First passage time statistics of Brownian motion with purely time dependent drift and diffusion

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model for water availability from surface runoff in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated

A note on aerosol sized particle deposition onto dense and tall canopies situated on gentle cosine hills

Micrometeorological measurements of aerosol sized dry particle deposition velocity ( V d ) onto forested canopies have significantly advanced over the past two decades and now include both—airborne and stationary platforms. However, the interpretation of these  V d measurements still relies on stationary and planar homogeneous flow assumptions only appropriate to flat-terrain conditions. Simplified model calculations were used to examine how variations in hill height ( H ) introduce biases in  V d when assumptions appropriate to flat terrain are applied to periodic and gentle 2-D cosine topography covered with tall and dense forested canopies. It was shown that increasing  H reduced the variability in  V d for all aerosol sized particle diameters ( d p ) inside the canopy when the hill slope ( H / L ) remained constant (=0.1), where  L is the cosine hill half-length. At the landscape scale, as may be monitored from airborne platforms, assumptions appropriate to flat-terrain appear accurate with increasing  H for a constant and gentle H/ L (= 0.1). Inside the canopy, variability in  V d tends to be larger than above the canopy for all  H values and  d p classes. DOI: 10.1111/j.1600-0889.2011.00528.

Delay-induced rebounds in CO_{2} emissions and critical time-scales to meet global warming targets

While climate science debates are focused on the attainment of peak anthropogenic CO2 emissions and policy tools to reduce peak temperatures, the human‐energy‐climate system can hold “rebound” surprises beyond this peak. Following the second industrial revolution, global per capita CO_{2} emissions (c_{c}) experienced a punctuated growth of about 100% every 60 years, mainly attributable to technological development and its global spread. A model of the human‐energy‐climate system capable of reproducing past punctuated dynamics shows that rebounds in global CO_{2} emissions emerge due to delays intrinsic to the diffusion of innovations. Such intrinsic delays in the adoption and spread of low‐carbon emitting technologies, together with projected population growth, upset the warming target set by the Paris Agreement. To avoid rebounds and their negative climate effects, model calculations show that the diffusion of climate‐friendly technologies must occur with lags one‐order of magnitude shorter (i.e., ∼6 years) than the characteristic timescale of past punctuated growth in c_{c}. Radically new strategies to globally implement the technological advances at unprecedented rates are needed if the current emission goals are to be achieved

Relation between the spectral properties of wall turbulence and the scaling of the Darcy-Weisbach friction factor

Empirical formulas describing the Darcy-Weisbach friction factor remain indispensable for applications in sciences and engineering dealing with turbulent flows. Despite their practical significance, these formulas have remained without theoretical interpretation for many decades. To close this knowledge gap, much research has been devoted to the development of the so-called "spectral link"introduced in the early 2000s. Such a theory is entirely based on elegant phenomenological arguments that make no contact with equations describing turbulent wall flows. The spectral link spawned alternative approaches, now labeled "cospectral budget"(or CSB) models, that describe how turbulent eddies contribute to wall stresses. The CSB overcomes some of the shortcomings of the phenomenological approach and is here employed to provide a thorough clarification of the link between spectral properties of velocity fluctuations and the scaling of friction factors in turbulent pipe flows in the hydraulically smooth and fully rough regimes

Inverse Cascade Evidenced by Information Entropy of Passive Scalars in Submerged Canopy Flows

Turbulent mixing of scalars within canopies is investigated using a flume experiment with canopy-like rods of height h mounted to the channel bed. The data comprised a time sequence of high-resolution images of a dye recorded in a plane parallel to the bed at z/h= 0.2. Image processing shows that von Kármán wakes shed by canopy drag and downward turbulent transport from upper canopy layers impose distinct scaling regimes on the scalar spectrum. Measures from information theory are then used to explore the dominant directionality of the interaction between small and large scales underlying these two spectral regimes, showing that the arrival of sweeps from aloft establishes an inertial-range spectrum with forward “information” cascade. In contrast, wake growth with downstream distance leads to persistent upscale transfer (inverse cascade) of scalar variance, which hints at their nondiffusive character and the significance of the stem diameter as an active length scale in canopy turbulence

Estimation of bare soil evaporation using skin temperature measurements

A simple model based on the Monin-Obukhov surface layer similarity theory of heat and momentum transport can be used to predict the latent heat flux for a variety of atmospheric and soil moisture conditions. Experiments were carried out on the Campbell Tract at the University of California, Davis, from 14 September to 23 November 1990. The latent heat flux was measured precisely with a large weighing lysimeter and the surface temperature by a thermal IR transducer. The evaporation predictions and lysimeter measurements overall were in good agreement (R2 = 0.86), including cases of dry surface conditions. Even low daily evaporation of the order of 1 mm could be modeled with the procedure studied

The spatial structure of turbulence at production wave-numbers using orthonormal wavelet

Orthonormal wavelet expansions are applied to surface-layer measurements of vertical wind speed under various atmospheric stability conditions. The orthonormal wavelet transform allows for the unfolding of these measurements into space and scale simultaneously to reveal the large intermittent behavior in space for the turbulent production wavenumbers. Both Fourier and wavelet power spectra indicated the existence of a -1 power law for the vertical velocity measurements at the production wavenumbers. The -1 power law in the turbulent production range was derived from surface-layer similarity theory. A dimensionless skewness structure function is applied to the wavelet decomposed vertical velocity field to trace the destruction of the shear- or buoyancy-induced anisotropy under various stability conditions. The structure skewness function revealed shear- or buoyancy-induced eddy asymmetry dependence on stability at each scale within the -1 power-law wavenumber range with more isotropy during propagation from smaller to larger wavenumbers. The asymmetry of these events at the turbulent production wavenumbers appeared very localized in space, as well as in scale, and could be described with a simple eddy-overturning model. It is demonstrated that the wavelet transform is suitable for such analysis