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Variogram Analysis

Variogram Analysis. Goal Determine sampling density (spacing) Method Measure property along transect at constant distance Requires large number of samples Record measurements Analyze semi-variance with statistical package. Variogram Analysis. Variogram Analysis.

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Variogram Analysis

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  1. Variogram Analysis • Goal • Determine sampling density (spacing) • Method • Measure property along transect at constant distance • Requires large number of samples • Record measurements • Analyze semi-variance with statistical package

  2. Variogram Analysis

  3. Variogram Analysis • Determining variation between spatial samples • Sum variation between samples • Sum 1 lag distance (samples 30 cm apart) • Sum 2 lag distances (samples 60 cm apart) • Sum 3 lag distances (samples 90 cm apart) • Etc. • Graph Semi-variance with lag distance • Determine nugget: how quickly semi-variance reaches maximum • Determine sill: maximum variation in measurement

  4. Variogram Analysis 8 lag distances  sample at 240 cm Nugget Sill

  5. Variogram Analysis: Guiyang Data 5 lag distances  sample at 150 cm Sill Nugget

  6. Applications of variogram analysis • Variogram analysis will help determine sampling frequency • Soil moisture measurements showed a sample frequency of 2.4 m in here • This technique can be applied in all spatial sampling applications • Sampling canopy interception and LAI • Electrical conductivity for soil analysis

  7. What is pF? • Water potential can be expressed in several ways: kPa, MPa, bars, cm H2O • -1 MPa = -1000 kPa = 10,000 cm H2O • pF is the log base 10 of water potential, in cm H2O. • Thus, -1 MPa = 10,000 cm H2O = 4 pF • 4 pF = log (10,000 cm H2O)

  8. Plant Canopy Analysis Colin S. Campbell, Ph.D. Decagon Devices and Washington State University

  9. Radiant energy and plant canopy analysis • Why do we care about the radiation environment of plant canopies? • Calculate Leaf Area Index (LAI) • Crop growth stage • Ecosystem health • Radiation use efficiency

  10. Radiant energy and plant canopy analysis • Must have detailed knowledge of light environment to use photosynthesis models • Partitioning ET into E and T • Need to know fraction of energy intercepted by canopy and fraction transmitted to soil

  11. Intercepted PAR and Biomass Production • Cumulative intercepted photosynthetically active radiation (PAR) linearly related to total biomass production

  12. Tools for detailed analysis • Radiation budget & view factors • Fisheye analysis • Plant canopy light environment • Fisheye analysis • Ceptometer – measures light interCEPTed by canopy

  13. Definitions • Zenith angle (Ψ) – angle between sun and the zenith (vertical) • Transmission coefficient (τ) – fraction of sunlight transmitted through canopy to ground • Direct beam radiation – sunlight coming directly from sun (leaves a shadow) • Diffuse radiation – sunlight that has been scattered Ψ

  14. Plant canopy light environment -leaf area index (LAI) • Leaf Area Index (LAI) – One-sided surface area of leaves/surface area of soil • Unit area basis: m2 m-2 • How do we measure • Destructive sampling • Light attenuation • Ceptometer • Fisheye photograph

  15. LAI – destructive sampling • Harvest leaves from 1 m2 canopyarea • Physically measure surface area with optical meter • Advantages: direct measurement • Disadvantages: destructive, time consuming, wilting

  16. LAI-light attenuation theory Leaf with area = a Unit ground Area a a A a • t is transmission and n is the number of leaves • This is only true if all of the leaves are horizontal LAI

  17. Real canopies (leaves aren’t all horizontal) • Leaf angle distribution parameter (χ) • Describes the orientation of the leaves spherical canopy χ= 1 (most canopies) vertical canopy χ= 0 (onions < 1) horizontal canopy χ= ∞ (strawberries χ= 3)

  18. Extinction coefficient • We can use the leaf angle distribution to determine an extinction coefficient (G) at a particular zenith angle What does G do for us? - allows us to relate τto LAI for any canopy, given c

  19. What parameters do we need to calculate LAI? • Zenith angle (ψ) • Time and location • latitude and longitude • Canopy extinction coefficient (G) • Calculate from leaf angle distribution (χ) = 1 for most canopies • Canopy transmission coefficient (τ) • Estimate from fisheye image • Use ceptometer to measure directly

  20. LAI from Ceptometers • Measure above-canopy radiation • Measure below-canopy radiation • Meter calculates τ

  21. LAI from Ceptometer • What else does a meter need to calculate LAI? • Time and location (zenith angle) • Estimate of leaf angle distribution parameter (χ) • Note: LAI measurements are best without beam radiation (only diffuse radiation) • broken clouds are worst (changing radiation conditions) Decagon Accupar LP-80 LI-COR LAI-2000

  22. Questions? • Download all presentations and additional information at: • www.decagon.com/soils_stuff/

  23. What is a fisheye analysis? • Simply a projection of a hemisphere onto a plane • In our case, a picture is taken through a special lens that projects a full 180 degree hemisphere onto the film

  24. What does this image allow us to do? • Determine view factors of surrounding objects • View factor determines radiative influence of one object on another • Determine light transmission coefficients through a canopy – diffuse and direct

  25. What does this image allow us to do? • Determine when a particular location will be in direct sunlight • Determine what percentage of time a location will be sunlit • Determine τ, LAI, and χ values

  26. Determining view factors • Simplest analysis • Aobject is the area of the picture taken up by the object of interest • Atotalis the total area of the photograph

  27. View Factors

  28. Determining transmission coefficients • Project the fisheye picture onto a grid

  29. 30 330 60 300 90 E 270 W 240 120 150 210 180 S

  30. Determining transmission coefficients • Visually estimate the fraction of sky visible in each grid sector (1 = full sky) • Average the value for each zenith angle band = τψ

  31. t ~ 0.05 30 t ~ 0.3 330 60 300 90 E 270 W 240 120 t = 1.00 150 210 180 S

  32. Calculating average understory radiant fluxes • τd is the transmission coefficient for diffuse radiation • But, if we average over a day or longer, it approximates the total radiation transmission coefficient so: Φbc = average radiant flux density below canopy ST avg = average total radiation above canopy

  33. Calculating times and duration of direct beam • Plot sun path on grid • Segment into time steps (hours) N E W S

  34. LAI from fisheye photo • First method • G58 = 0.5 for all leaf angle distributions! • Determine τ at ψ = 58° from fisheye photo

  35. LAI from fisheye photo(method 2: use solver in excel) • Determine τ at ψ=15, 45, and 75° from fisheye photo • Calculate G at each zenith angle with an arbitrary value of χ • Calculate new values of τ for each zenith angle using G from step 2 and an arbitrary LAI value 30 60

  36. LAI from fisheye photo(method 2: use solver in excel) • Calculate sum of squared errors (SSE) between τfisheye and τcalculated • Use solver to minimize SSE by adjusting arbitrary LAI and χ values • Results in fair estimate for both LAI and χ!

  37. LAI from fisheye photo(method 3: use software package) • HemiView software (ΔT Devices) • Import digitized fisheye photo • Software does all of the functions that we talked about doing manually • τ, LAI, χ

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