  Most environmental data come from a minority of well-monitored sites. An
ongoing challenge in the environmental sciences is transferring knowledge from
monitored sites to unmonitored sites. Here, we demonstrate a novel transfer
learning framework that accurately predicts depth-specific temperature in
unmonitored lakes (targets) by borrowing models from well-monitored lakes
(sources). This method, Meta Transfer Learning (MTL), builds a meta-learning
model to predict transfer performance from candidate source models to targets
using lake attributes and candidates' past performance. We constructed source
models at 145 well-monitored lakes using calibrated process-based modeling (PB)
and a recently developed approach called process-guided deep learning (PGDL).
We applied MTL to either PB or PGDL source models (PB-MTL or PGDL-MTL,
respectively) to predict temperatures in 305 target lakes treated as
unmonitored in the Upper Midwestern United States. We show significantly
improved performance relative to the uncalibrated process-based General Lake
Model, where the median RMSE for the target lakes is $2.52^{\circ}C$. PB-MTL
yielded a median RMSE of $2.43^{\circ}C$; PGDL-MTL yielded $2.16^{\circ}C$; and
a PGDL-MTL ensemble of nine sources per target yielded $1.88^{\circ}C$. For
sparsely monitored target lakes, PGDL-MTL often outperformed PGDL models
trained on the target lakes themselves. Differences in maximum depth between
the source and target were consistently the most important predictors. Our
approach readily scales to thousands of lakes in the Midwestern United States,
demonstrating that MTL with meaningful predictor variables and high-quality
source models is a promising approach for many kinds of unmonitored systems and
environmental variables.
