K-profile Parameterization Scheme Research Articles

Using NIW Observations to Assess Mixed Layer Parameterizations: A Case Study in the Tropical Atlantic

AbstractTropical sea surface temperature (SST) biases can cause atmospheric biases on global scales, hence SST needs to be represented well in climate models. A major source of uncertainties is the representation of turbulent mixing in the oceanic boundary layer, or mixed layer (ML). In the present study we focus on near‐inertial wave (NIW) induced mixing. The performance of two mixing schemes, Turbulent Kinetic Energy and K‐profile parameterization (KPP), is assessed at two sites (11.5°N, 23°W and 15°N, 38°W) in the tropical Atlantic. At 11.5°N, turbulence observations (eddy diffusivities, shear and stratification) are available for comparison. We find that the schemes differ in their representation of NIWs, but both under‐represent the observed enhanced diffusivities below the observed ML. However, we find that the models do mix below the ML at 15°N when a storm passes nearby. The near‐inertial oscillations remain below the ML for the following 10 days. Near‐inertial kinetic energy (NIKE) biases in the models are not directly correlated with the wind speed, the MLD biases, or the stratification at the ML base. Instead, NIKE biases are sensitive to the vertical mixing scheme parameterization. NIKE biases are lowest when the KPP scheme is used.

Langmuir Circulations Transfer Kinetic Energy from Submesoscales and Larger Scales to Dissipative Scales

Abstract Surface gravity wave effects on currents (WEC) cause the emergence of Langmuir cells (LCs) in a suite of high horizontal resolution (Δx = 30 m), realistic oceanic simulations in the open ocean of central California. During large wave events, LCs develop widely but inhomogeneously, with larger vertical velocities in a deeper mixed layer. They interact with extant submesoscale currents. A 550-m horizontal spatial filter separates the signals of LCs and of submesoscale and larger-scale currents. The LCs have a strong velocity variance with small density gradient variance, while submesoscale currents are large in both. Using coarse graining, we show that WEC induces a forward cascade of kinetic energy in the upper ocean up to at least a 5-km scale. This is due to strong positive vertical Reynolds stress (in both the Eulerian and the Stokes drift energy production terms) at all resolved scales in the WEC solutions, associated with large vertical velocities. The spatial filter elucidates the role of LCs in generating the shear production on the vertical scale of Stokes drift (10 m), while submesoscale currents affect both the horizontal and vertical energy fluxes throughout the mixed layer (50–80 m). There is a slightly weaker forward cascade associated with nonhydrostatic LCs (by 13% in average) than in the hydrostatic case, but overall the simulation differences are small. A vertical mixing scheme K-profile parameterization (KPP) partially augmented by Langmuir turbulence yields wider LCs, which can lead to lower surface velocity gradients compared to solutions using the standard KPP scheme.

A Fine Grid Tide-Wave-Ocean Circulation Coupled Model for the Yellow Sea: Comparison of Turbulence Closure Schemes in Reproducing Temperature Distributions

The performance of three turbulence closure schemes (TCSs), the generic length scale scheme (GLS), the Mellor–Yamada 2.5 scheme (MY2.5) and the K-profile parameterization scheme (KPP), embedded in the ocean model ROMS, was compared with attention to the reproduction of summertime temperature distribution in the Yellow Sea. The ROMS model has a horizontal resolution of 1/30° and 30 vertical sigma layers. For model validation, root mean square errors were checked, comparing model results with wave and temperature buoy data as well as tidal station data supplied by various organizations within the Republic of Korea. Computed temperature and vertical temperature diffusion coefficients were mainly compared along Lines A (36° N) and B (125° E) crossing the central Yellow Sea, Lines C (32° N) and E (34° N) passing over the Yangtze Bank and Line D off the Taean Peninsula. Calculations showed that GLS and MY2.5 produced vertical mixing stronger than KPP in both the surface and bottom layers, but the overall results were reasonably close to each other. The lack of observational data was a hindrance in comparing the detailed performance between the TCSs. However, it was noted that the simulation capability of cold patches in the tidal mixing front can be useful in identifying the better performing turbulence closure scheme. GLS and MY2.5 clearly produced the cold patch located near the western end of Line E (122° E–122.3° E), while KPP hardly produced its presence. Similar results were obtained along Line D but with a less pronounced tidal mixing front. Along Line C, GLS and MY2.5 produced a cold patch on the western slope of the Yellow Sea, the presence of which had never been reported. Additional measurements near 125° E–126° E of Line C and along the channel off the Taean Peninsula (Line D) are recommended to ensure the relative performance superiority between the TCSs.

Observation of vertical eddy diffusivity and mixing length during landfalling Super Typhoons

Understanding the vertical turbulent mixing processes in the planetary boundary layer (PBL) of tropical cyclones (TCs, or typhoons, hurricanes) and improving the PBL parameterization in numerical models of TCs is of paramount importance for TC modeling and forecasting. Based on the multi-level, high-resolution observations from Asia's tallest meteorological tower, the 356-m-high Shenzhen Meteorological Gradient Tower, this paper investigates the characteristics and vertical profiles of vertical eddy diffusivity and mixing length during two landfalling typhoons, namely Super Typhoons Mangkhut and Hato. The observed vertical eddy diffusivity and mixing length are compared with several widely-used parametrization schemes to assess the performance of the schemes. The results demonstrate that the K-profile parameterization scheme with the coefficient α = 1.5 satisfactorily portrays the magnitude and vertical distribution of the vertical eddy diffusivity. Moreover, a novel parametrization for mixing length is proposed, which is shown effective in reproducing the vertical mixing when used in conjunction with the Mellor–Yamada scheme. This study aims to enhance the understanding of vertical turbulent mixing in TC boundary layer and facilitate the numerical simulation of TCs over land.

Comparing the Performance of Turbulent Kinetic Energy and K-Profile Parameterization Vertical Parameterization Schemes over the Tropical Indian Ocean

The performance of vertical parameterization schemes, namely, turbulent kinetic energy (TKE) and K-profile parameterization (KPP), is evaluated over the domain [30E-120E; 20S-30N] in the Indian Ocean using the Nucleus for European Modeling of the Ocean (NEMO) regional model. The surface and sub-surface hydrography and mixed layer depth (MLD) of the simulations using TKE and KPP schemes have been compared. The KPP scheme produces higher bias (∼0.5 °C) of sea surface temperature (SST) in monsoon and post-monsoon seasons, which reduces on using the TKE scheme. The maximum surface salinity difference (0.45 psu) between TKE and KPP simulations is obtained over the head Bay of Bengal (BoB) in the post-monsoon months. The KPP scheme also overestimates MLD of the region. Barring highly convective regions as well as regions marked with very low and rapidly changing salinity, the TKE scheme performs better than KPP scheme in simulating the hydrography and MLD of the region. The differences between TKE and KPP simulations in the vertical stability and mixing are studied using buoyancy frequency, vertical shear of horizontal currents and energy required for mixing as quantifiers. The mixed layer heat budget analysis explains seasonal variability of SST and differences in vertical mixing parameterizations.

Max Planck Institute Earth System Model (MPI-ESM1.2) for the High-Resolution Model Intercomparison Project (HighResMIP)

Abstract. As a contribution towards improving the climate mean state of the atmosphere and the ocean in Earth system models (ESMs), we compare several coupled simulations conducted with the Max Planck Institute for Meteorology Earth System Model (MPI-ESM1.2) following the HighResMIP protocol. Our simulations allow to analyse the separate effects of increasing the horizontal resolution of the ocean (0.4 to 0.1∘) and atmosphere (T127 to T255) submodels, and the effects of substituting the Pacanowski and Philander (PP) vertical ocean mixing scheme with the K-profile parameterization (KPP). The results show clearly distinguishable effects from all three factors. The high resolution in the ocean removes biases in the ocean interior and in the atmosphere. This leads to the important conclusion that a high-resolution ocean has a major impact on the mean state of the ocean and the atmosphere. The T255 atmosphere reduces the surface wind stress and improves ocean mixed layer depths in both hemispheres. The reduced wind forcing, in turn, slows the Antarctic Circumpolar Current (ACC), reducing it to observed values. In the North Atlantic, however, the reduced surface wind causes a weakening of the subpolar gyre and thus a slowing down of the Atlantic meridional overturning circulation (AMOC), when the PP scheme is used. The KPP scheme, on the other hand, causes stronger open-ocean convection which spins up the subpolar gyres, ultimately leading to a stronger and stable AMOC, even when coupled to the T255 atmosphere, thus retaining all the positive effects of a higher-resolved atmosphere.

A Modified Vertical Mixing Parameterization for Its Improved Ocean and Coupled Simulations in the Tropical Pacific

AbstractClimate models suffer from significant biases over the tropical Pacific Ocean, including a too-cold cold tongue and too-warm temperature at the depth of the thermocline. The emergence of model biases can be partly attributed to vertical mixing parameterizations, in which there are great uncertainties in selections of functional forms and empirical parameters. In this paper, the impacts of two different vertical mixing schemes on the tropical Pacific temperature simulations are investigated using version 5 of the Modular Ocean Model (MOM5). One vertical mixing scheme is the widely used K-profile parameterization (KPP) scheme, and the other is a hybrid mixing scheme (the Chen scheme) by combining a Kraus–Turner-type bulk mixed layer (ML) model with Peters et al.’s shear instability mixing model (PGT model). It is shown that the Chen scheme works better than the KPP scheme for SST simulation but produces an exaggerated subsurface warm bias simultaneously. The better SST simulation can be attributed to the employment of the PGT model, which produces lower levels of shear instability mixing than its counterpart in the KPP scheme. Furthermore, a modified KPP scheme is presented in which its shear instability mixing model and constant background diffusivity are replaced by the PGT model and the Argo-derived background diffusivity, respectively. This new scheme is then employed into MOM5-based ocean-only and coupled simulations, demonstrating substantial improvements in temperature simulations over the tropical Pacific. The modified KPP scheme can be easily employed into other ocean models, offering an effective way to improve ocean simulations.

Evaluation of Planetary Boundary Layer Simulation in GFDL Atmospheric General Circulation Models

This study describes the performance of two Geophysical Fluid Dynamics Laboratory (GFDL) atmospheric general circulation models (AGCMs) in simulating the climatologies of planetary boundary layer (PBL) parameters, with a particular focus on the diurnal cycles. The two models differ solely in the PBL parameterization: one uses a prescribed K-profile parameterization (KPP) scheme with an entrainment parameterization, and the other employs a turbulence kinetic energy (TKE) scheme. The models are evaluated through comparison with the reanalysis ensemble, which is generated from European Centre for Medium-Range Weather Forecasts (ECMWF) twentieth-century reanalysis (ERA-20C), ERA-Interim, NCEP CFSR, and NASA MERRA, and the following systematic biases are identified. The models exhibit widespread cold biases in the high latitudes, and the biases are smaller when the KPP scheme is used. The diurnal cycle amplitudes are underestimated in most dry regions, and the model with the TKE scheme simulates larger amplitudes. For the near-surface winds, the models underestimate both the daily means and the diurnal amplitudes; the differences between the models are relatively small compared to the biases. The role of the PBL schemes in simulating the PBL parameters is investigated through the analysis of vertical profiles. The Sahara, which is suitable for focusing on the role of vertical mixing in dry PBLs, is selected for a detailed analysis. It reveals that compared to the KPP scheme, the heat transport is weaker with the TKE scheme in both convective and stable PBLs as a result of weaker vertical mixing, resulting in larger diurnal amplitudes. Lack of nonlocal momentum transport from the nocturnal low-level jets to the surfaces appears to explain the underestimation of the near-surface winds in the models.

수직 혼합 모수화 기법과 탁도에 따른 황해 수온 민감도 실험

Accurate prediction of sea water temperature has been emphasized to make precise local weather forecast and to understand change of ecosystem. The Yellow Sea, which has turbid water and strong tidal current, is an unique shallow marginal sea. It is essential to include the effects of the turbidity and the strong tidal mixing for the realistic simulation of temperature distribution in the Yellow Sea. Evaluation of ocean circulation model response to vertical mixing scheme and turbidity is primary objective of this study. Three-dimensional ocean circulation model(Regional Ocean Modeling System) was used to perform numerical simulations. Mellor- Yamada level 2.5 closure (M-Y) and K-Profile Parameterization (KPP) scheme were selected for vertical mixing parameterization in this study. Effect of Jerlov water type 1, 3 and 5 was also evaluated. The simulated temperature distribution was compared with the observed data by National Fisheries Research and Development Institute to estimate model`s response to turbidity and vertical mixing schemes in the Yellow Sea. Simulations with M-Y vertical mixing scheme produced relatively stronger vertical mixing and warmer bottom temperature than the observation. KPP scheme produced weaker vertical mixing and did not well reproduce tidal mixing front along the coast. However, KPP scheme keeps bottom temperature closer to the observation. Consequently, numerical ocean circulation simulations with M-Y vertical mixing scheme tends to produce well mixed vertical temperature structure and that with KPP vertical mixing scheme tends to make stratified vertical temperature structure. When Jerlov water type is higher, sea surface temperature is high and sea bottom temperature is low because downward shortwave radiation is almost absorbed near the sea surface.

Wave-modified Ekman current solutions for the vertical eddy viscosity formulated by K-Profile Parameterization scheme

A Fourier series solution is presented for the time-dependent wave-modified Ekman current resulting from the Stokes drift, wind input and wave dissipation for the vertical eddy viscosity formulated by the K-Profile Parameterization scheme. An exact steady solution can be concluded as a special example. The parameters involved in the solution can be determined by the two-dimensional surface wave spectrum, wind vector, the Coriolis parameter and the densities of air and water. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with those when wave is absent or includes only the effect of the Stokes drift by using the extended Donelan and Pierson (1987) spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. The exact solutions are also compared with well-known published observational data of the Ekman layer. It is shown that the solution presented is a reasonable analytic current model with the right dependence on wind, wave and Coriolis parameter for unstratified Ekman layer.

Application of wave‐induced vertical mixing to the K profile parameterization scheme

Surface‐wave‐induced vertical mixing is incorporated to modify the K profile parameterization (KPP) scheme. The effects of this modified KPP scheme on a quasi‐global oceanic general circulation model are examined by carrying out four test cases. To evaluate simulated upper layer temperature and surface mixed‐layer depth (MLD), the model seasonal cycle of temperature and MLD are compared with those from Levitus climatology. In this study, the MLD is defined as the depth that the temperature has changed 0.8°C from the reference depth of 10 m. Statistic analysis shows that test cases with the addition of wave‐induced vertical mixing can reduce the root‐mean‐square difference of upper layer temperature and increase the correlation with Levitus climatology. On the basis of the comparison with Levitus climatology, the surface‐wave‐induced mixing improves the simulation of MLD in summertime for both hemispheres. Comparing the MLD in different seasons, the wave‐induced mixing improves MLD in both hemispheres in summer more than in other seasons. The simulation results are sensitive to weighting coefficients of the wave‐induced mixing, suggesting that a preferred weighting coefficient be between 0.1 and 0.3 in the modified KPP scheme.

Sensitivity to Surface Forcing and Boundary Layer Mixing in a Global Ocean Model: Annual-Mean Climatology

Abstract The effects of more realistic bulk forcing boundary conditions, a more physical subgrid-scale vertical mixing parameterization, and more accurate bottom topography are investigated in a coarse-resolution, global oceanic general circulation model. In contrast to forcing with prescribed fluxes, the bulk forcing utilizes the evolving model sea surface temperatures and monthly atmospheric fields based on reanalyses by the National Centers for Environmental Prediction and on satellite data products. The vertical mixing in the oceanic boundary layer is governed by a nonlocal K-profile parameterization (KPP) and is matched to parameterizations of mixing in the interior. The KPP scheme is designed to represent well both convective and wind-driven entrainment. The near- equilibrium solutions are compared to a baseline experiment in which the surface tracers are strongly restored everywhere to climatology and the vertical mixing is conventional with constant coefficients, except where there is either conve...

Introduction to nonlinear science

A Fourier series solution is presented for the time-dependent wave-modified Ekman current resulting from the Stokes drift, wind input and wave dissipation for the vertical eddy viscosity formulated by the K-Profile Parameterization scheme. An exact steady solution can be concluded as a special example. The parameters involved in the solution can be determined by the two-dimensional surface wave spectrum, wind vector, the Coriolis parameter and the densities of air and water. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with those when wave is absent or includes only the effect of the Stokes drift by using the extended Donelan and Pierson (1987) spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. The exact solutions are also compared with well-known published observational data of the Ekman layer. It is shown that the solution presented is a reasonable analytic current model with the right dependence on wind, wave and Coriolis parameter for unstratified Ekman layer.