Documentation Accuracy and comparisons


After calculating model statistics by comparing Solargis model with good quality ground measurements in more than 220 sites across all type of climates, here is a summary of the accuracy of solar radiation data from Solargis:





Number of validation sites




Mean Bias for all sites



Tendency to overestimate or to underestimate the measured values, on average

Standard deviation



Indicator of the range of deviation of the model estimates for the validation sites

Expected range of bias outside validation sites (P90 uncertainty)

±4% to ±8%

±9% to ±14%

Depends on specific analysis on geography and availability of ground measurements

The maps below show detailed statistics for each validation site (click on the site marker to see the values). A detailed list is also available in the annex of the Solargis validation report (PDF, 1.7 MB).

Map of public validation sites for GHI

  • rMBD less than -4
  • rMBD from -4 to -2.5
  • rMBD between -2.5 and 2.5
  • rMBD from 2.5 to 4
  • rMBD more than 4

Map of public validation sites for DNI

  • rMBD less than -8
  • rMBD from -8 to -5
  • rMBD between -5 and 5
  • rMBD from 5 to 8
  • rMBD more than 8

Simplified characterization of bias distribution

For a practical use, the statistical measures of accuracy had to be converted into uncertainty, which better characterizes probabilistic nature of a possible error of the model estimate.

If we want to characterize the bias in general for sites out of the validation locations, we can take the simplified assumption of having a normal distribution of deviations between the model and the measured values for model estimates. When describing the normal distribution curve the following facts can be observed:

  • Average of biases is close to zero. This means that there is no systematic tendency either to overestimate or underestimate (distribution is symmetrically centered).
  • Standard deviation of bias is relatively low. This will be represented by a narrow probability distribution, i.e. the P90 value (value exceeded in the 90% of the cases) will be closer to the P50 (most expected value).

As with any other measuring approaches, users cannot expect zero uncertainty for satellite-based solar models. However, if the physics represented by the algorithms is correctly implemented, one can expect robust and uniform behavior of the model for the geographical conditions, for which it has been calibrated and validated.

Description of accuracy indicators

The performance of satellite-based models for a given site is characterized by validation statistics, which are calculated for each site for which comparisons with good quality ground measurements are available:

  • Bias or Mean Bias Deviation (MBD) characterizes systematic model deviation at a given site, i.e. systematic over- or underestimation. Bias values will be above zero when satellite modelled values are overestimating and below zero when underestimating (in comparison to ground measurements).
  • Root Mean Square Deviation (RMSD) and Mean Absolute Deviation (MAD) are used for indicating the spread of error for instantaneous values. RMSD indicates discrepancies between short-term modelled values (sub-hourly, hourly, daily, monthly) and ground measurements.

Typically, bias is considered as the first indicator of the model accuracy, however the interpretation of the model accuracy should be done analysing all measures. While knowing bias helps to understand a possible error of the long-term estimate, MAD and RMSD are important for estimating the accuracy of energy simulation and operational calculations (monitoring, forecasting). Usually validation statistics are normalized and expressed in percentage (e.g. rMBD is used for relative Mean Bias Deviation).

Other indicators can be calculated as well, like Kolmogorov-Smirnoff Index (KSI), which characterizes representativeness of distribution of values. It may indicate issues in the model’s ability to represent various solar radiation conditions. KSI is important for accurate CSP modelling, as the response of these systems is non-linear to irradiance levels. Even if bias of different satellite-based models is similar, other accuracy characteristics (RMSD, MAD and KSI) may indicate substantial differences in their performance. 

Representativeness of validation sites

Validation statistics for one site do not provide representative picture of the model performance in the given geographical conditions. This can be explained by the fact that such site may be affected by a local microclimate or by hidden issues in the ground-measured data.

Therefore, the ability of the model to characterize long-term annual GHI and DNI values should be evaluated at a sufficient number of validation sites. Good satellite models are consistent in space and time, and thus the validation at several sites within one geography provides a robust indication of the model accuracy in geographically comparable regions elsewhere.

As of today Solargis model has been validated at more than 220 sites worldwide. Although the number of reference stations is increasing with time, availability of high quality ground measurements for comparison is limited for some regions. In this case, if a number of validation sites within a specific geography shows bias and RMSD consistently within certain range of values, one can assume that the model will behave consistently also in regions with similar geography where validation sites are not available.

The results of this validation across the major climate classes (tropical, arid, temperate, cold and polar) are available in the chapter 4 of the Solargis validation report (PDF, 1.7 MB). A summary of the results according to climate classes, for GHI and DNI validation respectively, is available here:



The accuracy of the model can be calculated provided that the absolute majority of the validation data have been collected using high-accuracy instruments, applying the best measurement practices and strict quality control procedures.

Uncertainty ranges expected for Solargis model

An analysis on the distribution of the bias across different geographies and situations lead us to the following conclusions (summary in the table below):

  • In most situations the expected bias for annual values will be within ±4% for GHI values and ±9% for DNI values:
    • Most of Europe and North America (approx. below 50°) and Japan.
    • Mediterranean region, Arabian Peninsula (except the Gulf region) and Morocco.
    • South Africa, Chile, Brazil, Australia
    • Regions with good availability of high-quality ground measurements
  • Situations where the expected bias can be as high as ±8% for GHI values and ±14% for DNI values:
    • High latitudes (approx. above 50°)
    • Countries in humid tropical climate (e.g. equatorial regions of Africa, America and Pacific, Philippines, Indonesia and Malaysia) and coastal zones (approx. up to 15 km from water)
    • Regions with high and dynamically changing concentrations of atmospheric aerosols (Northern India, West Africa, Gulf region, some regions in China)
    • High mountains regions with regular snow and ice coverage and high-reflectance deserts
    • Regions with limited or no availability of high-quality ground measurements.

Based on the validation of Solargis data, a location specific uncertainty estimate can be derived on a case-by-case basis by looking at the model performance after analysing the local climatic and geographic features. 

More information about this can be found in chapter 5 of the Solargis validation report (PDF, 1.7 MB) and in the sections 2.8 and 2.9 of this scientific book chapter.

Calculation of confidence intervals

When assuming normal distribution, statistically one standard deviation characterizes 68% probability of occurrence. From the standard deviation, other confidence intervals can be constructed:


Probability of occurrence


One standard deviation



Two standard deviations



Three standard deviations



P75 uncertainty


± 0.675*STDEV

P90 uncertainty


± 1.282*STDEV

P95 uncertainty


± 1.645*STDEV

P97.5 uncertainty


± 1.960*STDEV

P99 uncertainty


± 2.326*STDEV

From confidence intervals we can calculate different probability scenarios. The P50 value will be the most expected value (center of the probability density curve), from which various levels of confidence can be expressed. For instance, in solar resource assessment the P90 value has become a standard and it represents a number that would be exceeded in 90% of the cases.


Probabilily of exceedance

Probabilily of non-exceedance


P50 value




P75 value



Mean - 0.675*STDEV

P90 value



Mean - 1.282*STDEV

P95 value



Mean - 1.645*STDEV

P97.5 value



Mean - 1.960*STDEV

P99 value



Mean - 2.326*STDEV