Yoshimura et al. (2010) presented the IsoRSM, which includes the isotopic species for water vapor (HDO and H{}_{{2}}{}^{{18}}218O) as tracers in the latest version of the Scripps Experimental Climate Prediction Center's regional spectral model (Kanamitsu et al., 2005). In the IsoRSM, the tracers can be incorporated into raindrops or cloud particles at every integration time step. Therefore, the interactions between the tracers and precipitation processes can be considered. In contrast, a general chemical transport model uses precipitation as an external forcing. Yoshimura (2011) and Saya et al. (2013) modified IsoRSM to enable the simulation of the transport of radioactive tracers. Isotopic variables were replaced with radioactive tracers (i.e., {}^{{131}}131I and {}^{{137}}137Cs), and dry and wet deposition processes caused by gravity and precipitation processes, respectively, were introduced. Saya et al. (2013) proposed a wet deposition process wherein the deposition is proportional to the ratio of the amount of condensed water to the total amount of water, whereas a traditional method (e.g., Maryon et al., 1991) considers only the amount of condensed water. In this study, the radioactive tracer mode of IsoRSM is used as an original framework.

In this study, the NDSL advection scheme replaces the spectral prognostic calculation of the tracers in the RSM. Once each tracer field is provided from the initial field on the regular grid space, the advection of these fields is calculated by the NDSL on the grid space without any spectral transformation during the model integration. This process prevents the Gibbs phenomenon. The NDSL has two characteristics: (1) non-iteration to compute the trajectories of each tracer and (2) a dimensional-splitting method. Figure 1 shows the basic concept of two-dimensional advection for both the traditional semi-Lagrangian scheme and the NDSL scheme (from Juang, 2008). The traditional backward (forward) semi-Lagrangian scheme assumes that the arrival (departure) points are located on the regular model grid (Fig. 1a). In this case, an initial guess and iterations to compute the trajectories are required, which means finding a midpoint wind and transferring the fluid particles from the departure points to the arrival points. These iterations make the semi-Lagrangian scheme expensive and inefficient. The NDSL scheme is a central scheme, which assumes a midpoint wind at the regular model grid point at time tt to find the departure point at time t-\Delta tt-Δt and the arrival point at time t+\Delta tt+Δt (Fig. 1b, also see Fig. 1 of Zhang and Juang, 2012). No initial guess or iteration is needed to find trajectories. Only one interpolation at the departure point and one remapping at the arrival point are needed. The wind in the central scheme can reduce numerical error better than the upstream scheme because no estimation or iteration occurs. During the advection process, the quantity of the tracer is assumed to be steady. The NDSL uses the dimensional-splitting method for 2-D advection, which simply splits the 2-D advection into a sequence of 1-D advections. Because it only needs 1-D interpolation and remapping, the method easily attains mass conservation. Another important advantage is that the 1-D method can be easily coded; thus, it is compatible with most numerical models.

For the implementation of the regional version of the NDSL in a real-data case, the boundary treatment must be considered. The global NDSL uses a cyclic boundary condition, which places a duplicated global domain at the western and eastern boundaries. This allows for the arrival or departure point to be located, even when it lies outside of the model domain. However, cyclic boundary conditions are not suitable for regional domains because the domain edge points differ in both longitude and latitude. Thus, the domain is treated as three sections: the boundary zone, the buffer zone, and inner domains. Figure 2 shows the structure of these sections in the lower-left corner of the model domain as an example; it assumes that the boundary and buffer zones are defined as three grid points each. The boundary zone (dark gray in Fig. 2a) is the area where the semi-Lagrangian advection calculation is not applied and where the values of the global base field are specified. This area is necessary to prevent the calculated departure point of tracers located outside of the model domain. The values in the inner domain are calculated entirely from the regional model. In the buffer zone (light gray in Fig. 2a), the global base field and the regional model field are combined, with the weighting determined by an inverse exponential function (Eq. 1, Fig. 2b), to smooth the gap between the boundary zone and the inner domain. \begin{array}[]{l}W_{\mathrm{G}}=\frac{1}{e^{{k}}}\\ W_{\mathrm{R}}=1-W_{\mathrm{G}}\\ \end{array}WG=1ekWR=1-WG Here, W_{\mathrm{G}}WG is the weighting for the global base field, W_{\mathrm{R}}WR is the weighting for the regional model field, and kk is the grid point of the buffer zone toward the inner domain. W_{\mathrm{G}}WG is defined according to Eq. (1) in the buffer zone but is specified as 1 and 0 in the boundary zone and the inner domain, respectively. Finally, the result over the model domain is defined by Eq. (2): F=W_{\mathrm{G}}F_{\mathrm{G}}+W_{\mathrm{R}}F_{\mathrm{R}}F=WGFG+WRFR where FF is the final result of a particular tracer, F_{\mathrm{G}}FG is the global base field, and F_{\mathrm{R}}FR is the field calculated by the regional model.

For the Fukushima case study, two experiments are performed. The first is the ORG run, which is identical to the control experiment of Saya et al. (2013), wherein tracer fields are calculated in the spectral space, as is performed in the original IsoRSM. The second is the SL run, wherein the specific humidity and radioactive material ({}^{{131}}131I and {}^{{137}}137Cs) tracer fields are calculated by the NDSL scheme. All configurations except the advection method for tracers are identical in the two experiments. Figure 5 shows the experimental domain for the case study, with horizontal grid spacing of 10 km. The number of grid points is 161 (east–west) by 200 (north–south). The number of vertical layers is 28 in terrain-following sigma coordinates; the lowest and highest sigma levels are 0.995 and 0.002, respectively. The red circle in Fig. 5 indicates the emission point, which is the location of the Fukushima Daiichi nuclear power plant. The physical processes used are the relaxed Arakawa–Schubert deep convection scheme (Moorthi and Suarez, 1992), the Noah land surface model (Ek et al., 2003), the Chou radiation scheme (Chou and Suarez, 1994), and a non-local planetary boundary scheme (Hong and Pan, 1996). The model simulation is integrated from 00:00 UTC 12 March 2011 to 00:00 UTC 28 March 2011 (16 days). Atmospheric initial and lateral boundary conditions are provided by the NCEP-Department of Energy (DOE) reanalysis (Kanamitsu et al., 2002). In the case that negative values are introduced in the initial field, correction is performed in regional interpolation process by replacing negative values with zero. If negative tracer quantities are produced by the physical parameterizations, those negative values are transported to the layer above and the original values are replaced by zero. The emission rate of the radioactive tracers from Chino et al. (2011) is used in this study. To determine the size of the boundary and buffer zones (Fig. 2) for this case study, the fastest wave is assumed to be a sound wave, which moves at a speed of 300 m s{}^{{-1}}-1. The estimated longest traveling distance of this wave in one time step (\Delta t=40Δt=40 s) is 12 km; this value is less than 2\Delta xΔx. Therefore, the fastest-moving tracer is confined within 2 grid points over one time step. Thus, it is impossible for tracers to enter from outside the domain when the boundary zone is larger than 2\Delta xΔx. In this study, the boundary zone is set to 5\Delta xΔx for safety. The buffer zone is the same size as the boundary zone.

When the NDSL advection is used (the SL experiment), the extra computation cost is 35 % higher with respect to the ORG run. However, the current version of the NDSL in the RSM still calculates spectral tracer advections even though the result is not used any more. It means that the computational burden with the current NDSL in the IsoRSM is purely the increased computational cost which is required for the NDSL tracer advections. In an updated release, this inefficiency will be solved.

Figure 6 shows column-integrated atmospheric radioactive tracer ({}^{{137}}137Cs) from the ORG and the SL experiments at 12:00 UTC, 15 March 2011, when the maximum emission rates occurred. The ORG run produces a very distinct noise in the zonal and meridional directions from the emission point (Fig. 6a). Additionally, a ring-shaped signal surrounds the emission point. This signal is the pattern of high-concentration, empty values; the ring shape extends from the center of the emission to outside the domain. These signals, also known as the ringing artifact, are typical of the Gibbs phenomenon. In the Fukushima case study, the discontinuity of the tracer field is pronounced because the tracers are emitted from a single grid point, which leads to significant noise from the spectral transformation processes in the ORG experiment. Widespread distributions of tracers with small concentrations occur over the domain. However, the SL experiment does not have any noise from the Gibbs phenomenon (Fig. 6b). Compared with the ORG run, the SL experiment produces a generally similar pattern of tracers, which advect northeast from the emission point. This result is the clearest advantage of the semi-Lagrangian advection scheme for tracer transport in the spectral model system. The simulated {}^{{131}}131I tracers have almost the same patterns with the {}^{{137}}137Cs in both the ORG and the SL runs (figure not shown). Figure 7 shows longitudinal–vertical cross sections of tracers averaged in the meridional direction over 36.5–37.5{}^{{\circ}}∘N, which includes the emission point. This figure shows that the ringing noises extend above the surface in the ORG experiment (Fig. 7a). The SL experiment shows transport in the vertical and horizontal directions without computational noise. Clearly, the semi-Lagrangian advection method can calculate the transport of tracers without computational noise, whereas the spectral representation of advection produces severe errors.

The SL experiment applies the semi-Lagrangian method to radioactive tracers and the humidity field. The humidity field is also a positive-definite field and spectrally exhibits the Gibbs phenomenon, although the discontinuity is not as strong as it is in the radioactive tracer fields. Figure 8 shows that the specific humidity in the ORG run exhibits some negative values in the lower troposphere (Fig. 8a, b). The SL experiment simulates detailed humidity distributions that are similar to those of the ORG experiment but without any negative values (Fig. 8c, d). Negatives in the ORG run indicate that the original RSM has a systematic problem representing the positive-definite field, even though the RSM is widely used and evaluated for regional downscaling. The 16-day accumulated precipitation fields from each experiment are quite similar (Fig. 9a, b). General rainfall patterns observed in the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) are well captured in both experiments (Fig. 9c). The spatial correlation coefficient of precipitation between the ORG run and the TMPA is 0.616, whereas the correlation coefficient between the SL run and the TMPA is 0.622. It means that the corrected humidity field by the NDSL scheme can slightly improve precipitation or keep the simulation skill of the original IsoRSM in the rainfall simulation. When we consider that the ORG experimental set has been widely used for various downscaling research, it is possible to understand that the regional NDSL can successfully calculate the transport and distribution of humidity in the RSM. One possible reason for why the improvement of the rainfall simulation by the NDSL scheme is not very significant is that the selected case in this study is not a heavy rainfall case. For a heavy rainfall case, the large discontinuity of a humidity field is expected, which means higher possibility of negative value occurrences in the original IsoRSM. Further studies will continue to examine how the NDSL can improve skills for the precipitation simulation in a heavy rainfall cases.

One can access the IsoRSM code through the Concurrent Versions System (CVS) server at the Center for Ocean-Atmospheric Prediction Studies (COAPS). Detailed descriptions on how to get the code and install the model can be found in the G-RSM home page (http://g-rsm.wikispaces.com/Installation). For further information or requests on the model, please contact E.-C. Chang (echang@kongju.ac.kr) or K. Yoshimura (kei@aori.u-tokyo.ac.jp).