# 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.

## Hourly¶

Scatter plot of the MERRA-2 hourly adjusted surface pressure (see info box below on the hypsometric equation) vs. the hourly station observations values from the selected NCEI ISD files for the years 2001 - 2019. Also compare the Daily surface pressure sections below of unadjusted vs. adjusted for the full justification of using the adjusted surface pressure for assessment purposes.

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.

Scatter plot of the re-gridded MERRA-2 daily un-adjusted pressure vs. the daily station observations values from the NCEI GSOD files for every 3rd year from 1981 – 2014.

Scatter plot of the re-gridded MERRA-2 daily adjusted surface pressure (see info box below on the hypsometric equation) vs. the daily station observations values from the NCEI GSOD files for every 3rd year from 1981 – 2014.

Comparing the unadjusted and adjusted surface pressure statistics in the scatter plots, there is an increase in Rsqrd (0.8078 vs 0.9967) and decrease in Bias (-8.5938 vs 0.0298) and RMSE (24.3998 vs 2.8153). Also note in the adjusted scatter plot, that the lowest 10% data pair per bin (ranging from 0 to 8241.8 and in dark blue color) represents the largest part of the scatter with 30.90% of the overall data pairs. The equivalent data pair per bins in the unadjusted surface pressure covers the lowest 30% ranging from 0 to 7784.7 and representing 86.16% of the overall data pairs. Therefore, the pressure adjusting method decreased the largest part of the scatter (dark blue color) from 86.16% to 30.90%. The color bar along the right side of the scatter plot provides a measure of the distribution of the NCEI, MERRA-2 surface pressure pairs in bins of 1 hPa. The left column along the vertical color bar shows that each data point in dark blue represents the number of ground site/MERRA-2 data pairs within 10% (i.e. <= 8,241.8) of the maximum number of data pairs in 1 hPa bins in the plot (i.e. 82,418). Additionally, from the right side of the vertical color bar it can be seen that all the points shown in dark blue contain 30.9% of the total number of ground site/MERRA-2 data pairs (6,544,757). The remaining 69.1% of the data pairs are concentrated along the 1:1 grey line.

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.