**6. Ocean forecasting**

120 Hydrodynamics – Natural Water Bodies

The results presented in Fig. 1 show the potential temperature (upper panel) and the chlorophyll-a (lower panel) from the last ten years of the fifty year simulation. By this point the model has passed through the spin-up phase and produces a relatively stable repeating annual cycle. The surface temperature varies between a maximum of approximately 26°C in summer and a winter minimum of 16.6°C. The shallow surface mixed layer, in which the temperature is relatively high and uniform, is clearly visible in summer when it extends from the surface to a depth of 30 m. It is driven mainly by wind mixing, which generates enough turbulent kinetic energy to mix the water against the density gradient. By autumn the surface begins to cool and as a result the water column begins to mix vertically due to free convection, as indicated by the deepening of the green shaded contour. The free convection is driven by gravitational instability of the water column due to cooling from above. By late winter (early to mid March) the mixed layer has deepened to it maximum extent of 190 m as indicated by the uniform cyan contour extending from the surface from late February through mid March. This cycle and the values of the temperature and mixed layer depth are consistent with the observations from this region (e.g., Hecht, et al., 1988;

The lower panel of Fig. 1 shows that chlorophyll-a (concentration in μM L-1), which is the proxy for phytoplankton biomass, is confined to the upper part of the water column where there is sufficient light for photosynthesis. Nutrients (mainly nitrate, phosphate, and silicate) are also necessary for the cells to function. The nutrients are injected into the upper layers from below the nutricline (begins at ~150-200 m and extends to ~ 600 m) during deep winter mixing or during wind induced upwelling events. They are rapidly depleted form the photic zone when photosynthesis commences. Chlorophyll-a in the figure exhibits a pattern that is typical for an oligotrophic sea such as the eastern Mediterranean. During spring and summer it is confined mainly to the upper 90-100 m. During the deep mixing in the latter part of winter, the phytoplankton are transported deeper by convective mixing. A combination of factors leads to reduced photosynthesis and biomass concentration during this period. Sun light is less intense and the phytoplankton spend less time in the photic zone. Also due to the deeper mixing they are distributed over a larger volume and therefore the concentration is lower as indicated by the cyan contour. The warmer colors indicate two important features on the marine ecosystem. In early spring the yellow contours show a layer of relatively high chlorophyll concentration extending from the surface to a depth of ~80 m and which lasts for 2-3 weeks. This phenomenon is referred to as the spring bloom. It occurs shortly after the end of the winter (i.e., end of net surface cooling) and the onset of net surface heating in the spring. As a result the free convective mixing ceases and the phytoplankton remain in the upper layers. At this time nutrients are abundant due to the import of high nutrient waters from the deeper layers during winter. These two factors combined with the increasing intensity of the sunlight lead to a rapid increase in photosynthesis and therefore a substantial increase in chlorophyll-a concentration. The nutrients are consumed by the photosynthetic activity of the cells. Since the nutrient source in deep water has been cut off by the cessation of free convection, the nutrients in the photic zone are rapidly depleted and the bloom ends within a few weeks. This is indicated by the transition to the green contours. Later in the summer a subsurface layer with high chlorophyll-a concentration appears at a depth of 70-90 m (yellow and orange contours). This phenomenon referred to as the deep chlorophyll maximum, DCM, is due to the complex interaction between light intensity, leakage of nutrients from the nutricline, and the density stratification. Its occurrence is quite common in the oligotrophic Mediterranean Sea

Manca et al., 2004; Ozsoy et al., 1993).

In this section we present another example of the powerful use and application of numerical ocean models as part of an operational forecasting system. In contrast to process studies or simulations which are designed to help us understand the particular dynamical process of interest, the goal of a forecasting system is to provide the most accurate prediction of the circulation at a particular instant in time, but within the constraint of producing the forecast in reasonably short period of time so that it considered to be useful. Clearly a 24 hour forecast that requires 24 hours of computer time has no value. A balance must therefore be reached between the acceptable level of forecast error and the time required to produce the forecast. Furthermore in a forecast system, in addition to the model itself, the specification of the initial conditions is a central consideration. Experience from numerical weather prediction has shown that during the first few days the forecast errors depend mainly on errors in the initial conditions, whereas at longer forecast lead times model errors and uncertainties have a larger impact on forecast errors. In addition to collecting data, accurate mathematical methods are necessary for interpolating the observations to the model grid while creating a minimal amount of numerical noise. This entire procedure, referred to as data assimilation (e.g., Kalnay, 2003), will not be discussed here. Our focus will be on the numerical model itself.

The development of the Mediterranean Forecasting System, MFS, began in 1998 as a cooperative effort of nearly 30 institutions with the goal of producing a prototype operational forecasting system and to demonstrate its feasibility. The project included components of in situ and remotely sensed data collection, data assimilation and model development. The model development component was structured to include a hierarchy of nested models with increasing resolution. The overall system was driven by the coarse resolution, full Mediterranean model. At the next level, sub-basin scale models, which covered large sections of the western, central, and eastern Mediterranean with a threefold increase in resolution, were nested in the full basin model. Nesting is the procedure through which the initial conditions were interpolated to the higher resolution grid, and the time dependent lateral boundary conditions were extracted from the coarser grid model. Finally, very high resolution local models for specific regions were nested in the sub-basin models with an additional two to threefold increase in resolution. An overall description of the prototype system and its implementation can be found in (Pinardi et al., 2003). While the initial model development focused on mainly climatological simulations with the nested model, the next phase led to the pre-operational implementation of short term forecasting with all three levels of models. This system has evolved into Mediterranean Operational Ocean Network, which is perhaps one of the most advanced operational ocean forecasting systems today (MOON, 2011). It routinely provides daily forecasts for the circulation at all scales and the ecosystem at the larger scales.

One component of MOON is a high resolution local model for the southeastern continental shelf zone of the eastern Mediterranean. The model was developed initially within MFS (Brenner, 2003) and has subsequently gone through a number of improvements and refinements. The version presented here is described in detail by (Brenner et al., 2007). It is

Numerical Modeling of the Ocean Circulation:

the pattern correlation.

anomaly correlation coefficient.

From Process Studies to Operational Forecasting – The Mediterranean Example 123

This model runs daily and produces forecasts of the temperature, salinity, free surface, and currents out to four days. As noted previously, the primary goal of a forecasting system is to produce the best possible prediction of the circulation at a specific instant in time. Thus forecast verification is an important aspect of assessing the usefulness of the system. In comparison to the atmosphere, ocean observations are extremely limited. The best spatial and temporal data are provided by satellites but are generally limited to sea surface temperature (SST) and sea surface height. The former are usually available several times daily while the latter are limited to approximately weekly, depending upon the path of the satellite. Other measurements are available from ships of opportunity or from fixed buoys but these are sporadic and limited in both time and space. With all of these reservations in mind, in the next few figures we present some examples of the verification of the forecasts produced by this model. In Fig. 3 we show the forecast skill of SST for a one year period as a function of forecast lead time. The skill scores used are the domain averaged root mean square error (RMSE) and the anomaly correlation coefficient. The former measures the magnitude of the forecast error while the latter provides a measure of the pattern error. The figure shows the forecast skill for the high resolution shelf model (red line) and for the coarser resolution regional model (green line). We also include the error for a persistence forecast (i.e., no change from the initial conditions), which is considered to be the minimum skill forecast. From both the RMSE and the anomaly correlation it is clear that the forecast skill degrades as the forecast length increases. The value added to the forecast by the high resolution model is substantial as it outperforms the regional model in both scores (i.e., lower error magnitude and higher pattern correlation). Both models also manage to significantly beat persistence for RMSE, but the regional model is only marginally better in

Fig. 3. Forecast skill for one year of forecasts in terms of root mean square error and

While the skill of the SST forecast is impressive, it is also important to validate the ability of the model to predict the subsurface fields. Unfortunately here the data are much more

based on the full three dimensional, primitive equations Princeton Ocean Model which was described above in Section 3. The horizontal grid spacing is 1.25 km and there are 30 vertical levels distributed on a terrain-following vertical coordinate. Data for the lateral boundary conditions are extracted from a sub-basin, regional model which covers most of the Levantine, Ionian, and Aegean basins. The domain and bathymetry of the model are shown in Fig. 2. The mathematical formulation of the boundary conditions along the two open boundaries consists of specifying the normal and tangential components of the horizontal velocity at all boundary grid points and the tracers (temperature and salinity) at inflow points. At outflow points the boundary values are extrapolated from the first interior grid point using a linearized advection equation.

Fig. 2. Domain and bathymetry of the high resolution southeastern Levantine model. Dots indicate locations were observations were available for verification.

based on the full three dimensional, primitive equations Princeton Ocean Model which was described above in Section 3. The horizontal grid spacing is 1.25 km and there are 30 vertical levels distributed on a terrain-following vertical coordinate. Data for the lateral boundary conditions are extracted from a sub-basin, regional model which covers most of the Levantine, Ionian, and Aegean basins. The domain and bathymetry of the model are shown in Fig. 2. The mathematical formulation of the boundary conditions along the two open boundaries consists of specifying the normal and tangential components of the horizontal velocity at all boundary grid points and the tracers (temperature and salinity) at inflow points. At outflow points the boundary values are extrapolated from the first interior grid

Fig. 2. Domain and bathymetry of the high resolution southeastern Levantine model. Dots

indicate locations were observations were available for verification.

point using a linearized advection equation.

This model runs daily and produces forecasts of the temperature, salinity, free surface, and currents out to four days. As noted previously, the primary goal of a forecasting system is to produce the best possible prediction of the circulation at a specific instant in time. Thus forecast verification is an important aspect of assessing the usefulness of the system. In comparison to the atmosphere, ocean observations are extremely limited. The best spatial and temporal data are provided by satellites but are generally limited to sea surface temperature (SST) and sea surface height. The former are usually available several times daily while the latter are limited to approximately weekly, depending upon the path of the satellite. Other measurements are available from ships of opportunity or from fixed buoys but these are sporadic and limited in both time and space. With all of these reservations in mind, in the next few figures we present some examples of the verification of the forecasts produced by this model. In Fig. 3 we show the forecast skill of SST for a one year period as a function of forecast lead time. The skill scores used are the domain averaged root mean square error (RMSE) and the anomaly correlation coefficient. The former measures the magnitude of the forecast error while the latter provides a measure of the pattern error. The figure shows the forecast skill for the high resolution shelf model (red line) and for the coarser resolution regional model (green line). We also include the error for a persistence forecast (i.e., no change from the initial conditions), which is considered to be the minimum skill forecast. From both the RMSE and the anomaly correlation it is clear that the forecast skill degrades as the forecast length increases. The value added to the forecast by the high resolution model is substantial as it outperforms the regional model in both scores (i.e., lower error magnitude and higher pattern correlation). Both models also manage to significantly beat persistence for RMSE, but the regional model is only marginally better in the pattern correlation.

Fig. 3. Forecast skill for one year of forecasts in terms of root mean square error and anomaly correlation coefficient.

While the skill of the SST forecast is impressive, it is also important to validate the ability of the model to predict the subsurface fields. Unfortunately here the data are much more

Numerical Modeling of the Ocean Circulation:

demonstrated by the examples presented.

174-267, Academic Press, London.

1-16, American Geophysical Union, Washington, DC.

barotropic vorticity equation. *Tellus*, Vol. 2, pp. 237-254.

13-353301-8, Englewood Cliffs, New Jersey.

**8. Acknowledgement** 

EVKT3-CT-2002-00075.

267-280.

287.

ISBN 9781-61209-644-5.

*Tellus*, Vol. 19, pp. 54-80.

**9. References** 

**7. Conclusion** 

From Process Studies to Operational Forecasting – The Mediterranean Example 125

In this chapter we have presented a concise overview of more than 40 years of research and development of numerical ocean circulation models. The pioneering work of Bryan & Cox (1967) set the stage for subsequent model development. The rapid development of computer technology of the past two decades has been a major factor allowing for the design of increasingly more complex and realistic models. By complementing field data and the associated gaps, numerical ocean models have proven to be an indispensible tool for enhancing our understanding of a wide range and variety of processes in oceanic hydrodynamics. Consequently, most modern oceanographic studies will almost always include a highly developed modeling component. Models are routinely used for processes studies and as the central component operational ocean forecasting systems as

The modeling results presented in this chapter were supported by the European Commission through the Sixth Framework Program European Coastal Sea Operational Observing and Forecasting System (ECOOP) Contract Number 36355, and Mediterranean Forecasting System Towards Environmental Prediction (MFSTEP) Contract Number

Arakawa and Lamb (1977). Computational design of the basic dynamical processes of the

Blumberg A. and Mellor, G.L. (1987). A description of a three-dimensional coastal ocean

Brenner, S. (2003). High-resolution nested model simulations of the climatological

Brenner, S. (2011). Circulation in the Mediterranean Sea, In: *Life in the Mediterranean Sea: A* 

Brenner, S., Gertman, I., and Murashkovsky, A. (2007). Pre-operational ocean forecasting

Bryan, K. and Cox, M.D. (1967). A numerical investigation of the oceanic general circulation.

Charney, J.G., Fjortoft, R. and von Neuman, J. (1950). Numerical integration of the

Cushman-Roisin, B. (1994). *Introduction to Geophysical Fluid Dynamics*, Prentice Hall, ISBN 0-

UCLA general circulation model. In: *Methods in Computational Physics*, Vol. 17, pp.

circulation model. In: *Three-Dimensional Coastal Ocean Models*, N. Heaps, editor, pp.

circulation in the southeastern Mediterranean Sea. *Annales Geophys*icae, Vol. 21, pp.

*Look at Habitat Changes*, N. Stambler, editor, chapter 4, Nova Science Publishers,

in the southeastern Mediterranean: Model implementation, evaluation, and the selection of atmospheric forcing. *Journal of Marine Systems,* Vol. 65, pp. 268-

limited in space and time. In Fig. 4 we show a scatter plot of the predicted versus the observed temperature taken from a sea level measurement station located offshore near Hadera (see map in Fig. 2 for location). The instrument was located at a depth of ~15 m below the surface and the bottom depth is ~27 m. The comparison shown here also covers a one year period. Overall the comparison is excellent with a correlation coefficient of nearly 0.97. During winter (low temperatures) and summer (high temperatures) the points tend to be roughly evenly scatter above and below the regression line thus indicating that there is no clear bias in the forecasts. During the transition seasons of spring and autumn (mid range temperatures), there is a strong tendency for the model to under predict the temperature and therefore develop a cold bias. This is most likely due to the more rapid temperature changes during the transitions seasons as compared to summer or winter.

Fig. 4. Scatter plot of the predicted versus measured temperature at a depth of 15 m at an offshore station.

Finally, as a measure of the spatial distribution of the prediction of the subsurface fields, a comparison was made between all measurements collected during a single, one day cruise in the late summer along a transect of points that extend westward from Haifa (see Fig. 2 for location). The measurements were obtained from an instrument that measures nearly continuous profiles of temperature and salinity from the surface to the bottom or to a depth of 1000 m, whichever is deeper. From below the surface mixed layer, the model did an excellent job of predicting the temperature and salinity at all depths and stations along the transect. In the mixed layer the model showed a warm bias with simulated temperatures that were too high by 1-2°C. This error is probably due to the specification of surface heat fluxes that were too high and/or winds that were too weak which prevented the model from creating a deep enough mixed layer. The high resolution forecast was significantly better than the regional model forecast in this area which again demonstrates the value added by a high resolution model. It should be noted however that this comparison was conducted for a single forecast only.
