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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
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
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
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
Maziar Bani Shahabadi
and
Mark Buehner

Abstract

Cloud-affected microwave humidity sounding radiances were excluded from assimilation in the hybrid four-dimensional ensemble–variational (4D-EnVar) system of the Global Deterministic Prediction System (GDPS) at Environment and Climate Change Canada (ECCC). This was due to the inability of the current radiative transfer model to consider the scattering effect from frozen hydrometeors at these frequencies. In addition to upgrading the observation operator to RTTOV-SCATT, quality control, bias correction, and 4D-EnVar assimilation components are modified to perform all-sky assimilation of Microwave Humidity Sounder (MHS) channel 2–5 observations over ocean in the GDPS. The input profiles to RTTOV-SCATT are extended to include liquid cloud, ice cloud, and cloud fraction profiles for the simulation and assimilation of MHS observations over water. There is a maximum (35%) increase in the number of channel 2 assimilated MHS observations with smaller increases for channels 3–5 in the all-sky experiment compared to the clear-sky experiment, mostly because of newly assimilated cloud-affected observations. The standard deviation (stddev) of difference between the observed global positioning system radio occultation (GPSRO) refractivity observations and the corresponding simulated values using the background state was reduced in the lower troposphere below 9 km in the all-sky experiment. Verifications of forecasts against the radiosonde observations show statistically significant reductions of 1% in the stddev of error for geopotential height, temperature, and horizontal wind for the all-sky experiment between 72- and 120-h forecast ranges in the troposphere in the Northern Hemisphere domain. Verifications of forecasts against ECMWF analyses also show small improvements in the zonal mean of stddev of error for temperature and horizontal wind for the all-sky experiment between 72- and 120-h forecast ranges. This work was planned for operational implementation in the GDPS in fall 2023.

Open access
Mariko Oue
,
Brian A. Colle
,
Sandra E. Yuter
,
Pavlos Kollias
,
Phillip Yeh
, and
Laura M. Tomkins

Abstract

Limited knowledge exists about ∼100-m-scale precipitation processes within U.S. northeast coastal snowstorms because of a lack of high-resolution observations. We investigate characteristics of microscale updraft regions within the cyclone comma head and their relationships with snowbands, wind shear, frontogenesis, and vertical mass flux using high-spatiotemporal-resolution vertically pointing Ka-band radar measurements, soundings, and reanalysis data for four snowstorms observed at Stony Brook, New York. Updraft regions are defined as contiguous time–height plotted areas with upward Doppler velocity without hydrometeor sedimentation that is equal to or greater than 0.4 m s−1. Most updraft regions in the time–height data occur on a time scale of seconds (<20 s), which is equivalent to spatial scales < 500 m. These small updraft regions within cloud echo occur more than 30% of the time for three of the four cases and 18% for the other case. They are found at all altitudes and can occur with or without frontogenesis and with or without snowbands. The updraft regions with relatively large Doppler spectrum width (>0.4 m s−1) occur more frequently within midlevels of the storms, where there are strong wind shear layers and moist shear instability layers. This suggests that the dominant forcing for the updrafts appears to be turbulence associated with the vertical shear instability. The updraft regions can be responsible for upward mass flux when they are closer together in space and time. The higher values of column mean upward mass flux often occur during snowband periods.

Significance Statement

Small-scale (<500 m) upward motions within four snowstorms along the U.S. northeast coast are analyzed for the first time using high-spatiotemporal-resolution millimeter-wavelength cloud radar pointed vertically. The analysis reveals that updrafts appear in the storms regardless of whether snowbands are present or whether there is larger-scale forcing for ascent. The more turbulent and stronger updrafts frequently occur in midlevels of storms associated with instability from vertical shear and contribute to upward mass flux during snowband periods when they are closer together in space and time.

Open access
Ron McTaggart-Cowan
,
David S. Nolan
,
Rabah Aider
,
Martin Charron
,
Jan-Huey Chen
,
Jean-François Cossette
,
Stéphane Gaudreault
,
Syed Husain
,
Linus Magnusson
,
Abdessamad Qaddouri
,
Leo Separovic
,
Christopher Subich
, and
Jing Yang

Abstract

The operational Canadian Global Deterministic Prediction System suffers from a weak-intensity bias for simulated tropical cyclones. The presence of this bias is confirmed in progressively simplified experiments using a hierarchical system development technique. Within a semi-idealized, simplified-physics framework, an unexpected insensitivity to the representation of relevant physical processes leads to investigation of the model’s semi-Lagrangian dynamical core. The root cause of the weak-intensity bias is identified as excessive numerical dissipation caused by substantial off-centering in the two time-level time integration scheme used to solve the governing equations. Any (semi)implicit semi-Lagrangian model that employs such off-centering to enhance numerical stability will be afflicted by a misalignment of the pressure gradient force in strong vortices. Although the associated drag is maximized in the tropical cyclone eyewall, the impact on storm intensity can be mitigated through an intercomparison-constrained adjustment of the model’s temporal discretization. The revised configuration is more sensitive to changes in physical parameterizations and simulated tropical cyclone intensities are improved at each step of increasing experimental complexity. Although some rebalancing of the operational system may be required to adapt to the increased effective resolution, significant reduction of the weak-intensity bias will improve the quality of Canadian guidance for global tropical cyclone forecasting.

Significance Statement

Global numerical weather prediction systems provide important guidance to forecasters about tropical cyclone development, motion, and intensity. Despite recent improvements in the Canadian operational model’s ability to predict tropical cyclone formation, the system systematically underpredicts the intensity of these storms. In this study, we use a set of increasingly simplified experiments to identify the source of this error, which lies in the numerical time-stepping scheme used to solve the model equations. By decreasing numerical drag on the tropical cyclone circulation, intensity predictions that resemble those of other global modeling systems are achieved. This will improve the quality of Canadian tropical cyclone guidance for forecasters around the world.

Open access
Wei-Ting Fang
,
Pao-Liang Chang
, and
Ming-Jen Yang

Abstract

Intensification of Typhoon Chanthu (2021) along the eastern coast of Taiwan was accompanied by pronounced asymmetry in eyewall convection dominated by wavenumber-1 features, as observed by a dense radar network in Taiwan. The maximum wind speed at 3-km altitude, retrieved from radar observations, exhibited a rapid increase of approximately 18 m s−1 within an 11-h period during the intensification stage, followed by a significant decrease of approximately 19 m s−1 within 8 h during the weakening stage. Namely, Chanthu underwent both rapid intensification (RI) and rapid weakening (RW) within the 24-h analyzed period, posing challenges for intensity forecasts. During the intensifying stages, the region of maximum eyewall convection asymmetry underwent a sudden cyclonic rotation from the eastern to the northern semicircle immediately after the initiation of terrain-induced boundary inflow from the south of the typhoon, as observed by surface station data. This abrupt rotation of eyewall asymmetry exhibited better agreement with radar-derived vertical wind shear (VWS) than that derived from global reanalysis data. This finding suggests that the meso-β-scale VWS is more representative for tropical cyclones than meso-α-scale VWS when the terrain-induced forcing predominates in the environmental conditions. Further examination of the radar-derived VWS indicated that the VWS profile pattern provided a more favorable environment for typhoon intensification. In summary, Chanthu’s RI was influenced by the three factors: 1) terrain-induced boundary inflow from the south of the typhoon, observed by surface station data; 2) low-level flow pointing toward the upshear-left direction; and 3) weak upper-level VWS.

Significance Statement

Tropical cyclone intensity change has been an important issue for both real-time operation and research, but the influence of terrain on intensity change has not been fully understood. Typhoon Chanthu (2021) underwent a significant intensity change near the complex terrain of Taiwan that was observed by a dense radar network. This study analyzes 24 h of radar and weather station data to investigate Chanthu’s evolution. The analyses indicate that the complex terrain affected the low-level flow near the TC. Such a change in flow pattern provided additional boundary inflow and a relatively favorable vertical wind shear pattern for TC intensification.

Open access