Light regime

Local analysis

While the estimation of the leaf area index (LAI) is an analysis of the whole canopy above the camera, the calculation of the radiation regime is a local analysis in the sense that it looks at light conditons prevailing at the very place at which the camera was set. It considers the hemispherical picture as a mask through which more or less light from the sun (direct radiation) or from the sky vault (diffuse radiation) can penetrate. Depending on the size and distribution of canopy gaps and corresponding sun flecks, incoming radiation can vary strongly in space and time. Caution is thus required when trying to extrapolate a local radiation analysis to a whole plant stand. On the other hand, this type of local results is appropriate if it comes for example to correlate with a vegetation survey done at the same set of locations within the stand.

Light transmission

The first step of a radiation analysis is the same as for the canopy LAI analyis: the hemispherical picture has to be transformed into a black-and-white picture by applying a threshhold. The obtained black-and-white picture is then used as a mask to calculate which proportion of the incoming light is let through this mask. This means that the mask determines the transmission of diffuse and of direct incoming radiation. Note that this approach makes sense only as long as the picture can be considered as representing the reality. For example, it does not make sense to use a summer picture with deciduous folaige to calculate the radiation regime over the winter.

Incoming radiation

The radiation regime under the canopy is determined not only by the transmission through this canopy but obviously also by how much incident radiation there is above the canopy, both direct and diffuse (indirect). The incoming radiation varies through time, with daily cycles and a yearly cycle. It changes also according to the weather. Measurements of direct and diffuse radiation may be available for some locations and over more or less long periods. Note that a measurement of the total incoming radiation is not sufficient because it is necessary to have separate values of direct and diffuse radiation, which requires a beam fraction sensor. In most cases, such meteorological data are not available and climatic data in form of a radiation model have to be used instead. This is also the case when it comes to predictions, which means for weather conditions that are not yet known. Radiation models exist for different areas. For Europe and North Africa, there is for example a model called PVGIS. This kind of models are mainly developped to predict the power that can be obtained from solar collectors. Combining these data with the mask of a hemispherical picture can thus predict the radiation power available under a plant canopy, but also on a solar collector with more or less shading from objects around it (like buildings or trees).

Time

The light regime is calculated as a function of the time of the day. Users can chose to use the legal time, the average solar time or the real solar time. See the effects of these settings by displaying the sun-tracks over a picture. With the legal time, it is further possible to ignore the daylight-saving shift that is applied in many countries during the summer. If the legal time is used, then the latitude and time zone of the site are taken into account.
The results are meant for an average year and not for any particular year. For this reason, they are always in years of 365 days and do not take into account the small shifts that occur during 4-year leap cycles. Dates at which summer daylight-saving begins and ends are also averages. This may shift by a few days in particular years and can also differ a bit between countries.

Results per month: the following table gives the first and last day of each month expressed as the day of the year. This can be usefull in order to display results per month.

Integrated radiation model

Hemisfer includes a model to predict the incoming direct and diffuse radiation. It is based on three parts:

Sun tracks: Knowing the location and orientation of a hemispherical picture, an astronomical model calculates the position of the sun over time. In Hemisfer, this is done minute by minute and the position of the solar disk is each time compared with the black or white pixels of the picture to determine how much direct solar radiation is transmitted. Sun tracks per month and per hour can be viewed on the picture by clicking on the sun-tracks button. A sun-track is displayed in red for the day at which the current picture was shot. On this track, the sun is also displayed at the position it had at the time the picture was taken. This can help to check if the orientation and the time of the picture are set correctly.

Direct and diffuse transmission: Radiation fluxes are calculated in W/m². The calculations in Hemisfer are derived (simplified) from the methods used in PVGIS. The only inputs required from the user are the normalised values of average transmissions, both for direct and for diffuse radiation. Normalised means here for the thickness of the atmosphere at sea level. For the direct radiation, a normal clear-sky transmission of 0.8 is supposed. The ratio between 0.8 and the normal direct transmission is thus equal to the probability of cloud interception, which is considered constant. If users have an estimation of cloud frequencies f at the site, then they may use it to calculate the direct normal transmission as 0.8*(1-f). The clear-sky direct transmission itself decreases with the zenith angle of the sun (because of a longer pathway through the atmosphere), but it increases with the elevation of the site. The elevation correction is calculated in a way that absorption by the atmosphere is a function of its mass above the site, that is of air pressure. The correction is thus called barometric. Note that it is also possible to turn off the elevation correction if the transmission is for the particular elevation of the site and not normalised at sea level. The diffuse radiation, on the other hand, decreases with the elevation (above the atmosphere, the sky is black). In Hemisfer, changes in diffuse light over time are set to respond proportionally to direct absorption (= 1 - transmission).
It is further possible to have a seasonality for both the direct and the diffuse transmission. This is achieved as a sinusoidal curve by indicating:

1. the day of the year at which the transmission is maximum,
2. the amplitude, i.e. the difference from the average to the maximum or minimum values.

Sky overcast model: Hemisfer uses the simple model known as standard overcast sky (SOC, Steven & Unsworth, 1977). This model requires one parameter (b) to be set by the user. In most cases, b varies around 1, which is thus used here as a default value. A uniform overcast sky (UOC) can also be modelled just by setting b = 0.

Combined approach

A way to improve the integrated radiation model of Hemisfer is to run an analysis with default transmission values and to compare the obtained incident radiation values with a fancier model like PVGIS. In a next step (or iteratively), the normalised transmissions can be adapted to come close to the model.

Slope and radiation

The radiation flux is calculated both for an horizontal surface and for the inclined surface given by the ground slope of the site, i.e. the flux normal to the ground. See the example of light regime results. If Hemisfer is used to predict the power delivered by a solar panel, then the slope and orientation of the panel should be entered as groud slope and aspect. This way, the normal radiation flux corresponds to the incoming power per panel area. If the flux on the inclined surface has to be reported (projected) onto an horizontal area, then it can simply be divided by the cosine of the slope.

Light indexes

Light indexes are often used to compare sites in terms of their radiation regime. A light index is actually a weighted average of the transmission through the canopy. Three indexes can be distinguished:

• diffuse light index (DLI): average transmission of diffuse (indirect) radiation,
• beam light index (BLI): average transmission of beam (direct) solar radiation,
• global light index (GLI): weighted average of diffuse and direct light indexes.

Because diffuse and beam radiation change with time, light indexes must be defined for a certain period of time, for example for the vegetation period. See the example of light regime results.