Contents
The site and the gap
Blodgett Forest is a ponderosa pine plantation in the Sierra Nevada foothills with a Mediterranean summer: no rain in July, the soil drying down through the month. ELM run there at a single point, with the tower's own GSWP3 forcing and satellite phenology, puts July 2004 GPP at a sixth of what the tower measured, and its water-stress index says why it thinks so.
- Site
- US-Blo, Blodgett Forest38.90°N 120.63°W
- Vegetation
- Ponderosa pineELM PFT 1, needleleaf evergreen temperate
- Window
- July 20041,488 steps of 30 min
- Tower GPP
- 7.20 ± 0.59gC m⁻² d⁻¹, FLUXNET2015 via ILAMB
- ELM GPP
- 1.14gC m⁻² d⁻¹, BTRAN 0.30
The parameters that govern water stress in ELM, the soil potentials at which stomata start to close and close fully and the two terms of the root profile, are the obvious suspects. Whether they can close the gap is a question about a month of coupled soil water, not about one routine at one instant, and that is the question a derivative through the whole step can answer.
From Fortran to a derivative
The engine reads ELM's Fortran and emits two things: a NumPy translation, gated bit-exact against the compiled original on state recorded from the running model, and a JAX port, gated to 32 ULP. Nothing on this page was ported by hand. The seven routines a step calls between canopy interception and drainage were each translated, recorded and gated, then chained: every quantity one routine writes and the next reads unchanged is carried from kernel to kernel instead of read back from the recording, so the soil water the month ends with is the chain's own.
Seven kernels inside one lax.scan over the month, one
checkpoint per step, and jax.grad of the month's GPP with
respect to the parameters. The forward pass reproduces the model's
soil water to 10⁻¹² relative at the end of July and its GPP to
10⁻¹⁴; the reverse pass takes 741 s for all parameters at once.
What the derivative gives is the total sensitivity along the
soil-water trajectory. When a parameter eases transpiration, the soil
dries faster and gives part of the gain back later in the month, and a
derivative taken through the month sees that. A derivative of one
routine at fixed soil water does not: for the closure potential
smpsc it predicted a x2.32 response to tripling the
parameter, where the month, and ELM itself, say x1.41.
The chain is the model
Daily mean GPP through July. On the left, the chain on the model's own parameters against the model's history tape. On the right, all four water parameters pushed to the edge of their plausible range at once: the chain's prediction, and what ELM produced when rerun from the same restart with those values in its parameter file. The band is the tower's monthly mean and its uncertainty.
What the derivative said
One reverse pass gives the month's elasticity to every parameter at once. The tower supplies one number, a monthly mean, so one parameter is determined and any pair is not; each parameter was therefore solved alone, as a bounded root of the forward in log-value, inside a factor of three of its default.
| Parameter, PFT 1 | What it sets | Elasticity | Alone at its bound | GPP | Gap closed |
|---|---|---|---|---|---|
| smpsc | soil potential at full stomatal closure | +0.319 | −255,000 → −765,000 mm | 1.61 | 7.8 % |
| roota_par | root profile, shallow term | −0.263 | 7 → 2.33 | 1.72 | 9.4 % |
| rootb_par | root profile, deep term | −0.589 | 2 → 0.67 | 1.77 | 10.4 % |
| smpso | soil potential where stress begins | +0.060 | −66,000 → −198,000 mm | 1.24 | 1.6 % |
| all four at bound | 2.85 | 28.2 % |
Elasticity is d ln GPP / d ln |p| over the month. Every fit ended AT BOUND.
Two of the four are not inputs of any chained routine.
roota_par and rootb_par set the root fraction
once, at initialization, through the two-exponential profile of Zeng
(2001) as ELM spells it. The same expression was evaluated in JAX from
the recorded soil layers; it reproduces the recorded root fraction to
2·10⁻¹⁶, and the fit moves the parameters through it.
Then the Fortran model was asked
A derivative of a translation is worth exactly what the original model would say. The July window was rerun in ELM, from the same restart, with the four values at their bounds written into the parameter file.
What this shows, and what it does not
The derivative is the model's. Reverse mode through a month of machine-translated ELM predicts the model's own response to a large, coupled parameter change to a fraction of a percent. There is no emulator to train and nothing to retrain when the Fortran changes: the translation is regenerated and gated.
The calibration answered honestly. Blodgett's GPP shortfall is not in the water-stress parameters. Inside plausible ranges, all four together close 28 % of the gap, and the model confirms it. What remains is structural: the soil column's depth and water holding, the forcing's precipitation, the prescribed leaf area. That is a finding about ELM at this site, reached in one reverse pass and one three-minute rerun.
One monthly tower value determines one parameter; the quartet at its bounds is an envelope, not a fit. The chain carries the water and energy path; radiation and phenology still come from the recording. A month at one site is a demonstration, not a calibration of ELM.
Method
ELM at E3SM e508436e, single point on the US-Blo
surface data, satellite phenology, GSWP3 forcing through the coupler
bypass, twelve months of spin-up from 2003-07-01. The recorder dumps
every argument of seven routines on every step of July 2004:
CanopyHydrology, CanopyFluxes, SoilTemperature, SoilFluxes, the
driver's patch-to-column averaging, HydrologyNoDrainage,
HydrologyDrainage. The chain carries 731 edges the flow audit found
unchanged on every step and reads 84 from the recording.
Observation: FLUXNET2015 monthly GPP as distributed by ILAMB, site US-Blo, 2004-07, 7.202 ± 0.590 gC m⁻² d⁻¹. Bounds: a factor of three either side of the parameter file's value, the rule used where no audited range exists. The model rerun: the window continued from the same restart with a copy of the parameter file, July FPSN read from the history tape.