GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-9-3817-2016PALADYN v1.0, a comprehensive land surface–vegetation–carbon cycle model of intermediate complexityWilleitMatteowilleit@pik-potsdam.dehttps://orcid.org/0000-0003-3998-6404GanopolskiAndreyPotsdam Institute for Climate Impact Research (PIK), Potsdam, GermanyMatteo Willeit (willeit@pik-potsdam.de)28October20169103817385715April201626April201614September20163October2016This 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://gmd.copernicus.org/articles/9/3817/2016/gmd-9-3817-2016.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/9/3817/2016/gmd-9-3817-2016.pdf
PALADYN is presented; it is a new comprehensive and computationally efficient
land surface–vegetation–carbon cycle model designed to be used in Earth
system models of intermediate complexity for long-term simulations and
paleoclimate studies.
The model treats in a consistent manner the interaction between atmosphere,
terrestrial vegetation and soil through the fluxes of energy, water and carbon.
Energy, water and carbon are conserved. PALADYN explicitly treats
permafrost, both in physical processes and as an important carbon pool.
It distinguishes nine surface types: five different vegetation
types, bare soil, land ice, lake and ocean shelf. Including the ocean shelf
allows the treatment of continuous changes in sea level and shelf area associated
with glacial cycles. Over each surface type, the model solves the surface
energy balance and computes the fluxes of sensible, latent and ground heat
and upward shortwave and longwave radiation. The model includes a single snow layer.
Vegetation and bare soil share a single soil column. The soil is vertically
discretized into five layers where prognostic equations for temperature,
water and carbon are consistently solved. Phase changes of water in the
soil are explicitly considered. A surface hydrology module computes
precipitation interception by vegetation, surface runoff and soil
infiltration. The soil water equation is based on Darcy's law.
Given soil water content, the wetland fraction is computed based on a
topographic index.
The temperature profile is also computed in the upper part of ice sheets
and in the ocean shelf soil.
Photosynthesis is computed using a light use efficiency model. Carbon
assimilation by vegetation is coupled to the transpiration of water through
stomatal conductance. PALADYN includes a dynamic vegetation module with
five plant functional types competing for the grid cell share with their
respective net primary productivity.
PALADYN distinguishes between mineral soil carbon, peat carbon, buried carbon
and shelf carbon. Each soil carbon type has its own soil carbon pools
generally represented by a litter, a fast and a slow carbon pool in each soil
layer. Carbon can be redistributed between the layers by vertical diffusion
and advection. For the vegetated macro surface type, decomposition is a
function of soil temperature and soil moisture. Carbon in permanently frozen
layers is assigned a long turnover time which effectively locks carbon in
permafrost. Carbon buried below ice sheets and on flooded ocean shelves is
treated differently. The model also includes a dynamic peat module.
PALADYN includes carbon isotopes 13C and 14C, which are tracked
through all carbon pools. Isotopic discrimination is modelled only
during photosynthesis.
A simple methane module is implemented to represent methane emissions
from anaerobic carbon decomposition in wetlands (including peatlands) and
flooded ocean shelf.
The model description is accompanied by a thorough model evaluation in
offline mode for the present day and the historical period.
Introduction
Land surface models (LSMs) represent an essential component of Earth
system models (ESMs) of different complexity. Currently, LSMs simulate the
interaction between atmosphere, vegetation, land surface and upper soil
through the fluxes of energy, water and carbon.
Modern LSMs are the result of a gradual convergence of initially separate
modelling approaches: climate, carbon cycle and vegetation dynamics models
e.g..
In the earlier climate models, very simple land surface schemes with bucket
hydrology and without explicit vegetation representation were used
. The second-generation LSMs simulated
soil temperature and moisture in several layers and the water and energy
exchange between the land surface and the atmosphere were mediated by
vegetation represented as a big leaf (e.g. ; BATS,
; and SiB, ). This step was
required because biological processes play a major role in controlling
evapotranspiration. In second-generation LSMs, the behaviour of leaf stomata,
which controls the rate of transpiration of water from plants, was
represented based on empirical relations with climate
e.g.. The third generation of LSMs included additionally
a mechanistic representation of photosynthesis
which could then directly be related to
stomatal conductance used to compute transpiration
.
Terrestrial biogeochemical models followed a separate line of development.
These models were designed to simulate the exchanges of carbon between
the atmosphere and terrestrial ecosystems for a given climate and
geographic vegetation distribution e.g..
Equilibrium biogeography models were developed alongside terrestrial carbon
cycle models to simulate the global vegetation distribution for given
climatic conditions .
However, equilibrium models do not simulate the processes of plant growth,
competition and mortality that govern the dynamics of vegetation changes.
Global dynamic vegetation models have been developed for this purpose
.
Since it was shown that climate–vegetation feedbacks may be important, the
first attempts to incorporate interactive vegetation into climate models were
made . While during the 1990s and
2000s climate models and then Earth system models based on coupled general
circulation models (GCMs) remained too expensive to perform long-term
simulations, a new class of models – Earth system models of intermediate
complexity (EMICs, ) – emerged. The EMIC CLIMBER-2
was one of the first Earth system models
which included both terrestrial carbon cycle and vegetation dynamics based on
VECODE and has been also used to estimate the
strength of the climate–vegetation feedback and the
carbon cycle feedback . Later, similar and more
comprehensive vegetation models were incorporated in both complex and
intermediate complexity ESMs
e.g..
A limitation of previous land surface modelling approaches is that
different model components are not necessarily consistent because initially they
were developed as stand-alone models. Additionally, initially LSMs
have been developed with the intention to capture the
processes which are important for climate change projections on the
timescales of centuries, thus missing processes which might play an
important role on longer timescales. This was fully justified by the fact
that complex ESMs were and are still too computationally expensive to be
used on much longer timescales, such as for simulations of glacial cycles.
Only recently some existing models have been adapted to include slower
processes, for example, peat carbon dynamics
. However,
the simulation of processes with long timescales, such as peat carbon
accumulation or inert permafrost carbon dynamics, require necessarily a transient
modelling approach, which is made feasible only by a fast model.
Here, we present a new land model primarily designed for paleoclimate
applications, and therefore named PAleo LAnd DYNamics model (PALADYN),
although also applicable to many other types of studies, including
multi-ensemble future projections. The model has been designed to represent
the land processes which are thought to be important both on short
and very long timescales. The physical and biochemical processes are consistently
coupled with each other. The model is intended to be used in the next
generation of the CLIMBER EMIC and to substitute VECODE. CLIMBER employs a statistical dynamical
atmosphere model. This type of model does not explicitly simulate weather,
and therefore PALADYN is designed to simulate climatological mean seasonal
cycle. Typical applications
of such model are simulations of Earth system dynamics on astronomical and
geological timescales. This is why particular attention is given to the
selection of the proper complexity of the different processes which are
represented in order to capture the main feedbacks in the system but at
the same time maintain the model computationally efficient.
We expect that PALADYN can also be used in other EMICs since most of
them still employ rather simplistic LSMs.
Model overview
PALADYN is designed to operate on coarse resolution required for long-term
simulations. Here, we test the model on a 5 × 5∘ horizontal resolution.
In each grid cell, the model distinguishes nine surface types (five vegetation types,
bare soil, ice sheets, lakes and ocean shelf) (Fig. a).
All surface type fractions can change over time. The fraction of vegetation
types and bare soil is computed by the dynamic vegetation module. The model
is also able to handle changes in the fraction of ice sheet and
ocean shelf, when given as input. This is necessary to simulate glacial
cycles. So far, lakes are implemented in the model only as a placeholder.
Over each surface type, except ocean shelf, the model
solves the surface energy balance and computes the fluxes of sensible,
latent and ground heat and upward shortwave and longwave radiation.
Vegetation and bare soil share a single soil column
(Fig. b) where temperature, moisture and carbon are
discretized in five vertical layers reaching down to a depth of 3.9 m. The
top soil layer is 20 cm thick. A single snow layer with prognostic
temperature and density is included in the model on top of the soil column. A
1-D heat diffusion equation is solved to compute snow and soil temperature with the
ground heat flux as top boundary condition. Snowmelt and phase changes of
water in the soil are explicitly considered. A surface hydrology module
computes rainfall intercepted by vegetation, surface runoff and infiltration.
Infiltration provides the top boundary condition for the solution of soil
water equation based on Darcy's law. Given soil water content, the wetland
fraction is computed following a simplified TOPMODEL approach
.
For the ice sheet fraction, the temperature of the snow layer and of the top
3.9 m of ice below is computed in the same way as for the soil, but
phase changes in the ice are inhibited. The temperature of the soil below the
shelf water is needed to calculate the decomposition rate of shelf carbon. It
is computed from a 1-D diffusion equation with the shelf water temperature prescribed
as top boundary condition and assuming that the soil is saturated with liquid
and/or frozen water. Phase changes are accounted for.
Photosynthesis is computed following and .
Carbon assimilation by vegetation is coupled to the transpiration of
water vapour through stomatal conductance.
PALADYN includes a dynamic vegetation module based on TRIFFID
with five plant functional types competing for the grid cell share with their
respective net primary production.
PALADYN includes a representation of soil carbon processes, including slow
processes that are thought to be relevant over multimillennial timescales associated with
glacial-interglacial transitions, when the appearance and disappearance
of continental ice sheets, changes in sea level and land area can potentially
strongly affect the land carbon cycle.
PALADYN therefore includes processes with a long timescale, such as
accumulation of carbon in peatlands, inert carbon locked in perennially
frozen ground and carbon buried below ice sheets. It also accounts for
changes in land area due to sea level variations and isostatic adjustment
of the lithosphere to the ice sheet loading. During periods of low sea level,
the model allows vegetation to grow on exposed ocean shelves. When sea level
is rising, the exposed shelf becomes flooded and the vegetation dies.
Illustration of the physical processes included in PALADYN. Energy
fluxes and variables are indicated in black while water fluxes and
hydrological variables are indicated in blue. Prognostic variables are in
bold and fluxes are accompanied by arrows.
Illustration of the carbon cycle processes represented in PALADYN.
Prognostic variables are in bold and fluxes are accompanied by
arrows.
The soil of the vegetated grid cell part, the soil below the ice sheet and
soil below the shelf water have their own carbon pools
(Fig. c) represented in general by a litter, a fast and a
slow carbon pool in each soil layer. Carbon can be redistributed between the
layers by vertical diffusion and advection. For the vegetated part,
decomposition of organic matter is a function of soil temperature and soil
moisture. Carbon in permanently frozen layers is assigned a long turnover
time which effectively locks carbon in permafrost. Carbon buried below ice
sheets and carbon on the flooded ocean shelf is treated separately, but is
not discussed in detail in this paper.
A representation of peatland dynamics is also included in PALADYN. In
inundated areas, peat is formed by accumulating carbon at the surface in
the seasonally anoxically decomposing acrotelm. When the acrotelm carbon
exceeds a critical value, carbon is transferred to the catotelm below the
water table.
PALADYN also includes carbon isotopes 13C and 14C, which are tracked
trough all carbon pools. Isotopic discrimination is modelled only during photosynthesis.
A simple methane module is implemented to represent methane emissions
from anaerobic carbon decomposition in wetlands (including peatlands) and
flooded ocean shelf.
The processes represented in PALADYN are illustrated in Figs.
and .
All physical model components and photosynthesis are integrated with an implicit
time-stepping scheme with a time step of 1 day. Dynamic vegetation and
soil carbon processes are integrated with an implicit time-stepping scheme
with a time step of 1 month.
The model is written in FORTRAN and uses the NCIO package
to handle input and output of data.
This paper describes the model representation of processes over ice free
land. Processes related to changes in land–ice–ocean mask, buried and
ocean shelf carbon will be described in a forthcoming paper.
Surface energy balance and fluxes
The surface energy balance equation at the land surface is written as
(1-α)SW↓+ϵLW↓-LW↑-H-LE-G=0,
where α is surface albedo, SW↓ is the incoming shortwave radiation,
ϵ is the surface emissivity for longwave radiation, LW↓ and
LW↑ are the incoming and outgoing longwave radiation at the surface,
H is the sensible heat flux, LE is the latent heat flux and G the ground
heat flux. Equation () is then solved for the skin
temperature, T∗, using the formulations for the energy fluxes
described next. All symbols are defined in Table .
Symbol definitions.
SymbolUnitsDefinitionΔ‰isotopic discriminationΔzlmthickness of soil layer lΛkgCm-2s-1litterfall rateΛburkgCm-2s-1vegetation carbon burial rate under ice sheetsΛlkgCm-2s-1leaf litterfall rateΛlockgCm-2s-1local litterfall rateΛpeatkgCm-2s-1litterfall rate over peatlandΛshelfkgCm-2s-1litterfall rate over ocean shelfΛvegkgCm-2s-1litterfall rate over vegetated grid cell areaαsurface albedoαafactor for APARαdiralbedo for direct radiationαdifalbedo for diffuse radiationαvisvisible broadband albedoαnirnear-infrared broadband albedoαcancanopy albedoαgground albedoαintssnowfall interception factorαintwrainfall interception factorαleafleaf albedoαsnsnow albedoαsncanalbedo of snow-covered canopyαsn,freshfresh snow albedoαsnfreesnow-free surface albedoαsnfreecanalbedo of snow-free canopyαsoilsnow-free soil albedoβθsoil moisture limitation factor for photosynthesisβssurface evaporation factorγνs-1PFT disturbance rateγν,mins-1minimum PFT disturbance rateγls-1leaf turnover rateγrs-1root turnover rateγss-1stem turnover rateϵlongwave emissivityηPassnow viscosityη0Pasreference snow viscosityθm3m-3volumetric total soil moistureθ1m3m-3top-layer volumetric soil moistureθcritm3m-3critical soil moisture for fireθfcm3m-3volumetric soil moisture at field capacityθim3m-3volumetric frozen soil moistureθrshape parameter for photosynthesisθsatm3m-3soil porosity
Continued.
θwm3m-3volumetric liquid soil moistureθwpm3m-3volumetric soil moisture at wilting pointκvon Karman constantλWm-1K-1heat conductivityλNPPNPP partitioning factorλaWm-1K-1heat conductivity of airλcratio of intercellular to atmospheric CO2λdryWm-1K-1heat conductivity of dry soilλiWm-1K-1heat conductivity of iceλsWm-1K-1heat conductivity of soilλs,1Wm-1K-1heat conductivity of top soil or snow layerλsatWm-1K-1heat conductivity of saturated soilλsnWm-1K-1heat conductivity of snowλwWm-1K-1heat conductivity of waterμradianssolar zenith angleνPFT fractional area coverageνseedPFT seed fractionρakgm-3air densityρacrokgCm-3acrotelm carbon densityρcatokgCm-3catotelm carbon densityρikgm-3density of iceρsnkgm-3density of snowρsn,freshkgm-3density of fresh snowρsn,minkgm-3minimum density of snowρwkgm-3density of liquid waterσWm-2K-4Stefan–Boltzmann constantτfiresfire return timescaleτsscanopy snow removal timescaleτwscanopy water removal timescaleϕphenology factorψmsoil matric potentialψsatmsaturated soil matric potentialAms-1vertical advection velocity for soil carbonAPARmolm-2day-1absorbed photosynthetically active radiationAggCm-2day-1daily gross assimilationAngCm-2day-1daily net assimilationAndgCm-2day-1daytime net assimilationCDNmneutral drag coefficient for momentumCDNhneutral drag coefficient for heat and waterCDmdrag coefficient for momentumCDhdrag coefficient for heat and waterCacrokgCm-2acrotelm carbon
Continued.
Cacro,critkgCm-2critical acrotelm carbon for catotelm formationCcanbelow canopy drag coefficientCcatokgCm-3catotelm carbon densityCfastkgCm-3fast soil carbon densityCiJkg-1K-1specific heat capacity of iceClitkgCm-3litter carbon densityClit,peatkgCm-2peat litter carbonCpJkg-1K-1specific heat capacity of air at constant pressureCpeatkgCm-2peat carbonCpeatcritkgCm-2minimum peat carbon content for peat survivalCslowkgCm-3slow soil carbon densityCvkgCm-2vegetation carbonCv,agkgCm-2aboveground vegetation carbonCv,highkgCm-2aboveground vegetation carbon parameter for fireCv,lkgCm-2leaf carbonCv,lowkgCm-2aboveground vegetation carbon parameter for fireCv,rkgCm-2root carbonCv,skgCm-2stem carbonCwJkg-1K-1specific heat capacity of waterDm2s-1vertical soil carbon diffusivityDbiom2s-1bioturbation carbon diffusivityDcryom2s-1cryoturbation carbon diffusivityEkgm-2s-1evapotranspirationEcankgm-2s-1canopy evaporation and sublimationEcanskgm-2s-1canopy sublimationEcanwkgm-2s-1canopy evaporationEskgm-2s-1snow sublimationGWm-2ground heat fluxHWm-2sensible heat fluxIcanskgm-2s-1canopy snow interceptionIcanwkgm-2s-1canopy rain interceptionJCgCm-2day-1RuBisCO-limited photosynthesis rateJEgCm-2day-1light-limited photosynthesis rateKKersten numberLJkg-1latent heat of vaporizationLaim2m-2leaf area indexLai,bm2m-2balanced leaf area indexLfJkg-1latent heat of fusion of waterLW↓Wm-2downward longwave radiation at the surfaceLW↑Wm-2upward longwave radiation at the surfaceMskgm-2s-1snowmeltNPPkgCm-2s-1net primary production
The surface emitted longwave radiation is given by the Stefan–Boltzmann law
with a surface-type-dependent emissivity ϵ (Sect. )
to account for the fact that the surface is not a perfect black body:
LW↑=ϵσT∗4.σ is the Stefan–Boltzmann constant.
The sensible heat flux is computed from the temperature gradient between
the surface and a reference height above the surface and an aerodynamic
resistance, ra (Sect. ),
using the bulk aerodynamic formula:
H=ρaCpra(T∗-Ta),
where ρa is air density, Cp is the specific
heat of air, ra is the aerodynamic resistance and Ta
is the temperature of the air at a reference level zref.
Continued.
Pskgm-2s-1snowfall ratePs,gkgm-2s-1snowfall rate reaching the groundPrkgm-2s-1rainfall ratePr,gkgm-2s-1rainfall rate reaching the groundRdgCm-2day-1leaf respirationRibulk Richardson numberRwkgm-2s-1surface water runoffSLAm2kgC-1specific leaf areaSaim2m-2stem area indexSW↓Wm-2downward shortwave radiation at the surfaceT0Kfreezing temperature of waterT∗Kskin temperatureTaKair temperature at height zrefTcmonmaxKmaximum coldest month temperature for establishmentTcmonminKminimum coldest month temperature for establishmentTcmonphenKcoldest month temperature for phenologyTgddbaseKbase temperature for phenologyTs,1Ktop soil layer or snow temperatureTsKsoil–snow temperatureTsnKsnow temperatureVPDkPavapour pressure deficitVams-1wind speed at height zrefVmgCm-2day-1maximum daily rate of net photosynthesisaCfactor for leaf respirationawhmallometric coefficient for plant heightawlkgCm-2allometric coefficientbClapp and Hornberger parameterbwlallometric coefficientcJm-3K-1volumetric heat capacityc1gmol-1factor for light-limited assimilationc2factor for RuBisCO-limited assimilationcamolmol-1atmospheric CO2 mole fractioncimolmol-1intercellular CO2 mole fractioncijPFT competition coefficientscqmolJ-1conversion factor for solar radiationcsJm-3K-1volumetric heat capacity of dry soilcsnJm-3K-1volumetric heat capacity of snowdmzero plane displacement
Continued.
dhhoursday lengthdr,1mroot distribution parameterdr,2mroot distribution parameterekgm-2s-1soil moisture removal by evapotranspirationf∇parameter for computation of water table depthfθsoil moisture factor for soil carbon decomposition ratefθ,peatsoil moisture factor for peat carbon decomposition ratefθ,satsoil moisture factor for soil carbon decomposition rate at saturationfTtemperature factor for soil carbon decomposition ratefμsolar zenith angle factor for snow albedofagesnow age factorfcanssnow-covered canopy fractionfcanwwater-covered canopy fractionffrz,critcritical fraction of frozen soil water for permafrost carbonficefraction of grid cell covered by ice sheetsfinertfrozen soil factor for soil carbon decompositionfinuninundated grid cell fractionflitrespfraction of decomposed litter carbon going to atmosphereflit→fastfraction of decomposed litter transferred to fast carbon poolflit→slowfraction of decomposed litter transferred to slow carbon poolfoxicfraction of litter and acrotelm respiring in oxic conditionsfpeatpeatland fractionfpeatminminimum peatland fractionfpeat,potpotential peatland fractionfsatsaturated grid cell fractionfsatmaxmaximum saturated grid cell fractionfshelffraction of grid cell below sea levelfsnsnow fractionfsvsky view factorfsvdirdirect beam sky view factorfsvdifdiffuse radiation sky view factorfveg→burfraction of vegetation carbon buried below ice sheetsfwetwetland fractiongms-2gravitational accelerationgddKgrowing degree days above Tgddbase
Continued.
gddcritKcritical growing degree days for phenologygddminKminimum growing degree days for establishmentg0ms-1cuticular canopy conductanceg1parameter in optimal stomatal conductance modelgcanms-1canopy conductancegminms-1minimum canopy conductancehsnmsnow thicknesshsoilmdepth of the soil columnhvmvegetation heightkkgm-2s-1hydraulic soil conductivitykacros-1acrotelm carbon turnover ratekacro→catos-1catotelm formation ratekcatos-1catotelm carbon turnover ratekextextinction coefficient for radiationkfasts-1fast carbon turnover ratekfast,10s-1fast soil carbon turnover rate at 10 ∘Ckinerts-1inert soil carbon turnover rateklits-1litter carbon turnover rateklit,10s-1litter carbon turnover rate at 10 ∘Cklit,peats-1peat litter carbon turnover rateksatkgm-2s-1hydraulic soil conductivity at saturationkslows-1slow soil carbon turnover ratekslow,10s-1slow soil carbon turnover rate at 10 ∘Ckρm3kg-1factor for density dependence of snow viscositykTK-1factor for temperature dependence of snow viscositynalmultiple of active layer thickness for cryoturbationpaPapartial pressure of atmospheric CO2piPapartial pressure of intercellular CO2qkgm-2s-1soil water fluxqakgkg-1air-specific humidity at height zrefqdrainkgm-2s-1soil water drainageqinfkgm-2s-1soil water infiltrationqinfmaxkgm-2s-1maximum soil water infiltrationqsatkgkg-1specific humidity at saturationrcumulative root fractionrasm-1aerodynamic resistancera,cansm-1below-canopy aerodynamic resistancerlroot fraction in layer l
Continued.
rssm-1canopy resistance to water vapour fluxwcanwkgm-2canopy liquid waterwcanskgm-2canopy snow water equivalentwikgm-2soil frozen water contentwsnkgm-2snow water equivalentwwkgm-2soil liquid water contentwwmaxkgm-2maximum soil liquid water contentz0bmbare soil roughness lengthz0imice roughness lengthz0snmsnow roughness lengthz0snfreemsnow-free roughness lengthz0vmvegetation roughness lengthz∇mgrid cell mean water table depthz∇minmminimum water table depthz∇peatmpeatland water table depthzacromacrotelm thicknesszalmactive layer thicknesszhmroughness length for scalarszmmroughness length for momentumzrefmreference height
Similarly, the latent heat flux over unvegetated surfaces is expressed in
terms of the specific humidity gradient between the surface and a reference
atmospheric level with the addition of a factor βs
(Sect. ) representing a possible limitation
in the moisture supply:
LE=Lρaraβsqsat(T∗)-qa.L is the latent heat of vaporization, qsat is the specific
humidity at saturation and qa is the specific humidity of air.
Over vegetation, the latent heat flux consists of contributions from
transpiration of water vapour through leaf stomata during photosynthesis,
soil–snow evaporation and sublimation from below the canopy and evaporation
and sublimation of precipitation intercepted by the canopy:
LE=Lρara+rsqsat(T∗)-qa+Lρara+ra,canβsqsat(Ts,1)-qa+L⋅Ecan.ra,can is the aerodynamic resistance between the soil surface
and the vegetation canopy (Sect. ) and
rs is the canopy resistance to water
vapour flux through the leaf stomata as described in detail in Sect. ). Ts,1 is the temperature
of the top soil layer, or the snow layer temperature if snow is present.
Canopy evaporation and sublimation, Ecan, is
computed using the skin temperature from the previous time step as described
in Sect. .
The ground heat flux is represented by conduction of heat between the skin
and the centre of the snow layer or top soil layer:
G=2λs,1T∗-Ts,1Δz1.λs,1 is the heat conductivity and Δz1 is the
thickness of the snow layer or top soil layer.
The prognostic terms in T∗ in the formulation of the
surface energy fluxes are then linearized using Taylor series expansion assuming that the temperature
at the new time step T∗,n+1=T∗,n+ΔT∗ with ΔT∗≪T∗:
T∗,n+14=T∗,n4+4T∗,n3(T∗,n+1-T∗,n),qsat(T∗,n+1)=qsat(T∗)+dqsatdT∗|T∗=T∗,n(T∗,n+1-T∗,n).
Equation () can then be solved explicitly for the
skin temperature at the new time step, T∗,n+1, separately for each
surface type.
If snow is present and the skin temperature is above freezing, the
surface energy fluxes are diagnosed first with the skin temperature greater then
0 ∘C and then with skin temperature set to 0 ∘C. The
difference between the sum of the energy fluxes is then added to the energy
available to melt the snow layer.
Given the new skin temperatures, the ground heat flux G and its derivative
with respect to top soil or snow temperature (∂G/∂Ts,1 )
are diagnosed and used as input for the soil heat diffusion equation.
After the top soil–snow temperature has been updated as described in Sect. , it is used to compute the total ground heat
flux Gnew=G+∂G/∂Ts,1ΔTs,1.
Skin temperature is then updated using Gnew and all remaining
surface energy and water fluxes are diagnosed.
In the next sections, the surface parameters needed for the solution of
the surface energy balance equation are described.
Surface albedo
PALADYN distinguishes between direct beam and diffuse albedo in the visible
and infrared spectral bands.
For ice sheets and bare soil the surface albedo is computed as
a weighted mean of snow-free (αsnfree) and snow (αsn) albedos:
α=fsnαsn+(1-fsn)αsnfree,bare soil, ice sheets.
The snow-free soil albedo in the visible and near-infrared band is prescribed
from . The fraction considered to be snow covered depends
on snow height (hsn) and snow-free roughness length
(z0snfree) of the surface (Sect. )
following :
fsn=hsnhsn+10z0snfree.
The albedo of grass and shrubs is computed by additionally separating
the snow-free albedo into bare soil and canopy albedo through a sky view
factor fsv:
α=fsnαsn+(1-fsn)(1-fsv)αsnfreecan+(1-fsn)fsvαsoil,grass,
shrubs.
The sky view factor is a function of the leaf area index (Lai), the
stem area index (Sai) and an extinction coefficient kext
(Table ) e.g.:
fsv=exp-kext(Lai+Sai).
Surface model parameters.
kext=0.5extinction coefficient for radiationαsn,freshvis,dif=0.95diffuse visible fresh snow albedoαsn,freshnir,dif=0.65diffuse near-infrared fresh snow albedoz0b=0.005mbare soil roughness lengthz0i=0.01mice roughness lengthz0sn=0.0024msnow roughness lengthCcan=0.006drag coefficient for fluxes below the canopyαintw=0.2canopy water interception parameterαints=0.5canopy snow interception parameterτw=1daycanopy water removal timescaleτs=10dayscanopy snow removal timescaleρsn,min=50kgm-3minimum snow densityη0=9×106Pasreference snow viscositykT=0.06K-1temperature parameter for snow viscositykρ=0.02m3kg-1density parameter for snow viscosityf∇=1.7parameter for saturated grid cell fraction
The forest albedo is computed as a weighted mean of canopy albedo
(αcan) and albedo of the ground below the canopy
(αg):
α=fsvαg+(1-fsv)αcan,forest.
The direct beam sky view factor for forest includes a daily radiation-weighted solar zenith angle (μ) dependence following :
fsvdir=exp-kext(Lai+Sai)cosμ.
The sky view factor for diffuse radiation is derived by fitting
the relation given by and is taken to be
fsvdif=exp-kext(Lai+Sai)cos45∘.
The albedo of the ground below the canopy, αg, is
computed as in Eq. ().
αcan varies between snow-free canopy albedo and
snow-covered canopy albedo depending on the canopy fraction covered by snow:
αcan=fcansαsncan+(1-fcans)αsnfreecan.
The canopy fraction covered by snow, fcans,
is described in Sect. .
For αsnfreecan the PFT-specific values
derived from MODIS data in for the TRIFFID PFTs
are used and αsncan values are taken from
based on MODIS data (Table ).
Snow albedo is parameterized as a function of the solar zenith angle and
a snow ageing factor. The diffuse albedo of freshly fallen snow is set to
0.95 in the visible band and to 0.65 in the near-infrared band.
The actual albedo of snow for diffuse radiation depends on a snow age factor
fage:
αsnvis,dif=αsn,freshvis,dif-0.05fage,αsnnir,dif=αsn,freshnir,dif-0.25fage.
The snow age factor is intended to represent the effect of snow grain size
increase on albedo . For simplicity and to account for
the fact that a statistical dynamical atmosphere does not resolve single
snowfall events but rather returns a smoothly varying daily snowfall rate,
fage is parameterized as a function of skin temperature and
snowfall rate as described in Appendix . If the skin
temperature is at melting point, the snow albedo is further reduced by 0.2
to account for the formation of melt ponds.
The direct beam snow albedo is then computed as in :
αsndir=αsndif+0.4fμ(1-αsndif),
where the solar zenith angle factor is slightly modified from
to correct for the bias highlighted by :
fµ=0.531+2cosμ-1.
Surface emissivity
The broadband emissivity (ϵ) used
to compute the net longwave radiation at the surface is a surface-type-dependent
parameter. It is taken to be equal to 0.96 for all vegetation
types, 0.9 for bare soil, 0.99 for snow-covered ground and 0.99 for ice
.
Aerodynamic resistances
The aerodynamic resistance, ra, is computed for each surface
type accounting for atmospheric stability through a bulk Richardson number
following BATS . The drag coefficients for neutral
stratification are obtained from boundary layer theory:
CDNm=κ2lnzref-dzm-2,drag coefficient for momentumCDNh=κ2lnzref-dzmlnzref-dzh-1,drag coefficient for heat and water.zref is a reference height above the surface and d is the
zero-plane displacement, the height above the ground at which zero wind
speed is achieved, and depends on the surface type.
zm is the roughness length for momentum and is computed as
the weighted mean of the roughness length of snow (z0sn)
and the roughness length of the snow-free surface (z0snfree):
zm=fsnz0sn+(1-fsn)z0snfree.
A logarithmic averaging would be more appropriate here ,
but for computational efficiency a simple linear weighting is preferred.
This simplification does not significantly affect the model results.
The snow-covered fraction is given by Eq. () for all
surface types.
For vegetated surfaces, z0snfree is given by
a weighted mean of vegetation (z0v) and bare soil
(z0b) roughness:
z0snfree=Vz0v+(1-V)z0b,
where the weight V depends on the vegetation state
V=Lai+Sai(Lai+Sai)crit,
and is limited to be lower than 1.
The critical value of (Lai+Sai)crit is set to 2.
showed that model results are not very sensitive to the
formulation of V.
z0v is taken as 1/10 of the vegetation
height (hv) and the displacement d=0.7Vhv. Vegetation
height varies over time for each PFT and differs between PFTs (see Eq. ).
For bare soil, snow and ice d=0 and the values of z0
are given in Table .
In general, the roughness length for heat and water vapour differs from the
roughness length for momentum and is defined by lnzmzh=2.zh is therefore almost an order of magnitude smaller than zm.
Although the surface energy balance equation in PALADYN is solved with a
daily time step, which implies that the diurnal cycle in atmospheric stability
can not be resolved by the model, the inclusion of a simple
Richardson number dependence based on daily mean temperatures in the
computation of the drag coefficients significantly improves the simulated
surface energy fluxes when the stratification is unstable.
The bulk Richardson number is calculated as :
Ri=gzref(1-T∗/Ta)Va2+1,
where g is the acceleration due to gravity and Va is the wind
speed at the reference level zref. The drag coefficients for
the unstable case (Ri<0) are then adjusted to account for
atmospheric stability:
CDm/h=CDNm/h1+24.5-CDNm/hRiRi<0.
Finally, the aerodynamic resistance for sensible and latent heat flux is
given by
ra=1CDhVa.
The aerodynamic resistance for the transfer of heat and water between the
ground and the canopy is parameterized as
ra,can=1-exp-Lai+SaiCcanVa.
The leaf and stem area index factor insures that ra,can
tends to zero when vegetation is vanishing.
The values of the drag coefficient Ccan is given in Table .
Surface resistance to water vapour fluxes
Additionally to the aerodynamic resistances, the flux of water vapour
from the ground or canopy is subject to additional resistances.
For evaporation from bare soil, this surface resistance is represented in
terms of a βs factor.
Different parameterizations of βs
have been proposed to be used in global climate models e.g..
The model results, in particular the geographic distribution and extent of
modelled bare soil, are strongly dependent on the formulation of the
βs factor. Thus, various surface resistance formulations
for bare soil evaporation are implemented in PALADYN with the default
βs depending on top soil moisture (θ1)
and field capacity (θfc) following :
βs=141-cosπθ1θfc2θ1<θfc1θ1≥θfc.
The resistance for transpiration of water through the leaf stomata is coupled
to the uptake of carbon during photosynthesis and is simply the inverse of the canopy
conductance calculated by the photosynthesis module (Sect. )
after conversion to units of ms-1:
rs=1gcan.
Evaporation and sublimation from the canopy and sublimation from snow and ice
are assumed to occur without surface resistance
(rs=0 and βs=1).
Snow and soil temperature
The heat transfer in the snow–soil column is represented by a one-dimensional
heat diffusion equation:
c∂Ts∂t=∂∂zλ∂Ts∂z.
Equation () assumes that the lateral heat transport and vertical
heat transport other than by conduction are small and can be neglected.
Other models include, for example, the vertical heat advection by the water
penetrating into the soil e.g.. Equation ()
also assumes that there are no heat sources inside the soil column.
Heat generated by organic matter decomposition is an example of
internally generated heat e.g..
In Eq. (), c is the volumetric heat capacity and
λ is the thermal conductivity of soil–snow.
Equation () is solved with the ground heat flux as top boundary
condition and zero heat flux at the bottom of the soil column. Eventually
the deep permafrost model of is going to be coupled
to PALADYN with the geothermal heat flux as the bottom boundary condition.
The numerical solution of Eq. () follows the fully
implicit formulation in .
The snow/soil temperature profile is calculated first without
phase change and then readjusted for phase change following .
If the new temperature of snow or of a soil layer containing frozen
water is greater than 0 ∘C, the excess energy is used to melt snow
or frozen soil water.
If all snow is melting during one time step and excess energy is remaining,
this energy is added to the top soil layer.
If soil temperature drops below 0 ∘C, soil water starts to freeze.
Observations show that liquid water exists in the soil at temperatures
well below 0 ∘C because of adsorption forces,
capillarity and ground heterogeneity e.g. and the presence
of solutes e.g.. To allow liquid water to coexist with ice
below 0 ∘C, a freezing point depression is included in the
model and the maximum liquid water content for soil temperatures Ts
below T0=273.15K is formulated as e.g.:
wwmax=ΔzρwθsatLf(Ts-T0)gTsψsat-1/b,
where Δz is the layer thickness, ρw the density
of water, θsat the porosity of the soil, Lf
the latent heat of fusion of water, ψsat is the matric
potential at saturation and b the Clapp–Hornberger parameter (Sect. ).
Snow and soil thermal properties
In winter, snow plays a crucial role in insulating the ground below from the cold
air temperatures. A realistic parameterization of snow thermal properties
is therefore fundamental to simulate frozen soil dynamics. In particular,
PALADYN is very sensitive to the parameterization of snow thermal
conductivity. Hence, several snow thermal conductivity formulations that
are all dependent on snow density are included in the model
. The default snow thermal conductivity
is from :
λsn=λa-1.06×10-5ρsn+3×10-6ρsn2.λa is the air thermal conductivity and the snow density
ρsn is described in detail in Sect. .
The volumetric heat capacity of snow depends on snow density and
specific heat capacity of ice (Ci):
csn=Ciρsn.
Soil heat capacity is a volume-weighted mean of dry soil and liquid and
frozen water:
c=(1-θsat)cs+θwρwCw+θiρiCi,
where cs is the volumetric heat capacity of dry soil (Table ),
θw and θi are the volumetric soil
liquid and frozen water contents, respectively, Cw is the
specific heat capacity of water and ρi is the density of
ice.
Soil model parameters.
cs=2.3× 106Jm-3K-1volumetric heat capacity of soilλs=5.0Wm-1K-1soil heat conductivity at saturationλdry=0.2Wm-1K-1dry soil heat conductivityθsat=0.43m3m-3soil porosityθfc=0.25m3m-3volumetric soil moisture at field capacityθwp=0.14m3m-3volumetric soil moisture at wilting pointψsat=-0.2msoil matric potential at saturationksat=520kgm-2day-1soil hydraulic conductivity at saturationb=6Clapp–Hornberger parameter
Soil heat conductivity is a combination of heat conductivity of water, ice
and dry soil following :
λ=Kλsat+(1-K)λdry,
with
λsat=λs1-θsatλwθwθθsatλiθiθθsat,
where θ is the total (liquid plus frozen) volumetric soil water
content.
The original logarithmic formulation of the Kersten number (K) is
approximated by a linear function of relative soil moisture:
K=11-0.35θθsat-0.35Ts≥0∘CθθsatTs<0∘C.K is limited to be between 0 and 1. λw and λi
are the thermal conductivities of water and ice, respectively.
λs and λdry
are globally uniform soil parameters (Table ).
Alternatively, the values can be chosen to be dependent on soil texture and
soil organic carbon content as described in Appendix .
The inclusion of variable λs and λdry
does not fundamentally affect the main model results; hence, for computational
efficiency the parameters are taken to be uniform in space and
constant in time by default.
HydrologyCanopy water
Re-evaporation of canopy-intercepted water contributes significantly to
the total water flux from the surface to the atmosphere e.g..
Therefore, PALADYN includes a representation of rain and snow intercepted by
vegetation. Rain is assumed to be intercepted only by trees while snow is
intercepted by all PFTs.
The prognostic equations for canopy liquid water (wcanw)
and snow (wcans) are similar and written in terms of canopy interception,
canopy evaporation/sublimation and a canopy water removal term as
dwcanw/sdt=Icanw/s-Ecanw/s-wcanw/sτw/s.
Canopy interception and evaporation are given by
Icanw/s=αintw/sPr/s1-exp-kext(Lai+Sai),Ecanw/s=ρara(qsat(T∗)-qa)fcanw/s.Pr is the rain rate and Ps the snowfall rate.
αintw and αints
are interception factors (Table ).
The wet canopy fraction fcanw and the snow-covered canopy fraction fcans
are assumed to increase linearly with wcanw and wcans,
respectively, up to a maximum water and snow amount that the canopy can hold,
wcanmax=0.2(Lai+Sai)e.g.
τw and τs
are the water and snow canopy removal timescales, respectively (Table ).
Negative canopy evaporation, that is dew deposition, is inhibited.
If skin temperature is greater than 0 ∘C, all snow is removed from the
canopy and added to the snow layer on the ground.
Finally Ecan=Ecanw+Ecans
is diagnosed and used in the solution of the surface
energy balance equation (Eq. ).
The rate of rain and snow reaching the ground is then derived as
Pr/s,g=Pr/s-Ecanw/s-dwcanw/sdt.
The area-weighted Pr/s,g over the vegetated and bare soil
surface tiles are then used as input to the surface hydrology module.
Snow
The snow water equivalent evolution of the single snow layer is determined
by the snowfall rate Ps,g,
the snowmelt rate Ms and sublimation Es:
dwsndt=Ps,g-Ms-Es.
To prevent an indefinite accumulation of snow, wsn is limited
to be below wsn,crit=1000kgm-2 and the snow
excess is added to frozen water runoff.
The density of snow is important because it determines the thickness of snow
and hence influences surface albedo and surface roughness and because it controls
the thermal properties of snow (Sect. ).
The parameterization of snow density is based partly on and
.
The density of freshly fallen snow is temperature dependent following :
ρsn,fresh=ρsn,min+1.7Ta-T0+151.5forT0-15<Ta<T0+2.ρsn,min is the minimum snow density (Table ).
The effect of self-loading on snow compaction is taken into account using
the relation proposed by as implemented in
and the prognostic equation for snow density accounting also for the density
of freshly fallen snow is written as dρsndt=0.5gρsnwsnη+Ps,gρsn,fresh-ρsnwsn,
where η is the viscosity depending both on the load and temperature:
η=η0⋅expkT(T0-Tsn)+kρρsn.
The values of the parameters η0, kT and kρ
are given in Table .
The effects of snow metamorphism and snow melting on snow density are
neglected.
Snow thickness is then computed as
hsn=wsnρsn.
Surface runoff and infiltration
Subgrid-scale surface hydrology is represented using a TOPMODEL approach
as implemented in .
The fraction of a grid cell that is assumed to be at saturation, fsat, is
determined by the grid cell mean water table position (z∇)
and the spatially varying maximum saturated fraction fsatmax
computed by from the compound topographic index (CTI)
derived from the high-resolution ETOPO1 topography as fsat=fsatmaxe-f∇z∇.f∇ is a parameter whose value is given in Table .
If the surface is snow free, the wetland fraction is set equal to the saturated
fraction (fwet=fsat), while it is set to zero otherwise.
The grid cell mean water table depth is estimated directly from the volumetric water
content in the soil column, the peat fraction (fpeat) and
the water table in peat (z∇peat) as
z∇=(1-fpeat)hsoil-∑lθlθsat,lΔzl+fpeatz∇peat.hsoil is the soil column depth and the sum is over all
soil layers. The peat water table is assumed
to follow the grid cell mean seasonal water table variations but with
an amplitude limited to the acrotelm thickness (Sect. ).
The maximum soil infiltration rate is then computed from the saturated
hydraulic conductivity (ksat)
assuming that infiltration can occur only in the unsaturated part of the grid cell:
qinfmax=ksat(1-fsat).
Surface runoff is then calculated assuming that all liquid water that
reaches the surface is rooted directly to runoff over the saturated fraction
of the grid cell and considering that the maximum infiltration rate can not
be exceeded:
Rw=fsat(Pr,g+Ms)+(1-fsat)⋅max0,Pr,g+Ms-qinfmax.
The actual soil infiltration rate is then computed as
qinf=Pr,g+Ms-Rw.
Soil hydrology
Water in the soil is assumed to be limited to flow in the vertical direction.
Making use of the conservation of mass, the change in volumetric water
content over time is then given by the vertical divergence of the water
flux and a sink term from soil water extraction by evapotranspiration (e):
ρwΔzldθw,ldt=ql-1-ql-el,
where l is the soil layer index.
This equation is solved with infiltration (qinf) as top
boundary condition and a free drainage bottom boundary condition, i.e.
the water flux at the bottom of the soil column (qdrain)
is set equal to the bottom hydraulic conductivity.
The soil water flux q is expressed by Darcy's law:
q=k∂(ψ-z)∂z,
where k is the hydraulic conductivity and ψ is the matric potential.
z is the vertical coordinate and is positive downwards from the surface.
The numerical solution of Eq. () follows the formulation
in .
The hydraulic conductivity and the matric potential are soil hydraulic
properties dependent on soil texture and volumetric soil water following
:
ψ=ψsatθwθsat-bk=ksatθwθsat2b+3.
Similarly to the discussion on soil thermal parameters in Sect. ,
hydraulic conductivity and matric potential at saturation,
ksat and ψsat, and the Clapp and Hornberger
parameter b are set to global uniform values by default (Table ).
However, a soil texture and soil organic matter content dependent formulation
of ksat, ψsat and b is also available (Appendix ).
Biogeochemistry and vegetation dynamicsPhotosynthesis
Daily photosynthesis is modelled following the general light use efficiency model
described in as implemented in
the LPJ dynamic vegetation model , with some modifications.
Compared to other models it has the advantage that it computes daily
integrated photosynthesis without the need to explicitly resolve the
diurnal cycle and therefore saves computing time. It also makes it
convenient to be coupled to the physical
PALADYN components, which are also integrated with a daily time step.
Daily gross photosynthesis is computed from a light-limited (JE) and a RuBisCO-limited
rate (JC) as
Ag=JE+JC-(JE+JC)2-4θrJEJC2θrβθ.JE=c1⋅APAR,JC=c2⋅Vm.θr is a shape parameter and APAR is the absorbed photosynthetically
active radiation computed as
APAR=0.5SW↓αa1-e-kextLaiΔt(1-αleaf)cq.
Half of the downwelling shortwave radiation is assumed to be in the
photosynthetically active wavelength range, αa
accounts for reductions in PAR utilization efficiencies in natural
ecosystems, the factor 1-e-kextLai scales
to the canopy, αleaf is the leaf albedo in the PAR
range, Δt is the length of day in seconds and cq
is a conversion factor from Jm-2 to molm-2.
Parameter values are given in Table and
more details on the formulation of c1 and c2 and the maximum daily
rate of net photosynthesis Vm are given in Appendix .
Photosynthesis model parameters .
θr0.7co-limitation parameterαleaf0.17leaf albedo in PAR rangeαa0.5fraction of PAR assimilated at ecosystem levelcq4.6 × 10-6molJ-1conversion factor for solar radiation at 550 nmaC30.015leaf respiration as a fraction of RuBisCO capacity in C3 plantsaC40.02leaf respiration as a fraction of RuBisCO capacity in C4 plants
PFT-specific model parameters.
Broadleaf treeNeedleleaf treeC3 grassC4 grassShrubdr,1root distribution parameter 6.57.011.011.07.0dr,2root distribution parameter 1.52.02.02.01.5αsnfreecan,vis,dirsnow-free visible canopy albedo for direct radiation 0.020.010.040.030.04αsnfreecan,vis,difsnow-free visible canopy albedo for diffuse radiation 0.030.010.050.040.04αsnfreecan,nir,dirsnow-free near-infrared canopy albedo for direct radiation 0.220.180.270.240.20αsnfreecan,nir,difsnow-free near-infrared canopy albedo for diffuse radiation 0.260.190.310.280.21αsncan,vis,dir/difsnow-free visible canopy albedo 0.440.310.700.700.55αsncan,nir,dir/difsnow-free near-infrared canopy albedo 0.330.240.480.480.37Tcmonmin(∘C)minimum coldest month temperature for establishment -17.0––15.5–Tcmonmax(∘C)maximum coldest month temperature for establishment –-5.015.5––gddmin(∘C)minimum gdd for establishment 1200350000Tcmonphen(∘C)coldest month temperature for phenology5.0–0.00.0–Tbasegdd(∘C)base temperature for gdd 5.02.02.05.02.0gddcrit(∘C)gdd for full phenology 300–100100–gmin(mms-1)minimum canopy conductance 0.50.30.50.50.5g1parameter in optimal stomatal conductance formulation 4.02.331.64.0Laimin(m2m-2)minimum leaf area index modified from 11111Laimax(m2m-2)maximum leaf area index modified from 86333SLA(m-2kgC-1)specific leaf area 2010404017γl(yr-1)leaf turnover rate 0.50.31.01.00.5γr(yr-1)root turnover rate0.50.30.50.50.5γs(yr-1)stem turnover rate modified from 0.0050.0050.20.20.05awl(kgCm-2)allometric coefficient2.02.00.010.010.5awhallometric coefficient for plant height3.560.150.171
Leaf respiration, Rd, is scaled to Vm as
Rd=aC3/4Vmβθ,
and daily net assimilation is then calculated as
An=Ag-Rd.
Daytime net assimilation can then be computed by adding nighttime respiration:
And=An+1-dh24Rd.
βθ is a soil-moisture-limiting factor:
βθ=∑lθw,l-θwpθfc-θwprl,θwp and θfc are the soil moisture values
at wilting point and field capacity, respectively. rl is the
fraction of roots in layer l (Sect. ). If the soil
temperature of layer l is below -2 ∘C, the corresponding term
in Eq. () is set to 0.
c1 and c2 depend on the intercellular partial pressure of CO2 (pi),
which is proportional to the atmospheric CO2 concentration (pa):
pi=λcpa.
In LPJ, λc is computed iteratively from potential and
actual evapotranspiration . To reduce the computation cost
and in light of recent developments, in PALADYN λc is
derived from the optimal stomatal conductance model ,
which predicts that canopy conductance for water vapour gcan is given by
gcan=g0+1+g1VPDAndca.VPD is the vapour pressure deficit between leaf surface and ambient air.
Since CO2 has to diffuse trough the stomata into the leaf interior
before being fixed by photosynthesis and at the same time water vapour
diffuses through the stomata from the leaf interior to the canopy air,
gcan and And are also related by
gcan=g0+1.6Andca-ci.ca and ci are the atmospheric and intercellular
CO2 mole fractions and g0 is a minimum canopy conductance:
g0=gmin(1-e-kextLai)βθ.
The values of gmin are given in Table .
From Eqs. () and (), λc can
simply be derived e.g.:
λc=1-1.61+g1/VPD.
To a first approximation, the values of g1 are taken to be constant
PFT-specific parameters (Table ) based on the data
reported in . As will be shown in Sect. ,
based on a simple model, the ratio of ci and ca is also the main
parameter determining the carbon isotopic discrimination during photosynthesis.
Therefore, the PFT-specific discrimination is used as an additional constraint
on g1 values.
Finally, maintenance respiration and growth respiration are computed and
net primary production (NPP) is derived as in .
Vegetation dynamics
There are a number of existing dynamic global vegetation
models spanning a large range of different approaches of varying complexity.
The appropriate model complexity for PALADYN, balancing low computational expenses
and a realistic representation of continental-scale vegetation dynamics,
is represented by the top-down modelling approach of the TRIFFID
dynamic global vegetation model . Another main
advantage of this type of model is that it does not require interannual
climate variability, which can not be provided by a statistical–dynamical
atmosphere model like CLIMBER.
The PALADYN dynamic vegetation scheme is therefore based on TRIFFID.
The model distinguishes five plant functional types: broadleaved trees,
needleleaved trees, C3 and C4 grass and shrubs.
Vegetation carbon Cv and fractional area coverage ν of each PFT i are
described by a coupled system of first order differential equations
based on the Lotka–Volterra approach for modelling competition between species:
dCv,idt=(1-λNPP,i)NPPi-Λloc,i,dνidt=λNPP,iNPPiCv,iνi,∗1-∑jcijνj-γν,iνi,∗.νi,∗=max(νi,νseed), where νseed
is a small seeding fraction used to ensure that a PFT is always seeded (Table ).
λNPP is a factor determining
the partitioning of NPP between increase of vegetation carbon of the
existing vegetated area (Eq. ) and spreading of the given
PFT (Eq. ) and is given by
λNPP=0Lai,b<LaiminLai,b-LaiminLaimax-LaiminLaimin≤Lai,b≤Laimax1Lai,b>Laimax.Lai,b is the balanced leaf area index that would be reached if the
plant was in full leaf and Laimin and Laimax
are PFT-specific parameters (Table ).
Λloc is the local litterfall rate:
Λloc=Λl+γrCv,r+γsCv,s.
Litterfall from leaf turnover is given by Λl=γlCv,l for evergreen plants
and is computed from the phenological status (Sect. )
for deciduous plants. The γ values are PFT-dependent turnover rates of
leaf, root and stem carbon (Table ).
Vegetation carbon Cv is directly related to the balanced leaf
area index through the relations of leaf (Cv,l), root (Cv,r)
and stem (Cv,s) carbon to Lai,b:
Cv,l=Lai,bSLA,Cv,r=Cv,l,Cv,s=awlLai,bbwl.Cv=Cv,l+Cv,r+Cv,s.SLA is the specific leaf area (one-sided leaf area per leaf carbon mass) and is PFT dependent following
(Table ). awl is a PFT-specific allometric
coefficient (Table ). In TRIFFID, a value of bwl=5/3
is used , although suggest bwl=4/3.
In PALADYN, bwl=1 is assumed, which greatly simplifies the
solution of Eq. (), and the awl values are
adjusted accordingly to compensate for the change in bwl.
The competition coefficients, cij, represent the impact of
vegetation type j on the vegetation type of interest i. TRIFFID is
based on a tree–shrub–grass dominance hierarchy with dominant types i
limiting the expansion of subdominant types j (cji=1), but not
vice versa (cij=0). While in TRIFFID the tree types and grass types
co-compete with competition coefficients dependent on their relative heights,
in PALADYN they compete only based on their NPP (cij=0.5 and cji=0.5).
Additionally, in PALADYN we implemented a dependence of the competition
coefficients on bioclimatic limits, i.e. the coldest month temperature
(Tcmonmin/max) and growing degree days
(gddmin) as given in Table .
In a given grid cell, PFTs outside of the bioclimatic limits are not
competitive and will be dominated by other PFTs, regardless of the
tree–shrub–grass dominance.
Dynamic vegetation model parameters.
νseed=0.001vegetation seed fractionγν,min=0.002yr-1minimum vegetation disturbance rateτfire=10yrfire return timescaleθcrit=0.15m3m-3critical soil moisture for fire disturbanceCv,low=0.2kgCm-2minimum aboveground vegetation carbonfor fire disturbanceCv,high=1.0kgCm-2maximum aboveground vegetation carbonfor fire disturbance
The last term in Eq. () represents vegetation disturbance.
In TRIFFID, the disturbance rate γν is taken
to be a constant PFT-specific parameter. In reality, on a global scale,
disturbance is mainly caused by fire, which shows a strong dependence on
climatic conditions and fuel availability e.g..
We therefore introduce a simple parameterization for fire disturbance based on
top soil moisture and aboveground biomass loosely following
and :
γν=γν,min+1τfiremax0,θcrit-θ1θcrit⋅max0,min1,Cv,ag-Cv,lowCv,high-Cv,low.γν,min is a minimum constant disturbance
rate intended to represent disturbances other than fire (e.g. windthrow,
, and insect outbreaks, among others, e.g. )
(Table ).
τfire is a characteristic fire return timescale, θcrit
is the critical soil moisture below which fires can occur and Cv,low
and Cv,high are values of aboveground biomass (Cv,ag)
that define the fuel availability limitation function. All parameter values
are listed in Table .
Vegetation height is assumed to vary linearly with the balanced leaf area index:
hv=awhLai,b.awh is a PFT-specific factor that relates
vegetation height with the balanced leaf area index (Table ).
awh values are selected to give plant heights in accordance with
data in . The stem area index, Sai, is taken to be 1/10 of Lai,b.
The dynamic vegetation model has a monthly time step.
Phenology
The phenology of the PFTs is controlled by the coldest month temperature
following .
If the coldest month temperature falls below a PFT-specific value
Tcmonphen (Table ), then the PFT in the grid cell
is assumed to be deciduous and Lai is computed from
Lai=ϕLai,b.ϕ increases linearly with the growing degree days (gdd) above a PFT-specific
base temperature Tbasegdd, at a PFT-specific rate
determined by gddcrit:
ϕ=gddgddcrit.
After ϕ reaches its maximum value of 1, it remains constant until
the air temperature drops below Tbasegdd. Then
leaf senescence starts when the temperature drops below
Tbasegdd and continues until all leaves are
lost to litter at 5 ∘C below Tbasegdd.
Raingreen phenology is not represented in the model.
Needleleaf trees are assumed to always be evergreen, independently of the climatic conditions. Given the relatively low
specific leaf area of needleleaf trees (Table ), they would not be competitive
in very cold regions if they were deciduous. In reality, deciduous
needleleaf trees have a much higher specific leaf area , which allows them to be competitive.
However, since evergreen and deciduous needleleaf trees are represented by a
single PFT in the model, the different traits of evergreen and deciduous trees cannot be distinguished.
Root distribution
The vertical distribution of roots in the soil plays an important role in
land surface models. It determines the water that is accessible by the plants
and hence controls the exchange of water between the surface and the atmosphere.
Water availability affects also plant productivity and consequently plays
an important role in the competition between plant functional types.
It also controls the vertical distribution of root litter input to the soil
which is an important factor determining vertical soil carbon distribution.
In PALADYN, we adopt the root distribution scheme proposed by .
The root fraction in each soil layer (rl) is derived from
the cumulative root fraction:
r(z)=1-0.5e-dr,1z+e-dr,2z.dr,1 and dr,2 are PFT-specific parameters (Table ).
Soil carbon
Traditionally, in terrestrial biosphere models, soil carbon has been represented
in terms of vertically integrated pools. Only recently vertically discretized
soil carbon has started to be included in these models e.g..
Vertically integrated models are unable to
represent soil carbon dynamics in permafrost areas, where only part of the
carbon stored in the soil column is affected by the seasonal thawing of
the upper soil. Large quantities of carbon are stored in the permanently
frozen soils around the Arctic
and to model the dynamics of this carbon stock it is necessary to
include carbon separately in different soil layers.
A proper representation of the permafrost carbon pool is important
especially for carbon cycle modelling over long timescales.
Therefore, PALADYN has carbon distributed over the different soil
layers where temperature and soil water are also computed.
Additionally, each grid cell distinguishes between soil carbon in four
different soil columns: mineral soil carbon and peat carbon below the
vegetated surface tile, buried carbon below ice sheets and shelf carbon
below the water on the ocean shelf (Fig. c).
Each layer generally contains three carbon pools with different
decomposability (Fig. ). For unfrozen mineral
soil carbon, the three pools are organized into litter, fast and slow carbon
following .
This structure is modified for peatlands, perennially frozen soils and
buried carbon.
Seasonal variation of zonal mean net radiation at the surface
modelled by PALADYN (left) and from ERA-Interim reanalysis
(middle). Right: modelled zonal annual mean net surface radiation compared to
ERA-Interim reanalysis .
The generic prognostic equations for litter, fast and slow soil carbon
pools are written as
∂Clit(z)∂t=Λ(z)-klit(z)Clit(z)+∂∂zD(z)∂Clit∂z+∂∂zA(z)Clit∂Cfast(z)∂t=(1-flitresp)flit→fastklit(z)Clit(z)-kfast(z)Cfast(z)+∂∂zD(z)∂Cfast∂z+∂∂zA(z)Cfast
∂Cslow(z)∂t=(1-flitresp)flit→slowklit(z)Clit(z)-kslow(z)Cslow(z)+∂∂zD(z)∂Cslow∂z+∂∂zA(z)Cslow.
Litter carbon is increased by litterfall Λ(z). A fraction flitresp
of the decomposed litter carbon goes directly into the atmosphere, while the
rest goes partly into the fast carbon pool (flit→fast)
and partly into the slow carbon pool (flit→slow) (Table ).
Each carbon pool decomposes at a specific rate k, which depends on soil
temperature and soil moisture. The vertical redistribution of soil carbon
between soil layers is represented as an advective–diffusive process
with diffusivity D(z) and advection velocity A(z).
Soil carbon model parameters.
flitresp=0.7fraction of decomposed litter carbon going to atmosphere flit→fast=0.985fraction of decomposed litter transferred to fast carbon pool flit→slow=0.015fraction of decomposed litter transferred to slow carbon pool Dbio=1×10-4m2year-1bioturbation rate Dcryo=5×10-4m2year-1cryoturbation rate klit,10=2.86yr-1litter carbon turnover rate at 10 ∘C kfast,10=33.3yr-1fast soil carbon turnover rate at 10 ∘C kslow,10=1000yr-1slow soil carbon turnover rate at 10 ∘C kacro,10=30yr-1acrotelm carbon turnover rate at 10 ∘Ckcato,10=1000yr-1catotelm carbon turnover rate at 10 ∘C kacro→cato=15×10-3yr-1catotelm formation rate fθ,peat=0.3soil moisture factor for peat carbon decomposition rate at saturation ρacro=20kgCm-3acrotelm carbon density ρcato=50kgCm-3catotelm carbon density Cacro,crit=5kgCm-2minimum acrotelm carbon content for catotelm formation Cpeatcrit=50kgCm-2minimum peat carbon content for peat survival fpeatmin=0.001minimum peatland fractiondCpeatdt|crit=10-3kgCm-2yr-1minimum peat carbon uptake for peat survival fCH4:Cwet=0.07fraction of carbon respired as methane from wetlands fCH4:Cpeat=0.2fraction of carbon respired as methane from peatlands
December–January–February (left) and June–July–August (right)
surface albedo as modelled by PALADYN (top) and derived from MODIS data
(bottom). The displayed surface albedo is a weighted mean
of visible and near-infrared broadband albedo for diffuse radiation. Spatial
correlation between model and data (corr) and root mean square error (RMSE)
are indicated in the top panels.
Over the vegetated grid cell part, the local litter, the litter
originating from competition between the PFTs and the litter from large-scale
disturbances are aggregated to give an average litterfall
(Λveg(z)) as in . Litter from the roots
is added to the different soil layers depending on the root fraction in
each layer, while litter from leaves and stem is added to the top soil layer.
When ice sheets are expanding into vegetated areas, a fraction
fveg→bur of the vegetation carbon
is assumed to be directly buried below the ice and the remaining is added
to the litter pools of the vegetated part:
Λbur(z)=fveg→burCv‾(z)ΔficeΛveg(z)=(1-fveg→bur)Cv‾(z)Δfice.Cv‾(z) is the mean vegetation carbon content of
the vegetated grid cell part in the different soil layers. For the purpose
of litter computation the aboveground vegetation carbon is considered to
be part of the top soil layer. Δfice is the increase of
ice sheet fraction in the grid cell.
When sea level is rising and shelf areas become flooded, the flooded
vegetation is assumed to die instantaneously and vegetation carbon is
added directly to the shelf litter pool:
Λshelf(z)=Cv‾(z)Δfshelf,
where Δfshelf is the increase in shelf fraction.
Vertical carbon diffusivity in unfrozen mineral soils is assumed to be
determined by bioturbation and D(z)=Dbio following
(Table ). In permafrost areas, the diffusivity represents
cryoturbation in the active layer. D(z) is set to a constant value in
the active layer and is assumed to linearly decrease below it to a value
of zero at a multiple (nal) of the active layer thickness zal:
D(z)=Dcryoz≤zalDcryo1-z-zal(nal-1)zalzal<z≤nalzal.
The value of Dcryo is given in Table .
To represent the effects of sedimentation on vertical carbon
movement in the soil an advection term is also included in Eqs. (), () and (),
similar to what has been introduced by and .
The advection velocity (A) is set to zero for now.
The decomposition rates for mineral soil carbon depend on temperature,
liquid water content in the soil layers and the inundated fraction of the grid cell:
kxmin(z)=(1-finun)kx,10fT(z)fθ(z)+finunkx,10fT(z)fθ,sat(z),
for x=lit,fast,slow. The inundated grid cell fraction is the
wetland fraction with the peatland fraction removed,
finun=fwet-fpeat.
klit,10, kfast,10 and kslow,10 are
the litter, fast and slow carbon decomposition rates at 10 ∘C and
field capacity and are given in Table . The temperature
dependence follows a modified Arrhenius equation :
fT(z)=exp308.56156.02-146.02+Ts(z)-T0.
The soil moisture dependence is taken from and
gives a linear increase of the decomposition rate up to field capacity
and a hyperbolic decrease above field capacity:
fθ(z)=θw(z)θfcθw(z)≤θfcθfcθw(z)θw(z)>θfc.
The soil moisture dependence factor for inundated land, fθ,sat,
is simply the value of fθ at saturation.
PALADYN allows for the possibility to effectively treat the carbon in
frozen soils as inert. If inert permafrost carbon is switched on,
the decomposition rates in Eq. () are additionally
weighted by a frozen soil factor, finert:
kxmin(z)=(1-finert(z))kxmin(z)+finert(z)kinert,
for x=lit,fast,slow.
All carbon is assumed to be inert if the fraction of frozen water in a
layer exceeds ffrz,crit:
finert(z)=min1,1ffrz,critθiθi+θw.
Therefore, in soil layers where at least a fraction ffrz,crit
of water is frozen all year round, carbon is effectively decomposing at the very
low rate kinert.
More details on the parameterization of carbon dynamics below ice sheets and
on the ocean shelf and of permafrost carbon will be given in a future paper
dedicated to processes active on glacial–interglacial cycle timescales.
Peatlands
Peat carbon is treated slightly differently from the other carbon pools.
We follow the approach of and distinguish between a
surface litter layer and an acrotelm layer where carbon is decomposed partly
under oxic and partly under anoxic conditions, depending on the position of
the water table. Both litter and acrotelm are assumed to be contained in
the top soil layer. In the layers below the catotelm, decomposition occurs
without oxygen all year round.
The prognostic equations for peat litter, acrotelm and catotelm carbon are
∂Clitpeat∂t=Λpeat-klitpeatClitpeat∂Cacro∂t=(1-flitresp)klitpeatClitpeat-kacro→catoCacro-kacroCacro∂Ccato(z)∂t=kacro→catoCacro-kcato(z)Ccato(z).
The transfer from acrotelm to catotelm carbon occurs only once a critical
acrotelm carbon content Cacro,crit=5kgCm-2 is
reached, as suggested by . Typical acrotelm carbon densities
are around 20 kgCm-3, so this threshold roughly corresponds to
assuming that transfer to the catotelm starts when the acrotelm reaches a
thickness of 25 cm, which is a typical value of observed acrotelm
thickness. When this threshold is exceeded, acrotelm carbon is transferred to
the catotelm in the second soil layer. Peat is assumed to grow thicker by
accumulating carbon on top and therefore in the model the catotelm is shifted
to lower soil layers once the catotelm carbon density ρcato
has been exceeded in a given layer. For the same reason, the vertical
diffusivity of peat carbon is set to 0. Litterfall over peatlands is assumed
to be the same as over mineral soil, but to be added to the top soil layer
only: Λpeat=∑zΛveg(z). The
decomposition rates for litter, acrotelm and catotelm are given by
klitpeat=klit,10fT(1)(foxic+(1-foxic)fθ,peat)kacro=kacro,10fT(1)(foxic+(1-foxic)fθ,peat)kcato(z)=kcato,10fT(z)fθ,peat.
Since peatland soil temperature is not separately computed by the model,
the temperature factor is calculated using the grid cell mean temperature.
fθ,peat is taken to be equal to 0.3 as in
and . The values of the reference decomposition
rates are given in Table .
The fraction of litter and acrotelm that is respiring in oxic conditions,
foxic, is determined from the mean grid cell water table depth z∇
and the minimum monthly water table position z∇min assuming
that the seasonal water table variations in the peatland fraction follow
the grid cell mean water table and that the amplitude of water table
variations in peatland is reduced compared to the grid cell mean and
limited to the acrotelm thickness:
foxic=minzacro,max0,z∇-z∇minzacro.
Peatland expansion and contraction is modelled partly following
. The grid cell fraction that is wetland for at least
3 months of the year is considered to be potential peatland area
fpeatpot.
The actual peatland area fpeat is simulated as
fpeat,n+1=min(1+r)fpeat,n,fpeatpotifdCpeatdt≥dCpeatdt|critorCpeat≥Cpeatcrit,max(1-r)fpeat,nfpeatminifdCpeatdt<dCpeatdt|critandCpeat<Cpeatcrit.
Peat is expanding if the annual mean rate of carbon uptake
(dCpeat/dt) is greater than
a critical value dCpeat/dt|crit
or if peat carbon exceeds a value Cpeatcrit;
otherwise peatland area is shrinking.
To account for inertia in lateral peatland expansion and contraction,
the relative areal change rate is limited to 1 %yr-1 (r=0.01yr-1).
When the peat area is changing, carbon is simply redistributed between
mineral soil and peat carbon pools, layer by layer, with the following rules:
Clitpeat↔Clit,
Cacro↔Cfast and
Ccato↔Cslow. A minimum peatland
extent in every grid cell (fpeatmin) insures that
peatlands are always “seeded”.
Methane emissions
Methane emissions are simulated as a constant fraction of heterotrophic
respiration when respiration occurs under anaerobic conditions, as is the
case in wetlands, peatlands and flooded ocean shelves. The fraction of carbon
that is respired as methane, fCH4:C, is different for wetlands,
peatlands and ocean shelves (Table ).
Carbon isotopes: 13C and 14C
The stable carbon isotope 13C and radiocarbon 14C are tracked
in PALADYN trough all carbon pools in vegetation and soil.
Discrimination is simulated only during photosynthesis and follows
the model outlined in .
The discrimination factor Δ for C3 and C4 photosynthesis is given by
Δ=4.4ca-cica+27cicaC34.4ca-cica+(-5.7+20⋅0.35)cicaC4.
Radiocarbon decay is ignored in the vegetation carbon pools because of
their fast turnover time relative to the 14C decay rate.
In all soil carbon pools, radiocarbon has a half life of 5730 years.
Global values of relevant model quantities over the time period 1981–2010 compared to observation-based estimates.
ModelObservation-based estimatesEvapotranspiration (×1015kgyr-1)7164–73 Runoff (×1015kgyr-1)3738–40 Permafrost area (mlnkm2)1613–18 GPP (PgCyr-1)132115–131 NPP (PgCyr-1)7042–70 Vegetation carbon (PgC)580470–650 Top metre soil carbon (PgC)1170890–1660 Soil carbon in permafrost area (PgC)5551100–1500 Peat carbon (PgC)510530–694 Maximum monthly wetland area (mlnkm2)5.15 Peatland area (mlnkm2)3.84.4 Total CH4 emissions (TgCH4yr-1)160115–215 Tropical CH4 emissions (TgCH4yr-1)9663–119 Extratropical CH4 emissions (TgCH4yr-1)7239–89
Climate forcing fields needed to run PALADYN in offline mode.
Surface air temperatureSurface air specific humidityDownwelling shortwave radiation at the surfaceDownwelling longwave radiation at the surfaceRainfallSnowfallWind speedSurface pressureModel spinup
Some of the processes related to vegetation and soil carbon dynamics
have very long intrinsic timescales, and therefore long simulations
of at least 10 000 years would be required to get the system into an
equilibrium state with prescribed boundary conditions.
Even though this is, in principle, feasible with
PALADYN, it is in fact impractical for test and tuning purposes.
Therefore, the possibility to run the vegetation
and carbon cycle modules with an artificially high internal integration
time step of 1000 or more years is implemented in PALADYN.
This is possible due to the fully implicit
formulation of the model components. In this equilibrium spinup mode,
the vegetation and carbon cycle modules are called only at the end of
each simulation year but using annually cumulated NPP and litterfall and
annual mean decomposition rates for soil carbon.
Using the equilibrium spinup mode brings the model close to equilibrium
already after around 100 years of simulation. A period of 100 years is also the
spinup time required to bring the physical state of the land model,
particularly permafrost related processes, into equilibrium with climate.
The equilibrium spinup mode can however not be applied to processes which
are intrinsically out of equilibrium such as peatlands and inert
permafrost carbon. To get the present state of these pools a
transient simulation over at least one glacial cycle is required.
Evaluation
In this section, the performance of PALADYN for the present day is presented
and discussed. The model is designed for large-scale applications, and
therefore the model evaluation is done at a global scale, although in
principle it would be possible to run the model in a single column mode
forced with site-level observations.
For the model evaluation, an offline transient simulation from 1901 to
2010 is performed. In offline mode, PALADYN needs several monthly climate
fields as input as listed in Table . In addition, the
annual atmospheric CO2 concentration has to be provided.
For the historical simulation of the past century the WATCH climate forcing
based on ERA-40 and
ERA-Interim reanalysis combined with GPCC precipitation
is used. CO2 is prescribed from
combined with Mauna Loa data .
Seasonal variation of zonal mean sensible heat flux modelled by
PALADYN (left) and from ERA-Interim reanalysis (middle).
Right: modelled zonal annual mean sensible heat flux compared to ERA-Interim
reanalysis .
Seasonal variation of zonally integrated evapotranspiration modelled
by PALADYN (left) and estimated by (middle). Right:
modelled zonal annual mean evapotranspiration compared to observation-based
estimates from and ERA-Interim reanalysis
.
Before running the transient experiment, the model is spun up for 30 000 years with the mean 1901–1930
climate as forcing and the 1901 CO2 concentration of 295 ppm.
To get a rough estimate of peatland area and carbon, during the first 4000 years of this spinup phase, the peatland module is enabled to allow
peatlands to establish. For the rest of the spinup phase peat carbon is kept constant.
Finally, the model is run in transient mode for the historical period forced with
annually varying climate and CO2 concentrations. Peatland
area is kept constant during this phase but peat carbon is interactive.
Depending on the time interval covered by the different observational
data products, the model climatology over the given time period is
computed and used to evaluate the different model components, as
described next.
Partitioning of modelled total annual evapotranspiration between
transpiration (top), surface evaporation (middle) and canopy evaporation
(bottom). The global percentage of each component is shown above the
corresponding plot.
Physical processes
The modelled net radiation absorbed at the surface is in good agreement
with reanalysis data both for the seasonal cycle and the annual mean (Fig. ).
With the downwelling shortwave and longwave radiation used as forcing,
the net surface radiation is determined by the modelled surface
emissivity and albedo. The surface albedo for winter and summer is well
simulated in the model (Fig. ).
A correct partitioning of the absorbed radiation between sensible, latent and
ground heat flux is of fundamental importance for a land model. The modelled
sensible heat flux compares well with ERA-Interim reanalysis data except for
the tropics, where it is systematically overestimated, and for the
subtropics, where it is underestimated in the model (Fig. ).
Evapotranspiration, and therefore the latent heat flux, tends to be
overestimated by the model everywhere except for the tropics when compared to
estimates from (Fig. ). However, it is in
good agreement with ERA-Interim. This is to be expected because
evapotranspiration strongly depends on surface air conditions which are used
to force the model, which are based on ERA-Interim. The discrepancy between
model and (model-based) estimates from might therefore
reflect a deficiency in the forcing rather than in the model. Modelled annual
global land evapotranspiration is
71 × 1015kgyr-1, in the range of observational
estimates (Table ).
Evapotranspiration is the sum of transpiration from vegetation, surface
evaporation and canopy interception and re-evaporation. The partitioning
of total evapotranspiration between the different components is shown in
Fig. . Transpiration is dominant in the tropics
and generally in densely vegetated areas. A significant amount of
precipitation is directly re-evaporated back to the atmosphere from plant
canopies, particulary in the tropics and over the boreal forest. Surface evaporation is the only
process acting in desert regions. Globally, transpiration, surface evaporation
and canopy evaporation account for around 50, 30 and 20 % of total
evapotranspiration, respectively.
This compares favourably with , who estimated
total global evapotranspiration to be partitioned in 48 % from
transpiration, 36 % from soil evaporation and 16 % from canopy
interception and re-evaporation using an ensemble of land surface models.
Seasonal variation of zonally integrated water runoff modelled by
PALADYN (left) and observations from UNH/GRDC (middle).
Right: modelled zonal annual mean runoff compared to observation-based
estimates from . Modelled and observed runoff is averaged
over the time period 1979–2010.
As a consequence of the overestimation of evapotranspiration, simulated
runoff is underestimated over Northern Hemisphere midlatitudes
(Fig. ). Compared to data from , the
modelled NH runoff from melting snow in spring tends to be less concentrated
to May and June and more gradually distributed over the whole summer
season. Global annual runoff is 37 × 1015kgyr-1 (Table ).
December–January–February (left) and June–July–August (right)
soil moisture. The modelled soil moisture (top) is the volumetric soil
moisture of the top soil layer (top 20 cm). The observed soil
moisture is from ESA-CCI and represents the
moisture content of the top few centimetres of soil. Snow-covered regions are
masked out. Spatial correlation between model and data (corr) and RMSE are indicated between the panels.
Modelled December–January–February (DJF) and June–July–August (JJA)
soil moisture shows generally a good agreement with
estimates from satellite data in the tropics,
while the model tends to simulate a dryer top soil in high northern
latitudes (Fig. ). This is partly a consequence of using a globally uniform soil porosity.
However, it has to be mentioned that the satellite data are
representative for the soil moisture of the top few centimetres of soil,
while the top model soil layer is 20 cm thick.
Monthly maximum wetland fraction over the time interval 1993–2007
as modelled by PALADYN (top) and inferred by GIEMS
(bottom).
Mean seasonal global wetland extent over the time interval
1993–2007 as modelled by PALADYN and inferred by GIEMS
.
The mean annual simulated wetland area is 3 mlnkm2. Some features
of the maximum monthly wetland extent are reasonably well captured by the
model (Fig. ). Compared to the multi-satellite product from
GIEMS the model simulates larger wetland extent
in tropical forest areas and northern peatland areas. However, if compared to
other wetland products based on data other than from satellite, GIEMS is
underestimating wetlands below dense forests (e.g. the Amazon forest)
() and in peatland regions of northern Canada and eastern
Siberia . In southeast Asia, the GIEMS wetland extent also
includes extensive rice cultivation areas, which are not represented in the
model. The modelled seasonal variation in global wetland area is in very good
agreement with GIEMS (Fig. ).
February to May snow water equivalent mean over the period
1980–2010 for PALADYN (top) compared to data from the GlobSnow project
(bottom). Spatial correlation between model and
data (corr) and RMSE are indicated in the top
panels.
Mean 1980–2010 seasonal evolution of the total Northern Hemisphere
snow mass compared to data from the GlobSnow project
.
Northern Hemisphere March snow mass anomalies from 1980 to 2010
compared to data from the GlobSnow project .
Left: modelled permafrost extent and active layer thickness compared
to the observed extent of continuous, discontinuous and isolated permafrost
(red lines, from dark red to light red) from . Right:
comparison of modelled (top) and observed (bottom) active layer thickness
over Yakutia. Active layer thickness data are from . The
modelled active layer thickness is calculated as the mean over the period
1981–2010 in grid cells that are permafrost during the whole time period.
Mean annual gross primary production (GPP) over the time interval
1980–2010 as modelled by PALADYN (top) and estimated by the model tree
ensemble approach (MTE) (bottom). Spatial
correlation between model and data (corr) and RMSE
are indicated in the top panel.
Net land carbon uptake for the historical simulation compared to
observations from IPCC.
The NH spring evolution of snow mass is compared to the GlobSnow dataset
in Fig. . The spatial
distribution of snow is well captured by the model. However, the model
tends to melt snow slightly too late in spring, as highlighted also by the seasonal
evolution of the total NH snow mass (Fig. ).
The overestimation of snow mass in spring is a feature common to many state-of-the-art
Earth system models .
The interannual variability of spring snow
over the NH is also largely in agreement with the GlobSnow data,
suggesting that the model has a reasonably good sensitivity
(Fig. ).
Modelled permafrost area is around 16 mlnkm2, which compares well
with observations (Table ).
The permafrost extent over Siberia and northern Canada are generally
well simulated by the model (Fig. ). Also the
active layer thickness over the Yakutia region is consistent with the
data from (Fig. ).
Biogeochemistry
The modelled annual mean gross primary productivity is compared to estimates
from , and in Fig. . Model and
data are generally in good agreement, except over the Amazon where the
model underestimates GPP. However, experiments using different climate
forcings show a much better agreement between modelled and observed
GPP over the Amazon basin, similarly to what shown by (not shown).
The simulated global annual
GPP of 133 PgCyr-1 is in the upper range of current estimates
(Table ).
Comparison of modelled plant functional types fraction (left) with
potential vegetation distribution adapted from as described
in Appendix (right).
The net global land carbon flux over the time period 1959–2010 is shown
in Fig. . The model is able to reproduce some of the
interannual variability in the net land carbon uptake, indicating that
the sensitivities of net primary production and soil respiration to
interannual climate variations are reasonably well represented in the model.
The dependence of the average percent coverages of PFTs on annual
precipitation in the model (top) compared to land cover data from MODIS
and precipitation from GPCC
(bottom). MODIS data are at
1 min spatial resolution and GPCC data are
interpolated to the MODIS data grid from the original 1∘ resolution.
MODIS data additionally include savanna as a land cover type, which is not
included in the model.
Comparison of modelled maximum annual leaf area index (top) with
observational estimates from MODIS (bottom). Spatial
correlation between model and data (corr) and RMSE
are indicated in the top panel.
Seasonality of leaf area index for different latitudinal bands in
the Northern Hemisphere as indicated in the individual panels. The modelled
seasonality (continuous lines) is compared to MODIS data (dashed lines)
.
Comparison of modelled vegetation carbon content (top) with the
observational estimates from the NDP-017b dataset
(bottom). Spatial correlation between model and data (corr)
and RMSE are indicated in the top panel.
The modelled potential vegetation distribution for the present day is
shown in Fig. , where it is compared to potential
vegetation estimates from . In general, the model has the
tendency to overestimate the areas covered by broadleaf trees in the
tropics. The boreal needleleaf forest is well reproduced by the model.
PALADYN tends to overestimate the shrub coverage, particulary over the NH,
while the area covered by grasslands is lower than in .
Desert area is overestimated over Australia.
Since vegetation cover strongly depends on the amount of precipitation, it
is useful to evaluate the ability of the model to reproduce the
observed PFT distribution as a function of precipitation .
The modelled bare soil fraction as a function of annual precipitation
perfectly matches the observed distribution (Fig. ).
As opposed to observations, the model tends to simulate more grass than
shrubs in arid regions. Where annual precipitation exceeds ≈ 500 mmyr-1
trees start to become the dominant PFT, both in model and observations.
In addition to the five PFTs represented in PALADYN, the land cover dataset
from MODIS, which is used as a reference in Fig. ,
also includes savanna as a land cover type. In the model, the space covered by
savanna is mostly occupied by forests, but partly also by shrubs and to a lesser
extend by grasslands. Overall the sensitivity of the different PFTs to precipitation is well
captured by the model.
Modelled annual flux-weighted discrimination during photosynthesis.
The annual maximum leaf area index is compared to estimates from MODIS
in Fig. . The modelled maximum LAI is generally higher than in MODIS,
particularly in the Tropics, in high northern latitudes and in arid regions.
The seasonality of the leaf area index over the Northern Hemisphere is
well simulated at latitudes south of 50∘ N, but is largely underestimated
north of 50∘ N (Fig. ) compared to MODIS data. This is because the latitudinal belt
between 50 and 70∘ N is dominated by evergreen needleleaf forests which have no
LAI seasonality in the model, while MODIS LAI is close to zero almost everywhere
in high northern latitudes during winter. The reduced LAI seasonality over the
boreal forest compared to observations is a common feature of many LSMs
and is possibly an artifact of
poor satellite data quality during winter .
Comparison of modelled and observed discrimination during
photosynthesis for different plant functional types. Observational data are
from .
Global modelled vegetation carbon is 580 PgC, comparable to
observations (Table ).
The geographic distribution of vegetation carbon content is in good
agreement with data from (Fig. ), but
is overestimated in tropical forests and underestimated in arid regions.
Top 1 m soil carbon as modelled by PALADYN (top) and derived
from the Harmonized World Soil Database (bottom). Spatial
correlation between model and data (corr) and RMSE
are indicated in the top panel.
The annual mean GPP-weighted isotopic discrimination during photosynthesis is shown in Fig. .
As expected, the lowest values are found in regions dominated by C4 grasses
in subtropical Africa and Australia. The highest discrimination values
are found in the tropical forests and in high northern latitudes, similar
to the results shown in .
Mean discrimination for each plant functional type is also compared with
observations from in Fig. . The
model successfully reproduces the observed differences in discrimination
between different PFTs, although it tends to consistently overestimate
the discrimination for all PFTs.
Comparison of modelled (top) soil carbon in northern permafrost
regions with estimates from the Northern Circumpolar Soil Carbon Database
(NCSCD) (bottom) for two
depth ranges: (left) 0–30 cm and (right) 0–100 cm. Spatial
correlation between model and data (corr) and RMSE
are indicated between the panels.
Peat fraction as modelled by PALADYN (left) compared to estimates
from the Northern Circumpolar Soil Carbon Database (NCSCD)
(right). The permafrost area
as defined in NCSCD is shown as a black line. No data are available from the
NCSCD dataset outside this area.
Top metre soil carbon from the HSWD dataset is well
reproduced by the model in the tropics (Fig. ). In high
northern latitudes, the model carbon content is higher than in the HSWD
dataset (Fig. ) but lower than in the NCSCD soil carbon
dataset for the permafrost region
(Fig. ).
The model underestimates carbon in peatland areas of the NH. Northern
permafrost areas store large amounts of carbon at depths greater than
1 m. The NCSCD soil carbon dataset contains estimates of soil carbon
down to a depth of 3 m in the permafrost regions. As expected, the
model in the setup used in the presented simulations can not reproduce the
large amounts of carbon stored in perennially frozen ground below 1 m
because the inert permafrost carbon pool is not included (not shown). To get
the carbon accumulation in permafrost, a transient simulation over at least
the last glacial cycle would be required. This is beyond the scope of this
work, but will be discussed in a future paper. Similarly to the discussion on
permafrost carbon, a proper estimate of peatland area and carbon content
would also require a long transient simulation. However, an attempt has been
made to estimate the peatland area and carbon using the equilibrium spinup
described above. The estimated peatland area from this idealized approach is
compared to NCSCD data in
Fig. .
Total modelled natural methane emissions for the present day are 160 TgCH4yr-1.
From these, 86 TgCH4yr-1 are from the tropics and 72 TgCH4yr-1
from the extratropics. These values compare well with recent estimates of
natural methane emissions (Table ). The spatial distribution
of annual methane emissions is shown in Fig. .
Conclusions
The PALADYN model presented here represents a new tool to model the land
processes which are relevant for climate and the carbon cycle on timescales
from years to millions of years.
Modelled annual methane emissions.
PALADYN serves as a land surface scheme, soil model, dynamic vegetation
model and land carbon cycle model. It also includes a representation of peatlands
and soil carbon pools in frozen ground. Compared to other land surface
models, it has the great advantage that all components are consistently
coupled.
Furthermore, PALADYN includes a representation of
the processes related to changes in land–ice–shelf area, making it
suitable for simulations over timescales where sea level and ice sheet
areas can not be considered as fixed boundary conditions. PALADYN is
therefore designed to be included in Earth system models of intermediate
complexity.
On a single CPU the model in its standard configuration (daily time step,
5 × 5∘ horizontal resolution and five soil layers) integrates 1 year
in about 1 s (or equivalently about 100 000 model years per day),
allowing to simulate, e.g. one glacial cycle in 1 day.
It is therefore indicated for paleoclimate applications or to perform
large ensembles of simulations to explore uncertainties and sensitivities.
PALADYN in its offline version has been shown to perform well
at reproducing a number of key characteristics of the present-day land surface,
soil, vegetation and land carbon cycle and is therefore ready to be
included in Earth system models in a coupled setup.
Code availability
The model code is available upon request from the authors.
Data availability
The ISLSCP II Monthly Background Soil Reflectance from Dazlich and Los (2009)
is available from 10.3334/ORNLDAAC/956. The Harmonized World Soil
Database from FAO/IIASA/ISRIC/ISSCAS/JRC (2012) can be accessed at
http://webarchive.iiasa.ac.at/Research/LUC/External-World-soil-database/HTML/.
The Global Soil Dataset for Earth System Modeling from Shangguan et
al. (2014) can be accessed at
http://globalchange.bnu.edu.cn/research/soilw. ERA-Interim reanalysis
data from Dee et al. (2011) are available at
http://apps.ecmwf.int/datasets/data/interim-full-daily/. GPCC
precipitation data from Schneider et al. (2014) are available at the GPCC
homepage http://gpcc.dwd.de. The ice core CO2 record from Bereiter
et al. (2015) can be downloaded from
http://www.ncdc.noaa.gov/paleo/study/17975 and annual CO2
concentration data for Mauna Loa from Keeling et al. (1976) are available
at http://www.esrl.noaa.gov/gmd/ccgg/trends/full.html. MODIS surface
albedo from Schaaf and Wang (2015) data are available at
10.5067/MODIS/MCD43C3.006. The merged benchmark synthesis product of
evapotranspiration of Mueller et al. (2013) is available after
registration at
http://www.iac.ethz.ch/group/land-climate-dynamics/research/landflux-eval.html.
The UNH/GRDC Global Composite Runoff Fields – V1.0 (Fekete et al., 2002) are accessible at
http://www.compositerunoff.sr.unh.edu/html/Data/index.html. The ESA CCI
soil moisture dataset from Liu et al. (2012) is available after registration
at http://www.esa-soilmoisture-cci.org/node/145. The GlobSnow snow
water equivalent dataset from Luojus et al. (2013) can be downloaded from
http://www.globsnow.info/swe/. The circum-arctic map of permafrost and
ground ice conditions from Brown et al. (1998) is available at
http://nsidc.org/data/docs/fgdc/ggd318_map_circumarctic/. The
active-layer thickness of Yakutia from Beer et al. (2013) is available at
10.1594/PANGAEA.808240. The GPP data from the MTE approach (Jung et
al., 2009) can be downloaded after registration at
https://www.bgc-jena.mpg.de/geodb/projects/Data.php. The MODIS land
cover data from Channan et al. (2014) are accessible at
ftp://ftp.glcf.umd.edu/glcf/Global_LNDCVR/UMD_TILES/Version_5.1/. The
MODIS leaf area index from Yuan et al. (2011) data are available after
registration at
http://globalchange.bnu.edu.cn/research/lai/lai_download.jsp. The
NDP-017b vegetation carbon data from Gibbs (2006) can be accessed at
10.3334/CDIAC/lue.ndp017.2006. The Northern Circumpolar Soil Carbon
Database (NCSCD) from Hugelius et al. (2013b) is accessible at
10.5879/ECDS/00000002.
Snow age factor
Snow age factor as a function of skin temperature and snowfall
rate.
The snow age factor, fage, is parameterized as a function
of skin temperature and snowfall rate Ps as
fage=1-ln(1+fageTPs,cPs)fageTPs,cPs,fageT=e0.05(T∗-T0)+e(T∗-T0).
The dependence of fage on temperature and snowfall rate
with Ps,c=2×10-5kgm-2s-1 is shown in
Fig. .
Soil thermal and hydraulic properties
Organic matter alters soil thermal and hydraulic properties substantially,
in particular because of the much higher porosity of organic soils
compared to mineral soils. The importance of accounting for organic
matter in land surface models has been discussed in, e.g.
, , , and .
In PALADYN, the fraction of soil that is considered to be organic for the determination
of the thermal and hydraulic soil properties is computed in each soil layer
from the total carbon density following :
forg=min1,Clit+Cfast+Cslowρorgmax.ρorgmax=50kgCm-3 is the
maximum soil carbon density, equivalent to a typical carbon density of peat.
Soil thermal and hydraulic properties are simply taken to be a linear
combination of mineral and organic values based on forg.
This linear combination is applied to porosity (θsat),
dry thermal conductivity (λdry),
solid soil thermal conductivity (λs),
saturated hydraulic conductivity (ksat),
saturation matric potential (ψsat) and b parameter.
Mineral soil properties are computed from sand and clay fractions
following , based on , and .
Sand and clay fractions are taken from
either or from ,
with the former set as default. Sand and clay fractions are considered to
be vertically uniform in each grid cell and constant in time.
Organic soil properties are also taken from , partly
based on and .
Photosynthesis
The maximum daily rate of net photosynthesis Vm is given by
Vm=1aC3/4c1c2(2θr-1)s-(2θrs-c2)σmAPAR.σm=1-c2-sc2-θr⋅s,
where
s=24dhaC3/4,
and dh is the day length in hours computed from orbital parameters.
All PALADYN PFTs follow the C3 photosynthetic pathway, except C4 grasses
which follow the C4 pathway. For C3 plants, c1 and c2
are given by
c1=αC3ftempCmasspi-Γ∗pi+Γ∗,c2=pi-Γ∗pi+Kc(1+O2/Ko).αC3=0.08 is the intrinsic quantum efficiency of CO2 uptake in C3 plants
and Cmass=12 is the atomic mass of carbon.
Γ∗ is the CO2 compensation point:
Γ∗=O22τ,
with O2=20.9 kPa, the atmospheric O2 partial pressure.
Kc,
Ko and τ are kinetic parameters whose temperature
dependence is modelled using a Q10 relationship .
ftemp is a PFT-specific temperature inhibition function .
For C4 plants, the same equations are used but with c1 and
c2 given by
c1=αC4ftemp,c2=1.αC4=0.053 is the intrinsic quantum efficiency of CO2 uptake in C4 plants.
Aggregation of potential vegetation
In order to compare the modelled with the potential vegetation distribution
of , the potential vegetation needs to be aggregated to
the plant functional types represented in PALADYN. We partly follow
and map vegetation classes of to the PALADYN
PFTs as described in Table . The grass class in
Table is divided into C3 and C4 grasses based on
the modelled grass type in each grid cell.
Mapping of potential vegetation classes to PALADYN PFTs.
The authors would like to thank Victor Brovkin and Daniela Dalmonech for
discussions, and Catherine Pringent for providing the GIEMS dataset.
M. Willeit acknowledges support by the German Science Foundation DFG
grant GA 1202/2-1.
Edited by: H. Sato
Reviewed by: two anonymous referees
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