The answer should be obvious! If we are talking about data, the only validated data are experimental data! However, any experimentalist should be conscious that his experiment is pregnant with theory. So, with field data you means data interpretation the situation can become more controversial. The scope of a theory is to furnish a way for rationalizing the existing rough data (this is that we call a model). A good theory should go over, forecasting unrevealed phenomena. And a further experiment can agree with the theory (which promoted the experiment itself) or can refuse it with new experimental data in disagreement with the model. So, my meaning should be clear: theories and models produce plausuble scenarios. The experiment is the way for disentangle concurrent models. In summary, experiment are not meaningful without a theory and the Popper's thinking remains valid up to day (in my opinion, of course).

Thank you for this answer, I agree with you totally

I don't want to compare field data and model outcome regarding a phenomenon under study; however the power of modelling is to predict something real, which could be tested experimentally, whether now or in the near future..

The answer should be obvious! If we are talking about data, the only validated data are experimental data! However, any experimentalist should be conscious that his experiment is pregnant with theory. So, with field data you means data interpretation the situation can become more controversial. The scope of a theory is to furnish a way for rationalizing the existing rough data (this is that we call a model). A good theory should go over, forecasting unrevealed phenomena. And a further experiment can agree with the theory (which promoted the experiment itself) or can refuse it with new experimental data in disagreement with the model. So, my meaning should be clear: theories and models produce plausuble scenarios. The experiment is the way for disentangle concurrent models. In summary, experiment are not meaningful without a theory and the Popper's thinking remains valid up to day (in my opinion, of course).

Data collected are obviously more important based on which a model can be verified or fitted.

Verified and Experimental results should complement each other.

Thank you all for this valuable replies, comments, and attachments.

Now we can say that:

If the field data is under restricted control and the measuring. Devices are precise and well calibrated, then we can trust the collected data and verrify and validate models by it

On the other hand, verrified models can provide more trustful data in theoretical base.

The answer to the main question seems straightforward at face value. Indeed the importance of accurate observations from well-calibrated sensors is undeniable. However, as others have mentioned, observing a high-dimensional complex system in a comprehensive manner is virtually impossible. This is the case for the Earth's atmosphere for example. In such a context, the value of a high-quality (well-constructed and well-tuned) numerical model also is undeniable.

The value of both models and observations is well-known in the discipline of data assimilation. Fairly accurate analyses of the four-dimensional state of the atmosphere are produced by combining, in an optimal way, the information provided by numerical models and observations. Such accurate analyses could not be possible by using models alone or using observations alone.

Also, there has been several well-documented instances where the comparison of model data with observations has allowed the detection of malfunctioning sensors. When statistics of differences between model and observations experience a sudden change or are characterized by a significant drift over time, this is often a sign that something is wrong with the observations. That is why numerical models are also used to monitor observation quality in the context of numerical weather prediction.

Elnesr: One of the three basic principles of statistical data collection is that 'no measuring device is perfect'. That is why in all laboratory experiments, data are collected more than once. Accordingly, assuming that the measuring device is perfect goes against statistical principles. Secondly, it is not that probabilistic uncertainty can always define the uncertainty concerned associated with a measurement. In fact, there are situations in which fuzzy uncertainty has to come into the picture.

Dear Francesco Aliotta,

I agree with You! But, some detaile. We have a fact - data with interpretation. Enterpretation is some (simple or complex) theory. But what is numerical model? I see it is part of theory at simple case (numerical solution of simple ODE for example) and it is a part of data at complex case (model of oceanic circulation for example). So we need a data and theory. In many case it wil be data+numerical model and physical Theory. It is only my opinion.

Our models of the physical world are basically mathematical ones. This idea originates from Plato, who believed that the 'mathematical world' is the projection of the real world. In other worlds, the mathematic equations can dominate our cosmos. This idea has been tested for thousands of years and so far it remains correct. So I think the answer to this question depends on whether our models ARE the projection of our real world, or rather whether they contain enough information for us to describe the real world with acceptable accuracy.

In theoretical physics, many scientists believe that a 'theory of everything' would soon be found and thus unravels the mysteries of the basic rules of the cosmos. Even so, however, I think things would still be different in engineering. Though we may well understand the behavior of a black hole, the description of the detailed performance of a vehicle on road still exceeds our ability. Due to this inability, we have to choose field experiments to validate our models.

Just to add some detali to the comment from Xiaohu Wang. There is no model that is the complete projection of the real word, in principle. As you correctly asserted, a model is just a description of the real word, in terms of a formal language, i. e. mathematics. However, mathematics, as well as any formal language (enough extended to include arithmetic) cannot be described as a fully axiomatic construct. It contains assertions which are synthetic "a priori", in the Kant sense. This point was well understood by Poincare, well before Kurt Godel destroyed the axiomatic buildig from Russel and Hilbert. So it is clear that the ultimate theory of the universe is just a dream that cannot become actualized. Far to be frustrating, such an idea tell us that never we will stop enjoing with our work! And, at the same time, should tell us which the roles of theory and experiment are.

"Cio che l'esperienza e il Senso insegna é da anteporsi a qualsiasi Ragionamento ancorché ne paresse assai fondato" Galileo Galilei

NB.: This what Prof. Gian Betini said but in English: "What that experience teaches is the Meaning and prevails over any reasoning even if it should seem very well founded "Galileo Galilei",

Through google translate.

A model validated by many and different field data is to be trusted because the computer will always give the same answer for the same case while the measuring instrument may be mechanically or electrically faulty once in a while!

The answer was given by Galileo Galilei in Italian of XVII Century, "CIò che l'esperienza ed il senso insegna è da anteporsi a qualsiasi ragionamento ancorchè ne paresse assai fondato".

Dear Prof. Rivano,

Galileo’s language is so rich and rigorous that it is very difficult to translate it in a schematic language like English, without subjunctive mood. The risk is to miss part of the meaning of the sentence translated. For this reason I preferred to leave the translation job to professional persons eventually involved.

Nevertheless, to follow your invitation, I will try to report here a free translation that on my opinion should be faithful to the Galilean Scientific Method.

"What is taught by experimental measurements and by (our) sensory functions must be placed above any reasoning line even if it would appear true (above any doubt)".

It must be considered that besides the five sensory functions, the only scientific instruments available to Galileo where, a ruler, a pair of compasses for space measurements, a clepsydra or pendulum, for time measurements.

Best regards,

G G Bentini

Thank you Prof. @Bentini,

The meaning of your answers and the quotes of Galileo is that we should trust field and experiments than any model or theories.

Am I right?

Yes Professor Elnesr, your conclusion is correct. I can add that almost all the Italian Physicists grow with this reasonig scheme, even if they can be excellent in computer modelling.

There is an appropriate place between the two cautionary advocations, because both are "wrong." Models are not simply "validated" using independent data, and experimental data are not "validated" via models. That approach to validity is misguided and unscientific. The engineering approach to developing theories and models is based on the recognition that "all models are wrong" - i.e., all models are inexact. The objective is to assess HOW inexact, in order to make an educated assessment of the appropriateness or suitability of that model for a specific application. The validation process - usually defined as assessing "... the degree of accuracy..." - becomes corrupted when assumptions about validity drive misguided conclusions like "proof." Do not trust any model until the validation process has quantified acceptable accuracy - and inaccuracy - of the model for its intended purposes. Do not trust your interpretation of experimental data - especially of complex systems - until the accuracies and inaccuracies of your model are sufficiently quantified, and uncertainties inherent in the data are sufficiently quantified.