Cven3501 Week 2 notes

CVEN3501 Water Resources Engineering

Fiona Johnson [email protected]

) EV#(+R#,'+N #N- EV#(+,R#N$('R#,'+N ).1 'ntroduction Water is re%oed fro% the surface of the earth to the at%os/here !" two distinct %echanis%s  ea/oration and trans/iration. oth descri!e a /rocess where!" i2uid water is transfor%ed to a gas water a/our4. ,his re2uires arge a%ounts of energ". ,herefore driing force !ehind a ea/oration is the 2uantit" of energ" receied fro% the sun. ,his is wh" we hae coered the energ" !aance of the earth in detai in the /reious sections. Ea/oration can so%ewhat o!ious"4 on" occur where and when i2uid water is aaia!e. 't aso re2uires that the at%os/here is not saturated so that the water a/our has so%ewhere to go once it eaes the surface. ,his cha/ter discusses the %echanis%s for ea/oration and ea/otrans/iration and %ethods for cacuating its contri!ution to the water c"ce. ,he i%/ortance of ea/oration can !e seen fro% the data in ,a!e )*1 which ists %onth" aerage rainfa and ea/oration for $"dne". ,he two fues are er" si%iar& indicating that runoff and infitration coud !e second order /rocesses. Table 2-1 Mean monthly distribution of rainfall and pan evaporation for Sydney (Australian Bureau of Meteorology, Stn 002!

Month

Mean "ainfall (mm!

Mean #an $vaporation (mm!

Januar"

101.1

16).7

Fe!ruar"

118.0

109.)

:arch

1)9.;

97.1

#/ri

1);.1

;8.0

:a"

119.9

58.9

June

13).0

37.0

Ju"

9;.6

67.5

#ugust

80.;

58.9

$e/te%!er

78.3

;5.0

+cto!er

;7.9

10).3

Noe%!er

83.9

1)9

-ece%!er

;;.7

137.6

1)11.8

1058.5

#nnua

#erage annua /reci/itation and ea/oration data for #ustraia is shown in Figure )*1 and Figure )*) sourced fro% the #ustraian ureau of :eteoroog" htt/<==www.!o%.go.au=ci%ate=aerages=%a/s.sht% htt/<==www.!o%.go.au=ci%ate=aerages=%a/s.sht%4. 4. 't can !e seen that for %an" /arts of #ustraia ea/oration is %uch arger than the rainfa. ,he tota ea/oration fro% continenta areas around the word is a//roi%ate" ;0> of tota /reci/itation oer the continents. 'n #ustraia the ratio is %uch arger with ea/oration accounting for a//roi%ate" 90> of the tota rainfa that occurs oer the continent.

ased on notes !" #shish $har%a& 'an #cworth

(age )*1



Ea/oration is an i%/ortant /art of the water !aance and has arge i%/acts on %an" water resources s"ste%s. Ea/oration osses fro% reseroirs are a su!stantia /ercentage of the tota storage ca/acit" genera" around )0> "ied4 and in so%e cases can eceed 50>. Ea/oration and ea/otrans/iration are aso i%/ortant for agricuture. 't is therefore ita that we correct" %easure or esti%ate ea/oration.

%igure 2-1 Average annual rainfall for Australia for the period 1&1-1&&0 (Australian Bureau of Meteorology #rodu't ode ) *+M00!

%igure 2-2 Average annual pan evaporation for Australia for the period 1&.-200. (Australian Bureau of Meteorology #rodu't ode )*+M000!


(age )*)



).) '%/ortant definitions ,here are a nu%!er of ?e" ter%s when thin?ing a!out ea/oration and ea/otrans/iration.

$vaporation/ the a%ount of water that /asses or coud /ass into the at%os/here across a soi=air or water=air interface

Transpiration/ the /rocess !" which water is re%oed fro% egetation into the at%os/here !" ea/oration fro% the /ant sto%ates. #ternate"& trans/iration is the trans/ort of that water within the /ant and its su!se2uent reease as a a/our into the at%os/here.

$vapotranspiration/ the co%!ined /rocess of ea/oration and trans/iration. 't descri!es the a%ount of water that /asses into the at%os/here across the /ant=air interface. 't is often used interchangea!" with ea/oration. Co%%on" ea/oration refers to an o/en water surface or !are soi and ea/otrans/iration is used when referring to soi surfaces with /ants.

#otential evaporationevapotranspiration ($T 0!/ the %ai%u% a%ount of water that can ea/oration or trans/ire fro% a surface when water aaia!iit" is not i%iting i.e. a we*watered surface or an o/en water !od"4. (otentia ea/oration is i%ited !" the a%ount of soar radiation that is aaia!e and the ca/acit" of the air to receie %ore water.

A'tual evaporationevapotranspiration ($T a!/ the actua a%ount of water that is ea/orated into the air. 't is i%ited !" the a%ount of water aaia!e in the soi for the ea/oration rather than the %oisture hoding ca/acit" of the air. #ctua ea/oration is awa"s e2ua to or ess than /otentia ea/oration.

"eferen'e 'rop evapotranspiration ($Tr'!/ the rate of ea/otrans/iration fro% an ideaised grass cro/ with an assu%ed cro/ height 0.1) %4& a fied cano/" resistance ;0 s=%4 and a!edo 0.)34.

rop 'oeffi'ient ('!/ the ratio of ea/otrans/iration of an" /ant=cro/ co%/ared to the reference cro/ defined a!oe.

).3 (h"sics of ea/oration ).3.1 'ntroduction ,he ea/oration /rocess is the resut of an echange of %oecues !etween water and the at%os/here. With an increase in the water te%/erature& the ?inetic energ" of the water %oecue increases. ,his ena!es so%e of the% to esca/e fro% the surface. When in the a/our /hase& each %oecue is se/arate fro% the others !" a arge distance& and hence the h"drogen !onding /ro/erties of the %oecues are a !ut a!sent. $o%e of the esca/ed %oecues coo down and tr" to re*enter the water  this /rocess is ter%ed condensation. Ea/oration is the difference !etween the nu%!er of %oecues eaing and those re*entering the water !od". ,here is a er" thin a"er of saturated water just a!oe the water surface. ,his is for%ed due to the esca/e of water %oecues for% the water surface and aso the re*entr" of so%e %oecues. When %oecues esca/e this a"er to the air a!oe& s/ace is crated for %ore ea/oration fro% the water surface. ,his conce/t is re/resented !" -atons aw< E = C (es − ea )

)*1

Where E is the ea/oration& C is a coefficient and es is the saturation a/our /ressure at the current air te%/erature4 and ea is the saturation a/our /ressure at the dew /oint te%/erature. Re%e%!er that the saturation a/our /ressure at the dew /oint te%/erature e d4 is the sa%e as the actua a/our /ressure at the /resent air te%/erature e4. ,his %eans that in E2uation )*1 it is the difference !etween the saturation a/our /ressure and the actua a/our /ressure that dries ea/oration. #s the air !eco%es %ore saturated& ea or e4 e2uas es and the ea/oration tends to Aero. #s the hu%idit" in sois is often cose to 100> i.e. es e2uas ea4 there is itte ea/oration fro% !eow the soi surface.


(age )*3



$aturation a/our /ressure is a function of the te%/erature. 't is ow at ow te%/eratures and increases at an e/onentia rate fro% there as shown in Figure )*3. Bence war% air can hod a ot %ore water than cod air. #n a//roi%ate reationshi/ for the saturation a/our /ressure is<

 17.27T    237.3 + T 

es = 0.6108 exp

)*)

Where , is the air te%/erature in C and es is the saturation a/our /ressure in ?(a.

7

6 ) a P k ( e r u s s e r P r u o p a V d e t a r u t a S

5

4

3

2

1

-10

0

10

20

30

40

Temperature (deg C)

%igure 2- Saturation vapour pressure relationship 3ith air temperature

).3.) #//ications of ea/oration in h"droog" Ea/oration is i%/ortant for the design and o/eration of water storage reseroirs and for soi %oisture. 't there has an i%/act on strea%fows and catch%ent "ieds. Ea/oration is ess i%/ortant during stor% eents& first" !ecause the actua a/our /ressure is cose to saturation during /reci/itation and second" !ecause stor%s do not usua" hae a er" ong duration. Water resources %anagers can change the wa" that the" o/erate reguated rier s"ste%s to ensure that the ea/oration osses are %ini%ised. For ea%/e it is !etter to reease water fro% a da% in arger 2uantities ess fre2uent" than to constant" reease s%aer a%ounts. ,his is !ecause the water de/ths in the rier wi !e shaower when s%aer a%ounts are reeased so the surface area to ou%e ratio wi !e higher and %ore ea/oration wi resut. #n ea%/e is the %anage%ent of :enindee Da?es in western New $outh Waes where o/eration of the a?es is !eing studied to %ini%ise ea/oration osses htt/<==www.water.nsw.go.au=Water* %anage%ent=Water*recoer"=-aring*$aings=-aring*water*saing 'n so%e cases& ea/oration can !e su//ressed !" /acing a thin fi% of certain che%ica e.g. cet" acoho4 that s/read oer the water surface and can reduce ea/oration !" as %uch as ;0>. Boweer the che%ica a"er can !e disru/ted !" wind and dust and can !rea? u/. ,his o/tion is therefore on" /ractica!e for s%a da%s where wind effects are %ini%a. roundwater storage da%s hae aso !een found to !e effectie in so%e arid areas where!" the da% is fied with sand or other reatie" /orous %ateria. Water is stored in the /ore s/aces and ea/oration is reduced.


(age )*6



nowedge of ea/oratie /rocesses has aso !een used to dis/ose of conta%inated water !" /acing it is in arge ea/oratie /onds. ,his sto/s the conta%inated water fro% running off or entering groundwater. ,he /onds are designed to !e shaow to increase the ea/oration rate. Ea%/es incude !rine fro% desaination /ants& waste water treat%ent /ants or %ine taiing water.

).6 Ea/oration %easure%ent ).6.1 Ea/oration /an ,he Cass # ea/oration /an is /ro!a!" the %ost wide" used instru%ent around the wod to %easure /otentia ea/oration. ,he Cass # /an is 1)0.; c% in dia%eter and )5 c% dee/ and is constructed fro% gaanised %eta. ,he /an is /aced in an o/en area and fenced to s/ot ani%as drin?ing fro% it. ,he water ee in the /an is %aintained at a constant de/th !" adding or su!tracting water fro% the /an each da". ,he ea/oration is cacuated !" considering a si%/e water !aance !" using the change in de/th of the water in the /an and the rainfa that has occurred in the /reious )6 hours. ,he surface of the /an can either !e eft o/en or a !ird gri added. When gris were added to /ans around #ustraia& ea/oration was decreased on aerage !" around ;>. Dong ter% records hae !een ho%ogenised to account for this error. # Cass # /an is shown in Figure )*6.

%igure 2- lass A evaporation pan in To3nsville (http/3334bom4gov4au5ldto3nsvilleimages$vap6#an6.047pg !

,he /an heats u/ %ore ra/id" than the ground around it and there are aso the side was of the /an which can receie so%e soar radiation. ,herefore ea/oration fro% a /an wi !e higher than fro% the eniron%ent. # correction factor is therefore nor%a" used to conert the /an ea/oration %easure%ent into true /otentia ea/oration. ,his /an factor is nor%a" !etween 0.7 to 0.8 and de/ends on the soi t"/e& surrounding egetation and ci%atic conditions. ,he /an coefficient can !e cai!rated for sites where enough data eists to aso direct" cacuated o/en water !od" ea/oration using the (en%an e2uation. 'n the a!sence of a oca" cai!rated aue& a ta!e of /an coefficients is /roided !" Allen et al. G1998H. htt/<==www.fao.org=docre/=I0690E=0690e08.ht%/an>)0ea/oration>)0%ethod Ksing this ta!e and aerage wind s/eed 3.7 %=s4 and reatie hu%idit" 75>4 for $"dne" a /an coefficient of 0.; woud !e chosen assu%ing 10 % of short green grass adjacent to the /an4.


(age )*5



,he e2uation to use the /an coefficient ?/an4 is< ET 0 = k pan × E pan

)*3

).6.) D"si%eter # "si%eter is a tan? of soi which is /anted with egetation and is h"droogica" seaed so that the water ea?age fro% the s"ste% is negigi!e. 't is used to %easure ea/otrans/iration in the fied and for stud"ing soi*water*/an reationshi/s under natura conditions. ,he "si%eter shoud !e re/resentatie of the surrounding natura soi /rofie and egetation t"/es. ,he rate of ea/otrans/iration fro% this instru%ent is o!tained !" underta?ing a soi water !udget. ,he /reci/itation on the "si%eter& the drainage through its !otto%& and the changes in soi %oisture within the "si%eter are a %easured. ,he a%ount of ea/otrans/iration is the a%ount necessar" to co%/ete the water !aance.

).6.3 Edd" coariance %easure%ent 'f the energ" fues at a site can !e %easured then ea/oration can !e cacuated direct". ,he ertica fuctuations of the wind and water a/our are %easured and then their correations cacuated oer so%e aeraging /eriod around 15 %inutes to an hour4.

't is on" in the ast 10 to 15 "ears that suita!e

instru%entation has !eco%e co%%ercia" aaia!e. Boweer the instru%entation is e/ensie and re2uires s/ecia s?i to o/erated and therefore this %ethod is on" used in research e/eri%ents. 't is the /referred %icro%eteoroogica techni2ue on the grounds that it is a direct %easure%ent with %ini%u% theoretica assu%/tions. # %a/ showing the ocations of edd" coariance stations in #ustraia is in Figure )*5.

%igure

2-.

8et3or

of

meteorologi'al

flu9

stations

in

Australia

and

8e3

:ealand

(http/3334o;flu94org4aumonitoringsitesinde94html!

).5 Ea/oration cacuations #s can !e seen fro% the %ethods a!oe the %easure%ent of ea/oration is a!our intensie and e/ensie. ,herefore in %ost cases ea/oration is cacuated !" considering the /h"sica reationshi/ !etween different ci%atic aria!es and the ea/oration rate. ,here are a nu%!er of different %ethods for cacuating ea/oration=ea/otrans/iration and a co%/rehensie reiew of the different %ethods is /roided !" McMahon et al. G)013H. 'n genera the %ethods can !e cassified as<

•

te%/erature*!ased %ethods


(age )*7


•

radiation*!ased %ethods

•

co%!ination %ethods resistance /us energ"4


'f a the re2uired ci%atic data are aaia!e then the (en%an :onteith %ethod a co%!ination a//roach4 is reco%%ended as the %ost accurate a//roach. -etais of this %ethod are /roided in the net section.

).5.1 Energ" !aance to drie e a/oration #s discussed a!oe ea/oration is drien !" energ" aowing water %oecues to esca/e fro% the water surface. ,herefore the genera /rinci/e of cacuating ea/oration is to use consider the energ" !udget. ,he aaia!e energ" A is the energ" !aance<

 =  − 

)*6

Where

•

# is #aia!e Energ"

•

Rn is Net 'nco%ing Radiation i.e. considering the soar and ongwae radiation co%/onents and directions4

•

 is the outgoing heat conduction into the soi

Knder %ost conditions the ter%s $& ( and # d are negected. ,he te%/orar" soi ou%e energ" $4 needs to !e considered when the energ" !aance is oer a forest. +er the course of a da"  is a//roi%ate" e2ua to Aero so can aso genera" !e negected if dai" ea/oration esti%ates are re2uired. ,herefore the aaia!e energ" can !e a//roi%ated as the net radiation. #s shown in E2uation )*5& the aaia!e energ" A can !e /artitioned into two co%/onents  sensi!e heat B and atent energ" λE i.e. the outgoing energ" in the for% of ea/oration4

 =  + 

)*5

,hus if there is i%ited water aaia!e for ea/oration& the sensi!e heat /artition wi !eco%e arger and the air te%/eratures wi !e higher. ,he ratio !etween sensi!e heat and atent heat is caed the owen Ratio and can !e used to su%%arise the aridit" of a ocation.

 = /

)*7

,a!e )*) ists owen ratios for a nu%!er of different ci%atic conditions. Table 2-2 Typi'al values of the Bo3en ration < Ladson, 200=>

onditions

Bo3en ratio

#rid conditions hot deserts4

10

$e%i*arid regions

)*7

,e%/erate forests and grass ands

0.6*0.8

,ro/ica rain forests

0.)

,ro/ica oceans

0.1

We watered short egetation with no wind and ow te%/eratures i.e. cose to Aero sensi!e heat fu4

L0

We watered egetation with ow hu%idit". 'n this case the eaf te%/erature can !e ess than the air te%/erature !ecause of ea/oratie cooing so the sensi!e heat is /roiding additiona energ" for ea/oration i.e. the owen ratio can !e negatie

M0


(age )*;



).5.) #aia!e energ" 'f we assu%e that the energ" oss to the ground is Aero reasona!e assu%/tion oer the course of a da" or onger4& then the aaia!e energ" is just the energ" !aance !etween the inco%ing and outgoing shortwae and ongwae radiation. A = Rn = Rns − Rnl

)*;

Where Rn is the net inco%ing radiation& R ns is the net shortwae radiation inco%ing  outgoing4 and R n is the net outgoing radiation inco%ing  outgoing4. #though oer the earth as a whoe& the net radiation is in !aance at an" one /oint and an" one ti%e& there wi !e an energ" in!aance and if the energ" in!aance is /ositie it wi ead to ea/oration and=or heating. We therefore need to !e a!e to cacuate the energ" in!aance at an" ocation and for an" ti%e of "ear !" finding the shortwae and ongwae radiation.

Short3ave (solar! radiation ,he etraterrestria soar radiation is the radiation receied at the to/ of the earths at%os/here on a horiAonta surface. 't changes throughout the "ear due to changes in the /osition of the sun and the ength of the da". 't is therefore a function of the atitude& date and ti%e of da". ,hese aues can !e su!stituted into *)

*1

the foowing e2uation to cacuate the etraterrestria soar radiation Ra :J % da" 4. R = a

118.1

π

(

)

d ω sin φ sin δ + cos φ cos δ sin ω r s s

)*8

where ωs re/resents the sunset hour ange<

ω s = arccos( − tan φ tan δ )

)*9

and φ is the atitude for the site negatie for $outhern Be%is/here4 with δ the soar decination in radians4& gien as<

 2π  J − 1.405   365 

δ = 0.4093 sin 

)*10

and J is the Juian da" nu%!er da" nu%!er fro% start of "ear4. ,he reatie distance !etween the earth and sun is cacuated as<

 2π  d = 1 + 0.033 cos J  r  365 

)*11

Not a the energ" at the to/ of the at%os/here reaches the earths surface and therefore soar radiation R s4 at the surface wi !e ess than etraterrestria soar radiation. +n a coudess da" cear s?" soar radiation R so4 is a//roi%ate" ;5> of the etraterrestria radiation. When there are couds the soar radiation wi !e een ower. $oar radiation Rs4 can !e cacuated using the #ngstro% for%ua< n   R = R  0.25 + 0.5  s a  N 

)*1)

Where n is the actua duration of sunshine hours4 and N is the %ai%u% /ossi!e duration of sunshine or da"ight hours hours4 cacuated as< N =

24

π

ω s


)*13

(age )*8



,he constants in the #ngstro% for%ua can ar" de/ending on ocation !ut the a!oe aues are reco%%ended !" Allen et al. G1998H in the a!sence of oca data. ,he net soar radiation Rns4 is the !aance !etween the inco%ing and refected soar radiation which is controed !" the a!edo 4. R = R (1 − α ) ns s

)*16

#n a!edo of 0.)3 is assu%ed for the reference cro/ discussed !eow4.

?ong3ave (terrestrial! radiation ,he ongwae energ" is descri!ed !" the $tefan*otA%ann aw which states that the energ" e%ission is /ro/ortiona to the a!soute te%/erature of the surface raised to the fourth /ower. Couds& water a/our& car!on dioide and dust can a!sor! the e%itted ongwae radiation and re*e%it towards earth. ,herefore net outgoing ongwae radiation wi !e s%aer when there is higher coudiness or hu%idit". ,his reationshi/ is shown in the foowing e2uation< 4 4  T max,    R K + T min, K   ( R = σ 0.34 − 0.14 ea ) 1.35 s − 0.35  nl   Rso 2    

)*15

Where< *)

*1

Rn is the net outgoing ongwae radiation :J % da" 4 *9

*)

*6

O is the $tefan otA%ann constant P 6.903  10 :J %  da"

*1

,%a& and ,%in& are the %ai%u% and %ini%u% dai" air te%/erature 4 ea is the actua a/our /ressure ?(a4 and Rso is found using<

(

)

−5 R = R 0.75 + 2 × 10 z so a

)*17

Where z is the station eeation % a!oe sea ee4. +nce again the constants in this e2uation can !e oca" cai!rated. :ore detais are /roided in Allen et al. G1998H.

8et radiation Net radiation is si%/" the difference !etween inco%ing net shortwae radiation and outgoing net ongwae radiation< Rn = Rns − Rnl

)*1;

+ther heat fues if significant4 are su!tracted fro% the net radiation in E2uation )*1; to arrie at the *)

*1

aaia!e energ" E2uation )*64. Note that the a!oe esti%ate is in :J % da" which can !e conerted to %% units !" diiding it !" the atent heat of a/orisation of water. ,he foowing conersion %a" !e used to conert energ" to other units< *)

*1

*)

1 :J % da" P 11.5; W % P 0.608 %% da"

*1

at )0°C4

)*18

).5.3 (en%an*:onteith e2uation Penman G1968H co%!ined the energ" !aance with the %ass transfer %ethod and deried an e2uation to

co%/ute the ea/oration fro% an o/en water surface fro% standard ci%atoogica records of sunshine& te%/erature& hu%idit" and wind s/eed. ,his so*caed co%!ination %ethod was further deeo/ed !" %an" researchers and etended to cro//ed surfaces !" introducing resistance factors.


(age )*9



#s was shown in E2uation )*1& ea/oration is controed !" the difference !etween the saturated a/our /ressure es and actua a/our /ressure ea e2uiaent to saturation a/our /ressure at the dew /oint te%/erature4. ,he a/our /ressure deficit is nor%a" denoted as - such that< D = es − ea

)*19

,he (en%an*:onteith a//roach is caed a co%!ination a//roach !ecause it cacuates ea/oration as the weighted co%!ination of the aaia!e energ" and the a/our /ressure deficit. ,he genera for% for the e2uation is therefore<

∆ A + ρ c p D λ E =

r a

∆ + γ (1 + r s r a )

)*)0

Where< λE is

*)

*1

the atent heat fu of ea/oration ?J % s 4 *1

E is the ea/oration rate % s 4 *1

λ is the atent heat of a/ourisation :J ?g 4 ∆ is the so/e of the saturated a/our /ressure  te%/erature cure which was shown in Figure )*3 *)

*1

# is the aaia!e energ" ?J % s 4 - is the a/our /ressure deficit ?(a4 *3

ρ is the densit" of air ?g % 4 c p is the s/ecific heat of %oist air ?J ?g

*1

*1

C 4 and is e2ua to 1.013

°

*1

rs is the surface resistance s % 4 *1

ra is the aerod"na%ic resistance s % 4 *1

γ is the /s"cho%etric constant ?(a C 4 °

,he so/e of the saturation a/our /ressure reationshi/ with res/ect to te%/erature is<

∆=

4098es

(237.3 + T )2

)*)1

,he atent heat of a/ourisation Q4 can !e cacuated using E2uation )*)) if the surface te%/erature of the water surface ,s4 in C is ?nown °

λ = 2.501 − 0.002361T s

)*))

Fina" the /s"cho%etric constant  γ4 is defined as<

γ = 0.00163

P

λ

)*)3

Where ( is the at%os/heric /ressure ?(a4. 'n the a!sence of data on at%os/heric /ressure an esti%ate can !e %ade using the site eeation A4 in units of %etres<

 293 − 0.0065 z  P = 101.3  293  

5.26

)*)6

,he co%!ination a//roach can !e seen %ore cear" if E2uation )*)0 is s/it into two co%/onents< ET 0 = ET rad + ET aero


)*)5

(age )*10



Where E,0 is the /otentia ea/otrans/iration and E,rad is the contri!ution fro% radiation energ" in/ut i.e. aaia!e energ"4 and E,aero is the contri!ution fro% the aerod"na%ic co%/onent drien !" the a/our /ressure deficit and adection fro% wind4. #ternatie" we can write the e2uation as< ET 0 = F A A + F D D

)*)7

'n this for% the weighting factors F# and F- de/end on whether ea/otrans/iration or o/en water !od" ea/oration is !eing cacuated. First" we wi oo? at the esti%ate for the reference cro/ ea/otrans/iration& and then with o/en water !od" ea/oration.

).5.6 (en%an*:onteith reference cro/ ea/otrans/iration #s descri!ed in the section on resistance a!oe& aerod"na%ic resistance wi ar" according to the /ant t"/e. ,herefore to standardise the esti%ates fro% the (en%an*:onteith e2uation& a reference cro/ has !een rc

*1

defined !" Allen et al. G1998H which has a surface resistance r c P ;0 s % . ,he reference cro/ is defined as a h"/othetica cro/ with a height of 0.1) % and an a!edo of 0.)3. ,he reference surface is assu%ed to !e of green grass of unifor% height which is actie" growing. '%/ortant" the cro/ is co%/ete" shading the ground and has ade2uate water so that it is for%s /otentia ea/otrans/iration conditions. ,he re2uire%ents that the grass surface shoud !e etensie and unifor% resut fro% the assu%/tion that a fues are one*di%ensiona u/wards G Allen et al.& 1998H. Ksing E2uation )*)0 and standard %eteoroogica o!serations and the infor%ation on the reference cro/& the reference cro/ ea/otrans/iration is esti%ated as<

900 0.408 ∆ A + γ u 2 D 273 + T ET rc = ∆ + γ (1 + 0.34 u 2 )

)*); *1

u) is the wind s/eed at ) % height % s 4 , is air te%/erature at ) % height  C4 °

*1

E,rc is reference cro/ ea/otrans/iration %% da" 4 *)

*1

*1

,he units for A shoud !e :J % da" and D in ?(a to gie the ea/otrans/iration in units of %% da" . Note *1

that the constant of 900 has units of ?J ?g . 'n /ractice actua a/our /ressure %a" not !e aaia!e if dew /oint te%/erature has not !een recorded4 and therefore it %a" need to !e cacuated fro% reatie hu%idit" %easure%ents. ecause the saturated a/our /ressure cure is non*inear& aerage saturated a/our /ressure cannot !e cacuated using aerage te%/erature. ,herefore aerage saturated a/our /ressure needs to !e cacuated using the %ini%u% and %ai%u% te%/eratures. Allen et al. G1998H reco%%ends the foowing /rocedures to esti%ate dai" aerage saturated and actua a/our /ressure es and ea res/ectie"4 o o es = 0.5 × e (T min ) + e (T max )

)*)8

o

Where e ,4 is the saturated a/our /ressure cacuated at a s/ecific te%/erature ,4 using E2uation )*) and ,%in and ,%a are the dai" %ini%u% and %ai%u% te%/eratures for which the a/our /ressures are cacuated. 'f %ai%u% and %ini%u% reatie hu%idit" data is aaia!e then the actua a/our /ressure e a4 is cacuated as< o o ea = 0.5 × e (T min ) × RH max + e (T max ) × RH min

)*)9

Where RB%a and RB%in are the %ai%u% and %ini%u% reatie hu%idites in >4 for the da". ,he idea is that the %ai%u% reatie hu%idit" genera" occurs in the %orning when te%/eratures are owest and the owest reatie hu%idit" occurs in the afternoon when te%/eratures are highest.


(age )*11



Refer to Allen et al. G1998H for detais of other %ethods to cacuate actua a/our /ressure in the a!sence of %ini%u% and=or %ai%u% reatie hu%idit" %easure%ents. 'f wind %easure%ents at a height of )% are not aaia!e& the foowing e2uation %a" !e used to conert %easure%ents fro% a height A% to corres/onding aues for a height of )%< u 2 = u z

ln(2 / 0.0023) ln( z m / 0.0023)

)*30

where uz is the wind s/eed %easured at a height of A %. Co%%on" wind s/eed %easure%ents are %ade at a height of 10 %.

).5.5 (en%an o/en water !od" ea/oration For o/en water !od" ea/oration the surface resistance can !e negected r s P 04 in E2uation )*)0 and thus the for% for the e2uation using standard %eteoroogica aria!es is< ET 0 =

∆ A + 6.43 γ ( 1 + 0.53u 2 ) D (∆ + γ )λ

)*31 *)

*1

#s for the reference cro/& the units for A shoud !e :J % da" and D in ?(a to gie the ea/oration in units of %% da"

*1

).5.7 +ther %ethods "adiation based e5uations ,he Priestley Taylor e2uation GPriestley and Taylor & 19;)H is a si%/er reationshi/ !etween reference cro/ ea/oration and the aaia!e energ"& eaing out the a/our /ressure deficit /art of the (en%an :onteith e2uation& on the !asis that the first ter% usua" eceeds the second !" a factor of four G Shuttleworth& 1993H. ,his is gien as< ET rc = α

∆A ∆ + γ

)*3)

where α has !een e%/irica" esti%ated as 1.;6 for arid ci%ates with reatie hu%idit" ess than 70> in the %onth with /ea? ea/oration and 1.)7 for hu%id ci%ates.

$mpiri'al e5uations ,here are a nu%!er of e%/irica" !ased e2uations& /articuar" !ased on te%/erature& that are wide" referenced or hae !een co%%on" used in the /ast G McMahon et al.& )013H. ,he /h"sica !asis for esti%ating ea/oration using te%/erature aone is that !oth radiation and a/our /ressure deficit are i?e" to hae so%e reationshi/ with te%/erature. 'n genera the on" justification of using esti%ation e2uations of this t"/e is that te%/erature is the on" aaia!e aria!e that has !een %easured. 'n this case it is unwise to %a?e ea/oration esti%ates for ess than a %onth" aeraging /eriod G Shuttleworth& 1993H. McMahon et al. G)013H aso reco%%end the use of /h"sica" !ased e2uations such as the (en%an*:ontheith %ethod4 shoud !e /referred co%/ared to the e%/irica reationshi/s  /articuar" for areas where the e%/irica coefficients were not deried. ,he ,hornthwaite %ethod GShaw & 1996H /roides esti%ates of /otentia ea/otrans/iration using on" %ean %onth" te%/erature data. ,he esti%ates are !ased on ci%atoogica aerage te%/eratures and therefore /roide a ci%atoogica esti%ate of ea/oration rather than true ea/oration for an" /articuar da" or %onth. a

 10T    I 

ET o = 16


)*33

(age )*1)



Where ' is a heat inde co%/uted using a %onth" aerage te%/eratures as< 1.514

 T j    I =  5 j =1   12

∑

)*36

#nd a is< −7 3

−5 2

−2

a = 6.75 × 10 I − 7.71× 10 I + 1.792 ×10 I + 0.49239

)*35

).5.; Cacuating actua ea/otrans/iration ,he water status of the soi is er" i%/ortant in esti%ating the actua ea/otrans/iration co%/ared to the /otentia ea/otrans/iration. ,his reationshi/ is shown !eow< ET a = f (θ ) ET o

)*37

# t"/ica reationshi/ for the soi %oisture etraction function is shown in E2uation .

 θ − θ wp   θ − θ wp    fc

f (θ ) = f 

)*3;

Where fc is the fied ca/acit" and  w/ is the witing /oint.

).7 References #en& R. .& D. $. (ereira& -. Raes& and :. $%ith 19984& Crop evapotranspiration  !uidelines "or computin# crop water re$uirements& F#+ * Food and #gricuture +rganiAation of the Knited Na%es& Ro%e. Dadson& #. R. )0084& %ydrolo#y& an Australian introduction& +ford uniersit" /ress. :c:ahon& ,.& :. (ee& D. Dowe& R. $ri?anthan& and ,. :cVicar )0134& Esti%ating actua& /otentia& reference cro/ and /an ea/oration using standard %eteoroogica data< a /rag%atic s"nthesis& %ydrolo#y and Earth System Sciences & '( 64& 1331*1373. (en%an& B. D. 19684& Natura Ea/oration fro% +/en Water& are $oi and rass& Proceedin# o" the )oyal Society o" *ondon+ Series A+ Mathematical and Physical Sciences & ',-103)4& 1)0*165. (rieste"& C. B.& and R. J. ,a"or 19;)4& #ssess%ent of $urface Beat*Fu and Ea/oration Ksing Darge*$cae (ara%eters& Monthly eather )eview & '//)4& 81*9). $haw& E. :. 19964& %ydrolo#y in Practice& Cha/%an S Ba& Dondon. $hutteworth& W. J. 19934& Ea/oration& in %and0oo1 o" %ydrolo#y & edited !" -. R. :aid%ent& :craw*Bi 'nc& New Tor?.


(age )*13

Cven3501 Week 2 notes

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