Zavisa Janjic

The Step-Mountain Eta Coordinate Model: Further Developments of the Convection, Viscous Sublayer, and Turbulence Closure Schemes

Abstract The step-mountain eta model has shown a surprising skill in forecasting severe storms. Much of the credit for this should be given to the Betts and Miller (hereafter referred to as BM) convection scheme and the Mellor-Yamada (hereafter referred to as MY) planetary boundary layer (PBL) formulation. However, the eta model was occasionally producing heavy spurious precipitation over warm water, as well as widely spread light precipitation over oceans. In addition, the convective forcing, particularly the shallow one, could lead to negative entropy changes. As the possible causes of the problems, the convection scheme, the processes at the air-water interface, and the MY level 2 and level 2.5 PBL schemes were reexamined. A major revision of the BM scheme was made, a new marine viscous sublayer scheme was designed, and the MY schemes were retuned. The deep convective regimes are postulated to be characterized by a parameter called “cloud efficiency.” The relaxation time is extended for low cloud effic...

The Step-Mountain Coordinate: Physical Package

Abstract A comprehensive physical package has been developed for a regional eta coordinate model with the steplike mountain representation. This paper describes the basic problems, concepts and numerical techniques developed, and reviews primarily those aspects of the performance of the model which reflect the effects of the parameterized physical processes. The Level 2.5 turbulence closure model in the Mellor-Yamada hierarchy was chosen to represent the turbulence above the surface layer. A severe instability encountered in the early experiments in the turbulent kinetic energy (TKF) equation was found to be of a numerical origin. The instability was removed by a suitably designed time-differencing scheme. As implemented in the eta-coordinate model, the Level 2.5 turbulence closure model is computationally remarkably inexpensive. An unconditionally stable, trivially implicit, time-differencing scheme is proposed for the vertical diffusion. The Mellor-Yamada Level 2 turbulence closure scheme is used for th...

The Step-Mountain Coordinate: Model Description and Performance for Cases of Alpine Lee Cyclogenesis and for a Case of an Appalachian Redevelopment

Abstract The problem of the pressure gradient force error in the case of the terrain-following (sigma) coordinate does not appear to have a solution. The problem is not one of truncation error in the calculation of space derivatives involved. Thus, with temperature profiles resulting in large errors, an increase in vertical resolution may not reduce and is even likely to increase the error. Therefore, an approach abandoning the sigma system has been proposed. It involves the use of “step” mountains with coordinate surfaces prescribed to remain at fixed elevations at places where they touch (and define) or intersect the ground surface. Thus, the coordinate surfaces are quasi-horizontal, and the sigma system problem is not present. At the same time, the simplicity of the sigma system is maintained. In this paper, design of the model (“silhouette” averaged) mountains, properties of the wall boundary condition, and the scheme for calculation of the potential to kinetic energy conversion are presented. For an ...

Assessment of the Land Surface and Boundary Layer Models in Two Operational Versions of the NCEP Eta Model Using FIFE Data

Abstract Data from the 1987 summer FIFE experiment for four pairs of days are compared with corresponding 48-h forecasts from two different versions of the Eta Model, both initialized from the NCEP–NCAR (National Centers for Environmental Prediction–National Center for Atmospheric Research) global reanalysis. One used the late 1995 operational Eta Model physics, the second, with a new soil and land surface scheme and revisions to the surface layer and boundary layer schemes, used the physics package that became operational on 31 January 1996. Improvements in the land surface parameterization and its interaction with the atmosphere are one key to improved summer precipitation forecasts. The new soil thermal model is an improvement over the earlier slab soil model, although the new skin temperature generally now has too large a diurnal cycle (whereas the old surface temperature had too small a diurnal cycle) and is more sensitive to net radiation errors. The nighttime temperature minima are often too low, b...

Nonlinear advection schemes and energy cascade on semi-staggered grids

Abstract A common problem with nonlinear advection schemes is the false accumulation of energy at the smallest resolvable scales. To keep this process under control, following Arakawa (1966), a number of energy and enstrophy conserving schemes for staggered and semi-staggered grids have been designed. In this paper, it is demonstrated that, in contrast to the staggered grid, the conservation of energy and enstrophy on the semi-staggered gods does not guarantee that the erroneous transport of energy from large to small scales will be effectively restricted. Using a new approach to the application of the Arakawa Jacobian, a scheme for a semi-staggered grid which exactly reflects the Arakawa theory for nondivergent flow is obtained for the first time. This is achieved by conservation of energy and enstrophy as defined on the staggered grid. These two quantities are of higher accuracy and cannot be calculated directly from the dependent variables on the semi-staggered grid. It is further demonstrated that the...

Assessment of Dynamic Downscaling of the Continental U.S. Regional Climate Using the Eta/SSiB Regional Climate Model

Abstract This study investigates the capability of the dynamic downscaling method (DDM) in a North American regional climate study using the Eta/Simplified Simple Biosphere (SSiB) Regional Climate Model (RCM). The main objective is to understand whether the Eta/SSiB RCM is capable of simulating North American regional climate features, mainly precipitation, at different scales under imposed boundary conditions. The summer of 1998 was selected for this study and the summers of 1993 and 1995 were used to confirm the 1998 results. The observed precipitation, NCEP–NCAR Global Reanalysis (NNGR), and North American Regional Reanalysis (NARR) were used for evaluation of the model’s simulations and/or as lateral boundary conditions (LBCs). A spectral analysis was applied to quantitatively examine the RCM’s downscaling ability at different scales. The simulations indicated that choice of domain size, LBCs, and grid spacing were crucial for the DDM. Several tests with different domain sizes indicated that the model...

The Impact of Land Surface Processes on Simulations of the U.S. Hydrological Cycle: A Case Study of the 1993 Flood Using the SSiB Land Surface Model in the NCEP Eta Regional Model

Abstract This paper describes a methodology for coupling the Simplified Simple Biosphere Model (SSiB) to the regional Eta Model of the National Centers for Environmental Prediction (NCEP), and presents the application of the coupled system in regional simulation studies. The coupled Eta–SSiB model is used to study the impact of land surface processes and land surface initialization on the regional water and energy cycle in an extreme climate event, by comparing the results from the Eta–SSiB with those from the Eta–bucket model. Simulations from both models spanned 3 months via a succession of 48-hr simulations over June, July, and August 1993, a summer of heavy flooding in the United States. The monthly and seasonal means from the simulations in both model runs are compared. The Eta–SSiB model produces more realistic monthly mean precipitation over the United States and the flood areas. The improvements are mainly manifested in the intensity of the heavy rainfall and its spatial distribution. The results ...

A Class of Conservative Fourth Order Advection Schemes and Impact of Enhanced Formal Accuracy on Extended Range Forecasts

Starting from three Eulerian second-order nonlinear advection schemes for semi-staggered Arakawa grids B/E, advection schemes of fourth order of formal accuracy were developed. All three second-order advection schemescontrolthenonlinear energycascadeincaseofnondivergentflowbyconservingquadraticquantities. Linearization of all three schemes leads to the same second-order linear advection scheme. The second-order term of the truncation error of the linear advection scheme has a special form so that it can be eliminated by modifying the advected quantity while still preserving consistency. Tests with linear advection of a cone confirm the advantage of the fourth-order scheme. However, if a localized, large amplitude and high wavenumber pattern is present in initial conditions, the clear advantage of the fourth-order scheme disappears. The new nonlinear fourth-order schemes are quadratic conservative and reduce to the Arakawa Jacobian for advected quantities in case of nondivergentflow. In case of generalflow the conservation properties of the new momentum advection schemes impose stricter constraint on the nonlinear cascade than the original second-order schemes. However, for nondivergent flow, the conservation properties of the fourth-order schemes cannot be proven in the same way as those of the original second-order schemes. Therefore, demanding long-term and low-resolution nonlinear tests were carried out in order to investigate how well the fourth-order schemes control the nonlinear energy cascade. All schemes were able to maintain meaningful solutions throughout the test. Finally, the impact was examined of the fourth-order momentum advection on global medium-range forecasts. The 500-hPa anomaly correlation coefficient obtained using the best performing fourth-order scheme did not show an improvement compared to the tests using its second-order counterpart.

A Stable Centered Difference Scheme Free of Two-Grid-Interval Noise

Abstract A procedure leading to a stable space-centered, leapfrog time-differencing scheme, capable of preventing the false two-grid-interval noise that arises when two large-scale solutions are separated an different elementary subgrids, is presented.

The Impact of Spring Subsurface Soil Temperature Anomaly in the Western U.S. on North American Summer Precipitation: A Case Study Using Regional Climate Model Downscaling

[1] This study explores the impact of spring subsurface soil temperature (SUBT) anomaly in the western U.S. on North American summer precipitation, mainly southeastern U.S., and possible mechanisms using a regional climate Eta model and a general circulation model (GCM). The GCM produces the lateral boundary condition (LBC) for the Eta model. Two initial SUBT conditions (one cold and another warm) on May 1st were assigned for the GCM runs and the corresponding Eta runs. The results suggest that antecedent May 1st warm initial SUBT in the western U.S. contributes positive June precipitation over the southern U.S. and less precipitation to the north, consistent with the observed anomalies between a year with a warm spring and a year with a cold spring in the western U.S. The anomalous cyclone induced by the surface heating due to SUBT anomaly propagated eastward through Rossby waves in westerly mean flow. In addition, the steering flow also contributed to the dissipation of perturbation in the northeastern U.S. and its enhancement in southeastern U.S. However, these results were obtained only when the Eta model run was driven by the corresponding GCM run. When the same reanalysis data were applied for both (cold and warm initial SUBT) Eta runs’ LBCs, the precipitation anomalies could not be properly produced, indicating the intimate dependence of the regional climate sensitivity downscaling on the imposed global climate forcing, especially when the impact was through wave propagation in the large-scale atmospheric flow.