Evaluation of Analyses and Forecasts Using Independent Data

In operational assimilation systems, the aim is to provide the best possible estimate of the ocean state, and so all available data are assimilated. However, some data-sets are not available in real-time and so can be used in delayed mode to validate the results. An example of this is the RAPID array which measures sub-surface ocean properties in the North Atlantic in order to produce estimates of the Atlantic Meridional Overturning Circulation (AMOC).

Qualitative inter-comparisons can be made between ocean model output of SSH and satellite ocean colour data (see for example Storkey et al. 2010). These can help to show the performance of the systems in reproducing the position of mesoscale eddies and fronts, but it is difficult to produce robust quantitative statistics using this sort of technique.

A method which is often used to validate ocean models in a hindcast setting is to withhold certain data from the data assimilation, and use this independent data for validating the results. This is a useful technique as it provides an independent check that the data assimilation system is working as expected. It is not possible to use this to assess the overall accuracy of the system as the unassimilated data would be assimilated in the operational system, but it can give a bound on the expected accuracy.

An example of this technique is shown in Oke et al. 2008 which shows results from the Bluelink Reanalysis system. Here some unassimilated Argo profiles are used to assess the RMSD in the assimilation run and the run without data assimilation. In all regions at almost all depths, the assimilation is improving the model's representation of sub-surface temperature when compared to the non-assimilating model.

Some data-sets provide information about variables which are not assimilated in most ocean forecasting systems at present. For instance, most of the current operational forecasting systems do not assimilate velocity data. Direct measurements of velocity are sparse, but there are some data in the tropical moorings and other time-series stations. There are also measurements of velocity from surface drifting

0.99

Dotted lines denote centred RMS (normalised wrt Obs)

b Dotted lines denote centred RMS (normalised wrt Obs)

Fig. 22.5 Taylor diagrams from a 2-year hindcast of the FOAM system for a SST comparison with AATSR data and b SSH comparison with a long-track altimeter data. The different colours and symbols represent the statistics for different geographical regions

b Dotted lines denote centred RMS (normalised wrt Obs)

+ Global

□ North Atlantic O Mediterranean A Tropical Atlantic x South Atlantic

□ North Pacific A Tropical Pacific

* South Pacific O Indian Ocean

* Southern Ocean

□ Arctic Stereo

+ Global

□ North Atlantic O Mediterranean A Tropical Atlantic x South Atlantic

□ North Pacific A Tropical Pacific

* South Pacific O Indian Ocean

* Southern Ocean

□ Arctic Stereo NATL12

A IND12 MED12

Fig. 22.5 Taylor diagrams from a 2-year hindcast of the FOAM system for a SST comparison with AATSR data and b SSH comparison with a long-track altimeter data. The different colours and symbols represent the statistics for different geographical regions a buoys and these provide near-global coverage. These can be used as an independent check on the surface ocean currents, an important variable for a number of users.

Surface drifters consist of a surface buoy which is attached to a subsurface drogue. This drogue is usually centred at 15 m depth. The buoy measures temperature (and sometimes other ocean/atmosphere properties) and the position of the drifter is usually inferred from satellite transmission information. The SST data and position of the drifter are disseminated via the global telecommunications system (GTS).

Three months of data from 1st January-31st March 2006 were quality controlled by checking the SST against climatology using a Bayesian technique, and by checking that the average daily velocity of the floats did not exceed 2 m/s. The daily mean velocity values from drifter data were calculated by estimating the distance in the latitudinal and longitudinal directions between the first and last float positions during each day, and dividing the distance by the difference in their reporting time. The modelled velocity corresponding to the observed velocity was calculated by interpolating the model's daily mean velocity fields to all of the observed drifter locations using a bilinear interpolation, and averaging the values for each day.

There are a number of issues with estimated velocities from surface drifters, for example aliasing of inertial oscillations, inaccuracy of position data, unknown drogue depths, un-drogued data and different reporting frequencies. The technique described in the previous paragraph also introduces errors as the curvature in the path of the drifter is not taken into account. Other techniques for comparing the model and observed velocities exist. For example one could input the starting position for each drifter on a particular day, run the model forward to estimate its position at the end of the day, and compare that with the final observed position of the drifter. Statistics on these position errors could then be calculated and assessed.

Various experiments were performed with the 1/9° resolution FOAM North Atlantic system (as it was in 2006, see Martin et al. 2007 for details) in order to assess the impact of different aspects of the system on the surface currents. Figure 22.6 shows the Taylor diagrams for a sample of these experiments for the u and v components of the velocities in the North Atlantic. The first experiment (in light blue) was a re-run of the operational FOAM system which shows that the variability in the model was close to the observed variability but that the correlation was very low with a fairly high RMSD. When not assimilating altimeter data (dark blue), the model's variability is much less, but the correlation coefficient is even worse. This implies that the altimeter assimilation is adding in variability to the model which is not naturally included in the model. One way of getting round this problem is to increase the viscosity in the model so that any spurious variability is damped. The results from a run of FOAM with an increased viscosity are shown in green. For comparison, the results from HYCOM and Mercator (as they were in 2006) are also shown in yellow and orange respectively. This shows improvements in the correlation and reduced RMSD compared to the other FOAM runs, giving similar results to HYCOM and Mercator.

Fig. 22.6 Taylor diagrams for the a u and b v components of surface currents for various model runs during the period 1 st January-31 st March 2006 compared to velocity from surface drifters. Dark blue—FOAM with no altimeter assimilation; light blue—FOAM with altimeter assimilation; green— FOAM with altimeter assimilation and increased viscosity; yellow—HYCOM; orange—Mercator

Fig. 22.6 Taylor diagrams for the a u and b v components of surface currents for various model runs during the period 1 st January-31 st March 2006 compared to velocity from surface drifters. Dark blue—FOAM with no altimeter assimilation; light blue—FOAM with altimeter assimilation; green— FOAM with altimeter assimilation and increased viscosity; yellow—HYCOM; orange—Mercator

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