Data Source Sensitivity in Solar Radiation Typical Meteorological Year (TMY) for Five Different Regions of Brazil

Generation of Cumulative Distribution Functions (CDFs)

The TMY generation procedure begins from hourly data of the 13-year time period for the following meteorological parameters: air temperature, relative humidity, wind speed and solar radiation. Ten daily weather indices are generated from this hourly data: maximum, minimum and mean dry air bulb temperature (T_max, T_min, T_mean) and relative humidity (RH_max, RH_min, RH_mean), maximum and mean windspeed (W_max, W), daily global solar radiation (GHI), and direct normal solar irradiation (DNI). For each calendar month, each of the 10 sets of daily indices were sorted into bins, and the CDFs were calculated by counting the cases in each bin. For N observations of a variable x that are sorted into an increasing order x₁, x₂, …, x_N, the CDF is given by the following function:

For each calendar month, a long term CDF is generated for the entire time period, as well as individual short term CDFs for each individual year. For example, for January, we calculate one long-term CDF consisting of the data for all 13 Januarys, as well as 13 individual CDFs for the January data from each year. This is done for each calendar month, and each daily index.

Using Finkelstein-Schafer statistics (FS), the monthly CDFs are compared to the long-term CDF for each index. This statistic gives a measure of the average absolute difference between the long-term CDF and the monthly CDF. The FS statistic for each index is calculated using the following equation (1):

where CDF_m is the long-term CDF for month m and CDF_y,m is the short-term CDF for month m in year y. N is the number of bins and x is the daily index.

The FS statistic is calculated for each calendar month, and for each daily meteorological index. To obtain a singular value for each calendar month, we must combine the FS statistics of every daily index. This can be done simply by calculating the sum of the FS statistics; however, this would assume that each daily index is equally as important as the others when determining the closeness of a month to its long-term average. For example, to generate a TMY for solar system performance, the global radiation is deemed to be much more important than the wind speed. In order to account for these differences, a weighted sum of the FS statistics is calculated, with different weighting factors corresponding to the importance of the daily index. In this study, we focus on TMY generation for solar energy systems, hence the significant weighting on radiation. A weighted sum of the FS statistics for the M daily indices is calculated using the following equation (2):

where the weighting factor, WFx, for each daily index can be found in Table, and the weighting factor, WFx, for each daily index is shown in Table 1.

This is the original weighting scheme suggested by Hall et al., 1978, however a modification was later suggested by Wilcox-Marion, 2008, to include Direct Normal Irradiance (DNI), rather than solely Global Horizontal Irradiance (GHI) and reduce the weighting on wind. Additionally, this later update to the Hall’s method utilized modelled solar radiation data. We refer to this updated Hall method as “TMY3”, and the weighting scheme for this method can be found in Table 1.

Later in this study, we investigate the use of different weighting schemes and investigate the sensitivity of the generated TMY to these weighting factors for weather indices. Various methods have been proposed in the literature (e.g., Marion-Urban,1995; Huang et al., 2014; Su et al., 2009), to select the final TMM once the weighted sums (WS) have been calculated. These involve imposing persistence criteria or calculating the root mean squared difference (RMSD), yet for the sake of simplicity for this paper we simply select the month with the smallest WS as our TMM.

The hourly data for each of the 12 TMMs are concatenated and smoothed for 6 hours on either side of month interfaces to account for discontinuities, thus producing the TMY. A final comparison of the CDF for the entire time period and the CDF of the TMY is calculated to demonstrate the closeness of the two datasets.

Data Used

The aims of this study were not only to produce a TMY for each of the 5 selected regions of Brazil, but also to compare the TMYs generated from different data sources. In theory, the TMYs generated from different sources of data should be the same for a specific location, however this study investigates whether we can be confident in the consistency of the TMY across different data sources.

The study used measured data from 5 stations collecting solarimetric data from the SONDA network (http://sonda.ccst.inpe.br/), representing the predominant climatic macro-regions in the country. The SONDA solarimetric network is maintained and operated by the National Institute for Space Research (INPE) and is linked to the Baseline Surface Radiation Network (BSRN-GEWEX), providing long-term and high-quality data series of solar irradiation, wind speed and other meteorological data. The stations were selected based on the representativeness of the climate, quality and continuity of the data and they are named: A009 Palmas – North A316, Caicó – Northeast; A001 Brasilia – Central-West; A707 Presidente Prudente – Southeast, and A803 Santa Maria – South.

It is difficult to obtain continuous hourly data for long time series of data (>10 years), so there are some gaps in the meteorological data provided. For short gaps in the data (less than 6 hours), the missing values are filled using linear interpolation based on previous values at that hour. For longer gaps, months containing more than 5 days of missing data (100 hours) were discarded from calculation of the TMY. This was done because otherwise a potential candidate for the TMM would contain more than 5 days of interpolated data, resulting in too much synthetic data in the TMY and defeating the purpose of using a TMY instead of the long-term average. In addition, a data quality control procedure was carried out to eliminate spurious values, such as non-zero solar radiation values at night or consistently unrealistic values for the chosen locations.

In TMY calculations, it is preferable to have as long a time period of data as possible to ensure that the long-term average is truly representative of the meteorological conditions in that region. In this study, we set our threshold for the sample size of years from which the TMM can be selected as 10 years. This enabled at most 3 months for each calendar month to be discarded. In some cases, we relax this condition to 9 years since it is difficult to obtain 10 years of reliable data in some areas of Brazil. For stations that did not meet this condition, an alternative station in that same region of Brazil was used to generate the TMY.

Ground observation data was obtained from automatic weather stations (AWS) from the Brazilian National Weather Service (INMET) located at the 5 locations of interest, as seen in Figure 1. For our initial TMY generation, hourly data for all 9 daily indices from these AWS stations was used. Since these stations do not contain data for Direct Normal Solar Radiation, the TMY weighting scheme from Table 1 was used to generate the observational TMY. The TMYs calculated from ground observation data are referred to as TMY_obs throughout the remainder of this report.

Satellite and ERA5 Modelled Solar Radiation

Numerical assessment of downward incoming solar irradiance employed a satellite-derived model for the 5 locations of interest as shown in Figure 1. The numerical physical-based model Brasil-SR (Pereira et al, 2017)) estimated the solar radiation incident components on the surface (GHI and DNI), combining the use of the two-flux method in the solution of the radiative transfer equation with the use of parameters determined from satellite images. The radiative transfer calculations follow a two-stream approximation with δ-Eddington scaling to estimate the downward surface GHI and to derive the other solar radiation components (Pereira et al., 2017; CasaGrande et al., 2021). This time-series Irradiance Model uses more than 17 years of satellite data from GOES/NOAA to derive modelled Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI). The Brazil-SR model was validated based on more than 300 in situ measurements AWS data from INMET and other sources, and Table 2 shows the validation metrics of the monthly averages of daily total horizontal global irradiation for each one of the Brazilian regions.

This modelled radiation data was used to replace the Global Horizontal Radiation (GHI) data from the solarimetric station data and allows for a further two TMYs to be calculated for each location. The first of these, TMY_mod, used only the modelled GHI data and therefore used the TMY weighting scheme. The second of these, TMY3_mod, used both the modelled GHI and DNI data, thereby using the TMY3 weighting scheme.

The final source of data used in this project was the ERA5-Land Hourly Reanalysis data from ECMWF (Muñoz Sabater, 2019). Reanalysis data combines modelled data with observations to create a complete and consistent dataset. However, since reanalysis data often has difficulties in resolving clouds, in this study we use the modelled GHI and DNI data in combination with the ERA5 data for the other daily weather indices (temperature, wind velocity and relative humidity). We include both GHI and DNI, and therefore use the TMY3 weighting scheme. The TMY generated from this data is referred to as TMY3_rea.

Central-West: Brasilia/DF (A001)

For the Brasilia station, there were at least 10 years from which TMM could be selected for each calendar month, therefore no alternative station was needed. The TMY was generated for each of the four different data sources and can be found in Table 3.

From the generated TMYs, we can see that there is agreement of at least 2 of the data sources for every calendar month, with 2 months (January and October) having the complete agreement of the TMM. The greatest similarity is between the TMY_mod and TMY3_mod results, with only 2 calendar months disagreeing, however this is not surprising since these TMYs only differ due to the inclusion of DNI in TMY3.

The CDF for each generated TMY is compared to the long term (LT) observed and modelled CDFs for the annual GHI, as shown in Figure 2. Evidently, these CDFs are extremely close to each other. The lower the value calculated for the Finkelstein-Schafer parameter, the closer the values of the two curves will be. In general, the calculated FS values are relatively low and close to each other, with the lowest value tabulated in Table 3 occurring for the observational data.

Figure 2

Southeast: Presidente Prudente/SP (A707)

For the Presidente Prudente station, there were at least 10 years from which TMM could be selected for each calendar month, therefore no alternative station was needed. The TMY was generated for each of the four different data sources and can be found in Table 4.

From the generated TMYs, we can see that there is agreement of at least 2 of the data sources for 10 calendar months, with 1 month (September) having the complete agreement of the TMM.

The CDF for each generated TMY is compared to the long term (LT) observed and modelled CDFs for the annual GHI, as shown in Figure 3. From this plot, we can see that there is a much greater discrepancy between the modelled and observed solar radiation at this location, compared to the A001 station, for example. Table 4 tabulates the Finkelstein-Schafer statistic for each TMY compared to its respective LT-CDF, in which case the TMY3_mod data showed the best FS statistics while the observational data showed the worst result.

Figure 3

South: Santa Maria/RS (A803)

For the Santa Maria station, there were at least 10 years from which TMM could be selected for each calendar month except for May, June, and July. For these months, there were only 9 years from which the TMM could be selected, yet this was deemed acceptable in the calculation of the TMY. The TMY was generated for each of the four different data sources and can be found in Table 5.

From the generated TMYs, we can see that there is agreement of at least 2 of the data sources for every calendar month, with 1 month (March) having the complete agreement of the TMM.

Again, the CDF for each generated TMY is compared to the long term (LT) observed and modelled CDFs for the annual GHI, as shown in Figure 4. From this plot, we can see that there is a good agreement between the modelled and observed solar radiation at this location. Table 5 tabulates the Finkelstein-Schafer statistics for each TMY compared to its respective LT-CDF. It can be seen that this station had the lowest FS values of all the stations analyzed, with a 75% quartile value below 0.0069. However, the TS value for observational data was higher at this station.

Figure 4

North: Palmas/TO (A009)

For the Palmas station, there are at least 10 years from which the TMM can be selected available for each calendar month, except for November. There are 9 years of data available for November, and this is deemed acceptable considering the difficulty in obtaining 10 years of stable measurements for Northern Brazil. The TMY was generated for each of the four different data sources and can be found in Table 6.

From the generated TMYs, we can see that there is agreement of at least 2 of the data sources for 11 calendar months, with 1 month (July) having the complete agreement of the TMM.The CDF for each generated TMY is compared to the long term (LT) observed and modelled CDFs for the annual GHI, as shown in Figure 5. From this plot, we can see that there is again a large discrepancy between the modelled and observed solar radiation at this location. In Table 6 the Finkelstein-Schafer statistic for each TMY compared to its respective LT-CDF are tabulated and the worst value was for the reanalysis data.

Figure 5

Northeast: Caicó/RN (A316)

For the Caicó station, there are only 8 or 9 years from which the TMM can be selected for each calendar month. Once again, this is not ideal, yet considering the difficulty in obtaining long term stable measurements for Northern Brazil, this is acceptable for our generation of the TMY. The TMY was generated for each of the four different data sources and can be found in Table 7.

From the generated TMYs, we can see that there is agreement of at least 2 of the data sources for every calendar month, with 2 months (April and June) having the complete agreement of the TMM.

The CDF for each generated TMY is compared to the long term (LT) observed and modelled CDFs for the annual GHI, as shown in Figure 6. From this plot, we can see that there is only a slight discrepancy between the modelled and observed solar radiation at this location, but not as large as at other locations. In Table 7 the Finkelstein-Schafer statistic for each TMY compared to its respective LT-CDF are tabulated and the worst value was for the reanalysis data.

Figure 6

From the TMYs generated for each of the 5 regions of Brazil, we can draw 4 main conclusions:

1. There is agreement in the TMMs between at least 2 data sources for at least 10 months for each region. This suggests that the typicality of the months is overall quite consistent, even if the data source is different.

2. Stations A001 and A803 have similar CDFs between observed/modeled and TMY/LT data, so they are not sensitive to data source selection. Although the TMMs may be slightly different, the overall CDF of the TMY is still very close to the LT. This is also reflected by the lowest FS values among all five stations studied.

3. For the A707, A009 and A316 stations there is discrepancy between the CDFs for observations and modelled data, meaning TMY may be sensitive to selection of data source at these locations. Table 8 shows the number of TMMs in agreement between TMY_obs and any of the TMYs calculated from modelled data for each station. Table 8 shows essentially no correlation between stations that have discrepancy between observed and modelled data and agreement in TMMs. Whilst the A707 station (which had a large discrepancy between modelled and observed data) only has three months in agreement, the A009 station which also had a large discrepancy has 6 months in agreement. This suggests that whilst the discrepancy of the data will be important in the generated TMY dataset, the choice of which months are the most typical is not greatly affected. These stations presented the highest FS values among the stations studied.

4. The stations A803 and A707 have shown the worst results compared with the observations (Figures 3 and 4, respectively). This is also reflected in the greater discrepancy in FS. The reason for it is due to the influence of the ENSO events of the dataset. It is well known that ENSO is very well (and positively) correlated with the south part of Brazil (which is represented by the station A803) while this is not so clear for the southeast Brazil (represented by the station A707). So, the presence of this event (ENSO) can modify the shape of the curve (e.g., Figure 3) and the difference between the input data (Figure 4).

To investigate this further, we could look at individual monthly CDFs, as opposed to the yearly CDF, as well as considering the ranking of the selected TMMs.