The radiation reaching the earth’s surface can be represented in a number of different ways. Global Horizontal Irradiance (GHI) is the total amount of radiation received from the sun on a surface horizontal to the ground. This value is of particular interest to photovoltaic installations and includes both Direct Normal Irradiance (DNI) and Diffuse Horizontal Irradiance (DIF).
The following chart shows the total GHI calculated from 52 years of weather station data at the Cranbrook airport.

The average is  1,203 kWh/kW/m2/yr  and the minimum /maximum are  1,056 and 1,311 respectively.

The dataset has two types of variances.

  1. The variance between GHI estimated and its actual value.  According to Environment Canada and NRCan that provided the data,  the root-mean-square error (RMSE) for hourly solar GHI amounts are typically around 30% .  The long term average error however is 5% or lower.
  2. The second variance is related to the year-to-year variation of solar irradiation, depending on the weather and other climatic factors.  The yearly Standard Deviation is 5.35 %.

As the two variances are independent,  the combined Standard Deviation  is their norm or 7.32%.


Solar data and statistics

The annual irradiation variance follow a normal distribution pattern (so-called bell curve)  as shown in the graph below.
According to  probability theory, 68% of the points are between plus and minus one sigma ( Standard deviation)  from the mean and 95% happens  between ± 2 sigma (the green points)


P90/P95 or Average?

In a normal distribution, half of the points will be below the mean and half above. It is thus risky to assess the performance and return of a solar project from the mean.  The results have 50% chance to be below the mean.

Solar developers and investors need greater certainty. For example, what is the minimum return that could be achieved 95% of the time over the project lifetime?   Or what is the minimum annual cash flow that could be generated  90% of the time.  This requires the calculation of the “exceedance probability”  (Pxx) i.e. the level of solar energy that would be exceeded x % of the time.

The following graph plot the cumulative probability of GHI solar data from the Cranbrook Airport Weather Station. The dotted blue curve plots the cumulative probability of annual data variations, the red curve, the combined variability of annual variations and monitoring errors, the yellow curve the 25-yr average variance. The purple dot represents the P90 level at one year, and the green dot P95 at 25-yr. It indicates a 90% chance that the GHI will exceed 1,090 kWh/kW/m2/yr in any particular year and 95% chance that the GHI 25-yr average will exceed 1,181.

These numbers can be used to make a solar project “investment-grade”.