Numerical Results for Shallow Water Model
The results obtained with divided differences show
significant inaccuracies compared with the
tangent-linear code.
Numerical results obtained with divided differences
grad-res 1 0.100000000E+01 0.000000000E+00 -.741678138E+08
grad-res 2 0.100000000E+01 0.000000000E+00 -.545557001E+05
grad-res 3 0.100000000E+01 0.000000000E+00 -.199637125E+05
grad-res 4 0.100000000E+01 0.000000000E+00 0.662637495E+04
grad-res 5 0.100000000E+01 0.000000000E+00 0.368561849E+05
grad-res 6 0.100000000E+01 0.000000000E+00 -.509516926E+05
grad-res 7 0.100000000E+01 0.000000000E+00 -.231536514E+07
grad-res 8 0.100000000E+01 0.000000000E+00 -.112640102E+08
grad-res 9 0.100000000E+01 0.000000000E+00 -.416056741E+07
grad-res 10 0.100000000E+01 0.000000000E+00 0.109824043E+07
grad-res 11 0.100000000E+01 0.000000000E+00 -.411637354E+07
grad-res 12 0.100000000E+01 0.000000000E+00 -.467818786E+07
grad-res 13 0.100000000E+01 0.000000000E+00 -.141970982E+07
grad-res 14 0.100000000E+01 0.000000000E+00 -.131850107E+07
grad-res 15 0.100000000E+01 0.000000000E+00 -.118033849E+07
grad-res 16 0.100000000E+01 0.000000000E+00 -.662371187E+06
grad-res 17 0.100000000E+01 0.000000000E+00 -.404622912E+06
grad-res 18 0.100000000E+01 0.000000000E+00 -.269512753E+06
grad-res 19 0.100000000E+01 0.000000000E+00 -.189654388E+06
grad-res 20 0.100000000E+01 0.000000000E+00 -.135756337E+06
grad-res 21 0.100000000E+01 0.000000000E+00 -.994484671E+08
grad-res 22 0.100000000E+01 0.000000000E+00 -.525248265E+07
grad-res 23 0.100000000E+01 0.000000000E+00 -.557542181E+07
grad-res 24 0.100000000E+01 0.000000000E+00 -.612261044E+07
grad-res 25 0.100000000E+01 0.000000000E+00 -.685431487E+07
grad-res 26 0.100000000E+01 0.000000000E+00 -.776360876E+07
grad-res 27 0.100000000E+01 0.000000000E+00 -.876970212E+07
grad-res 28 0.100000000E+01 0.000000000E+00 -.188268541E+08
grad-res 29 0.100000000E+01 0.000000000E+00 -.427404209E+08
grad-res 30 0.100000000E+01 0.000000000E+00 -.617185057E+07
grad-res 31 0.100000000E+01 0.000000000E+00 -.874768872E+07
grad-res 32 0.100000000E+01 0.000000000E+00 -.130023203E+08
grad-res 33 0.100000000E+01 0.000000000E+00 -.359195581E+07
grad-res 34 0.100000000E+01 0.000000000E+00 -.602176633E+07
grad-res 35 0.100000000E+01 0.000000000E+00 -.660278622E+07
grad-res 36 0.100000000E+01 0.000000000E+00 -.574423940E+07
grad-res 37 0.100000000E+01 0.000000000E+00 -.507589702E+07
grad-res 38 0.100000000E+01 0.000000000E+00 -.475596799E+07
grad-res 39 0.100000000E+01 0.000000000E+00 -.474043665E+07
grad-res 40 0.100000000E+01 0.000000000E+00 -.487058858E+07
grad-res 41 0.100000000E+01 0.000000000E+00 -.508048301E+08
grad-res 42 0.100000000E+01 0.000000000E+00 -.916278634E+07
grad-res 43 0.100000000E+01 0.000000000E+00 -.944943273E+07
grad-res 44 0.100000000E+01 0.000000000E+00 -.100193091E+08
grad-res 45 0.100000000E+01 0.000000000E+00 -.105620826E+08
grad-res 46 0.100000000E+01 0.000000000E+00 -.103335796E+08
grad-res 47 0.100000000E+01 0.000000000E+00 -.109521315E+08
grad-res 48 0.100000000E+01 0.000000000E+00 -.177608392E+08
grad-res 49 0.100000000E+01 0.000000000E+00 -.575633831E+08
grad-res 50 0.100000000E+01 0.000000000E+00 -.200777074E+08
grad-res 51 0.100000000E+01 0.000000000E+00 -.103310697E+08
grad-res 52 0.100000000E+01 0.000000000E+00 -.104515119E+08
grad-res 53 0.100000000E+01 0.000000000E+00 0.100236642E+08
grad-res 54 0.100000000E+01 0.000000000E+00 0.313310803E+05
grad-res 55 0.100000000E+01 0.000000000E+00 -.503539043E+07
grad-res 56 0.100000000E+01 0.000000000E+00 -.722193694E+07
grad-res 57 0.100000000E+01 0.000000000E+00 -.788961961E+07
grad-res 58 0.100000000E+01 0.000000000E+00 -.816225273E+07
grad-res 59 0.100000000E+01 0.000000000E+00 -.847049375E+07
grad-res 60 0.100000000E+01 0.000000000E+00 -.877222490E+07
grad-res 61 0.100000000E+01 0.000000000E+00 0.222967964E+08
grad-res 62 0.100000000E+01 0.000000000E+00 -.102624065E+08
grad-res 63 0.100000000E+01 0.000000000E+00 -.102831078E+08
grad-res 64 0.100000000E+01 0.000000000E+00 -.106096842E+08
grad-res 65 0.100000000E+01 0.000000000E+00 -.107957736E+08
grad-res 66 0.100000000E+01 0.000000000E+00 -.945062073E+07
grad-res 67 0.100000000E+01 0.000000000E+00 -.766100421E+07
grad-res 68 0.100000000E+01 0.000000000E+00 -.845406766E+07
grad-res 69 0.100000000E+01 0.000000000E+00 -.538908250E+08
grad-res 70 0.100000000E+01 0.000000000E+00 -.258903641E+08
grad-res 71 0.100000000E+01 0.000000000E+00 -.465851508E+07
grad-res 72 0.100000000E+01 0.000000000E+00 -.150308266E+08
grad-res 73 0.100000000E+01 0.000000000E+00 0.651124266E+07
grad-res 74 0.100000000E+01 0.000000000E+00 -.286121884E+07
grad-res 75 0.100000000E+01 0.000000000E+00 -.579893540E+07
grad-res 76 0.100000000E+01 0.000000000E+00 -.813218407E+07
grad-res 77 0.100000000E+01 0.000000000E+00 -.915781450E+07
grad-res 78 0.100000000E+01 0.000000000E+00 -.963682257E+07
grad-res 79 0.100000000E+01 0.000000000E+00 -.100155842E+08
grad-res 80 0.100000000E+01 0.000000000E+00 -.102674458E+08
grad-res 81 0.100000000E+01 0.000000000E+00 0.752101560E+08
grad-res 82 0.100000000E+01 0.000000000E+00 -.865193065E+07
grad-res 83 0.100000000E+01 0.000000000E+00 -.846663937E+07
grad-res 84 0.100000000E+01 0.000000000E+00 -.862921148E+07
grad-res 85 0.100000000E+01 0.000000000E+00 -.879824561E+07
grad-res 86 0.100000000E+01 0.000000000E+00 -.752548343E+07
grad-res 87 0.100000000E+01 0.000000000E+00 -.461185913E+07
grad-res 88 0.100000000E+01 0.000000000E+00 0.429906720E+07
grad-res 89 0.100000000E+01 0.000000000E+00 -.244333808E+08
grad-res 90 0.100000000E+01 0.000000000E+00 -.160989498E+08
grad-res 91 0.100000000E+01 0.000000000E+00 0.183507845E+08
grad-res 92 0.100000000E+01 0.000000000E+00 -.551193575E+07
grad-res 93 0.100000000E+01 0.000000000E+00 -.104202489E+07
grad-res 94 0.100000000E+01 0.000000000E+00 -.901254643E+07
grad-res 95 0.100000000E+01 0.000000000E+00 -.907406304E+07
grad-res 96 0.100000000E+01 0.000000000E+00 -.973017422E+07
grad-res 97 0.100000000E+01 0.000000000E+00 -.958221780E+07
grad-res 98 0.100000000E+01 0.000000000E+00 -.933077532E+07
grad-res 99 0.100000000E+01 0.000000000E+00 -.923623798E+07
grad-res 100 0.100000000E+01 0.000000000E+00 -.914932286E+07
grad-res 101 0.100000000E+01 0.000000000E+00 0.802135556E+08
grad-res 102 0.100000000E+01 0.000000000E+00 -.541512638E+07
grad-res 103 0.100000000E+01 0.000000000E+00 -.522108075E+07
grad-res 104 0.100000000E+01 0.000000000E+00 -.530666362E+07
grad-res 105 0.100000000E+01 0.000000000E+00 -.555334140E+07
grad-res 106 0.100000000E+01 0.000000000E+00 -.506435607E+07
grad-res 107 0.100000000E+01 0.000000000E+00 -.256241944E+07
grad-res 108 0.100000000E+01 0.000000000E+00 0.169677449E+08
grad-res 109 0.100000000E+01 0.000000000E+00 0.272900148E+08
grad-res 110 0.100000000E+01 0.000000000E+00 0.150894915E+08
grad-res 111 0.100000000E+01 0.000000000E+00 0.582580364E+08
grad-res 112 0.100000000E+01 0.000000000E+00 0.100128288E+08
grad-res 113 0.100000000E+01 0.000000000E+00 -.112607155E+08
grad-res 114 0.100000000E+01 0.000000000E+00 -.114713654E+08
grad-res 115 0.100000000E+01 0.000000000E+00 -.901355184E+07
grad-res 116 0.100000000E+01 0.000000000E+00 -.845302376E+07
grad-res 117 0.100000000E+01 0.000000000E+00 -.742649065E+07
grad-res 118 0.100000000E+01 0.000000000E+00 -.664838784E+07
grad-res 119 0.100000000E+01 0.000000000E+00 -.623625975E+07
grad-res 120 0.100000000E+01 0.000000000E+00 -.597360480E+07
grad-res 121 0.100000000E+01 0.000000000E+00 0.298965858E+08
grad-res 122 0.100000000E+01 0.000000000E+00 -.215299310E+07
grad-res 123 0.100000000E+01 0.000000000E+00 -.208856183E+07
grad-res 124 0.100000000E+01 0.000000000E+00 -.209260731E+07
grad-res 125 0.100000000E+01 0.000000000E+00 -.220427869E+07
grad-res 126 0.100000000E+01 0.000000000E+00 -.226617366E+07
grad-res 127 0.100000000E+01 0.000000000E+00 -.128541840E+07
grad-res 128 0.100000000E+01 0.000000000E+00 0.192293086E+08
grad-res 129 0.100000000E+01 0.000000000E+00 0.355864976E+08
grad-res 130 0.100000000E+01 0.000000000E+00 0.430805505E+08
grad-res 131 0.100000000E+01 0.000000000E+00 0.848697843E+08
grad-res 132 0.100000000E+01 0.000000000E+00 -.218280810E+08
grad-res 133 0.100000000E+01 0.000000000E+00 -.126896001E+08
grad-res 134 0.100000000E+01 0.000000000E+00 -.349141882E+07
grad-res 135 0.100000000E+01 0.000000000E+00 -.320797850E+07
grad-res 136 0.100000000E+01 0.000000000E+00 -.328889713E+07
grad-res 137 0.100000000E+01 0.000000000E+00 -.275217033E+07
grad-res 138 0.100000000E+01 0.000000000E+00 -.238908188E+07
grad-res 139 0.100000000E+01 0.000000000E+00 -.227512537E+07
grad-res 140 0.100000000E+01 0.000000000E+00 -.225182574E+07
grad-res 141 0.100000000E+01 0.000000000E+00 -.671157033E+08
grad-res 142 0.100000000E+01 0.000000000E+00 -.500149705E+06
grad-res 143 0.100000000E+01 0.000000000E+00 -.534189957E+06
grad-res 144 0.100000000E+01 0.000000000E+00 -.487624331E+06
grad-res 145 0.100000000E+01 0.000000000E+00 -.330581214E+06
grad-res 146 0.100000000E+01 0.000000000E+00 0.101239788E+06
grad-res 147 0.100000000E+01 0.000000000E+00 0.149332799E+07
grad-res 148 0.100000000E+01 0.000000000E+00 0.626783878E+07
grad-res 149 0.100000000E+01 0.000000000E+00 0.186710569E+09
grad-res 150 0.100000000E+01 0.000000000E+00 0.267835136E+09
grad-res 151 0.100000000E+01 0.000000000E+00 0.184507174E+09
grad-res 152 0.100000000E+01 0.000000000E+00 0.840418499E+08
grad-res 153 0.100000000E+01 0.000000000E+00 0.223719078E+07
grad-res 154 0.100000000E+01 0.000000000E+00 0.267848405E+07
grad-res 155 0.100000000E+01 0.000000000E+00 0.930796314E+06
grad-res 156 0.100000000E+01 0.000000000E+00 0.360969192E+06
grad-res 157 0.100000000E+01 0.000000000E+00 0.244476564E+06
grad-res 158 0.100000000E+01 0.000000000E+00 0.106052095E+06
grad-res 159 0.100000000E+01 0.000000000E+00 -.877004240E+05
grad-res 160 0.100000000E+01 0.000000000E+00 -.270125102E+06
Numerical results obtained with tangent-linear code
grad( 1 )= -74167779.0489114
grad( 2 )= -54555.7046145527
grad( 3 )= -19963.7206722904
grad( 4 )= 6626.36231346326
grad( 5 )= 36856.1737455821
grad( 6 )= -50951.6864239191
grad( 7 )= -2315365.04972718
grad( 8 )= -11264010.2152519
grad( 9 )= -4160567.38032823
grad( 10 )= 1098240.50479217
grad( 11 )= -4116373.40026658
grad( 12 )= -4678187.88347486
grad( 13 )= -1419709.75984788
grad( 14 )= -1318501.07162898
grad( 15 )= -1180338.48014448
grad( 16 )= -662371.178006576
grad( 17 )= -404622.906471553
grad( 18 )= -269512.752202257
grad( 19 )= -189654.383629407
grad( 20 )= -135756.341617346
grad( 21 )= -99448425.4853255
grad( 22 )= -5252475.00225610
grad( 23 )= -5575414.21796472
grad( 24 )= -6122602.94491424
grad( 25 )= -6854307.47906625
grad( 26 )= -7763602.16330200
grad( 27 )= -8769700.41241155
grad( 28 )= -18826858.0991215
grad( 29 )= -42740399.9798723
grad( 30 )= -6171849.64625867
grad( 31 )= -8747688.00169707
grad( 32 )= -13002331.1925580
grad( 33 )= -3591959.24617250
grad( 34 )= -6021763.80509457
grad( 35 )= -6602780.43379509
grad( 36 )= -5744232.75071394
grad( 37 )= -5075890.02867177
grad( 38 )= -4755960.70416425
grad( 39 )= -4740429.17546141
grad( 40 )= -4870581.00263907
grad( 41 )= -50804777.9440953
grad( 42 )= -9162792.58021089
grad( 43 )= -9449439.27379036
grad( 44 )= -10019315.9892082
grad( 45 )= -10562089.6233915
grad( 46 )= -10333586.5906494
grad( 47 )= -10952140.4934161
grad( 48 )= -17760844.1844033
grad( 49 )= -57563354.5554893
grad( 50 )= -20077706.1372401
grad( 51 )= -10331065.4422491
grad( 52 )= -10451530.6436189
grad( 53 )= 10023656.3434397
grad( 54 )= 31326.5561373311
grad( 55 )= -5035394.77088725
grad( 56 )= -7221942.34179568
grad( 57 )= -7889625.46294180
grad( 58 )= -8162258.61745325
grad( 59 )= -8470499.64002155
grad( 60 )= -8772230.83821072
grad( 61 )= 22296788.7755415
grad( 62 )= -10262413.6248127
grad( 63 )= -10283115.1648913
grad( 64 )= -10609691.7128647
grad( 65 )= -10795780.9135834
grad( 66 )= -9450627.21848539
grad( 67 )= -7661011.71727792
grad( 68 )= -8454071.83457481
grad( 69 )= -53890797.3680602
grad( 70 )= -25890365.1735897
grad( 71 )= -4658500.35321010
grad( 72 )= -15030856.0409306
grad( 73 )= 6511223.50330436
grad( 74 )= -2861226.06727685
grad( 75 )= -5798940.69225593
grad( 76 )= -8132190.38663810
grad( 77 )= -9157821.43199174
grad( 78 )= -9636829.63656930
grad( 79 )= -10015591.2785904
grad( 80 )= -10267452.8874659
grad( 81 )= 75210104.3231812
grad( 82 )= -8651935.77489616
grad( 83 )= -8466644.55371730
grad( 84 )= -8629216.76964764
grad( 85 )= -8798250.72291228
grad( 86 )= -7525487.72736520
grad( 87 )= -4611863.62018164
grad( 88 )= 4299065.45318266
grad( 89 )= -24433360.2296067
grad( 90 )= -16098954.6071847
grad( 91 )= 18350819.9509135
grad( 92 )= -5511971.91306098
grad( 93 )= -1042050.94861965
grad( 94 )= -9012555.15053639
grad( 95 )= -9074068.60360827
grad( 96 )= -9730179.96149936
grad( 97 )= -9582223.55311242
grad( 98 )= -9330780.86324223
grad( 99 )= -9236243.33812483
grad( 100 )= -9149328.09059412
grad( 101 )= 80213497.1906411
grad( 102 )= -5415129.20645297
grad( 103 )= -5221083.58550206
grad( 104 )= -5306666.53176013
grad( 105 )= -5553344.27166729
grad( 106 )= -5064358.53525832
grad( 107 )= -2562421.49312673
grad( 108 )= 16967746.1662109
grad( 109 )= 27290026.5392113
grad( 110 )= 15089485.2174926
grad( 111 )= 58258102.6366064
grad( 112 )= 10012790.5652936
grad( 113 )= -11260740.5220070
grad( 114 )= -11471372.6788198
grad( 115 )= -9013556.24106807
grad( 116 )= -8453027.97101048
grad( 117 )= -7426494.49199523
grad( 118 )= -6648391.27755910
grad( 119 )= -6236262.90783591
grad( 120 )= -5973607.79775447
grad( 121 )= 29896563.8385344
grad( 122 )= -2152994.38571170
grad( 123 )= -2088563.08838337
grad( 124 )= -2092608.56124427
grad( 125 )= -2204279.94126342
grad( 126 )= -2266174.79169372
grad( 127 )= -1285418.71552795
grad( 128 )= 19229311.0503077
grad( 129 )= 35586493.7509210
grad( 130 )= 43080543.3265077
grad( 131 )= 84869863.0173575
grad( 132 )= -21828115.4398711
grad( 133 )= -12689612.5213723
grad( 134 )= -3491420.59879100
grad( 135 )= -3207979.99871233
grad( 136 )= -3288898.93116643
grad( 137 )= -2752172.01325045
grad( 138 )= -2389083.38278614
grad( 139 )= -2275126.76803431
grad( 140 )= -2251827.09353001
grad( 141 )= -67115654.1921925
grad( 142 )= -500145.860395453
grad( 143 )= -534185.758458925
grad( 144 )= -487619.800264547
grad( 145 )= -330576.422182456
grad( 146 )= 101244.792273398
grad( 147 )= 1493333.49642891
grad( 148 )= 6267844.32905831
grad( 149 )= 186710537.993427
grad( 150 )= 267835126.185318
grad( 151 )= 184507261.652462
grad( 152 )= 84041851.6282041
grad( 153 )= 2237192.91082294
grad( 154 )= 2678486.54056733
grad( 155 )= 930798.241104315
grad( 156 )= 360971.081424388
grad( 157 )= 244478.722033326
grad( 158 )= 106054.597572290
grad( 159 )= -87697.5837177671
grad( 160 )= -270121.933151133