| Summary: | Data assimilation (DA) combines incomplete background values obtained via chemical transport model predictions with observational information. Several 3-Dimensional variational (3DVAR) and sequential methods (e.g., ensemble Kalman filter (EnKF)) are used to define model errors and build a background error covariance (BEC) and are important factors affecting the prediction performance of DA. The BEC determines the spatial range, where observation concentration is reflected in the model when DA is applied to an air pollution transport model. However, studies investigating the characteristics of BEC using air quality models remain lacking. In this study, horizontal length scale (HLS) and vertical length scale (VLS) analyses of a BEC were applied to EnKF and ensemble square root filter (EnSRF), respectively, and two ensemble-based DA methods were performed; the characteristics were compared with those of a BEC applied to 3DVAR. The results of 6 h PM<sub>2.5</sub> predictions performed for 42 days were evaluated for a control run without DA (CTR), 3DVAR, EnKF, and EnSRF. HLS and VLS respectively exhibited a high correlation with the ground wind speed and with the planetary boundary layer height for diurnal and daily variations; EnKF and EnSRF exhibited superior performances among all the methods. The root mean square errors were 11.9 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">g</mi><mo> </mo><mi mathvariant="normal">m</mi></mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> and 11.7 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">g</mi><mo> </mo><mi mathvariant="normal">m</mi></mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> for EnKF and EnSRF, respectively, while those for 3DVAR and CTR were 12.6 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">g</mi><mo> </mo><mi mathvariant="normal">m</mi></mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> and 18.3 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">g</mi><mo> </mo><mi mathvariant="normal">m</mi></mrow></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula>, respectively. Thus, we proposed a simple method to find a Gaussian function that best described the error correlation of the BEC based on the physical distance.
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