In our lab to detect gas evolution from liver samples and H2O2, we had used a filled but inverted bottle of water inside a tub of water (submerged) with the tube pointing to the mouth of the bottle. As the gas (in this case oxygen) is produced it displaces the water. If the bottle is graduated one can note volume of gas collected as a function of time. Can you do something similar at various sampling points in your rice field?
For method, see for example https://www.nuffieldfoundation.org/practical-biology/investigating-enzyme-controlled-reaction-catalase-and-hydrogen-peroxide-concentrat