Inertial currents in the Caspian Sea



[1] We present the first simulation of near-inertial oscillations in the Caspian Sea. Model amplitude is in good agreement with observations. Annual mean near-inertial oscillations are found to be up to 14 cm/s with a seasonal maximum in the summer approximately twice as great as in the winter. The energy increases away from the coast at a rate of up to 0.8 cm2 s−2 km−1; the strongest relationship is with distance from the 50 m depth contour. The peak amplitude also occurs later further from the coastline with a delay of the order of 1 day per 100 km distance. These features are consistent with propagating baroclinic and barotropic waves.

1. Introduction

[2] To date there have been no studies of the near inertial oscillations (NIOs) on the Caspian Sea, which is the world's largest enclosed body of water. Near-inertial waves are mainly wind-driven and are the most energetic form of internal waves [Kunze, 1985], comprising up to half of the near surface kinetic energy [Pollard and Millard, 1970]. These waves are considered vital for mixing at the base of the mixed layer [D'Asaro, 1985] and to maintain the meridional overturning circulation [Munk and Wunsch, 1988].

[3] Previous studies in the coastal ocean [e.g., Shearman, 2005; Jarosz et al., 2007] and in large lakes [e.g., Rao and Murthy, 2001; Zhu et al., 2001] showed through observations and modeling studies that near-inertial oscillations (NIOs) increase away from the shore. This is most likely due to barotropic and baroclinic wave propagation. In each case however the water depth similarly increases with distance from the coast, and so it is not clear whether depth or offshore distance is the driver of the increase in inertial response. Here we address this issue by comparing amplitude of NIOs with both depth and distance.

[4] Global studies of the distribution of near-inertial waves from measurements [e.g.,Park et al., 2005; Chaigneau et al., 2008; Elipot and Lumpkin, 2008] have shown large variability in the spatial structure and importance of these motions. Chaigneau et al. [2008]showed from drifter measurements that the global mean near-inertial current magnitude at 15 m depth is 10 cm/s, however local mean amplitudes range from a few cm/s to nearly 25 cm/s, while seasonal variations account for up to 20% of the magnitude. We will provide the first study of the spatial structure and seasonal variation of NIOs in the Caspian and compare with those seen elsewhere in the global oceans. The study uses a realistic ocean circulation model, driven by high spatio-temporal resolution atmospheric forcing, to compare model output with station current measurements, and to draw conclusions on the basin-wide NIOs based on simulation results.

2. Model and Data

[5] The model used in this study is Regional Ocean Modeling System (ROMS) [Haidvogel et al., 2000; Shchepetkin and McWilliams, 2005] run with a 4 km horizontal resolution, with the domain covering the whole of the Caspian Sea, and 32 vertical s-levels with increased resolution near the surface.Zhang et al. [2010]previously used this model to study near-inertial oscillations elsewhere. The model setup includes the sea-ice module ofBudgell [2005], as a portion of the northern Caspian freezes in winter, the LMD [Large et al., 1994] scheme for vertical mixing and quadratic bottom friction. The model bathymetry is a composite from the Caspian Environment Program, Azerbaijan Naval navigation charts, Turkmenistan hydrographic charts and side-scan sonar data in the area around the station used for validation. The model is initialised with basin averaged temperature and salinity profiles from the World Ocean Circulation Experiment with zero velocity fields and initially spun-up with ERA-40 reanalysis forcing for 40 years, then forcing from the WRF model is applied for 1 year as additional spin-up. The Caspian is non-tidal, allowing tides to be ignored.

[6] Near-inertial oscillations are known to be driven by high-frequency wind fluctuations, and previous studies noted the impact of high-frequency wind forcing on the modeled inertial response [e.g.,Alford, 2001]. Klein et al. [2004]used a 1-D model to show the importance of high temporal resolution winds, where inertial energy is reduced by a factor of 7 when daily wind forcing is applied, when compared to 3 hourly forcing. Therefore atmospheric forcing is applied at 3 hour intervals from the inner 4 km grid of a simulation of the Weather Research and Forecasting (WRF) model [Skamarock et al., 2005]. WRF is run on 3 nested grids of 36, 12 and 4 km, each with 38 vertical levels, where 6 hourly reanalysis fields from ERA-Interim are applied as boundary forcing on the outer nest.

[7] For this study the model is run for a year from 1st December 2007 to 1st December 2008 with a 1 minute time-step and currents output at 10 minute intervals to analyze the near-inertial motions. Comparison is made with currents recorded by an acoustic Doppler current profiler (ADCP) at 10 minute intervals from 1st December 2007 to 13th September 2008 at the Shah Deniz station (39.88N 50.37E) where the water depth is 92 m.

[8] The rotary spectral analysis methods of Gonella [1972]can be applied to a vector time series of currents to decompose into clockwise and counterclockwise spectral components. This is of particular use for the study of near-inertial oscillations, which in the Northern Hemisphere, show clockwise rotation.

3. Results

[9] Figure 1 shows the clockwise rotary spectrum of nine and a half months of measured data and simulated currents at 6 m depth at Shah Deniz. We can see from both spectra that there is a very clear peak near the local inertial frequency (0.053 /hr, 18.71 hrs), the peak frequencies in the measured and modeled spectra are 0.052 /hr and 0.054 /hr respectively. We use three quantitative methods to compare the measured and simulated spectra. The first is to perform complex demodulation, as described in Perkins [1976], which gives an amplitude for the inertial current; second is to calculate the percentage of the total current variance in the inertial band; finally the percentage of time the inertial current exceeds 5 cm/s as a measure of how often events occur. Table 1shows the inertial amplitude is around 5 cm/s and exceedance of 5 cm/s happens nearly 50% of the time at 6 m. Examining the time series, the NIOs are ubiquitous with no obvious decay time scale. The agreement between model and measurements is good, with a slight underprediction at 15 m, while the variance of around 30% is well represented. We therefore feel confident that our model accurately represents the observed near-inertial motions and next extend the analysis across the Caspian.

Figure 1.

Clockwise rotary spectra at 6 m depth from Shah Deniz station between 1st Dec 2007 and 13th Sept 2008. Measured currents - blue; simulated currents - green; coriolis frequency indicated as dashed line.

Table 1. Comparison of Measured and Simulated Near-Surface Inertial Currents 1st Dec 2007 to 13th Sept 2008a
  • a

    Inertial amplitude; percentage of total variance (10 days - 30 minutes) in inertial band (f ± 10%); and percentage of time inertial amplitude exceeds 5 cm/s.

Amplitude (cm/s)6 m5.185.27
 15 m4.223.86
Variance (%)6 m2830
 15 m2630
Exceedance (%)6 m4647
 15 m3226

[10] Figure 2ashows the peak surface near-inertial period andFigure 2bshows the local inertial period for comparison. As expected, the period decreases with latitude and follows closely the local inertial period. On average the model has a frequency 0.33% above the coriolis frequency. We also note that near-inertial oscillations are significant over much of the Caspian Sea, the areas where no significant peak is found correspond strongly to regions of shallow water with depths below approximately 20 m.

Figure 2.

Distribution of simulated inertial current characteristics. (a) Simulated peak near-inertial period (in hours) where significant at 95% level and (b) corresponding coriolis period; both have the 20 m bathymetry contour and Shah Deniz station indicated by a cross. (c) Simulated mean inertial amplitude (m/s) at 15 m depth with depth contours of 50, 100, 200, 400 and 600 m and (d) bias (m/s) of applied WRF wind forcing against Quikscat satellite data.

[11] We perform complex demodulation to find the amplitude at the local inertial period at 15 m depth for each model grid point to compare with the global study of Chaigneau et al. [2008]. Figure 2c shows that the amplitudes have large spatial variability and broadly follow the depth contours of the Caspian, with higher amplitudes at correspondingly larger local depths, while it can be seen that amplitude also increases towards the center of the basin and so may depend on distance from the coast. In the South Caspian in particular, amplitudes increase rapidly with offshore distance in the western part but more slowly in the eastern part. Mean inertial amplitudes of over 10 cm/s are seen over large parts of the interior of the Caspian, with a maximum amplitude of 14 cm/s.

[12] NIOs are known to be a function of mixed layer depth (MLD) and high-frequency wind speed. We find that the amplitude of NIOs decreases with model MLD as expected, while MLD tends to increase slightly with offshore distance (which should lead to the opposite effect i.e. a decrease in NIOs) but shows no trend with water depth. This implies that the increase in NIOs with depth and distance cannot be explained by spatial variation of MLD. We also compared the applied wind forcing with both water depth and offshore distance. The wind shows no relationship with water depth, however, winds do increase with distance from the coast, but only up to distances of around 80 km so this can't explain the distance dependence of NIOs beyond this. For validation, the wind fields were compared with Quikscat satellite data.Figure 2d shows the annual mean bias of −0.02 m/s. The mean RMSE is 2.9 m/s. The areas of largest errors don't correspond to the areas of strongest NIOs. Therefore the wind forcing is realistic and the spatial distribution cannot explain the increase in NIOs with water depth or offshore distance.

[13] To investigate further the dependence of inertial amplitude on distance from a coastline we binned each grid cell according to the local offshore distance and took a mean inertial amplitude amongst those points. Figure 3a shows that the amplitudes increase with distance out to 130 km from the coastline; at distances further than this there are fewer data points and the trend is less clear. The winter (DJF) amplitudes are around half of those in summer (JJA), while in spring and autumn the amplitudes are slightly less than in summer. This seasonality is generally consistent but larger than reported in previous studies [Park et al., 2005; Chaigneau et al., 2008].

Figure 3.

(a) Mean 15 m inertial amplitude for 2 km offshore distance bins. Data are averaged over Dec-Jan-Feb (blue); Mar-Apr-May (green); June-July-Aug (red); Sep-Oct-Nov (brown). (b) Annual mean 15 m inertial amplitude plotted against offshore distance (black) and water depth (red); inertial amplitude from idealised run with depth capped at 300 m against distance (blue) and depth (purple).

[14] We perform a similar comparison of annual mean inertial amplitude against water depth by binning each grid point into 5 m water depth bins. We see a trend of increasing amplitude with depth (Figure 3b), as we would expect from Figure 2c, where there is a rapid increase with depth up to nearly 100 m and then a slower increase above this to 1000 m. These results show a dependence of inertial amplitude on both water depth and offshore distance, and therefore to further investigate we perform an idealised simulation where the depths in our model are capped at 300 m. This idealised case is performed in the same way as before except the spin-up is reduced to 2 years of WRF forcing. The inertial amplitude results of this simulation were binned in terms of both offshore distance and the original water depth.Figure 3b shows that the amplitudes are largely unchanged by levelling the depths, which implies that the depth dependence is not robust and that the main factor in determining inertial amplitude is distance from a coastline rather than water depth.

[15] We see a linear dependence of the square of inertial amplitude on offshore distance, this relationship is strongest when taking the distance from the 50 m depth contour (results not shown). This result agrees with the measurements of Shearman [2005] where a linear relationship was observed between inertial kinetic energy and distance from the New England coastline. Shearman [2005]takes a latitude with depth of roughly 40–60 m and sees an increase of near-inertial energy of 0.8 ± 0.2 cm2 s−2 km−1 from this point, while we see an increase of between 0.4 and 0.8 cm2 s−2 km−1, depending on which depth contour we take as a reference for distance measurements. As expected from Figure 2c, amplitudes in the west of the South Caspian increase more quickly with distance from the shore than in the east, however the rate of increase in inertial amplitudes from the 50 m contour is similar for both regions (not shown).

[16] One further prediction from the idealised model of Kundu et al. [1983] and Shearman [2005] is that for an inertial event the peak amplitude observed at a given location occurs later further from the coastline. We look to see if this effect is present in our model by averaging the largest NIO event in each month and identifying the peak of amplitude associated with each event. Figure 4 shows that the peak inertial amplitude occurs later by about 1 day per 100 km distance from the coast. This analysis also confirms the earlier finding of amplitude increase from the coast. The same behaviour is observed moving away from the east coast of the South Caspian basin. This result further supports the hypothesis of Kundu et al. [1983] for the propagation of baroclinic waves from a coastline controlling inertial oscillations.

Figure 4.

Near-inertial amplitude for a composite of 12 events averaged over a box of 10-by-10 grid-cells. Plotted are amplitudes for four boxes along 39°N moving further away from the western coastline. Day 0 is the mean day of the event across the latitude belt.

4. Discussion

[17] We performed a high resolution Caspian Sea simulation using the ROMS model forced by high spatio-temporal output from the WRF atmosphere model. The model's near-inertial oscillations are compared with station measurements and found to accurately reproduce the observed spectrum, percentage of variance in the inertial band (around 30% of that at periods less than 10 days) and near-inertial amplitude. The model shows significant near-inertial oscillations over most of the Caspian basin, with the exception of areas with depths of less than about 20 m, the periods of which correspond closely with the local coriolis frequency. The seasonality shows greatest amplitudes in the summer months, when the mixed layer depth is shallowest, with slightly lower values in autumn and spring and much reduced amplitudes in the well mixed winter months. The magnitude of the seasonal variability is greater than seen previously on the oceanic scale [Park et al., 2005; Chaigneau et al., 2008].

[18] Previous studies [e.g., Shearman, 2005; Jarosz et al., 2007; Rao and Murthy, 2001; Zhu et al., 2001] have suggested that inertial oscillations increase with distance from the coast. The proposed mechanism is the interaction and propagation speed of baroclinic and barotropic waves originating from a coastline [e.g, Kundu et al., 1983; Shearman, 2005]. This could explain the pattern of inertial amplitudes seen in our Caspian Sea model, where maxima are located centrally in the basin. However, amplitudes of inertial currents also seem to follow depth contours; areas of significant near-inertial motions correspond strongly with the 20 m depth contour. We see an increase in inertial amplitude with both water depth and distance from the coastline. By performing a simulation where the water depths are limited to 300 m we confirm that depth is not the determining factor for amplitude of NIOs. The strongest relationship observed is a linear dependence of amplitude squared on distance from the 50 m depth contour.


[19] This study was supported by the National Environmental Research Council. We would also like to thank BP's Upstream Environmental Technology Program and Colin Grant.

[20] The Editor thanks two anonymous reviewers for their assistance evaluating this paper.