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David L. Williamson
and
Jerry G. Olson

Abstract

A semi-Lagrangian version of the National Center for Atmospheric Research Community Climate Model is developed. Special consideration is given to energy consistency aspects. In particular, approximations are developed in which the pressure gradient in the momentum equations is consistent with the energy conversion term in the thermodynamic equation. In addition, consistency between the discrete continuity equation and the vertical velocity ω in the energy conversion term of the thermodynamic equation is obtained. Simulated states from multiple-year simulations from the semi-Lagrangian and Eulerian versions are compared. The principal difference in the simulated climate appears in the zonal average temperature. The semi-Lagrangian simulation is colder than the Eulerian at and above the tropical tropopause. The terms producing the thermodynamic balance are examined. It is argued that the semi-Lagrangian scheme produces less computational smoothing of the temperature at the tropopause than the first-order finite-difference vertical advection approximations in the Eulerian version. Thus, by decreasing this particular computational error, the semi-Lagrangian produces less computational warming at the tropical tropopause. The net result is a colder tropical tropopause.

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David L. Williamson
and
Jerry G. Olson

Abstract

The differences in the polar lower-troposphere temperature simulated by semi-Lagrangian and Eulerian approximations are examined and their cause is identified. With grids having 8–10 layers below 500 mb, semi-Lagrangian simulations are colder than Eulerian by 2–4 K in the region poleward of 60°N and below 400 mb in winter. Diagnostic calculations with the NCAR CCM3 show that the semi-Lagrangian dynamical approximations tend to produce a cooling relative to the Eulerian at the 860-mb grid level. The difference occurs over land and sea ice where an inversion forms in the atmosphere with its top at the 860-mb grid level. The source of the difference is shown to be the different way the vertical advection approximations treat vertical structures found at the tops of marginally resolved inversions when the vertical velocity is reasonably vertically uniform surrounding the top of the inversion. The Eulerian approximations underestimate the cooling that should occur at the top of the inversion. This is also verified with diagnostic calculations on a grid with substantially increased resolution below 800 mb. On this grid, the adiabatic tendency differences between semi-Lagrangian and Eulerian approximations are small and the two approximations produce the same simulated lower-tropospheric temperature, which is also the same as that produced by the semi-Lagrangian approximations on the coarse grid. Compared to the NCEP reanalysis, the low vertical resolution Eulerian simulated temperature looks better than the semi-Lagrangian, but those approximations produce that “better” simulated temperature by an incorrect mechanism. For practical applications, the Eulerian approximations require higher vertical resolution below 800 mb than usually used today in climate models, but the semi-Lagrangian approximations are adequate on these coarser grids.

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Kevin E. Trenberth
and
Jerry G. Olson

Abstract

A detailed analysis of atmospheric temperatures at the South Pole and McMurdo Sound is presented. Missing data are common, especially in the stratosphere, and the usual practice of computing monthly means as an average of all available observations produces unreliable results because the annual cycle is aliased onto the interannual variations and longer term trends. A methodology to rectify this involves computation of the smoothed mean annual cycle for each day of the year and then subsequently analyzing the anomalies. The persistence of the anomalies within each month reveals that regular observations about every three days are required to produce a reliable climate record throughout the troposphere and lower stratosphere. A comparison of station data with lower stratospheric analyzed values from the National Meteorological Center (NMC) reveals big discrepancies at times arising mainly from methods used to produce the NMC analyses.

The mean annual cycle of temperature features the coreless winter at low levels at both stations. The largest amplitude annual cycle occurs at 10 mb with maximum temperatures in December. The maximum occurs progressively later at lower levels down to 200 mb, where it occurs in February. The seasonal transition occurs more rapidly in spring than in autumn. Interannual fluctuations are dominated by a quasi-biennial variation.

Noticeable downward trends in temperature were found mainly near the time of greatest variability, in late spring. Temperatures decreased between 50 and 100 mb in October and November and at 100 mb in December and January; but only from 1985 to 1987 have monthly means gone outside the range of previous variations. The most extreme anomalies, of as much as −21°C, were found in November 1987. The downward trends arise from a delay in the spring warming apparently brought about by the diminished solar heating due to low ozone amounts associated with the “ozone hole.” Trends from 1979 to 1986 or 1987, which is the period of satellite data on temperatures and ozone, are not representative of the overall record which begins in 1956.

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Kevin E. Trenberth
and
Jerry G. Olson

In order to help establish a global climate record data sets of global analyses from the U.S. National Meteorological Center (NMC) and the European Centre for Medium Range Weather Forecasts (ECMWF) have been comprehensively evaluated.

A detailed chronology of the changes in the analysis-forecast system at NMC and ECMWF has been compiled and the main impacts on the analyses have been identified. Discontinuities have been found in certain characteristics of the analyses when major changes occur. The main quantities so affected are the divergent wind component and associated vertical motion fields, and the moisture fields.

A detailed intercomparison of the two data sets and statistical results show fairly widespread agreement between the analyses from the two centers over the Northern Hemisphere extratropics. In general, the quality of the analyses is much lower in the tropics and Southern Hemisphere. This is reflected in much greater differences in wind fields south of 20°N, with root-mean-square differences in the north-south and east-west components often exceeding 5ms−1 above ~500 mb throughout most of this region. Much greater differences in geopotential height south of ~30°S exist.

Major problems at NMC prior to May 1986 occur south of ~50°S. ECMWF has also experienced difficulties over and around Antarctica, especially prior to 1982. In the tropics, there are major disagreements between the analyses of the divergent wind field and associated vertical motions which have become more intense and more realistic with time, but still appear to be poorly known. The relative humidity field is the poorest known and has undergone major changes with time at both centers. Possible reasons for these results are discussed and some implications and recommendations are given.

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David L. Williamson
and
Jerry G. Olson

Abstract

The authors compare short forecast errors and the balance of terms in the moisture and temperature prediction equations that lead to those errors for the Community Atmosphere Model versions 2 and 3 (CAM2 and CAM3, respectively) at T42 truncation. The comparisons are made for an individual model column from global model forecasts at the Atmospheric Radiation Measurement Program (ARM) Southern Great Plains site for the April 1997 and June–July 1997 intensive observing periods. The goal is to provide insight into parameterization errors in the CAM, which ultimately should lead to improvements in the way processes are modeled. The atmospheric initial conditions are obtained from the 40-yr ECMWF Re-Analysis (ERA-40). The land initial conditions are spun up to be consistent with those analyses. The differences between the model formulations that are responsible for the major differences in the forecast errors and/or parameterization behaviors are identified. A sequence of experiments is performed, accumulating the changes from CAM3 back toward CAM2 to demonstrate the effect of the differences in formulations.

In June–July 1997 the CAM3 temperature and moisture forecast errors were larger than those of CAM2. The terms identified as being responsible for the differences are 1) the convective time scale assumed for the Zhang–McFarlane deep convection, 2) the energy associated with the conversion between water and ice of the rain associated with the Zhang–McFarlane convection parameterization, and 3) the dependence of the rainfall evaporation on cloud fraction. In April 1997 the CAM2 and CAM3 temperature and moisture forecast errors are very similar, but different tendencies arising from modifications to one parameterization component are compensated by responding changes in another component to yield the same total moisture tendency. The addition of detrainment of water in CAM3 by the Hack shallow convection to the prognostic cloud water scheme is balanced by a responding difference in the advective tendency. A halving of the time scale assumed for the Hack shallow convection was compensated by a responding change in the prognostic cloud water. Changes to the cloud fraction parameterization affect the radiative heating, which in turn modifies the stability of the atmospheric column and affects the convection. The resulting changes in convection tendency are balanced by responding changes in the prognostic cloud water parameterization tendency.

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Kevin E. Trenberth
,
William G. Large
, and
Jerry G. Olson

Abstract

Computations of the surface wind stress and pseudostress over the global oceans have been made using surface winds from the European Centre for Medium Range Weather Forecasts for 7 years. The drag coefficient is a function of wind speed and atmospheric stability, and the air density is computed for each observation. Assuming a constant density, the effective drag coefficient required to convert the pseudostress into a stress has been computed for each month of the year using several methods. Because the drag coefficient varies from day-to-day and with the seasons, the effective drag coefficient cannot be uniquely defined and is a useful concept if only the very gross characteristics of the field are of interest and errors of the order of 10% are tolerable. Even then, the spatial and seasonal variations in CD must be taken into amount, and occasionally the wind stress may be greatly in error.

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Kevin E. Trenberth
,
William G. Large
, and
Jerry G. Olson

Abstract

The mean annual cycle in surface wind stress over the global oceans from surface wind analyses from the European Centre for Medium Range Weather Forecasts (ECMWF) for seven years (1980–86) is presented. The drag coefficient is a function of wind speed and atmospheric stability, and the density is computed for each observation. Annual and seasonal mean climatologies of wind stress, wind stress and Sverdrup transport and the first two annual harmonies of the wind stress are presented. The Northern and Southern hemispheres are contrasted as an the Pacific and Atlantic basins. The representativeness of the climatology is also assessed. The main shortcomings with the current results are in the topics.

The wind stress statistics over the southern ocean are believed to be the moon reliable because of the paucity of direct wind observations. Annual mean values exceed 2 dyn cm−2 over the eastern hemisphere near 50°S and locally exceed 3 dyn cm−2 in the southern Indian Ocean; values much larger than in previous climatologies. The 12 month variations dominate the annual cycle over most of the globe and are strongest in the Arabian Sea, North Pacific and North Atlantic. But strong semiannual components occur especially over the Southern Ocean and in the North Pacific. The former are associated with semiannual increases in the strength of the southern westerlies whereas in the North Pacific, the semiannual cycle occurs locally largely because of the annual variations in intensity and meridional movement of the Aleutian low and subtropical high.

The wind stress considerably from year to year. Over most of the world's ocean the mean annual cycle explains less then 45% of the monthly variance in each of the wind stress components and the curl of wind stress. In addition, mean values for the climatology differ significantly from those of previous periods. There is good reason to believe that these differences in the Northern Hemisphere an mostly real and represent climate variations on interannual and decadal time scales that have major implications for the circulation of the oceans. A related factor is that this period included two Pacific Warm Events (El Niños), but no Cold (La Niña) Events.

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David L. Williamson
,
Jerry G. Olson
, and
Byron A. Boville

Abstract

At the modest vertical resolutions typical of climate models, simulations produced by models based on semi-Lagrangian approximations tend to develop a colder tropical tropopause than matching simulations from models with Eulerian approximations, all other components of the model being the same. The authors examine the source of this relative cold bias in the context of the NCAR CCM3 and show that it is primarily due to insufficient vertical resolution in the standard 18-level model, which has 3-km spacing near the tropopause. The difference is first diagnosed with the Held and Suarez idealized forcing to eliminate the complex radiative–convective feedback that affects the tropopause formation in the complete model. In the Held and Suarez case, the tropical simulations converge as the vertical grid layers are halved to produce 36 layers and halved again to produce 72 layers. The semi-Lagrangian approximations require extra resolution above the original 18 to capture the converged tropical tropopause. The Eulerian approximations also need the increased resolution to capture the single-level tropopause implied by the 36- and 72-level simulations, although with 18 layers it does not produce a colder tropopause, just a thicker multilevel tropopause. The authors establish a minimal grid of around 25 levels needed to capture the structure of the converged simulation with the Held and Suarez forcing. The additional resolution is added between 200 and 50 mb, giving a grid spacing of about 1.3 km near the tropopause. With this grid the semi-Lagrangian and Eulerian approximations also create the same tropical structure in the complete model. With both approximations the convective parameterization is better behaved with the extra upper-tropospheric resolution. A benefit to both approximations of the additional vertical resolution is a reduction of the tropical temperature bias compared to the NCEP reanalysis. The authors also show that the Eulerian approximations are prone to stationary grid-scale noise if the vertical grid is not carefully defined. The semi-Lagrangian shows no indication of stationary vertical-grid-scale noise. In addition, the Eulerian simulation exhibits significantly greater transient vertical-grid-scale noise than the semi-Lagrangian.

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David L. Williamson
,
Jerry G. Olson
, and
Christiane Jablonowski

Abstract

Two flaws in the semi-Lagrangian algorithm originally implemented as an optional dynamical core in the NCAR Community Atmosphere Model (CAM3.1) are exposed by steady-state and baroclinic instability test cases. Remedies are demonstrated and have been incorporated in the dynamical core. One consequence of the first flaw is an erroneous damping of the speed of a zonally uniform zonal wind undergoing advection by a zonally uniform zonal flow field. It results from projecting the transported vector wind expressed in unit vectors at the arrival point to the surface of the sphere and is eliminated by rotating the vector to be parallel to the surface. The second flaw is the formulation of an a posteriori energy fixer that, although small, systematically affects the temperature field and leads to an incorrect evolution of the growing baroclinic wave. That fixer restores the total energy at each time step by changing the provisional forecast temperature proportionally to the magnitude of the temperature change at that time step. Two other fixers are introduced that do not exhibit the flaw. One changes the provisional temperature everywhere by an additive constant, and the other changes it proportionally by a multiplicative constant.

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Brian Medeiros
,
David L. Williamson
,
Cécile Hannay
, and
Jerry G. Olson

Abstract

Forecasts of October 2006 are used to investigate southeast Pacific stratocumulus in the Community Atmosphere Model, versions 4 and 5 (CAM4 and CAM5). Both models quickly develop biases similar to their climatic biases, suggesting that parameterized physics are the root of the climate errors. An extensive cloud deck is produced in CAM4, but the cloud structure is unrealistic because the boundary layer is too shallow and moist. The boundary layer structure is improved in CAM5, but during the daytime the boundary layer decouples from the cloud layer, causing the cloud layer to break up and transition toward a more trade wind cumulus structure in the afternoon. The cloud liquid water budget shows how different parameterizations contribute to maintaining these different expressions of stratocumulus. Sensitivity experiments help elucidate the origins of the errors. The importance of the diurnal cycle of these clouds for climate simulations is emphasized.

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