COINS: an integrative modelling shell for carbon accounting and general ecological analysis

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COINS:an integrative modelling shell for carbon
accounting and general ecological analysis
S.H.Roxburgh
a,b,
*
,I.D.Davies
a,b
a
Cooperative Research Centre for Greenhouse Accounting,GPO Box 1600,Canberra,ACT 2601,Australia
b
Ecosystem Dynamics Group,Research School of Biological Sciences,Institute of Advanced Studies,Australian National University,
Canberra ACT 0200,Australia
Received 21 May 2004;received in revised form 22 October 2004;accepted 3 November 2004
Available online 25 March 2005
Abstract
It is common for a range of models to be developed to investigate broadly similar ecological and environmental phenomena.This
inevitably results in collections of models that,although individually possessing unique characteristics,also share a number of key
similarities.Here we describe a new modelling shell called COINS (COmparison and INtegration Shell) within which many related
models can be co-located,and where model similarities are exploited to facilitate rapid model development and analysis.The
philosophy underlying COINS is to separate computer code that is shared across different models,such as common process
descriptions,or shared data input and output routines,from the core equations of each model.This reduces code redundancy,
allowing the modeller to more directly focus on the process of model formulation.As an integrative tool,COINS can be used to (i)
construct component models,(ii) integrate existing components to develop a simulation,and (iii) allow end users to run a simulation
for analysis and scenario comparison.The COINS software has been developed with a specific focus on modelling the terrestrial
carbon cycle,but its utility is potentially broader,particularly within the general area of ecological analysis and natural resource
management.Three examples based on terrestrial carbon accounting at a range of spatial scales (point,landscape,continental and
global) are used to illustrate major COINS features,including flexibility in the spatial deployment of models,the ability to combine
different models within the same simulation,and Monte Carlo sensitivity analyses.
￿ 2005 Published by Elsevier Ltd.
Keywords:Model integration;Carbon modelling;Simulation modelling
Software availability
Name of the software:COINS (Comparison and
Integration Shell)
Developers:Ian Davies and Stephen Roxburgh
Contact address:CRC for Greenhouse Accounting and
the Ecosystem Dynamics Group,Research
School of Biological Science,Institute of
Advanced Studies,The Australian National
University,Canberra ACT 0200,Australia
System requirements:Windows 95 or greater,512 MB
RAM
Program language:Delphi 7
Program size:6.5 MB
Availability:Available for non-commercial and educa-
tional use through an agreement with the
Cooperative Research Centre for Greenhouse
Accounting.For licence conditions see http://
www.greenhouse.crc.org.au
* Corresponding author.Cooperative Research Centre for Green-
house Accounting,GPO Box 1600,Canberra,ACT 2601,Australia.
Fax:C61 02 6249 5095.
E-mail address:roxburgh@greenhouse.crc.org.au (S.H.Roxburgh).
1364-8152/$ - see front matter ￿ 2005 Published by Elsevier Ltd.
doi:10.1016/j.envsoft.2004.11.006
www.elsevier.com/locate/envsoft
Environmental Modelling & Software 21 (2006) 359–374
1.Introduction
Recent advances in both software and hardware
technology have dramatically increased opportunities
for integrating different simulation models within the
same analysis frameworks (Rizzoli and Davis,1999).
Such model integration has many advantages,including
the ability to combine different models for addressing
complex issues such as those that arise in natural
resource management (Reed et al.,1999;Guariso et al.,
1996;Argent and Grayson,2003;Argent,2004),the
ability to compare model assumptions and behaviours
in a consistent and standardised way,and the ability to
re-use existing software (Rizzoli et al.,1998;Rizzoli
and Davis,1999).Integrative modelling activities
also facilitate the development of cross-disciplinary
research.
There exist a number of methods for integrating and
coordinating different models.One approach links
models at the level of the compiled code,for example
direct parsing of output from one model as input to
another (e.g.Villa and Costanza,2000),or the use of
component object model (COM) or related technologies
(e.g.Lam et al.,2004).In this case,controlling software
coordinates the communication between applications,
which themselves may reside on different machines,and
be running different operating systems (e.g.Villa and
Costanza,2000).Integrated model collections of this
nature have been called ‘federations’ (Maxwell,1999).
One major advantage is that no re-coding of the
component models is required;only a requirement to
establish a means of communication between the
controlling ‘master’ program and the component model
‘slaves’.However,this approach can be disadvantageous
if modification (even in a small way) of one of the
component models is required.
A second approach links models at the level of the
computer code,whereby different models are integrated
within the same software application or ‘shell’.This
option is more suited to the combined tasks of model
development (creating new models) and model integra-
tion (combining and running existing models).A
common criticism of this approach is that model
development or modification requires knowledge of
computer programming,therefore it is difficult for non-
specialists to become actively involved in transforming
conceptual models into simulations.
Finally,declarative approaches to modelling,which
seek to overcome some of the limitations discussed
above,are becoming increasingly popular.Within a de-
clarative framework the model is described,often using
graphical techniques,and this description becomes the
implementation.Therefore,specialists and non-special-
ists alike can participate in the model development
process.Examples and further discussion of the de-
clarative approach for the environmental sciences can be
found in Maxwell (1999),Fall and Fall (2001),Villa
(2001) and Muetzelfeldt and Massheder (2003).
In this article we describe the COINS integrative
software environment,which most closely corresponds
to the software ‘shell’ approach described above.
1.1.The concept of the modelling shell
A range of models is often developed to investigate
broadly similar ecological and environmental phenom-
ena.This inevitably results in a collection of models
that,although each possessing unique characteristics,
also share a number of key similarities.The philosophy
underlying a modelling shell is to take advantage of the
similarities,by extracting these common features and
embedding them centrally within the main code of the
shell,thereby simplifying the description and implemen-
tation of each component model.The common features
may be shared process descriptions,shared data input
and output routines,or algorithms for the presentation
of results.Co-locating many models within the same
software environment brings with it many advantages:
 The separation of shared model code and ancillary
functions from the ‘core’ model specification facil-
itates the rapid development of new models,and
the efficient modification of existing models.It also
aids in making transparent key underlying model
assumptions.
 Housing similar models within the same environ-
ment facilitates model inter-comparison activities by
ensuring consistency in both input data,and in the
presentation of model outputs.Model inter-compar-
isons can further lead to scientific insight,whereby
common processes across different models are more
readily identified,and differences between model
assumptions are highlighted.
 Housing similar models and model components
within the same environment provides opportunities
for combining separate algorithms,and allows the
construction of new analysis options.
A number of modelling shells have been developed
within the broad area of ecological modelling,with
varying aims,methods of implementation,and com-
plexity.They include products designed for the rapid
integration of knowledge for use in natural resource
decision making (Guariso et al.,1996;Reed et al.,1999;
Argent and Grayson,2003),tools for the analysis of
forest patch dynamics (Gignoux et al.,1998),landscape-
scale analysis (Lavorel et al.,2000;Yacoubi et al.,2003;
He et al.,2002),integrated risk assessment (Sydelko
et al.,2001),population viability analysis (Possingham
and Davies,1995) and general tools for ecological
analysis (Soetaert et al.,2002;Hillyer et al.,2003).
360 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
The COmparison and INtegration Shell (COINS)
modelling shell described here was developed initially
for the analysis of models of terrestrial carbon
dynamics.Our goal was to create a software environ-
ment within which new models could be developed and
existing models modified (i.e.model development
activities),in addition to the ability for end users to
take existing models and combine them for analysis and
scenario exploration (i.e.model integration and analysis
activities).A key specification of the project was to
design software capable of incorporating models oper-
ating at a wide range of temporal and spatial scales,
from days to centuries,and from ‘aspatial’ points to
GIS-type simulations of continental or global-scale
dynamics.A major differentiating feature of COINS is
its ability to run multi-model dynamic simulations,and
to have these embedded within a GIS-type framework.
Integrating GIS data within software optimised specif-
ically for dynamic modelling assists in overcoming issues
of inflexibility when one tries to perform such analyses
solely within commercially available GIS applications
(Argent,2004).This and other key features of the
COINS environment are described below,and are
further illustrated through three examples.
2.COINS overview
The COINS software is written with Borland
Delphi
￿
7 and designed with ModelMaker 6,a Unified
Modelling Language (UML) design tool.A flow-chart
of a COINS simulation illustrates the inter-relationships
among the major components (Fig.1a–q).Reference to
these components will be referred to throughout the text
where appropriate.
In developing COINS,features common to many
models were identified and made an integral part of the
software to provide a service to models within the
COINS library.Apart from input/output management
and spatial deployment,these include alternative ways
of deriving and modifying input ‘forcing’ or ‘driver’ data
(Fig.1b).Within COINS,it is possible for a model to
obtain this information from one of three sources;
directly from an existing database (Fig.1c),derived
from existing driver models or functions (Fig.1d),or
supplied directly by the user to the COINS interface
(Fig.1e).For example,precipitation is a key data
requirement for many ecological models.Example
‘precipitation driver’ sources include databases of
historical climate records,databases of long-term
average climate,or as output from a stochastic weather
generator.Other examples include pan evaporation,
which can be estimated from temperature range and
solar radiation (Hargreaves and Samani,1985),and
vapour pressure deficit,which can be estimated from
minimum and maximum temperature (Monteith and
Unsworth,1990).Other simple functions such as day
length (Collares-Pereira and Rabl,1979) and solar
radiation at the top of the atmosphere (Roderick,
1999) are also provided.Such a systemnot only provides
alternatives for deriving input data,but also guarantees
consistency in all input data supplied to models that are
run in parallel.An example of driver inter-changeability,
involving the calculation of net primary productivity
(NPP),is described in the first example.
Individual models are integrated within the COINS
shell to allow maximum flexibility.For example,models
are coded only once,but can then be specified by the
user,through the COINS interface,for use at any spatial
resolution deemed appropriate – from single-site anal-
yses through to spatially distributed maps.Similarly,the
input forcing data required for a given simulation can be
updated by the user without any need for model re-
coding,such as extending an analysis to new spatial
locations or regions,or spatially aggregating or disag-
gregating data to allow analyses at different resolutions.
Simplified class (Fig.2) and sequence (Fig.3)
diagrams illustrate the overall structure of the software,
and the object-oriented basis of its design.Because
models are coded independently of one-another (‘TU-
serModel’,Fig.2),with the only common dependency
among models being the option of shared driver data
functions and modifiers (‘TUserDriver’,‘TUserModi-
fier’,Fig.2),a wide range of different model types can be
incorporated within the COINS shell.This allows the set
of COINS models to be extended beyond the initial
scope of terrestrial carbon accounting.The sequence
diagram is discussed in greater detail in the next section,
and the class diagram is discussed in Section 3.2.
2.1.Spatial and temporal scaling
The basic spatial unit within COINS is the grid-cell.
A model can be run within a single grid-cell,which is
conceptually equivalent to running at a single ‘point’.
Several grid-cells can also be run simultaneously.
Alternatively,models can be embedded within a geo-
referenced map,allowing dynamic GIS simulations.
There are therefore two spatial modes,point and spatial.
The dimensions of the cells are open to the user to
define,therefore making the spatial scale of analysis
fully flexible.
There are also a number of ways in which models can
be spatially represented and combined.The simplest
option comprises a single model,which is associated
with a single set of parameters that is run uniformly
across the whole spatial domain.This is appropriate for
single-cell or ‘point’ applications,but is not generally
applicable across spatially heterogenous areas.More
often,when a model is applied across multiple cells,the
model parameters are themselves spatially varying.
361S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
Analyses simultaneously combining more than one
model provide opportunities for multi-model simula-
tions,where model behaviour can be compared and
contrasted within the same spatial and temporal de-
ployment while being driven by the same climate and
management scenario.The simplest example is where
different models are run at different locations (grid-
cells).An example might be an agricultural model
applied to one region of a landscape,and a forest model
in another.A more sophisticated approach is to allow
(a) Select model(s)
Model 1
Model 2
:
(b) Select source of forcing
data for each model
Model 1
Rainfall
VPD
LAI
Model 2
:
(f) Select reference system
(g) List the number of point locations, and
their latitudes and longitudes
(i) Select the GIS map which defines the
global analysis boundary (0-1 binary mask)
(h) For each point, define the proportional
occupancy of each selected model
(j) For each model, select a GIS map which
defines the models proportional occupancy
for each grid cell (0-100%)
(m) COINS simulation engine
Perform model calculations for this timestep,
as per the order in Figure 2.
Update runtime graphics: scalar values,
matrices, timelines, xy plots, GIS viewer ...
Autosave selected output as required
(k) Define simulation settings:
run duration, start date, etc.
Creation of *.CIS and *.INI files
(l) Apply model parameters.
Set time counter to 0.
Load initialisation (*.INI) file
(q) Post -simulation data
workbench
Increment
timer
(n) Apply
scheduled
events
Select next set
of model
parameters
YES
YES
YES
NO
NO
NO
POINT SPATIAL
Run
Complete?
(p)
Replicate
runs?
Replicate
runs
complete?
(o)
Monte-
Carlo run?
YES
NO
(c) COINS database
(d) COINS function
library
(e) COINS interface
Fig.1.Flow diagram of a COINS simulation.
362 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
up to n user-defined models (or different parameter-
isations of the same model) within a single grid-cell.In
this case the models are assigned to a proportion of the
total area of the grid-cell.This provides opportunities
for addressing within grid-cell heterogeneity,and issues
of spatial scaling.Finally,models with cellular-autom-
ata-like behaviour (for example horizontal transport
models) can be combined with standard process-based
or point models,allowing a range of spatial processes to
be represented within the same simulation.
With respect to temporal dynamics,there are three
scales at which models can be combined;daily,monthly
and yearly.The temporal resolution is implemented via
three nested loops,and models are called only when
appropriate.For example,within the same simulation,
model A could be running at a daily timestep,and
model B monthly.The simulation proceeds at a daily
timestep,but model B is called only at monthly
intervals.
There are a number of options for specifying the
order of events for a given model (Fig.3).Within a given
timestep the ‘driver’ method is called first (labelled
‘TUserDriver’ in Fig.3),which updates the driver data
for the current cell and timestep.If required,modifica-
tion of this data is then carried out (labelled ‘TUser-
Modifier’),followed by execution of the model code
(‘TUserModel’).The main code of the model resides
within the ‘onCellTimeStep’ event handler.Model code
can also be called immediately prior to or following the
main timestep code (labelled ‘openTimeStep’ and
‘closeTimeStep’ in Fig.3).This is useful for updating
or storing information that may change during the main
model calculation.
Although many models operate with discrete time-
steps,which fit within the COINS framework,models
with continuous functions can also be accommodated.
Models can make use of a library function for numerical
integration by supplying a call-back function.The
CASS model (Table 1) provides an example,whereby
the fourth-order adaptive Runge-Kutte algorithm of
Press et al.(1986) is used to integrate the model between
default COINS timesteps.
2.2.Model and function library
A summary of the default COINS library of models
and ancillary driver algorithms is given in Table 1.
Because COINS was developed specifically for terrestrial
carbon cycle modelling,most of the examples relate to
various aspects of the terrestrial carbon cycle,such as
vegetation growth and decay,and soil carbon dynamics.
Although optimised for individual grid-cell by grid-
cell calculations,where the behaviour of a grid-cell
is unaffected by that of the other grid-cells,spatially
interactive processes,such as hydrological flows or
fire-spread,are also compatible within the COINS
Fig.2.Simplified class diagram summarising the COINS software
design,and illustrating the three ways in which COINS may be
extended (TUserModel,TUserDriver,TUserModifier).See text for
further details.
time
update
update
modifier: TUserModifier
COINS: TCoins
driver: TUserDriver
model: TUserModel
[date pre]
openTimeStep
[date]
onCellTimeStep
[date location]
closeTimeStep
[date]
update
[date post]
update
[date pre]
[date post]
Fig.3.Simplified sequence diagramshowing the order of events during
model simulations.Driver data can be updated before (pre) the main
loop or at the end (post).Modifiers (if any) are updated immediately
when the associated driver completes its update.The openTimeStep
event and closeTimeStep event are called on specified dates if there are
cell events to process.The main model code is located within the
onCellTimeStep event.
363S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
architecture.In this context,a spatially interactive
process is one where changes in the state of a grid-cell
through time are determined by the states of adjacent
cells.Three cellular automata models are included to
illustrate this capability (Table 1).
Access to COINS models and functions is made
available to users through the COINS interface.Users
select the algorithm of choice from standard dialog
boxes and lists,and the software then prompts for any
additional user-input for the given selection,such as
specifying the type and location of driver data.
2.3.Databases
The data required by models within the COINS shell
can be provided in two broad formats.For single-cell or
point applications the required data is stored in a flat file
structure generated from a database such as Microsoft
ACCESS
￿
.The key to each record is the latitude,
longitude and date.Apart from the record key and the
site name,any user-defined model-specific fields can be
present in the file.
In spatial mode,data is input as arrays of 32-bit
floating point numbers,using ARCINFO
￿
floating
point number format,with associated *.hdr header files,
in geographic projection.Spatial data may either be
grids of temporally invariant numbers,such as a digital
elevation model or long-termaverage climate data,or be
both spatially explicit and temporally varying,such as
continental maps of historical monthly climate infor-
mation.In Fig.1,the combined spatial and non-spatial
data required by all models within a simulation is
labelled as the ‘COINS database’ (Fig.1c).Data must
be pre-processed and error checked prior to inclusion in
a simulation,although basic error checking,such as the
reporting unexpected non-numeric values,and missing
data values,is carried out by COINS as the data are
imported.
2.4.Visualisation of model outputs
Any combination of output variables can be viewed
as a simulation progresses,depending upon the type of
simulation selected (point vs.spatial),and the param-
eters and variables defined in the component models.
These outputs include scalar quantities,vectors,matri-
ces (e.g.maps) and XY-scatter plots (including plots of
output variables vs.time).There is also a dedicated
map-viewer with additional GIS-type capability.
Tables of observations can also be imported,and as
a simulation progresses these observations can be
graphically compared against the model outputs,allow-
ing ‘visual’ run-time validation of models.No formal
calibration or validation methods are provided,such as
sums of squares calculations for comparing observations
with model outputs,or iterative function minimisation
Table 1
Summary of the models and functions distributed with COINS
Brief description Reference
Carbon accounting models
3PG Forest growth model Landsberg and Waring (1997)
3PG
Spatial
Forest growth model Coops et al.(1998)
3PG
Diffuse
Forest growth model Nightingale and Davies (unpublished data)
CASS 1.2 General carbon cycle model Roxburgh (unpublished data)
PnetII Linked carbon,water and nutrient model Aber et al.(1995)
RothC Soil organic carbon model Coleman and Jenkinson (1999)
CenW Linked carbon,water and nutrient model Kirschbaum (1999)
Image 2.0 (carbon sub-model) Global carbon cycle model Klein Goldewijk et al.(1994)
NPP calculators
RFBN – Roderick et al.(2001)
TMS – Berry and Roderick
(unpublished data)
Miami – Lieth (1975)
Miami-Oz – This manuscript
Cellular automata models
Conway’s game of life – Gardner (1970)
Species invasion – Molofsky (1994)
Intermediate disturbance hypothesis – Roxburgh et al.(2004)
Miscellaneous calculations
Radiation at the top of atmosphere – Roderick (1999)
fPAR Fraction of photosynthetically active radiation
absorbed by a plant canopy
Roderick et al.(2001)
Vapour pressure deficit – Monteith and Unsworth (1990)
Pan evaporation – Hargreaves and Samani (1985)
Day length – Collares-Pereira and Rabl (1979)
364 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
techniques for parameter optimisation (c.f.Soetaert
et al.,2002).
Flexibility in the choice of run-time visualisation
options provides instantaneous feedback on the behav-
iour of almost any aspect of the simulation,and is
a valuable tool for debugging model behaviour.As
a simulation proceeds,a range of options is also
available for automatically logging model results for
post-simulation analyses.These include maps in GIS
format,time-lines of output variables in tabular format,
and XY plots (Fig.1m).
2.5.Monte Carlo analyses
Sensitivity analyses can be conducted via Monte
Carlo simulation (Fig.1o).The overall approach is to
run a simulation multiple times,each time selecting
parameter(s) from pre-defined probability distribution
functions.An interactive dialog box allows the user to
select parameter values from any one of 22 continuous
or 6 discrete probability distribution functions.This
allows sensitivity of model outputs to input parameters
to be readily assessed,and provides estimates of
uncertainty around model results.The Monte Carlo
interface is similar in design and function to the
commercially available @Risk software (Palisade,
2002).
An important consideration in conducting Monte
Carlo analyses when simultaneously varying more than
one parameter is specifying the appropriate correlation
structure.For example,independently drawing para-
meter values may produce meaningless outcomes,such
as high values for a ‘drought’ parameter being
associated with high values of a ‘growth’ parameter.In
COINS,multivariate correlations are specified via
a user-defined correlation matrix,and correlated ran-
dom deviates are drawn from the appropriate distribu-
tions using the method of Iman and Conover (1982).
Replicate model runs can also be conducted (Fig.1p).
This can be used to investigate the behaviour of models
that have embedded with them some stochasticity,for
example a random weather generator,or random seed
dispersal.The distinction between a replicate run of
a model,and a Monte Carlo analysis,is that in
a replicate run no changes are made to the input
parameters,and therefore any between-replicate vari-
ability in model output is due solely to the stochastic
elements of the models included in the simulation.
2.6.Event scheduling
An event scheduler allows complex simulations to be
built,specifying model-specific events such as distur-
bance and fertiliser addition to occur at particular times
during a simulation (Fig.1n).The scheduler also allows
repeated model runs to be performed,for example
performing factorial experiments via the sequential
modification of input parameters.The scheduler has
its own command syntax.Scheduler commands can also
be entered one-line-at-a-time through a command-line
prompt.
2.7.Miscellaneous utility tools
COINS also incorporates a selection of utility tools.
These include a toolbox that allows a number of vector
and layer-based operations to take place.Examples
include filling layers with various sorts of random and
regular patterns,rotation,editing,cropping,and ex-
porting layers in different formats.There is also a post-
analysis data workbench that allows a range of
graphical summaries of model outputs to be generated,
such as pairwise comparison of maps on a cell-by-cell
basis,and visualisation of the sensitivity of model
outputs to variations in model inputs from Monte
Carlo analysis (Fig.1q).Adatabase querying tool is also
provided to interrogate and display the contents of
spatial and non-spatial data.
3.Technical considerations
3.1.Initialising a simulation
A new simulation is set-up via a model configuration
wizard that sequentially prompts the user for all the
information required to define the model or models to
be used in the simulation,including the input data and
driver information required.The wizard automatically
creates the main COINS *.cis run file.This is a script file
that contains all of the information required to load and
run a simulation.Once created,it can be edited off-line
and re-opened for ‘batch-mode’ type operation.The
initialisation or ‘initial conditions’ script files (*.ini) are
kept separate from the model run file,to allow different
initialisation conditions to be specified and saved.In
short,the *.cis file contains the model parameter values,
file locations,and other information required to specify
the simulation.In contrast,the *.ini file contains only
the initial values of the output variables that are to be
loaded at the start of the simulation.The configuration
sequence is shown in Fig.1 as steps a–k.
3.2.Adding new models and driver functions
Adding a new model,driver or modifier function to
the COINS library requires coding the model within the
Borland Delphi environment as Delphi unit(s),using the
standard object-orientated programming techniques of
inheritance and virtual methods (Fig.2).To add
a model,a descendant of ‘TCNModel’ is declared and
model code added to the methods listed in each ancestor
365S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
class.The minimum requirement is to add model code
within the ‘onCellTimeStep’ event handler and to make
the model’s variables available to COINS through
‘registerPrivateData’,and declare any input require-
ments with ‘registerSharedData’ in ‘TCNComponent’.
To add an input driver,a descendant of ‘TCNDriver-
Function’ is made and a function written for the new
class together with an indication of its timestep,if any.
The driver should also list its immediate inputs (other
drivers) so that COINS can decide in what order the
drivers should be executed.All components have access
to the spatial domain through the ‘Location’ method,
and models have access to their sub-domain through the
‘subMask’ attribute.Example files and templates are
provided to assist with the creation of new modifier
functions,drivers and models.
One advantage of the design is that the addition of
a new function or model to COINS does not require any
knowledge of,or exposure to,existing COINS code.The
only constraint is the requirement to make the declara-
tions described above,which allow the new code to
interact with the rest of the shell.Once this is done,the
modeller is free to structure the new model in any way
that is deemed appropriate,e.g.with the code separated
across a set of separate units,or all of the code combined
within a single file.The entire COINS project is then
recompiled,with the newly developed model embedded
within a new COINS executable file.The main COINS
code is distributed as compiled object files.
4.Example 1:point and spatial model implementation
4.1.Simulation characteristics and
demonstrated features
Three examples are used to illustrate key aspects of
the COINS functionality.This first example demon-
strates the ability to apply the same model at both
a single point and as a landscape-scale simulation,and
also provides an example of the substitution of driver
data.The grid-cell resolution of the landscape simula-
tion is 25 m!25 m (or approximately 0.9 arc s),with
a total area of approximately 150 km
2
.The temporal
resolution is monthly.
4.2.Analysis background
The example is based on an analysis developed to
determine the carbonsequestrationpotential of aforested
landscape,located within the Kioloa region of south-
eastern coastal Australia (Roxburgh et al.,unpublished
data).Data from mature forests were used to calibrate
a simplified model of terrestrial carbon dynamics
(Fig.4).The model (‘CASS’) represents the pools of
carbon within,and the fluxes between,the main stores
of carbon in terrestrial ecosystems.These pools include
the living vegetation,the dead vegetation (litter),and the
soil.Loss of carbon from each pool is determined by
simple first-order rate constants,specified by the
residency times of carbon in the various pools.
4.3.COINS implementation
The main driver of the CASS model is net primary
productivity (NPP),which is the net amount of carbon
that is fixed by the vegetation,over a given period of
time.Because the CASS model was coded with NPP as
a COINS driver object,the user has a choice of methods
for supplying this input.In the simplest case NPP can be
treated as a constant,with the model applied to a single
grid-cell or ‘point’ (Fig.4a).
In order to more intensively investigate growth and
sequestration potential across the study landscape,the
constant NPP was replaced with a driver function that
Constant
Rad. top atmos.
Rad. top canopy
fPAR
TWI
NPP model
Stem
Litter
NPP
Leaf
Stem
Root
Leaf
Litter
Root
Litter
Soil
‘Fast’
Soil
‘Slow’
CASS carbon pool
model
Data layer
Constant
(a) ‘point’ application
(b) ‘spatial’ application
Top of atmosphere
radiation function
Day of year
Latitude
Current
date
Data layers
{Jan…Dec}
Current
location
Fig.4.Outline of the model used in the first example,showing the inter-changeability of model drivers.In (a) NPP is provided to the model as
a constant.In (b) it is provided as the output from a temporally and spatially varying NPP driver function.See text for further details.
366 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
provides spatio-temporally varying estimates of forest
growth,at a 25 m pixel resolution,using a modification
of the method of Roderick et al.(2001) (Fig.4b).The
NPP calculation is a function of spatially and tempo-
rally varying data (solar radiation at the top of the
canopy,solar radiation at the top of the atmosphere,
and additionally,a soil water modifier based on
a topographic wetness index (TWI)).
Note that in shifting from an aspatial model (Fig.4a)
to the spatial representation (Fig.4b) requires changing
the NPP driver source that is assigned to the CASS
model,and in the definition of the required underlying
data.These changes are all implemented by the user
within the COINS interface,and require no additional
programming to the CASS model,or the main COINS
code.The spatial output of the model is shown in Fig.5,
which also shows the number of the output visualisation
options.
5.Example 2:Monte Carlo analysis of Australian
continental net primary productivity
5.1.Simulation characteristics
and demonstrated features
This example demonstrates the Monte Carlo capa-
bility of COINS,where statistical uncertainty in model
parameters can be propagated through a simulation to
provide estimates of uncertainty around the model
predictions.The analysis is continental in scale,with
a grid-cell resolution of 0.05

!0.05

,and has an
annual timestep.
5.2.Analysis background
Net primary productivity (NPP) is a key ecological
process that reflects the myriad environmental
Fig.5.Screen image of the CASS model driven by spatially and monthly varying net primary productivity (NPP).(a) Three of the input data layers;
topographic wetness index (TWI),radiation at the top of the plant canopy (RTCM),and radiation at the top of the atmosphere (RTAM).(b) The
monthly trend in NPP for one of the grid-cells within the landscape,corresponding to a single field-plot location.(c) Spatially varying total annual
NPP for the Kioloa landscape (gC m
2
year
1
),displayed within the COINS map-viewer window.
367S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
constraints that determine vegetation growth in ecolog-
ical systems.One of the earliest approaches to modelling
NPP was the Miami model developed by Lieth (1975),
and involved the construction of empirical relationships
between mean annual temperature and precipitation
collected across a range of biomes,and then spatially
extrapolating those relationships using climate data.An
early application of the Miami model for the Australian
continent was conducted by Pittock and Nix (1986).A
similar analysis,based on data collected solely from
Australian ecosystems,was conducted by Graetz (1998).
Since those analyses,Barrett (2001) has compiled
a comprehensive database of fine-tissue NPP estimates
representative of mature vegetation for the Australian
continent,based predominantly on measurements of
litterfall.Because these are estimates from mature
vegetation,where rates of fine-tissue litterfall are
assumed to approximately equal to rates of fine-tissue
production,these data can be expanded to predictions
of total ecosystem NPP using the following relationship
(Graetz,1998;Barrett,2003).
NPP
t
ZNPP
f
=a
f
ð1Þ
where NPP
t
is the total productivity of the ecosystem,a
f
is the proportion of that productivity that is allocated to
plant fine-tissue components (e.g.leaves and fine twigs),
and NPP
f
is the fine-tissue component of that pro-
ductivity,i.e.the measured quantity.
The relationship between fine-tissue NPP and average
annual precipitation for a subset of the Barrett (2001)
database is shown in Fig.6a.This subset includes 148 of
the original 183 fine-tissue NPP measurements in the
database.The 35 measurements excluded from the
analysis include 28 that were based on potentially non-
comparable methods (biomass harvest rather than
litterfall),and 7 estimates measured during climatically
‘atypical’ periods,i.e.periods within which the annual
Fig.6.Components of the Miami-Oz Monte Carlo analysis.(a) Relationship between the VAST empirical above-ground fine-tissue NPP
measurements (Barrett,2001) and mean annual precipitation measured over the period each study was conducted.The curve represents the best-fit
Gompertz growth function fitted to the data.The shaded area shows the spread of best-fit Gompertz growth curves fitted to 5000 bootstrapped
re-samples of the original data.(b) Frequency distributions for each of the three fitted parameters in the Gompertz growth equation fitted to the 5000
bootstrapped re-samples of the data in (a),and the rank-correlation coefficients among those parameters.The bars showthe frequency distribution of
each best-fit parameter,and the line shows the continuous distribution which most closely approximates that distribution.In two cases the
distribution was Extreme-value (parameter K and r),and in one case Logistic (parameter C).
368 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
temperature or rainfall exceeded two standard devia-
tions of the long-term mean for that site.The fitted
function represents the best-fit three-parameter Gom-
pertz growth curve,forced through the origin (Gom-
pertz,1825).
NPP
f
ZKe
e
ðCr!PrecipÞ
Ke
e
ðCÞ
ð2Þ
where K,C and r are fitted parameters,and Precip is
mean annual precipitation.The shaded area in Fig.6a
shows the range of ‘best-fit’ Gompertz growth curves
derived from a bootstrapped re-sampling of the original
data (Manly,1991).For each of 5000 iterations,143 new
data points were selected at random,with replacement,
from the original 143 estimates,and the Gompertz
model was re-fitted by the method of least squares
minimisation,using the downhill simplex method (Press
et al.,1986).The best-fit distributions of the 5000
estimates for each parameter (corresponding to a family
of curves constrained within the shaded area of Fig.6a),
and the correlations among those parameters,are shown
in Fig.6b.This re-sampling procedure is one way of
quantifying the scatter in the relationship,and provides
the necessary information to conduct a formal Monte
Carlo uncertainty analysis within COINS.Note that this
statistical curve fitting was performed outside of the
COINS environment.
5.3.COINS implementation
In order to estimate Australian continental total NPP
(NPP
t
),Eqs.(1) and (2) were combined to yield:
NPP
t
Z
￿
Ke
e
ðCr!PrecipÞ
Ke
e
ðCÞ
￿
=a
f
ð3Þ
For each of 5000 iterations,parameters K,C and r
were drawn at random from their appropriate distribu-
tions (Fig.6b) under the constraints of the correlation
structure among the parameters (Fig.6b).The allocation
parameter a
f
(Eq.(1)) was estimated by Graetz (1998) to
be 0.34,and by Barrett (2001) to be in the range 0.58–
0.78.For the calculation here,a
f
was also included as
part of the Monte Carlo analysis,and was allowed to
vary at random and uniformly within the range 0.3–0.8.
For each of 5000 iterations a continental map of NPP
was calculated through combining Eq.(3) with an input
map of long-term average annual continental precipita-
tion,at a grid-cell resolution of 0.05

.The Monte
Carlo analysis yielded a mean continental NPP of
1.17 Gt Cyear
1
,with 95% of the values falling within
the range 0.60–2.02 Gt Cyear
1
(Fig.7).
6.Example 3:spatial scaling and multi-model
comparisons
6.1.Simulation characteristics and
demonstrated features
The final example illustrates how more than one
model can be combined within the same simulation,and
the ability to specify within grid-cell heterogeneity.The
analysis is global in scale,with a grid-cell resolution of
0.5

!0.5

,and has an annual timestep.
6.2.Analysis background
A particular challenge in environmental modelling is
encapsulating spatial and temporal variability.For
example,landscapes typically comprise mosaics of
different elements,such as forests,grasslands and
intensive agriculture.Whilst many individual forest,
grassland and agricultural models exist,performing
analyses in an integrated and holistic way across such
heterogenous areas poses particular challenges.One
solution is to combine,within the same simulation,
different models representative of the different compo-
nents of the system.
A second solution is to develop models that are
general enough such that the underlying heterogeneity
can be reflected through differences in the underlying
model calibration,such as changing vegetation growth
and decomposition parameters to reflect differences
between ‘forest’ and ‘grassland’ biomes in global
vegetation models (see e.g.Klein Goldewijk et al.,
1994;Foley,1995).This could be described as a ‘one-
size-fits-all’ approach,where the same model is used to
simulate the different landscape elements,and is the
approach used in this example.
A second challenge in quantifying natural variability
is deciding upon the appropriate spatial and temporal
scales on which to operate.For analyses based on
a representation of ‘space’ as a discretised raster of grid-
cells there is always the problem that no matter what
size the grid-cell,there will always be naturally occurring
within grid-cell variability that remains unaccounted
for.This could potentially lead to bias in the model
outcomes (Ruel and Ayres,1999;Medlyn et al.,2003).
One solution is to utilise the finest spatial (or temporal)
scales possible,in the hope that in so doing any resulting
biases will be minimised.Another solution is to
reformulate the problem (and therefore the model) in
such a way that parameters are quantified by probability
distribution functions and inter-parameter covariances,
that together statistically account for the underlying
variability (Welsh et al.,1988;Ruel and Ayres,1999;
Raupach et al.,2003).A third approach,and the one
considered below,is to allow sub-grid variability.
369S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
6.3.COINS Implementation
The example uses the terrestrial carbon component of
the Image 2.0 model (Klein Goldewijk et al.,1994) to
simulate global stocks and fluxes of carbon.The analysis
involves subdividing the earth’s ecosystems into 17
biomes,reclassified from the widely used Olson et al.
(1983) database (Leemans and van den Born,1994).The
version of the Olson classification used in this imple-
mentation of the model was the Global Land Cover
Characteristics Database (Loveland et al.,2000) that
identifies 96 Olson vegetation categories,derived from
AVHRR satellite imagery collected over the period
April 1992–March 1993.The geographic projection of
this database is provided at a resolution of 30 arc s,or
approximately 1 km!1 km,and comprises a gridded
layer,43,200 rows by 21,600 columns.Although this
dataset provides an extremely detailed classification of
the earth’s ecological systems (Fig.8a),in a simulation
environment there are logistical problems in handling
and storing all of the required model input and output
data at this resolution.One solution is to re-sample the
land cover dataset to a lower resolution,for example by
aggregating grid-cells by modal re-sampling (Fig.8b).
This has the disadvantage of decreasing the information
content of the original layer,and can lead to bias where
the less abundant land-cover types are potentiallylost due
to the re-sampling procedure (compare Fig.8a and b).
COINS offers the alternative of allowing different
biomes to have a proportional representation within
aggregated grid-cells (Fig.8c).This makes the data both
more manageable,and also more compatible with other
available global data (e.g.climate and soils databases
which are typically provided at a resolution of
Fig.7.Results of the Miami-Oz Monte Carlo analysis of total Australian continental NPP.The map shows the average NPP over 5000 Monte Carlo
runs,from selecting Gompertz model parameter values from the probability distributions in Fig.6b.The units are gC m
2
year
1
.The frequency
histogramshows the distribution of total continental NPP over all 5000 runs,and is displayed within the COINS post-analysis data workbench.The
distribution has a mean of 1.17 Gt C year
1
,with 95%of the values falling within the range 0.60–2.02 Gt C year
1
.
370 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
0.5

!0.5

grid-cells).Importantly,it avoids re-sam-
pling bias by retaining the original information on the
within grid-cell variability.
To implement the analysis within COINS,each
biome is associated with a new instance of the Image
2.0 model,each of which has a mask which defines that
biomes extent,and the proportion of each 0.5!0.5

grid-cell occupied by that biome (Fig.9a).Each biome is
then associated with a table of parameters that define
the rates of biomass production and decay (Table 1 of
Klein Goldewijk et al.,1994).In effect,17 versions of the
Image 2.0 model are run simultaneously,one for each
biome,and the final aggregated result for each grid-cell
is calculated as the sumover all biomes,weighted by the
within-cell percentage cover of each biome.
The model predicts long-term average carbon stocks
of 523 Gt C for the globe,corresponding to a global
average phytomass of 4.6 kg Cm
2
(Fig.9b).Although
these values are consistent with those previously reported
(e.g.Saugier et al.,2001),care should be taken in their
interpretation,as the implementation of the Image 2.0
model used in this example would not have activated
many of the growth feedback processes included in that
model.Rather,it was a minimal implementation
designed primarily to illustrate the spatial scaling and
multi-model capabilities of the COINS shell.
7.Limitations
As with any computer software,COINS has both
advantages and limitations.One of the major limitations
is the requirement for developers to code new models
and functions within the Borland Delphi programming
environment,which is potentially a constraint for
modellers not familiar with this product,and may limit
the extent to which the shell can be extended to include
models outside of the scope of terrestrial carbon
accounting.Note that Delphi does have the capacity
to interact more widely with code written in other
programming languages,such as.NET and COM
support,and is also able to be compiled to run under
the Linux operating system.
A second limitation is the temporal scaling options,
where each model is locked into either running at
a daily,monthly or yearly timestep.Finally,although
spatial interactions such as dispersal,fire-spread and
hydrological flows can be readily incorporated into
a COINS model,the COINS shell does not offer any
specific services for optimising or simplifying the task of
writing models with spatial interactions,and therefore
such coding remains the modellers responsibility.
Depending on the complexity of the problem,other
modelling environments might be more appropriate for
the development of spatially contagious processes,for
example LANDIS (He et al.,2002),LAMOS (Lavorel
et al.,2000),or LUCAS (Yacoubi et al.,2003).
8.Conclusions
The COINS modelling shell is a flexible software
environment for building,analysing and comparing
a wide range of models within the general area of
Fig.8.Illustration of within grid-cell variability in COINS.(a) The original land cover classification for a 2

!2

area of coastal Brazil,with a pixel
size of 0.03

(or approximately 1 km!1 km).(b) The result of re-sampling the original layer to a 0.5!0.5

resolution,showing the loss of
information incurred.(c) The COINS representation,whereby information on the percentage cover of each land cover type within 0.5!0.5

grid-cells is retained.
371S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
ecology and natural resource management.One of the
main advantages of integrating models within a common
environment is the gains in efficiency in model de-
velopment and modification,due primarily to the
removal of programming overheads involved with
linking the model code with associated data,and in
the graphical display of run-time and post-simulation
results.There are significant advantages for model users
as well,such as a greater choice of model options,and
the ability to alter and replace external driving data,
including changing the spatial domain and resolution
without the need to update model code.In COINS the
process of setting up a simulation is further streamlined
through the inclusion of a ‘wizard’ that sequentially
prompts the user for all of the information required to
configure a new simulation,including the choice of
model (or models) to be use in the simulation,the source
of the model drivers,the data requirements (either
spatial- or site-based) and their location.In this way,
users can rapidly build simulations from the existing
components within the shell.Other major innovations in
the COINS environment include full flexibility in the
spatial scale of analysis,the ability to combine and
compare more than one model within the same
simulation,the ability to define within grid-cell variabil-
ity,and a comprehensive Monte Carlo utility for
conducting sensitivity analyses.
Exploring and solving environmental problems is
typically a complex and expensive process involving
data collection,observation and experimentation.Sim-
ulation modelling provides one tool for integrating and
summarising this information into a single framework,
which can then be used to summarise existing knowl-
edge,and to explore various scenario options in
a temporally and spatially explicit format.Modelling
shells,such as the COINS environment,provide
a further tool for simulation model analysis and
scenario development,and provide significant potential
Fig.9.Image 2.0 analysis of global carbon stocks.(a) Example masks (0–1 fractional cover) for two land cover types (or biomes) – agricultural land
and tundra.(b) Modelled carbon stocks in living vegetation for the globe,in units gC m
2
year
1
.
372 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
for bringing together,with minimal effort,novel analysis
options and approaches that would otherwise not be
possible.
Acknowledgements
We gratefully acknowledge our many colleagues who
have either knowingly or unknowingly contributed to
the completion of this project.We especially thank
Guillaume Simioni for the translation of the CenW
model,and to Miko Kirschbaum for his contributions
during the early developmental stages of COINS.We
also thank Michael Hill,Brendan Mackey and two
anonymous reviewers who kindly commented on an
early draft of the manuscript.
References
Aber,J.D.,Ollinger,S.V.,Federer,C.A.,Reich,P.B.,Goulden,M.L.,
Kicklighter,D.W.,Melillo,J.M.,Lathrop,R.G.,1995.Predicting
the effects of climate change on water yield and forest production in
the Northeastern United States.Climate Research 5,207–222.
Argent,R.M.,2004.An overview of model integration for environ-
mental applications – components,frameworks and semantics.
Environmental Modelling and Software 19,219–234.
Argent,R.M.,Grayson,R.B.,2003.A modelling shell for participa-
tory assessment and management of natural resources.Environ-
mental Modelling and Software 18,541–551.
Barrett,D.J.,2001.NPP Multi-Biome:VAST calibration data,1965–
1998.Available on-line!http://www.daac.ornl.gov/O from Oak
Ridge National Laboratory Distributed Active Archive Center,
Oak Ridge,Tennessee,USA.
Barrett,D.J.,2003.Steady state turnover time of carbon in the
Australian terrestrial biosphere.Global Biogeochemical Cycles 16,
1108.
Coleman,K.,Jenkinson,D.S.,1999.Roth-C 26.3.A Model for the
Turnover of Carbon in Soil.IACR-Rothampsted,Rothampsted.
Collares-Pereira,M.,Rabl,A.,1979.The average distribution of solar
radiation – correlations between diffuse and hemispherical and
between daily and hourly insolation values.Solar 22,155–164.
Coops,N.C.,Waring,R.H.,Landsberg,J.J.,1998.Assessing forest
productivity in Australia and New Zealand using a physiologically-
based model driven with averaged monthly weather data and
satellite-derived estimates of canopy photosynthetic capacity.
Forest Ecology and Management 104,113–127.
Fall,A.,Fall,J.,2001.A domain-specific language for models of
landscape dynamics.Ecological Modelling 141,1–18.
Foley,J.A.,1995.An equilibrium model of the terrestrial carbon
budget.Tellus 47B,310–319.
Gardner,M.,1970.The fantastic combinations of John Conway’s new
solitaire game ‘‘life’’.Scientific American 223,120–123.
Gignoux,J.,Menaut,J.-C.,Noble,I.,Davies,I.D.,1998.A spatial
model of savanna function and dynamics:model description and
preliminary results.In:Newbery,D.M.,Prins,H.H.T.,Brown,N.
(Eds.),Dynamics of Tropical Communities.37th Symposium of
the British Ecological Society.Blackwell,Oxford.
Gompertz,B.,1825.On the nature of the function expressive of the
law of human mortality,and a new mode of determining the law of
live contingencies.Philosophical Transactions of the Royal Society
182,513–585.
Graetz,D.,1998.The terrestrial carbon pools of the Australian
continent:an assessment of their size,dynamics and tractability.
Reporting a project undertaken for the National greenhouse gas
inventory.Environment Australia,Department of the Environ-
ment and Territories,Canberra.
Guariso,G.,Hitz,M.,Werthner,H.,1996.An integrated simulation
and optimization modelling environment for decision support.
Decision Support Systems 16,103–117.
Hargreaves,G.H.,Samani,Z.A.,1985.Reference crop evapotranspi-
ration from temperature.Journal of Applied Engineering in
Agriculture 1,96–99.
He,H.S.,Larsen,D.R.,Mladenoff,D.J.,2002.Exploring component-
based approaches in forest landscape modelling.Environmental
Modelling and Software 17,519–529.
Hillyer,C.,Bolte,J.,van Evert,F.,Lamaker,A.,2003.The ModCom
modular simulation system.European Journal of Agronomy 18,
333–343.
Iman,R.L.,Conover,W.J.,1982.A distribution-free approach to
inducing rank correlation among input variables.Communications
in Statistics:Simulation and Computation 11,311–334.
Kirschbaum,M.U.F.,1999.CenW,a forest growth model with linked
carbon,energy,nutrient and water cycles.Ecological Modelling
118,17–59.
Klein Goldewijk,K.,van Minnen,J.G.,Kreileman,G.J.,
Vloedbeld,M.,Leemans,R.,1994.Simulation of the carbon flux
between the terrestrial environment and the atmosphere.Water,
Air and Soil Pollution 76,199–230.
Lam,D.,Leon,L.,Hamiltion,S.,Crookshank,N.,Bonin,D.,Swayne,D.,
2004.Multi-model integrationinadecisionsupport system:atechnical
user interfaceapproachfor watershedandlakemanagement scenarios.
Environmental Modelling and Software 19,317–324.
Landsberg,J.J.,Waring,R.H.,1997.A generalised model of forest
productivity using simplified concepts of radiation-use efficiency,
carbon balance and partitioning.Forest Ecology and Management
95,209–228.
Lavorel,S.,Davies,I.D.,Noble,I.R.,2000.LAMOS:a LAndscape
MOdelling Shell.In:Hawkes,B.C.,Flannigan,M.D.(Eds.),
Landscape Fire Modeling-Challenges and Opportunities.Northern
Forestry Centre Information Report NOR-X-371.Natural
Resources Canada,Canadian Forest Service,pp.25–28.
Leemans,R.,van den Born,G.J.,1994.Determining the potential
distribution of vegetation,crops and agricultural productivity.
Water,Air and Soil Pollution 76,133–161.
Lieth,H.,1975.Modeling the primary productivity of the world.In:
Lieth,h.,Whittaker,R.H.(Eds.),Primary Productivity of the
Biosphere.Springer-Verlag,New York,pp.237–263.
Loveland,T.R.,Reed,B.C.,Brown,J.F.,Ohlen,D.O.,Zhu,J.,Yang,L.,
Merchant,J.W.,2000.Development of a global land cover
characteristics database and IGBP DISCover from 1-km AVHRR
data.International Journal of Remote Sensing 21,1303–1330.
Manly,B.F.J.,1991.Randomization and Monte Carlo Methods in
Biology.Chapman and Hall,London.
Maxwell,T.,1999.A parsi-model approach to modular simulation.
Environmental Modelling and Software 14,511–517.
Medlyn,B.,Barrett,D.,Landsberg,J.,Sands,P.,Clement,R.,2003.
Conversion of canopy intercepted radiation to photosynthate:
review of modelling approaches for regional scales.Functional
Plant Biology 30,1–17.
Molofsky,J.,1994.Population dynamics and pattern formation in
theoretical populations.Ecology 75,30–39.
Monteith,J.L.,Unsworth,M.H.,1990.Principles of Environmental
Physics.Arnold,London.
Muetzelfeldt,R.,Massheder,J.,2003.The Simile visual modelling
environment.European Journal of Agronomy 18,345–358.
Olson,J.S.,Watts,J.A.,Allison,L.J.,1983.Carbon in live vegetation
of major world ecosystems.Report ORNL-5862.Oak Ridge,Oak
Ridge National Laboratory.
373S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374
Palisade,2002.@Risk.Palisade Corporation,Newfield.
Pittock,A.B.,Nix,H.A.,1986.The effect of changing climate on
Australian biomass production – a preliminary study.Climatic
Change 8,243–255.
Possingham,H.P.,Davies,I.,1995.Alex – a model for the viability
analysis of spatially structured populations.Biological Conserva-
tion 73,143–150.
Press,W.H.,Flannery,B.P.,Teukolsky,S.A.,Vetterling,W.T.,1986.
Numerical Recipes,The Art of Scientific Computing.Cambridge
University Press,Cambridge.
Raupach,M.R.,Barrett,D.J.,Briggs,P.R.,Kirby,M.J.,2003.
Terrestrial biosphere models and forest–atmosphere interactions.
In:Vertessy,R.,Elsenbeer,H.(Eds.),Forests and Water.IUFRO,
Vienna.
Reed,M.,Cuddy,S.,Rizzoli,A.E.,1999.A framework for modelling
multiple resource management issues – an open modelling
approach.Environmental Modelling and Software 14,503–509.
Rizzoli,A.E.,Davis,J.R.,1999.Integration and re-use of environmen-
tal models.Environmental Modelling and Software 14,493–494.
Rizzoli,A.E.,Davis,J.R.,Abel,D.J.,1998.Model and data
integration and re-use in environmental decision support systems.
Decision Support Systems 24,127–144.
Roderick,M.L.,1999.Estimating the diffuse component from daily
and monthly measurements of global radiation.Agricultural and
Forest Meteorology 95,169–185.
Roderick,M.L.,Farquhar,G.D.,Berry,S.L.,Noble,I.R.,2001.On
the direct effect of clouds and atmospheric particles on the
productivity and structure of vegetation.Oecologia 129,21–30.
Roxburgh,S.H.,Shea,K.,Wilson,J.B.,2004.The intermediate
disturbance hypothesis:patch dynamics and mechanisms of species
coexistence.Ecology 85,359–371.
Ruel,J.J.,Ayres,M.P.,1999.Jensen’s inequality predicts effects
of environmental variation.Trends in Ecology and Evolution 14,
361–366.
Saugier,B.,Roy,J.,Mooney,H.A.,2001.Estimations of global
terrestrial productivity:converging toward as single number?In:
Roy,J.,Saugier,B.,Mooney,H.A.(Eds.),Terrestrial Global
Productivity.Academic Press,San Diego,pp.543–557.
Soetaert,K.,deClippele,V.,Herman,P.,2002.FEMME,a flexible
environment for mathematically modelling the environment.
Ecological Modelling 151,177–193.
Sydelko,P.J.,Hlohowskyj,I.,Majerus,K.,Christiansen,J.,Dolph,J.,
2001.An object-oriented framework for dynamic ecosystem
modeling:application for integrated risk assessment.Science of
the Total Environment 274,271–281.
Villa,F.,2001.Integrating modelling architecture:a declarative
framework for multi-paradigm,multi-scale ecological modelling.
Ecological Modelling 137,23–42.
Villa,F.,Costanza,R.,2000.Design of multi-paradigm integrating
modelling tools for ecological research.Environmental Modelling
and Software 15,169–177.
Welsh,A.H.,Townsend Peterson,A.,Altmann,S.A.,1988.The fallacy
of averages.The American Naturalist 132,277–288.
Yacoubi,S.E.,Jai,A.E.,Jacewicz,P.,Pausas,J.G.,2003.LUCAS:an
original tool for landscape modelling.Environmental Modelling
and Software 18,429–437.
374 S.H.Roxburgh,I.D.Davies/Environmental Modelling & Software 21 (2006) 359–374