Model description

KiwiScience Soil Carbon Model · a monthly, multi-horizon, microbially explicit model for New Zealand land uses

Every equation below is implemented in js/model.js and carries the same number there, so the code and this page can be checked against each other.

0What this model is

A process model of soil organic carbon for New Zealand land uses. Click a block on KiwiMap, take the land use and fertiliser regime from KiwiFert, and it returns carbon stocks through time, the final profile, and a complete carbon mass balance — each with an uncertainty band rather than a single misleading line.

Most soil carbon tools ask for numbers nobody has: decay constants, specific surface area, microbial carbon use efficiency. This one asks instead for what a farm, a consultant or a research group is likely to know — a point on a map, a soil order, a crop, a stocking policy, a fertiliser programme — and fills the rest from libraries of published New Zealand values. Every one of those values is a plain JavaScript file you can open, read and overwrite.

What the model does

Soil carbon is split into pools that behave differently, because that is the difference between a change that lasts and one that does not:

  • Particulate organic matter — recognisable plant fragments, not protected by anything. It turns over in years, responds quickly to a change in management, and is just as quickly lost again.
  • Mineral-associated organic matter — carbon sorbed onto clay and oxide surfaces, turning over in decades to centuries. This is the pool worth building, and it saturates: a soil already near its capacity cannot store much more, whatever you add.
  • Microbial biomass — small, but every gram of carbon that becomes mineral-associated passes through it first. It moves years before the slow pools do, which makes it the early indicator.
  • Inert pyrogenic carbon — char, effectively permanent, which is why a single biochar application behaves so differently from an annual compost application.

Carbon leaves as carbon dioxide, as methane where the soil goes anaerobic, as dissolved organic carbon draining below the root zone, and in whatever is harvested or eaten. All of it is tracked and reported, so the Net Ecosystem Carbon Balance is an accounting result rather than an assertion.

Why the fertiliser is an input and not an afterthought

Soil carbon is oxidised by microorganisms, and two of the strongest controls on what those organisms manage to oxidise are the nitrogen supply and the pH. Both are set by what is spread on the block. Nitrogen relieves the immobilisation demand that holds back decomposition of nitrogen-poor residue while simultaneously repressing the oxidative enzymes that attack humified carbon; lime moves the pH towards the microbial optimum, which is the oldest observation in the subject. A soil carbon model that does not know the fertiliser and liming programme is guessing at some of its largest terms. Section 10 sets out exactly what the model does with a regime, and the Fertiliser tab can take one straight from KiwiFert.

Where the site comes from

The Site tab is a live KiwiMap. Click a block and the model reads the soil order, the New Zealand Soil Classification subgroup, the topsoil carbon with its mapped minimum and maximum, pH, cation exchange capacity, drainage, texture, depth, land cover, land use and the seasonal climate at that point, then writes them into the ordinary editable panels. Nothing is locked: a measurement from the block itself always outranks a national raster, and typing over an imported value is the expected thing to do rather than a workaround.

The monthly climate library is not replaced by any of that. KiwiMap carries seasonal mean temperatures but neither monthly rainfall nor evapotranspiration, so importing a point keeps the nearest station's monthly series from data/climate-nz.js and shifts its temperatures to match the mapped seasonal means. Rainfall and PET stay exactly as the station recorded them.

What it is not

It is a research and teaching tool. It is not a carbon accounting standard, it is not calibrated to any one site, and it should not be used to make a claim about a particular paddock without local measurements. The single most influential number in it — the decay constant for mineral-associated carbon — is uncertain by a factor of about five, which is why the model reports a band and why the band is often wide enough to include no change at all. That is not a defect in the model. It is the state of the knowledge.

Built to last

Plain HTML, three shared stylesheets and a handful of JavaScript files. No framework, no build step, no analytics, no external requests. Download the folder, open index.html, and the model works — on a plane, on a farm with no signal, or in ten years when whatever is fashionable now has been forgotten. Only the two panels that reach out to KiwiMap and KiwiFert need a local server, and each says so plainly when it does not have one; everything else keeps working without them.

1Structure

The model runs a monthly timestep over a user-set number of years. The profile is divided into horizons — by default an A, a B and a C — and each horizon carries five carbon pools. Above them sit two whole-profile surface pools.

PoolWhat it isTypical turnover
Litter (O horizon)Plant residue and dung lying on the surfaceMonths to a few years
MulchSurface-applied compost, wood chip, strawDepends on the material
POMParticulate organic matter: plant fragments in the soil, not protectedYears
POMoThe particulate carbon already present when the run starts. It receives no new input and only decaysYears, or millennia in a peat
MAOMMineral-associated organic matter, sorbed to clay and oxide surfacesDecades to centuries
MBCLiving microbial biomassWeeks to months
IOMInert pyrogenic carbon: char and condensed aromaticsCenturies to millennia

Why POM and POMo are separate

A single particulate pool forces this season's root litter and a soil's inherited organic matter to share one decay constant. In a mineral soil that is harmless, because the two are genuinely similar. In a peat it is not: the particulate carbon in a Waikato peat is thousands of years old and has already lost everything labile. Giving it the decay constant of fresh residue predicts losses of 40 t C/ha/yr on drainage instead of the 3 to 6 t C/ha/yr that is actually measured. POMo keeps the two apart. For every non-organic soil the two pools behave identically, so nothing else changes.

Order of operations within a month

  1. Find which phase of the rotation is running, and set the root depth distribution.
  2. Compute soil temperature at each horizon's midpoint.
  3. Run the water balance: rain, irrigation, drainage, evapotranspiration, water table.
  4. Add this month's plant carbon: litter, root litter, exudates; take out what is grazed, cut or burnt, and return dung.
  5. Add any organic amendment applied this month.
  6. Cultivate, if a pass falls in this month.
  7. Decompose the surface layers.
  8. Decompose each horizon in turn, from the top down, carrying dissolved carbon downward.

2From concentrations to stocks

A carbon percentage means nothing until it is multiplied by the mass of fine earth actually present, which is why bulk density and coarse fragments are not optional extras. For a horizon of thickness z centimetres:

(t/ha) Mfine = z × ρb × (1 − fcoarse) × 100

where ρb is bulk density in g/cm³, fcoarse is the volume fraction of stones over 2 mm, and 100 converts 1 cm of soil at 1 g/cm³ over one hectare into tonnes. Carbon stock is then Mfine × C% / 100.

Splitting the starting stock

The inert fraction at the start of a run follows Falloon et al. (1998):

IOM = 0.049 × TOC1.139

with TOC and IOM both in t C/ha, capped at a quarter of the total. The particulate share comes from the horizon's POM fraction and the microbial share from its microbial fraction; whatever is left is mineral-associated.

Mineral saturation capacity

Mineral surfaces can only hold so much. Hassink (1997) related the maximum carbon in the fine fraction to the mass of that fraction:

Cmax (g C/kg) = a + b × F<20µm,    MAOMcap = Cmax × Mfine / 1000

with a = 4.09 and b = 0.37 by default. F<20µm is the percentage of particles finer than 20 µm, taken from the texture class. A capFactor multiplies the result for mineralogies Hassink's temperate data set does not cover: allophanic soils (×2.6), pumice (×2.4) and oxidic clays (×1.6), where short-range-order minerals and iron oxides hold far more carbon than particle size alone implies.

Saturation is the most useful thing this model tells you, and the most often ignored. A New Zealand pasture topsoil already holding 85% of its capacity cannot be made to store much more stable carbon, no matter how much compost is applied. The compost will build particulate carbon, which is real but reversible.

3Soil temperature and water

Soil temperature

Decomposition is driven by soil temperature, but climate records give air temperature. The annual air wave is damped and delayed with depth, and damped again by canopy and litter cover:

(7) Tsoil(z) = T̄ + ΔToffset + [Tair(t − τ) − T̄] · e−z/d · ccover

T̄ is the annual mean air temperature, d the thermal damping depth (2 m by default), ccover a cover factor from the plant library (0.65 under closed native forest, 1.05 on bare soil), and the phase lag τ = 1.91 z/d months. ΔToffset is the amount by which mean annual soil temperature exceeds mean annual air temperature, normally 1 to 2 °C.

Water balance

A cascading bucket, one per horizon. Rain plus irrigation enters the top. Water above field capacity moves down, at a rate set by the drainage class — a well drained soil passes all of it, a very poorly drained soil only a tenth — and anything above saturation always leaves. Water is then withdrawn for evapotranspiration:

AET = Kc · PET · s + 0.12 · PET · θrel,1 (1 − Kc)

The first term is transpiration: the crop coefficient times reference evapotranspiration, reduced by a stress factor s = min(1, W̄/0.5), where W̄ is the root-weighted fraction of plant-available water remaining. Plants take water freely until half of it is gone, then increasingly struggle. The second term is evaporation from bare soil, which only matters when the canopy is open. Withdrawal from each horizon is proportional to root density × wetness and never goes below the wilting point, except in the top horizon where direct evaporation can dry the soil further.

Water table and water-filled pore space

Porosity is φ = 1 − ρb/2.65. The water table rises and falls with the profile-wide soil moisture deficit:

zwt = zwt,base + 1.4 · D,    WFPS = fsat + (1 − fsat) · θ/φ

D is the deficit in millimetres and 1.4 cm/mm follows from a specific yield near 0.07. zwt,base comes from the drainage class. fsat is the fraction of the horizon lying below the water table, which is saturated by definition. This is what switches on methanogenesis, so the drainage class is the single most consequential choice on the Soil tab for a wet site.

4Rate modifiers

Every decay constant in the model is a potential rate: what the pool would do at 10 °C, optimal moisture and pH 6.5. Six dimensionless modifiers scale it down. They are always multiplicative, so realised turnover in the field is always slower than k. A fertiliser and liming regime adds two more — one that speeds the labile pools up and one that slows the humified pool down — and moves the pH that Eq. 3 reads; both are set out in section 10.

Temperature

(1) fT = Q10(Tsoil − 10)/10

Q10 is 2.0 by default. Mineral-associated carbon has a higher activation energy, so it uses Q10 + 0.3.

Moisture

(2) fW = [ (W − 0.02) / (Wopt − 0.02) ]a · [ (1.05 − W) / (1.05 − Wopt) ]b

W is water-filled pore space, Wopt = 0.60. Below the optimum, substrate diffusion limits the microbes; above it, oxygen diffusion does. With the default exponents the function gives 0.28 at WFPS 0.10, 1.00 at 0.60, 0.59 at 0.80 and 0.07 at saturation.

pH

(3) fpH = exp[ −((pH − pHopt)/w)² ]

An asymmetric Gaussian with pHopt = 6.5, a narrower width on the acid side (1.8) than the alkaline side (2.4). A soil at pH 5.0 decomposes at half the rate of the same soil at pH 6.5.

Nitrogen availability

(4) fN = 1   for C:N ≤ C:Ncrit;    fN = exp[−s(C:N − C:Ncrit)]   otherwise

Applied to the soil's own C:N ratio, acting on the mineral-associated pool. Above the critical ratio of about 25, microbes must immobilise mineral nitrogen to build cells, and mineralisation slows.

Litter quality

(5) fQ = 1 / (1 + LN / LNhalf),    LN = lignin% / nitrogen%

The lignin-to-nitrogen ratio is the classic single predictor of litter decomposition rate (Melillo et al. 1982). Using the ratio rather than separate lignin and nitrogen multipliers avoids penalising woody litter twice for the same property, which would otherwise make forest litter decompose implausibly slowly. Pasture litter (LN ≈ 1.9) decomposes at 86% of its potential rate, wheat straw (LN ≈ 24) at 33%, pine litter (LN ≈ 40) at 23%. Above-ground values apply in the top horizon and root values below.

Mineral protection

(6) fprot = 1 / (1 + SSA / SSAref)

Applied only to the mineral-associated pool. Specific surface area is estimated from texture class where it has not been measured: under 2 m²/g for a quartz sand, 20 to 60 for a loam, over 100 for a smectitic clay, and 100 to 600 for an allophanic soil. Note the division of labour: surface area sets how strongly carbon is held and how much dissolved carbon sorbs; the fine fraction sets how much can be held at all. Using one property for both would double-count it.

5Carbon inputs

Above-ground net primary production for the month is the annual figure times that month's share of the growth curve. Below-ground production follows from the root:shoot ratio, and both are converted to carbon with the plant's carbon fraction.

NPP = ANPP (1 + rR:S) · fC,    GPP = NPP / (1 − ra)

ra is autotrophic respiration as a fraction of gross primary production, about 0.5 for herbaceous plants and 0.55 for forest. GPP is reported in the mass balance but does not otherwise enter the model.

Where above-ground carbon goes

A fraction is laid down as long-lived wood and does not reach the soil this year; it is reported separately so the account still balances. Of what remains, a fraction is grazed in place, a fraction is cut and carted off, and the rest falls as litter. A burnt fraction is emitted immediately as CO2, apart from a small pyrogenic residue that joins the inert pool.

Grazing

Intake carbon is partitioned by the livestock library:

Fate of intake carbonDairyBeefSheep
Returned as dung0.300.340.32
Returned as urine0.030.020.02
Leaves in animal product0.100.050.05
Enteric methane0.0600.0650.060
Animal respirationthe balancethe balancethe balance

Dung is partly humified already, so a share of its carbon goes straight to the mineral-associated pool and the rest joins the surface litter.

Below-ground carbon

Roots are distributed with depth by Gale & Grigal (1987): the cumulative fraction above depth d centimetres is 1 − βd. A fraction of below-ground production is released as exudates and rhizodeposits, which are taken up by microbes almost immediately; the rest becomes root litter and joins the particulate pool of each horizon in proportion to root density. Roots below the modelled profile are folded into the deepest horizon so nothing is lost from the account.

Below-ground inputs build soil carbon far more effectively than surface inputs. Two mechanisms in the model produce this: exudates are taken up by rhizosphere microbes already attached to mineral surfaces, so their necromass stabilises more efficiently (the exudate stabilisation bonus); and root carbon is delivered directly to depth, where it meets unsaturated mineral surfaces instead of the near-saturated topsoil.

Amendments

Each material is split three ways: an inert pyrogenic part straight to IOM, an already-humified part that sorbs to mineral surfaces, and a labile remainder that joins the surface mulch or, if incorporated, the particulate pool of the cultivated layer. Imported feed is routed through the livestock partition instead, since it only reaches the soil as dung.

6Decomposition and stabilisation

Each pool loses carbon by first-order decay. The exponential form is used rather than a simple product so the result is stable even when the monthly loss is large:

ΔC = C · [ 1 − exp(−k · E · Δt) ]

E is the product of the relevant modifiers from section 4 and Δt = 1/12 year. For the particulate pool E = fT A fpH fQ ftill; for the mineral-associated pool E = fT,MAOM A fpH fN fprot ftill,MAOM, where A is the oxygen-corrected activity from section 7.

Microbial uptake

Everything released by decomposition, plus exudates and the products of surface-layer breakdown, forms a pool of free carbon. Part dissolves; the rest is taken up by microbes and split between biomass and respiration by the carbon use efficiency:

CUEeff = CUE − m(Tsoil − 10),    assimilated = U · CUEeff,    respired = U (1 − CUEeff)

Efficiency falls as the soil warms, because maintenance respiration rises faster than growth, and falls again under anoxia where metabolism yields far less energy per unit of carbon.

Necromass and stabilisation

Microbes die at a first-order rate. What happens to the necromass is the heart of the model, because it is the only route from plant carbon to stable soil carbon:

(8) ε = εmax · (1 − MAOM / MAOMcap) · [1 + (βex − 1) · φex]

ε is the fraction of necromass that sorbs to mineral surfaces and becomes MAOM; the remainder becomes particulate. It falls to zero as the mineral surfaces fill. βex is the exudate stabilisation bonus and φex the share of this month's substrate that arrived as exudate. The same saturation limit is applied to every route into MAOM — amendments, dung and sorbed dissolved carbon included — so the capacity cannot be bypassed.

7Carbon dioxide and methane

Above a threshold water-filled pore space, oxygen diffusion cannot keep up with demand and part of the horizon respires anaerobically. Anaerobic metabolism is slow but does not stop, so the combined activity is a weighted mixture rather than simply the moisture response:

α = (WFPS − Wanox) / (1 − Wanox),    A = (1 − α) fW + α ranaer

Wanox is about 0.68 and ranaer, the anaerobic rate as a fraction of the aerobic optimum, about 0.15. That ratio is the reason peat accumulates under water and disappears once it is drained.

The anaerobic share of respiration is split between carbon dioxide and methane by the methanogenic fraction, about 0.5, which is what acetoclastic methanogenesis gives. Methane then has to escape through whatever aerobic soil lies above it, where methanotrophs consume it. That oxidation is first order along the path out:

(10) oxidised = 1 − exp(−λ zaer),    λ = −ln(1 − fox) / 20

zaer is the thickness of aerobic soil above the horizon in centimetres and fox the fraction oxidised in the first 20 cm. A wetland with the water table at the surface loses almost all of its methane to the atmosphere; the same soil with the water table at 60 cm loses almost none. Well drained soils are treated as a small net methane sink.

8Dissolved organic carbon

A fraction of everything released by decomposition enters solution rather than being respired or assimilated. Dissolved carbon produced in a horizon joins whatever percolated in from above. How much leaves depends on how much water drained relative to how much is held:

fleach = Q / (Q + θ),    sorbed = (1 − fleach) · DOC · fret · 2 · SSA/(SSA + SSAref)

Q is the month's drainage through the horizon in millimetres and θ its water content. Sorbed carbon joins the mineral-associated pool of that horizon, subject to its saturation limit; carbon that neither leaves nor sorbs is consumed in place. Whatever is still in solution at the base of the profile has left the system, and is reported as leached dissolved organic carbon.

This is the mechanism that builds subsoil carbon in a podzol, and the reason a high specific surface area matters at depth as well as in the topsoil.

9Cultivation and mixing

A cultivation pass does three things. It homogenises every pool through the working depth, weighted by each horizon's fine-earth mass. It buries the surface litter and mulch as particulate carbon. And it starts a decomposition pulse as aggregates break and occluded particulate carbon is exposed to microbes:

ftill(t) = 1 + (P − 1) · 2−t/h

P is the pulse multiplier (about 1.9), t the months since the pass, and h the half-life (about 4 months) over which aggregates re-form. Only a fraction of the pulse is applied to the mineral-associated pool, because cultivation exposes mainly particulate carbon.

Between cultivations, soil fauna carry particulate carbon downward from each horizon to the one below at a first-order bioturbation rate, and drag surface litter into the A horizon at the litter incorporation rate. In an earthworm-rich pasture soil that second flux is large.

Why cultivation is snapped to whole horizons

Each horizon is represented by a single value for each pool. If a plough pass were allowed to mix only the top few centimetres of the horizon below, that carbon would immediately be treated as though it were spread through the whole of that horizon — where the subsoil's large unused mineral capacity would stabilise it. Repeated every year, the model would turn ploughing into a carbon pump and report cultivation as beneficial, which is the opposite of what is observed.

Cultivation is therefore snapped to the nearest horizon boundary at or above the depth entered. To model deep ploughing, set the A horizon's base to the plough depth: a deep plough layer is a deep A horizon, and representing it that way keeps the physics honest. With the artefact removed, turning cultivation off in the Canterbury arable rotation adds about 5 t C/ha at equilibrium, in continuous maize about 12 t C/ha, and in an intensive vegetable rotation with three passes a year about 21 t C/ha.

10Fertiliser, lime and nitrogen

Soil organic carbon is oxidised by microorganisms, so a model of it is a model of what those organisms are able to do. Two of the strongest controls on that are the nitrogen supply and the pH, and both are set by what is spread on the block. A fertiliser and liming regime is therefore an input to this model, not a commentary on its output.

The whole of this section is inert while the Fertiliser tab is switched off: the nitrogen availability index is then zero, no lime or acid is applied, and every expression below reduces to one. A run without a regime gives exactly the numbers the model gave before the regime existed, which is what makes the comparison between the two meaningful.

Nitrogen supply

Three sources are added, in kilograms of nitrogen per hectare per year: fertiliser nitrogen as entered; nitrogen mineralised within the year from the organic materials in the imports panel, taken as each material's carbon input divided by its C:N ratio and multiplied by an available fraction of about 0.3; and, only if asked for, the nitrogen stock return in dung and urine. The last is off by default because it is internal recycling: the production figures in the plant library were measured on grazed swards and already contain it, so counting it again would double it.

The total is turned into a dimensionless index that saturates:

(6a) Nav = N / (N + Nhalf)

Nhalf is 90 kg N/ha/yr, so a New Zealand dairy platform at 150 kg N/ha/yr sits at about 0.63 and a cut-and-carry block with no nitrogen sits at zero.

What nitrogen does to decomposition

It does two opposite things, and the model has to carry both or it will get the sign wrong. Nitrogen-poor plant residue decomposes slowly because the microbes attacking it must immobilise mineral nitrogen to build cells; supply that nitrogen and the constraint is relieved. But the same mineral nitrogen represses the oxidative, ligninolytic enzyme systems that break down condensed, humified material, so the older and more processed the carbon, the more nitrogen slows it down. This is the pattern Fog (1988) set out, Berg and Matzner (1997) confirmed in litter, and the meta-analysis of Janssens et al. (2010) measured across temperate systems as a net reduction of roughly 15% in heterotrophic soil respiration.

(11) fN,lab = 1 + alab · Nav · (1 − fQ)

Applied to surface litter, to surface mulch and to the particulate pool. fQ is that material's own quality modifier from Eq. 5 (or Eq. 4 for mulch), so the acceleration is proportional to how nitrogen-limited the substrate already is: straw and wood chip speed up, a fertilised clover sward does not speed up twice. alab is 0.20.

(12) fN,hum = 1 − ahum · Nav

Applied to the mineral-associated pool, with ahum = 0.15 and a floor of 0.3 so the pool can never be switched off entirely.

(13) CUE0′ = CUE0 · (1 + aCUE · Nav)

Microbes that are not short of nitrogen respire less of the carbon they take up and build more of it into biomass, and biomass becomes necromass, which is the raw material of mineral-associated carbon. aCUE = 0.10. This adjusts the base efficiency CUE0 that section 6 then reduces for temperature and for anoxia; it does not replace either of those.

Acidity, lime and pH

Nitrification of fertiliser ammonium generates acid; lime consumes it. Both are expressed in the form a lime recommendation already uses — tonnes of calcium carbonate equivalent per hectare per year — so the two can simply be subtracted. The acidity per kilogram of nitrogen depends on the source and on how much of the resulting nitrate the plant takes up rather than losing to drainage: the conventional field figures are 1.8 kg CaCO3 per kg N for urea, 5.4 for ammonium sulphate and 3.6 for DAP, against theoretical limits of nothing and about 7.1. All of them are editable.

(14) ΔpH = (L − A) / [ B0 (1 + r |6.0 − pH| ) ] · sh

Applied once a year. L is the lime applied as CaCO3 equivalent, A the acid load, B0 the tonnes of carbonate needed to move the limed layer by one pH unit near pH 6 (9 t/ha by default, which is the New Zealand rule of thumb that four to five tonnes of lime lifts pH by about half a unit), and sh the share of horizon h that lies inside the limed layer. The buffer is not constant: below pH 6 the hydrolysis of exchangeable aluminium takes up acid in place of the soil solution, and above it base saturation approaches its ceiling and further carbonate simply accumulates, so r = 1.0 makes each successive pH unit cost more than the last and the trajectory approaches an asymptote instead of running away. pH is clamped to 3.5 to 8.4.

Two rules keep this honest. Maintenance lime stops once the limed layer reaches its target pH, because that is what a maintenance lime recommendation is for; without that test a standing order for lime would carry a soil to pH 8 over a long run, which no farm has ever managed. And the pH does not move during equilibration: the pH entered in the Soil tab is a measurement of the soil as it is now, and the trajectory describes the change from there under the regime entered, not three hundred years of invented history.

The pH so obtained feeds straight into Eq. 3, which multiplies every decay constant in the model. That is the mechanism behind the oldest observation in the subject — lime an acid soil and its organic matter starts to go — and it is usually the largest single effect a fertiliser regime has on the carbon line.

Production

(15) ΔDM = c · Nsat · [ 1 − exp(−Nfert+org / Nsat) ] / 1000 · kplant

Diminishing returns with an initial slope c of 10 kg DM per kg N and Nsat = 250 kg N/ha/yr, so 150 kg N/ha/yr on fully responsive pasture adds about 1.1 t DM/ha/yr. kplant scales it per plant (data/fertiliser.js): 1.0 for ryegrass and the cereals, 0.1 for lucerne, which fixes its own, 0.05 for mature native forest and 0 for a bare fallow. Grazing returns are excluded from Nfert+org here for the same reason as above, and a production figure pinned in the Production overrides table is left alone entirely: a typed figure is a measurement of the block as it is farmed now and already contains its own response. Without this equation nitrogen would appear in the model as nothing but a cost, which is wrong.

The carbon in the lime

Agricultural limestone is about 12% carbon by mass, and that carbon leaves as carbon dioxide as the carbonate dissolves — roughly 108 kg C per tonne of product spread. It is not soil organic carbon and it never was, so it is kept out of the pools and out of the Net Ecosystem Carbon Balance, and reported on its own line beneath the mass balance. Burnt and hydrated lime carry no carbonate carbon at all; their carbon dioxide was released in the kiln, which is upstream of this model.

11Mass balance and NECB

Every flux is tallied over the run. The Net Ecosystem Carbon Balance is the net flux across the boundary of the block:

(9) NECB = NPP + I − H − Panimal − CH4,enteric − Ranimal − B − Rh − CH4,soil − DOC − W

I is imported organic matter, H harvest, Panimal animal product, Ranimal animal respiration, B burning, Rh heterotrophic soil respiration and W carbon accumulating in woody biomass. A positive NECB means the block gained carbon.

NECB is computed from the fluxes, and the change in soil plus litter carbon is computed from the pools. They should be equal. The model reports the difference as a closure error, and the interface raises a warning if it exceeds 1% of the inputs. In normal use it is under a tenth of a tonne over fifty years.

12Uncertainty

Every uncertain quantity carries a minimum, a nominative value and a maximum. The central run uses the nominative values throughout. The uncertainty run repeats the whole simulation, drawing each quantity from a triangular distribution on its three values:

F(x) = (x−a)² / [(b−a)(c−a)] for x ≤ c;   1 − (b−x)² / [(b−a)(b−c)] otherwise

with a the minimum, c the nominative value and b the maximum. Triangular is used because those three numbers are exactly what the parameter library provides, and it uses them without inventing anything further.

All uncertain quantities are resampled together within a run, so the band shows the combined effect rather than one parameter at a time. The shaded band is the 5th to 95th percentile across runs. The generator is seeded, so a quoted result can be reproduced exactly.

The band is usually wide, and that is the honest answer. The decay constant for mineral-associated carbon is uncertain by a factor of about five, and it dominates any prediction beyond a decade. If your band spans zero, the model is telling you that the direction of change cannot be resolved from published parameters alone, and that you need site data — a repeat measurement, a radiocarbon age, or a long-term incubation.

13Assumptions and limits

What is assumed

  • Plant biomass is at steady state apart from the woody increment, which is tracked separately. Establishment years and the removal of standing biomass at harvest are not represented.
  • Root litter enters within the year it is produced. Fine root turnover is fast enough for this to hold in pasture and crops; in forest it slightly advances the timing of carbon inputs.
  • Horizons are internally uniform. Real profiles have gradients within a horizon, particularly the topsoil under no-till.
  • Nitrogen is an input, not a state variable. The nitrogen supply set in the Fertiliser tab acts on decomposition, on carbon use efficiency and on production (section 10), and the acid it generates moves the pH through the run. But there is no nitrogen pool: the model does not track mineralisation, immobilisation, leaching or denitrification, C:N ratios are entered rather than computed, and nitrogen limitation therefore cannot develop by itself over the course of a run. Nitrous oxide is not modelled at all, which matters to the greenhouse balance of a grazed system.
  • The rotation repeats unchanged for the whole run, and climate is the same every year apart from any warming trend.

What is not modelled

  • Erosion and deposition. On steep hill country this can dominate the carbon balance of a given point, and the model will not show it.
  • Nitrous oxide. It matters greatly to the greenhouse balance of a grazed system, but it is a nitrogen flux, not a carbon one.
  • Priming: the acceleration of old carbon decomposition by fresh input. There is good evidence it exists; there is no agreed way to parameterise it.
  • Soil fauna other than as a bulk bioturbation rate.
  • Preferential flow. Dissolved carbon is assumed to move with the bulk water flux, which understates leaching in a structured clay soil.
  • Lateral flow, run-off and irrigation-return flows.

A known disagreement worth stating

Repeated sampling of New Zealand dairy pasture on Allophanic soils has found carbon losses of roughly 1 t C/ha/yr. Run with library values, this model usually shows those soils as approximately stable or slowly gaining. The mechanism behind the measured loss is still contested — proposals include the effects of nitrogen fertiliser on decomposition, drainage changes, and sampling and bulk-density artefacts — and none of them is settled enough to encode. The model has not been tuned to reproduce the observation, because doing so would hide a genuine open question behind a fitted constant. If you are modelling that system, treat the result as a hypothesis and say so.

References the parameter values draw on

  • Berg, B. & Matzner, E. (1997) Effect of nitrogen deposition on decomposition of plant litter and soil organic matter in forest systems. Environmental Reviews 5, 1–25.
  • Fog, K. (1988) The effect of added nitrogen on the rate of decomposition of organic matter. Biological Reviews 63, 433–462.
  • Janssens, I.A. et al. (2010) Reduction of forest soil respiration in response to nitrogen deposition. Nature Geoscience 3, 315–322.
  • Falloon, P. et al. (1998) Estimating the size of the inert organic matter pool. Soil Biology and Biochemistry 30, 1207–1211.
  • Gale, M.R. & Grigal, D.F. (1987) Vertical root distributions of northern tree species. Canadian Journal of Forest Research 17, 829–834.
  • Hassink, J. (1997) The capacity of soils to preserve organic C and N by their association with clay and silt particles. Plant and Soil 191, 77–87.
  • Melillo, J.M., Aber, J.D. & Muratore, J.F. (1982) Nitrogen and lignin control of hardwood leaf litter decomposition dynamics. Ecology 63, 621–626.
  • Six, J. et al. (2002) Stabilization mechanisms of soil organic matter. Plant and Soil 241, 155–176.
  • Allen, R.G. et al. (1998) Crop evapotranspiration. FAO Irrigation and Drainage Paper 56. (Crop coefficients.)
  • NIWA climate normals, 1991–2020, for the station statistics behind the climate library.
  • Hewitt, A.E. (2010) New Zealand Soil Classification, 3rd edition. Manaaki Whenua Press.

The values in the libraries are national-typical starting points assembled from these sources and from published New Zealand agronomic data. They are not measurements from your site, and the model is not a substitute for making some.

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