Negative Perturbations Research Articles

Mesoscale field‐aligned irregularity structures (FAIs) of airglow associated with medium‐scale traveling ionospheric disturbances (MSTIDs)

AbstractIn this paper, we report the evolution (generation, amplification, and dissipation) of optically observed mesoscale field‐aligned irregularity structures (FAIs) (~150 km) associated with a medium‐scale traveling ionospheric disturbance (MSTID) event. There have not been observations of mesoscale FAIs of airglow before. The mesoscale FAIs were generated in an airglow‐depleted front of southwestward propagating MSTIDs that were simultaneously observed by an all‐sky imager, a GPS monitor, and a digisonde around Xinglong (40.4°N, 30.5° magnetic latitude), China, on 17/18 February 2012. A normalized cross‐correlation method has been used to obtain the velocities of mesoscale FAIs and MSTIDs. The mesoscale FAIs had an obvious northwestward relative velocity to main‐body MSTIDs (about 87.0 m/s on average). The direction of this relative velocity was roughly parallel to the depleted fronts. Furthermore, the evolution of the mesoscale FAIs was mostly controlled by the intensity of the depleted fronts. Occurred in a highly elevated ionosphere that had a total electron content depletion associated with large negative airglow perturbations (−25%), the mesoscale FAIs grew rapidly when they experienced southeastward wind, which had a speed of about 100 m/s and were measured by a Fabry‐Perot interferometer. A northeastward polarization electric field within a depleted airglow front can play a controlling role in the development of the mesoscale FAIs. The electric field can significantly elevate the ionosphere and move the mesoscale FAIs northwestward by the E × B drift. The processes for the generation and development of the polarization electric field and the mesoscale FAIs, however, need further study.

Sobolev inequalities for the Hardy–Schrödinger operator: extremals and critical dimensions

In this survey paper, we consider variational problems involving the Hardy–Schrodinger operator $$L_\gamma :=-\Delta -\frac{\gamma }{|x|^2}$$ on a smooth domain $$\Omega $$ of $$\mathbb {R}^n$$ with $$0\in \overline{\Omega }$$ , and illustrate how the location of the singularity 0, be it in the interior of $$\Omega $$ or on its boundary, affects its analytical properties. We compare the two settings by considering the optimal Hardy, Sobolev, and the Caffarelli–Kohn–Nirenberg inequalities. The latter can be stated as: $$\begin{aligned} C\left( \int _{\Omega }\frac{u^{2^*(s)}}{|x|^s}dx\right) ^{\frac{2}{2^*(s)}}\le \int _{\Omega } |\nabla u|^2dx-\gamma \int _{\Omega }\frac{u^2}{|x|^2}dx \quad \hbox {for all } u\in H^1_0(\Omega ), \end{aligned}$$ where $$\gamma <\frac{n^2}{4},\, s\in [0,2)$$ and $$2^\star (s):=\frac{2(n-s)}{n-2}$$ . We address questions regarding the explicit values of the optimal constant $$C:=\mu _{\gamma , s}(\Omega )$$ , as well as the existence of non-trivial extremals attached to these inequalities. Scale invariance properties often lead to situations where the best constants $$\mu _{\gamma , s}(\Omega )$$ do not depend on the domain, and hence they are not attainable. We consider two different approaches for “breaking the homogeneity” of the problem, and restoring compactness. One approach was initiated by Brezis–Nirenberg, when $$\gamma =0$$ and $$s=0$$ , and by Janelli, when $$\gamma >0$$ and $$s=0$$ . It is suitable for the case where the singularity 0 is in the interior of $$\Omega $$ , and consists of considering lower order perturbations of the critical nonlinearity. The other approach was initiated by Ghoussoub–Kang for $$\gamma =0,\, s>0$$ , and by C.S. Lin et al. and Ghoussoub–Robert, when $$\gamma \ne 0, s\ge 0$$ . It consists of considering domains, where the singularity 0 is on the boundary. Both of these approaches are rich in structure and in challenging problems. If $$0\in \Omega $$ , then a negative linear perturbation suffices for higher dimensions, while a positive “Hardy-singular interior mass” theorem for the operator $$L_\gamma $$ is required in lower dimensions. If the singularity 0 belongs to the boundary $$\partial \Omega $$ , then the local geometry around 0 (convexity and mean curvature) plays a crucial role in high dimensions, while a positive “Hardy-singular boundary mass” theorem is needed for the lower dimensions. Each case leads to a distinct notion of critical dimension for the operator $$L_\gamma $$ .

Dynamics of plasma density perturbations in the upper ionosphere and the magnetosphere under the action of powerful HF radio waves

Dynamics of the density perturbations of the main plasma components (electrons, oxygen and hydrogen ions) in the upper ionosphere and the magnetosphere under the action of powerful HF radio waves is discussed theoretically and numerically. For finite heating pulse and different effective powers the variations of the density perturbations in time at various heights are investigated. We argue that due to collisionless damping the magnetospheric duct along the whole field line is not formed. Instead positive and negative perturbations of the main plasma components propagating with the attenuation in the magnetosphere with two different speeds are predicted. Utilization of pulsed heating provides significant information concerning plasma perturbations in the upper ionosphere and the magnetosphere.

Remote impact of blocking highs on the sudden track reversal of tropical cyclones

Previous work showed that some tropical cyclones (TCs) in the western Pacific Ocean undergo sudden track reversal, and the onset, maintenance and decay of blocking highs (BHs) coexisted with 19 of the studied TCs with sudden track reversal. In these cases, the phase relations between the BH, the continental high (CH), the subtropical high (SH) and the suddenly reversed TCs could be classified into types A, B, C and D. Types C and D were the focal point of this follow-up study, in which Typhoon Pabuk (2007) and Lupit (2009) were employed to conduct numerical simulations. The results showed that the reversed tracks of Pabuk (2007) and Lupit (2009) could have been affected by the BH, particularly in terms of the turning location and the trend of movement after turning. Specifically, the two main features for Pabuk (2007) in the BH perturbations were the deflection of its turning point and a distinct anticlockwise rotation. Lupit (2009) deviated to the southwest and finally made landfall in the Philippines, or experienced further eastward movement, in the perturbed BH. The impact mechanisms can be attributed to the change in the vorticity field transported from the BH, leading to an intensity variation of midlatitude systems. BHs may have a positive feedback effect on the strength of the westerly trough (TR), as indicated by a weakened and strengthened TR corresponding to negative and positive BH perturbations, respectively.

A simulation study of the thermosphere mass density response to substorms using GITM

AbstractThe temporal and spatial variations of the thermospheric mass density during a series of idealized substorms were investigated using the Global Ionosphere Thermosphere Model (GITM). The maximum mass density perturbation of an idealized substorm with a peak variation of hemispheric power (HP) of 50 GW and interplanetary magnetic field (IMF) Bz of −2 nT was ~14% about 50 min after the substorm onset in the nightside sector of the auroral zone. The mass density response to different types of energy input has a strong local time dependence, with the mass density perturbation due to only an IMF Bz variation peaking in the dusk sector and the density perturbation due to only HP variation peaks in the nightside sector. Simulations with IMF Bz changes only and HP changes only showed that the system behaves slightly nonlinearly when both IMF and HP variations are included (a maximum of 6% of the nonlinearity) and that the nonlinearity grows with energy input. The neutral gas heating rate due to Joule heating was of same magnitude as the heating rate due to precipitation, but the majority of the temperature enhancement due to the heating due to precipitation occurs at lower altitude as compared to the auroral heating. About 110 min after onset, a negative mass density perturbation (~−5%) occurred in the night sector, which was consistent with the mass density measurement of the CHAMP satellite.

Theory and experiments of disorder-induced resonance shifts and mode-edge broadening in deliberately disordered photonic crystal waveguides

We study both theoretically and experimentally the effects of introducing deliberate disorder in a slow-light photonic crystal waveguide on the photon density of states. We first introduce a theoretical model that includes both deliberate disorder through statistically moving the hole centres in the photonic crystal lattice and intrinsic disorder caused by manufacturing imperfections. We demonstrate a disorder-induced mean blueshift and an overall broadening of the photonic density of states for various amounts of deliberate disorder. By comparing with measurements from a GaAs photonic crystal waveguide, we find good qualitative agreement between theory and experiment which highlights the importance of carefully including local field effects for modelling high-index contrast perturbations. Our work also demonstrates the importance of using asymmetric dielectric polarizabilities for modelling positive and negative dielectric perturbations when modelling a perturbed dielectric interface in photonic crystal platforms.

Global distribution of mineral dust and its impact on radiative fluxes as simulated by WRF-Chem

Dust aerosols make a considerable contribution to the climate system and atmospheric hydrological cycle through their radiative and ice nuclei effects. This underlines the need for investigating the sources of dust aerosols, their transport pathways, and radiative forcing. Seasonal distribution of mineral dust around the globe and its impact on radiation fluxes is estimated using two simulations: a model setup that did not include dust aerosols; and an interactive experiment that included dust aerosols and their feedback to the atmosphere. Simulations were performed by the Weather Research and Forecasting with Chemistry (WRF-Chem) model for a 1-year period. The global annual mean dust optical depth (DOD) at 0.55 $$\upmu$$ m is estimated to be 0.057, with a spring peak value of 0.081 and an autumn minimum value of 0.039. Seasonal variation of atmospheric dust loading is shown to be associated with similar significant variation in shortwave and longwave direct radiation perturbation by dust, both at the surface and top of the atmosphere (TOA). The presence of mineral dust in the interactive simulation is estimated to exert a maximum net direct radiation perturbation in summer with values of $$-$$ 2.85 and $$-$$ 1.63 W m $$^{-2}$$ in clear-sky conditions at the surface and TOA, respectively. It also exerts a global annual net direct radiation perturbation of $$-$$ 1.86 and $$-$$ 1.09 W m $$^{-2}$$ at the surface and TOA, respectively. The surface cooling is attributed to the extinction of incoming solar radiation by dust aerosols, while negative perturbation at the TOA (which demonstrates cooling of the Earth-atmosphere system) is predominantly attributed to an increase in outgoing shortwave radiation.

A model study of Abrahamsenbreen, a surging glacier in northern Spitsbergen

Abstract. The climate sensitivity of Abrahamsenbreen, a 20 km long surge-type glacier in northern Spitsbergen, is studied with a simple glacier model. A scheme to describe the surges is included, which makes it possible to account for the effect of surges on the total mass budget of the glacier. A climate reconstruction back to AD 1300, based on ice-core data from Lomonosovfonna and climate records from Longyearbyen, is used to drive the model. The model is calibrated by requesting that it produce the correct Little Ice Age maximum glacier length and simulate the observed magnitude of the 1978 surge. Abrahamsenbreen is strongly out of balance with the current climate. If climatic conditions remain as they were for the period 1989–2010, the glacier will ultimately shrink to a length of about 4 km (but this will take hundreds of years). For a climate change scenario involving a 2 m year−1 rise of the equilibrium line from now onwards, we predict that in the year 2100 Abrahamsenbreen will be about 12 km long. The main effect of a surge is to lower the mean surface elevation and thereby to increase the ablation area, causing a negative perturbation of the mass budget. We found that the occurrence of surges leads to a faster retreat of the glacier in a warming climate. Because of the very small bed slope, Abrahamsenbreen is sensitive to small perturbations in the equilibrium-line altitude. If the equilibrium line were lowered by only 160 m, the glacier would steadily grow into Woodfjorddalen until, after 2000 years, it would reach Woodfjord and calving would slow down the advance. The bed topography of Abrahamsenbreen is not known and was therefore inferred from the slope and length of the glacier. The value of the plasticity parameter needed to do this was varied by +20 and −20%. After recalibration the same climate change experiments were performed, showing that a thinner glacier (higher bedrock in this case) in a warming climate retreats somewhat faster.

Upper mantle structure beneath southern African cratons from seismic finite-frequency P- and S-body wave tomography

We present a 3D high-resolution seismic model of the southern African cratonic region from teleseismic tomographic inversion of the P- and S-body wave dataset recorded by the Southern African Seismic Experiment (SASE). Utilizing 3D sensitivity kernels, we invert traveltime residuals of teleseismic body waves to calculate velocity anomalies in the upper mantle down to a 700 km depth with respect to the ak135 reference model. Various resolution tests allow evaluation of the extent of smearing effects and help defining the optimum inversion parameters (i.e., damping and smoothness) for regularizing the inversion calculations.The fast lithospheric keels of the Kaapvaal and Zimbabwe cratons reach depths of 300–350 km and 200–250 km, respectively. The paleo-orogenic Limpopo Belt is represented by negative velocity perturbations down to a depth of ∼250 km, implying the presence of chemically fertile material with anomalously low wave speeds. The Bushveld Complex has low velocity down to ∼150 km, which is attributed to chemical modification of the cratonic mantle. In the present model, the finite-frequency sensitivity kernels allow to resolve relatively small-scale anomalies, such as the Colesberg Magnetic Lineament in the suture zone between the eastern and western blocks of the Kaapvaal Craton, and a small northern block of the Kaapvaal Craton, located between the Limpopo Belt and the Bushveld Complex.

An integrated carbon isotope record of an end-Permian crater lake above a phreatomagmatic pipe of the Siberian Traps

Abstract The largest mass extinction in Earth history occurred at the end-Permian (~ 252 million years ago) and is marked by a global negative carbon isotope excursion and the onset of Siberian Trap volcanism, prompting diverse hypotheses on the link between flood basalt volcanism, carbon cycle perturbations, and mass extinction. Phreatomagmatic pipes associated with Siberian Trap volcanism have been proposed as conduits for the release of 12C-enriched carbon gases from thermogenic and/or magmatic sources to the end-Permian atmosphere. Some of the pipes have preserved crater-lake sediments of volcaniclastic origin. This study examined the preserved evidence for 12C-enriched carbon release into the Western Oktyabrsk crater in east Siberia from the underlying volcanic basin. We find that the 13C/12C ratio of the carbonate cement, organic matter, and long-chain n-alkanes in the lacustrine crater sediments support the hypothesis that 12C-enriched carbon infiltrated the basal crater sediments and lake water immediately after crater formation. The values and trends of δ13CCarb, δ13CTOC, and δ13Cn-alkanes in the crater sediments are consistent with 12C-enriched carbon with isotopic values similar to that of carbon sourced from thermogenic and/or 12C-enriched magmatic sources. This implies that carbon release through the pipes in the Tunguska Basin may explain the source of the global negative carbon isotope perturbations, and their coincidence with Siberian Trap volcanism, at the end-Permian.

The interplay between cyclic AMP, MAPK, and NF-κB pathways in response to proinflammatory signals in microglia.

Cyclic AMP is an important intracellular regulator of microglial cell homeostasis and its negative perturbation through proinflammatory signaling results in microglial cell activation. Though cytokines, TNF-α and IL-1β, decrease intracellular cyclic AMP, the mechanism by which this occurs is poorly understood. The current study examined which signaling pathways are responsible for decreasing cyclic AMP in microglia following TNF-α stimulation and sought to identify the role cyclic AMP plays in regulating these pathways. In EOC2 microglia, TNF-α produced a dramatic reduction in cyclic AMP and increased cyclic AMP-dependent PDE activity that could be antagonized by Rolipram, myristoylated-PKI, PD98059, or JSH-23, implicating a role for PDE4, PKA, MEK, and NF-κB in this regulation. Following TNF-α there were significant increases in iNOS and COX-2 immunoreactivity, phosphorylated ERK1/2 and NF-κB-p65, IκB degradation, and NF-κB p65 nuclear translocation, which were reduced in the presence of high levels of cyclic AMP, indicating that reductions in cyclic AMP during cytokine stimulation are important for removing its inhibitory action on NF-κB activation and subsequent proinflammatory gene expression. Further elucidation of the signaling crosstalk involved in decreasing cyclic AMP in response to inflammatory signals may provide novel therapeutic targets for modulating microglial cell activation during neurological injury and disease.

The impact of salinity perturbations on the future uptake of heat by the Atlantic Ocean

AbstractAnthropogenic ocean heat uptake is a key factor in determining climate change and sea level rise. There is considerable uncertainty in projections of freshwater forcing of the ocean, with the potential to influence ocean heat uptake. We investigate this by adding either −0.1 Sv (sverdrup (106 m3/s)) or +0.1 Sv freshwater to the Atlantic in global climate model simulations, simultaneously imposing an atmospheric CO2 increase. The resulting changes in the Atlantic meridional overturning circulation are roughly equal and opposite (±2 Sv). The impact of the perturbation on ocean heat content is more complex, although it is relatively small (∼5%) compared to the total anthropogenic heat uptake. Several competing processes either accelerate or retard warming at different depths. While positive freshwater perturbations cause an overall heating of the Atlantic, negative perturbations produce insignificant net changes in heat content. The processes active in our model appear robust, although their net result is likely model dependent and experiment dependent.

Active Guard Ring to Improve Latch-Up Immunity

A new design concept named as active guard ring and related circuit implementation to improve the latch-up immunity of ICs are proposed. Using additional sensing circuit and active buffer to turn ON the electrostatic discharge (ESD) protection transistors, the large-dimensional ESD (or I/O) devices can provide or receive extra compensation current to the negative or positive current perturbation during the latch-up current test. The new proposed solution has been verified in 0.6-μm 5 V process to have much higher latch-up resistance compared with the conventional prevention method of guard ring in CMOS technology.

A review of aerosol optical properties and radiative effects

Atmospheric aerosols influence the earth’s radiative balance directly through scattering and absorbing solar radiation, and indirectly through affecting cloud properties. An understanding of aerosol optical properties is fundamental to studies of aerosol effects on climate. Although many such studies have been undertaken, large uncertainties in describing aerosol optical characteristics remain, especially regarding the absorption properties of different aerosols. Aerosol radiative effects are considered as either positive or negative perturbations to the radiation balance, and they include direct, indirect (albedo effect and cloud lifetime effect), and semi-direct effects. The total direct effect of anthropogenic aerosols is negative (cooling), although some components may contribute a positive effect (warming). Both the albedo effect and cloud lifetime effect cool the atmosphere by increasing cloud optical depth and cloud cover, respectively. Absorbing aerosols, such as carbonaceous aerosols and dust, exert a positive forcing at the top of atmosphere and a negative forcing at the surface, and they can directly warm the atmosphere. Internally mixed black carbon aerosols produce a stronger warming effect than externally mixed black carbon particles do. The semidirect effect of absorbing aerosols could amplify this warming effect. Based on observational (ground- and satellite-based) and simulation studies, this paper reviews current progress in research regarding the optical properties and radiative effects of aerosols and also discusses several important issues to be addressed in future studies.

Transforming circumnavigating Kelvin waves that initiate and dissipate the Madden–Julian Oscillation

Analyses of Lagrangian model simulations and atmospheric sonde data reveal a key component of the Madden–Julian Oscillation (MJO): circumnavigating equatorial Kelvin waves with dynamics that transform between dry and moist, which initiate and dissipate MJO convection. The same compositing procedure is applied to simulated and observed MJOs, which uses a coordinate system that moves with the precipitation centre, and treats developing, mature and dissipating stages separately. MJO structure and evolution are similar in the simulation and the observations. To the west of the developing convection, there is a broad region of low‐level (upper‐level) perturbation westerlies (easterlies), which is accompanied by a deep negative temperature perturbation. As this feature enters the MJO‐formation region, convection intensifies on its eastern edge, and the zonal wind perturbations decrease in zonal extent and propagation speed. This process is shown to be a dynamical consequence of a largely dry, first baroclinic Kelvin wave entering a region where large‐scale upward motion is mostly balanced by convective heating. As the MJO matures, a Kelvin wave of opposite sign emerges from its eastern edge, and makes the opposite transition (from moist to dry). The resulting wave, which includes low‐level (upper‐level) easterlies (westerlies) and a deep positive temperature perturbation, rapidly propagates around the world and dissipates MJO convection. The Kelvin wave that initiates MJO convection is shown to originate from the inactive phase of a previous MJO, so that the complete MJO cycle is characterized by the two kinds of Kelvin waves emerging from active and suppressed phases of MJO convection, circumnavigating the Tropics, and triggering the opposite phase.

Statistical analysis of geosynchronous magnetic field perturbations near midnight during sudden commencements

AbstractWhen an interplanetary (IP) shock passes over the Earth's magnetosphere, the geosynchronous magnetic field strength near noon is always enhanced except for the magnetopause crossing events. Near midnight, however, it increases or decreases. This indicates that the nightside magnetosphere is not always compressed by a sudden increase in the solar wind dynamic pressure. To understand midnight geosynchronous magnetic field responses to IP shocks, we statistically examined geosynchronous magnetic field perturbations, corresponding to 120 sudden commencements (SCs), observed when geosynchronous spacecraft were near midnight between 2200 and 0200 magnetic local times. Out of the 120 SCs, 107 SCs were identified by one geosynchronous spacecraft, and 13 SCs were identified by two geosynchronous spacecraft. Thus, 133 events were used in our statistical study. We observed 23 events in spring, 40 events in summer, 32 events in fall, and 38 events in winter, respectively. A statistical study of the midnight geosynchronous SC perturbations reveals the following characteristics. (1) In summer, all events show a positive enhancement (+ΔBT) in the magnetic field strength. (2) In winter, however, ΔBT exhibits a positive (+ΔBT) or negative (–ΔBT) enhancement. (3) In summer, the midnight geosynchronous SC perturbations in the BH component (positive northward) in VDH coordinates are mostly (∼88%, 35 out of 40 events) positive (+ΔBH), while the occurrence rate of the positive perturbation (∼43%) in the Bz component (positive northward) in GSM coordinates is lower than that of the negative perturbation (∼57%). (4) In winter, the negative perturbations in ΔBH (∼61%) and ΔBz (∼74%) are dominant. (5) Both the north‐south components (BH and Bz) in spring and fall are scattered around zero. To explain the observations, we suggest that SC‐associated cross‐tail current (JSC) has a peak intensity around geosynchronous orbit and thus is a main controlling factor of midnight geosynchronous magnetic field perturbations during SCs. Specifically, we suggest that the seasonal variation of the sign of ΔBH, ΔBz, and ΔBT is due to the seasonal variation of the spacecraft position relative to JSC.

Negative ion sound solitary waves revisited

AbstractSome years ago, a group including the present author and Padma Shukla showed that a suitable non-thermal electron distribution allows the formation of ion sound solitary waves with either positive or negative density perturbations, whereas with Maxwellian electrons only a positive density perturbation is possible. The present paper discusses the qualitative features of this distribution allowing the negative waves and shared with suitable two-temperature distributions.

Gyrokinetic particle simulation of nonlinear evolution of mirror instability

A gyrokinetic simulation model for nonlinear studies of the mirror instability is described. The model is set in a uniform, periodic slab with anisotropic ions and cold electrons. Particle‐in‐cell simulations with a noise reducing δfalgorithm show agreement with the linear theory of the mirror instability. Results of nonlinear simulations near marginal stability are presented. Single‐mode simulations show saturation due to trapping. Simulations with a spectrum of unstable modes show that the negative magnetic perturbations saturate at a lower amplitude and earlier than the positive magnetic perturbations, which results in the development of peaked saturated structures. The saturation amplitude of negative magnetic perturbations is in agreement with the trapped particle theory, while the saturation amplitude of the positive magnetic perturbations is determined by the local change in the β⟂ (ratio of perpendicular plasma pressure to magnetic pressure) parameter.

Sensitivity analysis to perturbations of the weight of a subset of items: The knapsack case study

In this paper, we study the sensitivity of the optimum to perturbations of the weight of a subset of items of both the knapsack problem (denoted KP) and knapsack sharing problem (denoted KSP). The sensitivity interval of the weight associated to an item is characterized by two limits, called lower and upper values, which guarantee the optimality of the solution at hand whenever the new weight’s value belongs to such an interval. For each perturbed weight, we try to establish approximate values of the sensitivity interval whenever the original problem is solved. We do it by applying a dynamic programming method where all established results require a negligible runtime. First, two cases are studied when considering an optimal solution of KP: (i) the case in which all perturbations are (non)negatives and (ii) the general case in which the set of the perturbed items is divided into two disjoint subsets (the first subset contains the nonnegative perturbations and the second one represents the subset of negative perturbations). Second, we show how we can adapt the results of KP to the KSP. All established results require a negligible runtime which grows the interest of such a study. Finally, for each of these problems, we will see the impact of the established results on an example while considering the various cases.

A Large-Eddy Simulation Study of Bottom-Heating Effects on Scalar Dispersion in and above a Cubical Building Array

AbstractThermal effects on scalar dispersion in and above a cubical building array are numerically investigated using the parallelized large-eddy simulation model (PALM). Two cases (no heating and bottom heating) are simulated, and scalar dispersion patterns in the two cases are compared. In the no-heating case, scalar ejections in the low-speed flow structures play an important role in transporting scalar upward above the building array. In the bottom-heating case, streamwise elongated and isolated scalar ejections appear below upper low-speed and upper high-speed regions above the building array. In both cases, bottom-emitted scalar flux is balanced by streamwise scalar advection and vertical turbulent scalar flux at the rooftop height. The vertical turbulent scalar flux at the rooftop height is mainly composed of scalar ejections and scalar sweeps that are related to low- and high-speed flow structures, respectively. Furthermore, the low- and high-speed flow structures at the rooftop height induce spanwise converging and spanwise diverging flow in the building array in both the no-heating and bottom-heating cases. Thus, the mean scalar concentration in the building array is high below the low-speed flow structures (above the building array) in both cases. Dominant scalar dispersion patterns in the building array are found to be spanwise scalar transport events that are composed of negative scalar concentration perturbation and spanwise flow therein. In the bottom-heating case, a large-scale secondary circular flow develops, causing stronger spanwise scalar dispersion patterns in the building array.