GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus GmbHGöttingen, Germany10.5194/gmd-8-939-2015A simple object-oriented and open-source model for scientific and
policy analyses of the global climate system – Hector v1.0HartinC. A.corinne.hartin@pnnl.govPatelP.SchwarberA.LinkR. P.https://orcid.org/0000-0002-7071-248XBond-LambertyB. P.https://orcid.org/0000-0001-9525-4633Pacific Northwest National Laboratory, Joint Global Change Research
Institute at the University of Maryland – College Park, 5825 University
Research Court, College Park, MD 20740, USAUniversity of Maryland, College Park, MD 20742, USAC. A. Hartin (corinne.hartin@pnnl.gov)1April20158493995514August201424October201426February20156March2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.geosci-model-dev.net/8/939/2015/gmd-8-939-2015.htmlThe full text article is available as a PDF file from https://www.geosci-model-dev.net/8/939/2015/gmd-8-939-2015.pdf
Simple climate models play an integral role in the policy and scientific
communities. They are used for climate mitigation scenarios within integrated
assessment models, complex climate model emulation, and uncertainty analyses.
Here we describe Hector v1.0, an open source, object-oriented, simple global
climate carbon-cycle model. This model runs essentially instantaneously while
still representing the most critical global-scale earth system processes.
Hector has a three-part main carbon cycle: a one-pool atmosphere, land, and
ocean. The model's terrestrial carbon cycle includes primary production and
respiration fluxes, accommodating arbitrary geographic divisions into, e.g.,
ecological biomes or political units. Hector actively solves the inorganic
carbon system in the surface ocean, directly calculating air–sea fluxes of
carbon and ocean pH. Hector reproduces the global historical trends of
atmospheric [CO2], radiative forcing, and surface temperatures. The
model simulates all four Representative Concentration Pathways (RCPs) with
equivalent rates of change of key variables over time compared to current
observations, MAGICC (a well-known simple climate model), and models from the
5th Coupled Model Intercomparison Project. Hector's flexibility, open-source
nature, and modular design will facilitate a broad range of research in
various areas.
Introduction
Projecting future impacts of anthropogenic perturbations on the climate
system relies on understanding the interactions of key earth system
processes. To accomplish this, a hierarchy of climate models with differing
levels of complexity and resolution are used, ranging from purely
statistical or empirical models, to simple energy balance models, and
fully coupled earth system models (ESMs) (Stocker, 2011).
Reduced-complexity or simple climate models (SCMs) lie in the middle of this
spectrum, representing only the most critical global-scale earth system
processes with low spatial and temporal resolution, e.g., carbon fluxes
between the ocean and atmosphere, primary production and respiration fluxes
on land. These models are relatively easy to use and understand and are
computationally inexpensive. Most SCMs have a few key features: (1)
calculating future concentrations of greenhouse gases (GHGs) from given
emissions while modeling the global carbon cycle, (2) calculating global mean
radiative forcing from greenhouse gas concentrations, and (3) converting the
radiative forcing to global mean temperature (e.g., Wigley, 1991; Meinshausen
et al., 2011a; Tanaka et al., 2007; Lenton, 2000).
With these capabilities, SCMs play an integral role in decision-making and
scientific research. For example, energy–economic–climate models or
integrated assessment models (IAMs) are used to address issues on energy
system planning, climate mitigation, stabilization pathways, and land-use
changes (Wigley et al., 1996; Edmonds and Smith, 2006; van Vuuren et al.,
2011). ESMs are too computationally expensive to use in these analyses.
Therefore, all IAMs rely on a simple representation of the global climate
system.
Depending on the purpose of the IAMs (economics, cost-benefit analysis, or
more physically based processes), the corresponding climate and carbon
component varies in complexity and resolution. For example, models like
DICE, FUND, and MERGE have a highly simplified carbon/climate system
(Nordhaus, 2008; Anthoff and Tol, 2014; Manne and Richels, 2005). IAMs
focusing more on the physical processes of the natural system and the
economy employ more complex representations of the climate/carbon system.
Models like GCAM (Global Change Assessment Model) and MESSAGE use MAGICC as
their SCM (Meinshausen et al., 2011a; Riahi et al., 2007; Calvin et al.,
2011). Increasing in complexity, some IAMs include the climate/carbon system
at gridded scales (e.g., IMAGE), and can be coupled to earth system models
of intermediate complexity (e.g., MIT IGSM) or, more recently, coupled to a
full earth system model (the iESM project) (Bouwman et al., 2006; Sokolov
et al., 2005; Bond-Lamberty et al., 2014; Di Vittorio et al., 2014; Collins
et al., 2015).
SCMs such as MAGICC, GENIE, and the climate emulation tool at RDCEP (Center for Robust Decision Making on Climate and Energy Policy) are also
used as emulators of more complex ESMs (Meinshausen et al., 2011c;
Schlesinger and Jiang, 1990; Challenor, 2012; Ratto et al., 2012; Lenton et
al., 2009; Castruccio et al., 2014). The behavior of SCMs can be constrained
to replicate the overall behavior of the more complex ESM. For instance, the
climate sensitivity of a SCM can be made equal to that of an ESM by altering
a single model parameter. In particular, the MAGICC model has been central
to the analyses presented in the Intergovernmental Panel on Climate Change
(IPCC) reports, and can be parameterized to emulate a large suite of ESMs
(Meinshausen et al., 2011a).
Lastly, SCMs are computationally efficient and inexpensive to run.
Therefore, they are used to run multiple simulations of future climate
change emissions scenarios, parameter sensitivity experiments, perturbed
physics experiments, large ensemble runs, and uncertainty analyses
(Senior and Mitchell, 2000; Hoffert et al., 1980; Harvey and Schneider,
1985; Ricciuto et al., 2008; Sriver et al., 2012; Irvine et al., 2012).
MAGICC, the Bern CC model, and SNEASY are examples of a few models used for
uncertainly analysis (Meinshausen et al., 2011c; Urban and Keller, 2010;
Joos et al., 2001b). SCMs have been useful in reducing uncertainties in
future CO2 sinks, quantifying parametric uncertainties in sea-level
rise, ice-sheet modeling, ocean-heat uptake, and aerosol forcing
(Ricciuto et al., 2008; Sriver et al., 2012; Applegate et al., 2012;
Urban and Keller, 2009).
This study introduces Hector v1.0, an open-source, object-oriented, simple
climate carbon-cycle model. Hector was developed with three main goals in
mind. First, Hector is an open-source model, an important quality given that
the scientific community, funding agencies, and journals are increasingly
emphasizing transparency and open source (White et al., 2013; Heron et al., 2013), particularly in climate change sciences
(Wolkovich et al., 2012). A large community of scientists
can access, use, and enhance open-source models, with the potential for
long-term utilization, improvement, and reproducibility (Ince et
al., 2012). Second, a clean design using an object-oriented framework is
critical for Hector development and future use. This allows for new
components to easily be added to Hector, i.e., the model's functionality to
be easily extended in the future. In addition, this framework allows for
easy coupling into IAMs, in particular GCAM. Lastly, Hector is a stand-alone
simple climate model used to answer fundamental scientific research
questions, uncertainty analysis, parameter sensitivities, etc.
One of the fundamental questions faced in developing a SCM is how much
detail should be represented in the climate system. Our goal is to introduce
complexity only where warranted, keeping the representations of the climate
system as simple as possible. This results in fewer calculations, faster
execution times, and easier analysis and interpretation of results. Sections 2, 3, and 4 describe the structure and components of Hector. Sections 5 and
6 describe the experiments, results and comparison of Hector against
observational data and other models (MAGICC and CMIP5).
Model architectureOverall structure and design
Hector is written in C++ and uses an object-oriented design that
enforces clean separation between its different parts, which interact via
strictly defined interfaces. The separation keeps each software module
self-contained, which makes the code easy for users to understand, maintain,
and enhance. Entities in the model include a command-line wrapper, the model
coupler, various components organized around scientific areas (carbon cycling, radiative
forcing, etc.) and visitors responsible for model output. Each of these is discussed
below.
Model coupler
Hector's control flow starts with the coupler, which is responsible for (1)
parsing and routing input data to the model components; (2) tracking how the
components depend on each other; (3) passing messages and data between
components; (4) providing facilities for logging, time series interpolation,
etc.; and (5) controlling the main model loop as it progresses through time.
Any errors thrown by the model are caught by the wrapper, which prints a
detailed summary of the error.
Input data are specified in flat text files, and during startup are routed
to the correct model component for its initialization. Some of the key
initial model conditions are summarized in Tables 1 and 2. For
more details of initial model conditions we urge the reader to download
Hector v1.0 (https://github.com/JGCRI/hector). Components can send messages
to each other during the model run, most often requesting data. The
messaging interface is also available to external subroutines, such as
components of IAMs or other linked models. The coupler handles message
routing (via the capability mechanism, below) and enforces mandatory type checking:
e.g., if a component requests mean global temperature in degrees Celcius but
the data are provided in kelvins, an error will be thrown (i.e., execution halts)
unless the receiving component can handle this situation.
Initial model conditions prior to the spinup phase. Carbon values
change slightly after spinning up to a steady state.
VariableDescriptionInitial ValueUnitsNotesCatmaAtmospheric carbon588.1PgCMurakami (2010)CDaDetritus carbon55.0PgCDenman et al. (2007)Land carbon (detritus, soiland vegetation) totaling∼ 2300 PgCCSaSoil carbon1782.0PgCCVaVegetation carbon550.0PgCCDODeep ocean26 000.0PgCDenman et al. (2007)Ocean carbon (deep,intermediate and surface)totaling ∼ 3800 PgCbCHLSurface ocean high latitude140.0PgCCIOIntermediate ocean8400.0PgCCLLSurface ocean low latitude770.0PgCFLAtmosphere–land carbon flux0.0PgC yr-1FOAtmosphere–ocean carbon flux0.0PgC yr-1NPP0Net primary production50.0PgC yr-1Approximate global valueNemani et al. (2003)TGGlobal temperature anomaly0.0∘CTHLTemperature of high-latitude surface ocean box2.0∘CLenton (2000)TLLTemperature of low-latitude surface ocean box22.0∘CLenton (2000)
a Parameters appearing in the input file.
b In order to obtain a steady state in Hector, carbon values in
the intermediate box are less than reported (Denman et al., 2007).
Model parameters for the land and ocean carbon components.
VariableDescriptionValueNotesfdsannual fraction of detritus carbon that is0.60the following fractions (f)transferred to soilwere selected to be generallyconsistent with previous simpleearth system models(e.g., Meinshausen et al., 2011a;Ricciuto et al., 2008);Murakami et al., 2010)fld*annual fraction of land use0.01change flux from detritusflsannual fraction of0.89land use change flux from soilflv*annual fraction of land use0.10change flux from vegetationfnd*annual fraction of NPP carbon0.60that is transferred to detritusfnsannual fraction of NPP carbon0.05that is transferred to soilfnv*annual fraction of NPP carbon0.35that is transferred to vegetationfrdannual fraction of respiration carbon0.25that is transferred to detritusfrsannual fraction of respiration carbon0.02that is transferred to soilfvdannual fraction of vegetation carbon0.034that is transferred to detritusfvsannual fraction of vegetation carbon0.001that is transferred to soilβ*Beta0.36Q10*Q10 respiration2.45TH*high-latitude circulation4.9e7 m3 s-1tuned to give ∼ 100 PgCfrom surface to deepTT*thermohaline circulation7.2e7 m3 s-1tuned to give ∼ 100 PgCfrom surface to deepEID*water mass exchange – intermediate1.25e7 m3 s-1Lenton (2000);to deepKnox and McElroy (1984)ELI*water mass exchange – low-latitude2.0e8 m3 s-1Lenton (2000);to intermediateKnox and McElroy (1984)
* Parameters appearing in the input file.
Visitor patterns are units of code that traverse all model components and
handle model output (Martin et al., 1997). Two visitors currently
exist: one saves an easily readable summary table to an output file, while
the other writes a stream of model data (both standard outputs and internal
diagnostics). After the model finishes, this “stream” file can be parsed and
summarized by R scripts (R Development Core Team, 2014) included
with Hector. Log files may also be written by any model entity, using
facilities provided by the coupler. The full sequence of events during a
model run is summarized in Fig. 1.
Components
Model components are submodels that communicate with the coupler. From the
coupler's point of view, components are fully defined by their
capabilities and dependencies. At model startup, before the run begins, components inform the
coupler of their capabilities, i.e., what data they can provide to or accept
from the larger model system. The coupler uses this information to route
messages, such as requests for data, between components. Components also
register their dependencies, i.e., what results they require from other
components in order to complete their computations. After initialization,
but before the model begins to run, the coupler uses this dependency
information to determine the order in which components will be called in the
main control loop.
The model's modular architecture and the capability/dependency systems described above
allow swapping, enabling and disabling of model components directly via the input
without recompiling. For example, this means that a user can test two
different ocean submodels and easily compare results without having to
rebuild the model.
Model phases for the coupler (left) and a typical component (right).
Arrows show flow of control and data. The greyed spinup step is optional.
Time step, spinup, and constraints
The model's fundamental time step is 1 year, although the carbon cycle can
operate on a finer resolution when necessary (Sect. 3.1). When the model is
on an integer date (e.g., 1997.0) it is considered to be the midpoint of that
particular calendar year, in accordance with Representative Concentration
Pathway (RCP) data (Meinshausen et al., 2011b).
Like many models, Hector has an optional “spinup” step, in which the model
runs to equilibrium in an a historical, perturbation-free mode
(Pietsch and Hasenauer, 2006). This occurs after model
initialization, but before the historical run begins, and ensures that the
model is in steady state when it enters the main simulation. During spinup,
the coupler repeatedly calls all the model components in their
dependency-driven ordering, using an annual time step. Each component
signals whether it needs further steps to stabilize, and this process
repeats until all components signal that they are complete.
Currently only the model's carbon cycle makes use of the spinup phase.
Spinup takes place prior to land use change or industrial emission inputs,
and the main carbon cycle moves from its initial, user-defined carbon pool
values to a steady state in which dC/dt < ε for
all pools. The convergence criterion ε is user-definable; by
default ε=1 Tg C yr-1. From its default values the
preindustrial carbon cycle will typically stabilize in 300–400 time steps.
Hector can be forced to match its output to a user-supplied time series.
This is helpful to isolate and test different components. Available
constraints currently include atmospheric CO2, global temperature
anomaly, total ocean–atmosphere carbon exchange, total land–atmosphere
carbon exchange, and total radiative forcing. Most constraints operate by
overwriting model-calculated values with user-supplied time series data
during the run. The atmospheric [CO2] constraint operates slightly
differently, as the global carbon cycle is subject to a continuous
mass-balance check. As a result, when the user supplies a [CO2] record
between arbitrary dates and orders the model to match it, the model
computes [CO2] at each time step, and any deficit (surplus) in comparison with
the constraint [CO2] is drawn from (added to) the deep ocean. The deep
ocean holds the largest reservoir of carbon; therefore, small changes in
this large pool have a negligible effect on the carbon cycle dynamics. When
the model exits the constraint time period, atmospheric [CO2] again
becomes fully prognostic.
Code availability and dependencies
All Hector code is open source and available at https://github.com/JGCRI/hector/. The repository includes model code that
can be compiled on Mac, Linux, and Windows input files for the four
RCPs cases discussed in Sect. 5, R
scripts to process model output, and extensive documentation. Software
dependencies are as limited as possible, with only the GNU Scientific
Library (GSL; Gough, 2009) and the Boost C++ libraries
(http://www.boost.org) required. HTML documentation can be
automatically generated from the code using the Doxygen tool (http://www.doxygen.org). All these tools and libraries are free and open
source.
In keeping with Hector's emphasis on modern, robust software design, the
code includes an optional (i.e., not needed to compile and run the model)
unit testing build target. Unit testing allows individual units of source
code to be tested in a standardized and automatic manner, ensuring that they
behave as expected after changes are made to the model source code. Current
tests verify the behavior of the model coupler (message passing and
dependency calculation), reading of input, time series, logging, and units
checking. This functionality requires the “googletest” library
(http://code.google.com/p/googletest).
Carbon cycle
In the model's default terrestrial carbon cycle, terrestrial vegetation,
detritus, and soil are linked with each other and the atmosphere by
first-order differential equations (Fig. 2). Vegetation net
primary production is a function of atmospheric [CO2] and temperature.
Carbon flows from the vegetation to detritus and then to soil, losing
fractions to heterotrophic respiration on the way. Land-use change emissions
are specified as inputs. An “earth” pool debits carbon emitted as
anthropogenic emissions, allowing a continual mass-balance check across the
entire carbon cycle.
Representation of Hector's carbon cycle, land, atmosphere, and
ocean. The atmosphere consists of one well-mixed box. The ocean consists of
four boxes, with advection and water mass exchange simulating thermohaline
circulation (see Table 2 for description of parameters). At steady state, the
high-latitude surface ocean takes up carbon from the atmosphere, while the
low-latitude surface ocean off-gases carbon to the atmosphere. The land
consists of a user-defined number of biomes or regions for vegetation,
detritus and soil. At steady state the vegetation takes up carbon from the
atmosphere while the detritus and soil release carbon back into the
atmosphere. The earth pool is continually debited with each time step to act
as a mass balance check on the carbon system.
More formally, any change in atmospheric carbon, and thus [CO2], occurs
as a function of anthropogenic fossil fuel and industrial emissions
(FA), land-use change emissions (FLC), and the atmosphere–ocean
(FO) and atmosphere–land (FL) carbon fluxes. The atmosphere is
treated as a single well-mixed box whose rate of change is
dCatmdt=FA(t)+FLC(t)-FO(t)-FL(t).
Note that the carbon cycle is solved under indeterminate time steps
(represented in the text by equations with d/dt), while most other submodels
of Hector are solved under a fixed time step of 1 year (equations with
Δ). Future versions of Hector will incorporate indeterminate time
steps within all components of the model. The overall terrestrial carbon
balance (Eq. 2) excluding user-specified land-use change fluxes at time
t is the difference between net primary production (NPP) and heterotrophic
respiration (RH). This is summed over user-specified n groups (each typically
regarded as a latitude band, biome, or political unit), with n≥1:
FLt=∑i=1nNPPit-RHi(t).
Note that NPP here is assumed to include non-LUC disturbance effects (e.g.,
fire), for which there is currently no separate term. For each biome i, NPP is
computed as a function of its preindustrial values NPP0, current
atmospheric carbon Catm, and the biome's temperature anomaly Ti,
while RH depends upon the pool sizes of detritus
(CD) and soil (CS), and global temperatures:
NPPit=NPP0×f(Catmβi)),fCatm,βi=1+βilogCatmC0,RHs,dt=Cs,d×frs,rd×Q10iTi(t)/10,Tit=TG(t)×δi.
These are commonly used formulations: NPP is modified by a user-specified
carbon fertilization parameter, β (Piao et al., 2013),
that is constant in time but not necessarily in space. For example, users
can define separate β values for different biomes. RH changes are
controlled by a biome-specific Q10 value. Biomes can experience
temperature changes at rates that differ from the global mean TG,
controlled by a user-specified temperature factor δI. Note
that in Eq. (5), soil RH depends on a running mean of past
temperatures, representing the slower propagation of heat through soil
strata. Land carbon pools (vegetation, detritus, and soil) change as a
result of NPP, RH, and land-use change fluxes, whose effects are partitioned
among these carbon pools. In addition, carbon flows from vegetation to
detritus and to soil (Fig. 2). Partitioning fractions (f) control
the flux quantities between pools (Table 2). For simplicity,
Eqs. (7–9) omit the time t and biome-specific i notations, but each pool is
tracked separately for each biome at each time step:
dCVdt=NPPfnv-CV(fvd+fvs)-FLCflv,dCDdt=NPPfnd+CVfvd-CDfds-RHdet-FLCfld,dCSdt=NPPfns+CVfvs+CDfds-RHsoil-FLCfls,
The ocean–atmosphere carbon flux is the sum of the ocean's surface fluxes
(Fi) (currently n=2, high- and low-latitude surface box):
FOt=∑i=1nFit.
The surface fluxes of each individual box are directly calculated from an
ocean chemistry submodel described in detail by Hartin et al. (2015).
We model the nonlinearity of the inorganic carbon cycle, calculating
pCO2, pH, and carbonate saturations based on equations from Zeebe and
Wolf-Gladrow (2001). The flux of CO2 for each box i is calculated
by
Fi(t)=kαΔpCO2,
where k is the CO2 gas-transfer velocity, α is the solubility of
CO2 in water based on salinity, temperature, and pressure, and
ΔpCO2 is the atmosphere–ocean gradient of pCO2 (Takahashi et al., 2009). The calculation of pCO2 in each surface
box is based on the concentration of CO2 in the ocean and its
solubility (a function of temperature, salinity, and pressure). At steady
state, the cold high-latitude surface box (> 55∘,
subpolar gyres) acts as a sink of carbon from the atmosphere, while the warm
low-latitude surface box (< 55∘) off-gases carbon back to
the atmosphere. Temperatures of the surface boxes are linearly related to
atmospheric global temperatures (see Sect. 4.1), THL=ΔT-13 and TLL=ΔT+7 (Lenton, 2000). The
ocean model, modeled after Lenton et al. (2000) and Knox and
McElroy (1984), circulates carbon through four boxes (two
surface, one intermediate depth, one deep), via water mass advection and
exchange, simulating a simple thermohaline circulation (Fig. 2).
At steady state, approximately 100 Pg of carbon are transferred from the
high-latitude surface box to the deep box based on the volume of the box and
transport (in Sv; 106 m3 s-1) between the boxes. The change in
carbon of any box i is given by the fluxes in and out, with Fatm→i as the atmosphere–ocean carbon flux:
dCidt=∑j=1inFj→i-∑j=1outFi→j+Fatm→i.
As the model advances, the carbon in PgC is converted to dissolved inorganic
carbon (DIC) in each box. The new DIC values are used within the chemistry
submodel to calculate pCO2 values at the next time step.
Adaptive time step solver
The fundamental time step in Hector is currently 1 year, and most model
components are solved at this resolution. The carbon cycle, however,
operates on a variable time step, ensuring accurate ODE solutions, even
under high-emissions scenarios. This will also allow for future subannual
applications where desired. The adaptive time step accomplished using the
gsl_odeiv2_evolve_apply solver package of GSL 1.16, which varies the time step to keep truncation
error within a specific tolerance when advancing the model. Thus, all the
carbon cycle components handle indeterminate time steps less than or equal
to 1 year and can signal the solver if a too-large time step is leading to
instability. The solver then retries the solution, using a series of
smaller steps. From the coupler's point of view, however, the entire model
continues to advance in annual increments.
Other componentsGlobal atmospheric temperature
Near surface global atmospheric temperature is calculated by
ΔT(t)=λ×RF(t)-FH(t),
where the user-specified λ is the climate feedback parameter,
defined as λ=S′/S, S′ is the climate sensitivity parameter (3 K)
and S is the equilibrium climate sensitivity for a doubling of CO2 (3.7 W m-2) (Knutti and Hegerl, 2008). RF is the total radiative
forcing and FH is the ocean heat flux. FH is calculated by a
simple sigmoidal expression of the ocean heat uptake efficiency k (W m-2 K-1) that decreases with increasing global temperatures) multiplied by
the atmospheric temperature change prior to the ocean's removal of heat from
the atmosphere (TH) (Raper et al., 2002).
ΔFH(t)=k×ΔTH(t)
As global temperatures rise, the uptake capacity of the ocean may diminish,
simulating both a saturation of heat in the surface and a slowdown in ocean
circulation with increased temperatures. Finally, the temperature effects
from atmospheric [CO2] are lagged in time, as there are numerous
real-world processes not simulated in Hector buffering the temperature
effects of increasing atmospheric [CO2].
Radiative forcing
Radiative forcing is calculated from a series of atmospheric greenhouse
gases, aerosols, and pollutants (Eqs. 15, 16, 18–22, 25, 29 and 30).
Radiative forcing is reported as the relative radiative forcing. The base
year user-specified forcings are subtracted from the total radiative forcing
to yield a forcing relative to the base year (1750).
CO2
Radiative forcing from atmospheric [CO2] (in W m-2) is calculated
based on Meinshausen et al. (2011a):
RFCO2=5.35×logCaC0,
where 5.35 W m-2 is a scaling parameter from Myhre et al. (1998), Ca is the current atmospheric [CO2] in ppmv and C0 is the
preindustrial [CO2] in ppmv.
Halocarbons
The halocarbon component of the model can accept an arbitrary number of gas
species, each characterized by a name, a lifetime τ (yr), a radiative
forcing efficiency α (W m-2 pptv-1), an optional
user-specified preindustrial concentration (pptv), and a molar mass (g). For
each gas, its concentration (Ci) at time t is then computed based on a
specified emissions time series E, assuming an exponential decay from the
atmosphere:
Ci(t)=C0×exp-1τ+E×τ×1-exp-1τ.E is corrected for atmospheric dry air mole constant (1.8) and the molar
mass of each halocarbon. The default model input files include these
parameters and a time series of emissions for C2F6, CCl4, CF4, CFC11, CFC12,
CFC113, CFC114, CFC115, CH3Br, CH3CCl3, CH3Cl, HCF22, HCF141b, HCF142b,
HFC23, HFC32, HFC125, HFC134a, HFC143a, HFC227ea, HFC245ca, HFC245fa,
HFC4310, SF6, halon1211, halon1301, and halon2402.
Radiative forcing by halocarbons and other gases controlled under the
Montreal Protocol, SF6, and ozone are calculated via
RF=α[Ci(t)],
where α is the radiative efficiency (input parameters; in
W m-2 ppbv-1) and [Ci] is the atmospheric
concentration.
Ozone
Tropospheric ozone concentrations are calculated from the CH4
concentration and the emissions of three primary pollutants, NOx,
CO, and NMVOCs (non-methane volatile organic compounds), modified from Tanaka
et al. (2007):
O3t=5.0×lnCH4+0.125×ENOx+0.0011×ECO+0.0033×EVOC,
where the constants are the ozone sensitivity factors for each of the
precursors (Ehhalt et al., 2001). The radiative
forcing of tropospheric ozone is calculated from a linear relationship using
a radiative efficiency factor (Joos et al., 2001a):
RFO3=0.042×O3.
BC and OC
The radiative forcing from black and organic carbon is a function of their
emissions (EBC and EOC).
RFBC=0.0743Wm-2Tg-1×EBCRFOC=-0.0128Wm-2Tg-1×EOC
The coefficients include both indirect and direct forcings of black and
organic carbon (fossil fuel and biomass) (Bond et al., 2013, Table C1).
Sulfate aerosols
The radiative forcing from sulfate aerosols is a combination of the direct
and indirect forcings (Joos et al., 2001a).
RFSOxDirect=-0.35Wm-2×ESOxtESOxt0RFSOxIndirect=-0.6Wm-2×(ln(ESN)+ESOxt)ESN⋅lnESN+ESOxt0ESN-1
The direct forcing by sulfate aerosols is proportional to the anthropogenic
sulfur emissions (Gg S yr-1) divided by the sulfate emissions from
2000. The indirect forcing by sulfate aerosols is a function of the
anthropogenic and natural sulfur emissions. Natural sulfur emissions,
denoted by ESN, are equal to 42 000 Gg S. A time series of annual mean volcanic
stratospheric aerosol forcing (W m-2) is supplied from Meinshausen et
al. (2011b) and added to the indirect and
direct forcing for a total sulfate forcing.
Methane (CH4)
The change in [CH4] is calculated directly from CH4 emissions, and
sinks of CH4 in the troposphere (based on the lifetime of OH),
stratosphere, and soil based on Wigley et al. (2002).
ΔCH4=E(CH4)2.78-[CH4]τOH-[CH4]τstrat-[CH4]τsoil,
where E is total CH4 emissions (Tg yr-1) from both natural and
anthropogenic sources, 2.78 (Tg ppb-1) is the conversion factor, and τ
are the lifetimes of the tropospheric sink (τOH), the stratospheric
sink (τstrat=120 years), and the soil sink (τsoil=160 years). Note that within Hector, natural emissions are held at a constant 300 Tg yr-1.
The lifetime of OH is a function of [CH4] and the emissions of
NOx, CO and VOC, based on Tanaka et al. (2007).
ln(OH)t=-0.32(ln[CH4]t-ln[CH4]t0)+0.0042(E(NOx)t)-(E(NOx)t0)-0.000 105(E(CO)t)-(E(CO)t0)-0.00315(E(VOC)t)-(E(VOC)t0)
The radiative forcing equation for CH4 (Joos et al., 2001a)
is a function of the concentrations (ppbv) of both CH4 and N2O:
RFCH4=0.036Wm-2[CH4](t)[CH4]t0-fCH4t,N2Ot0-fCH4t0,N2Ot0.
The function f accounts for the overlap in CH4 and N2O in their
bands is
fM,N=0.47×ln1+2.01×10-5×MN0.75+5.31×10-15×M×MN1.52
N2O
The change in [N2O] is a function of N2O emissions and the
lifetime of N2O based on Ward and Mahowald (2014).
ΔN2O=E(N2O)4.8-[N2O]τN2O,
where E is total N2O emissions (Tg N yr-1), both natural and
anthropogenic, 4.8 (Tg N ppbv-1) is the conversion factor, and
τN2O is the lifetime of N2O. We set natural emissions of
N2O to linearly decrease from 11 Tg N yr-1 in 1765, to
8 Tg N yr-1 in 2000 and are then held constant at 8 Tg N yr-1 to 2300.
The lifetime of N2O is a function of its initial lifetime (τ0) and
concentration ([N2O]t0).
τN2O=τ0×[N2O]t[N2O]t0-0.05
The radiative forcing equation for N2O (Joos et al., 2001a)
is a function of the concentration (ppbv) of both CH4 and N2O:
RFN2O=0.12Wm-2[N2O]t-[N2O]t0-fCH4t0,N2Ot-fCH4t0,N2Ot0.
The function f accounts for the overlap in CH4 and N2O in their
bands is the same as Eq. (27).
Stratospheric H2O from CH4 oxidation
The radiative forcing from stratospheric H2O is a function of the
[CH4] (Tanaka et al., 2007). The coefficient 0.05 is from Joos et
al. (2001a) based on the fact that the forcing contribution from
stratospheric H2O is about 5 % of the total CH4 forcing (IPCC,
2001). The 0.036 value of the coefficient corresponds to the same value used
in the CH4 radiative forcing equation.
RFstratH2O=0.05×0.036Wm-2×CH4t-CH4t0
Model experiments and data sources
A critical test of Hector's performance is to compare the major climatic
variables calculated in Hector, e.g., atmospheric [CO2], radiative
forcing, and atmospheric temperature, to observational records and both
simple and complex climate models. Within this study, Hector is run under
prescribed emissions from 1850 to 2300 for all four RCPs, freely available at http://tntcat.iiasa.ac.at/RcpDb/ (Moss et al., 2010; van Vuuren et al.,
2007; Clarke et al., 2007; Wise et al., 2009; Riahi et al., 2007; Fujino et
al., 2006; Hijioka et al., 2008; Smith and Wigley, 2006). The RCPs are
plausible future scenarios that were developed to improve our understanding
of the coupled human climate system. RCPs by definition are concentration
pathways; however, for all experiments within this study we use the
corresponding emissions trajectories from each RCP as input for Hector.
Comparison data was obtained from a series of models. We compared Hector
results to MAGICC, a SCM widely used in the scientific and IAM communities,
for global variables such as atmospheric CO2, radiative forcing, and
temperature (e.g., Raper et al., 2001; Wigley, 1995; Meinshausen et al.,
2011a). We also compare Hector to a suite of 11 earth system models
included in the 5th Coupled Model Intercomparison Project (CMIP5)
archive (Taylor et al., 2012) (Table 3). All CMIP5
data were converted to yearly global averages from the historical period
through the RCPs and their extensions. One standard deviation of the annual
global averages and the CMIP5 model range were calculated for each variable
using the RCMIP5 (http://github.com/JGCRI/RCMIP5) package in R.
All CMIP5 variables used in this study are from model runs with prescribed
atmospheric concentrations, except for comparisons involving atmospheric
[CO2] which are from the emissions-driven scenario (esmHistorical and
esmrcp85) (Figs. 3, 5). We acknowledge that this comparison, between
an emissions-forced model (Hector) and concentration-forced models (CMIP5),
is not perfect. However, very few CMIP5 models were run under prescribed
emissions scenarios.
We compare Hector to observations of atmospheric [CO2] from Law Dome
(1010–1975) and Mauna Loa (1958–2008), (Keeling and Whorf, 2005; Etheridge
et al., 1996). Global temperature anomalies are from HadCRUT4 (Morice et al.,
2012). Observations of air–sea and air–land fluxes are from the Global
Carbon Project (GCP) (Le Quéré et al., 2013). Lastly, observations of
surface ocean pH are from Bermuda Atlantic Time Series (BATS) and Hawaii
Ocean Time Series (HOTS) (Bates, 2007; Fujieki et al., 2013).
Historical atmospheric [CO2] from 1850 to 2005 for Hector
(blue); CMIP5 median, standard deviation, and model range (pink, n=4);
MAGICC6 (green); Law Dome (teal); and Mauna Loa (brown). Note CMIP5 data are
from the prescribed emissions historical scenario (esmHistorical). MAGICC6,
however, is constrained to match the observational record. Although Hector
can be run with similar constraints, in this study Hector was unconstrained
to highlight the full performance of the model. n=4 is the number of CMIP5
models used to produce this figure.
CMIP5 ESM models used within this study. We use the same
suite of models as found in Friedlingstein et al. (2014). Note,
not all variables are reported for each model under all scenarios.
ModelModel NameInstitutebcc-csm1-1Beijing Climate Center,Beijing Climate Center,Climate System Model, version 1.1China Meteorological Administration, ChinaCanESM2*Second Generation CanadianCanadian Center forEarth System ModelClimate Modeling and Analysis, BC, CanadaCESM1-BGC*Community Earth System Model,National Center for Atmospheric Research,version 1.0-BiogeochemistryUnited StatesGFDL-ESM2GGeophysical Fluid Dynamic LaboratoryGeophysical Fluid Dynamics Laboratory,Earth System Model with GOLD ocean componentUnited StatesHadGEM2-ESHadley Centre Global Environmental Model,Met Office Hadley Centre,version 2 (Earth System)United Kingdominmcm4Institute of Numerical MathematicsInstitute of Numerical Mathematics,Coupled Model, version 4.0RussiaIPSL-CM5A-LRL'Institut Pierre-Simon Laplace Coupled Model,Institut Pierre Simon Laplace,version 5A, coupled with NEMO, low resolutionFranceMIROC-ESM*Model for Interdisciplinary Research on Climate,Atmosphere and Ocean Research Institute; ,Earth System ModelNational Institute for Environmental StudiesJapan Agency for Marine-Earth Science and Technology,JapanMPI-ESM-LRMax Planck Institute Earth System Model,Max Planck Institute for Meteorology,low resolutionGermanyMRI-ESM1*Meteorological Research Institute Earth System Model,Meteorological Research Institute Earth,version 1JapanNorESM1-ME*Norwegian Earth System Model,Norwegian Climate Center,version 1, intermediate resolutionNorway
* Models used in emissions-forced scenarios (esmHistorical and esmrcp85).
Results and discussionHistorical
A critical test of Hector's performance is how well it compares to
historical and present day climate from observations, MAGICC, and a suite of
CMIP5 models. Rates of change and root mean square errors were calculated
for Hector's primary outputs, which are summarized in Table 4.
After spinup is complete in Hector, atmospheric [CO2] in 1850 is 286.0 ppmv, which compares well with observations from Law Dome of 285.2 ppmv.
Hector captures the global trends in atmospheric [CO2] (Fig. 3) with an average root mean square error (RMSE) of 2.85 ppmv
(Table 4a), when compared to observations, MAGICC6, and CMIP5 data
from 1850 to 2005. The rate of change of atmospheric [CO2] from 1850 to 2005 is
slightly lower than the observations, MAGICC6, and CMIP5. Hector can be
forced to match atmospheric [CO2] records (Sect. 2.4), but we
disabled this feature to highlight the full performance of the model. Note,
however, that in the MAGICC6 results a similar feature was used to force the
output to match the historical atmospheric [CO2] record.
Historical global temperature anomaly relative to 1850 for Hector
(blue); MAGICC6 (green); CMIP5 median, standard deviation and model range
(pink, n=8); and historical observations from HadCRUT4 (purple). Hector is
running without the effects of volcanic forcing, leading to a smoother
representation of temperature with time.
Historical global atmospheric temperature anomalies (relative to 1850) are
compared across Hector, MAGICC6, CMIP5, and observations from HadCRUT4
(Fig. 4). Atmospheric temperature change from Hector (0.98 ∘C) over the period 1850–2005 closely matches the CMIP5
temperature change (1.01 ∘C), both slightly higher than the
observational record. Over this time period Hector has an average RMSE of
0.14 ∘C. Note that simple climate models do not aim to capture
temperature variations due to interannual/decadal variability found in ESMs
or the real world; instead, they simulate the overall trends in global mean
temperature change.
Root mean square error (RMSE) for Hector versus
observations, CMIP5, and MAGICC for atmospheric [CO2], surface
temperature anomaly, radiative forcing, fluxes of carbon (ocean and land),
and low-latitude surface ocean pH and change (Δ) in atmospheric
[CO2], surface temperature anomaly and radiative forcing for Hector,
CMIP5, observations, and MAGICC6.
1 [CO2] observations are an average of Law Dome and Mauna Loa.
2 CMIP5 [CO2] only to 2100.
Future projections
Hector's strengths lie within policy-relevant timescales of decades to
centuries, and here we compare Hector to MAGICC and CMIP5 under differing
future climate projections. Results from all four RCPs are broadly similar
when comparing Hector, to MAGICC6, and CMIP5; we display here RCP8.5 results
as representative. Studies suggest that 80 % of the anthropogenic CO2
emissions have an average atmospheric lifetime of 300–450 years (Archer
et al., 1997; Rogner, 1997; Archer, 2005). Hector has all the necessary
components to model the climate system from present day through the next
approximately 300 years. Figure 5 highlights historical trends in
atmospheric [CO2], along with projections of atmospheric [CO2]
under esmrcp8.5 from 1850 to 2100. Note that the emissions-forced scenario
only extends to 2100 and not to 2300 like the concentration-forced scenarios
(e.g., Fig. 8). Both Hector and MAGICC6 are on the low end of the CMIP5
median but fall within one standard deviation and model range, with a RMSE
of 9.0 ppmv (Table 4b).
Atmospheric [CO2] from 1850 to 2100 under RCP 8.5 for Hector
(blue), MAGICC6 (green), Mauna Loa (brown), Law Dome (teal) and esmRCP 8.5
(prescribed emissions scenario) CMIP5 median, one standard deviation and
model range (pink, n=4 (1850–2000) and n=5 (2001–2100)). Note that the
CMIP5 models run under esmrpc85 do not extend to 2300.
Atmospheric [CO2] from 1850 to 2300 for RCP 2.6 (red), RCP 4.5
(green), RCP 6.0 (blue), RCP 8.5 (purple), Hector (solid) and MAGICC6
(dashed).
The CMIP5 archive does not provide emissions-prescribed scenarios for all
RCPs; we can only compare atmospheric [CO2] from Hector with MAGICC6
under all four RCP scenarios out to 2300 (Fig. 6). Hector's
change in [CO2] (1472.13 ppmv) from 1850 to 2300 is slightly lower than
MAGICC6 (1600.0 ppmv) for RCP 8.5. This is most likely due to different
representations of the global carbon cycle. We compare Hector to MAGICC6 for
changes in radiative forcing under the four RCPs (Fig. 7).
Radiative forcing was not provided within the CMIP5 archive and therefore we
can only compare Hector and MAGICC6. Over the period 1850–2300 Hector
(12.80 W m-2) and MAGICC6 (12.24 W m-2) are comparable in their
change in radiative forcing, with a RMSE of 0.26 W m-2. One noticeable
difference between MAGICC6 and Hector during the historical period is the
decreases in radiative forcing. This is due to the effects of volcanic
emissions on radiative forcing. For simplicity, we have chosen to run Hector
without these effects.
Figure 8 compares global temperature anomalies from Hector to
MAGICC6 and CMIP5 over the four RCPs, from 2005 to 2300. Hector simulates
the CMIP5 median more closely than MAGICC6 across all four RCPs, with a
temperature change under RCP 8.5 for Hector of 8.59 ∘C, compared
to MAGICC6 of 7.30 ∘C, while the temperature change for CMIP5 is
9.57 ∘C (Table 4c). To highlight this close comparison,
temperature change over the entire record (1850–2300) for Hector is 9.58 ∘C, which is within 1.0 ∘C of the CMIP5 median, while
MAGICC6's temperature change is greater than 2.5 ∘C away from the
CMIP5 median.
Relative radiative forcing from 1850 to 2300 for Hector (solid) and
MAGICC6 (dashed) for all four RCP scenarios: 2.6 (red), 4.5 (green), 6.0
(blue), and 8.5 (purple). Hector has the option to enable or disable radiative
forcing from historical volcanic emissions. We have opted to disable this for
ease of comparison across all RCPs.
Figures 9 and 10 present a detailed view of carbon fluxes
under RCP 8.5, for CMIP5 and observations (negative represents carbon flux
to the atmosphere). The ocean is a major sink of carbon through 2100,
becoming less effective with time in both Hector and the CMIP5 models.
MAGICC6 does not include air–sea fluxes in its output, and because it is not
open source we were unable to obtain these values. Therefore, we compare
air–sea fluxes of CO2 to MAGICC5.3, updated with explicit BC and OC
forcing as described in Smith and Bond (2014). Hector's
calculation of air–sea fluxes is within the large CMIP5 model range up to
2100. However, after that Hector peaks close to 2150, while the CMIP5 models
are beginning to decline. One potential reason for this discrepancy after
2100 is that in this version of Hector we do not simulate changes in ocean
circulation, potentially biasing fluxes too high after 2100. Most ESMs in
CMIP5 show a weakening of the Atlantic meridional overturning circulation by
2100 between 15 and 60 % under RCP 8.5 (Cheng et al.,
2013). A slowdown in ocean circulation may result in less carbon uptake by
the oceans. Another potential reason for this bias is Hector's constant pole
to Equator ocean temperature gradient. Studies show that the Artic is
warming faster than the rest of the globe (e.g., Bintanja and van der
Linden, 2013; Holland and Bitz, 2003; Bekryaev et al., 2010). A warmer high-latitude surface ocean in Hector would suppress the uptake of carbon,
potentially bringing the air–sea fluxes closer to the CMIP5 median after
2100.
Global temperature anomaly relative to 1850 for (a) RCP 2.6
(b) RCP 4.5 (c) RCP 6.0 and (d) RCP 8.5, comparing
Hector (blue), MAGICC6 (green), and CMIP5 median, standard deviation and
model range (pink). The CMIP5 models under RCP 6.0 used in this study do not
extend to 2300. Note the change in scales between the four panels. Number of
CMIP5 models in (a)n=7 (2006–2100) and n=5 (2101–2300),
(b)n=9 (2006–2100) and n=6 (2101–2300), (c)n=6
(2006–2100), (d)n=9 (2006–2100) and n=3 (2101–2300).
Global air–sea fluxes of carbon under RCP 8.5; Hector (blue);
MAGICC5.3 (purple, note that this is not the current version of MAGICC);
CMIP5 median, standard deviation, and model range (pink, n=9 (1850–2100)
and n=4 (2101–2300)); and observations from GCP (green) (Le Quéré
et al., 2013). The break in the graph at 2100 signifies a change in the
number of models that ran the RCP 8.5 extension.
Global air–land fluxes of carbon under RCP 8.5; Hector (blue); CMIP5
median, standard deviation, and model range (pink, n=8 (1850–2100) and
n=2 (2101–2300)); and observations from GCP (green) (Le Quéré et
al., 2013). The break in the graph at 2100 signifies a change in the number
of models that ran the RCP 8.5 extension.
CMIP models tend to show huge divergences in their land responses to
changing climate (e.g.,
Friedlingstein et al., 2006), which is evident by the large range in CMIP5
models (Fig. 10). Hector simulates the general trends of the
increasing carbon sink and then a gradual decline to a carbon source after
2100. Both land and ocean fluxes within Hector agree well the observations
from Le Quéré et al. (2013).
One feature in Hector that is unique amongst SCMs is its ability to actively
solve the carbonate system in the upper ocean (Hartin et al., 2015). This
feature allows us to predict changes ocean acidification, calcium carbonate
saturations and other carbonate system parameters. Figure 11 shows
low-latitude (< 55∘) pH for Hector compared to CMIP5 and
observations from 1850 to 2100 under RCP 8.5. The model projects a
significant drop in pH from present day through 2100, which may lead to
detrimental effects on marine ecosystems (e.g., Fabry et
al., 2008).
Low-latitude (< 55) ocean pH for RCP 8.5, from 1850 to 2100,
Hector (blue), CMIP5 median, standard deviation, and model range (pink,
n=6); and observations from BATS (green) and HOTS (purple).
Conclusions
Hector reproduces the large-scale couplings and feedbacks on the climate
system between the atmosphere, ocean, and land, falling within the range of
the CMIP5 model and matching MAGICC. It does not simulate the fine details
or parameterizations found in large-scale, complex ESMs, but instead
represents the most critical global processes in a reduced-complexity form.
This allows for fast execution times, ease of understanding, and
straightforward analysis of the model output.
Two of Hector's key features are its open-source nature and modular design.
This allows the user to edit the input files and code at will, for example,
to enable/disable/replace components, or include components not found within
the core version of Hector. For example, a user can design a new submodel
(e.g., sea ice) to answer specific climate questions relating to that
process. Hector is hosted on a widely used open-source software repository
(Github) and, thus, changes and improvements can be easily shared with the
scientific community. Because of these critical features, Hector has the
potential to be a key analytical tool in both the policy and scientific
communities. We welcome user input and encourage use, modifications, and
collaborations with Hector.
While Hector has many strengths, the current 1.0 version has some
limitations. For example, Hector does not currently simulate terrestrial
gross primary production, a key metric of comparison to e.g., the FLUXNET
database. Also, Hector does not have differential radiative forcing and
atmospheric temperature calculations over land and ocean. This may be a
problem, as land responds to changes in emissions of greenhouse gases and
aerosols much quicker than the ocean (Hansen et al., 2005). Hector does
not explicitly deal with oceanic heat uptake, except via a simple empirical
formula. Surface temperatures are calculated based on a linear relationship
with atmospheric temperature and we assume a constant pole to Equator
temperature gradient. We acknowledge that this assumption may not hold true
if the poles warm faster than the Equator.
Future plans with Hector include addressing some of the above limitations and
conducting numerous scientific experiments, using Hector as a stand-alone
simple climate carbon-cycle model. It is also being incorporated into Pacific
Northwest National Laboratory's Global Change Assessment Model for
policy-relevant experiments. Hector has the ability to be a key analytical
tool used across many scientific and policy communities due to its modern
software architecture, open-source, and object-oriented structure.
Code availability
Hector is freely available at https://github.com/JGCRI/hector. The
specific Hector v1.0 referenced in this paper, as well as code to reproduce
all figures and results shown here, is available at
https://github.com/JGCRI/hector/releases/tag/v1.0
C. A. Hartin and B. P. Bond-Lamberty developed the ocean and terrestrial carbon models,
respectively, and led the overall development of Hector. R. P. Link and
P. Patel wrote critical code for Hector's coupler and carbon cycle solver.
A. Schwarber helped with the development of the atmospheric forcing components.
C. A. Hartin wrote the manuscript with contributions from all co-authors.
Acknowledgements
This research is based on work supported by the US Department of Energy,
Office of Science, Integrated Assessment Research Program. The Pacific
Northwest National Laboratory is operated for DOE by Battelle Memorial
Institute under contract DE-AC05-76RL01830.
Edited by: C. Sierra
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