Formulating a Dynamic Limnological Model for the Dead Sea Selection of a computer code and preliminary simulations

The Princeton Oceanographic Model (POM) was chosen as the appropriate code for the formulation of the dynamic limnological model for the Dead Sea. The model, when completed, will simulate seawater mixing in the Dead Sea, as expected once the "Peace Conduit" is constructed. The POM code was developed in the late 1970's by Blumberg and Mellor (1987), with subsequent contributions from other people. It has been used for modeling of open oceans, coastal regions, estuaries and lakes. It is a public domain code, which has numerous available versions that can be combined for the purpose of simulating seawater inflow to Dead Sea. Additional advantages include the fact that Princeton University provides free on line consulting services, up to date information and supports a discussion group. These have already been used by us and shown to be valuable resources. The DTM map of the Dead Sea basin was used as the basis for the construction of the bathymetric input file. Most simulations were run using seawater for which the physical characteristics are well established and therefore allow verifying the validity of the changes and modification introduced by us to the code. Initial runs indicated that the more common σ-grid version of POM introduces pressure gradient errors and results in stability loss and unrealistically large velocities. These problems were eliminated when the Z-grid version was used. The next runs were stability tests on a stratified lake with no external forcing. These showed that the molecular diffusion coefficient, which is based on the smoothing role of the diffusion mechanism in ocean-scale, are too large and leads to the rapid erosion of stratification. These tests demonstrated that for the purpose of modeling the expected stratification in the Dead Sea, the molecular diffusion coefficient in the code should have the same order of magnitude as real ion diffusion coefficients, i.e., 4 orders of magnitude smaller than that used in the POM. Following the above modification, constant wind forcing was applied on a box filled with seawater and Dead Sea brine in order to determine the slope of the water and observe the development of the Ekman layer. These were compared with known analytical results and excellent agreements were found. The impact of wind forcing on the stratified lake (still filled with seawater) was then simulated with real wind data. The layered structure was preserved all over the year resulting in minor change in the thermoand halocline depth after a whole year of real wind. Finally, thermal forcing was introduced to the code and simulations were run on both seawater and Dead Sea brine, the latter using the equation of state of the Dead Sea. Other parameters were similar and are based on known or assumed seawater parameters. This also required incorporating a module to calculate the change in water mass and the impact on salinity (due to evaporation). Simulations on seawater with constant heat flux and no wind results in gradual formation of a stable thermocline, while loss of fresh water due to evaporation leads to formation of an unstable halocline, as expected. Introducing real, one year, meteorological data resulted in the development of a stabilizing thermocline and destabilizing halocline during the spring and summer months. During the following fall months, cooling sets in and both thermoand haloclines deepen significantly. Simulations done with Dead Sea brine resulted with similar general trends, but the maximum temperature at the end of the summer is slightly higher and absolute increase in salinity is much higher. The difference in salinity increase is explained by the effect of the relative water content in the brine, which is smaller than in seawater, and therefore the impact of evaporation is greater. This also explains the deeper stratification in the Dead Sea brine as compared with seawater at the end of the year because the destabilizing effect of the halocline in the brine is greater. The preliminary simulations runs using the POM indicate that the POM is a good platform for the development of the dynamic limnological model for the Dead Sea. They also emphasize the importance of step by step examination and modification of the code and the need to determine the appropriate and unique parameters for the Dead Sea and Dead Sea – seawater mixtures. Future work will include re-evaluation of the Boussinesq approximation, introduction of surface and groundwater inflows. parameterization of the code against known data, introduction to the code of the new equation of state developed for Dead Sea –seawater mixtures, saturation and mineral precipitation calculations, true light penetration coefficients etc. These tasks will be the next stage in the development of the model. Table of Content Introduction .......................................................................................................................1 Model Modification – Principals.......................................................................................2 The Princeton Oceanographic Model (POM)....................................................................3 Testing + Initial Modification of POM to the Dead Sea system .......................................5 1...Model geometry and stability ..........................................................................5 2...Wind forcing....................................................................................................7 3... Impact of wind forcing on stratification..........................................................8 4...Thermal forcing ...............................................................................................9 5...Water mass balance (evaporation).................................................................12 6...Heatand wind-driven stratification build up................................................13 7...A new equation of state for Dead Seaseawater mixtures ............................15 Gypsum precipitation experiments..................................................................................17 Future Work.....................................................................................................................19 References .......................................................................................................................21 Appendix A: Publications related to lake studies............................................................22 Appendix B: The Basics of POM....................................................................................25 List of Figures: Fig. 1. Number of POM users over years. Fig. 2. A digital terrain map (DTM) of the Dead Sea Fig. 3. Bathymetry and horizontal grid of the Dead Sea. Fig. 4. The vertical grid used in the model. Fig. 5. Flow pattern and surface elevation generated due to pressure gradient errors in σ-grid POM. Fig. 6. Comparison between zand s-grids. Fig 7. Maximal surface velocity with zero initial velocity and no forcing. Fig. 8. Profiles obtained with the POM default molecular diffusion (D = 10-5) with no external forcing Fig. 9. Model simulation and analytical solution for wind-driven surface elevation Fig. 10. Slopes of the wind-driven surface elevation of seawater vs Dead Sea brine. Fig. 11. Model simulation vs. analytical solution for Ekman layer. Fig. 12. Surface elevation and flow velocities for seawater and constant wind simulation. Fig. 13. N-S temperature cross-section for seawater and constant wind simulation. Fig. 14. Surface elevation with seawater and real wind simulation Fig. 15. N-S temperature cross-section with initial seawater stratification and real wind simulation Fig. 16. Initial and vertical temperature and salinity profiles for one year simulation with real wind and initial seawater stratification Fig. 17. Temperature and salinity distribution after 1 year simulation with seawater, constant heat flux of 400 W/m and zero wind. Fig. 18. Monthly vertical temperature and salinity distribution during 1 year simulation with seawater, constant heat flux and zero wind. Fig. 19. Monthly vertical temperature and salinity distribution during 1 year simulation with seawater and real wind. Fig. 20. Monthly vertical temperature and salinity distribution during 1 year simulation with Dead Sea brine and real wind. Fig. 21. Calculated densities; Pitzer’s vs. the new equation of state. Fig. 23. The σ coordinate system