The radiation budget in a regional climate model

Abstract

The long- and short-wave components of the radiation budget are among the most important quantities in climate modelling. In this study, we evaluated the radiation budget at the earth’s surface and at the top of atmosphere over Europe as simulated by the regional climate model CLM. This was done by comparisons with radiation budgets as computed by the GEWEX/SRB satellite-based product and as realised in the ECMWF re-analysis ERA40. Our comparisons show that CLM has a tendency to underestimate solar radiation at the surface and the energy loss by thermal emission. We found a clear statistical dependence of radiation budget imprecision on cloud cover and surface albedo uncertainties in the solar spectrum. In contrast to cloud fraction errors, surface temperature errors have a minor impact on radiation budget uncertainties in the long-wave spectrum. We also evaluated the impact of the number of atmospheric layers used in CLM simulations. CLM simulations with 32 layers perform better than do those with 20 layers in terms of the surface radiation budget components but not in terms of the outgoing long-wave radiation and of radiation divergence. Application of the evaluation approach to similar simulations with two additional regional climate models confirmed the results and showed the usefulness of the approach.

Appendices

Appendix 1: Results compared to other regional climate models

To see how our results with the regional model CLM compare to results with other regional climate models, we investigated simulations with the REMO regional climate model of the Max Planck Institute for Meteorology (Hamburg, Germany) (Jacob et al. 2001, 2007) and the ALADIN in climate mode of the Centre National de Recherches Météorologiques (Toulouse, France) (Sanchez-Gomez et al. 2008; Radu et al. 2008). These two regional climate models were applied in the EU-project ENSEMBLES (Hewitt and Griggs 2004) and we have analysed the corresponding simulations for Europe. The used simulations were ERA40 driven with a horizontal resolution of 0.5°. The REMO used 27 and ALADIN used 31 vertical layers, respectively.

The model bias of REMO (Fig. 10) relatively to SRB and ERA40 was small and for all parameters within the uncertainty range of the reference data. Opposite to CLM there was a small overestimation of TNS, which led to a larger solar divergence error than quantified for CLM. The model bias of ALADIN (Fig. 10) was of similar magnitude as of CLM, but in all cases with the opposite algebraic sign. Thus, ALADIN showed an overestimation of short-wave net radiation and an underestimation of long-wave net radiation. This shows that our evaluation approach is useful in identification of inter-model difference in radiation budget components.

Fig. 10

Same figure as Fig. 1 but additionally with biases of REMO and ALADIN

In terms of the identification of error sources the pattern of the dependence of flux errors on errors in the explaining quantities CFR, ALB, and TS in general was similar for all investigated models and setups (CLM20, CLM32, REMO, ALADIN). Figure 11 (upper panels) shows a strong dependence of the SNS differences in REMO and ALADIN on errors in CFR and ALB. For SNL (Fig. 11, lower panels) there was also a strong dependence on errors in CFR, while there was no dependence on errors in TS. These results compare very well to the results shown for CLM in Fig. 6.

Fig. 11

Same figure as Fig. 6 but for REMO and ALADIN and only for surface radiation components

The explained variances (not shown) also yielded similar results as those displayed for CLM in Fig. 7. Errors in CFR explain two to three times more than errors in ALB of the error variance in solar fluxes. For ALADIN explained variances for errors in ALB were with a range of about 11–22% clearly higher than for errors in TS, with a range of 0–7%. For REMO the values of explained variance for errors in ALB as well as for TS had a higher range than for ALADIN (for ALB 5–22%, for TS 2–22%). Thus, the investigation of REMO and ALADIN confirms the results with CLM that it is useful to invest some effort in relatively easily improvable parameters like CFR and ALB in further improvement of RCMs.

Appendix 2

By the help of a simplified calculation we wanted to discuss the impact of uncertainties in CFR, ALB, or TS on radiation fluxes. In the solar spectrum a cloud albedo of one and a transparent clear-sky atmosphere were assumed. Then the shortwave radiation components (SW) can be written to:

$$ \begin{gathered} {\text{SW}}_{\text{SFC}} \!\downarrow = \left( { 1- {\text{CFR}}} \right)\cdot{\text{SW}}_{\text{TOA}} \!\downarrow \hfill \\ {\text{SW}}_{\text{SFC}} \!\uparrow = {\text{ALB}}\cdot\left( { 1- {\text{CFR}}} \right)\cdot{\text{SW}}_{\text{TOA}} \!\downarrow \hfill \\ {\text{SW}}_{\text{TOA}} \!\uparrow = {\text{SW}}_{\text{TOA}} \!\downarrow \cdot\left[ {{\text{ALB}}\cdot\left( { 1- {\text{CFR}}} \right)^{ 2} + {\text\,{CFR}}} \right] \hfill \\ \end{gathered} $$

The indices SFC and TOA represent the surface or top of atmosphere and the arrows ↑ or ↓ represent the upwelling or downwelling fluxes. The net short-wave fluxes are given by:

$$ \begin{gathered} {\text{SNS}} = {\text{SW}}_{\text{SFC}} \!\downarrow - \,{\text{SW}}_{\text{SFC}} \!\uparrow = \left( { 1- {\text{ALB}}} \right)\cdot\left( { 1- {\text{CFR}}} \right)\cdot{\text{SW}}_{\text{TOA}} \!\downarrow \hfill \\ {\text{TNS}} = {\text{SW}}_{\text{TOA}} \!\downarrow - \,{\text{SW}}_{\text{TOA}} \!\uparrow = {\text{SW}}_{\text{TOA}} \!\downarrow \cdot\left[ { 1- {\text{ALB}}\cdot\left( { 1- {\text{CFR}}} \right)^{ 2} + {\text{CFR}}} \right] \hfill \\ \end{gathered} $$

The impact of errors in CFR and ALB is nearly linear, but (a) CFR is larger than ALB on average and (b) the error in CFR typically is larger than the error of ALB. The average values are given in Table 1 and applied in simple calculations summarised in Table 2. The results show that an overestimation in CFR and ALB led to a decrease in SNS and TNS and that the impact of errors in CFR was larger than the impact of errors in ALB on average.

Table 1 Mean values and typical errors (mean errors of all data) for CFR, ALB and TS in the model simulations discussed

Table 2 Example of a simplified calculation of typical errors in SNS (denoted by ∆SNS) and TNS (denoted by ∆TNS) to test the sensitivity to uncertainties in CFR (denoted by ∆CFR) and ALB (denoted by ∆ALB) under the assumption of SW_TOA↓ = 1367/4 W/m²

In case of long-wave radiation (LW) the single components are given by:

$$ \begin{gathered} {\text{LW}}_{\text{SFC}} \!\uparrow = \sigma \cdot{\text{TS}}^{ 4} \hfill \\ {\text{LW}}_{\text{SFC}} \!\downarrow = 0. 7 5\cdot\sigma \cdot{\text{TS}}^{ 4} \cdot\left( { 1+ 0. 2 2\cdot{\text{CFR}}^{ 2} } \right) \hfill \\ {\text{LW}}_{\text{TOA}} \!\uparrow = \, \left( { 1- {\text{CFR}}} \right)\cdot\sigma ^{*}\cdot{\text{TS}}^{k^{*}} + {\text{CFR}}\cdot\left( {\left( { 1- \varepsilon ^{*}} \right)\cdot\sigma ^{*}\cdot{\text{TS}}^{k^{*}} + \varepsilon ^{*}\cdot\sigma ^{*}\cdot{\text{TC}}^{k^{*}} } \right) \hfill \\ \end{gathered} $$

The SFC components were estimated following Ångström and Bolz (see Warnecke 1997) with σ the Stefan Boltzmann constant. The outgoing long-wave radiation LW_TOA↑ was approximated following Corti and Peter (2009). They estimated the parameters σ* and k* to 1.607 × 10⁻⁴ Wm⁻² K⁻⁴ and 2.528, respectively, by radiative calculations. For a mid-level cloud a cloud temperature TC = 255 K and an effective cloud emissivity ε* = 0.79 (Allen 1971) were assumed. The choice of the cloud emissivity was important for the respective impact of CFR and TS (the higher ε, the higher is the impact of CFR and the lower the impact of TS). SNL and TNL are the difference of the downwelling minus the upwelling component:

$$ \begin{gathered} {\text{SNL}} = {\text{LW}}_{\text{SFC}} \!\downarrow - {\text{ LW}}_{\text{SFC}} \!\uparrow = \sigma \cdot{\text{TS}}^{ 4} \cdot\left( {0. 1 6 5\cdot{\text{CFR}}^{ 2} - 0. 2 5} \right) \hfill \\ {\text{TNL}} = 0 - {\text{LW}}_{\text{TOA}} \!\uparrow = - \sigma ^{*}\cdot\left( {\left( { 1- {\text{CFR}}} \right)\cdot{\text{TS}}^{k^{*}} + {\text{CFR}}\cdot\left( {\left( { 1- \varepsilon ^{*}} \right)\cdot{\text{TS}}^{k^{*}} + \varepsilon ^{*}\cdot{\text{TC}}^{k^{*}} } \right)} \right) \hfill \\ \end{gathered} $$

For the example calculations in Table 3 typical errors of TS (denoted by ∆TS) and CFR (denoted by ∆CFR) were assumed (see Table 1). The table shows that the typical impact of errors in CFR was larger than in TS because of a partly compensation of terms with TS. In Table 3 it is also to see that ∆TNL in most cases was smaller than ∆SNL, while Fig. 1 shows a larger bias for TNL than for SNL. In combination with Fig. 7, where it can be seen that the explained variance for TNL was lower than for SNL, this shows that especially for TNL there were other important influencing factors besides CFR and TS. For example, Corti and Peter (2009) said that their parameterization could be improved by including a measure for the amount of absorption from water vapour, but they left it for simplification reasons.

Table 3 Example of a simplified calculation of typical errors in SNL (denoted by ∆SNL) and TNL (denoted by ∆TNL) to test the sensitivity to uncertainties in TS (denoted by ∆TS) and CFR (denoted by ∆CFR)