# Stochastic analysis of terrestrial systems

This research topic focuses on the uncertainty associated with numerical model predictions that calculate the transport of water, energy and solute in terrestrial systems. We focus on land surface model predictions which calculate water, energy and matter fluxes between the land surface and the atmosphere. Also predictions of exchange fluxes between streams and aquifers and between the unsaturated zone and aquifers (groundwater recharge) are of special interest. We want to characterize the prediction uncertainty and reduce it by incorporating different kinds of measurement data in the model predictions.

Most research projects in this topic are currently focused on the use of **sequential data assimilation methods** to reduce model prediction uncertainty. Sequential data assimilation corrects model predictions when measurements are available. The correction is based on a statistical approach which determines optimal weights for the different pieces of information (model prediction, measurement data) which are included in the data assimilation procedure. The model uncertainty is characterized using a Monte Carlo approach with many different model runs. Each of the model runs gives different predictions because model parameters and model forcings differ between the many model runs. The different model parameters and model forcings are sampled from statistical distributions. Data assimilation also takes measurement uncertainty into account. For each of the grid cells and each of the many model runs optimal weights are determined for the model prediction on one hand and each of the measurements on the other hand. This procedure results in an update of the predicted states for each of the model runs at all grid cells. Together with states also parameters can be updated, with help of an **augmented state vector approach**.

Concerning sequential data assimilation, currently and in the next years the following research topics are of special relevance:

**Multi-scale data assimilation**. This concerns the assimilation of different types of measurement data, measured at different scales. An example is soil moisture, measured at the field scale with cosmic ray probes and measured at a much larger scale by some of the remote sensing methods. We develop a methodology to optimally handle this multi-scale information in the data assimilation procedure.**Multivariate data assimilation**. In all branches of hydrology it is still uncommon to assimilate more than one data type. Most studies which are published focus on the assimilation of one (maximum a few) data types. However, we think that for an improvement of predictions with terrestrial system models it is especially important to assimilate many different data types. This concerns data which give complementary information: about the soil status, the vegetation status, the water cycle, the energy cycle and also fluxes between terrestrial compartments. We also look at methodological aspects of multivariate data assimilation.**Data assimilation for highly non-linear problems and Non-Gaussian distributions**. The most popular data assimilation method in geosciences is the Ensemble Kalman Filter method. This method is relatively robust for non-linearities, but does not perform optimally for non-linear problems and Non-Gaussian distributions. We are therefore also interested in alternative data assimilation methods which are more robust for non-linearity and non-Gaussianity. This is the reason why we also work on the particle filter method and the development of modified variants of the Ensemble Kalman Filter, that are more robust under those conditions.

The reducing of model prediction uncertainty by merging measurement data and model simulations is also addressed with help of **inverse modeling methods** (in groundwater studies), **upscaling and downscaling approaches** (e.g., for translating climate projections to the hydrological scale) and **other data fusion techniques** (e.g., geostatistical simulation approaches). For the appropriate handling of measurement data in simulation models we perform also statistical and other analyses to precisely analyze systematic and random errors of the data. This work results in the **development of measurement operators** to be used in data assimilation and inverse modeling studies.

Currently, the work in this research topic is organized in the following research projects:

- Improving the characterization of spatio-temporal variable streambeds and river-aquifer exchange fluxes by assimilation of piezometric head and temperature data
- Assimilating eddy covariance data with a particle filter
- Multi-scale assimilation of soil moisture data in land surface models
- Real-time optimization of irrigation of citrus fields in Spain
- Data assimilation with ParFlow-CLM
- Upscaling of biogeochemical fluxes to characterize regional carbon balance

The modeling activities result in the development of different software products. Often, existing software is enhanced with data assimilation routines (CLM, SPRING, HYDRUS). In rare cases, we develop also forward algorithms, adjoint codes and inversion routines ourselves (INVERTO). Most of the software is parallelized and run on the supercomputing facilities of the Forschungszentrum Jülich. Further information on supercomputing at Forschungszentrum Jülich and our computing activities can be found here:

Supercomputing at Forschungszentrum Jülich:

http://www.fz-juelich.de/ias/jsc/EN/Home/home_node.html

Specific computing activities in our team

Contact person:

Prof. Dr. Harrie-Jan Hendricks Franssen

Agrosphere (IBG-3)

Forschungszentrum Jülich GmbH

Leo Brandtstrasse

52425 Jülich

Germany

Tel. +49 02461 4462

E-mail: h.hendricks-franssen@fz-juelich.de

Publications of people contributing in this research topic