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.

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Two recently proposed turbulence closure schemes are compared against the conventional Mellor-Yamada (MY) model for stably stratified atmospheric flows. The Energy and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a "critical gradient Richardson number," both EFB and CSB models allow turbulence to exist at any gradient Richardson number R-t and predict a saturation of flux Richardson number (R-f -> R-fm) at sufficiently large R-i. The CSB approach further predicts the value of Rim and reveals a unique expression linking the Rotta and von Karman constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing R-i. However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as Rim is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.Peer reviewe

Turbulence organization and mean profile shapes in the stably stratified boundary layer: zones of uniform momentum and air temperature

A persistent spatial organization of eddies is identified in the lowest portion of the stably-stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al., J Atmos Sci 73(4):1815-1840, 2016) ranging in stability from neutral to nearly z-less stratification. The coherent turbulent structure is well approximated as a series of uniform momentum zones (UMZs) and uniform temperature zones (UTZs) separated by thin layers of intense gradients that are significantly greater than the mean. This pattern yields stairstep-like instantaneous flow profiles whose shape is distinct from the mean profiles that emerge from long-term averaging. However, the scaling of the stairstep organization is closely related to the resulting mean profiles. The differences in velocity and temperature across the thin gradient layers remain proportional to the surface momentum and heat flux conditions regardless of stratification. The vertical thickness of UMZs and UTZs is proportional to height above the surface for neutral and weak stratification, but becomes thinner and less dependent on height as the stability increases. Deviations from the logarithmic mean profiles for velocity and temperature observed under neutral conditions are therefore predominately due to the reduction in zone size with increasing stratification, which is empirically captured by existing Monin-Obukhov similarity relations for momentum and heat. The zone properties are additionally used to explain trends in the turbulent Prandtl number, thus providing a connection between the eddy organization, mean profiles, and turbulent diffusivity in stably stratified conditions.Comment: 35 pages, 12 figure

An objective method for determining principal time scales of coherent eddy structures using orthonormal wavelets

A new, parameter-free method, based on orthonormal wavelet expansions is proposed for calculating the principal time scale of coherent structures in atmospheric surface layer measurements. These organized events play an important role in the exchange of heat, mass, and momentum between the land and the atmosphere. This global technique decomposes the energy contribution at each scale into organized and random eddy motion. The method is demonstrated on vertical wind velocity measurements above bare and vegetated surfaces. It is found to give nearly identical results to a local thresholding approach developed for signal de-noising that assigns the wavelet coecients to organized and random motion. The eect of applying anti-and/or near-symmetrical wavelet basis functions is also investigated.

Multiple mechanisms generate Lorentzian and 1/f a power spectra in daily stream-flow time series

a b s t r a c t Power-law scaling is an ubiquitous feature of the power spectrum of streamflow on the daily to monthly timescales where the spectrum is most strongly affected by hydrologic catchment-scale processes. Numerous mechanistic explanations for the emergence of this power-law scaling have been proposed. This study employs empirical spectra obtained for eight river basins in the South Eastern US and synthetic spectra generated from a range of proposed mechanisms to explore these explanations. The empirical analysis suggested that streamflow spectra were characterized by multiple power-law scaling regimes with high-frequency exponents a in the range À1 to À5. In the studied basins, a tended to increase with drainage area. The power-law generating mechanisms analyzed included linear and nonlinear catchment water balance arguments, power-law recession behavior, autonomous and non-autonomous responses of channel hydraulics and the n-fold convolution of linear reservoirs underpinning Dooge or Nash hydrographs. Of these mechanisms, only n-fold convolutions with n = 2 or 3 generated power spectra with features that were consistent with the empirical cases. If the effects of daily streamflow sampling on truncating power spectra were considered, then the trends in a with drainage area were also consistent with this mechanism. Generalizing the linear convolution approach to a network of reservoirs with randomly distributed parameters preserved the features of the power spectrum and maintained consistency with empirical spectra

Multiple mechanisms generate Lorentzian and 1/f a power spectra in daily stream-flow time series

a b s t r a c t Power-law scaling is an ubiquitous feature of the power spectrum of streamflow on the daily to monthly timescales where the spectrum is most strongly affected by hydrologic catchment-scale processes. Numerous mechanistic explanations for the emergence of this power-law scaling have been proposed. This study employs empirical spectra obtained for eight river basins in the South Eastern US and synthetic spectra generated from a range of proposed mechanisms to explore these explanations. The empirical analysis suggested that streamflow spectra were characterized by multiple power-law scaling regimes with high-frequency exponents a in the range À1 to À5. In the studied basins, a tended to increase with drainage area. The power-law generating mechanisms analyzed included linear and nonlinear catchment water balance arguments, power-law recession behavior, autonomous and non-autonomous responses of channel hydraulics and the n-fold convolution of linear reservoirs underpinning Dooge or Nash hydrographs. Of these mechanisms, only n-fold convolutions with n = 2 or 3 generated power spectra with features that were consistent with the empirical cases. If the effects of daily streamflow sampling on truncating power spectra were considered, then the trends in a with drainage area were also consistent with this mechanism. Generalizing the linear convolution approach to a network of reservoirs with randomly distributed parameters preserved the features of the power spectrum and maintained consistency with empirical spectra