A functional coefficient model view of the Feldstein–Horioka puzzle

What does the saving–investment (SI) relation really measure and how should the SI relation be measured? These are two of the most discussed issues triggered by the so-called Feldstein–Horioka puzzle. Based on panel data we introduce a new variant of functional coefficient models that allows to separate long and short to medium run parameter dependence. The new modeling framework is applied to uncover the determinants of the SI relation. Macroeconomic state variables such as openness, the age dependency ratio, government current and consumption expenditures are found to affect the SI relation significantly in the long run.

A variational method to retrieve the extinction profile in liquid clouds using multiple field-of-view lidar

Liquid clouds play a profound role in the global radiation budget but it is difficult to remotely retrieve their vertical profile. Ordinary narrow field-of-view (FOV) lidars receive a strong return from such clouds but the information is limited to the first few optical depths. Wideangle multiple-FOV lidars can isolate radiation scattered multiple times before returning to the instrument, often penetrating much deeper into the cloud than the singly-scattered signal. These returns potentially contain information on the vertical profile of extinction coefficient, but are challenging to interpret due to the lack of a fast radiative transfer model for simulating them. This paper describes a variational algorithm that incorporates a fast forward model based on the time-dependent two-stream approximation, and its adjoint. Application of the algorithm to simulated data from a hypothetical airborne three-FOV lidar with a maximum footprint width of 600m suggests that this approach should be able to retrieve the extinction structure down to an optical depth of around 6, and total opticaldepth up to at least 35, depending on the maximum lidar FOV. The convergence behavior of Gauss-Newton and quasi-Newton optimization schemes are compared. We then present results from an application of the algorithm to observations of stratocumulus by the 8-FOV airborne “THOR” lidar. It is demonstrated how the averaging kernel can be used to diagnose the effective vertical resolution of the retrieved profile, and therefore the depth to which information on the vertical structure can be recovered. This work enables exploitation of returns from spaceborne lidar and radar subject to multiple scattering more rigorously than previously possible.

A global view of the extratropical tropopause transition layer from Atmospheric Chemistry Experiment Fourier Transform Spectrometer O3, H2O, and CO

The global behavior of the extratropical tropopause transition layer (ExTL) is investigated using O3, H2O, and CO measurements from the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on Canada’s SCISAT-1 satellite obtained between February 2004 and May 2007. The ExTL depth is derived using H2O-O3 and CO-O3 correlations. The ExTL top derived from H2O-O3 shows an increase from roughly 1–1.5 km above the thermal tropopause in the subtropics to 3–4 km (2.5–3.5 km) in the north (south) polar region, implying somewhat weaker tropospherestratosphere- transport in the Southern Hemisphere. The ExTL bottom extends ~1 km below the thermal tropopause, indicating a persistent stratospheric influence on the troposphere at all latitudes. The ExTL top derived from the CO-O3 correlation is lower, at 2 km or ~345 K (1.5 km or ~335 K) in the Northern (Southern) Hemisphere. Its annual mean coincides with the relative temperature maximum just above the thermal tropopause. The vertical CO gradient maximizes at the thermal tropopause, indicating a local minimum in mixing within the tropopause region. The seasonal changes in and the scales of the vertical H2O gradients show a similar pattern as the static stability structure of the tropopause inversion layer (TIL), which provides observational support for the hypothesis that H2O plays a radiative role in forcing and maintaining the structure of the TIL.

Seasonal pattern of regional carbon balance in the central Rocky Mountains from surface and airborne measurements

[1] High-elevation forests represent a large fraction of potential carbon uptake in North America, but this uptake is not well constrained by observations. Additionally, forests in the Rocky Mountains have recently been severely damaged by drought, fire, and insect outbreaks, which have been quantified at local scales but not assessed in terms of carbon uptake at regional scales. The Airborne Carbon in the Mountains Experiment was carried out in 2007 partly to assess carbon uptake in western U.S. mountain ecosystems. The magnitude and seasonal change of carbon uptake were quantified by (1) paired upwind-downwind airborne CO2 observations applied in a boundary layer budget, (2) a spatially explicit ecosystem model constrained using remote sensing and flux tower observations, and (3) a downscaled global tracer transport inversion. Top-down approaches had mean carbon uptake equivalent to flux tower observations at a subalpine forest, while the ecosystem model showed less. The techniques disagreed on temporal evolution. Regional carbon uptake was greatest in the early summer immediately following snowmelt and tended to lessen as the region experienced dry summer conditions. This reduction was more pronounced in the airborne budget and inversion than in flux tower or upscaling, possibly related to lower snow water availability in forests sampled by the aircraft, which were lower in elevation than the tower site. Changes in vegetative greenness associated with insect outbreaks were detected using satellite reflectance observations, but impacts on regional carbon cycling were unclear, highlighting the need to better quantify this emerging disturbance effect on montane forest carbon cycling.

Passive urban ventilation by combined buoyancy-driven slope flow and wall flow: Parametric CFD studies on idealized city models

This paper reports the results of a parametric CFD study on idealized city models to investigate the potential of slope flow in ventilating a city located in a mountainous region when the background synoptic wind is absent. Examples of such a city include Tokyo in Japan, Los Angeles and Phoenix in the US, and Hong Kong. Two types of buoyancy-driven flow are considered, i.e., slope flow from the mountain slope (katabatic wind at night and anabatic wind in the daytime), and wall flow due to heated/cooled urban surfaces. The combined buoyancy-driven flow system can serve the purpose of dispersing the accumulated urban air pollutants when the background wind is weak or absent. The microscopic picture of ventilation performance within the urban structures was evaluated in terms of air change rate (ACH) and age of air. The simulation results reveal that the slope flow plays an important role in ventilating the urban area, especially in calm conditions. Katabatic flow at night is conducive to mitigating the nocturnal urban heat island. In the present parametric study, the mountain slope angle and mountain height are assumed to be constant, and the changing variables are heating/cooling intensity and building height. For a typical mountain of 500 m inclined at an angle of 20° to the horizontal level, the interactive structure is very much dependent on the ratio of heating/cooling intensity as well as building height. When the building is lower than 60 m, the slope wind dominates. When the building is as high as 100 m, the contribution from the urban wall flow cannot be ignored. It is found that katabatic wind can be very beneficial to the thermal environment as well as air quality at the pedestrian level. The air change rate for the pedestrian volume can be as high as 300 ACH.

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.

Internal wave drag in stratified flow over mountains on a beta plane

The impact of the variation of the Coriolis parameter f on the drag exerted by internal Rossby-gravity waves on elliptical mountains is evaluated using linear theory, assuming constant wind and static stability and a beta-plane approximation. Previous calculations of inertia-gravity wave drag are thus extended in an attempt to establish a connection with existing studies on planetary wave drag, developed primarily for fluids topped by a rigid lid. It is found that the internal wave drag for zonal westerly flow strongly increases relative to that given by the calculation where f is assumed to be a constant, particularly at high latitudes and for mountains aligned meridionally. Drag increases with mountain width for sufficiently wide mountains, reaching values much larger than those valid in the non-rotating limit. This occurs because the drag receives contributions from a low wavenumber range, controlled by the beta effect, which accounts for the drag amplification found here. This drag amplification is shown to be considerable for idealized analogues of real mountain ranges, such as the Himalayas and the Rocky mountains, and comparable to the barotropic Rossby wave drag addressed in previous studies.

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge

Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states.

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

The effect of wind shear and curvature on the gravity wave drag produced by a ridge

The analytical model proposed by Teixeira, Miranda, and Valente is modified to calculate the gravity wave drag exerted by a stratified flow over a 2D mountain ridge. The drag is found to be more strongly affected by the vertical variation of the background velocity than for an axisymmetric mountain. In the hydrostatic approximation, the corrections to the drag due to this effect do not depend on the detailed shape of the ridge as long as this is exactly 2D. Besides the drag, all the perturbed quantities of the flow at the surface, including the pressure, may be calculated analytically.

Under what conditions does embedded convection enhance orographic precipitation?

Idealised convection-permitting simulations are used to quantify the impact of embedded convection on the precipitation generated by moist flow over midlatitude mountain ridges. A broad range of mountain dimensions and moist stabilities are considered to encompass a spectrum of physically plausible flows. The simulations reveal that convection only enhances orographic precipitation in cap clouds that are otherwise unable to efficiently convert cloud condensate into precipitate. For tall and wide mountains (e.g. the Washington Cascades or the southern Andes), precipitate forms efficiently through vapour deposition and collection, even in the absence of embedded convection. When embedded convection develops in such clouds, it produces competing effects (enhanced condensation in updraughts and enhanced evaporation through turbulent mixing and compensating subsidence) that cancel to yield little net change in precipitation. By contrast, convection strongly enhances precipitation over short and narrow mountains (e.g. the UK Pennines or the Oregon Coastal Range) where precipitation formation is otherwise highly inefficient. Although cancellation between increased condensation and evaporation still occurs, the enhanced precipitation formation within the convective updraughts leads to a net increase in precipitation efficiency. The simulations are physically interpreted through non-dimensional diagnostics and relevant time-scales that govern advective, microphysical, and convective processes.

Revisiting Asian monsoon formation and change associated with Tibetan Plateau forcing: I. Formation

Numerical experiments with different idealized land and mountain distributions are carried out to study the formation of the Asian monsoon and related coupling processes. Results demonstrate that when there is only extratropical continent located between 0 and 120°E and between 20/30°N and the North Pole, a rather weak monsoon rainband appears along the southern border of the continent, coexisting with an intense intertropical convergence zone (ITCZ). The continuous ITCZ surrounds the whole globe, prohibits the development of near-surface cross-equatorial flow, and collects water vapor from tropical oceans, resulting in very weak monsoon rainfall. When tropical lands are integrated, the ITCZ over the longitude domain where the extratropical continent exists disappears as a consequence of the development of a strong surface cross-equatorial flow from the winter hemisphere to the summer hemisphere. In addition, an intense interaction between the two hemispheres develops, tropical water vapor is transported to the subtropics by the enhanced poleward flow, and a prototype of the Asian monsoon appears. The Tibetan Plateau acts to enhance the coupling between the lower and upper tropospheric circulations and between the subtropical and tropical monsoon circulations, resulting in an intensification of the East Asian summer monsoon and a weakening of the South Asian summer monsoon. Linking the Iranian Plateau to the Tibetan Plateau substantially reduces the precipitation over Africa and increases the precipitation over the Arabian Sea and the northern Indian subcontinent, effectively contributing to the development of the South Asian summer monsoon.

Do soldiers' lives matter? A view from proportionality

A military operation is about to take place during an ongoing international armed conflict; it can be carried out either by aerial attack, which is expected to cause the deaths of enemy civilians, or by using ground troops, which is expected to cause the deaths of fewer enemy civilians but is expected to result in more deaths of compatriot soldiers. Does the principle of proportionality in international humanitarian law impose a duty on an attacker to expose its soldiers to life-threatening risks in order to minimise or avert risks of incidental damage to enemy civilians? If such a duty exists, is it absolute or qualified? And if it is a qualified duty, what considerations may be taken into account in determining its character and scope? This article presents an analytic framework under the current international humanitarian law (IHL) legal structure, following a proportionality analysis. The proposed framework identifies five main positions for addressing the above queries. The five positions are arranged along two ‘axes’: a value ‘axis’, which identifies the value assigned to the lives of compatriot soldiers in relation to lives of enemy civilians; and a justification ‘axis’, which outlines the justificatory bases for assigning certain values to lives of compatriot soldiers and enemy civilians: intrinsic, instrumental or a combination thereof. The article critically assesses these positions, and favours a position which attributes a value to compatriot soldiers’ lives, premised on a justificatory basis which marries intrinsic considerations with circumscribed instrumental considerations, avoiding the indeterminacy and normative questionability entailed by more expansive instrumental considerations.