Sap flow observations provide a basis for estimating transpiration and understanding forest water use dynamics and plant-climate interactions. This study developed a continental modeling approach using Long Short-Term Memory networks (LSTMs) to predict hourly tree-level sap flow across Europe based on the SAPFLUXNET database. We developed models with varying levels of training sets to evaluate performance in unseen conditions. The average Kling-Gupta Efficiency was 0.77 for gauged models trained on 50 % of time series across all forest stands and was 0.52 for ungauged models trained on 50 % of the forest stands. Continental models matched or exceeded performance of specialized and baseline models for all genera and forest stands, demonstrating the potential of LSTMs to generalize hourly sap flow across tree, climate, and forest types. This work highlights hence the potential of deep learning models to generalize sap flow for enhancing tree to continental ecohydrological investigations.

Estimating parameters for distributed hydrological models is a challenging and long studied task. Parameter transfer functions, which define model parameters as functions of geo-physical properties of a catchment, might improve the calibration procedure, increase process realism and can enable prediction in ungauged areas. We present the Function Space Optimization (FSO), a symbolic regression method for estimating parameter transfer functions for distributed hydrological models. FSO is based on the idea of transferring the search for mathematical expressions into a continuous vector space that can be used for optimization. This is accomplished by using a text generating neural network with a variational autoencoder architecture, that can learn to compress the information of mathematical functions. To evaluate the performance of FSO, we conducted a case study using a parsimonious hydrological model and synthetic discharge data. The case study consisted of two FSO applications: Single-criteria FSO, where only discharge was used for optimization and multi-criteria FSO, where additional spatiotemporal observations of model states were used for transfer function estimation. The results show that FSO is able to estimate transfer functions correctly or approximate them sufficiently. We observed a reduced fit of the parameter density functions resulting from the inferred transfer functions for less sensitive model parameters. For those it was sufficient to estimate functions resulting in parameter distributions with approximately the same mean parameter values as the real transfer functions. The results of the multi-criteria FSO showed that using multiple spatiotemporal observations for optimization increased the quality of estimation considerably.