Light behaviors

In this document:
Snags in light calculations
Light parameters
Quadrat-based GLI light behavior
GLI light behavior
Sail light behavior
Constant full GLI behavior
Beer's law light filter behavior
GLI Map Creator behavior
Gap Light behavior

Light is the key resource for trees in the SORTIE model. A tree's growth, and therefore its probability of mortality and reproductive ability, is a function of the amount of light it receives. Consequently, great care is taken in SORTIE to calculate the amount of light that each tree gets - in fact, these calculations take up more processing time than any other during model runs.

There are two basic light index types used by SORTIE to describe the amount of light a tree receives. The first is the Global Light Index, or GLI. GLI is the percentage of full sun received at a point. The second index is the Sail Light index, which is the proportion of shade seen at a point, from none to total. (The name Sail Light comes from the fact that the shape of shading neighbor tree crowns is approximated by a 2D rectangle, like a sail).

How light calculations work

In order to calculate the amount of light a tree gets, SORTIE simulates taking a fisheye photograph over each tree to determine which parts of the sky are blocked by taller trees nearby. SORTIE determines how much light comes from different parts of the sky and takes this into account, so shading neighbors in different directions will have different impacts on the total amount of light a tree gets.

The fisheye photo can be taken at one of two positions - either at the top of the crown or at mid-crown. The major difference between the two is that when the photograph is taken at mid-crown, trees near the same height as the target tree will be included in the shading effects. This can make a big difference in even-age stands.

Sky Simulation

At the beginning of a run, if light behaviors are being used, the amount of light coming from each part of the sky for the plot's location is calculated. The sun's position in the sky is tracked throughout the growing season. Diffuse radiation, assumed to be isotropic (coming equally from all directions), is then added to the direct beam radiation. Below the minimum solar angle, it is assumed that no light comes from those portions of the sky because of the density of the surrounding forest. (It is wise not to set this angle too low - otherwise SORTIE must look very far away for shading neighbors.)

To determine the amount of sun coming from each portion of the sky, the sky is first divided into a hemispherical grid. For GLI calculations, the grid cells are equal-area segments of a user-settable resolution. For Sail Light calculations, the sky is divided into one-degree-sized grid cells. For each day in the growing season, the times of sunrise and sunset are calculated, and then the sun's position in the sky grid is tracked at 5-minute intervals throughout the day. (The equations are below.) At each solar position, the amount of direct beam radiation received from the sun at that position is calculated, taking into account atmospheric effects. Each sky segment keeps track of the total amount of direct beam radiation coming from it for the duration of the growing season.

The total amount of light in the sky is the amount of direct beam radiation plus the amount of diffuse radiation. Once the total amount of direct beam radiation is known, the amount of diffuse radiation is calculated accordingly and added equally to all portions of the sky. Each sky segment is then relativized to hold the percentage of total light coming from that segment.

Determining a tree's light index

For each timestep, SORTIE calculates the amount of light each tree receives by simulating a fisheye photograph. To "take" the photo, the model looks at the hemisphere of sky around and above a tree and determines which portions of it are blocked by neighboring trees. It then totals up how much light is left to reach the tree.

Only tree crowns block light in the model. Trunks do not shade. Because seedlings are modeled as sticks with no crowns, they don't shade either.

The first step in creating the simulated fisheye photo is to determine how far from the tree to search for shading neighbors. For GLI, this is done by comparing the height of the fisheye photo to the maximum possible tree height and determining how far away a tree of this height could be and still have its crown appear in the sky above the minimum solar angle. All trees within this search radius that are taller than the height of the fisheye photo (and thus can be "seen" by it) are added into the "photo." For Sail Light, the search distance is specified by the user.

To add a shading neighbor to the photo, the light behavior determines the amount and location of sky covered by its crown. In a GLI calculation, neighbor crowns are approximated as cylinders. In a Sail Light calculation, neighbor crowns are approximated as 2-D rectangles with a width equal to their crown diameter and a height equal to their crown height (or, as an added simplification, the behavior can assume the crowns of shading neighbors extend all the way to the ground).

The amount of radiation received from the portion of the sky blocked by the shading neighbor is multiplied by the light extinction coefficient for the neighbor's species. The effects of multiple neighbors blocking the same patch of sky are multiplicative.

Once all shading neighbors have been added to the fisheye photo, the amount of light that can still be seen from each region of the sky is totaled up into the appropriate index.

Sky Simulation Equations

All equations are from Iqbal, 1983.

At a given (solar) time, the sun's zenith angle is calculated by:
cos θ = sin δ sinφ + cos δ cos φ cos ω

and its azimuth angle is calculated by:

cos ψ = (sin α sin φ - sin δ)/cos α cos φ

where:

Azimuth here is south zero, east positive.

Solar declination is calculated by

δ = 0.006918 - 0.399912 cos Γ + 0.070257 sin Γ - 0.006758 cos 2Γ + 0.000907 sin 2Γ - 0.002697 cos 3Γ + 0.00148 sin 3Γ

where δ = solar declination in radians and Γ is the day angle, in radians.

The day angle is calculated by Γ = 2π(d - 1)/365 where Γ is the day angle in radians and d is the Julian day number (day of the year between 1 and 365).

So, once we finally have the azimuth and altitude angles for the sun's position in the sky, we can calculate the amount of direct beam radiation coming from it and add it to the appropriate grid cell. The direct beam radiation equation is

I = E0m*cos(θ)

where

Eccentricity is calculated by

E0 = 1.000110 + 0.034221 cos Γ + 0.001280 sin Γ + 0.000719 cos 2Γ + 0.000077 sin 2Γ

where Γ is the day angle (equation above).

Optical mass of the atmosphere is calculated by

m = sec(θ)

where θ is the zenith angle of the sun. SORTIE uses a numerical approximation method instead of the sec to correct at low altitudes.

This process is repeated for each day in the growing season. The growing season starts with the First Day of Growing Season parameter and ends with the Last Day of Growing Season parameter.

Snags in light calculations

Snags are standing dead trees (more in the trees topic). They can block light like live trees do. For SORTIE purposes, snag crowns are frozen in the shape they had when the tree died, but they transmit more and more light as they lose branches. SORTIE tracks a snag's age in order to replicate this decay. You define three snag age classes and a light extinction coefficient for each. For as long as a snag stands, it will block the light of neighboring trees, but to a lesser degree through time.

You don't have to include snags in light calculations. If you do not have any behaviors in your run that either create snags or directly work with them, then your run is classified as "snag-unaware" and snags will not be created. In this case, the snag parameters are not required. However, if your run is "snag-aware" and snags may be created, you must supply the snag light extinction parameters.

Light parameters

Quadrat-based GLI light

For more on what GLI is and how it is calculated, see above.

How it works

This behavior uses a grid object, called Quadrat GLI, to help it assign GLI values to the trees to which it is assigned. The grid cells are the quadrats, in this case; this is a throwback to old SORTIE terminology. Each grid cell in which there is a tree to which this behavior applies has a GLI value calculated at its center, at a height that the user specifies. All other trees to which this behavior applies that are in that same grid cell get that same GLI value. This behavior saves having to calculate a different GLI value for each tree.

How to apply it

This behavior may be applied to seedlings, saplings, and adults of any species.

GLI light

For more on what GLI is and how it is calculated, see above.

How it works

This behavior calculates a Global Light Index (GLI) value for each individual of each tree type to which it is assigned.

How to apply it

This behavior may be applied to seedlings, saplings, and adults of any species.

Sail light

For more on what the Sail Light index is and how it is calculated, see above.

How it works

This behavior calculates a Sail Light index value for each individual of each tree type to which it is assigned.

How to apply it

This behavior may be applied to seedlings, saplings, and adults of any species.

Constant full GLI

How it works

This assigns a GLI value of full sun (100%) to all trees to which it is assigned.

How to apply it

This behavior may be applied to seedlings, saplings, and adults of any species.

Beer's law light filter

How it works

This behavior simulates a filter that reduces light according to Beer's Law.

Imagine a fog that hangs out on the forest floor and ends abruptly at a certain height. All trees shorter than the top of the fog layer will have their light attenuated but not blocked completely. The closer they get to the top of the fog the more light is let in. The amount of light which actually gets through is calculated according to Beer's Law, where transmission = e-az, where a is the Light Filter Light Extinction Coefficient parameter and z = thickness of the filter, in meters (which is the distance from the light point to the top of the filter - the Height of Light Filter, in m parameter). This filter behavior can be used to, for instance, replicate the effects of an herbaceous layer in reducing light to young seedlings. The height of the filter is randomized slightly each time the thickness of the filter over the light point is calculated to introduce a stochastic element.

Trees can be given a respite from the effects of the filter. This behavior does not set the respite counter but it will respect any values which another behavior has put in. Currently, only NZ Establishment supports filter respite counters.

Trees can be given a rooting height in addition to their normal height. This value is added to their existing height to get their effective height, which is what will be applied when determining the thickness of the filter overhead. Again, this behavior does not set this height but will use it if another behavior sets it.

This behavior DOES NOT ACTUALLY CALCULATE LIGHT LEVELS. Any tree species and types to which this filter is applied must also have one of the other light behaviors assigned to it. This behavior assumes the value is a GLI value; using Sail Light will probably not produce good results.

This behavior only affects tree types and species to which it is applied in the behavior list of the parameter file. It will ignore all other trees, even if they are short enough to be beneath the filter level.

How to apply it

This behavior may be applied to seedlings, saplings, and adults of any species.

GLI Map Creator

For more on what GLI is and how it is calculated, see above.

How it works

This behavior calculates a GLI value for each cell in a grid object called GLI Map. The height at which this GLI value is calculated is set by the Height at Which GLI is Calculated for GLI Map, in meters parameter. These values are not used by any other behavior. You can save the values in the GLI Map grid into a detailed output file and view the map data later.

How to apply it

This behavior may be applied to seedlings, saplings, and adults of any species.

Gap Light behavior

This behavior shortcuts the light calculation process by considering GLI to be binary: either full light (100%) or no light (0%). This simulates a simplified version of gap light dynamics.

How it works

This behavior uses a grid object called Gap Light to determine the basic position of plot gaps. If a grid cell contains no adult trees, it is considered a gap. If there are any adults of any species, then it is non-gap.

The trees to which this behavior has been applied get their GLI values based on the gap status of the grid cell in which they are located. If the gap status is TRUE, then they receive a GLI value of 100%. If it is FALSE, they receive a value of 0%.

How to apply it

This behavior may be applied to seedlings, saplings, and adults of any species.

08-Feb-2005 11:48 AM