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