This paper is a review of geophysical and climatic trends associated with extreme weather events and natural hazards, their implications for urban areas and the effects of continued environmental modification due to urban expansion. It... more
This paper is a review of geophysical and climatic trends associated with extreme weather events and natural hazards, their implications for urban areas and the effects of continued environmental modification due to urban expansion. It discusses how urban design, technological development and societal behaviour can either ameliorate or worsen climate-induced hazards in urban areas. Pressures – ranging from excessive rainfall causing urban flooding to urban temperature extremes driving air pollution – require more attention to understand, model and predict changes in hazards in urban areas. It concludes that involving different techniques for data analysis and system modelling is more appropriate for practical decision-making than a purely reductionist approach. Successfully determining the future environment of megacities will, however, require joint action with societally informed decision makers, grounded in sound scientific achievements.
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We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space Ḃ0∞,1,σ... more
We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space Ḃ0∞,1,σ (R2; L p(R+)) for 2 < p < ∞. Here the L p-integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space Ḃ0∞,1 contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous Besov spaces. For instance we provide and apply an operator-valued bounded H∞-calculus for the Laplacian in Ḃ0∞,1(Rn; E) for a general Banach space E. 1.
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In this study, the impacts of Mexican and southwestern U.S. agricultural and urban irrigation on North American monsoon (NAM) rainfall and other hydrometeorological fields are investigated using the Weather Research and Forecasting (WRF)... more
In this study, the impacts of Mexican and southwestern U.S. agricultural and urban irrigation on North American monsoon (NAM) rainfall and other hydrometeorological fields are investigated using the Weather Research and Forecasting (WRF) Model by implementing an irrigation scheme into the WRF–land surface model. Taking the 2000–12 monsoon seasons as examples, multiple WRF simulations with irrigation are conducted by designing different crops’ maximum allowable water depletions (SWm). In comparison with gridded rainfall observations in urban and rural area, the WRF simulations with/without irrigation generally capture the observations very well, but with underestimation along the western slope of the Sierra Madre Occidental (SMO) and overestimation over southern Mexico. The simulations of WRF with irrigation are slightly improved over those without irrigation, compared with rainfall and sounding observations. Sensitivity studies reveal that the impact of irrigation on rainfall varies...
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Nine dust storms in south-central Arizona, USA were simulated with the Weather Research and Forecasting with Chemistry model (WRF-Chem) at 2-km resolution. The windblown dust emission algorithm was the Air Force Weather Agency model. In... more
Nine dust storms in south-central Arizona, USA were simulated with the Weather Research and Forecasting with Chemistry model (WRF-Chem) at 2-km resolution. The windblown dust emission algorithm was the Air Force Weather Agency model. In comparison with ground-based PM10 observations, the model unevenly reproduces the dust storm events. The model adequately estimates the location and timing of the events, but it is unable to precisely replicate the magnitude and timing of the elevated hourly concentrations of particles 10 microns and smaller ([PM10]).Furthermore, the model under-estimated [PM10] in highly agricultural Pinal County because it under-estimated surface wind speeds and because the model's erodible fractions of the land surface data were too coarse to effectively resolve the active and abandoned agricultural lands. In contrast, the model over-estimated [PM10] in western Arizona along the Colorado River because it generated daytime sea breezes (from the nearby Gulf of C...
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This article explores regional impacts on near-surface air temperature and air conditioning (AC) electricity consumption due to projected urban expansion in a semiarid environment. In addition to the modern-day urban landscape setting,... more
This article explores regional impacts on near-surface air temperature and air conditioning (AC) electricity consumption due to projected urban expansion in a semiarid environment. In addition to the modern-day urban landscape setting, two projected urban expansion scenarios are analyzed with the Weather Research and Forecasting Model coupled to a multilayer building energy scheme. The authors simulate a 10-day extreme heat period at high spatial resolution (1-km horizontal grid spacing) over Arizona, one of the fastest-growing regions in the United States. Results show that replacement of natural land surfaces by buildings and pavement increases the local mean near-surface air temperature considerably. Furthermore, present-day waste heat emission from AC systems increases the mean nighttime 2-m air temperature by up to 1°C in some urban locations, but projected urban development aggravates the situation, increasing nighttime air temperatures by up to 1.5°–1.75°C. The contribution o...
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Physical mechanisms of incongruency between observations and Weather Research and Forecasting (WRF) Model predictions are examined. Limitations of evaluation are constrained by (i) parameterizations of model physics, (ii)... more
Physical mechanisms of incongruency between observations and Weather Research and Forecasting (WRF) Model predictions are examined. Limitations of evaluation are constrained by (i) parameterizations of model physics, (ii) parameterizations of input data, (iii) model resolution, and (iv) flux observation resolution. Observations from a new 22.1-m flux tower situated within a residential neighborhood in Phoenix, Arizona, are utilized to evaluate the ability of the urbanized WRF to resolve finescale surface energy balance (SEB) when using the urban classes derived from the 30-m-resolution National Land Cover Database. Modeled SEB response to a large seasonal variation of net radiation forcing was tested during synoptically quiescent periods of high pressure in winter 2011 and premonsoon summer 2012. Results are presented from simulations employing five nested domains down to 333-m horizontal resolution. A comparative analysis of model cases testing parameterization of physical processe...
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Research Interests: Applied Mathematics, Physics, Numerical Simulation, Classical Physics, Computational Science and Engineering, and 11 moreSpectral analysis, Space Time, Spatial Scale, Navier Stokes, High Resolution, Cross Section, Three Dimensional, Inertia, Vertical coordination, upper troposphere, and Group velocity
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For an idealized inertia-gravity wave, the Stokes drift, defined as the difference in end positions of a fluid parcel as derived in the Lagrangian and Eulerian coordinates, is exactly zero after one wave cycle in a deterministic flow.... more
For an idealized inertia-gravity wave, the Stokes drift, defined as the difference in end positions of a fluid parcel as derived in the Lagrangian and Eulerian coordinates, is exactly zero after one wave cycle in a deterministic flow. When stochastic effects are incorporated into the model, nonlinearity in the velocity field changes the statistical properties. Better understanding of the statistics of a passive tracer, such as the mean drift and higher order moments, leads to more accurate predictions of the pattern of Lagrangian mixing in a realistic environment. In this paper, we consider the inertia-gravity wave equation perturbed by white noise and solve the Fokker–Planck equation to study the evolution in time of the probability density function of passive tracers in such a flow. We find that at initial times the tracer distribution closely follows the nonlinear background flow and that nontrivial Stokes drift ensues as a result. Over finite times, we measure chaotic mixing bas...
Research Interests: Engineering, Stochastic Process, Physics, Fluid Dynamics, Mathematical Sciences, and 11 morePhysical sciences, FOkker Planck Equation, Stokes drift, Statistical Properties, PROBABILITY DENSITY, Probability Density Function, Velocity Field, Physics of Fluids, Chaotic Mixing, White Noise, and Higher order
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A time-stepping scheme is proposed. It is based on the leapfrog method and a fourth-order time filter. The scheme requires only one evaluation per time step and uses an implicit filter, but the effort needed to implement it in an explicit... more
A time-stepping scheme is proposed. It is based on the leapfrog method and a fourth-order time filter. The scheme requires only one evaluation per time step and uses an implicit filter, but the effort needed to implement it in an explicit manner is trivial. Comparative tests demonstrate that the proposed scheme produces numerical approximations that are more stable and highly accurate compared to the standard Robert–Asselin (RA) and the Robert–Asselin–Williams (RAW) filtered leapfrog scheme, even though both methods use filter coefficients that are tuned such that the 2Δt modes are damped at the same rate. Formal stability analysis demonstrates that the proposed method generates amplitude errors of O[(Δt)4], implying third-order accuracy. This contrasts with the O[(Δt)2] errors produced by the standard RA and RAW filtered leapfrog. A second scheme that produces amplitude errors of O[(Δt)6] is also presented. The proposed scheme is found to do well at controlling numerical instabilit...
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Research Interests: Engineering, Computer Science, Computational Physics, Atmospheric Modeling, Microscale Chemistry, and 12 moreStratosphere, Mesoscale Meteorology, Mathematical Sciences, Relaxation, Physical sciences, Boundary Conditions, Three Dimensional, Calculation, Boundary Condition, Tropopause, Weather Research and Forecasting Model, and Troposphere
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ABSTRACT
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We prove time-local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space Ḃ0... more
We prove time-local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space Ḃ0 ∞,1,σ(R;L(R+)) for 2 < p < ∞. Here the L-integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space Ḃ0 ∞,1 contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vectorvalued homogeneous Besov spaces. For instance we provide and apply an operator-valued bounded H-calculus for the Laplacian in Ḃ0 ∞,1(R;E) for a general Banach space E. Mathematical Subject Classification (2000). Primary: 76D05, Secondary: 76U05, 76D10
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In the Schrödinger picture, we find explicit solutions for two models of degenerate parametric oscillators in the case of multi-parameter squeezed input photons. The corresponding photon statistics and Wigner's function are also... more
In the Schrödinger picture, we find explicit solutions for two models of degenerate parametric oscillators in the case of multi-parameter squeezed input photons. The corresponding photon statistics and Wigner's function are also derived in coordinate representation. Their time evolution is investigated in detail. The unitary transformation and an extension of the squeeze/evolution operator are briefly discussed.
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Research Interests: Mathematics and Physics
High-resolution mesoscale and microscale simulations of wave breaking and laminated structures induced by mountain waves in the upper troposphere and lower stratosphere (UTLS) are presented for two Intense Observational Periods (IOPs) of... more
High-resolution mesoscale and microscale simulations of wave breaking and laminated structures induced by mountain waves in the upper troposphere and lower stratosphere (UTLS) are presented for two Intense Observational Periods (IOPs) of the Terrain-induced Rotor Experiment (T-REX) campaign of measurements. Vertical nesting and refined vertical gridding have been developed and applied in microscale simulations coupled the mesoscale Weather Research and Forecasting (WRF) model to resolve multi-scale nonlinear processes associated with mountain wave breaking. The finest nest of WRF is coupled with embedded microscale nests. The fully three-dimensional nonhydrostatic, compressible Navier-Stokes equations are solved with a stretched, adaptive grid in the vertical and improved resolution in the UTLS region. For nesting, both lateral and vertical boundary conditions are treated via relaxation zones where the velocity and temperature fields are relaxed to those obtained from the mesoscale ...
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In this paper, we study oscillating solutions of the 1D-quintic nonlinear Schrödinger equation with the help of Wigner's quasiprobability distribution in quantum phase space. An "absolute squeezing property", namely a... more
In this paper, we study oscillating solutions of the 1D-quintic nonlinear Schrödinger equation with the help of Wigner's quasiprobability distribution in quantum phase space. An "absolute squeezing property", namely a periodic in time total localization of wave packets at some finite spatial points without violation of the Heisenberg uncertainty principle, is analyzed in this nonlinear model.