Diurnal cycle of the dust instantaneous direct radiative forcing over the Arabian Peninsula

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Introduction
Mineral dust is an important and integral part of the Earth system. Dust aerosol perturbs radiation balance by changing optical properties of the atmosphere (Claquin Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | sensed and ground based aerosol optical depth (AOD, τ) measurements consistency (Yu et al., 2013). Osborne et al. (2011), Slingo et al. (2006), and Otto et al. (2007) have considered diurnal effects of dust. However, treatment of the surface optical properties was oversimplified (surface albedo was fixed). Jin et al. (2004) showed that measured broadband 5 ocean surface albedo (OSA) for a specific condition varies from about 0.04 at local noon to 0.3 when the sun is low. Li et al. (2006) considered several OSA parametrization schemes and pointed out that top of the atmosphere (TOA) reflected solar fluxes are biased by up to 20 W m −2 for simpler schemes. For the desert surface case, based on the Baseline Surface Radiation Network (BSRN) measurements at the Desert Rock 10 location, Roesch et al. (2004) showed that diurnal variation of the broadband albedo were confined to the 0.2 to 0.27 range. Surface albedo is also known to depend on the atmospheric conditions and on the ratio of direct and diffuse fluxes in particular. Increased surface diffuse flux tends to increase effective albedo during the local solar noon and decrease it when the sun is low (Lyapustin, 1999). Even though intrinsic vari- 15 ability of the surface albedo and impact of atmospheric conditions are believed to have a minor effect on climate energy balance, diurnal cycle of the surface albedo may be an important factor in determining the sign and improving the quantitative estimate of dust forcing. Daytime cycles of dust impact have also been studied using the observations from 20 the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) and Geostationary Earth Radiation Budget (GERB) instruments on Meteosat-9, by Ansell et al. (2014) and Banks et al. (2014). In each considered case (Geostationary Earth Radiation Budget Intercomparison of Longwave and Shortwave radiation campaign over North Africa during June 2007 and Fennec campaign in the central Sahara in June 2011, respec-25 tively) diurnal features reported were generally not due to diurnal cycle of the AOD itself, suggesting that the physics involved are playing a major role. The complexity of the mineral dust radiative effect is associated with several factors. Dust aerosol is optically active in both shortwave (SW) and longwave (LW)  It is one of the most absorbing aerosols after black carbon (Kinne et al., 2003). Its effect strongly depends on a number of parameters including dust particle size distribution and surface albedo, temperature, and water vapor mixing ratio, especially for the longwave case. Dust spatial, temporal, and microphysical patterns are known to vary depending on the location and source regions (Giles et al., 2012;Basart et al., 2009). 5 The current study aims at better quantification of the clear-sky mineral dust instantaneous direct radiative forcing (DRF) and its diurnal cycle over the Arabian Peninsula. This region is less studied and lacks in-situ observations, even though it represents one of the major sources of dust and occupies a significant part of the dust belt area. We pay close attention to the effects of the surface albedo, carefully define aerosol 10 characteristics, and study the the DRF diurnal cycle. In order to carry out numerical experiments, we developed a flexible framework for a standalone column Rapid Radiative Transfer Model (RRTM) and tested the model conducting radiation closure calculations using satellite and ground-based observations. The model description is given in Sect. 2. Numerical experiments were performed for King Abdullah University presented in Sect. 4. Mechanisms and parameters responsible for sensitivity of the diurnally resolved and daily mean DRF over the Arabian Peninsula are then discussed. We formulate conclusions in Sect. 5. monthly climatology derived from the Global Modeling Initiative (GMI) model monthly mean output. The GMI 3-D chemistry and transport model was integrated with meteorological fields from the Modern Era Retrospective-analysis for Research and Applications (MERRA) and includes full chemistry for both the troposphere and stratosphere (Strahan et al., 2011;Douglass et al., 1999). All calculations were performed on the 20 internal grid consisting of 37 vertical pressure levels. To avoid additional interpolation errors, boundaries were set up at constant ERA-Interim pressure levels. Corresponding heights were calculated from geopotential. All additional necessary variables were interpolated on this internal pressure grid. Introduction

Aerosols
The aerosol optical properties (extinction (λ), single scattering albedo ω(λ), and phase function p(λ)) are calculated for a given size distribution N(r) (van de Hulst, 1957) assuming the sphericity of particles using analytic Mie solution (Veihelmann et al., 2006). We assume that aerosol size distribution can be approximated by two log-5 normal modes (fine and coarse) with parameters r i and σ i (modal radius and SD of the radius for number distribution, respectively): where index i goes for coarse (c) and fine (f) modes, N i is a total number density of particles of a given mode, and r is a radius.

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Particles from the coarse and fine modes might have different refractive indices. We assume that aerosol is represented by one dominant type (dust, justified further). We assume that two modes are externally mixed, thus optical properties of the mixture could be obtained according to e.g., D'Almeida et al. (1991): where subscript m means mix aerosol and p i (λ), ω i (λ), i (λ) are calculated for each mode separately.
To define aerosol size distribution we use effective radius and SD of the fine and coarse modes from Aeronet inversion products (Dubovik and King, 2000). For a given mode, effective radius is related to the modal radius r i in the following way (Lacis and 5 Mishchenko, 1995): Aeronet provides column integrated values of AOD and, in order to define a plausible aerosol vertical profile, we collected Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO, Vaughan et al., 2004)  with uncertainty in the vertical profile have negligible impact in SW and are less than 1 Wm −2 in LW for about 0.1 AOD between considered profiles. According to CALIPSO, the ratio of the "not dust" and "dust" successful retrievals (screened) in the column between 0 and 5 km is 2.04 % . Hence, not surprisingly, dust is a dominant aerosol type over the Arabian Peninsula and therefore in calculations 5 we accounted only for dust. We used Balkanski et al. (2007) refractive indices (RIs) of the mineral dust internally mixed with 0.9, 1.5 and 2.7 % volume weighted hematite to calculate aerosol optical properties (referred to as B09, B15 and B27 respectively). Optical depths at 500 nm for each mode provided by the Aeronet Spectral Deconvolution Algorithm (SDA) were used to derive the total number of particles N i in Eq. (1) to 10 match the observed optical depth.

Surface optical properties
It is known that surface albedo is extremely important for calculation of the dust radiative effect (Houghton et al., 2001), as it defines bottom boundary conditions for the radiation transport in the atmospheric column. For each wavelength it is calculated as 15 a ratio of the reflected and incident surface radiation fluxes. However, surface albedo depends on several parameters and atmospheric conditions. Experimental and theoretical studies have shown its dependence on the solar zenith angle, ratio of the direct and diffuse fluxes and, in case of ocean surface, on wind speed (or surface roughness) and chlorophyll concentration (Lyapustin, 1999;Li et al., 2006;Jin et al., 2004). In this 20 section we discuss both land and ocean surface albedo.
The Moderate Resolution Imaging Spectroradiometer (MODIS) instrument aboard Terra and Aqua satellites views the entire Earth's surface every 1 to 2 days, acquiring data in 36 spectral bands. The MODIS multidate and multiangular remotely sensed surface reflectances are used to derive MODIS Bidirectional Reflectance Distribution 25 Function (BRDF)/Albedo product MCD43 based on the RossThickLiSparce-Reciprocal model (Shuai et al., 2008). The MCD43A1 product provides the parameters associated with this model sufficient to compute the black-sky (q bsa , direct radiation) and white-12310 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | sky (q wsa , diffuse radiation) albedos. Thus, in SW total albedo q can be obtained as a weighted sum: where λ is a wavelength, θ is a solar zenith angle, F dir and F dif are the direct and diffuse fluxes respectively.

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For ocean surface we adopted parametrization provided by Jin et al. (2004). In this case, SW total spectral albedo is a weighted sum of four components: where w is a wind speed, chl is a chlorophyll concentration, q dir s , q dif s , q dir w , and q dif w are 10 surface direct and diffuse and ocean volume direct and diffuse albedos, respectively. The effect of ocean foams (white caps) is also taken into account. Jin et al. (2004) show that their parametrization is in excellent quantitative and qualitative agreement with observations and correctly captures diurnal variations of the OSA. LW surface emissivity is mostly defined by the surface type. Over land it also de- 15 pends on the season and vegetation and is thus best observed from space. Daily land surface emissivities in LW were obtained by combining MODIS level 3 MOD11C1 and MYD11C1 products. LW emissivity for sea water was obtained from the Aster spectral library (Baldridge et al., 2009). This formulation of the surface albedo (both for land and ocean) introduces non-20 linearity in the radiation transport calculations, since surface albedo itself depends on F dir and F dif . Therefore, when calculating radiation transport in a given atmospheric column, an iterative approach was used to obtain the ratio r = F dif F dir (Li et al., 2006 During each iteration a new value of r is obtained and is used in the next step. The iterations continue until the convergence criteria |r i +1 −r i | < 35×10 −4 is satisfied, where i is the iteration number. Convergence criteria is chosen not to diminish the overall accuracy of the RRTM calculations. In order to facilitate the convergence, an initial guess value of r is chosen depending on the column optical depth.

3 Radiation closure
Observations over the Arabian Peninsula are scarce. Below we discuss the set of measurements that we were able to retrieve and employ in our study.

Ground observations
Since 1995 until 2003, the King Abdulaziz City for Science and Technology (KACST) and the National Renewable Energy Laboratory (NREL) have co-operated to establish a 12 station network of high quality radiation monitoring installations across the Kingdom of Saudi Arabia. The Solar Village site served as the Network Operations Center, calibration facility, and data retrieval and quality assessment center. One-and five-minute data are collected by a suite of instruments compatible with the BSRN 15 specifications, including upwelling and downwelling longwave and shortwave fluxes (Al-Abbadi et al., 2002).
In the scope of collaboration with the WHOI (Woods Hole Oceanographic Institution), a fully-instrumented shore-side tower was deployed at the KAUST campus in 2009 (Farrar et al., 2009) that routinely measures hourly average downward radiation 20 fluxes (data are available at: http://uop.whoi.edu/projects/KAUST/, last access: 17 January 2015). 15,2015 Diurnal cycle of the dust DRF over Arabian Peninsula

TOA observations
To test the simulated radiation fluxes at TOA we used satellite observations. Instantaneous footprint-level (20 km nominal spatial resolution) observed fluxes and cloud coverage were obtained from Clouds and the Earth's Radiant Energy System (CERES, Wielicki et al., 1996) Single Scanner Footprint TOA/Surface Fluxes and Clouds (SSF) 5 Level 2 Edition 3A product. Pixels from Aqua and Terra within 0.2 • distance were collected for comparison. These data were obtained from the NASA Langley Research Center Atmospheric Science Data Center. Additionally, we made use of the Geostationary Earth Radiation Budget High Resolution (GERB HR) product (available from 2004 onward) which provides continuous observations of the TOA outgoing fluxes available 10 every 15 min and which we re-gridded to 0.25 • spatial resolution (Harries et al., 2005;Dewitte et al., 2008). We also made a detailed comparison with the retrievals of SW and LW radiative forcing derived from GERB measurements, which are described in detail by Ansell et al. (2014) and investigated further by Banks et al. (2014). To empirically derive DRF one has to define the "pristine-sky" fluxes as a reference characteristic. In 15 the SW, pristine-sky surface albedo is derived from a regression of measured planetary albedo against SEVIRI AOD (Brindley and Russell, 2009) within a 0.25 • grid cell. The SW dust radiative effect is then calculated by multiplying this pristine-sky albedo by the incoming downwelling SW flux, and subtracting the measured TOA flux. Meanwhile in the LW, the pristine-sky TOA LW flux is derived for each timeslot using a 28 day rolling 20 reference window which also seeks to account for variations in atmospheric humidity and surface temperature (Brindley, 2007). As with the SW, the measured TOA LW flux is then subtracted from this pristine-sky LW flux.

Results
In this section we discuss clear-sky radiative transfer calculations conducted for dif-25 ferent locations over the Arabian Peninsula and the sensitivity studies. In each case ACPD 15,2015 Diurnal cycle of the dust DRF over Arabian Peninsula mineral dust DRF is calculated as a difference between perturbed (P) and control (C) experiments, where P experiments account for dust aerosol and C experiments do not. Both C and P experiment calculations are carried out using the same meteorology and atmospheric composition.

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In this section we conduct calculations for two specific locations: in the central Arabian desert at Solar Village and in the semi-desert area at the coastal plain of KAUST campus.
The first case study focuses on the 9-12 August 2002 DRF during fair-weather AOD conditions, based on Aeronet measurements at the Solar Village site established in 10 1999. For this case measurements of both the surface incident and reflected shortwave fluxes are available. They were used to estimate broadband surface albedo and compare it with the one derived from the model runs based on the MODIS BRDF/Albedo product. Description of the experiments and corresponding abbreviations are provided in Table 1. The first set of perturbed and control experiments (denoted as P and C, 15 respectively) uses surface temperature approximated from observations of the surface upwelling LW fluxes and the Stefan-Bolzmann law. The second set of experiments (denoted as PE and CE) follows a default setup (Sect. 2.2) and is based on surface temperature derived from ERA-Interim product. The third set of experiments (denoted as PA and CA) is identical to the first set, but does not model LW scattering and uses 20 absorption optical depth instead of extinction optical depth to exclude scattering effects.
The second case study deals with a major dust outbreak that occurred over the Arabian Peninsula during March 2012. The storm was observed by Aeronet at the KAUST campus site established in February 2012. The storm front first arrived on 18 March, causing strong AOD growth up to τ(0.5 µm) ∼ 1.6. Maximum value τ(0.5 µm) ∼  15,2015  Aeronet observations, simulations are only performed during the daytime at the exact time of each measurement. Fluxes from satellite retrieval products, ground-based observations and the model used in this study span different spectral ranges as summarized in Table 2. The broadband fluxes are integrated over wavelengths and are not very sensitive to the exact 5 position of the band's interfaces, as the interfaces are chosen to be in the regions of small intensities of the solar and terrestrial radiation (van de Hulst, 1957). However, cut off at 50 microns in LW may introduce positive bias up to about 14 W m −2 when RRTM fluxes are compared to ground based observations. In order to quantitatively compare time series of computed and observed quantities 10 (y c and y o ) we define the absolute error (root-mean-square error, RMSE) given by where N is the number of elements in the time series, deviation at a given time e i = y Similarly, relative error (RMSE r ) is given by:

Solar Village
This case study is characterized by naturally cloud free conditions and relatively low column AOD shown in Fig. 2. We were able to achieve good agreement with the SW downwelling surface direct fluxes shown in Fig. 2 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | sphericity assumption and/or underestimating number of large particles by Aeronet, Müller et al., 2010;McConnell et al., 2008) then in observations as indicated by the positively biased diffuse flux (RMSE a is 37 W m −2 and RMSE r is 20 %). As a result, total albedo q (Eq. 6) shifts more towards the q wsa . Nevertheless, taking into account that diffuse flux in the perturbed experiment is on average 3.5 times bigger then in 5 the control (not shown here), this bias has minor impact on effective albedo (Eq. 6). Abrupt "triangular-like" shape of the computed LW fluxes is due to linear interpolation of the 6 h meteorological data. In LW RMSE reaches 17 W m −2 , given the instrument uncertainty of ±10 W m −2 and RMSE r is 4.1 %. Bias due to difference in the RRTM and instrument spectral range contributes up 14 W m −2 to the error and discrepancies in 10 meteorological profiles have only minor impact. Figure 3 shows diurnal variations of the broadband surface albedo derived from BSRN measurements and calculated in the perturbed experiment. Since observations are attributed to a point location and the numerical experiment is based on the MODIS BRDF product attributed to a 500 m pixel, exact quantitative comparison with measure-15 ments is somewhat hindered. Nevertheless, MODIS BRDF parameters are adequate and qualitatively capture a strong diurnal cycle of the surface albedo up to solar zenith angles of about 75 • .
Due to positive bias in the surface downwelling flux (mostly due to diffuse components, Fig. 2) and in the surface albedo (Fig. 3), computed surface upwelling SW fluxes 20 shown in Fig. 4  Summary, available at: https://eosweb.larc.nasa.gov/project/ceres/quality_summaries/ CER_SSF_Terra_Edition3A.pdf, last access: 17 January 2015). Comparison of the TOA fluxes completes the radiation closure. Given a good agreement (with uncertainties close to instrumental) of the surface (downwelling and upwelling) and TOA (upwelling) fluxes and thus fairly accurate radia-10 tion closure, we focus on calculating the mineral dust radiative forcings. We first define total downward minus upward flux as: where F ↓ and F ↑ are the downward and upward fluxes, respectively. Thus, following the convention, the instantaneous forcing ∆F (either TOA or BOA) is defined as difference 15 of total downward minus upward fluxes in the P and C experiments: and atmospheric absorption ∆F A due to dust aerosol is then defined as a difference between TOA and BOA forcings: 20 The positive value of the radiative forcing ∆F TOA , ∆F BOA , ∆F A means heating of the atmospheric column, underlying surface or atmosphere respectively. Figure 6

KAUST campus
The time span of the numerical experiments for the KAUST case consists of several days of fair-weather AOD followed by the major dust outbreak that occurred over the 15 Arabian Peninsula on 18-20 March 2012 and several days of recovery. Figure 7 shows the impact of this dust event on the surface downwelling fluxes. vations since calculations are done for clear-sky conditions. Presence of clouds implies higher column optical depth than assumed in the model and thus observed SW downwelling fluxes are smaller than computed, which is consistent with the results shown on the top panel in Fig. 7. For this case study, GERB cloud-screened SW and LW TOA DRF are available 5 for comparison and are shown in Fig. 9. According to Ansell et al. (2014)

Diurnal cycle of SW DRF
In this section we focus on the sensitivity of the SW DRF diurnal cycle at the TOA and BOA and atmospheric absorption by aerosol, i.e. ∆F TOA , ∆F BOA and ∆F A , with respect to several parameters that span the range of values representative for the Arabian Peninsula. Specifically, we consider dependence on solar zenith angle θ and 20 sensitivity to the total column AOD τ, aerosol size distribution dN dr , aerosol refractive index RI and surface albedo q: While the middle Arabian Peninsula is extremely arid, coastal areas receive more precipitation, have more vegetation and are less reflective. The Red Sea reflects relatively ACPD 15,2015 Diurnal cycle of the dust DRF over Arabian Peninsula Unlike the Solar Village and KAUST case studies, in this section we conduct sensitivity analysis to model parameters rather then considering a specific time period. Size distribution statistics are derived from Aeronet Level 2.0 inversion product as a function of total column AOD over the Arabian Peninsula (Fig. 10). For fair-weather conditions, fine and coarse modes AOD are comparable to each other. For more severe events, coarse mode AOD contribution dominates and scales as 5 to 1 relative to the fine 15 mode. In terms of microphysical properties, scaling of the coarse mode AOD is accompanied by the shift towards larger radii and narrowing of the size distribution. Fine mode size distribution scaling is characterized by growth of their standart deviation σ. The same analysis for northern Africa shows similar scaling patterns of the aerosol size distribution and AOD. 20 Obtained statistics were fitted as a function of total column AOD covering the range from 0 to 3 as shown in Fig. 10. These scaling regimes were used in Eq. (1) to build the aerosol size distribution and calculate optical properties of dust aerosol.
In order to estimate the diurnal cycle of AOD we use AOD statistics derived from Aeronet AOT Level 2.0 product. Figure 11 shows the diurnal cycle of the AOD prob-25 ability density function (pdf) at KAUST and Solar Village. For each station pdf was computed by collecting AOD observations into AOD bins with 0.05 stepping at 30 min intervals, which then were normalized so that the integral of the pdf from zero to positive infinity is equal to 1 in a particular time slot. Figure 11 shows that AOD diurnal cycle at both locations is rather uniform with relatively weak tendency for higher AOD values in the morning and late afternoon. Banks et al. (2014) also reported low variability of the daytime cycle in mean SEVIRI and Aeronet AOD over the Bordj Badji Mokhtar site in the central Sahara.
We discuss below the sensitivity of the TOA SW DRF diurnal cycle computed for 5 different RIs, surface albedos, and AODs. In Fig. 12  ing local noon to exhibiting a symmetrical weakening around local noon. The contrast between peak forcing and this localised reductions (min-max-min structure, MMM) becomes more exacerbated with increased aerosol absorption and surface albedo, such that the maximum difference in forcing between morning/evening and local noon is seen for the most absorbing aerosol over the desert surface (bottom right panel). For 15 this case the sign of the forcing switches from negative to positive and then again to negative through the course of the day, indicating a SW cooling-heating-cooling of the Earth-atmosphere system. These results are consistent with those derived observationally by Ansell et al. (2014) and Banks et al. (2014) over northern Africa. Additionally, Fig. 12 shows that daily mean TOA DRF is not a linear function of the total AOD (red 20 line) and efficiency ( ∆F TOA τ ) of the daily mean forcing as a function total AOD declines faster over more reflective surfaces and for more absorbing aerosols.

Process analysis
SW TOA DRF shown in Fig. 12 has nontrivial shape and strong diurnal cycle. In order to qualitatively explain the mechanisms responsible for forming this shape and under- 25 stand the interplay of different factors, we consider a few special cases. We assume now that the surface albedo do not change during the daytime. We use the same ex-Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | periment setups presented in Sect. 4.2 but manually override certain parameters and assume that total column AOD is equal to 0.5. To demonstrate dependence on the surface albedo we consider black surface (q = 0 for all wavelengths), desert (measured during the B300 flight over Mauritania, Johnson and Osborne, 2011) and white surface (q = 1 for all wavelengths) albedo. To demonstrate dependence on aerosol absorp-5 tion and anisotropic scattering we consider absorbing (ω = ω * , same as in Sect. 4.2) and non-absorbing (ω = 1 for all wavelengths) dust, isotropic (g = 0 for all wavelengths, where g is a asymmetry parameter) and anisotropic (g = g * , same as in Sect. 4.2) scattering by aerosol (see Fig. 13). This approach allows us to extract the impact of each parameter on the DRF diurnal cycle. Let us consider first black body surface albedo 10 and non-absorbing dust (black curves in two left columns in Fig. 13). In this case surface does not reflect and TOA upward flux is only due to reflected radiation by the dust layer (F reflected dust ) and atmospheric Rayleigh scattering. Neglecting small changes in the atmospheric absorption, TOA DRF is almost equal to BOA DRF. F reflected dust does not depend on surface albedo. However, it does depend on the aerosol scattering phase 15 function. Due to dust anisotropic scattering, TOA, and thus BOA DRF in this case, have diurnal variation with MMM structure shown in the second column of Fig. 13. On the other hand, in the isotropic case (g = 0) both TOA and BOA DRF follow a simple diurnal cycle with one minimum at noon (left column in Fig. 13).
For the white body surface albedo case (blue curves), ∆F BOA is equal to zero. ∆F A 20 equals ∆F TOA and both are small. Due to smaller surface reflected flux, for any intermediate albedo case (including the real-case desert albedo, red curves) ∆F TOA is bounded by the black and white body albedo cases and the diurnal variation persists. In all cases ∆F A is small. To conclude the discussion of the non-absorbing aerosol case, we emphasize that both TOA and BOA DRF are strictly non-positive (if we neglect the 25 small changes in atmospheric absorption) over any surface and MMM structures are due to anisotropic scattering by dust. If we turn on the aerosol absorption (right two columns in Fig. 13) 20 In the previous section we considered SW DRF dependence on the parameters that do not have a diurnal cycle. In this section we quantify the effect of the albedo diurnal cycle on the SW TOA DRF. Airplane observations of the albedo usually are done at nadir. So, we define the reference albedo for the solar zenith angle at local noon, i.e.

Effect of the surface albedo
q fixed (r) = q(θ noon , r) The difference δF of the forcings calculated with the varying albedo q and the fixed albedo q fixed is a function of the solar zenith angle, optical depth and albedo: δF = ∆F (θ, τ, q(θ, r)) − ∆F (θ, τ, q(θ = θ noon , r)) (15) both at BOA and TOA. Figure 14 shows corresponding broadband albedo diurnal cycles at the desert, coastal plain, and ocean obtained from our numerical experiments. 5 Albedo in Fig. 14 is averaged over the range of optical depths (from 0 to 3) for a given refractive index (Balkanski 1.5 %). During the local solar noon q and q fixed coincide exactly (by construction), but they deviate as the solar zenith angle grows. Changes in the q fixed are solely due to variations of diffuse-to-direct flux ratio r. Figure 15 shows corresponding contribution to the SW TOA DRF associated with diurnal cycle of q compared to q fixed . Since surfaces tend to be more reflective with increasing solar zenith angle, δF is positive and causes a warming effect. The strongest effect is reached during the morning and evening hours and thus albedo diurnal cycle decreases the diurnal variability of the SW TOA DRF. The effect quickly saturates when AOD reaches 1. It is strongest over the ocean (up to 29 W m −2 ), weakening over desert (up to 24 W m −2 ) 15 and is smallest for the coastal plain (up to 11 W m −2 ).

Daily DRF sensitivity
In this section we focus on the daily mean dust DRF, discuss the contribution of the SW, LW and NET (SW plus LW) effects and their sensitivity to the surface albedo, and aerosol absorption efficiency. Similarly to Sect. 4.2.1, in calculations we use 0.5 20 as a reference column AOD at 674 nm. Figure 16 shows daily mean ∆F TOA , ∆F BOA and ∆F A for B09, B15 and B27 RI and for the ocean, coastal plain and desert surface albedos. In this figure surface albedo grows from left to right columns and inside each column aerosol absorption also grows from left to right. For all RIs and surface albedos dust causes the SW cooling of the atmospheric column (negative TOA DRF) and of the LW the sign of the forcings is opposite. In LW aerosol warms both the surface and the entire atmospheric column, but cools the atmosphere itself. Reduced variability of the LW DRF compared to SW DRF is a consequence of much smaller changes of the aerosol absorption and surface albedo or emissivity in LW than in SW. At BOA the LW forcing is weaker then SW forcing. At TOA SW cooling dominates LW warming of the 5 atmospheric column except the case for strongly absorbing B27 over the desert, where the NET forcing is positive. NET atmospheric absorption changes the sign between B09 and B15 refractive indices from negative to positive. Figure 16 also shows that SW BOA DRF is more sensitive to increasing absorption by dust than SW TOA DRF, as was discussed in Sect. 4.2.1. 10

Conclusions
A column radiation transport model was used to investigate dust instantaneous direct radiative forcing over the Arabian Peninsula for a range of optical depths covering fair-weather and dust storm conditions. According to CALIPSO product, dust is a dominant aerosol in this area. We calculated the forcing of the dust aerosol over ocean, 15 coastal plain and desert surfaces using a range of plausible refractive indices suggested by Balkanski et al. (2007) and were able to achieve good agreement of the surface and TOA fluxes with in-situ measurements and satellite retrievals. reported by Osborne et al. (2011) for the comparable AOD during June 2007 over land areas between Mauritania and Niger. The KAUST campus case during the dust storm conditions is characterized by a stronger cooling of atmospheric column due to lower surface albedo. Distinct diurnal cycle of the TOA DRFs is also present. Compiling aerosol statistics using Aeronet data, we found similar scaling patterns 5 between the Arabian Peninsula and North Africa. In particular, coarse and fine mode AODs at 674 nm on average scale as 5 to 1. Thus, similar to the measurements in Sahara during the ACE-2 campaign 1997 of Otto et al. (2007), coarse mode has a prevailing contribution to the total optical properties of the dust aerosol over the Arabian Peninsula. We found that SW TOA DRF, as a function of the solar zenith angle, has 10 three distinctive extrema structures and could be positive at small zenith angles. The forcing remains strictly negative over the ocean surface for the entire day. The diurnal variations are more prominent over the more reflective surfaces and, for the strongly absorbing dust B27 case, dust aerosol causes the warming of the atmospheric column over the desert during the local solar noon.
Process analysis for black and white surface albedo, non-absorbing dust, and isotropic scattering revealed that dust anisotropic scattering controls the diurnal variability of the SW BOA and TOA DRF. This emphasizes the importance of the assumptions about particle shape and thus the the phase function to correctly capture the maximum and minimum of the SW TOA DRF diurnal cycle. Due to prevailing forward 20 scattering by dust aerosol, BOA DRF is more sensitive to changes in single scattering albedo or absorption by dust, than TOA DRF. This also implies, that diurnal variations of the TOA DRF are less sensitive to changes in atmospheric absorption by dust then BOA DRF.
Daily mean dust DRF over the Arabian Peninsula for a 0.5 AOD at 674 nm showed 25 that in all considered cases dust causes cooling of the atmospheric column, while over the desert surface albedo and Balkanski 2.7 % refractive index case the effect is the opposite. For all considered surface albedo types, net atmospheric absorption due to dust changes the sign between Balkanski B09 and 1.5 % refractive indices. Several sources of the dust forcing uncertainty are currently known, which include refractive index, number size distribution and surface albedo. The treatment of the surface albedo is often oversimplified and albedo itself is assumed to be fixed. We found that intrinsic variability of the surface albedo and its dependence on the atmospheric conditions are important factors to be taken into account, especially for the desert sur-5 faces, where daily mean TOA DRF is close to zero.

ACPD
The main results could be formulated as follows: -Dust is a major aerosol over the Arabian Peninsula and its coarse mode mostly contributes to the total column AOD compared to fine mode.
-The developed model allows to carry out relatively accurate radiation closure.

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-The calculated fluxes are in a good agreement with best available observations.
-Dust DRF is estimated and compares well to the independently derived satellite values.
-Dust TOA DRF has strong diurnal cycle over desert, but three extrema structures are present over any surface.

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-Anisotropic scattering by dust significantly contributes to the diurnal cycle of the SW TOA and BOA DRF.
-Diurnal intrinsic variability of the surface albedo has a strong impact on the dust DRF diurnal cycle. Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Krishnamurthy, A., Moore, J. K., Mahowald, N., Luo, C., and Zender, C. S.: Impacts of atmospheric nutrient inputs on marine biogeochemistry, J. Geophys. Res.-Biogeo., 115, G01006, doi:10.1029/2009JG001115, 2010 Climate forcing, climate sensetivity, and climate response: a radiative modeling perspective on atmospheric aerosols, in: Aerosol Forcing of Climate, 5 Wiley, 1995. 12309 Levin, Z., Ganor, E., and Gladstein, V.: The effects of desert particles coated with sulfate on rain formation in the eastern Mediterranean, J. Appl. Meteorol., 35, 1511Meteorol., 35, -1523Meteorol., 35, , 1996. 12302 Li, J., Scinocca, J., Lazare, M., McFarlane, N., Von Salzen, K., and Solheim, L.: Ocean surface albedo and its impact on radiation balance in climate models, J. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | and Washington, R.: Optical properties of Saharan dust aerosol and contribution from the coarse mode as measured during the Fennec 2011 aircraft campaign, Atmos. Chem. Phys., 13, 303-325, doi:10.5194/acp-13-303-2013, 2013. 12303 Shao, Y., Ishizuka, M., Mikami, M., andLeys, J Hatching indicates the ∆F BOA edge and thus the opposite edge is ∆F TOA . The height of the bar corresponds to the absolute value of the atmospheric absorption due to dust or |∆F A | and color indicates the sign of the ∆F A (blue for negative or cooling, red for positive or warming). LW, SW values and their sum are shown in the top, bottom and the middle rows respectively. Total column AOD used in calculations is 0.5 at 674 nm.