SVERIGESLANTBRUKSUNIVERSITET

Simulation model for transpiration,evaporation and growth of plantcommunitiesSimuleringsmodell for transpiration,avdunstning och tillvaxt i vaxtbestand

Henrik Eckersten

SPAC-GROWTHModel description

Institutionen for markvetenskapAvdelningen for lantbrukets hydroteknik

Swedish University of Agricultural SciencesDepartment of Soil SciencesDivision of Agricultural Hydrotechnics

Rapport 164Report

Uppsala 1991ISSN 0348-1816

ISRN SLU-HY-R--164--SE

TABLE OF CONTENTS

1 INTRODUCTION2 MODEL

3 WATER SUBMODEL (SPAC)3.1 Plant water3.2 Canopy energy balance3.3 Resistances3.4 Rain interception3.5 Plant water change

4 BIOMASS SUBMODEL (GROWTH)5 SPECIAL FUNCTIONS

5.1 Resistances5.2 Other functions

6 ANALYTICAL INPUT VARIABLES6.1 Temperature6.2 Humidity6.3 Radiation6.4 Other variables

7 SIMULATION EXAMPLES7.1 Example 1: Minute input variables7.2 Example 2: Daily input variables

8 LIST OF SYMBOLS9 ACKNOWLEDGEMENTS10 SUMMARY (SAMMANFATTNING)

11 REFERENCES

................................. 5

................................. 6

................................. 7

................................. 7

................................. 8

................................. 91'1

•. ~"".""""""""."""" 1 "-

................................ 12

................................ 13

................................ 17

................................ 17

................................ 19

................................ 19

................................ 20

................................ 21

................................ 22

................................ 23

................................ 23

................................ 24

................................ 27

................................ 31

........................ 35

................................ 35

................................ 36

1 L~TRODUCTION

This paper aims to describe the theory of the SPAC-GROWTH model. The description servesas a tool when using the model and then should be used together with a manual (Eckersten,1991). The link to the manual is through the symbols given in the List of symbols. The textalways refers to the model and not directly to reality, unless otherwise stated. As regards thevalidity of the model, the reader is referred to other publications (see list of references) in whichtests of different parts of the model have been made. The software of the model is available fromthe author on request.

The model is a combined transpiration-growth model based on the Soil­Plant-Atrnosphere-Continuum (SPAC) concept (which simulates the flow of water from soilthrough the plant to the atmosphere). In short, the model works like this: The plant has a reservoirof water that regulates the transpiration rate which affects the total growth rate. The total growthis allocated to root, leaf+stem and grain, respectively. In turn, the size of the plam affects theevaporation of intercepted water and the transpiration through the leaf area and root development(Fig. 200). Although developed for crops, the model can be applied on species with onlyvegetative growth by cancelling the grain development. For woody plants like willow themaximum size of the plant water reservoir can be regulated with parameters. For plants olderthan one year, the biomass compartments of the model represent only the accumulated growthof the current year.

Some of the input variables to the model need to be given at a time scale of minutes. However,in many cases only daily values are available. Then the model can be applied by estimatingminute values of input variables from synoptic weather data using a special subroutine of themodel (see the special section on analytical input data).

The basic version of the transpiration calculations, which simulates the transpiration of a fixedplant that does not change in size, was described by Turner & Kowalik (1983) and Kowalik &Eckersten (1984). The transpiration-growth relations have to some extent been described byEckersten (1986 a,b) and allocation functions for assimilates within the plant are taken fromEckersten & Jansson (1991).

Since the model aims to be a research tool, although hopefully suitable for many practicalpurposes, it includes possibilities to choose among different hypotheses (see the section on specialfunctions) and will be modified as research makes progress. This model description henceincludes some processes that do not originate from other publications. New or modified equationsincluding these processes are denoted with an asterisk (*). Most new equations are related to therelations between water flows and the canopy size.

A section of the model description usually starts with a short general summary of its contents(written in italics) followed by a more detailed verbal (and graphic) description of the calculationprocedure. The section ends with the mathematical expressions. This enables understanding ofthe model regardless of whether or not the reader is familiar with mathematical expressions.Also, for the reader who is familiar with equations, this gives a good overview of the model.The numbers given to equations, figures and tables are related to the number of the subsectionconcerned.

5

2 MODEL

The model is conceptually divided into the water submodel and the biomass submodel. The watersubmodel consists of two compartments, one for easily available water located in the leaves andone for intercepted water on the canopy surface. The biomass submodel consists of threecompartments, the leaf plus stem biomass, the grain biomass and the root biomass.

The factors linking the two submodels are the transpiration rate calculated by the water submodeland the leaf area and root growth calculated by the biomass submodel (see Fig. 200). The rootgrowth is of use for the water submodel only as a special function (see the section on specialfunctions). The combined model is valid for horizontally uniform stands and the growth isassumed not to be limited by a shortage of nutrients other than nitrogen. The time step of thewater submodel is 1-4 minutes, whereas for the biomass submodel it is one day. Input data areminute values on global radiation, net radiation, air temperature, air relative humidity, windspeed and precipitation, registered above the canopy, and daily values on soil water potentialand leaf nitrogen concentration.

Water Biomass

1

~~/"\r'\

L;J~JW

9

Atmosphere

\~--/"-J"-JJI

l---------------l w,' ,

\ '-----------------

~-----------------!l---------------

v·I

Atmosphere

~

Soil

Figure 200. Schematic description of the SPAC-GROWTH model consisting of two "submodels": the watersubmodel (V) and the biomass submodel CVV). Indices are as follows: g=grain, i=intercepted, ls=leaf+stem andr=root Solid lines are flows of water or assimilates whereas dotted lines represent flows of information. Schematiskbeskrivning av SPAC-GROWTH modellen. Modellen bestdr av tvd "delmodeller"; en fOr vatten (V) och en forbiomassa (W)_ g=/dirna. i=intercepterat. ls=blad+stam och r=rot. lieldragna linjer iir [loden av vatten ellerassimilat. Streckade linjer iir informationsfloden.

6

3 WATER SUBMODEL (SPAC)

The leaves contain water which is easily available for transpiration. The transpiration occursduring day-time when stomata are open and the rate is determined by the radiation energyavailable, the drying "power" of the air and several factors regulating the flow of water fromthe plant to the atmosphere. The loss ofplant water is compensated by the uptake ofwater fromthe soil which, however, for several reasons can be delayed or is too small to meet thetram,piration demand. If, for instance, the root development is poor or soil water availability issmall, the plant water reservoir decreases. The plant then closes its stomata and the transpirationdecreases and the plant can stabilize its water status on a new lower level. During the night thestomata are closed and the plant loses water only very slowly through the cuticle. Then the plantcan recover to a plant water status close to that of the soil. The flow of water is described interms of water potentials and resistances.

3.1 Plant water

The amount of easily available water is proportional to the leaf area. It is decreased bytranspiration but increased through the root uptake created by the differences in water potentialsof the plant and the soil. A closed canopy typically contains much less water than is lost andgained daily through transpiration and uptake. Hence the water reservoir is replaced severaltimes a day.

Once leaves are present (see the biomass submodel) there is a reservoir of easily available waterin the plant (V) from which water can be transpired (FT)' The driving force for transpiration isthe vapour pressure difference (ea - es) between the ambient air and the air inside the stomatacavities. The flow is retarded by the resistances of stomata (re) and the air outside the leaf (rJ.As the plant loses water from its maximum value (VMax) the canopy water potential ('lfe) dropsbelow that of the soil ('lfJ. This difference is the force for uptake of water (Fu) against theresistances of the soil (rr) and the plant (rp)' Each unit of leaf area can maximally contain V0

amount of easily exchangeable water (see also section on special functions) corresponding to amaximum water potential ('lfeMax)' When the reservoir is emptied the canopy water potential is'lfeMin (Eqs. 311-313).

The difference in plant water content (oV) during a time-step (Ot) equals the integration of thedifference between FT and Fu during the period concerned. This integral is solved numericallyusing an iterating method that is described in the section on plant water change (Eq. 310).

oV =jFu-FT)dtwhere:Fu = ('lfs-'lfe)/(rr+rp)

'Ife = 'IfeMax-('IfeMax-'IfeMin)(1-VN Max)

pCp es-eaFT =-

y'A re+ra

FT?:O

VMax=VoAli

(310)

(311)(312)

(313)

7

3.2 Canopy energy balance

The radiation energy absorbed by the canopy is usedfor the evaporation ofwaterfrom the plant.The evaporation rate (latent heat flux) is also determined by other factors and often, duringday-time, more radiation is absorbed than is needed to meet the energy demand by evaporation.Then the canopy surface becomes warmer than the ambient air. The excess heat is leaving theplant through the sensible heat flUX. During night or at rainfall, normally the opposite occurs.We assume that the energy storage rate in leaf tissues is negligible in comparison with the otherflows. This assumption is not so good when the other flows are small, as at sunrise or sunset.The variables determining the partitioning ofsolar energy between the latent and sensible heatfluxes are for instance wind speed, air humidity and stomata resistance.

The surface temperature (Ts) is adjusted so that the canopy energy balance is fulfilled. Theradiation energy exchange between canopy and the surroundings is the net radiation interceptedby the canopy (Rn) which is the net radiation above canopy (Rna) minus the corresponding valuebelow canopy. The latter value is calculated according to Beers' law using a radiation extinctioncoefficient (k) and the leaf area index (A1J The energy balance is, in addition to R" also affGctedby the fluxes of sensible heat (H) and latent heat (AF.]') whereas storage of heat in plant tissuesis neglected (Eqs. 320-322).

The sensible heat flux is proportional to the difference between the surface temperature and theair temperature (Ta) divided by the resistance for flow of heat in the air which is assumed to bethe same as for vapour (ra) (see section on special functions). The latent heat flux (which isproportional to transpiration) is created by the vapour pressure difference between the surfaceof the stomata cavities (eS> and that of the surrounding air (ea> having a relative humidity equalto ha' The air in the stomata cavities is assumed to be at saturation. Ts is determined by changingiteratively its value until the sum of all three fluxes is below a certain limit (L1Max) (Eqs. 320,322-324).

Rn-H-AFT .::=; ~Max

Rn = Rna(l-exp(-kA1i»H = pCp(Ts- Ta)/raFT =Eq. 313es = aeexp((beT/ -ce)/(deT/-eel)ea = haaeexp((beTa' -ce)/(deTa' -eel)

8

Ts is changed until thisstatement is fulfilled

T/=Ts+273.l5Ta'=Ta+273.15

(320)

(321)(322)

(323)(324)

3.3 Resistances

The pathway for water flow from bulk soil to the atrnosphere is represented by four resistances:the soil-root resistance (rr) from the soil where the water potential is \ifs to the root surface, theplant resistance (rp)from the root surface to the mesophyll ofleaves, the stomata resistance (rcJfrom the leaj-mesophyll to the air just outside the leaf surface and finally, the aerodynamicresistance (rJ from close to the leaf surface to the ambient air above canopy. The resistancesvary with environmental conditions of the air and the soil as well as with the plant conditions.If, for instance, the wind speed or the radiation or the soil water potential increases then theresistance against water flow decreases (Fig. 330).

SPACAtmosphere

\.-..->---~~.-/'-.....-/'-....-/'-._~~-~a

~<-r--~ C ..?1r-- _. -==:==-)

r p t P'am

II!

I

~~so"

Figure 330. Schematic description ofthe pathway for water from soilthrough the plant to the atmosphere.For explanation of symbols, see text.Schematisk beskrivning av vattnetsvag frtln marken till atmosfaren.

The soil-root resistance (rr) is proportional to the root density factor (b) which accounts for thegeometry of the root system. The resistance increases with decreasing unsaturated hydraulicconductivity (al\jfr) which in turn decreases faster with decreasing soil water potentials (\jfs)when the "soil pore size factor" (n) is high. The size and depth of the root-system do not explicitlyaffect rr (see section on special functions). Instead, increased availability of water due to rootdevelopment can be considered by choosing appropriate values for the root density factor andthe soil water potential (Eq. 330) (Fig. 331).

50

40,--.,

CJ")---.0..J 30E

Cl')0

CLL

20.......,L

L

10

Q]

a b·1 0-5 n1.62 4 2.11.62 8 2.11.0 4 2.11.62 4 2.2

" "," '"' ..........~",......... ''' .....',.......

'''':::.:~>,.......~~.~

......~~'4:".....::::...:::;~-~~

-.5 -.5 -.4 -.3 -.2 -.1Soil \-Iot.er pot.entiol CMPo)

j

Figure 331. The soil-root resistanceas function of the soil water potential.Mark-rotmotstandet somfunktion avmarkens vattenpotentialen

9

The plant resistance (r) is assumed to be constant during the vegetative growth but increasesrapidly as grain development starts. rp is assumed to be proportional (arp ) to the grain biomass(Wg). (Eq. 331).

The stomata resistance per unit leaf area (rs) is affected either by the incoming short-waveradiation (~) or by the canopy water potential (\JfJ. Two separate mechanisms are assumed toregulate stomata, one represented by rs(Rs) and the other by rsC\Jfc)' Since there is only one reservoirof water in the canopy the water potential is the same for all leaves. However, the incomingradiation differs among leaves and for each sublayer (i) in the canopy, rs(Rs(i» is calculatedseparately. The radiation incident on the top of this layer (~(Ali(i», which depends on the leafarea above the layer (A1Ji», is intercepted by the leaf area of the layer (bAll) according to Beers'law and the radiation extinction coefficient (k). The actual value of rs is then the highest valuegiven by rs(Rs(i» and rs(\Jfc)' The resistances of single stomata are assumed to be coupled inparallel with each other. Then, assuming the number of stomata to be proportional to the leafarea, the resistance of the sublayer is inversely proportional to the leaf area of that layer. Thestomata resistance per unit of ground surface (re> is the sum of the conductances of sublayers(bAI/rs) (Eqs. 332-336) (Figs. 332 and 333).

~

-~

i\i

\

< ~

i oL ~--,----' --1----,--;

:~ ~j

r..... ; i

§: 1.0~-\-: I

'E o.8l(j) I

V' ~" ,-0 o.s~Q i \L r- \Q) I \

cl O.4~ \ I

~ \ \ J

L~O·t ~__jo I I, d-3 -2 -1 0

Canopy \iDler pot. CMPo)

1200 i ,'I' I ' I ' I ' I

r1000 r,

" 80J \'";- U~\E \~ 500 \," '"~~'" 400r

200lL

00 100 200 300 400' 500 500 700 800Rs CW m-2)

Figure 332. Stomata resistance as a functionof radiation. Stomatamotstandet somfunktionav straining.

Figure 333. Stomata resistance as a function of thecanopy water potentiaL Stomatamotstandet somfunktion av bladens vattenpotential.

The aerodynamic resistance (ra) is inversely proportional to the wind speed (u) measured abovethe canopy. ra is an increasing function of the smoothness of the surface which increases duringthe season as the leaf area index (Ali) increases (Lindroth equation; Persson & Lindroth, 1991).The values of the coefficients (au and brJ are related to the level of the input data on wind speed.(Eq.337).

10

br =- ~- n

I r al'V/

rp=rpo+~Wg

m

1/rc = 2: oAdrsCi)i=l

where:rs(i) = min CrsCRsCi» , fsC'VJ)where:

1rsC'Vc)=1 0 " -

Cac+bc'Vc'{c'Vc"+dc'Vc'+ec'Vc)

fsCR,Ci» = ""\"Ca,.+brrRsCl)+crRsClj")

where:RsCi) = RsCA1iCi))(1 +expC-koA1J )/2

fa = (aLi+bJjA1i)/u

m=number of layers

rsMin.::s;r:::;rs'vhx

"'R Co. R=rs:vlax It $ 1}<_ ~\Jin

(330)

(331)

C",..,,..,))jj~

(333)

(334)

(335)

(~""6),-" ..)

(337)

11

3.4 Rain interception

A fraction of the rain falling on the canopy (Fp) is intercepted on the vegetative surfaces andthereafter evaporated to the air. The rest (FG) falls onto the ground and is not included in thecalculations of the model any longer, although considered through the soil water potential inputvariable. The rain is assumed to be intercepted by the canopy in a similar way as the radiation.This means that the fractional interception of the rain is the same for all "sublayers" of leaf areain the canopy. Hence Beers' law is used but, instead of the radiation extinction coefficient, weuse the rain interception coefficient (kp). Grain is assumed to intercept rain in a similar way. Thecoefficient (kpg) used here is related to the grain biomass (Wg). The upper limit of waterinterception (VrMax) is determined by the maximum amount of water possible to be retained bythe unit leaf area (VIo) and the relative efficiency in interception between leaf and grain (Eqs.340-342).

The intercepted water evaporates (FI) in a way similar to that of the transpired water (FT) afterit has passed through the stomata. Hence, FIis calculated using the same equations as for FT butwith the stomata resistance (re) equal to zero. When there is intercepted water on the vegetativesurfaces the transpiration is assumed to stop and hence the plant water status can recover to thelevel determined by the soil conditions. Thereafter no uptake or change in plant water statusoccur as long as the canopy is wet. Since the evaporation takes place during the same time stepas the interception, the reservoir for water on the canopy (VI) often becomes zero already duringthe current time step (Eqs. 343-344).

oVI = (Fp-FG-FI)otwhere:VU,,fax = Vro(Ali+Wgkpglkp)FG= Fpexp(-kpAli-kpgWg)FI = FT in Eq. 313 but with rc=O

FT = 0

3.5 Plant water change

S;VIMax-V1(t-l)+(Fp-FG)ot (340)

(341)(342)

.;::0 ; if VI>O (343)

if Vr>O (344)

The calculation of the plant water change (Eq. 310) is basically according to the Euler methodof integration. Numerically, the change in plant water content (oV) is determined by changingthe plant water content (V) until a new balance between transpiration (FT)' uptake (Fu) and V isachieved.

The iterating method used for calculating the difference in V from one time (tl ) to the next (t2)

is as follows: First step U=l): FT and Fu are calculated for the meteorological variables and theplant water content at time t l (V(t l ». If this causes a change in V that corresponds to a changeof leaf water potential (\jIc) higher than a certain limit (.6.\jIcMax)' then we move to the second step.Second step U=j+1): using the new plant water status, FT and Fu are calculated again and if thechange of the resulting plant water status is too high compared to the previous one we go to the

12

third step (j=j+1). This procedure is repeated until the change in plant water status is below thespecified limit. The same values of the meteorological variables are used throughout. The lastvalues obtained for V, FT and Fc are those valid for time t2•

oV = V(12)-V(t1)

where:V(t2) = V(j +1)where:V(j+1) = VU)+(FuU)-FTU))(t2-t1)

CALCULATION PROCEDUREt=t 1

ifVU+l)-VU) is not too high

j=number of iteration

(350)

(351)

(352)

L >

.--->

i j=j+1!

NO!

ra, fp' rrVU)=V(t)

\JfcU)rcU)TsU)FT(j)FuU)V(j+1)

\JfcU+1)

l\JfcU+ l)-\JfcU)i ~ L1\JfcMax ?

< j=l------------·plant water content (Eq. 352)

canopy "vater potential (Eq. 312)stomata resistance (Eqs. 332-336)

canopy energy balance (Eqs. 313, 320-324)canopy energy balance (Eqs. 313,320-324)

root uptake (Eq. 311)plant water content (Eq. 352)

canopy \vater potential (Eq. 312)

--t=t+1 (=t2) i

YES!

4 BIOMASS SUBMODEL (GROWTH)

The plant is separated into three compartments ofbiomass: the root, the stem plus leafand thegrain. Through the open stomata of the leaves the plant receives carbon dioxide from theatmosphere, whereas when the stomata are closed (i.e. when the stomata resistance is atmaximum) no growth occurs. The assimilation rate is proportional to the transpiration rate.However, this proportion (water use efficiency) decreases for dry conditions because water isthen more readily lost than carbon dioxide is gained. Similarly, the water use efficiency changeswith leafnitrogen status. The assimilates are partitionedbetween roots and above-ground tissues.The root development is stimulated by low plant nitrogen and water status. The feedback onwater and nitrogen uptake of increased root growth is, however, not calculated by the model,but considered through the input variables on leaf nitrogen concentration and soil waterpotential. The rate of leaf area expansion increases with shoot growth but decreases withabove-ground biomass and at a certain high level ofabove-ground biomass no further expansion

13

occurs. The grain development starts when a function of air temperature and day-length risesabove a certain limit. The vegetative growth goes on also after this time, although considerablyaffected by the grain development. Litter-fall ofall kinds is neglected. However, since in realityno litter usually appears before the grain growth has started, we assume that the graindevelopment is overestimated by the litter amount (i.e. the grain compartrnent could be regardedas the grain plus litter compartment)

The day for start of growth (to), together with the initial amount of total biomass (W/to»at thistime, are input to the model. The initial assimilates are partitioned between leaf plus stem growth(Wls ') and root growth (W/) and developing leaf area following the ordinary equations forallocation (Eqs. 402-411). Once this flushing has occurred the transpiration through leaves startsand thereby the growth of the plant. The daily total growth per unit of soil surface (W/) isproportional to the transpiration (FT) according to the "water use efficiency" factor ('T) whichdecreases with increasing vapour pressure deficit of the ambient air (t3.e=ed-ea) and leaf nitrogenconcentration (n i) (Eqs. 400-401, Figs. 400 and 401).

0.012,-, ~

i jr 1, I

0.010 i- --~____ ~

,c:' i ~.-.-----_jI 0.0081- "" ' / / - ......----.... ~Cl , 0.uI2-0.1n l / ~~

6 i 0.011· 0.05n', / i:3 o.oos~ I l

I ,r '~ oooJ[) l

i

CD02~ I

i j

O~--L jo 0.01 0.02 0.03 0.04 0.05

nl C-)

0.012 ~ ,, I

'" 0.010 hi '~ 1\', 0.014f(ed-ea) -:

Ol r" '~ 0.000[1\\~ 0.021 fled-ea) ~

~ ~. 'Q~ \ i" I:::J ' I

-3 \ 1

0.004 ~'\~ JI \. i, ", 1

0.002 r ""'" '~ "- .j0

1, I --. ----:...:----- --__ J

o 10' 20 ' } ,~ed-ea ChPo) jO 40

Figure 400. Water use efficiency as functionof vapour pressure deficit. Vattenutnyttjandesomfunktion av luftens angtrycksdeficitet

Figure 401. Water use efficiency as function ofleafnitrogen concentration (Tom Ericsson unpublisheddata for Salix). Vattenutnyttjande somfunktion avbladens kviivehalt.

The amount of assimilates allocated to roots (W/) is a fraction (br ) of the total daily growthwhere br is the highest value of two functions. The first function depends on nl and has a minimumvalue (brMin) at or above the maximum (optimum) leaf nitrogen concentration (nlMax) and increasesas nl decreases. The second is a similar function but with the plant water status as independentvariable. The plant water status is here represented by the ratio between the actual (FT) and thepotential (FTp) transpiration, the latter being identically calculated to the actual, howeverassuming the plant water status to be at maximum (i.e. V=V M.x' see Eq. 312) (Eqs. 412-414, Fig.402).

14

~--'----'--'-----,~,Figure 402. Fraction of assim ilatesallocated to rools as function of leafnitrogen concentration. Andelenrouiliviixt som funktion av bladenskvii ve halt.

-ii

-i

..,

I!

!

~

ii

iI

n n(-\....l"UO

brMin = 0.15

brMin = 0.1

...~'.'~" ...-

............... -- -~ .... --. ----._---

,---~-:-

""',.., ...

M~\

,

1.00 "-,---,-Ir!

0.75~

-- ~I I----- t..oLO.50 r

~O.25~

~Ob O~1 Of'~ n~" r\n I,~-, "U I '~LJC::: 0"U.,j u"u4 ('-)"U~

n i (-)

The remaining part of the daily total growth «l-br)'vVt ') is allocated to the leaf plus stem biomass(We} At a certain day (tg) the vegetative growth is accompanied by the development of grains(Wg). This day appears earlier if the accumulated values of air temperature (Ta) and day length(Y) are high and is estimated to be the day when the grain switch (i g ) becomes equal to one (Eqs.405-408, Figs. 403 and 404).

n~

ILJv

OJ

30

i~7(., --;

..:~1·~·:~·: ..·~······1.•, Y

o18 ~J

x Y=18 0=.0252'1.25

o Y=18 b=.153 '1. 25i

t. Y=18 c=3.51 ,0, 75 ~

o Y=18 d=.301 '1. 25

10 20Ta (DC)

°0

0.01

0.03 '-1---,--,----,.--------,-------,

lI

0.02~

.9

ILJ'-'

r'\

Figure 403. Daily value of index related tostart of grain development as function of airtemperature. Indexforstartavkiirnans tillviixtsomfunktion av lufttemperaturen.

Figure 404. Daily value of index related to start ofgrain development as function of daylength. Indexfor start av kiirnans tillviixt som funktion avdagliingden.

The leaf area expansion (Ali'(in)) is such that a certain balance between the leaf area index (Ali)and the total above-ground biomass (W1s + Wg) is maintained. This balance is expressed as theratio (bi ) between the two variables and is an input function that decreases with plant size (bi =bio - billn(W\s+Wg)) (Fig. 405). From this function an expression for AI/(in) is derived. Alidecreases (AI/(ut)) when the leaf assimilates are allocated to grains (Eqs. 409-411).

15

'"....--[

:3:oOJ

"-1E

'---"

..0

0.025~\\\\ I

\\ J

r\\\ . -n n . I

0.020 \ \'\ b ; 0 -, u 4 b b [ 1 =. 00 S 4~

\,\ ~Djo=.053 bj1=.0054j, ., , "-

0.015~ ,...,.<~_.~ b i 0=' 048 b \ 1 =. 0058~

~". ---___ i

... ' ..... ~~~..................... :

0.010 --__ lL "" >----. !

1

1 .-••:-:.:-:.»-- 10.005, .... --.:-:::j

L --------- J--Jo Io ~OO 1000 -L-_ '1 c:;r:O

W!s+W g CgDW m-2 ) ,--,v

Figure 405. Leaf area toabove-ground biomass ratio asfunction of above-ground biomass.KVOfen mellan bladyta ochovanjordisk biomass somfunktion avovanjordisk biomassa.

r 1440\V/ =I>!(t)FT(t)

t=lwhere:'T(t) =min (arlfle , b"-c,,l1/n 1MaJ

W/ = br\V/ -bgWrwhere:br = 1+brMin-(1-x2)o.5

where:x =max ((111Max-I1I)!I1IMax) , (l-F1/FTp»

WIs ' = WIs'(in)-bgWIswhere:WIs'(in) = (l-br)Wr'

Wg' = bg(Wr+WIs)

tig=:r ag(l-exp(-bgg(Ta(t)-cg»(l-exp(-diY(t)-eg»

t=to

Ali ' = Ali'(in)-Ali'(ut)where:Ali ' (in) = (WIs' +Wg')(bio-bil (1+In(WIs+Wg»)AJj'(ut) =bgAli

16

.::;"C :\1:<:(

bg=O if ig<l

<1- '

0.::; x .::;0.99

bg=O if ig<1

bg=O if ig<l

T2.Cg, Y,2:eg

,2:0bg=O if ig<l

(400)

(401)

(402)

(403)

(404)

(405)

(406)

(407)

(408)

(409)

(410)(411)

5 SPECIAL FUNCTIONS

5.1 Resistances

In this section alternative or complementary calculations are presented. These are available inthe model and normally activated using the switch named Special.

The soil-root resistance (rr) that is a function of the soil water potential (Eq. 330) can be givena value that is inversely proportional (~) to the root biomass (WJ This modified resistance(rrCWr)) then reflects an increased efficiency in water uptake per unit of soil volume when theroot biomass increases (Eq. 510).

The stomata resistance (rJ can, in addition to the radiation (RJ and the canopy water potential(\jfJ, also be a function (rsCRs,L'l.e)) that decreases with the vapour pressure difference of the air(L'l.e). This function can either be the Lohammar equation (Eq. 512) or a polynomial function ofRs and L'l.e (Eq. 513). The actual stomata resistance is taken to be the highest value given by allthe "sub-functions" chosen to be included (Eqs. 511-513).

The aerodynamic resistance (rJ is modified by a factor named the Richardson number (Ri) whichaccounts for the effect of thermal convection on the transport of heat and vapour in the air. Thisfactoris proportional to the gravitation force (g), the distance from the canopy top to the roughnessheight (Zh-Zo) and the temperature difference between the surface and the air (Ts(t1)-Ta; t 1 meansthat the input value of the time step is used). Normally it is very small (Eqs. 514-515, Fig. 510).

Figure 510. The relative modificationof ra as function of wind speed fordiffereI1l values on the Richardsonnumber. Relativa dndringen iaerodynamiskarnotslandet somfunktion av vindhastighetenfor olikavdrden po Richardsontalet.

Ts - T a = +50%

Ta = -50%

'<C Z 0 = -50%Original:

zh=1, zo=0.1Ta =200CT -T =2 oCs a

1.00 I ~,¥-"...u flil ••·-W"$l!\l ail4T iIlIl Q-&UfI;SlStliUli

0.25

r0.75f-

I

i O.5°~1~ L,~

o0 5 1'0 1 I 1'5 20u Cm s- )

The aerodynamic resistance (rJ is inversely proportional to the wind speed (u) measured at height(Zt). Then, in the original version of the model, ra is also a function of the leaf area (Eq. 337).An alternative method is to let ra be a function of characteristic heights of the stand. ra decreaseswith the roughness height (zo) and the height at which the logarithmic wind profile (derived forthe conditions above the canopy) yields a wind speed equal to zero (Zct) (Eq. 516) (Fig. 511).

17

Figure 511. Aerodynamic resistanceas function of wind speed.Acrodynamiskarnotstdndet somfunktion av vindhastighctcn.

.J

iI

1-1

-I

0.1

0.10.05

0.1

ZoZd

0.70.70.350.7

25~1 \\ ~--,'\

20 1\ Zi\l h

15~' \\ ~~.5\

'\\ //1"\ / /

o 10 \\\ /1L \ \\

\ "~

~ \~

5~ '\''.=~, '.'-- ..,'.'-- I

[ __~"" .J

00 :; ,>"~=~~"c,J, 1~ _~I

U Cm s-1,) ,::; 20

(I)'-.../

,.-..,~

I

E

The height above ground for the wind speed measurements (Zh) can be placed in proportion (ah)to the above-ground biomass (W!s+Wg). The displacement height (Zct) and the roughness height(zo) used for calculating the aerodynamic resistance can, in their turn, be proportional to Zh (adand ao, respectively). Using these last relationships, however, implies that the aerodynamicresistance is affected by Zh only through the Richardson number (Eqs. 517-519).

In the original version of the model the aerodynamic resistances for heat and vapour are givenequal values. The resistance for heat (raH) could, however, be divided by a factor (8.,.a) as comparedto that for vapour (ra) (Eq. 519a).

rr(Wr) =rj(~Wr) (510)

rs =min (rs(Rs) , rs(\Vc) , rs(Rs,.6.e»where:rs(R,.6.e) =rsMin(bL.6.e+1)(Rs+aL)!(Rs)

= (a"+by.6.e+cy (RJl 00)2)

rs\finSrs.:S.rs\lax

if switch=lif switch=-l

(511)

(512)(513)

ra =ra/(1+lORi)where:Ri =g(zh-zo)(Ts(tl)-Ta)!((Ta+273.15)u2)

(514)

(515)

1n2( (Zh-zd)lzo)

r =----a ax2U

where:

Zh = ah(WIs+Wg)

Zd = adzh

Zo = aazh

(516)

(517)(518)(519)

raH =rJ~a (519a)

18

5.2 Other functions

The net radiation above canopy (Rno) should be an input variable. However, this variable is oftenlacking and then it can be estimated from the global radiation above canopy (Rs) (Eq. 520).

The maximum amount of easily available plant water (VMax) is proportional to the leaf area index(A!J However, with three coefficients (av, bvand cv) this dependency can be altered. For instance,for a large tree a high fraction of the water reservoir can be located in the stems and then it ispossible to put VMax in proportion to the leaf+stem biomass (WiS ) or to give it a high offset value(cv) (Eq. 521).

IRoo = aRR,-b"I

VMax = av(VoAli+bvW1s)+cy

6 ANALYTICAL INPUT VARIABLES

(520)

(521)

Most of the input weather variables to the SPAC-GROWTH model need to be given at a timescale of minutes. However, in many cases only synoptic or daily values are available. Then themodel can be applied by estimating minute values of the input variables from the daily values.The daily values needed are: (i) the daily maximum and minimum air temperature (for airtemperature), (ii) relative air humidity at three time points a day and minute values of airtemperature (for relative air humidity), (hi) daily sum of global radiation or the ratio betweenthis variable and the daily sum of global radiation below the clear sky (for global radiation), (iv)daily mean value of the wind-speed (for wind-speed) and (v) daily sums of precipitation (forprecipitation).

The methods used for estimating the analytical variables oftemperature and humidity have beendescribed by Eckersten (1986b) and for parts of the radiation routines by Eckersten (1985),whereas the other methods are presented for the first time here. Using the routines of this sectionmeans that errors will be introduced in the plant water and growth simulations as a consequenceof errors in the estimates of the analytical input variables. This effect has been examined byEckersten (1985 and 1986b) for temperature, humidity and radiation, showing that the analyticalinput variables works fairly well for daily outputs. The estimates of temperature and humidityalso work well for within-day simulations.

19

6.1 Temperature

Air temperature (TJ is estimated from daily values of maximum (Tx) and minimum (Tr) airtemperatures. Temperature is a sinusoidal function of time during the day, while it decreasesexponentially during the night. In order to prevent an unrealistic increase oftemperature duringnight, the sinusoidalfunction ofthe day is divided into 11vo parts. In the first part ofthe day, theminimum temperature ofthe last night is used, while for the second part we use the value ofthefollowing night.

The "day", from sunrise (l:c) to the sunrise on the following day (!cJ, is divided into three parts:(i) from !c to the time for maximum temperature (tx)' (ii) from tx to the time for sunset (ts) and(iii) from ts to !c+. During the first period Ta shows a sinusoidal increase over time (t) normalizedwith respect to the daylength (Y), from its minimum to its maximum value. Then, Ta starts todecrease in much the same way as it increased, however, with the amplitude determined by thedifference between the maximum temperature of this day and the minimum temperature of thefollowing day (TnJ. For the third period, Ta decreases exponentially over the time normalizedwith respect to the night length (Z), from the temperature at sunset (TaJ to Tn+- bT is the parameterthat regulates the rate of decrease (Eqs. 610-616, Fig. 610).

r,,.---.,... ~

Analytical air temperature T oCono!v t ic) C~'--·)

T --- --------"'\ I: \as- I I I 'r- I~Oi!\ If ; :l~ -~I I i i i / ~ I, ,! 'as"

I / ' I l: : I II ,:

____ : / : I . ----

T n

' ~ i ! ! ------------------'1

5

' ",!' T, Is 't' ' " n+_: n: t: " i11 .Jun " X I t I I

IS:t I12 Jun ! n+ I

1979 13 Jun ' I

Figure 610. Analytical air temperature during three days. Analytisk lufttemperatur fOr Ire dagar.

Ta =Tn+(Tx-Tn)sin(m'/(Y(l +2aT»)Ta =Tn++(Tx-Tn+)sin(m'/(Y(l +2aT»)Ta =Tn++(Tas-Tn+)exp(-bT(t'-Y)/Z)where:t' =t-!cY=!s-l:rZ=l:r+-!saT =(tx-12)jY

20

!c.::;t<txtx.::;t<ts

~t<l:r+

(610)(611)(612)

(613)(614)(615)(616)

6.2 Humidity

Minute values are estimatedfrom synoptic values ofthe relative air hUllzidity byjirst determiningthe absolute air humidity (weightper volume) which is much better suitedfor linear interpolationover time than relative air humidity. Then, together with minute values on air temperature, therelative air humidity can be calculatedfrom the interpolated values on absolute air humidity.

Using the values of relative air humidity (ha(1» for three fixed time points during the day (t1, t2,

t3) and the corresponding air temperature values (Ta'(i), Kelvins) from equations 610-616, theabsolute humidity (w(i)) can be calculated for each time point and also the last time point on theprevious day (t3J and the first of the following day (t1+). It is also necessary to estimate thesaturated vapour pressure of the air (ed) (Eqs. 620 and 621).

The absolute humidity of each minute (w) can be estimated by linear interpolation over timebetween the different values of w(i). Knowing also the minute values of the temperature (T;),the relative air humidity for every minute (hJ is determined. The ratio (a,J between the molecularweight for vapour (mv) and the universal gas constant (RJ is taken as constant (Eqs. 622 and624) (Fig. 620).

"1I

Relative and absolute analytical air humidity

100 r r--1\ i--\r .! ~

90 r- ,:. / '. "-

~I' I ,"--.

cf2. 80 /I!./·m : /

.= 70 / i \ /:sot ~ : ~ :50 I ----t-----l.---~-----.i.-.---.----.---~----.--~---,J

1

~'~. ..;..----- l!I :: 1

: i i : 1t

3i t

1i t_ i j t

3i t

15 I - ! 1 -~ 1: : +i 11 ~un 12 .Jun 13 Jun

15 rC0'E0'>~10

:s:

1979

Figure 620. Analytical air humidity during three days. Analytisk luftfuktighet fOr tre dagar.

w(i) =awha(i)ectCi)ffa' (i)where:

ed = aeexp«beTa' -ce)/(deTa' -ee))

i=t3.,t1,t2,t3,t1+ (620)

(621)

ha =wTa'/(awed)

where:Ta' =Ta+273.15aw =100mJRu

(622)

(623)(624)

21

6.3 Radiation

Daily sums of global radiation (300-3000 nm) above canopy (IDayRJ are converted into minutevalues (RJ by firstly determining the radiation for a typical clear and overcast day, respectively.The radiation below the clear sky (Rsct) is calculated from the solar constant (So, which is afunction of day-number (t», the solar elevation (~) and a parameter related to the air turbidity(gsJ· The radiation for the overcast condition (Rsov) is a fraction (go) of RSC1 (Eqs. 633-634 and637).

Assuming the cloudiness to be unifonnly distributed over the day, the "mean radiation" at eachminute (RM) equals the ratio (D) between the daily sums of Rs and RsC[' Cloudiness variationsfor periods within the day are simulated allowing the estimated actual radiation to vary (~Rs)

around the "mean radiation", using a very simple model that preserves the daily total of Rs• ~R

has a sinusoidal variation over time (t, hours) with a certain frequency (gf)' The amplitude oftl.R equals a factor (gd) times the difference between the "mean radiation" and RsCi or Rsov,depending on which one is the closest (Eqs. 630-632 and 635-636) (Fig. 630).

Analytical global radiation (W rTI- 2 )

I03 05 09 12

/~"O<J\'" Clear sky, R sCl -----e--/ \\/;" A. I \

/ \ '/ \~'Actua! , R s ',,----/ \/11 c \ Ove,cast . R sOv \ I~, \Ilv \ ~ I.r'il \f \\ /~!tl'\ I' \\.1"\ r\ \

/ 1', . I I i \/ ! , I I ! \ I! I, \

'\ ! ill.!I'!I\III\'\ /(\JI \J ~-y- V\1 \ \

' / ~~ '" LJ \ (~/ / " '\ I£,/ '~,,~

i ,~ /"1' 1"1"1' ~'- I 1 1 1 I 1 1 I , 0 ~ ,--, 18 clO

I ~, 1 1 1 I 1 I I, I 1 I. 24 03 05 O~ 1 2 ~1 ' 18 21 '"

lS7S061Z-1S7S061~

800

600

400

200

Figure 630. Analytical solar radiation during two days. Analytisk solstralning fOr Iva dagar.

R=RM+~Rs (630)

RM =DLnay(Rcl)D =Lnay(R)/LoaiRCl)RC[ = Sosin2~/(sin~+gs)

So = 1353+45.326cos(xt)+0.88018cos(xt)-0.00461cos(xt)+1.8037sin(xt)+0.09746sin(2xt)+0.18412sin(3xt)

x=2n/366

(631)(632)(633)(634)

~R = ARsin(gf2m)AR = gd min(Rscl-RsM , RsM-Rov)Rov ~ goRsCl

(635)(636)(637)

22

6.4 Other variables

Tvvo very simple approaches for calculating 'vvind speed and precipitatioll are presenred here.Wind speed is assumed to be low during the night and high during the day. This variation ismore pronounced when the wind is mainly influenced by local conditions. When larger weathersystems determine wind speed then smaller diurnal variations appear. Here J have assumed thelatter situation to be positively correlated with the average wind ,)peed. Records on dailyprecipitation are converted to a conSTant precipitation rate assuming a certain duration of therainfall.

Input data on wind speed are given as a short time (about 1O-minutes) average at time tu' Minutevalues of the wind speed (u) are a simple sinusoidal function of time (t, minutes) around thedaily mean (urn)' Maximum wind speed occurs at midday and minimum at midnight. Theamplitude is a fraction (Au) of Urn that decreases linearly from unity for low daily wind speedsto zero for Urn higher than parameter u,\rnp' llm is calculated from the infmmation on u(tu) and thediurnal variation of u (Eqs. 640-644).

To prevent a discontinuity occurring in u at midnigbt, because of different mean wind speeds ofadjacent days, a correction term UCorr is introduced. This term affects u from midnight to the timefor input variable (tJ. The non-cOlTected value for the wind speed at midnight (UNocorr(O) is thencorrected so as to yield the corresponding value calculated for the previous day (uYcsl(l440)).The correction term thereafter decreases linearly over time and is zero at time tu (Eq. 645, seeFig. 721d in the section on Input & Output variables).

Precipitation is given as a daily sum (LDayFp). By defining times for start and SlOp of rainfall (tpand tD) the daily sum of precipitation is convened into a rainfall of constant rate (Fp). Note thatminute values are used here (Eqs. 646-647).

u =lim(1+Ausin(2m/1440-n/2))+UCorrwhere:

Au= l-lim/uAmplim =x±(x2-u(lu)uAm/y)0.5

X =uAmp(l +1/y)/2y = sin(2ntj1440-n/2)

UCorr =(uYest(l440)-UNocorr(0»)(tu-t)/tu

Fp = (~alp)/tD

Fp =0

7 SIMULATION EXAMPLES

2::0

if t2::tp and LAccFP'::;~ayFp

otherwise

(640)

(641)(642)(643)(644)(645)

(646)(647)

Here the input and output var'iables of two simulation examples are presented. All input variablesare shown, except two: the soil water potential and the leaf nitrogen concentration. However,

we have assumed a very high soil water potential (i.e. no soil water limitations) and maximum

23

leaf nitrogen concentration (i.e. no nitrogen stress). Where a variable is denoted as artificial thismeans that the values are not measured but instead are chosen arbitrarily. Hence, the examplesdo not fully represent a special observed case. Instead they aim at presenting the variables neededby the model and which the model can calculate. For explanation of symbols, reference shouldbe made to the List of symbols.

7.1 Example 1: Minute input variables

The first example represents the most common type of simulation with the model and simulatesthe water flows in a Salix viminalis stand during a three-day period in August 1989 at Uppsala.The leaf area index was about 2.5.

Parameters are presented in the same way as they appear in the program of the model. The unitsare given in the list of symbols (Table 710).

Table 710. Parameter values used in simulation example 1. Explanation of symbols and theirunits are given in the List of symbols. Parametervarden anvanda i sirnuleringsexernpel I.

Parameter Value Parameter Value Parameter Value

START--------------------------------------

L'lM""L'l\jfeMax

oroTsooAliLatitudeA1i(tJ

0.10.083250.559.82.5

Tso -10

PLANT WATER

[ \Vc.\1in -2.7 \VeMax 0.0 IVo 100

RESISTA.~CE; STOMATA

~Mm 40~ 0.157Cc 0.001118a,. 0.001384RMin 30

RESISTANCE; OTHER

r,Max

bedebIT

10000.021442.617e-005-2.012e-005

Ccc,

2.301e-0074.216e-007

Ir l~2 b 4e-005 n 2.1 I<It-i 40 ~i 4

INTERCEPTION

[[ 0.2 I~ 1000

GROWTH

bio 0.048 bij 0.0064b,Mm 0.15k 0.5n1Max 0.05a,,(L'le) 0.014 biL'le) 0,01

24

The input variables were 1O-minute values of relative air humidity, air temperature, precipitation,wind speed, global radiation and net radiation above the canopy 71

3,b1989

Relative air humidity, h a('''/o) ~

100~~ ~ ~~ "~_~ ~80 r \ f ~/ '~v~~ \ ~50r ~,I/ j4 °~ ~I'y-./ ,

I­~O I

c::: 0 LF~ -,Air ten,perature , Ta (QC)25r­

:::'0 ~

~5 ~1 0 ~

r5f-

~ -lA A-0' -,- :1 A'-,Q

j

C, d

Precipitation, Fp (rnrn rnin- 1 ),-~ r-

~

1'1 L~ ~ /\3 f- /"0 '

' I~ i- /c:: f- ~__

L (

'1 t (o ,\\

~---"r"- \I ~,

r'=',:~ Wind speed. u , .•

2~ j M" 1 I I) .' ~~(_ ~"l

1

"fIN 'A/YII )'\ 1 ·r· ,',"'l ,i,-1" \ I '-"I \ ,', ' I I", \" I

~"lI~rJ~ f'nl~\I\jj! v:\ ~( .' \\),( 1,'V,(\jlicl.. JI ' IJ\ J 'I V' " M"'" iF' " I' Y \\

o I AI" jM.LI "'lA-! v'vAJ ~ I,M I"~ • V'L-w V"V •,_' \) ~L:Q --- "12-~A, ~~~ -- • .-1

e,f

800 Global radiation, As (W m-2 )

Olc,./ \ cJV "\. C'" .... I\I

12 Aug11 Aug

Net radiation, Rn(W rri2 )

10 Aug

700

ot, / J~-100 ;:===- 'L-' V \~d- "=-= =.r - '-vi ='\ ,j

Figures 710a-f. Input variables to water flow and growth simulation of example 1. Precipitation data is artificial.Indata till vattenf/odes och tillvaxtsimuleringarna i exempell. NederbOrdsdata ar inte verkliga.

25

The output variables selected are those represented in the schematic description of the watersubmodel (Fig. 200). The transpiration created a shortage of water in the plant which then createsa root uptake. When precipitation starts to fall the transpiration stops. Only a smaller fraction ofthe rain is intercepted on the canopy and evaporated. The rest falls to the ground (Fig. 711 a).The plant water decreases during day-time but increases to its maximum value during the nightor during rainfall (Fig. 711 b). The total growth rate increases with transpiration rate but decreaseswith dry air (Fig. 711c).

a

-,

II

1989Water flows (g m-2 s-1)

01S[ . -'Ion F. Tran:plrat 'T

<tUptaKe, F u

~ ~I , , ," le"., \ I 1', /\:.: \~;: i \ ,'"~I; :''0, if i i i i;Y \

I 11

(: . i ,,, 11 "~ ! preciPittlon, Fp~'l , :,I I: , . ,:\ ~~ __~ , , ~I I, Evapor tlon,F 1 \ ",.;. '\ I ,V,/I I' I' , ,I, \ ' IA'r

o.osL If To grOl-find

, FGAJ\I ::, i. __ ''''_.\ I :,1:0

;\ .I , " . , I ',~ , \ ~ ; I1 l \ ,

! " Ii ", " v ~-"'-", 11 \\ ,I j:' " ...- ,), ".. '1 At \\;~ I' I, '~I,\'"U, , G.F _r,' \\ f __ --;r \l !'oy . \ --ri j ~ J;.-- i\, SI ',e /\ugI; I 11 Augo 10 Aug

b

r---'I

I

Easily available plant vvater , V (g rn·2 )I

]100 1 ~ J

50 ~ 1o t1 _. l-- ~ ...,., .... !

200

300 rI

150

250

c

0.25 . 10-3 Total grovvth rate (gDVV m 2 8 1

hI \

)

r~,, 11~1

Io I I I I I I 11i 10 Aug I 11 Aug 12 Aug

Figures 711a-c. Output variables from water flow and growth simulation of example 1. Utdata fran vattenflodesoch tillviixtsimuleringarna i exempell.

26

7.2 Example 2: Daily input variables

The second example is similar to the first one except that the simulation is made over athree-month period instead of three days. For this rather long period, synoptic values were theonly input weather variables available. The synoptic variables were used to create minute valuesfor the weather variables which then could be used for the water and growth simulations similarto those of the first example (see above). Since no synoptic data were available for net radiationit was calculated as a linear function of the global radiation (Eq. 520). Compare to the previousexample plant growth was now simulated over a longerperiod comprising the grain development.

Several parameter values in addition to those of example I were needed for the simulation. Mostparameters, however, are related to the situation at the day for the start of simulation (to)' Thereason why they are not included among the input variables is purely technical (Table 720).

Table 720. Parameter values used in simulation example 2 in addition to those of Table 710.Explanations of symbols and their units are given in the List of symbols. Parametervardenanvanda i simuleringsexempel2 som ej finns medtagna i Tabell 710.

Parameter

STA,.~T

Value Parameter Value Parameter Value

1°' 15 I~I/~to) 0.25wt(ta) 100aR -23.0 ~ 0.649

PLA.NT WATER

[ Vo 50 IRESISTA.NCE; OTHER

Ill,p 0.1 _ IINTERCEPTION

lkpg 0.0002 ~

GROWTH

lb. 0.2 I~ 0.0252 bgg 0.153 cg 3.51Ug 0.301 eg 9.154

ANALYTIC; START

ha(t j , tJ 94 ha(G, tJ 60 ha(t3, to) 60h.(t3, to-I) 41t j 7 t2 13 t3 19Fp(~) 0Rs(ta) 26.5 LuavRso(ta) 26.5Tn(to) 9 Taita-1) 19.9 Tx(U 19.1t.(~) 20.5tu 720 u(tu, to)

ANALYTIC

ID 60 !p 600gd 1gf 12 er 0.2 er 0.25bO os

aT 0.1 ~. 2.6uAmp 10

27

The input variables during 1979 were daily values of maximum and minimum air temperatures,relative air humidity at7.00, 13.00 and 19.00 local time, ratio between sums ofactual and potentialglobal radiation, mean wind speed and precipitation sum (Figs 720a-g).

a 25 r Da.ily a.ir tempera.ture (oC)

~ iVlaximum. 'Iax-+, '"

-O~ ~~_ 1 \ ~~sl VVVVV,·~-JV~ r'V\J~

I 1"'\. ~i {I I'" \jr / \ 'i "" \. f \ "i ' ,~ I 1/\ ", f'.1 0 ~ o..liJ- \/J"., J \1'" '\/\\ ;iV\ j\ I 1/ \ f \! '\! .~, ( '\ /1, ,I \\ ~~r- \ '\ \, • \ R. )r ~, I / V • • ~ / ~. I I I

.I ~ / ...,f'of \J. \,!. \j ~,; \I \ ,/5 -"4 /"6 t; ~ "-d

~A' • ~:4"'"r- 4v.linlrrlUrr1~ I a.n-+-......

o I I ! .., ----,---,..Jun ..Ju j ,A '-'0

b Relative air humidity at 7.00 . 1'a,(T~) (=/=>100 ~ • .

::~VvVV'cJ(\J\J\/Vj"'f~\lVV \/VryJY\f

40~

20f-~

l1

i!

o IL,---T'--'---.---".....k ...l!, i

- -j------~

..J'-ll A'-IQ

C Rela.tive a.ir humidity at '13.00 • ha.(t -::>.) (=/=)100 I ~~. I

r A A ~ t t\ • t\ \ 1BO I I I \! V, : \ In" i (\ .Jr /\ 1\ !',!, r"

6 0 U~\ 1\ Itv! IIVi VVV \;V\ I \~.J V\) \1\ ,/\) \)1 \JI \ ~I ~ \ ~ v \1 if \! \ I" / \J I V" v ~L 'V \ i

40 l ~!

20t jo 1 -.J~n ....iul I AWQ~ I

Awe.Jwl

Rela.tive air humidity a.t '19.00 . ~(t~ ) (=/=)

lNVWVvJVV01A~\~d 100

BO

60

40

20

0.Jwn

\Nv\\..JL.Jrl

o I i j .4LJ

o.Ju'

0.2

Ra.tio betvveen actua.l and potential radiation . As /RsCl (-)1.0

e

28

f VVind speed at ,2.00 . u(1:u ) (rn s -'). . ~

10 l\ f'\ {\ ;\ /\ !""1 n. 1\ l, :\, 1\ ~8 ~ \ I J 'vi lA \ ,\ !,,;' \. i I \ ; \ ! \/ \, i \ .1 \ -j~'N \ VI i\ 1\ /, ,i"! I; I', !, 1\ "

6 ~ \ I N \;!\\ A IW\ rJ \ IVrJ d\i '\ I \I !i i \ r\1 \ l-4 ~ \ I VWl\j ~ /1 i /' \I I V J \ 1\1 \! 1,/' JJ

~ ~ , , \t \, ~ \I i j \ ,

I 1I, ".' -l2, V \ ~

o t , , ,- Ii ...J~'--' ...),-,1 /-"-..'-,1(;;;

I·1

r-- i --r----T"--r- -~I A'-'G:J

(1b 4

:3

2

1

o

Da.ily precipita:tion . Fp (rnnt d -'1)

Figures nOa-g. Input variables to calculations of analytical weather variables for simulation example 2. Windspeed and precipitation data are artificial. Indata tiff berakningarna av analytiska viiderdatafOr simuleringsexempei2. Vindhastighets och nederbOrdsdata ar ej verkliga.

The analytical weather variables were calculated for every IS-minutes during the wholethree-month period in 1979 although only five days (11 to 15 June) are shown in the figuresbelow (Figs 721a-d).

a bAir temperature, Ta (QC) Relative air humidity, h a(%)

20r 1100 - !I r fi iI '1

16lf\(\~"' j so~ I \ I \J \\ I \ !1/ '\" I I I . \ } I

1:~t / \1 ::[/,\)1 V V J I4 j cot 1a', " sol, ,i

c dWind speed, u (m s-1)

Global radiation, Fk (W m-2 ) Precipitation, FP (mm min-1 ) 1 0.11000

1 0, A N~. ~ f\V

0\ I J ) ( { If 0o 'I ( 11\, ( \ I I ,

13 14 1512 13 14 15

Figures nla-d. Analytical weather variables calculated by the model and used as input to the water flow andgrowth simulations of example 2. Analytiska vaderdata beraknade av modelien som sedan anvands som indata tillvattenflodes och tillviixtsimuleringarna i exempel 2.

29

Using the analytical weather variables shown in Figs. 72la-d as input, the transpiration andevaporation of intercepted water was simulated for every third minute during the summer of1979. These flows were summed up to daily values (Fig. 722a). The accumulated growth of leafplus stem and root biomass increased until the grain development started (Fig. 722b). The leafarea development and the water reservoir at midnight (which was always at maximum at thattime; Fig. 722c) were similar since the latter is proportional to the leaf area.

a

-i!

1J

5000 ~ ( --- T r 0 n s p , rOt , 0 n _ r- ~-\ IV! 1\ - - - - --0 E v 0 p 0 r . 0 fin t er, F II

'0 I1 I ;jr ' IN \~i (I ,

~ ~ I 1I I {\ ~ 1\ \ /1~ I I11 \ illI 1\ I: 1\ 1\ 1\ IIIE r I \ 1[1 \ /1 \ I ~ , '\ ' ,

6., I i '1 1 VII,I!! Iv!'--' r I' I \ I,J 1 I V, I

is I 'I i, 1 1\ I \ I i I~I'-- r I I i I \ I i I I, ,\! ,... ~ l ' I I I ~ I

CD r1 ll.P"jl \ll i I 11

i I 1\-0-> , "1 !'1 I \ '\,~ r- jf! II [j i I 'i I

.- ! i\. Ti f, ll, :11, \:1, P,I ! \ ',;; ~:: l 11\ JI~,:{. !0' l~;· ','l ~O;I" 6\ 0.1! 9 I ,~ ';" .... i' C?O' '0 . ....J

.Jun JUI i AL!g

b

C'J

E-9

300

Aug

AugJul

Avai lobi e pi on1. \.Io1.er. V ~

Leaf area index, AI i

-..Iul

- - - - -0

Leof+S1.em, W 1 sRoo1. _ Wr /I

Groi n W g ~ \

/ \,~/ \

f/ ---------------Lo (I Il" 'I" ~ 11 I 'r wl' ~ i ; i I ... g "11 ~; a "10" 11 I 'Ill' a .. Il' I' Il''' r .. 'ill

I I I I I I I I I [ I I I I I 0

(/)(/)CJE,'2=

,.-.,C'..J

~:3=0)'--'

Jun

C

5

4

3

2

1

0Jun

Figures 722a-c. Output variables for the water flow and growth simuJations of example 2. Utdatafran vattenflodesoch tillviixtssimuleringarna i exempel2.

30

8 LIST OF SYMBOLS

Unit Equation

MPa 311,312,333,334

MPa 311,330

MPa 312

\Jfc Canopy water potential

Symbols used only in the subroutine of analytical input variables are followed by the notationCA).

Symbol Description

'-Vs Soil water potential

\JfcMi."' Minimum and maximum canopy water potential\JfcMax

.6.\jfcMax

p

y

'A

<5

.6.'1ax

OAoi.6.e

oTgo

1:

't'Max

.0.Rs

~

(in)

(out)

Maximum allowed change of \jfc from one iteration to anotherfor accepting the water bahmce.

Specific density of moist air (=1.2047)

Psychrometric COnSk'lnt (=67)

Latent heat of water vaporisation (=2.4518 106)

Generally used for a difference during a time step

Maximum allowed deviation in canopy energy balance

Leaf area index of canopy internal layers

Vapour pressure difference between the air inside stomatacavities and the air above canopy

Initial increment of temperature for surface heat balancecalculations

Water use efficiency (Total growth divided by mmspiration)

Maximum water use efficiency

Variations around the analytical "mean radiation"

Sun elevation

Denotes the daily change of the symbol concerned

Denotes a positive change of the symbol concerned

Denotes a negative change of the symbol concerned

MPa

kg m-3

Pale

J kg l

Wm-2

hPa

or'--

gDWgHp-l

gDW gH20"1

W m-2 (A)

rad (A)

313,321

313

313,320

320

332,336

401,512,513

400,401

401

630,635

*

a

<1;, bi, ci , di ,

ei

Ali

Ali(i)

AR

A.

b

Denotes a fully or partly new equation which does not originatefrom another publication

Coefficient of saturated soil hydraulic conductivity

Coefficient names: i= '"C(water use eft), =c(r,(\JfJ),=d(displacement height), =e(saturated vapour pressure),=h(canopy height), =k(von Kannan's constant =0.41),=L(Lohammar eq.), =Li(Lindroth eq.), =o(roughness height),=r(r,(R,)), =R(net radiation), =ra(aerodynamic resistance),=rp(plant resistance), =rr(soil-root resistance), =T(analytictemperature), =v(r,(R".6.e)), =V(plant water), =w(analytichumidity)

Leaf area per unit ground surface (leaf area index)

Leaf area index accumulated from the canopy top to the top oflayer number i

Amplitude of the variations around the analytical "mean"radiation

Factor determining the amplitude of the within day variationsof the analytical wind speed

Root density resistance factor

g m-2 s-1 330

differs 323,324,331,334,335,337,401,408,510,512,513,516-521,610,611,616,620-622,

624

312,321,337,341,342,409-

411,521

336

W m-2 (A) 635,636

- (A) 640,641

MPa 330

31

bg Fraction of biomass in plant tissues tmnslocated to gram d-1 402,405,407,41 ]

bi Leaf area index to shoot biomass ralio m2 gDW- 1

bi1 Coefficient relating AIj to above-ground biomass gDW m-2 410

bio bi at unity above-ground biomass m2 gDW-1 410

br Fraction of daily total growth delivered to roots 402,403,406brMin br minimum 403c Specific heat per unit mass of air (= 1004) Jkt1 K-1 313,322p

D Ratio between the daily sums of actual global radimion and that - (A) 613,632of a clear day

ea Vapour pressure of the air above canopy hPa 313,324

ed Saturated vapour pressure of the air above canopy. hPa (A) 620-622

Vs Saturated vapour pressure of the air inside the stomata cavities. hPa 313,323

FG Flow of water to the ground gm-2 s-1 340,342

Fr Evaporation rate of intercepted water g m-2 S-1 340,343

Fp Precipitation rate g m-2 S-l 340,342,646,647

FT Transpiration rate g m-2 S-1 310,313,320,343,344,352,

400,404

FTp Potential transpiration rate g m-2 S-l 404

Fu Water uptake by roots g m-2 S-l 310,311,352

g Gravitational acceleration m S-2 (A) 515

& Parameter related to the magnitude of the variations around the - (A) 636analytical "mean" radiation

gf Parameter related to the frequency of the variations around the 11-' 635analytical "mean" radiation

go Ratio between global radiation under an overcast sky and that - (A) 637under a clear sky

gs Radiation parameter related to the air turbidity. - (A) 633

ha Relative air humidity above canopy 324,620,622

H Sensible heat flux from canopy to the air Wm-2 320,322

Accumulated, from the top, number of canopy sub-layers number 332,333,335,336,620

Ig Index determining the start of grain development 402,405,407,408,411

j Number of water balance iteration number 351,352

k Radiation extinction coefficient related to leaf area 321,336

!<p Rain interception coefficient related to leaf area 341,342

!<pg Rain interception coefficient related to grain biomass m2 gDW-1 341,342

m Total number of canopy layers number 332

mv Molecular weight for vapour (= 18.016) g mor1 (A) 624

n Soil pore size distribution factor 330

nl Leaf nitrogen concentration 401,404

nIMax Optimal leaf nitrogen concentration 401,404

ra Aerodynamic resistance sm-1 313,322,337,514,5l6,519a

raH Aerodynamic resistance specially for heat sm-1 519a

32

s m l 332,333,511

W m 2 333,335,336,511-513,520,

630,632

VI m-2 (A) 631-633,636,637

W m-2 CA) 630,631,636

s m-I 333,335,511

s m-I 333,511,512

W m-2 335

re

Ri

R"~

rp

fpo

rr

rr(Wr)

r,

R,

r,(\jfJ

r,(R"L'le)

r,(R,)

Rsa

R'Mr,Mu

r,Min

RsMin

R,Ov

Ru

So

t'

t1

t2

t1+, t1, lz, t3,

t3_

T.

Tas

Tas_

tntg

Tn

Tn+

r.,tp

~

Stomata resistance per unit ground surface

Richanison number

Canopy net radiation

Net radiation above c,mopy

Plant resistance

P!<mt resistance, constant value

Soil-root resistance

Soil-root resistance as a function root biomass

Stomata resistance per unit leaf area

Incident radiation intensity (300-3000nm) on :1 horizontalsurface

Sub function of the stomata resistance only dependem on thecanopy water potential

Sub function of the stomata resistance denendent on lheradiation and vapour pressure deficit "

Sub function of the stomata resistance only dependent on lheradiation

Global radiation under a clear sky

Analytical "me<m" radiation

Maximum stomata resistance

Minimum stomata resistance

Radiation limit below which the stomata resistance achievesits maximum value.

Global radiation for overcast conditions

The universal gas constant (=8.314)

Solar constant.

Time as seconds from midnight, minutes from midnight, hoursfrom midnight or day-number from January 1

Time since sunrise

Time at the beginning of a time-step

Time at the end of a time-step

Time for synoptic values ofrelative air humidity. The first valueof the following day, the fIrst, the second and the third of thepresent day and the last of the previous day, respectively

Air temperature

Analytical air temperature at sunset of the present day.

Analytical air temperature at sunset of the previous day.

Duration of rainfall

t at start of grain development

Minimum air temperature of the present day

Minimum air temperature of the following day

t at start of simulation

Time for start of rain during the day

Time for sunrise of the present day

J

srn-I

\V m-2

Wm-2

MPa s m2g-l

MPa s m2g"l

MPa s m2 g-l

MPa s m2 g-l

s nf1

s m-I

s m-I

W m-2 (A)

K-' CA)

W m-2 (A)

differs

min

s

sh (A)

QC

QC (A)

QC (A)

min CA)

day number

QC CA)

QC CA)

day number

min CA)

min CA)

313,332,343

514,515

320,321

321,520

311,331

331

311 ,330,510

510

333,334,511

511,512

333,335,511

636,637

624

633,634

310,340,400,401,408,610,611-613,634,635,640,645,

646

610-613

350,352,515

350,351

620

322,324,408,515,610,612,

620-623

612

646

408

610

611,612

408

646

610,613,614

33

t,.+ Time for sunrise of the following day min (A) 612,615

l" Time for sunset min 611,6]2,614,615

Ts Canopy surface temperature QC 320,322,323,515

Tsa Initial temperature for surface heat balance calculations QC

l" Time for daily records on wind speed min (A) 642,644,645

t. Time for maximum air temperature min (A) 610,611,616

Tx Daily maximum of air temperature GC (A) 610,611

u Wind speed above canopy m S-l 337,5]5,516,640,642

uAmp Upper limit ofdaily mean wind speed for which daily variations m S-l (A) 642,643occur

UCorr Correction term for analytical wind speed m S-l (A) 640,645

u'n Daily mean wind speed above canopy m S·l (A) 640-642

UNocorr Analytical wind speed not corrected will"! UCaITm sol (A) 645

UYcst Analytical wind speed calculated for the previous day In sol (A) 645

V Easily exchangeable water in the plant-0

310,312,350-gm -352

VI Water intercepted on the canopy surface (per unit ground,

340,343,344g rn ~

surface)

VlMax Maximum water intercepted on the canopy surface (per unit g m-2 340,341ground surface)

VIo Maximum water intercepted on the canopy surface per unit leaf g m-2 341area

VMax Maximum easily exchangeable water in the plant (per unit -0 312,521gm-ground surface).

V Maximum easily exchangeable water in the plant per unit leaf g m-2 3] 2,521aarea.

w Analytical absolute air humidity g m-3 (A) 620,622

Wg Grain biomass gDWm·2 331,341,342,407,410,517

W1s Leaf+stem biomass gDW m-2 405-407,410,517,521

Wr Root biomass gDW m-2 402,407,510

Wt Total biomass gDW m·2 400,402,406

y Day length h 408,610-612,614,616

Z Night length h (A) 612,615

Zd Displacement height m 516,518

Zh Height of reference measurements above canopy m 515-519

Za Roughness height m 515,516,519

34

9 ACKNOWLEDGEMENTS

Professor Bengt Torsell, Swedish University of Agricultural Sciences (SUAS) and ProfessorPiotr Kowalik, Technical University of Gdansk, Poland are acknowledged for their commentson the manuscript. This work was prepared at the Department of Soil Science, SUAS, Uppsala.However, much of the basic work concerning the formulation of the SPAC and the analyticaldriving variable routines were made at the Swedish Energy Forestry Project, Department ofEcology and Environmental Research, SUAS, Uppsala and funded by the Swedish EnergyAdministration. Nigel Rollison is acknowledged for the linguistic corrections.

10 SUMMARY

The theory of the simulation model SPAC-GROWTH is presented. The model simulatestranspiration, evaporation of intercepted water and growth for horizontally homogeneouscultivations for either non-woody or woody plants. The description aims to serve as a tool whenusing the model. Transpiration and evaporation simulations are based on the SPAC (Soil PlantAtmosphere Continuum) concept where the soil water potential and vapour pressure deficit ofthe air are input variables creating the driving force for water flow. The pathway of water throughthe system is represented by characteristic resistances. The growth is based on the "water useefficiency" concept and is allocated between leaf+stem, root and grain biomass. The plant sizeaffects the water flow mainly through the leaf area development. The presentation also includesfunctions for converting daily weather input data to minute values required by the water flowsimulations. Two simulation examples show all input needed by the model and some output ofthe model.

SAMMANFA1TNING

Har beskrivs teorin for simuleringsmodellen SPAC-GROWTH. Modellen simulerartranspiration, avdunstning av intereepterat vatten oeh tillviixt for horisontellt homogenaodlingar av sdviil ieke vedartade som vedartade viixter. Beskrivningen ar direkt avsedd attfungera som ett hjiilpmedel vid anvandningen av modellen. Transpirations- oehavdunstningssimuleringarna grundar sig pd SPAC-konceptet (Soil Plant AtmosphereContinuum). Markvattenpotentialen och luftens dngtryeksdejicit ar indata som skapardrivkraften for vattenflodet. Vattnets vag genom systemet representeras av karaktaristiskamotstdnd. Tillviixten grundar sig pd "vattenutnyttjande-koneeptet" oeh fordelar sig mellanblad+stam, rot oeh karna. Viixtens storlek pdverkar vattenflodet jramst genom utveekUngen avbladyta. Presentationen innehdller oeksd funktioner for konverteringen av dagUga varden pdindata av oUka vadervariabler till de minutvarden som behovs for vattenflodessimuleringarna.Tvd simuleringsexempel visar alla indata modellen behover och ndgra utav de utdata modelienger.

35

11 REFERENCES

Papers and reports published with relevance for the SPAC model and publications refened toin the text.

Eckersten, H. 1985. Transpiration of Salix simulated with low and high time resolutionweather data. Research Reports, Biotechnical Univ. E.K. of Ljubljana, Suppl. 10, pp49-55.

Eckersten, H. 1986a. Willow growth as a function of climate, water and nitrogen. Departmentof Ecology & Environmental Research, Swedish University of Agricultural Sciences,Report 25, 38 pp.

Eckersten, H. 1986b. Simulated willow growth and transpiration: the effect of high and lowresolution weather data. Agricultural and Forest Meteorology 38:289-306.

Eckersten, H. 1991. SPAC-GROWTH model, User's manual. Division of AgriculturalHydrotechnics, Communications 91:4, Dep. of Soil Sei., Swed. Univ. of Agric. Sei.,Uppsala. ISRN SLU-Hy-AVDM--9114--SE. 31 pp. (This report is a copy of the helpoption included in the program of the model)

Eckersten, H. & Jansson, P-E. 1991. Modelling water flow, nitrogen uptake and productionfor wheat. Fert. Res. 27:313-329.

Eckersten, H. & Kowalik, PJ. 1986. Measured and simulated leaf-air temperature differencesin a willow stand. In: Eckersten, H. (ed.). Willow growth as a function of climate,water and nitrogen. Department of Ecology and Environmental Research, SwedishUniversity of Agricultural Sciences. Report 25,31 pp.

Eckersten, H., Kowalik, P. & Lindroth, A. 1986. Simulation of diurnal changes of leaftemperature, transpiration and interception loss in willow energy forest. In: Institute ofWater Engineering and Water Management (Ed.). Hydrological processes in thecatchment. Cracow Technical University, Volume 1, 17-21 pp.

Eckersten, H. & Lindroth, A. 1986. Vattnet flodar i energiskogen. Pilarna har det svettigt.Uppsatser och Resultat Nr 53 (Biomassa och Energi 4), Inst. fOr skogsteknik, Sv.Lantb. Univ., Garpenberg, pp. 19-21.

Eckersten, H., Nilsson, L.O. & Perttu, K. 1984. Environment and production of energyforests. Poster abstract. In: Proc. from Bio Energy 1984, Goteborg, Sweden.Vasastadens bokbinderi, Goteborg. pp. 38.

Kowalik, P.J. & Eckersten, H. 1984. Water transfer from soil through plants to theatmosphere in willow energy forest. Ecological Modelling 26:251-284.

Kowalik, PJ. & Eckersten, H. 1989. Simulation of diurnal transpiration from willow. In: K.L.Perttu & P.J. Kowalik (Editors), Modelling of energy forestry - Growth, waterrelations and economy. Simulation Monographs, Pudoc, Wageningen, pp 97-119.

Kowalik, P.J. & Turner, N.C. 1983. Diurnal changes in the water relations and transpiration ofa soybean crop simulated during the development of water deficits. Irrig. Sci.,4:225-238.

Persson, G. & Lindroth, A. 1991. Assessment and parameterization of a soil water balancemade on a short rotation forest. Swedish University of Aigricultural Sciences,Uppsala. (Manuscript).

36

!·hrJl'('lnino ()VCr h~irl('n i ik;Jli()n~\cncn

SVI:lZICiLS LANTBRUKSUNIVERSITET, Ul'l'SALi\. INSTITUTJONl:N h)R \1,\IZKVI 11 NSK/\!'

i\VDLLNINCiLN FOR L\NTBRUKl:TS llYDROTEKNIK RAFPORTLR h U I1J nr 14)

j··+S J0l1SS00: It 198,:), C)rganiska oell syntetiska flhcrn1~Hcrial SZ)111 drjncrin~:\t!!lC'r 46 s.

).1() Fricson, L, Fabricius, M., Danie!sson, L, !Iullman, lL JUIO. 11. oc!J lIuhusaari. C. U8). De ocl!aJe

Norrbottens och \/~islCrb()ttcns ];jn. Rl s.

1 11j ~t .. il.kAfce, M. 1')8) The Rise and L:II ot" \'1 ()s~ar. /O~.

l-LS Johansson. W.. Crustalsson. E.-L & Mc/\fcc. M. 1()8). Descfl

soils (l4 s.

c~r" of i\\"cl vc cultivalccJ

I,!') Kreugcr, J. 198(). Kemisk vJllcnkvaiitet viJ s 9-)'J.

i!fikdosson, /\. \:..\: Krcugcr: J. 1986. Vaglcdning fc)[ bcdc)rnning. ,iV kcrnisk VJlh.:nk....falitcl vio bt:v~lnning, s ()1-7S.

1)0 !\J lndcf, S. l1J86..A1tcrnJti""~l bcvanni ngsfornv.:r. 2: ::'1"\"' ~rLlnclv:'ilk'nni YJn ():) s.

IS1 L~dling: P. l{)~(). Soil i\ir. y'olun1c anu eras ExchLlDgc.: :l\1cch8nis111s. 1.32~,

/\nJcr~sun, L. c\: CiCfV:JIS, P, 1'JS7. 1\1Llrkt)'r~k:Jncring ! NV Sk~ine 11leJ :--'~1L.'1l\1r .~2

hioJ11ctri och ning, }\\-'u. fDf t'i:'1rr;;n;ilv'", Box 7U;'). 7)0 ()7 l

2():-:., n':-.i.' ~ u:' ','n ....T: (O[

i~) Lincbtrc)!11, J. & klcl\fcc. 1\1. 1987, J\ir ::.lnd \v;;.Hcr i110VCiTlcnt in covers i'or rnine \\~i.sk', )() s.

1)4 Bjerketorp, A & Axe!son, U. 1987. Jl,.Jarkytesjunkning crter avvatlnin"

elt omrade i Emadalen. 67 s. !vJanuskripl.

LiHcr:.HU[- oeh fjllS!udicr i till

1)) (Juswfsson, E.-L 1987. Marktackning. Effckler pi1 olikajorcltyper. )<) s.

1)6 Johansson, W. & GustJt'sson, E.-L 1988. VattenWrseirjning, tillvax( (K'h cvapotranspiration hos korn

lerjordar. 100 s. Manuskripl.

rem

1)7 AnJcrsson, S. 1988. Om melOucr all mecl lItgangspunkt frfln binun

fbrl11agan. 30 s.

kurVdll hcnikna den iara ILLllllil';"-

158 Karlsson, 1. & Gusrafsson, E.-L 1988. Rotmiljei for yeUJrtaJ Vilxtlighcl: MarkunJerscikningar i sex

ytor. 77 s.

ngs-

159 Jarvis, N. J. 1989. CRACK - a model of water and solute movement in cracking clay soils: Technical description

and user notes. 54 s.

160 Berglund, K., Miller, U. & Persson,]. 1989. Gytrjejordar, dews S<ll11l11ansallning och egcnskaper. 106 s.

1()1 Karlsson,1. M. 1990. ]ordbrukets biclrag till fbroreningen av Gullmarsijoruen. 38 s.

162 Berglund, K., Carlgren, K, Ni!sson, G. & von Polgar, J. 1990. Markfbrbaltring och oJlingsanpassning pa lagav­

kastande jordar. 59 s.

163 Eckersten, H. 1991. Simulation model for growth anJ nitrogen dynJmics in short rotation forests. \VIGO: Model

Jescription. 36 s.

I(A Eckersten, H. 1991. Simulation model for twnspiration, eVJporation and growth of plant communities. SPAC­

GROWTH: Mode! Jescri ption. 3() s.