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Combining model uncertainty and uncertainty because of interannual variability

Components of uncertainty

For understanding the solar radiation model performance key indicators, it is important to consider the several factors that influence on the accuracy of the values, provided both by satellite-based modelling and on-site ground sensors.

On the modelling side, accuracy will be determined by cloud estimate (e.g. intermediate clouds), under/over estimation of atmospheric input data, terrain, microclimate and other effects, which are not captured by the model. Part of this discrepancy is natural - as satellites monitor large area (of approx. 3x4 km) while ground sensors see only micro area of approx. 1 squared centimetre. Due to higher complexity of the model, bias of satellite-based DNI is higher than GHI.

On the measurement side, the discrepancy will be determined by accuracy/quality and errors of the instrument, pollution of the detector, misalignment, data loggers, insufficient quality control, etc. Only quality-controlled measurements from high-standard sensors should be used for reliable validation of satellite-based solar models. Any issues in the ground measured data result in a skewed evaluation.

The most required value by project developers, technical consultants and finance industry is the uncertainty of the long-term yearly GHI or DNI estimate for the project site. The model uncertainty can be calculated from the validation statistics (Bias).

However, the uncertainty values should be also taking into account the fact that the measurements also include an uncertainty component itself. In addition, when assessing the uncertainty of one single year, inter-annual variability due to the climate factors should be evaluated as well.

In conclusion, assuming that the solar radiation values can be described using a normal probability distribution (similarly as we have done when characterizing the model bias distribution), the total combined uncertainty is calculated from:

  • Uncertainty of the Solargis model estimate
  • Uncertainty of the ground measurements
  • Inter-annual weather variability.

The influence of these three factors in the final uncertainty is calculated through the square root of the quadratic sum of each uncertainty.

Uncertainty of ground sensors

Estimate of the long-term uncertainty of ground measurements can be a bit subjective – it can be based on combination of the theoretical uncertainty of the instrument, results of quality control procedures and comparison of the redundant measurements.

Considering that the absolute majority of the validation data have been collected using high-accuracy instruments and applying the best measurement practices and strict quality control procedures, it is considered that a ±2.0% should be added from GHI measurements from pyranometers and ±1.0% from DNI measurements from pyrheliometers. This could serve as a good starting point for assessing annual uncertainty of solar instruments. It is known from other comparisons that these values could be exceeded in standard operating conditions.

On the other hand, utilization of the state-of-the-art instruments does not alone guarantee good results. Any measurements are subject to uncertainty and the information is only complete, if the measured values are accompanied by information on the associated uncertainty. Sensors and measurement process has inherent features that must be managed by quality control and correction techniques applied to the raw measured data.

The lowest possible uncertainties of solar measurements are essential for accurate determination of solar resource. Uncertainty of measurements in outdoor conditions is always higher than the one declared in the technical specifications of the instrument. The uncertainty may dramatically increase in extreme operating conditions and in case of limited or insufficient maintenance. Quality of measured data has significant impact on validation and regional adaptation of satellite models.

 

Theoretically-achievable daily uncertainty of GHI at 95% confidence level

 

Pyranometers

RSR

 

Secondary standard

First class

Second class

(After data post-processing)

GHI Hourly

±3%

±8%

±20%

±3.5% to ±4.5%

GHI Daily

±2%

±5%

±10%

±2.5% to ±3.5%

 

Theoretically-achievable daily uncertainty of DNI at 95% confidence level

 

Pyrheliometers

RSR

 

Secondary standard

First class

(After data post-processing)

DNI Hourly

±0.7%

±1.5%

±3.5% to ±4.5%

DNI Daily

±0.5%

±1.0%

±2.5% to ±3.5%

 

 

Interannual variability

Weather changes in cycles and it has also a stochastic nature. Therefore annual solar radiation in each year can deviate from the long-term average in the range of few percent. This is expressed by interannual variability, i.e. the magnitude of the year-by-year change.

The interannual variability for selected sites is calculated from the unbiased standard deviation of the yearly values over the available period of years, considering a simplified assumption of normal distribution of the annual sums. All sites show similar patterns of variation over the recorded period. This analysis can be made for longer periods, i.e. the uncertainty at different confidence levels expected for average values within more than one-year period. 

The historical period used for calculating the inter-annual variability may have some influence, although it is observed to be quite small (e.g. if we compare results from 10 years of data with results from 20 years of data). The expected difference for GHI would be less than 1% (depends on the climate zone). A higher influence may be found in data sets representing occurrence of large stratospheric volcano eruptions.

 

Table of GHI interannual variability of a period of 1, 5, 10 and 25 years for several sample sites

Nearby city

Country

Variability [%]

1 year

5 years

10 years

25 years

Kosice

Slovakia

3.8

1.7

0.5

0.1

Fresno

United States

2.5

1.1

0.4

0.1

Kurnool

India

2.3

1.0

0.3

0.1

Calama

Chile

1.3

0.6

0.2

0.0

Upington

South Africa

1.3

0.6

0.2

0.0

Comparing results

Good models have known and lowest possible uncertainty. On the other hand, the expected uncertainty for a specific site can be derived from the analysis of validation statistics for a sufficient number of validation points.

Assuming that the solar resource estimates from two different models follow a normal distribution, the combined uncertainty can be compared and represented in charts. The most expected value (P50) and its uncertainty will determine the position of the center and the width of the probability distribution respectively. The value exceeded with 90% probability (P90) can be calculated and identified in the probability distribution as well.

Using a solar model with proven higher accuracy like Solargis provides more probable estimates and less weather-related risk for the project. In other words, the distance between P50 and P90 values is smaller in such case.

In the sample below, the model A has a higher uncertainty than model B. Therefore the distribution of expected values in model A will be spread within a wider range. In other words, values expected by model B will occur with a higher probability.

 

Uncertainty of GHI values from two models at a sample site in Kosice, Slovakia

 

Model A

 [kWh/m2]

Model B

[kWh/m2]

Most expected value (P50)

1193

1230

Value exceeded with 90% probability (P90)

1069

1149

Uncertainty (P90 confidence interval)

±10.4%

±6.6%

Comparing2