The phrase "alarming decline" is correct and usable in written English.
It can be used to describe a significant and concerning decrease in something, such as performance, health, or numbers.
Example: "The alarming decline in bee populations has raised concerns among environmentalists."
Alternatives: "worrying decrease" or "disturbing drop".
Alarming decline in the number of phone booths.
Since then, scientists have searched for what might cause such an alarming decline.
Environmental activists, deeply concerned by the monarch's alarming decline, applauded the move.
A crane accident shuts down power to a third of Vietnam, and an alarming decline of frogs and salamanders is reported.
The Independent and Space for Giants' elephant campaign calls on world leaders at the forthcoming conference to take urgent steps to end the alarming decline of Africa's elephants.
A European Commission study undertaken in 2007 noted "an alarming decline in young people's interest for key science studies and mathematics" despite numerous efforts to reverse the trend.
It has rising rates of child malnutrition and alarming declines in reserves of its two main resources, oil and water.
— Jeff Gordinier NPD Group: Nationwide, after three years of alarming declines in customers' visits to restaurants that include children (called "parties with kids" in industry vernacular), such visits were flat – again — for the second consecutive year.
Some of the birds that have suffered the most alarming declines are the most well known species including the house sparrow which has fallen in number by 147m or 62%, the starling (53%) and skylark (46%).
The documentary has a complicated story to tell, involving (if I followed it correctly) how alarming declines in the red knot population led to the discovery of its special relationship with the horseshoe crab, which has it own problems, because eel and conch fishermen love to use it for bait.
Perhaps even more telling than the alarming declining rate of minority participation in American homeownership are the many contributing factors highlighted by the 2013 HMDA data.
