Modifying Covariance Localization to Mitigate Sampling Errors from the Ensemble Data Assimilation

<div>Influence of the CL and CL-MC on the Kalman gain matrix for model component <span class="nowrap"><svg height="8.8423pt" id="M196" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 31.112 8.8423" width="31.112pt" 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="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.181,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.444,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.684,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg>.</span> (a) Localization radius = 10. (b) Localization radius = 15. (c) Localization radius = 20. “K(none)” represents the without using localization scheme; “K(CL)” and “K(CL-MC)” represent using and without using modified Cholesky decomposition, respectively. “Kii” denotes the Kalman gain from each observation for CL, CL-MC, and without using the localization scheme.</div>

Advances in Meteorology

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Figure 3

Figure 3: Modifying Covariance Localization to Mitigate Sampling Errors from the Ensemble Data Assimilation 