Why do the maximum intensities in modeled tropical cyclones vary under the same environmental conditions?

In this study w e explored why the different initial tropical cyclone structures can result in different steady‐state maximum intensities in model simulations with the same environmental conditions. We discovered a linear relationsh ip between the radius of maximum wind (rm) and the absolute angular momentum that passes through rm (Mm) in the model simulated steady‐state tropical cyclones that rm = aMm+b. This nonnegligible intercept b is found to be the key to making a steady‐state storm with a larger Mm more intense. The sensitivity experiments show that this nonzero b results mainly from horizontal turbulent mixing and decreases with decreased horizontal mixing. Using this linear relationship from the simulations, it is also found that the degree of supergradient wind is a function of Mm as well as the turbulent mixing length such that both a larger Mm and/or a reduced turbulent mixing length result in larger supergradient winds

Time-correlated model error in the (ensemble) Kalman smoother

Data assimilation is often performed in a perfect-model scenario, where only errors in initial conditions and observations are considered. Errors in model equations are increasingly being included, but typically using rather ad-hoc approximations with limited understanding of how these approximations affect the solution and how these approximations interfere with approximations inherent in finite-size ensembles. We provide the first systematic evaluation of the influence of approximations to model errors within a time window of weak-constraint ensemble smoothers. In particular, we study the effects of prescribing temporal correlations in the model errors incorrectly in a Kalman Smoother, and in interaction with finite ensemble-size effects in an Ensemble Kalman Smoother. For the Kalman Smoother we find that an incorrect correlation time scale for additive model errors can have substantial negative effects on the solutions, and we find that overestimating of the correlation time scale leads to worse results than underestimating. In the Ensemble Kalman Smoother case, the resulting ensemble-based space-time gain can be written as the true gain multiplied by two factors, a linear factor containing the errors due to both time-correlation errors and finite ensemble effects, and a non-linear factor related to the inverse part of the gain. Assuming that both errors are relatively small, we are able to disentangle the contributions from the different approximations. The analysis mean is affected by the time-correlation errors, but also substantially by finite ensemble effects, which was unexpected. The analysis covariance is affected by both time-correlation errors and an in-breeding term. This first thorough analysis of the influence of time-correlation errors and finite ensemble size errors on weak-constraint ensemble smoothers will aid further development of these methods and help to make them robust for e.g. numerical weather prediction

Observation impact in data assimilation: the effect of non-Gaussian observation error.

Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure

Sequential Monte Carlo with kernel embedded mappings: the mapping particle filter

In this work, a novel sequential Monte Carlo filter is introduced which aims at an efficient sampling of the state space. Particles are pushed forward from the prediction to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between the posterior and the sequence of intermediate densities. The sequence of mappings represents a gradient flow based on the principles of local optimal transport. A key ingredient of the mappings is that they are embedded in a reproducing kernel Hilbert space, which allows for a practical and efficient Monte Carlo algorithm. The kernel embedding provides a direct means to calculate the gradient of the Kullback-Leibler divergence leading to quick convergence using well-known gradient-based stochastic optimization algorithms. Evaluation of the method is conducted in the chaotic Lorenz-63 system, the Lorenz-96 system, which is a coarse prototype of atmospheric dynamics, and an epidemic model that describes cholera dynamics. No resampling is required in the mapping particle filter even for long recursive sequences. The number of effective particles remains close to the total number of particles in all the sequence. Hence, the mapping particle filter does not suffer from sample impoverishment

Efficient fully nonlinear data assimilation for geophysical fluid dynamics

A potential problem with Ensemble Kalman Filter is the implicit Gaussian assumption at analysis times. Here we explore the performance of a recently proposed fully nonlinear particle filter on a high-dimensional but simplified ocean model, in which the Gaussian assumption is not made. The model simulates the evolution of the vorticity field in time, described by the barotropic vorticity equation, in a highly nonlinear flow regime. While common knowledge is that particle filters are inefficient and need large numbers of model runs to avoid degeneracy, the newly developed particle filter needs only of the order of 10-100 particles on large scale problems. The crucial new ingredient is that the proposal density cannot only be used to ensure all particles end up in high-probability regions of state space as defined by the observations, but also to ensure that most of the particles have similar weights. Using identical twin experiments we found that the ensemble mean follows the truth reliably, and the difference from the truth is captured by the ensemble spread. A rank histogram is used to show that the truth run is indistinguishable from any of the particles, showing statistical consistency of the method

Massively parallel implicit equal-weights particle filter for ocean drift trajectory forecasting

Forecasting of ocean drift trajectories are important for many applications, including search and rescue operations, oil spill cleanup and iceberg risk mitigation. In an operational setting, forecasts of drift trajectories are produced based on computationally demanding forecasts of three-dimensional ocean currents. Herein, we investigate a complementary approach for shorter time scales by using the recently proposed two-stage implicit equal-weights particle filter applied to a simplified ocean model. To achieve this, we present a new algorithmic design for a data-assimilation system in which all components – including the model, model errors, and particle filter – take advantage of massively parallel compute architectures, such as graphical processing units. Faster computations can enable in-situ and ad-hoc model runs for emergency management, and larger ensembles for better uncertainty quantification. Using a challenging test case with near-realistic chaotic instabilities, we run data-assimilation experiments based on synthetic observations from drifting and moored buoys, and analyze the trajectory forecasts for the drifters. Our results show that even sparse drifter observations are sufficient to significantly improve short-term drift forecasts up to twelve hours. With equidistant moored buoys observing only 0.1% of the state space, the ensemble gives an accurate description of the true state after data assimilation followed by a high-quality probabilistic forecast

Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing nonlinearity

We systematically compare the performance of ETKF-4DVAR, 4DVAR-BEN and 4DENVAR with respect to two traditional methods (4DVAR and ETKF) and an ensemble transform Kalman smoother (ETKS) on the Lorenz 1963 model. We specifically investigated this performance with increasing nonlinearity and using a quasi-static variational assimilation algorithm as a comparison. Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering (1) assimilation window length and observation interval size and (2) ensemble size to investigate the influence of hybrid background error covariance matrices and nonlinearity on the performance of the methods. For short assimilation windows with close to linear dynamics, it has been shown that all hybrid methods show an improvement in RMSE compared to the traditional methods. For long assimilation window lengths in which nonlinear dynamics are substantial, the variational framework can have diffculties fnding the global minimum of the cost function, so we explore a quasi-static variational assimilation (QSVA) framework. Of the hybrid methods, it is seen that under certain parameters, hybrid methods which do not use a climatological background error covariance do not need QSVA to perform accurately. Generally, results show that the ETKS and hybrid methods that do not use a climatological background error covariance matrix with QSVA outperform all other methods due to the full flow dependency of the background error covariance matrix which also allows for the most nonlinearity

Леся Українка та Олена Пчілка в контексті західно- української мемуаристики першої половини ХХ ст.

Розглядаються жанрові особливості та поетика деяких мемуарів західних теренів України (зокрема Галичини та Буковини), у яких постають образи Лесі Українки та Олени Пчілки.Рассматриваются жанровые особенности и поэтика некоторых мемуаров западного региона Украины (в особенности Галиции и Буковины), в которых постают образы Леси Украинки и Олены Пчилки.The article tells about genre peculiarities and poetics of memoirs of the Western Ukraine (in particular, Halychyna and Bukovyna), in which characters of Lesya Ukrainka and Olena Pchilka appear

Reply to comments on ‘On the steadiness of separating meandering currents’

The authors thank Nof et al. for their comments on the authors’ paper ‘‘On the steadiness of separating meandering currents.’’ The authors’ paper was motivated by a series of papers by Nof et al. Under a certain set of conditions (reduced gravity, steady state, no meridional velocity at outflow, and parallel outflow), Nof et al. showed that a separating and retroflecting frictionless current cannot be steady because of a momentum imbalance. The main conclusion of the authors’ paper was that they agree with the Nof et al. result that a momentum imbalance exists and extended the proof to all possible configurations of retroflecting currents, even including friction. The authors’ results point to a new mechanism for the generation of variability in the ocean that is not related to dynamical instability of the flow. The main claim in the comments is that the authors incorrectly argued in the appendix that the steadystate solutions presented by Nof et al. in several papers fulfill the extra constraint u2 5g9h. In the original paper, the authors showed that it follows from the geostrophic assumption stated implicitly in all these Nof et al. papers, because the flow is assumed to be parallel. Nof et al. now argue that the flow is only approximately geostrophic in all Nof et al. papers. The authors show in this reply that for steady weakly meandering outflows approximate geostrophy does lead to a momentum imbalance paradox as Nof et al. claim. However, for a steady strongly meandering outflow, approximate geostrophy is not enough and one has to use the method explored by van Leeuwen and De Ruijter to derive a momentum imbalance paradox