Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalisation of what is known as weakly constrained four dimensional variational assimilation (WC--4DVAR) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two point boundary value problem. For imperfect models, the trade off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. For (nearly) perfect models, this trade off turns out to be (nearly) trivial in some sense, yet allowing for some dynamical error is shown to have positive effects even in this situation. The presented formalism is dynamical in character; no assumptions need to be made about the presence (or absence) of dynamical or observational noise, let alone about their statistics.
The review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to the optimization of boundary conditions on rigid boundaries. As idealized and realistic model configurations are considered. It is shown that the optimization allows us to determine the most sensitive model operators and bring the model solution closer to the assimilated data.
This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the NN models using b…
Three-Dimensional Variational Data Assimilation with Rapid Update Cycling for Short-Range Precipitation Forecasting: A Case Study of Heavy Rainfall in Bali, Indonesia
Bandung Institute of Technology (ITB)（万隆理工学院）；Ronin Institute for Independent Scholarship（龙人独立学术研究学院）；School of Systems Science and Industrial Engineering, State University of New York (SUNY)（纽约州立大学系统科学与工业工程学院）
For many years, strongly and weakly constrained approaches were the only options to deal with errors in four-dimensional variational data assimilation (4DVar), with the aim of balancing the degrees of freedom and model constraints. Strong model constraints were imposed to reduce the degrees of freedom encountered when optimizing the strongly constrained 4DVar problem, and it was assumed that the models were perfect. The weakly constrained approach sought to distinguish initial errors from model errors, and to correct them separately using weak model constraints. Our proposed i4DVar* method exp…
Google Research（谷歌研究院）；Technical University of Munich（慕尼黑工业大学）；Harvard University（哈佛大学）
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their correspo…
Variational approaches to data assimilation, and weakly constrained four dimensional variation (WC-4DVar) in particular, are important in the geosciences but also in other communities (often under different names). The cost functions and the resulting optimal trajectories may have a probabilistic interpretation, for instance by linking data assimilation with Maximum Aposteriori (MAP) estimation. This is possible in particular if the unknown trajectory is modelled as the solution of a stochastic differential equation (SDE), as is increasingly the case in weather forecasting and climate modellin…
This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the evolution equations for the relevant moments of the model error statistics required in data assimilation procedures, along with an approximation suitable for application to large numerical models typical of environmental science. In this contribution we first derive the equations for the model error dynamics in the general case, and then for the particular situ…
EDF R&D（法国电力集团研发中心）；European Center for Research and Advanced Training in Scientific Computation (CERFACS)（欧洲科学计算高级研究与培训中心）；French National Research Center (CNRS)（法国国家科学研究中心）；Université de Toulouse（图卢兹大学）；Saint-Venant Laboratory for Hydraulics (LHSV)（圣维南水力学实验室）
Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be used for new scenarios. This raises the question of DA computational cost, as costly physics-based numerical models need to be reanalyzed. Reduction and metamodelling represent therefore interesting perspectives, for example proposed in recent contributions as hybridization between ensemble and variational methods, to combine their advantages (efficiency, non-l…
