We investigate the seasonal variability in the semidiurnal internal tide steric sea surface height (SSSH) and energetics using 8 km global Hybrid Coordinate Ocean Model (HYCOM) simulations with realistic forcing and satellite altimeter data. In numerous previous studies, SSSH has been used to explore the seasonal changes in internal tides. For the first time, we compare the seasonal variability in the semidiurnal internal tide SSSH with the seasonal variability in the semidiurnal baroclinic energetics. We explore the seasonal trends in SSSH variance, barotropic to baroclinic conversion rate, kinetic energy, available potential energy, and pressure flux for the semidiurnal internal tides. We find that the seasonal cycle of monthly semidiurnal SSSH variance in the Northern Hemisphere is out of phase with the Southern Hemisphere. This north–south phase difference and its timing are in agreement with altimetry. The amplitudes of the seasonal variability in SSSH variance are about 10 %–15 % of their annual mean values when zonally averaged. The normalized amplitude of the seasonal variability is higher for the SSSH variance than for the energetics. The largest seasonal variability is observed in Georges Bank and the Arabian Sea, where the seasonal trends of monthly SSSH variance and energetics are in phase. However, outside these hotspots, the seasonal variability in semidiurnal energetics is out of phase with semidiurnal SSSH variance, and a clear phase difference between the Northern Hemisphere and Southern Hemisphere is lacking. While the seasonal variability in semidiurnal energy is driven by seasonal changes in barotropic to baroclinic conversion, semidiurnal SSSH variance is also modulated by seasonal changes in surface stratification. Surface-intensified stratification at the end of summer enhances the surface perturbation pressures, which enhance the SSSH amplitudes.

The interaction between surface tides and bathymetry, in the presence of density stratification, leads to the generation of internal tides

The seasonal variability in internal tides has been observed and simulated in numerous studies.

Numerical model studies investigating the seasonal variability in internal tides mainly focus on regional areas

Only a few studies have used global numerical models to identify seasonal variability in internal tides

The variability in the internal tide at the generation site can be due to seasonal fluctuations in barotropic tidal forcing

The understanding of the seasonal variability in internal tides in the global ocean has been limited by the short duration of time series available from numerical experiments and the low spatial and temporal resolution of field measurements. While the SSH of internal tides has been used in previous studies to explore seasonal changes, the seasonal variability in internal tide SSH and energetics has never been compared. This study aims to answer the following questions: (a) Which areas in the global ocean have high seasonal variability in semidiurnal internal tides? (b) How do the spatial and temporal variabilities in internal tide SSH and energetics from a global HYCOM simulation compare? (c) What explains their differences? (d) What mechanisms cause the seasonal variability? To answer these questions, we analyze the seasonal variability in semidiurnal internal tides using two global HYCOM simulations with output durations of 5 years and 1 year. We examine the seasonal trends in SSSH variance, barotropic to baroclinic conversion rate, kinetic energy (KE), available potential energy (APE), and pressure flux for semidiurnal internal tides.

The rest of the paper is organized as follows: Sect. 2 explains the model simulation and the methodology applied. In Sect. 3, we compare the seasonal variability in the semidiurnal SSSH variance with the variability in the internal tide energetics. To confirm the accuracy of our findings, we also compare the model results with satellite altimeter observations. Section 4 discusses the causes of the disparity in seasonal trends between SSSH variance and internal tide energetics. Finally, Sect. 5 summarizes the key findings of the study.

This study uses two existing global non-data assimilative HYCOM simulations, expt 06.1 and expt 18.5, and an altimetry dataset. The list of datasets extracted from these simulations is given in Table

List of datasets used in this study.

For expt 06.1, the data are available for 1 year, from October 2011 to September 2012. We use SSSH and internal tide energy terms from this simulation. This non-data assimilative simulation is forced with realistic atmospheric and tidal forcing (

We use hourly SSSH snapshots subsampled at

We also use 5-year-long datasets from a global HYCOM simulation with a horizontal resolution of 8 km and 32 vertical layers to analyze the seasonal variability. This simulation features realistic atmospheric and tidal forcing. It is forced with four semidiurnal constituents (

To analyze the seasonal cycle in the semidiurnal internal tide SSSH, we use SSSH snapshots that are saved once per hour from 1 January 2005 to 31 December 2009. These snapshots are subsampled at 0.5° grid resolution.

We analyze the seasonal variability in the semidiurnal SSSH. Steric SSH is calculated in real time as part of the HYCOM simulation

We extract monthly

To calculate the seasonal variability in the semidiurnal internal tide SSSH variance, the annual cycle is fitted to the 5-year time series of the monthly semidiurnal SSSH variance (

We calculate the coefficient of determination (

We analyze the seasonal variability in the semidiurnal internal tide energetics and compare it with the SSSH variance. Following

The depth-integrated and time-averaged internal tide energy balance equation is written as

The depth-integrated and time-averaged conversion of baroclinic tides from barotropic tides for each

For expt 06.1, all variables (SSSH variance, barotropic to baroclinic conversion, KE, APE, total energy, and flux) are calculated for each month from October 2011 to September 2012. The exact number of hours per month is used. The hours for each month from October 2011 to September 2012 are as follows: 744, 720, 744, 744, 696, 744, 720, 744, 720, 744, 383, and 889. For August, we use the first 2 weeks of data because the model data for the third week were corrupted in storage. We add the last week of August to September, resulting in 5 weeks of data for September. However, the short months, February and August, show outlier values. The 14 d of August are not sufficient to resolve the

We decompose internal tide SSH and energetics into vertical modes to better understand the discrepancies in seasonal trends between SSSH variance and energy terms. For the calculation of mode 1 baroclinic SSH, KE, and APE, 3D HYCOM fields from expt 06.1a are decomposed into vertical modes following

To compare with SSSH, we compute the mode 1 SSH. For each

For calculation of the mode 1 semidiurnal KE and APE, we extract the harmonic constants for

The mode 1 variables are also linearly interpolated for February and August for each grid point using the same methodology as we employed for the undecomposed fields. Additionally, we subsample these variables at

We validate the seasonal variability in the HYCOM mode 1

The mean values over 12 months for semidiurnal SSSH variance, depth-integrated semidiurnal barotropic to baroclinic conversion rate, depth-integrated semidiurnal baroclinic energy, and depth-integrated semidiurnal baroclinic flux for expt 06.1 are shown in Fig.

The barotropic to baroclinic conversion rate in Fig.

The first objective is to analyze the seasonal variability in semidiurnal internal tide SSSH variance. We use the detrended monthly variance (

The internal tides generated in the coastal areas of Georges Bank and the Arabian Sea display the largest seasonal variability (Fig.

In this section, we analyze the seasonal trend in semidiurnal internal tide energetics and compare it with the seasonal trend in semidiurnal SSSH variance. To do so, we use 1-year data from expt 06.1 to calculate the monthly semidiurnal SSSH variance, depth-integrated conversion rate, KE, APE, energy, and flux for

To better visualize the seasonal trends, we zonally average the conversion rate, flux, SSSH variance, KE, APE, and total energy over 10° latitude bins for the Atlantic and the Pacific oceans for each 1-month period. The values in areas shallower than 100 m are excluded from the analysis because the model does not resolve internal tides satisfactorily in these areas. To derive the anomaly time series for these variables, we remove and normalize by their annual mean values. The anomaly plots are presented in Figs.

Zonally averaged anomaly time series of monthly semidiurnal

The same as Fig.

A seasonal cycle is observed in all variables (conversion rate, flux, SSSH variance, KE, APE, and total energy) in both the Pacific and Atlantic oceans (Figs.

The amplitude of the seasonal cycles in Figs.

In the Pacific Ocean, the seasonal signal for the SSSH variance in the tropical region, spanning

Area-averaged (left column) monthly semidiurnal SSSH variance (blue line) and KE (orange line) and (right column) normalized anomaly time series of monthly semidiurnal SSSH variance (blue line), KE (orange line), and conversion (black line) for regions marked by the red boxes in Fig.

To further compare the seasonal signals, we plot in Fig.

Our analysis indicates that the conversion rate is the primary factor responsible for the seasonal variability in internal tide energetics because the seasonal trends of conversion and other energy terms are similar. The amount of internal tide energy in the ocean is governed by the internal tide energy input over topography, which is computed with the conversion metric. However, the seasonal trends of SSSH variance are different from the trends in the energy terms, except for Georges Bank and the Arabian Sea, where the seasonal variability is the strongest. In Appendix

To validate the seasonal variability in our model, we compare the mode 1

Zonally averaged normalized anomaly time series of seasonal mean mode 1

The seasonal variability in both HYCOM and satellite altimeter

In this section, we explore the causes of the differences in the seasonal variability between SSSH variance and the energy terms. SSSH is strongly affected by the density of the surface layers, which varies significantly due to seasonal temperature changes

We compute the mode 1 semidiurnal baroclinic SSH variance, bottom perturbation pressure variance, KE, and APE for each month using 3D fields from expt 06.1a. These variables are based on reconstructed time series for the

We compare the seasonal trends in semidiurnal SSSH variance, mode 1 semidiurnal baroclinic SSH variance, KE, APE, bottom perturbation pressure variance, and

Zonally averaged normalized anomaly time series of monthly mean

The same as Fig.

The mode 1 SSH is computed as

Zonally averaged normalized anomaly time series of

Alternatively, we can also explain the modulation by considering APE. If we assume that the barotropic to baroclinic conversion rate remains constant throughout the year, we can assume that APE is constant. APE is proportional to

In this study, we compare the seasonal variability in semidiurnal steric sea surface height (SSSH) with internal tide energetics, which are extracted from two non-data assimilative global Hybrid Coordinate Ocean Model (HYCOM) simulations. We analyze the seasonal trends in SSSH variance, barotropic to baroclinic conversion rate, kinetic energy (KE), available potential energy (APE), and pressure flux for semidiurnal internal tides. The seasonal variability in the HYCOM simulation is also compared with the satellite altimeter data of

The seasonal cycle of the semidiurnal SSSH variance is 180° out of phase in the Northern Hemisphere and Southern Hemisphere, which indicates that stratification may be responsible for this seasonal variability. We find that the amplitude of the seasonal cycles is about 10 %–15 % of the annual mean values when zonally averaged. The strongest seasonal variability in the semidiurnal SSSH variance is observed in Georges Bank and the Arabian Sea.

We compare the seasonal trend in semidiurnal SSSH variance with depth-integrated semidiurnal barotropic to baroclinic energy conversion rate, baroclinic energy flux, KE, and APE. The seasonal trends in the energy terms are quite similar. The conversion rate is dominant in influencing the seasonal variability in the internal tide energetics. However, we observe differences in the seasonal cycles between SSSH variance and the energy terms. Seasonal maxima in energy terms and SSSH do not coincide in space and time. Moreover, the seasonal cycles in the Northern Hemisphere and Southern Hemisphere are not clearly out of phase as for SSSH. The seasonal cycles of SSSH variance and the energy terms are only in phase for Georges Bank and the Arabian Sea, where seasonal variability in internal tides is strong.

After comparing the seasonal variability in the HYCOM simulation with the satellite altimeter data from

Next, we investigate potential mechanisms that may explain the differences in the seasonal variability between semidiurnal SSSH variance and the energy terms. We explore the modulation of SSSH by the seasonal stratification. SSSH is strongly affected by the density of the surface layers, which varies significantly due to seasonal temperature changes. We compare the seasonal trends in semidiurnal SSSH variance with mode 1 semidiurnal SSH variance, bottom perturbation pressure variance, KE, APE, and buoyancy frequency. Although the seasonal cycles for both mode 1 SSH variance and the undecomposed SSSH variance are similar, they differ from the mode 1 bottom perturbation pressure variance, KE, and APE. The seasonal cycle in the mode 1 SSH variance is mostly due to changes in the mode 1 horizontal velocity eigenfunction at the surface and not due to changes in the mode 1 perturbation pressure amplitude. The strong stratification in summer causes the horizontal velocity eigenfunction to be surface intensified, which leads to an increase in semidiurnal surface perturbation pressure and SSSH variance.

Our analysis suggests that internal tide sea surface height may not be the most accurate indicator of the true seasonal variability in internal tides. Seasonal changes in the surface density stratification can modulate the seasonal variability in sea surface height. Because surface density values and stratification also change on weekly to monthly time scales, it may be that the internal tide nonstationarity

We compute the zonally averaged anomaly time series of steric sea surface height (SSSH) variance from expt 18.5 for all 5 years in a similar manner to expt 06.1. We calculate the semidiurnal SSSH variance using the harmonic time series constructed for

Zonally averaged anomaly time series of monthly variance in semidiurnal SSSH from expt 18.5 for the

Here, we show the seasonal trends for the non-normalized semidiurnal barotropic to baroclinic conversion rate, baroclinic energy flux, SSSH variance, baroclinic kinetic energy (KE), available potential energy (APE), and their sum for the Pacific and Atlantic oceans in Figs.

Zonally averaged anomaly time series of semidiurnal

The same as Fig.

In Section 3.3, we showed that KE, conversion rate, and SSSH variance exhibit similar seasonal trends in Georges Bank and the Arabian Sea (Fig.

Georges Bank and the Gulf of Maine are located in the Northwest Atlantic Ocean. Internal tides are generated on the northeast flank of Georges Bank and the Northeast Channel in this region (Fig.

In the Arabian Sea region, strong internal tides are generated on the shelf break, which generally propagate offshore

In conclusion, at both Georges Bank and the Arabian Sea, the seasonality in stratification greatly affects the conversion. However, at Georges Bank, these stratification changes occur mainly at the surface, whereas in the Arabian Sea, these changes mostly take place at depth.

Some Hybrid Coordinate Ocean Model (HYCOM) simulation data and code are available at

HK processed the data, plotted the results, and wrote the first version of the manuscript. MB, ZZ, and JFS collected and processed the data. All authors reviewed and edited the paper until its final version.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

Harpreet Kaur is funded by the National Aeronautics and Space Administration (NASA) grants 80NSSC18K0771 and 80NSSC20K1135 and Office of Naval Research (ONR) USA grant N00014-19-1-2704. Maarten Buijsman is funded by the National Aeronautics and Space Administration (NASA) grants 80NSSC18K0771 and 80NSSC20K1135 and Office of Naval Research (ONR) USA grants N00014-19-1-2704 and N00014-22-1-2576. Jay Shriver is supported by Office of Naval Research (ONR) Grant N0001423WX01413, which is a component of the Global Internal Waves project of the National Oceanographic Partnership Program (

This research has been supported by the National Aeronautics and Space Administration (grant nos. 80NSSC18K0771 and 80NSSC20K1135) and the Office of Naval Research (grant nos. N00014-19-1-2704, N00014-22-1-2576, and N0001423WX01413).

This paper was edited by Rob Hall and reviewed by two anonymous referees.