# Surface Pressure¶

In this section, MERRA-2 surface pressure is compared to observations reported to the National Center for Environmental Information (NCEI – formerly National Climatic Data Center). Selected surface sites from the NCEI Integrated Surface Database (ISD) files are used for the hourly MERRA-2 comparisons. Global "Summary of the Day" (GSOD) files are used for the comparison to the daily mean MERRA-2 surface pressure. Because of the difference in the grid box topography of MERRA-2 and the site elevation, the MERRA-2 surface pressure is adjusted by the difference. See the info box below on the hypsometric equation.

## Hourly¶

Density plot of the 2-D histograms comparing MERRA-2 hourly adjusted surface pressure with station observations from the selected NCEI ISD files for the years 2001 - 2019. Darker reds indicate a higher number of matched pairs within the 2-D histogram.

The hourly validation for the adjusted surface pressure shows good agreement with clustering around the 1:1 correlation line, especially for values above 700 hPa.

## Daily Average¶

The daily mean surface pressure is taken directly from the re-gridded MERRA-2 and represents estimates of the atmospheric pressure at 2 m above the local surface averaged from the original source spatial resolution.

Density plot of the 2-D histograms comparing MERRA-2 daily adjusted surface pressure with station observations from the NCEI GSOD files for 1981 – 2020.

Hypsometric Equation for Adjustment of Surface Pressure

The elevation of the MERRA-2 grid box is the mean elevation of the earth’s surface under the grid. In complex terrain one might expect to see a difference between the MERRA-2 elevation and that of the surface site resulting in a difference between the MERRA-2 pressure and that reported by the surface site. The Surface Pressure (Hypsometric Equation) scatter plot illustrates the improvements in the agreement between the MERRA-2 estimates of pressure and observational data by adjusting the MERRA-2 pressure using the hypsometric equation. The hypsometric equation, relates the thickness (h) between two isobaric surfaces to the mean temperature (T) of the layer as:

\begin{align}\ h = z_2 – z_1 = (RT/g) \times ln(p_1/p_2) \end{align}
\begin{align} Where: \\ z_1: & \text{ elevation of the MERRA-2 grid. } \\ z_2: & \text{ elevation of the reporting surface site. } \\ p_1: & \text{ MERRA-2 surface pressure. } \\ p_2: & \text{ Surface site pressure. } \\ R: & \text{ Gas constant for dry air. } \\ g: & \text{ Gravitational constant. } \\ T: & \text{ Temperature at mid-point between $z_1$ and $z_2$. } \\ \end{align}

Solving the hypsometric equation for p1 and substituting the known values for z1, z2, p1, R, and g, gives the adjusted MERRA-2 surface pressure (p1) at the elevation of the NCEI surface site.