Multivariate and multiscale data assimilation in terrestrial systems: a review

Abstract

More and more terrestrial observational networks are being established to monitor climatic, hydrological and land-use changes in different regions of the World. In these networks, time series of states and fluxes are recorded in an automated manner, often with a high temporal resolution. These data are important for the understanding of water, energy, and/or matter fluxes, as well as their biological and physical drivers and interactions with and within the terrestrial system. Similarly, the number and accuracy of variables, which can be observed by spaceborne sensors, are increasing. Data assimilation (DA) methods utilize these observations in terrestrial models in order to increase process knowledge as well as to improve forecasts for the system being studied. The widely implemented automation in observing environmental states and fluxes makes an operational computation more and more feasible, and it opens the perspective of short-time forecasts of the state of terrestrial systems. In this paper, we review the state of the art with respect to DA focusing on the joint assimilation of observational data precedents from different spatial scales and different data types. An introduction is given to different DA methods, such as the Ensemble Kalman Filter (EnKF), Particle Filter (PF) and variational methods (3/4D-VAR). In this review, we distinguish between four major DA approaches: (1) univariate single-scale DA (UVSS), which is the approach used in the majority of published DA applications, (2) univariate multiscale DA (UVMS) referring to a methodology which acknowledges that at least some of the assimilated data are measured at a different scale than the computational grid scale, (3) multivariate single-scale DA (MVSS) dealing with the assimilation of at least two different data types, and (4) combined multivariate multiscale DA (MVMS). Finally, we conclude with a discussion on the advantages and disadvantages of the assimilation of multiple data types in a simulation model. Existing approaches can be used to simultaneously update several model states and model parameters if applicable. In other words, the basic principles for multivariate data assimilation are already available. We argue that a better understanding of the measurement errors for different observation types, improved estimates of observation bias and improved multiscale assimilation methods for data which scale nonlinearly is important to properly weight them in multiscale multivariate data assimilation. In this context, improved cross-validation of different data types, and increased ground truth verification of remote sensing products are required.

Figure 1.

Ensemble-based DA system. Measurements are integrated into a DA framework by an observation operator for comparison with ensemble states for state (and parameter) updates. The scheme is presented for one time step only, the sequential character of DA is generated by new model forcings and new measurements initiating a new ensemble of forward models for the next time step.

Figure 2.

The importance resampling particle filter with 12 particles (modified according to van Leeuwen [86]). The model variable runs along the vertical axis, the weight of each particle corresponds to the size of the circles on this axis. t = 0, t = 10 and t = 20 denotes time, with observations at a time interval of 10 time units. All particles have equal weight at time zero. At time 10, the particles are weighted according to likelihood and resampled to obtain an equal-weight ensemble. Some studies perform a perturbation of states and/or parameters after resampling in order to avoid sample impoverishment.

Figure 3.

Schematic of the use of the observation operator for the assimilation of coarse-scale data into a fine-resolution 2D model. w_i,j stands for the weight of the model result in row i and column j in the calculation of the grid-averaged model result. Darker colors represent higher weights. θ stands for the model results, and darker values represent higher values. For simplicity, the .⁻ is omitted from the y and θ variables, and the time index k is omitted from all variables.

Figure 4.

Schematic of the use of prior downscaling for the assimilation of coarse-scale data into a fine-resolution model for a model with only one model layer. The symbols are identical to those in Figure 3. As in Figure 3, the .⁻ is omitted from the y and θ variables, and the time index k is omitted from all variables. DA refers to data assimilation.