I don't know of such conceptual model, however, there conservation science and environmental psychology could be two fields with appropriate concepts to use for your purpose.

When it comes to human attitude towards something, should be considered :

- affective component : emotions, feelings

- cognitive component : knowledge, beliefs, values, needs

- conative component : willingness and ability to act, habits, traditional behaviors..

Here, you've got a model of general perception : https://www.cairn.info/revue-natures-sciences-societes-2015-2-page-120.htm

Hope this can help a little.

In fact you need witness clues. for example since more than 35 years talks and debates related climatic changes and sea level rise however, the public do not see any noticeable changes on ground. This is a big problem.

A query about how scientific discourse might convince people about global warming will likely (and understandably) attract multiple suggestions touching, say, social marketing, storytelling, trust, etc. But, in the Attention Economy, the volume of research greatly exceeds its application in practice: and so, for one, researchers must pay greater attention to the production of their research findings in a flexible range of formats in recognition of the varied needs of the audiences they target.

Article Linking Research to Practice

I think it is simple, showing the level of the glaciers at dates. Take photographs of the nude walls that contained glaciers and mark the level at 1900, 1920, 1940, 1960 till now. People cannot not see the acceleration of warming.

it seems that the first answer which comes to mind is showing consequences of climate change to ordinary people but evaluations prove that countries which are suffering more from climate change impacts are less sensitive about it but countries with more globalist populations are more worry about climate change and its consequences, even if they do not sense it at the moment. so showing the consequences is one matter and proving that this is directly consequence of climate change to the ordinary people is another one which is more important.