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Consistency, in a narrow sense, denotes the alignment between the forecast-optimization strategy and the verification directive. The current recommended deterministic solar forecast verification practice is to report the skill score based on root mean square error (RMSE), which would violate the notion of consistency if the forecasts are optimized under another strategy such as minimizing the mean absolute error (MAE). This paper overcomes such difficulty by proposing a so-called "potential RMSE skill score," which depends only on (1) the cross-correlation between forecasts and observations and (2) the autocorrelation of observations. While greatly simplifying the calculation, the new skill score does not discriminate inconsistent forecasts as much, e.g., even MAE-optimized forecasts can attain a high RMSE skill score. [ABSTRACT FROM AUTHOR]

The current grid code in China in regard to solar forecasting is, in my opinion, underdeveloped, especially in contrast to the rate at which photovoltaics are being installed. As such, explaining the limitations of the grid code and resetting pathways to improve it are thought utilitarian for those scientists and policymakers who are responsible for or aware of the grid code but have not themselves worked on the problem of forecasting. In this perspective article, I should first explain with respect to China's grid code the perceived deficiencies in the current forecasting research and practices, and then outline a five-stage workflow that could completely mitigate the situation. Among other things, the over-reliance on accuracy as the basis for gauging the goodness of forecasts is identified as a root cause for the status quo, and thus, I advocate a holistic forecast verification procedure that encompasses consistency, quality, and value. With that in mind, the proposed workflow for better solar forecasting for grid integration purposes relies on the effective information flow among the weather department, grid operators, and individual plant owners, which is inline with the current grid code. What goes beyond this is that the proposal further introduces a couple of concepts called "hierarchical reconciliation" and "firm forecasting," which are new but are able to eliminate forecast errors wholly, thus making solar power dispatchable on the system level. With a slight premium incurred, it is now possible to manage solar plants, or variable renewables in general, in the same style as managing conventional fire-powered generators. [ABSTRACT FROM AUTHOR]

Fair forecast comparisons are exceedingly rare in the literature of solar forecasting. Since many published works have been operating under the condition "the proposed methods outperform the benchmarks," it is unlikely that the actual advancement in solar forecasting science is indeed successive in that the latter works supersede the former. It follows that one must hold fast to skepticism on those model superiority claims until they can be truly justified. In order to quantify the real progress, one needs to not only employ formal verification methods but also make inquiries on predictability, which, even in the field of statistics, is a controversial topic. Although predictability on its own is hard to define, let alone to quantify, one logically attractive proxy is to examine the performance of a short-range forecasting method relative to that of an optimal long-range forecasting method. This strategy is reasonable on the account that a climatological forecast in the short-range horizon marks the worst-case scenario, by which the relative improvement due to an alternative forecasting method can be gauged: situations with high predictability correspond to large relative improvements, and that with low predictability correspond to low relative improvements. If this argument can be considered admissible, the remaining task is to examine what properties ought the short-range forecasting method possess. This paper proposes, in this regard, a new measure of predictability for solar irradiance. [ABSTRACT FROM AUTHOR]

The procedure for splitting beam and diffuse components from the global radiation is known as separation modeling. Since the separation of irradiance components is required in a range of solar applications, hundreds of models with various complexities have been proposed in the literature. In this work, a new modeling philosophy, called the temporal-resolution cascade (TRC), is presented. The working principle of TRC models is to use low-resolution diffuse fraction estimates as input of a 1-min model. Based on a preliminary study, using two years (2019–2020) of data from seven locations, it is found that the TRC models are able to outperform most, if not all, existing separation models. All code and data are released for reproducibility. [ABSTRACT FROM AUTHOR]

The National Solar Radiation Database (NSRDB) offers satellite-derived irradiance over most of the Americas. The latest version of the NSRDB hosts broadband irradiance estimates at 5-min–2-km resolution, which have improved from the previous 30-min–4-km resolution. Whereas this new dataset is expected to continue providing invaluable solar resource information to researchers and practitioners worldwide, its accuracy needs to be validated. Validating high-resolution data must go beyond reporting the overall error metrics. To that end, time series features are used here to study the correspondence between the satellite-derived and measured irradiance transients. This paper also provides an in-depth discussion on the data quality issues observed during the validation. [ABSTRACT FROM AUTHOR]

High-resolution ground-based radiometry measurements are scarce, yet their importance in many solar engineering applications cannot be overstated. In this regard, a new model called the Dirichlet downscaling model (DDM), for synthetic downscaling of the global horizontal irradiance time series, is introduced in this paper. In its current version, the DDM is able to downscale any coarse input time series, with a resolution of 1-h or higher, to 1-min resolution. The DDM revolves around the adequate modeling for the concentration parameter of the Dirichlet distribution—a unique parameter that characterizes the Dirichlet distribution and allows generating downscaling probabilities. The concentration parameter captures all information relevant to downscaling from the input data. It is of particular interest that the DDM does not depend on local climate and weather regimes, facilitating worldwide applications. In the empirical part of the paper, the DDM is validated at 25 geographically dispersed locations. Excellent correspondence is obtained between the generated and measured time series in terms of the Kullback–Leibler divergence and the overlap coefficient. The Kolmogorov–Smirnov integral test is also used to quantify the effectiveness of the method at different timescales. Time order is evaluated by calculating the distribution of the autocorrelation function performed daily for each timescale per lag. To ensure full reproducibility and to facilitate the future uptake of the DDM, the R code is provided as the supplementary material. [ABSTRACT FROM AUTHOR]

The spatial scale mismatch between gridded irradiance products and in situ measurements is perhaps the least understood topic in solar resource assessment. However, it has a profound impact on virtually all solar applications that involve satellite-derived or reanalysis irradiance data. This paper investigates spatial scale mismatch through a kriging-based upscaling method. Point-location measurements from a monitoring network are upscaled to the size of a satellite-derived irradiance footprint. Subsequently, satellite-derived irradiance is validated against both the nearest point-location measurements and the upscaled areal averages, and the error reduction can, thus, be used to quantify the amount of spatial scale mismatch. In that, a new measure is proposed. The empirical part of the paper considers a synoptic scale satellite-derived irradiance product, namely, National Aeronautics and Space Administration's Clouds and the Earth's Radiant Energy System synoptic surface shortwave flux, and a mesoscale monitoring network, namely, the Oklahoma Mesonet. Based on two years of hourly data and the proposed measure, the spatial scale mismatch is found to be 45% for the U.S. state of Oklahoma. [ABSTRACT FROM AUTHOR]

Previously, in the study by Yang [J. Renewable Sustainable Energy 12, 016102 (2020)], probabilistic site adaptation was demonstrated for the first time. This technique leverages the ensemble model output statistics (EMOS), post-processes the empirical distribution formed by m gridded solar irradiance estimates from different satellite-derived and reanalysis databases, and thus obtains a final predictive distribution of the site-adapted irradiance, which has a normal density. That said, three questions were later thought of: (1) can post-processing the clear-sky index, instead of irradiance, lead to better site-adaptation performance; (2) will the parameter estimation strategy substantially affect model performance; and (3) how does the normality assumption hold in reality? In this paper, I revisit the probabilistic site-adaptation problem and aim to address these questions. In summary, it is found that (1) building EMOS models on irradiance and on the clear-sky index leads to similar model performance; (2) the choice of minimizing the continuous ranked probability score and the ignorance score needs to be tailored to the problem at hand; and (3) using a truncated normal predictive distribution in EMOS does not seem to possess an advantage over using a normal predictive distribution. [ABSTRACT FROM AUTHOR]

This paper is concerned with the choice of clear-sky model in solar forecasting. This issue is discussed from three perspectives: (1) accessibility, (2) forecast performance, and (3) statistical properties. Accessibility refers to the time and effort involved in obtaining clear-sky irradiance through a clear-sky model. Forecast performance is analyzed through a new concept called "mean square error (MSE) scaling," which allows one to decompose the MSE of reference irradiance forecasts into three terms, each carrying a notion of predictability. The decomposition, however, resides on the assumption that the clear-sky index time series is stationary. In this regard, the stationarity assumption is investigated using statistical hypotheses. It is found that even the best clear-sky models, such as the REST2 model, are not able to produce a stationary clear-sky index time series. Instead, the time series is only local stationary, which, in the present context, means that its statistical properties change slowly with the value of clear-sky irradiance. Contrary to the common belief that a better clear-sky model leads to better forecasts, no evidence suggests that the more intricate REST2 has an advantage over the simpler Ineichen–Perez model, in terms of forecast performance. In that, accessibility becomes the primary concern when opting a clear-sky model for forecasting purposes. At this point, the McClear model, available as a web service for worldwide locations at 1-, 15-, and 60-min resolutions, is highly recommended. [ABSTRACT FROM AUTHOR]

Short-term probabilistic solar forecasts are an important tool in decision-making processes in which uncertainty plays a non-negligible role. Purely statistical models that produce temporal or spatiotemporal probabilistic solar forecasts are generally trained individually, and the combined forecasts therefore lack the temporal or spatiotemporal correlation present in the data. To recover the spatiotemporal dependence structure, a copula can be employed, which constructs a multivariate distribution from which spatially and temporally correlated uniform random numbers can be sampled, which in turn can be used to generate the so-called space-time trajectories via the inverse probability integral transform. In this study, we employ the recently introduced ultra-fast preselection algorithm to leverage the spatiotemporal information present in a pyranometer network and compare its accuracy to that of quantile regression forecasts that only consider temporal information. We show that the preselection algorithm improves both the calibration and sharpness of the predictive distributions. Furthermore, we employ four copulas, i.e., (1) Gaussian, (2) Student-t, (3) Clayton, and (4) empirical, to generate space-time trajectories. The results highlight the necessity to rigorously assess the calibration of the space-time trajectories and the correct modeling of the spatiotemporal dependence structure, which we show through techniques introduced in atmospheric sciences. The code used to generate the results in this study can be found at https://github.com/DWvanderMeer/SpaceTimeTrajectories. [ABSTRACT FROM AUTHOR]

Suppose a location is within the spatial coverage of m gridded solar irradiance products, there is very little reason to rely on a single product, even if that product is known to be superior to its peers. In this paper, I discuss the ensemble performance of gridded irradiance estimates. First, I show the optimal convex combination of gridded irradiance estimates from different products almost always outperforms the best individual estimate under squared loss. Then, I extend the problem to the probability space and demonstrate how to construct predictive distributions for gridded irradiance estimates. Since the sample ensemble variances are often over- or under-dispersed, depending on the location, an ensemble model output statistics (EMOS) technique is used to correct such behaviors. The EMOS technique aims at minimizing the ignorance score, which is equivalent to maximizing the log-likelihood function of the underlying statistical model. In the language of solar engineers, EMOS is a probabilistic site-adaptation technique. At this point, this is the first work that (1) performs probabilistic site adaptation, (2) uses ensemble approaches for site adaptation, and (3) demonstrates formal probabilistic verification on site-adaptation problems. [ABSTRACT FROM AUTHOR]

Skill scores can be used to compare deterministic (also known as single-valued or point) forecasts made using different models at different locations and time periods. To compute the skill score, a reference forecasting method is needed. Nonetheless, there is no consensus on the choice of reference method. In this paper, three classes of commonly used references methods, namely, climatology, persistence, and their linear combination, are studied in a day-ahead solar forecasting scenario. Day-ahead global solar irradiance forecasts with an hourly resolution are generated using research-grade data from 32 sites around the globe, over a period of 1 year, in an operational manner. To avoid exaggerating the skill scores, it is generally agreed that the most accurate naïve forecasting method should be chosen as the standard of reference. In this regard, the optimal convex combination of climatology and persistence is highly recommended to be used as the standard of reference for day-ahead solar forecasting. [ABSTRACT FROM AUTHOR]

Global horizontal irradiance (GHI) forecasts by numerical weather prediction (NWP) often contain model-led bias. There is thus a strong consensus on using post-processing techniques, such as model output statistics (MOS), to correct such errors. As opposed to the conventional parametric methods, this article considers a nonparametric approach for post-processing, namely, kernel conditional density estimation (KCDE). Essentially, KCDE constructs a relationship between the bias error (difference between the NWP-based GHI forecast and measurement) and NWP output variables, such as clear-sky index, zenith angle, air temperature, humidity, or surface pressure. Hence, when a new set of explanatory variables becomes available, the conditional expectation of the bias error can be estimated. Since the ground-based GHI measurements are not available everywhere, the possibility of using satellite-derived GHI data to correct NWP forecasts is also explored. In the case study, two years of GHI forecasts made using the North American Mesoscale forecast system are corrected using both ground-measured and satellite-derived GHI references. As compared to Lorenz's fourth-degree polynomial MOS, additional 10%–16% (using ground-measured GHI) and 5%–13% (using satellite-derived GHI) reductions in the forecast error are observed at 7 test stations across the continental United States. [ABSTRACT FROM AUTHOR]

Separation models predict diffuse horizontal irradiance from other meteorological parameters such as the global horizontal irradiance or zenith angle. From a mathematical point of view, the separation modeling problem is a regression, where the regressors are observed or computed variables and the regressand is the unobserved diffuse fraction. The most successful minute-resolution separation model prior to 2016 was proposed by Engerer, which is constructed using a trend component (cloud enhancement) and a main effect (logistic function). Subsequently, the Starke model published in 2018 further improved the Engerer model. It is herein shown that the logistic-function type of model, and many other separation models, can be transformed into a (condition-based) multiple linear regression problem. Under this transformation framework, two new models are proposed, which strictly dominate the performance of the Engerer model and the Starke model, at all 7 test sites across the continental United States, making them probably the most accurate separation models to date. The new models are also tested at 5 European sites with unseen data (i.e., not involved during model parameter fitting); their performance again dominates all benchmarking models. The new separation models leverage half-hourly satellite-derived diffuse fraction. Since satellite data are available globally, the satellite-augmented separation models have universal applicability. However, despite their good performance, empirical separation models suffer from a series of issues. Hence, models driven by atmospheric physics are the "true gems" that one should pursue. [ABSTRACT FROM AUTHOR]

Satellite-derived irradiance data, as an alternative to ground-based measurements, offer a unique opportunity to verify gridded solar forecasts generated by a numerical weather prediction model. Previously, it has been shown that the mean square errors (MSE) evaluated against ground-based measurements and satellite-derived solar irradiance are comparable, which might warrant the use of satellite-based products for regional forecast verification. In this paper, the 24-h-ahead hourly forecasts issued by the North American Mesoscale forecast system are verified against both ground-based (Surface Radiation Budget Network, or SURFRAD) and satellite-based (National Solar Radiation Data Base, or NSRDB) measurements, at all 7 SURFRAD stations over 2015–2016. Three different MSE decomposition methods are used to characterize—e.g., through association, calibration, refinement, resolution, or likelihood—how well the two types of measurements can gauge the forecasts. However, despite their comparable MSEs, NSRDB is found suboptimal in its ability to verify forecasts as compared to SURFRAD. Nonetheless, if a new forecasting model produces significantly better forecasts than the benchmarking model, satellite-derived data are able to detect such improvements and make conclusions. This article comes with supplementary material (data and code) for reproducibility. [ABSTRACT FROM AUTHOR]

Over the past decade, significant progress in solar forecasting has been made. Nevertheless, there are concerns about duplication, long-term value, and reproducibility; this is referred to as the "solar forecasting bubble." There is an urgent need to reconcile and improve the current solar forecasting research practice. This discussion paper proposes a so-called "ROPES" guideline that describes the desirable characteristics of future solar forecasting studies. In short, ROPES stands for reproducible, operational, probabilistic and/or physically based, ensemble, and skill. This set of characteristics is intended to facilitate comparison, comprehension, and communication within the solar forecasting field and speed up its development. Compliance with ROPES is evaluated on 79 solar forecasting references published during 2017 January to 2018 July in 6 Elsevier energy journals. Although most current papers fall short of complying with ROPES, evidence suggests that a consensus is forming. [ABSTRACT FROM AUTHOR]

Analog ensemble (AnEn) is a popular probabilistic weather forecasting method based on similarity search. In that, forecasters are tasked to search for the top-m nearest neighbors (e.g., in terms of Euclidean distance) to a length-k query, from a set of historical data points in k-dimensional space. This is a straightforward yet time-consuming procedure, and few methods seem to be significantly better than a brute-force computation of all distances. To that end, I recommend using a kd-tree to perform AnEn, which appears to be one of (if not) the fastest approaches. [ABSTRACT FROM AUTHOR]