Solar radiation plays a key role in the atmospheric system but its distribution throughout the atmosphere and at the surface is still very uncertain in atmospheric models, and further assessment is required. In this study, the shortwave downward total solar radiation flux (SWD) predicted by the Weather Research and Forecasting (WRF) Model at the surface is validated over Spain for a 10-yr period based on observations of a network of 52 radiometric stations. In addition to the traditional pointwise validation of modeled data, an original spatially continuous evaluation of the SWD bias is also conducted using a principal component analysis. Overall, WRF overestimates the mean observed SWD by 28.9 W m−2, while the bias of ERA-Interim, which provides initial and boundary conditions to WRF, is only 15.0 W m−2. An important part of the WRF SWD bias seems to be related to a very low cumulus cloud amount in the model and, possibly, a misrepresentation of the radiative impact of this type of cloud.
Solar radiation is a primary driving force of the heat, mass, and momentum fluxes in the free atmosphere and at the surface. Thus, it is a key parameter for the entire global climate system (Ramanathan et al. 1989; Wild et al. 2013), including the energy closure at the land–atmosphere boundary (Geiger et al. 2009; Jimenez et al. 2014). However, considerable uncertainties still remain in the description of the distribution of the solar radiation budget in atmospheric models from the top of the atmosphere to the surface (Wild 2005). These uncertainties have been related to misrepresentations of clouds and aerosols (Wild et al. 1995, 2013; Bellouin et al. 2005; Wild 2005; Kim and Ramanathan, 2008; Oreopoulos et al. 2012).
Most of the studies that have evaluated the ability of atmospheric models to represent the surface solar radiation budget have been conducted using general circulation models (GCMs). Yang et al. (2006) evaluated the National Centers for Environmental Prediction Global Forecast System (GFS) over the southern Great Plains in Oklahoma. They found overestimations of 44 W m−2 of the daily maximum surface downward flux, consistent with underestimation of cloud fraction in the lower and midtroposphere. Paquin-Ricard et al. (2010) evaluated the Global Environmental Multiscale (GEM) Model also over the southern Great Plains and in Alaska. They found an excess in modeled surface downward flux in the middle of the day that they attributed to a combination of underestimated cloud fraction and very high solar transmissivity of optically thin clouds. Similar results are reported for other GCMs (Räisänen and Järvinen 2010; Thelen and Edwards 2013; Van Weverberg et al. 2015). In a more general framework, Wild (2005) found an average excess of 9 W m−2 in the modeled downward surface solar radiation in a multimodel global evaluation of 20 GCMs vis-à-vis surface solar observations from 760 sites of the Global Energy Balance Archive, with an average deviation from observations as large as 31 W m−2 for individual models. At regional to local scales, however, the models’ behavior may differ substantially from the averaged global performance. Moreover, at these scales, limited-area models (LAMs) constitute a more appropriate modeling framework to represent the small-scale processes in the atmosphere and the land surface. With initial and boundary conditions set typically from GCMs, LAMs downscale the numerical representation of the earth’s system, generally using grid spacing finer than 20 km, as well as subhourly time steps. However, the representation of the surface solar radiation budget resulting from LAMs still needs to be further assessed.
In this work, a multiyear multisite observational dataset of shortwave downward total flux at the surface (SWD) is used to evaluate the performance of the Weather Research and Forecasting (WRF) LAM (Skamarock et al. 2008) at describing the surface solar radiation budget. The WRF’s performance is analyzed comparatively with respect to the GCM from which it is nested here, namely, the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim; Dee et al. 2011). The study is conducted over Spain from January 2003 to December 2012, totaling 10 years. The present novelty is that, besides the conventional pointwise evaluation, the surface solar radiation budget is also analyzed from a spatiotemporal perspective. Specifically, the spatially distributed WRF SWD bias is evaluated based on the resulting analysis of a previous data assimilation process that adjusts the WRF’s outputs to meet the ground observations.
2. Observational dataset
The observations used in this study originate from 52 radiometric stations that belong to the Spanish National Weather Service (AEMet; AEMet 2014). Their locations are shown in Fig. 1 with yellow marks. The SWD measurements are acquired with Kipp and Zonen CM-11 or CM-21 pyranometers. These are secondary-standard instruments according to the ISO-9060 standard, and comply with the specifications for the high-quality class of sensors as defined in WMO (2008). Every other year, all these instruments are recalibrated at the AEMet headquarter in Madrid, Spain, against a reference radiometer that is directly traceable to the World Radiometric Reference at the World Radiometric Centre in Davos, Switzerland.
Data are acquired every minute and are quality controlled every day to prevent instrumental or malfunctioning errors such as unexpected shading, tracking errors, or soiling. Before being archived as hourly averages, they undergo standard quality-assessment procedures, including physical limits, climatological limits, and, whenever possible, verification of the fundamental radiation closure equation. The typical uncertainty that can be expected from these instruments under field conditions is ≈5% (Gueymard and Myers 2009).
3. Surface solar radiation budget modeling
WRF version 3.6 is used here to simulate SWD for the 10-yr period spanning January 2003–December 2012. The simulated domain spans the continental Spain and the Balearic Islands at 10-km spatial resolution.
Starting with version 3.6, WRF now includes a parameterization of the shortwave aerosol optical properties, which has been especially devised for the assessment of surface solar radiation. This parameterization is important in the present context because it provides an efficient way to evaluate the solar radiation extinction by atmospheric aerosols, using only two inputs with relatively widespread availability: the total (vertically integrated) aerosol optical depth at 550 nm (AOD), and the predominant type of aerosol aloft (Ruiz-Arias et al. 2013, 2014, 2015). For this numerical simulation, AOD is obtained from the Monitoring Atmospheric Composition and Climate (MACC) project reanalysis (Benedictow et al. 2013), which provides AOD every 3 h on a grid with a spatial resolution of 1.25° × 1.25°. A continental (or rural) aerosol type is assumed, which has proven a good performance over average turbidity conditions (Ruiz-Arias et al. 2014, 2015) as it is the case in Spain. The WRF numerical simulation is performed with initial and boundary conditions from the ERA-Interim (Dee et al. 2011).
The spatial setup consists of two domains having a two-way nesting with 30- and 10-km grid spacing, respectively, and 38 vertical layers. Grid nudging is applied to the meridional and zonal wind components, temperature, and water vapor mixing ratio above the 15th model’s vertical layer, which is located at approximately 560 hPa. The model runs are restarted every 8 days, with the first day always considered as model spinup. The model time step is 50 s and SWD is computed every 10 min. The physical configuration setup includes the WRF single-moment 6-class microphysics scheme (WSM6; Hong and Lim 2006), the Kain–Fritsch parameterization for the subgrid-scale cumulus clouds (Kain 2004), the Yonsei University parameterization for the PBL scheme (Hong et al. 2006), the Unified Noah parameterization for the land surface scheme (Tewari et al. 2004), and the Rapid Radiative Transfer Model for Global Climate Models (RRTMG) radiative transfer parameterization for the shortwave and longwave radiation schemes (Iacono et al. 2008).
4. Modeled surface solar radiation budget at the observation sites
In all what follows, the validation study is conducted at a monthly time scale. Thus, the validation dataset at each observational site consists, at most, of 120 monthly values. The pointwise comparison of the modeled and observed SWD values at all the validation sites combined (shown in Table 1) reveals that WRF significantly overestimates the observed SWD. The mean bias is 28.9 W m−2 (≈16%, with respect to the mean observed value), which is close to the maximum average deviation of 31 W m−2 found by Wild (2005) for individual GCMs. In the case of the ERA-Interim dataset, which defines SWD over a grid with 79-km spacing, SWD is also overestimated, but to a much lesser extent (15.0 W m−2). Note that the large WRF SWD bias cannot be explained on the basis of a hypothetical bias in AOD alone. Bellouin et al. (2013) estimated the total SW direct radiative effect (DRE) of aerosols over land to be about 11.5 ± 1.9 W m−2, using data from the MACC reanalysis. Thus, considering that, in this study, the aerosol SW DRE is also derived from the MACC AOD, most of the DRE should be already included in the SWD predictions. Based on the AOD DRE estimated by Bellouin et al. (2013), the worst-case contribution of aerosols to the present SWD bias should be roughly equal to the uncertainty they found (i.e., only a few watts per square meter). Mateos et al. (2013) estimated the SW DRE of clouds to be −78 W m−2, based on 6 yr of ground observations gathered in Granada (Spain), a location within our study area. Thus, a bias in the representation of clouds in WRF might well explain the SWD bias shown in Table 1. In turn, these results suggest that WRF could estimate a very low cloud amount, and/or underestimate the radiative impact of clouds.
The results presented so far are only strictly valid for the whole observational dataset combined. A more detailed spatially distributed estimation of the WRF SWD bias is performed in the next section, with the goal to gain an understanding of the spatiotemporal characteristics and causes of the bias.
5. Spatiotemporal characteristics of the WRF SWD bias
An optimal interpolation analysis of the WRF SWD monthly estimates is conducted month by month to match the observed pointwise SWD values over the study region. The process, which is described in detail in Ruiz-Arias et al. (2015), results in 120 monthly maps of gridded SWD with 10-km spacing. The maps are a spatially distributed estimate of the true SWD field throughout the 10-yr validation period during 2003–12. To evaluate the WRF representation of SWD, we focus on the analysis increments, defined as the difference between the raw WRF SWD estimates and the SWD analyses that result from the optimal interpolation process. The analysis increments are therefore a spatially continuous estimate of the WRF SWD bias error.
Figure 2a shows the average WRF SWD bias (positive if WRF overestimates compared to ground observations) in the study region over the 10-yr validation period. Throughout the entire region, the mean SWD bias is 27.3 W m−2, very close to its mean value at the 52 observational sites combined (28.9 W m−2) shown in Table 1. The SWD bias is smaller than 34.3 W m−2 in 90% of the region’s area. The 10% remaining areas are distributed mostly along the Cantabrian coast and the Cantabrian Mountains (see Fig. 1), hereafter collectively referred to as the Cantabrian region. Figures 2b–d show the average SWD bias from September to February (autumn/winter), from March to May (spring), and from June to August (summer), respectively. The SWD bias in autumn/winter and spring is relatively homogeneous throughout the entire validation area, with mean values of 18.5 and 37.6 W m−2, respectively. The summer season, however, presents a strong differential performance over the Cantabrian region, where bias values are greater than 50 W m−2, compared to the rest of the study region. For instance, the mean SWD bias over the whole country during summer is only 34.6 W m−2.
To explore the interrelationship that might exists between the overall SWD overestimation caused by WRF and a possible cloud amount underprediction, Figs. 2e–h show the total and seasonal WRF cloud fraction coverage (CFC) average differences with respect to the Climate Monitoring Satellite Application Facility (CMSAF) CFC product (Stengel et al. 2013) for the same 10-yr period as in Figs. 2a–d. Similar results are shown in Figs. 2i–l, but with respect to the ERA-Interim CFC. The annual mean CFC during the entire period is 49.3% according to CMSAF or 40.2% according to ERA-Interim, which are both significantly larger than the value predicted by WRF—only 30.8%. These results are consistent with the higher WRF SWD overprediction than with ERA-Interim’s, as discussed earlier (Table 1). On a seasonal basis, the WRF CFC is always smaller than the CMSAF CFC over the entire region. In contrast, although the ERA-Interim CFC is also smaller than the CMSAF CFC over most of the region (albeit with less underprediction than WRF’s), it also overestimates compared to the CMSAF satellite-derived CFC product over some areas, allowing ERA-Interim to achieve a lower SWD bias than WRF. During the summer season, the WRF SWD predictions largely overestimate compared to the observed SWD (i.e., the WRF SWD bias is positive) along the Cantabrian region (see Fig. 2d). Interestingly, this coincides with an unusually large underprediction of CFC by both WRF and ERA-Interim, compared to CMSAF (Figs. 2h and 2l). The relative importance and the possible causes of this SWD overprediction are assessed in the following subsection.
Principal component analysis of the WRF SWD bias
The temporal and spatial variability of the WRF SWD bias can be better understood using a principal component (PC) analysis (Von Storch and Zwiers 2002; Wilks 2011). This statistical multivariate analysis, which has been broadly applied in atmospheric dynamics, climate, and renewable energy studies, among others (Esteban-Parra et al. 1998; Pozo-Vázquez et al. 2001; Rattan and Hsieh 2004; Santos-Alamillos et al. 2012, 2014), also facilitates the identification of physical processes behind model errors. In this particular study case, if the WRF SWD bias dataset is interpreted as a collection of monthly bias time series (one time series at each model grid location), the PC analysis finds a new collection of monthly time series formed as linear combinations of the original ones. These combinations are performed such that the new time series, known as PCs, are orthogonal to each other and individually explain the maximum possible amount of variance of the original dataset under the constraint that only linear combinations are allowed.
The PC analysis is conducted here over the 10-km maps (i.e., 11 559 model grid cells in each map) of the monthly WRF SWD bias between 2003 and 2012 (i.e., 120 maps), resulting in a total of 11 559 monthly time series of 120 time steps. Figure 3a shows the first PC time series (PC_1) that results from the PC analysis. PC_1 is further renormalized to recast its units to watts per meters squared so it is directly comparable to the WRF SWD bias time series. It explains 72% of the total variability in the WRF SWD bias (i.e., almost three quarters of the total variance). In Fig. 3a, a very good agreement between PC_1 and the average WRF SWD bias time series (dashed line) is noticeable over the whole region. This is consistent with the large explained variance of PC_1. The WRF SWD bias is always positive, as is also apparent in Fig. 2. It has a very strong seasonal pattern, with maxima in the range 40–55 W m−2 from March to June, and minima in the range 10–15 W m−2 in November and December. Because these characteristics are fairly well reproduced by PC_1, which explains a very large fraction of the dataset variability, this seasonal pattern should be present in a large portion of the study area. This is confirmed in Fig. 3b, where PC_1 is correlated with the WRF SWD bias time series at each model grid location. The mean correlation coefficient throughout the whole region is very high (0.85) and 90% of its individual values are even greater than 0.73. Therefore, the bias error of the WRF Model at estimating SWD changes seasonally and very homogeneously throughout the entire study region. This bias can be mostly attributed, as discussed in section 4, to a systematic underestimation of the actual cloud amount and, possibly, a misrepresentation of the radiative effects of clouds.
Figure 3c shows the second PC time series (PC_2) that results from the PC analysis. Like PC_1, PC_2 is renormalized to recast its units to watts per meters squared so that it is directly comparable to the WRF SWD bias time series. PC_2 explains 10% of the total variability of the WRF SWD bias. Interestingly, it systematically reaches its yearly minima during the summer months (particularly, June and July) pointing out to some singularity during these periods. As with Fig. 3b for PC_1, Fig. 3d shows the correlation between the PC_2 and the WRF SWD bias time series at each model grid location. In this case, the correlation is not homogeneously distributed throughout the entire region. The absolute value of the correlation coefficient is larger than 0.6 only over the Cantabrian region, where PC_2 is actually anticorrelated with the WRF SWD bias. The location with the strongest anticorrelation is denoted as A in Fig. 3d, where the correlation coefficient is −0.67. The WRF SWD bias time series at this location is plotted in Fig. 3c (dashed line) to help compare it to PC_2. Note that the yearly minima of PC_2 perfectly agree in time with the yearly maxima of the WRF SWD bias at location A, as a result of their mutual anticorrelation.
Most precipitation in Spain occurs from November to March, and is associated with transient frontal systems coming from the Atlantic Ocean (Esteban-Parra et al. 1998; Rodriguez-Puebla et al. 1998; Serrano et al. 1999; Trigo et al. 2004; Muñoz-Díaz and Rodrigo 2004). During April and May, these systems reach the Iberian Peninsula only occasionally. As a consequence, since ground moisture and solar radiation during these months are high enough to trigger moist convection, cloudiness in spring is mostly convective. Summer months are dry and hot, except in the Cantabrian region where frontal systems and cloud convection episodes are common (Serrano et al. 1999; Trigo et al. 2002). These convective cloud regimes in Spain help explain the WRF SWD bias patterns described in section 5 for two reasons: (i) the high bias during spring (PC_1) is generalized and spatially homogenous and (ii) the summer overestimation peaks over the Cantabrian region (PC_2). All this suggests that these biases are tied to a deficient representation of cumulus clouds and/or their radiative impact.
Prior to WRF version 3.6, the radiative impact of subgrid-scale cumulus clouds generated with the Kain–Fritsch parameterization (the one used in the present study) was not considered in WRF, which is the case with the results presented so far. However, since that release, the radiative feedback of these clouds can be optionally accounted for via cloud fraction estimates of the subgrid-scale shallow and deep cumulus clouds (Alapaty et al. 2012). Then, in order to better discern the causes behind the WRF SWD bias, the radiative feedback of subgrid-scale cumulus clouds was activated in a new experiment simulating the 3-yr period of the observational dataset from 2010 to 2012.
Figures 4a–c show the average SWD bias during 2010–12 for three cases: (i) WRF without subgrid-scale cumulus clouds feedback to radiation, (ii) WRF with this feedback activated, and (iii) using ERA-Interim as a reference. The radiative impact of subgrid-scale cumulus clouds (Fig. 4b) reduces the overall WRF SWD bias by 4.5 W m−2 over the entire region on average, but WRF still underperforms with respect to ERA-Interim in almost the entire study region (Fig. 4c). The monthly spatial average of the SWD bias is shown in Fig. 4d. The highest WRF improvement occurs from April to June, when the bias decreases by ≈10 W m−2, consistent with the higher generalized cloud convection expected for these months. For the remaining months the bias decreases by ≈2 W m−2.
An interesting feature shown in Figs. 4a–c is that, over the Cantabrian region, WRF does provide the best SWD estimates, even better than ERA-Interim, when the subgrid-scale cumulus cloud radiation feedback is included. The rationale behind this finding is that this region is prone to orographic clouds in summer in addition to the other aforementioned cloud regimes. As shown in Fig. 1, the prevailing surface winds during summer blow from the coast (north) perpendicularly toward the Cantabrian Mountains (south), which have peaks higher than 2500 m above sea level. This situation tends to frequently create orographic clouds by the lift of the moist air from the sea. For the accurate representation of this type of clouds, a high-resolution resolved topography is required. In consequence, the high spatial resolution of WRF in combination with the radiative feedback of subgrid-scale cumulus clouds results in large benefits to reduce the SWD bias over this mountainous area.
The distribution of the solar radiation budget throughout the atmosphere and at the surface is still dubious in atmospheric models, mostly due to uncertainties in the representation of processes involving clouds, aerosols, and their mutual interactions. Although these uncertainties have been thoroughly evaluated in general circulation models, limited-area models, such as the WRF Model, still require further assessment. In this evaluation study, we use irradiance observations from 52 radiometric stations to validate the shortwave downward total solar radiation flux (SWD) predicted by WRF at the surface over the entire continental Spain during a 10-yr period. In addition to performing a conventional pointwise validation limited to the locations of the ground observations, the ground observations are also used to perform a principal component analysis based on an optimal interpolation of the data, thus resulting in a spatially continuous evaluation of the WRF SWD bias.
The comparison of the modeled and observed SWD values reveals that WRF significantly overestimates SWD by 28.9 W m−2 overall, whereas the bias in the ERA-Interim SWD predictions is only 15.0 W m−2. Considering that the latter provides the initial and boundary conditions to the former, the counterintuitive finding that the use of WRF can degrade—rather than improve—the initial surface irradiance estimates constitutes a concern for many potential applications of WRF. The spatiotemporal analysis undertaken here shows that the bias in the WRF predictions of SWD has a marked seasonal and spatially homogeneous variability pattern throughout the entire study area, with a mean bias varying from ≈15 W m−2 during winter months to ≈50 W m−2 in spring. In parallel, an independent comparison against satellite retrievals of cloud fraction coverage shows that the WRF SWD overprediction is consistent with its underprediction of cloud fraction coverage. Furthermore, the analysis of the principal modes of variation of the WRF SWD bias reveals that a significant part of the bias appears to be tied to an underprediction of the cumulus cloud amount, most particularly. This is further confirmed when the radiative feedback of subgrid-scale cumulus clouds is considered in WRF, since the SWD bias then decreases. However, on average, it only decreases by 4.5 W m−2, meaning that a greater cloud fraction amount is probably required for subgrid-scale cumulus clouds, particularly during spring and summer months.
Ongoing work is being conducted to further elucidate the role of the parameterization of the subgrid-scale deep and shallow cumulus clouds in the WRF Model and to determine whether this effectively leads to the anticipated improvement in the accuracy of SWD predictions.
The ground radiometric data used for this study belong to the Spanish National Weather Service (AEMet) and are available upon request (http://www.aemet.es). The ERA-Interim belongs to the European Centre for Medium-Range Weather Forecasts and are available following registration (http://www.ecmwf.int). The authors are supported by the Spanish Ministry of Science and Innovation under the Project CGL2011-30377-C02-01 and FEDER funds through the Junta de Andalucia research group TEP-220. José A. Ruiz-Arias is funded by the International Campus of Excellence Andalucia TECH of the University of Málaga (Spain) through a postdoctoral contract.