effect will be

greatest at the poles because the projected temperature increases are greatest

there. However, saturated vapor pressure is a non-linear function of tem-

perature and the rate of change in saturated vapor pressure with temperature

is more than twice as large at 29°C (typical of sea surface temperature at the

equator) than it is at 0°C (typical of sea surface temperature at the poles).

Answer 5

The answers below give one opinion but, as is generally the case in politics,

different people have different opinions. If your opinions differ, discuss them with

your instructor.

(a) The RWD Party is probably using the banner C. Malleable has Hadley

Circulation similar to on Earth. Having looked through a telescope at their

sister planet, RWD Party followers notice that the resulting falling air

currents at approximately 30°N and 30°S of the equator suppress the

formation of precipitation and give rise to warm deserts when this occurs

over continents, e.g. the Sahara Desert. Their proposal is to remove the

continents at this band of latitudes.

(b) The RTS Party is probably using the banner A. The oceans on Malleable are

currently arranged to inhibit the inclusion of cold polar water in oceanic

circulation towards the equator. Looking through a telescope, followers of

the RTS Party notice that on their sister planet Earth, there is a marked

difference in the general shape of continental areas between the two

hemispheres. Those in Earth’s Northern Hemisphere are similar to those

on Malleable and inhibit inclusion of polar water in oceanic circulation.

However, the more open nature of the continents in the Earth’s Southern

Hemisphere allows cold polar water to penetrate towards the equator in the

western Pacific and Atlantic oceans. On average, this reduces the sea

surface temperature of equatorial western oceans in the Earth’s Southern

Hemisphere, and this in turn inhibits the production of tropical storms in

these regions. The RTS Party argues for opening the channels that link



polar and tropical oceans on Malleable so as to encourage the inclusion of

colder water towards their planet’s tropical oceans via oceanic circulation.

(c) The MM Party is probably using the banner B. Looking through a telescope,

followers of the MM Party notice that on their sister planet Earth there is

strong hydroclimatic feature that involves a marked seasonal reversal in

wind direction between areas on land and ocean. By listening in to the

radio broadcasts of weather services on Earth they learn this is called a

Monsoon. They notice that when the land surface is preferentially heated

by the shifting axis of rotation of the Sun there is a seasonal flow which

brings moisture over land that falls as precipitation in some months and

this is useful for growing agricultural crops. They also notice the effect is

greater when the flow is between a warm tropical ocean and large areas of

land that have a boundary which lies roughly parallel to the equator, e.g.,

the Indian Ocean and the continent of Asia. They are therefore suggesting

the continents on Malleable are arranged to favor such Monsoon flows.

(d) The RWD Party’s argument for the REN Party forming a coalition with

them is quite strong. They point out that relative to the existing continental

distribution, their proposed redistribution will significantly reduce the

portion of Malleable’s tropical ocean in which the Trade Winds can estab-

lish ‘warm pools’. The REN Party is negotiating for a bigger proportion of

the available land area at the equator but is facing opposition from the more

conservative faction of the RWD Party who have grown up in cooler cli-

mates with marked seasons.

(e) The RTS Party’s argument for the REN Party forming a coalition with them

is also reasonably convincing. They point out that their proposal will much

lessen the distance the Trade Winds have to establish ‘warm pools’ because of

the reduced distance between their four (as opposed to two) continents, and

because each proposed continent has more land area at the equator relative to

the existing continents. The REN party is negotiating for yet more continents

with more of their land area at the equator if they agree to form a coalition.

Answer 6

(a) Solar radiation heats the atmosphere from below, while it heats the oceans

from above. This results in a buoyant mixed layer on the surface of the

oceans which is typically 100–1000 m deep, and separated from the lower

ocean by the thermocline. The oceanic structure is fairly constant in time

in tropical regions, but the mixing layer changes depth with season at mid-

latitudes, being shallower and warmer in summer months when surface

heating is greater and the ensuing buoyancy of the surface water is greater.

(b) The student was a ‘Northo-centralist’ and was wrong. She should have said

‘ocean currents tend to go away from the equator on the eastern sides of

continents, and towards the equator on the western side of continents.’

(c) The near-surface mixed layer circulation of the oceans is primarily influ-

enced by the prevailing low level wind fields. The ocean, being massive, in



effect acts like a filter, picking out and following the average wind flow. Sea

water tends to be blown easterly near the equator and westerly at mid-lati-

tudes, and the near-continent currents are formed as part of this circula-

tion. But nothing is quite that simple in the global system and thermocline

circulation caused by changes in density, mainly salt concentration, and

Coriolis acceleration also play a role.

(d) This is actually a very complex problem, but shape of the land masses sur-

rounding oceans clearly influence the surface currents of oceans. In par-

ticular, the presence of substantial land at high latitude tends to inhibit the

linkage between (say) the Atlantic Ocean and cold polar waters, see answer

7(b). South America and Africa tend to taper towards the south pole

(unlike in the north Atlantic) and there is little land south of 40 degrees

south. The Benguela current in the South Atlantic (like the Peru current in

the Pacific) can access cold polar water more easily than the Canary current

in the North Atlantic, and this results in a lower SST at about 10-20 degrees

from the equator in the eastern portion of the ocean.

Tropical storms and hurricanes are formed in a region about 10–20 degrees

north and south of the equator (because there is not enough Coriolis force

at the very low latitude), and initially tend to move east to west in the

prevailing Trade Winds. The SST in central and eastern portions of 10–20

degrees north of the equator in the Atlantic is warmer than the 26.5 degrees

required for formation of tropical cyclones for a substantial portion of the

year, and the islands of the Caribbean suffer in consequence. But south of

the equator the equivalent phenomenon is suppressed by the cooler SST in

the eastern tropical Atlantic, and partly because of this and partly because

it is nearer to the equator, the climate of northeastern Brazil, though still

subject to oceanic influence, is spared.

(e) The student realized that the relative proportion of surface radiation used

to evaporate water over the oceans is greater than over land where more is

used to warm the lower atmosphere. The yearly cycle in near-surface tem-

perature is therefore greater over land surfaces than it is over oceans, and

this seasonal temperature differential (between the Asian continent and the

Indian ocean) is the driving mechanism behind the South East Asian mon-

soon, which is a major hydroclimatological influence on that region of the

world where a large portion of human population is concentrated.

(f) For clouds to occur not only must there be a mechanism that gives ascent

and cooling, but there must also be (i) sufficient moisture available in the

atmosphere, and (ii) cloud condensation nuclei (CCN) for cloud droplets

to form around. However, there are usually enough CCN available in the

air hence, choosing between these two, moisture availability is probably the

limiting requirement. However, quite often the atmosphere has both

enough CCN and enough moisture and the absence of an atmospheric

ascent mechanism is then the limiting criterion.

(g) The molecular weight of water molecules is less than the average molecular

weight of the mixture of oxygen and nitrogen molecules that make up dry



air. At the same temperature and pressure, the moister air has the same

number of molecules as the drier air, but some of the heavier air molecules

are replaced by lighter vapor molecules. Rearranging the Ideal Gas Law for

moist air, gives:

ra = [P/(R

d T)] / [1 + 0.61(r

v / r

a )] = [P/(R

d T)] / [1 + 0.61q]

Rd is a constant so assuming the temperature and pressure are the same, if

a parcel of air is moister than its surroundings (i.e. if q is greater) its density

is less than the surrounding air and it will tend to rise. It is the effect of

this greater buoyancy which is allowed for by re-expressing potential

temperature as virtual potential temperature.

(h) In convective conditions parcels of air heated to a temperature above that

of the surrounding atmosphere near the ground can often keep on rising to

the cloud condensation level because both the air in the parcel and the sur-

rounding air cool with height. However, the ascending air cools at the dry

adiabatic lapse rate and the surrounding air cools less quickly so there can

be situations where ascent is suppressed prior to reaching the level at which

water vapor in the rising air parcels saturates, see answer 1(d).

(i) Once at the cloud condensation level, condensation and cloud formation

begins. This releases latent heat which further warms the air thus tending

to make the air more buoyant and enhancing its further ascent within the

cloud.

(j) In mid-latitude clouds with a temperature of –25°C all the phases of water

(solid, liquid or vapor) are likely to be present. In such clouds the Bergeron-

Findeison process is likely to be the most important process responsible for

cloud particle growth.

Answer 7

(a) Very open situations are not necessarily always the best rain gauge sites

because near-ground wind speeds tend to be higher and wind-related

blow-in/blow-out gauge errors possibly higher. Consequently an optimum

site might be surrounded by obstructions but should be located in a flat

open area of short mown grass and should be sufficiently far from up-wind

of obstructions that they all subtend a vertical angle of less than 30°. Ideally,

the gauge would be placed at the center of a pit in the ground (say) 1–2 m

across such that the top of the gauge is level with the ground. This avoids

splash-in errors. The top of the pit should be covered with an open mesh

(plastic mesh is cheap and easy to find) so that it has a similar aerody-

namic roughness to that of the surrounding grass. If this is done the near-

surface wind flow is essentially parallel to the ground and the effect of

wind on the gauge is minimized. Such a site might look like that shown

in Fig. 26.9.



(b) Over the period 1961–1990 the monthly average precipitation for the

months January through December for Tucson were 0.87, 0.7, 0.72, 0.30,

0.18, 0.20, 2.35, 2.19, 0.67, and 1.07 inches, respectively. The seasonality

index calculated using Equation (13.1) from these values is 0.55, which

implies a rainfall regime that is fairly seasonal.

(c) The monthly average precipitation for the months January through

December for Tucson given in (b) are plotted as a pie diagram in Fig. 26.10.

(d) The percentage mass curve for the rainstorm is given in Fig. 26.11. About

50% of the rain during this storm falls in the first quarter of the storm and

about 90% in the first half of the storm which suggests the storm is of con-

vective origin.

(e) The mean value of July Tanzanian rainfall for the years 1931 to 1960 is

24.57 mm while the median value is 6.5 mm. The large difference between

these two is because the probability distribution is so heavily skewed, see

Figure 13.3.

(f), (g), and (h) The required plots of 7-year running mean, mass curve, and

cumulative deviation for Tanzanian July rainfall data are given in Fig. 26.12

(i) The area-average precipitation values the farmer calculated for his field in

April, May, and June were 9.26, 36.18, and 42.47 mm, respectively.

Surrounding obstructions subtendan angle of less than 30� with

respect to the ground.

Gauge set in pit with top at ground level,surrounded by a plastic grid to simulate the

aerodynamic roughness of surrounding area.

30�

Figure 26.9 Preferred

arrangement for a rain gauge site.

Figure 26.10 Monthly-average

precipitation for the months

January through December

for Tucson over the period

1961–1990 plotted as a pie

diagram.

2%3%

6%

6%

8%10%

6%

10%

6%

20%

21%

2%

Percentage precipitation per month for tucson

Jan.Feb.March.Apr.May.June.July.Aug.Sept.Oct.Nov.Dec.



00

20

40

60

80

100

20 40 60

Percentage of time during storm

Percentage mass curve

80 100

Per

cent

age

of r

ainf

all d

urin

g st

orm

Figure 26.11 Mass curve for

the precipitation during a

storm measured using a siphon

rain gauge, see Fig. 26.2 and

Table 26.2.

7-year running mean80(a) (b)

(c)

70

60

50

40

30

20

10

0

Pre

cipi

tatio

n (m

m)

Mass curve800

700

600

500

400

300

200

100

0

Cum

mul

ativ

e pr

ecip

itatio

n (m

m)

Cummulative deviation100

50

0

−50

−100

−150

−200

−250

−300

1 6 11 16 21 26

Cum

mul

ativ

e de

viat

ion

(mm

)

Figure 26.12 The required (a) 7-year running mean values, (b) mass curve, and (c) cumulative deviation for Tanzanian

July rainfall data given Table 13.3 (a).



Answer 8

(a). Start from Equation (16. 46), the basic equation for conservation of water

vapor in the atmosphere, i.e.

∂ ∂ ∂ ∂ ∂ ∂ν∂ ∂ ∂ ∂ ∂ ∂ ∂

⎡ ⎤∂+ + + = + + + +⎢ ⎥

⎣ ⎦

2 2 2

2 2 2

qq

a a

Sq q q q q q q Eu v wt x y z x y z r r

and expand the variables u, q and ra as mean and fluctuating part, thus:

( ) ( )

∂ ∂ ∂ ∂∂ ∂ ∂

∂ ∂ ∂∂ ∂ ∂

+ ′ + ′ + ′ + ′+ + ′ + + ′ + + ′

∂⎡ ⎤+ ′ + ′ + ′

= + + + +⎢ ⎥+ ′ + ′⎣ ⎦

2 2 2

2 2 2

( ) ( ) ( ) ( )( ) ( ) ( )

( ) ( ) ( ) qq

a a a a

q q q q q q q qu u v v w w wt x y z

Sq q q q q q Ex y z

nr r r r

Multiply out and separate the factors, thus:

( ) ( )2 2 2 2 2 2

2 2 2 2 2 2

'

qq

a a a a

q q q q q qq q q qu u u u v v vt t x x x x y y y y

Sq q q q q q q q q q Ew w w wz z z z x x y y z z

′ ′⎡ ⎤ ⎡ ⎤ ⎡ ⎤′ ′ ′+ + + + + ′ + + + ′ + ′⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦ ⎣ ⎦′ ′ ⎡ ⎤⎡ ⎤ ′ ′ ′

+ + + ′ + ′ = + + + + + + +⎢ ⎥⎢ ⎥+ ′ + ′⎣ ⎦ ⎣ ⎦

∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

n

nr r r r

Average this equation and apply the Boussinesq approximation (in this case this just

means using average values for density because there is no buoyancy term), thus:

∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

⎡ ⎤⎡ ⎤ ⎡ ⎤′ ′ ′ ′ ′⎢ ⎥+ + + + ′ + ′ + + + ′ + ′⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

⎡ ⎤ ⎡ ⎤′ ′ ′ ′ ′⎢ ⎥ ⎢ ⎥+ + + ′ + ′ = + + + + + + +⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

2 2 2 2 2 2

2 2 2 2 2 2

qq

a a

q q q q q q q q q qu u u u v v vt t x x x x y y y y

Sq q q q q q q q q q Ew w w wz z z z x x y y z z

n

nr r

Apply Reynolds averaging to eliminate terms 2, 4, 5, 8, 9, 12, 13, 16, 18, and 20 and

to eliminate overbars on already averaged terms, thus:

∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤′ ′ ′⎡ ⎤ + + ′ + + ′ + + ′ = + + + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦

2 2 2

2 2 2

qq

a a

Sq q q q q q q q q q Eu u v w wt x x y y z z x y z

n nr r

Re-order the terms and rewrite the viscosity term in vector format, thus:

∂ ∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂

⎡ ⎤′ ′ ′+ + + = ∇ + + − ′ + ′ + ′⎢ ⎥

⎢ ⎥⎣ ⎦2.

qq

a a

Sq q q q q q qEu v w q u v wt x y z x y z

nr r



Multiply Equation (17.17) (the divergence equation for turbulent fluctuations in

the Atmospheric Boundary Layer) by q′, take the time average, then substitute the

resulting equation into the final term in the last equation to give:

( ) ( ) ( )∂ ∂ ∂∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂

⎡ ⎤′ ′ ′ ′ ′ ′⎢ ⎥+ + + = ∇ + + − + +⎢ ⎥⎣ ⎦

2.q

qa a

S u q v q w qq q q q Eu v w qt x y z x y z

nr r

In Equations (26.1) and Equations (26.2) the terms that become negligible with

the assumptions given in the question are as follows.

(b) q

a

S

r

(c) a

Er

and −a p

Ecr

(d) ∇

− n

a p

Rcr

(e) ∇2.q qn and ∇2

qu q

(f) ∂∂q

wz

and ∂∂

wzq

(g) ∂

∂′ ′( )u qx

, ∂

∂′ ′( )qy

n,

∂∂

′ ′( )uxq

and ∂

∂′ ′( )

yn q

(h) ∂∂q

ux

, ∂∂qy

n , ∂∂

uxq

and ∂∂ yq

n

(i) After making all of the above simplifying assumptions Equations (26.1)

and (26.2) become:

∂ ∂ ∂ ∂∂ ∂ ∂ ∂

′ ′ ′ ′= − = −

( ) ( )and

q w q wt z t z

q q

(j) At level (i) the temperature will be warmer and the humidity will change little.

Recalling that the chain rule gives:

∂ ∂ ∂ ∂∂ ∂∂ ∂ ∂ ∂ ∂ ∂

∂ ∂ ∂∂ ∂ ∂

′ ′ ′ ′ ′ ′′ ′= ′ + ′ = ′ + ′

′ ′ ′ ′= ′ + ′

( ) ( ). . ; . . ;

( ). .

u q q v q qu uu q v qx x x y y y

q w q ww qz z z

The final term in Equation (26.5) can be re-written to give the required prognostic

equation for mean humidity in the atmosphere, thus:

∂ ∂ ∂ ∂ ∂ ∂ ∂∂ ∂ ∂∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

⎡ ⎤′ ′ ′′ ′ ′+ + + = ∇ + + − ′ + ′ + ′ + ′ + ′ + ′⎢ ⎥

⎢ ⎥⎣ ⎦2.

qq

a a

Sq q q q q q qE u v wu v w q u q v q w qt x y z x x y y z z

nr r

(26.5)



(k) At level (ii) the temperature will be warmer and the humidity will change

little.

(l) At level (iii) the temperature will be warmer and the humidity will change

little.

(m) At level (iv) the temperature will be cooler and the humidity will be wetter.

(n) At level (v) the temperature will change little and the humidity will change

little.

Answer 9

(a) At 20°C the molecular diffusion coefficients are υ = 1.52 × 10−5 m2 s−1,

DH = 2.15 × 10−5 m2 s−1, D

V = 2.42 × 10−5 m2 s−1, and D

C = 1.47 × 10−5 m2 s−1.

If the in-canopy wind speed, U, is 0.5 m s−1 for (spherical plate) leaves 0.05 m in

diameter the Reynolds number, Re, is 1649. Selecting the relevant empirical equa-

tion from Table 21.1, the Nusselt number, Nu ≈ 0.62 × Re 0.5 ≈ 0.62 × 41 ≈ 25. From

Equation (21.9), the boundary-layer resistance for heat transfer for (spherical

plate) leaves 0.05 m in diameter is RH (flat leaf) ≈ 0.05/(2.15 × 10 −5 × 24) ≈ 92 s m−1.

(b) For (cylindrical) needles leaves, the Reynolds number is 82 and the Nusselt

number, Nu ≈ 0.62 × 9.1 ≈ 5.6. From Equation (21.9) the boundary-layer

resistance for heat transfer for (cylindrical) conifer needles is RH (needle) ≈

0.0025/(2.15 × 10−5 × 5.6) ≈ 21 s m−1.

Assuming the transfer from individual vegetative elements is always by forced

convection and the relative transfer resistances for other exchanges is determined

only by their relative diffusion coefficients, see Equations (21.10) and (21.11), the

boundary-layer resistance for:

(c) vapor transfer for coniferous needles is RV (needle) ≈ 0.93 × 21 ≈ 19 s m−1.

(d) carbon dioxide transfer for coniferous needles is RC (needle) ≈ 1.32 × 21 ≈

27 s m−1.

(e) The required plots of the ratio of zero plane displacement to vegetation

height versus leaf area index and of aerodynamic roughness to vegetation

height versus leaf area index are shown in Fig. 26.13.

As additional leaf area is included in a canopy (of fixed height) a progressively

greater proportion of the momentum is lost higher in the canopy – the limit of infinite

LAI it is equivalent to raising the ground to the level by h. Initially this additional leaf

area raises the aerodynamic roughness above that of the bare soil by putting taller

roughness elements into the air stream. However, after the canopy begins to ‘close’

(when LAI is around one) and becomes denser and denser, depressions in the top of

the canopy become less significant and the aerodynamic roughness progressively falls.

When LAI = 4 the values of (d/h) and (zo/h) required for use in (f) are 0.73 and

0.08, respectively.

(f) The required plot of the aerodynamic resistance for a 10 cm high grass

stand, a 1 m high crop stand, and a 30 m high forest stand (all with LAI = 4)

is given in Fig. 26.14. Notice the large difference between these values of



2

LAI (dimensionless)

3 4 5

1.0(a)

(b)

0.8

0.6

0.4

0.2

0.00 1

d/h

(dim

ensi

onle

ss)

2

LAI (dimensionless)

3 4 5

0.15

0.10

0.05

0.000 1

z0/h

(di

men

sion

less

)

Figure 26.13 (a) Ratio of zero

plane displacement to vegetation

height versus leaf area index, and

(b) aerodynamic roughness to

vegetation height versus leaf area

index calculated in question 9(e).

0 1 2 3 4

Wind speed (m s−1)

5 6 7 81

10

100

1000

Aer

odyn

amic

res

iste

nce

(s/m

)

Grass Crop Forest

Figure 26.14 Variation in

aerodynamic resistance for a

10 cm high grass stand, a 1 m

high crop stand, and a 30 m high

forest stand all with LAI = 4

calculated in question 9(f).



aerodynamic resistance as the height and roughness of the vegetation

stands increase.

(g) The required plots of gR, g

D, and g

T are given in Fig. 26.15.

(h) The required plots of gR, g

D , and g

T and the total stress function ( g

R g

D g

T g

M ,)

through the day are given in Fig. 26.16.

(i) The required plots of available energy, latent heat and sensible heat fluxes

are given in Fig. 26.17.

1.0

0.8

0.6

0.4

0.2

0.0

g s (

dim

ensi

onle

ss)

0 200 400 600 800 1000

1.0

0.8

0.6

0.4

0.2

0.0

g D (

dim

ensi

onle

ss)

0 1 2

VPD (k Pa)

3 4

1.0

0.8

0.6

0.4

0.2

0.0

g T (

dim

ensi

onle

ss)

0 105 20 2515Temperature ( �C)

30 4035

Solar Radiation (W m−2)

(c)

(b)

(a)


stomatal conductance stress

factor associated with

(a) radiation, (b) vapor pressure

deficit, and (c) temperature

calculated in question 9(g).



Answer 10

The spreadsheet calculations (equivalent to Tables 23.1, 23.2, 23.3 23.4 and 23.6)

made using the data for the three sites in Australia are given in Tables 26.7(a),

26.7(b), 26.7(c), 26.7(d), and 26.7(e), respectively.

1.0

0.8

0.6

0.4

0.2

0.00 6 12

Time (hrs)18 24

Radiation

Temperature

VPD

Total

Str

ess

Fac

tor

(dim

ensi

onle

ss)

Figure 26.16 Variation in gR,

gD and g

T and the total stress

function (gR, g

D g

T g

M,)

through the day calculated

in question 9(h).

800

700

600

500

400

300

200

100

0

−1000 6 12

Time (hrs)

18 24

Available EnergyLatent Heat

Sensible Heat

Ene

rgy

Flu

x (W

m−2

)


available energy, latent heat and

sensible heat fluxes through the

day calculated in question 9(i).


Table 26.7(b) Daily average net radiation for a crop calculated at three Australian sites

in question 10.


Day of year (none) 40 46 52Eccentricity factor (none) 1.0255 1.0232 1.0206Solar declination (radians) −0.2688 −0.2355 −0.1998Sunset hour angle (radians) 1.6691 1.6387 1.7033Latitude (deg) −19.62 −15.78 −33.13Latitude in radians (radians) −0.3424 −0.2754 −0.5782Extraterrestrial solar radiation (mm day−1) 16.61 16.34 15.68Cloud fraction (none) 0.40 0.10 -Solar at ground (cloudy sky) (mm day−1) 9.14 11.44 -Number of bright sunshine hours (hours) - - 4.00Maximum daylight hour (hours) - - 13.01Solar at ground (cloudy sky) (mm day−1) - - 6.33Solar at ground (cloudy sky) (mm day−1) 9.14 11.44 6.33Selected value for Albedo (none) 0.23 0.23 0.23Net solar radiation (mm day−1) 7.04 8.81 4.88Vapor pressure (k Pa) 1.863 1.593 1.313Effective emissivity (none) 0.149 0.163 0.180Solar at ground (clear sky) (mm day−1) 12.46 12.26 11.76Assigned site humidity (none) Humid Arid HumidCloud factor (none) 0.733 0.910 0.538Average temperature (°C) 23.50 28.20 17.25Net longwave (mm day−1) −1.68 −2.44 −1.37Net radiation (mm day−1) 5.35 6.37 3.51

Table 26.7(a) Daily average air temperature, saturated vapor pressure, vapor pressure,

vapor pressure deficit, and wind speed at 2 m calculated at three Australian sites in

question 10.


Maximum air temperature (°C) 29.10 35.00 23.00Minimum air temperature (°C) 17.90 21.40 11.50Average temperature (°C) 23.50 28.20 17.25Sat. vapor pressure (Max. temp) (kPa) 4.029 5.623 2.809Sat. vapor pressure (Min. temp) (kPa) 2.051 2.549 1.357Average sat. vapor pressure (kPa) 3.040 4.086 2.083Wet bulb psychrometric constant (kPa °C −1) 0.066 - -Dry bulb temperature (°C) 24.00 - -Wet bulb temperature (°C) 19.00 - -Vapor pressure (kPa) 1.863 - -Relative humidity (%) - 39 -Vapor pressure (kPa) - 1.593 -Dew point (°C) - - 11.00Vapor pressure (kPa) - - 1.313Vapor pressure deficit (kPa) 1.177 2.492 0.770Wind measurement height (m) 10.00 10.00 2.00Wind speed (m s−1) 5.60 4.70 3.70Modified wind speed (m s−1) 4.19 3.51 3.70


Table 26.7(c) Daily average open water evaporation calculated at three Australian sites

in question 10.


Average temperature (°C) 23.50 28.20 17.25Vapor pressure deficit (kPa) 1.177 2.492 0.770Modified wind speed (m/s) 4.19 3.51 3.70Solar at ground (cloudy sky) (mm day−1) 9.14 11.44 6.33Net longwave (mm day−1) −1.68 −2.44 −1.37Elevation (m) 12 44 30Air pressure (kPa) 101.16 100.78 100.95Latent heat (MJ kg−1) 2.446 2.434 2.460Delta (kPa °C −1) 0.1740 0.2217 0.1243Psychrometric constant (kPa °C −1) 0.0672 0.0674 0.0668Selected value for Albedo (none) 0.08 0.08 0.08Net solar radiation (mm day−1) 8.41 10.52 5.82Net radiation (mm day−1) 6.72 8.09 4.46Open water evaporation (mm day−1) 7.65 10.63 5.00

Table 26.7(d) Reference crop evaporation using the FAO, radiation-based, temperature-

based and pan-based methods calculated at three Australian sites in question 10.


Maximum air temperature (°C) 29.10 35.00 23.00Minimum air temperature (°C) 17.90 21.40 11.50Average temperature (°C) 23.50 28.20 17.25Vapor pressure deficit (kPa) 1.177 2.492 0.770Modified wind speed (m s−1) 4.19 3.51 3.70Extraterrestrial solar radiation (mm day−1) 16.61 16.34 15.68Net radiation (mm day−1) 5.35 6.37 3.51Assigned site humidity (none) Humid Arid HumidLatent heat (MJ kg−1) 2.446 2.434 2.460Delta (kPa °C−1) 0.1740 0.2217 0.1243Psychrometric constant (kPa °C−1) 0.0672 0.0674 0.0668Measured pan evaportion (mm) 7.6 11.2 4.9Value of Cp in Equ. (23.24) (s m−1) 224 224 224Value of (Apan/Arc) (none) 1.15 1.15 1.15Modified psychrometric const. (kPa °C−1) 0.1600 0.1456 0.1484rclim assigned in Equ. (23.26) (s m−1) 40 76 49Default pan coefficient (none) 0.88 0.82 0.88Wind corrected pan factor (none) 0.77 0.77 0.79Ref. Crop Evap. (FAO) (mm day−1) 5.78 8.62 3.75Ref. Crop Evap. (radiation based) (mm day−1) 4.87 8.50 2.87Ref. Crop Evap. (temperature based) (mm day−1) 5.28 6.38 4.29Ref. Crop Evap. (pan: default Kp) (mm day−1) 6.69 9.18 4.31Ref. Crop Evap. (pan: wind corr. Kp) (mm day−1) 5.85 8.59 3.87



Table 26.7(e) Daily average evaporation from unstressed crops calculated using the

Matt-Shuttleworth approach and the FAO crop factor method for an alfalfa crop, a

cotton crop, and a sugar cane crop calculated at three Australian sites in question 10.


Average temperature (°C) 23.50 28.20 17.25Vapor pressure deficit (kPa) 1.177 2.492 0.770Modified wind speed (m s−1) 4.19 3.51 3.70Extraterrestrial solar radiation (mm day−1) 16.61 16.34 15.68Net radiation (mm day−1) 5.35 6.37 4.20Assigned site humidity (none) Humid Arid HumidAir pressure (kPa) 101.16 100.78 100.95Latent heat (MJ kg−1) 2.446 2.434 2.460Delta (kPa °C−1) 0.1740 0.2217 0.1243Psychrometric constant (kPa °C−1) 0.0672 0.0674 0.0668Modified psychrometric constant (kPa °C−1) 0.1600 0.1456 0.1484Ref. Crop Evap. (FAO) (mm day−1) 5.78 8.62 3.75rclim (s m−1) 53 73 76(D50 / D2) (none) 1.21 1.28 1.19

Alfalfa cropCrop factor (none) 0.95 0.95 0.95Rc

50 (none) 196 196 196(rs)c (s/m) 127 127 127Re-modified psychrometric constant (kPa °C−1) 0.2494 0.2210 0.2270Matt-Shuttleworth estimate (mm day−1) 5.22 8.55 3.39FAO estimate (mm day−1) 5.49 8.19 3.56

CottonCrop factor (none) 1.18 1.18 1.18Rc

50 (none) 162 162 162(rs)c (s/m) 60 60 60Re-modified psychrometric constant (kPa °C−1) 0.1713 0.1552 0.1584Matt-Shuttleworth estimate (mm day−1) 7.17 11.36 4.77FAO estimate (mm day−1) 6.82 10.17 4.42

Sugar CaneCrop factor (none) 1.25 1.25 1.25Rc

50 (none) 124 124 124(rs)c (s/m) 63 63 63Re-modified psychrometric constant (kPa °C−1) 0.1673 0.1518 0.1924Matt-Shuttleworth estimate (mm day−1) 6.87 10.82 5.15FAO Estimate (mm day−1) 7.22 10.77 4.69


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Terrestrial Hydrometeorology (Shuttleworth/Terrestrial Hydrometeorology) || Example Questions and Answers