ChatGPT on predicting the weather [what are the limits of prediction for various phenomena?]

I’m interested in things we can predict and how we go about it. Newtonian mechanics gave us the means to predict the motion of the planets, so that’s now a solved problem – though I understand there are some nuances (chaos at the margins). Enormous effort goes into predicting the stock market. Much of that work is proprietary. In any event, I assume it’s an open problem.

What I’m really interested in is culture, such as Arthur De Vany’s work on predicting the success of a film once it’s released. He claims it’s impossible. I assume the same holds for books, records, and the like. Here we’ve got complex phenomena. Each title (movie, book, etc.) is an object of potentially unbounded complexity. The market is a population of people who have varying preferences for those complex objects. Perhaps the most interesting thing about this market place is that it has latent preferences (my coinage, though I wouldn’t be surprised if the concept, and even the term, is already in use; come to think of it, I’d be surprised if it isn’t). These preferences become visible only when an object is produced that satisfies them.

Now, one might observe of De Vany’s work that his method is crude. He trying to make predictions based on knowledge of producers, actors, directors, writers, and opening box-office. Maybe a more sophisticated set of variables, variables that tell us more about the films, would make prediction possible. Maybe, maybe some improvement is possible. But how much? What I’m wondering is whether or not these kinds of systems are computationally irreducible in the sense that Wolfram talks about. If so, then really accurate prediction would require a model as complex as the phenomenon itself.

All that’s by way of introduction. It provides context for this morning’s session with ChatGPT, where I asked it about weather prediction. My last question is about theoretical limits to accuracy. ChatGPT’s answers suggests that the weather system may ultimately be computationally irreducible. And, if you’re interested in long-term predictions, no matter how accurate your current model, if a large volcano blows the hurls enough dust into the atmosphere to affect the earth’s temperature, your predictions are now shot to hell.

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I’m interested in how we predict the weather. I know we use computer models. I know that weather is chaotic, in the mathematical sense, that is, it is sensitive to small variations in initial conditions. I’m interested in two things in particular: 1) How accurate are the forecasts over time? For example what’s the accuracy of a 3-day forecast vs. a 10-day forecast? 2) What’s the size of the data grid on which the models are based? My impression is that the resolution of the grid is stated in kilometers.

Predicting the weather is a complex task, and it relies on a combination of observational data, computer models, and our understanding of atmospheric physics. Let me address your two questions:

1. Accuracy of Weather Forecasts Over Time:

• Weather forecasts are generally more accurate for shorter timeframes and become less accurate as you extend the forecast period. The accuracy of a forecast depends on various factors, including the region, weather conditions, and the lead time.
  
• Short-term forecasts (e.g., 1-3 days) tend to be more accurate, with high precision in predicting temperature, precipitation, and wind patterns. These forecasts are often reliable for planning daily activities.
  
• Medium-range forecasts (around 4-7 days) are less precise and are subject to greater uncertainty. While they can provide general trends, they may not be accurate for specific details.
  
• Long-range forecasts (beyond 7-10 days) are even less accurate and are more like climatological trends rather than detailed weather predictions.

2. Grid Resolution of Weather Models:

• Numerical weather models divide the atmosphere into a three-dimensional grid to simulate the behavior of the atmosphere. The resolution of these grids is indeed stated in kilometers and is known as the "grid spacing" or "grid resolution."
  
• High-resolution models have smaller grid spacing (e.g., 1-10 kilometers) and can provide more detailed forecasts, especially for local or short-term weather events. These models are typically used for regional weather predictions.
  
• Coarser-resolution models have larger grid spacing (e.g., 10-50 kilometers or more) and are used for global weather forecasts, as they cover larger geographic areas. They are less detailed but can provide information on large-scale weather patterns.
  
• The choice of grid resolution depends on the specific goals of the forecast and the available computational resources. Weather agencies use a hierarchy of models with different resolutions to cater to various forecasting needs.

It's important to note that advances in technology and improved understanding of atmospheric processes have led to better weather predictions over the years. Weather forecast accuracy has significantly improved for short-term forecasts, and even medium-range forecasts have seen improvements. However, long-range forecasting remains challenging due to the chaotic nature of the atmosphere and the limitations of current modeling capabilities.

What’s the largest computers used in weather forecasting? How long does it take to run a simulation? Are there any weather models so complicated that it takes almost as much time to run the model as it takes for the weather to evolve?

Weather forecasting requires powerful supercomputers to run the complex numerical models that simulate the atmosphere. Some of the largest computers used in weather forecasting include:

1. IBM Blue Gene: The IBM Blue Gene supercomputers, like Blue Gene/P and Blue Gene/Q, have been used for weather modeling. These supercomputers are known for their high processing power and are used by various meteorological agencies.
2. Cray Supercomputers: Cray has also provided supercomputing solutions for weather forecasting, such as the Cray XT series and the Cray XC40 series. These supercomputers are designed to handle large-scale simulations.
3. Fujitsu Supercomputers: The Japanese Meteorological Agency (JMA) has used Fujitsu's supercomputers, such as the K computer, for high-resolution weather modeling.
4. Various National Supercomputing Centers: Many countries operate their own supercomputing centers for weather forecasting, and these centers use some of the world's most powerful supercomputers. For example, the European Centre for Medium-Range Weather Forecasts (ECMWF) uses its own supercomputer for global weather prediction.

The time it takes to run a weather simulation depends on several factors, including the model's resolution, the complexity of the simulation, and the available computational resources. High-resolution regional models, which cover smaller geographic areas, generally require less time compared to global models. On average, it may take anywhere from several minutes to a few hours to run a single simulation.

Regarding your question about models that take almost as much time to run as it takes for the weather to evolve, it's important to understand that weather simulations do not typically run in real-time. Running a weather model with a high grid resolution and a long forecast period can indeed take a significant amount of computational time. For example, running a global model with fine grid spacing over a long period (e.g., multiple weeks) would require a substantial amount of computing resources and can take hours or even longer. However, this is not a real-time process, and the results are used for forecasting the future weather.

To provide real-time forecasts, meteorological agencies use a combination of current observational data and the latest model output to generate forecasts quickly, often in a matter of minutes or hours, depending on the forecast duration (e.g., short-term vs. medium-range). The goal is to produce timely forecasts for operational use, which is critical for weather-related decision-making.

How do we gather the data that’s used in weather forecasting? If we’re using a 5 kilometer grid, that’s a lot of data points. Who gathers them? Do we have automated weather stations? How often is data collected?

Weather forecasting relies on a vast network of data collection, which includes both traditional manual observations and automated weather stations. Here's how data is gathered for weather forecasting:

1. Automated Weather Stations: Automated weather stations, also known as automatic weather stations (AWS), are equipped with various sensors to continuously monitor meteorological parameters. These stations are placed at various locations, including airports, research facilities, and remote areas. They collect data at high frequencies and transmit it in near real-time to meteorological agencies. Common measurements include temperature, humidity, wind speed and direction, atmospheric pressure, and precipitation.
2. Weather Radars: Weather radar systems are used to monitor precipitation, such as rain and snow. Radars provide information on the location, intensity, and movement of precipitation, which is essential for short-term weather forecasts.
3. Weather Satellites: Satellites in various orbits, such as geostationary and polar orbits, capture images and data on cloud cover, temperature, and other atmospheric parameters. Satellite data is crucial for monitoring large-scale weather patterns and tracking the movement of weather systems.
4. Weather Balloons (Radiosondes): Weather balloons equipped with radiosondes are launched from various locations around the world. These instruments measure temperature, humidity, and pressure as they ascend through the atmosphere. Data from radiosondes help meteorologists understand the vertical structure of the atmosphere.
5. Surface Weather Observations: Traditional manual weather stations are still in use and are often operated by trained meteorological observers. These stations record data, including temperature, humidity, wind, and precipitation, typically at least once an hour. Data from these stations are vital for local and regional weather forecasting.
6. Weather Buoys: In marine and coastal areas, weather buoys collect data on sea surface temperature, wave height, and atmospheric conditions. They are essential for marine weather forecasts.
7. Weather Drones: Unmanned aerial vehicles (UAVs) or drones are increasingly used to gather data in areas where it may be challenging to obtain information through other means. Drones can be equipped with various sensors to measure temperature, humidity, and other parameters.

Data collection typically occurs continuously, with observations made at regular intervals, such as hourly or even more frequently for critical parameters like temperature and pressure. The data is then transmitted to central data centers, where it is processed, quality-checked, and integrated into numerical weather prediction models. The use of automated systems and the rapid transmission of data allow meteorologists to receive real-time information, making it possible to provide timely and accurate weather forecasts, even on a 5-kilometer grid scale for high-resolution models used in regional forecasting.

Is there any theoretical limit to the accuracy possible? Assume we can get data at sub-kilometer resolution and that we have all the computing power we need, how accurate could forecasts get? Is there some point where, no matter how much data and how much computing, the results just wash-out?

In theory, there is a limit to the predictability of weather, known as the "butterfly effect." This concept is closely related to chaos theory and suggests that, for chaotic systems like the Earth's atmosphere, there is a point at which the sensitivity to initial conditions becomes so high that long-term weather forecasts are fundamentally uncertain. This means that even with perfect data at sub-kilometer resolution and unlimited computing power, there would still be a limit to the accuracy of weather forecasts for extended timeframes.

Several factors contribute to this inherent limit to weather predictability:

1. Sensitivity to Initial Conditions: As you mentioned, the atmosphere is sensitive to small variations in initial conditions. This sensitivity grows over time, making it challenging to accurately predict the evolution of the atmosphere beyond a certain point.
2. Complexity of the Atmosphere: The atmosphere is an incredibly complex system with many interacting processes and scales, from local weather patterns to large-scale global circulation. These complexities make long-term forecasts inherently uncertain.
3. Incomplete Understanding: While our understanding of atmospheric physics and modeling has improved significantly, there are still aspects of the atmosphere that are not fully understood. Sub-kilometer resolution data and vast computing power can help, but it cannot overcome our incomplete knowledge of all atmospheric processes.
4. Limitations in Data Collection: Even with sub-kilometer resolution data, we would need observations everywhere on the planet, including remote and less accessible regions, to minimize uncertainty. This is practically unattainable.
5. Non-Linear Processes: The atmosphere contains non-linear processes that can lead to rapid changes and unexpected behavior, contributing to forecast uncertainty.

While advances in technology, improved models, and more data can lead to more accurate short-term and medium-range forecasts, it's unlikely that we will ever be able to make highly accurate long-term predictions for extended periods (e.g., months or years) due to the inherent chaotic nature of the atmosphere. Instead, long-term climate projections focus on trends and statistical probabilities rather than precise weather details.

In summary, while there is no absolute limit to accuracy, there is a fundamental limit to the predictability of weather due to the chaotic nature of the atmosphere. No matter how much data and computing power are available, long-term weather forecasts will always have inherent uncertainty.