High sensitivity of Indian summer monsoon to Middle East dust absorptive properties

The absorptive properties of dust aerosols largely determine the magnitude of their radiative impacts on the climate system. Currently, climate models use globally constant values of dust imaginary refractive index (IRI), a parameter describing the dust absorption efficiency of solar radiation, although it is highly variable. Here we show with model experiments that the dust-induced Indian summer monsoon (ISM) rainfall differences (with dust minus without dust) change from −9% to 23% of long-term climatology as the dust IRI is changed from zero to the highest values used in the current literature. A comparison of the model results with surface observations, satellite retrievals, and reanalysis data sets indicates that the dust IRI values used in most current climate models are too low, tending to significantly underestimate dust radiative impacts on the ISM system. This study highlights the necessity for developing a parameterization of dust IRI for climate studies.

This Supplementary Information provides additional detailed information about model configuration, experimental design, and the model representation of dust emissions, aerosol mixing rules, and aeraosol optical properties.

Dust IRI values
The dust IRI values used in this study are listed in Table S1. Table S1. List of experiments with dust imaginary refractive indices at four wavelengths (unit: nm) used in various climate models. The real part of the dust refractive index is set to 1. 55

Description of model configuration and ensemble experimental design.
The key physical and chemical schemes used in WRF-Chem experiments are listed in Table S2. For shortwave and PBL scheme, multiple options are used to create physical and chemical perturbed ensemble simulations, which are listed in Table S3. The 16 ensemble simulations in the control and each of the six sensitivity experiments are created by selecting various schemes for physical and chemical processes to take into account the potential model uncertainties. These processes include the planetary boundary layer (2 options), aerosol chemical mixing rules (4 options), and shortwave radiation (2 options) and the details on the options for these processes are listed in Table S2. The reason for addressing these three processes is that they largely determine the radiative impacts of dust aerosols on the climate system.

Dust net radiative effect
The dust-induced net radiative effects and heating rates in the atmosphere at clear-sky conditions, except for heating rates of sensible and latent heat at all-sky conditions, because WRF-Chem calculates heating rates of sensible and latent only at all-sky conditions.

Relationship between AOD and ENSO
The relationship between AOD over the Arabian Sea and the Arabian Peninsula and ENSO is represented by the scatter plot of normalized AOD versus Niño 3.4 index, as shown in Figure S2. Based on Figure S2, AOD anomalies can occur in both La Niña and El Niño months. No solid evidence was found for a close relationship between AOD and ENSO in our analysis.  Figure S4a, based on Atmospheric Infrared Sounder (AIRS) satellite data, exhibits strong atmospheric warming effects within 900-600 hPa and 10°-25° N over the Arabian Sea and 900-300 hPa and 30°-35° N over the Iranian Plateau, with magnitudes of 1.0 and 1.5 K, respectively. The consistent heating patterns are also seen in the Modern Era-Retrospective Analysis for Research and Applications (MERRA) and ERA-I reanalysis data ( Figures S4b and S4c). Due to atmospheric heating over the Arabian Sea, a southerly wind anomaly is observed within 900-800 hPa and 5°-20° N as well as an upward wind anomaly within 900-500 hPa at around 20° N ( Figures S2b and S2c). Another important circulation change is the upward wind anomaly from the surface to the upper troposphere over the Iranian Plateau.

Dust-induced changes in vertical profiles of atmospheric temperature and circulation.
The simulated changes in atmospheric temperature show positive anomalies in the lowerto mid-troposphere over the Arabian Sea as well as in the upper troposphere over the Iranian Plateau ( Figure S4d), which are similar to satellite and reanalysis data, but with a smaller magnitude (0.5 K). Due to the positive temperature anomalies, upward wind anomalies are simulated over the Arabian Sea ( Figure S4d), which are similar to the observed wind anomalies ( Figures S4b and S4c). However, no significant wind change is simulated over the Iranian Plateau, which is probably due to the underestimation of atmospheric heating effects by the model in this area. As dust aerosols become less absorptive, the positive temperature anomalies become weaker in ( Figure S3 shows the rainfall responses in India to dust aerosols over the Arabian Sea and the Arabian Peninsula, which is discussed in the part of "Sensitivity of Monsoon rainfall changes to dust IRI" in the main text. Figure S4. Spatial patterns of (a)-(c) rainfall differences (mm day −1 ) from three observations based on the same composite analysis method as in Figure 3 and (e)-(i) the WRF-Chem ensemble means of the total rainfall (i.e. sum of stratiform and convective rainfall) responses (mm day −1 ) to dust aerosols in 16 members averaged for JJA 2008. Rainfall responses are calculated by subtracting rainfall in the control experiment without dust from rainfall in the sensitivity experiments with dust at various dust IRI values. The black dots represent grid points that have a 90 % confidence level based on a one-sided Student's t-test. The figure was created using NCAR (the National Center for Atmospheric Research) Command Language (NCL) of version 6.2.1 (http://dx.doi.org/10.5065/D6WD3XH5).

Dust emission
Dust emission is calculated by the Goddard Chemistry Aerosol Radiation and Transport model following Eq. (1.1) (Ginoux et al., 2001).
In Eq. (1.2), ρ d ,i is the density of dust aerosols, g is the gravitational accelerate velocity, R d ,i is the averaged radius of dust aerosols, and ρ air is the density of the air. In Eq. (1.3), represents the influence of soil moisture on the threshold of wind speed for dust emission, where w is defined by the volumetric soil moisture over soil porosity.
The mass of dust emission is then summed up over the five bins to get the total dust emission. Then 93% of mass of the total dust emission is assigned to the coarse mode (i.e. M dust ,coarse in Eq. (2.1)), and the remaining 7% goes into the accumulation mode. The 93% and 7% of the total emitted dust mass is also converted to the number concentrations and assigned to the coarse ( N coarse ) and accumulation ( N acc ) modes, respectively, assuming the number mean size and standard deviation of 0.3 µm and 1.7 for the accumulation mode and 6.0 µm and 2.2 for the coarse mode. The Hatch-Choate conversion equation for mean size is used for this conversion between mass and number mean sizes.
i f (w) Table 1. The size dependent parameters used in the GOCCART dust emission schemes, including the mean radius, lower, and upper radius boundaries of dust aerosols, the density of dust aerosols, and the fraction of each size bin of dust in emission. based on aerosol dynamical processes, which includes emission, nucleation, condensation, coagulation, dry deposition, and wet deposition. The subscript " s " stands for the eight species in the mixture of aerosols, including sulfate, nitrate, ammonium, black carbon (BC), organic carbon (OC), dust, sea salt, and water; the subscript " m " stands for the three modal modes. The standard deviation of aerosol size σ m is currently assumed to be 1.7, 2.0, and 2.5 at Aitken, accumulation, and coarse modes, respectively. Note that OC includes nine aerosol species.
The number averaged radius ( ) of aerosols at a specific mode is estimated using Eq.
(2.2) and (2.3): where V m and ρ s are the volume of all aerosol species at a specific mode and the density of a specific aerosol species. Water is not included in the summation of Eq. (2.2), because the size bins are defined by aerosol dry radius.
Aerosol mass and number from modal distribution is divided into individual sections or bins before passed into the Mie calculation. Currently the model use the same eight size bins as default MOSAIC aerosol scheme. The lower and upper boundaries of dry-diameter of aerosols are listed in Table 2.

The conversion from modal to sectional representation
The conversion of aerosol size distribution from modal to sectional representation is conducted using the Q-function. Q x ( ) is the probability that a normal random variable will have a larger value by x standard deviation than the mean. Given a known lognormal distribution, the probability that a random variable falls between the lower boundary of radius, D low ,b , and the upper boundary of radius, D up,b , is calculated by Eq. (3.1). Based on the characteristic of the lognormal distribution that the shape of this distribution is the same for all moments. In other words, if the number distribution is lognormal, the surface and mass distribution is also lognormal. However, the mass mean/median radius is different from the number mean/median radius. The median sizes of various order moments can be determined from a known distribution using the Hatch-Choate equation (Eq. (3.2)). For mass distribution, the order, , equals three.
where The mass of a specific aerosol species at an individual size bin, M s ,b , is calculated following Eq. (3.4). The number of total aerosols at a specific size bin, N b , is determined by Eq. (3.5).
So far, the mass and number of aerosols has been converted from the modal distribution to the sectional distribution. Now we need to calculate the aerosol averaged radius and complex refractive indices at each size bin, which are input of the Mie calculation.

Mixing rules of aerosols and their effective refractive indices
Eq. (4.1) determines the volume of each aerosol species at a specific size bin, V s ,b . The wet and core radii, r wet ,b and r core ,b , of aerosols are calculated through Eq. (4.2)-(4.5).
where V wet ,b , V shell ,b , and V BC ,b are respectively volumes of all aerosol species, all aerosols species but BC, and BC.
Mie code is used to calculate the optical properties of aerosols. There are three assumptions of mixing rules of aerosols: volume averaging, Maxwell-Garnett, and shell-core. The volume averaging method assumes the internal-mixing of aerosol compositions, which averages the refractive indices of all aerosol species weighted by their volumes at each size bin.
The shell-core method assumes a core composed of BC, which is surrounded by a shell composed of all other aerosol compositions.
where f b is the volume fraction of the core to the whole aerosol particle.

Aerosol optical properties
The Mie code takes in aerosol number concentration ( N b ), radius ( r wet ,b and r core ,b ), and complex refractive indices ( ! n λ ,b or ! n λ ,shell ,b and ! n λ ,core ) at each wavelength and bin to calculate the aerosol extinction efficiency ( ε λ ), scattering efficiency (ϖ λ ), asymmetry parameter ( g λ ), and backscattering efficiency ( b λ ) of a single particle. Multiplying the optical efficiencies of single aerosol particle with aerosol number concentration at a specific size bin and then summing these multiplications over the eight bins gives the aerosol optical properties at a specific wavelength, as formulated by Eqs. (5.1)-(5.5).
where τ λ and Δz are respectively aerosol optical depth at a specific model layer and the depth of the this model layer. Finally, τ λ , ϖ λ , and g λ are passed to RRTMG shortwave and longwave radiation scheme to determine aerosol's direct effect.
The terms in the left-hand side of Eqs (5.1)-(5.5) represent aerosol optical properties at the wavelength of λ in each model box. The column-integrated aerosol optical properties are determined following Eqs (5.6) and (5.7). For SSA, which is assumed homogenous in each model layer, the column-integrated value is calculated by weighting the extinction coefficients 62 , σ i , in the entire atmospheric column to make them comparable to satellite and AERONET observations, as shown in Eq (5.6). For AOD, the column-integrated value is the summation of all τ λ in the entire atmospheric column, as shown in Eq (5.7).
where i is the aerosol optical properties at the i th model layer. For additional information about the representation of aerosol's direct effect in climate model, please refer to 63,64 .