Abstract
Due to the importance of generating energy sustainably, with the Sun being a large solar power plant for the Earth, we study the crosscorrelations between the main meteorological variables (global solar radiation, air temperature, and relative air humidity) from a global crosscorrelation perspective to efficiently capture solar energy. This is done initially between pairs of these variables, with the Detrended CrossCorrelation Coefficient, ρ_{DCCA}, and subsequently with the recently developed Multiple Detrended CrossCorrelation Coefficient, \({\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}\). We use the hourly data from three meteorological stations of the Brazilian Institute of Meteorology located in the state of Bahia (Brazil). Initially, with the original data, we set up a color map for each variable to show the time dynamics. After, ρ_{DCCA} was calculated, thus obtaining a positive value between the global solar radiation and air temperature, and a negative value between the global solar radiation and air relative humidity, for all time scales. Finally, for the first time, was applied \({\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}\) to analyze crosscorrelations between three meteorological variables at the same time. On taking the global radiation as the dependent variable, and assuming that \({\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}={\bf{1}}\) (which varies from 0 to 1) is the ideal value for the capture of solar energy, our analysis finds some patterns (differences) involving these meteorological stations with a high intensity of annual solar radiation.
Similar content being viewed by others
Introduction
Nowadays, we know of the requirement to seek sustainable energy sources in order to preserve the environment for future generations on Earth. As is known, the Sun with its radiation can be increasingly used in order to generate energy renewably and sustainably. There are essentially two main ways of harnessing solar energy: direct electricity generation and heating water in a boiler. From the point of view of electric energy, the two systems that are the most widespread are the heliothermic system (the radiation is converted first into thermal energy and then into electric energy) and the photovoltaic system (the radiation is converted directly into electric energy). But, realistically speaking, there are several ways of generating electricity. For example, according to the Brazilian Ministry of Mines and Energy^{1}, the electrical matrix is made up of parts with the following percentages: Hydroelectric (63.7%), Thermal (27.2%), Wind (8.1%), and Solar (1.0%). We can see that most of the energy generation comes from hydroelectric plants, such as Itaipu (the world’s largest hydroelectric power plant). Of the 27% of nonrenewable thermal sources, 8.1% come from natural gas, 9.1% biomass, 6.2% oil, 2.3% coal, 1.2% nuclear, and 0.2% from others types^{1}.
Although hydroelectric plants use a renewable and a lowcost resource, they change the landscape, cause major deforestation, dam can break, as in Brumadinho^{2}, and in general they cause damage to the fauna and the flora also, in many cases, families are displaced from their homes^{3,4,5,6}.
Thus, there remains an incentive for research and development in this area for the furtherance of the policy of cleaner electricity generation, in order to replace nonrenewable thermal energy by a cleaner renewable source such as solar radiation. Specifically, in Brazil the incentive for solar power energy is justified by the fact that the country has large areas with a high incidence of solar radiation; the semiarid regions of the Northeast have the highest intensity of solar radiation over the year^{7,8}. Presently, in the case of solar energy powered by photovoltaic cell panels, there is the disadvantage of their high initial cost and their low process efficiency, from 15% to 25%. Another aspect to be considered is the environmental impact caused by the use of the silicon in the production chain of the photovoltaic cells. However, the current and recurring challenge is to establish innovative manufacturing processes and use highperformance materials in order to obtain more efficiency in the collecting surface of the photovoltaic cells.
The efficiency of the photovoltaic cells depends not only on internal manufacturing factors, but also on external factors. External factors include shading by trees and/or clouds, rain, dust, solar radiation, air temperature, relative air humidity, and the wind speed and direction, among others. Since the external factors are not controllable, there has been research to understand the their effects. Due to its strong influence on the performance of photovoltaic cells, the solar radiation and the air temperature have been the most studied external factors^{9,10,11,12}. There have also been many studies of the impact of the air temperature on photovoltaic cells, but there are still only a few studies that address the impact of these environmental factors in regions with a tropical climate, such as the Northeast of Brazil or that study how the variables are interrelated and interact^{13}. Thus, not only should our attention be focused on energy generation: it is also important to have robust statistical tools in the area of the environmental sciences, with the purpose of analyzing how the external meteorological variables are related, as will be proposed in this paper with the DCCA multiple crosscorrelation coefficient^{14}.
Data Set
Taking into consideration that the global solar radiations is measured while we have sunlight on the sensor (pyranometer), hence the data was taken hourly from 10 to 21 h UTC (Coordinated Universal Time). Our data were obtained from meteorological stations managed by Brazilian Institute of Meteorology (INMET)^{15}. Therefore, in order to study its potential for solar power we chose three meteorological stations localized in the state of Bahia (Brazil), see Fig. 1. These stations are important because they are the ones that have the best databases (about global solar radiation)^{15}, and because they have the following characteristics, see Table 1.
Our first choice of analysis was to temporally order the data in a color map, with the three meteorological variables side by side, which are:
(a) Global Solar Radiation (KJ/m^{2});
(b) Air Temperature (°C);
(c) Relative Air Humidity (%).
For each station, these variables can be see in Fig. 2 (Barreiras), Fig. 3 (Cruz da Almas), and Fig. 4 (Salvador). In these figures, a day (with 12 h) start at 10 h and ends at 21 h (UTC). It can be seen that the maximum global solar radiation is usually concentrated around the peak of sunlight (\(\simeq \)15 h). Logically, there are fluctuations in this value, depending on the season of the year or the time of day. We can also note in the color map a direct relation between the variables, but the color map is not able to robustly quantify that value; it gives us a beautiful visual display of information as to the dynamic changes in the variables. The next step is to quantitatively describe the features of the data for the whole of the period: for example, if we take the minimum and maximum values one can see:
BAR: 0 ≤ Rad. ≤ 4051 (KJ/m^{2})\(\therefore \)11 ≤ Temp. ≤ 40 (°C)\(\therefore \)8 ≤ Hum. ≤ 100 (%);
CRUZ: 0 ≤ Rad. ≤ 4148 (KJ/m^{2})\(\therefore \)14 ≤ Temp. ≤ 38 (°C)\(\therefore \)15 ≤ Hum. ≤ 100 (%);
SSA: 0 ≤ Rad. ≤ 4088 (KJ/m^{2})\(\therefore \)19 ≤ Temp. ≤ 35 (°C)\(\therefore \)33 ≤ Hum. ≤ 100 (%).
But, these statistics can be more refined if the seasons are considered. More details about these statistics can be seen in the results section below.
Results
Descriptive statistical
Initially as the results, we compute the mean values in the point of view of the annual seasons in the southern hemisphere. In this sense to simplify the climatological calculations and keep them uniform we choose the meteorological definition for seasons^{16} with:
Spring from September/01 to November/30;
Summer from December/01 to February/28;
Autumn from March/01 to May/31;
Winter from June/01 to August/31.
Figure 5 present these mean values (performed at every time (UTC)) for the global solar radiation, air temperature, and relative air humidity at each season (Spring, Summer, Autumn, Winter). It is possible to observe that the radiation in the sensor has a distribution (apparently normal) characterized by a mode varying with the season. The value for maximum solar global radiation is around 15 h (UTC) and this intensity depends on the location (see Table 2).
The maximum global solar radiation is at 15 h, except at Salvador in the spring and summer, that is at 16 h. The peak of maximum air temperature and minimum relative air humidity has a greater variation depending on the annual season. There is a clear inverse relation between air temperature and relative air humidity, more evidenced for Barreiras station, as shown in^{17}. But, depending on the location (northern hemisphere) such a relation is not always true^{18}. In this paper we also measured other moments, that are:
Standard deviation (%): \(sd( \% )=\frac{sd\,\ast \,100}{\langle x\rangle }\)
Skewness: \(sk\equiv \frac{n}{(n1)\,(n2)}\,{\sum }_{i=1}^{n}\,{(\frac{{x}_{i}\langle x\rangle }{sd})}^{3}\)
Kurtosis: \({K}_{e}\equiv \frac{\frac{1}{n}\,{\sum }_{i=1}^{n}\,{({x}_{i}\langle x\rangle )}^{4}}{{[\frac{1}{n}{\sum }_{i=1}^{n}{({x}_{i}\langle x\rangle )}^{2}]}^{2}}3\)
in this case, \(\langle x\rangle \) is the mean and sd is the sample standard deviation, see Table 3 with the results. We can see that the highest relative standard deviation is for the global solar radiation (≈35%), except in the Spring and Winter for Barreiras station, where the relative air humidity has the highest. For the skewness, we note in general values different from 0 (but close), indicating that our dataset diverges a little from the mean with positive or negative values. There is an excess Kurtosis, \({K}_{e}\ne 0\) for most of the values found in the Table 3, with \({K}_{e} < 0\) (platykurtic distribution) and with \({K}_{e} > 0\) (leptokurtic distribution). These results indicate that the meteorological time series is nonstationary. But, these descriptive statistics are well known and we want to propose something innovative in the study of direct or indirect relations between the main meteorological variables. With \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) and \(DM{C}_{{\rm{x}}}^{2}\), we will succeed.
DCCA crosscorrelation coefficient \({{\boldsymbol{\rho }}}_{{{\bf{x}}}_{{\boldsymbol{i}}},{{\bf{x}}}_{{\boldsymbol{j}}}}\)
Figure 6 presents the values of \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) for the crosscorrelations between global solar radiation × air temperature, global solar radiation × relative air humidity, and air temperature × relative air humidity (these are particular cases of \(DM{C}_{{\rm{x}}}^{2}\) for a pair of time series). We can see clearly that the variables are related for all time scales n and for all meteorological stations, because \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\ne 0\). Thus, due to the importance of the air temperature as a meteorological variable to solar power energy, Fig. 6 (◇) shows \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) between global solar radiation and air temperature. In this case \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}} > 0\), with a strong (mostly) DCCA crosscorrelation for all time scales n and meteorological stations. Specifically, for \(n < 360\) (30 days), Fig. 6 (◇) shows that \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) is lower for Barreiras than for with Cruz das Almas and Salvador at the same time scale. For \(n=360\), \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) has approximately the same value of 0.666 for these three stations. But, for \(n > 360\), there is a maximum value for \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) around \(n\approx 4400\) (≈365 days); this probably shows the cyclical annual effect. Analyzing the DCCA crosscorrelation between the global solar radiation and the relative air humidity in Fig. 6 () it is possible to observe that \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}} < 0\) for all time scales n and stations. Again, if we take as reference \(n=360\), patterns for each of the stations can be identified. For the DCCA crosscorrelation between air temperature and relative air humidity, Fig. 6 (), \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}} < 0\) which agrees with^{17}.
But, if we want to study a crosscorrelation between three (global solar radiation, air temperature and relative air humidity) or more variables, we must apply a method that generalizes \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\), such as \(DM{C}_{{\rm{x}}}^{2}\). The results of its application will be presented in the following.
DCCA multiple crosscorrelation coefficient \({\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}\)
Figure 7 presents \(DM{C}_{{\rm{x}}}^{2}(n)\) for global solar radiation, air temperature and relative air humidity at the same time. From this figure, it can be seen that the variables are related globally, because they have DCCA multiple crosscorrelations that range from weak to very strong. In an intuitive way, as introduced here, this result depends on the dependent variable {y}, the station, and the time scale involved. Figure 7 show that \(DM{C}_{{\rm{x}}}^{2}\) for {Air Temperature; (Global Radiation × Relative Humidity)} () behave similarly, for \(n < 360\), for all stations, but differ for \(n > 360\). Up to the value \(n\simeq 70\) {Air Temperature; (Global Radiation × Relative Humidity)} and {Relative Humidity; (Global Radiation × Air Temperature)} yield approximately the same value of \(DM{C}_{{\rm{x}}}^{2}\), going from very strong to strong DCCA multiple crosscorrelation. For the Salvador station, \(DM{C}_{{\rm{x}}}^{2}\) (□) are closer to ( and ) than they are for the Barreiras station, mainly for small time scales n.
Our goal here is to study how the meteorological variables are related. We believe that this can help promote the efficiency of capturing solar energy in photovoltaic cells located in a certain region with climatic variations. To this end, looking at \(DM{C}_{{\rm{x}}}^{2}(n)\) and taking as a dependent variable the global solar radiation, we have the following results, Fig. 8. Setting \(DM{C}_{{\rm{x}}}^{2}=1\) for maximum efficiency in capturing solar energy for all time scales, both in short and longterm, we can analyze separately each location and observe the dependence of \(DM{C}_{{\rm{x}}}^{2}\) on the time scale and location and define in this way the potential efficiency of each location. In our case study, all stations have \(DM{C}_{{\rm{x}}}^{2} > 0.2\) with levels of the multiple crosscorrelation lying between weak and very strong (see Table 4). For small time scales, \(n < 10\), we have, in decreasing order of their multiple crosscorrelation, Salvador (○), Cruz das Almas (), and Barreiras (). At \(n\simeq 360\) (30 days), all stations have approximately the same value, \(DM{C}_{{\rm{x}}}^{2}\simeq 0.6\). For long time scales, there is a peak of \(DM{C}_{{\rm{x}}}^{2}\) for Salvador and Barreiras at \(n\approx 3652\) (one year), of approximately 0.8, whereas for Barreiras this value is below 0.6.
Discussion
Taking into account the global solar radiation, the air temperature and the relative air humidity, we have studied the crosscorrelations from a global perspective, by using the multiple detrended crosscorrelation coefficient, \(DM{C}_{{\rm{x}}}^{2}\). Initially we provide, for better data visualization, the descriptive statistics of these time series. Then, with their mean values and with the capture and or generation of solar energy in view, we found the maximum global solar radiation value. It can be seen here that usually this maximum is concentrated at 15 h (UTC), but with different air temperature and relative air humidity depending on the season. Logically, with standard deviation, skewness, and kurtosis, we can infer whether or not the probability distribution function approach the normal distribution. In this paper, it can be seen that depending on the season, the distributions deviate from the normal, characterizing these time series as nonstationary. But, this classical statistical analysis only takes into consideration each variable separately. To analyze the relations between them in pairs (or more) we must apply a statistical tool that has this capability.
Developed by Zebende^{19}, Detrended Crosscorrelation Coefficient, \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\), was constructed in order to analyze the crosscorrelations between pairs of nonstationary time series. It is robust if compared, for example, with the Pearson’s coefficient^{20}. In this sense, the values of \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) between the global solar radiation, air temperature, and relative air humidity (in pairs) depend on the geographical location and the time scale, for these three meteorological stations chosen here. There is a positive relation between global solar radiation and air temperature and an inverse relation between global solar radiation and relative air humidity.
As mentioned in the introduction, the efficiency of a photovoltaic cell depends mainly on internal factors, but that the external factors are also important, as well as their interrelations. Our goal here was to apply the multiple DCCA crosscorrelation, \(DM{C}_{{\rm{x}}}^{2}\), to study globally the relation between three (main) variables involved in solar energy. It is noteworthy that such application has not yet been performed and this paper is the pioneer to treat together these three variables at the same time with \(DM{C}_{{\rm{x}}}^{2}\). Thus, assuming \(DM{C}_{{\rm{x}}}^{2}=1\) to be the ideal value for solar energy capture, if we have global solar radiation as the dependent variable, than for the meteorological stations of Barreiras, Cruz das Almas, and Salvador, located in the northeast of Brazil, an area with a high intensity of annual solar radiation, we did our analysis and noticed some patterns (differences). Because \(DM{C}_{{\rm{x}}}^{2}\) is a function of the time scale n, we can determine this multiple coefficient for small, medium, and long time scales. For example, for \(n=12\) (small time scale), the Salvador station has the best value for capture solar energy according to \(DM{C}_{{\rm{x}}}^{2}\), with verystrong value. For \(n=360\) (one month) all stations have an intermediate value for \(DM{C}_{{\rm{x}}}^{2}\), that is, between medium and strong. But, for long time scales, Barreiras and Cruz das Almas have the best values for capture solar energy if compared to Salvador.
Finally, it is worth pointing out that in a certain way the stations are close to each other, and that a study for other stations around the planet would be very welcome. But, the purpose of this paper was to apply a new method to the analysis of multiple crosscorrelations between meteorological variables in a global (innovative) way. In conclusion, as the expression for multiple correlation is quite general, other variables can be employed, such as atmospheric pressure and wind speed, among others, adding even more information to the calculation of \(DM{C}_{{\rm{x}}}^{2}\).
Methods
For DCCA multiple crosscorrelation coefficient^{14} presentation, we employ the DCCA crosscorrelation coefficient \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\)^{19}, which is defined in terms of the \({F}_{DFA}(n)\)^{21} and the \({F}_{DCCA}^{2}(n)\) fluctuation function^{22}:
The DCCA crosscorrelation coefficient in Eq. 1 ranges between −\(1\le {\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\le 1\), and has been applied in several papers, such as^{20,23,24,25,26,27}, among many others^{28}. It is possible to generalize the idea behind \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}\) to more than two variables, and such a new multiple coefficient is referred to as the DCCA multiple crosscorrelation coefficient, denoted by \(DM{C}_{{\rm{x}}}^{2}\)^{14}:
where,
is the detrended crosscorrelations vector between the independent variables (x_{i}) and the dependent variable (y), and \({\rho }^{1}(n)\) is the matrix inverse of the detrended crosscorrelation matrix of the independent variables, defined as
This matrix is symmetric because \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{j}}(n)={\rho }_{{{\rm{x}}}_{j},{{\rm{x}}}_{i}}(n)\), \({\rho }_{{{\rm{x}}}_{i},{{\rm{x}}}_{i}}(n)=1\), and \(0\le DM{C}_{{\rm{x}}}^{2}(n)\le 1\), see Table 4 for more details about the levels. For example, if the global solar radiation is {y}, the air temperature is {x_{1}}, and the relative air humidity is {x_{2}}, then
References
Ministério de Minas e Energia, http://www.mme.gov.br/ (2019).
Brumadinho dam collapse (guardian news on youtube), https://www.youtube.com/watch?v=sKZUZQytads (2019).
MartaAlmeida, M., Mendes, R., Amorim, F. N., Cirano, M. & ao M. Dias, J. Fundão Dam collapse: Oceanic dispersion of River Doce after the greatest Brazilian environmental accident. Marine Pollution Bulletin 112, 359–364 (2016).
do Carmo, F. F. et al. Fundão tailings dam failures: the environment tragedy of the largest technological disaster of Brazilian mining in global context. Perspectives in Ecology and Conservation 15, 145–151 (2017).
Guerra, M. B. B. et al. Postcatastrophe analysis of the Fundão Tailings Dam Failure in the Doce River System, Southeast Brazil: Potentially Toxic Elements in Affected Soils. Water Air Soil Pollut 228 (2017).
Omachi, C. Y. et al. Atlantic forest loss caused by the world’s largest tailing dam collapse (Fundão Dam, mariana, brazil). Remote Sensing Applications: Society and Environment 12, 30–34 (2018).
Tiba, C. & Fraidenraich, N. Atlas Solarimétrico do Brasil: banco de dados solarimétricos, http://www.cresesb.cepel.br/publicacoes/download/Atlas_Solarimetrico_do_Brasil_2000.pdf (Recife, UFPE, 2000).
for Space Research, I. N. I. LABREN  Laboratory of Modeling and Studies of Renewable Energy Resources (INPE, 2019).
Rehman, S. & Mohandes, M. Artificial neural network estimation of global solar radiation using air temperature and relative humidity. Energy Policy 36, 571–576 (2008).
Bindi, M. & Miglietta, F. Estimating daily global radiation from air temperature and rainfall measurements. Climate Research 1, 117–124 (1991).
Almorox, J., Hontoria, C. & Benito, M. Models for obtaining daily global solar radiation with measured air temperature data in madrid (spain). Applied Energy 88, 1703–1709 (2011).
Fernandes, D. S., Heinemann, A. B., de Oliveira Amorim, A. & da Paz, R. L. F. Estimativa da radiação solar global com base em observaç ões de temperatura para o estado de goiás. Revista Brasileira de Meteorologia 33, 558–566 (2018).
Cantor, G. A. R. Influência dos fatores climáticos no desempenho de môdulos fotovoltaicos em regiões de clima tropical. Master’s thesis, UFPB (2017).
Zebende, G. & da Silva Filho, A. Detrended multiple crosscorrelation coefficient. Physica A: Statistical Mechanics and its Applications 510, 91–97 (2018).
National Institute of Meteorology (inmet), http://www.inmet.gov.br/portal/ (2019).
Seasons: Meteorological and astronomical (time and date as 1995–2019), https://www.timeanddate.com/calendar/aboutseasons.html (2019).
Zebende, G., Brito, A., Filho, A. S. & Castro, A. ρ _{DCCA} applied between air temperature and relative humidity: An hour/hour view. Physica A: Statistical Mechanics and its Applications 494, 17–26 (2018).
Vassoler, R. & Zebende, G. DCCA crosscorrelation coefficient apply in time series of air temperature and air relative humidity. Physica A: Statistical Mechanics and its Applications 391, 2438–2443 (2012).
Zebende, G. F. DCCA crosscorrelation coefficient: Quantifying level of crosscorrelation. Physica A: Statistical Mechanics and its Applications 390, 614–618 (2011).
Kristoufek, L. Measuring crosscorrelation between nonstationary series with DCCA coefficient. Physica A: Statistical Mechanics and its Applications 402, 291–298 (2014).
Peng, C.K. et al. Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685–1689 (1994).
Podobnik, B. & Stanley, H. E. Detrended crosscorrelation analysis: A new method for analyzing two nonstationary time series. Phys. Rev. Lett 100, 1–4 (2008).
Zhao, X., Shang, P. & Huang, J. Several fundamental properties of DCCA crosscorrelation coefficient. Fractals 25, 1750017 (2017).
Zebende, G. F., Silva, M. F. & Filho, A. M. DCCA crosscorrelation coefficient differentiation: Theoretical and practical approaches. Physica A: Statistical Mechanics and its Applications 392, 1756–1761 (2013).
Wang, G.J., Xie, C., Chen, S. & Han, F. Crosscorrelations between energy and emissions markets: New evidence from fractal and multifractal analysis. Mathematical Problems in Engineering 2014, 1–13 (2014).
Marinho, E., Sousa, A. & Andrade, R. Using detrended crosscorrelation analysis in geophysical data. Physica A: Statistical Mechanics and its Applications 392, 2195–2201 (2013).
Kwapień, J., Oświeçimka, P. & Drożdż, S. Detrended fluctuation analysis made flexible to detect range of crosscorrelated fluctuations. Phys. Rev. E 92, 052815 (2015).
DCCA crosscorrelation coefficient: quantifying level of crosscorrelation (citations on academic google), https://scholar.google.com.br/scholar?oi=bibs&hl=ptBR&cites=6351233990136499122 (2019).
Acknowledgements
A.A. Brito thanks the FAPESB (Fundação de Amparo à Pesquisa do Estado da Bahia) (Grant BOL 0262/2017) and G.F. Zebende thanks the CNPq (Conselho Nacional de Desenvolvimento Cientfico e Tecnológico) (Grant 304362/20174), Brazilian agencies. We all thanks the National Institute of Meteorology for the availability of the data, the UFPE Renewable Energy Center for the rich discussions and the Earth Science and Environment Modeling Program (UEFS) by the scientific support. We also thanks Dra. Jocimara Lobão of PPGM UEFS for help in the Fig. 1.
Author information
Authors and Affiliations
Contributions
A.A. Brito, H.A. de Araújo and G.F. Zebende did a data mining, analysed the results and reviewed all the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Brito, A.d.A., Araújo, H.A.d. & Zebende, G.F. Detrended Multiple CrossCorrelation Coefficient applied to solar radiation, air temperature and relative humidity. Sci Rep 9, 19764 (2019). https://doi.org/10.1038/s41598019561146
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598019561146
This article is cited by

Urban heat island (UHI) spatiotemporal pattern in comparison with NDBI before–after COVID19 pandemic in Sleman Regency, Indonesia
Modeling Earth Systems and Environment (2024)

Associating daily meteorological variables of a local climate using DCCA, sample entropy, Lévyindex and Hurst–Kolmogorov exponents: a case study
Meteorology and Atmospheric Physics (2024)

Artificial neural network model with different backpropagation algorithms and meteorological data for solar radiation prediction
Scientific Reports (2022)

Multifractal detrended crosscorrelation heatmaps for time series analysis
Scientific Reports (2022)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.