We developed a multilayered physical snowpack model named Snow Metamorphism and Albedo Process (SMAP), which is intended to be incorporated into general circulation models for climate simulations. To simulate realistic physical states of snowpack, SMAP incorporates a state-of-the-art physically based snow albedo model, which calculates snow albedo and solar heating profile in snowpack considering effects of snow grain size and snow impurities explicitly. We evaluated the performance of SMAP with meteorological and snow impurities (black carbon and dust) input data measured at Sapporo, Japan during two winters: 2007–2008 and 2008–2009, and found SMAP successfully reproduced all observed variations of physical properties of snowpack for both winters. We have thus confirmed that SMAP is suitable for climate simulations. With SMAP, we also investigated the effects of snow impurities on snowmelt at Sapporo during the two winters. We found that snowpack durations at Sapporo were shortened by 19 days during the 2007–2008 winter and by 16 days during the 2008–2009 winter due to radiative forcings caused by snow impurities. The estimated radiative forcings due to snow impurities during the accumulation periods were 3.7 W/m2 (it corresponds to albedo reduction in 0.05) and 3.2 W/m2 (albedo reduction in 0.05) for the 2007–2008 and 2008–2009 winters, respectively. While during the ablation periods they were 25.9 W/m2 (albedo reduction in 0.18) and 21.0 W/m2 (albedo reduction in 0.17) for each winter, respectively.
 Snow cover affects terrestrial climate system through its high albedo, thermal insulating properties (low thermal conductivity), and the ability to change phase [Armstrong and Brun, 2008]. The retreat of snow cover induced by global warming causes a positive feedback known as snow albedo feedback [e.g., Budyko, 1969; Sellers, 1969; Hall, 2004; Qu and Hall, 2007], wherein the albedo decrease from snow covered surface to snow free surface enhances warming. The feedback process accelerates melting of snow and ice. The low thermal conductivity of snow obstructs energy exchanges between the ground and the atmosphere. The ability of snow to change its phases makes itself to play a role in retarding warming of both the ground and the atmosphere during ablation period because large amount of energy is required to melt ice.
 Light-absorbing impurities such as black carbon (BC) and dust in snow and ice have recently been recognized as possible contributors to global warming because they generally reduce snow and ice albedos.Hansen and Nazarenko estimated that BC on snow and ice contributed about one-quarter of observed global warming during 1880–2000.Flanner et al.  showed that BC in snowpack can provoke a disproportionately large springtime climate response because the forcing tends to coincide with the onset of snowmelt and results in the triggering of more rapid snowmelting and snow albedo feedback. Painter et al.  demonstrated that snow cover duration in a seasonally snow covered mountain range (San Juan Mountains, Colorado, USA) was shortened by 18 to 35 days during ablation periods in 2005 and 2006 as a result of surface shortwave radiative forcing caused by deposition of disturbed desert dust (17–37 W/m2 in 2005 and 39–59 W/m2 in 2006) using the snow energy balance model SNOBAL [Marks et al., 1998], which uses a two-layer snowmelt approach with an active 25 cm surface layer and the reminder of the snowpack as a second layer.
 Recently several authors have developed physically based snow albedo models for LSMs to improve the accuracy of GCM climate simulations [Flanner and Zender, 2005; Gardner and Sharp, 2010; Yasunari et al., 2011; Aoki et al., 2011]. Flanner and Zender developed a two-stream, multilayer, Snow, Ice, and Aerosol Radiation (SNICAR) model to calculate snow albedo and solar heating profile in snowpack.Gardner and Sharp  developed a computationally simple, theoretically based parameterization for the broadband albedo of snow and ice. Their parameterization depends on the specific surface area (SSA) of snow or ice, BC concentration, solar zenith angle, cloud optical thickness, and snow depth. Kuipers Munneke et al.  implemented this parameterization into a regional climate model for Antarctica and improved the model performance. Yasunari et al.  developed a snow albedo model that was a function of snow impurity, solar zenith angle, and SSA. Incorporation of the model into their LSM led to an improvement of snow depth estimates. Aoki et al. developed a physically based snow albedo model (PBSAM) to calculate snow albedo and solar heating profile in snowpack. In PBSAM factors that affect snow albedo are explicitly taken into account by using a look-up table calculated with a spectrally detailed radiative transfer model for the atmosphere-snow system [Aoki et al., 1999, 2000, 2003]. PBSAM takes into consideration the spectral distribution of the shortwave radiant flux in snowpack by dividing the broadband into several spectral sub-bands.
 These considerations motivated us to develop a multilayered physical snowpack model for climate studies. The model, named Snow Metamorphism and Albedo Process (SMAP), incorporates PBSAM and is able to bring out PBSAM's potential accuracy in LSMs. In the SMAP model, PBSAM [Aoki et al., 2011] calculates snow albedo and solar heating profile in snowpack with profiles of snow grain size and snow water equivalent (SWE) calculated in SMAP, together with snow impurities externally given from in situ measurements or host GCMs. SMAP also introduces processes of energy and mass balance in snowpack, snow settlement, phase changes, water percolation, and snow metamorphism.
 The purposes of this paper are to describe the processes that SMAP simulates, to validate the predictions of the model with observations, and to demonstrate the availability of SMAP for climate studies. The model validation utilizes in situ data from the two winters of 2007–2008 and 2008–2009 at Sapporo, Japan. The simulated parameters compared with observations are snow depth, column-integrated SWE, Column-average snow density, snow grain shape profiles, snow surface temperature, snow grain size in the top 2 cm, and broadband albedos. Because we employed the same data asAoki et al. , we were able to determine whether SMAP could exploit PBSAM's potential by comparing the accuracy of simulated broadband albedos with their results. The comparison was informative because they calculated broadband albedos with measured (1) vertical profiles of snow grain size, (2) mass concentrations of snow impurities, and (3) SWE, whereas SMAP simulates the first and third of these parameters. Finally, we demonstrated the application of SMAP to climate studies by investigating the effects of snow impurities on snowmelt at Sapporo by carrying out a simulated “pure snow experiment” wherein no snow impurities were assumed. We presented the effects in terms of changes in snowpack durations, radiative forcings, and albedo reductions due to snow impurities. In general, qualities and quantities of snow impurities differ from place to place. It in turn implies that their impacts on reducing broadband albedos also vary by location. Thus it is worth employing SMAP to assess snow impurity effects on snowmelt at Sapporo, where climate conditions and snow impurity types are different from other places investigated by the previous works [e.g., Painter et al., 2007].
2. Model Description
 SMAP is a one-dimensional multilayered snowpack model for calculating the temporal evolution of the physical characteristics of snow. SMAP models snowpack as an accumulation of snow layers composed of ice, water, and moist air. Some unique input parameters are required in addition to the meteorological parameters ordinarily required as input by other snowpack models [e.g.,Langlois et al., 2009] (Table 1). The unique parameters are the mass concentrations of snow impurities, the downward ultraviolet (UV)-visible (wavelengthλ = 0.2–0.7 μm) and near-infrared (λ = 0.7–3.0 μm) radiant fluxes, and their diffuse fractions. These parameters are used in the PBSAM component of SMAP. When the downward UV-visible and near-infrared radiant fluxes, and their diffuse fractions are not available, SMAP calculates them from the downward shortwave (λ = 0.2–3.0 μm) radiant flux, which is necessary in this case, following a scheme by Goudriaan  as functions of cloud fraction and solar zenith angle. In this option SMAP calculates cloud fraction following the approach by van den Broeke et al. [2004, 2006]as functions of internally calculated net longwave radiant fluxes at the snow surface and air temperature. The model calculates all snow physical parameters relevant to snow-atmosphere interactions such as broadband albedos, snow surface temperature, and energy fluxes at the snow surface (Table 2). SMAP calculates broadband albedos in the UV-visible, near-infrared, and shortwave spectra. SMAP also calculates internal physical parameters of snowpack such as snow temperature, snow density, snow grain size, and snow grain shape.
Table 1. Input Parameters of SMAP
Downward shortwave radiant flux is possible, alternatively.
Downward UV-visible and near-infrared radiant fluxesa
Diffuse components of UV-visible and near-infrared radiant fluxesa
Downward longwave radiant flux
Ground heat flux
Mass concentrations of snow impurities (BCb and dust)
Table 2. Representative Output Parameters of SMAP
Snow surface temperature
Net shortwave radiant flux
Net longwave radiant flux
Sensible heat flux
Latent heat flux
Energy exchange due to rainfall
Conductive heat flux
Snow temperature (in each layer)
Snow density (in each layer)
Snow water equivalent (in each layer, and column-integrated)
Liquid water content (in each layer, and column-integrated)
Bottom runoff rate
Snow grain size (in each layer)
Sphericity (in each layer)
Dendricity (in each layer)
Snow grain shape (in each layer)
 The following sections describe the physical processes and numerical solutions used in SMAP (Table 3). Further attempts will be needed to optimize SMAP for LSMs. For example, computational costs can be reduced by neglecting some processes that have little effect on snow-atmosphere interactions [Loth and Graf, 1998; Armstrong and Brun, 2008]. However, such optimization is beyond the scope of this paper.
 We assume that total heat and radiant energy are conserved within snowpack and are exchanged at both the snow surface and bottom of the snowpack. In snowpack the zcoordinate is taken to be positive in a downward direction from the snow surface. SMAP formulates energy conservation in snowpack by using a one-dimensional diffusion equation that takes solar heating in snowpack and melt-freeze cycles into account:
where cs is the specific heat capacity of snow at constant pressure, ρs is snow density, Ts is snow temperature, t is time, keff is the effective thermal conductivity of snow, Snet is the net shortwave radiant flux in snowpack, Lf is the latent heat of fusion, and Rmr is the difference between the melting and refreezing rates. Here ρs is defined as
where ρi, ρw and ρa are the densities of ice, water, and air, respectively, and θi, θw, and θa are the volumetric fractions of ice, water, and air, respectively. Again cs is defined as
where ci, cw and ca are the specific heat capacities of ice, water, and air, respectively.
 The integral of equation (1) determines the temporal evolution of Ts following specification of its initial value, which is the temperature for new snow or surface hoar. We assume the initial temperature to equal the ground wet bulb temperature Tw when snowfall occurred. In this numerical procedure (see section 2.5), we prescribe Neumann boundary conditions both at the snow surface and the bottom of snowpack. At the snow surface the condition is written as
where Lnet, HS, HL, and HR are the net longwave radiant flux, sensible heat flux, latent heat flux, and energy exchange due to rainfall, respectively, at the snow surface. At the bottom of snowpack the condition is
where HG is the ground heat flux. Energy fluxes such as Snet, Lnet, HS, HL, HP, and HG are defined to be positive when they are directed downward. We calculate keff (W/mK) with a simple parameterization as a function of ρs (kg/m3) [Devaux, 1933]:
 We calculate the divergence of the net shortwave radiant flux ∂Snet/∂z and snow albedo in the shortwave spectrum α with PBSAM [Aoki et al., 2011]. The input snow parameters for PBSAM are vertical profiles of snow grain size, mass concentrations of snow impurities, and SWE. The input parameters needed to calculate solar illumination conditions for PBSAM are the solar zenith angle, downward radiant fluxes in the UV-visible and near-infrared bands, their diffuse fractions, and the underlying surface albedos. The relationship between ∂Snet/∂z and the downward shortwave radiant flux S↓ is written as follows:
where D is snow depth, and S↓ is taken directly from input data. According to Aoki et al. , one UV-visible subband and three near-infrared subbands are necessary in PBSAM to obtain accurate estimates of broadband albedos. In addition, they showed that the accuracy of broadband albedos obtained with three or more subbands in both the UV-visible and near-infrared bands is almost the same when the number of model snow layers is fixed. They also demonstrated that more than three subbands in both the UV-visible and near-infrared bands were necessary to obtain a sufficiently accurate solar heating profile in snowpack. In the present paper we employed four UV-visible subbands (λ = 0.200–0.475, 0.475–0.550, 0.550–0.625, and 0.625–0.700 μm) and for near-infrared subbands (λ = 0.700–0.950, 0.950–1.125, 1.125–1.400, and 1.400–3.000 μm), respectively, as explained in section 2.5.
 SMAP equates the net longwave radiant flux Lnetto the difference between the downward longwave radiant flux determined from input data and the upward longwave radiant flux calculated by using the Stefan-Boltzmann law with snow surface temperatureTs0, together with a snow surface emissivity of 0.98 [Armstrong and Brun, 2008].
 SMAP calculates both the sensible heat flux HS and latent heat flux HL at the snow surface by the bulk method, which utilizes values of wind speed at a measurement height and differences in potential temperature and specific humidity between a measurement height and the snow surface. These two turbulent fluxes are expressed by
where cpa is the specific heat capacity of air at constant pressure, Lv is the latent heat of sublimation or evaporation, κ is von Kármán constant, u is ground wind speed, Θ and Θs0 are potential temperature at the ground and the snow surface, respectively, q and qs0 are specific humidity at the ground and the snow surface, respectively, ΨM and ΨH are profile functions for momentum and heat, respectively, zref is a measurement height above the snow surface, z0, zH, and zQ are roughness lengths for momentum, heat, and moisture, respectively, and L is Obukhov length. SMAP calculates Θs0 and qs0 directly from Ts0 by using the assumption that the snow surface is saturated.
 To obtain these turbulent heat fluxes, SMAP first calculates the bulk Richardson number Ri, which is a measure of stability conditions in the atmospheric boundary layer, as follows:
SMAP calculates roughness lengths for heat and moisture (zH and zQ) according to Andreas :
where R* is the roughness Reynolds number. The choice of profile functions (ΨM, ΨH) depends on stability conditions in the atmospheric boundary layer. When the atmosphere is stable, SMAP assumes that ΨM = ΨH and calculates the profile functions according to Holtslag and De Bruin :
When the atmosphere is unstable, SMAP carries out the calculations with functions determined by Paulson :
where x is defined as
In general, z0 for the snow surface is of the order of 10−4 to 10−3 m depending on the condition of the snow surface. In this study, we treat z0 as a constant parameter equal to 2.3 × 10−4 m, which is the value obtained by Kondo and Yamazawa  for seasonal snow.
 Finally, HR is written as
where cpw is the specific heat capacity of water at constant pressure, Rr is rainfall rate, and we assume that the rain temperature equals Tw [Loth et al., 1993].
2.2. Mass Balance of Snowpack
 SMAP expresses the mass of the snowpack in terms of water equivalent. Snowfall, rainfall, and surface hoar add to the mass of the snowpack. Surface sublimation and liquid water runoff at the bottom of the snowpack decrease the mass of the snowpack. The mass balance is formulated as follows:
where Min,p is the precipitation (snowfall and rainfall) rate, Min,sh is the surface hoar rate, Mout,r is the runoff rate at the bottom of the snowpack, and Mout,ss is the surface sublimation rate. SMAP calculates the change in mass during a simulation period, which can be arbitrary, and equation (19) is always valid during the period.
 SMAP partitions the precipitation rate, which is taken directly from the input data, into snow and rain rates by using the algorithm to calculate snow:rain ratios as a function of Tw parameterized by Yamazaki [1998, 2001]. Surface hoar is created when SMAP determines that HL is positive and ground wind speed is less than 3 m/s [Föhn, 2001]. This constrains SMAP not to create much surface hoar because SMAP sets HL equal to 0 when Ri exceeds the critical Richardson number as explained in section 2.1. In order to confirm whether the above mentioned modeling procedure is robust or not, it is necessary to perform detailed snow pit observations together with micrometeorological measurements and modeling work in the future. In contrast, surface sublimation occurs when SMAP determines HL to be negative. |HL/Lv| is equivalent to surface hoar rate or surface sublimation rate.
 Snow settlement, melting and refreezing, and water percolation affect ρs and Mout,r and thus the mass balance of the snowpack. We describe snow settlement in section 2.3 and the other processes in section 2.5.
2.3. Snow Settlement
 Snow settlement increases ρs, and is given by a densification equation:
This equation performs well for seasonal snow, though it tends to underestimate η for polar snow [Morris et al., 1997]. To initialize ρs for new snow or surface hoar, we have to calculate new snow density. Unfortunately, a parameterization of new snow density that can be applicable globally has not been developed yet. For example, when Yamaguchi et al.  applied SNOWPACK [Bartelt and Lehning, 2002; Lehning et al., 2002a, 2002b] to the wet-snow region in Japan, they employed an empirical parameterization as functions of air temperature and wind speed obtained from data gathered in the northern part of Honshu Island, Japan instead of the original function of SNOWPACK [Lehning et al., 2002b]. Although SMAP is equipped with the functions by Yamaguchi et al.  and Lehning et al. [2002b], we employ a parameterization for new snow density ρs,new (kg/m3) as a function of wind speed u (m/s) introduced by Yamazaki [1998, 2001]:
because it was developed and well validated under the climate condition at Sapporo. When SMAP is applied to global climate simulations, the parameterization can be inadequate. In this case it should be changed.
2.4. Snow Metamorphism
 Snow metamorphism processes control temporal changes in optically equivalent snow grain radius ropt (in this paper, we refer to “snow grain size”). To simulate the processes, we employ the model geometry for a snow grain developed by the SNOWPACK model [Lehning et al., 2002a], where a neck connects two spherical ice particles and the related prognostic parameters are calculated (Figure 1). The parameters are the geometric snow grain radius rg, bond size rb, dendricity dd, and sphericity sp, where rg is the radius of each ice particle, rb is the minimum constriction in a neck [Lehning et al., 2002a], dd describes the part of the original snow grain shape that is still remaining in a snow layer, and sp describes the ratio of rounded versus angular snow grain shapes [Brun et al., 1992]. Both dd and sp range between 0 and 1. The assumption for new snow is that dd = 1 and sp = 0.5. Combinations of these four parameters and water content determine snow grain shape [Lehning et al., 2002a]. The model geometry of the two connected ice particles considered here is a geometrically nonspherical particle. A geometrically nonspherical particle is optically represented by a collection of independent spheres that have the same volume-to-surface-area (V/A) ratio as the nonspherical particle [Grenfell and Warren, 1999; Neshyba et al., 2003; Grenfell et al., 2005]. SMAP therefore calculates ropt with the following equation [Grenfell and Warren, 1999]:
where SSAv is SSA per unit volume, and SSAv is written as a function of the model geometry's volume Vg and surface area Ag as
From the model geometry (Figure 1), Vg and Ag are calculated as
SMAP employs the same prognostic equations, which describe temporal changes in rg, rb, dd, and sp, as those used in SNOWPACK [Lehning et al., 2002a], in which three types of snow metamorphism processes are considered: (1) equi-temperature metamorphism, (2) temperature gradient metamorphism, and (3) wet snow metamorphism. Equi-temperature metamorphism occurs when snow is dry and the absolute snow temperature gradient is small (less than 5 K/m). This process forms decomposing and fragmented precipitation particles as well as rounded grains. Temperature gradient metamorphism occurs when snow is dry and the absolute snow temperature gradient is large (more than 5 K/m). Faceted crystals and depth hoar are formed through this process. Wet snow metamorphism occurs when snow contains liquid water. Melt forms are created in this case. However, recentlyPinzer and Schneebeli demonstrated that small rounded grains can be formed even when the temperature gradient is large if the sign of the temperature gradient changes with a 24-h cycle. We implicitly consider this kind of snow metamorphism under an alternating temperature gradient regime by forcing the temperature gradient metamorphism not to occur in the top 20 cm of the snowpack. We discuss the validity of this procedure insection 4.4.
 To calculate the temporal evolution of ropt it is necessary to initialize ropt for both new snow and surface hoar. For this purpose, we use ropt0 (μm), which is the initial value of ropt, and the following empirical equation as a function of air temperature Ta (°C):
 SMAP assumes each snow layer to have a thickness d that is allowed to range between dmin and dmax. When d exceeds dmax, SMAP divides the layer into two layers that have the same snow physical parameters. On the other hand, when d becomes less than dmin, SMAP adds this thin layer to the adjacent lower layer. When new snow falls or surface hoar forms, SMAP adds a new snow layer to the top of the snowpack. A grid point retaining the values of simulated snow physical parameters is located at the center of each snow layer. Using forcing provided by input data SMAP approximates and solves the energy balance equation (1)with the Crank-Nicolson finite difference implicit method where Neumann boundary conditions, which is prescribed in terms of snow temperature gradients at both the snow surface and the bottom of the snowpack (equations (4) and (5)), are imposed. In this numerical procedure, we have to pay attention to the values of the time step Δt, d, and keff to avoid possible numerical instabilities. We discuss the values chosen for these parameters in section 4.
 SMAP diagnoses snowmelting and refreezing at every time step with Ts predicted by the energy balance equation. When Ts is positive, melting occurs. In contrast, when Ts is negative and liquid water exists, refreezing occurs. In both cases SMAP expresses the change in θw during one time step, Δθw, by
In cases where Ts is positive, SMAP sets Ts to 0°C after this calculation.
 When the snowpack retains liquid water, the water may move downward. We treat liquid water displacement in terms of the mass fraction of water, θwm. SMAP assumes that liquid water greater than the maximum θwm descends to the adjacent lower layer. SMAP assumes the maximum values of θwm to be 0.2 for layers in the top 5 cm of the snowpack and 0.1 for the lower layers [Yamazaki, 1998, 2001]. If excess liquid water exists at the bottom layer of the snowpack, liquid water runs off. In this case, SMAP assumes that the excess liquid water penetrates into the ground.
3. Field Measurements at Sapporo
3.1. Meteorological Measurements
 During 2007–2009 we carried out meteorological measurements at an automated weather station (AWS) installed at the Institute of Low Temperature Science, Hokkaido University (43°04′56″N, 141°20′30″E, 15 m a.s.l), which is located in an urban area of Sapporo city, Hokkaido, Japan [Aoki et al., 2006]. We used data averaged every 30 min or integrated over every 30 min (precipitation only) as input and validation values for SMAP.
 For input data, we corrected measured precipitation for catch efficiencies for snow and rain as functions of gauge type and wind speed with algorithms developed by Yokoyama et al. . The downward UV-visible radiant flux (λ = 0.305–0.708 μm) was not measured directly but instead was calculated by subtracting the measured downward near-infrared radiant flux (λ = 0.708–2.8 μm) from the measured downward shortwave radiant flux (λ = 0.305–2.8 μm). The diffuse/direct ratios of the downward radiant fluxes in both the UV-visible and the near-infrared regions were also not measured directly. They were obtained by assuming these ratios to be the same as the corresponding ratio for downward shortwave radiant flux, though this approximation can cause a small error in calculated broadband snow albedo [Aoki et al., 2011]. We also corrected the ground heat flux measured during the ablation period (March and April) because diurnal variations in this flux are enhanced when the ground is exposed. If simulated melting is delayed compared to observed one, large variations in the ground heat flux have a proportionate effect on the model simulations. To minimize this effect, we assumed constant ground heat fluxes during the ablation period while the observed snow depth was less than 0.2 m. These values were −2.35 W/m2 in the winter of 2007–2008 and −1.95 W/m2 in the winter of 2008–2009. We obtained these values when the measured snow depth was 0.2 m. They are very similar to the value of −2 W/m2 employed in CROCUS when the snow temperature at the bottom of the snowpack was 0°C [Brun et al., 1989, 1992; Essery et al., 1999].
 For model validation we used the measured snow depth, snow surface temperature, and broadband albedos. Broadband albedos were calculated by the downward and upward radiant fluxes for UV-visible, near-infrared, and shortwave spectra, where the unmeasured upward UV-visible radiant flux was obtained in a similar way with the downward UV-visible radiant flux.
 Model validation of broadband albedos requires close attention to the observed data [Yamanouchi, 1983; Aoki et al., 2011, Brandt et al., 2011] because accurate knowledge of the instrument's shadowing correction would be needed. In the present study we corrected the observed broadband albedo data that we used in this study considering the effect of a pyranometer mounting frame, which blocked 3.56% of the upward flux in the case of isotropic upward radiation [Aoki et al., 2011]. The value was comparable with that obtained by Yamanouchi  (3–5%) at Mizuho station in east Antarctica.
3.2. Snow Pit Observations
 During the winters of 2007–2008 and 2008–2009, we carried out snow pit observations twice a week at about 1100 local time near the AWS. Observed parameters were snow depth, the snow grain shape profile, snow grain size, and Column-average snow density. We used the snow depth and Column-average snow density to calculate the column-integrated SWE. Snow grain size was observed for the top 2 cm and top 10 cm depths because we focused near-surface snow grain size, which strongly affects the broadband albedos.Aoki et al. [2000, 2003]defined snow grain size measured manually as one-half the branch width of dendrites or as one-half the width of the narrower portion of broken crystals “r2.” On the other hand snow grain shape was observed in the entire snowpack as we intended to confirm whether SMAP could reproduce detailed layer structure of snowpack or not. We simultaneously collected snow samples for the top 2 cm and top 10 cm of the snowpack to measure the mass concentrations of dust and elemental carbon (EC) [Kuchiki et al., 2009; Aoki et al., 2011]. In this study we assumed EC to be equivalent to BC following Aoki et al. . Aoki et al.  showed that snow impurities at Sapporo are characterized by high BC concentrations (an average during the two winters of 0.215 ppmw for the top 2 cm of the snowpack), which is much higher than those in Arctic snow.
 We used the measured mass concentrations of BC and dust for input data in this study. We equated the values in the top 2 cm model layers of the snowpack to the corresponding observed values. For the lower model layers of the snowpack, we gave the observed values for the top 10 cm of the snowpack equally. Data gaps existed for the days between snow pit observations. We estimated the missing data by using the values measured at the nearest points in time. For model validation we used vertical profiles of snow grain shape, the grain size of the snow in the top 2 cm of the snowpack, column-integrated SWE, and Column-average snow density.
3.3. Meteorological and Snow Conditions at Sapporo
 Sapporo is located in the southwest part of Hokkaido, Japan. It faces the Sea of Japan and is exposed to the cold winter northwesterly monsoon, which brings frequent snowfalls. The record of daily mean air temperature and half-hourly snow depth measured at Sapporo during the winters of 2007–2008 and 2008–2009 (Figure 2) shows that the first winter was colder than the second. During the second winter air temperature often rose above 0°C (Figure 2b). Average daily mean air temperatures during the period from December to March were −1.58°C for the first winter and −0.34°C for the second. Snow depth after late January was greater during the first winter than during the second. In this paper we refer to November, December, January, and February as the “accumulation period” and March and April as the “ablation period.”
4. Model Validation with Data from Sapporo
 We evaluated SMAP with the data obtained during the winters of 2007–2008 and 2008–2009 at Sapporo. We compared the snow depth, column-integrated SWE, Column-average snow density, snow grain shape profile, snow surface temperature, snow grain size in the top 2 cm of the snowpack, and broadband albedos simulated by SMAP with in situ measurements. To assess the performance of the model we used the correlation coefficient (r), root mean square error (RMSE), and mean error (ME; the average of the difference between simulated values and observed values) obtained from a comparison of measured and simulated data during the period from November to April for both winters (Table 4).
Table 4. Comparison of SMAP Simulation Results With Measurements
Periods are November to April for both 2007–2008 and 2008–2009 winters.
Root mean square error.
Mean error (the average of the difference between simulated values and observed values).
Snow depth [m]
Snow density [kg/m3]
Snow surface temperature [°C]
Snow grain size [mm]
 SMAP requires as input the values of some model parameters, including the number of subbands used in PBSAM, Δt, dmin, dmax, and the maximum value of keff. Except for the number of subbands, SMAP requires these parameters to solve the energy balance equations with the Crank-Nicolson finite difference implicit method (section 2.5). To demonstrate the expected maximum potential of SMAP, we chose somewhat computationally demanding values for the number of subbands, Δt, dmin, and dmax. We employed four subbands for both the UV-visible and near-infrared bands. We solved the energy balance equations with Δt = 50 s and forced d to range between dmin = 0.005 m and dmax = 0.03 m. In addition we restricted keff not to exceed 1.0 W/mk in the present study.
4.1. Snow Depth, SWE, and Snow Density
 In general it is possible for snowpack models to reproduce column-integrated SWE if energy and mass balance considerations are imposed precisely. To reproduce snow depth, snowpack models are required to simulate multifarious physical processes, namely snow settlement, phase changes, water percolation, and snow metamorphism accurately in addition. Thus in this section we validated snow depth, column-integrated SWE, and Column-average snow density to assess the overall performance of SMAP. Before the validation we investigated the sensitivities of three parameterizations for new snow density mentioned insection 2.3 (Yamaguchi et al. , Lehning et al. [2002b], and Yamazaki [1998, 2001]) in terms of half-hourly snow depth in order to verify the availability of the function byYamazaki [1998, 2001] at Sapporo. SMAP with the function by Yamaguchi et al.  obtained RMSE of 0.073 m and 0.089 m for 2007–2008 winter and 2008–2009 winter, respectively. When we employed the function by Lehning et al. [2002b] we obtained RMSE of 0.075 m and 0.080 m for 2007–2008 winter and 2008–2009 winter, respectively. Finally, we acquired RMSE of 0.064 m and 0.075 m for 2007–2008 winter and 2008–2009 winter, respectively if we chose the parameterization by Yamazaki [1998, 2001]. From these results we confirmed the usefulness of the function by Yamazaki [1998, 2001] at least in Sapporo. However, when we apply SMAP to global climate simulations, we have to investigate sensitivities and performances of these parameterizations again. Furthermore, it is necessary to develop a physically based function to calculate new snow density in the future.
 We began our model validation with a comparison of half-hourly snow depths observed by AWS and simulated by SMAP. SMAP reproduced very well the seasonal variations in snow depth during both winters (Figures 2c and 2d and Table 4). A comparison of RMSE values and ME values (Table 4) indicates that SMAP modeled snow depth with comparable accuracy during both winters and tended to somewhat overestimate observed depths. To more carefully explore the accuracy of the simulated snow depths we examined the accuracy of the modeled column-integrated SWE and Column-average snow density.
 A comparison of column-integrated SWE and bottom runoff simulated by SMAP with the column-integrated SWE from snow pit observations revealed that SMAP successfully reproduced seasonal variations of column-integrated SWE (Figure 3), however, SMAP tended to underestimate column-integrated SWE in all periods for both winters (Figure 4), with the bias being more pronounced during the winter of 2008–2009 than 2007–2008 (Table 4). During January to February 2009, a large amount of SWE (about 100 mm) drained off from the snowpack as air temperature frequently rose above 0°C (Figure 3). However, at the end of the ablation period, the calculated and observed column-integrated SWEs were similar in both winters. This result suggests that modeled water movement in snowpack especially during the accumulation period can be sometimes unrealistic and inadequate. In some cases the maximum water content can be higher than the simple present setting described insection 2.5. In order to eliminate the uncertainty in the water movement process, it will be necessary to treat the maximum water content as a function of snow microstructure as pointed out by Bartelt and Lehning .
 Since snow density is increased by overburden pressure, underestimates of SWE can result in underestimates of snow density. We checked the accuracy of the simulated Column-average snow density by comparing them with the snow pit observations (Figure 5). Although SMAP reproduced seasonal variations of Column-average snow density for both winters, SMAP underestimated Column-average snow density (Figure 6) and this tendency was more pronounced during warm 2008–2009 winter when air temperature were often above 0°C even during accumulation period (Figures 5 and 6 and Table 4).
 Overall the simulated mass balance during the winter of 2008–2009 was not as accurate as during the winter of 2007–2008, though the accuracy of simulated snow depth was comparable during both winters. The result that larger amount of SWE drained off from the snowpack during January to February in relatively warm 2009 winter compared to 2008 winter suggest that inadequacies of the water movement simulation during accumulation period appear to be primarily responsible for the inaccuracy of the model simulations. If more SWE remains in the snowpack, snow compaction can proceed more rapidly. To improve the accuracy of the mass balance during the 2008–2009 winter, it is needed to consider realistic water percolation and retention processes.
4.2. Snow Grain Shape
 Since air temperatures at Sapporo were often greater than 0°C during the accumulation period (Figure 2), melt forms were often observed in the snow pits. A comparison of the temporal evolution of the vertical profiles of snow grain shape observed in the snow pits and those simulated by SMAP (Figure 7) shows that SMAP successfully reproduced the overall stratigraphy for both winters. SMAP reproduced well, in particular, the temporal evolution of precipitation particles, decomposing and fragmented precipitation particles, and rounded grains. However, the fact that SMAP did not simulate depth hoar and faceted crystals observed in the lower layers during January–February 2008 indicates a need for improvement in the simulated process of temperature gradient metamorphism, which generally develops depth hoar and faceted crystals. SMAP also sometimes simulated melt forms in surplus. For example, SMAP simulated excessive melt forms in the upper layers in early February 2008. The likely cause is underestimation of snow albedo, which is discussed in section 4.5. Finally, SMAP could not reproduce the ice formations that we frequently observed during the warm winter of 2008–2009. To reproduce ice formations it will be necessary to improve water retention and percolation processes during accumulation period questioned in the previous section.
4.3. Snow Surface Temperature
 It is possible for us to assess whether energy exchanges at the snow surface were modeled adequately or not in terms of snow surface temperature. A comparison of temporal sequences of half-hourly snow surface temperature for snow covered periods observed with AWS and those simulated by SMAP (Figure 8) indicates that SMAP reproduced diurnal variations of snow surface temperature fairly well for both winters (r = 0.914 for the 2007–2008 winter and 0.913 for the 2008–2009 winter). There were no obvious biases for either winter (ME = −0.301°C for 2007–2008 winter and ME = −0.666°C for 2008–2009 winter). However, SMAP occasionally underestimated snow surface temperatures at night when surface cooling was enhanced, for example during 7–9 March 2008. During these days the sky conditions at Sapporo were clear, and the winds were calm. The conditions at night were therefore quite stable. A possible cause of the underestimation in this case is the treatment of turbulent heat fluxes under very stable conditions when Ri exceeds the critical Richardson number explained in section 2.1. Under these conditions SMAP assumes that turbulence ceases. To improve the model performance it can be effective to introduce a windless transfer coefficient employed in SNTHERM [Jordan, 1991; Jordan et al., 1999; Andreas et al., 2004; Helgason and Pomeroy, 2011], or a modification formulation for bulk transfer coefficients implemented in CROCUS by Martin and Lejeune  to ensure minimum heat exchanges even under very stable conditions. However, since they are quite empirical, they should be validated carefully through detailed micrometeorological observations such as turbulence measurements with the eddy covariance technique before introducing them to SMAP.
 Another possible cause of the underestimation of snow surface temperatures at night is an uncertainty of the effective thermal conductivity of snow. In the present formulation (see section 2.1), the low density of snow near the surface obstructs heat transfer between the lower layers and near-surface layers. Since the effective thermal conductivity of snow depends qualitatively on the morphological state of the snowpack [Sturm et al., 1997; Schneebeli and Sokratov, 2004; Kaempfer et al., 2005], simple parameterizations of the effective thermal conductivity of snow as a function of snow density are inadequate.
4.4. Snow Grain Size
 As explained in section 2.1, SMAP employs PBSAM, which calculates snow albedo and solar heating profiles in snowpack, with vertical profiles of snow grain size, SWE, snow impurities, and solar illumination conditions as input. In situ measurements or host GCMs provide profiles of snow impurities as external inputs, whereas SMAP calculates profiles of snow grain size and SWE internally. The snow grain size profile is one of the most important prognostic outputs of SMAP.
 We first examined the effect of the implicit consideration of snow metamorphism under alternating temperature gradients described in section 2.4 by comparing the simulated snow grain size in the top 2 cm of the snowpack with the snow grain size observed in the snow pits (Figure 9). The implicit consideration remarkably improved the accuracy of the snow grain size simulations in January of both winters (Figures 9a and 9b). By employing the implicit consideration, SMAP kept the simulated snow grain sizes during these periods to less than 0.05 mm, and the simulated values closely approached the observed snow grain sizes. We therefore employed the implicit consideration as the default setting of SMAP. Although the implicit consideration accomplished to some degree in the present study, it goes without saying that the explicit formulations of snow metamorphism under alternating temperature gradients should be developed in the future because the implicit consideration cannot reproduce observed high mass turnover [Pinzer and Schneebeli, 2009] accurately.
 The results with the implicit consideration (Figures 9a and 9b) and the correlation coefficients (0.763 and 0.840 for the 2007–2008 and 2008–2009 winters, respectively) indicate that SMAP approximately reproduces the characteristics of the seasonal variation of snow grain size, i.e., small during the accumulation period and rapidly growing during the ablation period. However, SMAP tends to overestimate observed snow grain sizes less than about 0.1 mm and to underestimate snow grain sizes during the ablation period (Figure 10). A possible cause of the overestimates is errors in new snow grain size calculated by equation (27). There is a possibility that equation (27) slightly overestimates new snow grain size especially when the air temperature is negative. New snow grain size could be affected by not only air temperature but also the shape of new snow, wind speed, and relative humidity. A physically based parameterization of new snow grain size that explicitly considers those effects should be developed in the future. Finally, the underestimates during the ablation period could be related to wet snow metamorphism. The grain growth rate under wet snow metamorphism can be higher than the present formulation.
4.5. Broadband Albedos
 Snow albedo plays an important role in controlling energy exchanges between the snow surface and the atmosphere. We therefore sought to determine whether SMAP could bring out PBSAM's potential accuracy by comparing the accuracy of simulated broadband albedos estimated with SMAP to those calculated by Aoki et al. .
 We conducted the validation of broadband albedos in the same manner as Aoki et al. by employing only the daily half-hourly broadband albedos measured from 1130 to 1200 local time around local noon. A comparison of broadband albedos observed with AWS and simulated by SMAP (Figure 11) shows that albedo variations for the three spectra were well reproduced for both winters, although some discrepancies are apparent. Broadband albedos were underestimated in early February 2008. During that period SMAP simulated excessive melt forms in the upper layers (Figure 7a) and overestimated snow surface temperature (Figure 8). In general, reduced shortwave albedo can induce snowmelt in the upper layers and cause snow surface temperature to approach 0°C. This cycle triggers wet snow metamorphism and in turn accelerates snow grain growth. Furthermore, snow grain growth affects broadband albedos by reducing especially near-infrared albedo. We thus confirmed the repeated occurrence during the study period of the positive feedback between the increase in snow temperature and snow grain growth [Colbeck, 1975; Wiscombe and Warren, 1980].
 During the 2008–2009 winter, observed broadband albedos (especially near-infrared albedos) often fluctuated rapidly in the short term. This behavior was not reproduced well by SMAP. For example, SMAP did not simulate the rapid albedo reduction observed during late December 2008. A likely cause is the failure of SMAP to simulate very shallow snow depths. In late March 2009, SMAP simulated unrealistic increases in albedo. We attribute this error to failure of the algorithm that calculates the snow:rain ratio for new snow (seesection 2.2). In contrast, we attribute the poor reproducibility of the large fluctuations that we measured from January to early March 2009 to errors in the simulation water movement processes (questioned in section 4.1) because the processes affect profiles of water content and snow grain size. If more SWE remains in snowpack, snow grain size develops more rapidly in proportion to higher water content [Brun et al., 1992; Lehning et al., 2002a] and reduced the albedo can be reproduced.
RMSE values of the shortwave albedo obtained by SMAP were 0.051 and 0.084 for the winters of 2007–2008 and 2008–2009, respectively. We attribute the relatively large RMSE value for the 2008–2009 winter mainly to errors that we found during late December 2008 when SMAP failed to simulate rapid complete melting and during late March 2009 when SMAP simulated unrealistic increases in albedo. In fact the RMSE value of the shortwave albedo simulated by SMAP was 0.048 from 1 January 2009 to 15 March 2009. RMSE values of the shortwave albedo obtained by PBSAM were 0.052 and 0.042 for the winters of 2007–2008 and 2008–2009, respectively [Aoki et al., 2011]. These results confirm that SMAP can exploit PBSAM's potential accuracy.
5. Effects of Snow Impurities on Snowmelt at Sapporo
 We investigated the effects of snow impurities on snowmelt by using the data collected during the 2007–2008 and 2008–2009 winters at Sapporo. For this purpose, we carried out a “pure snow experiment” with SMAP by assuming that there were no snow impurities (Figure 12). A comparison of simulated snow depths for snow containing impurities (“CTL” simulation: same as Figures 2c and 2d), and for snow without impurities (“PURE” simulation) (Figures 12a and 12b, respectively) revealed a remarkable effect of snow impurities on the ablation period for both winters. The presence of impurities caused the duration of the snowpack to be shortened by 19 days and 16 days in the first and second winters, respectively.
 To qualitatively assess the effects of snow impurities we estimated the surface radiative forcing [Hansen and Nazarenko, 2004] of snow impurities by calculating the difference between the PURE and CTL simulated shortwave radiant fluxes absorbed by the snowpack. Averaged over the entire period of snow cover, the simulated radiative forcings due to snow impurities were 9.0 W/m2 and 8.1 W/m2 for the 2007–2008 and 2008–2009 winters, respectively. The contrast of the simulated radiative forcing between accumulation periods and ablation periods was remarkable. The estimated radiative forcings of snow impurities averaged during only the accumulation periods were 3.7 W/m2 and 3.2 W/m2 for the 2007–2008 and 2008–2009 winters, respectively. These values correspond to 0.05 reductions in shortwave albedo due to snow impurities for both the 2007–2008 and 2008–2009 winters. In contrast, the estimated radiative forcings of snow impurities averaged during only the ablation periods were 25.9 W/m2 and 21.0 W/m2 for the 2007–2008 and 2008–2009 winters, respectively. These values correspond to 0.18 and 0.17 reductions in shortwave albedo due to snow impurities for the 2007–2008 and 2008–2009 winters, respectively. Aoki et al.  indicated seasonal variations of mass concentrations of snow impurities at Sapporo during two winters: 2007–2008 and 2008–2009, which are also used in this study as input parameters for SMAP. The variations show that mass concentrations of snow impurities during accumulation period are not significantly low compared to those during ablation period. Therefore, the contrast of the simulated radiative forcing between accumulation periods and ablation periods can be attributed to (1) the contrast of downward shortwave radiant flux; and (2) the difference in snow grain size. As for (1) downward shortwave radiant flux is much higher during spring ablations periods compared to winter accumulation periods. Regarding (2) snow grain size during ablation periods develops rapidly through wet snow metamorphism, while it is relatively low during accumulation periods as demonstrated in Figures 9a and 9b. In general, radiation penetrates deeper in more coarsely grained snow and encounters more absorbing materials before it can reemerge from the snowpack [e.g., Warren and Wiscombe, 1980; Aoki et al., 2011], and these result in lower broadband albedo and enhanced solar heating in snowpack.
Painter et al.  showed that snow cover duration in San Juan Mountains was shortened by 18 to 35 days during ablation periods in 2005 and 2006 as a result of surface shortwave radiative forcing (17–37 W/m2 in 2005 and 39–59 W/m2 in 2006) caused by deposition of disturbed desert dust. Comparison our results with theirs indicates that changes in snowpack durations as well as radiative forcings due to snow impurities are almost the same order between Sapporo and San Juan Mountains, though the qualities of snow impurities in Sapporo (BC and dust) and San Juan Mountains (dust) are essentially different.
 The importance of snow impurities on snowmelt in turn indicates that mass concentrations of snow impurities are important prognostic parameters for GCMs with detailed snow albedo models, because temporal changes in snow impurities (e.g., timing when impurities deposit on snowpack, quantities and qualities of impurities, and how impurities move in snowpack) significantly affect not only the physical states of snowpack but also the surface energy balance in response to seasonal variations of meteorological conditions.
6. Summary and Conclusions
 Snow albedo plays an important role in terrestrial climate systems. Recently, several authors have developed physically based snow albedo models for GCMs to improve the accuracy of climate simulations [Flanner and Zender, 2005; Flanner et al., 2007; Gardner and Sharp, 2010; Yasunari et al., 2011; Aoki et al., 2011]. As these models require either snow grain size or SSA as an input parameter, GCMs should calculate these parameters accurately. In general, temporal changes in snow grain size or SSA depend on snow metamorphism processes, which are controlled by physical states of snowpack such as snow temperature and water content. Hence an optimum snowpack model for LSMs, which reproduces realistic physical states of snowpack, is necessary to utilize these snow albedo models and to bring out their potential accuracy in climate simulations.
 In the present study we developed a multilayered physical snowpack model named SMAP, which incorporates PBSAM [Aoki et al., 2011] and is able to bring out PBSAM's potential accuracy with respect to snow albedo simulation. SMAP takes energy balance, mass balance, snow settlement, phase changes, water percolation, and snow metamorphism into account. The PBSAM component of SMAP calculates snow albedo and solar heating profiles by using profiles of snow grain size and SWE calculated by SMAP, together with mass concentrations of snow impurities externally provided by in situ measurements or host GCMs. Snow grain size is calculated with the use of a model geometry that envisions two spherical ice particles connected by a neck [Lehning et al., 2002a]. SMAP obtains snow grain sizes by calculating SSA per unit volume with the nonspherical model geometry. SMAP calculates the temporal evolution of snow grain size with the same formulations as SNOWPACK [Lehning et al., 2002a], which take into consideration equi-temperature metamorphism, temperature gradient metamorphism, and wet snow metamorphism. SMAP also implicitly considers the effects of snow metamorphism under alternating temperature gradients [Pinzer and Schneebeli, 2009] by forcing the temperature gradient metamorphism not to occur in the top 20 cm of the model layers, although this method cannot reproduce observed high mass turnover accurately. SMAP is now implemented into the Meteorological Research Institute Earth System Model version1 (MRI-ESM1) [Yukimoto et al., 2011] through the integrated land surface framework named Hydrology, Atmosphere, and Land surface (HAL) (M. Hosaka et al., manuscript in preparation, 2012), which provides input data for SMAP. However, we restrict the number of model snow layers by eight at present due to high computational costs of SMAP.
 We evaluated SMAP with meteorological and snow data observed during two winters from 2007 to 2009 at Sapporo, Japan. We compared the simulated snow depth, column-integrated SWE, Column-average snow density, snow grain shape profile, snow surface temperature, grain size in the top 2 cm of the snowpack, and broadband albedos with in situ measurements. SMAP reproduced well all observed seasonal variations of these parameters for both winters.RMSE values of shortwave albedo obtained by SMAP were 0.051 and 0.084 for the 2007–2008 and 2008–2009 winters, respectively. The RMSE value for the 2007–2008 winter is comparable to that obtained by PBSAM (0.052) [Aoki et al., 2011]. Although the RMSE for the 2008–2009 winter is somewhat large compared to that obtained by PBSAM (0.042) [Aoki et al., 2011], we attribute the discrepancy mainly to errors found during late December 2008, when SMAP failed to simulate rapid complete melting, and during late March 2009, when SMAP simulated unrealistic increases in albedo. Except for these periods (i.e., from 1 January 2009 to 15 March 2009, during which time the simulated snowpack existed continuously), SMAP obtained an RMSE value of 0.048. These results confirm that SMAP is able to bring out the potential accuracy of PBSAM and can be served for climate simulations by GCMs.
 Finally, we investigated the effects of snow impurities on snowmelt at Sapporo during the 2007–2008 and 2008–2009 winters with a sensitivity test in which we assumed an absence of snow impurities. Snow depths simulated by the sensitivity test indicated that snow impurities forced snowpack durations at Sapporo to be shortened by 19 days and 16 days during the 2007–2008 and 2008–2009 winters, respectively. Most of the changes occurred during the ablation period. The estimated surface radiative forcings of snow impurities were quite low during ablation periods (around 3.5 W/m2) compared to accumulation periods (25.9 W/m2 for 2007–2008 and 21.0 W/m2 for 2008–2009) for both winters. These radiative forcings were consequences of reductions in shortwave albedo by around 0.05 during accumulation periods, while around 0.175 during ablation periods. The seasonal contrast was attributed to (1) the contrast of downward shortwave radiant flux; and (2) the difference in snow grain size between accumulation and ablation periods. Above mentioned results highlight the fact that GCMs, which incorporate detailed snow albedo models that calculate snow albedo explicitly, need to calculate mass concentrations of snow impurities accurately. For that purpose it is necessary for aerosol transport models implemented into GCMs to simulate aerosol depositions onto the snow surface accurately. In addition, we have to develop a formulation for movements of impurities in snowpack, which were not considered in this study.
 We are grateful to Michael Lehning at WSL Institute for Snow and Avalanche Research SLF, for providing us with the SNOWPACK model, from which we learned the essence of snow metamorphism processes. We thank Teppei J. Yasunari, Yuki Sawada, Kou Shimoyama, Tetsuo Sueyoshi, Junko Mori, Masahiro Takahashi, Tomoyasu Kuno, Hayato Oka, Taro Nakai, Kazuhiro Okuzawa, Tsutomu Watanabe, Shun Tsutaki, Chusei Fujiwara, Kohei Ohtomo, Niyi Sunmonu, Masaki Okuda, Tatsuya Nakayama, Hirokazu Hirano, and Etsuko Tanaka for help with snow pit observations during two winters at the Institute of Low Temperature Science of Hokkaido University. We also thank Masae Igosaki for performing the laboratory measurements of snow impurities. We gratefully appreciate the very helpful comments by Ruzica Dadic and an anonymous reviewer. This study was supported in part by (1) the Experimental Research Fund for Global Environment Conservation, the Ministry of the Environment of Japan, (2) the Grant for Joint Research Program, the Institute of Low Temperature Science, Hokkaido University, (3) the Global Change Observation Mission – Climate (GCOM–C) / the Second–generation GLobal Imager (SGLI) Mission, the Japan Aerospace Exploration Agency (JAXA), and (4) Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (S), 23221004.