Delta Electronics SS1-UM-1.05 user manual Derivation of Wood’s SunScan canopy analysis equations

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Equation fitting and inversion

The results of the computer modelling, while accurate, are not suitable for use in a field instrument. It takes many minutes of processing on a fast PC to calculate light transmission for any given conditions using the model, and the Psion Workabout is not a fast computer!. The model calculates values of light transmission for a given LAI, whereas the SunScan measures light transmission. This means that the functions have to be inverted to work back to LAI, which is more difficult.

To give you immediate results in the field, computable functions have been fitted to the model data, and it is these that are solved to give LAI to reasonable accuracy from the parameters measured by the SunScan system.

Note! Wood’s SunScan equations are copyright, and you should not copy them without written permission unless for purposes of scientific debate or publication, in which case they should be fully acknowledged.

Theory versus reality

We believe that Wood’s SunScan equations accurately reflect the assumptions that the modelling is based on.

By far the largest uncertainties are bound to be caused by

•the mismatch between the real canopy architecture and the simplifying assumptions built into the fundamental analysis

•to a lesser extent the uncertainty in the numerical values of ELADP estimated for your canopy.

With these caveats, the values of LAI for your canopy, even if of uncertain accuracy, will provide valid trends for a given canopy (e.g. canopy growth in a season), and valid comparisons between different canopies of similar architecture (e.g. trial plots of different cultivars of the same species). If you are able to compare SunScan estimates with actual harvested samples from time to time, this will enable you to calibrate out any systematic errors due to your canopy not matching the SunScan assumptions.

If you wish, you can force the SunScan calculations to be equivalent to older, less sophisticated inversions by setting some of the parameters to appropriate values. For example, setting ELADP to 1024 (horizontal leaves) and Absorption to 1.0 will give you the simple Beer’s law inversion.

Derivation of Wood’s SunScan canopy analysis equations

The major assumptions

•The canopy is an infinite, uniform, horizontal slab, with leaf elements randomly distributed in proportion to the surface area of an ellipsoid, as described by Campbell.

•The incident light consists of a component from a point source at a given zenith angle (the Direct beam); and a Diffuse component of equal intensity from every point in the sky (Uniform Overcast Sky).

•The canopy either has sufficiently high LAI that light reflected back from the ground below is negligible, or the reflectance of the ground is similar to that of the canopy.

•Of the light intercepted by the leaf element, a fraction a (absorption) is totally absorbed. The remainder is re-emitted uniformly in all directions.

SunScan User Manual v 1.05

LAI theory • 55

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Contents SS1-UM-1.05 SunScanCE conformity CopyrightAcknowledgements TrademarksContents Technical Reference section Menus and Screens More Psion and file handling notesMeasurement options LAI theoryIndex AppendicesOrganisation of this manual How to use the manualsIntroduction SunScan Canopy Analysis SystemData Collection Terminal Field accessoriesSunScan probe Beam Fraction sensorPreliminary checks Getting StartedWorkabout and SunScan probe Checking the Workabout hardware What the s/w does Installing the SunData s/w in your PCInstalling the s/w SunData s/w DisketteRunning SunData Setting up your PCs COM portSunScan probe to PC Communication checksWorkabout to PC Running SunData in Windows About this tutorial SunScan TutorialWorking with the Workabout Starting SunData in the Workabout What to do if you get lostStarting the PC software Using a PC instead of the WorkaboutThis page is intentionally blank Working through the menu options Setting up a measurement sessionHot Keys File SavingTaking readings Using the Emulator modeWithout a Beam Fraction Sensor Connecting the SunScan probeConnecting the Beam Fraction Sensor Measuring Leaf Area Index without a Beam Fraction Sensor Averages Reviewing your data fileFrom the Workabout Transferring the data file to your PCTo the PC Initiating the file transfer from the Workabout Meanwhile, on the PC Conclusion of the Tutorial RS232 communication problemsSunData Screens on the Workabout Menus and Screens SettingsFile Utils ContdQuit Navigating the Psion directories and screens More Psion and file handling notesNavigating Psion directories and screens Workabout User GuidePsion subdirectory usage in file select dialogs Deleting unwanted Workabout files Re-installing the SunData application iconFlashcards reformatting SunData Configuration files Configuration and data file handlingData memory management Data files Default .cfgCreating a configuration file Restoring a configuration.PRN file Displaying data files on your PC.CSV file Data file layouts and data groups Page Experiment design Measurement optionsAbove-canopy reference requirements Canopy type and BFS practicalities Canopy Sampling volumeCanopy type and LAI estimates Planning for the sun’s position Preferred light and weather conditionsSetting Eladp Advice on Absorption and Eladp valuesAbsorption Estimating Eladp in the field Relationship between Mean Leaf Angle and EladpSunScan System Measurement modes Workabout setupLAI, PAR and All displays Autolog function Levelling the probe Measurement procedures in the fieldProbe handling in the field Probe GO buttonWorkabout Using the tripodBFS handling in the field Use of the tripodLevelling the BFS Finding North, and setting the shade ringExtension cables, and the location of the BFS Recalibrate option PAR calibrationsFactory light calibration Checking the probe/BFS matchingComparing the calibration with other PAR sensors Routine maintenance and cleaningRestoring the factory calibration Effect of the shade ring on the BFSSunScan probe and Beam Fraction Sensor Environmental and moisture protectionIngredients of the LAI computation method LAI theoryMajor assumptions Derivation of Wood’s SunScan canopy analysis equationsTheory versus reality Campbells Ellipsoidal LAD equations Beers law for canopy absorptionTransmission of Diffuse Light Transmission fraction τ Is given by I/I0 Diffuse light transmission cosine corrected sensor Modelling the canopy transmissionDetail Diffuse light hemispherical response sensor Functions used to model canopy transmissionAccuracy of LAI calculations Diffuse light cosine response sensorExp 0.1 . x . atan 0.9 Atan L Q Spher Modelling incomplete PAR absorption and scatteringCalculating zenith angles Scientific referencesSummary Jones, Hamlyn G Plants and Microclimate second edition. CUP SunScan probe batteries Maintenance and repairTechnical Reference section Checking the batteriesChecking the desiccant Checking the PAR calibration Re-setting the factory calibrationFactory calibration method While running SunData TroubleshootingProblems running the SunData application Psion WorkaboutInsufficient power to write data reported Technical Support Data Collection Terminal type DCT1 Psion Workabout SpecificationsSunScan Probe Type SS1 Beam Fraction Sensor type BF1Logging Cables Carrying Case type SCC1Telescopic Tripod type BFT1 Spares Kit type SPS1Spectral response PAR PerformanceSunScan system cosine response Cosine responses of probe and BFSLogging the probe as a Linear Quantum Sensor AppendicesLogging the Beam Fraction sensor Revision History Upgrading the SunScan systemSunData PC s/w Workabout SunData s/wWorkabout Remote Link File transfer between Workabout and PCChoice of different programs PsiWinSlink and Rcom Example using SlinkDrives on the PC are referred to as REMA, Remc REM = remote Documentation of Rcom and Slink Example using RcomSending a file to a serial printer Using the Workabout Comms applicationAlternative file transfer mechanisms Sending a file to a Communication programGlossary Page Accuracy IndexIndex Field use 39, 46, 48, 50, 51, 58

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