Leaf angle and GPS

Using measurements from the accelerometer / magnetometer and GPS receiver, the LI-600 computer software calculates the leaf angle relative to the sun at a given time and place, which is the angle of incidence.1

Figure 9‑2. The angle of incidence of a leaf.


The accelerometer and magnetometer measure three aspects of a leaf's angle:

Pitch: slope from horizontal in degrees (accelerometer)

Roll: rotation from the horizontal in degrees (accelerometer)

Heading: rotation from North in degrees (magnetometer)

Figure 9‑3. Pitch, roll, and heading.


If GPS is enabled in the instrument settings and there are a minimum of 3 satellite signals, a GPS map pin will appear in the upper left of the device screen. To view the number of satellites available, go to Instrument Settings on the device, select GPS, then NumSats.

GPS information is logged into a separate variable group as follows.

Table 9‑4. The GPS variable group.
Description Label Units
UTC Offset utcoffset hours
latitude latitude degrees
longitude longitude degrees
altitude altitude m
number of satellites nsats  
horizontal dilution of prescision hdop  

Leaf angle software calculations

The LI-600 software application combines data from GPS and rotational information to compute parameters related to solar position and leaf angle position relative to the sun. The angle of incidence of a surface (here, a leaf) arbitrarily oriented with respect to the sun at a given time and place can be given by:


where angle_incleaf is the incidence angle between the leaf and direct sunlight (angle_incleaf = 0 for leaf plane perpendicular to direct sunlight). Equation 9-48 is Equation 47 from Reda & Andreas 2004. Input parameters are calculated from either GPS location information or accelerometer/magnetometer information as follows below.

The proportion of direct sunlight incident on the leaf at the given angle can also be calculated


where directpct is the % of available photons incident on the leaf relative to the amount of photons if the leaf were normal to direct sunlight.

Solar position calculations

Location and time from GPS are used to calculate solar parameters. The solar parameters can be solved using equations from Michalsky 2008. Those equations are valid for the years 1950-2050 with uncertainty of ±0.01°.

Leaf plane calculations

Two parameters are needed to describe the plane of the leaf:

slopeleaf Inclination of a surface from the horizontal position

azleaf Surface azimuth angle or deviation of the normal to the surface with respect to the south

The following equations are similar to those from Escribano-Rocafort et al. 2014 with modifications to fit the LI-600 framework.



Equation 4 requires additional quadrant corrections. Equation 1 requires astronomers zenith angle, 180 from the topocentric zenith angle (equation 46 R&A 2004).

Leaf angle group calculation variables

Calculation variables are added to the LEAF_ANGLE group as follows.

Table 9‑5. The leaf angle variable group.
Description Label Units Range
slope from horizontal pitch degrees  
rotation from horizontal roll degrees  
rotation from North heading degrees  
Angle of incidence between leaf and sun angle_inc_leaf degrees 0-90
Proportion of Direct Irradiance incident on leaf direct_pct % 0-100
Leaf Inclination from horizontal slope_leaf degrees 0-90
Leaf rotation from South az_leaf degrees ± 180 (0 south, + west)
angular position of sun wrt to equator dec_solar degrees ± 180
Solar rotation az_solar degrees ± 180
Solar zenith angle zenith_solar degrees 0-90


With the addition of GPS, the LI-600 reports two different time stamps in the data file: a date/time stamp in the SYS group, and a date/time stamp in the GPS group. The date/time stamp in the SYS group is either set manually by the user or synced to GPS time (when available).

GPS not available

If the user is unable to view enough satellites to acquire GPS, then the clock needs to be set manually (Instrument Settings > Set Time > Manual). In this case, the SYS Date/Time will update based on user settings. GPS time will not be available and is logged as time = '0:00:00' and date = '0000-00-00'.

GPS available

When GPS is available, the GPS clock will accurately reflect Universal Time. The user can use the SYNC function to update the SYS clock and account for UTC offset to get the local time (Instrument Settings > Set Time > GPS Sync).

If SYS time is not synced to GPS time, the time reported in the SYS group will reflect the last manual update, and not necessarily match the GPS clock. The real-time clock counting for the SYS group will drift over time, typically a few seconds a month, therefore it is good practice to sync with GPS once lock is achieved before taking measurements. In a logged data set, the SYS and GPS clocks can be compared to determine the UTC offset that is used. UTC offset is maintained through power cycling of the instrument.