Structural Equation Model of Total Phosphorus Loads in the Red River of the North Basin, USA and Canada

Karen R. Ryberg

Attribution of the causes of trends in nutrient loading is often limited to correlation, qualitative reasoning, or references to the work of others. This paper represents efforts to improve causal attribution of water-quality changes. The Red River of the North basin provides a regional test case because of international interest in the reduction of total phosphorus loads and the availability of long-term total phosphorus data and ancillary geospatial data with the potential to explain changes in water quality over time. The objectives of the study are to investigate structural equation modeling methods for application to water-quality problems and to test causal hypotheses related to the drivers of total phosphorus loads over the period 1970 to 2012. Multiple working hypotheses that explain total phosphorus loads and methods for estimating missing ancillary data were developed, and water-quality related challenges to structural equation modeling (including skewed data and scaling issues) were addressed. The model indicates that increased precipitation in season 1 (November-February) or season 2 (March-June) would increase total phosphorus loads in the basin. The effect of agricultural practices on total phosphorus loads was significant, although the effect is about one-third of the effect of season 1 precipitation. The structural equation model representing loads at six sites in the basin shows that climate and agricultural practices explain almost 60% of the annual total phosphorus load in the Red River of the North basin. The modeling process and the unexplained variance highlight the need for better ancillary long-term data for causal assessments.