Internal variability of a 3-D ocean model

Abstract

The Defence Centre for Operational Oceanography runs operational forecasts for the Danish waters. The core setup is a 60-layer baroclinic circulation model based on the General Estuarine Transport Model code. At intervals, the model setup is tuned to improve ‘model skill’ and overall performance. It has been an area of concern that the uncertainty inherent to the stochastical/chaotic nature of the model is unknown. Thus, it is difficult to state with certainty that a particular setup is improved, even if the computed model skill increases. This issue also extends to the cases, where the model is tuned during an iterative process, where model results are fed back to improve model parameters, such as bathymetry.

An ensemble of identical model setups with slightly perturbed initial conditions is examined. It is found that the initial perturbation causes the models to deviate from each other exponentially fast, causing differences of several PSUs and several kelvin within a few days of simulation. The ensemble is run for a full year, and the long-term variability of salinity and temperature is found for different regions within the modelled area. Further, the developing time scale is estimated for each region, and great regional differences are found – in both variability and time scale. It is observed that periods with very high ensemble variability are typically short-term and spatially limited events.

A particular event is examined in detail to shed light on how the ensemble ‘behaves’ in periods with large internal model variability. It is found that the ensemble does not seem to follow any particular stochastic distribution: both the ensemble variability (standard deviation or range) as well as the ensemble distribution within that range seem to vary with time and place. Further, it is observed that a large spatial variability due to mesoscale features does not necessarily correlate to large ensemble variability. These findings bear impact on the way data assimilation should be addressed – especially in relation to operational forecasts.

• Baroclinic
• ensemble modelling
• salinity
• temperature
• elevation
• Skagerrak
• Baltic Sea

8. Acknowledgements

We would like to thank our colleagues at FCOO for good discussions, constructive criticism and liberal feedback. Also, we acknowledge our colleagues at BSH, DMI and SMHI for the data provided for the FCOO operational setup – data which have also been used for the present study. The reviewers are thanked for comments and suggestions, which have led to improvements of the manuscript.

Notes

¹For a 20-sample draw from a Gaussian (normal) distribution, the ratio RANGE/STDDEV has an average/expected value of 3.8 with a standard deviation of 0.40. Using Monte Carlo simulations, we find the equivalent 0.1%, 1%, 99% and 99.9% percentiles to be, respectively, 2.8, 3.0, 4.8 and 5.1.

²An animation of the initial development of the surface and bottom salinity standard deviation in the Danish waters is presented as part of the online material: dk.salt-std.surfbott-15min.avi.

³This event is presented as animation in online material as gbight.salt-std.surfbott-15min-jump.avi.

⁴Repeat until convergence.

⁵A figure including surface salinity data for all 20 members is available as part of the online material: dk.salt-data.surface.20130301.png.

⁶A figure including surface salinity anomalies for all 20 members is available as part of the online material: dk.salt-anomaly.surface.20130301.png.

⁷A13-area.salt.surface.dstd-dl3.avi.

⁸A13-area.salt.surface.d19-d13.avi.