Form Approved REPORT DOCUMENTATION PAGE OMB No. 074-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Proiect (0704-0188), Washington, DC 20503 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 11996 Pro ress Re ort Jul 1996 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Study of the Spatial Structure of Arctic Ocean Variability Subcontract No. 4500033242 6. AUTHOR(S) N.G. Yakovlev, A.S. Sarkisyan, & S.V. Pisarev 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Marine Science International Corporation MSIC Report No. 3/96 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING / MONITORING AGENCY REPORT NUMBER SERDP 901 North Stuart St. Suite 303 N/A Arlington, VA 22203 11. SUPPLEMENTARY NOTES This work was supported in part by SERDP under Subcontract No. 4500033242. The United States Government has a royalty-free license throughout the world in all copyrightable material contained herein. All other rights are reserved by the copyright owner. 12a. DISTRIBUTION /AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release: distribution is unlimited A 13. ABSTRACT (MaxImum 200 Words) There were three directions to this study-theoretical modeling, collection and systemization of experimental data, and analysis of long-term variations in the Arctic Basin. The work with the experimental data included: 1. The creation of a new version of the Arctic basin Data Base. 2. The collection & preliminary analysis of the archive data on the water exchange through the Fram Strait... 3. A comparison of the heat content variability in the Atlantic layer in different oceanographic regions.... 4. A comparison of salinity variations in the upper ocean layers in these regions. 14. SUBJECT TERMS 15. NUMBER OF PAGES SERDP, Long-term variations, Arctic Basin 23 16. PRICE CODE N/A 17. SECURITY CLASSIFICATION 18. SECURITY 19. SECURITY CLASSIFICATION 20. LIMITATION OF OF REPORT CLASSIFICATION OF ABSTRACT ABSTRACT unclass. OF THIS PAGE unclass. UL unclass. NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-1 8 298-102 'I9114 ~UA17 )~ I PETB ~ 127-1996 MARINE SCIENCE INTERNATIONAL CORPORATION STUDY OF THE SPATIAL STRUCTURE OF ARCTIC OCEAN VARIABILITY PROGRESS REPORT Subcontract NO. 4500033242 N.G. Yakovlev A.S.Sarkisyan (Section 1) S.V.Pisarev (Section II) MSIC Report No. 3/96 1996 STUDY OF THE SPATIAL STRUCTURE OF ARCTIC OCEAN VARIABILITY PROGRESS REPORT N.G. Yakovlev A.S. Sarkisyan (Section I) S.V. Pisarev (Section II) ABSTRACT There were three directions to this study- theoretical modeling, collection and systematization of experimental data, and analysis of long-term variations in the Arctic Basin. The work with the experimental data included: I. The creation of a new version of the Arctic Basin Data Base by combining the WOA-94, MOODS, and the historical Russian data. The data base will be used for studying the evolution of large-scale thermohaline anomalies, as well as further development of the theoretical model. 2. The collection and preliminary analysis of the archive data on the water exchange through Fram Strait and the runoff of the Siberian rivers as important factors influencing the oceanographic and ice conditions in the Arctic Ocean. (These data will be used later for modeling of the Arctic Ocean response to external impacts). 3. A comparison of the heat content variability in the Atlantic layer in different oceanographic regions outlined in the report "Climatic variability of the Arctic ocean" (Final report, MSIC, 1996). 4. A comparison of salinity variations in the upper ocean layers in these regions. The aim of the theoretical work was to improve the numerical scheme for modeling the Atlantic water inflow into the Arctic Basin, and was performed by N.G. Iakovlev. The results of the modeling are described in Section I of the Report. A description of the new version of the Arctic Basin Data Base is presented in Section II. TABLE OF CONTENTS page I. NUMERICAL MODELING OF THE ARCTIC OCEAN RESPONSE TO 4 EXTERNAL FORCING 1.1. The development of the new numerical scheme 4 1.1.1. Rationale 4 1.1.2. New formulation of the general circulation model 4 1.1.3. The new time scheme 8 1.1.4. Results and problems 9 1.2. Comments on the choice of turbulent mixing/diffusion coefficients 17 II. THE CURRENT VERSION OF THE ARCTIC BASIN OCEANOGRAPHIC 18 DATA BASE 2.1. Introduction 18 2.2. The new version of CTD data in the Arctic part of the WOA-94 18 2.3. The preliminary results of merging the Arctic Master Oceanographic 20 Observation Data Set and the World Ocean Atlas -1994 2.4. The current composition of the Arctic Basin Data Base 21 REFERENCES 23 2 LIST OF FIGURES page Fig. 1.1. Flow velocity at 250m for the nonslip boundary condition 10 Fig. 1.2. Flow velocity at 250m for the slip condition 11 Fig. 1.3. Flow velocity at the 25m depth 13 Fig. 1.4. Flow velocity at the 500m depth 14 Fig. 1.5. Test for the velocity oscillation at the side boundary 15 Fig. 1.6. Flow velocity averaged over four grid points 16 LIST OF TABLES page Table 1.1. The coefficients of horizontal mixing in different models 17 Table 2.1. The distribution of the profiles of the CD-ROM 19 "Replacement CTD data - 96" and the WOA-94 Table 2.2. The distribution of the profiles from the MOODS and the WOA-94 20 Table 2.3. Miscellaneous information about the current Arctic Basin Data Base 21-23 3 I. ON NUMERICAL MODELING OF THE ARCTIC OCEAN RESPONSE TO EXTERNAL FORCING 1. 1. The development of the new numerical scheme 1.1.1. Rationale One of the prominent features of the water circulation in the Arctic Ocean is the existence of narrow coastal jets, one of which is the West Spitsbergen current supplying the Arctic with warm Atlantic water. In the previous version of our general ocean circulation model, this current was almost absent because of comparatively low spatial resolution and nonslip boundary conditions for the velocity components at the side boundary, and at the bottom. The width of the Fram Strait is about 400 km, i.e. - four grid steps. To allow for the Atlantic water inflow we had to specify a model of the bottom bathymetry deeper than that in reality, thus making it necessary for us to develop a new numerical scheme. The first, direct, way to improve the simulation of the coastal jets is to refine both the horizontal and vertical spatial discretization. This demands no changes in computer programming and, at first glance, may seem very attractive. However, even when we choose a grid size three times smaller, it barely allows us to get results on the circulation sensitivity in reasonable "real" time. Moreover, the nonslip boundary condition for the velocity is acceptable only when the grid size is much less than the internal Rossby radii - for the Arctic, it is about 10 km, i.e., 10 times less than the grid size used in the model. The second way is to design a special coordinate system refining the areas of interest. The simplest versions of this approach have been proposed by S. Hakkinen (USA) and by G. Semjonov (AARI, Russia). The approach is fine, but, unfortunately, the area considered changes in time. We decided to change the boundary conditions and assume conditions with free slip at the side boundary and quadratic friction at the bottom. This approach does not contradict the first and second approaches, but may even complement them. if necessary. 1.1.2. New formulation of the general circulation model The basic features of the new model are the same as in the previous version, but the boundary conditions for the horizontal components of the velocity are different. Let us consider the system of equations of large-scale ocean dynamics under commonly used assumptions in a 3D area ! bounded by plane z = 0 and sufficiently smooth bottom topography z=H(x, y). To simplify the presentation, we use the Cartesian coordinate system (x, y, z). S+ Lu - v = - + Du Tt P ax 0 V+ Lv+lu= - -P+Dv at PO aY "T = Pg 4 au (cid:127)+ av + aw =o0 (1) aJx , ay az -a+T LT =DTT at S +.LS = DS at p = p(T, S) Here u, v, w are the components of the velocity u along the axes x, y, z respectively, P is the pressure, T, S are the temperature and the salinity, p is the density anomaly compared with the constant Po, 1 is the Coriolis parameter, g is the gravity acceleration, and t is time. L, D, DT, Ds are the operators of advection, turbulent mixing of momentum, and turbulent diffusion of heat and salt, respectively. We specify the advection as L4= UO + .v + WO, X y oz and turbulent mixing and diffusion as a a+++ a a + , ag az az ax ax ay ay Let the boundary consist of two parts: F = Fo U [,i, where F. is a "liquid" boundary (passages and rivers). As for the first part of the boundary, let Fo = F., U 0, where no is an intersection of U with the plane z = 0, and Fs is a "solid" boundary representing the land. Let the boundary conditions for momentum be as follows: vp0 au- T , vpo a- = T()on 1-0, un =0 on , ons (2) w= at on 90, U= U b , V =V b onE . 1 For temperature and salinity we specify the following boundary conditions: aT as N- =QT, QS on 7 , 0 T = Tb, S = Sb on I',. Here (x, y, t) = P(x, yO, t) is the sea surface elevation, n is the outer normal vector, u, is Pog the velocity component along the vector n, ) g a) is the conormal derivative corresponding to the momentum turbulent mixing. Derivatives 5NT - and are specified in the same way. Functions T(x),'(Y) , ub , vb, Tb, Sb, QT, and QS aNs are assumed to be known. The initial conditions at t =0 are as follows: u=u() ,v=v(0), T=T(0), S=S(0) and,=ý(0). Note 1. In general, the linearized kinematic condition w = -L on z = 0 is valid for <«< H. This condition is not satisfied in the vicinity of F, nflo. However, in a discrete model, after applying the finite element technique, we find mn H(x, y)-- 1Oi , while the scale of level variationsi s about im. To develop a finite element scheme we pose a projection form of the problem (1)-(2), where functions 2tJ,7t2,7CT,[S E W2 (n ) are equal to zero on F, ,and functions nr , nt , 7rp E W1( a): 3 4 (- 7c,)-B(u, tn)-(lv,n,) =--(- -xr,T )-[u,7rt]+f , 1 at' Po ax (-atv(cid:127)7 2 )- B(vtn.) +(IME2) =--_I_ aopT(, n 2) -tvn]+ fl I (-a-z,' It3) = (pg,7 t3) - (w,--)=f3 ax ay az aT (Tt ,17T)-B(T,UnT)=-[T,n] IT +fT aast I,,) - B(s, u,,7s)= -IS,nslIs +: ,, (Ptp)= (p(T,S),itp) The following denotations are used here: (a,b) =f abdK2 , (a b oy + aw B(aukb)= auTx +av-ab+ aw-b)M r( )aa b Daa b aa ab [a,b]=J T -Mi- ~ v- d aax ayay azaz} and [a,b], is specified in similar way. The right-hand sides fl, f2, f3, fr, andfs are generated by boundary conditions. As in the previous version of the model, we choose right triangular prisms to be the finite elements. Let the bases of the prisms lie on the planes z = zk, k = 1,..., K0, and the vertexes of the prisms belong to the set of points Pi(x,y),i = 1 M...,MLe. t each index 5. correspond to the 6 integer number KL(i) < K , hence ZKL(i) will be treated as a depth at point P(i). On the finite 0 elements, we specify the basis functions Iti,k =(Pi(x,y)Yk(z) , where (pi(x,y) are 2D finite linear piecewise functions defined on triangular finite elements and Wk (z) are ID finite linear piecewise functions, so called "the roofs" (Marchuk and Agoshkov, 1981; Zienkiewicz, 1977). The approximate solution is represented by sums of the form Dh = XIDi,k7ti,k . Probe functions i,k 7ti, i=1,...,4, 7ET, 7tS, 7tp are also chosen among ;i,k. The vector of coefficients (Di,k will be denoted by "= ((D], I .... (cid:127)IP ,KL( I) ,cY2,1 ..... ¢D2,KL( 2).... DpM ,KL( M) )TT. = It is obvious, that ýh is approximated by the sum of pi (x, y) . We constantly apply the so called "lumping-method" to derive the system of ordinary differential equations for vectors U,V,w,P,T,S,-T,'Z. Instead of Gram matrix G for functions nri,k we use the diagonal matrix M with the elements (M)(i,k),(I,m) = 8(i,k),(!,m) fI ti,kdQ' 0h where 8(i,k),(1,m) = 1, ifi= (cid:127) and k = m L0, ifi (cid:144)1or k (cid:144)m The Gram matrix G, for functions 7ti,k in a space with the scalar product weighted by 1i is substituted for the diagonal matrix C with the elements (C)(i,k),(!,m) = 8(i,k),(1,m)li fItci,kdgi2h ah The gradient approximation is defined by the formulae: M f (Vh-)ik = (hPlk j-)1)i kdab I (VyT)i,k = (XPl,k L)Tci,kd(cid:127)h J KL(i) (Vhzp)i'k = (X Pl~k- )7ri,kd2(cid:127)' d~~M ah f m=1 -~ The trilinear form B-- uis~ !h a'p proxima5te)id`d kahcfc-o( rdinYgP lt oU t'hk~e form)u(nlai~:k(P) o lldg Oh ah m=l lD and the two rest terms are approximated in a similar way. The matrix approximation of B will be denoted as A. Applying the lumping method for the turbulent mixing/diffusion operators, we obtain the matrices D, DT and Ds derived with the use of the approximate equality 7 f J.L -N~kdUŽ f ji(Y,1, k ) 41 ah xh 1= x ax (and the same for the last terms). The coefficients of turbulent mixing/diffusion are assumed to be constant over a finite element. As a result we have the following system of ordinary differential equations: M du- + AW - CV _.LI vhx 1 + DIT +fi dt PO M-dv-+AV+C =- IVhP+O5D +2, dt PO +2 Vh P=gM" -(Vhx)T(cid:127)-(Vhy)T7-(vh)TIW=j(cid:127) (3) MdT +AT=DTT+fT, dt MdS-+AS =DsS + fs dt T = (cid:127)TS 1.1.3. The new time scheme In the previously used version of the model, there was a time step limit stipulated by the Coriolis term approximation in time, and there was the explicit "leap-frog" scheme for the Coriolis force. According to the CFL criterion, one can conclude that the time step should not be greater than 1.9 hours. This limitation may turn out to be too severe, therefore the next step necessary to enhance the efficiency of the model is to change the Coriolis term time approximation. We used the Crank-Nicholson time approximation, so that CY = I!c(wj+l +Wi-s). 2 The new scheme leads to some additional difficulties which arise because the matrix for sea level was nonsymmetric, and the conjugate gradients method, used before, is no longer valid. The nonsymmetricity is due to the method of deriving the matrix. To obtain the system of equations for ýj+l, we substitute .jj+I, Vj+I in the discrete integral continuity equation: j+Il I) h f (pidfJ h+ At ~ h h + f ((u h )j+! D(P--i +(vhlS+l a_¢Pi)dj~h = Fi , i = I,.... M ah ax ay 8