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Short-termintense precipitation (SIP; i.e., convective precipitation exceeding 20mmh21) nowcasting is important for urban flood warning and natural hazards management. This paper presents an algorithm for coupling automatic weather station data and single-polarization S-band radar data with a graph model and a random forest for the nowcasting of SIP. Different from the pixel-by-pixel precipitation nowcasting algorithm, this algorithm takes the convective cells as the basic units to consider their interactions and focuses on multicell convective systems. In particular, the following question could be addressed: Will a multicell convective system cause SIP events in the next hour? First, a method based on spatiotemporal superposition between cells is proposed for multicell systems identification. Then, the graph model is used to represent cell physical attributes and the spatial distribution of the entire system. For each graph model, a fusion operation is used to form a 42-dimensional graph feature vector. Finally, combined with the machine learning approaches, a random forest classifier is trained with the graph feature vector to predict the precipitation. In the experiment, this algorithm achieves a probability of detection (POD) of 79.2% and a critical success index (CSI) of 68.3% with the data between 2015 and 2016 in North China. Compared with other precipitation nowcasting algorithms, the graph model and random forest could predict SIP events more accurately and produce fewer false alarms. [ABSTRACT FROM AUTHOR]

In Part I of this two-part paper a new method of predicting the total lightning flash rate in thunderstorms was introduced. In this paper, the implementation of this method into the convection-permitting Consortium for Small Scale Modeling (COSMO) model is presented. The new approach is based on a simple theoretical model that consists of a dipole charge structure, which is maintained by a generator current and discharged by lightning and, to a small extent, by a leakage current. This approach yields a set of four predictor variables, which are not amenable to direct observations and consequently need to be parameterized (Part I). Using an algorithm that identifies thunderstorm cells and their properties, this approach is applied to determine the flash frequency of every thunderstorm cell in the model domain. With this information, the number of flashes that are accumulated by each cell and during the interval between the activation of the lightning scheme can be calculated. These flashes are then randomly distributed in time and beneath each cell. The output contains the longitude, the latitude, and the time of occurrence of each simulated discharge. Simulations of real-world scenarios are presented, which are compared to measurements with the lightning detection network, LINET. These comparisons are done on the cloud scale as well as in a mesoscale region composing southern Germany (two cases each). The flash rates of individual cumulonimbus clouds at the extreme ends of the intensity spectrum are realistically simulated. The simulated overall lightning activity over southern Germany is dominated by spatiotemporal displacements of the modeled convective clouds, although the scheme generally reproduces realistic patterns such as coherent lightning swaths. [ABSTRACT FROM AUTHOR]

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 (2.58 at the equator) with that of theTLMcurrently 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. [ABSTRACT FROM AUTHOR]

This paper extends on the first part of this series by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii) from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps. [ABSTRACT FROM AUTHOR]

This paper describes a region-tree-based precipitation forecast verification approach, which is then used to assess the performance of a numerical model forecast at various scales. In this verification approach, the forecast and observation fields are first represented using region-tree structures. The verification approach consists of three procedures: calculation of spatial structural properties of the forecast and observation trees, matching the forecast tree with the observation tree, and deforming the forecast tree to resemble the observation tree. Based on these procedures, the tree-based verification approach aims at determining the spatial structural differences, displacement errors, and intensity errors between the forecast and the observation at different scales. The behavior of the proposed verification approach is investigated by applications to a standard verification dataset from the spatial forecast verification intercomparison project. [ABSTRACT FROM AUTHOR]

Following the recent development of a three-dimensional ensemble–variational (3DEnVar) data assimilation algorithm for the AROME-France NWP system, this paper examines different approaches to reduce the sampling noise in the ensemble-derived background error covariances in this new scheme without modifying the background ensemble generation strategy. We first examine two variants of scale-dependent localization: one method consists of applying different amounts of localization to different ranges of background error covariance spatial scales, while simultaneously assimilating all of the available observations. Another separate approach uses time-lagged forecasts in order to increase the effective ensemble size, up to a factor of 3 here. This approach of time-lagged forecasts is considered both on its own and together with scale-dependent localization. When the background error covariances are derived from the most recent 25-member ensemble forecasts, the results from data assimilation cycles over a 33-day winter period show that avoiding cross covariances between scales in the scale-dependent localization formulation first proposed by Buehner performs better than the more recent formulation of Buehner and Shlyaeva. However, when increasing the effective ensemble size to 75 members with time-lagged forecasts, the two scale-dependent formulations provide similar forecast improvements overall. It is also found that the lagged-members approach outperforms scale-dependent localization on its own. The largest forecast improvements are obtained when combining the two approaches. [ABSTRACT FROM AUTHOR]

A novel object-based algorithm capable of identifying and tracking convective outflow boundaries in convection-allowing numerical models is presented in this study. The most distinct feature of the proposed algorithm is its ability to seamlessly analyze numerically simulated density currents and bores, both of which play an important role in the dynamics of nocturnal convective systems. The unified identification and classification of these morphologically different phenomena is achieved through a multivariate approach combined with appropriate image processing techniques. The tracking component of the algorithm utilizes two dynamical constraints, which improve the object association results in comparison to methods based on statistical assumptions alone. Special attention is placed on some of the outstanding challenges regarding the formulation of the algorithm and possible ways to address those in future research. Apart from describing the technical details behind the algorithm, this study also introduces specific algorithm applications relevant to the analysis and prediction of bores. These applications are illustrated for a retrospective case study simulated with a convection-allowing ensemble prediction system. The paper highlights how the newly developed algorithm tools naturally form a foundation for understanding the initiation, structure, and evolution of bores and convective systems in the nocturnal environment. [ABSTRACT FROM AUTHOR]

In the standard four-dimensional variational data assimilation (4D-Var) algorithm the background error covariance matrix remains static over time. It may therefore be unable to correctly take into account the information accumulated by a system into which data are gradually being assimilated. A possible method for remedying this flaw is presented and tested in this paper. A hybrid variational-smoothing algorithm is based on a reduced-rank incremental 4D-Var. Its consistent coupling to a singular evolutive extended Kalman (SEEK) smoother ensures the evolution of the matrix. In the analysis step, a low-dimensional error covariance matrix is updated so as to take into account the increased confidence level in the state vector it describes, once the observations have been introduced into the system. In the forecast step, the basis spanning the corresponding control subspace is propagated via the tangent linear model. The hybrid method is implemented and tested in twin experiments employing a shallow-water model. The background error covariance matrix is initialized using an EOF decomposition of a sample of model states. The quality of the analyses and the information content in the bases spanning control subspaces are also assessed. Several numerical experiments are conducted that differ with regard to the initialization of the matrix. The feasibility of the method is illustrated. Since improvement due to the hybrid method is not universal, configurations that benefit from employing it instead of the standard 4D-Var are described and an explanation of the possible reasons for this is proposed. [ABSTRACT FROM AUTHOR]

In the Kalman filter standard algorithm, the computational complexity of the observational update is proportional to the cube of the number y of observations (leading behavior for large y). In realistic atmospheric or oceanic applications, involving an increasing quantity of available observations, this often leads to a prohibitive cost and to the necessity of simplifying the problem by aggregating or dropping observations. If the filter error covariance matrices are in square root form, as in square root or ensemble Kalman filters, the standard algorithm can be transformed to be linear in y, providing that the observation error covariance matrix is diagonal. This is a significant drawback of this transformed algorithm and often leads to an assumption of uncorrelated observation errors for the sake of numerical efficiency. In this paper, it is shown that the linearity of the transformed algorithm in y can be preserved for other forms of the observation error covariance matrix. In particular, quite general correlation structures (with analytic asymptotic expressions) can be simulated simply by augmenting the observation vector with differences of the original observations, such as their discrete gradients. Errors in ocean altimetric observations are spatially correlated, as for instance orbit or atmospheric errors along the satellite track. Adequately parameterizing these correlations can directly improve the quality of observational updates and the accuracy of the associated error estimates. In this paper, the example of the North Brazil Current circulation is used to demonstrate the importance of this effect, which is especially significant in that region of moderate ratio between signal amplitude and observation noise, and to show that the efficient parameterization that is proposed for the observation error correlations is appropriate to take it into account. Adding explicit gradient observations also receives a physical justification. This parameterization is thus proved to be useful to ocean data assimilation systems that are based on square root or ensemble Kalman filters, as soon as the number of observations becomes penalizing, and if a sophisticated parameterization of the observation error correlations is required. [ABSTRACT FROM AUTHOR]

In this paper, a new iterative algorithm for computing a steady-state Kalman gain is proposed. This algorithm utilizes two model forecasts with statistically independent random perturbations to determine the error covariance used to define a Kalman gain matrix for steady-state data assimilation. It is based on the assumption that the error process is weakly stationary and ergodic. The algorithm consists of an iterative procedure for improving the covariance estimate, which requires a fixed observation network. Two twin experiments using a simple wave model and an operational storm surge prediction model are performed to demonstrate the performance of the proposed algorithm. The experiments show that the results obtained by using the proposed algorithm converge to the ones produced by the classic Kalman filter algorithm. An additional experiment using the three-variable Lorenz model is also performed to demonstrate its potential applicability in unstable dynamical systems. [ABSTRACT FROM AUTHOR]

The stability of semi-implicit schemes for the hydrostatic primitive equations system has been studied extensively over the past 20 yr, since this temporal scheme and this system represented a standard for NWP. However, with the increase of computational power, the relaxation of the hydrostatic approximation through the use of nonhydrostatic fully elastic systems is now emerging for future NWP as an attractive solution valid at any scale. In this context, several models employing the so-called Euler equations together with a constant- coefficients semi-implicit time discretization have already been developed, but no solid justification for the suitability of this algorithmic combination has been presented so far, especially from the point of view of robustness. The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This study is restricted to the impact of thermal and baric residual terms (metric residual terms linked to the orography are not considered here). It is shown that, conversely to what occurs with hydrostatic primitive equations, the choice of the prognostic variables used to solve the system in time is of primary importance for the robustness with Euler equations. For an optimal choice of prognostic variables, unconditionally stable schemes can be obtained (with respect to the length of the time step), but only for a smaller range of reference states than in the case of hydrostatic primitive equations. This study also indicates that (i) vertical coordinates based on geometrical height and on mass behave similarly in terms of stability for the problems examined here, and (ii) hybrid coordinates induce an intrinsic instability, the practical importance of which is, however, not completely elucidated in the theoretical context of this paper. [ABSTRACT FROM AUTHOR]

This paper addresses real-time precipitation forecasts from a multianalysis–multimodel superensemble. The methodology for the construction of the superensemble forecasts follows previous recent publications on this topic. This study includes forecasts from multimodels of a number of global operational centers. A multianalysis component based on the Florida State University (FSU) global spectral model that utilizes TRMM and SSM/I datasets and a number of rain-rate algorithms is also included. The difference in the analysis arises from the use of these rain rates within physical initialization that produces distinct differences among these components in the divergence, heating, moisture, and rain-rate descriptions. A total of 11 models, of which 5 represent global operational models and 6 represent multianalysis forecasts from the FSU model initialized by different rain-rate algorithms, are included in the multianalysis–multimodel system studied here. In this paper, “multimodel” refers to different models whose forecasts are being assimilated for the construction of the superensemble. “Multianalysis” refers to different initial analysis contributing to forecasts from the same model. The term superensemble is being used here to denote the bias-corrected forecasts based on the products derived from the multimodel and the multianalysis. The training period is covered by nearly 120 forecast experiments prior to 1 January 2000 for each of the multimodels. These are all 3-day forecasts. The statistical bias of the models is determined from multiple linear regression of these forecasts against a “best” rainfall analysis field that is based on TRMM and SSM/I datasets and using the rain-rate algorithms recently developed at NASA Goddard Space Flight Center. This paper discusses the results of real-time rainfall forecasts based on this system. The main results of this study are that the multianalysis–multi... [ABSTRACT FROM AUTHOR]

This paper is the second of a series and focuses on developing an algorithm to objectively identify tropical cyclone (TC) vorticity centers using single-Doppler radar data. The first paper dealt with the formulation of a single-Doppler radar TC wind retrieval technique, the ground-based velocity-track-display (GBVTD), and the results are verified using analytical TCs. It has been acknowledged that the quality of the GBVTD-retrieved TC circulation strongly depends on accurately knowing its center position. However, existing single-Doppler radar center finding algorithms are limited to estimate centers for axisymmetric TCs. The proposed algorithm uses a simplex method to objectively estimate the TC vorticity center by maximizing GBVTD-retrieved mean tangential wind. When tested with a number of axisymmetric and asymmetric analytical TCs, the accuracy of the TC centers estimated by the GBVTD-simplex algorithm is ≈340 m from the true center. When adding 5 m s[sup -1] random noise to the Doppler velocities, the accuracy of the TC centers is nearly unchanged at 350 m. When applying the GBVTD-simplex algorithm to Typhoon Alex (1987), the estimated uncertainty varies between 0.1 and 2 km. When the overall velocity gradient is weak, the uncertainties in the retrieved TC centers are usually large. The GBVTD-simplex algorithm sometimes has problems finding a solution when a large sector of Doppler radar data is missing in conjunction with weak velocity gradients. The GBVTD-simplex algorithm significantly reduces the uncertainties in estimating TC center position compared with existing methods and improves the quality of the GBVTD-retrieved TC circulation. The GBVTD-simplex algorithm is computationally efficient and can be easily adapted for real-time applications. [ABSTRACT FROM AUTHOR]

This paper reviews the development of the ensemble Kalman filter (EnKF) for atmospheric data assimilation. Particular attention is devoted to recent advances and current challenges. The distinguishing properties of three well-established variations of the EnKF algorithm are first discussed. Given the limited size of the ensemble and the unavoidable existence of errors whose origin is unknown (i.e., system error), various approaches to localizing the impact of observations and to accounting for these errors have been proposed. However, challenges remain; for example, with regard to localization of multiscale phenomena (both in time and space). For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window. This motivates a focus on approaches for maintaining balance during the EnKF update. Also discussed are limited-area EnKF systems, in particular with regard to the assimilation of radar data and applications to tracking severe storms and tropical cyclones. It seems that relatively less attention has been paid to optimizing EnKF assimilation of satellite radiance observations, the growing volume of which has been instrumental in improving global weather predictions. There is also a tendency at various centers to investigate and implement hybrid systems that take advantage of both the ensemble and the variational data assimilation approaches; this poses additional challenges and it is not clear how it will evolve. It is concluded that, despite more than 10 years of operational experience, there are still many unresolved issues that could benefit from further research. Contents APPENDIX A...36 Types of Filter Divergence...36 [ABSTRACT FROM AUTHOR]

Part I of this paper examined nine trace constituent advection algorithms as applied in channel versions of the University of Wisconsin hybrid isentropic-sigma (Φ-σ) and sigma (σ) models. This paper examines the performance of 12 semi-Lagrangian transport (SLT) algorithms in the same models. The interpolants of trace constituent include second- through twelfth-order Lagrangian, an overlapping polynomial, a quasi-monotonic scheme, and two sixth-order schemes that employ derivative estimates. Additional experiments are performed that emulate the SLT algorithm in the NCAR Community Climate Model 2. As in Part I, these three-dimensional simulations are under adiabatic conditions so that conservation of the initial trace constituent maximum on an isentropic surface, and conservation of the areas between any two constituent contours, can be used as objective measures of SLT algorithm accuracy. Further, the experiments provide comparisons not only between the different SLT formulations but also between their performance in models using Φ and σ coordinates. Similar to Part I, an important result of the experiments is that comparison of algorithms is most revealing under three-dimensional transport within a baroclinic wave in which vertical transport is important. The experiments also show 1) that the 'cascade' interpolation scheme is a reasonable method of greatly reducing computation time in SLT without affecting accuracy; 2) that 'shape-preserving' interpolation schemes reduce accuracy in both the Φ-σ and σ models; and 3) that Lagrangian interpolants of tenth and twelfth order do not significantly improve results. Comparisons to results in Part I suggest that the conservation of second-order moments advection scheme is the most consistent of all options tested. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Four-dimensional variational data assimilation (4D-Var) produces unavoidable inaccuracies in the models initial state vector. In this paper the authors investigate a novel variational error estimation method to calculate these inaccuracies. The impacts of model, background, and observational errors on the state estimate produced by 4D-Var are analyzed by applying the variational error estimation method. The structure of the method is similar to the conventional 4D-Var, with the differences in that (i) instead of observations it assimilates observational errors, and (ii) the original model equations (used in 4D-Var as constraints) are first linearized with respect to a small perturbation in the initial state vector and then used as the constraints. The authors then carry out a proof-of-concept study and validate the reliability of this method through multiple twin experiments on the basis of a 2D shallow-water model. All required differentiated models were generated by means of algorithmic differentiation directly from the nonlinear model source code. The experiments reveal that the suggested method works well in a wide range of assimilation windows and types of observational and model errors and can be recommended for error estimation and prediction in data assimilation. [ABSTRACT FROM AUTHOR]

Since mid-February 2013, the ensemble Kalman filter (EnKF) in operation at the Canadian Meteorological Centre (CMC) has been using a 600 × 300 global horizontal grid and 74 vertical levels. This yields 5.4 × 107 model coordinates. The EnKF has 192 members and uses seven time levels, spaced 1 h apart, for the time interpolation in the 6-h assimilation window. It follows that over 7 × 1010 values are required to specify an ensemble of trial field trajectories. This paper focuses on numerical and computational aspects of the EnKF. In response to the increasing computational challenge posed by the ever more ambitious configurations, an ever larger fraction of the EnKF software system has gradually been parallelized over the past decade. In a strong scaling experiment, the way in which the execution time decreases as larger numbers of processes are used is investigated. In fact, using a substantial fraction of one of the CMC's computers, very short execution times are achieved. As it would thus appear that the CMC's computers can handle more demanding configurations, weak scaling experiments are also performed. Here, both the size of the problem and the number of processes are simultaneously increased. The parallel algorithm responds well to an increase in either the number of ensemble members or the number of model coordinates. A substantial increase (by an order of magnitude) in the number of assimilated observations would, however, be more problematic. Thus, to the extent that this depends on computational aspects, it appears that the meteorological quality of the Canadian operational EnKF can be further improved. [ABSTRACT FROM AUTHOR]

Current ensemble-based Kalman filter (EnKF) algorithms are not robust to gross observation errors caused by technical or human errors during the data collection process. In this paper, the authors consider two types of gross observational errors, additive statistical outliers and innovation outliers, and introduce a method to make EnKF robust to gross observation errors. Using both a one-dimensional linear system of dynamics and a 40-variable Lorenz model, the performance of the proposed robust ensemble Kalman filter (REnKF) was tested and it was found that the new approach greatly improves the performance of the filter in the presence of gross observation errors and leads to only a modest loss of accuracy with clean, outlier-free, observations. [ABSTRACT FROM AUTHOR]

This paper describes a three-dimensional immersed boundary method (IBM) that facilitates the explicit resolution of complex terrain within the Weather Research and Forecasting (WRF) model. Two interpolation methods-trilinear and inverse distance weighting (IDW)-are used at the core of the IBM algorithm. This work expands on the previous two-dimensional IBM algorithm of Lundquist et al., which uses bilinear interpolation. Simulations of flow over a three-dimensional hill are performed with WRF's native terrain-following coordinate and with both IB methods. Comparisons of flow fields from the three simulations show excellent agreement, indicating that both IB methods produce accurate results. IDW proves more adept at handling highly complex urban terrain, where the trilinear interpolation algorithm fails. This capability is demonstrated by using the IDW core to model flow in Oklahoma City, Oklahoma, from intensive observation period 3 (IOP3) of the Joint Urban 2003 field campaign. Flow in Oklahoma City is simulated concurrently with an outer domain with flat terrain using one-way nesting to generate a turbulent flow field. Results from the IBM-WRF simulation of IOP3 compare well with observations from the field campaign, as well as with results from an urban computational fluid dynamics code, Finite Element Model in 3-Dimensions and Massively Parallelized (FEM3MP), which used body-fitted coordinates. Using the FAC2 performance metric from Chang and Hanna, which is the fraction of predictions within a factor of 2 of observations, IBM-WRF achieves 100% and 71% for velocity predictions using cup and sonic anemometer observations, respectively. For the passive scalar, 53% of the model predictions meet the FAC5 (factor of 5) criteria. [ABSTRACT FROM AUTHOR]

Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given all the observations on a time window of interest, plays a central conceptual role. The aim of this paper is to use this Bayesian posterior probability distribution as a gold standard against which to evaluate various commonly used data assimilation algorithms. A key aspect of geophysical data assimilation is the high dimensionality and limited predictability of the computational model. We study the 2D Navier-Stokes equations in a periodic geometry, which has these features and yet is tractable for explicit and accurate computation of the posterior distribution by state-of-the-art statistical sampling techniques. The commonly used algorithms that we evaluate, as quantified by the relative error in reproducing moments of the posterior, are 4DVAR and a variety of sequential filtering approximations based on 3DVAR and on extended and ensemble Kalman filters. The primary conclusions are that, under the assumption of a well-defined posterior probability distribution: (i) with appropriate parameter choices, approximate filters can perform well in reproducing the mean of the desired probability distribution; (ii) however they do not perform as well in reproducing the covariance; (iii) the error is compounded by the need to modify the covariance, in order to induce stability. Thus, filters can be a useful tool in predicting mean behavior, but should be viewed with caution as predictors of uncertainty. These conclusions are intrinsic to the algorithms when assumptions underlying them are not valid and will not change if the model complexity is increased. [ABSTRACT FROM AUTHOR]

This paper explores the temporal evolution of cloud microphysical parameter uncertainty using an idealized 1D model of deep convection. Model parameter uncertainty is quantified using a Markov chain Monte Carlo (MCMC) algorithm. A new form of the ensemble transform Kalman smoother (ETKS) appropriate for the case where the number of ensemble members exceeds the number of observations is then used to obtain estimates of model uncertainty associated with variability in model physics parameters. Robustness of the parameter estimates and ensemble parameter distributions derived from ETKS is assessed via comparison with MCMC. Nonlinearity in the relationship between parameters and model output gives rise to a non-Gaussian posterior probability distribution for the parameters that exhibits skewness early and multimodality late in the simulation. The transition from unimodal to multimodal posterior probability density function (PDF) reflects the transition from convective to stratiform rainfall. ETKS-based estimates of the posterior mean are shown to be robust, as long as the posterior PDF has a single mode. Once multimodality manifests in the solution, the MCMC posterior parameter means and variances differ markedly from those from the ETKS. However, it is also shown that if the ETKS is given a multimode prior ensemble, multimodality is preserved in the ETKS posterior analysis. These results suggest that the primary limitation of the ETKS is not the inability to deal with multimodal, non-Gaussian priors. Rather it is the inability of the ETKS to represent posterior perturbations as nonlinear functions of prior perturbations that causes the most profound difference between MCMC posterior PDFs and ETKS posterior PDFs. [ABSTRACT FROM AUTHOR]

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. The authors show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an 'ensemble of Kalman filters' operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, the authors consider the construction of the PKF through an 'ensemble' of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). It is shown that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, the authors also introduce a resampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed. [ABSTRACT FROM AUTHOR]

Smoothers are increasingly used in geophysics. Several linear Gaussian algorithms exist, and the general picture may appear somewhat confusing. This paper attempts to stand back a little, in order to clarify this picture by providing a concise overview of what the different smoothers really solve, and how. The authors begin addressing this issue from a Bayesian viewpoint. The filtering problem consists in finding the probability of a system state at a given time, conditioned to some past and present observations (if the present observations are not included, it is a forecast problem). This formulation is unique: any different formulation is a smoothing problem. The two main formulations of smoothing are tackled here: the joint estimation problem (fixed lag or fixed interval), where the probability of a series of system states conditioned to observations is to be found, and the marginal estimation problem, which deals with the probability of only one system state, conditioned to past, present, and future observations. The various strategies to solve these problems in the Bayesian framework are introduced, along with their deriving linear Gaussian, Kalman filter-based algorithms. Their ensemble formulations are also presented. This results in a classification and a possible comparison of the most common smoothers used in geophysics. It should provide a good basis to help the reader find the most appropriate algorithm for his/her own smoothing problem. [ABSTRACT FROM AUTHOR]

In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. o3o3 is a variant or generalization of the third-order spectral element method (SEM3). It uses third-order piecewise polynomials for the representation of a field and piecewise third-degree polynomials for fluxes. For the discretization, SEM3 uses the irregular Legendre–Gauss–Lobatto grid while o3o3 uses a regular collocation grid. o3o3 can be regarded as an inhomogeneous finite-difference scheme on a uniform grid, which means that the finite-difference equations are different for each group with three points. A particular version of o3o3 is set as an example of many possibilities to construct LGM schemes on piecewise polynomial spaces in which the basis functions used are continuous at corner points and function spaces having continuous derivatives are shortly discussed. We propose a standard o3o3 scheme and a spectral o3o3 scheme as alternatives to the standard method of using the quadrature approximation. These two particular schemes selected were chosen for ease of implementation rather than optimal performance. In one dimension, compared to standard SEM3, o3o3 has a larger CFL condition benefiting from the use of a regular collocation grid. While SEM3 uses the irregular Legendre–Gauss–Lobatto collocation grid, o3o3 uses a regular grid. This is considered an advantage for physical parameterizations. The shortest resolved wave is marginally smaller than that with SEM3. In two dimensions, o3o3 is implemented on a sparse grid where only a part of the points on the underlying regular grid are used for forecasting. [ABSTRACT FROM AUTHOR]

In large-sized atmospheric or oceanic applications of square root or ensemble Kalman filters, it is often necessary to introduce the prior assumption that long-range correlations are negligible and force them to zero using a local parameterization, supplementing the ensemble or reduced-rank representation of the covariance. One classic algorithm to perform this operation consists of taking the Schur product of the ensemble covariance matrix by a local support correlation matrix. However, with this parameterization, the square root of the forecast error covariance matrix is no more directly available, so that any observational update algorithm requiring this square root must include an additional step to compute local square roots from the Schur product. This computation generates an additional numerical cost or produces high-rank square roots, which may deprive the observational update from its original efficiency. In this paper, it is shown how efficient local square root parameterizations can be obtained, for use with a specific square root formulation (i.e., eigenbasis algorithm) of the observational update. Comparisons with the classic algorithm are provided, mainly in terms of consistency, accuracy, and computational complexity. As an application, the resulting parameterization is used to estimate maps of dynamic topography characterizing a basin-scale ocean turbulent flow. Even with this moderate-sized system (a 2200-km-wide square basin with 100-km-wide mesoscale eddies), it is observed that more than 1000 ensemble members are necessary to faithfully represent the global correlation patterns, and that a local parameterization is needed to produce correct covariances with moderate-sized ensembles. Comparisons with the exact solution show that the use of local square roots is able to improve the accuracy of the updated ensemble mean and the consistency of the updated ensemble variance. With the eigenbasis algorithm, optimal adaptive estimates of scaling factors for the forecast and observation error covariance matrix can also be obtained locally at negligible additional numerical cost. Finally, a comparison of the overall computational cost illustrates the decisive advantage that efficient local square root parameterizations may have to deal simultaneously with a larger number of observations and avoid data thinning as much as possible. [ABSTRACT FROM AUTHOR]

Most mesoscale models can be run with either one-way (parasitic) or two-way (interactive) grid nesting. This paper presents results from a linear 1D shallow-water model to determine whether the choice of nesting method can have a significant impact on the solution. Two-way nesting was found to be generally superior to one-way nesting. The only situation in which one-way nesting performs better than two-way is when very poorly resolved waves strike the nest boundary. A simple filter is proposed for use exclusively on the coarse-grid values within the sponge zone of an otherwise conventional sponge boundary condition (BC). The two-way filtered sponge BC gives better results than any of the other methods considered in these tests. Results for all wavelengths were found to be robust to other changes in the formulation of the sponge boundary, particularly with the width of the sponge layer. The increased reflection for longer-wavelength disturbances in the one-way case is due to a phase difference between the coarse- and nested-grid solutions at the nested-grid boundary that accumulates because of the difference in numerical phase speeds between the grids. Reflections for two-way nesting may be estimated from the difference in numerical group velocities between the coarse and nested grids, which only becomes large for waves that are poorly resolved on the coarse grid. [ABSTRACT FROM AUTHOR]

Applying a flow-dependent background error covariance (&BsansserB; matrix) in variational data assimilation has been a topic of interest among researchers in recent years. In this paper, an ensemble-based four-dimensional variational (En4DVAR) algorithm, designed by the authors, is presented that uses a flow-dependent background error covariance matrix constructed by ensemble forecasts and performs 4DVAR optimization to produce a balanced analysis. A great advantage of this En4DVAR design over standard 4DVAR methods is that the tangent linear and adjoint models can be avoided in its formulation and implementation. In addition, it can be easily incorporated into variational data assimilation systems that are already in use at operational centers and among the research community. A one-dimensional shallow water model was used for preliminary tests of the En4DVAR scheme. Compared with standard 4DVAR, the En4DVAR converges well and can produce results that are as good as those with 4DVAR but with far less computation cost in its minimization. In addition, a comparison of the results from En4DVAR with those from other data assimilation schemes [e.g., 3DVAR and ensemble Kalman filter (EnKF)] is made. The results show that the En4DVAR yields an analysis that is comparable to the widely used variational or ensemble data assimilation schemes and can be a promising approach for real-time applications. In addition, experiments were carried out to test the sensitivities of EnKF and En4DVAR, whose background error covariance is estimated from the same ensemble forecasts. The experiments indicated that En4DVAR obtained reasonably sound analysis even with larger observation error, higher observation frequency, and more unbalanced background field. [ABSTRACT FROM AUTHOR]

The primary circulation of atmospheric vortices, such as tropical cyclones and tornadoes, can be estimated from single-Doppler radar observations using the ground-based velocity track display (GBVTD) algorithm. The GBVTD algorithm has limitations in the following four areas: 1) distortion in the retrieved asymmetric wind fields, 2) a limited analysis domain, 3) the inability to resolve the cross-beam component of the mean wind, and 4) the inability to separate the asymmetric tangential and radial winds. This paper presents the generalized velocity track display (GVTD) algorithm, which eliminates the first two limitations inherent in the GBVTD technique and demonstrates the possibility of subjectively estimating the mean wind vector when its signature is visible beyond the influence of the vortex circulation. In this new paradigm, the GVTD algorithm fits the atmospheric vortex circulation to a new variable VdD/RT in a linear azimuth angle (θ′), rather than the Doppler velocity Vd in a nonlinear angle (ψ), which is used in GBVTD. Key vortex kinematic structures (e.g., mean wind, axisymmetric tangential wind, etc.) in the VdD/RT space simplify the interpretation of the radar signature and eliminate the geometric distortion inherent in the Vd display. This is a significant improvement in diagnosing vortex structures in both operations and research. The advantages of using VdD/RT are illustrated using analytical atmospheric vortices, and the properties are compared with GBVTD. The characteristics of the VdD/RT display of Typhoon Gladys (1994) can be approximated by a constant mean wind plus an axisymmetric vortex. [ABSTRACT FROM AUTHOR]

In this paper it is argued that ensemble prediction systems can be devised in such a way that physical parameterizations of subgrid-scale motions are utilized in a stochastic manner, rather than in a deterministic way as is typically done. This can be achieved within the context of current physical parameterization schemes in weather and climate prediction models. Parameterizations are typically used to predict the evolution of grid-mean quantities because of unresolved subgrid-scale processes. However, parameterizations can also provide estimates of higher moments that could be used to constrain the random determination of the future state of a certain variable. The general equations used to estimate the variance of a generic variable are briefly discussed, and a simplified algorithm for a stochastic moist convection parameterization is proposed as a preliminary attempt. Results from the implementation of this stochastic convection scheme in the Navy Operational Global Atmospheric Prediction System (NOGAPS) ensemble are presented. It is shown that this method is able to generate substantial tropical perturbations that grow and “migrate” to the midlatitudes as forecast time progresses while moving from the small scales where the perturbations are forced to the larger synoptic scales. This stochastic convection method is able to produce substantial ensemble spread in the Tropics when compared with results from ensembles created from initial-condition perturbations. Although smaller, there is still a sizeable impact of the stochastic convection method in terms of ensemble spread in the extratropics. Preliminary simulations with initial-condition and stochastic convection perturbations together in the same ensemble system show a promising increase in ensemble spread and a decrease in the number of outliers in the Tropics. [ABSTRACT FROM AUTHOR]

Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmosphere. Applying variational data assimilation to these systems requires a tangent linearization of the nonlinear dynamics about a background state for the cost function minimization. The tangent linearization may be accurate for limited time scales. Here it is proposed that linearized assimilation systems may be accurate if the assimilation time period is less than the tangent linear accuracy time limit. In this paper, the cycling representer method is used to test this assumption with the Lorenz attractor. The outer loops usually required to accommodate the linear assimilation for a nonlinear problem may be dropped beyond the early cycles once the solution (and forecast used as the background in the tangent linearization) is sufficiently accurate. The combination of cycling the representer method and limiting the number of outer loops significantly lowers the cost of the overall assimilation problem. In addition, this study shows that weak constraint assimilation corrects tangent linear model inaccuracies and allows extension of the limited assimilation period. Hence, the weak constraint outperforms the strong constraint method. Assimilated solution accuracy at the first cycle end is computed as a function of the initial condition error, model parameter perturbation magnitude, and outer loops. Results indicate that at least five outer loops are needed to achieve solution accuracy in the first cycle for the selected error range. In addition, this study clearly shows that one outer loop in the first cycle does not preclude accuracy convergence in future cycles. [ABSTRACT FROM AUTHOR]

This study examines a few approaches to isolate the balanced component of the initial corrections from the Canadian Meteorological Centre energy-norm-based key analysis error algorithm, in an attempt to capture the part of the key analysis errors responsible for short-range forecast errors. The best results were obtained with the nonlinear balance potential vorticity (PV) inversion technique. It was shown that the PV component of the initial corrections contains the essential information for reducing short-range forecast errors. The remaining imbalance part of the initial corrections does not grow in time and does not contribute to the improvement of the forecast. The removal of the imbalance part of the initial corrections makes the corrected analysis slightly closer to the observations, but remains systematically farther away as compared with the original analysis. Thus the balanced part of the key analysis errors cannot justifiably be associated to analysis errors. A methodology to balance the divergent part of the initial corrections, which reduces significantly the spinup in the vertical motion corrections, is also presented. Finally, in light of the results presented in this paper, some recommendations to improve the key analysis error algorithm are proposed. [ABSTRACT FROM AUTHOR]

Assimilation of salinity into ocean and climate general circulation models is a very important problem. Argo data now provide far more salinity observations than ever before. In addition, a good analysis of salinity over time in ocean reanalyses can give important results for understanding climate change. Here it is shown from the historical ocean database that over large regions of the globe (mainly midlatitudes and lower latitudes) variance of salinity on an isotherm S(T) is often less than variance measured at a particular depth S(z). It is also shown that the dominant temporal variations in S(T) occur more slowly than variations in S(z), based on power spectra from the Bermuda time series. From ocean models it is shown that the horizontal spatial covariance of S(T) often has larger scales than S(z). These observations suggest an assimilation method based on analyzing S(T). An algorithm for assimilating salinity data on isotherms is then presented, and it is shown how this algorithm produces orthogonal salinity increments to those produced during the assimilation of temperature profiles. It is argued that the larger space and time scales can be used for the S(T) assimilation, leading to better use of scarce salinity observations. Results of applying the salinity assimilation algorithm to a single analysis time within the ECMWF seasonal forecasting ocean model are also shown. The separate salinity increments coming from temperature and salinity data are identified, and the independence of these increments is demonstrated. Results of an ocean reanalysis with this method will appear in a future paper. [ABSTRACT FROM AUTHOR]

In this paper a Godunov-type methodology is applied to three-dimensional global atmospheric modeling. Numerical issues are addressed regarding the formulation of the tracer advection problem, the application of dimensional splitting, and the implementation of a Godunov-type scheme, based on the WAF approach, on spherical geometries. Particular attention is paid to addressing the problems that arise because of the convergence of the grid lines toward the Poles. A three-dimensional model is then built on the sphere that is based on a uniform longitude-latitude-height grid. This provides the framework within which an adaptive mesh refinement (AMR) algorithm is applied, to enhance the efficiency and accuracy with which results are obtained. These methods are not commonly used in the area of atmospheric modeling, but AMR in particular is commonly used with great success in other areas of computational fluid dynamics. The model is initially validated using a series of idealized case studies that have exact solutions, but is then developed into an offline model of tracer advection, forced by data from meteorological analyses, suitable to study the evolution of trace chemical species in the atmosphere. [ABSTRACT FROM AUTHOR]

In this paper extensions to an existing tracking algorithm are described. These extensions implement adaptive tracking constraints in the form of regional upper-bound displacements and an adaptive track smoothness constraint. Together, these constraints make the tracking algorithm more flexible than the original algorithm (which used fixed tracking parameters) and provide greater confidence in the tracking results. The result of applying the new algorithm to high-resolution ECMWF reanalysis data is shown as an example of its effectiveness. [ABSTRACT FROM AUTHOR]

The method of frequency-wavenumber 'beamsteering' is a familiar tool in seismic applications and radar work where it is commonly used to detect coherent, propagating disturbances in 'noisy' data. However, its use in meteorological situations is not well documented. In this paper the beamsteering method is summarized and its application in a meteorological context is discussed. Three different algorithms are used to detect single waves in artificial data with varying signal-to-noise ratios. Two of these are different beamsteering algorithms: one is a low-resolution scheme where the frequency-wavenumber spectrum is estimated using a fixed wavenumber window and the other a high-resolution method where the wavenumber window is effectively optimized for each wavenumber. These are compared with a method based on the cross-correlation function, which is more routinely used in meteorological studies. The results from this analysis provide a quantifiable measure of the performance and reliability of the three methods when detecting single waves at a given frequency. The performance of the high-resolution beamsteering algorithm is then tested in a similar manner with two waves at the same frequency. [ABSTRACT FROM AUTHOR]

Ensemble-variational data assimilation algorithms that can incorporate the time dimension (four-dimensional or 4D) and combine static and ensemble-derived background error covariances (hybrid) are formulated in general forms based on the extended control variable and the observation-space-perturbation approaches. The properties and relationships of these algorithms and their approximated formulations are discussed. The main algorithms discussed include the following: 1) the standard ensemble 4DVar (En4DVar) algorithm incorporating ensemble-derived background error covariance through the extended control variable approach, 2) the 4DEnVar neglecting the time propagation of the extended control variable (4DEnVar-NPC), 3) the 4D ensemble-variational algorithm based on observation space perturbation (4DEnVar), and 4) the 4DEnVar with no propagation of covariance localization (4DEnVar-NPL). Without the static background error covariance term, none of the algorithms requires the adjoint model except for En4DVar. Costly applications of the tangent linear model to localized ensemble perturbations can be avoided by making the NPC and NPL approximations. It is proven that En4DVar and 4DEnVar are mathematically equivalent, while 4DEnVar-NPC and 4DEnVar-NPL are mathematically equivalent. Such equivalences are also demonstrated by single-observation assimilation experiments with a 1D linear advection model. The effects of the non-flow-following or stationary localization approximations are also examined through the experiments. All of the above algorithms can include the static background error covariance term to establish a hybrid formulation. When the static term is included, all algorithms will require a tangent linear model and an adjoint model. The first guess at appropriate time (FGAT) approximation is proposed to avoid the tangent linear and adjoint models. Computational costs of the algorithms are also discussed. [ABSTRACT FROM AUTHOR]

A previous Lagrangian linear advection scheme (trajectory-tracking scheme) is modified to achieve local mass conservation in this paper, which is more favorable to climate modeling. The discretized tracer parcels are volumes with interfaces instead of centroids. In 2D problems, the parcels are polygons and the interfaces are described by polygonal edges with a finite number. Because polygons will deform under the background wind field, a curvature-guard algorithm (CGA) is devised to retain accurate representation of the deformed interfaces among parcels. The tracer mass carried by parcels is mapped onto the regular latitude-longitude mesh by a first-order conservative remapping algorithm that can handle concave polygons. Several standard test cases have been carried out to show the effectiveness of the new scheme. [ABSTRACT FROM AUTHOR]

An adaptive ensemble covariance localization technique, previously used in ''local'' forms of the ensemble Kalman filter, is extended to a global ensemble four-dimensional variational data assimilation (4D-VAR) scheme. The purely adaptive part of the localization matrix considered is given by the element-wise square of the correlation matrix of a smoothed ensemble of streamfunction perturbations. It is found that these purely adaptive localization functions have spurious far-field correlations as large as 0.1 with a 128-member ensemble. To attenuate the spurious features of the purely adaptive localization functions, the authors multiply the adaptive localization functions with very broadscale nonadaptive localization functions. Using the Navy''s operational ensemble forecasting system, it is shown that the covariance localization functions obtained by this approach adapt to spatially anisotropic aspects of the flow, move with the flow, and are free of far-field spurious correlations. The scheme is made computationally feasible by (i) a method for inexpensively generating the square root of an adaptively localized global four-dimensional error covariance model in terms of products or modulations of smoothed ensemble perturbations with themselves and with raw ensemble perturbations, and (ii) utilizing algorithms that speed ensemble covariance localization when localization functions are separable, variable-type independent, and/or large scale. In spite of the apparently useful characteristics of adaptive localization, single analysis/forecast experiments assimilating 583 200 observations over both 6- and 12-h data assimilation windows failed to identify any significant difference in the quality of the analyses and forecasts obtained using nonadaptive localization from that obtained using adaptive localization. [ABSTRACT FROM AUTHOR]

A truly variance-minimizing filter is introduced and its performance is demonstrated with the Korteweg–DeVries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four-dimensional variational data assimilation (4DVAR)-like methods relying on perfect model dynamics have difficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When observations are available, the so-called importance resampling algorithm is applied. From Bayes's theorem it follows that each ensemble member receives a new weight dependent on its “distance” to the observations. Because the weights are strongly varying, a resampling of the ensemble is necessary. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be formulated that way. Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However, in the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, governed by strongly nonlinear dynamics, shows that the method is working satisfactorily. The strong and weak points of the method are discussed and possible improvements are proposed. [ABSTRACT FROM AUTHOR]

A three-dimensional ensemble-variational (3DEnVar) data assimilation algorithm has been developed for the high-resolution AROME NWP system. Building on previous work on 3DEnVar for AROME, we describe a formulation of the 3DEnVar that is based on the traditional square-root preconditioning. The localization may be performed either in gridpoint or spectral space, and allows for cross-covariances between surface pressure and the three-dimensional variables. The scheme has capacity for dual resolution, with the ensemble running at a lower 3.2-km spatial resolution than the deterministic AROME running at 1.3 km. This formulation is compatible with the variational bias correction scheme used in AROME. Hybrid covariances are implemented with climatological covariances at 1.3-km resolution being combined with ensemble perturbations that are interpolated to high resolution on the fly in the computation of the gradient. Hybrid 3DEnVar has an increased computational cost compared to 3DVar, which is partly mitigated by the use of dual resolution and the adoption of a flexible convergence criterion in the minimization. To get the full benefit from the ensemble scheme, it is recommended 1) to increase ensemble size from 25 to 50 members and 2) to decrease the localization length scale for the benefit of high-density radar observations. With those changes, the 3DEnVar outperforms the operational AROME-France 3DVar by a significant margin on the first 12 h of forecast range, as evidenced by a 3-month summer experiment. Finally, a case study reports on the improved prediction of heavy rainfall that frequently occurs in the Mediterranean region. [ABSTRACT FROM AUTHOR]

Lagrangian detection and tracking algorithms are frequently used to study the development, distribution, and trends of extratropical cyclones. Past research shows that results from these algorithms are sensitive to both spatial and temporal resolutions of the gridded input fields, with coarser resolutions typically underestimating cyclone frequency by failing to capture weak, small, and short-lived systems. The fifth-generation atmospheric reanalysis from the European Centre for Medium-Range Weather Forecasts (ERA5) offers finer resolution, and, therefore, more precise information regarding storm locations and development than previous global reanalyses. However, our sensitivity tests show that using ERA5 sea level pressure fields at their finest-possible resolution does not necessarily lead to better cyclone detection and tracking. If a common number of nearest neighbors is used when detecting minima in sea level pressure (like past studies), finer spatial resolution leads to noisier fields that unrealistically break up multicenter cyclones. Using a common search distance instead (with more neighbors at finer resolution) resolves the issue without smoothing inputs. Doing this also makes cyclone frequency, life span, and average depth insensitive to refining spatial resolution beyond 100 km. Results using 6- and 3-h temporal resolutions have only minor differences, but using 1-h temporal resolution with a maximum allowed propagation speed of 150 km h−1 leads to unrealistic track splitting. This can be counteracted by increasing the maximum propagation speed, but modest sensitivity to temporal resolution persists for several cyclone characteristics. Therefore, we recommend caution if applying existing algorithms to temporal resolutions finer than 3 h and careful evaluation of algorithm settings. Significance Statement: Many researchers use computer algorithms that automate detection of extratropical storms and then track those storms through time to better understand how they develop, where they impact people, and how they are changing as the world warms. Conventional wisdom is that using finer spatial and temporal resolutions as inputs to these algorithms improves results by capturing more storms more accurately. However, we find that storm frequency is more sensitive to algorithm settings than to spatial resolution. Making temporal resolution 1-hourly instead of 3-hourly or 6-hourly incorrectly breaks up the tracks of some storms into several smaller pieces. In either case, our datasets have improved enough so that a finer resolution is no longer always better. [ABSTRACT FROM AUTHOR]

Large-scale cloud features referred to as cloudbands are known to be related to widespread and heavy rain via the transport of tropical heat and moisture to higher latitudes. The Australian northwest cloudband is such a feature that has been identified in simple searches of satellite imagery but with limited investigation of its atmospheric dynamical support. An accurate, long-term climatology of northwest cloudbands is key to robustly assessing these events. A dynamically based search algorithm has been developed that is guided by the presence and orientation of the subtropical jet stream. This jet stream is the large-scale atmospheric feature that determines the development and alignment of a cloudband. Using a new 40-yr dataset of cloudband events compiled by this search algorithm, composite atmospheric and ocean surface conditions over the period 1979–2018 have been assessed. Composite cloudband upper-level flow revealed a tilted low pressure trough embedded in a Rossby wave train. Composites of vertically integrated water vapor transport centered around the jet maximum during northwest cloudband events reveal a distinct atmospheric river supplying tropical moisture for cloudband rainfall. Parcel backtracking indicated multiple regions of moisture support for cloudbands. A thermal wind anomaly orientated with respect to an enhanced sea surface temperature gradient over the Indian Ocean was also a key composite cloudband feature. A total of 300 years of a freely coupled control simulation of the ACCESS-D system was assessed for its ability to simulate northwest cloudbands. Composite analysis of model cloudbands compared reasonably well to reanalysis despite some differences in seasonality and frequency of occurrence. [ABSTRACT FROM AUTHOR]

Model errors and sampling errors produce inaccurate sample covariances that limit the performance of ensemble Kalman filters. Linearly hybridizing the flow-dependent ensemble-based covariance with a time-invariant background covariance matrix gives a better estimate of the true error covariance. Previous studies have shown this, both in theory and in practice. How to choose the weight for each covariance remains an open question especially in the presence of model biases. This study assumes the weighting coefficient to be a random variable and then introduces a Bayesian scheme to estimate it using the available data. The scheme takes into account the discrepancy between the ensemble mean and the observations, the ensemble variance, the static background variance, and the uncertainties in the observations. The proposed algorithm is first derived for a spatially constant weight and then this assumption is relaxed by estimating a unique scalar weight for each state variable. Using twin experiments with the 40-variable Lorenz 96 system, it is shown that the proposed scheme is able to produce quality forecasts even in the presence of severe sampling errors. The adaptive algorithm allows the hybrid filter to switch between an EnKF and a simple EnOI depending on the statistics of the ensemble. In the presence of model errors, the adaptive scheme demonstrates additional improvements compared with standard enhancements alone, such as inflation and localization. Finally, the potential of the spatially varying variant to accommodate challenging sparse observation networks is demonstrated. The computational efficiency and storage of the proposed scheme, which remain an obstacle, are discussed. [ABSTRACT FROM AUTHOR]

As global data assimilation systems continue to evolve, observing system simulation experiments (OSSEs) need to be updated to accurately quantify the impact of proposed observing technologies in weather forecasting. Earlier OSSEs with radio occultation (RO) observations have been updated, and the impact of the originally proposed Constellation Observing System for Meteorology, Ionosphere and Climate-2 (COSMIC-2) mission, with high-inclination and low-inclination components, has been investigated by using the operational data assimilation system at NOAA and a one-dimensional bending-angle RO forward operator. It is found that the impact of the low-inclination component of the originally planned COSMIC-2 mission (now officially named COSMIC-2) has significantly increased as compared with earlier studies, and significant positive impact is now found globally in terms of mass and wind fields. These are encouraging results as COSMIC-2 was successfully launched in June 2019 and data have been recently released to operational weather centers. Earlier findings remain valid indicating that globally distributed RO observations are more important to improve weather prediction globally than a denser sampling of the tropical latitudes. Overall, the benefits reported here from assimilating RO soundings are much more significant than the impacts found in previous OSSEs. This is largely attributed to changes in the data assimilation and forecast system and less to the more advanced one-dimensional forward operator chosen for the assimilation of RO observations. [ABSTRACT FROM AUTHOR]

To produce more precise descriptions of air–sea exchanges under tropical cyclones (TCs), spaceborne synthetic aperture radar (SAR) instruments provide unique capabilities to probe the ocean surface conditions, at very high spatial resolution, and on synoptic scales. Using highly resolved (3 km) wind fields, an extensive database is constructed from RadarSat-2 and Sentinel-1 SAR acquisitions. Spanning 161 tropical cyclones, the database covers all TC intensity categories that have occurred in 5 different TC basins, and include 29 cases coincident with SFMR measurements. After locating the TC center, a specific methodology is applied to filter out areas contaminated by heavy precipitation to help extract, for each acquisition, the maximum wind speed (Vmax), its associated radius (Rmax), and corresponding outer wind radii (R34/50/64 kt). These parameters are then systematically compared with best track (BTK), and when available, SFMR airborne measurements. For collocated SFMR and SAR observations, comparisons yield root-mean-squares of 3.86 m s-1 and 3 km for ocean surface wind speeds and TC Rmax, respectively. High correlations remain for category-5 cases, with Vmax exceeding 60 m s-1. The largest discrepancies are found between BTK and SAR Rmax estimates, with Rmax fluctuations poorly captured by BTK, especially for rapidly evolving category-3, -4, and -5 TCs. In heavy precipitation (>35 mm h-1), the SAR C-band measurements may be impacted, with local ambiguities associated with rain features, as revealed by external rain measurements. Still, this large dataset demonstrates that SAR measurements have unique high-resolution capabilities, capturing the inner- and outer-core radial structure of the TC vortex, and provide independent and complementary measurements than those used for BTK estimates. [ABSTRACT FROM AUTHOR]

The viability of a parameterless hybrid data assimilation algorithm is investigated. As an alternative to the traditional hybrid covariance scheme hybrid gain data assimilation (HGDA) was proposed to blend the gain matrix derived from the variational method and the ensemble-based Kalman filter (EnKF). A previously proposed HGDA algorithm uses a two-step process applying the EnKF with a variational update. The algorithm is modified here to limit the variational correction to the subspace orthogonal to the ensemble perturbation subspace without the use of a hybrid weighting parameter as the optimization of such a parameter is nontrivial. The modified HGDA algorithm is investigated with a quasigeostrophic (QG) model. Results indicate that when the climatological back ground error covariance matrix Band the observation error covariance R are well estimated state estimates from the parameterless HGDA are more accurate than the parameter-dependent HGDA. The parameterless HGDA not only has potential advantages over the standard HGDA asanon line data assimilation algorithm but can also serve as a valuable diagno stictool fortuning the B and R matrices. It is also found that in this QG model the empirically best static B matrix for the standalone 3DVAR has high variance at larger spatial scales which degrades the accuracy of the HGDA systems and may not be the best choice for hybrid methods in general. A comparison of defining the orthogonal subspace globally or locally demonstrates that global orthogonality is more advantageous for stabilizing the hybrid system and maintains large-scale balances. [ABSTRACT FROM AUTHOR]

The use of single-precision arithmetic in ECMWF's forecasting model gave a 40% reduction in wall-clock time over double-precision, with no decrease in forecast quality. However, using reduced-precision in 4D-Var data assimilation is relatively unexplored and there are potential issues with using single-precision in the tangent-linear and adjoint models. Here, we present the results of reducing numerical precision in an incremental 4D-Var data assimilation scheme, with an underlying two-layer quasigeostrophic model. The minimizer used is the conjugate gradient method. We show how reducing precision increases the asymmetry between the tangent-linear and adjoint models. For ill-conditioned problems, this leads to a loss of orthogonality among the residuals of the conjugate gradient algorithm, which slows the convergence of the minimization procedure. However, we also show that a standard technique, reorthogonalization, eliminates these issues and therefore could allow the use of single-precision arithmetic. This work is carried out within ECMWF's data assimilation framework, the Object Oriented Prediction System. [ABSTRACT FROM AUTHOR]

We apply spectral empirical orthogonal function (SEOF) analysis to educe climate patterns as dominant spatiotemporal modes of variability from reanalysis data. SEOF is a frequency-domain variant of standard empirical orthogonal function (EOF) analysis, and computes modes that represent the statistically most relevant and persistent patterns from an eigendecomposition of the estimated cross-spectral density matrix (CSD). The spectral estimation step distinguishes the approach from other frequency-domain EOF methods based on a single realization of the Fourier transform, and results in a number of desirable mathematical properties: at each frequency, SEOF yields a set of orthogonal modes that are optimally ranked in terms of variance in the L2 sense, and that are coherent in both space and time by construction. We discuss the differences between SEOF and other competing approaches, as well as its relation to dynamical modes of stochastically forced, nonnormal linear dynamical systems. The method is applied to ERA-Interim and ERA-20C reanalysis data, demonstrating its ability to identify a number of well-known spatiotemporal coherent meteorological patterns and teleconnections, including the Madden–Julian oscillation (MJO), the quasi-biennial oscillation (QBO), and the El Niño–Southern Oscillation (ENSO) (i.e., a range of phenomena reoccurring with average periods ranging from months to many years). In addition to two-dimensional univariate analyses of surface data, we give examples of multivariate and three-dimensional meteorological patterns that illustrate how this technique can systematically identify coherent structures from different sets of data. The MATLAB code used to compute the results presented in this study, including the download scripts for the reanalysis data, is freely available online. [ABSTRACT FROM AUTHOR]

Cloud trails are primarily thermally forced bands of cloud that extend downwind of small islands. A novel algorithm to classify conventional geostationary visible-channel satellite images as cloud trail (CT), nontrail (NT), or obscured (OB) is defined. The algorithm is then applied to the warm season months of five years at Bermuda comprising 16 400 images. Bermuda's low elevation and location make this island ideal for isolating the role of the island thermal contrast on CT formation. CTs are found to occur at Bermuda with an annual cycle, peaking in July, and a diurnal cycle that peaks in midafternoon. Composites of radiosonde observations and ERA-Interim data suggest that a warm and humid low-level environment is conducive for CT development. From a Lagrangian perspective, wind direction modulates CT formation by maximizing low-level heating on local scales when winds are parallel to the long axis of the island. On larger scales, low-level wind direction also controls low-level humidity through advection. [ABSTRACT FROM AUTHOR]