It is very complex. There are equations involved, but more indirectly in the form of climate models. Here's an explanation of how modeling works. Look at it all, but your question is sort of directed to the part about inputs and outputs of a model, and what goes on within the black box. You can imagine how changing even just one certain trend to get an estimate will generate a remarkably different picture over time.
Ask Science
Ask a science question, get a science answer.
Community Rules
Rule 1: Be respectful and inclusive.
Treat others with respect, and maintain a positive atmosphere.
Rule 2: No harassment, hate speech, bigotry, or trolling.
Avoid any form of harassment, hate speech, bigotry, or offensive behavior.
Rule 3: Engage in constructive discussions.
Contribute to meaningful and constructive discussions that enhance scientific understanding.
Rule 4: No AI-generated answers.
Strictly prohibit the use of AI-generated answers. Providing answers generated by AI systems is not allowed and may result in a ban.
Rule 5: Follow guidelines and moderators' instructions.
Adhere to community guidelines and comply with instructions given by moderators.
Rule 6: Use appropriate language and tone.
Communicate using suitable language and maintain a professional and respectful tone.
Rule 7: Report violations.
Report any violations of the community rules to the moderators for appropriate action.
Rule 8: Foster a continuous learning environment.
Encourage a continuous learning environment where members can share knowledge and engage in scientific discussions.
Rule 9: Source required for answers.
Provide credible sources for answers. Failure to include a source may result in the removal of the answer to ensure information reliability.
By adhering to these rules, we create a welcoming and informative environment where science-related questions receive accurate and credible answers. Thank you for your cooperation in making the Ask Science community a valuable resource for scientific knowledge.
We retain the discretion to modify the rules as we deem necessary.
Thanks. The article in the link explains a lot
"Do they just calculate the current trends of temperature growth and take the causes of it into account"
yep, held against historical data for context.
"Is it basically some model y = a1x1 + a2x2 + ... or something more complex"
The more complex algorithms are for predicting and imminent weather patterns. "climate" itself, like ice age trends, global warming and future projections are based on data analysis and extrapolation.
y = a1x1 + a2x2 + ...
Just a quick markdown tip: If you want the asterisks to show up, you need to escape them with backslashes, otherwise they are rendered as italics.
y = a1\*x1 + a2\*x2 + ...
Renders as:
y = a1*x1 + a2*x2 + ...
Thx, fixed.