The calculation of geopotential and the pressure gradient in the ECMWF atmospheric model: Influence on the simulation of the polar atmosphere and on temperature analyses

The spectral atmospheric model used for prediction at the European Centre for Medium Range Weather Forecasts (ECMWF) is modified to change the spectrally‐represented thermodynamic variable from temperature to the deviation of temperature from a reference profile which depends analytically on pressure. There is only a minor change to the form of the thermodynamic equation, and the calculation of the pressure gradient is modified to eliminate some of the cancellation between the Δ and RT ΔIn p terms which occurs in the standard formulation. At T42 resolution the revised scheme significantly improves southern hemispheric forecasts, with differences originating over Antarctica. There is also a small improvement over the Arctic. Sensitivity is much less at T106 resolution, but a minor advantage can still be seen in high southern latitudes, and there is a reduction in noise in the vertical velocity field near the Andes at tropical latitudes. Similar results are found for a version in which surface pressure, rather than its logarithm, is chosen as a spectrally represented prognostic variable. This gives mass conservation but the stability of the semi‐implicit time integration is somewhat reduced. The improvement seen at high latitudes is also captured by a simpler revision which retains temperature as the spectrally‐represented variable, and uses a reference temperature only in the computation of the pressure‐gradient terms in gridpoint space. Results indicate that much of the systematic difference in behaviour between T42 and T106 simulations at high latitudes can be removed by changing the pressure‐gradient calculation. In particular, the new schemes correct a systematic tendency for erroneously high pressures east of the Ross Ice Shelf over Antarctica in lower resolution simulations at medium and longer time ranges. Improvement occurs because the schemes reduce an inconsistent treatment of the Δ and RT ΔIn p terms in the model's semi‐implicit treatment of the vorticity equation. The reference temperature profile has also been used in data assimilation to reduce a systematic error in the calculation of first‐guess geopotential heights at standard pressure levels. The resulting height analyses agree slightly better with radiosonde measurements, and initialization causes less of a degradation of the fit to observed data. Temperatures are systematically warmer in the upper troposphere (by almost 0.5 K in the global mean at 200 hPa) and cooler in the lower troposphere, and are closer to observed values. Results from forecasts carried out after one and two days of assimilation show small improvements in the short and early medium range, and are inconclusive at longer time ranges.