We study soil water flow and the associated transport of nonreactive solutes with a focus on the role of soil's multiscale heterogeneity and its intermittent forcing. So far, we considered the atmosphere as the system's stochastic driver but steadily move towards representing the true coupling between soil and atmosphere. Similarly for vegetation for which we start to consider a dynamic coupling all the way to the formation of vegetation patterns. The spatial scales of our prime interest range from a few centimeters to a few hundred meters.

The goal of our research is to develop and demonstrate fundamental methods that are eventually applicable to real systems. We do not aim for actual engineering solutions. Challenges of real systems are the typically complicated and little known architecture of soils, their largely unknown material properties, the diversity of processes, not all of them known let alone understood, and the stochastic and dynamic coupling to other systems like vegetation and atmosphere that are not represented explicitly. Our approach closely integrates experimental methods, theory-based modeling, high-resolution numerical simulations, and data assimilation methods.

## Experiments

Our current experiments at the lab-scale mainly involve Hele-Shaw cells with light-transmission measurements. They include studies of saturated and unsaturated water flow in heterogeneous architectures as well as active transport associated with the evaporation of saline water and $\mathrm{CO_2}$ sequestration.

The current work crew: Philipp Kreyenberg, Marvin Lasetzki, Christin Proß, Jasper Rippberger, Jule Thome

## Modeling & Theory

Our main contributions so far were on flow and transport in heterogeneous porous media and on exploring non-equilibrium flow processes during infiltration into unsaturated soil. We currently embark on studying these processes in more realistic environments that include surface topography, dynamic root systems, weather, and vegetation patterns.

The current work crew: Hannes Bauser, Edoardo Martini

## Simulation

We routinely deploy a range of numerical PDE-solvers, for unsaturated flow of water (SWMS and MuPhi), for solute transport (particle trackers and MuPhi), and for the propagation of electromagnetic fields (MEEP). On occasion, special solvers are implemented, so far for the thermal and hydraulic dynamics of permafrost soils (using COMSOL), for the turbulent wind field above sand dunes (using FEniCS), for the dynamics of vegetation patterns (using Octave and MATLAB), and for soil hydrology in realistic environments (DORiE, using DUNE). For high-performance computing, we rely on the Parallel Computing Group at the Interdisciplinary Center for Scientific Computing (IWR) of Heidelberg University.

The current work crew: Santiago OspinaLukas Riedel

## Inversion - Data Assimilation - Knowledge Fusion

Process models for environmental systems are hardly ever known to the extent that direct simulations are quantitatively useful. The situation is particularly severe for non-uniform domains or with dominating boundaries, both difficulties are typically encountered in terrestrial systems. We separate three aspects:

1. Incomplete process representations are manifest in highly uncertain values of effective parameters. More often though also the very parameterizations are uncertain and even the process model itself is only valid within a subset of naturally occurring states. An example is soil water flow that is modeled by Richards equation, for instance with the Mualem-van Genuchten parameterization. The escalation of conceptual uncertainties here is: (i) the parameters, most importantly $K_0$, $n$, and $\alpha$, (ii) the parameterization itself, often already its shape (Mualem-Brooks-Corey, multimodel,…), certainly its behavior for very high and very low saturations, and (iii) the model, for instance with respect to preferential flow or mechanical deformations.
2. For systems with boundaries, uncertainties extend to the relation between the system and its environment. These uncertainties reach from the accuracy and precision of the forcing quantity all the way to a possible true coupling of the system with its environment, where the feedback between them is no more negligible. Again looking at soil water flow as an example, this would range from inaccurate precipitation information all the way to the soil-precipitation feedback.
3. Observations bring in a plethora of further uncertainties that range from instrument noise on the simple end to scale-discrepancies, weak proxy-relations, and insufficient sampling in space, time, and quantity on the difficult end.

To cope with our insufficient knowledge, we adapt and explore inversion methods for situations where just some parameters are uncertain. With further components uncertain, we attempt data assimilation schemes, currently ensemble Kalman (EnKF) and particle filters. Our eventual goal, however, is to develop and demonstrate knowledge fusion, the optimal representation of some observed reality.

Our current main focus is soil hydrology together with its observation systems like TDR, GPR, soil-weather stations. In addition a strong link develops to CCEES, both for the development of assimilation and fusion methods as well as for their application to analyze complicated high-dimensional systems.

The current work crew: Hannes Bauser, Daniel Berg, Sven Peyinghaus

## Off our General Track

Occasionally, a project explores beyond our general track, invariably if the person who pushes it has direct access to the required specialist understanding, usually through cooperation with respective groups. Such forays help to keep our perspective wide.

### Projects:

Frictional Control of Cross-Equatorial Flow
Dion Häfner, working in TeamOcean at Niels Bohr Institute, Copenhagen