---
title: Earth models that show their uncertainty: covariance maps, unseen wells, and climate surrogates
description: In preprints, an inversion method returns a map of where data constrain the model, a groundwater model forecasts at wells it was not trained on, and a climate model is calibrated to two different sensitivity values.
canonical: https://hangingcontext.com/stories/2026-11-01/earth-models-show-their-uncertainty/
last-updated: 2026-11-01
url: https://hangingcontext.com/stories/2026-11-01/earth-models-show-their-uncertainty/
published: 2026-11-01T12:23:19Z
edition: 2026-11-01T12
newsroom: research-science
beat: None
trust: confirmed
source_count: 4
cited_manifest_ids: ['1793529133974313504', '1793526038967795182', '1793526038966493052', '1793522006065704601']
---

# Earth models that show their uncertainty: covariance maps, unseen wells, and climate surrogates

*In preprints, an inversion method returns a map of where data constrain the model, a groundwater model forecasts at wells it was not trained on, and a climate model is calibrated to two different sensitivity values.*

Confirmed · 4 sources · Research & Science · Published 2026-11-01 12:23 UTC

## Key facts

- In a preprint, a stochastic variational inference framework for electrical resistivity tomography and time-domain induced polarization uses adjoint-state gradients for mean and covariance updates and offers a computationally efficient alternative to Markov chain Monte Carlo. (self-reported) [cites: 1793529133974313504]
- In a preprint, GeoAI-GWFM-KR outperforms per-well long short-term memory networks in groundwater level forecasting at 7, 30, and 90-day horizons. (self-reported) [cites: 1793526038967795182]
- In a preprint, E3SMv3 can be calibrated to an equilibrium climate sensitivity of 2.69 K or 4.67 K using a machine learning surrogate model, against a default of 3.89 K. (self-reported) [cites: 1793526038966493052]
- In a preprint, a four-step workflow converts TensorFlow-based seismic phase pickers to PyTorch without retraining while preserving original model weights. (self-reported) [cites: 1793522006065704601]

## Inversion that maps its own limits

In a preprint, the useful output of an inversion is not only a subsurface image but a statement about where that image can be trusted. The stochastic variational inference framework for electrical resistivity tomography and time-domain induced polarization provides a computationally efficient alternative to Markov chain Monte Carlo by using adjoint-state gradients for both mean and covariance updates. Efficiency here is a practical claim: the same gradient machinery updates the central estimate and its spread. [cites: 1793529133974313504]

The recovered covariance in the framework serves as a spatial map indicating where geophysical data constrain the subsurface model. Where the map shows strong constraint, the data are doing the work; where it does not, the model is filling in. Field application at the Hongqi Reservoir demonstrates the ability of the framework to identify conductivity and chargeability structures associated with seepage outlets, so the map is tied to features with a physical reading, not only to abstract uncertainty. [cites: 1793529133974313504]

## Groundwater at wells never trained on

A second preprint addresses a different kind of uncertainty: what happens at a location with no training record of its own. Foundation models adapted with low-rank adapters can accurately forecast groundwater levels at unseen wells without per-well training, according to the preprint. The test is direct, since the wells in question were not part of per-well training, and the model must transfer what it learned elsewhere. [cites: 1793526038967795182]

> **From Synorb** — Run the cited Manifests yourself. Every claim in this paper points to a Manifest id. Get a Synorb Key and read the Manifests behind it. The 72 Hour Agent Demo key needs no email. It lasts 72 hours and can pull up to 25 Manifests. It includes 5 Beacons; all of them are starter Beacons. [Get a key](https://synorb.com/connect/start)


GeoAI-GWFM-KR, a time-series foundation model adapted to the Korean monitoring network, outperforms per-well long short-term memory networks in groundwater level forecasting at 7, 30, and 90-day horizons. The comparison spans short, medium, and longer horizons, so the result is not confined to one forecast window. Physics-informed loss functions did not improve the accuracy of per-well long short-term memory networks in this study, which is a useful negative result: adding physics-flavored training terms did not help the baseline it was tested on. [cites: 1793526038967795182]

## A climate model tuned two ways

A third preprint makes model uncertainty explicit by calibrating one climate model to two different answers. E3SMv3 can be calibrated to achieve an equilibrium climate sensitivity of 2.69 K or 4.67 K using a machine learning surrogate model, while the default equilibrium climate sensitivity of E3SMv3 is 3.89 K. The spread between the two calibrated values is wider than the distance from either value to the default, which shows how much room calibration choices leave. [cites: 1793526038966493052]

A 400-member perturbed parameter ensemble, varying 14 atmospheric parameters, is sufficient to train a surrogate model consistent with 46 climate variables from satellite and reanalysis data. The ensemble size, the parameter count, and the variable count together describe the training basis for the surrogate. This suggests that the surrogate is not a shortcut around physics but a compressed map of many model runs, and that its value depends on whether that map stays consistent across the variables it was trained to match. [cites: 1793526038966493052]

## Tools that move without retraining

A fourth preprint concerns tooling rather than a single model result, but it fits the same theme of stated fidelity. A four-step workflow enables the conversion of TensorFlow-based seismic phase pickers to PyTorch without retraining, preserving original model weights. Conversion without retraining matters because retraining can change behavior in ways that are hard to trace back to the original model. [cites: 1793522006065704601]

Converted EQCCT models, named EQCCTP and EQCCTS, exhibit mean absolute errors between 1.46 times ten to the power of negative nine and 1.82 times ten to the power of negative nine compared with original TensorFlow implementations. Those errors are small in absolute terms, and reporting them gives users a number for how much conversion changed the output. Across all four preprints, the pattern is consistent: the result is reported together with a measure of where it holds, where it weakens, or how far it moved. [cites: 1793522006065704601]

## What is still unresolved

- Whether the covariance map from the inversion framework generalizes beyond the Hongqi Reservoir field application
- Whether groundwater forecasts at unseen wells hold outside the Korean monitoring network tested here
- Which calibrated equilibrium climate sensitivity value, if either, better matches observations beyond the 46 variables used
- Whether converted phase pickers perform as closely on data beyond the comparison reported here

## Decision card

- **Useful for:** Modelers who need uncertainty, transfer, or calibration limits stated alongside a result; Teams choosing between per-site training and foundation-model transfer for groundwater or subsurface work
- **Not for:** Treating a surrogate-calibrated sensitivity value as a new best estimate on its own; Assuming that a method that works at unseen wells in one network works everywhere
- **Compare against:** Markov chain Monte Carlo inversion, per-well long short-term memory networks, and the default E3SMv3 calibration, which these preprints use as baselines

## Provenance ledger

| Manifest id | Title | Source | Claims used | Published |
|---|---|---|---|---|
| `1793529133974313504` | Stochastic Variational Inference for Electrical Resistivity Tomography and Time-Domain Induced Polarization with Adjoint-State Gradients | [ess-open-archive-geology-minerals-geophysics](https://essopenarchive.org/doi/full/10.22541/essoar.15011381/v1) | 1793529910545449031, 1793529910548795939, 1793529910550229030 | 11-01 00:00 |
| `1793526038967795182` | Forecasting groundwater levels at unseen wells without per-well training: GeoAI-GWFM-KR, a time-series foundation model adapted to the Korean monitoring network | [ess-open-archive-geospatial-remote-sensing-ai](https://essopenarchive.org/doi/full/10.22541/essoar.15011386/v1) | 1793526237048473801, 1793526237051306910, 1793526237053042831 | 11-01 00:00 |
| `1793526038966493052` | Calibration of E3SMv3 for Low and High Equilibrium Climate Sensitivity Using a Machine Learning Surrogate Model | [ess-open-archive-geospatial-remote-sensing-ai](https://essopenarchive.org/doi/full/10.22541/essoar.176265632.20461249/v2) | 1793526237307644393, 1793526237309201940, 1793526237311208193 | 11-01 00:00 |
| `1793522006065704601` | Porting Deep-Learning Phase Pickers from TensorFlow to PyTorch for SeisBench Without | [ess-open-archive-ocean-cryosphere-sea-level](https://essopenarchive.org/doi/full/10.22541/essoar.15011367/v1) | 1793522864202293458, 1793522864203940398 | 11-01 00:00 |

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Cited Manifest ids:

- `1793529133974313504`
- `1793526038967795182`
- `1793526038966493052`
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done
```

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