The short version
- Refining a climate model's grid does not cost what people assume. Halving the spacing quarters the cell area, but a dynamical model must also shorten its timestep to stay stable, so cost grows as the inverse cube of grid spacing in two dimensions.
- Moving from 50 km to 1 km is a factor of 125,000 in two dimensions and 6.25 million in three. Then multiply by the ensemble size you need for any honest statement about uncertainty.
- An AI emulator has no timestep to shorten, and a decomposed emulator evaluates subdomains independently. Wall-clock time becomes a function of how many you can run at once.
- That turns compute from a physical ceiling into a budget line, which is the difference between a country owning its climate intelligence and renting it.
Ask a Caribbean ministry why its climate projections are at 25 or 50 km and you will usually get an answer about data availability or capacity. Both are real. Neither is the binding constraint.
The binding constraint is that the arithmetic of refining a grid is worse than almost everyone outside the field expects, and once you see the exponent you understand why a whole region has been planning coastal infrastructure and agricultural policy off fields too coarse to distinguish one parish from the next.
The Exponent
Two effects compound.
The first is obvious. Halving the grid spacing quarters the cell area, so cell count grows as the inverse square of spacing. Going from 50 km to 1 km multiplies the number of cells by 2,500.
The second is not obvious unless you have written the code. A dynamical model integrates the equations of motion forward in discrete steps, and the step length is bounded by how far information can travel across one cell in one step. This is the Courant condition:
Violate it and the numerical scheme does not merely lose accuracy, it blows up. So when you shrink the cell you must shrink the step, and the number of steps grows as the inverse first power of spacing on top of the cell count. That takes the total to the inverse cube. Refine the vertical as well and the exponent reaches four.
In round numbers: 125,000 times the cost in two dimensions to go from 50 km to 1 km, or 6.25 million in three. And that is one run. A single deterministic run tells you what happened in one draw of a chaotic system. To say anything defensible about probability you need an ensemble, so multiply again by the ensemble size.
This is the whole reason AI emulation exists as a research field. It is also why the answer to "just run a finer model" has been no for thirty years.
What an Emulator Changes
An emulator learns the mapping from a coarse field to a fine one. It does not integrate forward in time, so there is no timestep and therefore no Courant condition to satisfy. Its total work still grows with the number of cells, so it still grows as the inverse square, but it sheds the extra factor. At 1 km that is about fifty times cheaper than the two-dimensional dynamical route and 2,500 times cheaper than the three-dimensional one.
Decomposition does something further, and it is the part that matters for procurement. If the domain is split into subdomains that are evaluated independently, then the memory a machine needs is set by the size of one subdomain rather than by the size of the country. The subdomains do not wait for one another.
That converts the question from "can we afford a supercomputer" to "how many parallel workers do we want to pay for this month". A meteorological service asking whether a method fits in a line item is asking a different and much more answerable question than one asking whether it can build a data centre.
Why This Is a Sovereignty Question
Renting climate intelligence has three costs that do not show up on the invoice.
You cannot interrogate what you did not build. When a vendor's projection says a coastal road has a 1-in-50-year flood exposure, somebody in the ministry has to be able to ask what driving model that came from, what its bias over the Caribbean is, and how the number moves if that bias is corrected. If nobody can ask, the number gets used anyway.
You cannot re-run what you do not control. Emergency management needs answers on the timescale of the emergency. A contract with a quarterly deliverable cycle does not produce a flood footprint for a storm that forms on Tuesday.
You cannot extend what you do not own. Every country in this region has a hazard nobody else models: a specific gully, a specific reservoir, a specific stretch of coast. Those get added by the people who live there or they do not get added.
None of this is an argument for building everything from scratch. It is an argument for owning the layer where local knowledge enters, and for that layer being cheap enough to run repeatedly.
What Is Actually Being Built
The research behind this article is doctoral work at the Climate Studies Group Mona, in the Department of Physics at The University of the West Indies, Mona, which has been doing Caribbean climate science since 1994.
The technical contribution is narrow, which is how research should work. Physics-constrained downscaling models already enforce one conservation law: the average of the fine field should match the coarse input. That law assumes the coarse driver is unbiased, which holds in a controlled experiment and fails in operation, and global models carry documented rainfall biases over this basin. There is a second law nobody has enforced, which is that what leaves one subdomain through a face must equal what enters its neighbour through the same face. That constraint binds the fine field to itself, so it does not inherit the driver's bias.
There are no results yet. The scaling argument above is arithmetic and stands on its own; the claim about the second conservation law is a hypothesis with a pre-registered experiment attached, and the experiment is designed so that a null result is publishable. The full technical version is here.
Four Questions for the Procurement File
If your ministry, utility or insurer is evaluating climate intelligence, these four separate a usable system from a demonstration.
- What is the native resolution over land? Not the delivery resolution. Interpolating a 50 km field onto a 1 km grid adds pixels and no information, and it is a very common practice.
- What does one run cost, in currency, per simulated year? Almost nobody in this field publishes that figure. It decides whether you can run the ensembles you need or only the single run the vendor demonstrated.
- How does skill degrade when the driving model is biased? Ask for the degradation curve, not the headline score. Every operational deployment runs on a biased driver.
- What result would make you say this model had failed? If nobody on the vendor's side can answer, you are buying a demonstration.
The Part I Am Least Sure Of
The cost argument is arithmetic and I will defend every digit of it. The claim that a cheaper model is a better model is not arithmetic, and it is not established. An emulator trained on one climate can fail when the climate moves, and testing that properly needs scenario runs that do not exist yet. The honest position today is that emulation makes kilometre-scale output affordable, and that whether it makes it trustworthy is the open question the next two years of work has to answer.
Frequently Asked Questions
Does this mean dynamical climate models are obsolete?
No. Emulators are trained on dynamical model output, so the dynamical models are the source of the physics. What changes is where the expensive runs get spent: a small number of reference simulations, instead of every ensemble member of every scenario for every region.
How much would a Caribbean government actually pay?
I am not going to invent a figure. Cost per downscaled simulated year, in currency, at each subdomain size, is a number that has to come out of the experiments, and it is almost never published in this literature. When it exists it will be reported.
Could this run on a phone?
That is the design target. Because a decomposed emulator evaluates one subdomain at a time, the memory needed is bounded by subdomain size rather than domain size, so a phone would run the subdomain covering its own location. The scaling argument for that is established. The deployment is not, and treating it as a current capability would be wrong.
Where does StarApple AI fit?
StarApple AI is the Caribbean's first AI company and works on applied AI systems across the region. The climate emulation research described here is academic work at UWI Mona and is separate from any commercial product. Keeping that line visible matters, because a methods claim published under a company banner invites a discount it should not have to carry.