The highly nonlinear dynamics of earthquake sequences and the limited availability of stress observations near subsurface faults make it very difficult, if not impossible, to forecast earthquakes. Ensemble data-assimilation methods provide a means to estimate state variables and parameters of earthquake sequences that may lead to a better understanding of the associated fault-slip process and contribute to the forecastability of earthquakes. We illustrate the challenges of data assimilation in earthquake simulation with an overview of three studies, each with different objectives and experiments.

In the first study, by reconstructing a laboratory experiment with an advanced numerical simulator we perform synthetic twin experiments to test the performance of an ensemble Kalman Filter (EnKF) and its ability to reconstruct fault slip behaviour in 1D and 3D simulations. The data assimilation estimates and forecasts earthquakes, even when having highly uncertain observations of the stress field. In these experiments, we assume the friction parameters to be perfectly known, which is typically not the case in reality.

A bias in a friction parameter can cause a significant change in earthquake dynamics, which will complicate the application of data assimilation in realistic cases. The second study addresses how well state estimation and state-parameter estimation can account for friction-parameter bias. For this, we use a 0D model for earthquake recurrence with a particle filter with sequential importance resampling. This shows that in case of intermediate to large uncertainty in friction parameters, combined state-and-parameter estimation is critical to correctly estimate earthquake sequences. The study also highlights the advantage of a particle filter over an EnKF for this nonlinear system.

The post- and inter-seismic deformations following an earthquake are rather gradual and do not pose the same challenges for data assimilation as the deformation during an earthquake event. To estimate the model parameters of surface displacements during these phases, a third study illustrates the application of the Ensemble Smoother-Multiple Data Assimilation and the particle filter with actual GPS data of the Tohoku 2011 earthquake.

Based on the comparison of the various experiments, we discuss the choice of data-assimilation method and -approach in earthquake simulation and suggest directions for future research.

How to cite: Vossepoel, F., Banerjee, A., Diab Montero, H., Li, M., Marsman, C., Govers, R., and van Dinther, Y.: Nonlinear Data Assimilation for State and Parameter Estimation in Earthquake Simulation, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-9529, https://doi.org/10.5194/egusphere-egu23-9529, 2023.

Slowly varying ocean heat content is one of the most important variables when describing cli-
mate variability on interannual to decadal time scales. Since observation-based estimates of
ocean heat content require extensive observational coverage, incomplete observations are often
combined with numerical models via data assimilation to simulate the evolution of oceanic heat.
However, incomplete observations, particularly in the subsurface ocean, lead to large uncertain-
ties in the resulting model-based estimate. As an alternative approach, Kadow et al (2020) have
proven that artificial intelligence can successfully be utilized to reconstruct missing climate in-
formation for surface temperatures. In the following, we investigate the possibility to train their
three-dimensional convolutional neural network to reconstruct missing subsurface temperatures
to obtain ocean heat content estimates with a focus on the North Atlantic ocean.
The network is trained and tested to reconstruct a 16 member Ensemble Kalman Filter assimi-
lation ensemble constructed with the Max-Planck Institute Earth System Model for the period
from 1958 to 2020. Specifically, we examine whether the partial convolutional U-net represents
a valid alternative to the Ensemble Kalman Filter assimilation to estimate North Atlantic sub-
polar gyre ocean heat content.
The neural network is capable of reproducing the assimilation reduced to datapoints with ob-
servational coverages within its ensemble spread with a correlation coefficient of 0.93 over the
entire time period and of 0.99 over 2004 – 2020 (the Argo-Era). Additionally, the network is
able to reconstruct the observed ocean heat content directly from observations for 12 additional
months with a correlation of 0.97, essentially replacing the assimilation experiment by an extrap-
olation. When reconstructing the pre-Argo-Era, the network is only trained with assimilations
from the Argo-Era. The lower correlation in the resulting reconstruction indicates higher un-
certainties in the assimilation outside of its ensemble spread at times with low observational
density. These uncertainties are highlighted by inconsistencies in the assimilation’s represen-
tations of the North Atlantic Current at times and grid points without observations detected
by the neural network. Our results demonstrate that a neural network is not only capable of
reproducing the observed ocean heat content over the training period, but also before and after
making the neural network a suitable candidate to step-wise extend or replace data assimilation.

How to cite: Lentz, S., Brune, Dr. S., Kadow, Dr. C., and Baehr, P. Dr. J.: Reconstructing North Atlantic Ocean Heat Content Using Convolutional Neural Networks, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-14985, https://doi.org/10.5194/egusphere-egu23-14985, 2023.

There is a history of simple error growth models designed to capture the key properties of error growth in operational numerical weather prediction models. We propose here such a scalar model that relies on the previous ones, but captures the effect of small scales on the error growth via additive noise in a nonlinear stochastic differential equation (SDE). We nondimensionalize the equation and study its behavior with respect to the error saturation value, the growth rate of small errors, and the magnitude of noise. We show that the addition of noise can change the curvature of the error growth curve. The SDE model seems to improve substantially the fit to operational error growth curves, compared to the deterministic counterparts.

How to cite: Ghil, M., Bach, E., and Crisan, D.: Forecast error growth: A stochastic differential equation model, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-8640, https://doi.org/10.5194/egusphere-egu23-8640, 2023.

Instead of combining data from an ensemble of different models after the simulations are already performed, as in a standard multi-model ensemble, we let the models interact with each other during their simulation. This ensemble of interacting models is called a supermodel. By exchanging information, models can compensate for each other's errors before the errors grow and spread to other regions or variables. Effectively, we create a new dynamical system. The exchange between the models is frequent enough such that the models synchronize, in order to prevent loss of variance when the models are combined. In previous work, we experimented successfully with combining atmospheric models of intermediate complexity in the context of parametric error. Here we will show results of combining two different AGCMs, NorESM1-ATM and CESM1-ATM. The models have different horizontal and vertical resolutions. To combine states from the different grids, we convert the individual model states to a ‘common state space’ with interpolation techniques. The weighted superposition of different model states is called a ‘pseudo-observation’. The pseudo-observations are assimilated back into the individual models, after which the models continue their run. We apply recently developed methods to train the weights determining the superposition of the model states, in order to obtain a supermodel that will outperform the individual models and any weighted average of their outputs.

How to cite: Schevenhoven, F., Shen, M.-L., Keenlyside, N., Weiss, J. B., and Duane, G. S.: Supermodelling: synchronising models to further improve predictions, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-7480, https://doi.org/10.5194/egusphere-egu23-7480, 2023.

Data assimilation theory relies on the assumption that the background, model, and observations are unbiased. However, this is often not the case and, if biases are left uncorrected, this can cause significant systematic errors in the analysis. When bias is only present in the observations, Variational Bias Correction (VarBC) can correct for observation bias, and when bias is only present in the model, Weak-Constraint 4D Variational Assimilation (WC4DVar) can correct for model bias. However, when both observation and model biases are present, it can be very difficult to understand how the different bias correction methods interact, and the role of anchor (unbiased) observations becomes crucial for providing a frame of reference from which the biases may be estimated. This work presents a systematic study of the properties of the network of anchor observations needed to disentangle between model and observation biases when correcting for one or both types of bias in 4DVar.

We extend the theory of VarBC and WC4DVar to include both biased and anchor observations, to find that the precision and timing of the anchor observations are important in reducing the contamination of model/observation bias in the correction of observation/model bias. We show that anchor observations have the biggest impact in reducing the contamination of bias when they are later in the assimilation window than the biased observations, as such, operational systems that rely on anchor observations that are earlier in the window will be more susceptible to the contamination of model and/or observation biases. We also compare the role of anchor observations when VarBC/WC4DVar/both are used in the presence of both observation and model biases. We find that the ability of VarBC to effectively correct for observation bias when model bias is present, is very dependent on precise anchor observations, whereas correcting model bias with WC4DVar or correcting for both biases performs reasonably well regardless of the precision of anchor observations (although more precise anchor observations reduces the bias in the state analysis compared with less precise anchor observations for all three cases). This demonstrates that, when it is not possible to use anchor observations, it may be better to correct for both observation and model biases, rather than relying on only one bias correction technique.

We demonstrate these results in a series of idealised numerical experiments that use the Lorenz 96 model as a simplified model of the atmosphere.

How to cite: Francis, D., Fowler, A., Lawless, A., Migliorini, S., and Eyre, J.: The role of anchor observations in disentangling observation and model bias corrections in 4DVar, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-7719, https://doi.org/10.5194/egusphere-egu23-7719, 2023.

All-sky radiance assimilation often has non-Gaussian observation error distributions, which can be exacerbated by high model spatial resolutions due to better resolved nonlinear physical processes. For ensemble Kalman filters, observation ensemble perturbations can be approximated by linearized observation operator (LinHx) that uses the observation operator Jacobian of ensemble mean rather than full observation operator (FullHx). The impact of observation operator on infrared radiance data assimilation is examined here by assimilating synthetic radiance observations from channel 1025 of GIIRS with increased model spatial resolutions from 7.5 km to 300 m. A tropical cyclone is used, while the findings are expected to be generally applied. Compared to FullHx, LinHx provides larger magnitudes of correlations and stronger corrections around observation locations, especially when all-sky radiances are assimilated at fine model resolutions. For assimilating clear-sky radiances with increasing model resolutions, LinHx has smaller errors and improved vortex intensity and structure than FullHx. But when all-sky radiances are assimilated, FullHx has advantages over LinHx. Thus for regimes with more linearity, LinHx provides stronger correlations and imposes more corrections than FullHx; but for regimes with more nonlinearity, LinHx provides detrimental non-Gaussian prior error distributions in observation space, unrealistic correlations and overestimated corrections, compared to FullHx.

How to cite: Lei, L.: Impacts of Observation Forward Operator on Infrared Radiance Data Assimilation with Fine Model Resolutions, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3011, https://doi.org/10.5194/egusphere-egu23-3011, 2023.

In this presentation we introduce coupled assimilation activities conducted in support of seamless Earth system approach developments for Numerical Weather Prediction and climate reanalysis at the European Centre for Medium-Range Weather Forecasts (ECMWF). For operational applications coupled assimilation requires to have reliable and timely access to observations in all the Earth system components and it relies on consistent acquisition and monitoring approaches across the components. We show recent and future infrastructure developments and implementations to support consistent observations acquisition and monitoring for land and ocean at ECMWF. We discuss challenges of surface sensitive observations assimilation and we show ongoing forward operator and coupling developments to enhance the exploitation of interface observations over land and ocean surfaces. We present plans to use new and future observation types from future observing systems such as the Copernicus Expansion missions.

How to cite: de Rosnay, P., browne, P., de Boisséson, E., Fairbairn, D., Garrigues, S., Herbert, C., Ochi, K., Schepers, D., Weston, P., and Zuo, H.: Coupled data assimilation for numerical weather prediction at ECMWF, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-16806, https://doi.org/10.5194/egusphere-egu23-16806, 2023.

We developed an ensemble based data assimilation (DA) system for an integrated hydrological model to facilitate real-time operational simulations of water quantity and quality. The integrated surface and subsurface hydrologic model HydroGeoSphere (HGS) (Brunner & Simmons, 2012) which simulates surface water and variably saturated groundwater flow as well as solute transport, was coupled with the Parallel Data Assimilation Framework (PDAF) (Nerger et al., 2005). The developed DA system allows joint assimilation of multiple types of observations such as piezometric heads, streamflow, and tracer concentrations. By explicitly considering tracer and streamflow data we substantially expand the hydrologic information which can be used to constrain the simulations.    Both the model states and the parameters can be separately or jointly updated by the assimilation algorithm.  

A synthetic alluvial plain model set up by Delottier et al., (2022) was used as an example to test the performance of our DA system.  For flow simulations, piezometric head observations were assimilated, while for transport simulations, noble gas concentrations (²²²Rn, ³⁷Ar, and ⁴He) were assimilated. Both model states (e.g., hydraulic head or noble gas concentrations) and parameters (e.g. hydraulic conductivities and porosity) are jointly updated by the DA. Results were evaluated by comparing the estimated model variables with independent observation data between the assimilation runs and the free run where no data assimilation was conducted. In a further evaluation step, a real-world, field scale model featuring realistic forcing functions and material properties was set up for a site in Switzerland and carried out for numerical simulations with the developed DA system. The synthetic and real-world examples demonstrate the significant potential in combing state of the art numerical models, data assimilation and novel tracer observations such as noble gases or Radon.

How to cite: Tang, Q., Delottier, H., Schilling, O. S., Kurtz, W., and Brunner, P.: A coupled data assimilation framework with an integrated surface and subsurface hydrological model, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-15189, https://doi.org/10.5194/egusphere-egu23-15189, 2023.

Land data assimilation aims to monitor the evolution of soil and vegetation variables. These variables are driven by climatic conditions and by anthropogenic factors such as agricultural practices. Monitoring terrestrial surfaces involves a number of variables of the soil-plant system such as land cover, snow, surface albedo, soil water content and leaf area index. These variables can be monitored by integrating satellite observations into models. This process is called data assimilation. Integrating observations into land surface models is particularly important in changing climate conditions because environmental conditions and trends never experienced before are emerging. Because data assimilation is able to weight the information coming from contrasting sources of information and to account for uncertainties, it can produce an analysis of terrestrial variables that is the best possible estimation. In this work, data assimilation is implemented at a global scale by regularly updating the model state variables of the ISBA land surface model within the SURFEX modelling platform: the LDAS-Monde sequential assimilation approach. Model-state variable analysis is done for initializing weather forecast atmospheric models. Weather forecast relies on observations to a large extent because of the chaotic nature of the atmosphere. Land variables are not chaotic per se but rapid and complex processes impacting the land carbon budget such as forest management (thinning, deforestation, ...), forest fires and agricultural practices are not easily predictable with a good temporal precision. They cannot be monitored without integrating observations as soon as they are available. We focus on the assimilation of leaf area index (LAI), using land surface temperature (LST) for verification. We show that (1) analyzing LAI together with root-zone soil moisture is needed to monitor the impact of irrigation and heat waves on the vegetation, (2) LAI can be forecasted after properly initializing ISBA. This paves the way to more interactive assimilation of land variables into numerical weather forecast and seasonal forecast models, as well as in atmospheric chemistry models.

How to cite: Calvet, J.-C., Bonan, B., and Xu, Y.: Recent offline land data assimilation results and future steps towards coupled DA at Meteo-France, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-1095, https://doi.org/10.5194/egusphere-egu23-1095, 2023.

Assimilation of sea ice and ocean observational data into coupled sea-ice, ocean and atmosphere models is known as an efficient approach for providing a reliable sea-ice prediction (Mu et al. 2022). However, implementations of the data assimilation in the coupled systems still remain a challenge. This challenge is partly originated from the chaoticity possessed in the atmospheric module, which leads to biases and, therefore, to divergence of predictive characteristics. An additional constrain of the atmosphere is proposed as a tool to tackle the aforementioned problem. To test this approach, we use the recently developed AWI Coupled Prediction System (AWI-CPS). The system is built upon the AWI climate model AWI-CM-3 (Streffing et al. 2022) that includes FESOM2.0 as a sea-ice ocean component and the Integrated Forecasting System (OpenIFS) as an atmospheric component. An Ensemble-type Kalman filter within the Parallel Data Assimilation Framework (PDAF; Nerger and Hiller, 2013) is used to assimilate sea ice concentration, sea ice thickness, sea ice drift, sea surface height, sea surface temperature and salinity, as well as temperature and salinity vertical profiles. The additional constrain of the atmosphere is introduced by relaxing, or “nudging”, the AWI-CPS large-scale atmospheric dynamics to the ERA5 reanalysis data. This nudging of the large scale atmospheric circulation towards reanalysis has allowed to reduce biases in the atmospheric state, and, therefore, to reduce the analysis increments. The most prominent improvement has been achieved for the predicted sea ice drift. Comprehensive analyses will be presented based upon the new system’s performance over the time period 2003 – 2022.

Mu, L., Nerger, L., Streffing, J., Tang, Q., Niraula, B., Zampieri, L., Loza, S. N. and H. F. Goessling, Sea-ice forecasts with an upgraded AWI Coupled Prediction System (Journal of Advances in Modeling Earth Systems, 14, e2022MS003176. doi: 10.1029/2022MS003176.

Nerger, L. and Hiller, W., 2013. Software for ensemble-based data assimilation systems—Implementation strategies and scalability. Computers & Geosciences, 55, pp.110-118.

Streffing, J., Sidorenko, D., Semmler, T., Zampieri, L., Scholz, P., Andrés-Martínez, M., Koldunov, N., Rackow, T., Kjellsson, J., Goessling, H., Athanase, M., Wang, Q., Sein, D., Mu, L., Fladrich, U., Barbi, D., Gierz, P., Danilov, S.,  Juricke, S., Lohmann, G. and Jung, T. (2022) AWI-CM3 coupled climate model: Description and evaluation experiments for a prototype post-CMIP6 model, EGUsphere, 2022, 1—37, doi: 10.5194/egusphere-2022-32

How to cite: Losa, S. N., Mu, L., Athanase, M., Streffing, J., Andrés-Martínez, M., Nerger, L., Semmler, T., Sidorenko, D., and Goessling, H. F.: Combining sea-ice and ocean data assimilation with nudging atmospheric circulation in the AWI Coupled Prediction System, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-14227, https://doi.org/10.5194/egusphere-egu23-14227, 2023.