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In oceanography, a shallow-water wave is a wave whose wavelength is significantly larger than the ocean depth. A wave enters shallow water when the ratio of the water depth to its wavelength becomes smaller than 1/20. Changes in ocean depths can slow the wave, causing it to change direction. Essentially, for tsunami to behave as a shallow-water wave, the depth of the ocean must be less than one-twentieth of the wavelength of the tsunami wave.

With the understanding from Step 1, assess each of the options:\n\nOption a suggests that the wavelength of the tsunami must be comparable to or longer than the ocean depth. This definition aligns with the definition of a shallow water wave, where the wavelength is significantly larger than the water depth.\n\nOption b suggests that the wavelength should be shorter than the ocean depth. This is in contradiction to the definition of a shallow water wave and, therefore, is incorrect.\n\nOption c suggests that the wavelength can have any value. This is also incorrect as the wavelength has to be in a specific relation to the ocean depth for the wave to be considered a shallow water wave.\n\nTherefore, the correct answer is Option A.

Review the facts to confirm the choice. A tsunami is considered a shallow-water wave when its wavelength is longer than the ocean depth. Hence, option A must be the correct answer.