Estimation of the equivalent depth of the 1 Pekeris mode using reanalysis data

Abstract

used and the horizontal/temporal averaging operations.The method of calculating the equivalent depths of the Lamb and Pekeris modes for the resulting vertical temperature profile is described in Section 3. The results of the calculation are presented in Section 4. Summary and discussion are given in Section 5.


Data and averaging methods

We use pressure-level (Hersbach, et al., 2023) andmodel-level (Hersbach, et al., 2017) temperature data in ERA5 (Hersbach, et al., 2020), the latest atmospheric reanalysis dataset produced by the European Centre for Medium-Range Weather Forecasts (ECMWF).The reason for using both pressure-level data and model-level data is that, as described in the next section, it is necessary to know the temperature profile up to near the mesopause when solving the vertical structure equation in order to accurately calculate the values of the equivalent depths of the free oscillation modes (Ishioka, 2023).Since the ERA5 pressure-level data are only available up to 1 hPa, the model-level data provided up to 0.01 hPa are used in conjunction with the pressure-level data.Specifically, the model-level data are used for the 54 levels from 0.01 hPa to 71.1187 hPa (each model level is defined in a hybrid coordinate, but down to that level it is completely identical to a pressure level), and the pressure-level data are used for the 27 levels from 100 hPa to 1000 hPa.The longitude-latitude grid interval we use is 1 • × 1 • for the model-level data, while 0.25 • × 0.25 • for the pressure-level data.For the time of data used, three types of data are used: hourly data at 08 UTC rage for January 2022; and data for the annual average for 2022.As mesospheric temperatures are known to be influenced by the 11-year solar activity cycle (Li, et al., 2021), the monthly ave

ge f
r January 2014, the most rec

t pe
k month, is also examined for comp

aver
ge from January 2011 to December 2020 to check what the equivalent depths are in a climatological state.

To investigate the dependence of equivale t depths on the locations, the weighted average temperature T (p) is

ed w
th a horizontal averaging operation o

take
in the north of HTHH: :
(λ 0 , ϕ 0 ) = (λ T , ϕ T + 20 • ).
Here, (λ T , ϕ T ) = (−175.39• , −20.55 • ) is the long ude represents south latitude), and c in (2) represents the angular distance along the great circle from the center point of longitude λ 0 and latitude ϕ 0 .In (2), the function on the right-hand side gives a Gaussian-like weight function on the sphere.Here, α = 16 is specif distribution with a spread of approximately 15 • from the center point (Fig. 1).When the integrals in (1) are computed Fig. 1 using the grid data, the integration in the longitude direction is performed by simply summing up the grid

lues
and multiplying by the grid spacing in the longitude direction, while the Clenshaw-Curtis quadrature is used in the latitude direc

on.
Computation of equivalent depths

This section briefly describes a method for calculating the equivalent depths of free oscillation modes by numerically solving

he v
rtical structure equation.The method is b

ically based on Ishioka
(2023), where the geometric height is used as the vertical coordinate for consistency with Salby (1979), but here the logarithmic pressure coordinate is used as the vertical coordinate.This is because the ERA5 data are given in pressure coordinates.Since a fixed value of the scale height H has no meaning in the calculation of the equivalent depth itself, we set H = 1 (dimensionless)

and define the logarithmic pressure coordinate ẑ = − ln(p/p 0 ), where p 0 is the surface pressure.With this setting, the vertical structure