Many of the organisms in the ocean are nutrient-limited. if you wanted to investigate this phenomenon, one reasonable approach would be to many of the organisms in the ocean are nutrient-limited. if you wanted to investigate this phenomenon, one reasonable approach would be to compare nutrient concentrations between the photic zone and the benthic zone in various marine locations contrast nutrient uptake by autotrophs in marine locations that are different temperatures experimentally enrich some areas of the ocean and compare their productivity to that of untreated areas observe antarctic ocean productivity from year to year to see if it changes

None of the provided options are reasonable. comparing nutrient concentrations between the photic zone and the benthic zone can not tell you whether differences in concentrations between the photic and benthic zone are due to uptake by phytoplankton or because nutrients are sinking to the sea bottom and ocean stratification is preventing mixing.  The approach of contrasting nutrient uptake by autotrophs at different locations under different temperatures would not provide useful information on limiting nutrients. but rather uptake rates at different temperatures.  It is likely that experimentally enriching some areas of the ocean and compare their productivity to that of untreated areas can provide an indication of limiting nutrients, but this is not advisable, as it would have to be done on a large scale, and one cannot be sure of the ecological consequences. Also, because it would not be a controlled experiment, other factors could create 'noise' in the data. The last option, observe antarctic ocean productivity from year to year to see if it changes, also does not help, as there is no correlation between nutrient concentrations using this approach. The best approaches would be either the last approach, but with the additional monitoring of nutrient concentrations, or under a controlled laboratory experiment.