Zonal average models

Fig. 2.25 Temporal mean (left) and standard deviation (right) of the zonal mean volatilisation rate over 10 years [kg/(kg s)]. Dashed lines show volatilisation rates derived from zonal mean SST and wind speed (denoted as zonally averaging model). Solid lines show volatilisation rates derived from zonally resolved SST and wind speed, which were zonally averaged afterwards (denoted as zonally resolved model).

Significant economies of computation are possible in systems that consist of a one-dimensional chain of identical reservoirs. Chapter 7 describes such a system in which there is just one dependent variable. An illustrative example is the climate system and the calculation of zonally averaged temperature as a function of latitude in an energy balance climate model. In such a model, the surface temperature depends on the balance among solar radiation absorbed, planetary radiation emitted to space, and the transport of energy between latitudes. I present routines that calculate the absorption and reflection of incident solar radiation and the emission of long-wave planetary radiation. I show how much of the computational work can be avoided in a system like this because each reservoir is coupled only to its adjacent reservoirs. I use the simulation to explore the sensitivity of seasonally varying temperatures to such aspects of the climate system as snow and ice cover, cloud cover, amount of carbon dioxide in the atmosphere, and land distribution. 

I also applied the revised computational method to calculate zonally averaged temperature as a function of latitude. I introduced an energy balance climate model, which calculates surface temperature for absorbed solar energy, emitted planetary radiation, and the transport of heat between... 

FIGURE 14.22 Model-calculated percentage (a) increase in Os (zonal average) in July and (b) the corresponding contributions to instantaneous radiative forcing calculated as a function of latitude and altitude from preindustrial times to the present (adapted from Chalita et al., 1996). 

With the same model we also calculated the HO concentration distributions. Figure 1 shows the calculated zonally averaged, meridional distribution of the diumally averaged HO concentrations. They show strong maxima in the tropics, largely due to high intensities of ultraviolet radiation as a consequence of a minimum in the ozone column (units of 105 molecules/cm3). Consequently the atmospheric oxidation efficiency is strongly determined by tropical processes. For instance, most CH4 and CO are mostly removed from the atmosphere by reaction with HO in the tropics. 

The model tropopause is defined by a PV level of 3.5 pvu poleward of 20° latitude, and by a -2 K km 1 temperature lapse rate equatorward of 20° latitude. Consequently, in this study the troposphere is defined as the volume between the surface and the simulated tropopause. Because the model does not consider typical stratospheric chemical reactions explicitly, ozone concentrations are prescribed from 1-2 levels above the model tropopause up to the top of the model domain at 10 hPa. In both hemispheres we apply monthly and zonally averaged distributions from a 2D stratospheric chemistry model [31]. In the present version of the model, we use the simulated PV and the regression analysis of the MOZAIC data (Section 2) to prescribe ozone in the NH extratropical lower stratosphere, which improves the representation of ozone distributions influenced by synoptic scale disturbances [32, 33]. Furthermore, the present model contains updated reaction rates and photodissociation data [34]. 

Figure 1. Annual (2015) and zonal average increases of ozone volume mixing ratios due to aircraft emissions [ppbv] calculated by six 3-D models. The IMAGES/BISA model does not give results above 14 km, and the HARVARD model does not give results above 12 km.

On the basis of the OEOS ozone data, two model experiments were carried out experiment "A" - with 3-D ozone and experiment B - with zonal averaged ozone distribution. The model calculations started at the first day of the GEOS ozone data... 

The same physical principles are utilized to develop isotopic models which better account for the transport of air masses at a regional scale, such as done by Fisher (1992) using a regional stable isotope model coupled to a zonally averaged global model. Other authors such as Eriksson (1965) and more recently Hendricks et al. (2000) considered the transport of water both by advective and eddy diffusive processes, the latter inducing less fractionation. 

Fisher D. A. (1992) Stable isotope simulations using a regional stable isotope model coupled to a zonally averaged global model. Cold Reg. Sci. Technol. 21, 61-77. 

Garcia, R.R., and S. Solomon, A numerical model of the zonally averaged dynamical and chemical structure of the middle atmosphere. J Geophys Res 88, 1379, 1983. 

Kasting, J.F., and R.G. Roble, A zonally averaged chemical-dynamical model of the lower thermosphere. J Geophys Res 86, 9641, 1981. 

Apruzese, J.P., M R. Schoeberl, and D.F. Strobel, Parameterization of IR cooling in a middle atmosphere dynamics model, 1. Effects of the zonally averaged circulation. J Geophys Res 87, 8951, 1982. 

FIGURE 1 The calculated change (%) in the July zonally averaged concentration of tropospheric ozone between 1850 and 1990 simulated by the IMAGES model using the IS92a emission scenario. 

FIGURE 21.1 Zonally averaged components of the absorbed solar flux and emitted thermal infrared flux at the top of the atmosphere. The + and — signs denote energy gain and loss, respectively. (From Radiation and Cloud Processes in the Atmosphere Theory Observation and Modeling by Kuo-Nan Liou. Copyright 1992 by Oxford University Press, Inc. Used by permission of Oxford University Press, Inc.)... 

In summaiy, the EP flux is a vector in the meridional plane whose components, in quasi-geostrophic theory, measure the zonally averaged northward eddy fluxes of momentum and temperature. Maps of the EP flux and its divergence may be prepared from observations or the results of model calculations. Such maps may be used to infer where and to what extent the eddy motions are acting to change the mean flow and where transient, nonconservative eddy motions are present. 

This simple approach was used in the plumbosolvency control programme in Wales (Hayes et al., 2008) and enabled a zonal emission model to be calibrated that good validation of predicted RDT sample results was obtained from actual RDT sample results indicated that this simple methodology was adequate for estimating the percentage of houses with a lead pipe. However, to put this into perspective, over 11,000 results were available across 29 water supply systems, with an average of 383 RDT sample results per scheme. 

A37. Lelieveld, J. Cmtzen, P.J. Rodhe, H., 1989 Zonal Average Cloud Characteristics for Global Atmospheric Chemistry Modelling , Report CM-76, UDC 551.510.4, Glomac 89/1. International Meteorological Institute in Stockholm, University of Stockholm, 54 pp. 

Basing models on zonal mean wind speed and sea surface temperature is averaging over regions where very different regimes of interaction of wind speed, SST and volatilisation rate prevail. In a long-term mean this leads to an underestimation of the volatilisation rate and its variabilty. 

Figure 2. Zonal mean temperature (K) at approximately 85°N and SOhPa as a function of the day of year. Thick lines are observations (from FUB analyses) and thin lines are from the IGCM. For both observations and the model, average (solid line), maximum and minimum (dashed lines) temperatures are shown. The observations use the years 1972 to 1981 whilst the model results are from the simulation using an ozone scenario representative of 1979 (see text for more details).

---