## Modern-Era Retrospective analysis for Research and Applications (MERRA)

### Pressure levels intersecting the surface

Many modern atmospheric numerical models use terrain following vertical coordinates, meaning that the pressure of the lowest model level tracks the topography and does not intersect the surface. ERA40 and NCEP reanalyses have produced pressure level data extrapolated downward beneath the Earth's surface. The result is that for 850, 925 and 1000 mb levels etc, continuous grids are available. Previous versions of GEOS models and assimilation systems have not extrapolated data beneath the surface, favoring to provide undefined values when the surface pressure is lower than a given pressure level.

For instantaneous analyses, comparing GEOS5 pressure levels to other reanalyses would be straight forward, once the undefined value is considered. However, monthly averages pose a problem. There are some regions and pressure levels where the number of valid values may be available for a fraction of the times. If all valid values of GEOS5 are averaged and reported, the average would not be representative or comparable to NCEP or ERA40 reanalyses which made averages of all times.

Figure 1 850 mb temperature RMS error between GOES5 and NCEP analyses for different criteria of the sampling of missing data in the GEOS5 time series. At the left of the graphs, lower criteria allow undersampling of the monthly time series to be compared with NCEP complete monthly mean. Far right, rejects points that have missing data in the time series, so there are fewer data points, but the comparisons to NCEP are more completely sampled. (Click figure to enlarge)

This can lead to an increase in the squared error and systematic bias between GEOS5 and other reanalyses because of the temporal sampling at the edges of topography. This is also noticeable in global and regional map comparisons. We computed global monthly averages testing a range of criteria for rejecting a monthly average. The criteria are applied at each grid point and are based on the percentage of valid data over the month. In Figure 1, on the far left, if data are valid only 1% of the time during a month, a valid monthly mean value is saved. Moving right, at 20%, a grid point with valid data 20% of the month produce a monthly mean (fewer than 20% are reported as undefined). At the farthest right, the strictest criteria requires that for each gridbox to produce a monthly average much have gridpoints that have valid data 100% of the time. The two figures are global land only and North America (20-70, -170- -60). At higher pressure, there are more points affected by sub-sampling, and the errors are most noticeable in these large area averages. For higher altitudes, the large scale error drops slowly for criteria greater than 20% (more points valid 100% of the time).

Figure 2 Comparison between GEOS5 and NCEP for different criteria, and a map of the sampling percentage. At 20% criteria (data is valid only 20% of the month) large differences are apparent. These are reduced at 80%. At 100% the data should be showing only differences between full monthly averages, no effect of sampling. There are some artifacts because these figures have interpolated NCEP to the GEOS5 ½degree resolution. Differences near topography can be significant and misleading (to one not knowing about the character of the data). (Click figure to enlarge)

To address this issue in the monthly mean MERRA products, only means which include counts that exceed a threshold of 20% valid data are included in the mean. Otherwise, the monthly mean value is reported as undefined. This low value is defined to provide as much information as possible.

One difficulty that may arise is the lack of a 1000-500 mb thickness diagnostic. This was produced in some previous versions of GEOS5. However, in revising the pressure level interpolation code for MERRA, the calculation of 1000 mb height has been left out, and so, 1000-500 mb height is not available. Also, consider that the 1000 mb analyses will have undefined data over large areas of the globe (land and ocean). Lowest model level data are also available that may be suitable for some purposes, instead of the 1000mb level.

M. Bosilovich