A Continuous Semi-nonparametric Isotope-Based Mixing Model for Multimodal Water Uptake Patterns

Abstract

Isotope mixing models have become increasingly prevalent in the partitioning of root water uptake. However, many models fail to incorporate site physical information in a physically meaningful manner, whereas others adopt discrete approaches to segmenting the soil profile rather than continuous approaches that aptly treat the soil as a continuum of physical properties and conditions. Here, we present the novel ‘multimodal physically-based root water uptake isotope mixing estimation’ model (Multi-PRIME). The model utilizes a flexible, continuous and multimodal probability density function in conjunction with water-stable isotopes and additional site physical information, combined in a process-based linear mixing framework. To evaluate the approach, estimates of water uptake from boreal forest Pinus banksiana trees were compared with those of the PRIME and MixSIAR approaches. The models yielded comparable results; however, because of the highly flexible nature of its semi-nonparametric water uptake function, Multi-PRIME reduced the bias and uncertainty associated with soil segmentation of the discrete model MixSIAR and with the specification of parametric functions and initial parameter values of the PRIME model. Furthermore, the multimodal nature of Multi-PRIME provided a superior ability to describe water uptake patterns in cases with multiple potential source regions of uptake. In addition, due to its continuous and process-based nature, Multi-PRIME surpassed the discrete, empirically-based MixSIAR in both accuracy and certainty. These findings illustrate the benefits of adopting a process-based modelling framework that utilizes a semi-nonparametric, continuous and multimodal water uptake function, thereby providing an improvement in our ability to confidently estimate water uptake apportionment.