Building Ensemble-Based Data Assimilation Systems for High-Dimensional Models

Different strategies for implementing ensemble-based data assimilation systems are discussed. Ensemble filters like ensemble Kalman filters and particle filters can be implemented so that they are nearly independent from the model into which they assimilate observations. This allows to develop implementations that clearly separate the data assimilation algorithm from the numerical model. For coupling the model with a data assimilation software one possibility is to use disk files to exchange the model state information between model and ensemble data assimilation methods. This offline coupling does not require changes in the model code, except for a possible component to simulate model error during the ensemble integration. However, using disk files can be inefficient, in particular when the time for the model integrations is not significantly larger than the time to restart the model for each ensemble member and to read and write the ensemble state information with the data assimilation program. In contrast, an online coupling strategy can be computational much more efficient. In this coupling strategy, subroutine calls for the data assimilation are directly inserted into the source code of an existing numerical model and augment the numerical model to become a data assimilative model. This strategy avoids model restarts as well as excessive writing of ensemble information into disk files. To allow for ensemble integrations, one of the subroutines modifies the parallelization of the model or adds one, if a model is not already parallelized. Then, the data assimilation can be performed efficiently using parallel computers. As the required modifications to the model code are very limited, this strategy allows one to quickly extent a model to a data assimilation system. In particular, the numerics of a model do not need to be changed and the model itself does not need to be a subroutine. The online coupling shows an excellent computational scalability on supercomputers and is well suited for high-dimensional numerical models. Further, a clear separation of the model and data assimilation components allows to continue the development of both components separately. Thus, new data assimilation methods can be easily added to the data assimilation system. Using the example of the parallel data assimilation framework [PDAF, http://pdaf.awi.de] and the ocean model NEMO, it is demonstrated how the online coupling can be achieved with minimal changes to the numerical model

ITR: A Computational Framework for Observational Science: Data Assimilation Methods and their Application for Understanding North Atlantic Zooplankton Dynamics

This project will develop a modular data assimilation system, investigate several algorithms to make data assimilation more efficient, and will apply this system to investigate zooplankton dynamics in the North Atlantic. The goal of data assimilation is to find the value of the control variables (typically, the initial conditions or boundary conditions or model parameters) producing the best agreement between the model and the data. A data assimilation system consists of a forward model representing known dynamics. This model is integrated and the deviation between its predictions and available observations are quantified by a cost function. An adjoint model, representing the inverse of the known dynamics, is then run to determine the dependence of the cost function on the control variables. From the results of the adjoint model, the control variables are adjusted and the entire procedure repeats until the system converges on an answer. Because of the many iterations of the forward/adjoint system are required to find an answer, data assimilation is a computationally intensive process. The proposed data assimilation system will attempt to improve the effciency through parallelization and algorithmic improvements. Specifically, this project will evaluate three standard minimization algorithms and a new algorithm based on multigrid techniques. Using this system, data from the Continous Plankton Recorder survey, the only ongoing basin-wide plankton survey, will be assimilated to provide an accurate, quantitative description of the seasonal and interannual changes of North Atlantic zooplankton populations (especially, Calanus finmarchicus) in the Gulf of Maine and across the entire North Atlantic. This description will provide a better mechanistic understanding of the processes responsible for observed patterns in these populations. Such an understanding is prerequisite for predicting the impact of climate variability and change on zooplankton populations and the ecosystems they support.Broader Impacts: The proposed data assimilation system is a general model for many data assimilation problems including operational oceanography and numerical weather prediction. This project\u27s association with the Cornell Theory Center (CTC) allows a unique opportunity to share its data assimilation system to a wide audience. With the help of CTC staff, a web interface to the system running on CTC\u27s .NET cluster will be built. This interface will allow researchers and students across the world to access a high-performance data assimilation system. The development of the data assimilation system will be integrated into a series of computational tools courses offered at Cornell. This project will also provide research opportunities for both graduate students and undergraduates

Application of an Ensemble Smoother to Precipitation Assimilation

Assimilation of precipitation in a global modeling system poses a special challenge in that the observation operators for precipitation processes are highly nonlinear. In the variational approach, substantial development work and model simplifications are required to include precipitation-related physical processes in the tangent linear model and its adjoint. An ensemble based data assimilation algorithm "Maximum Likelihood Ensemble Smoother (MLES)" has been developed to explore the ensemble representation of the precipitation observation operator with nonlinear convection and large-scale moist physics. An ensemble assimilation system based on the NASA GEOS-5 GCM has been constructed to assimilate satellite precipitation data within the MLES framework. The configuration of the smoother takes the time dimension into account for the relationship between state variables and observable rainfall. The full nonlinear forward model ensembles are used to represent components involving the observation operator and its transpose. Several assimilation experiments using satellite precipitation observations have been carried out to investigate the effectiveness of the ensemble representation of the nonlinear observation operator and the data impact of assimilating rain retrievals from the TMI and SSM/I sensors. Preliminary results show that this ensemble assimilation approach is capable of extracting information from nonlinear observations to improve the analysis and forecast if ensemble size is adequate, and a suitable localization scheme is applied. In addition to a dynamically consistent precipitation analysis, the assimilation system produces a statistical estimate of the analysis uncertainty

Uncertainty Quantification of Nonlinear Lagrangian Data Assimilation Using Linear Stochastic Forecast Models

Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact Bayesian formulae for the state estimation of high-dimensional systems. In this paper, an analytically tractable mathematical framework for continuous-in-time Lagrangian data assimilation is developed. It preserves the nonlinearity in the observational processes while approximating the forecast model of the underlying flow field using linear stochastic models (LSMs). A critical feature of the framework is that closed analytic formulae are available for solving the posterior distribution, which facilitates mathematical analysis and numerical simulations. First, an efficient iterative algorithm is developed in light of the analytically tractable statistics. It accurately estimates the parameters in the LSMs using only a small number of the observed tracer trajectories. Next, the framework facilitates the development of several computationally efficient approximate filters and the quantification of the associated uncertainties. A cheap approximate filter with a diagonal posterior covariance derived from the asymptotic analysis of the posterior estimate is shown to be skillful in recovering incompressible flows. It is also demonstrated that randomly selecting a small number of tracers at each time step as observations can reduce the computational cost while retaining the data assimilation accuracy. Finally, based on a prototype model in geophysics, the framework with LSMs is shown to be skillful in filtering nonlinear turbulent flow fields with strong non-Gaussian features

Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean

This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the Tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both methods produce similarly good results. However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error

Short-term fire front spread prediction using inverse modelling and airborne infrared images

A wildfire forecasting tool capable of estimating the fire perimeter position sufficiently in advance of the actual fire arrival will assist firefighting operations and optimise available resources. However, owing to limited knowledge of fire event characteristics (e.g. fuel distribution and characteristics, weather variability) and the short time available to deliver a forecast, most of the current models only provide a rough approximation of the forthcoming fire positions and dynamics. The problem can be tackled by coupling data assimilation and inverse modelling techniques. We present an inverse modelling-based algorithm that uses infrared airborne images to forecast short-term wildfire dynamics with a positive lead time. The algorithm is applied to two real-scale mallee-heath shrubland fire experiments, of 9 and 25 ha, successfully forecasting the fire perimeter shape and position in the short term. Forecast dependency on the assimilation windows is explored to prepare the system to meet real scenario constraints. It is envisaged the system will be applied at larger time and space scales.Peer ReviewedPostprint (author's final draft

Development of an oceanographic application in HPC

High Performance Computing (HPC) is used for running advanced application programs efficiently, reliably, and quickly. In earlier decades, performance analysis of HPC applications was evaluated based on speed, scalability of threads, memory hierarchy. Now, it is essential to consider the energy or the power consumed by the system while executing an application. In fact, the High Power Consumption (HPC) is one of biggest problems for the High Performance Computing (HPC) community and one of the major obstacles for exascale systems design. The new generations of HPC systems intend to achieve exaflop performances and will demand even more energy to processing and cooling. Nowadays, the growth of HPC systems is limited by energy issues Recently, many research centers have focused the attention on doing an automatic tuning of HPC applications which require a wide study of HPC applications in terms of power efficiency. In this context, this paper aims to propose the study of an oceanographic application, named OceanVar, that implements Domain Decomposition based 4D Variational model (DD-4DVar), one of the most commonly used HPC applications, going to evaluate not only the classic aspects of performance but also aspects related to power efficiency in different case of studies. These work were realized at Bsc (Barcelona Supercomputing Center), Spain within the Mont-Blanc project, performing the test first on HCA server with Intel technology and then on a mini-cluster Thunder with ARM technology. In this work of thesis it was initially explained the concept of assimilation date, the context in which it is developed, and a brief description of the mathematical model 4DVAR. After this problem’s close examination, it was performed a porting from Matlab description of the problem of data-assimilation to its sequential version in C language. Secondly, after identifying the most onerous computational kernels in order of time, it has been developed a parallel version of the application with a parallel multiprocessor programming style, using the MPI (Message Passing Interface) protocol. The experiments results, in terms of performance, have shown that, in the case of running on HCA server, an Intel architecture, values of efficiency of the two most onerous functions obtained, growing the number of process, are approximately equal to 80%. In the case of running on ARM architecture, specifically on Thunder mini-cluster, instead, the trend obtained is labeled as "SuperLinear Speedup" and, in our case, it can be explained by a more efficient use of resources (cache memory access) compared with the sequential case. In the second part of this paper was presented an analysis of the some issues of this application that has impact in the energy efficiency. After a brief discussion about the energy consumption characteristics of the Thunder chip in technological landscape, through the use of a power consumption detector, the Yokogawa Power Meter, values of energy consumption of mini-cluster Thunder were evaluated in order to determine an overview on the power-to-solution of this application to use as the basic standard for successive analysis with other parallel styles. Finally, a comprehensive performance evaluation, targeted to estimate the goodness of MPI parallelization, is conducted using a suitable performance tool named Paraver, developed by BSC. Paraver is such a performance analysis and visualisation tool which can be used to analyse MPI, threaded or mixed mode programmes and represents the key to perform a parallel profiling and to optimise the code for High Performance Computing. A set of graphical representation of these statistics make it easy for a developer to identify performance problems. Some of the problems that can be easily identified are load imbalanced decompositions, excessive communication overheads and poor average floating operations per second achieved. Paraver can also report statistics based on hardware counters, which are provided by the underlying hardware. This project aimed to use Paraver configuration files to allow certain metrics to be analysed for this application. To explain in some way the performance trend obtained in the case of analysis on the mini-cluster Thunder, the tracks were extracted from various case of studies and the results achieved is what expected, that is a drastic drop of cache misses by the case ppn (process per node) = 1 to case ppn = 16. This in some way explains a more efficient use of cluster resources with an increase of the number of processes