The phrase "automatically rise" is correct and usable in written English.
It can be used in contexts where something increases or elevates without manual intervention, often in technical or scientific discussions.
Example: "When the temperature reaches a certain threshold, the pressure in the system will automatically rise."
Alternatives: "increase on its own" or "elevate by itself.".
"About 15 months from now, the officials said, the standard will automatically rise to three banks.
Auction sites like eBay allow people to specify the most they are willing to pay for an item, and their bids automatically rise as others bid higher.
Washington has been fretting for months over the so-called "fiscal cliff," the Jan . 1deadline when taxes automatically rise and government spending drastically falls.
And at the end of 2012 an even bigger threat looms: taxes will automatically rise and spending shrink unless Congress votes to override existing legislation.
Compulsory summer school was belatedly introduced to end "social promotion", whereby pupils automatically rise a grade each year even if they have not met adequate educational levels.
Other Republicans, however, have shown more willingness to accept the president's plan, knowing that taxes will automatically rise without action by Congress.
Also, because its taxes are lower and social-safety nets less generous, America has fewer "automatic stabilisers" than Europe, where spending on unemployment benefits automatically rises further in a downturn.
At present, teachers' pay automatically rises according to their experience.
(And paying for it means that European government spending automatically rises quite a bit during recessions).
The ratio automatically rises as an economy develops and shifts to more capital-intensive production.
Even manufacturers who played fair had an incentive to bump up their costs, with contracts written so that profits automatically rose by a similar proportion.
