To solve this question, we need to look at the processes that generate hydroxyl radicals (OH) in the troposphere. The hydroxyl radical is a crucial component in the atmosphere as it acts as a natural "detergent," playing a significant role in the breakdown of pollutants.

1. Understanding the Processes:
   • \(\text{O}(^1\text{D}) + \text{H}_2\text{O}\): This process involves an excited state oxygen atom reacting with water to produce hydroxyl radicals.
   • \(\text{O}(^3\text{P}) + \text{H}_2\text{O}\): Here, the ground-state oxygen atom does not have enough energy to react with water to form hydroxyl radicals.
   • \(\text{HCHO} + h\nu\): Formaldehyde can undergo photolysis, which can lead to the generation of hydroxyl radicals among other products.
   • \(\text{HNO}_2 + h\nu\): Nitrous acid is known to photolyze to produce hydroxyl radicals and nitrogen monoxide.
2. Identifying the Non-contributing Process:
   • The key here is recognizing the energy states and whether they can facilitate the production of hydroxyl radicals.
   • The reaction \(\text{O}(^3\text{P}) + \text{H}_2\text{O}\) involves oxygen in its ground state, which does not have the requisite energy to produce an OH radical from water.
3. Conclusion:
   • Thus, the process that does not generate hydroxyl radicals is \(\text{O}(^3\text{P}) + \text{H}_2\text{O}\).