# Site-Adaptation of Modeled Solar Radiation Data: The SiteAdapt Procedure

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## Abstract

**:**

## 1. Introduction

- the treatment of the effect of clouds in solar radiation attenuation;
- the irradiance modeling under clear sky conditions;
- the area integrated by the satellite pixel leads to inaccuracies mainly during intermittent cloudy weather and changing aerosol load, which is the so-called “nugget effect” [18];
- terrain effects and the high reflective albedo of deserts and snow

## 2. Materials and Methods

#### 2.1. Solar Radiation Data

#### 2.1.1. Ground Measured Data

- Baseline surface radiation network (BSRN). The BSRN is a project managed under by the World Climate Research Program (WCRP), and imposes high quality standards, both in instrumentation and maintenance. Global horizontal solar irradiation (GHI) and direct normal solar irradiation (DNI) data were used in this work.
- UO SRML: The activity of the solar radiation monitoring laboratory of the University of Oregon started in 1977, with the creation of a five-station global network under the auspices of the Pacific northwest regional commission, motivated by the lack of available and accurate solar radiation data. This network covers the States of Idaho, Montana, Oregon, Utah, Washington and Wyoming, with 39 stations. The data are recorded with an hourly interval before 1995 and of 5 min afterward, and the associated estimated uncertainties for daily irradiances are 2% for DNI and 5% for GHI. The radiometers are calibrated on a yearly basis with periodic on-site checks with reference radiometers.

#### 2.1.2. Modeled Data

- The NSRDB (national solar radiation data base), that provides solar irradiance at a 4-km horizontal resolution for each 30-min interval from 1998 to 2016 over the United States and regions of the surrounding countries [28]. It was computed by the National Renewable Energy Laboratory’s (NREL’s) physical solar model (PSM) and products from the National Oceanic and Atmospheric Administration’s (NOAA’s) geostationary operational environmental satellite (GOES), the National Ice Center’s (NIC’s) interactive multisensor snow and ice-mapping system (IMS) and the National Aeronautics and Space Administration’s (NASA’s) moderate resolution imaging spectroradiometer (MODIS) and modern era retrospective analysis for research and applications, version 2 (MERRA-2).
- The CAMS-RAD database, provided by the atmosphere service of Copernicus, the European program for the establishment of a European capacity for earth observation with respect to land, marine and atmosphere monitoring, emergency management, security and climate change [29]. This database was calculated by means of the Heliosat-4 method [15], a fully physical model using a fast, but still accurate approximation of radiative transfer modeling. It is composed of two models based on abaci, also called lookup tables: the McClear [30] model calculating the irradiance under cloud-free conditions and the McCloud model calculating the extinction of irradiance due to clouds. Both were constructed by using the LibRadtran [31] radiative transfer model. The main inputs to Heliosat-4 are aerosol properties, total column water vapor and ozone content as provided by the CAMS global services every 3 h. Cloud properties are derived from images of the Meteosat Second Generation (MSG) satellites in their 15 min temporal resolution using an adapted APOLLO (AVHRR processing scheme over clouds, land and ocean) scheme.

#### 2.2. The SiteAdapt Procedure

#### 2.2.1. Preprocessing

- GHI preprocessing. It relies on the regression of the measured clearness index (kt, the ratio of GHI to top-of-atmosphere solar irradiance on the same plane) on the best combination of the following variables: α; kt of modeled series; relative air mass (m, based on Kasten formulation [34]); modeled clear-sky index (kc, the ratio between modeled GHI and its corresponding value under clear-sky conditions, calculated through the McClear model [30]).
- DHI preprocessing: it relies on the regression of the ratio DHI to GHI (kd, diffuse ratio) of measured data on the following variables: m; Kc; α; kt
_{m}designed to diminish the solar zenith angle dependence of kt by normalizing it with respect to a standard clear-sky GHI profile, normalized to 1 for a relative air mass of 1 [35] Equation (1):$$k{t}_{m}=kt/\left(1.031\xb7\mathrm{exp}\left[-1.4/\left(0.9+9.4/m\right)\right]+0.1\right)$$ - DNI preprocessing: it is calculated from both preprocessed GHI and DHI by the closure Equation (2):$$GHI=DNI\xb7\mathrm{cos}\left(\theta \right)+DHI$$
_{m}provides better results than simply using kt_{m}.

#### 2.2.2. Empirical Quantile Mapping (eQM) Correction

_{m}, to a probability domain and subsequently applies the inverse transformation using the cumulative distribution function (CDF) of the observational data to obtain the corrected data, χ

_{adapted}[38] Equation (3):

_{meas}and CDF

_{model}are the cumulative distribution functions of the observed and modeled data, respectively. This procedure is carried out employing the R-package ‘hyfo’ (hydrology and climate forecasting) version 1.4.0 [39] and it is applied separately to solar data under clear and cloudy skies, which are defined by modeled time series as in Section 2.2.1.

#### 2.2.3. Postprocessing

- Extreme values. To determine extremely high values, it was imposed that the maximum annual values measured (and validated) for GHI and DNI are not exceeded by 5% and that the DHI does not exceed 700 W/m
^{2}. Negative solar data have were also defined as erroneous data.

#### 2.3. Statistical Indicators

- Class A: relative mean bias difference (relbias); relative mean absolute difference (relMAD); relative root mean square difference (relRMSD). These indicators quantify the dispersion (or “error”) of individual points (their value would be 0 for a perfect model);
- Class C: Kolmogorov–Smirnov test Integral (KSI) and OVER [42]. These indicators quantify the distribution similarity (a lower value indicates better distributions similarity). KSI estimates the area between the CDFs of the datasets to be compared and OVER is also an estimate of the area between the CDFs, but only for the parts where a critical value distance is exceeded.

#### 2.4. Case Study

^{th}to 75

^{th}percentiles) is calculated for the same cases, to assess in detail both the performance and robustness of the site-adaptation methodology.

## 3. Results

#### 3.1. Preprocessing

^{2}) between parameters found in 2007, 2009 and 2010 is >0.99 and also the R

^{2}of the parameters found at these years with respect to all period is >0.99. On the contrary, the R

^{2}of the parameters found in 2008 show lower R

^{2}values with respect to individual years (R

^{2}= 0.92) and with all periods (R

^{2}= 0.96). This suggests that both the model and its correction do not have a homogeneous behavior: although the model can be corrected well with most years, there may be specific years whose behavior is especially different from the others in view of the correlation results obtained (however, this difference is slight). It is also interesting to highlight the stability of the kt predictor value in all cases analyzed at SBO site: The average of their values found for different years (1.8211) is very close to the one found using all period available (1.8366). In addition, their values found at different years are close between them (their standard deviation is 3.7% of their average). The combination of kt with Kc and with m also shows stability between the different cases analyzed.

#### 3.2. Site-Adaptation Performance

^{2}, which is markedly corrected after the adaptation procedure (purple, right graph).

#### 3.3. Prediction of Site-Adaptation Performance

^{2}values. It is worth highlighting an almost perfect match of R

^{2}, NSE and WIA for GHI and DNI, with slopes between 0.986 and 0.999 and R

^{2}= 1.000. Similarly, relMAD and relRMSD show an R

^{2}> 0.999, but with slightly higher slopes (in this case, prediction underestimates actual values by ~4% or less). KSI is almost exactly predicted for DHI, but it is underestimated for GHI and DNI with predictable behavior, reflected in R

^{2}of 0.951 for GHI and 0.905 for DNI. CPI is also underestimated for GHI, DNI and DHI (ranging from 31% to 46%), but also with great predictability (with R

^{2}between 0.991 and 0.991). Finally, both OVER and relbias are not well predicted for both GHI and DNI (R

^{2}< 0.207), for different reasons: adapted relbias are usually <1% in absolute value, but with great variability within its range, and OVER predicted with a single year of measurements provides low values (<3%), whereas their actual values are up to 40%.

## 4. Discussion

^{2}, NSE and WIA) are almost perfectly correlated (R

^{2}> 0.999), others (KSI, CPI) are highly correlated (R

^{2}> 0.9) and the rest (relbias and OVER) in general show low values after site-adaptation (<0.5% and <15%, respectively), allowing for an accurate description of the site-adaptation procedure with only one year of overlapped measurements and models.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CAMS | Copernicus atmospheric monitoring services |

CDF | cumulative distribution function |

CPI | combined performance index |

ECDF | empirical cumulative distribution function |

eQM | empirical quantile mapping |

kc | clear-sky index |

KSI | Kolmogorov–Smirnov test integral |

Kt | clearness index |

kt_{m} | clearness index formulation independent of the zenith angle |

m | relative air mass |

NSRDB | national solar radiation database |

NSE | Nash–Sutcliffe’s efficiency |

OVER | estimate of the area between the CDFs over a critical value distance |

R2 | coefficient of correlation |

relbias | relative mean bias difference |

relMAD | relative mean absolute difference |

relRMSD | relative root mean square difference |

WIA | Willmott’s index of agreement |

α | solar elevation above the horizon |

Θ | solar zenith angle |

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**Figure 1.**Measurement sites selected for this study, with a color code showing the climate zone to which each one belongs.

**Figure 2.**Empirical quantile mapping (eQM)correction for quantile 50 of modeled direct normal solar irradiance (DNI) data (blue) to match measured data (red).

**Figure 3.**DNI scatterplots between daytime modeled (left) and adapted (right) DNI with respect to the measured ones at GOB site (2013–2017) using the year 2013 for the site-adaptation.

**Figure 6.**Empirical cumulative distribution function (ECDF) of daytime measured (red marker), modeled (blue line) and site-adapted (purple line) GHI (left) and DNI (right) at Gobabeb site using the year 2013 for the site-adaptation.

**Figure 7.**Scatter plots between statistical indicators of DNI site-adaptation performance calculated with 1 year of coincident measured and modeled data with respect to the actual values calculated in the whole period available.

Site | Code | Country | Latitude (°, +N) | Longitude (°, +E) | Elevation (m ASL) | Climate | Network | Source of Modeled Data | Period |
---|---|---|---|---|---|---|---|---|---|

Payerne | PAY | Switzerland | 46.815 | 6.944 | 491 | Temperate oceanic | BSRN | CAMS | 2007–2017 |

Burns | BRN | USA | 43.519 | 119.022 | 1265 | Cold semi-arid | UO SRML | NSRDB | 2007–2013 |

Boulder | BOU | USA | 40.050 | −105.007 | 1577 | Cold semi-arid^{1} | BSRN | NSRDB | 2009–2013 |

Sede Boqer | SBO | Israel | 30.859 | 34.779 | 500 | Hot desert, arid | BSRN | CAMS | 2007–2012 |

Izaña | IZA | Spain | 28.309 | −16.499 | 2373 | Mediterranean | BSRN | CAMS | 2009–2016 |

Tamanrasset | TAM | Algeria | 22.790 | 5.529 | 1385 | Hot desert, arid | BSRN | CAMS | 2008–2016 |

Petrolina | PTR | Brazil | −9.068 | −40.319 | 387 | Hot semi-arid | BSRN | CAMS | 2009–2017 |

Gobabeb | GOB | Namibia | −23.56 | 15.04 | 407 | Hot desert, arid | BSRN | CAMS | 2013–2017 |

De Aar | DAA | South Africa | −30.6667 | 23.9930 | 1287 | Cold semi-arid | BSRN | CAMS | 2015–2018 |

^{1}with some overlap of a humid subtropical climate, due to its relatively high yearly precipitation.

**Table 2.**Conditions and limits defined for evaluating the consistency between global horizontal solar irradiation (GHI), direct normal solar irradiance (DNI) and diffuse horizontal solar irradiance (DHI).

Ratio | Conditions | Limits Allowed |
---|---|---|

$\frac{GHI}{DHI+DNI\xb7\mathrm{cos}\left(\theta \right)}$ | $SZA<75\xb0ANDDHI+DNI\xb7\mathrm{cos}\left(\theta \right)50W/{m}^{2}$ | 1% ± 8% |

$75\xb0<SZA93\xb0ANDDHI+DNI\xb7\mathrm{cos}\left(\theta \right)50W/{m}^{2}$ | 1% ± 15% |

**Table 3.**Set of variables and coefficients for the site-adaptation of kt at the three locations in different periods.

Variables ^{1} | DAA | GOB | SBO | ||||
---|---|---|---|---|---|---|---|

Entire Period | Entire Period | Entire Period | 2007 | 2008 | 2009 | 2010 | |

(Intercept) | 0.1765 | 0.1434 | −0.0687 | −0.1356 | −0.2644 | −0.0360 | −0.0389 |

kt | 0.6282 | 1.0375 | 1.8366 | 1.8941 | 1.7559 | 1.7744 | 1.8601 |

m | 0.0114 | 0.0047 | 0.0322 | 0.0437 | 0.0468 | 0.0268 | 0.0326 |

kc | 0.1769 | −0.1059 | 0.2761 | 0.3274 | 0.6636 | 0.2682 | 0.1715 |

α | 0.0032 | 0.0015 | −0.0021 | −0.0027 | 0.0018 | −0.0015 | −0.0031 |

kt: kc | 0.1473 | – | −1.0933 | −1.1168 | −1.3100 | −1.0488 | −1.0196 |

kt:α | – | −0.0097 | 0.0033 | 0.0039 | 0.0085 | 0.0066 | – |

m:α | −0.0043 | −0.0019 | – | – | – | – | – |

kc:α | −0.0020 | 0.0071 | – | – | −0.0076 | −0.0034 | 0.0035 |

kt:m | 0.0819 | 0.0344 | −0.0487 | −0.0464 | - | −0.0536 | −0.0507 |

m:kc | −0.0608 | −0.0131 | −0.0404 | −0.0517 | −0.0830 | −0.0337 | −0.0374 |

^{1}The sign “:” refers to the combination of the input variables.

Component | Source | relbias | relMAD | relRMSD | R^{2} | NSE | WIA | KSI | OVER | CPI |
---|---|---|---|---|---|---|---|---|---|---|

GHI | Modeled | −1.8 | 11.3 | 17.9 | 0.92 | 0.91 | 0.98 | 76.8 | 17.3 | 32.5 |

Adapted | 0.1 | 8.7 | 14.6 | 0.94 | 0.94 | 0.98 | 23.1 | 0.7 | 13.3 | |

DNI | Modeled | −2.3 | 24.5 | 34.9 | 0.71 | 0.67 | 0.90 | 222.2 | 141.0 | 108.2 |

Adapted | 0.3 | 19.2 | 29.8 | 0.79 | 0.78 | 0.94 | 57.6 | 12.1 | 32.3 | |

DHI | Modeled | −0.2 | 35.9 | 51.7 | 0.59 | 0.54 | 0.84 | 146.5 | 87.7 | 84.4 |

Adapted | 1.1 | 28.4 | 43.3 | 0.71 | 0.67 | 0.91 | 45.3 | 14.3 | 36.5 |

**Table 5.**Slope and R

^{2}of the linear fit of statistical indicators calculated with one year of measured and modeled data versus their actual values calculated in the whole period available.

Statistical Indicator | GHI | DNI | DHI | |||
---|---|---|---|---|---|---|

Slope | R^{2} | Slope | R^{2} | Slope | R^{2} | |

relbias | −0.086 | 0.009 | 0.166 | 0.046 | 0.999 | 1.000 |

relMAD | 1.038 | 1.000 | 1.040 | 1.000 | 0.997 | 1.000 |

relRMSD | 1.036 | 0.999 | 1.035 | 0.999 | 1.001 | 1.000 |

R^{2} | 0.996 | 1.000 | 0.989 | 1.000 | 1.000 | 1.000 |

NSE | 0.997 | 1.000 | 0.986 | 1.000 | 1.026 | 0.854 |

WIA | 0.999 | 1.000 | 0.997 | 1.000 | 1.031 | 0.999 |

KSI | 1.906 | 0.951 | 1.914 | 0.905 | 0.976 | 0.999 |

OVER | 213.198 | 0.030 | 8.019 | 0.207 | 2.242 | 0.870 |

CPI | 1.318 | 0.991 | 1.457 | 0.950 | 1.376 | 0.937 |

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**MDPI and ACS Style**

Fernández-Peruchena, C.M.; Polo, J.; Martín, L.; Mazorra, L.
Site-Adaptation of Modeled Solar Radiation Data: The SiteAdapt Procedure. *Remote Sens.* **2020**, *12*, 2127.
https://doi.org/10.3390/rs12132127

**AMA Style**

Fernández-Peruchena CM, Polo J, Martín L, Mazorra L.
Site-Adaptation of Modeled Solar Radiation Data: The SiteAdapt Procedure. *Remote Sensing*. 2020; 12(13):2127.
https://doi.org/10.3390/rs12132127

**Chicago/Turabian Style**

Fernández-Peruchena, Carlos M., Jesús Polo, Luis Martín, and Luis Mazorra.
2020. "Site-Adaptation of Modeled Solar Radiation Data: The SiteAdapt Procedure" *Remote Sensing* 12, no. 13: 2127.
https://doi.org/10.3390/rs12132127