Temperature zonally averaged

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. 

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. 

The calculation is performed in terms of degrees Celsius, including values both above and below zero. It is not convenient, therefore, to use the relative increment of temperature as a test for step size in subroutine CHECKSTEP. I use absolute increments instead. At the end of subroutine SPECS, I set incind equal to 3 for all equations, limiting the absolute increment in temperature to 3° per time step. Zonally averaged heat capacity as a function of latitude is calculated in subroutine CLIMINP in terms of land fraction and the heat capacity parameters specified in SPECS. It is returned in the array heap. 

Fig. 7-9. Calculated values of seasonally varying temperatures at three latitudes in the Southern Hemisphere, plotted as solid lines. Observed zonally averaged temperatures at these latitudes are plotted as symbols.

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... 

Zonally averaged, 10-y temperature trend in °C/y for 1993 to 2003 caloulated using a ieast squares fit from in situ data. Source After Wiiiis, J. K., et al. (2004). Journal of Geophysioal Research 109, Cl 2036. (See companion website for coior version.)... 

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 5.17 Pearson correlation coefficient (R) between the WIBIX and 360° zonally averaged winter anomalies (JFM) in the air temperature derived from (WCP, 1987) for slices of five degrees between 15°N and 85°N during of the last continental climate mode (1951-1986) vertical hues mark the 95% confidence level (/-distribution) while the box indicates the averaged belt of the planetary frontal zone with imbedded westerlies note the increasing poleward correlation due to the increasing effect of the AO. 

WCP, 1987. Monthly, zonally averaged air temperature at the sea level. World Climate Programme. Climate System Monitoring Monthly Bulletin 3. 

Figure 3.2. Zonally averaged temperature (K) from the surface to approximately 120 km altitude in January, based on Fleming et al. (1988). Note the temperature minimum (less than 200 K) at the tropical tropopause, the temperature maximum (280 K) at the summer stratopause and the temperature minimum (less than 140 K) at the summer mesopause. The height of the mesopause increases from approximately 90 km in summer to 100 km in winter.

Figure 3.7. Zonally averaged distribution of the potential temperature unbroken lines, in K) from the surface to approximately 30 km altitude 10 hPa). The isolines for the absolute temperature (dashed lines, in K) are also shown. The tropopause is represented by the dotted line. Note that isentropes corresponding to potential temperatures larger than 380 K are located exclusively in the stratosphere (an area called the overworld ). Air parcels located in the lowermost stratosphere between the tropopause and the 380 K isentrope (an area called the middle world) are susceptible to crossing the tropopause when adiabatically transported, and entering the troposphere also called the underworld). From Holton et al. (1995), based on Appenzeller 1994).

Figure 3.9. Zonally averaged distribution of the modified potential vorticity (unbroken lines in 10-4K m2s-1kg-1) from the surface to approximately 30 km altitude (10 hPa). The potential temperature (K) is represented by dashed lines and the tropopause by a dotted line. From Appenzeller (1994).

Figure 3.32. Zonally averaged temperature in the vicinity of the mesopause (65 to 105 km) observed in July by the HRDI instrument on board the Upper Atmosphere Research Satellite (UARS). From Ortland et al, 1997.

Figure 6.19. Observations of the zonally averaged temperatures in the Arctic for 82° N near 18 km, from the National Center for Environmental Prediction (NCEP) meteorological database for two illustrative recent years, together with Antarctic observations at 82°S in 1997 (shifted by six months for comparison).

This prediction can be checked with the help of radiosonde data. The instrumentation normally is not suitable to measure the low abundance of water in the upper troposphere and stratosphere, so that the data are restricted to altitudes below 7 km. Oort and Rasmussen (1971) have compiled zonally averaged, mean monthly specific humidities (H20 mass mixing ratios) as a function of height for the northern hemisphere. Average water vapor pressures computed from their values are shown in Fig. 8-1 as a function of temperature. If, as a precaution, one uses only data for altitudes... 

FIGURE 15 Latitude-time distribution of the zonal mean difference in surface air temperature (K) in response to the quadrupling of CO2. Zonal averaging is taken over both oceans and continents. [From Manabe, S., and Stouffer, R. J. (1980). J. Geophys. Res. 85, 5529-5554. Reproduced by permission of American Geophysical Union.]... 

Barotropic instability. Barotropic instability can result from a basic state with horizontal shear but no vertical shear of the zonal average wind. By the thermal wind relationship, the basic-state horizontal temperature gradient vanishes and temperature advection does not occur. Furthermore, it is assumed that the perturbed flow is purely horizontal, and therefore, by necessity, nondivergentinthe horizontal plane with no vertical shear. In this situation the potential vorticity reduces to the absolute vorticity. H.-L. Kuo showed in 1949 that such a flow is susceptible to instability. A necessary condition for barotropic instability may be derived that states that somewhere in the fluid... 

The vector F is the quasi-geostrophic EP flux. Its components are the zonally averaged northward eddy flux of zonal momentum and the zonally averaged northward eddy flux of temperature (because d dp is proportional to temperature through the hydrostatic approximation). Equation (117) shows that the EP flux divergence, defined by Eq. (115), induces changes in the basic state. 

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. 

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).

---