scholarly journals First Application of the Local Ensemble Tangent Linear Model (LETLM) to a Realistic Model of the Global Atmosphere

2018 ◽  
Vol 146 (7) ◽  
pp. 2247-2270 ◽  
Author(s):  
Sergey Frolov ◽  
Douglas R. Allen ◽  
Craig H. Bishop ◽  
Rolf Langland ◽  
Karl W. Hoppel ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Data Assimilation ◽  
Linear Model ◽  
Weather Prediction ◽  
Computational Cost ◽  
Maximum Size ◽  
Realistic Model ◽  
Sensitivity Studies ◽  
The Difference ◽  
The Cost

Abstract The local ensemble tangent linear model (LETLM) provides an alternative method for creating the tangent linear model (TLM) and adjoint of a nonlinear model that promises to be easier to maintain and more computationally scalable than earlier methods. In this paper, we compare the ability of the LETLM to predict the difference between two nonlinear trajectories of the Navy’s global weather prediction model at low resolution (2.5° at the equator) with that of the TLM currently used in the Navy’s four-dimensional variational (4DVar) data assimilation scheme. When compared to the pair of nonlinear trajectories, the traditional TLM and the LETLM have improved skill relative to persistence everywhere in the atmosphere, except for temperature in the planetary boundary layer. In addition, the LETLM was, on average, more accurate than the traditional TLM (error reductions of about 20% in the troposphere and 10% overall). Sensitivity studies showed that the LETLM was most sensitive to the number of ensemble members, with the performance gradually improving with increased ensemble size up to the maximum size attempted (400). Inclusion of physics in the LETLM ensemble leads to a significantly improved representation of the boundary layer winds (error reductions of up to 50%), in addition to improved winds and temperature in the free troposphere and in the upper stratosphere/lower mesosphere. The computational cost of the LETLM was dominated by the cost of ensemble propagation. However, the LETLM can be precomputed before the 4DVar data assimilation algorithm is executed, leading to a significant computational advantage.

scholarly journals Four-dimensional ensemble-variational data assimilation for global deterministic weather prediction

2013 ◽  
Vol 20 (5) ◽  
pp. 669-682 ◽  
Author(s):  
M. Buehner ◽  
J. Morneau ◽  
C. Charette
Keyword(s):  
Data Assimilation ◽  
Weather Prediction ◽  
Weighted Average ◽  
Variational Data Assimilation ◽  
Tropical Region ◽  
Model Configuration ◽  
The Difference ◽  
The Cost ◽  
The Tropics ◽  
Forecast Quality

Abstract. The goal of this study is to evaluate a version of the ensemble-variational data assimilation approach (EnVar) for possible replacement of 4D-Var at Environment Canada for global deterministic weather prediction. This implementation of EnVar relies on 4-D ensemble covariances, obtained from an ensemble Kalman filter, that are combined in a vertically dependent weighted average with simple static covariances. Verification results are presented from a set of data assimilation experiments over two separate 6-week periods that used assimilated observations and model configuration very similar to the currently operational system. To help interpret the comparison of EnVar versus 4D-Var, additional experiments using 3D-Var and a version of EnVar with only 3-D ensemble covariances are also evaluated. To improve the rate of convergence for all approaches evaluated (including EnVar), an estimate of the cost function Hessian generated by the quasi-Newton minimization algorithm is cycled from one analysis to the next. Analyses from EnVar (with 4-D ensemble covariances) nearly always produce improved, and never degraded, forecasts when compared with 3D-Var. Comparisons with 4D-Var show that forecasts from EnVar analyses have either similar or better scores in the troposphere of the tropics and the winter extra-tropical region. However, in the summer extra-tropical region the medium-range forecasts from EnVar have either similar or worse scores than 4D-Var in the troposphere. In contrast, the 6 h forecasts from EnVar are significantly better than 4D-Var relative to radiosonde observations for both periods and in all regions. The use of 4-D versus 3-D ensemble covariances only results in small improvements in forecast quality. By contrast, the improvements from using 4D-Var versus 3D-Var are much larger. Measurement of the fit of the background and analyzed states to the observations suggests that EnVar and 4D-Var can both make better use of observations distributed over time than 3D-Var. In summary, the results from this study suggest that the EnVar approach is a viable alternative to 4D-Var, especially when the simplicity and computational efficiency of EnVar are considered. Additional research is required to understand the seasonal dependence of the difference in forecast quality between EnVar and 4D-Var in the extra-tropics.

scholarly journals On the Impact of Unmanned Aerial System Observations on Numerical Weather Prediction in the Coastal Zone

2018 ◽  
Vol 146 (2) ◽  
pp. 599-622 ◽  
Author(s):  
David D. Flagg ◽  
James D. Doyle ◽  
Teddy R. Holt ◽  
Daniel P. Tyndall ◽  
Clark M. Amerault ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Data Assimilation ◽  
Numerical Weather Prediction ◽  
Research Laboratory ◽  
Weather Prediction ◽  
Ocean Model ◽  
Naval Research ◽  
Unmanned Aerial System ◽  
Numerical Weather ◽  
The Impact

Abstract The Trident Warrior observational field campaign conducted off the U.S. mid-Atlantic coast in July 2013 included the deployment of an unmanned aerial system (UAS) with several payloads on board for atmospheric and oceanic observation. These UAS observations, spanning seven flights over 5 days in the lowest 1550 m above mean sea level, were assimilated into a three-dimensional variational data assimilation (DA) system [the Naval Research Laboratory Atmospheric Variational Data Assimilation System (NAVDAS)] used to generate analyses for a numerical weather prediction model [the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS)] with a coupled ocean model [the Naval Research Laboratory Navy Coastal Ocean Model (NCOM)]. The impact of the assimilated UAS observations on short-term atmospheric prediction performance is evaluated and quantified. Observations collected from 50 radiosonde launches during the campaign adjacent to the UAS flight paths serve as model forecast verification. Experiments reveal a substantial reduction of model bias in forecast temperature and moisture profiles consistently throughout the campaign period due to the assimilation of UAS observations. The model error reduction is most substantial in the vicinity of the inversion at the top of the model-estimated boundary layer. Investigations reveal a consistent improvement to prediction of the vertical position, strength, and depth of the boundary layer inversion. The relative impact of UAS observations is explored further with experiments of systematic denial of data streams from the NAVDAS DA system and removal of individual measurement sources on the UAS platform.

scholarly journals Using machine learning to correct model error in data assimilation and forecast applications

2021 ◽  
Author(s):  
Alban Farchi ◽  
Patrick Laloyaux ◽  
Massimo Bonavita ◽  
Marc Bocquet
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Data Science ◽  
Weather Prediction ◽  
Realistic Model ◽  
Model Error ◽  
Underlying Assumption ◽  
Correct Model ◽  
Recent Developments ◽  
Spatiotemporal Processes

<p>Recent developments in machine learning (ML) have demonstrated impressive skills in reproducing complex spatiotemporal processes. However, contrary to data assimilation (DA), the underlying assumption behind ML methods is that the system is fully observed and without noise, which is rarely the case in numerical weather prediction. In order to circumvent this issue, it is possible to embed the ML problem into a DA formalism characterised by a cost function similar to that of the weak-constraint 4D-Var (Bocquet et al., 2019; Bocquet et al., 2020). In practice ML and DA are combined to solve the problem: DA is used to estimate the state of the system while ML is used to estimate the full model. </p><p>In realistic systems, the model dynamics can be very complex and it may not be possible to reconstruct it from scratch. An alternative could be to learn the model error of an already existent model using the same approach combining DA and ML. In this presentation, we test the feasibility of this method using a quasi geostrophic (QG) model. After a brief description of the QG model model, we introduce a realistic model error to be learnt. We then asses the potential of ML methods to reconstruct this model error, first with perfect (full and noiseless) observation and then with sparse and noisy observations. We show in either case to what extent the trained ML models correct the mid-term forecasts. Finally, we show how the trained ML models can be used in a DA system and to what extent they correct the analysis.</p><p>Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models, Nonlin. Processes Geophys., 26, 143–162, 2019</p><p>Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization, Foundations of Data Science, 2 (1), 55-80, 2020</p><p>Farchi, A., Laloyaux, P., Bonavita, M., and Bocquet, M.: Using machine learning to correct model error in data assimilation and forecast applications, arxiv:2010.12605, submitted. </p>

scholarly journals Some Aspects of Sensitivity Analysis in Variational Data Assimilation for Coupled Dynamical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Sergei Soldatenko ◽  
Peter Steinle ◽  
Chris Tingwell ◽  
Denis Chichkine
Keyword(s):  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Weather Prediction ◽  
Computational Cost ◽  
Variational Data Assimilation ◽  
Practical Implementation ◽  
Parameter Uncertainties ◽  
Sensitivity Functions ◽  
Sensitivity Analysis Method

Variational data assimilation (VDA) remains one of the key issues arising in many fields of geosciences including the numerical weather prediction. While the theory of VDA is well established, there are a number of issues with practical implementation that require additional consideration and study. However, the exploration of VDA requires considerable computational resources. For simple enough low-order models, the computational cost is minor and therefore models of this class are used as simple test instruments to emulate more complex systems. In this paper, the sensitivity with respect to variations in the parameters of one of the main components of VDA, the nonlinear forecasting model, is considered. For chaotic atmospheric dynamics, conventional methods of sensitivity analysis provide uninformative results since the envelopes of sensitivity functions grow with time and sensitivity functions themselves demonstrate the oscillating behaviour. The use of sensitivity analysis method, developed on the basis of the theory of shadowing pseudoorbits in dynamical systems, allows us to calculate sensitivity functions correctly. Sensitivity estimates for a simple coupled dynamical system are calculated and presented in the paper. To estimate the influence of model parameter uncertainties on the forecast, the relative error in the energy norm is applied.

scholarly journals Multiplicative and Additive Incremental Variational Data Assimilation for Mixed Lognormal–Gaussian Errors

2014 ◽  
Vol 142 (7) ◽  
pp. 2521-2544 ◽  
Author(s):  
Steven J. Fletcher ◽  
Andrew S. Jones
Keyword(s):  
Data Assimilation ◽  
Lognormal Distribution ◽  
Weather Prediction ◽  
Variational Data Assimilation ◽  
Incremental Formulation ◽  
Incremental Scheme ◽  
Observational Errors ◽  
Mixed Approach ◽  
The Cost ◽  
Gaussian Space

Abstract An advance that made Gaussian-based three- and four-dimensional variational data assimilation (3D- and 4DVAR, respectively) operationally viable for numerical weather prediction was the introduction of the incremental formulation. This reduces the computational costs of the variational methods by searching for a small increment to a background state whose evolution is approximately linear. In this paper, incremental formulations for 3D- and 4DVAR with lognormal and mixed lognormal–Gaussian-distributed background and observation errors are presented. As the lognormal distribution has geometric properties, a geometric version for the tangent linear model (TLM) is proven that enables the linearization of the observational component of the cost functions with respect to a geometric increment. This is combined with the additive TLM for the mixed distribution–based cost function. Results using the mixed incremental scheme with the Lorenz’63 model are presented for different observational error variances, observation set sizes, and assimilation window lengths. It is shown that for sparse accurate observations the scheme has a relative error of ±0.5% for an assimilation window of 100 time steps. This improves to ±0.3% with more frequent observations. The distributions of the analysis errors are presented that appear to approximate a lognormal distribution with a mode at 1, which, given that the background and observational errors are unbiased in Gaussian space, shows that the scheme is approximating a mode and not a median. The mixed approach is also compared against a Gaussian-only incremental scheme where it is shown that as the z-component observational errors become more lognormal, the mixed approach appears to be more accurate than the Gaussian approach.

scholarly journals Linear Filtering of Sample Covariances for Ensemble-Based Data Assimilation. Part I: Optimality Criteria and Application to Variance Filtering and Covariance Localization

2015 ◽  
Vol 143 (5) ◽  
pp. 1622-1643 ◽  
Author(s):  
Benjamin Ménétrier ◽  
Thibaut Montmerle ◽  
Yann Michel ◽  
Loïk Berre
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Weather Prediction ◽  
Computational Cost ◽  
Analytical Framework ◽  
Companion Paper ◽  
Optimality Criteria ◽  
Linear Filtering ◽  
Sampling Errors ◽  
Output Only

Abstract In data assimilation (DA) schemes for numerical weather prediction (NWP) systems, the estimation of forecast error covariances is a key point to get some flow dependency. As shown in previous studies, ensemble data assimilation methods are the most accurate for this task. However, their huge computational cost raises a strong limitation to the ensemble size. Consequently, covariances estimated with small ensembles are affected by random sampling errors. The aim of this study is to develop a theory of covariance filtering in order to remove most of the sampling noise while keeping the signal of interest and then to use it in the DA scheme of a real NWP system. This first part of a two-part study presents the theoretical aspects of such criteria for optimal filtering based on the merging of the theories of optimal linear filtering and of sample centered moments estimation. Its strength relies on the use of sample estimated quantities and filter output only. These criteria pave the way for new algorithms and interesting applications for NWP. Two of them are detailed here: spatial filtering of variances and covariance localization. Results obtained in an idealized 1D analytical framework are shown for illustration. Applications on real forecast error covariances deduced from ensembles at convective scale are discussed in a companion paper.

scholarly journals Toward a variational assimilation of polarimetric radar observations in a convective-scale numerical weather prediction (NWP) model

2020 ◽  
Vol 13 (5) ◽  
pp. 2279-2298
Author(s):  
Guillaume Thomas ◽  
Jean-François Mahfouf ◽  
Thibaut Montmerle
Keyword(s):  
Data Assimilation ◽  
Numerical Weather Prediction ◽  
Weather Prediction ◽  
Numerical Weather ◽  
Observation Operator ◽  
Weather Radars ◽  
Convective Scale ◽  
The Difference ◽  
Input Variables ◽  
Nwp Model

Abstract. This paper presents the potential of nonlinear and linear versions of an observation operator for simulating polarimetric variables observed by weather radars. These variables, deduced from the horizontally and vertically polarized backscattered radiations, give information about the shape, the phase and the distributions of hydrometeors. Different studies in observation space are presented as a first step toward their inclusion in a variational data assimilation context, which is not treated here. Input variables are prognostic variables forecasted by the AROME-France numerical weather prediction (NWP) model at convective scale, including liquid and solid hydrometeor contents. A nonlinear observation operator, based on the T-matrix method, allows us to simulate the horizontal and the vertical reflectivities (ZHH and ZVV), the differential reflectivity ZDR, the specific differential phase KDP and the co-polar correlation coefficient ρHV. To assess the uncertainty of such simulations, perturbations have been applied to input parameters of the operator, such as dielectric constant, shape and orientation of the scatterers. Statistics of innovations, defined by the difference between simulated and observed values, are then performed. After some specific filtering procedures, shapes close to a Gaussian distribution have been found for both reflectivities and for ZDR, contrary to KDP and ρHV. A linearized version of this observation operator has been obtained by its Jacobian matrix estimated with the finite difference method. This step allows us to study the sensitivity of polarimetric variables to hydrometeor content perturbations, in the model geometry as well as in the radar one. The polarimetric variables ZHH and ZDR appear to be good candidates for hydrometeor initialization, while KDP seems to be useful only for rain contents. Due to the weak sensitivity of ρHV, its use in data assimilation is expected to be very challenging.

A Hybrid Differential-Ensemble Linear Forecast Model for 4D-Var

2021 ◽  
Vol 149 (1) ◽  
pp. 3-19
Author(s):  
T. J. Payne
Keyword(s):  
Data Assimilation ◽  
Linear Model ◽  
Numerical Weather Prediction ◽  
Weather Prediction ◽  
Forecast Model ◽  
Regression Technique ◽  
Time Step ◽  
Dynamical Core ◽  
Numerical Weather ◽  
Better Than

AbstractA key component of the 4D-Var data assimilation method used widely for numerical weather prediction is the linear forecast model, which is approximately tangent linear to the forecast model. Traditionally this has been based on differentiating the forecast model, though recently some authors have experimented with an ensemble regression technique, the localized ensemble tangent linear model (LETLM). We propose a hybrid of the two, in which a simplified conventional tangent-linear model (e.g., just the dynamical core) is used together with an LETLM-like adjustment every time step to account for the remaining processes (in this example, the parameterized physics). This is much cheaper than the LETLM, and in tests using the Met Office’s linear model performs considerably better than either a pure LETLM (with a very large ensemble) or the existing linear model.

scholarly journals Regionally Enhanced Global (REG) 4D-Var

2018 ◽  
Vol 146 (12) ◽  
pp. 4015-4038
Author(s):  
Michael A. Herrera ◽  
Istvan Szunyogh ◽  
Adam Brainard ◽  
David D. Kuhl ◽  
Karl Hoppel ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Prediction Models ◽  
Initial Conditions ◽  
Weather Prediction ◽  
Computational Cost ◽  
Limited Area ◽  
Atmospheric Flow ◽  
Forecast Performance ◽  
Limited Area Model ◽  
Area Model

Abstract A regionally enhanced global (REG) data assimilation (DA) method is proposed. The technique blends high-resolution model information from a single or multiple limited-area model domains with global model and observational information to create a regionally enhanced analysis of the global atmospheric state. This single analysis provides initial conditions for both the global and limited-area model forecasts. The potential benefits of the approach for operational data assimilation are (i) reduced development cost, (ii) reduced overall computational cost, (iii) improved limited-area forecast performance from the use of global information about the atmospheric flow, and (iv) improved global forecast performance from the use of more accurate model information in the limited-area domains. The method is tested by an implementation on the U.S. Navy’s four-dimensional variational global data assimilation system and global and limited-area numerical weather prediction models. The results of the monthlong forecast experiments suggest that the REG DA approach has the potential to deliver the desired benefits.

scholarly journals Screen-level non-GTS data assimilation in a limited-area mesoscale model

2010 ◽  
Vol 10 (6) ◽  
pp. 1129-1149 ◽  
Author(s):  
M. Milelli ◽  
M. Turco ◽  
E. Oberto
Keyword(s):  
Boundary Layer ◽  
High Resolution ◽  
Data Assimilation ◽  
Planetary Boundary Layer ◽  
Prediction Models ◽  
Mesoscale Model ◽  
Positive Impact ◽  
Weather Prediction ◽  
Limited Area ◽  
Very High

Abstract. The forecast in areas of very complex topography, as for instance the Alpine region, is still a challenge even for the new generation of numerical weather prediction models which aim at reaching the km-scale. The problem is enhanced by a general lack of standard observations, which is even more evident over the southern side of the Alps. For this reason, it would be useful to increase the performance of the mathematical models by locally assimilating non-conventional data. Since in ARPA Piemonte there is the availability of a great number of non-GTS stations, it has been decided to assimilate the 2 m temperature, coming from this dataset, in the very-high resolution version of the COSMO model, which has a horizontal resolution of about 3 km, more similar to the average resolution of the thermometers. Four different weather situations have been considered, ranging from spring to winter, from cloudy to clear sky. The aim of the work is to investigate the effects of the assimilation of non-GTS data in order to create an operational very high-resolution analysis, but also to test the option of running in the future a very short-range forecast starting from these analyses (RUC or Rapid Update Cycle). The results, in terms of Root Mean Square Error, Mean Error and diurnal cycle of some surface variables such as 2 m temperature, 2 m relative humidity and 10 m wind intensity show a positive impact during the assimilation cycle which tends to dissipate a few hours after the end of it. Moreover, the 2 m temperature assimilation has a slightly positive or neutral impact on the vertical profiles of temperature, eventhough some calibration is needed for the precipitation field which is too much perturbed during the assimilation cycle, while it is unaffected in the forecast period. So the stability of the planetary boundary layer, on the one hand, has not been particularly improved by the new-data assimilation, but, on the other hand, it has not been destroyed. It has to be pointed out that a correct description of the planetary boundary layer, even only the lowest part of it, could be helpful to the forecasters and, in general, to the users, in order to deal with meteorological hazards such as snow (in particular snow/rain limit definition), or fog (description of temperature inversions).

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