Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Müller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.

Structure oil-absorption relationships during deep-fat frying

Analysis of the oil-absorption process in deep-fat fried potato cylinders (frying temperatures of 155degreesC, 170degreesC, and 185degreesC) allowed to distinguish 3 oil fractions: structural oil (absorbed during frying), penetrated surface oil (suctioned during cooling), and surface oil. Results showed that a small amount of oil penetrates during frying because most of the oil was picked up at the end of the process, suggesting that oil uptake and water removal are not synchronous phenomena. After cooling, oil was located either on the surface of the chip or suctioned into the porous crust microstructure, with an inverse relationship between them for increasing frying times.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

Initiation of deep convection at marginal instability in an ensemble of mesoscale models: a case-study from COPS

The present study investigates the initiation of precipitating deep convection in an ensemble of convection-resolving mesoscale models. Results of eight different model runs from five non-hydrostatic models are compared for a case of the Convective and Orographically-induced Precipitation Study (COPS). An isolated convective cell initiated east of the Black Forest crest in southwest Germany, although convective available potential energy was only moderate and convective inhibition was high. Measurements revealed that, due to the absence of synoptic forcing, convection was initiated by local processes related to the orography. In particular, the lifting by low-level convergence in the planetary boundary layer is assumed to be the dominant process on that day. The models used different configurations as well as different initial and boundary conditions. By comparing the different model performance with each other and with measurements, the processes which need to be well represented to initiate convection at the right place and time are discussed. Besides an accurate specification of the thermodynamic and kinematic fields, the results highlight the role of boundary-layer convergence features for quantitative precipitation forecasts in mountainous terrain.

Cloud-resolving simulations of deep convection over a heated mountain

Cloud-resolving numerical simulations of airflow over a diurnally heated mountain ridge are conducted to explore the mechanisms and sensitivities of convective initiation under high pressure conditions. The simulations are based on a well-observed convection event from the Convective and Orographically Induced Precipitation Study (COPS) during summer 2007, where an isolated afternoon thunderstorm developed over the Black Forest mountains of central Europe, but they are idealized to facilitate understanding and reduce computational expense. In the conditionally unstable but strongly inhibited flow under consideration, sharp horizontal convergence over the mountain acts to locally weaken the inhibition and moisten the dry midtroposphere through shallow cumulus detrainment. The onset of deep convection occurs not through the deep ascent of a single updraft but rather through a rapid succession of thermals that are vented through the mountain convergence zone into the deepening cloud mass. Emerging thermals rise through the saturated wakes of their predecessors, which diminishes the suppressive effects of entrainment and allows for rapid glaciation above the freezing level as supercooled cloud drops rime onto preexisting ice particles. These effects strongly enhance the midlevel cloud buoyancy and enable rapid ascent to the tropopause. The existence and vigor of the convection is highly sensitive to small changes in background wind speed U0, which controls the strength of the mountain convergence and the ability of midlevel moisture to accumulate above the mountain. Whereas vigorous deep convection develops for U0 = 0 m s−1, deep convection is completely eliminated for U0 = 3 m s−1. Although deep convection is able to develop under intermediate winds (U0 = 1.5 m s−1), its formation is highly sensitive to small-amplitude perturbations in the initial flow.

Moisture vertical structure, column water vapor, and tropical deep convection

The vertical structure of the relationship between water vapor and precipitation is analyzed in 5 yr of radiosonde and precipitation gauge data from the Nauru Atmospheric Radiation Measurement (ARM) site. The first vertical principal component of specific humidity is very highly correlated with column water vapor (CWV) and has a maximum of both total and fractional variance captured in the lower free troposphere (around 800 hPa). Moisture profiles conditionally averaged on precipitation show a strong association between rainfall and moisture variability in the free troposphere and little boundary layer variability. A sharp pickup in precipitation occurs near a critical value of CWV, confirming satellite-based studies. A lag–lead analysis suggests it is unlikely that the increase in water vapor is just a result of the falling precipitation. To investigate mechanisms for the CWV–precipitation relationship, entraining plume buoyancy is examined in sonde data and simplified cases. For several different mixing schemes, higher CWV results in progressively greater plume buoyancies, particularly in the upper troposphere, indicating conditions favorable for deep convection. All other things being equal, higher values of lower-tropospheric humidity, via entrainment, play a major role in this buoyancy increase. A small but significant increase in subcloud layer moisture with increasing CWV also contributes to buoyancy. Entrainment coefficients inversely proportional to distance from the surface, associated with mass flux increase through a deep lower-tropospheric layer, appear promising. These yield a relatively even weighting through the lower troposphere for the contribution of environmental water vapor to midtropospheric buoyancy, explaining the association of CWV and buoyancy available for deep convection.