Optimization of numerical weather model parameterizations for solar irradiance prediction in the tropics

In this study, Weather Research and Forecasting (WRF) model ³⁰⁾ version 3.6.1 is applied to forecast solar irradiance. This is a physical meteorological model with fully compressible non-hydrostatic equations developed by the National Center for Atmospheric Research (NCAR) and the National Center for Environmental Prediction (NCEP). It is used not only for real-time numerical weather forecasting, but also for research using idealized conditions, data assimilation, etc. It contains many physical parameterization options for meteorological micro-processes, e.g. planetary boundary layer (PBL) physics and cumulus parameterization, and users select schemes suited to their purpose. In the world, there are variety of weather conditions due to regional and climatic conditions. Suitable options should be selected for WRF to obtain appropriate computation of the weather. However, their selection is still empirical for users.

It can simulate two-way nesting and apply across scales ranging from hundreds of meters to thousands of kilometers. It is open-source software and is widely used throughout the world.

This meteorological phenomenon usually spreads horizontally and moves in a horizontal direction, e.g. stratus and wind near the ground. Most meteorological models employ this feature for the formulation of principal equations. However, cumulus and cumulonimbus are common clouds in the tropics, which grow vertically, and their behavior negatively impacts the accuracy of meteorological simulations. Therefore, in this study, we seek the optimal combination of the schemes of the physical parameterization options for the solar irradiance simulation with WRF in the tropical zone.

Figure 1 shows the topography of Thailand and the computational domains in this study. It is three-level nesting. The coarse domain is Domain 1, and its child domain is Domain 2. Domain 3 is the child domain of Domain 2. The horizontal resolutions of Domains 1, 2 and 3 are 18, 6 and 2 km, respectively. The National Electronics and Computer Technology Center (NECTEC) is at the center of Domain 3, and observes the global horizontal solar irradiance and some meteorological parameters with a pyranometer and a weather station as a reference of the WRF simulation.

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The computational settings of weather simulation with WRF are summarized in Table I. The final analysis data of the NCEP operational Global Forecast System (GFS) 0.25-degree grids (horizontal resolution 0.25° × 0.25°, three-hourly interval) ³¹⁾ are used as the initial and boundary conditions and data assimilation for model simulation. The NCEP data are re-analyzed as part of the forecasted data, NCEP GFS-0.25, which are used by the authors to forecast the solar irradiance in Thailand. ¹²⁾

The computed global horizontal irradiance at the target point is output every 10 min, and the accuracy of the simulation is evaluated by comparison with the observation data.

The target period of simulation is a whole year from January to December in 2019. Before simulation, spin-up computation was performed for one day.

The global horizontal solar irradiance and meteorological parameters, e.g. wind speed and ambient temperature, are observed at NECTEC, which is in the center of Domain 3 in Fig. 1, for references of the simulation, as previously explained. The sampling interval of the observation is 1 min. Since the WRF output is a 10 min interval, 10 min average observational data is used in this study.

First, we selected six primary physical parameterization options; PBL, surface layer, cumulus, shortwave radiation, longwave radiation and microphysics, which may affect the accuracy of weather simulation in the tropics. Then one-year WRF simulations were performed with different combinations of schemes of the options. Then, the accuracy of the simulations was evaluated with a statistical error index, and the optimal combination of schemes is found. However, the weather simulation is computationally expensive, and since there are numerous combinations of the options it is not feasible to compute all of them. Consequently, the most commonly used schemes are selected and tested for the sensitive analysis in this study.

There are several statistical error indices, e.g. correlation coefficient (Corr) and rms error (RMSE). In this study, we employ the Corr of the irradiance as an evaluation index of the simulation error to the observation because it can assess the accuracy of the short-period variations, less than one day, of the irradiance.

The Corr and RMSE are defined as follows:

$$\begin{eqnarray}&&{\rm{Corr}}=\displaystyle \frac{\displaystyle {\sum }_{i=1}^{n}\left({x}_{i}-\bar{x}\right)\left({y}_{i}-\bar{y}\right)}{\sqrt{\displaystyle {\sum }_{i=1}^{n}{\left({x}_{i}-\bar{x}\right)}^{2}\displaystyle {\sum }_{i=1}^{n}{\left({y}_{i}-\bar{y}\right)}^{2}}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\rm{RMSE}}=\sqrt{\displaystyle \frac{1}{n}\displaystyle {\sum }_{i=1}^{n}{\left({x}_{i}-{y}_{i}\right)}^{2}},\end{eqnarray} \tag{ 2 }$$

where x_i and y_i are simulated and observed diurnal irradiances, $\bar{x}$ and $\bar{y}$ are averages of x and y, respectively, and n is the number of data x_i or y_i .

If the Corr is large, the simulation error on the RMSE may be caused by the tendencies of WRF itself, e.g. overestimation, and it may be improved with a post-processing of WRF simulation. We will adopt this approach in future work.

We seek the optimal combination of schemes of physical parameterization options in a similar way to Arasa et al. ¹⁵⁾ A total of 20 simulations with different schemes have been performed progressively. The combinations of schemes for the simulations are listed in Table II. First, we performed WRF computation with the initial setup of schemes (Experimental name: INI). They are MYNN2, ^32,33) Eta sim, ^34–37) KF, ³⁸⁾ Dudhia, ³⁹⁾ RRTMG ⁴⁰⁾ and Thomson ⁴¹⁾ for the options PBL, surface layer, cumulus, shortwave radiation, longwave radiation and microphysics, respectively. Next, the microphysics option changed from Thomson to WSM3, ⁴²⁾ WSM6 ⁴³⁾ and SBU-Lin ⁴⁴⁾ in order, and the best scheme for the microphysics option was determined from the Corr of the solar irradiance between WRF simulation and observation. Then, the microphysics option was fixed with the best scheme, and the longwave radiation option was changed from RRTMG to Goddard, ^45,46) RRTM ⁴⁷⁾ and FLG. ^48,49) Similar processes were performed for cumulus with BMJ, ³⁵⁾ Grell 3D ^50,51) and New SAS, ⁵²⁾ and for PBL with YSU, ⁵³⁾ MYJ, ³⁵⁾ QNSE, ⁵⁴⁾ ACM2, ⁵⁵⁾ MYNN3, ^32,33) UW ⁵⁶⁾ and GBM. ⁵⁷⁾ The surface layer was changed by following PBL, because its selection is briefly dependent on the PBL. Table III shows the Corrs of each experimental case, and Table IV shows the optimal combination of schemes of the parameterization options selected with the sensitive analysis. The experimental case PBL1 has the highest Corr, as in Table III, and it is the optimal one. The RMSE for each case is also printed as a reference. For the experimental cases LWR3, SWR2 and PBL3 the numerical simulations were not completed due to instability of the model, and neither Corr nor RMSE was evaluated, as shown in the table. Therefore, their applicability could not be determined. The instability may occur at sudden change in the weather, and neither the time-step nor the grid resolution is responsible for the change.

The schemes of the parameterization options selected are summarized. SBU-Lin for microphysics considers quick growth of ice crystals (riming). Goddard for longwave radiation focuses on the solar irradiance transmission. Dudhia for shortwave radiation was developed under the winter conditions of the South China Sea. KF for cumulus parameterization contains the large-scale convection process with time scale of downdrafts or convective available potential energy. MM5 for the surface layer is the scheme developed for the former weather model MM5 (Fifth-Generation Penn State/NCAR Mesoscale Model). ^58–60) YSU for PBL represents convection reduction with high accuracy.

Brief explanations of the other schemes listed in Table II are in the Appendix A·I.

The Corrs with the initial setup (Experiment INI) and the optimal schemes (Experiment PBL1) are 0.773 and 0.814, respectively, as in Table III. The Corr increases 0.041 by the optimization. The evaluation index for the optimization is Corr, but the RMSE is also improved from 241.5 to 204.7 W m⁻² by introducing the optimal ones.

Figure 2 shows 30-day moving averages of statistical error indices, Corr and RMSE of the solar irradiance simulations of all experimental cases. Winter in Thailand, from November to the next mid-March, has dry weather and is usually fine. As the Corr under the initial setting (INI) in Fig. 2(a), the WRF can simulate solar irradiance with high accuracy in this season. On the other hand, in summer, from mid-March to mid-May, there are cloudy and rainy days and the solar irradiance changes due to shading by clouds. Simulation of the irradiance with WRF becomes difficult and its accuracy reduces, as shown by the Corr in the figure. In the rainy season, from mid-May to October, the weather is even worse for the solar irradiance simulation, and its Corr drops to 0.7.

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The Corr of the case with the optimal combination is not at its highest in all months, as shown in Fig. 2(a), but it is the highest over the year, as listed in Table III. The Corr in the rainy season improved compared to the one in summer, by about 0.8, by introducing the optimal combination of schemes, as shown in the figure. However, there is very little improvement in simulation accuracy in summer, as shown in the figure. The application of the optimal schemes does not contribute to the improvement in this season. Since sufficient accuracy had already been obtained in winter with the initial setup of the schemes, the improvement in accuracy with the optimal schemes was limited.

The Corrs of monthly simulations improved throughout the year by introducing the optimal combination of schemes, as shown in Fig. 2(a). Only in February, does the Corr of the optimal schemes deteriorate, but only slightly.

The monthly RMSEs in Fig. 2(b) show the same trend as the Corrs in Fig. 2(a); higher accuracy in winter than in the other seasons. The RMSEs are reduced throughout the year by introducing the optimal schemes. The optimization of the parameterization options is for improving Corr only, but as a result, the RMSE is also improved by the optimization. The improving of monthly Corrs by the optimal schemes is limited in winter and summer, but the RMSEs are reduced by the optimal schemes in all the seasons.

The correlation maps of observed and simulated solar irradiance in April are plotted in Fig. 3. April is in summer, and the irradiance fluctuates strongly due to cloud shading. The fluctuation makes forecasting or representation of the irradiance difficult in this season. The red lines in the graphs are regression lines. Their slopes with (a) the initial and (b) the optimal combinations of schemes are 1.131 and 1.048, respectively. As can be seen in Fig. 3(a), WRF overestimates the irradiance, and the slope of the regression line is more than unity. The overestimation is canceled by introducing the optimal schemes, as shown in Fig. 3(b). Similar trends to in April are observed in other months. In April, the Corr is not improved by introducing the optimal schemes, but the RMSE is improved, as shown in Fig. 2. The reason is the cancellation of WRF overestimation, as shown in Fig. 3.

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As shown in Figs. 2 and 3, the introduction of the optimal combination of scheme is effective throughout the year, especially in rainy season, from mid-May to October.

Figures 4 and 5 show the simulated and observed solar irradiance from July 26–28, 2017 during the rainy season. The weather was unstable and the solar irradiance fluctuated due to cloud shading, as shown in the figures. During the rainy season the solar irradiance varies quickly due to the clouds. Therefore, forecasting or representation of the weather and the irradiance with WRF is difficult, as shown in the figures.

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Figure 4 shows all the simulated solar irradiance with the combination of schemes listed in Table II. There are large variations between the experimental cases, and this indicates the importance of setting up the parameterization options. In this figure, the simulated irradiance is larger than the observation in most of the experimental cases on 26 July. On the other hand, the irradiance is underestimated in most of the cases on 27 July. It can also be seen in the figure that the short-period variations do not correlate well with the simulation in this period.

Figure 5 shows the solar irradiance simulated with (a) the initial combination of schemes and (b) the optimal one. By introducing the optimal schemes, the simulated irradiance is reduced and comes near to the observation on 26 July. After a few days, the irradiance simulated with the optimal schemes is larger than the one with the initial conditions, and the simulation accuracy is improved with the optimal ones. The simulated short-period fluctuations of the irradiance are also improved and match the observation by introducing the optimal combination of schemes of the physical parameterization options.

In this study, the optimal combination of schemes is found, and its introduction improves the simulation accuracy. However, there is room for improvement in the simulation accuracy, as shown in Fig. 4(b). A complete simulation with an NWP model is not feasible due to its imperfections. A method to improve accuracy is to introduce a post-processing for NWP simulation, e.g. Zhang and Zou. ⁶¹⁾ Probabilistic forecasting, e.g. Liu et al. ⁶²⁾ may also be useful for weather and solar irradiance forecasting.

Table IV shows the changes in Corrs depending on each change in parameterization option. The changes in RMSE are also printed as a reference. We had expected that the accuracy of solar irradiance would be greatly affected by shortwave radiation processes and cumulus parameterization because of its large fluctuation due to cloud cover. However, Table IV shows that the surface layer and PBL display the largest change for improving Corr. This indicates that the surface layer and PBL have the greatest influence on the simulation accuracy of the solar irradiance. The surface layer process is a physical process that describes the exchange of heat and water vapor between the ground surface and the atmosphere, and the PBL process is a physical process that describes turbulent mixing in PBL. In considering the factors that significantly affect the accuracy of solar irradiance computations, the development of convective clouds, e.g. cumulus, should be discussed. The conditions for the development of convective clouds require unstable atmosphere and upwelling in the lower layers that triggers convection, or upwelling that lifts the entire air layer with unstable convection. Some lower-level upwelling is convection caused by heating of the ground surface. This is caused by heating of the ground surface by solar irradiance, which warms the atmosphere from the bottom. This convection occurs within the PBL, which includes the ground layer. Consequently, the surface layer and PBL are highly relevant to the prediction of convective clouds in the tropics.

The optimal schemes selected in the previous studies and the results in this study are compared here. Table V shows the list of the optimal schemes obtained in this study and by Zempila et al. ²⁸⁾ and Verbois et al. ²⁹⁾ Meteorological data sets for initial and boundary conditions are also indicated in the table. The schemes used in Arasa et al. ¹⁵⁾ and Aryaputera et al. ¹¹⁾ are also listed as a reference because Arasa et al. ¹⁵⁾ also optimized schemes, not for solar irradiance, but for wind. The target area of Aryaputera et al. ¹¹⁾ is Singapore, near Thailand, but their work did not include optimization of the options, and all the schemes are fixed from the beginning. The six parameterization options that are used in this study are listed in the table. The only target option for the optimization in both Zempila et al. ²⁸⁾ and Verbois et al. ²⁹⁾ is shortwave radiation. Other schemes were fixed from the beginning. They are indicated with parentheses in the table. The target area of Verbois et al. ²⁹⁾ is Singapore and it is near our target area, Thailand. The distance between them is about 1,500 km. However, the two points are about 13° apart in latitude, with Singapore at 1.4° and Thailand at 14.1°, in terms of north-south relationship.

As shown in the table, the optimal scheme for the shortwave radiation option in both previous studies, Zempila et al. ²⁸⁾ and Verbois et al. ²⁹⁾ is Dudhia, which is the same as in this study. Arasa et al. ¹⁵⁾ also selected Dudhia as the optimal scheme for shortwave radiation, even though the target areas and climates are different. The scheme is relatively old, simple and has a low computational cost compared to the others. These results suggest that newer, more sophisticated, higher-order schemes are not necessarily better, but the combination with other parameterization options is more important.

When our optimal schemes are compared with the results of Arasa et al. ¹⁵⁾ in Table V, only the longwave radiation option is different, Goddard and RRTMG, respectively. Our and their target areas are Thailand and southern Spain, and their climates are tropical and Mediterranean. In the process to evaluate the transmission of the irradiance, Goddard simply evaluates the absorption coefficient with the reference pressure and temperature. On the other hand, RRTM and its advanced scheme, RRTMG, evaluate the absorption coefficient along the optical path of the irradiance under various atmospheric conditions by paying a high computational cost. Therefore, for the atmosphere with high non-homogeneity, RRTMG evaluates the irradiance with higher accuracy than Goddard. This is the physical reason for the difference between the optimal longwave scheme in our study and that of Arasa et al. ¹⁵⁾ The difference in climates may be the cause of the difference in the longwave radiation option.

In previous studies, Zempila et al. ²⁸⁾ and Verbois et al., ²⁹⁾ some parameterization options are fixed from the beginning, and they are different to the ones that are derived as the optimal ones in this study, as shown in Table V. The simulation accuracy with different schemes in the table are compared here. As discussed in the previous section, PBL and surface layer options make a large contribution to the simulation accuracy. The accuracy of the schemes for the options are listed in Table VI. The schemes for the surface layer option in both Zempila et al. ²⁸⁾ and Verbois et al. ²⁹⁾ are not known. Thus, we compare the schemes of PBL options only in the table. The Corr and RMSE for each scheme are listed in the table. The Corr of the experiment with the YSU scheme is 0.01 higher than the others, and its RMSE is also smaller.

As shown in Table V, the shortwave radiation option of the optimal combination in this study is Dudhia, which is the same as the optimal one in the previous studies. From this table, one can see the commonality of each optimal combination or setting for the parameterization options for forecasting solar irradiance or for forecasting in the tropics. This result will be helpful for other researchers to set up NWPs under similar conditions.