Per-Pixel Uncertainty and Physical Understanding as the Basis for Trust

In July I wrote about a question that changed how I think about my work — a question about whether validation data ever actually changes the retrieval model, or just checks it. That question led to months of conversation with Nicolas Rouquette (formal methods and systems engineering) and Amy Braverman (statistical uncertainty quantification at JPL), and eventually to a white paper we submitted to NASA’s Earth Science Decadal Survey 2028 Request for Information.

The paper is not about a mission or a project. It is about a gap in method.

The problem

When several instruments estimate the same geophysical quantity — snow water equivalent, soil moisture, sea-ice thickness, biomass — their products often disagree. Averaging does not resolve the disagreement; it hides it. Operational users fall back on decades of personal experience, which works but cannot be scaled, transferred, or defended in a coordination meeting.

What users need is not another estimate. It is a way to know how much to trust the estimate they have: a per-pixel, per-acquisition uncertainty, delivered as a data layer alongside the value itself.

Two halves of trust

Today’s products carry one half each:

• Physics-based products carry the understanding — measurement principles, stated assumptions — but their uncertainty stops at aggregate validation. No per-pixel number travels with the value.
• Machine-learning products carry a statistical uncertainty — they learn from all the data and can put a number on their own spread — but nothing says why the number is what it is. No physics to explain where it breaks.

Combining finished products loses both halves, because nothing in the process carries the physics through.

The proposal

Start from the instrument. Every satellite mission already documents how its signal becomes a geophysical quantity — assumptions, approximations, conditions — in an Algorithm Theoretical Basis Document. What has not been done is turning those documented assumptions into a per-pixel number: propagating the instrument’s error through the forward model so the uncertainty travels with the value.

Then check it against what the data say. Post hoc methods can estimate an operational retrieval’s error from its own data, independently. Where the physics-derived uncertainty and the data-learned uncertainty agree, the product can be trusted. Where they disagree, the physics is incomplete — and that is where it advances.

Two worked examples

The paper uses snow water equivalent (where users have stated their requirements with unusual precision) and soil moisture (where a decade of passive microwave and new active radar data are converging) as worked examples. But the method applies to any quantity estimated from more than one instrument.

Where this goes

This is a framing for discussion, not a finished answer. We submitted it to the Decadal Survey because we believe the next decade — budget-constrained, measurement-rich — needs this shift: from accuracy validation to uncertainty quantification, from fusing finished products to integrating at the level of measurement principles.

The five points we offer:

1. Trust needs two things: quantified uncertainty and physical understanding. Deliver both.
2. Two uncertainties — physics-derived and data-learned — checked against each other, pixel by pixel.
3. Integrate at the measurement level, not the finished product level.
4. Let the user own the threshold: deliver the number and the error bar.
5. Derive the next measurement from what the current system cannot see.

Full paper (PDF): Per-Pixel Uncertainty and Physical Understanding as the Basis for Trust in Multi-Instrument Products

Authors: Xiaolan Xu, Nicolas Rouquette, Amy Braverman — Jet Propulsion Laboratory, California Institute of Technology

Submitted: August 2026, to the National Academies ESAS 2028 Decadal Survey Request for Information