# Evaluation of NASA POWER Reanalysis Products to Estimate Daily Weather Variables in a Hot Summer Mediterranean Climate

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}) higher than 0.82, with normalized root mean square error (NRMSE) varying, from 8 to 20%, and a normalized mean bias error (NMBE) ranging from –9 to 26%, for those variables. Based on these results, and in order to improve the accuracy of the NASA POWER dataset, two bias corrections were performed to all weather variables: one for the Alentejo Region as a whole; another, for each location individually. Results improved significantly, especially when a local bias correction is performed, with Tmax and Tmin presenting an improvement of the mean NRMSE of 6.6 °C (from 8.0 °C) and 16.1 °C (from 20.5 °C), respectively, while a mean NMBE decreased from 10.65 to 0.2%. Rs results also show a very high goodness of fit with a mean NRMSE of 11.2% and mean NMBE equal to 0.1%. Additionally, bias corrected RH data performed acceptably with an NRMSE lower than 12.1% and an NMBE below 2.1%. However, even when a bias correction is performed, Ws lacks the performance showed by the remaining weather variables, with an NRMSE never lower than 19.6%. Results show that NASA POWER can be useful for the generation of weather data sets where ground weather stations data is of missing or unavailable.

## 1. Introduction

^{–2}d

^{–1}for maximum and minimum temperatures, and solar radiation, respectively. Negm et al. [25] assessed the suitability of NASA POWER to estimate reference evapotranspiration through daily maximum, minimum and average air temperatures, relative humidity, global solar radiation and wind speed, in Sicily, Italy. Results showed a RMSE for those variables, respectively of 3.6 °C, 5.0 °C, 3.2 °C, 12.2%, 2.7 MJ m

^{–2}d

^{–1}and 2.4 m s

^{−1}, allowing them to conclude that NASA POWER had agreement with the corresponding measured values on ground weather stations. However, inaccurate estimations of relative air humidity occurred for the coastal weather stations. Monteiro et al. [26], performed a similar study in Brazil, found similar agreement for the same variables. Aboelkhair et al. [1] evaluated NASA POWER reanalysis data for surface monthly average maximum, minimum, average and dew point temperatures, and relative humidity in comparison the observed data in Egypt. The results showed that there is a significant correlation between NASA POWER reanalysis and observed data for all temperature parameters (RMSE lower than 5 °C) but failed to accurately simulate relative humidity (with an average RMSE of 11.6%). However, none of those previous studies evaluated the impact of bias correction on reanalysis products.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Agroclimatic Data

#### 2.3. Evaluation Criteria

_{i}and P

_{i}(i = 1, 2, …, n) represent pairs of values of each variable using locally collected data and the NASA POWER estimated data, respectively, and $\overline{\mathrm{O}}$ and $\overline{\mathrm{P}}$ are the respective mean values and n is the number of samples of each variable:

- The coefficients of regression and determination, relating the observed and simulated data, b and R
^{2}, respectively, are defined as:

^{2}values of 0.25, 0.50 and 0.75 match weakly, moderately and significantly fit, respectively.

- The root mean square error, RMSE, and its normalization, NRMSE, which characterizes the variance of the estimation error:

- The mean bias error, MBE, and its normalization, NMBE, that measures the systematic error between the predicted and observed values:

- The Nash and Sutcliffe [29] modelling efficiency, EF, that is the ratio of the mean square error to the variance in the observed data, subtracted from unity:

#### 2.4. Correction of Bias

_{NASA}is the uncorrected NASA POWER’s daily weather variable and X

_{obs}is the observed daily weather variable. In the equation an overbar denotes the average over the considered period and σ the standard deviation. The ratio of the standard deviation performs the scaling while the difference of the averages performs the shifting of bias.

## 3. Results

#### 3.1. Bias Correction Equations

#### 3.2. Evaluation of Maximum Temperature Accuracy

^{2}and EF higher than 0.82 and 0.68, respectively, a mean NRMSE of 7.59% and an average NMBE equal to −2.56%. If a regional bias correction is applied, results show a slightly better performance: mean b increases by 2.2% (to 1.00), while the average RMSE decreases 9.2% (1.74 °C day

^{–1}), and the mean MBE increases 104.4% (to 0.03 °C day

^{–1}). Similarly, if a local bias correction is adopted, the accuracy metrics tend to improve with the mean RMSE, MBE and EF: the mean root mean square error decreases 17.0% (RMSE = 1.59 °C day

^{–1}), the average mean bias error decreases 97.5% (MBE = −0.02 °C day

^{–1}) and the mean modelling efficiency increases by 2.8% (EF = 0.95).

#### 3.3. Evaluation of Minimum Temperature

^{2}higher than 0.85, showing an excellent accuracy of NASA POWER when compared with observed data. These results were obtained when adopting the calibrated and validated bias correction equations presented in Table 3. If no bias correction is performed, minimum temperature can be estimated with an EF averaging 0.84, with a mean RMSE of 2.01 °C day

^{–1}and a mean MBE of 1.03 °C day

^{–1}. Results tend to improve when a bias correction is applied: for a regional correction, mean b decreases by 8.9% (to 0.99), while the mean RMSE and MBE show a decrease of 16.4% (to 1.68 day

^{–1}) and 105.2% (to −0.05 °C day

^{–1}), respectively; if a local bias correction is applied, the average RMSE is even lower (with a decrease of 21.3% to 1.58 °C day

^{–1}) with mean MBE equal to −0.02 °C day

^{–1}, representing a decrease of 101.8% when compared with raw data. The modelling efficiency tends to increase on both correction schemes to an average 0.89 and 0.90 for regional and local bias correction, respectively.

#### 3.4. Evaluation of Solar Radiation

^{2}value higher than 0.91, as high as 0.97 for Redondo and Vidigueira (Table S3), representing an excellent accuracy. NASA POWER Rs present a RMSE lower than 2.73 MJ m

^{–2}d

^{–1}with a normalization of 16.12% and a mean EF of 0.93. NASA POWER tends to slight overestimate solar radiation (MBE averaging 0.65 MJ m

^{–2}d

^{–1}). If NASA POWER Rs bias is regionally corrected, all accuracy metrics tend to increase resulting in a b, RMSE, MBE and EF averaging 1.00, 1.99 MJ m

^{−2}day

^{−1}, −0.01 MJ m

^{−2}day

^{−1}and 0.94, respectively. For all locations, the accuracy metrics show an even better goodness of fit and agreement between the observed and simulated solar radiation when the bias is locally corrected with mean RMSE decreasing 10.2% (RMSE = 2.10 MJ m

^{−2}day

^{−1}), mean MBE decreases 98.6% (MBE = 0.01 MJ m

^{−2}day

^{−1}) and a modelling efficiency improving by 1.5% (EF = 0.94).

#### 3.5. Evaluation of Relative Humidity

^{2}of 0.82 (as high as 0.88). However, for Odemira (Table S4) the coefficient of determination is equal to 0.40, showing low correlation and with fit between observed and simulated RH; this may be due to the station closeness to the sea, and the influence of both Atlantic Ocean and Mediterranean Sea. The EF values average 0.61 and range from –0.08 to 0.79. Additionally, for raw NASA POWER RH data, the RMSE averages 9.24% day

^{–1}(with an NRMSE of 13.00%), with MBE averaging –5.17% day

^{–1}(with an NMBE of –7.27%). However, the bias is corrected, results improve significantly with both correction schemes showing an increase of the mean b of 7.7% (to 1.01) and a mean EF increasing by 30.7% 8 to 0.80). The mean RMSE decreases to 28.8 and 30.0% for a regional and local bias correction, respectively, with normalizations below 9.25%. The most frequent EF (Supplementary Figure S4) for both schemes is higher than 0.80, with more than 93% of all stations having an NMBE between −1.0 and 1.0%.

#### 3.6. Evaluation of Wind Speed

^{2}(0.79) was recorded for Beja while the minimum values of R

^{2}(0.52) was obtained for Elvas (Table S5), showing a moderate to high fit between reanalysis and observed wind speed data. Results for the uncorrected NASA POWER wind speed data (Table 8) show a mean coefficient of regression of 1.40, with an average RMSE of 1.10 m s

^{−1}, a mean NRMSE equal to 62.50% and an average modelling efficiency of −0.88. Wind speed is overestimated by NASA POWER for all weather stations, with an MBE that varies from 0.12 to 1.44 m s

^{–1}. Bias correction increases the accuracy of NASA POWER wind speed estimation significantly. The mean EF increased to 0.40 (an improvement of 146.3%), for a regional correction, and to 0.53 (an increase of 160.7%), when locally correcting the bias. The RMSE decreased 37.4% (to 0.69 m s

^{−1}), for the former, and 45.7% (to 0.60 m s

^{−1*}, for the latter. The most frequent (Supplementary Figure S5) NMBE and EF for the raw NASA POWER wind speed data is higher than 60% (42% of all locations) a lower than 0 (71% of all locations), respectively; however, if the dataset is locally bias corrected, the most frequent NMBE ranging −10.0 to 10.0%, with more than 60% of the stations showing an EF higher than 0.50.

## 4. Discussion

^{–1}for Tmax and for Tmin, and from 0.65 to 0.01 MJ m

^{−2}day

^{−1}for Rs. Additionally, a local bias correction of NASA POWER Tmax, Tmin and Rs improved the mean RMSE values from 1.91 °C, 2.01 °C and 2.10 MJ m

^{−2}day

^{−1}to 1.59 °C, 1.58 °C and 1.89 MJ m

^{−2}d

^{−1}, respectively. Similar results for those variables were found by Bai et al. [24] in China, by Monteiro et al. [26] in Brazil and by Negm et al. [25] in Italy. White el al. [23], for continental USA, and Aboelkhair et al. [1], for Egypt, also reported similar results and concluded that NASA POWER can accurately estimate maximum and minimum temperature. Therefore, the presented results show that NASA POWER can simulate maximum, minimum temperatures and solar radiation with a high goodness of fit and agreement, when compared with observed data.

^{–1}and 0.78% day

^{–1}, respectively. This represent an improvement from raw RH data, where a mean RMSE of 9.24% day

^{–1}and a mean MBE of −5.71% day

^{–1}were found. However, for coastal stations the estimation still needs improvement. Similar conclusions were drawn by Negm et al. [25], Monteiro et al. [26] and Aboelkhair et al. [1]. Nonetheless, one can conclude that NASA POWER can simulate RH with good accuracy, when compared with observed data.

^{−1}with a coefficient of regression equal to 1.40. Results tend to improve with a bias correction; however, the lowest NRMSE is of 19.6%, thus one can conclude that wind speed lacks the performance showed by the remaining weather variables. Previous studies [25,26,32] also found that NASA POWER fails to estimate wind speed with acceptable accuracy. Despite the improvements if a bias correction is performed, the NASA POWER wind speed reanalysis data show unsatisfactory correlation and does not agree with most of the ground observations and still needs improvement.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Aboelkhair, H.; Mostafa, M.; El Afandi, G. Assessment of agroclimatology NASA POWER reanalysis datasets for temperature types and relative humidity at 2 m against ground observations over Egypt. Adv. Space Res.
**2019**, 64, 129–142. [Google Scholar] [CrossRef] - Trenberth, K.E.; Toshio, K.; Kazutoshi, O. Progress and prospects for reanalysis for weather and climate. Eos Trans. Am. Geophys. Union
**2008**, 89, 234–235. [Google Scholar] [CrossRef] - Sheffield, J.; Gopi, G.; Eric, F.W. Development of a 50-year high-resolution global dataset of meteorological forcings for land surface modeling. J. Clim.
**2006**, 19, 3088–3111. [Google Scholar] [CrossRef][Green Version] - Sheffield, J.; Ziegler, A.D.; Wood, E.F.; Chen, Y. Correction of the high-latitude rain day anomaly in the NCEP–NCAR reanalysis for land surface hydrological modeling. J. Clim.
**2004**, 17, 3814–3828. [Google Scholar] [CrossRef][Green Version] - Schneider, D.P.; Deser, C.; Fasullo, J.; Trenberth, K.E. Climate data guide spurs discovery and understanding. Eos Trans. Am. Geophys. Union
**2013**, 94, 121–122. [Google Scholar] [CrossRef] - Dee, D.P.; Uppala, S.M.; Simmons, A.J.; Berrisford, P.; Poli, P.; Kobayashi, S.; Andrae, U.; Balmaseda, M.A.; Balsamo, G.; Bauer, P.; et al. The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc.
**2011**, 137, 553–597. [Google Scholar] [CrossRef] - Kobayashi, S.; Yukinari, O.T.A.; Harada, Y.; Ebita, A.; Moriya, M.; Onoda, H.; Onogi, K.; Kamahori, H.; Kobayashi, C.; Miyaoka, K.; et al. The JRA-55 reanalysis: General specifications and basic characteristics. J. Meteorol. Soc. Jpn. Ser. II
**2015**, 93, 5–48. [Google Scholar] [CrossRef][Green Version] - Kanamitsu, M.; Ebisuzaki, W.; Woollen, J.; Yang, S.K.; Hnilo, J.J.; Fiorino, M.; Potter, G.L. Ncep–doe amip-ii reanalysis (r-2). Bull. Am. Meteorol. Soc.
**2002**, 83, 1631–1644. [Google Scholar] [CrossRef] - Rienecker, M.M.; Suarez, M.J.; Gelaro, R.; Todling, R.; Bacmeister, J.; Liu, E.; Bosilovich, M.G.; Schubert, S.D.; Takacs, L.; Kim, G.K.; et al. MERRA: NASA’s modern-era retrospective analysis for research and applications. J. Clim.
**2011**, 24, 3624–3648. [Google Scholar] [CrossRef] - Chandler, W.S.; Stackhouse, P.W., Jr.; Hoell, J.M.; Westberg, D.; Zhang, T. NASA prediction of worldwide energy resource high resolution meteorology data for sustainable building design. In Proceedings of the Solar 2013 Conference of American Solar Energy Society, Baltimore, Maryland, 16–20 April 2013. [Google Scholar]
- Bao, X.; Zhang, F. Evaluation of NCEP–CFSR, NCEP–NCAR, ERA-interim, and ERA-40 reanalysis datasets against independent sounding observations over the Tibetan Plateau. J. Clim.
**2013**, 26, 206–214. [Google Scholar] [CrossRef][Green Version] - Dile, Y.T.; Srinivasan, R. Evaluation of CFSR climate data for hydrologic prediction in data-scarce watersheds: An application in the Blue Nile River Basin. J. Am. Water Resour. Assoc.
**2014**, 50, 1226–1241. [Google Scholar] [CrossRef] - Liu, J.; Shanguan, D.; Liu, S.; Ding, Y. Evaluation and hydrological simulation of CMADS and CFSR reanalysis datasets in the Qinghai-Tibet Plateau. Water
**2018**, 10, 513. [Google Scholar] [CrossRef][Green Version] - Chen, S.; Gan, T.Y.; Tan, X.; Shao, D.; Zhu, J. Assessment of CFSR, ERA-Interim, JRA-55, MERRA-2, NCEP-2 reanalysis data for drought analysis over China. Clim. Dyn.
**2019**, 53, 737–757. [Google Scholar] [CrossRef] - Solman, S.A.; Sanchez, E.; Samuelsson, P.; Da Rocha, R.P.; Li, L.; A Marengo, J.; Pessacg, N.L.; Remedio, A.R.; Chou, S.C.; Berbery, H.; et al. Evaluation of an ensemble of regional climate model simulations over South America driven by the ERA-Interim reanalysis: Model performance and uncertainties. Clim. Dyn.
**2013**, 41, 1139–1157. [Google Scholar] [CrossRef] - Paredes, P.; Martins, D.S.; Pereira, L.S.; Cadima, J.; Pires, C. Accuracy of daily estimation of grass reference evapotranspiration using ERA-Interim reanalysis products with assessment of alternative bias correction schemes. Agric. Water Manag.
**2018**, 210, 340–353. [Google Scholar] [CrossRef] - Chen, G.; Iwasaki, T.; Qin, H.; Sha, W. Evaluation of the warm-season diurnal variability over East Asia in recent reanalyses JRA-55, ERA-Interim, NCEP CFSR, and NASA MERRA. J. Clim.
**2014**, 27, 5517–5537. [Google Scholar] [CrossRef] - Tsujino, H.; Urakawa, S.; Nakano, H.; Small, R.J.; Kim, W.M.; Yeager, S.G.; Danabasoglu, G.; Suzuki, T.; Bamber, J.L.; Bentsen, M.; et al. JRA-55 based surface dataset for driving ocean–sea-ice models (JRA55-do). Ocean Model.
**2018**, 130, 79–139. [Google Scholar] [CrossRef] - Trenberth, K.E.; Guillemot, C.J. Evaluation of the atmospheric moisture and hydrological cycle in the NCEP/NCAR reanalyses. Clim. Dyn.
**1998**, 14, 213–231. [Google Scholar] [CrossRef] - Maurer, E.P.; O’Donnell, G.M.; Lettenmaier, D.P.; Roads, J.O. Evaluation of the land surface water budget in NCEP/NCAR and NCEP/DOE reanalyses using an off-line hydrologic model. J. Geophys. Res. Atmos.
**2001**, 106, 17841–17862. [Google Scholar] [CrossRef][Green Version] - Reichle, R.H.; Draper, C.S.; Liu, Q.; Girotto, M.; Mahanama, S.P.; Koster, R.D.; De Lannoy, G.J. Assessment of MERRA-2 land surface hydrology estimates. J. Clim.
**2017**, 30, 2937–2960. [Google Scholar] [CrossRef][Green Version] - Draper, C.S.; Reichle, R.H.; Koster, R.D. Assessment of MERRA-2 land surface energy flux estimates. J. Clim.
**2018**, 31, 671–691. [Google Scholar] [CrossRef] - White, J.W.; Hoogenboom, G.; Stackhouse, P.W.; Hoell, J.M. Evaluation of NASA satellite- and assimilation model-derived longterm daily temperature data over the continental US. Agric. For. Meteorol.
**2008**, 148, 1574–1584. [Google Scholar] [CrossRef][Green Version] - Bai, J.; Chen, X.; Dobermann, A.; Yang, H.; Cassman, K.; Zhang, F. Evaluation of NASA satellite- and model-derived weather data for simulation of maize yield potential in China. Agron. J.
**2010**, 102, 9–16. [Google Scholar] [CrossRef] - Negm, A.; Jabro, J.; Provenzano, G. Assessing the suitability of American National Aeronautics and Space Administration (NASA) agro-climatology archive to predict daily meteorological variables and reference evapotranspiration in Sicily, Italy. Agric. For. Meteorol.
**2017**, 244–245, 111–121. [Google Scholar] [CrossRef] - Monteiro, A.L.; Sentelhas, P.C.; Pedra, G.U. Assessment of NASA/POWER satellite-based weather system for Brazilian conditions and its impact on sugarcane yield simulation. Int. J. Climatol.
**2018**, 38, 1571–1581. [Google Scholar] [CrossRef] - Henseler, J.; Ringle, C.; Sinkovics, R. The use of partial least squares path modeling in international marketing. Adv. Int. Mark.
**2009**, 20, 277–320. [Google Scholar] - Willmott, C.J.; Matsuura, K. On the use of dimensioned measures of error to evaluate the performance of spatial interpolators. Int. J. Geogr. Inf. Sci.
**2006**, 20, 89–102. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Legates, D.R.; McCabe, G.J., Jr. Evaluating the use of goodness-of-fit measures in hydrologic and hydroclimatic model validation. Water Resour. Res.
**1999**, 35, 233–241. [Google Scholar] [CrossRef] - Berg, A.A.; Famiglietti, J.S.; Walker, J.P.; Houser, P.R. Impact of bias correction to reanalysis products on simulations of North American soil moisture and hydrological fluxes. J. Geophys. Res.
**2003**, 108, 4490. [Google Scholar] [CrossRef][Green Version] - Leander, R.; Buishand, T.A. Resampling of regional climate model output for the simulation of extreme river flows. J. Hydrol.
**2007**, 332, 487–496. [Google Scholar] [CrossRef]

**Figure 2.**Annual climate of maximum (

**a**) and minimum (

**b**) temperatures, mean relative humidity (

**c**), solar radiation (

**d**) and mean wind speed (

**e**) over Alentejo.

**Figure 3.**Flow chart presenting the procedures to correct the bias of NASA POWER data and comparing with observations using two bias correction methods.

**Table 1.**Weather stations coordinates, elevation, distance to the sea and date ranges of the weather data series.

Weather Station | Latitude (N) | Longitude (W) | Elevation (m) | Date Range |
---|---|---|---|---|

Aljustrel | 37° 58′ 17′′ | 08° 11′ 25′′ | 104 | Sep/2001–Sep/2020 |

Alvalade do Sado | 37° 55′ 44′′ | 08° 20′ 45′′ | 79 | Sep/2001–Sep/2020 |

Beja | 38° 02′ 15′′ | 07° 53′ 06′′ | 206 | Sep/2001–Sep/2020 |

Castro Verde | 37° 45′ 21′′ | 08° 04′ 35′′ | 200 | Oct/2001–Sep/2020 |

Elvas | 38° 54′ 56′′ | 07° 05′ 56′′ | 202 | Sep/2001–Sep/2020 |

Estremoz | 38° 52′ 20′′ | 07° 35′ 49′′ | 404 | Feb/2006–Sep/2020 |

Évora | 38° 44′ 16′′ | 07° 56′ 10′′ | 246 | Feb/2002–Sep/2020 |

Ferreira do Alentejo | 38° 02′ 42′′ | 08° 15′ 59′′ | 74 | Sep/2001–Sep/2020 |

Moura | 38° 05′ 15′′ | 07° 16′ 39′′ | 172 | Sep/2001–Sep/2020 |

Odemira | 37° 30′ 06′′ | 08° 45′ 12′′ | 92 | Jul/2002–Sep/2020 |

Redondo | 38° 31′ 41′′ | 07° 37′ 40′′ | 236 | Sep/2001–Sep/2020 |

Serpa | 37° 58′ 06′′ | 07° 33′ 03′′ | 190 | May/2004–Sep/2020 |

Viana do Alentejo | 38° 21′ 39′′ | 08° 07′ 32′′ | 138 | Mar/2006–Sep/2020 |

Vidigueira | 38° 10′ 37′′ | 07° 47′ 35′′ | 155 | Nov/2007–Sep/2020 |

**Table 2.**Annual mean and standard deviation of maximum (Tmax) and minimum (Tmin) temperatures, mean relative humidity (RH), solar radiation (Rs) and mean wind speed (Ws) at the selected weather stations.

Weather Station | T Max (°C) | T Min (°C) | RH (%) | Rs (MJ m^{–2} day^{−1}) | Ws (m s^{–1}) |
---|---|---|---|---|---|

Aljustrel | 24.5 (±7.5) | 9.9 (±5.1) | 72.3 (±14.8) | 16.4 (±7.7) | 1.9 (±0.9) |

Alvalade do Sado | 24.8 (±7.3) | 10.3 (±5.1) | 73.1 (±13.2) | 16.9 (±8.1) | 2.1 (±0.9) |

Beja | 24.0 (±7.8) | 10.4 (±4.8) | 70.2 (±15.8) | 18.1 (±8.6) | 2.0 (±0.8) |

Castro Verde | 24.2 (±7.7) | 9.9 (±4.9) | 72.3 (±16.1) | 17.5 (±8.0) | 2.7 (±1.2) |

Elvas | 24.5 (±8.4) | 9.5 (±5.7) | 67.9 (±18.0) | 16.9 (±8.1) | 1.8 (±0.9) |

Estremoz | 22.5 (±8.1) | 9.4 (±4.9) | 70.2 (±17.3) | 16.9 (±8.5) | 1.4 (±0.7) |

Évora | 23.8 (±7.9) | 9.0 (±5.3) | 71.3 (±14.7) | 16.0 (±7.7) | 2.0 (±1.3) |

Ferreira do Alentejo | 24.8 (±7.4) | 9.8 (±5.2) | 72.4 (±14.3) | 16.7 (±7.9) | 1.6 (±0.7) |

Moura | 25.0 (±8.2) | 8.5 (±6.0) | 69.1 (±17.7) | 16.4 (±7.8) | 1.3 (±0.7) |

Odemira | 21.3 (±4.8) | 11.1 (±3.9) | 76.7 (±10.9) | 17.9 (±8.0) | 2.0 (±0.9) |

Redondo | 24.2 (±8.1) | 10.4 (±5.2) | 68.4 (±16.8) | 16.5 (±7.9) | 2.5 (±1.3) |

Serpa | 25.2 (±7.9) | 10.5 (±5.1) | 69.4 (±15.7) | 16.8 (±8.1) | 1.4 (±0.8) |

Viana do Alentejo | 23.7 (±7.8) | 10.0 (±4.7) | 72.3 (±16.1) | 16.8 (±7.9) | 2.2 (±0.9) |

Vidigueira | 25.0 (±7.9) | 10.0 (±5.2) | 69.0 (±16.9) | 17.3 (±8.3) | 1.6 (±0.8) |

**Table 3.**Calibrated and validated bias correction equations for NASA POWER maximum (Tmax) and minimum (Tmin) temperatures, solar radiation (Rs), mean relative humidity (RH) and mean wind speed (Ws).

Location | Equation | ||||
---|---|---|---|---|---|

Alentejo | Tmax’ = 0.96 × Tmax + 1.56 | Tmin’ = 0.95 × Tmin − 0.57 | Rs’ = 0.99 × Rs − 0.44 | RH’ = 0.85 × RH + 16.01 | Ws’ = 0.88 × Ws − 0.64 |

Aljustrel | Tmax’ = 0.97 × Tmax + 1.89 | Tmin’ = 1.01 × Tmin − 1.35 | Rs’ = 0.97 × Rs − 1.06 | RH’ = 0.82 × RH + 17.88 | Ws’ = 0.78 × Ws − 0.57 |

Alvalade | Tmax’ = 0.95 × Tmax + 2.51 | Tmin’ = 0.99 × Tmin − 0.76 | Rs’ = 1.01 × Rs − 1.25 | RH’ = 0.74 × RH + 24.87 | Ws’ = 0.81 × Ws − 0.45 |

Beja | Tmax’ = 0.94 × Tmax + 1.60 | Tmin’ = 0.86 × Tmin + 1.09 | Rs’ = 1.04 × Rs + 0.08 | RH’ = 0.82 × RH + 18.01 | Ws’ = 0.73 × Ws − 0.05 |

Castro Verde | Tmax’ = 1.00 × Tmax + 0.59 | Tmin’ = 0.98 × Tmin − 1.06 | Rs’ = 1.02 × Rs − 0.72 | RH’ = 0.91 × RH + 11.54 | Ws’ = 1.02 × Ws − 0.23 |

Elvas | Tmax’ = 0.96 × Tmax + 2.36 | Tmin’ = 0.95 × Tmin − 0.28 | Rs’ = 0.99 × Rs − 0.18 | RH’ = 0.87 × RH + 12.62 | Ws’ = 0.83 × Ws − 0.44 |

Estremoz | Tmax’ = 0.97 × Tmax − 0.36 | Tmin’ = 0.89 × Tmin + 0.06 | Rs’ = 1.03 × Rs − 1.22 | RH’ = 0.91 × RH + 11.54 | Ws’ = 0.62 × Ws − 0.62 |

Évora | Tmax’ = 0.95 × Tmax + 1.82 | Tmin’ = 0.93 × Tmin − 0.63 | Rs’ = 0.93 × Rs − 0.28 | RH’ = 0.76 × RH + 22.88 | Ws’ = 1.07 × Ws − 0.75 |

Ferreira do Alentejo | Tmax’ = 0.95 × Tmax + 2.41 | Tmin’ = 1.02 × Tmin − 1.31 | Rs’ = 0.96 × Rs + 0.01 | RH’ = 0.82 × RH + 19.02 | Ws’ = 0.70 × Ws − 0.73 |

Moura | Tmax’ = 0.95 × Tmax + 2.52 | Tmin’ = 1.01 × Tmin − 2.38 | Rs’ = 0.94 × Rs + 0.19 | RH’ = 0.86 × RH + 15.85 | Ws’ = 0.67 × Ws − 0.81 |

Odemira | Tmax’ = 0.79 × Tmax + 3.95 | Tmin’ = 0.92 × Tmin − 0.82 | Rs’ = 1.00 × Rs − 0.11 | RH’ = 0.86 × RH + 15.09 | Ws’ = 0.67 × Ws − 0.78 |

Redondo | Tmax’ = 0.97 × Tmax + 1.56 | Tmin’ = 0.94 × Tmin + 0.77 | Rs’ = 0.96 × Rs + 0.00 | RH’ = 0.87 × RH + 12.07 | Ws’ = 1.23 × Ws − 0.70 |

Serpa | Tmax’ = 0.96 × Tmax + 1.78 | Tmin’ = 0.91 × Tmin + 0.34 | Rs’ = 1.03 × Rs − 1.51 | RH’ = 0.80 × RH + 19.47 | Ws’ = 0.69 × Ws − 0.67 |

Viana do Alentejo | Tmax’ = 1.01 × Tmax − 0.28 | Tmin’ = 0.92 × Tmin − 0.39 | Rs’ = 0.97 × Rs − 0.18 | RH’ = 0.93 × RH + 11.12 | Ws’ = 0.80 × Ws − 0.13 |

Vidigueira | Tmax’ = 0.95 × Tmax + 2.17 | Tmin’ = 0.94 × Tmin − 0.02 | Rs’ = 1.02 × Rs − 0.39 | RH’ = 0.89 × RH + 12.63 | Ws’ = 0.77 × Ws − 0.67 |

**Table 4.**Mean and range values of the accuracy metrics relative to NASA POWER maximum temperature with and without bias correction for the full data set of all 14 locations.

Bias Correction Scheme | b | R^{2} | RMSE | NRMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | |

No Bias Correction | 0.98 | 0.02 | 0.95 to 1.03 | 0.95 | 0.04 | 0.82 to 0.97 | 1.91 | 0.31 | 1.36 to 2.67 | 7.95 | 1.53 | 5.73 to 12.55 |

Regional Bias Correction | 1.00 | 0.03 | 0.97 to 1.06 | 0.95 | 0.04 | 0.82 to 0.97 | 1.74 | 0.34 | 1.38 to 2.8 | 7.25 | 1.81 | 5.70 to 13.12 |

Local Bias Correction | 1.00 | 0.00 | 0.98 to 1.00 | 0.95 | 0.04 | 0.82 to 0.97 | 1.59 | 0.18 | 1.36 to 2.04 | 6.60 | 1.00 | 5.64 to 9.59 |

Bias Correction Scheme | MBE | NMBE | EF | |||||||||

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | ||||

No Bias Correction | −0.64 | 0.65 | −1.40 to 0.57 | −2.56 | 2.69 | −5.71 to 2.68 | 0.92 | 0.07 | 0.68 to 0.97 | |||

Regional Bias Correction | 0.03 | 0.65 | −0.72 to 1.30 | 0.22 | 2.84 | −2.93 to 6.12 | 0.93 | 0.08 | 0.65 to 0.97 | |||

Local Bias Correction | −0.02 | 0.12 | −0.42 to 0.08 | −0.08 | 0.52 | −1.85 to 0.31 | 0.95 | 0.04 | 0.81 to 0.97 |

^{2}—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error; MBE—mean bias error; NMBE—normalized mean bias error; EF—modelling efficiency.

**Table 5.**Mean and range values of the accuracy metrics relative to NASA POWER minimum temperature with and without bias correction for the full data set of all 14 locations.

Bias Correction Scheme | b | R^{2} | RMSE | NRMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | |

No Bias Correction | 1.08 | 0.04 | 0.99 to 1.15 | 0.90 | 0.02 | 0.85 to 0.93 | 2.01 | 0.38 | 1.57 to 3.17 | 20.51 | 5.28 | 14.98 to 37.05 |

Regional Bias Correction | 0.99 | 0.03 | 0.90 to 1.05 | 0.90 | 0.02 | 0.85 to 0.93 | 1.68 | 0.28 | 1.28 to 2.50 | 17.10 | 3.90 | 12.93 to 29.2 |

Local Bias Correction | 0.99 | 0.01 | 0.98 to 1.00 | 0.90 | 0.02 | 0.85 to 0.93 | 1.58 | 0.25 | 1.29 to 2.25 | 16.12 | 3.53 | 12.36 to 26.35 |

Bias Correction Scheme | MBE | NMBE | EF | |||||||||

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | ||||

No Bias Correction | 1.03 | 0.54 | −0.15 to 2.24 | 10.65 | 6.05 | −1.41 to 26.22 | 0.84 | 0.07 | 0.65 to 0.91 | |||

Regional Bias Correction | −0.05 | 0.53 | −1.20 to 1.16 | −0.35 | 5.52 | −11.52 to 13.59 | 0.89 | 0.03 | 0.82 to 0.93 | |||

Local Bias Correction | −0.02 | 0.05 | −0.15 to 0.08 | −0.19 | 0.52 | −1.33 to 0.76 | 0.90 | 0.03 | 0.84 to 0.93 |

^{2}—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error; MBE—mean bias error; NMBE—normalized mean bias error; EF—modelling efficiency.

**Table 6.**Mean and range values of the accuracy metrics relative to NASA POWER solar radiation with and without bias correction for the full data set of all 14 locations.

Bias Correction Scheme | b | R^{2} | RMSE | NRMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | |

No Bias Correction | 1.03 | 0.03 | 0.95 to 1.08 | 0.94 | 0.02 | 0.91 to 0.97 | 2.10 | 0.31 | 1.51 to 2.73 | 12.44 | 1.92 | 8.75 to 16.12 |

Regional Bias Correction | 1.00 | 0.03 | 0.92 to 1.05 | 0.94 | 0.02 | 0.91 to 0.97 | 1.99 | 0.30 | 1.48 to 2.53 | 11.72 | 1.64 | 8.92 to 14.87 |

Local Bias Correction | 1.00 | 0.00 | 0.99 to 1.01 | 0.94 | 0.02 | 0.91 to 0.97 | 1.89 | 0.27 | 1.43 to 2.50 | 11.15 | 1.53 | 8.62 to 14.73 |

Bias Correction Scheme | MBE | NMBE | EF | |||||||||

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | ||||

No Bias Correction | 0.65 | 0.59 | −0.84 to 1.62 | 3.93 | 3.51 | −0.65 to 9.86 | 0.93 | 0.02 | 0.89 to 0.97 | |||

Regional Bias Correction | −0.01 | 0.59 | −1.49 to 0.96 | 0.06 | 3.39 | −8.24 to 5.84 | 0.94 | 0.02 | 0.9 to 0.96 | |||

Local Bias Correction | 0.01 | 0.07 | −0.11 to 0.16 | 0.05 | 0.44 | −0.68 to 0.97 | 0.94 | 0.02 | 0.9 to 0.97 |

^{2}—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error; MBE—mean bias error; NMBE—normalized mean bias error; EF—modelling efficiency.

**Table 7.**Mean and range values of the accuracy metrics relative to NASA POWER relative humidity with and without bias correction for the full data set of all 14 locations.

Bias correction scheme | b | R^{2} | RMSE | NRMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | |

No Bias Correction | 0.93 | 0.01 | 0.92 to 0.96 | 0.82 | 0.12 | 0.40 to 0.88 | 9.24 | 0.84 | 7.81 to 11.18 | 13.00 | 0.98 | 11.41 to 14.57 |

Regional Bias Correction | 1.01 | 0.01 | 0.99 to 1.04 | 0.82 | 0.12 | 0.40 to 0.88 | 6.58 | 0.92 | 5.50 to 9.24 | 9.25 | 1.18 | 7.60 to 12.04 |

Local Bias Correction | 1.01 | 0.01 | 1.00 to 1.02 | 0.82 | 0.12 | 0.40 to 0.88 | 6.47 | 0.99 | 5.44 to 9.30 | 9.10 | 1.26 | 7.45 to 12.12 |

Bias Correction Scheme | MBE | NMBE | EF | |||||||||

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | ||||

No Bias Correction | −5.17 | 0.88 | −6.23 to −2.93 | −7.27 | 1.22 | −9.02 to −4.28 | 0.61 | 0.21 | −0.08 to 0.79 | |||

Regional Bias Correction | 0.74 | 0.90 | −0.17 to 3.04 | 1.07 | 1.33 | −0.24 to 4.45 | 0.80 | 0.15 | 0.26 to 0.88 | |||

Local Bias Correction | 0.78 | 0.41 | 0.09 to 1.51 | 1.09 | 0.57 | 0.13 to 2.07 | 0.80 | 0.15 | 0.25 to 0.88 |

^{2}—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error; MBE—mean bias error; NMBE—normalized mean bias error; EF—modelling efficiency.

**Table 8.**Mean and range values of the accuracy metrics relative to NASA POWER wind speed with and without bias correction for the full data set of all 14 locations.

Bias Correction Scheme | b | R^{2} | RMSE | NRMSE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | |

No Bias Correction | 1.40 | 0.24 | 0.96 to 1.79 | 0.67 | 0.07 | 0.52 to 0.79 | 1.10 | 0.29 | 0.62 to 1.63 | 62.50 | 25.93 | 23.08 to 105.62 |

Regional Bias Correction | 0.95 | 0.17 | 0.65 to 1.2 | 0.67 | 0.07 | 0.52 to 0.79 | 0.69 | 0.17 | 0.52 to 1.14 | 36.60 | 6.92 | 27.22 to 46.37 |

Local Bias Correction | 0.86 | 0.10 | 0.64 to 0.98 | 0.67 | 0.08 | 0.51 to 0.79 | 0.60 | 0.11 | 0.4 to 0.79 | 32.51 | 8.41 | 19.59 to 50.46 |

Bias Correction Scheme | MBE | NMBE | EF | |||||||||

Mean | St. Dev. | Range | Mean | St. Dev. | Range | Mean | St. Dev. | Range | ||||

No Bias Correction | 0.85 | 0.39 | 0.12 to 1.44 | 49.86 | 28.01 | 4.54 to 94.54 | −0.88 | 1.21 | −3.03 to 0.71 | |||

Regional Bias Correction | −0.12 | 0.38 | −0.84 to 0.38 | −2.85 | 18.26 | −33.15 to 22.75 | 0.41 | 0.14 | 0.23 to 0.67 | |||

Local Bias Correction | −0.20 | 0.17 | −0.5 to 0.04 | −12.25 | 10.50 | −32.68 to 2.03 | 0.53 | 0.17 | 0.16 to 0.73 |

^{2}—coefficient of determination; RMSE—root mean square error; NRMSE—normalized root mean square error; MBE—mean bias error; NMBE—normalized mean bias error; EF—modelling efficiency.

**Table 9.**Mean and standard deviation values of all the accuracy metrics relative to NASA POWER weather variables, with and without bias correction.

Variable | Bias Correction | Accuracy Metric | |||||
---|---|---|---|---|---|---|---|

b | RMSE | NRMSE | MBE | NMBE | EF | ||

Maximum Temp. | No Bias Correction | 0.98 (±0.02) | 1.91 (±0.31) | 7.95 (±1.53) | −0.64 (±0.65) | −2.56 (±2.69) | 0.92 (±0.07) |

Regional Bias Correction | 1.00 (±0.03) | 1.74 (±0.34) | 7.25 (±1.81) | 0.03 (±0.65) | 0.22 (±2.84) | 0.93 (±0.08) | |

Local Bias Correction | 1.00 (±0.00) | 1.59 (±0.18) | 6.60 (±1.00) | −0.02 (±0.12) | −0.08 (±0.52) | 0.95 (±0.04) | |

Minimum Temp. | No Bias Correction | 1.08 (±0.04) | 2.01 (±0.38) | 20.51 (±5.28) | 1.03 (±0.54) | 10.65 (±6.05) | 0.84 (±0.07) |

Regional Bias Correction | 0.99 (±0.03) | 1.68 (±0.28) | 17.10 (±3.9) | −0.05 (±0.53) | −0.35 (±5.52) | 0.89 (±0.03) | |

Local Bias Correction | 0.99 (±0.01) | 1.58 (±0.25) | 16.12 (±3.53) | −0.02 (±0.05) | −0.19 (±0.52) | 0.90 (±0.03) | |

SolarRadiation | No Bias Correction | 1.03 (±0.03) | 2.10 (±0.31) | 12.44 (±1.92) | 0.65 (±0.59) | 3.93 (±3.51) | 0.93 (±0.02) |

Regional Bias Correction | 1.00 (±0.03) | 1.99 (±0.30) | 11.72 (±1.64) | −0.01 (±0.59) | 0.06 (±3.39) | 0.94 (±0.02) | |

Local Bias Correction | 1.00 (±0.00) | 1.89 (±0.27) | 11.15 (±1.53) | 0.01 (±0.07) | 0.05 (±0.44) | 0.94 (±0.02) | |

Relative Humidity | No Bias Correction | 0.93 (±0.01) | 9.24 (±0.84) | 13.00 (±0.98) | −5.17 (±0.88) | −7.27 (±1.22) | 0.61 (±0.21) |

Regional Bias Correction | 1.01 (±0.01) | 6.58 (±0.92) | 9.25 (±1.18) | 0.74 (±0.9) | 1.07 (±1.33) | 0.80 (±0.15) | |

Local Bias Correction | 1.01 (±0.01) | 6.47 (±0.99) | 9.10 (±1.26) | 0.78 (±0.41) | 1.09 (±0.57) | 0.8 (±0.15) | |

Wind Speed | No Bias Correction | 1.40 (±0.24) | 1.10 (±0.29) | 62.50 (±25.93) | 0.85 (±0.39) | 49.86 (±28.01) | −0.88 (±1.21) |

Regional Bias Correction | 0.95 (±0.17) | 0.69 (±0.17) | 36.60 (±6.92) | −0.12 (±0.38) | −2.85 (±18.26) | 0.41 (±0.14) | |

Local Bias Correction | 0.86 (±0.10) | 0.60 (±0.11) | 32.51 (±8.41) | −0.20 (±0.17) | −12.25 (±10.5) | 0.53 (±0.17) |

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## Share and Cite

**MDPI and ACS Style**

Rodrigues, G.C.; Braga, R.P.
Evaluation of NASA POWER Reanalysis Products to Estimate Daily Weather Variables in a Hot Summer Mediterranean Climate. *Agronomy* **2021**, *11*, 1207.
https://doi.org/10.3390/agronomy11061207

**AMA Style**

Rodrigues GC, Braga RP.
Evaluation of NASA POWER Reanalysis Products to Estimate Daily Weather Variables in a Hot Summer Mediterranean Climate. *Agronomy*. 2021; 11(6):1207.
https://doi.org/10.3390/agronomy11061207

**Chicago/Turabian Style**

Rodrigues, Gonçalo C., and Ricardo P. Braga.
2021. "Evaluation of NASA POWER Reanalysis Products to Estimate Daily Weather Variables in a Hot Summer Mediterranean Climate" *Agronomy* 11, no. 6: 1207.
https://doi.org/10.3390/agronomy11061207