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Geir Evensen
,
Femke C. Vossepoel
, and
Peter Jan van Leeuwen

Abstract

This paper identifies and explains particular differences and properties of adjoint-free iterative ensemble methods initially developed for parameter estimation in petroleum models. The aim is to demonstrate the methods’ potential for sequential data assimilation in coupled and multiscale unstable dynamical systems. For this study, we have introduced a new nonlinear and coupled multiscale model based on two Kuramoto–Sivashinsky equations operating on different scales where a coupling term relaxes the two model variables toward each other. This model provides a convenient testbed for studying data assimilation in highly nonlinear and coupled multiscale systems. We show that the model coupling leads to cross covariance between the two models’ variables, allowing for a combined update of both models. The measurements of one model’s variable will also influence the other and contribute to a more consistent estimate. Second, the new model allows us to examine the properties of iterative ensemble smoothers and assimilation updates over finite-length assimilation windows. We discuss the impact of varying the assimilation windows’ length relative to the model’s predictability time scale. Furthermore, we show that iterative ensemble smoothers significantly improve the solution’s accuracy compared to the standard ensemble Kalman filter update. Results and discussion provide an enhanced understanding of the ensemble methods’ potential implementation and use in operational weather- and climate-prediction systems.

Open access
Koryu Yamamoto
,
Keita Iga
, and
Akira Yamazaki

Abstract

A cutoff low that covered central Europe in the middle of July 2021 brought heavy rainfall and severe flooding, resulting in more than 200 fatalities. This low was formed by a trough on 11 July and merged with another cutoff low around 12–13 July. Analysis of the energy budget and potential vorticity suggests that the main cutoff low was maintained through the merger with another cutoff low; this was the dominant contributor to maintenance of the main cutoff low around 12–13 July. The results of Lagrangian trajectory analyses support this conclusion. Analysis of diabatic PV modification during the merger indicates that radiation acts mainly to enhance the potential vorticity of the parcels when they move from another cutoff low into the main cutoff low, especially in the upper layer. However, that effect is not pronounced in the lower layer. These results demonstrate that cutoff lows can be maintained through a merger with another cutoff low and underline the need to consider diabatic processes when investigating mergers.

Significance Statement

This study examines an upper-tropospheric cyclone called a cutoff low, which caused a high-impact weather event over Europe in the middle of July 2021, and investigates its maintenance mechanism. This cutoff low merged with another, suggesting a contribution to the maintenance. Diabatic processes during the merger are also investigated. The results of this study suggest that not only do cyclone regions merge, but diabatic modification of the vortex structure can be seen when two cutoff lows merge, and the modification process may differ in different vertical layers of the cutoff low.

Open access
Free access
Xiangzhou Song
,
Xuehan Xie
,
Yunwei Yan
, and
Shang-Ping Xie

Abstract

Based on data collected from 14 buoys in the Gulf Stream, this study examines how hourly air–sea turbulent heat fluxes vary on subdaily time scales under different boundary layer stability conditions. The annual mean magnitudes of the subdaily variations in latent and sensible heat fluxes at all stations are 40 and 15 W m−2, respectively. Under near-neutral conditions, hourly fluctuations in air–sea humidity and temperature differences are the major drivers of subdaily variations in latent and sensible heat fluxes, respectively. When the boundary layer is stable, on the other hand, wind anomalies play a dominant role in shaping the subdaily variations in latent and sensible heat fluxes. In the context of a convectively unstable boundary layer, wind anomalies exert a strong controlling influence on subdaily variations in latent heat fluxes, whereas subdaily variations in sensible heat fluxes are equally determined by air–sea temperature difference and wind anomalies. The relative contributions by all physical quantities that affect subdaily variations in turbulent heat fluxes are further documented. For near-neutral and unstable boundary layers, the subdaily contributions are O(2) and O(1) W m−2 for latent and sensible heat fluxes, respectively, and they are less than O(1) W m−2 for turbulent heat fluxes under stable conditions.

Significance Statement

High-resolution buoy observations of air–sea variables in the Gulf Stream provide the opportunity to investigate the physical factors that determine subdaily variations in air–sea turbulent heat fluxes. This study addresses two key points. First, the observed subdaily amplitudes of heat fluxes are related to various processes, including wind fields and air–sea thermal effect differences. Second, the global sea surface heat budget is known to not be in near-zero balance and it ranges from several to tens of watts per square meter. Therefore, consideration of the relatively strong influence of subdaily variability in air–sea turbulent heat fluxes could provide a new strategy for solving the global heat budget balance problem.

Open access
Javier Amezcua
,
Sven Peter Näsholm
, and
Ismael Vera-Rodriguez

Abstract

Infrasound waves generated at the Earth’s surface can reach high altitudes before returning to the surface to be recorded by microbarometer array stations. These waves carry information about the propagation medium, in particular, temperature and winds in the atmosphere. It is only recently that studies on the assimilation of such data into atmospheric models have been published. Intending to advance this line of research, we here use the Modulated Ensemble Transform Kalman Filter (METKF) –commonly used in satellite data assimilation– to assimilate infrasound-related observations in order to update a column of three vertically varying variables: temperature and horizontal wind speeds. This includes stratospheric and mesospheric heights, which are otherwise poorly observed. The numerical experiments on synthetic data but with realistic reanalysis product atmospheric specifications (following the Observing System Simulation Experiment paradigm) reveal that a large ensemble is capable of reducing errors, especially for the wind speeds in stratospheric heights close to 30 – 60 km. While using a small ensemble leads to incorrect analysis increments and large estimation errors, the METKF ameliorates this problem and even achieves error reduction from the prior to the posterior mean estimator.

Open access
Connell S. Miller
,
Gregory A. Kopp
,
David M.L. Sills
, and
Daniel G. Butt

Abstract

Currently, the Enhanced Fujita scale does not consider the wind-induced movement of various large compact objects such as vehicles, construction equipment, farming equipment / haybales, etc. that are often found in post-event damage surveys. One reason for this is that modelling debris in tornadoes comes with considerable uncertainties since there are many parameters to determine, leading to difficulties in using trajectories to analyze wind speeds of tornadoes. This paper aims to develop a forensic tool using analytical tornado models to estimate lofting wind speeds based on trajectories of large compact objects. This is accomplished by implementing a Monte Carlo simulation to randomly select the parameters and plotting cumulative distribution functions showing the likelihood of lofting at each wind speed. After analyzing the debris lofting from several documented tornadoes in Canada, the results indicate that the method provides threshold lofting wind speeds that are similar to the estimated speeds given by other methods. However, the introduction of trajectories produces estimated lofting wind speeds that are higher than the EF-scale rating given from the ground survey assessment based on structural damage. Further studies will be required to better understand these differences.

Open access
Joël Stein
and
Fabien Stoop

Abstract

A procedure for evaluating the quality of probabilistic forecasts of binary events has been developed. This is based on a two-step procedure: pooling of forecasts on the one hand and observations on the other hand, on all the points of a neighborhood in order to obtain frequencies at the neighborhood length scale and then to calculate the Brier divergence for these neighborhood frequencies. This score allows the comparison of a probabilistic forecast and observations at the neighborhood length scale, and therefore, the rewarding of event forecasts shifted from the location of the observed event by a distance smaller than the neighborhood size. A new decomposition of this score generalizes that of the Brier score and allows the separation of the generalized resolution, reliability, and uncertainty terms. The neighborhood Brier divergence skill score (BDnSS) measures the performance of the probabilistic forecast against the sample climatology. BDnSS and its decomposition have been used for idealized and real cases in order to show the utility of neighborhoods when comparing at different scales the performances of ensemble forecasts between themselves or with deterministic forecasts or of deterministic forecasts between themselves.

Significance Statement

A pooling of forecasts on the one hand and observations on the other hand, on all the points of a neighborhood, is performed in order to obtain frequencies at the neighborhood scale. The Brier divergence is then calculated for these neighborhood frequencies to compare a probabilistic forecast and observations at the neighborhood scale. A new decomposition of this score generalizes that of the Brier score and allows the separation of the generalized resolution, reliability, and uncertainty terms. This uncertainty term is used to define the neighborhood Brier divergence skill score which is an alternative to the popular fractions skill score, with a more appropriate denominator.

Open access
Jingnan Wang
,
Xiaodong Wang
,
Jiping Guan
,
Lifeng Zhang
,
Tao Chang
, and
Wei Yu

Abstract

The forecast uncertainty, particularly for precipitation, serves as a crucial indicator of the reliability of deterministic forecasts. Traditionally, forecast uncertainty is estimated by ensemble forecasting, which is computationally expensive since the forecast model is run multiple times with perturbations. Recently, deep learning methods have been explored to learn the statistical properties of ensemble prediction systems due to their low computational costs. However, accurately and effectively capturing the uncertainty information in precipitation forecasts remains challenging. In this study, we present a novel spatiotemporal transformer network (ST-TransNet) as an alternative approach to estimate uncertainty with ensemble spread and probabilistic forecasts, by learning from historical ensemble forecasts. ST-TransNet features a hierarchical structure for extracting multiscale features and incorporates a spatiotemporal transformer module with window-based attention to capture correlations in both spatial and temporal dimensions. Additionally, window-based attention can not only extract local precipitation patterns but also reduce computational costs. The proposed ST-TransNet is evaluated on the TIGGE ensemble forecast dataset and Global Precipitation Measurement (GPM) precipitation products. Results show that ST-TransNet outperforms both traditional and deep learning methods across various metrics. Case studies further demonstrate its ability to generate reasonable and accurate spread and probability forecasts from a single deterministic precipitation forecast. It demonstrates the capacity and efficiency of neural networks in estimating precipitation forecast uncertainty.

Open access
Free access
Joshua Chun Kwang Lee
,
Javier Amezcua
, and
Ross Noel Bannister

Abstract

Two aspects of ensemble localization for data assimilation are explored using the simplified nonhydrostatic ABC model in a tropical setting. The first aspect (i) is the ability to prescribe different localization length scales for different variables (variable-dependent localization). The second aspect (ii) is the ability to control (i.e., to knock out by localization) multivariate error covariances (selective multivariate localization). These aspects are explored in order to shed light on the cross-covariances that are important in the tropics and to help determine the most appropriate localization configuration for a tropical ensemble–variational (EnVar) data assimilation system. Two localization schemes are implemented within the EnVar framework to achieve (i) and (ii). One is called the isolated variable-dependent localization (IVDL) scheme and the other is called the symmetric variable-dependent localization (SVDL) scheme. Multicycle observation system simulation experiments are conducted using IVDL or SVDL mainly with a 100-member ensemble, although other ensemble sizes are studied (between 10 and 1000 members). The results reveal that selective multivariate localization can reduce the cycle-averaged root-mean-square error (RMSE) in the experiments when cross-covariances associated with hydrostatic balance are retained and when zonal wind/mass error cross-covariances are knocked out. When variable-dependent horizontal and vertical localization are incrementally introduced, the cycle-averaged RMSE is further reduced. Overall, the best performing experiment using both variable-dependent and selective multivariate localization leads to a 3%–4% reduction in cycle-averaged RMSE compared to the traditional EnVar experiment. These results may inform the possible improvements to existing tropical numerical weather prediction systems that use EnVar data assimilation.

Open access