1,651
edits
Charts - Solar charts: Difference between revisions
From Cumulus Wiki
Jump to navigationJump to search
m
→Using Numerical Integration
mNo edit summary |
|||
| Line 34: | Line 34: | ||
''Solar irradiance is often integrated over a given time period in order to report the radiant energy emitted into the surrounding environment (joule per square metre, J/m2) during that time period. This integrated solar irradiance is called solar irradiation, solar exposure, solar insolation, or insolation.'' | ''Solar irradiance is often integrated over a given time period in order to report the radiant energy emitted into the surrounding environment (joule per square metre, J/m2) during that time period. This integrated solar irradiance is called solar irradiation, solar exposure, solar insolation, or insolation.'' | ||
So if we take R for Radiation (which we sample in field 19) we get for a time period of a day: | So if we take R for Radiation (which we sample in field 19) we get for a time period of a day: | ||
<math>\int | <math>\int{R} \, dt</math> | ||
But because we do not have continuous measurement we have to approximate this by taking the samples of the ''Solar Radiation'' we do have for the sampling interval we use (1, 5, 10 etc... minutes). Assuming equal distance between the samples and a not too disruptive radiation function we get an approximation for the integral as: | But because we do not have continuous measurement we have to approximate this by taking the samples of the ''Solar Radiation'' we do have for the sampling interval we use (1, 5, 10 etc... minutes). We use the theory of [https://en.wikipedia.org/wiki/Numerical_integration#Quadrature_rules_based_on_interpolating_functions Numerical Integration]. Assuming equal distance <math>\Delta t</math> between the samples and a not too disruptive radiation function we get an approximation for the integral as: | ||
<math>\sum_{ | <math>\sum_{0}^{\sum_{\Delta t}} ({field19} \times \, \Delta t)</math> | ||
for all samples, assuming the measured value is the midpoint of | for all samples, assuming the measured value is the midpoint of | ||
<math>t + \frac{1}{2} | <math>t + \frac{1}{2}\times \Delta t</math> and <math>t - \frac{1}{2}\times \Delta t</math>. | ||
However this interval appears not to be constant in the reality of ''CumulusMX''. | === Variable interval === | ||
However this interval appears not to be constant in the reality of ''CumulusMX''. Not only appears the user to change the interval once in a while but also in the start and stop sequence of CMX and for other reasons unknown there appear to be smaller and larger 'gaps' in the data resulting in time interval changes which have been found to be unpredictable. As a result an algorithmic solution has been applied to reduce the influence of the interval size. With a bit of grandeur you might say it is an integration with variable step size. | |||
=== Method of calculation === | |||
#A list of monthly logfile entries is created for each day where the theoretical solar max radiation is above zero (i.e. the sun is up) | |||
#The interval in minutes is the sampling interval (loginterval) the user has assigned in the CumulusMX settings (1, 5, 10, 15, 20 or 30 minutes) | |||
#Then in a loop over all values, each time it is checked if the interval setting corresponds with the realised interval. If not the interval is adjusted to the new value. | |||
#If the interval is larger then 30 minutes the gap is too large and the value is skipped, no addition is made, the calculation is restarted at the next entry. | |||
#The Energy over the interval is calculated as <math>{SolarRad} \times {Interval} \times 60</math> to get the energy in Ws and summed up to the total for the day. | |||
#At the end of the day the total energy in Ws is converted to KWh by dividing the energy sum by <math>{energy} \div {3600 \div 1000}</math> | |||
=== Solving the variability of the interval === | === Solving the variability of the interval === | ||
