first joint calibration pass at the cal/val sites

[divine7022]

Report status and follow-up — 20 October 2026

Historical first-pass calibration report. The Russell “reproduced without calibration” claim was explicitly withdrawn; preserve that correction with these results. This report is not a current transferable parameter set.

Implementation: parameters/targets #245, multisite fit #247, Russell inputs/targets #276, and documentation #249. Later calibration artifacts and retrieval instructions are in the calibration repository. Same-day Modesto contrasts are implemented in the later example; site weighting, covariance, runtime input/version checks and parameter–target coupling still need evidence for each new fit. The carbon-saturation experiment is reported in the later pass-5 record; it is not an unperformed request.

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Joint calibration of SIPNET soil carbon at the cal/val sites, first pass

Purpose

The sensitivity analysis (#268) picked out the soil biogeochemistry parameters that control
soil carbon. This pass calibrates them against the curated cal/val observations. Physiological
parameters stay at their priors, per the split we agreed: strong priors on physiology,
calibration aimed at the biogeochemistry.

This is a first pass. It ran end to end and gave a clear answer, but several design questions
are still open and are listed at the bottom.

What was run

item	value
model	SIPNET master d2fc7a2
observations	ccmmf/cal-val-data
method	ensemble Kalman inversion with likelihood tempering
ensemble	50 particles, 3 tempering steps
cost	4,600 model runs

Fitted: 101 soil carbon observations. Salinas stock over 8 systems and 7 years, 2005-2011,
0-30 cm. Russell Ranch stock over 11 rotations and 5 years.

Calibrated: som_respiration_rate and fracLitterRespired, both on their soil PFT priors.
The unamended Salinas control constrains the base respiration rate and the seven compost
systems constrain the litter respired fraction, which is how the earlier single-site Salinas
pass was set up.

Fixed: soil_respiration_Q10 at 2.0. It is confounded with som_respiration_rate along
som_respiration_rate x Q10^(T/10), so it is scanned outside the inversion rather than fitted
alongside. Initial soil carbon is pinned per treatment at that treatment's first fitted
measurement.

How the likelihood is built

Every observation becomes one slot, keyed by variable, site, treatment and year. A slot holds
the measured value, a variance, and the model prediction for that same treatment and window.
The estimator aligns on slot name and never sees a site or a variable, so adding a site or a
variable only makes the vector longer.

Slot variance comes from replicate spread where replicates exist, and from the reported
standard error otherwise.

Every slot currently carries equal weight, and that is a known problem. With 56 Salinas
slots against 45 Russell slots, Salinas holds 55 percent of the likelihood, and it holds that
share because the trial happens to have 8 systems measured over 7 years rather than because it
carries more information about the model. The same applies within a site: a site with 20
treatments would dominate one with 10 for no methodological reason.

Weighting by site rather than by observation is the obvious correction and is not implemented
in this pass. Flagging it because it affects how much of the result below is really about
Salinas.

Result: the parameters

parameter	prior	posterior
som_respiration_rate	0.01052 +/- 0.00499	0.01468 +/- 0.00044
fracLitterRespired	0.49660 +/- 0.05947	0.60000, at the upper bound

som_respiration_rate moves up and narrows sharply. fracLitterRespired hits its upper bound
on the first tempering step and stays there.

Prior and posterior for the base soil respiration rate. The observations narrow it
considerably and move it above the prior median.

param_trace.png

Parameter mean and spread by tempering step. Grey dashed lines are the parameter bounds.

Result: soil carbon against observations

	RMSE	bias	coverage
Salinas, prior	22.31	+19.90	0.00
Salinas, calibrated	19.63	+17.54	0.00
Russell, prior	2.91	+0.22	0.47
Russell, calibrated	3.67	-1.35	0.04

Mg C ha-1. Coverage is the fraction of observations falling inside the ensemble's 90 percent
band.

Russell Ranch comes out right without any calibration. The bias at the priors is 0.22 Mg C ha-1
on a stock of about 33.5, and the ensemble contains the observation about half the time.
Calibrating makes each of those slightly worse.

Russell Ranch at the priors. Blue is the ensemble, black the median, red the observations.

Salinas is the opposite. The model runs 19.9 Mg C ha-1 above the measured stock at the priors.
Calibration brings that to 17.5 and pulls the ensemble in tight, but the trajectory itself
hardly moves, and the ensemble never contains the observation at any step. The compost systems
gain carbon in the model while the measured stocks stay flat, and the two parameters calibrated
here do not change that.

PRIOR:

CALIBRATED:

Salinas before and after. The narrow band on the right is the ensemble collapsing, not a
better fit.

The compost effect: the model does not saturate

The absolute stock above is the weaker way to look at Salinas. The treatment contrast is more
informative, and it is what the earlier(MVP) proof-of-concept reported

Compost systems (mean of seven) minus the unamended control, Mg C ha-1:

year	measured	model, prior	model, calibrated
2005	11.2	15.7	15.6
2006	10.5	20.3	19.7
2007	7.5	23.1	21.8
2008	9.3	27.0	25.1
2009	12.9	30.3	27.8
2010	17.4	34.4	31.3
2011	12.2	38.3	34.6
mean	11.6	27.0	25.1

The measured compost effect is approximately flat. It starts at 11.2 in 2005, ends at 12.2 in
2011, and moves between 7.5 and 17.4 in between with no trend. The field reaches an offset and
holds it.

The modelled effect grows steadily, from 15.7 to 38.3 over the same period, and calibration
barely changes that: 15.6 to 34.6. The model keeps accumulating compost carbon year after year.

That difference is a saturation signature, not a rate error, which is consistent with neither
calibrated parameter being able to close it. Both change how fast carbon moves; neither changes
whether the soil stops accepting it.

SIPNET has a soil carbon saturation mechanism and it was off in these runs.
CARBON_SATURATION is defined in src/common/context.c with a default of off, alongside
NITROGEN_CYCLE, ANAEROBIC, FLOODING and LITTER_POOL, which we set explicitly. We did not
set this one, so it took its default. With it enabled, the fraction of soil carbon input that
reaches the soil pool declines as the pool approaches a saturation limit, and the remainder is
redirected to the litter pool as fast-turnover carbon, following Stewart et al. (2007).

This has not been tested. It is a structural change rather than a parameter, it needs a
soilCSaturation value we do not currently have a prior for, and turning it on is a design
decision rather than a calibration one. Raising it because the mechanism is present, is
currently inactive, and its absence matches the pattern in the table above.

A note on total against delta

This pass fitted the absolute stock. Fitting the change instead is the better construction,
since initial soil carbon is pinned and the only thing model behaviour controls is how it
moves from there.

The result here is already mostly a trajectory error rather than a level offset, because
soilInit is pinned at each treatment's first measurement, so the model starts on the data and
diverges. The next pass fits the change; the disagreement above does not go away when it does.

N2O

The 27 N2O observations were held out of the likelihood in this pass. There are two separate
reasons, and the second is the more important one.

The comparison is not well defined. The N2O data is chamber data, taken at nine time points
in a year. Nine chamber measurements are not an annual flux and cannot simply be summed and
compared against an annual model output. Two workable approaches:

1. compare instantaneously: take the day a chamber measurement was made, ask the model for its
   rate on that day, and compare directly
2. integrate piecewise across the season, summing the area under lines connecting the
   measurement points, and compare against an annual model value

The first is cleaner. The second is commonly done but is a poor estimate of the annual total.
This pass implements neither properly and that is why the N2O numbers below are reported as
diagnostics rather than as a fit.

CARB guidance is that chamber data should not be used to estimate field-level fluxes. It can be
used to measure treatment differences. That points away from fitting an absolute N2O flux at
all and towards fitting a contrast, which is a different target construction than the one used
here.

Including N2O as-is distorts the carbon parameters. In a trial run with the 27 observations
in the likelihood, the model sat about an order of magnitude above the Modesto chamber
measurements, and that single residual accounted for roughly 99 percent of the total misfit.
The update became a Modesto N2O fit: it improved Modesto sevenfold, barely moved Salinas, and
made Russell worse. The nitrogen residual was being absorbed by the carbon parameters.

The proposed fix is structural, in the likelihood rather than in the target list. Build the
likelihood so that a site only informs the parameters its data speaks to: a site with only N2O
does not move the carbon parameters, and a site with only soil carbon does not move the
nitrogen parameters. That keeps the calibration joint, all sites in one inversion, while
stopping a nitrogen residual from being absorbed by a carbon parameter. It is a cleaner answer
than dropping sites, and it is not implemented yet.

Held-out diagnostics, ratio of means:

	prior	calibrated
Bouldin, 9	1.1x	0.4x
Modesto, 18	9.5x	17.2x

Calibrating on soil carbon moves both away from their observations, which is the same effect
seen from the other direction.

Limitations

Met, initial conditions and management are pinned to one realization so that the ensemble
spread comes from the parameters alone. That makes the posterior spread a parameter range
under fixed inputs, not a calibration uncertainty, and it should not be quoted as one.

The Salinas likelihood variance comes from within-year replicate spread and has no
between-year term in it. Within-cell standard deviation is 5.05 Mg C ha-1 at about four
replicates, while the cross-system annual means move by 10.7 Mg C ha-1 from year to year.

The Russell stock is derived rather than measured. Carbon concentration and bulk density were
combined on an equivalent soil mass basis at a reference mass of 3661 Mg ha-1, at treatment-year
level. The source publication provides its own equations for computing the stock, and those
should be the authoritative version once they are applied and added to cal-val-data. The 45
Russell observations used here may be superseded.

Salinas 2003 and 2004 sit outside the run. 2005 is the first fully differentiated season.

Where this leaves us

The configuration runs end to end: 23 forward blocks, per-treatment run windows, held-out
validation, parameters bounded to their support with the posterior checked against it.

It does not give a parameter set to use. Russell is already reproduced at the priors, and
Salinas is not resolved by the two parameters calibrated here.

the target for model behaviour is the general response of these systems,
not the behaviour of any one site. A poor fit at Salinas is a result to understand rather than
a failure to correct at that site, and no prior was adjusted to chase it. Adjusting a prior
using information from one of our own sites would put that information into the calibration
twice and would compromise any later validation against it.

Open questions

Input welcome on any of these. They are the things that determine what the next pass looks
like.

1. The N2O observation operator. Instantaneous same-day comparison, or piecewise
   integration to an annual value? The first looks cleaner, but the model output would need to
   be read at the right resolution.
2. Fitting an N2O contrast rather than a flux, given the CARB guidance on chamber data. If
   the target becomes a treatment difference, both the operator and the variance construction
   change.
3. Parameter blocking in the likelihood, so that a site informs only the parameters its
   data constrains. This looks like the right way to keep the fit joint without a nitrogen
   residual reaching a carbon parameter. Worth confirming before it is built.
4. Weighting by site rather than by observation. Straightforward to implement; the question
   is whether to weight equally across sites, or across treatments within a site, or both.
5. The Russell stock derivation. Confirming that the source publication's equations replace
   the equivalent soil mass derivation used here, and when that lands in cal-val-data.
6. Delta SOC as the fitted target for the next pass, in place of the absolute stock.
7. Whether to enable CARBON_SATURATION. The mechanism is in the model and currently off by
   default. Its absence is consistent with the modelled compost effect growing while the
   measured one holds flat. Enabling it needs a soilCSaturation value, and it is a structural
   choice rather than something to calibrate.

Data gaps

• Delta-site N2O observations exist in the curated data but were not brought into this pass
  while the model inputs for those sites are still being settled.
• The Russell soil carbon stock is not in cal-val-data as a stock; it is derived here from
  concentration and bulk density.
• The Modesto event file used here was rebuilt from managements.csv in the curated data. A
  script or README documenting that derivation still needs to go into the repository alongside
  the event file.

[divine7022]

Correction to the Russell result above.

The Russell stocks used here were derived by equivalent soil mass at a 3661 Mg/ha reference. Tautges et al. 2019 computes them by fixed depth (Eq. 1, section 2.6) and does not use ESM. The reference mass was also wrong on its own terms: measured 1992 bulk density gives 4457 Mg/ha to 30 cm, so 3661 covered about 24.6 cm.

Recomputed by the paper's method, 1993 is 40.6 Mg C/ha rather than 33.0, and the 19-year change is -4.9 rather than +0.87. The sign reverses.

So "Russell Ranch is reproduced without calibration, bias 0.22" does not hold. It was scored against the incorrect series, and soilInit was pinned per treatment to the same incorrect 1993 value. Withdrawing that result. Russell is out of the next pass until the stocks are precomputed into cal-val-data. @AritraDey-Dev

Salinas is unaffected; those stocks come from the curated data directly. The Salinas findings and the parameter results remain unchanged.