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TECHNICAL REPORTS18

Max-Planck-Institut für Biogeochemie

ISSN 1615-7400

A simple global land surface model for biogeochemical studies

byP. Porada , S. Arens , C. Buendia , F. Gans ,

S. J. Schymanski and A. Kleidon

Technical Reports - Max-Planck-Institut für Biogeochemie 18, 2010

Max-Planck-Institut für BiogeochemieP.O.Box 10 01 6407701 Jena/Germanyphone: +49 3641 576-0fax: + 49 3641 577300http://www.bgc-jena.mpg.de

A simple global land surface model for biogeochemical

studies

P. Porada∗, S. Arens∗, C. Buendıa∗, F. Gans∗, S. J. Schymanski∗ and A. Kleidon ∗

Abstract

A simple and global model of terrestrialbiogeochemistry is presented here. Themodel accounts for the most importantfluxes of carbon and water at the land sur-face, such as evapotranspiration, runoff andNet Primary Productivity. Its main featureis modularity, meaning that the differentparts of the model can be exchanged. Atthe moment, for instance, the model con-sists of a vegetation and a soil model, whichare able to run independently and can alsobe connected to other models. The modelis fast and it is able to reproduce a range ofobservational datasets with good accuracy.It can subsequently be used as a predictivetool in terrestrial biogeochemistry.

1. Introduction

The aim of this paper is to present andevaluate a simple and fast model of terres-

∗Max Planck Institut fur Biogeochemie; P.O.Box: 10 01 64, 07701 Jena, Germany

trial biogeochemistry that runs on a globalscale. The model consists of three systems,corresponding to soil, vegetation and atmo-sphere. In the presented version, the soilsystem is described by the model JESSY(JEna Soil SYstem model), the vegetationsystem by the model SIMBA (SIMulatorof Biospheric Aspects) and the atmospheresystem is represented by a forcing dataset. The systems communicate by meansof fluxes of matter and energy. Root wateruptake, for instance, is written as a flowof water from the soil system to the vege-tation system. In this way, carbon, waterand heat balances can be quantified.

Due to the compartmentalised modelstructure, it is easy to replace processesand integrate additional ones into the mod-els. In the current version, for example,JESSY is able to run without SIMBA andcan also be connected to a different veg-etation model. In turn, SIMBA could becoupled to different kinds of soil models. Itis also straightforward to include processessuch as weathering or cycling of phosphorus

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MPI-BGC Tech Rep 18: Porada et al., 2010

into the model (e.g. (Arens and Kleidon,2008)).

SIMBA has already been described inLunkeit et al. (2004), but never been ex-plicitly evaluated. Moreover, the version ofSIMBA used in this study has been exten-sively modified in order to make it com-patible with the modular structure of thewhole model. Hence, SIMBA is presentedhere together with JESSY.

In accordance with the modular struc-ture of the framework, the variable namesconsist of the name of the substance theyrepresent, its phase, and the systems theyrefer to (see Table 1 and 2). This makesthe variable names precise and easy to un-derstand.

At the beginning of this paper, the nam-ing convention for the model and the vari-ables and parameters of the model are de-scribed. This is followed by a descriptionof the components of JESSY and SIMBAand an evaluation of the model. The pa-per closes with a discussion and some briefconclusions.

This article, a user manual and thesource code of the model can be found un-der the following link:

http://www.bgc-jena.mpg.de/service/pr/technical reports/18/

2. Model description

2.1. Model structure

Figure 1 gives an overview of the structureof JESSY and SIMBA.

Daily Climate Data

INP

UT

MO

DE

L C

OU

PLI

NG Soil Vegetation

Heat

Water

CarbonCarbon

Water

OU

TP

UT Runoff

EvaporationRoot Water UptakeSoil MoistureSoil Carbon ...

TranspirationPlant Water ContentNPPRespirationBiomass ...

Figure 1: Diagram showing the structure of themodel, the processing sequence and the most im-portant output variables. JESSY corresponds tothe soil part and SIMBA to the vegetation part.

2.2. Variable names

In the JESSY and SIMBA models a nam-ing convention for variables has been intro-duced to secure easy recognition of theirmeaning. State variables are convention-ally named rAc

b or xAcb (r for extensive vari-

ables, x for intensive ones) where A is achemical compound, e.g. H2O, a form ofenergy, e.g. heat Q or a state variable suchas temperature T , b is the state of matter,e.g. solid, and c is the location, e.g. atmo-sphere (see Table 1). Fluxes have names ofthe form fAcc

bb, where bb is start and endstate (to consider phase change) and cc isthe start and end location. Root uptake ofwater from soil to vegetation is thus namedfH2Osv

l .

2


Table 1: Abbreviations in variable names

Abbreviation

State solid sliquid lgaseous gdissolved dstructural biomass osugars & starch c

Reservoir atmosphere avegetation vsoil sriver channel c

The model parameters are partitionedinto effective parameters (pname), whichare taken from the literature or calibrated,and measurable constants (cname). Wher-ever possible, the parameter names areadapted to the naming convention. Thetype of parameter is abbreviated by a let-ter, e.g. K for conductivity or τ for timescale, and the phase as well as the locationare abbreviated as described above. Theconductivity for water at the soil-root inter-face, for instance, is written as pKH2Osv

l .Some important variables and model pa-

rameters are listed in Table 2 and Table 3in the appendix.

2.3. Soil Heat

2.3.1. General setup

JESSY-HEAT is a heat diffusion schemethat is responsible for calculating heatfluxes into and out of the soil as well asfreezing and thawing of soil water. It is theonly part of the model that has a vertical

structure and uses more than one verticallayer. In the standard version the thick-ness of the layers is set to 1 m so that onlythe first layer is coupled to the other modelparts. The soil water content, for exam-ple affects only the thermal properties ofthe first layer while all the other layers aremodelled with fixed water content.

The module JESSY-HEAT uses a fixednumber of soil layers pnlayer, each having athickness equal to the soil depth p∆Zs andbeing characterised by a dynamic temper-ature, heat capacity and heat conductivity.In the following equations indices i and jalways denote the soil layer, layer 1 beingthe top layer. The heat flux from layer i toj is calculated by

fQs,ij =2(xKQs,i + xKQs,j)(xT s,i

− xT s,j)

p∆Zs,i + p∆Zs,j

(1)The soil conductivities are updated at eachtime step and depend on the water con-tent of the soil layer (see below). Thereare two schemes for heat exchange of thesoil with the atmosphere, depending on thesnow cover. If there is no snow, then theheat flux is only determined by the surfacetemperature and the soil heat conductiv-ity:

fQas =2(xKQs,1)(xT as

− xT s,1)

p∆Zs,1(2)

In the case of surface snow the snow acts asan additional layer. The heat flux betweenthe air and the snow layer is parametrizedas:

fQas = pDQas· (xT as

− xT s,0) (3)

where pDQas = 12.44W/Km2 is asnow/atmosphere boundary heat diffusiv-ity. The value of pDQas is derived fromthe PlaSim model (Lunkeit et al., 2004).

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The heat exchange between the snow layerand the first soil layer is calculated accord-ing to Equation 1. Note that the radiationbudget is not considered here.

2.3.2. Coupling to soil water

In its standard version the model is runwith a layer thickness of 1 m. Thus,only the first layer is affected by soil wa-ter. For the heat capacity this means thatthe heat capacity of the soil water sim-ply adds to the dry soil heat capacity. Toinclude the effect of additional heat con-ductivity added by the soil water, at eachtime step the Kersten number is calculatedas Nk = 0.7 · log10(rH2Os

l /pmaxH2Osl )

for liquid water (Blackburn et al., 1997).If the temperature is below the meltingpoint, the Kersten number is defined asNk = rH2Os

l /pmaxH2Osl . The soil heat

conductivity is then estimated as:

xKQs = pminKQs + (pmaxKQs

− pminKQs) ·Nk(4)

The water content also has substantial in-fluence on the temperature profile when themelting point is reached. Then the heatadded to or removed from the layer is di-rectly transformed into latent heat of fu-sion. When all the soil water has changedits state, the temperature will change againaccording to the additional heat flux.

2.4. Water balance

Flows of water across the boundary of thesoil system and changes in soil water con-tent are described in JESSY-WATER bymeans of a bucket model. It allows for thequantification of bare soil evaporation, root

water uptake, surface runoff and slow base-flow. Water at the land surface is describedby means of three state variables: Soilwater rH2Os

l , soil ice rH2Oss, and snow

rH2Oass which have the unit [m]. The state

of the soil water is characterised by thedegree of saturation, rH2Os

l /pmaxH2Osl ,

where pmaxH2Osl is the maximum water

storage capacity of the bucket. pmaxH2Osl

is a product of soil depth p∆Zs and therelative soil water content at saturation(pΘss − pΘrs) for the soil type sandy loam(see Table 3). Dependent on soil tempera-ture, a certain fraction of the soil water isfrozen as soil ice. This water cannot be partof the exchange flows of water and thereforeresults in a reduced bucket size. The par-titioning between soil water and soil ice iscalculated in JESSY-HEAT. Snow is storedin a reservoir above the soil.

The input of water into the soil systemconsists of rainfall fH2Oas

l and water fromsnow-melt fH2Oas

sl . If there is no snowcover on the soil, it is assumed that all rain-fall infiltrates into the soil, losses due to in-filtration excess flow and evaporation of in-tercepted rainfall are neglected. If a snowcover exists, however, it is assumed thatthe soil surface is frozen and all rainfall isconverted into surface runoff. Snow meltis calculated in JESSY-HEAT (see Section2.3) and is added to rainfall. In addition tomelting, snow is lost due to the movementof glaciers into the ocean, fH2Oso

s . This isdescribed by fH2Oso

s = rH2Oass ·pτH2Oas

s .

The flows of water out of the soil arequantified as functions of the state of soilwater and other variables. Water can leave

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the soil in form of surface runoff fH2Oacl ,

bare soil evaporation fH2Osag , root wa-

ter uptake fH2Osvl and baseflow fH2Osc

l .Surface runoff fH2Oac

l is calculated as sat-uration excess flow:

fH2Oacl = max

(

0, fH2Oasl + fH2Oas

sl

+rH2Os

l + rH2Oss − pmaxH2Os

l

pdt

) (5)

where pdt is the time step of JESSY. Baresoil evaporation takes place if soil mois-ture is high enough. This is assumed to bethe case when the expression pmaxH2Os

l −

rH2Osl − rH2Os

s is smaller than 0.01 m.Bare soil evaporation is described as theminimum between available soil water andthe potential evaporation under equilib-rium conditions (McNaughton and Jarvis,1983). It is written as:

fH2Osag = min

(

rH2Osl + rH2Os

s + 0.01

pdt

−pmaxH2Os

l

pdt, fpotH2Osa

g

) (6)

where

fpotH2Osag =

dsdTdsdT+cγ

· fnetΓ

cQH2Olg

with

dsdT =epsa1·

zTpsa2+zT · psa1 · psa2 · psa3

(psa2 + zT )2

· cρH2Ol

(7)

where dsdT is the slope of the satura-tion vapour pressure versus temperature re-lationship. zT corresponds to (tempera-ture in K - melting temperature of water,cTH2Osl) and fnetΓ is net radiation. Thevalues of the parameters cQH2Olg, psa1,

psa2, psa3, cρH2Ol and cγ can be found inTable 3). fH2Osa

g is multiplied by the frac-tion of bare soil in each grid cell since tran-spiration dominates over evaporation in thepresence of vegetation. Note that the phasetransition from liquid soil water to watervapour during evaporation (fH2Oss

lg ) is notexplicitly modelled here.Root water uptake depends on the differ-

ence in water saturation between the soiland the vegetation:

fH2Osvl = pKH2Osv

l

(

rH2Osl

pmaxH2Osl

−rH2Ov

l

pmaxH2Ovl

) (8)

where pKH2Osvl is the conductivity for

water flow at the soil-root interface (see Ta-

ble 3).rH2Ov

l

pmaxH2Ovl

is the relative water con-

tent of the vegetation given by SIMBA. Thevalue of fH2Osv

l is transferred to SIMBAwhere transpiration of water is quantified.Baseflow is formulated as a function of

soil moisture and calculated as:

fH2Oscl =

(rH2Osl )

2

pmaxH2Osl · pτH2Os

l

(9)

where pτH2Osl is the time scale of base-

flow. The quadratic increase of fH2Oscl

with soil water content accounts for thepositive feedback of soil moisture on thehydraulic conductivity of the soil. Theflows of water out of the soil are limitedto the available water content of the soil.If fH2Osv

l exceeds rH2Osl , for instance, it

is reduced to rH2Osl /pdt. fH2Osc

l is thenset to zero since it is assumed to be a slowerprocess than fH2Osv

l .After the calculation of all flows of wa-

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ter, the change in soil water content of thebucket is calculated by the mass balance:

d

dtrH2Os

l = fH2Oasl + fH2Oas

sl

− fH2Osag − fH2Osv

l

− fH2Oacl − fH2Osc

l

− fH2Ossls + fH2Oss

sl

(10)

where fH2Ossls is the amount of water that

freezes to soil ice and fH2Osssl is the amount

of melting soil ice, which are both calcu-lated in JESSY-HEAT. The mass balancefor the snow reservoir is described by:

d

dtrH2Oas

s = fH2Oass − fH2Oas

sl − fH2Osos (11)

The balance of soil ice is written as:

d

dtrH2Os

s = fH2Ossls − fH2Oss

sl (12)

2.5. Soil carbon

2.5.1. Soil organic carbon

The accumulation and decomposition ofsoil organic matter rCs

o is modelled throughthe influx of litter from SIMBA, fCvs

o (de-scribed in Section 2.6, Equation 34) anda Q10 relationship (Knorr and Heimann,1995):

fCssog =

rCso

pτCso

· pq10ssrTs

−cTH2Osl−10.0

10.0 (13)

where pq10ss is the Q10 value, pτCso is the

residence time of organic matter in the soiland cTH2Osl is the melting temperature ofwater in K.

2.5.2. Soil CO2

The parametrisations of the CO2 balanceof the soil are basically the same as inFang and Moncrieff (1999), but for a boxmodel, i.e. there is only one soil layer.The input of CO2 to the soil comes fromthree parts: autotrophic/root respiration,litter decomposition/heterotrophic respira-tion and CO2 dissolved in rain. The lossof CO2 happens through diffusion throughthe surface, runoff and plant uptake of wa-ter. The total amount of CO2 in the soilrCO2s, is

rCO2s = rCO2sg + rCO2sd = Cg ·Vg +Cl ·Vl (14)

where Cg and Cl are the concentrations ofCO2 in the gas and water phases, respec-tively, and Vg and Vl denote the volumesof those same phases. The combined airand water volume corresponds to the totalporosity of the soil, which is constant.In each time step the total flux of CO2

into the soil from respiration and rain iscalculated. However, the variation of theair volume of the soil also plays a role. Theair volume in each time step is calculatedbased on soil wetness. If the air volumeis larger than in the time step before, airhas diffused in from the atmosphere andthus atmospheric CO2 has been added. Ifthe air volume is less than before, air andthus CO2 has been pushed out of the soil.The water phase contains CO2 that is up-dated to the current time step using thefluxes of CO2 from the previous time stepfor rain, plant water uptake and runoff.The new concentrations of CO2 in air andwater are assumed to reach equilibrium in-stantaneously. The equilibrium concentra-tions are calculated, first for a closed sys-tem, i.e. where there is no diffusion outof the system. After this the diffusion tothe atmosphere is calculated and finally the

6


equilibrium calculation is repeated withoutthe diffused CO2. The equilibriums are cal-culated as follows: The dissolution of CO2

in water under acidic conditions can be de-scribed by the following reactions and equi-librium constants:

CO2(g) +H2O(l) ⇔ H2CO3(aq) (15)

K1 =[H2CO3]

pCO2

(16)

where pCO2 is the partial pressure of CO2

in the soil air (dimensionless) and K1 is thetemperature dependent Henry’s law con-stant.

H2CO3 ⇔ H+ +HCO−

3 (17)

K2 =[H+][HCO−

3 ]

[H2CO3](18)

where K2 = 4.1115 · 10−7 and finally

HCO−

3 ⇔ H+ + CO2−

3 (19)

K3 =[H+][CO2−

3 ]

[HCO−

3 ](20)

K2 and K3 are constants for the ionizationreactions of the hydrogen carbonates. Theconcentration of CO2 in the liquid phase isthe sum of the three carbonate species.

Cl = [H2CO3] + [HCO−

3 ] + [CO2−

3 ] (21)

[CO2−3 ] can be left out because [CO2−

3 ] ≪[HCO−

3 ] under acidic conditions. Then,this can be rewritten to

Cl =

(

K1 +K1K2

[H+]

)

· pCO2 · 1000 (22)

where pCO2 is the partial pressure ofCO2 in the soil air and the factor 1000is to change Cl from units of [mol/l] to

[mol/m3]. pCO2 can be related to Cg:

pCO2 = D · Cg (23)

where Cg is in units of [mol/m3] and

D =RT

pAIR(24)

where R = 8.314Jmol−1K−1 is the molargas constant and pAIR is the air pressurein Pa. Combining Equations (16) and (18)we get

K1K2 · pCO2 = [H+][HCO−

3 ] (25)

Since we have left out [CO2−3 ], [H+] ≈

[HCO−

3 ]

[H+] =√

K1K2 · pCO2 =√

K1K2D · Cg (26)

From Equation (14):

Cg =rCO2s − ClVl

Vg

(27)

substituting (23) and (26) into Equation(22) gives a new expression

Cl =

(

K1 +K1K2

√

K1K2 ·D · Cg

)

·D ·Cg ·1000 (28)

where the factor 1000 changes Cl fromunits of [mol/l] to [mol/m3]. This can bemanipulated into a 2nd order equation forCl or Cg by applying Equation (27).

2.6. Vegetation

The vegetation module is a simplified dy-namic parametrisation of terrestrial vegeta-tion accounting for the general water andcarbon fluxes through vegetation. Orig-inally, the vegetation module was a part

7


of the Planet Simulator, PlaSim, (Lunkeitet al., 2004). Now it is presented as asub-module on its own with considerablechanges to the one presented in the PlaSimmodel documentation. Its main purposeis to predict large-scale vegetation statesand fluxes, e.g. the exchange of water andcarbon between vegetation, soil and atmo-sphere. Climate and soil properties set theconstraints to vegetation, and vegetationfeeds back on the water and carbon fluxesto and from the soil. In the following wewill explain how we represent vegetation interms of the water and carbon fluxes.

2.6.1. Carbon fluxes

Net CO2 uptake by photosynthesis, or grossprimary productivity (GPP), is calculatedas the minimum of CO2-demand and CO2-supply. The demand is driven by the light-dependent reactions of photosynthesis, thesupply is limited by the inflow of CO2 intothe leaf, which is coupled to the transpira-tion of water (Monteith et al., 1989; Dewar,1997; Kleidon, 2004, 2006):

fCO2avgc = min(fCO2avgc [light],

fCO2avgc [water])(29)

where the light-driven GPP is defined us-ing a light-use efficiency approach:

fCO2avgc [light] = ǫlue · Fleaf · fΓav (30)

where ǫlue is a globally uniform factor ac-counting for light-use efficiency, Fleaf is thefraction of the surface covered by leaves andfΓav is the amount of short-wave solar ra-diation. The water-limited gross primaryproductivity is described using a water-use

efficiency approach:

fCO2avgc [water] = ǫwue ·xµCO2ag − xµCO2vlxµH2Ov

l − xµH2Oag

· fH2Ovag

(31)

where ǫwue is a factor that accounts forwater-use efficiency and also includes thelower diffusion of CO2 with respect to watervapour, xµH2Ov

l −xµH2Oag is the gradient

between plant water potential and atmo-spheric water vapour potential. xµH2Ov

lis described as a linear function of plantwater content (Roderick and Canny, 2005;Schymanski, 2007):

xµH2Ovl = pwiltH2Os

l ·

(

rH2Ovl

pmaxH2Ovl

−max

(

1.0,rH2Ov

l

pmaxH2Ovl

))

· cGrav

(32)

where pwiltH2Osl is the permanent wilt-

ing point, cGrav is the gravitational accel-eration and

rH2Ovl

pmaxH2Ovl

is the relative plant

water content. xµH2Oag is calculated ac-

cording to Kleidon and Schymanski (2008).xµCO2ag − xµCO2vl is the gradient in thechemical potential of CO2 across the leaf-air interface. Both xµCO2ag and xµCO2vlare derived as functions of pressure, tem-perature and tabulated values of the energyof formation (Engel and Reid, 2006). CO2

inside the leaf is assumed to be 70% of theatmospheric CO2 (Wong et al., 1979).Respiration, which accounts for plant

growth costs and maintenance is calculatedin each time step as 50% of the GPP (Ryan,1991). From the respired carbon half goesto the soil (fCO2vscg) and half goes to the at-mosphere (fCO2vacg ). Therefore the net pri-

8


mary productivity NPP is calculated as thedifference between GPP and respiration:

fCvco = fCO2avgc − (fCO2vacg + fCO2vscg) (33)

Litter fall fCvso is calculated using a res-

idence time pτCvo of structural biomass in

the soil:fCvs

o =rCv

o

pτCvo

(34)

2.6.2. Water fluxes

Transpiration is calculated as the minimumbetween the water stored in the vegetationand the atmospheric demand.

fH2Ovag = min

(

fpotH2Osag ,

rH2Ovl

pdt+ fH2Osv

l

) (35)

where the atmospheric demandfpotH2Osa

g is calculated according toEquation 7. As with bare soil evaporation,the phase transition from liquid to gaseouswater inside the leaf is not explicitlymodelled here. Root water uptake fH2Osv

l

is calculated in JESSY-WATER (Equation8).

2.6.3. Balance equations

The pool of sugars and starch in the vege-tation rCv

c and the structural biomass rCvo

are the result from the balance between car-bon uptake, respiration and litter fall.

d

dtdCv

c = fCO2avgc − fCO2vacg

− fCO2vscg − fCvco (36)

d

dtdCv

o = fCvco − fCvs

o (37)

From the total vegetation biomass theproportion of green biomass, or vegeta-tive cover, is estimated from an empiricalparametrisation:

Cover =(

arctan

(

pav · rCvo − pbv

pcv

)

/pdv

+ pev)

· pfv

(38)

where the parameters pav to pf v are setto values which result in a realistic distri-bution of forested area with respect to theborders of the Taiga and Savannah biomes.The vegetative cover is limited to values be-tween 0 and 1.The amount of water in vegetation is lim-

ited to be positive and is determined by thebalance between water uptake and evapo-transpiration:

d

dtrH2Ov

l = fH2Osvl − fH2Ova

l (39)

3. Model setup

3.1. Climate input data

To evaluate JESSY and SIMBA forpresent-day conditions, they are run withclimate data from the NASA Land Sur-face and Hydrology archive from the years1971 to 2006 (Sheffield et al., 2006). Thisdata includes daily values of short-wave ra-diation, downwelling long-wave radiation,precipitation, daily average air tempera-ture and daily minimum air temperature.The temperature data is measured at 2m height and it is assumed that it is ap-

9


proximately equal to the surface tempera-ture xT as in the model. Since the modelneeds terrestrial long-wave radiation, theupwelling long-wave radiation is subtractedfrom the downwelling one. Upwelling long-wave radiation is derived from the sur-face temperature according to the Stefan-Boltzmann-law and is then multiplied byan emissivity of 0.97. The model needs alsorelative humidity as input data. Hence,the saturation vapour pressure is calcu-lated according to the equation psat =

0.6108e17.27T−273

T−35.7 where T is the daily meantemperature in degrees Kelvin (Allen et al.,1998). The same is done for the minimumdaily temperature assuming that the ac-tual vapour pressure is equal to psat(Tmin).Relative humidity then results from RH =psat(Tmin)/psat(T ).It has to be mentioned that feedbacks

with the climate forcing are not simulatedin this study for reasons of computationalspeed. It is, however, possible to cou-ple JESSY and SIMBA to an atmosphericmodel.

3.2. Setup of the simulations

The model is run on a global rectangu-lar grid with a resolution of 2.8125 degrees(T42 resolution). The length of one simu-lation is 470 years, such that all variables,particularly the thickness of the ice sheetsin the polar regions and the amount of soilcarbon have reached a steady state in themodel. To control the assumption of steadystate, a 2070-year model run is used. Themodel outputs of the two runs differ by

around 5 percent.All model output variables are derived by

averaging over the last 10 years of the sim-ulation. Averaging over longer periods, e.g.30 years, does not change the model outputmuch, the difference between the values isless than 5 percent. If the averaging pe-riod is shorter, however, some output vari-ables of the model change, which is not sur-prising. The Budyko-curve, for instance, isbased on the assumption of zero change insoil water storage, which is only valid forlonger periods of time.

3.3. Datasets used for model

evaluation

To evaluate JESSY and SIMBA, themodel output is compared to a number ofdatasets. These datasets contain in ourview the most important variables to char-acterise the water and carbon budgets atthe land surface: Runoff, evapotranspira-tion, Net Primary Productivity (NPP), andsoil carbon.

3.3.1. Runoff

Runoff output from JESSY is comparedto river basin discharge data from the 35largest catchments by area of the world.To identify the grid cells of the modelcontributing to a certain basin, the maskfrom Vorosmarty et al. (2000) is used.The discharge data is taken from Dai andTrenberth (2002). This dataset contains200 river basins sorted by discharge vol-ume. Consequently, some basins which

10


have a large area but show no or onlylittle amounts of runoff are not included.The runoff values for these basins are de-rived from additional literature (Probstand Tardy, 1987; Shahin, 1989; Aladinet al., 2005; Meshcherskaya and Golod,2003). Since the dataset does not allowfor a distinction between surface runoff andbaseflow, the sum of the model output vari-ables fH2Oac

l and fH2Oscl (see Section

2.4) is compared to the river basin dis-charge data.

3.3.2. Evapotranspiration

Complete global datasets of directly mea-sured evapotranspiration are, to our knowl-edge, not available. We therefore usean indirect method to evaluate JESSYand SIMBA in this respect, based on theBudyko-curve (Budyko, 1974) which is con-firmed by a large amount of empirical data(Budyko, 1951, 1961; Donohue et al., 2007).The Budyko-curve predicts evapotranspira-tion as a function of a climate index, whichonly depends on net radiation and precip-itation. These two variables are both pro-vided by the climate dataset used as modelinput. The agreement between model out-put and the Budyko-curve is estimated bycalculating the climate index for each of the35 largest river basins as a function of themean net radiation and precipitation overthe basin. The predicted evapotranspira-tion is then compared to the mean mod-elled evapotranspiration over the basin.

3.3.3. Net Primary Productivity and

Soil carbon

A global estimate of Net Primary Produc-tivity (NPP) is provided by Cramer et al.(1999). This estimate results from themean of the predictions of NPP of 17 dif-ferent vegetation models. It consequentlyallows for drawing a comparison betweenSIMBA and other global vegetation mod-els. Soil carbon data for the first meterof the soil column is taken from IGBP-DIS(1998). For both NPP and soil carbon lat-itudinal profiles of model output and dataare compared.

4. Model evaluation

4.1. Model output

JESSY and SIMBA allow for the quantifi-cation of several biogeochemical reservoirsand fluxes such as soil moisture, soil car-bon, runoff, evapotranspiration and NPP.As an example, two of these variables areshown in Figure 2.

4.2. Sensitivity analysis

The output variables used for the sensi-tivity analysis of JESSY and SIMBA arethe latitudinal pattern of Net Primary Pro-ductivity (NPP) and the ratio of runoffto evapotranspiration, expressed by theBudyko-curve (Budyko, 1974). These twoquantities largely determine the patternsand values of the other variables used forthe evaluation of the model: Runoff, evap-otranspiration and soil carbon. The model

11


b)a)

Figure 2: Global distribution of a) soil moisture and b) NPP, the values are averages over the last 10years of a simulation.

sensitivity is tested with respect to all pa-rameters that have unknown values. Theseinclude soil depth, soil type, conductivityat the soil-root-interface, time scale of base-flow , parameters controlling water-use effi-ciency and light-use efficiency, and the soilcarbon turnover time scale (see Table 3).

The model is most sensitive to the con-ductivity at the soil-root-interface, whichcontrols transpiration by vegetation andwhich subsequently strongly influences thepartitioning between evapotranspirationand runoff. It also affects the latitudinalpattern of NPP, which can be explained bythe fact that NPP becomes limited by evap-otranspiration in case of declining root wa-ter uptake.

The parameters controlling water-use ef-ficiency and light-use efficiency, ǫwue andǫlue, have a strong effect on the totalvalue of NPP, which can be easily seenfrom Equations (30) and (31). Further-more, the proportion of ǫwue to ǫlue de-termines where vegetation is water limited

and where it is light limited.

The value of the conductivity at the in-terface between soil and river channel con-trols the ratio of surface runoff to base-flow. Low values of this parameter lead toslightly enhanced evapotranspiration, sincebaseflow is reduced and therefore plantscan transpire more water. This has a posi-tive influence on NPP.

The soil type is characterised by two pa-rameters (van Genuchten, 1980; Mualem,1976) which determine soil water storagecapacity. The influence of these parame-ters on runoff, however, is small and thebucket is not sensitive to soil type.

Changing soil depth p∆Zs affects the wa-ter storage capacity of the bucket. Conse-quently, the ratio of surface runoff to base-flow is shifted towards surface runoff withdecreasing soil depth. Also total runoffincreases slightly, since the water that isavailable for the vegetation is reduced atshallow soil depths. This also leads to aslight reduction of NPP with decreasing soil

12


depth.While the latitudinal pattern of soil car-

bon is strongly influenced by NPP, its totalamount depends also on the time scale ofsoil carbon turnover, pτCs

o .In summary, the conductivity at the soil

root interface has the strongest effect onthe model output, since it controls bothevapotranspiration and NPP. Varying soilproperties and the parameters controllingwater-use efficiency and light-use efficiency,however, only leads to small changes inthe model output. Thus, given the dataused to evaluate the model, more than oneparametrisation of the model leads to goodpredictions of the data. The parameter val-ues shown in Table 3 are one example ofa model parametrisation that generates arealistic model output with respect to theBudyko-curve and the latitudinal patternof NPP, considering the datasets from Sec-tion (3).

4.3. Comparing the model with

observational data

The results of the comparison betweenmodel output and data are presented inFigure 3. It can be seen that the gen-eral patterns of runoff, evapotranspiration,NPP and soil carbon simulated by themodel correspond well with the availableempirical observations. Also the absolutevalues agree relatively well with the onesfrom the evaluation data sets. However,modelled runoff in the northern temperateregions seems to be slightly too high ac-cording to the Budyko-curve. Furthermore,

modelled runoff in arid catchments seemsto be higher than the observed one. A pos-sible reason for these results is given in thediscussion.

5. Discussion

Although model output and evaluationdata show good agreement in general, someaspects of the climate input data and thedatasets used for evaluating the model needfurther discussion.A thorough analysis of the quality of the

input data lies beyond the scope of thisstudy. Nevertheless, the consistency of theriver basin discharge dataset and the LSHclimate data is checked using the Budyko-curve (see Section 3). The climate databased runoff from each of the 35 largestriver basins can be derived by subtract-ing the evapotranspiration predicted by theBudyko-curve from the mean precipitationover the respective basin. This is then com-pared to the river basin discharge data.The agreement between climate data basedrunoff and measured one is reasonable (seeFigure 4).In general, runoff derived by the Budyko-

curve seems to be smaller than the mea-sured one, especially for regions in highlatitudes and some arid regions (Figure3). These regions exhibit large-scale flood-ing events which prevent the vegetationfrom taking up the available water. Conse-quently, the Budyko-curve probably over-estimates the amount of water available forevapotanspiration since it is based on an-nual mean values of precipitation and

13


a) b)

c) d)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2

ET / Epot

P / Epot

1e-10

1e-09

1e-08

1e-07

1e-10 1e-09 1e-08 1e-07

Data from 35 largest river basins [m/s]

Model output from 35 largest river basins [m/s]P / Epot

ET

/ E

pot

Dat

a fro

m 3

5 la

rges

t riv

er b

asin

s [m

/s]

Model output from 35 largest river basins [m/s]S

oil C

arbo

n in

[kg/

m²]

LatitudeLatitude

NP

P in

[kg/

m²/

yr]

Figure 3: a) Modelled evapotranspiration averaged over a basin plotted against the theoretical Budyko-curve (magenta, dashed) for the 35 world’s largest river basins. b) scatterplot of modelled runoff andobserved runoff for the 35 largest river basins of the world (Dai and Trenberth, 2002). • correspondsto humid tropical, � humid subtropical, ⊡ temperate, > cold continental and × (semi) arid climateregions. c) latitudinal pattern of modelled NPP (blue, solid) and the mean NPP of 17 global vegetationmodels (magenta, dashed). d) latitudinal pattern of modelled (blue, solid) and measured (magenta,dashed) soil carbon, both accumulated over the first meter of the soil. All model estimates are averagevalues over the last 10 years of a simulation .

14


1e-10

1e-09

1e-08

1e-07

1e-10 1e-09 1e-08 1e-07

mean b

asin

runoff fro

m d

ata

[m

/s]

mean basin runoff from Budyko-curve & climate [m/s]

mea

n ba

sin

runo

ff fro

m d

ata

[m/s

]

mean basin runoff from Budyko curve & climate [m/s]

Figure 4: scatterplot of measured runoff and runoffderived by combining the Budyko-curve and cli-mate input data for the 35 largest river basins ofthe world. • corresponds to humid tropical, � tohumid subtropical, ⊡ to temperate, > to cold con-tinental and × to (semi) arid climate regions.

radiation. A temporal separation of wa-ter supply and demand is not explicitlyconsidered in Budyko’s framework (Kosterand Suarez, 1999). Assuming that theriver basin discharge data is not biased,another explanation for the difference be-tween runoff data and predictions by theBudyko-curve could be a general under-estimation of precipitation in the climatedata in northern temperate regions, whichis not unrealistic (Milly and Dunne, 2002).Hence, the small overestimation of runoffby the bucket models used in JESSY withrespect to the Budyko-curve can be ex-plained by the possible underestimation ofrunoff by the Budyko-curve in certain re-gions of the world.

Comparing the model output with runoffdata from the 35 world’s largest catch-ments, runoff seems to be overestimated inarid regions (Figure 3). Assuming the cli-mate data in these regions to be correct,a possible explanation for this result is theextraction of water by agriculture in mostof the respective catchments, which is notaccounted for in the model and demonstra-bly leads to a strong decrease in runoff.The slight underestimation of runoff by themodel in northern temperate regions mightresult from underestimation of precipita-tion in the climate data in this region asmentioned above.

6. Summary and conclusions

The JESSY/SIMBA model allows for asimple and fast modelling of land sur-face processes at the global scale. Globalbiogeochemical fluxes such as evapotran-spiration, runoff and NPP and reservoirssuch as soil moisture or soil carbon canbe quantified. In spite of its simplicity,the JESSY/SIMBA model is able to re-produce a variety of global observationaldatasets with reasonable accuracy. This isimportant, since it shows that earth systemmodels do not have to be complex to pro-duce good results. Increasing model com-plexity usually leads to a higher numberof unknown model parameters which haveto be determined by calibrating the modelagainst empirical datasets. By doing so,however, it is implicitly assumed that dif-ferences between model output and dataare due to the unknown parameter values

15


and the remainder of the model is correct.This is a very general problem faced byalmost every model used in earth systemanalysis. The number of unknown param-eters should consequently be reduced to aminimum. The model presented here couldbe used as a basis for a more parsimoniousapproach to biogeochemical modelling.

7. Acknowledgements

The authors want to thank Ryan Pavlick,Bjorn Reu and Nate Brunsell for their help-ful support. This study has been finan-cially supported by the Helmholtz Alliancefor Planetary Evolution and Life.

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A. Variables and parameters used in

the model

18


Table 2: Description of variables

Symbol Description Units

pools rH2Ovl water in vegetation m

rH2Osl soil water m

rH2Oss frozen soil water m

rH2Oass snow pack m

rCvo structural biomass of vegetation kg C m−2

rCvc sugars & starch in vegetation kg C m−2

rCso soil organic matter kg C m−2

rCO2s total CO2 in soil moles m−2

rCO2sd CO2 dissolved in soil water moles m−2

rCO2sg CO2 in soil air moles m−2

fluxes fH2Oasl precipitation m s−1

fH2Osvl root water uptake m s−1

fH2Ovag transpiration m s−1

fH2Osag evaporation m s−1

fH2Oacl surface runoff m s−1

fH2Oscl baseflow m s−1

fH2Oassl snow melt m s−1

fCO2avgc vegetation gross carbon uptake GPP kg C m−2s−1

fCO2vco vegetation net carbon uptake NPP kg C m−2s−1

fCO2vacg leaf respiration kg C m−2s−1

fCO2vscg root respiration kg C m−2s−1

fCvso Litter production kg C m−2s−1

fCO2ssog soil respiration kg C m−2s−1

fCO2asd input of CO2 though rain moles m−2s−1

fCO2sag soil CO2 efflux moles m−2s−1

fQas heat flux into the soil W m−2

fQsi heat flux from soil column i into column i+1 W m−2

states xT s,i soil temperature in the ith layer KxT as surface temperature KxKQs,i soil heat conductivity in the ith layer W m−1K−1

xµH2Oag water vapour potential m2 s−2

xµH2Ovl vegetation water potential m2 s−2

19


Table 3: Description of model parameters. Parameters with the reference > are set by personal assess-ment while parameters marked by ⊚ are calibrated to values which lead to reasonable model outputconsidering the data used to evaluate the model.

Parameter Description Value Units Reference

cQH2Olg latent heat of vaporization 2.45E6 J kg−1

cρH2Ol density of liquid water 1000.0 kg m−3

cγ psychometric constant 65.0 Pa K−1

cTH2Osl melting temperature 273.15 K

ccpH2Os heat capacity of ice 2.05E6 J m−3K−1

ccpH2Ol heat capacity of water 4.18E6 J m−3K−1

psa1 parameter to calculate vapour

pressure

17.269 (Allen et al., 1998)


pressure

237.3 K (Allen et al., 1998)


pressure

610.8 Pa (Allen et al., 1998)

pτH2Oass snow loss time scale 3.0e-10 s−1

>

pKH2Osvl

soil-root conductivity 5.5E-08 m s−1 ⊚

pτH2Osl

timescale of baseflow 3.0e+7 s ⊚

p∆Zs soil depth 1.0 m ⊚

pmaxH2Osl

relative soil water content at satu-

ration

0.345 m p∆Zs· (pΘss − pΘrs)

pΘrs residual relative soil water content 0.065 (sandy loam) (Carsel and Parrish, 1988)

0.068 (clay)

0.045 (sand)

pΘss maximum relative soil water con-

tent

0.41 (sandy loam) (Carsel and Parrish, 1988)

0.38 (clay)

0.43 (sand)

ǫlue factor for light-use efficiency 120 ⊚

ǫwue factor for water-use efficiency 3.5e-10 ⊚

pwiltH2Osl

permanent wilting point 150.0 m (Hillel, 1998)

pmaxH2Ovl

relative plant water content at sat-

uration

1.0 m >

pτCvo carbon residence time in vegetation 3.1e+8 s >

pτCso soil carbon turnover time scale 1.2e+9 s ⊚

pq10ss Q10 value of litter decomposition 2.0 (Knorr and Heimann, 1995)

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