BACkground Conditions And low- frequenCy vAriABility. Some elements of weather and higher-frequency climate variability that are targeted by YOTC depend on characteristics of the conditions set up by lower-frequency climate variability. For example, the spatial characteristics and manifestations of intraseasonal variability (e.g., MJO) can be modified by the conditions of ENSO and the Indian Ocean dipole (e.g., Hendon et al. 1999; Kessler 2001; Waliser et al. 2001; Lau 2005; Hendon et al. 2007; Rao et al. 2007; Ajayamohan et al. 2009). Moreover, these low-frequency tropical climate conditions influence the manifestations of extratropical patterns of atmospheric variability (e.g., Horel and Wallace 1982; Renwick and Wallace 1996; Kumar and Hoerling 1998; Newman and Sardeshmukh 1998; Wallace 2000; Ambaum et al. 2001; Giannini et al. 2001; Hastenrath and Greischar 2001; Ostermeier and Wallace 2003). For these reasons, we begin by documenting the background conditions and evolution of low-frequency climate patterns, including a couple of the more significant extratropical modes of climate variability. Figure 1 shows the anomalous characteristics of sea surface temperature (SST) in the three tropical ocean basins during the YOTC period. Starting with the Pacific, the early half the YOTC period is characterized by modest La Niña conditions, while the latter half is characterized by modest El Niño conditions. Closer examination shows that the 2008/09 boreal winter period is cool and the 2009/10 boreal winter period is warm, both spring-to-summer periods tend to exhibit warming conditions, and the 2008 (2009) boreal fall undergoes cooling (warming) conditions. Overall the largest and longer-lived anomalous conditions tend to be more strongly exhibited in the western half of the Pacific basin compared to the eastern half. This evolution in anomalous SST (i.e. La Niña vs El Niño) between the first half and the second half of the YOTC period represents an excellent contrast for studying its effects on tropicalconvection characteristics.
Ann Shelly 1 , Prince Xavier 1 , Dan Copsey 1 , Tim Johns 1 , José M. Rodr´ıguez 1 , Sean Milton 1 , and Nicholas Klingaman 2
1 Met Oﬃce, Exeter, UK, 2 Department of Meteorology, University of Reading, Reading, UK
Abstract This study investigates the impact of a full interactive ocean on daily initialized 15 day hindcasts of the Madden-Julian Oscillation (MJO), measured against a Met Oﬃce Uniﬁed Model atmosphere control simulation (atmospheric general circulation model (AGCM)) during a 3 month period of the Year of TropicalConvection. Results indicate that the coupled conﬁguration (coupled general circulation model (CGCM)) extends MJO predictability over that of the AGCM, by up to 3–5 days. Propagation is improved in the CGCM, which we partly attribute to a more realistic phase relationship between sea surface temperature (SST) and convection. In addition, the CGCM demonstrates skill in representing downwelling oceanic Kelvin and Rossby waves which warm SSTs along their trajectory, with the potential to feedback on the atmosphere. These results imply that an ocean model capable of simulating internal ocean waves may be required to capture the full eﬀect of air-sea coupling for the MJO.
Numerical model simulations show that when convection occurs in an environment of non-zero vertical vorticity, updraughts amplify the vorticity by the process of vortex-tube stretching (Hendricks et al. 2004, Saunders and Montgomery 2004, Montgomery et al. 2006, Nguyen et al. 2008, Rozoff 2007, Wissmeier and Smith 2011). Using a cloud model, Wissmeier and Smith (2011) showed that even moderately deep clouds can produce a large amplification (by one to two orders of magnitude) of the vertical component of absolute vorticity on time scales of an hour, and even for a background rotation rate typical of the undisturbed tropical atmosphere. The vorticity so produced has a maximum in the lower troposphere and persists long after the initial updraught has decayed. The authors showed also that the induced tangential wind speeds by a single updraught are typically no more than a few meters per second with a horizontal scale on the order of a kilometer, and would be barely detectable by normal measurement methods in the presence of an ambient wind field. Their results suggest that all tropicalconvection away from the equator is vortical to some degree and can significantly amplify the vertical vorticity locally. It is not hard to imagine, then, that the stretching of vertical vortex tubes by a developing cumulus cloud is a fundamental process and that it may be an important process in tropical cyclogenesis. In fact, vortical convective clouds have been identified as fundamental building blocks during both the tropical cyclone genesis and intensification process (Hendricks et al. 2004, Montgomery et al. 2006, Nguyen et al. 2008, Braun et al. 2010, Fang and Zhang 2010).
the theory can be applied to three-dimensional cases with non-idealised wind profiles. The large standard deviations for the shear ratios and angles make it difficult to provide thresholds for which new cells can be expected. Furthermore, there are regions where the amount of shear ahead of and behind the leading edge of the cold pool seem to be comparable, but no new cell development occurs (see Fig. 5.10b, red box). In these cases, convection might be suppressed due to unfavourable mid-tropospheric environments (Wilson and Schreiber 1986, Rao and Fuelberg 2000). Lafore and Moncrieff (1989, 1990) studied the organisation and interaction of convective regions of tropical squall lines and found that the strength and form of the low-level shear is important for the longevity and intensity of these storm systems, a result that is consistent with the RKW-theory. However, when systems with extensive stratiform regions are considered, other factors can influence the evolution and characteristics of the storm system, such as the wind profile in the mid- to upper-levels, and the differential movement of convective cells. Thus, while the fulfilment of the RKW-criterion might be a necessary condition, it is not always sufficient for convective development.
While convection stabilizes the large scale environment on time scales given by the gravity wave speed, the large scale forcing acts on much slower timescales. In particular, while the large scale forcing changes on time scales of about a day or longer (Arakawa and Schubert, 1974), Cohen and Craig (2004) used an atmospheric model simulation to show that con- vection adjusts to a change in the forcing within approximately one hour. This time-scale separation has led to the so called quasi-equilibrium hypothesis, introduced by Arakawa and Schubert (1974), which suggests that convection is in statistical equilibrium with the forc- ing. As the large scale forcing renders the atmosphere unstable to convection at a given rate, convection stabilizes the atmosphere at the same rate. In case of a constant external forcing, this would not be surprising, but that it is a valid approximation despite continually changing external forcing is due to the timescale separation between convective adjustment and the time scale on which the large scale forcing changes. We have already mentioned in section 1.1.3, that this hypothesis is a key ingredient of convection parametrization schemes as it allows the estimation of the convective mass flux from the large scale conditions. So far we have discussed how the combined effect of gravity waves, induced by convective cells, results in large scale stabilization and thus affects the amount, rather than the spatial distribution, of convection. For completeness, we note however that some studies have sug- gested that, as gravity waves spread, they may play a role in the triggering or intensification of convection (e.g. Mapes, 1993; Stephan et al., 2016). On comparing an atmospheric model simulation with observations Stephan et al. (2016), for example, investigated the spreading of gravity waves from two independent convective regions, separated by about 700 kilome- ters. They found that the arrival of a gravity-wave-related, low level, positive vertical velocity perturbation caused by one of the convective cells coincided with a significant increase in convective activity at the second convective cell, potentially indicating a gravity wave in- duced intensification of convection. As the relevance of the impact of gravity wave induced triggering and intensification of new convection is still uncertain we will not consider this mechanism in this thesis.
The overall model configuration was as described in Pearson et al. (2010) based on that used by Lean et al. (2008) who tested the implications for convection over the UK. The UM version 7.1 (Davies et al. 2005) was run as a Local Area Model over a West Africa test region at 3 different resolutions (approximately 12 km, 4 km and 1.5 km) and with a variety of representations of the convection process. The models were one-way nested inside a run from the next coarser domain that provided the initial state and lateral boundary conditions. The 12 km simulations were initialised using analysis fields from the European Centre for Medium-Range Weather Forecasts and updates to the models were subsequently applied solely through the lateral boundary conditions. As a result, the simulations did not run in a “forecast” mode but were still guided by the large-scale circulatory environment. Any comparison with observation must, therefore, be carried out statistically. The domains are plotted in Figure 1. All the domains used a rotated coordinate system with the North pole at [180 ◦ W,79 ◦ N]. The details are summarised in Table I.
To study entrainment and mixing among different types of clouds, I used the high-resolution simulation of tropical oceanic deep convection described in (Khairout- dinov et al., 2010). The simulation was performed with the System for Atmospheric Modeling (SAM) (Khairoutdinov and Randall, 2003). Constant large-scale forcing ide- alized from the Global Atmospheric Research Program’s Atlantic Tropical Experiment (GATE) is applied for 24 simulated hours (no diurnal cycle). SAM is run as a large eddy simulation (LES), in which the grid scale is chosen to be small enough to resolve most of the turbulent eddies responsible for entrainment. The horizontal grid spacing is 100 m with a full domain size of 204.8 km by 204.8 km. There are 256 vertical levels with a spacing of 50 m in the lowest 1 km expanding linearly to a spacing of 100 m by 5 km height. Because this simulation contains one billion grid points, it is called the Giga-LES. Convection in the simulation reaches a statistically steady state after 12 hours, and all analysis is performed on the second 12 hours of the simulation. The Giga-LES domain is large enough to contain many deep cumulonimbus size clouds as well as many smaller cumulus congestus and cumulus humilis size clouds throughout their life-cycles.
A photograph o f the basic apparatus consisting o f the convection tank mounted on the rotating table is shown in Figure 3.1. The experim ents were conducted in a rectangular perspex cavity o f height H = 15cm, length L = 200cm and width B = 60cm, giving a fixed longitudinal aspect ratio o f A = 0.075. H eat exchangers formed the two vertical end walls of the tank (Figure 3.2) and consisted of a 3.0cm thick aluminium block with 1.2cm square grooves through which heated or cooled water was pumped. To ensure an even temperature distribution over the heat exchanger surface, a 1.0cm thick block of copper was in contact with the working fluid. Copper was chosen because o f its high therm al conductivity and adequate resistance to corrosion. Thermistors embedded in the copper and aluminium plates allowed both the temperature gradient between the plates, and the temperature in contact with the fluid to be measured. With the end walls calibrated (Appendix A), the heat flux into the fluid could be calculated from the temperature gradient. Three hypodermic tubes inserted through the end walls allowed dye to be continuously gravity fed into the fluid to visualize the flow.
When the corrugation is placed at the lower plate, the most intense convection occurs for the corrugation wavelengths comparable to the slot height. The intensity of convection rapidly decreases as the corrugation wavelength is either increased or decreased away from its optimum. It has been found that the optimal wavelength corresponds to 1.53 regardless of the Rayleigh number Ra, the Prandtl number Pr and the corrugation amplitude. The intensity of convection initially increases proportionally Ra and then its growth rapidly accelerates when Ra approaches conditions giving rise to secondary flows in smooth slots. An increase of the corrugation amplitude results in an increase of the convection intensity proportionally to the amplitude but the system begins to saturate and the growth slows down when an excessively large amplitude is used. Transfer of the corrugation to the upper plate results in a similar convection whose properties can be deduced from the properties of convection occurring when the corrugation is placed at the lower plate. Placement of corrugations on both plates may either significantly increase or decrease the convection intensity depending on the phase shift between both corrugation systems. The most intense convection results from the phase shift c = 0
In the preceding sections we have considered largely external natural convection in which the ambient medium away from the ﬂow is extensive and stationary. However, there are many natural convection ﬂows that occur within enclosed regions, such as ﬂows in rooms and buildings, cooling towers, solar ponds, and furnaces. The ﬂow domain may be completely enclosed by solid boundaries or may be a partial enclosure with openings through which exchange with the ambient occurs. There has been growing interest and research activity in buoyancy-induced ﬂows arising in partial or complete enclosures. Much of this interest has arisen because of applications such as cooling of electronic circuitry (Jaluria, 1985b; Incropera, 1999), building ﬁres (Emmons, 1978, 1980), materials processing (Jaluria, 2001), geothermal energy extraction (Torrance, 1979), and environmental processes. The basic mechanisms and heat transfer results in internal natural convection have been reviewed by several researchers, such as Yang (1987) and Ostrach (1988). Some of the important basic considerations are presented here.
The shredding radius is calculated as described in Section 2.1. In Figures 6 and 8, the shredding radii of each companion are marked with an X. As the companion inspirals, it releases energy with the decreasing orbital radius. For companions which tidally disrupt closer to the primary’s core, the change in orbital energy, and thus the energy that can contribute to unbinding the envelope, is greater than for those companions which disrupt closer to the surface. The energy that can contribute to unbinding the envelope will be maximized if the companion’s shredding radius is deeper than the lower boundary of the SCCR. The convection within the SCCR aids in reducing the energy available for unbinding the envelope, as it carries the energy to the surface to be radiated away. This is discussed further in Section 3.
Like many other natural-convection flows, for faster convergence Boussinesq model has been used. This model treats density as a constant value (which has been supplied as the Material Property taking air as a working fluid) in all transport equations, except for the buoyancy term in the momentum equation. As the Boussinesq ap- proximation is only valid when the temperature differ- ence between the hotter and cooler wall is less where as for the present numerical experimentation that has been always considered as 50˚C for air as working fluid [1,6]. All the relevant material properties for working fluid and
evolution of sublithospheric convection is studied using two-dimensional whole mantle convection models with temperature- and depth-dependent viscosity and an endothermic phase transition. Scaling laws for the breakdown of layered convection as well as the strength of convection are derived as a function of viscosity layering, the phase buoyancy parameter, and the thermal Rayleigh number. Our results suggest that layered convection in the upper mantle is maintained only for a couple of overturns, with plausible mantle values. Furthermore, scaling laws for the onset of convection, the stable Richter rolls, and the breakdown of layered convection are all combined to delineate possible dynamic regimes beneath evolving lithosphere. Beneath long-lived plates, the development of longitudinal convection rolls is suggested to be likely in the upper mantle, as well as its subsequent breakdown to whole mantle-scale convection. This evolutionary path is suggested to be consistent with the seismic structure of the Pacific upper mantle. I NDEX T ERMS : 3040 Marine Geology and Geophysics: Plate tectonics (8150, 8155, 8157, 8158); 8120 Tectonophysics: Dynamics of lithosphere and mantle—general; 8121 Tectonophysics: Dynamics, convection currents and mantle plumes; 8180 Tectonophysics: Tomography; K EYWORDS : convection, upper mantle, scaling laws
 Rahman, M. M., Öztop, H. F., Rahim, N. A., Saidur, R., & Al- Salem, K. (2011). MHD mixed convection with joule heating effect in a lid-driven cavity with a heated semi- circular source using the finite element technique. Numerical Heat Transfer, Part A: Applications, 60(6), 543-560.
Plant “ “tropical forest refugia tropical forest refugia” ” based based on centers of plant diversity are on centers of plant diversity are correlated with areas of wet correlated with areas of wet conditions during dry periods conditions during dry periods — the Refugia Debate
the western Mediterranean, the model was run using the two-way interactive grid-nesting method (Stein et al. 2000) with two nested grids, a horizontal grid mesh of 15 and 2.5 km and a vertical grid with 62 levels. Otherwise, the model was run with the coarser grid only. The model includes parameterisations for radiation (Mlawer et al. 1997), turbulence (Cuxart et al. 2000), subgrid shallow convection (Pergaud et al. 2009), mixed-phase microphysics (Pinty and Jabouille 1998), subgrid cloud cover and condensate content (Chaboureau and Bechtold 2005) and surface exchanges (Masson et al. 2013). The convection scheme of Bechtold et al. (2001), was activated for the 15-km grid, while convection was assumed to be explicitly resolved for the 2.5-km grid (648 by 480 grid points, see the domain in Figure 8). From the model outputs available every 3 hours, brightness temperatures were computed using the radiative transfer code RTTOV (Radiative Transfer for Tiros Operational Vertical Sounder) version 11 (Saunders et al. 2005). The scattering properties of frozen hydrometeors were those calculated by Geer and Baordo (2014) for dendrite snowflakes using the discrete dipole approximation, while precomputed Mie tables were used for other hydrometeors. The simulation of brightness temperatures from the model outputs allowed a direct comparison with passive microwave observations. Such a comparison, the so-called model-to-satellite approach has already been performed successfully at various wavelengths and has shown the overall performance of the Meso-NH model to correctly predict cloud and rain fields (Chaboureau et al. 2008; S¨ohne et al. 2008; Clark and Chaboureau 2010; Chaboureau et al. 2012a,b, amongst others). In this study, the comparison is restricted to the inner model (2.5-km grid) where the convection is resolved. For each mesh point of the model, the MHS synthetic brightness temperatures are computed and the DC and COV criteria are applied. The normalised occurrence of DC and COV is then computed for a 0.2 ˚ grid to be compared with those derived from MHS observations.
Tropical algebraic geometry is a piecewise linear shadow of algebraic geometry, in which varieties are replaced by polyhedral complexes. This area has grown significantly in the past decade and has had great success in numerous applications, such as Mikhalkin’s calculation of Gromov- Witten invariants of P 2 [Mik05], the work of Cools-Draisma-Payne-Robeva [CDPR12] and Jensen- Payne [JP14,JP16] on Brill-Noether theory, and the Gross-Siebert program in mirror symmetry [Gro11].
∂y = s(x, y, t), (15) where p, q are positive diﬀusion coeﬃcients, and a(x, y), b(x, y) are variable convection coeﬃcients in x- and y-directions, respectively. Therefore, the unique solvability of nu- merical solution of the CCD method for solving the above 2D/3D unsteady convection- diﬀusion equations subject to periodic boundary conditions can also be obtained. How- ever, the results obtained in this paper cannot be directly adopted for the fractional order case as given in [37, 38].