The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

The ocean's gravitational potential energy budget in a coupled climate model

This study examines, in a unified fashion, the budgets of ocean gravitational potential energy (GPE) and available gravitational potential energy (AGPE) in the control simulation of the coupled atmosphere–ocean general circulation model HadCM3. Only AGPE can be converted into kinetic energy by adiabatic processes. Diapycnal mixing supplies GPE, but not AGPE, whereas the reverse is true of the combined effect of surface buoyancy forcing and convection. Mixing and buoyancy forcing, thus, play complementary roles in sustaining the large scale circulation. However, the largest globally integrated source of GPE is resolved advection (+0.57 TW) and the largest sink is through parameterized eddy transports (-0.82 TW). The effect of these adiabatic processes on AGPE is identical to their effect on GPE, except for perturbations to both budgets due to numerical leakage exacerbated by non-linearities in the equation of state.

Thermobaric control of gravitational potential energy generation by diapycnal mixing in the deep ocean

Sources and sinks of gravitational potential energy (GPE) play a rate-limiting role in the large scale ocean circulation. A key source is turbulent diapycnal mixing, whereby irre- versible mixing across isoneutral surfaces is enhanced by turbulent straining of these surfaces. This has motivated international observational efforts to map diapycnal mixing in the global ocean. However, in order to accurately relate the GPE supplied to the large scale circulation by diapycnal mixing to the mixing energy source, it is first necessary to determine the ratio, ξ , of the GPE generation rate to the available potential energy dissipation rate associated with turbulent mixing. Here, the link between GPE and hydro- static pressure is used to derive the GPE budget for a com- pressible ocean with a nonlinear equation of state. The role of diapycnal mixing is isolated and from this a global cli- matological distribution of ξ is calculated. It is shown that, for a given source of mixing energy, typically three times as much GPE is generated if the mixing takes place in bottom waters rather than in the pycnocline. This is due to GPE destruction by cabbelling in the pycnocline, as opposed to thermobaric enhancement of GPE generation by diapycnal mixing in the deep ocean.

Estimating the direct aerosol radiative perturbation: impact of ocean surface representation and aerosol non-sphericity

Atmospheric aerosols are now actively studied, in particular because of their radiative and climate impacts. Estimations of the direct aerosol radiative perturbation, caused by extinction of incident solar radiation, usually rely on radiative transfer codes and involve simplifying hypotheses. This paper addresses two approximations which are widely used for the sake of simplicity and limiting the computational cost of the calculations. Firstly, it is shown that using a Lambertian albedo instead of the more rigorous bidirectional reflectance distribution function (BRDF) to model the ocean surface radiative properties leads to large relative errors in the instantaneous aerosol radiative perturbation. When averaging over the day, these errors cancel out to acceptable levels of less than 3% (except in the northern hemisphere winter). The other scope of this study is to address aerosol non-sphericity effects. Comparing an experimental phase function with an equivalent Mie-calculated phase function, we found acceptable relative errors if the aerosol radiative perturbation calculated for a given optical thickness is daily averaged. However, retrieval of the optical thickness of non-spherical aerosols assuming spherical particles can lead to significant errors. This is due to significant differences between the spherical and non-spherical phase functions. Discrepancies in aerosol radiative perturbation between the spherical and non-spherical cases are sometimes reduced and sometimes enhanced if the aerosol optical thickness for the spherical case is adjusted to fit the simulated radiance of the non-spherical case.

Estimates of global multicomponent aerosol optical depth and direct radiative perturbation in the Laboratoire de Météorologie Dynamique general circulation model

The global cycle of multicomponent aerosols including sulfate, black carbon (BC),organic matter (OM), mineral dust, and sea salt is simulated in the Laboratoire de Me´te´orologie Dynamique general circulation model (LMDZT GCM). The seasonal open biomass burning emissions for simulation years 2000–2001 are scaled from climatological emissions in proportion to satellite detected fire counts. The emissions of dust and sea salt are parameterized online in the model. The comparison of model-predicted monthly mean aerosol optical depth (AOD) at 500 nm with Aerosol Robotic Network (AERONET) shows good agreement with a correlation coefficient of 0.57(N = 1324) and 76% of data points falling within a factor of 2 deviation. The correlation coefficient for daily mean values drops to 0.49 (N = 23,680). The absorption AOD (ta at 670 nm) estimated in the model is poorly correlated with measurements (r = 0.27, N = 349). It is biased low by 24% as compared to AERONET. The model reproduces the prominent features in the monthly mean AOD retrievals from Moderate Resolution Imaging Spectroradiometer (MODIS). The agreement between the model and MODIS is better over source and outflow regions (i.e., within a factor of 2).There is an underestimation of the model by up to a factor of 3 to 5 over some remote oceans. The largest contribution to global annual average AOD (0.12 at 550 nm) is from sulfate (0.043 or 35%), followed by sea salt (0.027 or 23%), dust (0.026 or 22%),OM (0.021 or 17%), and BC (0.004 or 3%). The atmospheric aerosol absorption is predominantly contributed by BC and is about 3% of the total AOD. The globally and annually averaged shortwave (SW) direct aerosol radiative perturbation (DARP) in clear-sky conditions is �2.17 Wm�2 and is about a factor of 2 larger than in all-sky conditions (�1.04 Wm�2). The net DARP (SW + LW) by all aerosols is �1.46 and �0.59 Wm�2 in clear- and all-sky conditions, respectively. Use of realistic, less absorbing in SW, optical properties for dust results in negative forcing over the dust-dominated regions.