PhD project offered by the IMPRS-gBGC in July 2025

Hybrid modeling of riverine carbon fluxes across scales using machine learning

Shijie Jiang, Sung-Ching Lee, Elisa Calamita, Alexander Brenning

Project description

Riverine carbon dynamics form a key link between land and ocean carbon cycles and contribute significantly to the global carbon budget. Rivers and streams release substantial amounts of gaseous carbon through interactions among hydrology, catchment carbon inputs, biogeochemical processes, and gas exchange at the air–water interface (Dean et al., 2025). Despite their importance, large uncertainties remain in quantifying these emissions due to limited understanding of the coupled physical and biogeochemical controls that govern carbon fluxes across spatial and temporal scales (Battin et al., 2023).

This PhD project aims to improve the quantification of gaseous carbon fluxes from river systems by developing a differentiable hybrid modeling framework that integrates physical process representations with machine learning (Shen et al., 2023). The model combines water and carbon mass balance principles (e.g., Butman et al., 2016) with machine learning to represent processes that are difficult to model explicitly, such as gas transfer velocities and microbial transformations. The hybrid model will be trained on public river monitoring data and applied across a range of hydrological and biogeochemical settings. Modeling will begin at the catchment scale to investigate key controls, then extend to larger spatial domains to estimate inland water carbon emissions across regions and over time. The successful PhD student will work at the interface of environmental modeling and machine learning, gaining experience in hybrid model development and in analyzing environmental processes and carbon cycle dynamics across scales.

Working group & collaboration

The successful candidate will work in the Department of Biogeochemical Integration at the Max Planck Institute for Biogeochemistry and will also be affiliated with Friedrich Schiller University, Jena. The working group offers long-standing expertise in hydrology, carbon cycling, environmental systems modeling, and hybrid and interpretable machine learning. The PhD candidate will work closely with the ELLIS Unit Jena as part of the European Lab for Learning and Intelligent Systems (ELLIS), with access to a strong machine learning research network. For further information, please contact Shijie Jiang.

Requirements

Applications to the IMPRS-gBGC are open to well-motivated and highly-qualified students from all countries. Prerequisites for this PhD project are:

Master's degree in environmental science, earth system science, biogeosciences, climate science, computer science, or related field
Background in either environmental processes with exposure to machine learning, or machine learning with interest in environmental systems
Experience in environmental modeling or machine learning; familiarity with neural networks is a strong plus
Programming skills (e.g., Python, R); experience with deep learning libraries (e.g. PyTorch, TensorFlow) is desirable
Broad interest in carbon cycling, process-based and data-driven environmental modeling, and large-scale Earth system dynamics
Fluency in spoken and written English
Willingness to work in an interdisciplinary environment with geoscientists, modelers, and computational scientists

The Max Planck Society (MPS) strives for gender equality and diversity. The MPS aims to increase the proportion of women in areas where they are underrepresented. Women are therefore explicitly encouraged to apply. We welcome applications from all fields. The Max Planck Society has set itself the goal of employing more severely disabled people. Applications from severely disabled persons are expressly encouraged.

References

Dean, J.F., Coxon, G., Zheng, Y. et al. Old carbon routed from land to the atmosphere by global river systems. Nature 642, 105–111 (2025).
Battin, T.J., Lauerwald, R., Bernhardt, E.S. et al. River ecosystem metabolism and carbon biogeochemistry in a changing world. Nature 613, 449–459 (2023).
Shen, C., Appling, A.P., Gentine, P. et al. Differentiable modelling to unify machine learning and physical models for geosciences. Nat Rev Earth Environ 4, 552–567 (2023).
Butman, D., Stackpoole, S., Stets, E., McDonald, C.P., Clow, D.W. & Striegl, R.G. Aquatic carbon cycling in the conterminous United States and implications for terrestrial carbon accounting, Proc. Natl. Acad. Sci. U.S.A. 113 (1) 58-63 (2016).