[counters]

Which is *exactly* why ultra-high resolution global weather simulation has dubious prospects for improving forecasts. When you're at spatial scales where you need to parameterize convection, there's an inherent "smoothness" to model solutions that suppresses noisy errors. If you go to cloud-resolving scales - which is needed for simulations like the ones here - you don't get the benefit of that smoothness anymore, because you need to actually resolve scales of motion that are incredibly fine. It's a losing proposition; you'll never get it "perfect", so you're much more likely to spin up an error cascade with significant impacts on forecast down the line, through things like the structure of organized convection.

But dynamically uninteresting, quasi-balanced setups and modes? There's far less to worry about in terms of the butterfly effect, and any errors you might worry about will be dwarfed by the fact that we don't have good data to assimilate in places like the remote oceans anyways.

It's also worth pointing out that the mathematics and understanding of error / perturbation growth in the atmosphere are well-understood. In fact, this fundamentally underpins how we've developed data assimilation approaches over the past two or three decades that allow us to effectively leverage new datasets such as satellite data to increase forecast quality and reliability at longer lead times. So it's somewhat trivial to actually directly quantify these "butterflies."

[Maursault]

If we're ever going to get to the femtometer resolution required for very precise 100 day weather forecasting, we have to start somewhere, so let them waste their time. It's not as though this is part of a growing trend to abandon conventional weather and climate modeling.

[counters]

Why do you think that we need "femtometer resolution" for "very precise" 100 day weather forecasting? What even is "very precise" 100 day weather forecasting? I think it's very amusing to do the math on how much memory would be required to run a crude primitive equation dycore over even the tiniest of domains at femtometer resolution :)

> It's not as though this is part of a growing trend to abandon conventional weather and climate modeling.

The thing is, there *absolutely is* a trend towards private investment in weather modeling going towards faux-moonshot ideas like cubesat constellations without demonstrated ROI and that would require evolutionary leaps forward in data assimilation, or for deep learning to replace weather models. A miniature version of this already played out with precipitation nowcasting - probably the easiest weather forecasting problem that you could approach with an AI system, yet the approaches that have been developed so far barely improve over optical flow or other simple approaches, let alone advance our capability to forecast, say, convective initiation.

The future of weather forecasting is larger ensembles (O(100-500) ensemble members, across 2-5 different models) of near-convective-resolving global models at meso-gamma (2-10 km resolution) fed into slightly more sophisticated statistical post-processing systems - almost certainly trained using simple AI/ML techniques on large-scale reforecasts of these parent model systems, or brute-forcing purely Bayesian statistical approaches.

[Maursault]

> Why do you think that we need "femtometer resolution" for "very precise" 100 day weather forecasting?

Due to sensitive dependence on initial conditons. Even using measurements at meter resolution will cause the accuracy of a forecast to begin to break down after only a few days.

> What even is "very precise" 100 day weather forecasting?

Anywhere from accurate to exact.

> I think it's very amusing to do the math on how much memory would be required to run a crude primitive equation dycore over even the tiniest of domains at femtometer resolution

And Bill Gates thought 64K should be enough for anybody. Do you really think computers will only have a few GB of memory 50 years from now?

> there absolutely is a trend towards private investment in weather modeling going towards faux-moonshot ideas like cubesat constellations without demonstrated ROI and that would require evolutionary leaps forward in data assimilation, or for deep learning to replace weather models

This straw man does not exactly demonstrate that conventional weather and climate modeling is being abandoned anytime soon. If the unconventional private investments aren't profitable, the market will deal with them.

> The future of weather forecasting is

much like the local weather, impossible to predict with any accuracy years into the future, and yet the tools used to measure it are consistently getting more accurate, cheaper and smaller. Maybe like bottle-openers, weather sensors may superfluously start appear on everything. The more widespread the measurements, the more data descibing initial conditions, the better the forecast will be at any interval.

[nine_k]

* You don't have the density of sensors to see even at a meter resolution, to say nothing of femtometer. Actually in oceans you don't have many sensors at all, and most data come from satellite observations that give rather indirect information. Even if you had a capability to compute a model at femtometer resolution, I don't see how much of it would you be able to fit to observations.

* It's pretty hard to predict weather for 100 days, because you would also need to predict many other events in the future: forest fires, volcano eruptions, and many kinds of human activity that also affect weather. However great are your fluid dynamic models, and however well were they able to predict the future state from today's state, they wont help that.

[Maursault]

> You don't have the density of sensors to see even at a meter resolution, to say nothing of femtometer.

At the moment, no. But maybe there will be a way to accurately sense weather data at any location from LEO. IR thermometers are pretty neat, maybe something metaphorically along those lines, a satellite with a laser technology that could beam back accurate weather data from any location, and all atmospheric locations it can see along its orbit, sending the data to ground-based ultra-computer networks running simulations.

In 1933, no one would have believed that GPS was 40 years away. In 1985 most would not have been able to understand how flat and thin color monitors were only a decade away, nor that mRNA vaccines were less that 30 years away. Similarly, we really don't know what the future of weather sensing and prediction will be like in 2070, and if we could know, we wouldn't understand how it would be possible.

[counters]

> Due to sensitive dependence on initial conditons. Even using measurements at meter resolution will cause the accuracy of a forecast to begin to break down after only a few days.

That's an extremely simplistic take on things. In reality, one of the largest issues with high-resolution weather forecasts (1-3 km scale, convection-permitting simulations) is the fact that you small errors in the initialization or model dynamics lead to changes in small-scale storm structure that feedback onto larger scales of motions, disrupting the forecast. Ultra-fine measurements and simulation resolutions only exacerbate this tendency.

> Anywhere from accurate to exact.

You didn't answer the question. Are you trying to predict convective initiation at 100 days lead time? Are you trying to predict a particular synoptic system? Are you trying to predict whether or not it will be warmer than average or not? These are vastly different weather prediction problems which require different approaches.

> And Bill Gates thought 64K should be enough for anybody. Do you really think computers will only have a few GB of memory 50 years from now?

Modern weather and climate modeling is already a tera- or peta-scale endeavor, depending on exactly what one is trying to do. The sorts of simulations alluded to in the OP push into the exascale.

As other commenters have noted, your odd choice of femotometer (10^-15 meters) would lead to memory requirements larger than the number of atoms in the real atmosphere.

> This straw man does not exactly demonstrate that conventional weather and climate modeling is being abandoned anytime soon. If the unconventional private investments aren't profitable, the market will deal with them.

Of course it does. The age of heterogeneous compute for weather/climate models is just beginning, yet you do not see NVIDIA optimizing NWP systems to run on GPUs or Google porting them to run on TPUs, do you? Instead, you see these organizations pursuing AI/DL, while core NWP development is limited to federal research labs and agencies, but they are increasingly struggling to attract developer and research scientist talent to pursue these activities.

This is a very real challenge that is frequently talked about within the weather community in the United States. I'd hazard the guess that you are not a member of this community?

> much like the local weather, impossible to predict with any accuracy years into the future, and yet the tools used to measure it are consistently getting more accurate, cheaper and smaller. Maybe like bottle-openers, weather sensors may superfluously start appear on everything. The more widespread the measurements, the more data descibing initial conditions, the better the forecast will be at any interval.

There is virtually no data assimilation technology to support the ingestion of the vast majority these data, and we do not even run weather models with suitable configurations to take advantage of them if we had the DA support in the first place. And, as I've mentioned repeatedly, not every measurement leads to an improvement in forecast quality. This is simply _not_ the low- or even high-hanging fruit regarding improvements to weather forecast quality and impact.

I've worked in this exact domain of developing novel weather sensing and observation systems and leveraging them to try to improve forecast quality - across federally-funded research and more than one private company over the past ten years - and it's mostly a fools errand. If one wants to develop improved, impactful, useful weather forecasts, this is not the path to pursue.

[contravariant]

You want to know the precise shape of the Earth's surface in femtometer precision?

There are some profound problems with that idea once you get below 10 meter or so, but I'll let you think that one through yourself.

[Maursault]

No, but I wouldn't mind weather measuments every cubic femtometer of the lower atmosphere and a fast enough computer with enough memory to cruch the data and accurately report what the weather will be like on 29 February.

[doctor_eval]

Are we thinking about the same femtometer? 10^-15 of a meter?

https://en.wikipedia.org/wiki/Femtometre

I mean you can’t even fit a thermometer into a cubic femtometer..?

[Certhas]

I think Maursault has thoroughly demonstrated their lack of serious thought or reading on the subject. But just for giggles and for the casual reader, the lattice spacing of silicon is 200,000 femtometer. So if you encode only one bit per cube of this fm cubic lattice, and you manage to encode this into single atoms of silicon, you need a volume of silicon 8,000,000,000,000,000 times larger than the system you model.

[Maursault]

> I think Maursault has thoroughly demonstrated their lack of serious thought

When you can't beat the argument, pull out the ad hominem fallacy and attack the man. Fallacy, of course, is faulty reasoning.

> So if you encode only one bit per cube of this fm cubic lattice, and you manage to encode this into single atoms of silicon, you need a volume of silicon 8,000,000,000,000,000 times larger than the system you model.

This explanation is indicative of linear thinking. Apparently Google Earth is not possible, as it would require a computer the size of the planet. Digitizing the Library of Congress apparently requires a memory stick the size of Congress. Seriously? You just can not comprehend how things could ever get better than your current understanding of how things are right now? Consider that if you lived in 1500BC, were an expert at the time in farming, and a plough was described to you, you would mock the person describing it, and insist that tilling soil was impossible.

[Maursault]

What is the smallest possible width of a photon? How do IR thermometers work without fitting them in anywhere? You just never know how it might be done.

[adgjlsfhk1]

there's a very good physical argument that this is impossible. if you want to store 1 bit per femptometer simulated, at current computer sizes, we are taking about a computer billions the size of the earth. even if you use 1 atom per bit, your computer will be almost as big as the earth. such a computer will collapse under it's own gravity.

[Maursault]

> at current computer sizes

This. No, not at all at current computer sizes, but at future computer sizes. This is the same mistake someone in the 1970's might make about billions having a smartphone today (supercomputer by their standards). Consider how everything at current computer sizes is effectively two dimensional, even stacked processors are still fundamentally 2D designs. There is still a lot of computing advancement ahead. 40 years from now they'll look back and think the same things we think when we look back 40 years, that the machines were so primitive, hardly anything could be done with them, and some will be nostalgic for them, talk about their strengths, while others will shake their heads and think even messing with the fastest workstation today is a waste of time. Just because we can't conceive of how, doesn't mean it's not possible, some day.

[adgjlsfhk1]

do the math at 1 atom per bit.

[adrianN]

It's extremely unlikely that we'll ever get anywhere near that. Even meter precision is impractical.

[Maursault]

Unless you know it to be physically or logically impossible, you could not really know how likely it is or isn't. Ask anyone in the mid-1970's how likely it is that billions of people would be walking around with a supercomputer in their pockets, and they'd come up with all sorts of reasons why it was extremely unlikely, such as no individual would ever need so much computing power. The practicality of the precision only depends on the ability to measure and the ability to manipulate and simulate large amounts of data, both of which are extremely likely to get better, and better faster and faster, as time and technology progresses.

[adrianN]

A femtometer is a few orders of magnitude smaller than an atom. There are about 2*140 atoms in the atmosphere. You can't even count to that number, let alone do any fluid dynamics to that. I'm confident that we won't have femtometer scale simulations of the atmosphere before the sun becomes a red giant and swallows the earth.

[Maursault]

> A femtometer is a few orders of magnitude smaller than an atom.

Thank you for telling me what a femtometer is, as though my using the word wasn't a pretty good indicator I knew what it was. You mean a femtometer is a real thing? And I just made that up out of thin air to mean a meter stick to give to women. What are the odds?

> There are about 2*140 atoms in the atmosphere. You can't even count to that number, let alone do any fluid dynamics to that.

Would you like me to explain how your argument is a straw man, or can I trust you to figure it out?

> I'm confident that we won't have femtometer scale simulations of the atmosphere before the sun becomes a red giant and swallows the earth.

Very colorful, but all you're really saying is that you are pessimistic about technology and about any staggeringly large advancements in computer design or weather sensor tech, while I, otoh, optimistically say I just don't know, but I bet computers will get faster, smaller and cheaper, and that within only a hundred years there will be weather tech that we are incapable of conceiving of today.

Sure, a femtometer is mind-bogglingly small, but it's only 15 orders of magnitude smaller than a meter. It's way bigger than a zeptometer. How is it even possible femtometers can be described so simply? But of course, there could never be any more advancements in mathematics, physics, computer engineering or our current understanding of weather and climate. We basically know all there is to know right now. Huh.

[adrianN]

Maybe read https://arxiv.org/pdf/quant-ph/9908043.pdf before you think about computers operating on 2*140 objects and try to be less aggressive in your comments.