Delta Electronics SS1-UM-1.05 user manual Functions used to model canopy transmission

Page 60

Accuracy of LAI calculations

When used to predict LAI from transmitted fraction, the functions used in the SunData software are accurate to within ±10% ±0.1 over the range of LAI less than 10 and Zenith Angle less than 60° when compared to the output of the full model.

The errors become larger for highly vertical leaves with a strong low sun, and users should avoid these conditions if possible.

In practice, the greatest errors are likely to follow from the differences between the real canopy and the idealised assumptions in the model.

Functions used to model canopy transmission

Diffuse light - cosine response sensor

The transmission of diffuse light through a canopy, as measured by a cosine corrected sensor, can be modelled by the following functions:

Given:

 

 

 

 

 

 

 

 

A ( x )

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.

 

 

 

1.38

 

 

0.007

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.15 x

 

 

 

 

 

 

 

 

 

 

 

 

B ( x )

 

 

4.32

 

 

 

2.60.exp( 2.75. x )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C( x )

 

 

0.57

 

 

 

0.23.exp( 1.40. x )

 

 

 

 

 

 

 

 

 

 

 

τ

( x , L )

 

exp(

 

L )

 

 

 

A( x ). L3

.exp

 

B ( x ).LC( x)

 

diff

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

These curves give maximum errors of 0.009 in τ diff, with a maximum 6% error for

τdiff greater than 0.01 over the range L = 0 to 10 and x = 0 to 1000.

Diffuse light - hemispherical response sensor.

The previous analysis of diffuse light transmission is appropriate for a cosine- corrected sensor as it only considers the vertical component of the incident and transmitted light. This works as long as the leaf absorption in the PAR band is complete, and there is no scattering of the incoming light.

When we consider leaves with incomplete PAR absorption, some of the absorbed light is re-emitted in different directions to the original incoming light. Because of this we have to account for all of the incoming light, both horizontal and vertical components, and also be aware that the spatial intensity distribution of the light is modified by the canopy and varies through the canopy depending on the canopy leaf angle distribution.

The above analysis is now repeated to find the transmission of uniform diffuse light as measured by a sensor with a hemispherical response. The equivalent equation for the transmission fraction is:

 

 

 

 

 

 

 

π

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

.

2

. π .

 

 

 

.

 

 

 

 

 

.

 

τ

spher( x , L )

 

 

 

 

sin(

θ

)

exp(

 

K( x ,

θ

)

θ

 

 

 

 

 

 

 

 

2.π

2

 

 

 

 

 

L ) d

 

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

60 • LAI theory

Document code: SS1-UM-1.05

Page 59 Page 61
Image 60
Page 59 Page 61
Contents SunScan SS1-UM-1.05Copyright AcknowledgementsTrademarks CE conformityContents Menus and Screens More Psion and file handling notes Measurement optionsLAI theory Technical Reference sectionAppendices IndexHow to use the manuals IntroductionSunScan Canopy Analysis System Organisation of this manualField accessories SunScan probeBeam Fraction sensor Data Collection TerminalGetting Started Preliminary checksWorkabout and SunScan probe Checking the Workabout hardware Installing the SunData s/w in your PC Installing the s/wSunData s/w Diskette What the s/w doesSetting up your PCs COM port Running SunDataCommunication checks SunScan probe to PCWorkabout to PC Running SunData in Windows SunScan Tutorial About this tutorialWorking with the Workabout 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 AveragesTransferring the data file to your PC From the WorkaboutTo the PC Initiating the file transfer from the Workabout Meanwhile, on the PC RS232 communication problems Conclusion of the TutorialSunData Screens on the Workabout Settings Menus and ScreensFile Contd UtilsQuit More Psion and file handling notes Navigating Psion directories and screensWorkabout User Guide Navigating the Psion directories and screensPsion subdirectory usage in file select dialogs Re-installing the SunData application icon Deleting unwanted Workabout filesFlashcards reformatting Configuration and data file handling SunData Configuration filesData memory management Default .cfg Creating a configuration fileRestoring a configuration Data filesDisplaying data files on your PC .PRN file.CSV file Data file layouts and data groups Page Measurement options Experiment designAbove-canopy reference requirements Canopy Sampling volume Canopy type and BFS practicalitiesCanopy type and LAI estimates Preferred light and weather conditions Planning for the sun’s positionAdvice on Absorption and Eladp values Setting EladpAbsorption Relationship between Mean Leaf Angle and Eladp Estimating Eladp in the fieldWorkabout setup SunScan System Measurement modesLAI, PAR and All displays Autolog function Measurement procedures in the field Probe handling in the fieldProbe GO button Levelling the probeUsing the tripod BFS handling in the fieldUse of the tripod WorkaboutFinding North, and setting the shade ring Levelling the BFSExtension cables, and the location of the BFS PAR calibrations Factory light calibrationChecking the probe/BFS matching Recalibrate optionRoutine maintenance and cleaning Restoring the factory calibrationEffect of the shade ring on the BFS Comparing the calibration with other PAR sensorsEnvironmental and moisture protection SunScan probe and Beam Fraction SensorLAI theory Ingredients of the LAI computation methodDerivation of Wood’s SunScan canopy analysis equations Major assumptionsTheory versus reality Beers law for canopy absorption Campbells Ellipsoidal LAD equationsTransmission of Diffuse Light Transmission fraction τ Is given by I/I0 Modelling the canopy transmission Diffuse light transmission cosine corrected sensorDetail Functions used to model canopy transmission Accuracy of LAI calculationsDiffuse light cosine response sensor Diffuse light hemispherical response sensorModelling incomplete PAR absorption and scattering Exp 0.1 . x . atan 0.9 Atan L Q SpherScientific references Calculating zenith anglesSummary Jones, Hamlyn G Plants and Microclimate second edition. CUP Maintenance and repair Technical Reference sectionChecking the batteries SunScan probe batteriesChecking the desiccant Re-setting the factory calibration Checking the PAR calibrationFactory calibration method Troubleshooting Problems running the SunData applicationPsion Workabout While running SunDataInsufficient power to write data reported Technical Support Specifications SunScan Probe Type SS1Beam Fraction Sensor type BF1 Data Collection Terminal type DCT1 Psion WorkaboutCarrying Case type SCC1 Telescopic Tripod type BFT1Spares Kit type SPS1 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 Upgrading the SunScan system SunData PC s/wWorkabout SunData s/w Revision HistoryFile transfer between Workabout and PC Choice of different programsPsiWin 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 SlinkUsing the Workabout Comms application Alternative file transfer mechanismsSending a file to a Communication program Sending a file to a serial printerGlossary Page Index AccuracyIndex Field use 39, 46, 48, 50, 51, 58

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