Model Hierarchies

Isaac Held noticed something troubling about climate science in 2005: a gap had opened between understanding and simulation. Climate scientists had two kinds of models — very simple idealized ones that could sometimes be thoroughly understood, and enormously complex Earth system models (ESMs) that could simulate the climate with high fidelity but couldn't be completely understood because of their complexity. The gap between these extremes was mostly empty. Held's diagnosis was that the field needed a hierarchy of models to bridge it, just as biologists have a hierarchy of organisms (bacteria, fruit fly, mouse, human) at increasing levels of complexity.¹

More than a decade later, a team at the Community Earth System Model project (CESM) took Held's challenge seriously and began building that hierarchy. Their argument is worth understanding not just for climate science but for any field that uses complex simulations — which increasingly means all of them.

The Problem With Complexity

Modern Earth system models are staggering in their ambition. They simulate atmosphere, ocean, land surface, ice, biogeochemical cycles, and their interactions at high resolution. Running them requires the most expensive supercomputers available. The result is a simulation that can generate accurate climate projections, but at a cost: the models are too complex to understand why they produce the results they do.¹

"Earth system models may be good for simulating the climate system but may not be as valuable for understanding it." This is the core tension. A model that reproduces observed behavior but can't explain it has limited scientific value — you can't use it to develop intuition, test hypotheses about mechanisms, or identify which processes matter most. You also can't explore its parameter space because each run takes too long and costs too much.

Held's biological analogy is illuminating: imagine if molecular biologists could only study humans. No bacteria, no fruit flies, no mice — just the full complexity of human biology. Progress would be glacial. The reason biology has advanced so rapidly is that "nature has provided us with a hierarchy of biological systems of increasing complexity that are amenable to experimental manipulation." The nature of evolution ensures that insights from simpler organisms are often directly relevant to more complex ones.¹

Climate science doesn't get this gift for free — it has to build the hierarchy deliberately. That's what the CESM project did.

The Bookends

The first two models released are bookends of the atmospheric hierarchy:¹

The dynamical core is the simplest: it solves only the fluid dynamics equations, with all other physical processes massively simplified. It's a pure atmosphere in motion, with no clouds, no radiation, no chemistry. This lets researchers study how atmospheric circulation works in isolation — the "grammar" of the atmosphere before you add the vocabulary of weather.

The aquaplanet is nearly as complex as the full atmospheric model, with one radical simplification: all land has been eliminated. Earth's entire surface is ocean. This removes the complicating effects of continents, mountain ranges, and land-surface processes, while keeping the full physics of clouds, radiation, and atmospheric chemistry. It lets researchers ask: what would weather and climate look like on a water world?

Between these extremes, the hierarchy can be filled in. Single-column models that simulate a vertical slice of atmosphere. Ocean models of varying complexity. Land models stripped to essentials. Each level adds one source of complexity, so that when behavior changes, you know what caused it.

Models of Lasting Value

The most provocative aspect of the proposal is that some models in the hierarchy should be deliberately frozen. ESMs are under constant development — every year brings new parameterizations, higher resolution, better physics. But the simpler models should be "forcefully shielded from the relentless cycle of model improving and updating." Their value comes precisely from being unchanged. If a model stays the same for decades, researchers can understand it in depth. New observations and theories can be tested against a stable reference. Students can master the concepts before confronting the full complexity of an ESM.¹

This goes against every instinct in computational science, where "update to the latest version" is dogma. But Held's point — and Polvani and colleagues echo it — is that understanding requires stability. You can't deeply understand a model that changes every year. The simple models are not stepping stones to be discarded but permanent intellectual infrastructure.

Beyond Climate

The idea of model hierarchies applies far beyond climate science. Ecological modeling faces the same gap: process-based models of ecosystem function are either too simple to test or too complex to understand. The International Biological Programme failed in the 1960s partly because it tried to measure everything without a hierarchy of models to organize the measurements. World3, the Limits to Growth model, sits at one end of a systems-dynamics hierarchy — it's useful precisely because it's simple enough to understand in full, and its structural properties (overshoot, oscillation, collapse) are clearly traceable to specific feedback loops.¹

The same principle operates in machine learning. Researchers who study only the largest language models can characterize their behavior but often can't explain it. Those who also study small, interpretable models — and trace how behavior changes as models scale up — develop genuine mechanistic understanding. The hierarchy is the method.

I think the deepest lesson here is epistemological. Simulating a system is not the same as understanding it. A perfect simulation — one that reproduces every observable detail of the target system — is no more understandable than the system itself. Understanding requires compression: finding the minimal description that captures the essential dynamics. Model hierarchies are a systematic way to perform that compression, not by simplifying blindly, but by removing one source of complexity at a time and watching what changes.