Comparison of the Atmospheric 200 hPa Jet’s Analyses between Proper Orthogonal Decomposition and Advanced Dynamic Mode Decomposition Method

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Number of modes</td><td class="align_center">Error of <svg height="11.9348pt" id="M242" style="vertical-align:-3.18146pt" version="1.1" viewbox="-0.0498162 -8.75334 51.2033 11.9348" width="51.2033pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.969,0)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.484,0)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,29.177,3.132)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.728,3.132)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,43.836,3.132)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g></svg></td><td class="align_center">Error of <svg height="12.0627pt" id="M243" style="vertical-align:-3.309361pt" version="1.1" viewbox="-0.0498162 -8.75334 48.3718 12.0627" width="48.3718pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.969,0)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.484,0)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,29.177,3.132)"><path d="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,34.3,3.132)"><path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,41.016,3.132)"><path d="M43 650V622C120 616 128 612 128 526V124C128 39 120 33 34 27V0H270C392 0 492 25 567 83C643 141 690 230 690 350C690 444 655 517 605 565C543 625 450 650 323 650H43ZM213 547C213 587 217 598 226 604C236 612 262 617 304 617C371 617 429 604 474 576C554 529 592 439 592 336C592 176 505 36 319 36C246 36 213 55 213 131V547Z"></path></g></svg></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">11 modes</td><td class="align_center">0.0971</td><td class="align_center">0.1100</td></tr><tr><td class="align_left">17 modes</td><td class="align_center">0.0671</td><td class="align_center">0.0843</td></tr><tr><td class="align_left">25 modes</td><td class="align_center">0.0593</td><td class="align_center">0.0640</td></tr><tr><td class="align_left">47 modes</td><td class="align_center">0.0443</td><td class="align_center">0.0383</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The average relative error of the POD/SPDMD reduced-order model.</div>

Advances in Meteorology

tab2

Table 2

Table 2: Comparison of the Atmospheric 200 hPa Jet’s Analyses between Proper Orthogonal Decomposition and Advanced Dynamic Mode Decomposition Method 