Comment on gmd-2022-18

This study investigates the factors contributing to the delay in the rapid intensification (RI) of Hurricane Ida (2021). Using data assimilation to modify the steering flow and environmental moisture, several mechansims responsible for the RI onset delay during Ida’s development can be identified. Specifically, we show that the presence of dry air in the Gulf of Mexico is the dominant inhibiting factor for Ida’s RI delay, rather than the land effects associated with Ida’s passage over Cuba or other large-scale conditions. This dry-air intrusion could extend deeply into the storm’s inner core, suppressing deep convection and preventing Ida’s further intensification even after the storm has developed a sufficiently organized structure. Comparing two data assimilation approaches based on the local ensemble transform Kalman filter (LETKF) and three-dimensional variational data assimilation (3DVAR) shows further that LETKF more effectively isolates environmental conditions responsible for Ida’s RI delay. This is largely due to LETKF’s ability to generate ensemble-based analyses and incorporate model uncertainty in the background covariance matrix through the use of multiple physics. These findings are robust across sensitivity experiments and underscore the strong dependence of RI onset predictability on tropical cyclone (TC) track such that evaluating environmental conditions at one particular time or location is generally insufficient for real-time RI forecasting. In this regard, our results have significant implications for future observing strategies such as the design or deployment of reconnaissance missions targeting RI onset and its predictability. Significance Statement This study makes use of data assimilation techniques to examine different environmental factors causing the delay of rapid intensification (RI) for Hurricane Ida (2021). Our results show the key role of the large-scale moisture environment during Ida’s RI delay, which was strongly influenced by a persistent dry-air intrusion to the west of its track. Analysis of different data assimilation experiments reveals a critical window within the next 24–30 h after a potential RI onset moment, during which any inimical environmental conditions can disrupt tropical cyclone (TC) development and restrain RI. In contrast, land effects associated with Ida’s passage over Cuba play a minor role for the case of Ida, given its short duration and limited ability to inhibit RI. These findings highlight the importance of observing environmental conditions for more accurate RI forecasting.

In two recent studies, the authors presented a new data assimilation (DA) method for precipitation observations that does not require Gaussianity or linearity assumptions. The method, called localized ensemble mosaic assimilation (LEMA), initializes the new ensemble forecast by relaxing the background ensemble (prior) toward a single analysis composed of different column states taken from the ensemble members with the lowest error in the precipitation forecast. However, a limitation of the LEMA method is that relaxing the background ensemble toward that analysis severely reduces the spread of the ensemble, thus, limiting its usefulness for cycled DA applications. This study presents a new version of LEMA, called localized ensemble mosaic assimilation sequence (LEMAS), suitable for cycled DA operations. LEMAS constructs an ensemble of analysis mosaics using a small group of members closer to the observations instead of only the closest one. The new ensemble forecast is then initialized by recentering the prior ensemble around the mean of the analysis ensemble while scaling the original background perturbations to match the spread of the analysis mosaics. A series of ideal and real DA experiments are used to evaluate the potential of LEMAS for the assimilation of hourly accumulation observations. A comparison of LEMAS with the local ensemble transform Kalman filter (LETKF) using idealized experiments shows that LEMAS produces similar or slightly better forecast quality than the LETKF in temperature, water vapor, winds, and precipitation. Extending this comparison to real DA experiments assimilating Stage-IV precipitation observations shows that both methods produce precipitation forecasts of comparable quality.

Data assimilation (DA) based on Bayes' theorem helps improve the accuracy of numerical models and simultaneously enables the estimation of unknown parameters used in the numerical model by combining simulation results with observational data. We applied the local ensemble transform Kalman filter (LETKF), a computationally efficient and accurate DA methodology, to a phase-field model of dendritic solidification in a binary alloy. We demonstrated the efficiency of LETKF through numerical experiments (twin experiments) wherein we estimated the unknown state of the solidification and the model parameters from synthetic observation datasets of a growing dendrite morphology. Results of the twin experiments show that using LETKF we could successfully estimate three-dimensional (3D) time evolution of the solute concentration-field in the liquid phase. Further, we could inversely identify multiple model parameters, including interfacial energy between the solid and liquid phases and the solute diffusion coefficient in the liquid phase only from the 3D morphological information of a growing dendrite. We demonstrated that the LETKF-based DA method is a promising methodology for performing accurate phase-field simulations in conjunction with experimental data.

This paper develops a parallel implementation of the ensemble Kalman filter (EnKF) based on shrinkage covariancematrix estimation. The EnKF is a sequential Monte Carlo method for parameter and state estimation of highly nonlinearmodels. In the context of ensemble based methods, background error correlations are estimated via anensemble of model realizations. In practice, the model dimension (number of model components) is several timeslarger than the ensemble size owing to the computational effort involved in one single model propagation. Thisconstraint yields to spurious correlations (correlation between distant model components in space) in the backgrounderror estimations. Commonly, localization methods are utilized in order to reduce the impact of spuriouscorrelations. For instance, correlations of model components are reduced based on some function of their physicaldistances. Some EnKF implementations are formulated in such manner that, localization methods are implicitlyinvolved in the assimilation of observations. In this context, one of the best ensemble Kalman filter implementationsis the local ensemble transform Kalman filter (LETKF). In the LETKF, each model component is surrounded by alocal box of size r and then, the information contained within the local domain (i.e., observed components) is used toperform the assimilation. However, for sparse observational networks, r can become sufficiently large with respectto the ensemble size and therefore, the local analysis corrections can be impacted by spurious correlations. Wepropose an ensemble Kalman filter implementation in which the background error covariance matrix is estimated viathe Rao-Blackwell Ledoit and Wolf (RBLW) estimator. This estimator has proven to be better conditioned than thetrue (background) error covariance matrix. In addition, the explicit computation of the RBLW estimator is notrequired in our formulation. This implies enormous savings in terms of memory considering the typical order ofbackground error covariance matrices O(10e8) Furthermore, the proposed EnKF implementation can be efficientlyperformed in parallel: each model component is surrounded by a local box, a local background error covariancematrix is estimated based on the RBLW estimator and then, the ensemble Kalman filter equations are locally used inorder to compute the local analysis corrections. After the local assimilation, each model component is mapped backonto the full model domain from where the global analysis solution is obtained. In operational data assimilation, EnKF implementations are attractive owing to their potential for parallelization. Experiments are performed making use of the Atmospheric General Circulation Model SPEEDY. The proposed method is coded in FORTRAN and MPI is used for the local assimilation of observations. The predicted variables are the zonal and meridional wind components, the temperature and the specific humidity. For each model variable, 8 layers with the T-63 resolution (192 x 96 grid points) are considered which provide a total number of 589,824 model components. The ensemble size is 94. The number of processors utilized are 96, 256, 512, 768, 1024 and 1536. The results reveal that, the use of the RBLW estimator can mitigate the impact of spurious correlations under sparse observational networks and even more, for different number of processors, the computational effort of the proposed EnKF implementation is comparable to that of the LETKF where no covariance estimation is performed. In terms of accuracy, the proposed implementation performs better than the LETKF formulation in the Root Mean Square Error sense.

Super-resolution (SR) in deep learning is a technique to generate high-resolution (HR) outputs from low-resolution (LR) inputs. Recently, combining SR with data assimilation (DA) has been proposed, leading to the development of super-resolution data assimilation (SRDA). The SRDA method simultaneously performs SR and DA by inputting LR simulation results and observations into a neural network. This study develops a four-dimensional SRDA (4D-SRDA) model to predict temporal evolutions of three-dimensional quasi-geostrophic flows in a baroclinic jet system. To evaluate the performance of 4D-SRDA, we compare it with a Local Ensemble Transform Kalman Filter (LETKF), which uses an HR model. 4D-SRDA successfully reproduces both small- and large-scale structures of potential vorticity, visually similar to those produced by the LETKF. We compare grid-wise and pattern-similarity errors to quantify the accuracy of the analysis and forecast states. Despite using an LR fluid model, 4D-SRDA achieves accuracy comparable to that of the LETKF. Comparing the computational time required for prediction reveals that 4D-SRDA is substantially more efficient than the LETKF. These results suggest that 4D-SRDA is a promising approach for predicting HR atmospheric flows.

A particle filter (PF) is an ensemble data assimilation method that does not assume Gaussian error distributions. Recent studies proposed local PFs (LPFs), which use localization as in the ensemble Kalman filter, to apply the PF for high-dimensional dynamics efficiently. Among others, Penny and Miyoshi developed an LPF in the form of the ensemble transform matrix of the Local Ensemble Transform Kalman Filter (LETKF). The LETKF has been widely accepted for various geophysical systems including numerical weather prediction (NWP) models. Therefore, implementing consistently with an existing LETKF code is useful. This study developed a software platform for the LPF and its Gaussian mixture extension (LPFGM) by making slight modifications to the LETKF code with a simplified global climate model known as Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY). A series of idealized twin experiments were accomplished under the ideal model assumption. With large inflation by the relaxation to prior spread, the LPF showed stable filter performance with dense observations but became unstable with sparse observations. The LPFGM showed more accurate and stable performances than the LPF with both dense and sparse observations. In addition to the relaxation parameter, regulating the resampling frequency and the amplitude of Gaussian kernels was important for the LPFGM. With a spatially inhomogeneous observing network, the LPFGM was superior to the LETKF in sparsely observed regions where the background ensemble spread and non-Gaussianity are larger. The SPEEDY-based LETKF, LPF, and LPFGM systems were available as open-source software on Github (https://github.com/skotsuki/speedy-lpf) and can be adapted to various models relatively easily like the LETKF.

A particle filter (PF) is an ensemble data assimilation method that does not assume Gaussian error distributions. Recent studies proposed local PFs (LPFs), which use localization as in the ensemble Kalman filter, to apply the PF for high-dimensional dynamics efficiently. Among others, Penny and Miyoshi developed an LPF in the form of the ensemble transform matrix of the Local Ensemble Transform Kalman Filter (LETKF). The LETKF has been widely accepted for various geophysical systems including numerical weather prediction (NWP) models. Therefore, implementing consistently with an existing LETKF code is useful. This study developed a software platform for the LPF and its Gaussian mixture extension (LPFGM) by making slight modifications to the LETKF code with a simplified global climate model known as Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY). A series of idealized twin experiments were accomplished under the ideal model assumption. With large inflation by the relaxation to prior spread, the LPF showed stable filter performance with dense observations but became unstable with sparse observations. The LPFGM showed more accurate and stable performances than the LPF with both dense and sparse observations. In addition to the relaxation parameter, regulating the resampling frequency and the amplitude of Gaussian kernels was important for the LPFGM. With a spatially inhomogeneous observing network, the LPFGM was superior to the LETKF in sparsely observed regions where the background ensemble spread and non-Gaussianity are larger. The SPEEDY-based LETKF, LPF, and LPFGM systems were available as open-source software on Github (https://github.com/skotsuki/speedy-lpf) and can be adapted to various models relatively easily like the LETKF.

Abstract. Prediction of spatiotemporal chaotic systems is important in various fields, such as numerical weather prediction (NWP). While data assimilation methods have been applied in NWP, machine learning techniques, such as reservoir computing (RC), have recently been recognized as promising tools to predict spatiotemporal chaotic systems. However, the sensitivity of the skill of the machine-learning-based prediction to the imperfectness of observations is unclear. In this study, we evaluate the skill of RC with noisy and sparsely distributed observations. We intensively compare the performances of RC and local ensemble transform Kalman filter (LETKF) by applying them to the prediction of the Lorenz 96 system. In order to increase the scalability to larger systems, we applied a parallelized RC framework. Although RC can successfully predict the Lorenz 96 system if the system is perfectly observed, we find that RC is vulnerable to observation sparsity compared with LETKF. To overcome this limitation of RC, we propose to combine LETKF and RC. In our proposed method, the system is predicted by RC that learned the analysis time series estimated by LETKF. Our proposed method can successfully predict the Lorenz 96 system using noisy and sparsely distributed observations. Most importantly, our method can predict better than LETKF when the process-based model is imperfect.

Groundwater contamination assessment can be useful in taking proper actions during environmental emergency. A three-dimensional deterministic model was taken into consideration to simulate the advective-diffusive transport of non-conservative contaminant in groundwater. Multiple stochastic data assimilation techniques, such as, ensemble Kalman filter (EnKF), local ensemble transform Kalman filter (LETKF), and the global form of the LETKF, denoted as GETKF were applied to the model. The results show that data assimilation improved contaminant concentration prediction. The EnKF method reduced the root-mean-square-error (RMSE) of the contaminant prediction from 12.5 mg/L to 1.31 mg/L, whereas the LETKF reduced that to 0.46 mg/L and GETKF reduced that to 0.38 mg/L. Approximately 89.48%, 96.30% and 96.82% improvement were made by EnKF, LETKF, and GETKF, respectively. The sensitivity analysis suggest that these data assimilation techniques are very sensitive to the observation noise, process noise, and ensemble size.

Abstract. Reliable estimates of Earth system conditions are important for weather forecasting, hydrological modelling and their downstream applications. Both real-time prediction systems and historical reanalyses use a combination of observations and physical laws embedded in numerical models to generate gapless and accurate estimates of weather, climate and hydrological conditions. Data assimilation systems merge information from model estimates and observations in an objective way, accounting for their respective uncertainties. In this work we present a regional reanalysis system, focusing on the land surface component. The system uses a multi-layer snow model together with the ensemble-based Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme. The system is run for a 4 year period over the European Arctic, assimilating in situ snow depth observations. Evaluation of the new snow depth analysis showed reduced errors compared to existing products and positive impact of the data assimilation over the domain. Furthermore, a significant difference in total accumulated snow water was seen over the domain, implying a potential impact on downstream hydrological applications. The ensemble correlations between the total snow depth and the multivariate control vector indicated that the ensemble was able to represent snow compaction processes. The LETKF is thus able to account for processes which are often neglected in snow depth data assimilation. The system presented in this study allows for future extensions, including other types of observations and analyses beyond snow variables.

This study aims to improve precipitation forecasts by estimating model parameters of a numerical weather prediction model with an ensemble‐based data assimilation method. We implemented the parameter estimation algorithm into a global atmospheric data assimilation system NICAM‐LETKF, which incorporates Nonhydrostatic Icosahedral Atmospheric Model (NICAM) and the Local Ensemble Transform Kalman Filter (LETKF). This study estimated a globally uniform model parameter of a large‐scale condensation scheme known as the B1 parameter of Berry's parameterization. We conducted an online estimation of the B1 parameter using the Global Satellite Mapping of Precipitation (GSMaP) data and successfully reduced NICAM's precipitation forecast bias relative to the GSMaP data, especially for weak rains. The estimated B1 parameter evolved toward the optimal value obtained by manual tuning. The parameter estimation also mitigated a dry bias for the lower troposphere in the Tropics. However, the estimated B1 intensified biases for cloud water mixing ratio and outgoing long‐wave radiation in the regions where shallow clouds are dominant. This is because only precipitation data were used to estimate the optimal value of B1, and more constraints will be required to obtain a suitable value for climatological simulations.

Data assimilation methods that work in high-dimensional systems are crucial to many areas of the geosciences: meteorology, oceanography, climate science and so on. The equivalent weights particle filter (EWPF) has been designed for, and recently shown to scale to, problems that are of use to these communities. This article performs a systematic comparison of the EWPF with the established and widely used local ensemble transform Kalman filter (LETKF). Both methods are applied to the barotropic vorticity equation for different networks of observations. In all cases, it was found that the LETKF produced lower root mean–squared errors than the EWPF. The performance of the EWPF is shown to depend strongly on the form of nudging used, and a nudging term based on the local ensemble transform Kalman smoother is shown to improve the performance of the filter. This indicates that the EWPF must be considered as a truly two-stage filter and not only by its final step which avoids weight collapse.

The analyses produced by a data assimilation system may be unbalanced, which is dynamically inconsistent with the forecasting model, leading to noisy forecasts and reduced skill. While there are effective procedures to reduce synoptic-scale imbalance, the situation on the convective scale is less clear because the flow on this scale is strongly divergent and nonhydrostatic. In this study, we compare three measures of imbalance relevant to convective-scale data assimilation: (i) surface pressure tendencies, (ii) vertical velocity variance in the vicinity of convective clouds, and (iii) departures from the vertical velocity prescribed by the weak temperature gradient (WTG) approximation. These are applied in a numerical weather prediction system, with three different data assimilation algorithms: 1) latent heat nudging (LHN), 2) local ensemble transform Kalman filter (LETKF), and 3) LETKF in combination with incremental analysis updates (IAUs). Results indicate that surface pressure tendency diagnoses a different type of imbalance than the vertical velocity variance and the WTG departure. The LETKF induces a spike in surface pressure tendencies, with a large-scale spatial pattern that is not clearly related to the precipitation pattern. This anomaly is notably reduced by the IAU. LHN does not generate a pronounced signal in the surface pressure but produces the most imbalance in the other two measures. The imbalances measured by the partitioned vertical velocity variance and WTG departures are similar and closely coupled to the convective precipitation. Between these two measures, the WTG departure has the advantage of being simpler and more economical to compute.

<p>Reanalysis is a procedure to merge numerical model integrations and observations to obtain a synergetic representation of the past climatological state of a system, e.g., of the atmosphere. An alternative to running a full reanalysis scheme is a so-called surface reanalysis. Here, an existing reanalysis is used as prior information (for the near-surface state). This first guess is then corrected in a data assimilation step preferrably by applying observations not used in the original assimilation. In such a scheme, an additional downscaling is often performed to enhance the spatial representation of the surface reanalysis.</p><p>We present here the development of a new approach aiming to establish such a data set based on the COSMO-REA6 regional reanalysis of the Hans-Ertel-Centre and Deutscher Wetterdienst (DWD). The data assimilation step is based on the operational Local Ensemble Transform Kalman Filter (LETKF) of DWD. While the data assimilation is often performed univariately in such surface reanalysis schemes, here we apply it to various parameters at once thus conserving the covariances among the parameters and allowing for a consistent multivariate utilization of the data. Further, this reanalysis will not be restricted to the ground level and near-surface parameters. Instead, it will be extended to the lower part of the boundary layer aiming at an improved representation of wind speeds in wind turbine hub heights especially relevant for renewable energy applications. The envisaged resolution is approximately 1km and therefore enables an enhanced representation of spatial variability and heterogeneity on small scales. In addition, the LETKF is an ensemble-based data assimilation scheme which also provides uncertainty estimates through an ensemble of the re-analyzed parameters which can also be used as input for downstream applications.</p>

The assimilation of radar reflectivity data is of great interest for numerical weather prediction (NWP) models at the convective scale since these observations are very dense both in space and time and they are related to microphysical prognostic variables. So far, the assimilation of reflectivity in operational frameworks has been limited to derived products, like precipitation rates and humidity profiles. This approach is also adopted at ARPAE‐SIMC, the Hydro‐Meteo‐Climate Structure of the Regional Agency for Prevention, Environment and Energy of Emilia‐Romagna region in Italy, where latent heat nudging (LHN) is employed to assimilate precipitation rates in the COSMO‐2I model, the convection‐permitting version of the regional model developed by the COnsortium for Small‐scale MOdelling (COSMO) which is run operationally to provide high‐resolution forecasts over Italy. However, to fully exploit the information contained in these observations, the whole reflectivity volume should be directly assimilated. Nevertheless, despite several promising studies, its implementation in an operational framework has not yet been achieved. In this study, a set‐up designed to assimilate reflectivities operationally in the COSMO‐2I model through a local ensemble transform Kalman filter (LETKF) has been evaluated over 37 days in 2018 and performed 303 forecasts. The comparison with the current operational set‐up based on LHN reveals an average improvement in quantitative precipitation forecasts (QPFs) up to 7 hr, even if the impact on convective cases is much stronger than that observed in conditions of stratiform precipitation. Moreover, a small but positive impact is noticed for the RMSE of upper‐air variables, while the impact on bias is mixed. Mixed results are also obtained when considering surface variables. In the light of the results of this study, a pre‐operational parallel system in which COSMO‐2I analyses are generated replacing LHN by the direct assimilation of reflectivity volumes was implemented in April 2020.