Ocean Science Operational forecast of hydrophysical fields in the

Ocean Sci 7 793ndash803 2011wwwocean-scinet77932011doi105194os-7-793-2011copy Author(s) 2011 CC Attribution 30 License

Ocean Science

Operational forecast of hydrophysical fields in the Georgian BlackSea coastal zone within the ECOOP

A A Kordzadze and D I Demetrashvili

M Nodia Institute of Geophysics Iv Javakhishvili Tbilisi State University 1 M Alexidze Str 0173 Tbilisi Georgia

Received 31 December 2010 ndash Published in Ocean Sci Discuss 21 February 2011Revised 26 August 2011 ndash Accepted 1 November 2011 ndash Published 25 November 2011

Abstract One of the parts of the Black Sea Nowcast-ingForecasting System is the regional forecasting system forthe easternmost part of the Black Sea (including the Georgianwater area) which has been developed within the context ofthe EU International projects ARENA and ECOOP A coreof the regional system is a high-resolution baroclinic regionalmodel of the Black Sea dynamics developed at M Nodia In-stitute of Geophysics (RM-IG) This model is nested in thebasin-scale model of Marine Hydrophysical Institute (MHISevastopolUkraine) The regional area is limited to theCaucasian and Turkish coastal lines and the western liquidboundary coinciding with the meridian 3936 E Since June2010 we have regularly been computing 3 daysrsquo forecasts ofcurrent temperature and salinity for the easternmost part ofthe Black Sea with 1 km spacing In this study the results oftwo forecasts are presented The first forecast correspondsto summer season and covers the prognostic interval from0000 h 6 August to 0000 h 9 August 2010 The secondone corresponds to autumn season and covers the prognos-tic interval from 0000 h 26 October to 0000 h 29 October2010 Data needed for the forecasts ndash the initial and prog-nostic hydrophysical fields on the open boundary also 2-Dprognostic meteorological fields at the sea surface ndash windstress heat fluxes evaporation and precipitation rates for ourregional area are being placed on the MHI server every dayand we are available to use these data operatively Prognostichydrophysical fields are results of forecast by the basin-scalemodel of MHI and 2-D meteorological boundary fields rep-resent the results of forecast by regional atmospheric modelALADIN All these fields are given on the grid of basin-scalemodel with 5 km spacing and with one-hour time step fre-quency for the integration period The analysis of predicted

Correspondence toD I Demetrashvili(demetr48yahoocom)

fields shows that to use the model with high resolution isvery important factor for identification of nearshore eddiesof small sizes It should be noted the very different characterof regional circulation in summer and autumn seasons in theeasternmost part of the Black Sea

1 Introduction

Large scientific and technical achievement of the Black Seaoperational oceanography for the last decade is the devel-opment of the Black Sea NowcastingForecasting Systemwhich allows to carry out continuous control over a currentstate of the Black Sea and its change for some days forward(Besiktepe 2003 Korotaev and Eremeev 2006) Creationof such system was promoted by the leading oceanographicCenters of the Black Sea riparian countries within the EUInternational scientific and technical projects ARENA andECOOP Coordination of this work was carried out by Ma-rine Hydrophysical Institute (MHI Sevastopol Ukraine) ofthe National Academy of Sciences of Ukraine Functioningof the system in operative mode is especially important forcoastal and shelf areas which undergoes the greatest anthro-pogenous loading

The main structure of the NowcastingForecasting Sys-tem is described by Korotaev et al (2006) and Kubryakovet al (2006) One of the parts of the System is the re-gional forecasting system for the easternmost part of theBlack Sea (including the Georgian water area) the core ofwhich is a high-resolution baroclinic regional model (RM-IG) of the Black Sea dynamics developed at M Nodia Insti-tute of Geophysics by Kordzadze and Demetrashvili (20082010) This model is nested in the basin-scale model (BSM)of the Black Sea dynamics of MHl (Demyshev and Koro-taev 1992) Note that the pilot near-real time operation of

Published by Copernicus Publications on behalf of the European Geosciences Union

794 A A Kordzadze and D I Demetrashvili Operational forecast of hydrophysical fields in the Georgian Black Sea

the Black Sea NowcastingForecasting System (including re-gional forecasting system for the Georgian water area) wassuccessfully carried out for the first time in July 2005 dur-ing five days (Kubryakov et al 2006 Kordzadze and Deme-trashvili 2008)

Since June 2010 at M Nodia Institute of Geophysics 3daysrsquo forecasts of 3-D fields of current temperature andsalinity with high resolution have been regularly carried outfor the easternmost part of the Black Sea All input dataneeded for initial and boundary conditions are available fromthe MHI server

In this study we consider the regional forecasting systemfor the easternmost part of the Black Sea To demonstratethe functioning of the system two forecasts of hydrophysicalfields for summer and autumn seasons are discussed

2 Regional forecasting system

The main component of the regional forecasting system(RM-IG) is developed by adaptation of the BSM of the BlackSea dynamics of M Nodia Institute of Geophysics (Ko-rdzadze and Demetrashvili 2004 Kordzadze et al 2008Demetrashvili et al 2008) to the easternmost part of thebasin and one-way nesting in the BSM of MHI (without feed-back from RM-IG to BSM) It is necessary to note that in turnthe BSM of Institute of Geophysics is an improved version ofthe prognostic model of the Black Sea dynamics (Kordzadzeand Skiba 1973 Marchuk et al 1975 1979 Marchuk andKordzadze 1986 Kordzadze 1989) originally developed inthe early 1970s at the Computing Center of Siberian Branchof the Academy of Sciences USSR (Novosibirsk Akadem-gorodok)

21 Model description

The RM-IG is based on a primitive system of ocean hydro-thermodynamics equations in hydrostatic approximationwhich is written inz-coordinates for deviations of thermody-namic values from their standard vertical distributions (Ko-rdzadze and Demetrashvili 2008 2010)

The model equation system is given in Appendix A Themodel takes into account nonstationary atmospheric windand thermohaline forcing quasi-realistic bottom relief theabsorption of solar radiation by the sea upper layer space-temporal variability of horizontal and vertical turbulent ex-change (Appendix B)

Atmospheric forcing is taken into account by boundaryconditions on the sea surface which is considered as a rigidsurface where Neumann conditions are used by given windstress components heat fluxes precipitation and evaporationfrom the sea surface On the sea bottom the velocity compo-nents heat and salt fluxes are equal to zero On the lateralsurfaces two kinds of boundary conditions are considered(1) on the rigid boundaries sharing the sea from the land

components of current velocity gradients of temperature andsalinity normal to the boundary surface are equal to zero (2)on the liquid boundary prognostic values of velocity com-ponents temperature and salinity computed on the base ofBSM of MHI are used

22 Method of solution

The existence and uniqueness theorems of 3-D nonsta-tionary problem of the sea dynamics are proved bySukhonosov (1981) and Kordzadze (1982) To solve theproblem we used the two-cycle method of splitting themodel equation system with respect to both physical pro-cesses and coordinate planes and lines which was proposedto solve problems of ocean and atmosphere dynamics byMarchuk (1967 1974)

Let us describe the numerical algorithm briefly Aftersplitting the model equation system (see Appendix A) withrespect to physical processes the following main stages areallocated (1) the transfer of the physical fields taking into ac-count eddy viscosity and diffusion (2) the adaptation of thephysical fields with division of the solution into barothropicand baroclinic components For approximation on time of allsplit problems the Krank-Nickolson scheme is used

At the transfer stage after using two-cycle splittingmethod with respect to coordinates and correspondingtransformation we receive one-dimensional finite-differenceequations on coordinatesx y andz for grid functions ofvelocity componentsu andv temperature deviationsT andsalinity deviationsS The received equations are solved bythe factorization method

At the adaptation stage the barothropic and barocliniccomponents are allocated The barothropic task is reduced tosolution of 2-D finite-difference equations for integral streamfunction

The differential operator of the baroclinic problem is pre-liminary splitting with the purpose of allocating the term de-scribing the Coriolis force action as an independent stageAfter using finite-difference approximation the remainingpart of the differential operator of the baroclinic problemsplits into vertical coordinate planeszx andzy As a resulta set of 2-D problems for baroclinic components on verticalplanes are received which then also are reduced to the equa-tions for analogs of stream functions

Thus the adaptation problem as a whole is reduced to so-lution of sequence of the same type 2-D problems for thestream function and analogs of stream functions which areefficiently realized within the framework of uniform iterativealgorithm (Kordzadze 1989) The exception is a task con-sidering the Coriolis force action which is explicitly real-ized by solution of algebraic equations At the transfer stageall required grid functions are defined in grid points with in-teger indexes and at the stage of adaptation the functionsare defined on the shifted grids Transition from one grid to

Ocean Sci 7 793ndash803 2011 wwwocean-scinet77932011

A A Kordzadze and D I Demetrashvili Operational forecast of hydrophysical fields in the Georgian Black Sea 795

another is carried out by the linear interpolation at each timestep

The finite-difference schemes received at each elementarystage of splitting are absolutely steady energetically bal-anced and provide the second order accuracy on time andspace coordinates (in case of uniform grid) The use of thesplitting method substantially simplifies the implementationof complex physical model and enables us to reduce solutionof 3-D nonstationary problem to solution of more simple 2-Dand 1-D problems

23 Methodology of nested grid modeling and someinput parameters

The high-resolution RM-IG covers the regional area boundedwith the Caucasus and Turkish shorelines and the westernliquid (open) boundary coincident with 3936 E with a gridhaving 193times 347 points on horizons (grid step 1 km) Ona vertical the non-uniform grid with 30 calculated levels ondepths 2 4 6 8 12 16 26 36 56 86 136 206 306 2006 m are considered The time step is equal to 05 h

The RM-IG is nested in the BSM of MHI with grid step5 km In addition there is applying one-way nesting whichprovides forcing of basin-scale processes on the regional pro-cesses via the open boundary Data needed for the regionalforecasts ndash the 3-D initial and 2-D prognostic fields of veloc-ity components temperature and salinity on the open bound-ary also 2-D prognostic meteorological fields at the sea sur-face ndash wind stress heat fluxes evaporation and precipitationrates for our regional area are providing from MHI via ftp siteand we are available to use these data operatively Prognos-tic hydrophysical fields on the open boundary are results offorecast from BSM of MHI and 2-D meteorological bound-ary fields represent results of forecast from the regional at-mospheric model ALADIN All these fields are given on thegrid of BSM with one-hour time step frequency within the4-days period With the purpose of using the received data asinitial and boundary conditions (on upper and open bound-aries) during model implementation these fields are trans-ferred to grid of RM-IG with 1 km spacing by interpolationThus on each time step on the western liquid boundary wehave forecasted values of flow velocity components temper-ature and salinity which are used as open boundary condi-tions for the RM-IG It should be noted that via ftp site weobtain also 3-D hydrophysical fields forecasted from BSM ofMHI and corresponding to our regional domain This fact en-ables us to compare results of forecasts obtained from bothRM-IG and BSM of MHI

Concerning the input data it is necessary to note the fol-lowing The input data which are given on a course gridprovide to run for 4-days but we consider that the RM-IGgives forecast only for three days as during the first day thecoastal model runs in the prognostic mode only to have betteradjustment of the fine resolution to the coarse initial condi-tions provided by the BSM of MHI

The software of the problem is developed on the basis ofthe algorithmic language ldquoCompaq Visual Fortran 61rdquo andrealization of the forecasting system is carried out by meansof PC Pentium-4 with 300 GHz The system allows to calcu-late 3-D fields of current temperature salinity and density inthe Black Sea coastal zone with 1 km resolution At 24 48and 72 h after starting the forecast visualization of the flowtemperature and salinity fields on horizons 0 10 20 50 100200 500 1000 m is carried out using the System softwareldquoSurfer-8rdquo Transition from calculated levels to these ones iscarried out by the linear interpolation

3 Simulation and forecast of regional circulationprocesses

To demonstrate the operation of the regional forecasting sys-tem there are considered two examples of the forecast cor-responding to summer and autumn seasons when circulatingfeatures of waters of the Georgian Black Sea coastal zonearea extremely differed from each other Before to analyzeforecast results simulated fields of SST are compared withsatellite SST

31 Validation of simulated SST

With the purpose of validating the regional system compar-ison of predicted fields with real data have been done dur-ing the pilot experiment within the project ARENA in 2005which showed an ability of the RM-IG to predict hydrophys-ical fields with sufficient accuracy (Kubryakov et al 2006)In this study we have carried out comparison of simulatedSST corresponding to 2010ndash2011 with satellite images SSTderived from NOAA The remote-sensing data were avail-able from the Black Sea data archive of the National SpaceAgency of Ukraine (httpdvsnetuamp) Mostly the dayswere selected when the sky was cloud-free over the east-ernmost Black Sea The analysis of results of compari-son showed a good qualitative correspondence between fore-casted and observed temperature fields Quantitative differ-ence in many cases does not exceed 07ndash08C

Some examples of validation of forecasted SST are shownin Fig 1 Here periods August and October 2010 are cho-sen which are considered in the next subsection to analyzeforecast results Fig 1a and c correspond to forecast start at5 August 2010 0000 h (here and after local time is used)and Fig 1e ndash to forecast start at 25 October 2010 0000 hIt is necessary to note that because of using of differentcolor scales (for example satellite images are given in con-tinuous spectrum while simulated SST ndash in discrete spec-trum) close similarity between the forecasted and satelliteSST at once is not obvious visually but their careful analy-sis shows that simulated and observed temperature fields arein a good agreement to each other For example as a resultof comparison of Fig 1a and b it is easy to notice that both

wwwocean-scinet77932011 Ocean Sci 7 793ndash803 2011


11

5

10

15

20

25

30

35

40

45

Fig 1 Forecasted (on the left side) and satellite SST derived from NOAA (on the right side)

50

(a)

(b) 6082010 235 GMT

(c)

(d) 7082010 0011 GMT

(e)

(f) 26102010 714 GMT

Fig 1 Forecasted (on the left side) and satellite SST derived fromNOAA (on the right side)

the simulated and measured SST patterns equally reflect themain features of the temperature field for example alongndashshore water transport with relatively high temperature and azone with relatively lower temperature approximately in thecentral part of the considered area The same can be noted atcomparison between Fig 1c and d

It should be noted that in October for the forecasting pe-riod presented here cloudiness dominated over the Black Seaincluding the easternmost part Only on 26 October 2010the sky was relatively cloud-free over the easternmost part ofthe sea basin but in this case some clouds in the central andnorth-western parts of the basin were observed too (Fig 1f)According to simulated and observed data (Fig 1e and f) acommon tendency of water cooling is observed in process ofincrease of distance from the sea coast Concerning quanti-

12

(a)

(b)

(c)

(d)

Fig 2 Current field at 5082010 0000 h on depths of 0 m (a) 50 m (b) 200 m (c)

and 500 m (d)

5

10

Fig 2 Current field at 5 August 2010 0000 h on depths of 0 m(a)50 m(b) 200 m(c) and 500 m(d)

tative comparison in the most part of the considered domaindifferences between forecasted and observed values of SSTdo not exceed 05C but there are some points where aresignificant differences

32 Forecast for summer season

The forecasting time period lasted from 0000 h 6 August to0000 h 9 August 2010 but according to discussed aboveintegration of model equations began one day earlier ieat 0000 h 5 August At this moment the current field inthe regional area on the different depths is shown in Fig 2From this Figure it is clear that the main element of the re-gional circulation is the anticyclonic eddy (called the Batumieddy) with diameter about of 150ndash200 km which covers thesignificant part of the considered area This vortex practi-cally does not change in the upper 200 m layer only cur-rent speed decreases from maximal value equal to 24 cm sminus1

till 11 cm sminus1 below 200 m the vortex gradually decreases insizes (Fig 2d) At deeper levels the Batumi eddy graduallydisappeared

The temperature and salinity fields on the Black Sea sur-face and horizonz= 100 m at the beginning of integration ofmodel equation system are presented in Figs 3 and 4 Hor-izontal distribution of the surface temperature is typical forthe summer period warmer waters are in the nearshore zoneto Caucasus sealine On the horizonz= 100 m the cold in-termediate layer (CIL) which covers a considerable part of



13

(a)

(b)

Fig 3 Temperature field (deg C) at 5082010 0000 h on depths of 0 m (a) and 100 m (b)

5

(a)

(b)

Fig 4 Salinity field (psu) at 5082010 0000 h on depths of 0 m (a) and 100 m (b) 10

Fig 3 Temperature field (deg C) at 5 August 2010 0000 h ondepths of 0 m(a) and 100 m(b)

13

(a)

(b)


5

(a)

(b)


Fig 4 Salinity field (psu) at 5 August 2010 0000 h on depths of0 m (a) and 100 m(b)

the allocated water area is well observed (CIL is boundedwith isotherm of 8C) The Batumi anticyclonic eddy makesappreciable impact on formation of salinity field in the con-sidered area General feature of this field is that the area ofrelatively low salinity waters coincides with allocation of an-ticyclonic eddy (compare Figs 2 and 4) It is easy to explainthis fact to that descending streams which develop in the an-ticyclonic vortex transfer fresher waters from the upper layerdownwards (Stanev et al 1988 Kordzadze 1989)

The analysis of the wind stress fields for the forecast-ing period showed that atmospheric circulation significantlychanged during this period

The surface current fields after 24 and 72 h (time iscounted from the initial moment of the forecast 0000 h6 August 2010) predicted by the RM-IG are presented inFig 5 and the same fields predicted by the BSM of MHI atthe same time moments are shown in Fig 6

The comparative analysis of Figs 5 and 6 shows that fore-casted regional circulation patterns obtained from RM-IGand BSM of MHI have common features but it is evidentthat there are also distinctive features The common featureis that accordance to both models the Batumi eddy is rather

14

(a) t = 24 h

(b) t = 72 h

5

Fig 5 The surface current fields predicted by RM-IG at 24 h (a) and 72 h (b) (the forecasting

period is 6082010 0000 h ndash 9082010 0000 h)

(a) t = 24 h

(b) t = 72 h

Fig 6 The surface current fields predicted by BSM of MHI at 24 h (a) and 72 h (b) (the 10

forecasting period is 6082010 0000 h ndash 9082010 0000 h)

Fig 5 The surface current fields predicted by RM-IG at 24 h(a)and 72 h(b) (The forecasting period is 6 August 2010 0000 hndash9August 2010 0000 h)

14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h



Fig 6 The surface current fields predicted by BSM of MHI at 24 h(a) and 72 h(b) (the forecasting period is 6 August 2010 0000 hndash9August 2010 0000 h)

stable formation and it is observed during all forecasting pe-riod without strong changes despite nonstationarity of atmo-spheric forcing It must be noted that formation of the anticy-clonic eddy in the south-east part of the Black Sea basin andits stability in warm season is a well-known fact (Oguz etal 1993 Korotaev et al 2003) The main differences arein the narrow zone with width about 20ndash25 km along theCaucasian shoreline The system of currents in this zoneby results of RM-IG is characterized by the clear tendencyto vortex formation of very small sizes and nonstationaritywhereas results of BSM specify about smoothness and prac-tically non-stationary character of current in this zone Forexample unlike results of the BSM in Fig 5a formation of asmall cyclonic eddy with a diameter about 15ndash20 km near theSukhumi water area is observed att = 24 h which becomesmore clear tot = 72 h Likewise near shoreline between Potiand Khopa the process of formation of very small unstableeddies is observed att = 24 h but to the momentt = 72 hthey are disappeared The existence of rather unstable eddiesof small sizes of cyclonic and anticyclonic characters near the



15

t = 24 h

t = 72 h

Fig 7 The temperature fields (deg C) on depth of 10 m predicted by RM-IG at 24 h and

(b) 72 h (the forecasting period is 6082010 0000 h ndash9082010 0000 h)

5

t = 24 h

t = 72

Fig 8 The salinity fields (psu) on depth of 10 m predicted by RM-IG at 24 h (a) and 72 h (b)

(the forecasting period is 6082010 0000 h ndash9082010 0000 h)

10

Fig 7 The temperature fields (deg C) on depth of 10 m predictedby RM-IG at 24 h and(b) 72 h (the forecasting period is 6 August2010 0000 hndash9 August 2010 0000 h)

15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10

Fig 8 The salinity fields (psu) on depth of 10 m predicted by RM-IG at 24 h(a) and 72 h(b) (the forecasting period is 6 August 20100000 hndash9 August 2010 0000 h)

Georgian shoreline is known from observations (Jaoshvili1986) but their identification by the mathematical models ispossible by providing very high resolution that is achievedin the RM-IG

According to results of the RM-IG the narrow coastal zoneof vortex formation makes certain impact on configuration ofBatumi anticyclonic eddy and consequently on velocity dis-tribution within the eddy This zone plays a role of the in-terfering factor for the right peripheral current of the Batumieddy to reach the Georgian coast For example from Fig 5 iswell visible that the small anticyclonic eddy near Sukhumiwater area represents an obstacle for peripheral current ofthe Batumi eddy and the current is passing through relativelynarrow strip between the center of Batumi eddy and the smalleddy near Sukhumi area Therefore here a zone of cur-rents intensification with speeds about 30ndash32 cm sminus1 is ob-served The above phenomenon of regional circulation is notobserved according to the results of BSM of MHI (Fig 6)

Temperature and Salinity fields predicted by the RM-IGare presented in Figs 7 and 8 and the same fields predictedby the BSM of MHI ndash in Figs 9 and 10 In both cases these

16

(a) t = 24 h

(b) t = 72 h

Fig 9 The temperature fields (deg C) on depth of 10 m predicted by BSM of MHI at 24 h (a)

and 72 h (b) (the forecasting period is 6082010 0000 h ndash9082010 0000 h)

5

(a) t = 24 h

(b) t = 72 h

Fig 10 The salinity fields (psu) on depth of 10 m predicted by BSM of MHI at 24 h (a) and

72 h (b) (the forecasting period is 6082010 0000 h ndash9082010 0000 h)

10

15

Fig 9 The temperature fields (deg C) on depth of 10 m predictedby BSM of MHI at 24 h(a) and 72 h(b) (the forecasting period is6 August 2010 0000 hndash9 August 2010 0000 h)

16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15

Fig 10The salinity fields (psu) on depth of 10 m predicted by BSMof MHI at 24 h (a) and 72 h(b) (the forecasting period is 6 August2010 0000 hndash9 August 2010 0000 h)

fields are shown on depth of 10 m and at moments 24 and72 h after start of the forecast Comparison between Figs 7and 9 shows some differences of temperature patterns com-puted on the basis RM-IG and BSM of MHI From these Fig-ures it is visible that in both cases colder waters are observedin the central area of the Batumi eddy than on its peripheriesbut this feature is more expressed in the temperature fieldpredicted by the BSM (Fig 9) Comparison of Figs 8 and10 obviously demonstrate efficiency of the higher resolutionmodel to simulate a salinity field in the coastal zone withhigher adequacy From Fig 8 it is well visible the zone withhigh salinity having a form of concave tongue that appar-ently shows transfer of more salty waters from the open partof the sea into the Georgian water area by the Batumi eddyThe coarse resolution model is unable to reproduce this phe-nomenon (Fig 10) whereas the fine intrusion of waters ofdifferent salinity is well resolved by the high resolution RM-IG



17

(a) t =0 h

(b)

(c)

(d)

Fig 11 Current field at 25102010 0000 h on depths of 0 m (a) 50 m (b)

200 m (c) and 500 m (d)

5

10

15

Fig 11 Current field at 25 October 2010 0000 h on depths of 0 m(a) 50 m(b) 200 m(c) and 500 m(d)

18

(a)

(b)

Fig 12 Temperature field (deg C) at 25102010 0000 h on depths of 0 m (a) and

100 m (b)

5

(a)

(b)

Fig 13 Salinity field (psu) at 25102010 0000 h on depths of 0 m (a) and 100 m (b)

10

15

Fig 12 Temperature field (deg C) at 25 October 2010 0000 h ondepths of 0 m(a) and 100 m(b)

33 Forecast for autumn season

The second example of the forecast concerns to the autumnwhen the forecasting period was from 0000 h 26 October to0000 h 29 October 2010 Like the previous case integrationof model equation system began one day earlier at 0000 h25 October

The velocity pattern on some horizons at the beginningof integration is shown in Fig 11 It is interesting to note

18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15

Fig 13 Salinity field (psu) at 25 October 2010 0000 h on depthsof 0 m (a) and 100 m(b)

19

t = 24 h

t = 72 h

Fig 14 The surface current fields predicted by RM-IG at 24 h (a) and 72 h (b)

(the forecasting period is 26102010 0000 h ndash 29102010 0000 h)

5

(a) t = 24 h

(b) t = 72 h

Fig 15 The surface current fields predicted by BSM of MHI at 24 h (a) and 72 h (c) (the

forecasting period is 26102010 0000 h ndash 29102010 0000 h) 10

Fig 14 T he surface current fields predicted by RM-IG at 24 h(a)and 72 h(a) (the forecasting period is 26 October 2010 0000 h ndash29October 2010 0000 h)

that the character of the regional circulation is quite differentfrom circulation taking place on 5 August 2010 (see Fig 2)The general structure of the regional circulation on 0000 h25 October is characterized by formation of cyclonic and an-ticyclonic eddies of small sizes Such structure is qualita-tively kept up to deep levels with gradual reduction of themaximal speed of the flow from 32 cm sminus1 up to 4 cm sminus1 onhorizonz= 500 m Accordingly horizontal distributions oftemperature and salinity fields (Figs 12 and 13) differ fromdistribution of the same fields at 0000 5 August 2010 (seeFigs 3 and 4)

The Atmospheric wind above the regional area consider-ably changed during the forecasting interval

The prognostic surface regional circulation patterns com-puted by the RM-IG are presented in Fig 14 and the samepatterns computed by the BSM of MHI are demonstrated inFig 15 at times of 24 and 72 h after start of the forecastinginterval Comparison of these two Figures shows that ac-cording to results of RM-IG during the forecasting intervalthe regional circulation is characterized by intensive forma-tion deformation and disappearance of the small eddies with



19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h



Fig 15 The surface current fields predicted by BSM of MHI at24 h (a) and 72 h(c) (the forecasting period is 26 October 20100000 hndash29 October 2010 0000 h)

20

t = 48 h

t = 72 h

Fig 16 The temperature fields (deg C) on depth of 10 m predicted by RM-IG at 48 h (a) and

72 h (b) (forecasting period is 26102010 0000 h ndash 29102010 0000 h)

5

(a) t = 48 h

(b) t = 72 h

Fig 17 The salinity fields (psu) on depth of 10 m predicted by RM-IG at 48 h (a) and

72 h (b) (forecasting period is 26102010 0000 h ndash 29102010 0000 h ) 10

Fig 16 The temperature fields (deg C) on depth of 10 m predictedby RM-IG at 48 h(a) and 72 h(b) (forecasting period is 26 October2010 0000 hndash29 October 2010 0000 h)

diameter about 15ndash20 km while these properties of the re-gional circulation are much less expressed by results of theBSM of MHI This fact once again directs us to the ideathat high resolution of numerical model is a major factor forimproving identification of small unstable eddies which arepermanently formed in the Georgian coastal zone

The prognostic fields of temperature and salinity com-puted by the RM-IG are shown in Figs 16 and 17 and thesame fields predicted by the BSM are presented in Fig 18and 19 These fields are shown on the depth of 10 m after 48and 72 h after the initial moment of the forecast The com-parative analysis of the fields predicted by both RM-IG andBSM shows that in this case general features of temperatureand salinity fields predicted by the both models are similarand qualitatively are close to each other but they differ fromeach other quantitatively and with some separate nuances ofthe thermohaline fields

20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h



Fig 17The salinity fields (psu) on depth of 10 m predicted by RM-IG at 48 h(a) and 72 h(b) (forecasting period is 26 October20100000 hndash29 October2010 0000 h)

21

(a) t = 48 h

(b) t = 72 h

Fig 18 The temperature fields (deg C) on depth of 10 m predicted by BSM of MHI at 48 h (a) and

72 h (b) (forecasting period is 26102010 0000 h ndash 29102010 0000 h) 5

(a) t = 48 h

(b) t = 72 h

Fig 19 The salinity fields (psu) on depth of 10 m predicted by BSM of MHI at 48 h (a) and 10

72 h (b) (the forecasting period is 26102010 0000 h ndash 29102010 0000 h)

Fig 18The temperature fields (deg C) on depth of 10 m predictedby BSM of MHI at 48 h(a) and 72 h(b) (forecasting period is 26October 2010 0000 hndash29 October 2010 0000 h)

4 Conclusions

A regional forecasting system allowed to predict flow tem-perature and salinity fields with 1 km spacing in the eastern-most part of the Black Sea (including Georgian water area)is elaborated The core of the forecasting system is the hy-drostatic baroclinic regional model of the Black Sea dynam-ics developed at M Nodia Institute of Geophysics which isnested in the BSM of MHI

The simulation and 3 daysrsquo forecasts of 3-D hydrophysicalfields were performed for the summer and autumn seasons2010 using the prognostic data of BSM of MHI and atmo-spheric dynamics model ALADIN

The model simulation shows the seasonal differences be-tween regional dynamical processes Our results once againshow already known fact that in summer the main elementof the regional circulation in the considered area is the Ba-tumi anticyclonic eddy Unlike the summer circulation inautumn the circulation has a vortical character with forma-tion of cyclonic and anticyclonic eddies with diameters about



21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h


72 h (b) (the forecasting period is 26102010 0000 h ndash 29102010 0000 h) Fig 19 The salinity fields (psu) on depth of 10 m predicted byBSM of MHI at 48 h(a) and 72 h(b) (the forecasting period is 26October 2010 0000 hndash29 October 2010 0000 h)

15ndash20 km These eddies are not stable formations and de-compose or undergo some modifications in time

The comparative analysis of predicted fields by both RM-IG and BSM of MHI shows that to use the model withhigh resolution is very important factor for identification ofcoastal eddies of small sizes In case of forecast of summercirculation more differences are observed in the narrow zonealong Caucasus shoreline In this near-shore zone the flowpredicted by the RM-IG is characterized by nonstationarityand the tendency to form eddies of small sizes Such char-acter of the sea flow along the Georgian near-shore zone isknown from observations (Jaoshvili 1986) In case of fore-cast of autumn circulation considerable differences betweenthe predicted current fields are observed the vortex forma-tion processes are more intensive at using of the RM-IG It isalso interesting fact that in summer when the Batumi eddyis well developed penetration of more salty waters from theopen part of the Black Sea into the Georgian water area isdistinctly observed by the results of the RM-IG

The regional forecasting system presented in this study isa base for further development of a coupled modeling sys-tem allowing to predict not only dynamic processes also dif-ferent ecological processes including dispersion of oil andother polluting substances in the Georgian coastal zone inaccidental situations The hydrodynamic module of the cou-pled system ndash the RM-IG will be improved by taking intoconsideration a free surface and nonhydrostatic effects

Appendix A

Model equation system

The RM-IG equation system which describes the hydro andthermodynamic processes in the sea basin is following

partu

partt+div uuminus lv+

1

ρ0

partpprime

partx= nablamicronablau+

part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime

party= nablamicronablav+

part

partzνpartv

partz

partpprime

partz= gρprime div u = 0

partT prime

partt+div uT prime

+γT middotw= nablamicroTnablaT prime+part

partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime

+γSw=nablamicroSnablaSprime+part

partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz

T = T (zt)+T primeS= S(zt)+Sprimeρ= ρ(zt)+ρprime

p= p(zt)+pprime

nablamicronabla =part

partxmicropart

partx+part

partymicropart

party I = η(1minusA)I0e

minusαz

I0=asinh0minusbradic

sinh0 sinh0=sinϕsinψ+cosϕcosψcosπ

12t

η= 1minus(a+ bn)n

αT = partfpart T = minus10minus3(00035+000938T +00025S)

αS = partfpart S= 10minus3(0802minus0002T )

Here the following notations are useduv andw are thecomponents of the current velocity vector along the axesxy andz respectively (the axesx y andz are directed east-ward northward and vertically downward from the sea sur-face respectively)T primeSprimeP primeρprime are the deviations of temper-ature salinity pressure and density from their standard ver-tical distributionsT SP ρ l= l0+β y is the Coriolis pa-rameter whereβ = dldy g c andρ0 are the gravitationalacceleration the specific heat capacity and average density ofseawater respectivelymicromicroT SννT S are the horizontal andvertical eddy viscosity heat and salt diffusion coefficientsrespectivelyI0 ndash the total flux of solar radiation atz= 0A is the albedo of a sea surfaceh0 is the zenithal angle ofthe Sunϕ is the geographical latitude9 is the parameterof declination of the Sunη is the factor which takes intoaccount influence of a cloudiness on a total radiation and de-pends upon ball of nebulosityn (Berlyand 1960)a b a bare the empirical factorsα is the parameter of absorption ofshort-wave radiation by seawater



Appendix B

Parameterization of the turbulent field

Factors of horizontal viscosity and diffusion for temperatureand saltmicromicroT S where calculated by the formulas (Zilitinke-vich and Monin 1971)

micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS

where1x and1y are horizontal grid steps alongx andyrespectivelycT andcS are some constants equal to 10

Factors of vertical turbulent diffusion for heat and saltνT Swere calculated by using the modified Oboukhov formulapresented by Marchuk et al (1980) as

νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz

Here h is the depth of the turbulent surface layer which isdefined by the first pointzm in which following condition issatisfied

(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0

T Sν0T S = 1 cm2 sminus1

Vertical turbulent viscosity factor

ν=

50 cm2 sminus1 zle 55 m10 cm2 sminus1 zgt55 m

In case of unstable stratification which might appear dur-ing integration of the equations (partρ

partzlt 0) the realization of

this instability in the model is taken into account by increaseof factor of turbulent diffusionνT S 20 times in appropriatecolumns from the surface to the bottom

AcknowledgementsThe Authors would like to thank theEU projects ARENA and ECOOP coordinators G KorotaevOle Krarup Leth Paolo Oddo A Kubryakov also all othercolleagues with which the authors fruitfully cooperated within theimplementation of these projects

Edited by G Korotaev

References

Berlyand G G Method of climatological calculation of the netradiation (in Russian) Meteorologia i gidrologia Moscow 6 9ndash12 1960

Besiktepe S T Development of the regional forecasting systemfor the Black Sea Proceed of the ldquoSecond International Con-ference on Oceanography of Eastern Mediterranean and BlackSea Similarities and Differences of Two Interconnected BasinsrdquoAnkara Turkey 14ndash18 October 2002 297ndash306 2003

Demetrashvili D I Kvaratskhelia D U and Gvelesiani A IOn the vortical motions in the Black Sea obtained by the 3-Dhydrothermodynamical numerical model Adv Geosci 14 295ndash299doi105194adgeo-14-295-2008 2008

Demyshev S G and Korotaev G K Numerical energy-balancedmodel of baroclinic currents in the ocean with bottom topographyon the C-grid in Numerical Models and Results of Intercalibra-tion Simulations in the Atlantic Ocean edited by Sarkisyan AMoscow 163ndash231 1992 (in Russian)

Jaoshvili Sh V The river alluvium and the beach formation of theGeorgian Black Sea coast Tbilisi 155 pp 1986 (in Russian)

Kordzadze A A Mathematical Problems of Solving Problems ofOcean Dynamics VTs SO AN SSSR Novosibirsk 148 pp 1982(in Russian)

Kordzadze A A Mathematical modelling of sea currents (theoryalgorithms numerical experiments) Moscow OVM AN SSSR218 pp 1989 (in Russian)

Kordzadze A A and Skiba Yu N Numerical calculations ofthe Black Sea with a three-dimensional model Preprint Com-puter Center Siberian Branch of Russian Academy of SciencesNovosibirsk 32 pp 1973 (in Russian)

Kordzadze A A and Demetrashvili D I Numerical modeling ofinner-annual variability of the hydrological regime of the BlackSea with taking into account of alternation of different types ofthe wind above its surface Proceed of Intern Conference ldquoAyear after Johanesburg-Ocean Governance and Sustainable De-velopment Ocean and Coasts ndash a Glimpse into the Futurerdquo KievUkraine October 27ndash30 2003 495ndash505 2004

Kordzadze A and Demetrashvili D I Simulation and forecast ofhydrophysical fields in the part of the Georgian Black Sea coastalzone J Georgian Geoph Soc 12 7ndash16 2008

Kordzadze A and Demetrashvili D I Modeling of dynamicalprocesses in the Black Sea Georgian Electronic Scientific Jour-nal (GESJ) Physics 1 25ndash45httpgesjinternet-academyorggephys 2010

Kordzadze A A Demetrashvili D I and Surmava A A Nu-merical modeling of hydrophysical fields of the Black Sea un-der the conditions of alternation of atmospheric circulation pro-cesses Izvestiya RAS Atmospheric and Oceanic Physics 44213ndash224 2008

Korotaev G K and Eremeev V N Introduction in operativeoceanography of the Black Sea Sevastopol HPC ldquoEKOCI-Gidrofizikardquo 382 pp 2006 (in Russian)

Korotaev G Oguz T Nikiforov A and Koblinsky C Seasonalinterannual and mesoscale variability of the Black Sea upperlayer circulation derived from altimeter data J Geophys Res108 3122doi1010292002JC001508 2003

Korotaev G Cordoneanu E Dorofeev V Fomin V Grig-oriev A Kordzadze A Kubriakov A Oguz T RatnerYu Trukhchev D and Slabakov H Near-operational BlackSea nowcastingforecasting system in European OperationalOceanography Present and Future 4th EuroGOOS Conference6ndash9 June 2005 Brest France 269ndash275 2006

Kubryakov A Grigoriev A Kordzadze A Korotaev GTrukhchev D and Fomin V NowcastingForecasting subsys-tem of the circulation in the Black Sea nearshore regions inEuropean Operational Oceanography Present and Future 4thEuroGOOS Conference 6ndash9 June 2005 Brest France 605ndash6102006



Marchuk G I Numerical methods in weather predictionLeningrad Gidrometeoizdat 353 pp 1967 (in Russian)

Marchuk G I Numerical Solution of Problems of Atmosphericand Oceanic Dynamics Gidrometeoizdat Leningrad 303 pp1974 (in Russian)

Marchuk G I and Kordzadze A A Perturbation theory and theformulation of inverse problems of ocean dynamics Proceedengsof Tbilisi State University Mathematica Mekhanica Astrono-mia 259 49ndash65 1986 (in Russian)

Marchuk G I Kordzadze A A and Skiba Yu N Calcula-tion of major hydrological fields of the Black Sea on the basisof the splitting method Izvestiya USSR Atmos Ocean Phys11 379ndash393 1975

Marchuk G I Kordzadze A A and Zalesnyi V B Problem ofmathematical modelling of sea and ocean currents in Differen-tial and Integral Equations Boundary-Value Problems Tbilisi99ndash151 1979 (in Russian)

Marchuk G I Kochergin V P Sarkisyan A S Bubnov M AZalesny V B Klimok V I Kordzadze A A Kuznetsov VI Protasov A B Sukhorukov B A Tsvetova E A andScherbakov A B Mathematical models of ocean circulation Nauka Novosibirsk 288 pp 1980 (in Russian)

Oguz T Latun V S Latif M A Vladimirov V V Sur H IMarkov A A Ozsoy E Kotovshchikov B B Eremeev VV and Unluata U Circulation in the surface and intermediatelayers in the Black Sea Deep Sea Res 40 1597ndash1612 1993

Stanev E Truhchev D and Roussenov V The Black Sea circu-lation and its numerical modelling Sofia Kliment Ohridski 222pp 1988 (in Russian)

Sukhonosov V I On the correctness as a whole of a 3D problem ofocean dynamics in Mechanics of Inhomogeneous Continuousmedia Computer Center Siberian Branch of Russian Academyof Sciences Novosibirsk 52 37ndash53 1981 (in Russian)

Zilitinkevich S S and Monin A S Turbulence in Dynamic Mod-els of the Atmosphere Nauka Leningrad 41 pp 1971 (in Rus-sian)



the Black Sea NowcastingForecasting System (including re-gional forecasting system for the Georgian water area) wassuccessfully carried out for the first time in July 2005 dur-ing five days (Kubryakov et al 2006 Kordzadze and Deme-trashvili 2008)

Since June 2010 at M Nodia Institute of Geophysics 3daysrsquo forecasts of 3-D fields of current temperature andsalinity with high resolution have been regularly carried outfor the easternmost part of the Black Sea All input dataneeded for initial and boundary conditions are available fromthe MHI server

In this study we consider the regional forecasting systemfor the easternmost part of the Black Sea To demonstratethe functioning of the system two forecasts of hydrophysicalfields for summer and autumn seasons are discussed

2 Regional forecasting system

The main component of the regional forecasting system(RM-IG) is developed by adaptation of the BSM of the BlackSea dynamics of M Nodia Institute of Geophysics (Ko-rdzadze and Demetrashvili 2004 Kordzadze et al 2008Demetrashvili et al 2008) to the easternmost part of thebasin and one-way nesting in the BSM of MHI (without feed-back from RM-IG to BSM) It is necessary to note that in turnthe BSM of Institute of Geophysics is an improved version ofthe prognostic model of the Black Sea dynamics (Kordzadzeand Skiba 1973 Marchuk et al 1975 1979 Marchuk andKordzadze 1986 Kordzadze 1989) originally developed inthe early 1970s at the Computing Center of Siberian Branchof the Academy of Sciences USSR (Novosibirsk Akadem-gorodok)

21 Model description

The RM-IG is based on a primitive system of ocean hydro-thermodynamics equations in hydrostatic approximationwhich is written inz-coordinates for deviations of thermody-namic values from their standard vertical distributions (Ko-rdzadze and Demetrashvili 2008 2010)

The model equation system is given in Appendix A Themodel takes into account nonstationary atmospheric windand thermohaline forcing quasi-realistic bottom relief theabsorption of solar radiation by the sea upper layer space-temporal variability of horizontal and vertical turbulent ex-change (Appendix B)

Atmospheric forcing is taken into account by boundaryconditions on the sea surface which is considered as a rigidsurface where Neumann conditions are used by given windstress components heat fluxes precipitation and evaporationfrom the sea surface On the sea bottom the velocity compo-nents heat and salt fluxes are equal to zero On the lateralsurfaces two kinds of boundary conditions are considered(1) on the rigid boundaries sharing the sea from the land

components of current velocity gradients of temperature andsalinity normal to the boundary surface are equal to zero (2)on the liquid boundary prognostic values of velocity com-ponents temperature and salinity computed on the base ofBSM of MHI are used

22 Method of solution

The existence and uniqueness theorems of 3-D nonsta-tionary problem of the sea dynamics are proved bySukhonosov (1981) and Kordzadze (1982) To solve theproblem we used the two-cycle method of splitting themodel equation system with respect to both physical pro-cesses and coordinate planes and lines which was proposedto solve problems of ocean and atmosphere dynamics byMarchuk (1967 1974)

Let us describe the numerical algorithm briefly Aftersplitting the model equation system (see Appendix A) withrespect to physical processes the following main stages areallocated (1) the transfer of the physical fields taking into ac-count eddy viscosity and diffusion (2) the adaptation of thephysical fields with division of the solution into barothropicand baroclinic components For approximation on time of allsplit problems the Krank-Nickolson scheme is used

At the transfer stage after using two-cycle splittingmethod with respect to coordinates and correspondingtransformation we receive one-dimensional finite-differenceequations on coordinatesx y andz for grid functions ofvelocity componentsu andv temperature deviationsT andsalinity deviationsS The received equations are solved bythe factorization method

At the adaptation stage the barothropic and barocliniccomponents are allocated The barothropic task is reduced tosolution of 2-D finite-difference equations for integral streamfunction

The differential operator of the baroclinic problem is pre-liminary splitting with the purpose of allocating the term de-scribing the Coriolis force action as an independent stageAfter using finite-difference approximation the remainingpart of the differential operator of the baroclinic problemsplits into vertical coordinate planeszx andzy As a resulta set of 2-D problems for baroclinic components on verticalplanes are received which then also are reduced to the equa-tions for analogs of stream functions

Thus the adaptation problem as a whole is reduced to so-lution of sequence of the same type 2-D problems for thestream function and analogs of stream functions which areefficiently realized within the framework of uniform iterativealgorithm (Kordzadze 1989) The exception is a task con-sidering the Coriolis force action which is explicitly real-ized by solution of algebraic equations At the transfer stageall required grid functions are defined in grid points with in-teger indexes and at the stage of adaptation the functionsare defined on the shifted grids Transition from one grid to

















11

5

10

15

20

25

30

35

40

45


50

(a)

(b) 6082010 235 GMT

(c)

(d) 7082010 0011 GMT

(e)

(f) 26102010 714 GMT




12

(a)

(b)

(c)

(d)


and 500 m (d)

5

10









13

(a)

(b)


5

(a)

(b)



13

(a)

(b)


5

(a)

(b)







14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h




14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h







15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10


15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10





16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15


16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15





17

(a) t =0 h

(b)

(c)

(d)


200 m (c) and 500 m (d)

5

10

15


18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15





18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15


19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h









19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h




20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h






20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h




21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h




4 Conclusions






21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References













































11

5

10

15

20

25

30

35

40

45


50

(a)

(b) 6082010 235 GMT

(c)

(d) 7082010 0011 GMT

(e)

(f) 26102010 714 GMT




12

(a)

(b)

(c)

(d)


and 500 m (d)

5

10









13

(a)

(b)


5

(a)

(b)



13

(a)

(b)


5

(a)

(b)







14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h




14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h







15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10


15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10





16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15


16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15





17

(a) t =0 h

(b)

(c)

(d)


200 m (c) and 500 m (d)

5

10

15


18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15





18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15


19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h









19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h




20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h






20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h




21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h




4 Conclusions






21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References































11

5

10

15

20

25

30

35

40

45


50

(a)

(b) 6082010 235 GMT

(c)

(d) 7082010 0011 GMT

(e)

(f) 26102010 714 GMT




12

(a)

(b)

(c)

(d)


and 500 m (d)

5

10









13

(a)

(b)


5

(a)

(b)



13

(a)

(b)


5

(a)

(b)







14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h




14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h







15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10


15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10





16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15


16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15





17

(a) t =0 h

(b)

(c)

(d)


200 m (c) and 500 m (d)

5

10

15


18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15





18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15


19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h









19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h




20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h






20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h




21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h




4 Conclusions






21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References































13

(a)

(b)


5

(a)

(b)



13

(a)

(b)


5

(a)

(b)







14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h




14

(a) t = 24 h

(b) t = 72 h

5



(a) t = 24 h

(b) t = 72 h







15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10


15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10





16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15


16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15





17

(a) t =0 h

(b)

(c)

(d)


200 m (c) and 500 m (d)

5

10

15


18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15





18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15


19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h









19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h




20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h






20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h




21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h




4 Conclusions






21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References































15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10


15

t = 24 h

t = 72 h



5

t = 24 h

t = 72



10





16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15


16

(a) t = 24 h

(b) t = 72 h



5

(a) t = 24 h

(b) t = 72 h



10

15





17

(a) t =0 h

(b)

(c)

(d)


200 m (c) and 500 m (d)

5

10

15


18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15





18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15


19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h









19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h




20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h






20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h




21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h




4 Conclusions






21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References































17

(a) t =0 h

(b)

(c)

(d)


200 m (c) and 500 m (d)

5

10

15


18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15





18

(a)

(b)


100 m (b)

5

(a)

(b)


10

15


19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h









19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h




20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h






20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h




21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h




4 Conclusions






21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References































19

t = 24 h

t = 72 h



5

(a) t = 24 h

(b) t = 72 h




20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h






20

t = 48 h

t = 72 h



5

(a) t = 48 h

(b) t = 72 h




21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h




4 Conclusions






21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References































21

(a) t = 48 h

(b) t = 72 h



(a) t = 48 h

(b) t = 72 h






Appendix A



partu


1

ρ0

partpprime


part

partzνpartu

partz

partv

partt+div uv+ lu+

1

ρ0

partpprime


part

partzνpartv

partz

partpprime


partT prime

partt+div uT prime


partzνTpartT prime

partz+partνT γT

partz

minus1

cρ0

partI

partzminuspartT

partt

partSprime

partt+div uSprime


partzνSpartSprime

partz+partνSγS

partzminuspartS

partt

ρprime=αT T

prime+αSS

prime γT =partT

partzγS =

partS

partz


p= p(zt)+pprime


partxmicropart

partx+part

partymicropart


minusαz



12t

η= 1minus(a+ bn)n






Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References































Appendix B



micro=1x middot1y

radic2

(partu

partx

)2

+

(partu

party+partv

partx

)2

+2

(partv

party

)2

microT =micro

cTmicroS =

microS

cS



νT S = (005h)2

radic(partu

partz

)2

+

(partv

partz

)2

minusg

ρ0

partρ

partz


(005zm)2

radic(partu

partz

)2

+

(partv

partz

)2g

ρ0

partρ

partzleν0



ν=







References










































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Ocean Science Operational forecast of hydrophysical fields in the