Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Tropical cyclones”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Objective Operational Utilization of Satellite Microwave Scatterometer Observations of Tropical Cyclones

This study has demonstrated that high-resolution scatterometer measurements in tropical cyclones and other high-marine surface wind regimes may be retrieved accurately for wind speeds up to about 35 mls (1-hour average at 10 m) when the scatterometer data are processed through a revised geophysical model function, and a spatial adaptive algorithm is applied which utilizes the fact that wind direction is so tightly constrained in tile inner core of severe marine storms that wind direction may be prescribed from conventional data. This potential is demonstrated through case studies with NSCAT data in a severe West Pacific Typhoon (Violet, 1996) and an intense North Atlantic hurricane (Lili, 1996). However, operational scatterometer winds from NSCAT and QuickScat in hurricanes and severe winter storms are biased low in winds above 25 m/s. We have developed an inverse model to specify the entire surface wind field about a tropical cyclone from operational QuickScat scatterometer measurements within 150 nm of a storm center with the restriction that only wind speeds up to 20 m/s are used until improved model function are introduced. The inverse model is used to specify the wind field over the entire life-cycle of Hurricane Floyd (1999) for use to drive an ocean wave model. The wind field compares very favorably with wind fields developed from the copious aircraft flight level winds obtained in this storm.

Cardone, Vincent J.↗

The Influence of African Easterly Waves on Atlantic Tropical Cyclone Tracks and Landfall in Large Ensembles

African easterly waves (AEWs) are an important precursor or “seed” for Atlantic tropical cyclones (TCs), with 60%–80% of major hurricanes observed to originate from AEWs. However, climate model simulations indicate that AEWs are not necessary to maintain annual Atlantic TC frequency. Furthermore, small ensembles suggest that AEWs may impact the spatial distribution and landfall of Atlantic TCs. Here, we investigated the influence of AEWs on the spatial distribution of Atlantic TC tracks and landfall using 50-member ensembles of TC-permitting regional model simulations for five hurricane seasons characterized by different levels of TC activity. The control simulations are seasonal hindcasts in which AEWs were prescribed through the eastern lateral boundary condition using reanalysis. In the experiments, we suppressed AEWs by applying a 2–10 day filter to the eastern lateral boundary condition. In response to AEW suppression, we discovered statistically significant increases in Atlantic TC frequency (10%–26%) and landfall (16%–44%), a westward shift in TC genesis location and tracks with increased landfall over the Caribbean Islands, southwestern Gulf Coast, and southeastern US coast, and increases in mid-tropospheric relative humidity in the main development region. In addition, we evaluated TC genesis mechanisms in the absence of AEWs and found evidence that the intertropical convergence zone (ITCZ) intensified and extended northward, resulting in ITCZ wave-breaking that shed vortices which served as TC seeds. By uncovering the connections between TC seed types and the likelihood of TC landfall, this research can provide Atlantic coastal and island communities with useful information to prepare for TC impacts.

African easterly waves↗

Tropical Cyclones Feed More Heavy Rain in a Warmer Climate

The possible linkage of tropical cyclones (TC) to global warming is a hotly debated scientific topic, with immense societal impacts. Most of the debate has been focused on the issue of uncertainty in the use of non-research quality data for long-term trend analyses, especially with regard to TC intensity provided by TC forecasting centers. On the other hand, it is well known that TCs are associated with heavy rain during the processes of genesis and intensification, and that there are growing evidences that rainfall characteristics (not total rainfall) are most likely to be affected by global warming. Yet, satellite rainfall data have not been exploited in any recent studies of linkage between tropical cyclones (TC) and global warming. This is mostly due to the large uncertainties associated with detection of long-term trend in satellite rainfall estimates over the ocean. This problem, as we demonstrate in this paper, can be alleviated by examining rainfall distribution, rather than rainfall total. This paper is the first to use research-quality, satellite-derived rainfall from TRMM and GPCP over the tropical oceans to estimate shift in rainfall distribution during the TC season, and its relationships with TCs, and sea surface temperature (SST) in the two major ocean basins, the northern Atlantic and the northern Pacific for 1979-2005. From the rainfall distribution, we derive the TC contributions to rainfall in various extreme rainfall categories as a function to time. Our results show a definitive trend indicating that TCs are contributing increasingly to heavier rain events, i.e., intense TC's are more frequent in the last 27 years. The TC contribution to top 5% heavy rain has nearly doubled in the last two decades in the North Atlantic, and has increased by about 10% in the North Pacific. The different rate of increase in TC contribution to heavy rain may be related to the different rates of different rate of expansion of the warm pool (SST >2S0 C) area in the two oceans.

Lau, K.-M.↗

Observational Analysis of Atlantic Basin Tropical Cyclone Squall Lines and Relationship to the Diurnal Cycle

Previous studies on the tropical cyclone (TC) diurnal cycle have shown in observations and modeling the presence of outward propagating squall lines. These squall lines were observed in several TCs during recent Atlantic hurricane seasons. Of these squall lines, one observed in Hurricane Laura made landfall over 14 hours prior to the hurricane’s eye. This squall was responsible for 40 tornado warnings, which disrupted preparations and evacuations ahead of the storm’s landfall. This study seeks to characterize these squall lines and their environmental and thermodynamic characteristics, determine whether they behave more like midlatitude squall lines or tropical cyclone rain bands, and assess the performance of the convection-allowing High Resolution Rapid Refresh model in forecasting them over the ocean and over land. By using a combination of operational radar data, a network of surface weather observations from land and sea, satellite data, and HRRR model output, this case will undergo an extensive evaluation based on criteria from past literature in order to better understand these features as a whole and in relation to the diurnal cycle.

Vivian Brasfield↗

Investigating Sensitivity to Saharan Dust in Tropical Cyclone Formation Using Nasa's Adjoint Model

As tropical cyclones develop from easterly waves coming of the coast of Africa they interact with dust from the Sahara desert. There is a long standing debate over whether this dust inhibits or advances the developing storm and how much influence it has. Dust can surround the storm and absorb incoming solar radiation, cooling the air below. As a result an energy source for the system is potentially diminished, inhibiting growth of the storm. Alternatively dust may interact with clouds through micro-physical processes, for example by causing more moisture to condense, potentially increasing the strength. As a result of climate change, concentrations and amount of dust in the atmosphere will likely change. It it is important to properly understand its effect on tropical storm formation. The adjoint of an atmospheric general circulation model provides a very powerful tool for investigating sensitivity to initial conditions. The National Aeronautics and Space Administration (NASA) has recently developed an adjoint version of the Goddard Earth Observing System version 5 (GEOS-5) dynamical core, convection scheme, cloud model and radiation schemes. This is extended so that the interaction between dust and radiation is also accounted for in the adjoint model. This provides a framework for examining the sensitivity to dust in the initial conditions. Specifically the set up allows for an investigation into the extent to which dust affects cyclone strength through absorption of radiation. In this work we investigate the validity of using an adjoint model for examining sensitivity to dust in hurricane formation. We present sensitivity results for a number of systems that developed during the Atlantic hurricane season of 2006. During this period there was a significant outbreak of Saharan dust and it is has been argued that this outbreak was responsible for the relatively calm season. This period was also covered by an extensive observation campaign. It is shown that the adjoint can provide insight into the sensitivity and reveals a relatively low sensitivity to dust compared to, for example, the thermodynamic variables. However a secondary sensitivity though moisture is seen. If dust dries the air it can significantly reduce the cyclone intensity through the moisture.

Tropical Cyclones↗

Estimating Tropical Cyclone Threats to Floating Rigs in the Gulf of Mexico

Offshore drilling operations in the Gulf of Mexico are particularly vulnerable during hurricane season. When a weather threat arises, a decision to evacuate the rig and/or move to a safe location may need to be made. Securing the well, evacuating, and/or moving to a safe location can take a considerable amount of time. This transition time is called T-time. T-time is not only rig dependent, but also depends on the activity being performed at the time of the threat. For these reasons, it is important to assess tropical cyclone threats and the estimated time it will take the storm to reach the rig location from the time it is first detected. The objective of this study is to use 50 years of cyclone history from a National Oceanic and Atmospheric Administration’s (NOAA) database, the International Best Track Archive for Climate Stewardship (IBTrACS) to estimate cyclone threats at any location in the Gulf of Mexico. The cyclone threat is estimated based on the rig location as well as the start date and duration of the offshore activity. By threat, it is meant the likelihood that a specific location with an associated offshore activity lies within the forecasted track cone and storm size of the upcoming cyclone. Three representative rig locations in the Gulf of Mexico were selected as assessment sites to evaluate the threat of incoming cyclones for different T-times. To conduct this tropical cyclone study, an Excel spreadsheet tool was developed to automate the analysis of the tropical cyclone data. The spreadsheet tool allows the user to input any location (i.e., longitude and latitude) in the Gulf of Mexico and displays a list of historical cyclones that have passed within 150 nautical miles of that location during the activity period selected by the user. In addition, the tool allows the user to input any T-time to assess the threat of cyclones that would not provide adequate time to secure the well, evacuate, and/or move to a safe location.

Offshore Oil Drilling↗

Lower-stratospheric/upper-tropospheric exchange processes associated with tropical cyclones as observed by TOMS

Total ozone associated with western Atlantic and Pacific tropical cyclones at various stages of development were analyzed for the purpose of monitoring storm intensity and/or intensity changes. The analysis is based on total ozone measurements from the Nimbus 7 Total Ozone Mapping Spectrometer (TOMS). Since ozone may be considered a passive tracer in the lower stratosphere and the ozone gradients are strongest just above the tropopause, fluctuations of total ozone are due to variations in tropopause height and/or changes in concentration within the column caused by vertical and horizontal advection. In the subtropical northern Pacific during August and September 1981, a negative correlation greater than 0.60 was found between upper-tropospheric geopotential heights near the tropopause level and total ozone. Preliminary results suggest that TOMS can be used to resolve the upper-troposphere structure in and around tropical cyclones and can provide an indication of those processes that help to intensify and maintain these storms.

Rodgers, Edward B.↗

Improving NASA's Multiscale Modeling Framework for Tropical Cyclone Climate Study

One of the current challenges in tropical cyclone (TC) research is how to improve our understanding of TC interannual variability and the impact of climate change on TCs. Recent advances in global modeling, visualization, and supercomputing technologies at NASA show potential for such studies. In this article, the authors discuss recent scalability improvement to the multiscale modeling framework (MMF) that makes it feasible to perform long-term TC-resolving simulations. The MMF consists of the finite-volume general circulation model (fvGCM), supplemented by a copy of the Goddard cumulus ensemble model (GCE) at each of the fvGCM grid points, giving 13,104 GCE copies. The original fvGCM implementation has a 1D data decomposition; the revised MMF implementation retains the 1D decomposition for most of the code, but uses a 2D decomposition for the massive copies of GCEs. Because the vast majority of computation time in the MMF is spent computing the GCEs, this approach can achieve excellent speedup without incurring the cost of modifying the entire code. Intelligent process mapping allows differing numbers of processes to be assigned to each domain for load balancing. The revised parallel implementation shows highly promising scalability, obtaining a nearly 80-fold speedup by increasing the number of cores from 30 to 3,335.

tropical cyclone interannual variability↗

The Role of Tropical Cyclone—Ocean Interactions in Future Changes in Hurricane Katrina

Tropical cyclone (TC) intensity and precipitation are projected to increase in the future. However, some projections are based on atmosphere‐only models in which sea surface temperatures are prescribed, whereas projections based on global atmosphere‐ocean coupled models can be subject to long‐term ocean biases. We investigated the role of TC‐ocean interactions in future changes in TC intensity and precipitation in Hurricane Katrina. We performed four‐member ensembles using convection‐permitting atmosphere‐only and atmosphere‐ocean regional models for the historical climate and four future climates. We found that although future TC intensity and precipitation increased regardless of ocean coupling, ocean coupling dampened the future minimum sea‐level pressure decrease by half and amplified future precipitation scaling. Compared to future changes in upper‐ocean temperature, changes in salinity contributed little to future changes in TC intensity. This study highlights the importance of considering TC‐ocean interactions to reduce uncertainty in the magnitude of future TC intensity and precipitation projections.

climate change↗

Deepti: Deep Learning-Based Tropical Cyclone Intensity Estimation

We present the development of a deep learning model for objective estimation of tropical cyclone intensity at a higher temporal frequency, deployment of the model in production, design and implementation of the tropical cyclone monitoring and intensity estimation system and development of an interactive portal for situational awareness and evaluation of intensity estimation.

Maskey, Manil↗

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗

Evolution of Tropical Cyclone Properties Across the Development Cycle of the GISS-E3 Global Climate Model

The next-generation global climate model from the NASA Goddard Institute for Space Studies, GISS-E3, contains many improvements to resolution and physics that allow for improved representation of tropical cyclones (TCs) in the model. This study examines the properties of TCs in two different versions of E3 at different points in its development cycle, run for 20 years at 0.5 degree resolution, and compares these TCs with observations, the previous generation GISS model, E2, and other climate models. E3 shares many TC biases common to global climate models, such as having too few tropical cyclones, but is much improved from E2. E3 produces strong enough TCs that observation-based wind speed thresholds can now be used to detect and track them, and some storms now reach hurricane intensity; neither of these was true of E2. Model development between the first and second versions of E3 further increased the number and intensity of TCs and reduced TC count biases globally and in most regions. One-year sensitivity tests to changes in various microphysical and dynamical tuning parameters are also examined. Increasing the entrainment rate for the more strongly-entraining plume in the convection scheme increases the number of TCs (though also affecting other climate variables, and in some cases increasing biases). Variations in divergence damping did not have a strong effect on simulated TC properties, contrary to expectations based on previous studies. Overall, the improvements in E3 make it more credible for studies of TC activity and its relationship to climate.

Tropical Cyclones↗

Tropical Cyclone Ecology: A Scale-Link Perspective

Tropical cyclones are increasing in intensity and size and, thus, are poised to increase in importance as disturbance agents. Our understanding of cyclone ecology is biased towards the North Atlantic Basin, because cyclone effects do differ across oceanic basins. Cyclones have both short and long-term effects across the levels of biological organization, but we lack a scale-perspective of cyclone ecology. Effects on individual trees, such as defoliation or branch stripping and uprooting, are mechanistically linked to effects at the community and ecosystem levels, including forest productivity and stand regeneration time. Forest dwarfing via the gradual removal of taller trees by cyclones over many generations illustrates that cyclones shape forest structure through the accumulation of short-term effects over longer timescales.

54 ENVIRONMENTAL SCIENCES↗

Ocean internal tides suppress tropical cyclones in the South China Sea

Abstract Tropical Cyclones (TCs) are devastating natural disasters. Analyzing four decades of global TC data, here we find that among all global TC-active basins, the South China Sea (SCS) stands out as particularly difficult ocean for TCs to intensify, despite favorable atmosphere and ocean conditions. Over the SCS, TC intensification rate and its probability for a rapid intensification (intensification by ≥ 15.4 m s −1 day −1 ) are only 1/2 and 1/3, respectively, of those for the rest of the world ocean. Originating from complex interplays between astronomic tides and the SCS topography, gigantic ocean internal tides interact with TC-generated oceanic near-inertial waves and induce a strong ocean cooling effect, suppressing the TC intensification. Inclusion of this interaction between internal tides and TC in operational weather prediction systems is expected to improve forecast of TC intensity in the SCS and in other regions where strong internal tides are present.

54 ENVIRONMENTAL SCIENCES↗

Understanding Uncertainties in Tropical Cyclone Rainfall Hazard Modeling Using Synthetic Storms

Tropical cyclone (TC) rainfall hazard assessment is subject to the bias in TC climatology estimation from climate simulations or synthetic downscaling. In this study, we investigate the uncertainty in TC rainfall hazard assessment induced by this bias using both rain gauge and radar observations and synthetic-storm-model-coupled TC rainfall simulations. We identify the storm’s maximum intensity, impact duration, and minimal distance to the site to be the three most important storm parameters for TC rainfall hazard, and the relationship between the important storm parameters and TC rainfall can be well captured by a physics-based TC rainfall model. The uncertainty in the synthetic rainfall hazard induced by the bias in TC climatology can be largely explained by the bias in the important storm parameters simulated by the synthetic storm model. Correcting the distribution of the most biased parameter may significantly improve rainfall hazard estimation. Bias correction based on the joint distribution of the important parameters may render more accurate rainfall hazard estimations; however, the general technical difficulties in resampling from high-dimensional joint probability distributions prevent more accurate estimations in some cases. The results of the study also support future investigation of the impact of climate change on TC rainfall hazards through the lens of future changes in the identified important storm parameters.

54 ENVIRONMENTAL SCIENCES↗

An explicit three-dimensional nonhydrostatic numerical simulation of a tropical cyclone

A nonhydrostatic numerical simulation of a tropical cyclone is performed with explicit representation of cumulus on a meso-beta scale grid and for a brief period on a meso-gamma scale grid. Individual cumulus plumes are represented by a combination of explicit resolution and a 1.5 level closure predicting turbulent kinetic energy (TKE).

Tripoli, G. J.↗