Delta Electronics SS1-UM-1.05 Scientific references, Calculating zenith angles, Summary

Page 62
(extreme vertical leaves) and

The results were then analysed in terms of La, the LAI of a canopy of black leaves that would give the same transmission as a canopy of LAI L assuming incomplete absorption, all other factors being equal.

L a L.( 1 g( 1 a ) )

L is the "true" LAI, La is the LAI that when used in the black leaf model, gives the same transmission as L used in the complete model. a is the leaf absorptivity in the PAR band.

The function g varied with all the other parameters in a complex way, but most strongly with x, the leaf angle distribution parameter, and with solar zenith angle for the direct beam. The following equations represent quite a crude approximation to the full model, but give satisfactory results for most situations. If any given transmission fraction is inverted using the approximation, the LAI calculated is within ±10% ±0.1 of the "true" LAI indicated by the full model, except for x near 0

zenith angle > 60 ° (strong low sun).

For diffuse light:

g diff

 

 

0.5

 

1.5.x ).

 

 

 

 

 

0.7.zen2

 

 

 

0.2.zen5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For direct beam:

g dir

 

 

exp(

 

 

0.2

 

 

 

 

 

 

 

 

 

0.3

 

 

 

 

 

 

 

 

 

 

 

 

 

where: x is the ellipsoidal leaf angle distribution parameter zen is the solar zenith angle in radians.

The full equation thus becomes:

τ

 

f

.exp

 

 

 

K ( x , θ ).

 

1

 

g

.( 1

 

a )

 

.L

 

...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

 

 

 

 

 

 

 

 

dir

 

 

 

 

 

 

 

 

 

 

+

1

 

f

 

 

.

exp

 

 

 

L

 

 

 

 

 

A ( x ).L

3.exp

 

 

 

B ( x ).L

C( x )

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

a

 

 

 

 

 

a

 

a

Direct part

Diffuse

This looks hard to invert to get LAI from τ , but an iterative solution is fairly straightforward given the computing power, and is much simpler than the full numerical solution.

Calculating zenith angles

Zenith angles are calculated from latitude, longitude, and local time using standard astronomical equations as given in Practical Astronomy. These give zenith angles accurate to better than 0.1° and times of sunrise or sunset to within a few seconds.

Summary

A computer model has been created which calculates accurately the transmitted light below the canopy based on the assumptions given. This has been run over the whole range of each of the different variables, i.e. Direct beam angle, Direct beam fraction, Leaf Angle Distribution, Leaf Absorption and Leaf Area Index. The results of these runs, taking many hours of computer time, have been collected and functions found to fit them.

These approximating functions are used in the SunData software to predict LAI from the measured inputs in the field. The LAI values calculated by the SunData software are within ± 10% ± 0.1 of the LAI that would have been calculated by the full model.

Scientific references

Campbell G S (1986). Extinction coefficients for radiation in plant canopies using an ellipsoidal inclination angle distribution. Agric. For. Meteor., 36:317-321.

62 • LAI theory

Document code: SS1-UM-1.05

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Contents SunScan SS1-UM-1.05Trademarks CopyrightAcknowledgements CE conformityContents LAI theory Menus and Screens More Psion and file handling notesMeasurement options Technical Reference sectionAppendices IndexSunScan Canopy Analysis System How to use the manualsIntroduction Organisation of this manualBeam Fraction sensor Field accessoriesSunScan probe Data Collection TerminalWorkabout and SunScan probe Getting StartedPreliminary checks Checking the Workabout hardware SunData s/w Diskette Installing the SunData s/w in your PCInstalling the s/w What the s/w doesSetting up your PCs COM port Running SunDataWorkabout to PC Communication checksSunScan probe to PC Running SunData in Windows Working with the Workabout SunScan TutorialAbout this tutorial What to do if you get lost Starting SunData in the WorkaboutUsing a PC instead of the Workabout Starting the PC softwareThis page is intentionally blank Setting up a measurement session Working through the menu optionsFile Saving Hot KeysUsing the Emulator mode Taking readingsConnecting the SunScan probe Without a Beam Fraction SensorConnecting the Beam Fraction Sensor Measuring Leaf Area Index without a Beam Fraction Sensor Reviewing your data file AveragesTo the PC Transferring the data file to your PCFrom the Workabout Initiating the file transfer from the Workabout Meanwhile, on the PC RS232 communication problems Conclusion of the TutorialSunData Screens on the Workabout File SettingsMenus and Screens Contd UtilsQuit Workabout User Guide More Psion and file handling notesNavigating Psion directories and screens Navigating the Psion directories and screensPsion subdirectory usage in file select dialogs Flashcards reformatting Re-installing the SunData application iconDeleting unwanted Workabout files Data memory management Configuration and data file handlingSunData Configuration files Restoring a configuration Default .cfgCreating a configuration file Data files.CSV file Displaying data files on your PC.PRN file Data file layouts and data groups Page Above-canopy reference requirements Measurement optionsExperiment design Canopy type and LAI estimates Canopy Sampling volumeCanopy type and BFS practicalities Preferred light and weather conditions Planning for the sun’s positionAbsorption Advice on Absorption and Eladp valuesSetting Eladp Relationship between Mean Leaf Angle and Eladp Estimating Eladp in the fieldLAI, PAR and All displays Workabout setupSunScan System Measurement modes Autolog function Probe GO button Measurement procedures in the fieldProbe handling in the field Levelling the probeUse of the tripod Using the tripodBFS handling in the field WorkaboutExtension cables, and the location of the BFS Finding North, and setting the shade ringLevelling the BFS Checking the probe/BFS matching PAR calibrationsFactory light calibration Recalibrate optionEffect of the shade ring on the BFS Routine maintenance and cleaningRestoring the factory calibration Comparing the calibration with other PAR sensorsEnvironmental and moisture protection SunScan probe and Beam Fraction SensorLAI theory Ingredients of the LAI computation methodTheory versus reality Derivation of Wood’s SunScan canopy analysis equationsMajor assumptions Transmission of Diffuse Light Beers law for canopy absorptionCampbells Ellipsoidal LAD equations Transmission fraction τ Is given by I/I0 Modelling the canopy transmission Diffuse light transmission cosine corrected sensorDetail Diffuse light cosine response sensor Functions used to model canopy transmissionAccuracy of LAI calculations Diffuse light hemispherical response sensorModelling incomplete PAR absorption and scattering Exp 0.1 . x . atan 0.9 Atan L Q SpherSummary Scientific referencesCalculating zenith angles Jones, Hamlyn G Plants and Microclimate second edition. CUP Checking the batteries Maintenance and repairTechnical Reference section SunScan probe batteriesChecking the desiccant Factory calibration method Re-setting the factory calibrationChecking the PAR calibration Psion Workabout TroubleshootingProblems running the SunData application While running SunDataInsufficient power to write data reported Technical Support Beam Fraction Sensor type BF1 SpecificationsSunScan Probe Type SS1 Data Collection Terminal type DCT1 Psion WorkaboutSpares Kit type SPS1 Carrying Case type SCC1Telescopic Tripod type BFT1 Logging CablesPAR Performance Spectral responseCosine responses of probe and BFS SunScan system cosine responseAppendices Logging the probe as a Linear Quantum SensorLogging the Beam Fraction sensor Workabout SunData s/w Upgrading the SunScan systemSunData PC s/w Revision HistoryPsiWin File transfer between Workabout and PCChoice of different programs Workabout Remote LinkExample using Slink Slink and RcomDrives on the PC are referred to as REMA, Remc REM = remote Example using Rcom Documentation of Rcom and SlinkSending a file to a Communication program Using the Workabout Comms applicationAlternative file transfer mechanisms Sending a file to a serial printerGlossary Page Index AccuracyIndex Field use 39, 46, 48, 50, 51, 58

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