Modeling canopy transpiration using time series analysis: A case study illustrating the effect of soil moisture deficit on Pinus taeda

Bulk sap flow measurements are widely used to assess and model the hydrological process of canopy transpiration (Ec); however, common analysis techniques of these data do not identify and/or incorporate time lag effects, multiple variables affecting canopy transpiration at different temporal scales or thresholds, and interactions of environmental variables. Here, we describe how autoregressive-integrated-moving average (ARIMA) time series models can be used with bulk sap flow and climate data to empirically estimate Ec. We illustrate parameterizing and forecasting the ARIMA model using bulk sap flow data collected in a plantation of Pinus taeda trees during a period of relatively high soil moisture (wet period) and use this model to predict Ec during a seasonal drought (dry period). The time series model that best fit the data during the wet period was an ARIMA model of order (3, 1, 1). The environmental variable that explained the most partial variance was vapor pressure deficit (D). Photosynthetically active radiation (PAR) was significant, but only explained a small amount of partial variance. When the wet period model was used to forecast daily Ec during the dry period, a systematic overestimate occurred compared to measured values. The difference between actual and forecasted Ec for the 25-day dry period was 12.29 mm, or an overestimate of 29%. In general, the model did not perform well when soil moisture dropped below 0.25 fractional soil moisture content (θ). We added a step intervention term to the model to represent this threshold effect of θ on Ec. The intervention term was significant and explained a higher amount of partial variance in the dry period than did PAR. The ARIMA model explained more than 97% of the total variance in the data and performed well during the wet and dry periods, as well as during an independent validation period that was intermediate in soil moisture and similar in climatic conditions. We discuss the assumptions and limitations of common analysis techniques of bulk sap flow data and suggest that these approaches be carefully considered when using sap flow measurements to estimate either Ec or canopy conductance, gc.