On dimension reduction in Gaussian filters

A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is often obtained from the truncated Karhunen-Loeve expansion of the prior distribution. For high-dimensional inverse problems equipped with smoothing priors, this technique can lead to drastic reductions in parameter dimension and significant computational savings. In this paper, we extend the concept of a priori dimension reduction to non-stationary inverse problems, in which the goal is to sequentially infer the state of a dynamical system. Our approach proceeds in an offline-online fashion. We first identify a low-dimensional subspace in the state space before solving the inverse problem (the offline phase), using either the method of "snapshots" or regularized covariance estimation. Then this subspace is used to reduce the computational complexity of various filtering algorithms - including the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within a novel subspace-constrained Bayesian prediction-and-update procedure (the online phase). We demonstrate the performance of our new dimension reduction approach on various numerical examples. In some test cases, our approach reduces the dimensionality of the original problem by orders of magnitude and yields up to two orders of magnitude in computational savings

Data Assimilation by Artificial Neural Networks for an Atmospheric General Circulation Model: Conventional Observation

This paper presents an approach for employing artificial neural networks (NN) to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation. The assimilation methods are tested in the Simplified Parameterizations PrimitivE-Equation Dynamics (SPEEDY) model, an atmospheric general circulation model (AGCM), using synthetic observational data simulating localization of balloon soundings. For the data assimilation scheme, the supervised NN, the multilayer perceptrons (MLP-NN), is applied. The MLP-NN are able to emulate the analysis from the local ensemble transform Kalman filter (LETKF). After the training process, the method using the MLP-NN is seen as a function of data assimilation. The NN were trained with data from first three months of 1982, 1983, and 1984. A hind-casting experiment for the 1985 data assimilation cycle using MLP-NN were performed with synthetic observations for January 1985. The numerical results demonstrate the effectiveness of the NN technique for atmospheric data assimilation. The results of the NN analyses are very close to the results from the LETKF analyses, the differences of the monthly average of absolute temperature analyses is of order 0.02. The simulations show that the major advantage of using the MLP-NN is better computational performance, since the analyses have similar quality. The CPU-time cycle assimilation with MLP-NN is 90 times faster than cycle assimilation with LETKF for the numerical experiment.Comment: 17 pages, 16 figures, monthly weather revie

A wildland fire model with data assimilation

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An ensemble Kalman filter technique with regularization is then used to assimilate temperatures measured at selected points into running wildfire simulations. The assimilation technique is able to modify the simulations to track the measurements correctly even if the simulations were started with an erroneous ignition location that is quite far away from the correct one.Comment: 35 pages, 12 figures; minor revision January 2008. Original version available from http://www-math.cudenver.edu/ccm/report

Efficiency and Sensitivity Analysis of Observation Networks for Atmospheric Inverse Modelling with Emissions

The controllability of advection-diffusion systems, subject to uncertain initial values and emission rates, is estimated, given sparse and error affected observations of prognostic state variables. In predictive geophysical model systems, like atmospheric chemistry simulations, different parameter families influence the temporal evolution of the system.This renders initial-value-only optimisation by traditional data assimilation methods as insufficient. In this paper, a quantitative assessment method on validation of measurement configurations to optimize initial values and emission rates, and how to balance them, is introduced. In this theoretical approach, Kalman filter and smoother and their ensemble based versions are combined with a singular value decomposition, to evaluate the potential improvement associated with specific observational network configurations. Further, with the same singular vector analysis for the efficiency of observations, their sensitivity to model control can be identified by determining the direction and strength of maximum perturbation in a finite-time interval.Comment: 30 pages, 10 figures, 5 table

Multi-source data assimilation for physically based hydrological modeling of an experimental hillslope

Data assimilation has recently been the focus of much attention for integrated surface–subsurface hydrological models, whereby joint assimilation of water table, soil moisture, and river discharge measurements with the ensemble Kalman filter (EnKF) has been extensively applied. Although the EnKF has been specifically developed to deal with nonlinear models, integrated hydrological models based on the Richards equation still represent a challenge, due to strong nonlinearities that may significantly affect the filter performance. Thus, more studies are needed to investigate the capabilities of the EnKF to correct the system state and identify parameters in cases where the unsaturated zone dynamics are dominant, as well as to quantify possible tradeoffs associated with assimilation of multi-source data. Here, the CATHY (CATchment HYdrology) model is applied to reproduce the hydrological dynamics observed in an experimental two-layered hillslope, equipped with tensiometers, water content reflectometer probes, and tipping bucket flow gages to monitor the hillslope response to a series of artificial rainfall events. Pressure head, soil moisture, and subsurface outflow are assimilated with the EnKF in a number of scenarios and the challenges and issues arising from the assimilation of multi-source data in this real-world test case are discussed. Our results demonstrate that the EnKF is able to effectively correct states and parameters even in a real application characterized by strong nonlinearities. However, multi-source data assimilation may lead to significant tradeoffs: the assimilation of additional variables can lead to degradation of model predictions for other variables that are otherwise well reproduced. Furthermore, we show that integrated observations such as outflow discharge cannot compensate for the lack of well-distributed data in heterogeneous hillslopes.</p

Final Report of the DAUFIN project

DAUFIN = Data Assimulation within Unifying Framework for Improved river basiN modeling (EC 5th framework Project

Application and testing of the extended-Kalman-filtering technique for determining the planetary boundary-layer height over Athens, Greece

The final publication is available at Springer via http://dx.doi.org/10.1007/s10546-020-00514-zWe investigate the temporal evolution of the planetary boundary-layer (PBL) height over the basin of Athens, Greece, during a 6-year period (2011–2016), using data from a Raman lidar system. The range-corrected lidar signals are selected around local noon (1200 UTC) and midnight (0000 UTC), for a total of 332 cases: 165 days and 167 nights. In this dataset, the extended-Kalman filtering technique is applied and tested for the determination of the PBL height. Several well-established techniques for the PBL height estimation based on lidar data are also tested for a total of 35 cases. The lidar-derived PBL heights are compared to those derived from radiosonde data. The mean PBL height over Athens is found to be 1617¿±¿324 m at 1200 UTC and 892¿±¿130 m at 0000 UTC for the period examined, while the mean PBL-height growth rate is found to be 170¿±¿64 m h-1 and 90¿±¿17 m h-1 during daytime and night-time, respectively.The research leading to these results has received additional funding from the European Union 7th Framework Program (FP7/2011-2015) and Horizon 2020/2015-2021 Research and Innovation program (ACTRIS) under grant agreements nos 262254, 654109, and 739530, as well as from Spanish National Science Foundation and FEDER funds PGC2018-094132-B-I00. CommSensLab-UPC is a María-de-Maeztu Excellence Unit, MDM-2016-0600, funded by the Agencia Estatal de Investigación, Spain.Peer ReviewedPostprint (author's final draft