Pieter de Visser& Gerhard Buck-Sorlin

1. Simulation of light absorption and photosynthesis in a greenhouse crop: effect of light node types & shaders Pieter de Visser& Gerhard Buck-Sorlin Wageningen UR Greenhouse Horticulture* P.O. Box 430, 6700 AK Wageningen, The Netherlands

2. Evolution of lighting systems

3. Observed light distribution

4. Why studying this? • improve light interception, being driver of production • even only 1% yield increase is appreciated: fine-tuning • check stakeholders’ ideas about light climate with model • efficient lighting strategies reduce energy use

5. Modelling platform: GroIMP

6. Main model parts: Inversed path tracer model from GroIMP Iight distribution 3D mockup in XL of existing crop Iight absorption/reflection/transmission ? Photosynthesis (Kim & Lieth, 2004)

7. Design of the virtual greenhouse

8. Measuring light with virtual sensors • Sensor types • perceiving • sphere with radius r • hemispheric view • (upper or upper/lower hemisphere) • absorbing • planar • area ∼ amount of absorbed light • any planar object (e.g. leaf) can • measure its light absorption directly

9. T RL L7 L7 L6 L6 L5 L5 RL (“hanging down”of leaflets) RU (divergence) L4 L4 LENi+1 RH (tilting) DIAM L3 L3 LEN L2 L2 LENi L1 L1

12. SONT + LED at Improvement Centre, Bleiswijk, NL

13. Shader parameterization: a virtual set-up

14. Light types Point light Directional light Spotlight

15. SONT HPS-lamps Measured light distribution (two vertical planes, perpendicular): max. opening angle 140°

16. Model of a SON-T lamp • New class SONT: extension of PointLight class of GroIMP • Directional distribution of emitted light incorporated into the rendering process by overwriting method getDensityAt() (computes for a given direction probability density of choosing this direction.): • 1) Transformation of direction vector ω = (x,y,z), |ω| = 1 into a polar form, where polar angles are: φ = atan2 ϕ = atan2(y,x) θ= acos(z) azimuth [-π < ϕ< π] elevation [-π < θ < π] where atan2 = variant of arcus tangens function

17. 2) Angles ϕand θused as indices for the lookup table λ of luminosity values. λ is discretized as an array of 36 by 180 values, for ϕ, respectively θ. Mapping the values of ϕ and θto λ and obtaining lower and higher indices for the two angles: float a = (phi+PI) * 18 / PI; float b = (theta+PI) * 90 / PI; int phi0 = (int) a % 36; int phi1 = (phi0+1) % 36; int theta0 = (int) b; int theta1 = min(179, theta0+1);

18. Obtaining the array values from the lookup table: float d00 = li[phi0][theta0]; float d01 = li[phi0][theta1]; float d10 = li[phi1][theta0]; float d11 = li[phi1][theta1]; 3) Bilinear interpolation to weight four drawn array values  smoothing of spatial light distribution: float wa = 1 - (a-floor(a)); float wb = 1 - (b-floor(b)); float w00 = wa*wb; float w01 = wa*(1-wb); float w10 = (1-wa)*wb; float w11 = (1-wa)*(1-wb);

19. Multiplication of weighting factors with read luminosity values to obtain probability density of the ray for the given direction: float density = w00*d00 + w01*d01 + w10*d10 + w11*d11;

20. Visualisation of light distribution of a SON-T assimilation lamp. • Next step: implementation of such a lamp as a new light source in the modelling environment

21. Implementation of a Hortilux GreenPower SON-T lamp First version (improper interpolation between array values) Update: bilinear interpolation between array values; 3 different lamp angles to a reflecting sheet

22. Grid of 21 SON-T broad beam reflector lamps 0.5 m reflection screen at increasing distance below the lamps

23. Quantifying light distribution in row crop: light type

24. Effect light type on distribution Plant shading is more stable at use of spot lights:

25. How many buffer rows?

26. Validation of light module of tomato model Check poster on comparison of two light models of tomato

27. Lighting strategies: • change SON-T position (horizontal & vertical) & angle • LED position above or between crop rows • path width between rows (at same plant density) • SON-T distribution wide vs. deep reflector • reflection via screen increases light use efficiency? • Effect lamp colour

28. Lamp light direction

29. Lamp type, height; crop structure

30. Testing opening angle

31. Effect opening angle (≃ type reflector): Available light in scene and crop absorption at 27 Phyto: (umol in total)

32. LED scenarios: Relation to LED position in the crop: in path, in row, height Wireframe in sideview Virtual crop White: rows of virtual sensors

33. Vertical light distribution depending on LED position N.B.: data averaged from 2 rows incl. path

34. Light absorption in crop: LED positioning in row

35. Light absorption in crop: LED positioning in path

36. Conclusions: • Type of reflector hardly affects light utilization • Row structure (path width) has some impact on light use • LED positioning strongly affects light use • GroIMP platform suitable for this approach

37. Next steps and outlook: • Further optimize lighting strategy incl. screens • Include wavebands in light source and photosynthesis • Determine energy requirements for scenarios • Light on rose • Not a static, but a growing, adapting crop • Improve path tracer (Göttingen) • ..

38. Thank you for your attention! Funded by: Horticultural Production Board & Ministry of Agriculture