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

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>

Revisiting albedo from a fuzzy perspective

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Morteza Pakdaman ◽  
Majid Habibi Nokhandan ◽  
Yashar Falamarzi
Keyword(s):  
Differential Equation ◽  
Energy Balance ◽  
Fuzzy Number ◽  
Climate Models ◽  
Energy Balance Model ◽  
Fuzzy Differential Equation ◽  
Balance Model ◽  
Content Type ◽  
Fuzzy Energy ◽  
Fuzzy Derivative

PurposeThe aim of this paper is to revisit the albedo for uncertainty. The albedo is considered as a fuzzy value due to some realistic reasons which they will be discussed in details. After defining an appropriate uncertain albedo by using fuzzy set theory, the related energy balance model is also redefined as a fuzzy differential equation by using the concept of fuzzy derivative.Design/methodology/approachThe well-known Earth energy balance model is redefined as a fuzzy differential equation by using the concept of fuzzy derivative. Thus, instead of an ordinary differential equation, a fuzzy differential equation arises which it's solution procedure will be discussed in details.FindingsResults indicate that the fuzzy uncertainty for albedo causes more real results after solving the fuzzy energy balance equation. Considering albedo as a fuzzy number is more realistic than considering a single certain number for albedo of a surface. This is due to this fact that the Earth's surface coverage is not crisp and the boundaries of different types of lands are not consistent. The proposed approach of this paper can help us to provide more realistic climate models and construct dynamical models which can model the albedo based on its variability.Originality/valueIn this paper, we defined fuzzy energy balance model as a fuzzy differential equation for the first time. We also, considered albedo as a fuzzy number which is another novel approach.

scholarly journals The cloud-free global energy balance and inferred cloud radiative effects: an assessment based on direct observations and climate models

2018 ◽  
Vol 52 (7-8) ◽  
pp. 4787-4812 ◽  
Author(s):  
Martin Wild ◽  
Maria Z. Hakuba ◽  
Doris Folini ◽  
Patricia Dörig-Ott ◽  
Christoph Schär ◽  
...  
Keyword(s):  
Energy Balance ◽  
Climate Models ◽  
Radiative Effects ◽  
Global Energy ◽  
Global Energy Balance ◽  
Direct Observations ◽  
Cloud Radiative Effects

scholarly journals Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations

2018 ◽  
Vol 52 (3) ◽  
pp. 893-944 ◽  
Author(s):  
Raphaèle Herbin ◽  
Jean-Claude Latché ◽  
Trung Tan Nguyen
Keyword(s):  
Energy Balance ◽  
Kinetic Energy ◽  
Internal Energy ◽  
Euler Equations ◽  
Left Hand ◽  
Isentropic Euler Equations ◽  
Space Discretization ◽  
Face Centered ◽  
The Stability ◽  
Stability And Consistency

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.

scholarly journals A general framework for understanding the response of the water cycle to global warming over land and ocean

2013 ◽  
Vol 10 (12) ◽  
pp. 15263-15294 ◽  
Author(s):  
M. L. Roderick ◽  
F. Sun ◽  
W. H. Lim ◽  
G. D. Farquhar
Keyword(s):  
Energy Balance ◽  
Surface Energy ◽  
Surface Energy Balance ◽  
Climate Models ◽  
Climate Model ◽  
Water Cycle ◽  
Specific Humidity ◽  
Water Vapour Content ◽  
Long Wave ◽  
Small Change

Abstract. Climate models project increases in globally averaged atmospheric specific humidity at the Clausius–Clapeyron (CC) value of around 7% K−1 whilst projections for precipitation (P) and evaporation (E) are somewhat muted at around 2% K−1. Such global projections are useful summaries but do not provide guidance at local (grid box) scales where impacts occur. To bridge that gap in spatial scale, previous research has shown that the following relation, Δ(P − E) &amp;propto; P − E, holds for zonal averages in climate model projections. In this paper we first test whether that relation holds at grid box scales over ocean and over land. We find that the zonally averaged relation does not hold at grid box scales. We further find that the zonally averaged relation does not hold over land – it is specific to zonal averages over the ocean. As an alternative we tested whether the long-standing Budyko framework of catchment hydrology could be used to synthesise climate model projections over land. We find that climate model projections of Δ(P − E) out to the year 2100 conform closely to the Budyko framework. The analysis also revealed that climate models project little change in the net irradiance at the surface. To understand that result we examined projections of the key surface energy balance terms. In terms of global averages, we find the climate model projections are dominated by changes in only three terms of the surface energy balance; an increase in the incoming longwave irradiance while the responses are (mostly) restricted to the outgoing longwave irradiance with a small change in the evaporative flux. Because the change in outgoing longwave irradiance is a function of the change in surface temperature, we show that the precipitation sensitivity (i.e. 2% K−1) is an accurate summary of the partitioning of the greenhouse-induced surface forcing. With that we demonstrate that the precipitation sensitivity (2% K−1) is less than the CC value (7% K−1) because most of the greenhouse-induced surface forcing is partitioned into outgoing longwave irradiance (instead of evaporation). In essence, the models respond to elevated [CO2] by an increase in atmospheric water vapour content that increases the incoming long-wave irradiance at the surface. The surface response is dominated by a near equal increase in outgoing long-wave irradiance with only minor changes in other terms of the surface energy balance.

scholarly journals Evaluating multi-year, multi-site data on the energy balance closure of eddy-covariance flux measurements at cropland sites in southwestern Germany

2019 ◽  
Vol 16 (2) ◽  
pp. 521-540 ◽  
Author(s):  
Ravshan Eshonkulov ◽  
Arne Poyda ◽  
Joachim Ingwersen ◽  
Hans-Dieter Wizemann ◽  
Tobias K. D. Weber ◽  
...  
Keyword(s):  
Energy Balance ◽  
Eddy Covariance ◽  
Wind Direction ◽  
Climate Models ◽  
Global Climate Models ◽  
Energy Balance Closure ◽  
Prevailing Wind ◽  
Atmospheric Conditions ◽  
Prevailing Wind Direction ◽  
Wide Range

Abstract. The energy balance of eddy-covariance (EC) measurements is typically not closed, resulting in one of the main challenges in evaluating and interpreting EC flux data. Energy balance closure (EBC) is crucial for validating and improving regional and global climate models. To investigate the nature of the gap in EBC for agroecosystems, we analyzed EC measurements from two climatically contrasting regions (Kraichgau – KR – and Swabian Jura – SJ) in southwestern Germany. Data were taken at six fully equipped EC sites from 2010 to 2017. The gap in EBC was quantified by ordinary linear regression, relating the energy balance ratio (EBR), calculated as the quotient of turbulent fluxes and available energy, to the residual energy term. In order to examine potential reasons for differences in EBC, we compared the EBC under varying environmental conditions and investigated a wide range of possible controls. Overall, the variation in EBC was found to be higher during winter than summer. Moreover, we determined that the site had a statistically significant effect on EBC but no significant effect on either crop or region (KR vs SJ). The time-variable footprints of all EC stations were estimated based on data measured in 2015, complimented by micro-topographic analyses along the prevailing wind direction. The smallest mean annual energy balance gap was 17 % in KR and 13 % in SJ. Highest EBRs were mostly found for winds from the prevailing wind direction. The spread of EBRs distinctly narrowed under unstable atmospheric conditions, strong buoyancy, and high friction velocities. Smaller footprint areas led to better EBC due to increasing homogeneity. Flow distortions caused by the back head of the anemometer negatively affected EBC during corresponding wind conditions.

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