On the stability of the Earth's radiative energy balance: Response to the Mt. Pinatubo eruption

In this paper, we build and analyze the stability and consistency of decoupled schemes, involving only explicit steps, for the isentropic Euler equations and for the full Euler equations. These schemes are based on staggered space discretizations, with an upwinding performed with respect to the material velocity only. The pressure gradient is defined as the transpose of the natural velocity divergence, and is thus centered. The velocity convection term is built in such a way that the solutions satisfy a discrete kinetic energy balance, with a remainder term at the left-hand side which is shown to be non-negative under a CFL condition. In the case of the full Euler equations, we solve the internal energy balance, to avoid the space discretization of the total energy, whose expression involves cell-centered and face-centered variables. However, since the residual terms in the kinetic energy balance (probably) do not tend to zero with the time and space steps when computing shock solutions, we compensate them by corrective terms in the internal energy equation, to make the scheme consistent with the conservative form of the continuous problem. We then show, in one space dimension, that, if the scheme converges, the limit is indeed an entropy weak solution of the system. In any case, the discretization preserves by construction the convex of admissible states (positivity of the density and, for Euler equations, of the internal energy), under a CFL condition. Finally, we present numerical results which confort this theory.

Download Full-text

Stochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing

Discrete and Continuous Dynamical Systems - Series S ◽

10.3934/dcdss.2021165 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Gregorio Díaz ◽

Jesús Ildefonso Díaz

Keyword(s):

Energy Balance ◽

Wiener Process ◽

Climate Models ◽

Random Parameter ◽

Parabolic Problems ◽

Change Of Variables ◽

Wiener Processes ◽

Cylindrical Wiener Process ◽

The Stability ◽

Suitable Change

<p style='text-indent:20px;'>We consider a class of one-dimensional nonlinear stochastic parabolic problems associated to Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forcing. Our results use in an important way that, under suitable assumptions on the Wiener processes, a suitable change of variables leads the problem to a pathwise random PDE, hence an essentially "deterministic" formulation depending on a random parameter. Two applications are also given: the stability of solutions when the Wiener process converges to zero and the asymptotic behaviour of solutions for large time.</p>

Download Full-text

Evaporation suppression and energy balance of water reservoirs covered with self-assembling floating elements

Hydrology and Earth System Sciences ◽

10.5194/hess-22-4015-2018 ◽

2018 ◽

Vol 22 (7) ◽

pp. 4015-4032 ◽

Cited By ~ 10

Author(s):

Milad Aminzadeh ◽

Peter Lehmann ◽

Dani Or

Keyword(s):

Energy Balance ◽

Water Storage ◽

Climatic Conditions ◽

Heat Fluxes ◽

Conservation Strategy ◽

Radiative Energy ◽

Water Reservoirs ◽

Local Climate ◽

Self Assembling ◽

Evaporation Suppression

Abstract. The growing pressure on natural freshwater resources and the projected climate variability are expected to increase the need for water storage during rainy periods. Evaporative losses present a challenge for the efficiency of water storage in reservoirs, especially in arid regions with chronic water shortages. Among the available methods for suppressing evaporative losses, self-assembling floating elements offer a simple and scalable solution, especially for small reservoirs. The use of floating elements has often been empirically based; we thus seek a framework for systematic consideration of floating element properties, local climate and reservoir conditions to better predict evaporative loss, energy balance and heat fluxes from covered water reservoirs. We linked the energy balance of the water column with energy considerations of the floating elements. Results suggest significant suppression of evaporative losses from covered reservoirs in which incoming radiative energy is partitioned to sensible and long wave fluxes that reduce latent heat flux and thus increase the Bowen ratio over covered water reservoirs. Model findings were consistent with laboratory-scale observations using an uncovered and covered small basin. The study offers a physically based framework for testing design scenarios in terms of evaporation suppression efficiency for various climatic conditions; it hence strengthens the science in the basis of this important water resource conservation strategy.

Download Full-text

Correction to: Importance of the green color, absorption gradient, and spectral absorption of chloroplasts for the radiative energy balance of leaves

Journal of Plant Research ◽

10.1007/s10265-018-1014-0 ◽

2018 ◽

Vol 131 (3) ◽

pp. 569-569 ◽

Cited By ~ 1

Author(s):

Atsushi Kume

Keyword(s):

Energy Balance ◽

Radiative Energy ◽

Spectral Absorption ◽

Green Color ◽

Absorption Gradient

Download Full-text

A Method to Accelerate Convergence and to Preserve Radiative Energy Balance in Solving the P1 Equation by Iterative Methods

Journal of Heat Transfer ◽

10.1115/1.1423318 ◽

2002 ◽

Vol 124 (3) ◽

pp. 580-582 ◽

Cited By ~ 8

Author(s):

Genong Li and ◽

Michael F. Modest

Keyword(s):

Energy Balance ◽

Boundary Conditions ◽

Iterative Methods ◽

Radiative Energy ◽

The Third ◽

Iterative Solutions ◽

Accelerate Convergence ◽

Acceleration Method

An acceleration method is proposed particularly for the P1 equation. The radiative energy balance is used as a constraint to correct iterative solutions. The method not only accelerates convergence but also preserves the radiative energy balance, the latter being of great importance when radiation calculations are coupled with flow calculations. This acceleration method can be applied to other elliptical problems with boundary conditions of the second and/or the third kind.

Download Full-text

A benchmark dataset of in situ Antarctic surface melt rates and energy balance

Journal of Glaciology ◽

10.1017/jog.2020.6 ◽

2020 ◽

Vol 66 (256) ◽

pp. 291-302

Author(s):

Constantijn L. Jakobs ◽

Carleen H. Reijmer ◽

C. J. P. Paul Smeets ◽

Luke D. Trusel ◽

Willem Jan van de Berg ◽

...

Keyword(s):

Energy Balance ◽

Climate Model ◽

Ice Sheet ◽

Benchmark Dataset ◽

Shortwave Radiation ◽

Balance Model ◽

Ice Shelves ◽

Surface Melt ◽

The Stability

AbstractSurface melt on the coastal Antarctic ice sheet (AIS) determines the viability of its ice shelves and the stability of the grounded ice sheet, but very few in situ melt rate estimates exist to date. Here we present a benchmark dataset of in situ surface melt rates and energy balance from nine sites in the eastern Antarctic Peninsula (AP) and coastal Dronning Maud Land (DML), East Antarctica, seven of which are located on AIS ice shelves. Meteorological time series from eight automatic and one staffed weather station (Neumayer), ranging in length from 15 months to almost 24 years, serve as input for an energy-balance model to obtain consistent surface melt rates and energy-balance results. We find that surface melt rates exhibit large temporal, spatial and process variability. Intermittent summer melt in coastal DML is primarily driven by absorption of shortwave radiation, while non-summer melt events in the eastern AP occur during föhn events that force a large downward directed turbulent flux of sensible heat. We use the in situ surface melt rate dataset to evaluate melt rates from the regional atmospheric climate model RACMO2 and validate a melt product from the QuikSCAT satellite.

Download Full-text