Machine learning for Swiss river flow estimation


River flow is a key component of the terrestrial water cycle and of special relevance for ecosystems and societies. Dependable information on river flow is essential for advancing both environmental research, and water resources management as well as for anticipating and mitigating floods and droughts.

To date, observations at gauging stations constitute the most accurate way to measure this quantity along river systems. However, observation networks only monitor a small number of locations, leaving many gaps on maps of regional river flow.

The proposed project MACH-Flow aims to bridge this gap by advancing our capabilities for estimating daily river flow at ungauged locations in Switzerland using data science methods. To this end, MACH-Flow will expand upon recent advances for modeling water-cycle variables by fusing sparse in situ observations with spatially continuous predictor variables using machine learning.

A special focus will be on making existing methods fit for application at the national scale, by tackling conceptual hurdles that arise when modeling daily river flow at the very high spatial resolution (i.e. 200×200 to 500×500 meters) that is relevant for water management. In particular, the MACH-Flow project will develop a machine-learning based reconstruction of spatially resolved daily river flow covering all of Switzerland. This product will be the first of its type and be relevant for a range of practical and scientific applications.


September 2021


PI / Partners


  • Dr. Lukas Gudmundsson 
  • Dr. Etienne Fluet
  • Prof. Sonia I. Seneviratne


  • Dr. Massimiliano Zappa



This project deals with the modeling of river flows, with a focus on streams in Switzerland. Current state-of-the-art spatially distributed hydrological models are too computationally expensive to be run over entire Switzerland at a fine spatial resolution and often lead to mediocre river flow estimates at ungauged locations (out-of-sample predictions). We wish to develop various probabilistic models which are computationally scalable, propagate uncertainty adequately, and yield satisfactory flow predictions at ungauged locations.

Proposed approach:

We are currently developing two models in parallel. The first one is a recurrent neural network with long short-term memory (LSTM) cells, adapted for multiple gauging stations which are connected by the river network seen as a directed graph. The second model builds on the first principles by combining additive models (with group ridge-penalized splines) for every gauging station and propagating the predicted discharge through the network (routing). We plan on exploring a third approach, primarily for uncertainty quantification, based on Gaussian processes defined on river networks.


The successful development of such models, and their application to the entire network of river streams in Switzerland, will have important implications for water resources management. Furthermore, if run in an online fashion, these models would greatly improve drought and flood monitoring, with possible deployment beyond Switzerland.


Ghiggi, G., Humphrey, V., Seneviratne, S. I., and Gudmundsson, L. (2021). G-RUN ENSEMBLE: A multi-forcing observation-based global runoff reanalysis. Water Resources Research, 57 (5), 1-13.

Jia, X. et al. (2021). Physics-Guided Recurrent Graph Model for Predicting Flow and Temperature in River Networks. Proceedings of the 2021 SIAM International Conference on Data Mining (SDM), 612-620. The Society for Industrial and Applied Mathematics: 

Asadi, P., Davison, A. C., and Engelke, S. (2015). Extremes on river networks. Ann. Appl. Stat. 9 (4), 2023-2050. Extremes on river networks: