ATLANTIDA3.1_2014 FOR WINDOWS: A SOFTWARE FOR TIDAL
Contents
1. However this discrepancy is small since all the seven analyzed stations are located in the middle latitudes where the values predicted by our model for ASP and DDW NH barely differ Fig 6 In order to compare the results derived for these two models we carried out detailed additional processing of the gravimetric data obtained at the Syowa Antarctic station operated by Japan Kim et al 2011 These data are mainly interesting by the fact that they are acquired at very high latitude 69 007 S At the same time this station is marked with rather wide scatter of the amplitudes and phases of the oceanic tidal models Nevertheless it was shown that irrespective of the oceanic tidal model used almost in 70 cases for 14 oceanic models and 12078 12079 eight waves the application of the theoretical delta factors of DDW NH model for calculating the oceanic effect observed at the Syowa station leads to poorer results in comparison with the application of the modeled amplitude factors used in the ATLANTIDA3 1_2014 program 1 1627 1 1622 pm a as ka 1 1617 m am o 1 1612 1 1607 1 1602 O O oO O O O O O oO O oO 0 Ta uw wT m N PREM AS5Pf91 cesses DOW_H DDW _NH Fig 6 Latitude dependence of M2 amplitude delta factor calculated Spiridonov 2014 for Earth s structure models PREM and IASP91 in comparison with DDW H and DDW NH models of Dehant et2. Spiridonov 2013b 3 2 The delta factors for the oceanless Earth We compared the amplitude factors for oceanless Earth obtained in Spiridonov 2014 and applied in ATLANTIDA3 1_2014 with the observations using the results presented in Ducarme B et al 2009 In the quoted study the authors analyzed the measurements by seven modern instruments of the GGP network in Europe the CT and CD series The effect of the ocean was considered as the average over nine oceanic models The results are presented for the M2 O1 and K1 waves In more than half cases the empirical values differed from the model predictions by about 0 01 for PREM and by about 0 1 in the other cases In this respect it is worth noting that the standard deviation of the amplitudes for nine oceanic models used in Ducarme B et al 2009 mainly corresponded to the error of 0 1 Nevertheless the slightly closer agreement between the observations and model predictions in our calculations was obtained for the JASP9 model The discrepancies between the theory and observations in most cases do not exceed a few hundredths percent Spiridonov 2014 Tables 3 and 4 It was also found that the standard deviation of the differences between the delta factors estimated with the use of the model of Spiridonov 2014 and the observations at all the seven stations and for the three waves is almost 8 4 lower than the estimation based on the DDW NH model 8 794 107 against 9 600 1074
3. 12819 0 00000 0 00000 0 00000 4 57114 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 75464 0 00000 0 00000 0 00000 0 74981 0 00000 4 46744 0 69984 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 TAU1 TO 01 OR RO1 RQ Q1 QSIG SIG1 2Q1 MSQM MTM MSTM MF MSF MM MSM SSA SA 186 MOSO 0 932583 0 929684 0 928932 0 898264 0 896129 0 893407 0 892934 0 866977 0 859381 0 721500 0 132715 0 106756 0 075321 0 070317 0 062103 0 033716 0 028844 0 004710 0 002428 0 000141 0 000000 0 940016 0 932582 0 929683 0 928931 0 898263 0 896128 0 893406 0 892933 0 866976 0 859380 0 249951 0 130596 0 106446 0 073806 0 070155 0 060132 0 033701 0 028697 0 003425 0 000913 0 000140 463 481 450 461 439 449 412 438 406 410 394 405 387 392 369 386 352 368 283 349 206 281 174 204 140 171 118 139 92 117 53 91 40 52 21 39 11 18 3 9 1 2 3 95233 1 95353 303 02724 1 04220 11 02046 0 54121 58 01826 0 55459 9 26549 7 67667 0 33202 2 07906 0 39489 10 85895 0 95163 5 73751 1 09728 5 05292 0 80223 4 55421 51 30260 0 93501 0 93015 0 92954 0 92680 0 89810 0 89598 0 89324 0 89279 0 86181 0 85695 0 14093 0 10949 0 10464 0 07320 0 06773 0 03629 0 03143 0 00548 0 00274 0 00015 0 00000 1 15405 1 15406 1 14443 1 15408 1 15408 1 15408 1 16337 1 15404 1
4. Spiridonov E Vinogradova O 2013 Gravimetric oceanic loading effect Lambert Acad Publishing 2013 in Russian Spiridonov Evgeny 2013 Oceanic Loading Effect for Gravity Prospecting SPE Arctic and Extreme Environments Technical Conference and Exhibition 15 17 October Moscow Russia 2013 Society of Petroleum Engineers DOI http dx doi org 10 2118 166838 RU ISBN 978 1 61399 284 5 V 1 pp 380 412 Spiridonov E A and Vinogradova O Yu 2014 Comparison of the Model Oceanic Gravimetrical Effect with the Observations Izvestiya Physics of the Solid Earth 2014 Vol 50 No 1 pp 118 126 Spiridonov E A 2014 Tidal Amplitude Delta Factors and Their Dependence on Latitude Geophysical Research Abstracts Vol 16 EGU2014 1296 2014 Spiridonov E A Afanasyeva L V 2014 The Program for the Oceanic Gravimetric Effect Computation ATLANTIDA 3 0 Proceedings IAG Symposium on Terrestrial Gravimetry Static and Mobile Measurements Saint Petersburg Russia 2013 Van Camp M and Vanterin P 2005 T soft graphical and interactive software for the analysis of the time series and Earth tides Computers and Geosciences 31 631 640 Vinogradova O Yu Spiridonov E A 2012 Comparative Analysis of Oceanic Corrections to Gravity Calculated from the PREM and IASP91 Models Izvestiya Physics of the Solid Earth 2012 Vol 48 No 2 pp 162 170 Vinogradova O Yu 2012 Oceanic tidal loads near the European coast calculate
5. WHR OO WO WN DU BR WN FH OO ETA2 KSI2 K2 R2 S2 T2 TL2 L2 LM2 M2 MNI NI2 NIN N2 NMI MI2 MIN 2N2 NEP EPS2 3N2 222 V1 OV 001 OJ J1 THE1 FI1 PSI1 K1 KS S1 P1 PI1 PIC CH1 CHM M1 MTU MAIN WAVE theoretical parameters Delta factors and phase lags for the Earth with ocean lt From To Cycle Day 2 935321 3 937897 2 53244 2 935174 2 039339 2 182843 2 005623 2 039177 2 003032 2 005622 2 000619 2 003031 1 998287 2 000456 1 997115 1 997493 1 968876 1 997114 1 968271 1 968875 1 932421 1 968270 1 931817 1 932420 1 901459 1 931816 1 900545 1 901458 1 896602 1 900544 1 895363 1 896601 1 865167 1 895362 1 864253 1 865166 1 861663 1 864252 1 859071 1 861662 1 830685 1 859070 1 827342 1 830684 1 822633 1 826136 1 719381 1 822486 1 111613 1 216397 1 080797 1 109950 1 073202 1 078825 1 039193 1 073201 1 036910 1 039192 1 010333 1 036748 1 007904 1 008655 1 003651 1 007903 1 002575 1 003650 1 001826 1 002574 0 997734 1 001825 0 995143 0 997733 0 989049 0 995142 0 971598 0 989048 0 970994 0 971597 0 968566 0 970993 0 963399 0 968565 0 940017 0 963398 Numbers 1168 1200 1110 1166 1035 1107 1007 1034 996 1004 991 995 984 988 980 982 956 979 950 955 904 949 895 901 871 894 865 870 855 863 843 854 818 842 813 816 804 812 795 802 779 794 771 777 763 769 733 761 686 731 663 683 644 662 613 643 606 612 584 604 576 581 569 575 557 568 553
6. al 1999 CONCLUSIONS We have considered the main characteristics and possibilities of ATLANTIDA_3 1_2014 the new program for tidal prediction and described the internal structure of the methods that were applied for its design We briefly described the comparison of the output of ATLANTIDA_3 1_2014 program with the observations Of course the further testing will significantly expand the comparative analysis 12079 12080 Even in the next version ATLANTIDA_3 1_2015 whose release is expected in the fall 2015 it is planned to increase the number of the oceanic models and to include the program for calculating the observed delta factors and phase shifts After this we will take into account the latitudinal variations of delta factors for the waves of the zero third and fourth order and expand the program package by the calculations of the potential deformations and displacements we will also update the computations of the tilts the present version of our program only calculates the tilts for the oceanic effect The comments on the operation of the program and the suggestions for the further improvements are greatly appreciated REFERENCES Agnew D C SPOTL Some programs for ocean tide loading SIO Ref Ser 98 8 35 pp Scripps Inst of Oceanogr La Jolla Calif 1996 Agnew D C NLOADF A program for computing ocean tide loading J Geophys Res 102 5109 5110 1997 Dehant V Defraigne P Wahr J
7. briefly discuss some numerical results that we obtained when developing and testing our program These results are provided by the different variants of calculations of the oceanic gravimetric effect and amplitude delta factors for the oceanless Earth 3 1 Oceanic Effect in Europe 3 1 1 Earth models PREM and IASP The differences in the amplitudes of ocean loading effect calculated for the PREM and IASP91 models in Europe reach 0 1 ugal M2 wave near the Moroccan coast and increase to 0 3 ugal at the western coasts of Portugal and France Vinogradova Spiridonov 2012 Here the maximum discrepancies in phases do not exceed 0 1 However near the tip of Cape Cornwall and close to the Irish seaboard in the region of Le Havre and Calais the differences in the amplitudes and phases reach 0 35 0 4 ugal and 3 5 respectively The maximum differences in amplitude for sums of semidiurnal and all semidiurnal and diurnal waves were observed near Cape Lands End Cornwall and reach to 0 5 0 55 ugal In Britany these values reach to 0 35 ugal and up to 0 2 ugal near southern coasts of Europe and Morocco The difference for the sum of diurnal waves is negligible and it do not exceeds as rule 0 01 ugal 3 1 2 Dissipation Dissipation induces variations in the amplitude of M2 wave which do not typically exceed 0 1 ugal in the immediate proximity of the coastline Vinogradova 2012 Vinogradova Spiridonov 2013a Somewhat higher values up
8. calculations can be conducted in two models of the Earth s structure PREM Dzeiwonski A M amp Anderson D L 1981 and a later IASP91 model Kennett B L N Engdahl E R 1991 Although some authors in their calculations use in fact several Earth s models e g besides PREM the 1066A model which is obsolete or modified versions of PREM this approach has not yet become common and still less is it popular when designing the programs for tidal computations In each and every program calculating the oceanic loading effect this effect 1s determined by the convolution of the tidal height with the Green s functions In these calculations it is common to separate the near zone 2 5 degrees within which the data are subjected to the procedure of interpolation Thus the high spatial frequencies of tidal height are taken from the near zone whereas the data falling beyond this area are coarsely described by the values at the grid nodes of the oceanic model In our opinion this approach is not quite reasonable because first the high frequency components affect the entire Earth and therefore they should be calculated over the entire surface Second instead of the near zone it is the far zone that provides the largest contribution to the modeled oceanic gravimetric effect and the calculations for the far zone are less accurate Therefore when designing our program we implemented a different approach which is based on the spherical harmonic
9. of the following seven messages appears if the latitude specified for a site or for a grid node falls beyond the interval from 90 to 90 degrees or if the longitude is lower than 180 degrees or higher than 180 degrees or if the value of the lower latitude longitude in the grid calculations is greater than or equal to the larger latitude LatFin is not valid 90 90 LATITUDE is not valid 90 90 LATITUDE LatStart gt LatFin LONGITUDE is not valid 180 180 LONGITUDE LongStart gt LongFin LongFin is not valid 180 180 for GRID LongStart is not valid 180 180 for GRID MONTH is not valid 1 12 The number of the month specified in the initial date in the calculations of the time series should range from to 12 NO sp exe The program warns that the installation package lacks the sp exe program which checks the completeness of the whole package This check is executed every time the ATLANTIDA3 1 program is run NO subject computing OCEAN LOAD or ROWS must be YES The both OCEAN_LOAD and ROWS options are set to NO NO WAVES This is the most frequent message warning that the waves for calculating the oceanic effect in the selected tidal model are not specified To specify the waves click on the WAVES button select the desired waves in the popup menu and press SAVE This message often appears if the user had selected the waves but changed some other settings afterwards Option ROWS for TILT does not work in this versio
10. uF aC 0 0000 ETAZ LUSS 1Li07 L16154 0 0000 KSI2 1007 1034 1 16154 0 0000 K2 996 1004 Le dort OS a ae a al S R2 991 995 1 13647 6 7515 S2 964 9868 1 14409 6 6810 a Program Terminated with exit code SS Exit Window ae Fig 5 The popup window of program termination If the program was successfully terminated with exit code 55 press YES Otherwise exit code 0 press NO and reinstall the whole program package or contact the author of the program Program termination with exit code 55 informs the user that failures were absent at all the steps of the calculations 12070 12071 2 4 Program messages The program issues more than thirty different messages overall Below we present short comments on each message The messages are listed in the alphabetical order By checking the messages the user can also obtain the information on some limitations assumed in a given version of the program 0 lt N_DAYS lt 9800 The number of the days used for constructing the tidal series should be at most 9800 26 8 years Access violation in CC3260MT DLL This system message appears if the program is installed in other than a root directory ALTITUDE is not valid The height of the observation site specified for the program should range within 9000 to 9000 m DAY is not valid The day of the month starting from which the user would like to calculate the tidal time series should be specified in the range from to 31 FILE FILE_NAME
11. 0 to 9999 You can calculate only one wave for GRID The calculations of the amplitudes and phases of the oceanic effect at the grid nodes are only possible for a single wave of the selected tidal oceanic model This message appears if the user specifies many waves 2 5 The Results Files The files of the results are located in ATLANTIDA31 RESULTS For the example shown in the Fig 2 the program displays the following three files in the RESULTS directory LISBON_FES12_IASP_L_DY_MN_LAT_DEP_YES_GRAV dat LISBON_FES12_IASP_L_DY_MN_LAT_DEP_YES_GRAV prn LISBON_FES12_IASP_L_DY_MN_LAT_DEP_YES_GRAV grw The first file DAT contains the tidal time series the second file PRN contains the constants used in the calculations the amplitude delta factors and phase shifts for the Earth without and with the ocean for the groups of the waves The amplitude factors and phase shifts for the Earth with ocean are only calculated for the waves for which the oceanic effect is calculated These waves can easily be distinguished in the list of the waves by the non zero phase shifts Table 1 The third file GRW contains the amplitudes and phases of the gravity oceanic effect the Newtonian attraction of water masses the loading effect and their sum In the TILT mode the NS and EW components are provided 12073 Table 1 O CON DU BP UU N be B B BP WWW wWwWwwwWwWWN NY NN NNN NNN RP RP RP BR RP RP RB perhe He Ne OW WAN DU BRP WNH PO WO WN DU BP
12. 1 and SPOTL programs Agnew 1996 1997 The detailed intercomparison of these programs and the analysis of their performance against the ATLANTIDA3 1 _2014 program fall beyond the scope of the present work However we briefly outline the main features of our program which distinguish it from the previous programs First for calculating the Love numbers and delta factors of the body tides we applied the latitudinal dependences of these parameters obtained in Spiridonov E A 2014 These dependences differ from those calculated by Dehant V et al 1999 for the DDW NH model Our curves have a somewhat steeper latitudinal gradient which 1s particularly important in the prediction of tidal data at high latitudes see Fig 6 The latitudinal dependence used in our work does not depend on the form of the tidal or loading potential Besides we also calculated the 12062 12063 latitudinal variations of the loading Love numbers and delta factors This is the first distinction of our program from the other programs The calculations of the loading Love numbers take into account dissipation of tidal energy in the mantle according to the logarithmic creep function Dissipation is allowed for by some but not all programs For instance LOAD97 does not consider this dependence despite the fact that nothing prevents this program from specifying the loading Green s functions calculated with the allowance for the dissipation In ATLANTIDAS 1_2014
13. 12062 ATLANTIDAS3 1_2014 FOR WINDOWS A SOFTWARE FOR TIDAL PREDICTION E Spiridonov O Vinogradova E Boyarskiy and L Afanasyeva Schmidt Institute of Physics of the Earth Russian Academy of Sciences ul B Gruzinskaya 10 Moscow 123995 Russia e mail sp287 mail ru In this paper we describe the possibilities of the ATLANTIDA3 1_2014 software which was recently developed for predicting tidal parameters on the Earth These possibilities include the calculation of the gravimetric oceanic effect the amplitude delta factors for oceanless Earth as well as the modeled amplitude factors and phase shifts for the Earth with ocean The program also calculates the tidal series We present the highlights of the program and discuss the underlying theoretical and methodical ideas The detailed installation guidelines and user manual are presented The results of the calculations are compared with the observations INTRODUCTION At present there are about ten programs for calculating the prognostic delta factors and phase shifts of the tides as well as oceanic gravimetric effect Among the first group of the software the most popular are the PREDICT program of the ETERNA package developed by Wenzel Wenzel G 1996 7 soft Van Camp amp Vanterin 2005 and MTSOw programs CET The calculations of the oceanic effect are conducted by the LOAD97 ETERNA 3 3 Francis O and Mazzega P 1990 GOTIC2 Matsumoto et al 2001 OLFG Scherneck 199
14. 15399 1 15397 1 34442 1 15753 1 15754 1 15767 1 15770 1 15794 1 15800 1 15884 1 15924 1 16144 1 00000 12075 0 00000 0 00000 0 62527 0 00000 0 00000 0 00000 1 39957 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 The names of these files only differ by their extensions The filename consists of the following parts LISBON site name In the GRID mode instead of the site name this part of the filename is composed of the wave name and a flag that is indicative of the GRID mode for example M2_GR_ FESI2 oceanic model FES2012 L local phase G Greenwich DY dissipation YES or DN dissipation NO MN mass correction NO or MY mass correction YES LAT_DEP_YES dependence from latitude YES or LAT_DEP_ NO GRAV gravimetric effect or TILT If only the oceanic effect is calculated ROWS NO a single file with GRW extension is yielded The content of the Results file for the parameters shown in Figure 1 can be found in the ATLANTIDAS31 EXAMPLE directory The theoretical and practical results that were used when designing the program are described in some ours papers All these publications are available in the ATLANTIDAS1 PAPERS directory 12075 12076 3 SOME NUMERICAL ESTIMATES OBTAINED DURING THE DEVELOPMENT OF THE ATLANTIDA3 1_2014 PROGRAM In this section we
15. 556 546 552 537 544 532 536 525 530 521 523 515 519 494 512 482 492 12074 AMPL nm s 2 0 91451 7 01912 3 23297 1 87187 57 82324 1 77965 212 74914 12 43269 3 23189 12 92498 3 37194 457 27659 1 57185 16 62923 0 81804 87 55012 0 94334 13 98132 0 35759 11 58524 0 65254 3 37798 1 30356 0 55939 2 49611 0 62659 13 03706 3 95301 23 83138 4 55719 6 06752 3 33251 426 17775 0 23882 3 33228 140 99789 8 24189 0 19465 4 55788 0 14720 23 83207 2 23608 FREQUENCY Cycle Day 2 97161 2 89841 2 04177 2 00577 2 00548 2 00274 2 00000 1 99726 1 96918 1 96857 1 96371 1 93227 1 92954 1 90084 1 89872 1 89598 1 86729 1 86455 1 86424 1 85969 1 83311 1 82826 1 82340 1 79196 1 11223 1 10676 1 07594 1 07046 1 03903 1 03417 1 00821 1 00548 1 00274 1 00243 1 00000 0 99726 0 99452 0 97404 0 97130 0 96918 0 96645 0 96097 Amplitude Factor 1 03900 1 07338 1 16154 1 16154 1 13705 1 13647 1 14409 1 11181 1 16154 1 10354 1 16154 1 06495 1 16154 1 16154 1 16154 1 00349 1 16154 1 16154 1 16154 0 94940 1 16154 1 16154 1 16154 1 16000 1 15605 1 15605 1 15610 1 15631 1 15894 1 15685 1 17011 1 26954 1 12803 1 13841 1 08476 1 14204 1 15054 1 15272 1 15351 1 15360 1 15366 1 15376 12074 Phase Lag Deg 0 00000 0 00000 0 00000 0 00000 6 77168 6 75150 6 68103 6 44535 0 00000 6 82502 0 00000 7 96007 0 00000 0 00000 0 00000 7
16. M Tides for a convective Earth J Geophys Res 1999 104 1035 1058 Ducarme B Rosat S Vandercoilden L Xu J Q Sun H P European Tidal Gravity Observations Comparison with Earth Tide Models and Estimation of the Free Core Nutation FCN Parameters M G Sideris ed Observing our Changing Earth International Association of Geodesy Symposia 133 Springer Verlag Berlin Heidelberg 2009 pp 523 531 Dzeiwonski A M Anderson D L 1981 Preliminary Reference Earth Model Phys Earth planet Inter 25 297 356 Francis O Mazzega P Global charts of ocean tide loading effects J geophys Res 1990 95 11411 11424 Kennett B L N Engdahl E R 1991 Traveltimes for global earthquake location and phase identification Geophys J Int 1991 105 429 465 Kim Tae Hee et al Validation of global ocean tide models using the superconducting gravimeter data at Syowa Station Antarctica and in situ tide gauge and bottom pressure observations Elsevier Polar Science 5 2011 21 39 Matsumoto K T Sato T Taanezawa and M Ooe GOTIC2 A program for computation of oceanic tidal loading effect J Geod Soc Jpn 2001 47 243 248 2001 Molodenskiy S M Tides nutation and Earth s structure AN SSSR IPE Moscow 1984 219D 12080 12081 Scherneck H G A parameterized Earth tide observation model and ocean tide loading effects for precise geodetic measurements Geophys J Int 106 677 695 1991
17. already exist Replace it Y or N This message may only appear in the case of repeated computations for the same site if the calculation is fully identical to the previous one or if a different set of the waves is selected for this oceanic model By pressing Y and Enter you can rewrite the new file over the old one replace the old file by the new one If you press No and Enter the program terminates The file can be copied from the RESULTS directory to any other directory The following three messages are concerned with specifying the frequency band in the calculations of the tidal time series They appear if the lower specified frequency is higher than the higher frequency or if the specified frequencies are negative Frequency2 must be greater then frequencyl Frequency is not valid Frequency2 is not valid GREENWICH PHASE does not work with ROWS option The option of selecting the Greenwich phase in our program is only available for calculating the amplitudes and phases of the oceanic effect This option does not work with the mode of constructing the tidal series ROWS Latitude for this model must be gt 78 deg This message only concerns the CSR3 0 and Schwiderski tidal oceanic models Latitude for this model must be gt 85 deg This message only concerns the FES95 tidal oceanic model 12071 12072 Latitude for this model must be from 89 75 to 89 75 deg This message only concerns the NAO99b tidal oceanic model One
18. d from Green s functions Izvestiya Physics of the Solid Earth 2012 Vol 48 No 1 8 pp 572 586 Vinogradova O Yu Spiridonov E A 2013a Comparison of Two Methods for Calculating Tidal Loads Comparison of Two Methods for Calculating Tidal Loads Izvestiya Physics of the Solid Earth 2013 Vol 49 No I pp 83 92 Vinogradova O Yu Spiridonov E A 2013b Some Features of TOPEX POSEIDON Data In 2 Application in Gravimetry Z Altamimi and X Collilieux eds Reference Frames for Applications in Geosciences International Association of Geodesy Symposia 138 DOI 10 1007 978 3 642 32998 2 35 Springer Verlag Berlin Heidelberg 2013 pp 229 235 Wenzel H G The Nanogal Software Earth Tide Data Processing Package Eterna3 30 Bull D Inf Maree Terr 1996 124 9425 9439 12081
19. d section in fact presents the user s manual Finally in the third part we show some results of our calculations and compare the output of our program to the observations 1 MAIN COMPUTATIONAL PROCEDURES The general flow chart of the calculations that are carried out when preparing the initial data for the ATLANTIDA3 1_2014 program and the calculations that are carried out directly by our program are illustrated by Fig 1 The general flow chart of the calculations that are carried by ATLANTIDAS3 1 2014 Numerical integration ofthe boundary value problem describing the loaded state o the elastic gravitati p t a Soe es compressible sphere A r ue hn kn On CSR4 0 FES2014 SCW80 etc ATLANTIDA 3 1 Newtonian direct attraction PROLET Fig 1 The general flow chart of the calculations In the calculations of the oceanic loading effect Love numbers and delta factors of the body tide we applied as was mentioned above two models of the interior structure of the Earth 12064 12065 namely PREM and IASP91 Vinogradova Spiridonov 2012 Spiridonov 2014 The second model for example more adequately describes the structure of the crust and upper mantle of Europe and is more advanced For the both models the velocity curves of the seismic compressional and shear waves were recalculated from the reference period of s to the periods of the tidal waves using the logarithmic creep f
20. decomposition of tidal height after the preliminary interpolation of all the data of the oceanic models with the degree of detail that is not worse than in the near zone in the calculations of the other authors Thus the near zone covers the entire Earth Strictly speaking the approaches that are based on the application of the Green s functions and spherical harmonic decomposition of the tidal height are fully identical from the mathematical standpoint At the same time the attempt to specify the near zone e g in the LOAD97 model with a size of a few tens of degrees infinitely increases the time of the computations and the obtained result tends to our estimates obtained without the allowance for the dissipation In addition our program also provides the possibility of calculating the oceanic effect at the grid nodes However in the case of the calculations at a point the program separately yields the 12063 12064 loading and Newtonian direct attraction components of the oceanic effect as well as their sum By no means all programs provide this option In contrast to almost all the other programs of this kind ATLANTIDA3 1_2014 has a intuitively transparent user friendly interface which enables the user to run the program straightforwardly without referencing to the manual In the first section of this work we discuss the general principles of the program and the physical sense of the corresponding computational procedures The secon
21. ed on the obtained expansions and loading delta factors the program calculates the value of the loading effect direct Newtonian attraction by the mass of water and their sum The amplitudes and phases of the oceanic gravimetric effect as well as the delta factors of the body tide calculated by the program for 63 groups of the waves are inputted to the PROLET program developed by E A Boyarsky and L V Afanasyeva Being the part of the ATLANTIDA3 1_2014 package PROLET calculates the prognostic values of delta factors and phase shifts for the Earth with ocean as well as the tidal series for the time interval of interest The prognostic amplitude delta factors are only calculated for those waves for which the oceanic effect is known The time series are separately calculated for the oceanic and body tide as well as for their sum The computational scheme of PROLET largely follows the PREDICT program from the Wenzel s ETERNA 3 3 package The expansion of tidal potential into 1200 Tamura s waves 1987 is applied The corrections for the conversion from UTC to TDT time are taken from the USNO website http maia usno navy mil ser7 deltat data and decimated in such a way that for the time after 1973 the error of the correction does not exceed 1 s the error of the tidal effect is less than 1 nm s 2 HOW TO WORK WITH THE PROGRAM 2 1 Downloading and installation To download the program please follow the link https yadi sk d hszRKIngcrDSC or h
22. ed the bugs associated with introducing the station height corrections and mass correction in the FES95 and SCW80 models The LOADO7 program has its own HELP only available in Russian in this version of the program 2 3 Running and operation of the program After specifying all the required settings click OK The names of the results files are generated automatically If the OCEAN_LOAD YES option calculation of the oceanic gravimetric effect is selected immediately after the start of the program a popup window will appear Fig 4 This window displays the number of the wave for which the calculations are being conducted and the total number of the waves specified for calculating the oceanic effect 12069 12070 C Windows system32 cmd exe oj B OCEAN EFFECT CALCULATION WAVE 1 from 14 Fig 4 The popup window of calculations of the oceanic effect Immediately upon the completion of the calculations of the oceanic effect ATLANTIDA3 1 passes the control to the PROLET program This only occurs if the ROWS YES option is selected The PROLET program calculates the tidal series as well as the prognostic values of delta factors and phase shifts for those waves for which the oceanic effect has been calculated previously After the termination the program displays the popup window shown in Fig 5 Prot eee l0 xi E Time tidal series calculations Please wait 2015 0505 0000 E M4 11668 1200 1 03900 0 0000 M3 1110 1166
23. n The tidal series of the tilts are not calculated in this version ROWS option latitude must be from 89 to 89 degrees In the calculations of the tidal time series the latitudes should range within 89 and 89 degrees STEP gt NDAYS 24 60 The time step in minutes indicated for the calculations of the time series cannot be longer than the length of the series The following three messages appear if in the calculations of the oceanic effect on the numerical grid the selected step of calculations along the latitude longitude is larger than the entire range of calculations or if it is negative 12072 12073 Step by latitude is too large the step along the latitude exceeds the entire latitudinal range of the calculations Step by longitude is too large Step by latitude or longitude is not valid the specified step is negative TILT GRID is not possible in this version The grid calculations of the amplitude and phase of the oceanic effect for the tilts are not possible in this version of the program The ocean model wave WAVE_NAME is outside the rows frequency band These waves will exclude from the list of the ocean model This is a purely informational message The waves of the oceanic effect that were not included in the frequency band selected for calculating the tidal series are excluded from the further calculations YEAR is not valid The first year of calculations of the tidal series should fall in the interval from 100
24. ogradova Larisa Afanasyeva Fig 2 The ATLANTIDA 3 1_2014 interface 2 2 Selecting the options 2 2 1 General options OCEAN_LOAD YES or NO Calculate or not calculate the oceanic effect ROWS YES or NO Calculate or not calculate the tidal time series LAT_DEP To take or not to take into account the latitudinal dependence of the ordinary and loading delta factors After the desired options are selected this version of the program can be used in either of the two possible modes GRAVITY or TILT For tilt it 1s only possible now to compute ocean tide loading in the NS and EW directions EARTH_MODEL Selecting the Earth model PREM or IASP91 12067 12068 2 2 2 Selecting the parameters of calculations of the oceanic gravimetric effect OCEAN_MODELS Selecting the tidal ocean model YES if OCEAN_LOAD 1s selected The calculations for the selected oceanic model can be conducted with the allowance for dissipation DISSIPATION and mass correction MASCOR The DISSIPATION option only applies to the loading delta factors By default the delta factors of the body tides are calculated with dissipation You can select the phase LOCAL or GREENWICH If the ROWS option is enabled the GRENWICH option is unavailable When calculating the oceanic effect OCEAN_LOAD YES you should also specify the set of the waves for the selected oceanic model For doing this click on the WAVES bottom select the desired waves in the pop
25. on of the oceanic tidal heights up to n 720 have revealed minimal discrepancies in the results at distances exceeding 50 100 km off the coast Vinogradova Spiridonov 2013a The differences in the amplitudes of the effect are on the order of a few tenths of microgal and the phase differences are hundredths and thousandths of a degree In the immediate neighborhood of the coast in the zones of moderate gradients these discrepancies do not typically exceed 0 2 0 3 ugal and a few tenths of a degree respectively In the very narrow zones the amplitude differences may reach 0 5 0 8 ugal and this situation certainly requires further analysis In any case the discrepancies make up at most 2 2 5 of the studied values The expansion of the tidal heights in the higher order spherical harmonics does not change this pattern significantly 3 1 4 The latitudinal dependence of the oceanic gravimetric effect The calculations by the ATLANTIDA3 1_2014 program have shown that the latitudinal dependence of the loading Love numbers only slightly affects the calculated oceanic loading effect Significant contribution was only revealed for the islands in the open ocean and for the zones with high gradient of the amplitudes of the oceanic effect For example in the Canary Islands the difference between the amplitudes of the oceanic effect for the M2 wave calculated with and without the allowance for the latitudinal variations reaches 0 15 ugal which make
26. r of the M2 wave and the average values of these ratios over two models The need for calculating the average over two models was motivated by the fact that the latitudinal average delta factor for the M2 wave obtained for the PREM model fell within 0 004 accuracy between the delta factors of this wave in the DDW H and DDW NH models At the same time the averages for IASP91 have practically coincided with the averages for DDW NH see section 3 Based on the values of the ordinary and loading Love numbers the corresponding amplitude delta factors are calculated In contrast to the loading delta factors up to order 10000 and their latitudinal dependence with a step of 0 1 degree which were calculated a priori and in fact served as the input data for the program the second order delta factors of the body tide are calculated every time the program is run The load was specified by the tidal masses of the six tidal models CSR3 0 FES95 2 the Schwiderski model SCW80 NAO99b CSR4 1 and FES2012 The tidal heights were 12065 12066 expanded into the spherical harmonic series up to order 720 up to order 1120 for FES2012 For doing this we used the system of recurrent formulas for the integrals of the Legendre polynomials and associated polynomials Spiridonov Afanasyeva 2014 Spiridonov 2013 The obtained coefficients of the expansion together with the loading delta factors composed the input data for the ATLANTIDA3 1_2014 program Bas
27. s up 0 2 0 25 of the amplitude of the body tide for this wave 3 1 5 Comparison of oceanic effect with observations The comparative analysis of the oceanic gravitational effect calculated in this study with the observations is based on the results obtained by different authors at 21 stations using 22 instruments Two stations are located on the Canary Islands two on Svalbard five stations carried out measurements with SLR instruments in Europe 12 stations with superconducting gravimeters are part of the GGP network The instruments included 12 superconducting gravimeters eight LaCoste_Romberg gravimeters and two Askania gravimeters Besides comparing our calculations with the observations we also compared them with the model predictions by other authors using the programs based inter alia on the regional oceanic models 12077 12078 The number of cases n in which the results of ATLANTIDA 3 1 are closer to those observed than calculations performed by other programs are Canary Islands 62 Spitsbergen 69 European LCR stations 64 GGP network 59 In 77 of the cases obtained in this study the results are closer to the observations than those computed using the package Load97 from ETERNA3 30 More results of this analysis refers to the article Spiridonov E A Vinogradova O Yu 2014 Low frequency sea level T P non tidal perturbations give the magnitude of the gravimetric load effect of order 1 mgal Vinogradova
28. to 0 2 0 3 ugal are only observed near the mentioned St Matthew and Land s End Capes which sharply project into the ocean Again the specific structure of the isolines in the Irish Sea and English Channel is remarkable The phase differences do not normally exceed a few hundredths of a degree and can reach several degrees only in the specific knotty zones mentioned above At more than 100 km distance from coastline the influence of dissipation is smaller than 0 01 ugal The geographical distribution of considered differences derived for sums semidiurnal and all waves practically repeat the scheme of M2 In fact in the transition from M2 to the sum of all semidiurnal waves the amplitude of differences increases upon the average to 0 05 ugal and considering the sum of eight waves it reaches 0 15 0 2 ugal Almost half the discussed difference is obtained already even upon the transition from a reference period of s to 200 s The transition from 12 h to 24 h yields the corrections below 0 005 ugal to the amplitude and 0 1 degree to the phase 12076 12077 So the dissipation contributes 0 1 0 2 ugal to the amplitude and typically with a few hundredths of a degree to the phase of the total oceanic gravimetric effect near the coast of Europe 3 1 3 Spherical harmonic expansion of the oceanic tidal heights The comparison between the methods of calculating the oceanic load effect through Green s functions and by spherical harmonic expansi
29. ttps drive google com open id 0B PQJHBLMMBrWnpfanpYTO1qgeEE amp authuser 0 and download the ATLANTIDA EXE file to your computer This a self extracting archive which should be installed to the root directory on any desired disc Attention Unless installed to a root directory the program won t run To run the program hit ATLANTIDA31 ATLANTIDA31 EXE Select the desired options see Fig 2 below in the dropdown menu Warning In the work with this menu the separator between the integer part and fractional part of the entered numbers is a dot However by default the WINDOWS settings prescribe this separator to be a comma In order to correctly run the program one should either replace the 12066 12067 separator in the form of a comma in the WINDOWS settings by the separator in the form of a dot or to fill the menu prompts using the separator in the form of a comma In the next versions of the program we intend to make it independent on this OS setting Ef ATLANTIDA 3 1_2014 _ jes OCEAN LOAD LAT DEP oO YES NO S Oo YES NO GRAVITY POTENTIAL DEFORMATION TILT OCEAN MODELS CSR3 CSR4 0 FES2012 FES952 FES99 GOTOO SCW80 NAO99b TPX 0 5 CALCULATED BY LATITUDE LONGITUDE ALT NAME 90 90 180 180 LAT FROM STEP LONG FROM STEP E E bo foo poo INITIAL DATE STEP minutes N DAYS FREQUENCY cycl day FROM 0 00 3 94 TO Evgeny Spiridonov Ernst Boyarskiy Olga Vin
30. uency band is subdivided into 63 groups of waves Table 1 If the user specifies a limited frequency band the group of the waves that contains the boundaries of this band is selected as a whole for the further calculations If some of the waves that were previously selected for calculating the oceanic effect do not fall in the last frequency band the program automatically removes them and issues the warning message NOTE The additional GRID mode creation of the gridded ocean loading data only works in the GRAVITY mode with ROWS NO Here you may only select a single wave from WAVES The additional TILT mode only works for POINT and ignores ROWS mode by default WARNING In this version of the program the ALT N DAYS and STEP fields are integers In case of a wrong choice of the parameters the program displays the error message see section 2 4 The interface has also a button that runs the LOADO7 program This program is completely identical to the LOAD89 97 program of the Wenzel s ETERNA3 3 package At the same time LOADO7 has a convenient user friendly interface which makes it possible to conduct calculations both at a single point and on a grid and to select the waves of interest for the user This interface was designed by Ernst Aronovich Boyarskiy in 2011 Later two updates were introduced into the program They provided the possibility to account for the effect of the M2 wave of FES95 2 model which was previously impossible and fix
31. unction Then with the use of the obtained values the Love parameters density curves and the curves of gravitational acceleration were calculated These four dependences as well as the curves of compression and its derivative served as the main input data required for numerical integration of the boundary value problem describing the loaded state of the elastic gravitating compressible sphere with the allowance for the latitudinal variations in the elastic parameters and potential The problem is described by the set of the six ordinary first order differential equations with three boundary conditions on the Earth s surface and three conditions on the mantle core boundary Spiridonov 2014 The method of numerical integration of the boundary problem is most thoroughly expanded in Spiridonov E and Vinogradova O 2013 Vinogradova Spiridonov 2013b Integration was carried out with a 0 1 km step along the depth When determining the delta factors of the M2 wave the corresponding corrections for the effects of inertia forces presented in Molodenskiy S M 1984 were added to the Love numbers k and ho For the diurnal waves we applied the resonance curve 24 from Dehant V et al 1999 We constructed this curve for the amplitude delta factors of the waves in the near diurnal period range for the DDW H and DDW NH models After this for the same models we calculated the ratios of the obtained delta factors of diurnal waves to the delta facto
32. up window and be sure to hit the SA VE button Fig 3 SYP ATLANTIDA 3 1_2014 o amp XG OCEAN _ LOAD YES NO GRAVITY POTENTIAL DEFORMATION TILT M M2 v KOJ vps EARTH MODEL PREM CSR3 CSR4 0 FES2012 FES952 FES99 GOTOO SCW80 NAO99b TPX 0 5 PHASE E LOCAL GREENWICH IASP91 CALCULATED BY LATITUDE LONGITUDE NAME ALT 90 90 180 180 WAVES LAT FROM STEP LONG FROM WAVES a INITIAL DATE STEP minutes 05 05 2014 365 0 00 3 94 TO Evgeny Spiridonov Ernst Boyarskiy Olga Vinogradova Larisa Afanasyeva FREQUENCY cycl day FROM Fig 3 The ATLANTIDA 3 1_2014 program interface with the pop up window to select the Waves 2 2 3 The name and location of the site By default all the options listed above except for the selection of the waves and tidal time series parameters are set optimal by the program To get started you should only specify the name of the station NAME the site latitude LATITUDE in degrees longitude LONGITUDE in degrees and altitude ALT in meters and tidal time series parameters 12068 12069 2 2 4 The parameters of calculation of the time series Then in order to construct the time series in the ROWS mode you should specify the start date INITIAL DATE the time step in minutes STEP min the number of the days N DAYS and the frequency band FREQUENCY in cycles per day The entire tidal freq
Download Pdf Manuals
Related Search