h.a. den hollander, j.c.h. van eijkeren, d. van de meent...] are computed as the product of a...

RIVM report 601200003 page 1 of 68

RIVM report 601200003/2004

SimpleBox 3.0: multimedia mass balance model for evaluating the fate of chemical in the envi-ronment

H.A. den Hollander, J.C.H. van Eijkeren, D. van de Meent

This investigation has been performed for the account of the Directorate-General for Envi-ronmental Protection, Directorate for Chemicals, Waste and Radiation, in the context of the project "Uitvoeringsinstrumentarium", RIVM-project no. 601200.

National Institute of Public Health and the Environment, P.O. Box 1, 3720 BA Bilthoven, The Netherlands. telephone: 0031 - 30 - 274 9111; telefax: 0031 - 30 - 274 2971


Abstract

p.m.


Contents

1 INTRODUCTION ................................................................................................................................ 11

2 MODEL DESCRIPTION .................................................................................................................... 13

2.1 CONCEPT .......................................................................................................................................... 13 2.2 SPATIAL SCALES .............................................................................................................................. 13 2.3 COMPARTMENTS AND PHASES .........................................................................................................15 2.4 PROCESSES ....................................................................................................................................... 16

Emission ........................................................................................................................................... 16 Advection .......................................................................................................................................... 16 Intermedia transport ........................................................................................................................ 16 Degradation ..................................................................................................................................... 18 Removal ............................................................................................................................................ 20

2.5 CALCULATIONS ................................................................................................................................ 21 Steady state solution ......................................................................................................................... 21 Transient solution............................................................................................................................. 22

3 OPERATION ........................................................................................................................................ 26

3.1 SIMPLEBOX WORKBOOK STRUCTURE ..............................................................................................26 3.2 STEADY STATE COMPUTATIONS AND OUTPUT .................................................................................28 3.3 LEVEL 4 COMPUTATIONS AND OUTPUT ............................................................................................29

REFERENCES ......................................................................................................................................... 32

APPENDIX: EQUATIONS AND MODEL PARAMETERS OF THE SPREADSHEET SIMPLEBOX 3.0.XLS ............................................................................................................................. 33


Samenvatting

Dit document is bedoeld als technisch achtergronddocument en beschrijft de opbouw, werking en de technische details van het herziene multimedia lotgevallen model Sim-plebox 3.0. Ter illustratie van het model is een voorbeeldberekening opgenomen. Simplebox is door het RIVM toegepast voor het berekenen van een stelsel van mili-eukwaliteitsdoelstellingen en is (gedeeltelijk) opgenomen in het "European Union System for the Evaluation of Substances" (EUSES). Simplebox is een “genest” model van het “Mackay type”. Het milieu is gemodelleerd als een verzameling van (totaal veertig) homogene compartimenten (lucht, oppervlak-te- en zeewater, sediment-, bodem- en vegetatiecompartimenten) op een lokale, regio-nale, continentale en globale ruimtelijke schaal. De globale schaal vertegenwoordigt het noordelijk halfrond en is verdeeld in een gematigde, een arctische en een tropische zone. Het model gebruikt emissies en transformatiesnelheidsconstanten van stoffen als input en berekent hiermee de steady-state concentraties van die stoffen in de diver-se milieucompartimenten. Bovendien kan met een bijgeleverd integratieprogramma het concentratieverloop als functie van de tijd bepaald worden. Simplebox is een ge-neriek model; het kan worden aangepast om elke gewenste specifieke milieusituatie te simuleren. Vergeleken met de versie 2.0 is er een aantal wijzigingen doorgevoerd. De belangrijk-ste hiervan zijn het toevoegen van een lokale schaal en het verfijnen van de zeewater-stromen op en tussen de regionale, continentale en "gematigde" globale schaal. Even-eens is een volledige naamswijziging van parameters doorgevoerd en is de lay-out van het model gewijzigd.


Summary

This document describes the technical details, construction and operation of the fully revised multimedia fate model Simplebox 3.0. Former versions of Simplebox have been used for prediction of intermedia concentration ratios in order to harmonisation of environmental quality objectives. Also Simplebox is (partly) built in the "European Union System for the Evaluation of Substances" (EUSES) As an illustration a fully worked out example computation is admitted Simplebox 3.0 is a nested multi-media fate model of the “Mackay type”. The environment is modelled as a set of forty well-mixed, homogeneous compartments (air, fresh water and marine water compartments, sediment, soil and vegetation compartments) on a local., regional, continental and global scale. The global scale represents the Northern Hemisphere and contains a moderate, arctic and tropical zone. The model needs substance properties, emission rates and transformation rate constants as input and computes steady-state concentra-tions for all boxes as output. Simplebox is a generic model in the sense that it can be customised to represent specific environmental situations. With respect to Simplebox 2.0, several changes have been made. The main modifica-tions are the addition of a local scale nested in the regional scale and refinement of the seawater currents between the regional, continental and moderate zone of the global scale. All parameters are renamed and the lay out of the model has been changed


1 Introduction

This report describes version 3.0 of the spreadsheet model SimpleBox: a multimedia mass balance models of the so-called Mackay type. Detailed technical descriptions have been given in earlier RIVM reports [1, 1,2]. The aim of the present report is to technically present details of the updated SimpleBox version 3.0, in a condensed for-mat. The report consists of three main blocks: Model description (chapter 2) Model operation (chapter 3) Technical details of equations and default settings (Appendix 2) Informed readers are advised to turn to Appendix 2 immediately.

Evolution of SimpleBox The earliest example, exactly reproducing Mackay and Paterson’s ‘Calculating fu-gacity’ [3] (in Multiplan for Apple IIe), was created in 1984 as ‘SimpleSal’. Later ver-sions (in Lotus 123 for MS-DOS PC) [1] have maintained the original concepts of ge-neric model settings and description of intermedia transport velocities as functions substance properties, but took the classical concentration approach. The first model version (Lotus 123 for MS-DOS) with the name ‘SimpleBox’ was published in 1993 [1]. SimpleBox 1.0, a generic, open, 8-compartment model, was was used for two specific regulatory purposes in The Netherlands (i) risk assessment and prioritization new and existing chemicals, and (ii) harmonization of environmen-tal quality objectives [4]. A second SimpleBox version (Excel for Windows) was published in 1996 [2]. To bet-ter serve the purposes of calculating overall persistence in the environment, and toxic impact assessment in LCA, SimpleBox 2.0 used nesting of spatial scales. Since that time, SimpleBox has been used as the regional distribution module for the EUropean System for the Evaluation of Substances, EUSES [5]. Validation studies have support-ed the use of SimpleBox 2.0 for harmonizing environmental quality objectives [6,7]. In the course of time many small and major changes have been made to the model. In the present version of SimpleBox, all these have been accomodated. The differences

1 SimpleBox 1.0 2 SimpleBox 2.0 3 Calculating fugacity 4 Van de Meent and De Bruijn 5 EUSES 6 Struijs J, Peijnenburg WJGM. 2002. Predictions by the multimedia environmental fate mod-el SimpleBox compared to field data: Intermedia concentration ratios of two phthalate esters. Report nr. 607220 008. RIVM, Bilthoven, The Netherlands. 7 Bakker J, Brandes LJ, Den Hollander HA, Van de Meent D, Struijs J. 2003. Validating Sim-pleBox-Computed Steady-State Concentration Ratios Report nr. 607220 010. RIVM, Bilt-hoven, The Netherlands

between SimpleBox 3.0 and the earlier versions are described in Table 1. Major point

of difference are addition of a local spatial scale, remodeling the regional sea water

compartment, and complete revision of the spreadsheet, including variable names. In

its default settings, SimpleBox 3.0 models an area of 100 km2 around an emission

source somewhere in the Rhine/MeuseScheldt basins, including a 10x100km coastal

strip in the Southern North Sea.

Table 1: Evolution of SimpleBox

Model Year Platform Main characteristics Ref SimpleSal 1984 Multiplan/Apple IIe algebraic fugacity model [3] SimpleRisk 1989 Lotus-123/MSDOS generic, open mass balance model; concentration-based [1]

air, water, suspended matter, biota, sediment, 2 soil compartments level III (matrix inversion) and level IV (numeric inte-gration) calculation

SimpleBox 1.0 1993 Lotus-123/MSDOS as SIMPLERISK [1] 3 soil compartments default settings: NL

SimpleBox 2.0 1996 Excel/Windows as SimpleBox 1.0 [2] different spatial scales: regional, continental, 3 climate zones soil depth based on chemical-specific penetration depth vegetation compartments at regional and continental scales transient level IV calculation default settings: northern hemisphere, continent=EU, region=NL

SimpleBox 3.0 2004 Excel/Windows as SimpleBox 2.0 local scale nested inside regional scale [8] regional seawater compartment remodelled according to EU TGD solid phase turbation/advection accounted for in pene-tration depth air-soil transfer rate based on penetration depth spreadsheet redesigned, removing sewage treatment plant and integrating vegetation compartment; variables renamed default settings: region=Rhine/Meuse/Scheldt basin, local: 10x10km

8 Roelofs en Van de Meent


2 Model description

2.1 Concept Simplebox is a multimedia environmental fate model in which the environmental compartments are represented by homogeneous boxes. Intermedia mass flows [mol.s-

1] are computed as the product of a transport coefficient [m3.s-1] and the concentration in the compartment from which the mass flow originates [mol.m-3]. The transport co-efficients are found as the product of intermedia mass transfer coefficients [m.s-1] and the interfacial areas [m2]. Simplebox provides guidelines and in most cases estimation equations to derive the mass transfer coefficients from properties of the chemicals and characteristics of the environment.

The concentration of a chemical in a box is the result of mass flows of the chemical to and from the box. A mass balance equation is written for each of the boxes. The mass balance equations have the following format:

Vi . dCi = EMISi + ADVij + DIFFij - REM i - DEGRDi 1dt

with Vi : volume of box i [m3] Ci : concentration of the chemical in box i [mol.m-3] t : time [s] EMISi : mass flow of the chemical into box i by emission [mol.s-1] ADVi j : mass flow of the chemical from one box to another by advective transport [mol.s-1]

DIFFi j : mass flow of the chemical from one box to another by diffusive exchange [mol.s-1] REMi: mass flow of the chemical from box i to outside the system by removal [mol.s-1] DEGRDi : mass flow of the chemical from box i due to degradation [mol.s-1]

The chemical can be emitted into a box, transported to and from other boxes by means of advective or diffusive processes, removed from a box to outside the system, for instance by escape to the stratosphere, or be degraded.

The terms of the mass balance equations each represent a mass flow of the chemical [mol.s-1]. Generally, the magnitudes of these mass flows depend on the concentration of the chemical in the boxes. If mathematical expressions that relate the mass flows to the concentrations are available, the set of mass balance equations (one for each box) can be solved: the concentrations in each of the boxes can be computed.

2.2 Spatial scales Simplebox 3.0 models the Northern Hemisphere as a nested set of spatial scales. It consists of six spatial scales; a local, regional and continental scale and a three global scales reflecting arctic, moderate and tropic climate zones (Figure 1).

Figure 1: Spatial structure of SimpleBox 3.0. The overall model represents the Northern

ARCTIC MODERATE TROPICAL

CONTINENTAL

REGIONAL

LOCAL

Hemisphere, which is spilt into climate zones. A continental, regional and local scale are nested in the moderate climate zone.

The local scale is a small scale within the regional scale. This gives the possibility to simulate the immediate vicinity of a single emission source, e.g. an industrial area within the regional scale. The default settings of the local scale are generic; the local scale is not modeled after any particular place. The default settings of the regional scale are set to match the Rhine-Meuse-Scheldt basin. The default settings of the con-tinental scale are set such as these represent the European region. The global scales are added to serve as background for the continental and regional scales. These scales reflect the polar, moderate and tropic zones of the Northern Hemisphere. The way in which transport between these scales is defined is shown in Figure 2.

AIR FLOW WATER FLOW

A

T

M

C

R L

R L

C

T

A

M

land

water

Figure 2: Advection of air and water between the spatial scales in SimpleBox.


2.3 Compartments and phases The regional and continental environments modelled consist of ten compartments: air, fresh water, seawater, fresh water sediment, marine sediment, three soil compartments and vegetation on natural and agricultural soil. The local scale is identical to these scales, but does not contain a marine water compartment. The global scales consist of four compartments: air, seawater, sediment and soil. All compartments but vegetation consist of several physical phases, which are considered to be in thermodynamic equi-librium at all times. The distribution over these phases is dependent of the chemico-physical properties of the substance modeled. In the air compartment Simplebox makes a distinction between gas, rain and aerosol. The water compartments contain water, suspended particles, and biota; the soil com-partments consist of solids, water, air and plant roots, and sediments consist of solids and water. The vegetation compartments consists only of one phase (crops, grass, etc.). The SimpleBox systems comprises 40 compartments (boxes) in total (Table 2).

Table 2: Compartments of SimpleBox Comp. Medium Scale Comp. Medium Scale aL air local scale s1C natural soil continental scale wL fresh water local scale s2C agricultural soil continental scale sdL fresh water sediment local scale s3C other soil continental scale s1L natural soil local scale v1C natural vegetation continental scale s2L agricultural soil local scale v2C agricultural vegetation continental scale s3L other soil local scale aM air moderate zone v1L natural vegetation local scale wM seawater moderate zone v2L agricultural vegetation local scale sdM marine sediment moderate zone aR air regional scale s1M natural soil moderate zone w1R fresh water regional scale s2M agricultural soil moderate zone w2R seawater regional scale s3M other soil moderate zone sd1R fresh water sediment regional scale aT air tropical zone sd2R marine sediment regional scale wT seawater tropical zone s1R natural soil regional scale sdT marine sediment tropical zone s2R agricultural soil regional scale s1T natural soil tropical zone s3R other soil regional scale s2T agricultural soil tropical zone v1R natural vegetation regional scale s3T other soil tropical zone v2R agricultural vegetation regional scale aA air arctic zone aC air continental scale wA seawater arctic zone w1C fresh water continental scale sdA marine sediment arctic zone w2C seawater continental scale s1A natural soil arctic zone sd1C fresh water sediment continental scale s2A agricultural soil arctic zone sd2C marine sediment continental scale s3A other soil arctic zone

2.4 Processes

Emission Emissions are the only source of substances; zero autochtonous production is as-sumed. Emissions are considered to take place in air, water and soil only. Emission rates are to be specified by the user, optionally as the product of production volume and emission factor.

Advection Large-scale air- and ocean water currents transport chemicals between spatial scales (Figure 2). The importance of advection flows is most pronounced at the smaller spa-tial scales, where air- and water flow results in high renewal rates, and relatively little time is available for the slower intermedia transport and degradation processes.

Air flow Air flows between spatial scales are characterized by residence times. By default, air residence times are calculated by assuming a constant linear flow (default windspeed: 3 m.s-1 at all spatial scales) through a completely mixed, cylindrical air mass.

Water flow SimpleBox attempts to model the complete water cycle. By default, river flows are deduced from user-specified net prcipitation, and fractions that run off to fresh water systems and infiltrate into soil to become groudwater, which is not explicitely mod-eled. Water flows in the marine environment are modeled to be reflective of large-scale sea currents and small-scale dispersive water movements. The regional sea water com-partment means to represent the plume of a major river in a coastal zone, controled by a user-specified current along the coast and a user-specified dispersive lateral ex-change with the continental sea water compartment. Default flows of water between the larger spatial scales are based on user-specified residence times of ocean water in the systems.

Sediment flow SimpleBox attempts to maintain closed sediment balances. By default, net flows of solids between spatial scales, and sediment accumulation rates accordingly, are com-puted as the balance of steady-state inputs and outputs of suspended matter in water bodies.

Intermedia transport Transport between different environmental media occurs by advection and diffusion. Diffusive intermedia transport is always directed toward the medium in which the fu-


gacity is smallest; its magnitude is controlled by the departure from equilibrium (ef-

fective concentration difference), which depends on the intermedia partition coeffi-

cient. Volatilization from water to air is an example of diffusive intermedia transport.

Atmospheric deposition to soil and water by aerosol particles and rain droplets is an

example of advective intermedia transport. The direction of advective intermedia

transport is determined only by the direction of the carrier flow. Intermedia advection

may carry the chemical against fugacity gradients.

The intermedia transport mechanisms accounted for in SimpleBox are:

Atmospheric deposition

SimpleBox models three parallel mechanisms of advective transport from the atmos-

phere to the earth’s surface.

Dry deposition of aerosol-bound substance is modeled with a user-specified deposi-

tion velocity of aerosol particles (default value: 10-3 m.s-1). Washout of aerosol-bound

chemical by rain water is modeled with a user-specified dimensionless aerosol collec-

tion efficiency (default value: 2x105), which describes the volume of air that is com-

pletely scavenged by a unit volume of rain water. Washout of the gaseous chemical by

rain water is modeled by assuming complete equilibrium between the gas phase of air

and rain water, given by the Henry’s Law Constant.

Deposition fluxes from the atmosphere to water, soil and vegetation are deduced, ac-

counting for

fractions of the chemical in the gas- and aerosol phases (see below)

interception by vegetation;

Exchange of gaseous substances

Diffusive exchange of gaseous chemical is treated differently

Exchange of gaseous substances

- absorption to and volatilization from water

- absorption to and volatilization from soil

- absorption to and volatilization from vegetation

Exchange between sediment and water

- sedimentation of suspended particles

- resuspension of sediment

- adsorption to and desorption from sediment

Run-off from soil to surface water

- dissolved in run-off water

- associated with eroded soil particles

Net uptake from soil by vegetation

- transpiration flow from soil to plant

- litter fall from plant to soil

Default estimation routines for intermedia mass transfer coefficients make use of in-termedia (equilibrium) partition coefficients. These partition coefficients are the prin-cipal input data for SimpleBox. By default, partition coefficients are estimated from the basis substance properties as follows:

Equilibrium between gas phase and aerosol

Equilibrium between air and water

Equilibrium between soil or sediment and water

Equilibrium between air and soil

Equilibrium between air and vegetation

Equilibrium between vegetation and water

Degradation Degradation is the major route of elimination of the modeled chemical from the sys-tem. It takes place in all compartments, on all spatial scales and is assumed to obey (pseudo) first order kinetics. Degradation mass flows follow are controlled by the deg-radation rate constants that are specified by the user. By default, Simplebox offers in-dicative estimations.

Air Degradation in the atmosphere is assumed to take place in the gas phase only. By de-fault, reaction is assumed to be dominated by oxidation with OH-radicals. A standard pseudo-first order rate constant for reaction in the gas phase, kdeg.air [s-1], is calculat-ed from

Ea.OHrad

kdeg.air C.OHrad k0.OHrad e-

RT

in which k0.OHrad (default: 7.9x10-11 cm3.s-1) is the second-order rate constant for OH-radical attack, C.OHrad (default: 5x105 molec.cm-3) is the concentration of OH-radicals in the gas phase, Ea (6 kJ.mol-1) is the activation energy for this reaction, R


(=8.314) is the gas constant, and T (=298 K) is the temperature. The default estima-tion leads to a half life of 160 days: a minimum estimate for organic substances. Default atmospheric degradation rate constants at the various spatial scales (and, thus, other temperatures) are derived from the standard kdeg.air, applying i Correction for the fraction of the substance in the gas phase. By default, this is

done using the Junge-Pankow equation; ii Correction for differences in OH-radical concentration; iii Correction for differences in temperature.

Water Degradation in the water compartments is assumed to take place in solution only. By default, a standard first order rate constant for reaction in the water phase, kdeg.water [s-1], is calculated from

ln2kdeg.water biodeg

in which biodeg is the biodegradation half life in water, as obtained from the EU Technical Guidance Documents [9] and results of standard biodegradation tests10. De-fault degradation rate constants in water at the various spatial scales are derived from kdeg.air, applying i Correction for the fraction of the substance in solution; ii Correction for differences in bacteria concentration concentration. This assumes

that first-order degradation rates in solution are proportional to the total bacteria concentration; kdeg.water is multiplied by the ratio of the actual bacteria con-centyration and the assumed bacteria concentration in the biodegradation test.

iii Correction for differences in temperature. This is done assuming an increase of re-activity of a factor Q.10 (default: 2) for an increase in temperature for every 10 de-grees (K or oC)

Sediment and soil Default degradation rate constants in sediment, kdeg.sed, and soil, kdeg.soil, are are taken from EU Technical Guidance Documents [9], on the basis of results of standard biodegradation tests and sediment/soil-water partition coefficients10. In line with the TGD, degradation in sediment is assumed to be 10 times as slow as degradation in soil. Default degradation rate constants for the different compartments are derived from kdeg.sed and kdeg.soil by applying the Q.10-based temperature correction factor as used for water.

9 TGD 10 Values in the TGD are interpreted as applying an environmental temperature of 12 12 oC, and recalculated to standard temperature of 25 oC, using a Q.10 of 2.

Vegetation By default, the degradation rate constant for vegetation is assumed to be a factor of 10 greater than the (temperature-dependent) degradation rate constant in soil.

Removal Besides degradation, some other routes of removal from the system are formulated in SimpleBox.

From air SimpleBox models the lower atmosphere (troposphere) only; ‘escape to the strato-sphere’ is modeled with a first-order removal constant (default: 3.66x10-10 s-1, equiva-lent with a removal half life of 60 yr).

From sediment SimpleBox models the top layer of a sediment system only. Burial of sediment under freshly deposited material accounts for an apparent removal of chemical from the sys-tem. This is described as a sediment burial mass transfer coefficient. By dfault, Sim-pleBox uses the net sedimentation rate (sedimentation minus resuspension) that re-sults from incoming and outgoing suspended matter loads as specified in the model settings.

From soil SimpleBox describes the top layer of the soil system only. Downward transport with percolating water removes chemical from soil system. Default estimtion of the leach-ing mass transfer coefficients assumes that (i) the top soil layer is completely mixed11, and (ii) percolating water is in equilibrium with soil.

Below-surface parts of plants are described in SimpleBox as part of the soil system. Removal of plant roots, therefore, acts as a mechanism that removes chemical from the system. This is simulated with a removal mass transfer coefficient. By default, roots removal is assumed zero for naural soil, and 2.1x10-3 m.s-1 (equivalent with re-moval half life of 66 yr at 0.2 m soil mixing depth).

From vegetation SimpleBox describes vegetation as invariable (constant volume, etc.) in time. Periodic harvesting is described as constant removal from the vegetation compartment, given by a first-order harvesting coefficient. Default assumptions are zero harvest of natural vegetation, and annual harvest of 59% of the agricultural vegetation.

11 This assumption neglects the empirical observation that usually concentrations in soil steep-ly decease in increasing depth, and may seriously overestimate the actual leaching mass flow.


2.5 Calculations Simplebox can perform two types of calculations: 1. Steady-state or "level 3" calculation. If the conditions (loadings and environ-mental conditions) remain constant in time for a sufficiently long period of time, eventually a steady state, in which all mass flows and concentrations are constant in time, will develop. At steady state, the sum of the mass balance equation terms is equal to zero for all boxes, and the n steady-state concentrations can be solved from the n linear mass balance equations. This steady-state solution is obtained in Simple-box by means of matrix inversion on the."engine-sheet" The mass flows and concen-trations that characterize this steady state are written by Simplebox in output tables on the "level 3 output-sheet". 2. Quasi-dynamic or "level 4" calculation. If a steady-state is not developed yet, mass flows and concentrations still change to that new steady state, according to the mass balance equations. The "level 4" computation is done by numerical integration of the set of mass balance equations from time zero, with all concentrations at zero, to infinite time with all concentrations constant at steady state. The numerical integration is carried out by the external program "Integrat.exe". Input for this program is gener-ated in the spreadsheet on the "level 4-sheet". The output of the integration program is put on this same worksheet. A built-in VBA-macro in the worksheet generates an in-put-file to be used by "Integrat.exe", starts the integrator and copies its output into the Simplebox spreadsheet. Because the values of the elements of the model matrix are needed for level 4-computations the correct order is to compute the steady-state solution first and option-ally carry out the dynamic response computation afterwards.

Steady state solution The model description in Simplebox consists of the mass balance equations described in paragraph @@. In Simplebox fourty boxes are distinguished: the regional and con-tinental system contain ten boxes each, the global scales consists of four boxes; the local scale contains eight boxes. In The SimpleBox systems comprises 40 compart-ments (boxes) in total (Table 2).

Table 2, the box numbers are given for the compartments of the different scales.

At steady state, all the forty mass balances become equal to zero:

dCiV . = EMIS + ADV + DIFF - REM - DEGRD 0i i ij ij i idt In matrix-format, the set of these forty mass balances reads:

CNST = CF.Css with

CNST : vector of constant terms of mass balance equations (emissions) CF : matrix of coefficients (removal, degradation and transport) Css : vector of steady-state concentrations

As the product of a matrix and its inverse is equals to 1, the solution of the set of mass balances can be obtained by multiplying the left and right parts by the inverse of the matrix of coefficients:

1 1CF .CF.Css Css CF .CNST

Simplebox uses this matrix-inversion method to calculate the steady-state concentra-tions.

Transient solution As an option, the response of the system to changes in emissions, i.e. the development to steady state, may be computed. As the phase of evolution to steady state is often referred to as the transient phase, the computation is referred to as “transient-dynamics computation”. The most commonly used loading scenario is a "block scenario", in which the loading have the value used in the steady-state computation for a period of time, long enough to approach the steady state, followed by the value zero for an equally long period of time. Using this scenario, both the development toward the steady state that has been computed and the recovery upon elimination of sources are computed. This computa-tion is known in "Mackay-nomenclature" as "level 4 computation". The transient-dynamics computation is described by the following.

The mass balances between the boxes are rewritten in the following format:

N

E I f ci i ,dc i j j i j1 (1)

dt vi

with ci : concentration in box i [mol.m-3] t : time [s] Ei : emission mass flow into box i [mol.s-1]

Ii : import mass flow into box i [mol.s-1]

, : flow from box j into box i [m3 (of medium i) s-1] fi j


vi : volume of box i [m3] N : number of boxes

In these mass balance equations, the parameters vi and f , have the same values as i j

their equivalents Vi and CFi j in equations (284) and (285), used for computation of the steady-state solution. These parameter values are written into a settings table, which is read by the integration routine. The parameters Ei and Ii are read by the transient computation routine from a scenario table.

Equation (1) can be written as a system of coupled equations:

dc Ac b

dt (2) c(0) c 0

with c b c 0 :, , vectors with dimension N A : coupling matrix with dimension N N

and E I fi j,i ibi ; A , (3)i j v vi i

The general solution to this problem is

t ( ) exp( t ) c 0 exp( A b dc t A )

0 (4)

) A I exp( t ) exp( tA c 0 1 A b

which is easily verified by differentiation. The last equality sign only holds when b is time-independent as in the “level-4” computations. When lim exp( tA ) 0 , then the

t

1steady state solution is c A b . For convenience it is assumed that the matrix A is

non-singular. The case where A has one zero-eigenvalue has been taken care of in the

routine. A zero eigenvalue exists when there is no decay whatsoever in the system, or when al decays are described as transfers to compartments that contain the decayed substance, i.e., when one keeps the mass balance of the total system, including de-cayed substances, to be zero.

In (4)

1 2 2 1 3 3tA) I tA 2! t A 3! t A (5)exp(

is the matrix obtained by the formal series expansion of the exponential function. The exponent of a matrix is not known, generally, but the exponent of a diagonal matrix

e1

1 2

e 2 exp( ) exp (6)

n e n

Now, let us assume that the system matrix A in (2), i.e. the matrix of the system of

equations (306) in the report, can be diagonalized. It is well known that such a diago-nalization can be performed when there exist eigenvalues and eigenvectors s , such that As s .

Let the columns of the matrix S ( , s ,,s s ) consist of the eigenvectors of A1 2 n

with corresponding eigenvalues 1, ,,n : 2

AS S (7)

then

1 1 1 1 2 1 1 3exp(tA ) exp(StS ) I tS S (tSS ) (tS S ) 2! 3!

1 1 2 1 1I tS S 2! t SS S S (8) 2 2 1 1 t S S exp(t) S I t 2!

1 S

and the solution in equation (4) is:

t 1 1c t ( ) S exp(t) S c 0 exp()S b d 0 (9) 1 1 1exp(t)S c 0 S I exp(t) S S b

where the last equality assumes b to be constant. When all eigenvalues (or all real parts of the eigenvalues) are smaller than 0, then the steady state solution is


1 1 1c S S b A b (10)

The computations thus consist of the computations of eigenvalues and corresponding eigenvectors, inverting the matrix S of eigenvectors and then calculating the last line

of equation (9) for different time points.

3 Operation

3.1 SimpleBox workbook structure The SimpleBox 3.0 model was developed as an Excel97 spreadsheet. The workbook contains 13 worksheets. An overview of these sheets and their function is given in Table 3:

Version Short version description Database Database of physico-chemical properties of @@ substances Input Substance identification and declaration of emissions and

physico-chemical properties level 3 output Tables and figures of output of the steady state computations level 4 Input and output of the "level 4" (transient) calculations Local Description of the environment and processes on the local

scale Regional Description of the environment and processes on the regional

scale Continental Description of the environment and processes on the conti-

nental scale Moderate Description of the environment and processes on the moder-

ate global scale Arctic Description of the environment and processes on the arctic

global scale Tropic Description of the environment and processes on the tropic

global scale Engine all the level 3 computations variable names variable administration

Table 3: The worksheets of the SimpleBox 3.0 workbook.

In the previous version, SimpleBox 2.0, each worksheet representing a spatial scale had the same basic structure, consisting of an input block, a computation block and an output block. As a consequence a lot of redundant input was required and the output was scattered. SimpleBox 3.0 has a slightly different structure. On the "input" sheet all relevant substance properties and emissions can be filled in. The characteristics of the spatial scales are defined on the worksheets with the corresponding titles. Since all the environment settings have default values, only the data on the "input" sheet are strictly needed to make a "level 3" computation. These computations are made on the "engine" sheet. The principle of the calculations are described in paragraph 2.@@. All tables and figures of the level 3 computation are given at the "level 3 output" sheet. On the "database"sheet the relevant substance properties and emissions for a number of chemicals are listed. These substances can easily be selected by means of the spin


button in cell H5 of the "Input"sheet or by filling in a number in cell I7 corresponding

with the row number of the substance on the "database" sheet. In SimpleBox 3.0 a

macro "SeriesCalculation"is built in to perform series calculations by using the data of

this list Relevant output of these calculations is written to the columns "AK" through

"AR". On the "level 4" sheet the necessary input to perform the transient solution can

be generated. Also the outcome of these computations are placed here. How to per-

form the level 4 computation is discussed in paragraph 3.3

All the Simplebox variables are defined in the worksheets as named cell ranges. Fig-

ure 3 shows a part of the "input-sheet". The worksheets that represent a spatial scale

and the "input-sheet" are built up in a similar way. The variables on the sheets are

listed in rows. Furthermore:

In the columns "A" to "F" a textual description of the variables is given

In the "G"-column the name of the variable is given

The "H"-column contains the unit in which the variable should be given

The "I"-column is reserved for user input to overrule the default values

The "J"-column (input-sheet: "K"-column) contains formulas that calculate values

for the variables. The "J"-column of the "input-sheet" contains values for com-

pound properties and/or emissions originating from the "database-sheet".

The "K"-column (input-sheet: "L"-column) contains values for variables which

are constants.

In the "L"-column (input-sheet: "M"-column) conditional statements are evaluated

to adopt either the result of the user input, the estimation formula or the default

value as model input and converts this value into SI-units that are internally used

in SimpleBox. SimpleBox calculations are performed with these ultimate results.

3.2 Steady state computations and output

To perform a steady-state computation in SimpleBox all relevant substance properties

and emissions must be filled in on the "input" sheet. The environmental characteristics

of the different scales are defined on the worksheets with names of the corresponding

scale and can be adjusted to every specific situation. If "Calculation" in Excel is set to

"Automatic" (in Excel97: Tools/Options/Calculation-Automatic) level 3 computations

will be done instantaneously after changing anything in the SimpleBox workbook.

The steady state computation output is summarized in the following tables:

Table 1: Concentrations, Fugacities, Toxic pressure, Emissions and Hold-up mass at Steady-state

Steady state concentrations for all compartments.

Fugacities (i.e. the tendency for a substance to move from one environmental

compartment to another) for all boxes.

Toxic pressure for all water, sediment and soil compartments.

An overview of the applied emissions.

An overview of the amount of the chemical present in each of the compartments at

steady state.This distribution is given in tons and as a percentage of the total mass

per scale. The summarised amounts per scale are also given as a percentage of the

total hold-up mass of the system.

Table 2: Half lives of removal from the enviromental compartments

The calculated half-lives for all occurring processes for any environmental

compartment. These values provide a clear insight of the relative importance of

each of the processes. Half lives are mentioned in days.

Table 3: Steady-state mass flows

The steady-state mass flows due to all occurring processes within and between

boxes are represented in this table. As a check for the integrity of the steady-state

computation, these mass flows are summed for each of the boxes. Because of the

principle "what goes in must go out" these mass flow balance of all compartments

and thus of all scales must be zero. Mass flows are given in tons/year.

Graphical overview of the steady state mass flows per scale

All mass flows within and between the various spatial scales are represented

graphically in the range (BL1..CI227) on the "level 3 output-sheet"


3.3 Level 4 computations and output

With SimpleBox 3.0 the "Transient.exe" program is supplied. This program gives the possibility to consider concentration development during non steady-state and gives the opportunity to study emission scenarios. These level 4 computations can be per-formed by executing the built-in "Transient"-macro. Since this macro executes the "Transient.exe" program, drive and path where this program is located should be giv-en. This can be performed by editing the following lines in the "Transient"-macro:

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

ChDrive "D" 'the drive letter and…. ChDir "\Usr" 'the working directory where you placed 'integrat.exe'" XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

The principal of the transient solution is described in section @@of this document. The "Transient.exe" program needs input (emission scenario) in the form of a text-file called "integrat.scn". Therefor, the range "scenario" (S51..BI185) on the "level 4-sheet" is exported as a tab delimited text file.

Figure @@3: Screenshot of the scenario-range on the "level 4-sheet"

Figure 4 shows a part of the "level 4"-sheet. For reasons of clarification some areas are colored, however, in the SimpleBox workbook this is not the case. The level 4 scenario file begins with the declaration of the number of boxes (40) which means that a 40 by 40 matrix must be solved. In the second line the time interval in years is declared (here: calculation of the current concentrations each ten years) and subse-quently the initial concentrations in the boxes. Normally these initial concentrations are zero because the integration starts at t=0 and no emissions have taken place at that time. See the pink block in Figure@@3. Below this two or more blocks are given that are built up in the same way. The first block begins in cell S55 of the "level 4" sheet; the second block starts at cell S97, the

third one at cell S139 and so on. These blocks begin with declaration of "time". In the first block time is equal to zero. Hereafter, forty lines are given all starting with "BALANCE i" (grey area).After this the emission rates (mol.s-1) valid at time zero divided by the volume of box i are given (yellow area) followed by all elements of the model matrix (blue area, derived from the "engine"-sheet) divided by the volume of box i. Generally spoken "time" in the first block is set to zero and the emissions are set to zero. Since the emission rates are set to zero consequently all concentrations will be zero. The next blocks begin with the declaration of the begin time whereupon the new emission rates become valid. It is clear that this time must be equal to or greater than the time step. The values in the yellow block reflect the emission rates as from this "time" until the next "time". A number of time blocks can be defined in this way. The scenario file must end with a line that contains the end time. The area of the Range "scenario" must of course be adjusted so it contains all the time blocks and the last line containing the end time. In order to simplify the creation of the scenario file in the range S4..X45 the different "times" and emissions can be given. The values filled in here are taken over by the appropriate cells in the scenario file. It should be noted that three blocks are prede-fined. If more blocks are needed users must expand the scenario file by copying a time block below the third block and take care that the values are taken over properly. Also the area of scenario should be adjusted in that case.

Mass of Chemical in the Environment

0%

25%

50%

75%

100%

0 1 2 3 4 5 Time [years]

Mas

s/sc

ale

(% o

f Max

.M

ass/

scal

e)

MassL

MassR

MassC

MassM

MassA

MassT

MassTOT

Start. Emissions = 0

T=0.2. Emissions = X T = 2. Emissions = 0.1X

T = 4.End

Figure @@: Typical output of the level 4 calculations.


The quasi-dynamic computation is carried out by executing the "Transient"-macro in SimpleBox 3.0. This macro first creates the text file that is necessary to perform the level 4 calculations: the range scenario of the "level 4"-sheet is copied to a text file with the name Integrat.scn. Consequently the transient.exe program is run. The pro-gram writes its results to the file Integrat.out. This output consists of concentrations in mol.m-3 for each box at each time step from t=0 to t=end time. Subsequently the mac-ro reads the results from this file and produces several graphs on the "level 4" sheet. Because the readability off the graphs all "transient" results are scaled to the steady-state results.

1 Van de Meent, D. 1989. SIMPLERISK, a model for estimating local concentrations in water and soil. Report nr. 718706 001. RIVM, Bilthoven, The Netherlands. (in Dutch)

References

Van de Meent, D. 1989. SIMPLERISK, a model for estimating local concentrations in water and soil. Report nr. 718706 001. RIVM, Bilthoven, The Netherlands. (in Dutch)

SimpleBox 1.0 SimpleBox 2.0 Calculating fugacity Van de Meent and De Bruijn EUSES Struijs J, Peijnenburg WJGM. 2002. Predictions by the multimedia environmental fate

model SimpleBox compared to field data: Intermedia concentration ratios of two phthalate esters. Report nr. 607220 008. RIVM, Bilthoven, The Netherlands.

Bakker J, Brandes LJ, Den Hollander HA, Van de Meent D, Struijs J. 2003. Validat-ing SimpleBox-Computed Steady-State Concentration Ratios Report nr. 607220 010. RIVM, Bilthoven, The Netherlands

Roelofs en Van de Meent TGD to be completed ….


Appendix: Equations and model parameters of the spreadsheet SimpleBox 3.0.xls

Variable name Formula / Value Unit Cell address ADSORBflow.w1C.sd1C =(kwsd.water.wC * kwsd.sed.sdC) / (kwsd.water.wC + kwsd.sed.sdC) * FRw.w1C * (SYSTEMAREA.C *

AREAFRAC.w1C) [m3.s-1] =continental!$L$208

ADSORBflow.w1R.sd1R =(kwsd.water.wR * kwsd.sed.sdR) / (kwsd.water.wR + kwsd.sed.sdR) * FRw.w1R * (SYSTEMAREA.R * AREAFRAC.w1R)

[m3.s-1] =regional!$L$204

ADSORBflow.w2C.sd2C =(kwsd.water.wC * kwsd.sed.sdC) / (kwsd.water.wC + kwsd.sed.sdC) * FRw.w2C * (SYSTEMAREA.C * AREAFRAC.w2C)

[m3.s-1] =continental!$L$210

ADSORBflow.w2R.sd2R =(kwsd.water.wR * kwsd.sed.sdR) / (kwsd.water.wR + kwsd.sed.sdR) * FRw.w2R * (SYSTEMAREA.R * AREAFRAC.w2R)


ADSORBflow.wA.sdA =(kwsd.water.wA * kwsd.sed.sdA) / (kwsd.water.wA + kwsd.sed.sdA) * FRw.wA * SYSTEMAREA.A * AREAFRAC.wA

[m3.s-1] =arctic!$L$88

ADSORBflow.wL.sdL =(kwsd.water.wL * kwsd.sed.sdL) / (kwsd.water.wL + kwsd.sed.sdL) * FRw.wL * (SYSTEMAREA.L * AREAFRAC.wL)

[m3.s-1] =local!$L$174

ADSORBflow.wM.sdM =(kwsd.water.wM * kwsd.sed.sdM) / (kwsd.water.wM + kwsd.sed.sdM) * FRw.wM * SYSTEMAREA.M * AREAFRAC.wM

[m3.s-1] =moderate!$L$93

ADSORBflow.wT.sdT =(kwsd.water.wT * kwsd.sed.sdT) / (kwsd.water.wT + kwsd.sed.sdT) * FRw.wT * SYSTEMAREA.T * AREAFRAC.wT

[m3.s-1] =tropic!$L$88

ADVflow.w2C.w2R =WIDTH.w2R * DEPTH.w2R * SEAcurrent.w2C.w2R [m3.s-1] =continental!$L$79 ADVflow.wM.w2C =(VOLUME.w2C / SQRT(SYSTEMAREA.C * AREAFRAC.w2C)) * SEAcurrent.wM.w2C [m3.s-1] =moderate!$L$34 AEROSOLdeprate.A 1.00E - 03 [m.s-1] =arctic!$L$67 AEROSOLdeprate.C 1.00E - 03 [m.s-1] =continental!$L$149 AEROSOLdeprate.L 1.00E - 03 [m.s-1] =local!$L$123 AEROSOLdeprate.M 1.00E - 03 [m.s-1] =moderate!$L$71 AEROSOLdeprate.R 1.00E - 03 [m.s-1] =regional!$L$145 AEROSOLdeprate.T 1.00E - 03 [m.s-1] =tropic!$L$67 AerosolWashout.A =RAINrate.A * (1 - FRg.aA) * COLLECTeff.A [m.s-1] =arctic!$L$65 AerosolWashout.C =RAINrate.C * (1 - FRg.aC) * COLLECTeff.C [m.s-1] =continental!$L$147 AerosolWashout.L =RAINrate.L * (1 - FRg.aL) * COLLECTeff.L [m.s-1] =local!$L$121 AerosolWashout.M =RAINrate.M * (1 - FRg.aM) * COLLECTeff.M [m.s-1] =moderate!$L$69

AerosolWashout.R =RAINrate.R * (1 - FRg.aR) * COLLECTeff.R [m.s-1] =regional!$L$143 AerosolWashout.T =RAINrate.T * (1 - FRg.aT) * COLLECTeff.T [m.s-1] =tropic!$L$65 AIRflow.aA.aM =VOLUME.aA / TAU.aA [m3.s-1] =arctic!$L$29 AIRflow.aC.aM =VOLUME.aC / TAU.aC - AIRflow.aC.aR [m3.s-1] =continental!$L$66 AIRflow.aC.aR =AIRflow.aR.aC [m3.s-1] =continental!$L$69 AIRflow.aL.aR =VOLUME.aL / TAU.aL [m3.s-1] =local!$L$59 AIRflow.aM.aA =AIRflow.aA.aM [m3.s-1] =moderate!$L$30 AIRflow.aM.aC =AIRflow.aC.aM [m3.s-1] =moderate!$L$29 AIRflow.aM.aT =AIRflow.aT.aM [m3.s-1] =moderate!$L$31 AIRflow.aR.aC =VOLUME.aR / TAU.aR - AIRflow.aR.aL [m3.s-1] =regional!$L$68 AIRflow.aR.aL =AIRflow.aL.aR [m3.s-1] =regional!$L$71 AIRflow.aT.aM =VOLUME.aT / TAU.aT [m3.s-1] =tropic!$L$29 AlphaS - 2.56E + 00 [g.kg-1] =input!$M$43 AlphaW - 4.26E + 00 [g.L-1] =input!$M$41 AREAFRAC.s1C =0.27 * (AREAland.C / (SYSTEMAREA.C + SYSTEMAREA.R)) [ - ] =continental!$L$22 AREAFRAC.s1L 0.27 [ - ] =local!$L$17 AREAFRAC.s1R =0.27 * (AREAland.R / (SYSTEMAREA.R + SYSTEMAREA.L)) [ - ] =regional!$L$24 AREAFRAC.s2C =0.6 * (AREAland.C / (SYSTEMAREA.C + SYSTEMAREA.R)) [ - ] =continental!$L$23 AREAFRAC.s2L 0.6 [ - ] =local!$L$18 AREAFRAC.s2R =0.6 * (AREAland.R / (SYSTEMAREA.R + SYSTEMAREA.L)) [ - ] =regional!$L$25 AREAFRAC.s3C =0.1 * (AREAland.C / (SYSTEMAREA.C + SYSTEMAREA.R)) [ - ] =continental!$L$24 AREAFRAC.s3L 0.1 [ - ] =local!$L$19 AREAFRAC.s3R =0.1 * (AREAland.R / (SYSTEMAREA.R + SYSTEMAREA.L)) [ - ] =regional!$L$26 AREAFRAC.sA =1 - AREAFRAC.wA [ - ] =arctic!$L$13 AREAFRAC.sM =1 - AREAFRAC.wM [ - ] =moderate!$L$13 AREAFRAC.sT =1 - AREAFRAC.wT [ - ] =tropic!$L$13 AREAFRAC.w1C =0.03 * (AREAland.C / (SYSTEMAREA.C + SYSTEMAREA.R)) [ - ] =continental!$L$20 AREAFRAC.w1R =0.03 * (AREAland.R / (SYSTEMAREA.R + SYSTEMAREA.L)) [ - ] =regional!$L$22 AREAFRAC.w2C =AREAsea.C / (SYSTEMAREA.C + SYSTEMAREA.R) [ - ] =continental!$L$21 AREAFRAC.w2R =LENGTH.w2R * WIDTH.w2R / (SYSTEMAREA.R + SYSTEMAREA.L) [ - ] =regional!$L$23 AREAFRAC.wA 0.6 [ - ] =arctic!$L$12 AREAFRAC.wL 0.03 [ - ] =local!$L$16


AREAFRAC.wM 0.5 [ - ] =moderate!$L$12 AREAFRAC.wT 0.7 [ - ] =tropic!$L$12 AREAland.C 3.71E + 06 [km2] / [m2] =continental!$L$18 AREAland.R 2.29E + 05 [km2] / [m2] =regional!$L$18 AREAsea.C =AREAland.C / 1000000 [km2] / [m2] =continental!$L$19 AREAsea.R =LENGTH.w2R * WIDTH.w2R / 1000000 [km2] / [m2] =regional!$L$19 BACT.test 4.00E + 04 [CFU.mL-1] =input!$M$32 BACT.wA 4.00E + 04 [CFU.mL-1] =arctic!$L$104 BACT.wC 4.00E + 04 [CFU.mL-1] =continental!$L$233 BACT.wL 4.00E + 04 [CFU.mL-1] =local!$L$196 BACT.wM 4.00E + 04 [CFU.mL-1] =moderate!$L$109 BACT.wR 4.00E + 04 [CFU.mL-1] =regional!$L$229 BACT.wT 4.00E + 04 [CFU.mL-1] =tropic!$L$104 BCFfish.A =FATfish.A * Kow [L.kg-1] =arctic!$L$48 BCFfish.M =FATfish.M * Kow [L.kg-1] =moderate!$L$52 BCFfish.T =FATfish.T * Kow [L.kg-1] =tropic!$L$48 BCFfish1.C =FATfish1.C * Kow [L.kg-1] =continental!$L$97 BCFfish1.L =FATfish1.L * Kow [L.kg-1] =local!$L$82 BCFfish1.R =FATfish1.R * Kow [L.kg-1] =regional!$L$93 BCFfish2.C =FATfish2.C * Kow [L.kg-1] =continental!$L$104 BCFfish2.R =FATfish2.R * Kow [L.kg-1] =regional!$L$100 BetaS 4.41E - 01 [g.kg-1] =input!$M$44 BetaW 4.40E - 01 [ - ] / [g.l-1] =input!$M$42 biodeg i [r / r - / i / p] =input!$M$31 BIOmass.w1C 1.00E + 00 [mg.L-1] / [kg.m-3] =continental!$L$99 BIOmass.w1R 1.00E + 00 [mg.L-1] / [kg.m-3] =regional!$L$95 BIOmass.w2C 1.00E + 00 [mg.L-1] / [kg.m-3] =continental!$L$106 BIOmass.w2R 1.00E + 00 [mg.L-1] / [kg.m-3] =regional!$L$102 BIOmass.wA 1.00E + 00 [mg.L-1] / [kg.m-3] =arctic!$L$50 BIOmass.wL 1.00E + 00 [mg.L-1] / [kg.m-3] =local!$L$84 BIOmass.wM 1.00E + 00 [mg.L-1] / [kg.m-3] =moderate!$L$54 BIOmass.wT 1.00E + 00 [mg.L-1] / [kg.m-3] =tropic!$L$50

BURIALflow.sd1C =NETsedrate.w1C * SYSTEMAREA.C * AREAFRAC.w1C [m3.s-1] =continental!$L$244 BURIALflow.sd1R =NETsedrate.w1R * SYSTEMAREA.R * AREAFRAC.w1R [m3.s-1] =regional!$L$239 BURIALflow.sd2C =NETsedrate.w2C * SYSTEMAREA.C * AREAFRAC.w2C [m3.s-1] =continental!$L$245 BURIALflow.sd2R =NETsedrate.w2R * SYSTEMAREA.R * AREAFRAC.w2R [m3.s-1] =regional!$L$240 BURIALflow.sdA =NETsedrate.wA * SYSTEMAREA.A * AREAFRAC.wA [m3.s-1] =arctic!$L$110 BURIALflow.sdL =NETsedrate.wL * SYSTEMAREA.L * AREAFRAC.wL [m3.s-1] =local!$L$205 BURIALflow.sdM =NETsedrate.wM * SYSTEMAREA.M * AREAFRAC.wM [m3.s-1] =moderate!$L$115 BURIALflow.sdT =NETsedrate.wT * SYSTEMAREA.T * AREAFRAC.wT [m3.s-1] =tropic!$L$110 C.OHrad 5.00E + 05 [cm-3] =input!$M$27 C.OHrad.aA 5.00E + 05 [cm-3] =arctic!$L$101 C.OHrad.aC 5.00E + 05 [cm-3] =continental!$L$229 C.OHrad.aL 5.00E + 05 [cm-3] =local!$L$193 C.OHrad.aM 5.00E + 05 [cm-3] =moderate!$L$106 C.OHrad.aR 5.00E + 05 [cm-3] =regional!$L$225 C.OHrad.aT 5.00E + 05 [cm-3] =tropic!$L$101 ChemID =input!$M$6 ChemName =input!$M$5 COLLECTeff.A 2.00E + 05 [ - ] =arctic!$L$69 COLLECTeff.C 2.00E + 05 [ - ] =continental!$L$151 COLLECTeff.L 2.00E + 05 [ - ] =local!$L$125 COLLECTeff.M 2.00E + 05 [ - ] =moderate!$L$73 COLLECTeff.R 2.00E + 05 [ - ] =regional!$L$147 COLLECTeff.T 2.00E + 05 [ - ] =tropic!$L$69 CORG 2.00E - 02 [ - ] =input!$M$17 CORG.s1C 2.00E - 02 [ - ] =continental!$L$117 CORG.s1L 2.00E - 02 [ - ] =local!$L$92 CORG.s1R 2.00E - 02 [ - ] =regional!$L$113 CORG.s2C 2.00E - 02 [ - ] =continental!$L$122 CORG.s2L 2.00E - 02 [ - ] =local!$L$97 CORG.s2R 2.00E - 02 [ - ] =regional!$L$118 CORG.s3C 2.00E - 02 [ - ] =continental!$L$127 CORG.s3L 2.00E - 02 [ - ] =local!$L$102


CORG.s3R 2.00E - 02 [ - ] =regional!$L$123 CORG.sA 2.00E - 02 [ - ] =arctic!$L$58 CORG.sd1C 5.00E - 02 [ - ] =continental!$L$109 CORG.sd1R 5.00E - 02 [ - ] =regional!$L$105 CORG.sd2C 5.00E - 02 [ - ] =continental!$L$112 CORG.sd2R 5.00E - 02 [ - ] =regional!$L$108 CORG.sdA 5.00E - 02 [ - ] =arctic!$L$53 CORG.sdL 5.00E - 02 [ - ] =local!$L$87 CORG.sdM 5.00E - 02 [ - ] =moderate!$L$57 CORG.sdT 5.00E - 02 [ - ] =tropic!$L$53 CORG.sM 2.00E - 02 [ - ] =moderate!$L$62 CORG.sT 2.00E - 02 [ - ] =tropic!$L$58 CORGsusp.A 1.00E - 01 [ - ] =arctic!$L$46 CORGsusp.L 1.00E - 01 [ - ] =local!$L$80 CORGsusp.M 1.00E - 01 [ - ] =moderate!$L$50 CORGsusp.T 1.00E - 01 [ - ] =tropic!$L$46 CORGsusp1.C 1.00E - 01 [ - ] =continental!$L$95 CORGsusp1.R 1.00E - 01 [ - ] =regional!$L$91 CORGsusp2.C 1.00E - 01 [ - ] =continental!$L$102 CORGsusp2.R 1.00E – 01 [ - ] =regional!$L$98 DataBaseRowNr =input!$M$7 Deff.s1C =DIFFgas * FRACa.s1C^ 1.5 * (1 - FRw.s1C - FRs.s1C) / FRACa.s1C + DIFFwater * FRACw.s1C^ 1.5 *

FRw.s1C / FRACw.s1C + SOLIDdiff.s1C * FRs.s1C / FRACs.s1C [m2.s-1] =continental!$L$34

Deff.s1L =DIFFgas * FRACa.s1L^ 1.5 * (1 - FRw.s1L - FRs.s1L) / FRACa.s1L + DIFFwater * FRACw.s1L^ 1.5 * FRw.s1L / FRACw.s1L + SOLIDdiff.s1L * FRs.s1L / FRACs.s1L

[m2.s-1] =local!$L$27

Deff.s1R =DIFFgas * FRACa.s1R^ 1.5 * (1 - FRw.s1R - FRs.s1R) / FRACa.s1R + DIFFwater * FRACw.s1R^ 1.5 * FRw.s1R / FRACw.s1R + SOLIDdiff.s1R * FRs.s1R / FRACs.s1R


Deff.s2C =DIFFgas * FRACa.s2C^ 1.5 * (1 - FRw.s2C - FRs.s2C) / FRACa.s2C + DIFFwater * FRACw.s2C^ 1.5 * FRw.s2C / FRACw.s2C + SOLIDdiff.s2C * FRs.s2C / FRACs.s2C



[m2.s-1] =local!$L$33



Deff.s3C =DIFFgas * FRACa.s3C^ 1.5 * (1 - FRw.s3C - FRs.s3C) / FRACa.s3C + DIFFwater * FRACw.s3C^ 1.5 * FRw.s3C / FRACw.s3C + SOLIDdiff.s3C * FRs.s3C / FRACs.s3C



[m2.s-1] =local!$L$39



Deff.sA =DIFFgas * FRACa.sA^ 1.5 * (1 - FRw.sA - FRs.sA) / FRACa.sA + DIFFwater * FRACw.sA^ 1.5 * FRw.sA / FRACw.sA + SOLIDdiff.sA * FRs.sA / FRACs.sA


Deff.sM =DIFFgas * FRACa.sM^ 1.5 * (1 - FRw.sM - FRs.sM) / FRACa.sM + DIFFwater * FRACw.sM^ 1.5 * FRw.sM / FRACw.sM + SOLIDdiff.sM * FRs.sM / FRACs.sM


Deff.sT =DIFFgas * FRACa.sT^ 1.5 * (1 - FRw.sT - FRs.sT) / FRACa.sT + DIFFwater * FRACw.sT^ 1.5 * FRw.sT / FRACw.sT + SOLIDdiff.sT * FRs.sT / FRACs.sT


DEPflow.aA.sA =(DRYDEPaerosol.A + AerosolWashout.A + GasWashout.A) * (SYSTEMAREA.A * AREAFRAC.sA) [m3.s-1] =arctic!$L$63 DEPflow.aA.wA =(DRYDEPaerosol.A + AerosolWashout.A + GasWashout.A) * (SYSTEMAREA.A * AREAFRAC.wA) [m3.s-1] =arctic!$L$62 DEPflow.aC.s1C =(DRYDEPaerosol.C * (1 - IFDRYaerosol.v1C) + AerosolWashout.C * (1 - IFWETaerosol.v1C) +

GasWashout.C * (1 - IFWETgas.v1C)) * (SYSTEMAREA.C * AREAFRAC.s1C) [m3.s-1] =continental!$L$141

DEPflow.aC.s2C =(DRYDEPaerosol.C * (1 - IFDRYaerosol.v2C) + AerosolWashout.C * (1 - IFWETaerosol.v2C) + GasWashout.C * (1 - IFWETgas.v2C)) * (SYSTEMAREA.C * AREAFRAC.s2C)


DEPflow.aC.s3C =(DRYDEPaerosol.C + AerosolWashout.C + GasWashout.C) * (SYSTEMAREA.C * AREAFRAC.s3C) [m3.s-1] =continental!$L$143 DEPflow.aC.v1C =(DRYDEPaerosol.C * IFDRYaerosol.v1C + AerosolWashout.C * IFWETaerosol.v1C + GasWashout.C *

IFWETgas.v1C) * (SYSTEMAREA.C * AREAFRAC.s1C) [m3.s-1] =continental!$L$144

DEPflow.aC.v2C =(DRYDEPaerosol.C * IFDRYaerosol.v2C + AerosolWashout.C * IFWETaerosol.v2C + GasWashout.C * IFWETgas.v2C) * (SYSTEMAREA.C * AREAFRAC.s2C)


DEPflow.aC.w1C =(DRYDEPaerosol.C + AerosolWashout.C + GasWashout.C) * (SYSTEMAREA.C * AREAFRAC.w1C) [m3.s-1] =continental!$L$139 DEPflow.aC.w2C =(DRYDEPaerosol.C + AerosolWashout.C + GasWashout.C) * (SYSTEMAREA.C * AREAFRAC.w2C) [m3.s-1] =continental!$L$140 DEPflow.aL.s1L =(DRYDEPaerosol.L * (1 - IFDRYaerosol.v1L) + AerosolWashout.L * (1 - IFWETaerosol.v1L) +

GasWashout.L * (1 - IFWETgas.v1L)) * (SYSTEMAREA.L * AREAFRAC.s1L) [m3.s-1] =local!$L$115

DEPflow.aL.s2L =(DRYDEPaerosol.L * (1 - IFDRYaerosol.v2L) + AerosolWashout.L * (1 - IFWETaerosol.v2L) + GasWashout.L * (1 - IFWETgas.v2L)) * (SYSTEMAREA.L * AREAFRAC.s2L)

[m3.s-1] =local!$L$116

DEPflow.aL.s3L =(DRYDEPaerosol.L + AerosolWashout.L + GasWashout.L) * (SYSTEMAREA.L * AREAFRAC.s3L) [m3.s-1] =local!$L$117


DEPflow.aL.v1L =(DRYDEPaerosol.L * IFDRYaerosol.v1L + AerosolWashout.L * IFWETaerosol.v1L + GasWashout.L * IFWETgas.v1L) * (SYSTEMAREA.L * AREAFRAC.s1L)

[m3.s-1] =local!$L$118

DEPflow.aL.v2L =(DRYDEPaerosol.L * IFDRYaerosol.v2L + AerosolWashout.L * IFWETaerosol.v2L + GasWashout.L * IFWETgas.v2L) * (SYSTEMAREA.L * AREAFRAC.s2L)

[m3.s-1] =local!$L$119

DEPflow.aL.wL =(DRYDEPaerosol.L + AerosolWashout.L + GasWashout.L) * (SYSTEMAREA.L * AREAFRAC.wL) [m3.s-1] =local!$L$114 DEPflow.aM.sM =(DRYDEPaerosol.M + AerosolWashout.M + GasWashout.M) * (SYSTEMAREA.M * AREAFRAC.sM) [m3.s-1] =moderate!$L$67 DEPflow.aM.wM =(DRYDEPaerosol.M + AerosolWashout.M + GasWashout.M) * (SYSTEMAREA.M * AREAFRAC.wM) [m3.s-1] =moderate!$L$66 DEPflow.aR.s1R =(DRYDEPaerosol.R * (1 - IFDRYaerosol.v1R) + AerosolWashout.R * (1 - IFWETaerosol.v1R) +

GasWashout.R * (1 - IFWETgas.v1R)) * (SYSTEMAREA.R * AREAFRAC.s1R) [m3.s-1] =regional!$L$137

DEPflow.aR.s2R =(DRYDEPaerosol.R * (1 - IFDRYaerosol.v2R) + AerosolWashout.R * (1 - IFWETaerosol.v2R) + GasWashout.R * (1 - IFWETgas.v2R)) * (SYSTEMAREA.R * AREAFRAC.s2R)


DEPflow.aR.s3R =(DRYDEPaerosol.R + AerosolWashout.R + GasWashout.R) * (SYSTEMAREA.R * AREAFRAC.s3R) [m3.s-1] =regional!$L$139 DEPflow.aR.v1R =(DRYDEPaerosol.R * IFDRYaerosol.v1R + AerosolWashout.R * IFWETaerosol.v1R + GasWashout.R *

IFWETgas.v1R) * (SYSTEMAREA.R * AREAFRAC.s1R) [m3.s-1] =regional!$L$140

DEPflow.aR.v2R =(DRYDEPaerosol.R * IFDRYaerosol.v2R + AerosolWashout.R * IFWETaerosol.v2R + GasWashout.R * IFWETgas.v2R) * (SYSTEMAREA.R * AREAFRAC.s2R)


DEPflow.aR.w1R =(DRYDEPaerosol.R + AerosolWashout.R + GasWashout.R) * (SYSTEMAREA.R * AREAFRAC.w1R) [m3.s-1] =regional!$L$135 DEPflow.aR.w2R =(DRYDEPaerosol.R + AerosolWashout.R + GasWashout.R) * (SYSTEMAREA.R * AREAFRAC.w2R) [m3.s-1] =regional!$L$136 DEPflow.aT.sT =(DRYDEPaerosol.T + AerosolWashout.T + GasWashout.T) * (SYSTEMAREA.T * AREAFRAC.sT) [m3.s-1] =tropic!$L$63 DEPflow.aT.wT =(DRYDEPaerosol.T + AerosolWashout.T + GasWashout.T) * (SYSTEMAREA.T * AREAFRAC.wT) [m3.s-1] =tropic!$L$62 DEPTH.s1C =IF(PENdepth.s1C> 1, 1, IF(PENdepth.s1C< 0.03, 0.03, PENdepth.s1C)) [m] =continental!$L$30 DEPTH.s1L =IF(PENdepth.s1L> 1, 1, IF(PENdepth.s1L< 0.03, 0.03, PENdepth.s1L)) [m] =local!$L$23 DEPTH.s1R =IF(PENdepth.s1R> 1, 1, IF(PENdepth.s1R< 0.03, 0.03, PENdepth.s1R)) [m] =regional!$L$32 DEPTH.s2C =IF(PENdepth.s2C> 1, 1, IF(PENdepth.s2C< 0.2, 0.2, PENdepth.s2C)) [m] =continental!$L$36 DEPTH.s2L =IF(PENdepth.s2L> 1, 1, IF(PENdepth.s2L< 0.2, 0.2, PENdepth.s2L)) [m] =local!$L$29 DEPTH.s2R =IF(PENdepth.s2R> 1, 1, IF(PENdepth.s2R< 0.2, 0.2, PENdepth.s2R)) [m] =regional!$L$38 DEPTH.s3C =IF(PENdepth.s3C> 1, 1, IF(PENdepth.s3C< 0.03, 0.03, PENdepth.s3C)) [m] =continental!$L$42 DEPTH.s3L =IF(PENdepth.s3L> 1, 1, IF(PENdepth.s3L< 0.03, 0.03, PENdepth.s3L)) [m] =local!$L$35 DEPTH.s3R =IF(PENdepth.s3R> 1, 1, IF(PENdepth.s3R< 0.03, 0.03, PENdepth.s3R)) [m] =regional!$L$44 DEPTH.sA =IF(PENdepth.sA> 1, 1, IF(PENdepth.sA< 0.03, 0.03, PENdepth.sA)) [m] =arctic!$L$17 DEPTH.sd1C 3.00E + 00 [cm] / [m] =continental!$L$28 DEPTH.sd1R 3.00E + 00 [cm] / [m] =regional!$L$30

DEPTH.sd2C 3.00E + 00 [cm] / [m] =continental!$L$29 DEPTH.sd2R 3.00E + 00 [cm] / [m] =regional!$L$31 DEPTH.sdA 3.00E + 00 [cm] / [m] =arctic!$L$16 DEPTH.sdL 3.00E + 00 [cm] / [m] =local!$L$22 DEPTH.sdM 3.00E + 00 [cm] / [m] =moderate!$L$16 DEPTH.sdT 3.00E + 00 [cm] / [m] =tropic!$L$16 DEPTH.sM =IF(PENdepth.sM> 1, 1, IF(PENdepth.sM< 0.03, 0.03, PENdepth.sM)) [m] =moderate!$L$17 DEPTH.sT =IF(PENdepth.sT> 1, 1, IF(PENdepth.sT< 0.03, 0.03, PENdepth.sT)) [m] =tropic!$L$17 DEPTH.w1C 3.00E + 00 [m] =continental!$L$26 DEPTH.w1R 3.00E + 00 [m] =regional!$L$28 DEPTH.w2C 2.00E + 02 [m] =continental!$L$27 DEPTH.w2R 1.00E + 01 [m] =regional!$L$29 DEPTH.wA 1.00E + 03 [m] =arctic!$L$15 DEPTH.wL 3.00E + 00 [m] =local!$L$21 DEPTH.wM 1.00E + 03 [m] =moderate!$L$15 DEPTH.wT 1.00E + 03 [m] =tropic!$L$15 DESORBflow.sd1C.w1C =((kwsd.water.wC * kwsd.sed.sdC) / (kwsd.water.wC + kwsd.sed.sdC)) / Ksdw1.C * (SYSTEMAREA.C *

AREAFRAC.w1C) [m3.s-1] =continental!$L$209

DESORBflow.sd1R.w1R =((kwsd.water.wR * kwsd.sed.sdR) / (kwsd.water.wR + kwsd.sed.sdR)) / Ksdw1.R * (SYSTEMAREA.R * AREAFRAC.w1R)


DESORBflow.sd2C.w2C =((kwsd.water.wC * kwsd.sed.sdC) / (kwsd.water.wC + kwsd.sed.sdC)) / Ksdw2.C * (SYSTEMAREA.C * AREAFRAC.w2C)


DESORBflow.sd2R.w2R =((kwsd.water.wR * kwsd.sed.sdR) / (kwsd.water.wR + kwsd.sed.sdR)) / Ksdw2.R * (SYSTEMAREA.R * AREAFRAC.w2R)


DESORBflow.sdA.wA =(kwsd.water.wA * kwsd.sed.sdA / (kwsd.water.wA + kwsd.sed.sdA)) / Ksdw.A * SYSTEMAREA.A * AREAFRAC.wA


DESORBflow.sdL.wL =((kwsd.water.wL * kwsd.sed.sdL) / (kwsd.water.wL + kwsd.sed.sdL)) / Ksdw.L * (SYSTEMAREA.L * AREAFRAC.wL)

[m3.s-1] =local!$L$175

DESORBflow.sdM.wM =(kwsd.water.wM * kwsd.sed.sdM / (kwsd.water.wM + kwsd.sed.sdM)) / Ksdw.M * SYSTEMAREA.M * AREAFRAC.wM


DESORBflow.sdT.wT =(kwsd.water.wT * kwsd.sed.sdT / (kwsd.water.wT + kwsd.sed.sdT)) / Ksdw.T * SYSTEMAREA.T * AREAFRAC.wT



DIFFgas 7.69E - 06 [m2.s-1] =input!$M$11 DIFFwater 7.98E - 10 [m2.s-1] =input!$M$12 DRYDEPaerosol.A =AEROSOLdeprate.A * (1 - FRg.aA) [m.s-1] =arctic!$L$64 DRYDEPaerosol.C =AEROSOLdeprate.C * (1 - FRg.aC) [m.s-1] =continental!$L$146 DRYDEPaerosol.L =AEROSOLdeprate.L * (1 - FRg.aL) [m.s-1] =local!$L$120 DRYDEPaerosol.M =AEROSOLdeprate.M * (1 - FRg.aM) [m.s-1] =moderate!$L$68 DRYDEPaerosol.R =AEROSOLdeprate.R * (1 - FRg.aR) [m.s-1] =regional!$L$142 DRYDEPaerosol.T =AEROSOLdeprate.T * (1 - FRg.aT) [m.s-1] =tropic!$L$64 DSPcoeff.w2Cw2R =WIDTH.w2R^ 2 / (2 * (LENGTH.w2R - WIDTH.w2R)) * SEAcurrent.w2C.w2R [m2.s-1] =continental!$L$82 DSPcoeff.wMw2C 1.84E + 04 [m2.s-1] =moderate!$L$37 DSPflow.w2Cw2R =(DSPcoeff.w2Cw2R / (WIDTH.w2R / 2)) * (LENGTH.w2R + 2 * WIDTH.w2R) * DEPTH.w2R [m3.s-1] =continental!$L$81 DSPflow.wMw2C =6 * DEPTH.w2C * DSPcoeff.wMw2C [m3.s-1] =moderate!$L$36 E.aA [t.yr-1] / [mol.s-1] =input!$M$97 E.aC [t.yr-1] / [mol.s-1] =input!$M$77 E.aL [t.yr-1] / [mol.s-1] =input!$M$49 E.aM [t.yr-1] / [mol.s-1] =input!$M$92 E.aR [t.yr-1] / [mol.s-1] =input!$M$62 E.aT [t.yr-1] / [mol.s-1] =input!$M$102 E.s1C [t.yr-1] / [mol.s-1] =input!$M$80 E.s1L [t.yr-1] / [mol.s-1] =input!$M$51 E.s1R [t.yr-1] / [mol.s-1] =input!$M$65 E.s2C [t.yr-1] / [mol.s-1] =input!$M$81 E.s2L [t.yr-1] / [mol.s-1] =input!$M$52 E.s2R [t.yr-1] / [mol.s-1] =input!$M$66 E.s3C [t.yr-1] / [mol.s-1] =input!$M$82 E.s3L [t.yr-1] / [mol.s-1] =input!$M$53 E.s3R [t.yr-1] / [mol.s-1] =input!$M$67 E.sA [t.yr-1] / [mol.s-1] =input!$M$99 E.sM [t.yr-1] / [mol.s-1] =input!$M$94 E.sT [t.yr-1] / [mol.s-1] =input!$M$104 E.w1C [t.yr-1] / [mol.s-1] =input!$M$78 E.w1R [t.yr-1] / [mol.s-1] =input!$M$63

E.w2C [t.yr-1] / [mol.s-1] =input!$M$79 E.w2R [t.yr-1] / [mol.s-1] =input!$M$64 E.wA [t.yr-1] / [mol.s-1] =input!$M$98 E.wL [t.yr-1] / [mol.s-1] =input!$M$50 E.wM [t.yr-1] / [mol.s-1] =input!$M$93 E.wT [t.yr-1] / [mol.s-1] =input!$M$103 Ea.OHrad 6.00E + 00 [kJ.mol-1] / [J.mol-1] =input!$M$29 Efact.aC 1.30E - 01 [ - ] =input!$M$84 Efact.aL 2.50E - 03 [ - ] =input!$M$55 Efact.aR 1.30E - 01 [ - ] =input!$M$69 Efact.s1C 0.00E + 00 [ - ] =input!$M$87 Efact.s1L 0.00E + 00 [ - ] =input!$M$57 Efact.s1R 0.00E + 00 [ - ] =input!$M$72 Efact.s2C 0.00E + 00 [ - ] =input!$M$88 Efact.s2L 0.00E + 00 [ - ] =input!$M$58 Efact.s2R 0.00E + 00 [ - ] =input!$M$73 Efact.s3C 2.10E - 01 [ - ] =input!$M$89 Efact.s3L 2.00E - 04 [ - ] =input!$M$59 Efact.s3R 2.10E - 01 [ - ] =input!$M$74 Efact.w1C 1.40E - 01 [ - ] =input!$M$85 Efact.w1R 1.39E - 01 [ - ] =input!$M$70 Efact.w2C 0.00E + 00 [ - ] =input!$M$86 Efact.w2R 1.40E - 03 [ - ] =input!$M$71 Efact.wL 3.00E - 02 [ - ] =input!$M$56 EROSION.s1C 3.00E - 02 [mm.yr-1] / [m.s-1] =continental!$L$218 EROSION.s1L 3.00E - 02 [mm.yr-1] / [m.s-1] =local!$L$182 EROSION.s1R 3.00E - 02 [mm.yr-1] / [m.s-1] =regional!$L$214 EROSION.s2C 3.00E - 02 [mm.yr-1] / [m.s-1] =continental!$L$219 EROSION.s2L 3.00E - 02 [mm.yr-1] / [m.s-1] =local!$L$183 EROSION.s2R 3.00E - 02 [mm.yr-1] / [m.s-1] =regional!$L$215 EROSION.s3C 3.00E - 02 [mm.yr-1] / [m.s-1] =continental!$L$220 EROSION.s3L 3.00E - 02 [mm.yr-1] / [m.s-1] =local!$L$184


EROSION.s3R 3.00E - 02 [mm.yr-1] / [m.s-1] =regional!$L$216 EROSION.sA 3.00E - 02 [mm.yr-1] / [m.s-1] =arctic!$L$94 EROSION.sM 3.00E - 02 [mm.yr-1] / [m.s-1] =moderate!$L$99 EROSION.sT 3.00E - 02 [mm.yr-1] / [m.s-1] =tropic!$L$94 FATfish.A 5.00E - 02 [ - ] =arctic!$L$49 FATfish.M 5.00E - 02 [ - ] =moderate!$L$53 FATfish.T 5.00E - 02 [ - ] =tropic!$L$49 FATfish1.C 5.00E - 02 [ - ] =continental!$L$98 FATfish1.L 5.00E - 02 [ - ] =local!$L$83 FATfish1.R 5.00E - 02 [ - ] =regional!$L$94 FATfish2.C 5.00E - 02 [ - ] =continental!$L$105 FATfish2.R 5.00E + 00 [ - ] =regional!$L$101 FRAC.w1C.w1R 0.00E + 00 [ - ] =continental!$L$77 FRAC.wL.w1R 1.00E + 00 [ - ] =local!$L$69 FRACa.s1C 2.00E - 01 [ - ] =continental!$L$48 FRACa.s1L 2.00E - 01 [ - ] =local!$L$41 FRACa.s1R 2.00E - 01 [ - ] =regional!$L$50 FRACa.s2C 2.00E - 01 [ - ] =continental!$L$51 FRACa.s2L 2.00E - 01 [ - ] =local!$L$44 FRACa.s2R 2.00E - 01 [ - ] =regional!$L$53 FRACa.s3C 2.00E - 01 [ - ] =continental!$L$54 FRACa.s3L 2.00E - 01 [ - ] =local!$L$47 FRACa.s3R 2.00E - 01 [ - ] =regional!$L$56 FRACa.sA 2.00E - 01 [ - ] =arctic!$L$23 FRACa.sM 2.00E - 01 [ - ] =moderate!$L$23 FRACa.sT 2.00E - 01 [ - ] =tropic!$L$23 FRACinf.s1C 2.50E - 01 [ - ] =continental!$L$250 FRACinf.s1L 2.50E - 01 [ - ] =local!$L$210 FRACinf.s1R 2.50E - 01 [ - ] =regional!$L$245 FRACinf.s2C 2.50E - 01 [ - ] =continental!$L$251 FRACinf.s2L 2.50E - 01 [ - ] =local!$L$211 FRACinf.s2R 2.50E - 01 [ - ] =regional!$L$246

FRACinf.s3C 2.50E - 01 [ - ] =continental!$L$252 FRACinf.s3L 2.50E - 01 [ - ] =local!$L$212 FRACinf.s3R 2.50E - 01 [ - ] =regional!$L$247 FRACinf.sA 2.50E - 01 [ - ] =arctic!$L$113 FRACinf.sM 2.50E - 01 [ - ] =moderate!$L$118 FRACinf.sT 2.50E - 01 [ - ] =tropic!$L$113 FRACl.v1C 1.50E - 02 [ - ] =continental!$L$134 FRACl.v1L 1.50E - 02 [ - ] =local!$L$109 FRACl.v1R 1.50E - 02 [ - ] =regional!$L$130 FRACl.v2C 1.20E - 02 [ - ] =continental!$L$135 FRACl.v2L 1.20E - 02 [ - ] =local!$L$110 FRACl.v2R 1.20E - 02 [ - ] =regional!$L$131 FRACrun.s1C 2.50E - 01 [ - ] =continental!$L$221 FRACrun.s1L 2.50E - 01 [ - ] =local!$L$185 FRACrun.s1R 2.50E - 01 [ - ] =regional!$L$217 FRACrun.s2C 2.50E - 01 [ - ] =continental!$L$222 FRACrun.s2L 2.50E - 01 [ - ] =local!$L$186 FRACrun.s2R 2.50E - 01 [ - ] =regional!$L$218 FRACrun.s3C 2.50E - 01 [ - ] =continental!$L$223 FRACrun.s3L 2.50E - 01 [ - ] =local!$L$187 FRACrun.s3R 2.50E - 01 [ - ] =regional!$L$219 FRACrun.sA 2.50E - 01 [ - ] =arctic!$L$95 FRACrun.sM 2.50E - 01 [ - ] =moderate!$L$100 FRACrun.sT 2.50E - 01 [ - ] =tropic!$L$95 FRACs.s1C =1 - FRACa.s1C - FRACw.s1C [ - ] =continental!$L$50 FRACs.s1L =1 - FRACa.s1L - FRACw.s1L [ - ] =local!$L$43 FRACs.s1R =1 - FRACa.s1R - FRACw.s1R [ - ] =regional!$L$52 FRACs.s2C =1 - FRACa.s2C - FRACw.s2C [ - ] =continental!$L$53 FRACs.s2L =1 - FRACa.s2L - FRACw.s2L [ - ] =local!$L$46 FRACs.s2R =1 - FRACa.s2R - FRACw.s2R [ - ] =regional!$L$55 FRACs.s3C =1 - FRACa.s3C - FRACw.s3C [ - ] =continental!$L$56 FRACs.s3L =1 - FRACa.s3L - FRACw.s3L [ - ] =local!$L$49


FRACs.s3R =1 - FRACa.s3R - FRACw.s3R [ - ] =regional!$L$58 FRACs.sA =1 - FRACa.sA - FRACw.sA [ - ] =arctic!$L$25 FRACs.sdA =1 - FRACw.sdA [ - ] =arctic!$L$27 FRACs.sdC =1 - FRACw.sdC [ - ] =continental!$L$58 FRACs.sdL =1 - FRACw.sdL [ - ] =local!$L$51 FRACs.sdM =1 - FRACw.sdM [ - ] =moderate!$L$27 FRACs.sdR =1 - FRACw.sdR [ - ] =regional!$L$60 FRACs.sdT =1 - FRACw.sdT [ - ] =tropic!$L$27 FRACs.sM =1 - FRACa.sM - FRACw.sM [ - ] =moderate!$L$25 FRACs.sT =1 - FRACa.sT - FRACw.sT [ - ] =tropic!$L$25 FRACw.s1C 2.00E - 01 [ - ] =continental!$L$49 FRACw.s1L 2.00E - 01 [ - ] =local!$L$42 FRACw.s1R 2.00E - 01 [ - ] =regional!$L$51 FRACw.s2C 2.00E - 01 [ - ] =continental!$L$52 FRACw.s2L 2.00E - 01 [ - ] =local!$L$45 FRACw.s2R 2.00E - 01 [ - ] =regional!$L$54 FRACw.s3C 2.00E - 01 [ - ] =continental!$L$55 FRACw.s3L 2.00E - 01 [ - ] =local!$L$48 FRACw.s3R 2.00E - 01 [ - ] =regional!$L$57 FRACw.sA 2.00E - 01 [ - ] =arctic!$L$24 FRACw.sdA 8.00E - 01 [ - ] =arctic!$L$26 FRACw.sdC 8.00E - 01 [ - ] =continental!$L$57 FRACw.sdL 8.00E - 01 [ - ] =local!$L$50 FRACw.sdM 8.00E - 01 [ - ] =moderate!$L$26 FRACw.sdR 8.00E - 01 [ - ] =regional!$L$59 FRACw.sdT 8.00E - 01 [ - ] =tropic!$L$26 FRACw.sM 2.00E - 01 [ - ] =moderate!$L$24 FRACw.sT 2.00E - 01 [ - ] =tropic!$L$24 FRACw.v1C 8.00E - 01 [ - ] =continental!$L$132 FRACw.v1L 8.00E - 01 [ - ] =local!$L$107 FRACw.v1R 8.00E - 01 [ - ] =regional!$L$128 FRACw.v2C 8.50E - 01 [ - ] =continental!$L$133

FRACw.v2L 8.50E - 01 [ - ] =local!$L$108 FRACw.v2R 8.50E - 01 [ - ] =regional!$L$129 FRg.aA =1 - (SURFaerosol.A * JungeConst) / (PLT.A + (SURFaerosol.A * JungeConst)) [ - ] =arctic!$L$40 FRg.aC =1 - (SURFaerosol.C * JungeConst) / (PLT.C + (SURFaerosol.C * JungeConst)) [ - ] =continental!$L$89 FRg.aL =1 - (SURFaerosol.L * JungeConst) / (PLT.L + (SURFaerosol.L * JungeConst)) [ - ] =local!$L$74 FRg.aM =1 - (SURFaerosol.M * JungeConst) / (PLT.M + (SURFaerosol.M * JungeConst)) [ - ] =moderate!$L$44 FRg.aR =1 - (SURFaerosol.R * JungeConst) / (PLT.R + (SURFaerosol.R * JungeConst)) [ - ] =regional!$L$85 FRg.aT =1 - (SURFaerosol.T * JungeConst) / (PLT.T + (SURFaerosol.T * JungeConst)) [ - ] =tropic!$L$40 FRs.s1C =FRACs.s1C / (FRACa.s1C * Kh.C / (Kp.s1C * RHOsolid / 1000) + FRACw.s1C / (Kp.s1C * RHOsolid /

1000) + FRACs.s1C) [ - ] =continental!$L$115

FRs.s1L =FRACs.s1L / (FRACa.s1L * Kh.L / (Kp.s1L * RHOsolid / 1000) + FRACw.s1L / (Kp.s1L * RHOsolid / 1000) + FRACs.s1L)

[ - ] =local!$L$90

FRs.s1R =FRACs.s1R / (FRACa.s1R * Kh.R / (Kp.s1R * RHOsolid / 1000) + FRACw.s1R / (Kp.s1R * RHOsolid / 1000) + FRACs.s1R)

[ - ] =regional!$L$111

FRs.s2C =FRACs.s2C / (FRACa.s2C * Kh.C / (Kp.s2C * RHOsolid / 1000) + FRACw.s2C / (Kp.s2C * RHOsolid / 1000) + FRACs.s2C)

[ - ] =continental!$L$120


[ - ] =local!$L$95



FRs.s3C =FRACs.s3C / (FRACa.s3C * Kh.C / (Kp.s3C * RHOsolid / 1000) + FRACw.s3C / (Kp.s3C * RHOsolid / 1000) + FRACs.s3C)



[ - ] =local!$L$100



FRs.sA =FRACs.sA / (FRACa.sA * Kh.A / (Kp.sA * RHOsolid / 1000) + FRACw.sA / (Kp.sA * RHOsolid / 1000) + FRACs.sA)

[ - ] =arctic!$L$56

FRs.sM =FRACs.sM / (FRACa.sM * Kh.M / (Kp.sM * RHOsolid / 1000) + FRACw.sM / (Kp.sM * RHOsolid / 1000) + FRACs.sM)

[ - ] =moderate!$L$60

FRs.sT =FRACs.sT / (FRACa.sT * Kh.T / (Kp.sT * RHOsolid / 1000) + FRACw.sT / (Kp.sT * RHOsolid / 1000) + FRACs.sT)

[ - ] =tropic!$L$56


FRw.s1C =FRACw.s1C / (FRACa.s1C * Kh.C + FRACw.s1C + FRACs.s1C * Kp.s1C * RHOsolid / 1000) [ - ] =continental!$L$114 FRw.s1L =FRACw.s1L / (FRACa.s1L * Kh.L + FRACw.s1L + FRACs.s1L * Kp.s1L * RHOsolid / 1000) [ - ] =local!$L$89 FRw.s1R =FRACw.s1R / (FRACa.s1R * Kh.R + FRACw.s1R + FRACs.s1R * Kp.s1R * RHOsolid / 1000) [ - ] =regional!$L$110 FRw.s2C =FRACw.s2C / (FRACa.s2C * Kh.C + FRACw.s2C + FRACs.s2C * Kp.s2C * RHOsolid / 1000) [ - ] =continental!$L$119 FRw.s2L =FRACw.s2L / (FRACa.s2L * Kh.L + FRACw.s2L + FRACs.s2L * Kp.s2L * RHOsolid / 1000) [ - ] =local!$L$94 FRw.s2R =FRACw.s2R / (FRACa.s2R * Kh.R + FRACw.s2R + FRACs.s2R * Kp.s2R * RHOsolid / 1000) [ - ] =regional!$L$115 FRw.s3C =FRACw.s3C / (FRACa.s3C * Kh.C + FRACw.s3C + FRACs.s3C * Kp.s3C * RHOsolid / 1000) [ - ] =continental!$L$124 FRw.s3L =FRACw.s3L / (FRACa.s3L * Kh.L + FRACw.s3L + FRACs.s3L * Kp.s3L * RHOsolid / 1000) [ - ] =local!$L$99 FRw.s3R =FRACw.s3R / (FRACa.s3R * Kh.R + FRACw.s3R + FRACs.s3R * Kp.s3R * RHOsolid / 1000) [ - ] =regional!$L$120 FRw.sA =FRACw.sA / (FRACa.sA * Kh.A + FRACw.sA + FRACs.sA * Kp.sA * RHOsolid / 1000) [ - ] =arctic!$L$55 FRw.sM =FRACw.sM / (FRACa.sM * Kh.M + FRACw.sM + FRACs.sM * Kp.sM * RHOsolid / 1000) [ - ] =moderate!$L$59 FRw.sT =FRACw.sT / (FRACa.sT * Kh.T + FRACw.sT + FRACs.sT * Kp.sT * RHOsolid / 1000) [ - ] =tropic!$L$55 FRw.w1C =1 / (1 + Kp.susp1C * SUSP.w1C / 1000 + BCFfish1.C * BIOmass.w1C / 1000) [ - ] =continental!$L$93 FRw.w1R =1 / (1 + Kp.susp1R * SUSP.w1R / 1000 + BCFfish1.R * BIOmass.w1R / 1000) [ - ] =regional!$L$89 FRw.w2C =1 / (1 + Kp.susp2C * SUSP.w2C / 1000 + BCFfish2.C * BIOmass.w2C / 1000) [ - ] =continental!$L$100 FRw.w2R =1 / (1 + Kp.susp2R * SUSP.w2R / 1000 + BCFfish2.R * BIOmass.w2R / 1000) [ - ] =regional!$L$96 FRw.wA =1 / (1 + Kp.suspA * SUSP.wA / 1000 + BCFfish.A * BIOmass.wA / 1000) [ - ] =arctic!$L$44 FRw.wL =1 / (1 + Kp.suspL * SUSP.wL / 1000 + BCFfish1.L * BIOmass.wL / 1000) [ - ] =local!$L$78 FRw.wM =1 / (1 + Kp.suspM * SUSP.wM / 1000 + BCFfish.M * BIOmass.wM / 1000) [ - ] =moderate!$L$48 FRw.wT =1 / (1 + Kp.suspT * SUSP.wT / 1000 + BCFfish.T * BIOmass.wT / 1000) [ - ] =tropic!$L$44 g.v1C 1.00E - 03 [m.s-1] =continental!$L$191 g.v1L 1.00E - 03 [m.s-1] =local!$L$163 g.v1R 1.00E - 03 [m.s-1] =regional!$L$187 g.v2C 1.00E - 03 [m.s-1] =continental!$L$192 g.v2L 1.00E - 03 [m.s-1] =local!$L$164 g.v2R 1.00E - 03 [m.s-1] =regional!$L$188 GASABSflow.aA.sA =FRg.aA * (kas.air.aA * kas.soil.sA) / (kas.air.aA * (Kh.A / Ksw.A) + kas.soil.sA) * (SYSTEMAREA.A *

AREAFRAC.sA) [m3.s-1] =arctic!$L$75

GASABSflow.aA.wA =FRg.aA * (kaw.air.aA * kaw.water.wA / (kaw.air.aA * Kh.A + kaw.water.wA)) * SYSTEMAREA.A * AREAFRAC.wA


GASABSflow.aC.s1C =FRg.aC * (kas.air.aC * kas.soil.sC) / (kas.air.aC * (Kh.C / Ks1w.C) + kas.soil.sC) * (SYSTEMAREA.C * AREAFRAC.s1C)






GASABSflow.aC.v1C =FRg.aC * g.v1C * LAI.v1C * SYSTEMAREA.C * AREAFRAC.s1C [m3.s-1] =continental!$L$187 GASABSflow.aC.v2C =FRg.aC * g.v2C * LAI.v2C * SYSTEMAREA.C * AREAFRAC.s2C [m3.s-1] =continental!$L$189 GASABSflow.aC.w1C =FRg.aC * (kaw.air.aC * kaw.water.wC / (kaw.air.aC * Kh.C + kaw.water.wC)) * SYSTEMAREA.C *

AREAFRAC.w1C [m3.s-1] =continental!$L$173

GASABSflow.aC.w2C =FRg.aC * (kaw.air.aC * kaw.water.wC / (kaw.air.aC * Kh.C + kaw.water.wC)) * SYSTEMAREA.C * AREAFRAC.w2C


GASABSflow.aL.s1L =FRg.aL * (kas.air.aL * kas.soil.sL) / (kas.air.aL * (Kh.L / Ks1w.L) + kas.soil.sL) * (SYSTEMAREA.L * AREAFRAC.s1L)

[m3.s-1] =local!$L$151


[m3.s-1] =local!$L$153


[m3.s-1] =local!$L$155

GASABSflow.aL.v1L =FRg.aL * g.v1L * LAI.v1L * SYSTEMAREA.L * AREAFRAC.s1L [m3.s-1] =local!$L$159 GASABSflow.aL.v2L =FRg.aL * g.v2L * LAI.v2L * SYSTEMAREA.L * AREAFRAC.s2L [m3.s-1] =local!$L$161 GASABSflow.aL.wL =FRg.aL * (kaw.air.aL * kaw.water.wL / (kaw.air.aL * Kh.L + kaw.water.wL)) * (SYSTEMAREA.L *

AREAFRAC.wL) [m3.s-1] =local!$L$147

GASABSflow.aM.sM =FRg.aM * (kas.air.aM * kas.soil.sM) / (kas.air.aM * (Kh.M / Ksw.M) + kas.soil.sM) * (SYSTEMAREA.M * AREAFRAC.sM)


GASABSflow.aM.wM =FRg.aM * (kaw.air.aM * kaw.water.wM / (kaw.air.aM * Kh.M + kaw.water.wM)) * SYSTEMAREA.M * AREAFRAC.wM


GASABSflow.aR.s1R =FRg.aR * (kas.air.aR * kas.soil.sR) / (kas.air.aR * (Kh.R / Ks1w.R) + kas.soil.sR) * (SYSTEMAREA.R * AREAFRAC.s1R)






GASABSflow.aR.v1R =FRg.aR * g.v1R * LAI.v1R * SYSTEMAREA.R * AREAFRAC.s1R [m3.s-1] =regional!$L$183 GASABSflow.aR.v2R =FRg.aR * g.v2R * LAI.v2R * SYSTEMAREA.R * AREAFRAC.s2R [m3.s-1] =regional!$L$185


GASABSflow.aR.w1R =FRg.aR * (kaw.air.aR * kaw.water.wR / (kaw.air.aR * Kh.R + kaw.water.wR)) * (SYSTEMAREA.R * AREAFRAC.w1R)


GASABSflow.aR.w2R =FRg.aR * (kaw.air.aR * kaw.water.wR / (kaw.air.aR * Kh.R + kaw.water.wR)) * (SYSTEMAREA.R * AREAFRAC.w2R)


GASABSflow.aT.sT =FRg.aT * (kas.air.aT * kas.soil.sT) / (kas.air.aT * (Kh.T / Ksw.T) + kas.soil.sT) * (SYSTEMAREA.T * AREAFRAC.sT)


GASABSflow.aT.wT =FRg.aT * (kaw.air.aT * kaw.water.wT / (kaw.air.aT * Kh.T + kaw.water.wT)) * SYSTEMAREA.T * AREAFRAC.wT


GasWashout.A =RAINrate.A * FRg.aA / Kh.A [m.s-1] =arctic!$L$66 GasWashout.C =RAINrate.C * FRg.aC / Kh.C [m.s-1] =continental!$L$148 GasWashout.L =RAINrate.L * FRg.aL / Kh.L [m.s-1] =local!$L$122 GasWashout.M =RAINrate.M * FRg.aM / Kh.M [m.s-1] =moderate!$L$70 GasWashout.R =RAINrate.R * FRg.aR / Kh.R [m.s-1] =regional!$L$144 GasWashout.T =RAINrate.T * FRg.aT / Kh.T [m.s-1] =tropic!$L$66 GROSSSEDrate.w1C =IF(SETTLvelocity.C * SUSP.w1C / (FRACs.sdC * RHOsolid)> NETsedrate.w1C, SETTLvelocity.C *

SUSP.w1C / (FRACs.sdC * RHOsolid), NETsedrate.w1C) [m.s-1] =continental!$L$198

GROSSSEDrate.w1R =IF(SETTLvelocity.R * SUSP.w1R / (FRACs.sdR * RHOsolid)> NETsedrate.w1R, SETTLvelocity.R * SUSP.w1R / (FRACs.sdR * RHOsolid), NETsedrate.w1R)

[m.s-1] =regional!$L$194

GROSSSEDrate.w2C =IF(SETTLvelocity.C * SUSP.w2C / (FRACs.sdC * RHOsolid)> NETsedrate.w2C, SETTLvelocity.C * SUSP.w2C / (FRACs.sdC * RHOsolid), NETsedrate.w2C)

[m.s-1] =continental!$L$200

GROSSSEDrate.w2R =IF(SETTLvelocity.R * SUSP.w2R / (FRACs.sdR * RHOsolid)> NETsedrate.w2R, SETTLvelocity.R * SUSP.w2R / (FRACs.sdR * RHOsolid), NETsedrate.w2R)


GROSSSEDrate.wA =IF(SETTLvelocity.A * SUSP.wA / (FRACs.sdA * RHOsolid)> NETsedrate.wA, SETTLvelocity.A * SUSP.wA / (FRACs.sdA * RHOsolid), NETsedrate.wA)

[m.s-1] =arctic!$L$82

GROSSSEDrate.wL =IF(SETTLvelocity.L * SUSP.wL / (FRACs.sdL * RHOsolid)> NETsedrate.wL, SETTLvelocity.L * SUSP.wL / ((FRACs.sdL) * RHOsolid), NETsedrate.wL)

[m.s-1] =local!$L$168

GROSSSEDrate.wM =IF(SETTLvelocity.M * SUSP.wM / (FRACs.sdM * RHOsolid)> NETsedrate.wM, SETTLvelocity.M * SUSP.wM / (FRACs.sdM * RHOsolid), NETsedrate.wM)

[m.s-1] =moderate!$L$87

GROSSSEDrate.wT =IF(SETTLvelocity.T * SUSP.wT / (FRACs.sdT * RHOsolid)> NETsedrate.wT, SETTLvelocity.T * SUSP.wT / (FRACs.sdT * RHOsolid), NETsedrate.wT)

[m.s-1] =tropic!$L$82

GROWTHrate.v1C 2.88E - 08 [s-1] =continental!$L$161 GROWTHrate.v1L 2.88E - 08 [s-1] =local!$L$135

GROWTHrate.v1R 2.88E - 08 [s-1] =regional!$L$157 GROWTHrate.v2C 1.27E - 07 [s-1] =continental!$L$162 GROWTHrate.v2L 1.27E - 07 [s-1] =local!$L$136 GROWTHrate.v2R 1.27E - 07 [s-1] =regional!$L$158 H0sol 1.00E + 01 [kJ.mol-1] / [J.mol-1] =input!$M$23 H0vap 5.00E + 01 [kJ.mol-1] / [J.mol-1] =input!$M$21 HARVEST.v1C =HARVESTeff.v1C * GROWTHrate.v1C * VOLUME.v1C [m3.s-1] =continental!$L$257 HARVEST.v1L =HARVESTeff.v1L * GROWTHrate.v1L * VOLUME.v1L [m3.s-1] =local!$L$217 HARVEST.v1R =HARVESTeff.v1R * GROWTHrate.v1R * VOLUME.v1R [m3.s-1] =regional!$L$252 HARVEST.v2C =HARVESTeff.v2C * GROWTHrate.v2C * VOLUME.v2C [m3.s-1] =continental!$L$258 HARVEST.v2L =HARVESTeff.v2L * GROWTHrate.v2L * VOLUME.v2L [m3.s-1] =local!$L$218 HARVEST.v2R =HARVESTeff.v2R * GROWTHrate.v2R * VOLUME.v2R [m3.s-1] =regional!$L$253 HARVESTeff.v1C 0.00E + 00 [ - ] =continental!$L$163 HARVESTeff.v1L 0.00E + 00 [ - ] =local!$L$137 HARVESTeff.v1R 0.00E + 00 [ - ] =regional!$L$159 HARVESTeff.v2C 5.90E - 01 [ - ] =continental!$L$164 HARVESTeff.v2L 5.90E - 01 [ - ] =local!$L$138 HARVESTeff.v2R 5.90E - 01 [ - ] =regional!$L$160 HEIGHT.aA 1.00E + 03 [m] =arctic!$L$14 HEIGHT.aC 1.00E + 03 [m] =continental!$L$25 HEIGHT.aL 1.00E + 03 [m] =local!$L$20 HEIGHT.aM 1.00E + 03 [m] =moderate!$L$14 HEIGHT.aR 1.00E + 03 [m] =regional!$L$27 HEIGHT.aT 1.00E + 03 [m] =tropic!$L$14 IFDRYaerosol.v1C 1.00E - 01 [ - ] =continental!$L$152 IFDRYaerosol.v1L 1.00E - 01 [ - ] =local!$L$126 IFDRYaerosol.v1R 1.00E - 01 [ - ] =regional!$L$148 IFDRYaerosol.v2C 5.00E - 02 [ - ] =continental!$L$153 IFDRYaerosol.v2L 5.00E - 02 [ - ] =local!$L$127 IFDRYaerosol.v2R 5.00E - 02 [ - ] =regional!$L$149 IFWETaerosol.v1C 5.00E - 02 [ - ] =continental!$L$154 IFWETaerosol.v1L 5.00E - 02 [ - ] =local!$L$128


IFWETaerosol.v1R 5.00E - 02 [ - ] =regional!$L$150 IFWETaerosol.v2C 2.50E - 02 [ - ] =continental!$L$155 IFWETaerosol.v2L 2.50E - 02 [ - ] =local!$L$129 IFWETaerosol.v2R 2.50E - 02 [ - ] =regional!$L$151 IFWETgas.v1C 0.00E + 00 [ - ] =continental!$L$156 IFWETgas.v1L 0.00E + 00 [ - ] =local!$L$130 IFWETgas.v1R 0.00E + 00 [ - ] =regional!$L$152 IFWETgas.v2C 0.00E + 00 [ - ] =continental!$L$157 IFWETgas.v2L 0.00E + 00 [ - ] =local!$L$131 IFWETgas.v2R 0.00E + 00 [ - ] =regional!$L$153 JungeConst 1.72E - 01 [Pa.m] =input!$M$24 k0.OHrad 7.90E - 11 [cm3.s-1] =input!$M$28 kas.air.aA 1.05E - 03 [m.s-1] =arctic!$L$77 kas.air.aC 1.05E - 03 [m.s-1] =continental!$L$185 kas.air.aL 1.05E - 03 [m.s-1] =local!$L$157 kas.air.aM 1.05E - 03 [m.s-1] =moderate!$L$82 kas.air.aR 1.05E - 03 [m.s-1] =regional!$L$181 kas.air.aT 1.05E - 03 [m.s-1] =tropic!$L$77 kas.soil.sA =Veff.sA + Deff.sA / PENdepth.sA [m.s-1] =arctic!$L$78 kas.soil.sC =Veff.s1C + Deff.s1C / PENdepth.s1C [m.s-1] =continental!$L$186 kas.soil.sL =Veff.s1L + Deff.s1L / PENdepth.s1L [m.s-1] =local!$L$158 kas.soil.sM =Veff.sM + Deff.sM / PENdepth.sM [m.s-1] =moderate!$L$83 kas.soil.sR =Veff.s1R + Deff.s1R / PENdepth.s1R [m.s-1] =regional!$L$182 kas.soil.sT =Veff.sT + Deff.sT / PENdepth.sT [m.s-1] =tropic!$L$78 kaw.air.aA =0.01 * (0.3 + 0.2 * WINDspeed.A) * ((0.018 / Molweight)^ (0.67 * 0.5)) [m.s-1] =arctic!$L$73 kaw.air.aC =0.01 * (0.3 + 0.2 * WINDspeed.C) * ((0.018 / Molweight)^ (0.67 * 0.5)) [m.s-1] =continental!$L$177 kaw.air.aL =0.01 * (0.3 + 0.2 * WINDspeed.L) * ((0.018 / Molweight)^ (0.67 * 0.5)) [m.s-1] =local!$L$149 kaw.air.aM =0.01 * (0.3 + 0.2 * WINDspeed.M) * ((0.018 / Molweight)^ (0.67 * 0.5)) [m.s-1] =moderate!$L$77 kaw.air.aR =0.01 * (0.3 + 0.2 * WINDspeed.R) * ((0.018 / Molweight)^ (0.67 * 0.5)) [m.s-1] =regional!$L$173 kaw.air.aT =0.01 * (0.3 + 0.2 * WINDspeed.T) * ((0.018 / Molweight)^ (0.67 * 0.5)) [m.s-1] =tropic!$L$73 kaw.water.wA =0.01 * (0.0004 + 0.00004 * WINDspeed.A^ 2) * ((0.032 / Molweight)^ (0.5 * 0.5)) [m.s-1] =arctic!$L$74 kaw.water.wC =0.01 * (0.0004 + 0.00004 * WINDspeed.C^ 2) * ((0.032 / Molweight)^ (0.5 * 0.5)) [m.s-1] =continental!$L$178

kaw.water.wL =0.01 * (0.0004 + 0.00004 * WINDspeed.L^ 2) * ((0.032 / Molweight)^ (0.5 * 0.5)) [m.s-1] =local!$L$150 kaw.water.wM =0.01 * (0.0004 + 0.00004 * WINDspeed.M^ 2) * ((0.032 / Molweight)^ (0.5 * 0.5)) [m.s-1] =moderate!$L$78 kaw.water.wR =0.01 * (0.0004 + 0.00004 * WINDspeed.R^ 2) * ((0.032 / Molweight)^ (0.5 * 0.5)) [m.s-1] =regional!$L$174 kaw.water.wT =0.01 * (0.0004 + 0.00004 * WINDspeed.T^ 2) * ((0.032 / Molweight)^ (0.5 * 0.5)) [m.s-1] =tropic!$L$74 KDEG.aA =FRg.aA * kdeg.air * (C.OHrad.aA / C.OHrad) * Tempfactor.aA [s-1] =arctic!$L$100 KDEG.aC =FRg.aC * kdeg.air * (C.OHrad.aC / C.OHrad) * Tempfactor.aC [s-1] =continental!$L$228 kdeg.air 3.51E - 06 [s-1] =input!$M$26 KDEG.aL =FRg.aL * kdeg.air * (C.OHrad.aL / C.OHrad) * Tempfactor.aL [s-1] =local!$L$192 KDEG.aM =FRg.aM * kdeg.air * (C.OHrad.aM / C.OHrad) * Tempfactor.aM [s-1] =moderate!$L$105 KDEG.aR =FRg.aR * kdeg.air * (C.OHrad.aR / C.OHrad) * Tempfactor.aR [s-1] =regional!$L$224 KDEG.aT =FRg.aT * kdeg.air * (C.OHrad.aT / C.OHrad) * Tempfactor.aT [s-1] =tropic!$L$100 KDEG.s1C =Tempfactor.wsdsC * kdeg.soil [s-1] =continental!$L$238 KDEG.s1L =Tempfactor.wsdsL * kdeg.soil [s-1] =local!$L$199 KDEG.s1R =Tempfactor.wsdsR * kdeg.soil [s-1] =regional!$L$233 KDEG.s2C =Tempfactor.wsdsC * kdeg.soil [s-1] =continental!$L$239 KDEG.s2L =Tempfactor.wsdsL * kdeg.soil [s-1] =local!$L$200 KDEG.s2R =Tempfactor.wsdsR * kdeg.soil [s-1] =regional!$L$234 KDEG.s3C =Tempfactor.wsdsC * kdeg.soil [s-1] =continental!$L$240 KDEG.s3L =Tempfactor.wsdsL * kdeg.soil [s-1] =local!$L$201 KDEG.s3R =Tempfactor.wsdsR * kdeg.soil [s-1] =regional!$L$235 KDEG.sA =Tempfactor.wsdsA * kdeg.soil [s-1] =arctic!$L$107 KDEG.sd1C =Tempfactor.wsdsC * kdeg.sed [s-1] =continental!$L$235 KDEG.sd1R =Tempfactor.wsdsR * kdeg.sed [s-1] =regional!$L$231 KDEG.sd2C =Tempfactor.wsdsC * kdeg.sed [s-1] =continental!$L$236 KDEG.sd2R =Tempfactor.wsdsR * kdeg.sed [s-1] =regional!$L$232 KDEG.sdA =Tempfactor.wsdsA * kdeg.sed [s-1] =arctic!$L$106 KDEG.sdL =Tempfactor.wsdsL * kdeg.sed [s-1] =local!$L$198 KDEG.sdM =Tempfactor.wsdsM * kdeg.sed [s-1] =moderate!$L$111 KDEG.sdT =Tempfactor.wsdsT * kdeg.sed [s-1] =tropic!$L$106 kdeg.sed 6.58E - 10 [s-1] =input!$M$34 KDEG.sM =Tempfactor.wsdsM * kdeg.soil [s-1] =moderate!$L$112 kdeg.soil 6.58E - 09 [s-1] =input!$M$36


KDEG.sT =Tempfactor.wsdsT * kdeg.soil [s-1] =tropic!$L$107 KDEG.v1C =KDEG.s1C * 10 [s-1] =continental!$L$241 KDEG.v1L =KDEG.s1L * 10 [s-1] =local!$L$202 KDEG.v1R =KDEG.s1R * 10 [s-1] =regional!$L$236 KDEG.v2C =KDEG.s2C * 10 [s-1] =continental!$L$242 KDEG.v2L =KDEG.s2L * 10 [s-1] =local!$L$203 KDEG.v2R =KDEG.s2R * 10 [s-1] =regional!$L$237 KDEG.w1C =kdeg.water * Tempfactor.wsdsC * (BACT.wC / BACT.test) * FRw.w1C [s-1] =continental!$L$231 KDEG.w1R =kdeg.water * Tempfactor.wsdsR * (BACT.wR / BACT.test) * FRw.w1R [s-1] =regional!$L$227 KDEG.w2C =kdeg.water * Tempfactor.wsdsC * (BACT.wC / BACT.test) * FRw.w2C [s-1] =continental!$L$232 KDEG.w2R =kdeg.water * Tempfactor.wsdsR * (BACT.wR / BACT.test) * FRw.w2R [s-1] =regional!$L$228 KDEG.wA =kdeg.water * Tempfactor.wsdsA * (BACT.wA / BACT.test) * FRw.wA [s-1] =arctic!$L$103 kdeg.water 1.32E - 07 [s-1] =input!$M$30 KDEG.wL =kdeg.water * Tempfactor.wsdsL * (BACT.wL / BACT.test) * FRw.wL [s-1] =local!$L$195 KDEG.wM =kdeg.water * Tempfactor.wsdsM * (BACT.wM / BACT.test) * FRw.wM [s-1] =moderate!$L$108 KDEG.wT =kdeg.water * Tempfactor.wsdsT * (BACT.wT / BACT.test) * FRw.wT [s-1] =tropic!$L$103 kesc.aA 3.66E - 10 [s-1] =arctic!$L$99 kesc.aC 3.66E - 10 [s-1] =continental!$L$227 kesc.aL 3.66E - 10 [s-1] =local!$L$191 kesc.aM 3.66E - 10 [s-1] =moderate!$L$104 kesc.aR 3.66E - 10 [s-1] =regional!$L$223 kesc.aT 3.66E - 10 [s-1] =tropic!$L$99 Kh =IF(Pvap25> 100000, (100000 / Sol25) / (8.314 * 298) , (Pvap25 / Sol25) / (8.314 * 298)) [ - ] =input!$M$19 Kh.A =Kh * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.A)) * EXP( - (H0sol / 8.314) * (1 / 298 - 1 / TEMP.A)) *

(298 / TEMP.A) [ - ] =arctic!$L$39

Kh.C =Kh * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.C)) * EXP( - (H0sol / 8.314) * (1 / 298 - 1 / TEMP.C)) * (298 / TEMP.C)


Kh.L =Kh * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.L)) * EXP( - (H0sol / 8.314) * (1 / 298 - 1 / TEMP.L)) * (298 / TEMP.L)

[ - ] =local!$L$73

Kh.M =Kh * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.M)) * EXP( - (H0sol / 8.314) * (1 / 298 - 1 / TEMP.M)) * (298 / TEMP.M)

[ - ] =moderate!$L$43

Kh.R =Kh * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.R)) * EXP( - (H0sol / 8.314) * (1 / 298 - 1 / TEMP.R)) * (298 / TEMP.R)


Kh.T =Kh * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.T)) * EXP( - (H0sol / 8.314) * (1 / 298 - 1 / TEMP.T)) * (298 / TEMP.T)

[ - ] =tropic!$L$39

Kow 1.35E + 03 [ - ] =input!$M$16 Kp 2.16E + 01 [ - ] =input!$M$15 Kp.s1C =Kp * (1000 / RHOsolid) * (CORG.s1C / CORG) [L.kg-1] =continental!$L$116 Kp.s1L =Kp * (1000 / RHOsolid) * (CORG.s1L / CORG) [L.kg-1] =local!$L$91 Kp.s1R =Kp * (1000 / RHOsolid) * (CORG.s1R / CORG) [L.kg-1] =regional!$L$112 Kp.s2C =Kp * (1000 / RHOsolid) * (CORG.s2C / CORG) [L.kg-1] =continental!$L$121 Kp.s2L =Kp * (1000 / RHOsolid) * (CORG.s2L / CORG) [L.kg-1] =local!$L$96 Kp.s2R =Kp * (1000 / RHOsolid) * (CORG.s2R / CORG) [L.kg-1] =regional!$L$117 Kp.s3C =Kp * (1000 / RHOsolid) * (CORG.s3C / CORG) [L.kg-1] =continental!$L$126 Kp.s3L =Kp * (1000 / RHOsolid) * (CORG.s3L / CORG) [L.kg-1] =local!$L$101 Kp.s3R =Kp * (1000 / RHOsolid) * (CORG.s3R / CORG) [L.kg-1] =regional!$L$122 Kp.sA =Kp * (1000 / RHOsolid) * (CORG.sA / CORG) [L.kg-1] =arctic!$L$57 Kp.sd1C =Kp * (1000 / RHOsolid) * (CORG.sd1C / CORG) [L.kg-1] =continental!$L$108 Kp.sd1R =Kp * (1000 / RHOsolid) * (CORG.sd1R / CORG) [L.kg-1] =regional!$L$104 Kp.sd2C =Kp * (1000 / RHOsolid) * (CORG.sd2C / CORG) [L.kg-1] =continental!$L$111 Kp.sd2R =Kp * (1000 / RHOsolid) * (CORG.sd2R / CORG) [L.kg-1] =regional!$L$107 Kp.sdA =Kp * (1000 / RHOsolid) * (CORG.sdA / CORG) [L.kg-1] =arctic!$L$52 Kp.sdL =Kp * (1000 / RHOsolid) * (CORG.sdL / CORG) [L.kg-1] =local!$L$86 Kp.sdM =Kp * (1000 / RHOsolid) * (CORG.sdM / CORG) [L.kg-1] =moderate!$L$56 Kp.sdT =Kp * (1000 / RHOsolid) * (CORG.sdT / CORG) [L.kg-1] =tropic!$L$52 Kp.sM =Kp * (1000 / RHOsolid) * (CORG.sM / CORG) [L.kg-1] =moderate!$L$61 Kp.sT =Kp * (1000 / RHOsolid) * (CORG.sT / CORG) [L.kg-1] =tropic!$L$57 Kp.susp1C =Kp * (1000 / RHOsolid) * (CORGsusp1.C / CORG) [L.kg-1] =continental!$L$94 Kp.susp1R =Kp * (1000 / RHOsolid) * (CORGsusp1.R / CORG) [L.kg-1] =regional!$L$90 Kp.susp2C =Kp * (1000 / RHOsolid) * (CORGsusp2.C / CORG) [L.kg-1] =continental!$L$101 Kp.susp2R =Kp * (1000 / RHOsolid) * (CORGsusp2.R / CORG) [L.kg-1] =regional!$L$97 Kp.suspA =Kp * (1000 / RHOsolid) * (CORGsusp.A / CORG) [L.kg-1] =arctic!$L$45 Kp.suspL =Kp * (1000 / RHOsolid) * (CORGsusp.L / CORG) [L.kg-1] =local!$L$79


Kp.suspM =Kp * (1000 / RHOsolid) * (CORGsusp.M / CORG) [L.kg-1] =moderate!$L$49 Kp.suspT =Kp * (1000 / RHOsolid) * (CORGsusp.T / CORG) [L.kg-1] =tropic!$L$45 Ks1w.C =FRACa.s1C * Kh.C + FRACw.s1C + FRACs.s1C * Kp.s1C * RHOsolid / 1000 [ - ] =continental!$L$113 Ks1w.L =FRACa.s1L * Kh.L + FRACw.s1L + FRACs.s1L * Kp.s1L * RHOsolid / 1000 [ - ] =local!$L$88 Ks1w.R =FRACa.s1R * Kh.R + FRACw.s1R + FRACs.s1R * Kp.s1R * RHOsolid / 1000 [ - ] =regional!$L$109 Ks2w.C =FRACa.s2C * Kh.C + FRACw.s2C + FRACs.s2C * Kp.s2C * RHOsolid / 1000 [ - ] =continental!$L$118 Ks2w.L =FRACa.s2L * Kh.L + FRACw.s2L + FRACs.s2L * Kp.s2L * RHOsolid / 1000 [ - ] =local!$L$93 Ks2w.R =FRACa.s2R * Kh.R + FRACw.s2R + FRACs.s2R * Kp.s2R * RHOsolid / 1000 [ - ] =regional!$L$114 Ks3w.C =FRACa.s3C * Kh.C + FRACw.s3C + FRACs.s3C * Kp.s3C * RHOsolid / 1000 [ - ] =continental!$L$123 Ks3w.L =FRACa.s3L * Kh.L + FRACw.s3L + FRACs.s3L * Kp.s3L * RHOsolid / 1000 [ - ] =local!$L$98 Ks3w.R =FRACa.s3R * Kh.R + FRACw.s3R + FRACs.s3R * Kp.s3R * RHOsolid / 1000 [ - ] =regional!$L$119 Ksdw.A =FRACw.sdA + FRACs.sdA * Kp.sdA * RHOsolid / 1000 [ - ] =arctic!$L$51 Ksdw.L =FRACw.sdL + FRACs.sdL * Kp.sdL * RHOsolid / 1000 [ - ] =local!$L$85 Ksdw.M =FRACw.sdM + FRACs.sdM * Kp.sdM * RHOsolid / 1000 [ - ] =moderate!$L$55 Ksdw.T =FRACw.sdT + FRACs.sdT * Kp.sdT * RHOsolid / 1000 [ - ] =tropic!$L$51 Ksdw1.C =FRACw.sdC + FRACs.sdC * Kp.sd1C * RHOsolid / 1000 [ - ] =continental!$L$107 Ksdw1.R =FRACw.sdR + FRACs.sdR * Kp.sd1R * RHOsolid / 1000 [ - ] =regional!$L$103 Ksdw2.C =FRACw.sdC + FRACs.sdC * Kp.sd2C * RHOsolid / 1000 [ - ] =continental!$L$110 Ksdw2.R =FRACw.sdR + FRACs.sdR * Kp.sd2R * RHOsolid / 1000 [ - ] =regional!$L$106 Ksw.A =FRACa.sA * Kh.A + FRACw.sA + FRACs.sA * Kp.sA * RHOsolid / 1000 [ - ] =arctic!$L$54 Ksw.M =FRACa.sM * Kh.M + FRACw.sM + FRACs.sM * Kp.sM * RHOsolid / 1000 [ - ] =moderate!$L$58 Ksw.T =FRACa.sT * Kh.T + FRACw.sT + FRACs.sT * Kp.sT * RHOsolid / 1000 [ - ] =tropic!$L$54 Kv1a.C =Kv1w.C / Kh.C [ - ] =continental!$L$128 Kv1a.L =Kv1w.L / Kh.L [ - ] =local!$L$103 Kv1a.R =Kv1w.R / Kh.R [ - ] =regional!$L$124 Kv1w.C =FRACw.v1C + FRACl.v1C * (Kow)^ 0.95 [ - ] =continental!$L$130 Kv1w.L =FRACw.v1L + FRACl.v1L * (Kow)^ 0.95 [ - ] =local!$L$105 Kv1w.R =FRACw.v1R + FRACl.v1R * (Kow)^ 0.95 [ - ] =regional!$L$126 Kv2a.C =Kv2w.C / Kh.C [ - ] =continental!$L$129 Kv2a.L =Kv2w.L / Kh.L [ - ] =local!$L$104 Kv2a.R =Kv2w.R / Kh.R [ - ] =regional!$L$125 Kv2w.C =FRACw.v2C + FRACl.v2C * (Kow)^ 0.95 [ - ] =continental!$L$131

Kv2w.L =FRACw.v2L + FRACl.v2L * (Kow)^ 0.95 [ - ] =local!$L$106 Kv2w.R =FRACw.v2R + FRACl.v2R * (Kow)^ 0.95 [ - ] =regional!$L$127 kwsd.sed.sdA 2.78E - 08 [m.s-1] =arctic!$L$91 kwsd.sed.sdC 2.78E - 08 [m.s-1] =continental!$L$213 kwsd.sed.sdL 2.78E - 08 [m.s-1] =local!$L$177 kwsd.sed.sdM 2.78E - 08 [m.s-1] =moderate!$L$96 kwsd.sed.sdR 2.78E - 08 [m.s-1] =regional!$L$209 kwsd.sed.sdT 2.78E - 08 [m.s-1] =tropic!$L$91 kwsd.water.wA 2.78E - 06 [m.s-1] =arctic!$L$90 kwsd.water.wC 2.78E - 06 [m.s-1] =continental!$L$212 kwsd.water.wL 2.78E - 06 [m.s-1] =local!$L$176 kwsd.water.wM 2.78E - 06 [m.s-1] =moderate!$L$95 kwsd.water.wR 2.78E - 06 [m.s-1] =regional!$L$208 kwsd.water.wT 2.78E - 06 [m.s-1] =tropic!$L$90 LAI.v1C 3.90E + 00 [ - ] =continental!$L$59 LAI.v1L 3.90E + 00 [ - ] =local!$L$52 LAI.v1R 3.90E + 00 [ - ] =regional!$L$61 LAI.v2C 2.70E + 00 [ - ] =continental!$L$60 LAI.v2L 2.70E + 00 [ - ] =local!$L$53 LAI.v2R 2.70E + 00 [ - ] =regional!$L$62 LEACHflow.s1C =FRACinf.s1C * RAINrate.C / Ks1w.C * SYSTEMAREA.C * AREAFRAC.s1C [m3.s-1] =continental!$L$247 LEACHflow.s1L =FRACinf.s1L * RAINrate.L / Ks1w.L * SYSTEMAREA.L * AREAFRAC.s1L [m3.s-1] =local!$L$207 LEACHflow.s1R =FRACinf.s1R * RAINrate.R / Ks1w.R * SYSTEMAREA.R * AREAFRAC.s1R [m3.s-1] =regional!$L$242 LEACHflow.s2C =FRACinf.s2C * RAINrate.C / Ks2w.C * SYSTEMAREA.C * AREAFRAC.s2C [m3.s-1] =continental!$L$248 LEACHflow.s2L =FRACinf.s2L * RAINrate.L / Ks2w.L * SYSTEMAREA.L * AREAFRAC.s2L [m3.s-1] =local!$L$208 LEACHflow.s2R =FRACinf.s2R * RAINrate.R / Ks2w.R * SYSTEMAREA.R * AREAFRAC.s2R [m3.s-1] =regional!$L$243 LEACHflow.s3C =FRACinf.s3C * RAINrate.C / Ks3w.C * SYSTEMAREA.C * AREAFRAC.s3C [m3.s-1] =continental!$L$249 LEACHflow.s3L =FRACinf.s3L * RAINrate.L / Ks3w.L * SYSTEMAREA.L * AREAFRAC.s3L [m3.s-1] =local!$L$209 LEACHflow.s3R =FRACinf.s3R * RAINrate.R / Ks3w.R * SYSTEMAREA.R * AREAFRAC.s3R [m3.s-1] =regional!$L$244 LEACHflow.sA =FRACinf.sA * RAINrate.A / Ksw.A * SYSTEMAREA.A * AREAFRAC.sA [m3.s-1] =arctic!$L$112 LEACHflow.sM =FRACinf.sM * RAINrate.M / Ksw.M * SYSTEMAREA.M * AREAFRAC.sM [m3.s-1] =moderate!$L$117 LEACHflow.sT =FRACinf.sT * RAINrate.T / Ksw.T * SYSTEMAREA.T * AREAFRAC.sT [m3.s-1] =tropic!$L$112


LENGTH.w2R 1.00E + 02 [km] / [m] =regional!$L$20 LITTERflow.v1C.s1C =(1 – HARVESTeff.v1C) * GROWTHrate.v1C * VOLUME.v1C [m3.s-1] =continental!$L$159 LITTERflow.v1L.s1L =(1 – HARVESTeff.v1L) * GROWTHrate.v1L * VOLUME.v1L [m3.s-1] =local!$L$133 LITTERflow.v1R.s1R =(1 – HARVESTeff.v1R) * GROWTHrate.v1R * VOLUME.v1R [m3.s-1] =regional!$L$155 LITTERflow.v2C.s2C =(1 – HARVESTeff.v2C) * GROWTHrate.v2C * VOLUME.v2C [m3.s-1] =continental!$L$160 LITTERflow.v2L.s2L =(1 – HARVESTeff.v2L) * GROWTHrate.v2L * VOLUME.v2L [m3.s-1] =local!$L$134 LITTERflow.v2R.s2R =(1 – HARVESTeff.v2R) * GROWTHrate.v2R * VOLUME.v2R [m3.s-1] =regional!$L$156 Molweight 200 [g.mol-1] / [kg.mol-1] =input!$M$13 NETsedrate.w1C =((EROSION.s1C * AREAFRAC.s1C * FRACs.s1C + EROSION.s2C * AREAFRAC.s2C * FRACs.s2C +

EROSION.s3C * AREAFRAC.s3C * FRACs.s3C) * SYSTEMAREA.C * RHOsolid + PRODsusp.w1C -SUSP.w1C * (WATERflow.w1C.w1R + WATERflow.w1C.w2C)) / (FRACs.sdC * RHOsolid) / (SYSTEMAREA.C * AREAFRAC.w1C)


NETsedrate.w1R =(SUSP.w1C * WATERflow.w1C.w1R + SUSP.wL * WATERflow.wL.w1R + (EROSION.s1R * AREAFRAC.s1R * FRACs.s1R + EROSION.s2R * AREAFRAC.s2R * FRACs.s2R + EROSION.s3R * AREAFRAC.s3R * FRACs.s3R) * SYSTEMAREA.R * RHOsolid + PRODsusp.w1R - SUSP.w1R * (WA-TERflow.w1R.w2R - WATERflow.w1R.wL)) / (FRACs.sdR * RHOsolid) / (SYSTEMAREA.R * AREAFRAC.w1R)


NETsedrate.w2C =(SUSP.wM * WATERflow.wM.w2C + SUSP.w1C * WATERflow.w1C.w2C + SUSP.w2R * WATER-flow.w2R.w2C + PRODsusp.w2C - SUSP.w2C * (WATERflow.w2C.w2R + WATERflow.w2C.wM)) / (FRACs.sdC * RHOsolid) / (SYSTEMAREA.C * AREAFRAC.w2C)


NETsedrate.w2R =(SUSP.w1R * WATERflow.w1R.w2R + SUSP.w2C * WATERflow.w2C.w2R + SUSP.wL * WATER-flow.wL.w2R + PRODsusp.w2R - SUSP.w2R * WATERflow.w2R.w2C) / (FRACs.sdR * RHOsolid) / (SYSTEMAREA.R * AREAFRAC.w2R)


NETsedrate.wA =(SUSP.wM * WATERflow.wM.wA + PRODsusp.wA - SUSP.wA * WATERflow.wA.wM) / (FRACs.sdA * RHOsolid) / (SYSTEMAREA.A * AREAFRAC.wA)

[m.s-1] =arctic!$L$85

NETsedrate.wL =(SUSP.w1R * WATERflow.w1R.wL + (EROSION.s1L * AREAFRAC.s1L * FRACs.s1L + EROSION.s2L * AREAFRAC.s2L * FRACs.s2L + EROSION.s3L * AREAFRAC.s3L * FRACs.s3L) * SYSTEMAREA.L * RHOsolid + PRODsusp.wL - SUSP.wL * (WATERflow.wL.w1R + WATER-flow.wL.w2R)) / (FRACs.sdL * RHOsolid) / (SYSTEMAREA.L * AREAFRAC.wL)

[m.s-1] =local!$L$171

NETsedrate.wM =(SUSP.w2C * WATERflow.w2C.wM + SUSP.wA * WATERflow.wA.wM + SUSP.wT * WATER-flow.wT.wM + PRODsusp.wM - SUSP.wM * (WATERflow.wM.w2C + WATERflow.wM.wA + WATER-flow.wM.wT)) / (FRACs.sdM * RHOsolid) / (SYSTEMAREA.M * AREAFRAC.wM)

[m.s-1] =moderate!$L$90

NETsedrate.wT =(SUSP.wM * WATERflow.wM.wT + PRODsusp.wT - SUSP.wT * WATERflow.wT.wM) / (FRACs.sdT * RHOsolid) / (SYSTEMAREA.T * AREAFRAC.wT)

[m.s-1] =tropic!$L$85

PENdepth.s1C =(Veff.s1C + SQRT(Veff.s1C^ 2 + 4 * KDEG.s1C * Deff.s1C)) / (2 * KDEG.s1C) [m] =continental!$L$31 PENdepth.s1L =(Veff.s1L + SQRT(Veff.s1L^ 2 + 4 * KDEG.s1L * Deff.s1L)) / (2 * KDEG.s1L) [m] =local!$L$24 PENdepth.s1R =(Veff.s1R + SQRT(Veff.s1R^ 2 + 4 * KDEG.s1R * Deff.s1R)) / (2 * KDEG.s1R) [m] =regional!$L$33 PENdepth.s2C =(Veff.s2C + SQRT(Veff.s2C^ 2 + 4 * KDEG.s2C * Deff.s2C)) / (2 * KDEG.s2C) [m] =continental!$L$37 PENdepth.s2L =(Veff.s2L + SQRT(Veff.s2L^ 2 + 4 * KDEG.s2L * Deff.s2L)) / (2 * KDEG.s2L) [m] =local!$L$30 PENdepth.s2R =(Veff.s2R + SQRT(Veff.s2R^ 2 + 4 * KDEG.s2R * Deff.s2R)) / (2 * KDEG.s2R) [m] =regional!$L$39 PENdepth.s3C =(Veff.s3C + SQRT(Veff.s3C^ 2 + 4 * KDEG.s3C * Deff.s3C)) / (2 * KDEG.s3C) [m] =continental!$L$43 PENdepth.s3L =(Veff.s3L + SQRT(Veff.s3L^ 2 + 4 * KDEG.s3L * Deff.s3L)) / (2 * KDEG.s3L) [m] =local!$L$36 PENdepth.s3R =(Veff.s3R + SQRT(Veff.s3R^ 2 + 4 * KDEG.s3R * Deff.s3R)) / (2 * KDEG.s3R) [m] =regional!$L$45 PENdepth.sA =(Veff.sA + SQRT(Veff.sA^ 2 + 4 * KDEG.sA * Deff.sA)) / (2 * KDEG.sA) [m] =arctic!$L$18 PENdepth.sM =(Veff.sM + SQRT(Veff.sM^ 2 + 4 * KDEG.sM * Deff.sM)) / (2 * KDEG.sM) [m] =moderate!$L$18 PENdepth.sT =(Veff.sT + SQRT(Veff.sT^ 2 + 4 * KDEG.sT * Deff.sT)) / (2 * KDEG.sT) [m] =tropic!$L$18 PLT.A =IF(Tm> 298, EXP( - 6.79 * (1 - Tm / 298)) * Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.A)),

Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.A))) [Pa] =arctic!$L$42

PLT.C =IF(Tm> 298, EXP( - 6.79 * (1 - Tm / 298)) * Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.C)), Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.C)))

[Pa] =continental!$L$91

PLT.L =IF(Tm> 298, EXP( - 6.79 * (1 - Tm / 298)) * Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.L)), Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.L)))

[Pa] =local!$L$76

PLT.M =IF(Tm> 298, EXP( - 6.79 * (1 - Tm / 298)) * Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.M)), Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.M)))

[Pa] =moderate!$L$46

PLT.R =IF(Tm> 298, EXP( - 6.79 * (1 - Tm / 298)) * Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.R)), Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.R)))

[Pa] =regional!$L$87

PLT.T =IF(Tm> 298, EXP( - 6.79 * (1 - Tm / 298)) * Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.T)), Pvap25 * EXP((H0vap / 8.314) * (1 / 298 - 1 / TEMP.T)))

[Pa] =tropic!$L$42

PRODsusp.w1C 1.00E + 01 [g.m-2.yr-1] / [kg.s-1] =continental!$L$205 PRODsusp.w1R 1.00E + 01 [g.m-2.yr-1] / [kg.s-1] =regional!$L$201 PRODsusp.w2C 5.00E + 00 [g.m-2.yr-1] / [kg.s-1] =continental!$L$206 PRODsusp.w2R 1.00E + 01 [g.m-2.yr-1] / [kg.s-1] =regional!$L$202 PRODsusp.wA 1.00E + 00 [g.m-2.yr-1] / [kg.s-1] =arctic!$L$86 PRODsusp.wL 1.00E + 00 [g.m-2.yr-1] / [kg.s-1] =local!$L$172


PRODsusp.wM 1.00E + 00 [g.m-2.yr-1] / [kg.s-1] =moderate!$L$91 PRODsusp.wT 1.00E + 00 [g.m-2.yr-1] / [kg.s-1] =tropic!$L$86 Pvap25 1.33E - 01 [Pa] =input!$M$20 Q.10 2.00E + 00 [ - ] =input!$M$33 Q.v1C 8.40E - 09 [m.s-1] =continental!$L$168 Q.v1L 8.40E - 09 [m.s-1] =local!$L$142 Q.v1R 8.40E - 09 [m.s-1] =regional!$L$164 Q.v2C 2.50E - 08 [m.s-1] =continental!$L$169 Q.v2L 2.50E - 08 [m.s-1] =local!$L$143 Q.v2R 2.50E - 08 [m.s-1] =regional!$L$165 RAINflow.aC.w1C =RAINrate.C * AREAFRAC.w1C * SYSTEMAREA.C [m3.s-1] =continental!$L$73 RAINflow.aC.w2C =RAINrate.C * AREAFRAC.w2C * SYSTEMAREA.C [m3.s-1] =continental!$L$84 RAINflow.aL.wL =RAINrate.L * AREAFRAC.wL * SYSTEMAREA.L [m3.s-1] =local!$L$65 RAINflow.aR.w1R =RAINrate.R * AREAFRAC.w1R * SYSTEMAREA.R [m3.s-1] =regional!$L$75 RAINflow.aR.w2R =RAINrate.R * SYSTEMAREA.R * AREAFRAC.w2R [m3.s-1] =regional!$L$80 RAINrate.A 2.50E + 02 [mm.yr-1] / [m.s-1] =arctic!$L$68 RAINrate.C 7.00E + 02 [mm.yr-1] / [m.s-1] =continental!$L$150 RAINrate.L 7.00E + 02 [mm.yr-1] / [m.s-1] =local!$L$124 RAINrate.M 7.00E + 02 [mm.yr-1] / [m.s-1] =moderate!$L$72 RAINrate.R 7.00E + 02 [mm.yr-1] / [m.s-1] =regional!$L$146 RAINrate.T 1.30E + 03 [mm.yr-1] / [m.s-1] =tropic!$L$68 RESUSPflow.sd1C.w1C =RESUSPrate.sd1C * SYSTEMAREA.C * AREAFRAC.w1C [m3.s-1] =continental!$L$195 RESUSPflow.sd1R.w1R =RESUSPrate.sd1R * SYSTEMAREA.R * AREAFRAC.w1R [m3.s-1] =regional!$L$191 RESUSPflow.sd2C.w2C =RESUSPrate.sd2C * SYSTEMAREA.C * AREAFRAC.w2C [m3.s-1] =continental!$L$197 RESUSPflow.sd2R.w2R =RESUSPrate.sd2R * SYSTEMAREA.R * AREAFRAC.w2R [m3.s-1] =regional!$L$193 RESUSPflow.sdA.wA =RESUSPrate.sdA * SYSTEMAREA.A * AREAFRAC.wA [m3.s-1] =arctic!$L$81 RESUSPflow.sdL.wL =RESUSPrate.sdL * SYSTEMAREA.L * AREAFRAC.wL [m3.s-1] =local!$L$167 RESUSPflow.sdM.wM =RESUSPrate.sdM * SYSTEMAREA.M * AREAFRAC.wM [m3.s-1] =moderate!$L$86 RESUSPflow.sdT.wT =RESUSPrate.sdT * SYSTEMAREA.T * AREAFRAC.wT [m3.s-1] =tropic!$L$81 RESUSPrate.sd1C =GROSSSEDrate.w1C - NETsedrate.w1C [m.s-1] =continental!$L$199 RESUSPrate.sd1R =GROSSSEDrate.w1R - NETsedrate.w1R [m.s-1] =regional!$L$195 RESUSPrate.sd2C =GROSSSEDrate.w2C - NETsedrate.w2C [m.s-1] =continental!$L$201

RESUSPrate.sd2R =GROSSSEDrate.w2R - NETsedrate.w2R [m.s-1] =regional!$L$197 RESUSPrate.sdA =GROSSSEDrate.wA - NETsedrate.wA [m.s-1] =arctic!$L$83 RESUSPrate.sdL =GROSSSEDrate.wL - NETsedrate.wL [m.s-1] =local!$L$169 RESUSPrate.sdM =GROSSSEDrate.wM - NETsedrate.wM [m.s-1] =moderate!$L$88 RESUSPrate.sdT =GROSSSEDrate.wT - NETsedrate.wT [m.s-1] =tropic!$L$83 RHO.v1C 9.00E + 02 [kg.m-3] =continental!$L$63 RHO.v1L 9.00E + 02 [kg.m-3] =local!$L$56 RHO.v1R 9.00E + 02 [kg.m-3] =regional!$L$65 RHO.v2C 9.00E + 02 [kg.m-3] =continental!$L$64 RHO.v2L 9.00E + 02 [kg.m-3] =local!$L$57 RHO.v2R 9.00E + 02 [kg.m-3] =regional!$L$66 RHOsolid 2.50E + 03 [kg.m-3] =input!$M$18 ROOTSremoval.s1C =0 * SYSTEMAREA.C * AREAFRAC.s1C / (365 * 24 * 3600) [m3.s-1] =continental!$L$254 ROOTSremoval.s1L =0 * SYSTEMAREA.L * AREAFRAC.s1L / (365 * 24 * 3600) [m3.s-1] =local!$L$214 ROOTSremoval.s1R =0 * SYSTEMAREA.R * AREAFRAC.s1R / (365 * 24 * 3600) [m3.s-1] =regional!$L$249 ROOTSremoval.s2C =0.0021 * SYSTEMAREA.C * AREAFRAC.s2C / (365 * 24 * 3600) [m3.s-1] =continental!$L$255 ROOTSremoval.s2L =0.0021 * SYSTEMAREA.L * AREAFRAC.s2L / (365 * 24 * 3600) [m3.s-1] =local!$L$215 ROOTSremoval.s2R =0.0021 * SYSTEMAREA.R * AREAFRAC.s2R / (365 * 24 * 3600) [m3.s-1] =regional!$L$250 RUNOFFflow.s1C.w1C =(RAINrate.C * FRACrun.s1C / Ks1w.C + EROSION.s1C) * SYSTEMAREA.C * AREAFRAC.s1C [m3.s-1] =continental!$L$215 RUNOFFflow.s1L.wL =(RAINrate.L * FRACrun.s1L / Ks1w.L + EROSION.s1L) * SYSTEMAREA.L * AREAFRAC.s1L [m3.s-1] =local!$L$179 RUNOFFflow.s1R.w1R =(RAINrate.R * FRACrun.s1R / Ks1w.R + EROSION.s1R) * SYSTEMAREA.R * AREAFRAC.s1R [m3.s-1] =regional!$L$211 RUNOFFflow.s2C.w1C =(RAINrate.C * FRACrun.s2C / Ks2w.C + EROSION.s2C) * SYSTEMAREA.C * AREAFRAC.s2C [m3.s-1] =continental!$L$216 RUNOFFflow.s2L.wL =(RAINrate.L * FRACrun.s2L / Ks2w.L + EROSION.s2L) * SYSTEMAREA.L * AREAFRAC.s2L [m3.s-1] =local!$L$180 RUNOFFflow.s2R.w1R =(RAINrate.R * FRACrun.s2R / Ks2w.R + EROSION.s2R) * SYSTEMAREA.R * AREAFRAC.s2R [m3.s-1] =regional!$L$212 RUNOFFflow.s3C.w1C =(RAINrate.C * FRACrun.s3C / Ks3w.C + EROSION.s3C) * SYSTEMAREA.C * AREAFRAC.s3C [m3.s-1] =continental!$L$217 RUNOFFflow.s3L.wL =(RAINrate.L * FRACrun.s3L / Ks3w.L + EROSION.s3L) * SYSTEMAREA.L * AREAFRAC.s3L [m3.s-1] =local!$L$181 RUNOFFflow.s3R.w1R =(RAINrate.R * FRACrun.s3R / Ks3w.R + EROSION.s3R) * SYSTEMAREA.R * AREAFRAC.s3R [m3.s-1] =regional!$L$213 RUNOFFflow.sA.wA =(RAINrate.A * FRACrun.sA / Ksw.A + EROSION.sA) * SYSTEMAREA.A * AREAFRAC.sA [m3.s-1] =arctic!$L$93 RUNOFFflow.sM.wM =(RAINrate.M * FRACrun.sM / Ksw.M + EROSION.sM) * SYSTEMAREA.M * AREAFRAC.sM [m3.s-1] =moderate!$L$98 RUNOFFflow.sT.wT =(RAINrate.T * FRACrun.sT / Ksw.T + EROSION.sT) * SYSTEMAREA.T * AREAFRAC.sT [m3.s-1] =tropic!$L$93 SEAcurrent.w2C.w2R 3.50E - 02 [m.s-1] =continental!$L$80 SEAcurrent.wA.wM 1.00E - 02 [m.s-1] =arctic!$L$35


SEAcurrent.wM.w2C 0.00E + 00 [m.s-1] =moderate!$L$35 SEAcurrent.wT.wM 1.00E – 02 [m.s-1] =tropic!$L$35 SEDflow.w1C.sd1C =(GROSSSEDrate.w1C * FRACs.sdC * RHOsolid / SUSP.w1C) * ((Kp.susp1C * SUSP.w1C / 1000) *

FRw.w1C) * (SYSTEMAREA.C * AREAFRAC.w1C) [m3.s-1] =continental!$L$194

SEDflow.w1R.sd1R =(GROSSSEDrate.w1R * FRACs.sdR * RHOsolid / SUSP.w1R) * ((Kp.susp1R * SUSP.w1R / 1000) * FRw.w1R) * (SYSTEMAREA.R * AREAFRAC.w1R)


SEDflow.w2C.sd2C =(GROSSSEDrate.w2C * FRACs.sdC * RHOsolid / SUSP.w2C) * ((Kp.susp2C * SUSP.w2C / 1000) * FRw.w2C) * (SYSTEMAREA.C * AREAFRAC.w2C)


SEDflow.w2R.sd2R =(GROSSSEDrate.w2R * FRACs.sdR * RHOsolid / SUSP.w2R) * ((Kp.susp2R * SUSP.w2R / 1000) * FRw.w2R) * (SYSTEMAREA.R * AREAFRAC.w2R)


SEDflow.wA.sdA =(GROSSSEDrate.wA * FRACs.sdA * RHOsolid / SUSP.wA) * ((Kp.suspA * SUSP.wA / 1000) * FRw.wA) * SYSTEMAREA.A * AREAFRAC.wA


SEDflow.wL.sdL =(GROSSSEDrate.wL * FRACs.sdL * RHOsolid / SUSP.wL) * ((Kp.suspL * SUSP.wL / 1000) * FRw.wL) * (SYSTEMAREA.L * AREAFRAC.wL)

[m3.s-1] =local!$L$166

SEDflow.wM.sdM =(GROSSSEDrate.wM * FRACs.sdM * RHOsolid / SUSP.wM) * ((Kp.suspM * SUSP.wM / 1000) * FRw.wM) * SYSTEMAREA.M * AREAFRAC.wM


SEDflow.wT.sdT =(GROSSSEDrate.wT * FRACs.sdT * RHOsolid / SUSP.wT) * ((Kp.suspT * SUSP.wT / 1000) * FRw.wT) * SYSTEMAREA.T * AREAFRAC.wT


SETTLvelocity.A 2.89E – 05 [m.s-1] =arctic!$L$84 SETTLvelocity.C 2.89E – 05 [m.s-1] =continental!$L$202 SETTLvelocity.L 2.89E – 05 [m.s-1] =local!$L$170 SETTLvelocity.M 2.89E – 05 [m.s-1] =moderate!$L$89 SETTLvelocity.R 2.89E – 05 [m.s-1] =regional!$L$198 SETTLvelocity.T 2.89E – 05 [m.s-1] =tropic!$L$84 Sol25 [mg.L-1] / [mol.m-3] =input!$M$22 SOLIDadv.s1C 6.34E - 12 [m.s-1] =continental!$L$33 SOLIDadv.s1L 6.34E - 12 [m.s-1] =local!$L$26 SOLIDadv.s1R 6.34E - 12 [m.s-1] =regional!$L$35 SOLIDadv.s2C 6.34E - 12 [m.s-1] =continental!$L$39 SOLIDadv.s2L 6.34E - 12 [m.s-1] =local!$L$32 SOLIDadv.s2R 6.34E - 12 [m.s-1] =regional!$L$41 SOLIDadv.s3C 6.34E - 12 [m.s-1] =continental!$L$45

SOLIDadv.s3L 6.34E - 12 [m.s-1] =local!$L$38 SOLIDadv.s3R 6.34E - 12 [m.s-1] =regional!$L$47 SOLIDadv.sA 6.34E - 12 [m.s-1] =arctic!$L$20 SOLIDadv.sM 6.34E - 12 [m.s-1] =moderate!$L$20 SOLIDadv.sT 6.34E - 12 [m.s-1] =tropic!$L$20 SOLIDdiff.s1C 6.37E - 12 [m2.s-1] =continental!$L$35 SOLIDdiff.s1L 6.37E - 12 [m2.s-1] =local!$L$28 SOLIDdiff.s1R 6.37E - 12 [m2.s-1] =regional!$L$37 SOLIDdiff.s2C 6.37E - 12 [m2.s-1] =continental!$L$41 SOLIDdiff.s2L 6.37E - 12 [m2.s-1] =local!$L$34 SOLIDdiff.s2R 6.37E - 12 [m2.s-1] =regional!$L$43 SOLIDdiff.s3C 6.37E - 12 [m2.s-1] =continental!$L$47 SOLIDdiff.s3L 6.37E - 12 [m2.s-1] =local!$L$40 SOLIDdiff.s3R 6.37E - 12 [m2.s-1] =regional!$L$49 SOLIDdiff.sA 6.37E - 12 [m2.s-1] =arctic!$L$22 SOLIDdiff.sM 6.37E - 12 [m2.s-1] =moderate!$L$22 SOLIDdiff.sT 6.37E - 12 [m2.s-1] =tropic!$L$22 SURFaerosol.A 1.50E - 04 [m2.m-3] =arctic!$L$43 SURFaerosol.C 1.50E - 04 [m2.m-3] =continental!$L$92 SURFaerosol.L 1.50E - 04 [m2.m-3] =local!$L$77 SURFaerosol.M 1.50E - 04 [m2.m-3] =moderate!$L$47 SURFaerosol.R 1.50E - 04 [m2.m-3] =regional!$L$88 SURFaerosol.T 1.50E - 04 [m2.m-3] =tropic!$L$43 SUSP.w1C 1.50E + 01 [mg.L-1] / [kg.m-3] =continental!$L$96 SUSP.w1R 1.50E + 01 [mg.L-1] / [kg.m-3] =regional!$L$92 SUSP.w2C 5.00E + 00 [mg.L-1] / [kg.m-3] =continental!$L$103 SUSP.w2R 5.00E + 00 [mg.L-1] / [kg.m-3] =regional!$L$99 SUSP.wA 5.00E + 00 [mg.L-1] / [kg.m-3] =arctic!$L$47 SUSP.wL 1.50E + 01 [mg.L-1] / [kg.m-3] =local!$L$81 SUSP.wM 5.00E + 00 [mg.L-1] / [kg.m-3] =moderate!$L$51 SUSP.wT 5.00E + 00 [mg.L-1] / [kg.m-3] =tropic!$L$47 SYSTEMAREA.A 4.25E + 07 [km2] / [m2] =arctic!$L$11


SYSTEMAREA.C =(AREAland.C + AREAsea.C - SYSTEMAREA.R) / 1000000 [km2] / [m2] =continental!$L$17 SYSTEMAREA.L 100 [km2] / [m2] =local!$L$15 SYSTEMAREA.M 8.50E + 07 [km2] / [m2] =moderate!$L$11 SYSTEMAREA.R =(AREAland.R + AREAsea.R - SYSTEMAREA.L) / 1000000 [km2] / [m2] =regional!$L$17 SYSTEMAREA.T 1.28E + 08 [km2] / [m2] =tropic!$L$11 SystemName.A =arctic!$L$5 SystemName.C =continental!$L$5 SystemName.L =local!$L$5 SystemName.M =moderate!$L$5 SystemName.R =regional!$L$5 SystemName.T =tropic!$L$5 TAU.aA =(SQRT(SYSTEMAREA.A * PI() / 4) / WINDspeed.A) / (3600 * 24) [d] / [s] =arctic!$L$30 TAU.aC =(SQRT(SYSTEMAREA.C * PI() / 4) / WINDspeed.C) / (3600 * 24) [d] / [s] =continental!$L$67 TAU.aL =(SQRT(SYSTEMAREA.L * PI() / 4) / WINDspeed.L) / (3600 * 24) [d] / [s] =local!$L$60 TAU.aR =(SQRT(SYSTEMAREA.R * PI() / 4) / WINDspeed.R) / (3600 * 24) [d] / [s] =regional!$L$69 TAU.aT =(SQRT(SYSTEMAREA.T * PI() / 4) / WINDspeed.T) / (3600 * 24) [d] / [s] =tropic!$L$30 TAU.wA =(SQRT(SYSTEMAREA.A * AREAFRAC.wA) / SEAcurrent.wA.wM) / (3600 * 24) [d] / [s] =arctic!$L$34 TAU.wT =(SQRT(SYSTEMAREA.T * AREAFRAC.wT) / SEAcurrent.wT.wM) / (3600 * 24) [d] / [s] =tropic!$L$34 TEMP.A - 1.00E + 01 [oC] / [K] =arctic!$L$41 TEMP.C 1.20E + 01 [oC] / [K] =continental!$L$90 TEMP.L 1.20E + 01 [oC] / [K] =local!$L$75 TEMP.M 1.20E + 01 [oC] / [K] =moderate!$L$45 TEMP.R 1.20E + 01 [oC] / [K] =regional!$L$86 TEMP.T 2.50E + 01 [oC] / [K] =tropic!$L$41 Tempfactor.aA =EXP((Ea.OHrad / 8.314) * (TEMP.A - 298) / 298^ 2) [ - ] =arctic!$L$102 Tempfactor.aC =EXP((Ea.OHrad / 8.314) * (TEMP.C - 298) / 298^ 2) [ - ] =continental!$L$230 Tempfactor.aL =EXP((Ea.OHrad / 8.314) * (TEMP.L - 298) / 298^ 2) [ - ] =local!$L$194 Tempfactor.aM =EXP((Ea.OHrad / 8.314) * (TEMP.M - 298) / 298^ 2) [ - ] =moderate!$L$107 Tempfactor.aR =EXP((Ea.OHrad / 8.314) * (TEMP.R - 298) / 298^ 2) [ - ] =regional!$L$226 Tempfactor.aT =EXP((Ea.OHrad / 8.314) * (TEMP.T - 298) / 298^ 2) [ - ] =tropic!$L$102 Tempfactor.wsdsA =Q.10^ ((TEMP.A - 298) / 10) [ - ] =arctic!$L$105 Tempfactor.wsdsC =Q.10^ ((TEMP.C - 298) / 10) [ - ] =continental!$L$234

Tempfactor.wsdsL =Q.10^ ((TEMP.L - 298) / 10) [ - ] =local!$L$197 Tempfactor.wsdsM =Q.10^ ((TEMP.M - 298) / 10) [ - ] =moderate!$L$110 Tempfactor.wsdsR =Q.10^ ((TEMP.R - 298) / 10) [ - ] =regional!$L$230 Tempfactor.wsdsT =Q.10^ ((TEMP.T - 298) / 10) [ - ] =tropic!$L$105 Tm 4.30E + 01 [oC] / [K] =input!$M$25 TRANSflow.s1C.v1C =Q.v1C * TSCF.v1C / Ks1w.C * (SYSTEMAREA.C * AREAFRAC.s1C) [m3.s-1] =continental!$L$166 TRANSflow.s1L.v1L =(Q.v1L * TSCF.v1L / Ks1w.L) * (SYSTEMAREA.L * AREAFRAC.s1L) [m3.s-1] =local!$L$140 TRANSflow.s1R.v1R =(Q.v1R * TSCF.v1R / Ks1w.R) * (SYSTEMAREA.R * AREAFRAC.s1R) [m3.s-1] =regional!$L$162 TRANSflow.s2C.v2C =Q.v2C * TSCF.v2C / Ks2w.C * (SYSTEMAREA.C * AREAFRAC.s2C) [m3.s-1] =continental!$L$167 TRANSflow.s2L.v2L =(Q.v2L * TSCF.v2L / Ks2w.L) * (SYSTEMAREA.L * AREAFRAC.s2L) [m3.s-1] =local!$L$141 TRANSflow.s2R.v2R =(Q.v2R * TSCF.v2R / Ks2w.R) * (SYSTEMAREA.R * AREAFRAC.s2R) [m3.s-1] =regional!$L$163 TSCF.v1C =0.784 * EXP( - ((LOG(Kow) - 1.78)^ 2) / 2.44) [ - ] =continental!$L$170 TSCF.v1L =0.784 * EXP( - ((LOG(Kow) - 1.78)^ 2) / 2.44) [ - ] =local!$L$144 TSCF.v1R =0.784 * EXP( - ((LOG(Kow) - 1.78)^ 2) / 2.44) [ - ] =regional!$L$166 TSCF.v2C =0.784 * EXP( - ((LOG(Kow) - 1.78)^ 2) / 2.44) [ - ] =continental!$L$171 TSCF.v2L =0.784 * EXP( - ((LOG(Kow) - 1.78)^ 2) / 2.44) [ - ] =local!$L$145 TSCF.v2R =0.784 * EXP( - ((LOG(Kow) - 1.78)^ 2) / 2.44) [ - ] =regional!$L$167 Use.C [t.yr-1] / [ - ] =input!$M$83 Use.L [t.yr-1] / [mol.s-1] =input!$M$54 Use.R [t.yr-1] / [mol.s-1] =input!$M$68 Veff.s1C =(RAINrate.C * FRACinf.s1C) * (FRw.s1C / FRACw.s1C) + SOLIDadv.s1C * (FRs.s1C / FRACs.s1C) [m.s-1] =continental!$L$32 Veff.s1L =(RAINrate.L * FRACinf.s1L) * (FRw.s1L / FRACw.s1L) + SOLIDadv.s1L * (FRs.s1L / FRACs.s1L) [m.s-1] =local!$L$25 Veff.s1R =(RAINrate.R * FRACinf.s1R) * (FRw.s1R / FRACw.s1R) + SOLIDadv.s1R * (FRs.s1R / FRACs.s1R) [m.s-1] =regional!$L$34 Veff.s2C =(RAINrate.C * FRACinf.s2C) * (FRw.s2C / FRACw.s2C) + SOLIDadv.s2C * (FRs.s2C / FRACs.s2C) [m.s-1] =continental!$L$38 Veff.s2L =(RAINrate.L * FRACinf.s2L) * (FRw.s2L / FRACw.s2L) + SOLIDadv.s2L * (FRs.s2L / FRACs.s2L) [m.s-1] =local!$L$31 Veff.s2R =(RAINrate.R * FRACinf.s2R) * (FRw.s2R / FRACw.s2R) + SOLIDadv.s2R * (FRs.s2R / FRACs.s2R) [m.s-1] =regional!$L$40 Veff.s3C =(RAINrate.C * FRACinf.s3C) * (FRw.s3C / FRACw.s3C) + SOLIDadv.s3C * (FRs.s3C / FRACs.s3C) [m.s-1] =continental!$L$44 Veff.s3L =(RAINrate.L * FRACinf.s3L) * (FRw.s3L / FRACw.s3L) + SOLIDadv.s3L * (FRs.s3L / FRACs.s3L) [m.s-1] =local!$L$37 Veff.s3R =(RAINrate.R * FRACinf.s3R) * (FRw.s3R / FRACw.s3R) + SOLIDadv.s3R * (FRs.s3R / FRACs.s3R) [m.s-1] =regional!$L$46 Veff.sA =(RAINrate.A * FRACinf.sA) * (FRw.sA / FRACw.sA) + SOLIDadv.sA * (FRs.sA / FRACs.sA) [m.s-1] =arctic!$L$19 Veff.sM =(RAINrate.M * FRACinf.sM) * (FRw.sM / FRACw.sM) + SOLIDadv.sM * (FRs.sM / FRACs.sM) [m.s-1] =moderate!$L$19 Veff.sT =(RAINrate.T * FRACinf.sT) * (FRw.sT / FRACw.sT) + SOLIDadv.sT * (FRs.sT / FRACs.sT) [m.s-1] =tropic!$L$19


VEGmass.v1C 1.20E + 00 [kg.m-2] =continental!$L$61 VEGmass.v1L 1.20E + 00 [kg.m-2] =local!$L$54 VEGmass.v1R 1.20E + 00 [kg.m-2] =regional!$L$63 VEGmass.v2C 1.80E + 00 [kg.m-2] =continental!$L$62 VEGmass.v2L 1.80E + 00 [kg.m-2] =local!$L$55 VEGmass.v2R 1.80E + 00 [kg.m-2] =regional!$L$64 VOLATflow.s1C.aC =(kas.air.aC * kas.soil.sC) / (kas.air.aC + kas.soil.sC / (Kh.C / Ks1w.C)) * (SYSTEMAREA.C *

AREAFRAC.s1C) [m3.s-1] =continental!$L$180

VOLATflow.s1L.aL =(kas.air.aL * kas.soil.sL) / (kas.air.aL + kas.soil.sL / (Kh.L / Ks1w.L)) * (SYSTEMAREA.L * AREAFRAC.s1L)

[m3.s-1] =local!$L$152

VOLATflow.s1R.aR =(kas.air.aR * kas.soil.sR) / (kas.air.aR + kas.soil.sR / (Kh.R / Ks1w.R)) * (SYSTEMAREA.R * AREAFRAC.s1R)


VOLATflow.s2C.aC =(kas.air.aC * kas.soil.sC) / (kas.air.aC + kas.soil.sC / (Kh.C / Ks2w.C)) * (SYSTEMAREA.C * AREAFRAC.s2C)



[m3.s-1] =local!$L$154



VOLATflow.s3C.aC =(kas.air.aC * kas.soil.sC) / (kas.air.aC + kas.soil.sC / (Kh.C / Ks3w.C)) * (SYSTEMAREA.C * AREAFRAC.s3C)



[m3.s-1] =local!$L$156



VOLATflow.sA.aA =(kas.air.aA * kas.soil.sA) / (kas.air.aA + kas.soil.sA / (Kh.A / Ksw.A)) * (SYSTEMAREA.A * AREAFRAC.sA)


VOLATflow.sM.aM =(kas.air.aM * kas.soil.sM) / (kas.air.aM + kas.soil.sM / (Kh.M / Ksw.M)) * (SYSTEMAREA.M * AREAFRAC.sM)


VOLATflow.sT.aT =(kas.air.aT * kas.soil.sT) / (kas.air.aT + kas.soil.sT / (Kh.T / Ksw.T)) * (SYSTEMAREA.T * AREAFRAC.sT)


VOLATflow.v1C.aC =g.v1C / Kv1a.C * LAI.v1C * SYSTEMAREA.C * AREAFRAC.s1C [m3.s-1] =continental!$L$188 VOLATflow.v1L.aL =g.v1L / Kv1a.L * LAI.v1L * SYSTEMAREA.L * AREAFRAC.s1L [m3.s-1] =local!$L$160

VOLATflow.v1R.aR =g.v1R / Kv1a.R * LAI.v1R * SYSTEMAREA.R * AREAFRAC.s1R [m3.s-1] =regional!$L$184 VOLATflow.v2C.aC =g.v2C / Kv2a.C * LAI.v2C * SYSTEMAREA.C * AREAFRAC.s2C [m3.s-1] =continental!$L$190 VOLATflow.v2L.aL =g.v2L / Kv2a.L * LAI.v2L * SYSTEMAREA.L * AREAFRAC.s2L [m3.s-1] =local!$L$162 VOLATflow.v2R.aR =g.v2R / Kv2a.R * LAI.v2R * SYSTEMAREA.R * AREAFRAC.s2R [m3.s-1] =regional!$L$186 VOLATflow.w1C.aC =(kaw.air.aC * kaw.water.wC / (kaw.air.aC * Kh.C + kaw.water.wC)) * Kh.C * FRw.w1C *

SYSTEMAREA.C * AREAFRAC.w1C [m3.s-1] =continental!$L$174

VOLATflow.w1R.aR =(kaw.air.aR * kaw.water.wR / (kaw.air.aR * Kh.R + kaw.water.wR)) * Kh.R * FRw.w1R * (SYSTEMAREA.R * AREAFRAC.w1R)


VOLATflow.w2C.aC =(kaw.air.aC * kaw.water.wC / (kaw.air.aC * Kh.C + kaw.water.wC)) * Kh.C * FRw.w2C * SYSTEMAREA.C * AREAFRAC.w2C


VOLATflow.w2R.aR =(kaw.air.aR * kaw.water.wR / (kaw.air.aR * Kh.R + kaw.water.wR)) * Kh.R * FRw.w2R * (SYSTEMAREA.R * AREAFRAC.w2R)


VOLATflow.wA.aA =(kaw.air.aA * kaw.water.wA / (kaw.air.aA * Kh.A + kaw.water.wA)) * Kh.A * FRw.wA * SYSTEMAREA.A * AREAFRAC.wA


VOLATflow.wL.aL =(kaw.air.aL * kaw.water.wL / (kaw.air.aL * Kh.L + kaw.water.wL)) * Kh.L * FRw.wL * (SYSTEMAREA.L * AREAFRAC.wL)

[m3.s-1] =local!$L$148

VOLATflow.wM.aM =(kaw.air.aM * kaw.water.wM / (kaw.air.aM * Kh.M + kaw.water.wM)) * Kh.M * FRw.wM * SYSTEMAREA.M * AREAFRAC.wM


VOLATflow.wT.aT =(kaw.air.aT * kaw.water.wT / (kaw.air.aT * Kh.T + kaw.water.wT)) * Kh.T * FRw.wT * SYSTEMAREA.T * AREAFRAC.wT


VOLUME.aA =SYSTEMAREA.A * HEIGHT.aA [m3] =arctic!$L$7 VOLUME.aC =SYSTEMAREA.C * HEIGHT.aC [m3] =continental!$L$7 VOLUME.aL =SYSTEMAREA.L * HEIGHT.aL [m3] =local!$L$7 VOLUME.aM =SYSTEMAREA.M * HEIGHT.aM [m3] =moderate!$L$7 VOLUME.aR =SYSTEMAREA.R * HEIGHT.aR [m3] =regional!$L$7 VOLUME.aT =SYSTEMAREA.T * HEIGHT.aT [m3] =tropic!$L$7 VOLUME.s1C =SYSTEMAREA.C * AREAFRAC.s1C * DEPTH.s1C [m3] =continental!$L$12 VOLUME.s1L =SYSTEMAREA.L * AREAFRAC.s1L * DEPTH.s1L [m3] =local!$L$10 VOLUME.s1R =SYSTEMAREA.R * AREAFRAC.s1R * DEPTH.s1R [m3] =regional!$L$12 VOLUME.s2C =SYSTEMAREA.C * AREAFRAC.s2C * DEPTH.s2C [m3] =continental!$L$13 VOLUME.s2L =SYSTEMAREA.L * AREAFRAC.s2L * DEPTH.s2L [m3] =local!$L$11 VOLUME.s2R =SYSTEMAREA.R * AREAFRAC.s2R * DEPTH.s2R [m3] =regional!$L$13


VOLUME.s3C =SYSTEMAREA.C * AREAFRAC.s3C * DEPTH.s3C [m3] =continental!$L$14 VOLUME.s3L =SYSTEMAREA.L * AREAFRAC.s3L * DEPTH.s3L [m3] =local!$L$12 VOLUME.s3R =SYSTEMAREA.R * AREAFRAC.s3R * DEPTH.s3R [m3] =regional!$L$14 VOLUME.sA =SYSTEMAREA.A * AREAFRAC.sA * DEPTH.sA [m3] =arctic!$L$10 VOLUME.sd1C =SYSTEMAREA.C * AREAFRAC.w1C * DEPTH.sd1C [m3] =continental!$L$10 VOLUME.sd1R =SYSTEMAREA.R * AREAFRAC.w1R * DEPTH.sd1R [m3] =regional!$L$10 VOLUME.sd2C =SYSTEMAREA.C * AREAFRAC.w2C * DEPTH.sd2C [m3] =continental!$L$11 VOLUME.sd2R =SYSTEMAREA.R * AREAFRAC.w2R * DEPTH.sd2R [m3] =regional!$L$11 VOLUME.sdA =SYSTEMAREA.A * DEPTH.sdA * AREAFRAC.wA [m3] =arctic!$L$9 VOLUME.sdL =SYSTEMAREA.L * AREAFRAC.wL * DEPTH.sdL [m3] =local!$L$9 VOLUME.sdM =SYSTEMAREA.M * DEPTH.sdM * AREAFRAC.wM [m3] =moderate!$L$9 VOLUME.sdT =SYSTEMAREA.T * DEPTH.sdT * AREAFRAC.wT [m3] =tropic!$L$9 VOLUME.sM =SYSTEMAREA.M * AREAFRAC.sM * DEPTH.sM [m3] =moderate!$L$10 VOLUME.sT =SYSTEMAREA.T * AREAFRAC.sT * DEPTH.sT [m3] =tropic!$L$10 VOLUME.v1C =SYSTEMAREA.C * AREAFRAC.s1C * VEGmass.v1C * 1 / RHO.v1C [m3] =continental!$L$15 VOLUME.v1L =SYSTEMAREA.L * AREAFRAC.s1L * VEGmass.v1L * 1 / RHO.v1L [m3] =local!$L$13 VOLUME.v1R =SYSTEMAREA.R * AREAFRAC.s1R * VEGmass.v1R * 1 / RHO.v1R [m3] =regional!$L$15 VOLUME.v2C =SYSTEMAREA.C * AREAFRAC.s2C * VEGmass.v2C * 1 / RHO.v2C [m3] =continental!$L$16 VOLUME.v2L =SYSTEMAREA.L * AREAFRAC.s2L * VEGmass.v2L * 1 / RHO.v2L [m3] =local!$L$14 VOLUME.v2R =SYSTEMAREA.R * AREAFRAC.s2R * VEGmass.v2R * 1 / RHO.v2R [m3] =regional!$L$16 VOLUME.w1C =SYSTEMAREA.C * AREAFRAC.w1C * DEPTH.w1C [m3] =continental!$L$8 VOLUME.w1R =SYSTEMAREA.R * AREAFRAC.w1R * DEPTH.w1R [m3] =regional!$L$8 VOLUME.w2C =SYSTEMAREA.C * AREAFRAC.w2C * DEPTH.w2C [m3] =continental!$L$9 VOLUME.w2R =SYSTEMAREA.R * AREAFRAC.w2R * DEPTH.w2R [m3] =regional!$L$9 VOLUME.wA =SYSTEMAREA.A * DEPTH.wA * AREAFRAC.wA [m3] =arctic!$L$8 VOLUME.wL =SYSTEMAREA.L * AREAFRAC.wL * DEPTH.wL [m3] =local!$L$8 VOLUME.wM =SYSTEMAREA.M * DEPTH.wM * AREAFRAC.wM [m3] =moderate!$L$8 VOLUME.wT =SYSTEMAREA.T * DEPTH.wT * AREAFRAC.wT [m3] =tropic!$L$8 WATERflow.w1C.w1R =(RAINflow.aC.w1C + WATERrun.s1C + WATERrun.s2C + WATERrun.s3C) * FRAC.w1C.w1R [m3.s-1] =continental!$L$71 WATERflow.w1C.w2C =(RAINflow.aC.w1C + WATERrun.s1C + WATERrun.s2C + WATERrun.s3C) * (1 - FRAC.w1C.w1R) [m3.s-1] =continental!$L$72 WATERflow.w1R.w2R =RAINflow.aR.w1R + WATERrun.s1R + WATERrun.s2R + WATERrun.s3R + WATERflow.w1C.w1R +

WATERflow.wL.w1R - WATERflow.w1R.wL [m3.s-1] =regional!$L$74

WATERflow.w1R.wL =RAINflow.aL.wL + WATERrun.s1L + WATERrun.s2L + WATERrun.s3L [m3.s-1] =regional!$L$73 WATERflow.w2C.w2R =ADVflow.w2C.w2R + DSPflow.w2Cw2R [m3.s-1] =continental!$L$78 WATERflow.w2C.wM =(RAINflow.aC.w2C + WATERflow.w1C.w2C) + (WATERflow.w2R.w2C - WATERflow.w2C.w2R) +

WATERflow.wM.w2C [m3.s-1] =continental!$L$83

WATERflow.w2R.w2C =RAINflow.aR.w2R + WATERflow.wL.w2R + WATERflow.w1R.w2R + WATERflow.w2C.w2R [m3.s-1] =regional!$L$79 WATERflow.wA.wM =VOLUME.wA / TAU.wA [m3.s-1] =arctic!$L$33 WATERflow.wL.w1R =(RAINflow.aL.wL + WATERrun.s1L + WATERrun.s2L + WATERrun.s3L + WATERflow.w1R.wL) *

FRAC.wL.w1R [m3.s-1] =local!$L$63

WATERflow.wL.w2R =(RAINflow.aL.wL + WATERrun.s1L + WATERrun.s2L + WATERrun.s3L + WATERflow.w1R.wL) * (1 - FRAC.wL.w1R)

[m3.s-1] =local!$L$64

WATERflow.wM.w2C =ADVflow.wM.w2C + DSPflow.wMw2C [m3.s-1] =moderate!$L$33 WATERflow.wM.wA =WATERflow.wA.wM [m3.s-1] =moderate!$L$38 WATERflow.wM.wT =WATERflow.wT.wM [m3.s-1] =moderate!$L$39 WATERflow.wT.wM =VOLUME.wT / TAU.wT [m3.s-1] =tropic!$L$33 WATERrun.s1C =AREAFRAC.s1C * FRACrun.s1C * RAINrate.C * SYSTEMAREA.C [m3.s-1] =continental!$L$74 WATERrun.s1L =AREAFRAC.s1L * FRACrun.s1L * RAINrate.L * SYSTEMAREA.L [m3.s-1] =local!$L$66 WATERrun.s1R =AREAFRAC.s1R * FRACrun.s1R * RAINrate.R * SYSTEMAREA.R [m3.s-1] =regional!$L$76 WATERrun.s2C =AREAFRAC.s2C * FRACrun.s2C * RAINrate.C * SYSTEMAREA.C [m3.s-1] =continental!$L$75 WATERrun.s2L =AREAFRAC.s2L * FRACrun.s2L * RAINrate.L * SYSTEMAREA.L [m3.s-1] =local!$L$67 WATERrun.s2R =AREAFRAC.s2R * FRACrun.s2R * RAINrate.R * SYSTEMAREA.R [m3.s-1] =regional!$L$77 WATERrun.s3C =AREAFRAC.s3C * FRACrun.s3C * RAINrate.C * SYSTEMAREA.C [m3.s-1] =continental!$L$76 WATERrun.s3L =AREAFRAC.s3L * FRACrun.s3L * RAINrate.L * SYSTEMAREA.L [m3.s-1] =local!$L$68 WATERrun.s3R =AREAFRAC.s3R * FRACrun.s3R * RAINrate.R * SYSTEMAREA.R [m3.s-1] =regional!$L$78 WIDTH.w2R 1.00E + 01 [km] / [m] =regional!$L$21 WINDspeed.A 3.00E + 00 [m.s-1] =arctic!$L$31 WINDspeed.C 3.00E + 00 [m.s-1] =continental!$L$68 WINDspeed.L 3.00E + 00 [m.s-1] =local!$L$61 WINDspeed.M 3.00E + 00 [m.s-1] =moderate!$L$79 WINDspeed.R 3.00E + 00 [m.s-1] =regional!$L$70 WINDspeed.T 3.00E + 00 [m.s-1] =tropic!$L$31