A Copula Approach for Predicting Tree Sap Flow Based on Vapor Pressure Deficit

Abstract

While using sap-flow sensor measurements is a well-established technique for quantifying leaf water transpiration in tree species, installing and maintaining a large number of sensors and data loggers in large-scale plantations to obtain accurate measurements is both costly and time-consuming. We developed a copula-based approach to predict sap flows based on readily available vapor pressure deficits (VPDs) and found that the Normal copula was the best among five commonly used copulas. The Normal-copula approach was validated using our field-measured eastern cottonwood (Populus deltoides (Bartr. ex Marsh.)) sap flow data, yielding solid statistical measures, including Mann–Kendall’s τ = 0.59, R2 = 0.81, and p-value < 0.01. The approach was applied to predict sap flows of eastern cottonwood during the growing period from 1 March to 31 October 2015 as well as the 5-year growing period from 2019 to 2023. It successfully replicated the characteristic diurnal sap flow pattern, with rates increasing during the day and decreasing at night, as well as the typical seasonal pattern, with rates rising from winter to summer and decreasing from summer to next winter. Our study suggests that the copula-based approach is a reliable tool for estimating sap flows based on VPD data.