Search NASASearch

SEARCH · Search NASA

Results for “air/sea interaction”

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.

Research in Observations of Oceanic Air/Sea Interaction

The primary purpose of this research has been: (1) to develop an innovative research radar scatterometer system capable of directly measuring both the radar backscatter and the small-scale and large-scale ocean wave field simultaneously and (2) deploy this instrument to collect data to support studies of air/sea interaction. The instrument has been successfully completed and deployed. The system deployment lasted for six months during 1995. Results to date suggest that the data is remarkably useful in air/sea interaction studies. While the data analysis is continuing, two journal and fifteen conference papers have been published. Six papers are currently in review with two additional journal papers scheduled for publication. Three Master's theses on this research have been completed. A Ph.D. student is currently finalizing his dissertation which should be completed by the end of the calendar year. We have received additional 'mainstream' funding from the NASA oceans branch to continue data analysis and instrument operations. We are actively pursuing results from the data expect additional publications to follow. This final report briefly describes the instrument system we developed and results to-date from the deployment. Additional detail is contained in the attached papers selected from the bibliography.

Long, David G.

BOMEX bulletin, no. 10

Radiosonde and radar echo measurements on area of air/sea interactions over tropical ocean surface with numerical weather forecasting

Source record

Characterization and Correction of Aquarius Long Term Calibration Drift Using On-Earth Brightness Temperature Refernces

The Aquarius/SAC-D mission was launched on June 10, 2011 from Vandenberg Air Force Base. Aquarius consists of an L-band radiometer and scatterometer intended to provide global maps of sea surface salinity. One of the main mission objectives is to provide monthly global salinity maps for climate studies of ocean circulation, surface evaporation and precipitation, air/sea interactions and other processes. Therefore, it is critical that any spatial or temporal systematic biases be characterized and corrected. One of the main mission requirements is to measure salinity with an accuracy of 0.2 psu on montly time scales which requires a brightness temperature stability of about 0.1K, which is a challenging requirement for the radiometer. A secondary use of the Aquarius data is for soil moisture applications, which requires brightness temperature stability at the warmer end of the brightness temperature dynamic range. Soon after launch, time variable drifts were observed in the Aquarius data compared to in-situ data from ARGO and models for the ocean surface salinity. These drifts could arise from a number of sources, including the various components of the retrieval algorithm, such as the correction for direct and reflected galactic emission, or from the instrument brightness temperature calibration. If arising from the brightness temperature calibration, they could have gain and offset components. It is critical that the nature of the drifts be understood before a suitable correction can be implemented. This paper describes the approach that was used to detect and characterize the components of the drift that were in the brightness temperature calibration using on-Earth reference targets that were independent of the ocean model.

Aquarius

Impact of Satellite Sea Surface Salinity Observations on ENSO Predictions from the GMAO S2S Forecast System

Sea surface salinity (SSS) observations from space allow us to investigate if improved estimates of near-surface density stratification and associated mixing can positively impact seasonal to interannual variability of tropical Pacific Ocean dynamics as well as dynamical ENSO forecasts. For the first part of the presentation, we utilize our intermediate-complexity coupled model. Baseline experiments assimilate satellite sea level (multi-satellite gridded AVISO, 2013), SST (Reynolds et al., 2004), and in situ subsurface temperature and salinity observations (GTSPP NODC, 2006). These baseline experiments are then compared with experiments that additionally assimilate Aquarius (V5.0 Lilly and Lagerloef, 2008) and SMAP (V4.0 Fore et al., 2016) SSS. Twelve-month forecasts are initialized for each month from September 2011 to September 2017. For initialization of the coupled forecast, the positive impact of SSS assimilation is brought about by surface freshening near the eastern edge of the western Pacific warm pool and density changes that lead to shallower mixed layer between 10S-5N. This pattern enhances air/sea interaction and amplifies the equatorial Kelvin wave signal. We find that including satellite SSS significantly improves NINO3.4 sea surface temperature anomaly validation over most forecast lead times. We next assess how different satellite SSS products impact the validation of ENSO forecasts. SMAP V4 reduces the salty bias in the western Pacific and so is an improvement upon SMAP V2 and SMOS V2 (Boutin et al., 2017) has similar validation characteristics as a combination of Aquarius and SMAP V4. Next we shift to present results from the NASA GMAO Sub-seasonal to seasonal (S2S_v2.1) production coupled model (i.e. the same model that contributes ENSO forecasts to the North American Multi-Model Ensemble Experiment). From March to June 2015, the availability of two overlapping satellite SSS instruments, Aquarius and SMAP, allows a unique opportunity to compare and contrast forecasts initialized with the benefit of these two satellite SSS observation types. We assess the impact of satellite sea surface salinity (SSS) observations on dynamical ENSO forecasts for the big 2015 El Nino event. We will present distinct experiments for the overlap period that include 1) freely evolving SSS (i.e. no satellite SSS as the production system), 2) Aquarius, and 3) SMAP initialization. Our results show that using Aquarius slightly improves validation of the reanalysis (including sea level and temperature statistics). Our production system without SSS assimilation generated too warm forecasts for the 2015 El Nino from March initial conditions. Incorporating Aquarius into initialization of the coupled system leads to a deeper, more realistic MLD that acts to damp the downwelling Kelvin signal and slightly cool NINO3.4 SST. With Aquarius the forecasts better match the observed amplitude of the 2015 event. On the other hand, SMAP V2 relaxation generally degrades validation statistics. At forecast initialization, SMAP is much too salty within 10o of the equator, leading to deeper MLD east of 165W. This deeper MLD leads to over-damping of the downwelling signal (i.e. relative upwelling), in turn leading to relatively too cool ENSO forecasts.

Hackert, E.

Impact of Satellite Sea Surface Salinity Observations on ENSO Predictions from the GMAO S2S Forecast System

El Nino/Southern Oscillation (ENSO) has far reaching global climatic impacts and so extending useful ENSO forecasts would be of great benefit for society. However, one key variable that has yet to be fully exploited within coupled forecast systems is accurate estimation of near-surface ocean density. Satellite Sea Surface Salinity (SSS), combined with temperature, help to identify ocean density changes and associated mixing near the ocean surface. We assess the impact of satellite SSS observations for improving near-surface dynamics within ocean analyses and how these impact dynamical ENSO forecasts using the NASA GMAO (Global Modeling and Assimilation Office) Sub-seasonal to Seasonal (S2S_v2.1) coupled forecast system (Molod et al. 2018 - i.e. NASA's contribution to the NMME (National Multi-Model Ensemble) project). For all initialization experiments, all available along-track absolute dynamic topography and in situ observations are assimilated using the LETKF ( Local Ensemble Transform Kalman Filter) scheme similar to Penny et al., 2013. A separate reanalysis additionally assimilates Aquarius V5 (September 2011 to June 2015) and SMAP (Soil Moisture Active Passive) V4 (March 2015 to present) along-track data.We highlight the impact of satellite SSS on ocean reanalyses by comparing validation statistics of experiments that assimilate SSS versus our current prediction system that withholds SSS. We find that near-surface validation versus observed statistics for salinity are slightly degraded when assimilating SSS. This is an expected result due to known biases between SSS (measured by the satellite at approximately 1 centimeter) and in situ measurements (typically measured by Argo floats at 3 meters). On the other hand, a very encouraging result is that both temperature, absolute dynamic topography, and mixed layer statistics are improved with SSS assimilation. Previous work has shown that correcting near-surface density structure via gridded SSS assimilation can improve coupled forecasts. Here we present results of coupled forecasts that are initialized from the GMAO S2S reanalyses that assimilates/withholds along-track (L2) SSS. In particular, we contrast forecasts of the overestimated 2014 El Nino, the big 2015 El Nino, and the minor 2016 La Nina. For each of these ENSO scenarios, assimilation of satellite SSS improves the forecast validation. Improved SSS and density upgrades the mixed layer depth leading to more accurate coupled air/sea interaction.

Hackert, E.

Impact of Satellite Sea Surface Salinity Observations on ENSO Predictions from the GMAO Seasonal Forecast System

El Nino/Southern Oscillation (ENSO) has far reaching global climatic impacts and so extending useful ENSO forecasts would be of great benefit for society. However, one key variable that has yet to be fully exploited within coupled forecast systems is accurate estimation of near-surface ocean density. Satellite sea surface salinity (SSS), combined with temperature, help to identify ocean density changes and associated mixing near the ocean surface. We assess the impact of satellite SSS observations for improving near-surface dynamics within ocean analyses and how these impact dynamical ENSO forecasts using the NASA GMAO (Global Modeling and Assimilation Office) Sub-seasonal to Seasonal (S2S_v2.1) coupled forecast system (Molod et al. 2018 - i.e. NASA's contribution to the NMME (North American Multi-Model Ensemble) project). For all initialization experiments, all available along-track absolute dynamic topography and in situ observations are assimilated using the LETKF (Local Ensemble Transform Kalman Filter) scheme similar to Penny et al., 2013. A separate reanalysis additionally assimilates Aquarius V5 (September 2011 to June 2015) and SMAP (Soil Moisture Active Passive satellite) V4.1 (March 2015 to present) along-track data.We highlight the impact of satellite SSS on ocean reanalyses by comparing validation statistics of experiments that assimilate SSS versus our current prediction system that withholds SSS. We find that near-surface validation versus observed statistics for salinity are slightly degraded when assimilating SSS. This is an expected result due to known biases between SSS (measured by satellite at approximately 1-centimeter depth) and in situ measurements (typically measured by Argo floats at 3-meters depth). On the other hand, a very encouraging result is that both temperature, absolute dynamic topography, and mixed layer statistics are improved with SSS assimilation. Previous work has shown that correcting near-surface density structure via gridded SSS assimilation can improve coupled forecasts. Here we present results of coupled forecasts that are initialized from GMAO S2S spring reanalyses that assimilate/withhold along-track (L2) SSS. In particular, we contrast forecasts of the big 2015 El Nino, the 2017 La Nina and the 2018 weak El Nino. For each of these ENSO scenarios, assimilation of satellite SSS improves the forecast validation. Improved SSS and density upgrade the mixed layer depth leading to more accurate coupled air/sea interaction. From March to June 2015, the availability of two overlapping satellite SSS instruments, Aquarius and SMAP, allows a unique opportunity to compare and contrast forecasts initialized with the benefit of these two satellite SSS observation types. We assess the impact of gridded satellite sea surface salinity observations on dynamical ENSO forecasts for the big 2015 El Nino.

Hackert, E.

Satellite Sea Surface Salinity Observations Impact on El Niño/Southern Oscillation Predictions: Case Studies from the NASA GEOS Seasonal Forecast System

El Niño/Southern Oscillation (ENSO) has far reaching global climatic impacts and so extending useful ENSO forecasts would have great societal benefit. However, one key variable that has yet to be fully exploited within coupled forecast systems is accurate estimation of near-surface ocean salinity. Satellite sea surface salinity (SSS), combined with temperature, help to improve the estimates of ocean density changes and associated near-surface mixing. For the first time, we assess the impact of satellite SSS observations for improving near-surface dynamics within ocean reanalyses and how these initializations impact dynamical ENSO forecasts using NASA’s coupled forecast system (GEOS-S2S-2). For all initialization experiments, all available sea level and in situ temperature and salinity observations are assimilated. Separate observing system experiments (OSE) additionally assimilate Aquarius, and SMAP, SMOS, and these datasets combined. We highlight the impact of satellite SSS on ocean reanalyses by comparing experiments with and without the application of SSS assimilation. Next, we compare case studies of coupled forecasts for the big 2015 El Niño, the 2017 La Niña, and the weak El Niño in 2018 that are initialized from GEOS-S2S-2 spring reanalyses that assimilate and withhold along-track SSS. For each of these ENSO-event case studies, assimilation of satellite SSS improves the forecast validation with respect to observed NINO3.4 anomalies (or at least reduces the forecast uncertainty). Satellite SSS assimilation improved characterization of the mixed layer depth leading to more accurate coupled air/sea interaction and better forecasts. These results further underline the value of satellite SSS assimilation into operational forecast systems.

Eric Hackert

Effect of Rain-Adjusted Satellite Sea Surface Salinity on ENSO Predictions from the GMAO S2S Forecast System

ENSO has a significant impact on climate variability throughout the world and so has been the key focus for improving coupled ocean-atmosphere forecasts. Assimilation of altimetry and in situ data lead to improved short-term forecasts of the coupled system. However, few studies have focused on improving the near-surface density/mixing through assimilation of satellite sea surface salinity (SSS). For expediency, most projects that do assimilate SSS do so as if these data were observed at the top model layer instead of at the surface. In rainy regions where buoyant water sits as a fresh lens at the surface, this assumption is likely invalid. Therefore, we adjust SSS so that it more accurately represents the salinity at the first model layer. The Rain Impact Model (RIM) uses a simple diffusion model to determine the near surface salinity gradient (i.e., 1 cm to 5 m). Satellite SSS data are modified using this near-surface salinity gradient, so the salinity values are now valid at the first model layer (we call this SSS@5m). We assess the impact of satellite SSS observations for near-surface dynamics within ocean reanalyses and how these impact dynamical ENSO forecasts using the NASA GMAO S2S coupled system. For all reanalysis experiments, all available along-track sea level and in situ observations are assimilated for 2011 to 2020 using the LETKF scheme (Penny et al., 2013). One reanalysis assimilates Aquarius /SMAP SSS as before. An additional reanalysis is performed assimilating the SSS@5m data. Validation statistics are compared for experiments that assimilate SSS (sub-optimally as before) versus the SSS@5m. We also compare results of coupled forecasts that are initialized from these reanalyses in spring. For all but the big La Niña in 2017, all NINO3.4 forecasts were improved by using the RIM. We will show that improved SSS estimates upgrades density and near-surface mixing leading to more accurate coupled air/sea interaction and better forecasts.

ENSO

Improving Ocean Reanalyses and ENSO Forecasts By Assimilation of Rain-Corrected Satellite Sea Surface Salinity Using the GMOA S2s Forecast System

The ENSO phenomenon has a significant global socio-economic impact and has been the key focus for improving coupled ocean-atmosphere forecasts. Assimilation of satellite altimetry and subsurface temperature and salinity from (mostly) Argo help improve the initialization of the thermocline, while satellite SST aids in constraining surface heat-fluxes, leading to improved coupled system sub-seasonal to seasonal forecasts. However, few studies have focused on improving the near-surface density and mixing through satellite sea surface salinity (SSS) assimilation. The few ocean models that assimilate satellite SSS, bias correct to normalize towards the near-surface Argo data for expediency. This assumption is likely inadequate in rainy regions, where buoyant water forms a fresh surface lens. In previous work, we showed that adjusting SSS to bulk salinity (Sb) using the Rain Impact Model (RIM) of Santos-Garcia et al., 2014 improves the near-surface density and mixed layer depth, leading to deeper thermocline and improved NINO3.4 SST forecasts. We now utilize the Soil Moisture and Ocean Salinity rain-corrected (SMOS_RC) SSS, available in SMOS-CATDS products, to represent Sb more accurately at the first model layer (e.g., 5 m). Rather than a diffusivity model as RIM, SMOS_RC uses a statistical correction dependent on Integrated Multi-satellitE Retrievals for GPM (IMERG) rain rates, established on observed SMOS SSS decreases related to Sb in the presence of rain (Supply et al., 2020). For all experiments, all available along-track absolute dynamic topography and in situ observations are assimilated using the LETKF scheme (Penny et al., 2013). One reanalysis additionally assimilates SMOS SSS data as is, and a separate reanalysis assimilates SMOS_RC. We assess the impact on near-surface and subsurface dynamics by validating against observations and explore how SSS assimilation (SMOS vs SMOS_RC) impacts ENSO forecasts using the NASA GMAO Sub-seasonal to Seasonal coupled forecast system (S2S-v3, Molod et al. 2020). We show that improved estimates of density and near-surface mixing led to more accurate coupled air/sea interaction and better ENSO forecasts. The increased SSS, resulting from the removal of the instantaneous rain effect, modifies the ocean state by enhancing mixing and deepening the thermocline.

Veronica Ruiz Xomchuk

Improving Ocean Reanalyses and ENSO Forecasts By Assimilation of Rain Corrected Satellite Sea Surface Salinity Using the GMAO S2S Forecast System

During the past years, we have seen that the La Nina to El Nino transition has had a significant global socio-economic impact and so has been the key focus for improving coupled ocean-atmosphere forecasts. Assimilation of satellite altimetry and subsurface temperature and salinity from (mostly) Argo help to improve the initialization of the thermocline, while satellite Sea Surface Temperature (SST) aids in constraining surface heat-fluxes, leading to improved subseasonal to seasonal forecasts of the coupled system. However, few studies have focused on improving the fresh-water flux and near-surface density and mixing through assimilation of satellite sea surface salinity (SSS). For expediency, the few ocean models that do assimilate SSS bias-correct the satellite SSS data to normalize towards the near-surface Argo data. However, in rainy regions, where buoyant water sits as a fresh lens at the surface, this assumption is likely inadequate. In previous work, we have shown that adjusting SSS data to bulk salinity (Sb) using the Rain Impact Model (RIM) of Santos-Garcia et al., 2014 has improved the near-surface density and mixed layer depth, leading to deeper thermocline and improved the NINO3.4 SST forecasts. Now we utilize the Soil Moisture/Ocean Salinity, Rain Corrected (SMOS_RC) SSS product provided by the Centre Aval de Traitement des données SMOS (CATDS CPDC) to represent the Sb more accurately at first model layer (in our case 5 m). Rather than using a diffusivity model as with RIM, SMOS_RC relies on an observed relationship between the spatial heterogeneity of SMOS SSS and instantaneous rain rate (RR) (Supply et al., 2020). In order to test the impact of SMOS_RC versus SMOS, we compare two reanalyses over the period 2014 to 2021. For both reanalysis experiments, all available along-track absolute dynamic topography and in situ observations are assimilated using the LETKF scheme (Penny et al., 2013). One reanalysis additionally assimilates SMOS SSS data as is (i.e., with the fresh bias), and a separate reanalysis is performed assimilating the SMOS_RC data. We assess the impact for near-surface and subsurface dynamics within ocean reanalyses by validating against observations and explore how SSS assimilation (SMOS versus SMOS_RC) impacts dynamical ENSO forecasts using the NASA GMAO Sub-seasonal to Seasonal coupled forecast system (GEOS S2S-3, Molod et al., 2020, Hackert et al., 2023). We will show that improved SSS estimates and near-surface density and mixing led to more accurate coupled air/sea interaction and better ENSO forecasts.

Eric Hackert

Revisiting the validity of eddy viscosity models for predicting airflow over water waves

In this study, we revisit the validity of eddy viscosity models for predicting wave-induced airflow disturbances over ocean surface waves. We first derive a turbulence curvilinear model for the phase-averaged Navier–Stokes equations, extending the work of Cao, Deng & Shen (2020 J. Fluid Mech. 901, A27), by incorporating turbulence stress terms previously neglected in the linearised viscous curvilinear model. To verify our formulation, we perform a priori tests by numerically solving the model using mean wind and turbulence stress profiles from large-eddy simulations (LES) of airflow over waves across various wave ages. Results show that including turbulence stress terms improves wave-induced airflow predictions compared with the previous viscous curvilinear model. We further show that using a standard mixing-length eddy viscosity yields inaccurate predictions at certain wave ages, as it fails to capture wave-induced turbulence, which fundamentally differs from mean shear-driven turbulence. The LES data show that accurate representations of wave-induced stresses require a complex-valued eddy viscosity. The maximum magnitude of this eddy viscosity scales as ∼𝑢 𝜏 ⁢𝜁 𝑖𝑛𝑛𝑒𝑟 , where 𝑢 𝜏 is the friction velocity and 𝜁 𝑖𝑛𝑛𝑒𝑟 is the inner-layer thickness, the height at which the eddy-turnover time matches the wave advection time scale. This scaling aligns with the prediction by Belcher & Hunt (1993 J. Fluid Mech. 251, 109–148). Overall, the findings demonstrate that traditional eddy viscosity models are inadequate for capturing wave-induced turbulence. More sophisticated turbulence models are essential for the accurate prediction of airflow disturbances and form drag in wind–wave interaction models.

16 TIDAL AND WAVE POWER

Numerical Analysis of Offshore Wind-Farm-Induced Drag Effects on Coastal Upwelling Dynamics

Wind farms extract momentum from the atmospheric flow, generating wind-speed deficits both within the plant, and extending downstream. When located offshore, these deficits modulate air-sea coupling, potentially impacting coastal upwelling in sensitive regions. We investigate impacts of wind farms on coastal upwelling using kilometre-scale, three-way-coupled simulations with the coupled ocean-atmosphere-wave-sediment transport system for the US West Coast. Wind-farm effects are represented by a generalised turbine drag formulation, an idealised, height-dependent body force whose magnitude is systematically varied. This approach isolates the leading-order fluid-dynamical response in a realistic coastal configuration. The atmospheric adjustment exhibits an approximately linear relation between drag force and wind-speed deficit, with wakes that expand downstream and increase in magnitude as drag increases. An empirical orthogonal function analysis of sea-surface-temperature anomalies reveals the emergence of a canonical dipole pattern under strong drag forcing. Subsurface diagnostics show consistent shoaling of the mixed layer and suppressed upward velocities in areas near wind-farm region, accompanied by compensating enhancements of shoaling closer to the coast. These results identify turbine drag as a control parameter in assessing interactions between wind-farm wake and coastal upwelling and provide scaling relationships for understanding offshore wind-farm effects on the coastal circulation dynamics.

16 TIDAL AND WAVE POWER

Implementation of a Three-Dimensional Planetary Boundary Layer Parameterization in a Coupled Modeling System and Evaluation of "Gray Zone" Simulations of a Wind-Wave Event Off the US California Coast Using Observations

A three-dimensional (3D) planetary boundary layer (PBL) parameterization was added to the Coupled Ocean Atmosphere Wave Sediment Transport (COAWST) model and the first coupled atmosphere/wave "gray zone" simulations were carried out using the 3D PBL parameterization. A case study of a significant wind-wave event from 4-8 November 2020 off the US west coast was examined, with a focus on the impacts of the event within an approximate 280x280 km central California coastal region covering the Bureau of Ocean Energy Management Morro Bay wind energy lease area. Simulations with both one-dimensional (1D; Yonsei University) and 3D PBL parameterizations were examined in this nest with ..delta..x=400 m. Two-way coupling was active, with near-surface winds feeding back to the wave model and bulk wave statistics feeding back to the atmospheric model. Both simulations compared favorably with buoy observations in capturing the timing and magnitude of wind speed, temperature, dewpoint, and significant wave height, as the front associated with the maritime weather system moved southward across coastal California. However, wind speed errors over land were larger. Time series of the vertical profile of winds below z=250 m from the simulations compared favorably with observations from the US Dept. of Energy Morro Bay Doppler lidar buoy. Differences between the coupled 1D and 3D PBL simulations were minor. The most notable difference was that the simulation using the 3D PBL parameterization had approximately 10 % weaker winds at the peak of the event causing 10 % lower significant wave heights. This difference was shown to be mostly due to differences in the vertical mixing treatment between the parameterizations, in particular the nonlocal downward mixing of higher momentum air in the 1D Yonsei University parameterization in convective conditions. Overall, this work demonstrates that the 3D PBL parameterization can be used in a coupled atmosphere/wave modeling framework with similar behaviors as traditional PBL parameterizations that do not provide horizontal turbulent variances and fluxes.

16 TIDAL AND WAVE POWER

Offline GCSS Intercomparison of Cloud-Radiation Interaction and Surface Fluxes

Simulations of deep tropical clouds by both cloud-resolving models (CRMs) and single-column models (SCMs) in the GEWEX Cloud System Study (GCSS) Working Group 4 (WG4; Precipitating Convective Cloud Systems), Case 2 (19-27 December 1992, TOGA-COARE IFA) have produced large differences in the mean heating and moistening rates (-1 to -5 K and -2 to 2 grams per kilogram respectively). Since the large-scale advective temperature and moisture "forcing" are prescribed for this case, a closer examination of two of the remaining external types of "forcing", namely radiative heating and air/sea hear and moisture transfer, are warranted. This paper examines the current radiation and surface flux of parameterizations used in the cloud models participating in the GCSS WG4, be executing the models "offline" for one time step (12 s) for a prescribed atmospheric state, then examining the surface and radiation fluxes from each model. The dynamic, thermodynamic, and microphysical fluids are provided by the GCE-derived model output for Case 2 during a period of very active deep convection (westerly wind burst). The surface and radiation fluxes produced from the models are then divided into prescribed convective, stratiform, and clear regions in order to examine the role that clouds play in the flux parameterizations. The results suggest that the differences between the models are attributed more to the surface flux parameterizations than the radiation schemes.

Tao, W.-K.