Simulations and Numerical Experiments < rdctheory.cloud
There are two types of computer-based methods for representing objects and phenomena: simulations and numerical experiments. However, most people do not pay attention to the difference between simulations and numerical experiments. Of course, they are not clearly and completely separable, but should be classified according to which of their attributes they are closer to.
The purpose is literally to simulate. To do this, there must be an object or phenomenon to simulate. In other words, simulation begins with the target to be simulated. It is impossible to simulate something that does not exist. The more details that can be reproduced, the more successful the simulation will be. Of course, the model becomes more complex as it tries to reproduce details, but the complexity of the model is not a problem in simulation. The model can be as complex as necessary to reproduce the details of the target. For example, if you can reproduce the details of a target using 8000 numerical expressions, there is nothing wrong with that.
On the other hand, as long as the target can be reproduced, that is, as long as the target looks the same, it is not necessary to correctly understand the physical mechanism behind the target.
Computer graphics used in movies is probably the best example. For example, computer graphics are often used in scenes where a high speed car crashes and breaks because it would be too expensive to actually break the car. It is important to note that the process of breaking a car does not necessarily have to be based on strict physical laws. Even without solving the equations of motion that the structural elements of the car must obey, by assuming appropriate polynomials that express the motion of the elements, and by tuning the coefficients (parameters) of the polynomial well (parameter tuning), it is possible to create the illusion that the car is actually breaking when the audience sees it.
They are experiments. The ultimate goal is to understand an object or phenomenon physically. A numerical experiment begins with a hypothesis. The model is created based on the assumption of the physical laws that underlie the target under study. If the model can correctly represent the target in the end, the experiment is a success, which means that the hypothesis assumed at the beginning was correct and the target is understood by this mechanism. Conversely, if the model fails to correctly represent the target, then the initial assumption about the laws of physics was incorrect.
For example, in the case of car destruction, the goal of a numerical experiment is to find the cause of the car's destruction and perhaps modify the structure to make it less susceptible to destruction. Therefore, it is necessary to correctly implement the destruction process of the car based on the laws of physics. It is not necessary to be concerned with the detailed appearance as in simulation, and implementations that model only the car frame, for example, are common.
The simpler the initial hypothesis, the better. If a numerical experiment with 8000 governing equations can correctly represent a subject, it does not mean that a human being understands the subject. The model used in a numerical experiment must be simple enough to be understood by humans.
On the other hand, detailed reproduction of the target is secondary. As long as the target can be roughly described, the target is understood in the first sense, and differences in detail can be ignored. If you are concerned about the details, you can replace the initial hypothesis with a more detailed one to explain the details.
For example, the example of a pendulum is often used in introductory physics. A pendulum is a volumeless mass point attached by a massless string to a frictionless fulcrum. But think about it. There is no volumeless mass point, massless string, or frictionless fulcrum in the world. It may seem pointless to think in terms of these nonexistent things, but it is not. This simplification extracts the essence of the pendulum and the phenomenon of its motion and makes it much easier to understand. If the model roughly reproduces the actual motion of the pendulum, it can be shown that the attributes omitted in the simplification have no significant effect on the motion of the pendulum. If the size of the weight, the mass of the string, the friction at the fulcrum, etc. are important, then later the model can be refined to represent these secondary differences. Note that the pendulum, which starts out as a pure model, becomes more and more like a simulation as more and more details are implemented. If you are aiming for simulation, you are on the right track, but if you are aiming for experimentation, the first step to understand the phenomenon with the simplest possible mechanism is the most important step.
Simulations and numerical experiments have different goals and methods, and they differ in what they value.
Weather forecast is an important example of simulation. As with other simulations, there are indeed parts of the weather forecasting model that are implemented based on the laws of physics. However, the internal structure of the model is not the essence of weather forecast. The purpose of weather forecast is to reproduce current and future atmospheric conditions. If it is possible to reproduce atmospheric conditions that closely resemble reality, it does not matter if every part of the model is represented by a set of polynomial equations that have nothing to do with the laws of physics. Weather forecast can predict disasters and warn people. It is valuable in terms of social welfare.
But we said above that simulation requires the existence of an target to be simulated. The future state of the atmosphere does not yet exist in this world. In fact, the state of tomorrow's atmosphere cannot be obtained until 24 hours have passed. Nevertheless, simulation is possible in weather forecasting. Why is this? Because weather phenomena repeat themselves. There are many weather maps and torrential rain patterns that have been observed before under similar conditions. Even if the weather phenomenon to be predicted is represented by a polynomial that has no physical meaning, it is possible to tune the polynomial to predict the phenomenon in question by statistically applying past observation data to it and determining the unknown coefficient (parameter) values that appear in the polynomial (parameter tuning). And then the polynomial is the final product for the weather forcasting.
[NOTE]
Furthermore, once the forecast period has passed, actual observations can be used to verify if the weather forecast itself was correct or not.
This period is short enough for model implementers.
This latest result is also added to the weather database.
The growing amount of information in the database allows for parameter tuning and further model refinement.
[NOTE]
Understanding the physical mechanisms of atmospheric phenomena
is not necessarily essential for weather forecasting.
Even without understanding,
weather forecasting is possible with sufficient parameter tuning.
However,
this does not mean that an understanding of meteorological phenomena is meaningless.
Understanding the physics of weather phenomena can help
improve the accuracy of weather prediction by confirming the validity of parameterization,
and by complementing prediction methods other than parameter tuning for phenomena
for which there is insufficient data for parameter tuning.
On the other hand, what about climate prediction? The climate in 100 years will not be known until 100 years have passed. In this case, can we use the same method as weather forecasting? If the same phenomenon as the current global warming had happened many times in the past, then we could use the same method as weather forecasting. Given the archean climate, there may have been similar or even more intense warming, however, nothing essentially identical to the current human-caused situation. There has never been a situation where human beings appeared on Earth, started the Industrial Revolution, and, with the help of satellites, dug up and burned all kinds of fossil fuels. In other words, climate phenomena do not repeat themselves. While parameter tuning, namely simulation, may be possible for past climates, it is not possible to describe changes that will occur in the future. Although "simulation for climate change" is a commonly used term, it is self-contradictory for future climate. We have no target to be simulated.
[NOTE]
Some statistical climate studies are very good.
In the example of the study cited in our paper,
it is possible to treat a warming situation and conversely a cold situation
by statistically looking at observations of the current atmosphere,
dividing the entire globe into summer and winter hemispheres.
Simulations using this approach are possible,
but limited to the range of warming now occurring.
Therefore, simulations that reproduce the phenomena are essentially ineffective in predicting the climate 100 years from now. Even if researchers believe they are predicting the climate, as long as they continue to do simulation-based research, they will only develop even better weather forecasts. Their models only apply to the future if atmospheric properties remain essentially unchanged, and they are powerless against climate change that changes atmospheric properties such as radiative transfer. The only way to predict climate is to configure numerical experiments in which the basic mechanisms work no matter how the nature of the atmosphere changes, and then to apply them to future conditions. Once the mechanism is understood, it makes sense to apply it to an unknown situation.
Of course, confirmation for the climate predictions can only be made under limited conditions, even if we understand the climate mechanisms. A direct answer can only be given when the atmospheric conditions are actually observed 100 years later.
We have found that RDC dominates the transport from the inside to the outside of cumulus clouds. We believe that RDC plays a key role in the water vapor feedback, which has a significant impact on warming. The RDC scheme is based on fundamental physical laws that should make good physical sense even when applied to unknown future warming conditions.
To make it easier to figure out, we have presented the RDC implementation method as a kind of cumulus parameterization. Strictly speaking, however, it is more accurate to call it an RDC scheme. This is because the main implementation of the RDC scheme is not parameter tuning as the DD method in the conventional cumulus parameterization of the simulation base. Of course, parameter tuning is required also in the RDC scheme to enable its practical use in the model, but it is limited to a secondary part that determines how it should be constrained when the full RDC flow cannot be realized. It should be recognized that the RDC scheme is fundamentally different from conventional cumulus parameterization.
In general, simulations can often show a detailed atmospheric structure, while numerical experiments can only show a coarse structure. This is due to the differences between the approaches of the two methods as described above. However, one should always be aware that such differences in appearance can lead people to underestimate the importance of simple numerical experiments and to place too much trust in eye-catching simulations.
It is one of the best examples, unfortunately, that RDC derived from simple numerical experiments have been ignored by people for a long time. But let us give you an opposite example. A fellow researcher once told me about the bright future of the simulation in which he was involved in. The development of computers is amazing. At this rate, it will be possible to simulate all the phenomena on Earth, like Populous and SimCity :) If we can simulate people on Earth together with their intellectual activities, people in the box may be able to solve the climate problem. We could use the research in the simulator as a reference to develop real solutions to climate problems. Certainly, with the recent development of artificial intelligence systems, such a pipe dream may seem realistic. It is possible that many people will agree with it.
We do not know how many bits of information are needed to describe all the phenomena on Earth, but perhaps one day we will be able to build a simulator with that many bits. But even if that were to happen, the answer to his dream is unfortunately NO. Do you guess why?
Suppose there is a computer called "Globe Simulator (GS)" with the same number of bits, let us say N, as the number of bits needed to represent all the phenomena on Earth, and that all the phenomena on Earth can be simulated on GS. Then,
[NOTE]
As some of you may have already noticed,
there is actually only one way to solve this bit number paradox problem.
We can place GS outside of the Earth to be simulated.
In this case, however,
the virtual people cannot use GS and must solve the climate problem on their own.
In this sense, they are not faithful simulation of us.
It has been said that it is rare to find something new in atmospheric science from a model study. But this is to be expected, because the most model studies are simulations, and the goal is to complete the model itself. In simulations, if you succeed in reproducing the phenomenon, that's the end of the study. There is no further discovery. Rather, if something other than the expected phenomenon occurs, it is discarded as a simulation failure. This is the correct and steady approach for weather forecasting, but not for climate prediction, in which we have nothing to expect. In any case, do not be fooled by the eye-catching appearance of simulation. Simulation is only an "imitation", a reproduction of a known phenomenon. No new discoveries can be made from it. Although it has social utility when limited to weather forecasting, it is not permissible to apply the method directly to climate prediction.
In contrast, in numerical experiments consisting of fundamental physics, the research begins when the model is complete. We do not know what results the model calculations will produce, and we must analyze each of them as it might be possible. Some may be meaningless due to model inadequacies, but others may be new discoveries that we did not expect. In our fortunate case, RDC, together with its result of vertically constant relative humidity which is maintained against warming, and subcloud layer warming effect are examples. Numerical experiments are simply not popular with the general public because their results tend to be simple and less striking in appearance. Professionals should gain insight into the deeper physical meaning hidden in the simplicity. While the world is united in its focus on climate simulation, we believe that more information about climate change can be obtained by conducting their own numerical experiments.
To say the truth, when we worked in organizations, it was very stressful to discuss things with the people there. They often assumed that simulation was the numerical method, which was far from what we expected from numerical experiments. Surprisingly, most of the people, even the most advanced researchers, confuse simulation with numerical experiments. Many of them kindly advised us that our model was too simple and that we should add various physical processes to make it more similar to the real atmosphere. While this would make the model indeed a better simulation with more realistic phenomena in the model, it would also make the interpretation of the physical processes occurring in the model more complex and difficult. Although we were working with similar numerical models, the goals were quite different. To make meaningful climate predictions, these two numerical methods must be clearly separated.
Our RDC scheme follows the approach of the numerical experiment. It is not a kind of tuning of parameter sets to some observed values, but rather starts from fundamental physical laws. Therefore, unlike the DD method, which starts by tuning to the observed values, there is no guarantee that the actual observed values can be reproduced. Nevertheless, from its basic structure and the results of simple model calculations performed so far, it can be applied to unknown climate conditions and is expected to represent more possible atmospheric structures than DD, such as a moist atmosphere and the maintenance of relative humidity during warming. Many of you may be reluctant to introduce the RDC scheme because you think it is too simple and not realistic. Let's start with the first basic point, and you will be amazed at the good results you can get with such a simple method. Secondary detailed adjustments to fit reality can be made later.
Simulations and Numerical Experiments < rdctheory.cloud
Exhibited on 2024/05/07
Last Updated on 2024/06/21
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