In the LPJmL model vegetation is represented by different plant functional
types (PFTs) that can establish concurrently within a cell. These
established PFTs share the same soil stand and compete for light, water, and
nitrogen resources, while crop functional types (CFTs) are established
exclusively at sowing on their own soil stand.
In the predecessor version LPJmL3.5, all organic matter pools (vegetation,
soil) were represented as carbon pools. We now also implemented a
corresponding N pool for each of these carbon pools and pools
for inorganic reactive N forms (NH4+, NO3-) in the
soil (Fig. ). Nitrogen dynamics have been incorporated in
other dynamical vegetation models, e.g., in LPJ-GUESS
. In addition to LPJ-GUESS our model considers
not only natural vegetation but also takes into account managed crops.
Furthermore, nitrogen transformation in soils is simulated in a more
sophisticated way incorporating the immobilization of nitrogen. In the following
sections we describe the implementation of the plant N demand,
uptake, allocation, the effects of N limitation, photosynthesis,
maintenance respiration, and N inputs, and transformations and
losses in and/or from soils. All processes are computed at a daily time step, except
for fire events (annual) and the allocation of carbon and N in plants,
which is computed daily only for crops but annually for natural vegetation
and before each harvest event for managed grasslands. Soil processes are
vertically resolved in six soil layers including one bedrock layer.
Nitrogen demand
Daily photosynthesis and maximum carboxylation capacity (Vmax) are
computed based on absorbed photosynthetically active radiation (APAR) and
canopy conductance reflecting the level of water stress
. This water-stressed carboxylation capacity
Vmax determines the demand for N of trees, grasses, and crops in
the leaves. Depending on PFT-specific requirements for Vmax, the
N demand of leaf, Nleaf (g N m-2), is calculated
according to based on
as
Nleaf=25⋅0.02314815/daylength⋅Vmax⋅exp(-0.02⋅(T-25))⋅fLAI(LAI)+0.00715⋅Cleaf,
where Cleaf is the actual leaf carbon content (g C m-2)
and daylength is the duration of daylight (h). The function
fLAI(LAI) is a modifier dependent on current leaf area
index (LAI) accounting for a stronger leaf N content decline with
canopy depth compared to incoming sunlight.
fLAI(LAI)=max(0.1,LAI)forLAI<1exp(0.08⋅min(LAI,7))otherwise
The pre-factor 0.12 in the exponential term of
has been replaced by 0.08 for two reasons.
First, we find that canopy C : N ratios are too low for the original value.
Second, the computed values for the average leaf C : N ratio of the canopy
should monotonically increase with LAI, whereas they decline again at higher
LAI. This unwanted decline is not completely prevented with our pre-factor of
0.08 but much weaker and occurs only at much higher LAI values than in the
original implementation (see Fig. S1 in the Supplement). We choose a maximum
of LAI=7 and for LAI<1 a linear decrease to avoid
too-high respiration rates at low LAI levels, where C : N ratios would
become very small otherwise. Daily gross photosynthesis Agd
depends on the light-limited photosynthesis rate JE and Rubisco-limited
photosynthesis rate JC:
Agd=JE+JC-(JE+JC)2-4⋅θ⋅JE⋅JC(2⋅θ)⋅daylength,
where θ is the shape parameter describing the co-limitation of light
and Rubisco activity. The value of θ of LPJmL3.5 has been changed from
0.7 to 0.9, which is in better agreement with and
results in lower Rubisco demand to reach the light-limited photosynthesis
rate (see Fig. S2). The factor αa determining the fraction of
photosynthetic active radiation (PAR) assimilated at ecosystem level relative
to leaf level has been changed from 0.5 to 0.6 to counterbalance the
reduction of GPP due to additional nitrogen limitations.
Because the allocation of carbon and nitrogen for grass and tree PFTs is done
on a yearly time interval, the actual carbon stored in leaves
Cleaf,t at time t of the current year is calculated from the
carbon stored in leaves at the end of the previous year Cleaf:
Cleaf,t=Cleaf+fleaf⋅∑t′=1tNPPt′,
where ∑t′NPPt′ is the accumulated biomass increment and
fleaf is the fraction of biomass that was allocated to leaves at
the end of the previous year. Then the total N demand is determined by
the actual (t) carboxylation-based demand for N in leaves
Nleaf,t (see Eq. ), the current N content
of the other organs (roots Nroot and sapwood
Nsapwood for trees), and the approximated N demand for
the newly accumulated NPP (Eq. ). For this approximation, we
use the allocation shares of the previous year (froot,
fsapwood):
Ndemand,t=Nleaf,t+Nroot+Nsapwood+NleafCleaf⋅(froot/R1+fsapwood/R2)⋅∑t′=1tNPPt′,
where R1 and R2 are the prescribed PFT-specific C : N ratios of roots
and sapwood relative to the C : N ratio of leaves (Table ).
C : N ratios relative to the leaf C : N ratio Ri for the
different plant compartments.
Plant
Root R1
Sapwood R2
Storage organ R3
Pool R4
Tree
1.16
6.9
Grass
1.16
Temperate cereals
1.16
0.99
3
Rice
1.16
1.30
3
Maize
1.16
0.83
3
Tropical cereals
1.16
0.79
3
Pulses
1.16
0.45
3
Potatoes
1.16
1.74
3
Sugar beet
1.16
4.46
3
Tropical roots
1.16
3.27
3
Sunflower
1.16
1.04
3
Soybeans
1.16
0.42
3
Groundnut
1.16
0.68
3
Rapeseed
1.16
0.76
3
Sugarcane
1.16
4.57
3
The daily allocation scheme of crops enables the calculation of nitrogen
demand by using the carbon compartment itself. Plants maintain a store of
labile N, Nstore (g N m-2), to buffer fluctuations
between N demand and supply from the soil mineral N pool
. N demand is therefore increased by a
factor of kstore=1.15 for trees and kstore=1.3 for
grass and crops. Thus, the optimum N uptake fulfilling the demand
Nuptake,opt can be calculated from the demand increment.
Nuptake,opt=(Ndemand,t-Ndemand,t-1)⋅kstore
Nitrogen uptake
The mechanism for the uptake of N (Nuptake in
g N m-2 d-1) is the same for trees, crops, and grasses. Following
, plant Nuptake is determined by
soil mineral N concentrations, fine root mass, soil temperature and
porosity, and plant demand for N. This is computed for all soil layers
individually and summed up to compute overall N uptake:
Nuptake=∑l=1nsoillayer2⋅Nup,root⋅fN(Navail,l)⋅fT(Tsoil,l)⋅fNC(NCplant)⋅Croot⋅rootdistl,
where Nup,root is the maximum N uptake rate per unit of fine
root mass in each layer, fN(Navail) parameterizes
the dependence on available N, fT(Tsoil) parameterizes
the temperature dependence, fNC parameterizes the dependence on
plant N : C ratio, Croot is the carbon stored in the roots,
nsoillayer is the number of soil layers
(nsoillayer=6), and rootdistl determines the fraction
of roots in each layer. Nup,root is 2.8×10-3 g N g C-1 d-1 for trees and 5.51×10-3 g N g C-1 d-1 for crops and grasses
. The available N is the sum of
NO3- and NH4+ in the soil layer l.
Navail,l=NO3,soil,l-+NH4,soil,l+
The function fN can be parameterized by Michaelis–Menten
kinetics:
fN(Navail,l)=kN,min+Navail,lNavail,l+KN,min⋅θmax⋅dsoil,l,
where dsoil,l is the soil column depth (m), θmax is
the soil-type-specific fractional pore space (dimensionless),
KN,min is 1.48 g N m-3 for woody and 1.19 for grassy
PFTs (half-saturation concentration of fine root N uptake), and
kN,min (dimensionless) is 0.05, which is the basal rate of
N uptake that is not associated with Michaelis–Menten kinetics. The
function fNC(NCplant) is from
:
fNC(NCplant)=NCleaf,high-NCplantNCleaf,high-NCleaf,low,
where NCleaf,low and NCleaf,high
are the lower and upper limits of N : C ratios and
NCplant is the actual plant N : C ratio. The lower and
upper limits NCleaf,low and
NCleaf,high are derived from the TRY database
. Their reciprocal C : N values for each PFT are
shown in Table . The actual plant N : C ratio is calculated
according to
NCplant=Nleaf+NrootCleaf+Croot.
The temperature function fT for N uptake is given by
:
fT(Tsoil,l)=(Tsoil,l-T0)⋅(2⋅Tm-T0-Tsoil,l)(Tr-T0)⋅(2⋅Tm-T0-Tr),
where T0<Tr<2⋅Tm-T0. For the chosen Tm=15 ∘C,
Tr=15 ∘C, and T0=-25 ∘C, the maximum of 1 is reached
at 15∘ and the function is positive above -25 ∘C.
The root distribution rootdistl can be calculated from the
proportion of roots from the surface to soil depth z, rootdistz, as
in :
rootdistz=∫0z(βroot)z′dz′∫0zbottom(βroot)z′dz′=1-(βroot)z1-(βroot)zbottom,
where βroot is a PFT-specific parameter (for parameter
values,
see Table ); rootdistl is then given by the
difference rootdistz(l)-rootdistz(l-1). If the soil
depth of the layer l is greater than the thawing depth then
rootdistl is reduced accordingly. The nonzero
rootdistl values are rescaled so that their sum is normalized to 1,
accounting for the modified root distribution under freezing conditions. Soil
NH4+ and soil NH3- pools are reduced accordingly every
simulation day t.
NO3,soil,l,t+1-=NO3,soil,l,t-⋅1-rootdistl⋅Nuptake∑l=1nsoillayerNavail,lNH4,soil,l,t+1+=NH4,soill,t+⋅1-rootdistl⋅Nuptake∑l=1nsoillayerNavail,l
PFT-specific βroot based on
and minimum and maximum leaf C : N ratios
based on the TRY database with data from
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
, and
.
The C : N ratios for C3 and C4 grasses and crops are based on
.
Functional type
CNleaf,low
CNleaf,high
βroot
Tropical broad-leaved evergreen tree
15.6
46.2
0.962
Tropical broad-leaved raingreen tree
15.4
34.6
0.961
Temperate needle-leaved evergreen tree
31.8
63.8
0.976
Temperate broad-leaved evergreen tree
15.6
46.2
0.964
Temperate broad-leaved summergreen tree
15.4
34.6
0.966
Boreal needle-leaved evergreen tree
31.8
63.8
0.943
Boreal broad-leaved summergreen tree
15.4
34.6
0.943
Boreal needle-leaved summergreen tree
18.4
36.9
0.943
C3 perennial grass
10.5
37.9
0.972
C4 perennial grass
17.4
66.9
0.943
Bioenergy tropical tree
15.6
46.2
0.976
Bioenergy temperate tree
15.4
34.6
0.976
Bioenergy C4 grass
17.4
66.9
0.976
Crops
14.3
58.8
0.972
Nitrogen allocation and turnover in plants
Carbon allocation to plant compartments follows functional and allometric
rules as described by and is computed annually
for natural vegetation and daily for crops .
The allocation rules account for the functional relationships that leaf area
needs to be supported by sufficient sapwood (in trees) and fine root biomass.
Fine root biomass increases relative to leaf biomass under water stress and
also under nitrogen limitation. The allometric rules specify the relationship
of stem diameter to plant height and crown diameter
. Plants require N in varying amounts to
satisfy organ-specific C : N ratios. Leaf N content is determined by
photosynthetic potential and structural requirements and can vary within
PFT-specific limits of C : N ratios. The PFT-specific range of possible
C : N ratios is based on the TRY database
Table .
The allocation of N (Ninc) to plant compartments follows
the allocation rules for carbon and ensures distribution between
plant compartments as established with the relative ratios given for the
C : N ratio of, e.g., roots in comparison to leaves (CNroot /
CNleaf). These relative ratios for natural vegetation are taken
from Table 4.
For crops the C : N ratios for the storage organ are derived from
. Therefore, average crop-functional-type-specific leaf
C : N ratios as simulated by LPJmL5.0 were used to estimate the factors R3
that relate leaf C : N ratios to storage organ C : N ratios
(Table ).
The allocation scheme follows the algebraic solution of the following set of
equations when there are n plant compartments.
N1+a1⋅NincC1=R1⋅N2+a2⋅NincC2N1+a1⋅NincC1=R2⋅N3+a3⋅NincC3⋮N1+a1⋅NincC1=Rn-1⋅Nn+an⋅NincCn∑i=1nai=1
C1,C2,…,Cn, N1, N2, …,
Nn are the C and N pools of plant compartments 1,2,…,n, and R1,R2,…Rn-1 are the relative C : N ratios in
comparison to leaves. The system is solved for a1,a2,…an so that
the relative ratios R1,…,Rn-1 are ensured. Thus, the model has to
solve the equation system for n=2 pools for grass, n=3 pools for
trees, and n=4 pools for crops. If the N : C ratio for a pool is below
the PFT-specific minimum N : C ratio allowed, then the excess carbon is put
into the litter pools. To avoid overly large C fluxes from excess
carbon to the litter pools in N-limited environments, we have
introduced a sink limitation for the photosynthesis of trees. For this, the
excess carbon from the sapwood pool is stored in an additional carbon pool
Cexcess. If this excess pool is filled and if there is a
minimum Csapwood pool of at least 1 kg m-2,
photosynthesis is downregulated by a scaling factor s in the following year
(Eq. ). At the end of the year, the newly acquired
carbon (NPP) and the Cexcess are allocated to the plant
organs according to the usual allocation rules. If all carbon can be
allocated within allowed compartment-specific C : N ratios, the
Cexcess pool is empty afterwards and photosynthesis is no
longer downregulated.
s=(1+KM)⋅ff+KM,f=min1,NsapwoodCsapwood+Cexcess⋅R2NCleaf,low,
where KM=0.1 is the Michaelis constant of the Michaelis–Menten
kinetics and R2 is the relative C : N ratio of sapwood with respect to
leaves.
Similar to water stress, we assume that plants allocate more biomass to roots
under N limitation. For this, the leaf to root mass ratio
(lmtorm) is modified by the minimum of the N limitation
factor vscal and the water limitation factor wscal.
Both factors are computed as growing season means with daily updates, i.e.,
for the entire calendar year for natural vegetation, between harvest events
for managed grasslands, and since sowing for crops.
LPJmL employs PFT-specific turnover rates for living leaves and fine roots.
At turnover the corresponding amount of carbon is moved into the litter
pools, whereas not all of the associated N is disposed of but remains in
the plant. We assume that grasses and deciduous trees recover
kturn=70 % of their N upon biomass turnover, whereas
evergreen trees only recover kturn=20 %. At turnover sapwood
carbon is transformed into heartwood carbon. Not all nitrogen from sapwood
turnover goes into heartwood, and only a fraction fheartwood=0.7
of nitrogen is transformed.
Nitrogen transformation in soils
Nitrogen occurs in soils in different reactive forms, mainly the organic forms
nitrate (NO3-) and ammonium (NH4+), which are represented
by different pools in LPJmL5.0. Transformations between different forms of
N in the soil are represented by mineralization, immobilization,
nitrification, and denitrification and are simulated in sequential order.
Each soil and litter pool consists of carbon and nitrogen stocks and the
resulting C : N ratios are flexible. Losses from the soil are represented
by the implemented nitrification, leaching, denitrification, and
volatilization processes. The corresponding pools and fluxes are depicted in
Fig. and described, including their parameterization
(see Table S2), in this section.
Nitrogen transformations and losses in soils. Pools and fluxes are
denoted by boxes and arrows, respectively.
![]()
Mineralization of nitrogen
The mineralization of N from soil organic matter and the decomposition of
litter pools follow that of carbon as described by
. First, for each soil layer the fluxes of
carbon from the soil into the atmosphere are calculated and the respective
fluxes of N, reflecting the actual C : N ratios of the material, are
transferred to the NH4+ soil pool of the corresponding soil layer.
Fluxes (F) of carbon and nitrogen for slow (s) and fast (f) pools (P)
depend on parameters ksoil10f=0.03,
ksoil10s=0.001 (per year), and R(T,M) as a function of
temperature (T) and soil moisture (M) per soil layer (l).
Flx=max(0,Plx⋅(1-exp(-ksoil10x⋅R(Tl,Ml))),x∈(s,f),
where
R(Tl,Ml)=Tl⋅(0.04021601-5.00505434⋅Ml3+4.26937932⋅Ml2+0.71890122⋅Ml).
The mineralization of soil N, Nminer,soil,l, in
soil layer l is given by
Nminer,soil,l=Flf+Fls.
Whereas the mineralization fluxes of carbon go completely to the atmosphere
as CO2, mineralized N goes to the mineral pools, where it is
subject to further transformation .
The decomposition of N in soil organic material (Ndecom)
consists of a mineralization part (Af=0.6, dimensionless) that forms
NH4+ and a humification part (1-Af), in which organic N
from the litter pool is transferred to the soil pools. The humification flux
is divided into fluxes to slow (s) and fast (f) N soil pools (P)
for which the parameter Ff=0.98 (dimensionless) specifies the portion that
goes to the fast soil pool.
Pl,t+1f=Pl,tf+Ff⋅(1-Af)⋅Ndecom⋅Nshift,lf,Pl,t+1s=Pl,ts+(1-Ff)⋅(1-Af)⋅Ndecom⋅Nshift,ls,
where the annual shift rates Nshift,ls,f describe the
organic matter input from the different PFTs into the respective layer due to
cryoturbation and bioturbation .
Net mineralized material Nminer,litter,l is
Nminer,litter,l=Af⋅Ndecom⋅Ff⋅Nshift,lf+(1-Ff)⋅Nshift,ls,
which adds N to an intermediate N mineralization pool
Nminer,l=Nminer,soil,l+Nminer,litter,l.
In contrast to in which 20 % of this pool is
directly nitrified to NO3-, we follow
and transfer all mineralized N to the NH4+ pool.
NH4,soil,l,t+1+=NH4,soil,l,t++Nminer,l
Nitrogen immobilization
Immobilization, i.e., the transformation of mineral N to organic
N in soils, is determined per soil layer directly after soil and
litter mineralization, following the LM3V land model described by
. If available mineral soil N is
constraining immobilization, mineral N is first immobilized into the
fast soil pool and then into the slow soil pool. The immobilized N,
Nimmo,l, is calculated according to
Nimmo,l=Ff⋅(1-Af)⋅Cdecom/CNsoil-Ndecom⋅Nshift,lf⋅Nsum,l/dsoil,lkN+Nsum,l/dsoil,l,
where CNsoil is the desired soil C : N ratio of 15
(dimensionless) for all soil types, dsoil,l is the soil depth
of layer l in meters, kN=5×10-3 (g N m-3) is the half-saturation concentration for immobilization in soils
, and Nshift,lf is the parameter
that determines the distribution of the humified organic matter in the
topsoil to the different soil layers l .
The available mineral N in the soil layer l (Nsum,l in
g N m-2) is the sum of NH4+ and NO3-.
Nsum,l=NH4,soil,l++NO3,soil,l-
The immobilized N (Nimmo,l) is added to the fast soil
N pool of layer l and subtracted from the NH4+ and
NO3- pools.
Psoil,l,t+1f=Psoil,l,tf+min(Nimmo,l,Nsum,l)
NH4,soil,l,t+1+=NH4,soil,l,t+-NH4,soil,l,t+⋅min(Nimmo,l/Nsum,l,1)NO3,soil,l,t+1-=NO3,soil,l,t--NO3,soil,l,t-⋅min(Nimmo,l/Nsum,l,1)
The immobilization into the slow soil N pool
(Psoil,l,t+1s) is computed accordingly as in
Eq. () but with (1-Ff) instead of Ff.
Nitrification
Nitrogen fluxes from nitrification in the soil are modeled modified after
with the schematic representation of a series
of pipes for the main flow from NH4+ over NO3- to
N2 from which N2O leaks in between. As suggested by
Eq. 2, nitrification is computed as a
fixed fraction of the mineralization flux (see Sect. )
and an explicit transformation flux FNO3- from ammonium to
nitrate in g N m-2 d-1, which is described here.
FNO3-=Kmax⋅F1(Tsoil,l)⋅F1(Wsat,l)⋅F(pH)⋅NH4,soil,l+,
where NH4,soil,l+ is the model-derived soil ammonium
concentration (g N m-2), Kmax is the maximum nitrification rate
of NH4+ (Kmax=0.1 d-1), F1(Tsoil,l) is
the limiting function for temperature, and F1(Wsat,l) the
corresponding limiting function for water saturation Wsat,l.
show nitrification rates after data from
in Table 3 without a formula. Using these
data from three different sites in the US, Canada, and Australia, we fitted a
bell-shaped function for the temperature dependence:
F1(Tsoil,l)=exp(-(Tsoil,l-a)2/(2⋅b2)),
where a=18.79 ∘C and b=5.26 give the best fist to the data (see
Fig. S3). The function is also applicable for negative values.
The soil water response function F1(Wsat) is parameterized
according to as described in
:
F1(Wsat,l)=Wsat,l-bnitanit-bnitdnit⋅(bnit-anit)/(anit-cnit)⋅Wsat,l-cnitanit-cnitdnit,
where Wsat,l is the water-filled pore space of soil layer l,
and
parameters anit to dnit are given for sandy and
medium soil (Table S2).
This soil pH function is based on .
F(pH)=0.56+arctan(π⋅0.45⋅(-5+pH))/π
Soil pH values are taken from the WISE data set . Part of the
N during nitrification is lost to the atmosphere as nitrous oxide
(N2O). assume that the N2O flux
FN2O (in g N m-2 d-1) is proportional to the
nitrification rate with
FN2O=K2⋅FNO3-,
where K2 is the fraction of nitrified N lost as N2O flux (K2=0.02). Finally, soil NO3- and NH4+ are updated
accordingly.
NO3,soil,l,t+1-=NO3,soil,l,t-+(1-K2)⋅FNO3-NH4,soil,l,t+1+=NH4,soil,l,t+-FNO3-
Denitrification
The reduction of NO3- to NO2 and N2 is determined
for each soil layer using the implementation in SWIM .
DNO3-=F2(Wsat,l)⋅F2(Tsoil,l,Corg,l)⋅NO3,soil,l-,
where F2(Wsat,l) is the water response function and F2(T,C)
the soil temperature and carbon reaction function. The water response
function depends on the water-filled pore space Wsat,l in the
following way.
F2(Wsat,l)=6.664096×10-10⋅exp(21.12912⋅Wsat,l)
The water response function shows a qualitatively similar behavior to
Eq. (151) from SWIM while ensuring continuity (see Fig. S4). Parameters are
fitted and adjusted so that for full soil water saturation, the value is not
greater than 1. The soil temperature and carbon reaction function is
parameterized according to
F2(Tsoil,l,Corg,l)=1-exp(-CDN⋅F2(Tsoil,l)⋅Corg,l),
where CDN=1.4 is the shape coefficient ,
Corg,l is the sum of the fast and slow C pools,
and F2(Tsoil,l) is the soil temperature reaction function.
F2(Tsoil,l) is replaced by Eq. (C5) from
, which is only valid for positive
Tsoil,l. The original function from the soil and water
assessment tool (SWAT) approaches 1 for high temperatures, whereas the
function from Smith declines, which seems more sensible. Equation (C5) of
is taken from .
F2(Tsoil,l)=0.0326forTsoil,l≤0∘C0.0326+0.00351⋅Tsoil,l1.652for0∘C<Tsoil,l<45.9∘C-Tsoil,l41.7487.190forTsoil,l≥45.9∘C
assume that the N2O flux from
NO3-, FN2O (in g N m-2 d-1), is proportional
to the denitrification rate DNO3- with
FN2O=rmx⋅DNO3-,
where rmx=0.11 is the fraction of denitrified N lost as
N2O flux. The N2 flux FN2 is then derived by
FN2=(1-rmx)⋅DNO3-.
The soil NO3- pools have to be reduced by the denitrification flux.
NO3,soil,l,t+1-=NO3,soil,l,t--DNO3-
Nitrogen leaching and movement
Nitrate movement with water fluxes is simulated as in SWAT
. Nitrate is assumed to be fully
dissolved in water and moves with surface runoff, lateral runoff, and
percolation water. To compute the amount of nitrate transported with the
water from a soil layer, we first calculate the concentration of nitrate in
the mobile water. This concentration is then multiplied by the volume of
surface runoff, lateral runoff, or percolation water between soil layers or
into the aquifer. The amount of nitrate leached depends on the
climatic and soil conditions and on the type and intensity of soil management
(e.g., plant cover, soil treatment, fertilization).
The concentration of nitrate in the mobile water
concNO3-,mobile,l in layer l
(kg N m-3) is
concNO3-,mobile,l=NO3,soil,l-⋅1-exp-wmobile,l(1-θ)⋅SATlwmobile,l,
where NO3,soil,l- is the content of nitrate in layer
l (g N m-2), wmobile is the amount of mobile water in
the layer (mm), θ=0.4 is the fraction of porosity from which anions
are excluded 0.5 in, and SATl is
the saturated water content of the soil layer (mm).
The mobile water wmobile,l in the layer l is the amount of
water lost by surface runoff, lateral flow, and percolation:
wmobile,l=Qsurf+Qlat,l=1+wperc,l=1forl=1Qlat,l+wperc,lforl>1,
where Qsurf is the surface runoff (only in the topsoil layer; mm),
Qlat,l is the water discharged from the layer by lateral flow
(mm), and wperc,l is the amount of water percolating to the
underlying soil layer on a given day.
Finally, the amount of nitrate that is removed with surface runoff
NO3-surf and lateral flow
NO3-lat,l is calculated as
NO3-surf=βNO3-⋅concNO3-,mobile⋅Qsurf,NO3-lat,l=1=βNO3-⋅concNO3-,mobile⋅Qlat,l=1,
for the top layer and
NO3-lat,l=concNO3-,mobile,l⋅Qlat,l
for the lower soil layers, where βNO3- is the nitrate
percolation coefficient. It controls the amount of NO3- removed
from the surface layer in runoff relative to the amount removed via
percolation . The value for βNO3-
can range from 0.01 to 1.0. For βNO3-→0, the
concentration of nitrate in the runoff approaches 0. For
βNO3-=1.0, surface runoff has the same concentration of
nitrate as the percolating water. We choose for βNO3- a
value of 0.4.
Nitrate moved to the lower soil layer with percolation
NO3-perc,l is calculated as
NO3-perc,l=concNO3-,mobile⋅wperc,l.
NO3-perc,l is subtracted from the current NO3- in
the soil layer and added to the NO3- pool of the following soil
layer.
NO3,soil,l,t+1-=NO3,soil,l,t--NO3-perc,l-NO3-surf-NO3-lat,lforl=1NO3,soil,l,t-+NO3-perc,l-1-NO3-perc,l-NO3-lat,lforl>1
Nitrogen volatilization
The volatilization of NH4+ is parameterized according to
. A convective mass transfer model is applied
in which the flux varies with air temperature, air velocity over the surface,
and the NH3 concentration gradient between the ammonium
(NH4+) in solution and in the air:
JNH3=hm⋅[NH3]gas-[NH3]air,
where JNH3 is the NH3 volatilization flux
(g NH3-N m-2 s-1), hm is the convective mass
transfer coefficient (m s-1), [NH3]gas is the concentration
of gaseous NH3 in equilibrium with dissolved NH3 in solution
(g NH3 - N m-3 air), and [NH3]air is the concentration of
NH3 in ambient air (g NH3 - N m-3 air), which is usually very
small and can be neglected. The convective mass transfer coefficient
hm is a function of temperature T (in K), air velocity U (in
m s-1), and characteristic length L (m) of the emitting surface.
hm=0.000612⋅U0.8⋅T0.382⋅L-0.2
The concentration of gaseous NH3 in equilibrium with the dissolved
NH3 is determined using Henry's law. The Henry's law Kh
constant relates the concentration of dissolved NH3 in water to an
equilibrium concentration of NH3 in the air.
Kh=[NH3]gas[NH3]solution
The Henry's law constant Kh can be parameterized as a function of
air temperature Tair (K).
Kh=Kh(Tair)=(0.2138/Tair)⋅106.123-1825/Tair
The fraction of total ammoniacal N present as NH3 can be
estimated using equilibrium thermodynamic principles:
fNH3=[NH3]solution[NH3]solution+[NH4+]solution,=11+[H+]Ka=11+10-pHKa,
where Ka is the dissociation constant, [H+] is the proton
concentration in solution, and pH =-log([H+]). The dissociation
constant Ka is parameterized as a function of temperature T (K).
Ka=Ka(T)=100.05-2788/T
Then the volatilization flux Fvol (in g N m-2 d-1)
is calculated according to
Fvol=86400⋅hm(U,T,L)⋅Kh(T)⋅11+10-pHKa(T)⋅NH4,soil,l=1+/dsoil,l=1,
and soil NH4+ is reduced in the top layer l=1 accordingly:
NH4,soil,l=1,t+1+=NH4,soil,l=1,t+-Fvol.