Improving the Sectional MOSAIC Aerosol models of WRF-Chem with the 1 revised Gridpoint Statistical Interpolation System and multi-wavelength aerosol 2 optical measurements : DAO-K experiment 2019 at Kashi , near the Taklamakan 3 Desert , northwestern China 4 5

Abstract. The Gridpoint Statistical Interpolation data assimilation (DA) system was developed for the four-size bin sectional Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) aerosol mechanism in the Weather Research and Forecasting-Chemistry (WRF-Chem) model. The forward and adjoint operators for the aerosol optical depth (AOD) analysis were derived from WRF-Chem aerosol optical code. We applied three-dimensional variational DA to assimilate the multi-wavelength AOD, ambient aerosol scattering coefficient, and aerosol absorption coefficient, measured by the sun-sky photometer, nephelometer, and aethalometer, respectively. These were undertaken during a dust observation field campaign at Kashi in northwestern China in April 2019. The results showed that the DA analyses decreased the low biases in the model aerosols; however, it had had some deficiencies. Assimilating the surface particle concentration increased the coarse particles in the dust episodes, but AOD, and the coefficients for aerosol scattering and absorption, were still lower than observed values. Assimilating aerosol scattering coefficient separately from AOD improved the two optical quantities. However, it caused an overestimation of the particle concentrations at the surface. Assimilating the aerosol absorption coefficient yielded the highest positive bias in the surface particle concentration, aerosol scattering coefficient, and AOD. The positive biases in the DA analysis were caused by the forward operator underestimating particle scattering and absorption efficiency. As a compensation, the DA system increased particle concentrations excessively so as to fit the observed optical values. The best overall improvements were obtained from the simultaneous assimilation of the surface particle concentration and AOD. The assimilation did not substantially change the aerosol chemical fractions. After DA, the clear-sky aerosol radiative forcing at Kashi was −10.5 W m−2 at the top of the atmosphere, which was 46 % higher than the background radiative forcing value.



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Data assimilation (DA) blends the information from observations with a priori background 53 fields from deterministic models to obtain an optimal analysis (Wang et al., 2001;Bannister,

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This study verifies the effectiveness of our revised GSI system by incorporating multi- conditions (Hong et al., 2006), and the rapid radiative transfer model for general circulation 172 models (RRTMG) scheme for shortwave and longwave radiation (Iacono et al., 2008). The 173 gas-phase chemistry was simulated using the carbon bond mechanism (Zaveri and Peters, compositions, aerosol number concentration, and aerosol water content. The aerosol 184 compositions included hydrophilic particulates (i.e., SO4 2-, NO3 -, NH4 + , Cl -, Na + ) and 185 hydrophobic particulates (i.e., BC, OC, and OIN). The dust emission was simulated using the 186 GOCART dust scheme (Ginoux et al., 2001). The dust mass was included in the OIN 187 concentration determination and aerosol optical calculation. The aerosol compositions were 188 externally mixed between the size bins and internally mixed in each size bin. The internal 189 mixing refractive index was the volume-weighted mean refractive index of each composition.

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The revised GSI DA system is based on the official GSI (https://dtcenter.org/community-

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The official GSI version only works with the GOCART aerosols for assimilating the surface-206 layer PM2.5 and PM10 (denoted as PMx in the context) concentrations, and the 550 nm MODIS 207 AOD. Our revised GSI system assimilates PMx concentrations, multi-wavelength aerosol 208 scattering/absorption coefficients, and AOD. Figure 1 shows the workflow of our DA system.

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According to the AOD calculation in WRF-Chem, we can either choose the aerosol number 210 concentration (option 1), or aerosol mass concentration (option 2) as control variables. Option 211 1 is described in Li et al. (2020). In this study, we selected option 2, which is described in the 212 following subsections.

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where eext,z,k is the extinction cross section of a single mixing particle in the k-th size bin at the 280 z-th model layer, nz,k is the aerosol number concentration, and Hz is the layer thickness. The 281 extinction cross section eext,z,k of a wet particle with radius rwet,z,k is:

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where pext,z,k is the extinction coefficient, given the desired mixing refractive indexes and the  309 310 The first term on the righthand side of Eq. (7) indicates the change in AOD as the perturbation 311 of extinction cross section. According to Eq. (4), considering that the particle radius is  328 surrounding the point with the desired mixing refractive indexes, and the wet particle radius.

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The changes in interpolation weights are determined as:

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The third term on the righthand side of Eq.

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The adjoint operator for the aerosol absorption coefficient measured by aethalometer is 421 422 423 426

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where the symbols have the same meaning as before. The subscript one denotes the surface 432 layer, while. sca and abs denote "scattering" and "absorption," respectively.

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As shown in the adjoint operators, the gradients of the aerosol mass concentrations rely on the

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However, we found that using the latitude-binning strategy overestimated the surface PMx 500 concentration when assimilating aerosol optical observations. One reason for this was related 501 to the model bias in particle extinction efficiency, as discussed in Section 3.3. Another

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'anthropogenic aerosols') had maximum errors in the second particle size. The background 519 error for OIN composition was higher than that for anthropogenic aerosols by a factor of two 520 or three, because of the high background dust concentration in the city.

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The horizontal and vertical correlation length scales determine the range of observation

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The background model errors were independent of particle size, which would have tended to

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(2020) for more details about the field campaign. Table 1

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Kashi is in the junction between the Tian Shan Mountains to the west and the Taklamakan

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Desert to the east (Figure 5a). In the Tarim Basin, the prevailing surface wind is easterly or 609 northeasterly, which raises dust levels and carries the particles westward (Figure 5b). An

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The low bias in PM2.5 was mainly in the dust storm on 24-25 April (Figure 6a). This indicates 647 that the DA system preferentially modified the coarse particle concentrations because the Research Testbed). They claimed that WRF-Chem underestimated the AOD and low-level 680 aerosol extinction coefficient because the model had a low bias in relative humidity, which 681 led to less AWC and lowered the single-particle extinction. As a compensation, the DA 682 system overestimated the total particle concentration to fit the observed AOD value. In the 683 arid area of Kashi, PM10 was strongly overestimated when assimilating AOD. We speculate 684 that WRF-Chem also lowers the dust extinction efficiency. Table 3 shows the ratios of the AOD and aerosol scattering/absorption coefficients to the

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Another reason for the low ratio of AOD to PM10 is related to our approach for modeling 708 BEC. It is important to remember that our BEC represents the possible error effects owing to 709 model bias in aerosols. The coarse particle accounts for a large mass portion of PMx, and its 710 bias dominates the model error. However, we cannot say that this background error 711 assessment is unbiased. As our BEC gave a high background error to the coarse particle for its 712 sufficient concentration, the DA system tended to increase PM10, which was not as effective 713 in increasing AOD as PM2.5. If the background error of the coarse particle were too high, the 714 BEC would falsely lower the ratio of AOD to PM10 in the analysis.

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To reduce the overestimate in PMx concentrations, we set the gridded standard deviation for 717 the OIN for Kashi in place of the latitude-binning standard deviation, as discussed in Section 718 2.3. Figure 12 shows the analyzed vertical profiles of PMx concentrations. Higher

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Chem strongly underestimated the single-particle absorption efficiency, and the low bias was 734 too strong to be compensated by the overestimated aerosol number concentration.

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Assimilating the AOD increased the diurnal variation in the DA analyses. There was a higher 737 increase in the concentration at noon (06:00 UTC) (Figure 10d). At the hot time of the day,  752 However, the surface particle concentrations were overestimated (i.e., positive biases by 32% 753 for PM2.5, and 84% for PM10), with a substantial increase in the coarse particle of OIN.

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Overestimations appeared during the mild dust episodes (Figure 6b). This again indicated that 755 WRF-Chem underestimated the particle scattering efficiency, which was represented by the 756 ratio of the scattering coefficient to PM10 (

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The maximum increase in the mean value was at 06:00 UTC, also because of the strong 770 noontime heating in the model. As the particle concentration increased, the aerosol scattering 771 coefficient was overfitted to 849.0 Mm -1 , higher than the observed levels by a factor of four.

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The monthly mean AOD was improbably up to 1.95. The improvement of the absorption 773 coefficient (which was 65.1 Mm -1) was insufficient, and was 21% lower than the observed 774 levels.

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Unlike DA_AOD and DA_Esca, assimilating the absorption coefficient cannot increase the

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Dust redistributes the energy between the land and the atmosphere. The atmosphere gains 899 more shortwave energy as the dust particle absorption; the warming atmosphere also emits 900 more longwave energy as it absorbs shortwave energy. The change in energy budget at the 901 surface is correspondingly the opposite of that in the atmosphere. As shown in

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Simultaneous assimilation of the PM2.5 and PM10 concentrations improved the model aerosol 946 concentrations, with significant increases in the coarse particles; meanwhile, the analyzed 947 AOD was 56% lower than observed levels. The assimilation of AOD significantly improved 948 the AOD but overestimated the surface PM10 concentration by a factor of at least two.

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Assimilating the aerosol scattering coefficient improved the scattering coefficient in the 950 analysis but overestimated the surface PM10 concentration by 84%. It therefore seems that 951 WRF-Chem underestimated the particle extinction efficiency. As a compensation, the DA 952 system overestimated the aerosol concentration to fit the observed optical values, yielding 953 overly high particle concentrations.

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A notable problem was the assimilation of the absorption coefficient, which greatly

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Our design of control variables allowed the DA system to adjust the aerosol chemical

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When assimilating surface particles and AOD, the instantaneous clear-sky ADRF at Kashi 985 were -10.5 Wm -2 at the TOA, +19.5 Wm -2 within the atmosphere, and -30.0 Wm -2 at the 986 surface, respectively. Since the DA analyses still lowered the AOD value, the aerosol 987 radiative forcing values assimilating the observations were also underestimated.

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The limitations that necessitate further research include:

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(1) The binning strategy. The desired strategy should link the circulation flow and 991 particle emission sources. A better hybrid DA coupled with the ensemble Kalman filter will 992 be more effective for estimating the aerosol background error.

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(2) The observational error. This could be elaborated further. The PM10 included the Figure 1. The workflow of aerosol DA in the revised GSI system for the sectional MOSAIC aerosols in WRF-Chem. The contents in blue are the portions we developed. The arrows in gray indicate the workflow of option 2 that we did in this study. Only option 2 can assimilate the aerosol scattering/absorption coefficients.