The Impact of Radiation on the GABLS3 Large-Eddy Simulation through the Night and during the Morning Transition

Abstract

Large-eddy simulation in the GABLS3 intercomparison is concerned with the developed stable boundary layer (SBL) and the ensuing morning transition. The impact of radiative transfer on simulations of this case is assessed. By the time of the reversal of the surface buoyancy flux, a modest reduction of the lapse rate in the developed SBL is apparent in simulations that include longwave radiation. Subsequently, with radiation, the developing mixed layer grows significantly more quickly, so that four hours after the transition the mixed layer is roughly 40 % deeper; the resulting profiles of potential temperature and specific humidity are in better agreement with observations. The inclusion of radiation does not substantively alter the shape of turbulent spectra, but it does indirectly reduce the variance of temperature fluctuations in the mixed layer. The deepening of the mixed layer is interpreted as a response to the reduction of the strength of the capping inversion, resulting from cumulative radiative cooling in the residual layer and around the top of the former SBL. Sensitivity studies are performed to separate the two effects. Solar radiative heating of the atmosphere has a smaller impact on the development of the mixed layer than does longwave radiative cooling and slightly reduces its rate of growth, compared to simulations including longwave radiation alone. These simulations demonstrate that nocturnal radiative processes have an important effect on the morning transition and that they should be considered in future large-eddy simulations of the transition.

Appendix

1.1 The Radiation Scheme: Technical Details

The treatment of radiation was discussed in general terms in Sect. 3, where it was noted that the GABLS3 community had taken the view that a very simplified scheme should be used in this case to facilitate use in different models. The purpose of this Appendix is to record the technical details of the scheme.

Within the domain of a particular LES of the boundary layer, only small relative variations in the pressure and absolute temperature are expected. (In the present case, temperatures lie within the range 285–300 K.) This permits the linearization of the Planckian function in temperature and allows us to neglect variations in gaseous absorption coefficients within the domain. As a result, it is possible to produce a very compact scheme for radiative transfer that is simple to incorporate into different models and is adequate for simulating clear-sky radiation in a limited computational domain. It is also necessary to provide a set of parameters for the scheme and these must be derived from a more sophisticated radiation scheme. The set of parameters is specific to the case in question, and for conditions other than GABLS3 these would have to be rederived.

The scheme is based on the correlated $k$-distribution method, with radiation treated in a number of pseudo-monochromatic intervals. Downward fluxes are calculated using Eq. 2 and its analogue for upward fluxes. Within the $j$th interval, the Planckian function is linearized as,

$$\begin{aligned} B_j(T) = \beta _{0j} +\beta _{1j} T. \end{aligned}$$

(11)

The optical depth of the $i$th layer in the $j$th interval is written as,

$$\begin{aligned} \Delta \tau _{ij} = (k_{0j} + k_{1j} q_i + k_{2j} q_i^2) \rho _i \,\Delta z_i, \end{aligned}$$

(12)

where $q_i$ is the specific humidity in the layer, $\rho _i$ is its density and $\Delta z_i$ is its physical thickness. The parameters, $k_{lj}, l=0,1,2$ represent absorption by the well-mixed gases ($l=0$), water vapour lines and the foreign-broadened continuum ($l=1$) and the self-broadened continuum ($l=2$).

Because of the non-locality of radiative transfer, conditions above the domain of the LES cannot be neglected completely and it is necessary to specify the downward flux in each interval at the top of the domain. For this purpose, atmospheric profiles above the domain must be assumed. To ensure a smooth profile of radiative heating rates at the top of the domain, the downward fluxes are calculated for the assumed atmospheric profile and for profiles with temperatures 2 K higher or lower. A linear fit to the fluxes in terms of the temperature at the top of the model is then derived,

$$\begin{aligned} F^-_j(z_N) = f_{0j} +f_{1j} T(z_N). \end{aligned}$$

(13)

It is now necessary to specify the parameters $k_{0j}, k_{1j}, k_{2j}, \beta _{0j}, \beta _{1j}, f_{0j}$ and $f_{1j}$ in each spectral interval. These are derived using the full radiation code described by Edwards and Slingo (1996) and Cusack et al. (1999), which is itself based on the correlated-$k$ approach and has been compared with line-by-line reference results (e.g. Oreopoulos et al. 2012). In this code, the number of pseudo-monochromatic intervals can be varied. For the specific case of GABLS3, 55 pseudo-monochromatic intervals have been used. The parameters $k_{0j}, k_{1j}$ and $k_{2j}$ are taken as the corresponding values implied by the full code at a height of 400 m. The concentration of carbon dioxide is set to 380 ppmv (Solomon et al. 2007), as appropriate for the calendar year 2006. The atmospheric profile for these calculations is constructed by taking the initial profile for the LES at 0000 UTC, extended throughout the depth of the atmosphere, by adding on the mid-latitude profile of McClatchey et al. (1972). The extension could have been carried out in other ways, perhaps by using a profile from the single-column models, but the profiles encountered in GABLS3 are sufficiently similar to this standard profile that there will be little impact on radiative heating rates in the boundary layer. The downward radiative flux at the surface would be more sensitive to the profile above the large-eddy domain, but the radiative fluxes at the surface are not relevant in this case. Longwave heating rates derived from the simple scheme agree with those from the full code to within 5 % up to 500 m, except when the reference heating rates are close to zero, showing that the simple scheme is adequate for the present case.

As previously noted, the impact of shortwave radiation is small and, by comparison with full radiation calculations, it has been found that it is sufficient simply to relate the shortwave temperature tendency within the computational domain, $\dot{T}_{\mathrm{SW}}$, to the incident shortwave flux at the top of the atmosphere, $S_0$,

$$\begin{aligned} \dot{T}_{\mathrm{SW}} = 2.23\times 10^{-8} S_0, \end{aligned}$$

(14)

where $\dot{T}_{\mathrm{SW}}$ has units of K s$^{-1}$ and $S_0$ units of W m$^{-2}$.