Effects of Aggregation on Chlorophyll-Phosphorus Relations in Missouri Reservoirs

ABSTRACT

Using chlorophyll and phosphorus data from 119 Missouri reservoirs we show how data aggregation-averaging data into seasonal means or long-term lake means – influences our ability to make inferences from large-scale statistical regression analyses. We demonstrate the most obvious phenomenon of data aggregation, that relations between variables estimated from aggregated data are generally stronger than the same relations estimated from unaggregated data. Averaging reduces the often large variation in the response of chlorophyll to phosphorus (Chl-TP) that characterizes measurements of these variables in lakes. We also demonstrate that inferences made from statistical regression analyses apply only to situations that match the level of aggregation used to produce the model. Using lake means we found a strong positive Chl-TP relation. This strong cross-sectional pattern among lakes in the study, however, did not always reflect the relation of these variables to one another in individual lakes. And the cross-sectional pattern has limited value in predicting conditions in unaggregated data. The effect of aggregation on the estimated strength of a regression relation serves as a caution in transferring inferential statements about the effect of TP on Chi between temporal scales and among lakes.

Key Words:

• chlorophyll
• phosphorus
• aggregation
• models