When AI Weather Models Learn to Fake Conservation

The Invisible Drift

In the basement of a computing cluster in Boulder, Colorado, an AI model was learning to simulate Earth's atmosphere. It was getting better at its job—or so every diagnostic said. The model produced precipitation fields that closed the global water budget to machine precision, meaning the moisture falling from the sky balanced, exactly, what evaporated from the oceans and was stored in the atmosphere. It was a clean, elegant result. Conservation laws held. The researchers celebrated.

Then they looked closer.

The model's raw prediction—the numbers it generated before any physical correction was applied—had developed a severe drinking problem. Over just 18 training cycles, the uncorrected precipitation rate had plummeted nearly 20% below where it should have been. The model was producing a desert and then papered over the shortfall with an ever-larger correction. By the end, the corrector was adjusting precipitation by 24%—more than a fifth of the total—to compensate for a raw prediction that had wandered into nonsense.

The researchers had stumbled onto a subtle but critical flaw in how AI weather models are trained to obey physical law. The fix, once understood, is straightforward. But the implications extend far beyond one errant model: this is a warning about the seductive danger of enforcing constraints without watching what those constraints are hiding.

"The delivered field closed the moisture budget to machine precision," says William Chapman, an atmospheric scientist at the University of Colorado Boulder and the paper's lead author. "But the raw precipitation was collapsing. The conservation diagnostic was green across the board, and the model was silently getting worse in exactly the dimension it was supposed to protect."

The finding, published as a "lessons learned" paper in Artificial Intelligence for the Earth Systems, matters because AI weather and climate models are no longer laboratory curiosities. They are being deployed for operational forecasting, climate projection, and scientific discovery. When they drift—quietly, invisibly, while reporting perfect conservation—the consequences could compound over decades of simulated climate time.

The Science

Teaching Machines to Forecast the Sky

Weather prediction has always been a computational arms race. Numerical weather prediction (NWP) models—the workhorses of forecasting for seventy years—solve fundamental physics equations on grid cells spanning the globe, step by step, hour by hour. They are mathematically rigorous and physically interpretable. They are also extraordinarily expensive: a single ten-day forecast can require weeks of supercomputer time.

AI emulators take a different approach. Rather than solving physics from scratch, they learn from vast archives of model output or reanalysis data—essentially, they learn to map current atmospheric states to subsequent ones. Train a neural network on fifty years of six-hourly atmospheric snapshots, and it can learn to produce tomorrow's weather from today's. The results have been startling. Models like NVIDIA's FourCastNet, DeepMind's GraphCast, and Google's Pangu-Weather now match or exceed traditional NWP on many forecast metrics, often completing in seconds what conventional models take hours.

But these neural emulators have an embarrassing problem: they don't inherit physics by default. A network learns to minimize a loss function—some measure of error between its output and the truth—but nothing in that process forces conservation of mass, water, or energy. The network can, and does, violate fundamental balances that the real atmosphere maintains without thinking about it. Precipitation can exceed evaporation over a year. Total atmospheric moisture can mysteriously appear or vanish. These are not minor bookkeeping gripes; they're the kind of errors that compound over long simulations, causing drift, instability, and eventually complete physical nonsense.

The Promise and Practice of Conservation

The AI weather community has known about this vulnerability for years, and they've developed strategies to address it. The two main approaches are called soft and hard constraints.

Soft constraints add a penalty term to the loss function. If a model violates energy conservation, you add the magnitude of that violation to its training objective. The network learns to minimize both its prediction error and its physical infidelity, and the relative weight between them is a tuning choice. It works, but it requires careful calibration, and exact closure is never guaranteed.

Hard constraints take a different approach. After the network produces its prediction, you apply a correction that enforces the desired balance exactly. A common method rescales precipitation globally—multiplying every grid cell's value by whatever factor is needed to make precipitation match evaporation minus storage. Do this after every forward pass, and the delivered output closes the water budget to machine precision, no tuning required.

This is the strategy used in the CREDIT framework, which stands for Climate Emulator with Reinforced Implementation Training—a collaboration between NCAR, Google, and several universities that has produced some of the most capable AI climate models to date. CREDIT uses hard correctors to enforce conservation of dry mass, energy, and water during training and inference. Prior work showed that these correctors improved forecast stability and reduced precipitation bias (Sha et al., 2025; Watt-Meyer et al., 2025). The approach seemed solved.

"The hard corrector is very attractive," Chapman explains. "It guarantees closure without you having to decide how much you care about conservation relative to other things. Every sample that comes out satisfies your constraint. It's clean."

Clean, but not without cost.

The Model and the Experiment

Chapman's team was fine-tuning an emulator called CAMulator—a global atmospheric model based on the WXFormer architecture, trained to reproduce the output of CAM6, a conventional climate model developed at NCAR. CAMulator operates on a one-degree grid with 32 atmospheric levels, predicting winds, temperature, moisture, surface pressure, and precipitation at six-hour intervals.

During fine-tuning, they enabled the hard water-budget corrector that had become standard in the CREDIT framework. The corrector computes the global total of water tendency, evaporation (the source), and precipitation (the sink). If they don't balance, it rescales precipitation by the factor needed to close the budget.

The standard configuration evaluated the training loss—the signal that drives learning—on the corrected output. Every prediction satisfied conservation. The diagnostic dashboard glowed green.

But the researchers, following a hunch, began tracking something the loss couldn't see: the raw prediction before correction.

What they found was alarming.

What They Found

The required correction grew monotonically, epoch after epoch. When fine-tuning began, the corrector needed to adjust precipitation by about 2.4%—slightly above the natural variation in the target data (CAM6 itself requires only 0.024% correction on average). By the eighteenth epoch, that number had climbed to 24.1%.

Growth of Required Water-Budget Correction Over 18 Training Epochs

Label	Value
Epoch 1	2.4
Epoch 4	5.5
Epoch 8	11.2
Epoch 12	17.8
Epoch 16	21.5
Epoch 18	24.1

The delivered field, remember, still closed the water budget perfectly. The corrector was simply working harder, multiplying precipitation by a factor of 1.24 to compensate for a raw prediction that had wandered low. A 24% correction factor means the model's underlying precipitation estimate was producing only about 80% of the moisture it should have been—the rest was being supplied by the corrector.

The raw precipitation error tells the full story. Against the CAM6 reference, the model's uncorrected precipitation had drifted from 4% too low to nearly 20% too low. This was not noise or temporary fluctuation; it was a systematic collapse in the model's ability to estimate how much rain should fall.

Raw Precipitation Bias vs CAM6 Target Over Training

Label	Value
Epoch 1	-4
Epoch 4	-7.2
Epoch 8	-11.5
Epoch 12	-15.1
Epoch 16	-18.3
Epoch 18	-19.8

Yet the corrected output looked fine. The post-correction error—precipitation measured after applying the corrector, against the same CAM6 target—was only -0.5% by epoch 18. The corrector had done its job. The loss, which was evaluated on the corrected output, saw only that fine number and had no signal that anything was wrong.

The researchers ran several checks to rule out alternative explanations. They applied the same budget calculation to CAM6 data and found near-zero mean imbalance, confirming the target data weren't to blame. They ran a second independent training from the same starting point and watched the correction grow even larger—peaking above 60%. The mass and energy correctors, meanwhile, remained stable at 0.01% throughout, showing this wasn't a general model instability. Higher-precision arithmetic changed the correction by only a few tenths of a percent, nowhere near enough to explain the 24% signal.

The conclusion was inescapable: the coupling between the corrector and the loss was causing the drift.

The Scale Degeneracy

To understand what went wrong, you need to appreciate a mathematical property of multiplicative correctors: they are invariant under uniform rescaling.

Consider what happens if you take the raw precipitation field and multiply every value by some constant alpha. The spatial pattern—the relative distribution of where it rains—doesn't change, only the overall amplitude. Now pass this through the corrector. The corrector rescales the field again to close the water budget, but this second rescaling exactly cancels the first. The delivered output is identical to what it would have been without the alpha scaling.

Mathematically, if P is the raw precipitation and r is the correction factor, then C(αP) = C(P). The corrector collapses any uniform scaling of the raw field onto a single point.

This means the loss, evaluated on the corrected output, cannot see uniform changes in raw amplitude. They lie in what's called the null space of the correction operator—a direction in the space of all possible predictions where the loss provides no gradient, no information, no restoring force. The network is free to drift in that direction without any learning signal pulling it back.

To verify this, Chapman's team took CAM6 precipitation and uniformly rescaled it by factors of 0.5, 0.75, 1.0, 1.25, and 1.5. The correction factor scaled inversely (r ∝ 1/α), exactly compensating. The corrected output was unchanged to machine precision. The loss evaluated on the corrected field was flat across all five scalings. The loss evaluated on the raw field, and the imbalance penalty they later introduced, both responded strongly.

The invariance was real and complete.

But invariance under uniform scaling explains why the loss can't see drift—it's silent on why the drift went consistently downward rather than up or in random directions. The researchers don't isolate the culprit definitively, but they note several plausible candidates. Strongly supervised fields like temperature and humidity share decoder weights with precipitation, and their gradients could tug precipitation in one direction. Mean-squared-error loss has a known tendency to favor under-prediction for spatially displaced, heavy-tailed distributions like precipitation—it's a documented pathology in the statistics literature. Weight decay was disabled in these runs, removing a potential stabilizer.

The plateau in raw precipitation at around 19.8% below target likely marks when the uniform rescaling assumption breaks down: once the drift becomes large enough that the spatial pattern or other jointly predicted fields are affected, opposing gradients re-enter.

The Contrast Between Correctors

Why did only the water corrector drift? Mass and energy corrections operate on different fields—temperature, humidity, surface pressure—and those fields remain supervised across many levels through coupled terms. After the precipitation corrector rescales precipitation, there is no comparable supervision on its global amplitude. The raw precipitation amplitude is, in the language of the paper, a "weakly supervised model degree of freedom."

The key insight is that a null direction produces visible runaway only when it overlaps a degree of freedom that the remaining objective does not strongly constrain. Precipitation amplitude is exactly such a degree of freedom in the standard corrected-output-supervision setup. Mass and energy fields are more tightly constrained, so their null directions don't cause comparable drift—not because those correctors lack null spaces, but because the other training pressures happen to constrain them.

The Fix and the Ablation

Once the researchers understood the mechanism, the fix was obvious: supervise the prediction before correction, not after. Move the loss so it sees raw precipitation directly, restoring the gradient along the amplitude direction that the corrector had erased.

They also added a soft penalty on the squared closure deviation, (r-1)²—a term that penalizes large correction factors directly. This encourages the network to produce predictions that close the budget on their own, reducing reliance on the corrector.

The hard corrector remained in the forward pass, so the delivered field continued to close the budget exactly. But now the loss could see the raw amplitude, and there was an explicit pressure to keep the correction small.

Starting from the degenerate checkpoint—where the correction had grown to 24%—this configuration reduced the required correction from 24% to below 1% within a single epoch. The model held near zero for the next 64 epochs, with a mean correction of 0.4% and a standard deviation of 0.9% over the final five.

But this recovery changed both variables at once: the loss target and the penalty weight. To isolate which change mattered, the researchers ran a controlled 2×2 ablation crossing loss placement (corrected vs. pre-correction) with penalty weight (0 vs. 0.1), yielding four cells.

Only one cell drifted: Cell A, which used corrected-output supervision with no penalty—the production failure mode. Its correction climbed to 60-70% within a single epoch before partially receding. The raw precipitation collapsed to about 1.0×10¹⁰ kg/s, roughly 40% below the CAM6 reference.

The other three cells remained stable. Cell B (corrected output with penalty) held at a mean correction of 0.5%. Cell C (pre-correction output without penalty) drifted only slightly to 1.1%. Cell D (pre-correction with penalty) stayed at 0.1%.

Ablation Study: Correction Magnitude by Configuration

Label	Value
Cell A: Corrected + No Penalty	65
Cell B: Corrected + Penalty	0.5
Cell C: Pre-corr + No Penalty	1.1
Cell D: Pre-corr + Penalty	0.1

The conclusion was unambiguous: the runaway requires the specific combination of corrected-output supervision with no competing constraint. Restoring pre-correction supervision alone suppresses it. Adding the penalty alone suppresses it. Either change breaks the degenerate configuration.

"The ablation tells you that both fixes work individually," Chapman says. "But they're not equivalent. The penalty route is tuning-dependent—you have to choose a weight, and the right weight might depend on your model, your data, your learning rate. Pre-correction supervision constrains amplitude directly without that extra knob to turn."

Why This Changes Things

A General Diagnostic Principle

The paper's contribution extends beyond the specific precipitation corrector to a general framework for thinking about what hard constraints hide.

When a corrector C(·) is applied to the network output and the supervised loss is evaluated on C(x̂), any perturbation v that satisfies J_C(x̂)v = 0—meaning it lies in the null space of the correction Jacobian—produces zero gradient in the loss. The perturbation is locally invisible. If v corresponds to a physically meaningful property of the raw prediction, and no other training term constrains that property, the model is non-identifiable in that direction. It can drift without the loss knowing.

For a multiplicative global rescaling, this null direction is exactly raw amplitude. The fix, similarly, is general: supervise the prediction before correction, or add a constraint on the null direction, or both.

The broader point is about evaluation. After a hard correction, a closed budget is no longer an independent diagnostic. "You can always close the budget with a corrector," Chapman says. "That's what it's designed to do. The question is whether the model is doing any of the work."

The researchers therefore recommend tracking the raw residual and the size of the correction factor alongside skill metrics in both raw and corrected fields. A growing correction is a warning sign, even when the delivered field looks fine.

Implications for the Field

Several prominent AI climate models use the same corrected-output-supervision strategy that proved vulnerable here. The Ai2 Climate Emulator (ACE2), which has demonstrated stable long integrations and realistic precipitation climatology, uses a precipitation corrector of the same form (a globally uniform multiplicative factor). Its published diagnostics are computed after correction and do not include the correction factor or the raw precipitation field.

"ACE2 contains the same precipitation-amplitude null direction," the paper notes carefully. "Its published diagnostics do not establish whether training produced meaningful drift along that direction, which is exactly the post-correction blind spot we document."

The researchers are careful not to claim ACE2 exhibits the drift they observed. Their experiments used CAMulator under specific fine-tuning conditions. The comparison is at the level of diagnostics: ACE2's published metrics are post-correction-only and thus cannot rule out hidden amplitude drift. "We do not claim that ACE2 exhibits the raw-amplitude degradation documented here," they emphasize.

But the concern is legitimate. If operational models contain the same vulnerability—corrected-output supervision with no check on raw amplitude—then the same silent drift could be occurring in production systems, invisible to the metrics being reported.

"There's a distinction between 'the model conserves' and 'the model learned conservation,'" Chapman says. "Those can come apart completely. You can get perfect post-correction closure while the underlying network is learning something entirely different about how much it should rain."

The Stakes of Long Integration

Why does this matter beyond the immediate training dynamics? Because AI climate models are increasingly used for simulations spanning decades or centuries—the timescales relevant for understanding climate change.

In a free-running simulation, the corrected state feeds back at every step. The model generates a prediction, the corrector adjusts it, the adjusted state becomes the input for the next step. If the corrector is compensating for a raw amplitude that drifts ever further from physical reality, that drift compounds over time. The corrector's scalar adjustment becomes increasingly responsible for setting precipitation amplitude, displacing the network's learned physics.

At some point, the network's raw prediction may depart so far from the correction null space—departing from uniform rescaling—that the corrector can no longer fully compensate. Regional errors emerge that a single global scalar cannot fix. The model enters territory its training never prepared it for.

The researchers have not demonstrated this failure in long free-running runs. Their experiments span short fine-tuning cycles, not multi-year integrations. The stable configuration held for 64 epochs, but that is not evidence of stability over decades of simulated climate time. "We have not shown that the corrected product degrades," they acknowledge. "The cost is the lost diagnostic information, and the risk that drift carries the model outside the correction null space."

This is a genuine open question. The vulnerability is real; its manifestation in long climate runs is not yet measured.

What's Next

Verification and Best Practices

The most immediate implication is methodological: AI weather and climate model developers should audit their training configurations for the same vulnerability.

The diagnostic checklist is straightforward. Track the raw prediction alongside the corrected one. Monitor the correction factor—not just whether it's nonzero, but how it's evolving over training. If it's growing, that's a warning sign. If it's growing while skill metrics look fine, that's a red flag.

The fix is also straightforward: evaluate the loss on pre-correction predictions, not corrected ones, or add an explicit penalty on correction magnitude, or both. This is not a fundamental redesign of conservation training; it's a correction of a subtle but consequential configuration error.

"It's a one-line change to where the loss is evaluated," Chapman notes. "But you have to know you need to make it."

Open Questions

Several questions remain open.

First, how does this vulnerability manifest in long climate integrations? The paper's experiments are short fine-tuning cycles. Demonstrating stable behavior over decades of simulated time, with the pre-correction-supervision fix in place, is the next critical evidence.

Second, how does the vulnerability interact with autoregressive drift—the tendency of AI models to diverge from reality over long self-feeding simulations? If the corrector is compensating for raw amplitude drift, and the simulation feeds back corrected states, the interaction could produce complex dynamics not visible in the training experiments.

Third, are there corrector designs that don't have this problem? The paper analyzes multiplicative global correctors specifically. Other constraint operators—projections, learned corrections, spatially varying adjustments—may have different null space structures. The general principle is clear (track what's hidden from the loss), but the specific vulnerabilities vary by architecture.

Fourth, what is the optimal balance between pre-correction supervision, soft imbalance penalties, and hard correction? The ablation shows both fixes work independently, but the paper doesn't compare their long-term skill implications. Pre-correction supervision constrains amplitude directly; the penalty is tuning-dependent but can shape the learned prediction in ways that pure supervision might not. The tradeoffs are not yet mapped.

The Broader Lesson

AI weather and climate models have achieved remarkable things in a remarkably short time. In five years, they've gone from interesting research prototypes to operational tools being evaluated by national weather services worldwide. The pace of progress has been exhilarating—and, for anyone who cares about the reliability of scientific tools, occasionally vertiginous.

This paper is a reminder that the pace does not eliminate the need for the slow, careful work of understanding failure modes. The vulnerability Chapman and his colleagues found is not obvious. It requires understanding the mathematical structure of correction operators, the geometry of loss landscapes, and the distinction between "the model satisfies the constraint" and "the model learned the physics." It would be easy to miss.

It was missed, perhaps, in prior work that reported benefits from conservation training without monitoring what the corrector was hiding. The authors are careful to credit that prior work—the CREDIT framework's successes are real—but they add a nuance: those successes came with a diagnostic gap that could have concealed the very problem the conservation training was meant to prevent.

"Conservation is still a good idea," Chapman says. "The hard correctors in CREDIT are genuinely useful. What we're saying is: watch what they're doing to your loss. Make sure the thing you're trying to conserve is actually being learned, not just being corrected into existence."

The atmosphere doesn't know it's being simulated. It simply balances water, energy, and mass, continuously, globally, without effort or correction. Teaching AI models to emulate that behavior—to learn the physics rather than outsource it to a corrector—is the real goal. This paper is a step toward understanding what that takes.

The green dashboard told one story. The raw numbers told another. In climate modeling, as in medicine, the most important diagnostic is sometimes the one you haven't thought to run yet.