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."
> 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.
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.
* 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.
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.
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.
https://en.wikipedia.org/wiki/Femtometre
I mean you can’t even fit a thermometer into a cubic femtometer..?
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.
