Lowenberg-DeBoer, Lambert, Bongiovanni 1 Appropriate On-Farm Trial Designs for Precision Farming J....

Lowenberg-DeBoer, Lambert, Bongiovanni

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Appropriate On-Farm Trial Appropriate On-Farm Trial Designs for Precision FarmingDesigns for Precision Farming

J. Lowenberg-DeBoerJ. Lowenberg-DeBoer11, D. Lambert, D. Lambert11, , R. BongiovanniR. Bongiovanni22

11Purdue University, Site-Specific Management Center, Department of Agricultural Purdue University, Site-Specific Management Center, Department of Agricultural Economics, Purdue University, West Lafayette, IndianaEconomics, Purdue University, West Lafayette, Indiana

22Precision Agriculture Project, National Institute for Agricultural Technology (INTA), Precision Agriculture Project, National Institute for Agricultural Technology (INTA), Manfredi, Córdoba, ArgentinaManfredi, Córdoba, Argentina

[email protected]@purdue.edu


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• Objective of on-farm trials is different from Objective of on-farm trials is different from research trialsresearch trials

• Farmers want to make the best economic Farmers want to make the best economic decisions for their operationdecisions for their operation

• Most farmers do not care about underlying Most farmers do not care about underlying mechanisms or whether results are generalizablemechanisms or whether results are generalizable

• For on-farm trials we need to shift focus away For on-farm trials we need to shift focus away from research to farm management decision from research to farm management decision makingmaking

MotivationMotivation

Photo: Farmphotos.com


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Feedback from US FarmersFeedback from US Farmers• For hybrid and variety trials, filling planters with For hybrid and variety trials, filling planters with

small quantities of seed and cleaning boxes for the small quantities of seed and cleaning boxes for the next hybrid or variety takes too much time.next hybrid or variety takes too much time.

• In larger operations, seed is often purchased in bulk. In larger operations, seed is often purchased in bulk. This makes it difficult to fill the planter with small This makes it difficult to fill the planter with small quantities. Hybrid and variety strip trials work better quantities. Hybrid and variety strip trials work better with seed in bags.with seed in bags.

• Split planter trials are convenient only if your Split planter trials are convenient only if your combine head is exactly half the width of the planter. combine head is exactly half the width of the planter. That is not always the case.That is not always the case.

• For narrow row soybeans, many producers prefer to For narrow row soybeans, many producers prefer to harvest at a diagonal to the rows. This makes it harvest at a diagonal to the rows. This makes it impossible to detect narrow strips on the yield maps.impossible to detect narrow strips on the yield maps.


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SOURCE: Malzer et al., 2000. University of Minnesota Dept. of Soil Sciences

102

4

N191

P275

K184

103

1

N0

P0

K0

104

5

N286

P585

K211

105

3

N158

P371

K102

201

4

N241

P479

K179

202

2

N82

P165

K60

203

1

N0

P0

K0

204

3

N105

P105

K109

205

5

N255

P340

K218

301

3

N105

P105

K109

302

5

N255

P292

K211

303

1

N0

P0

K0

304

2

N65

P100

K53

305

4

N245

P495

K179

401

5

N250

P333

K211

402

4

N237

P556

K153

403

1

N0

P0

K0

404

3

N130

P201

K105

405

2

N80

P160

K60

HubTelephonepole

Road

96.4'63.9"

Hub

Hub

HubLath-pole

Flags

Flags

65.0'

63.8'

87.0'

109.0

92.0'83.9'

Sleepy Eye Christensen Farms 1999Brown County 10.7 acre North

190.3'

130.1'

154.7'

135.0'

200'

120ft pipe

pipe

pipe

800

feet

700

fee t

700

feet

100

feet

900

feet

360 ft24ft

TreatmentsSwine Manure1. Check2. 2000 gals/acre3. 4000 gals/acre4. 6000 gals/acre5. 8000 gals/acre

101

2

N62

P83

K53

406

7

407

6

408

9

410

8

409

1

add ons 5 tr.see back for tr.

add ons 5 tr.

Problem:Yield monitors provide many correlated observations at low cost. Can explicit modeling of the spatial error structure lead to good farm management decisions based on large block designs and fewer repetitions?

Farmers prefer large block designs


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Soil Density Trials, LeRoy, IL, USA, are an example

Photo: Russ Munn


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Field were split into large blocks (>10 ha)and yield data averaged by soil type polygon


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Tracked Equipment Advantage Occurred Mainly with Corn on Lowland Fields with Clay Soils

Net Return from Tracked Equipment

$38$49

$109

-$25-$15

$46

-$40

-$20

$0

$20

$40

$60

$80

$100

$120

LightSilt

Loam

SiltLoam

SiltyClay

Loam

LightSilt

Loam

SiltLoam

SiltyClay

Loam

$/ha

--Upland Fields----Lowlands--


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On-farm trials provide experience with different designs, but do not tell us

which is best.


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Why use a Monte Carlo Simulation in developing alternative trial designs?

• It is cheaper to narrow the range of alternative designs with simulation before doing expensive field testing

• With spatial heterogeneity field testing cannot entirely answer the question since one can only do one trial in one place in a given year

• Simulation allows us to test different designs on the same set of spatial characteristics with the same weather years


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Pilot Test of Monte Carlo Approach

8 scenarios total

• Two experimental designs (3 treatments, no blocks; 3 treatments, 5 blocks)

• Two estimation methods (OLS and SAR)

• Two levels of spatial autocorrelation (rho = 0.5 and 0.9)

• 100 Monte Carlo trials for each scenario


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Monte Carlo experimental design: detail• 2 15 x 15 grids • N treatments: 0, 75, 150 kg ha-1

• Topography zones from the Las Rosas (Argentina) trials.• OLS slope coefficients from the Argentina trial were used to simulate yields in each grid cell

Hilltop (3)

Slope W (4)

Slope E (2)

Low E (1)

132 kg/ha

Hilltop (3)

Slope W (4)

Slope E (2)

Low E (1)


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Two Experimental Designs Simulated

150

0

TOP1

TOP2

TOP3

TOP4

0150

75 750

TOP1

TOP2

TOP3

TOP4

75150

75150

150

0750 075150

5 blocks with 3 N treatments in each block

3 blocks with 3 N treatments in each block


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• Treatments were randomly assigned in blocks; Blocks were randomly assigned over the grid• Quadratic model to generate yields (with Las Rosas OLS coefficients):

y* = βo + β1N + β2N2 + δi + interaction terms + u

• Spatial model to induce correlation: y* = Xβ + (I – ρW)-1u*• u*; a randomly drawn i.i.d. innovation~N(0, σ2); σ2 is from the Las Rosas trial.• The same vector of disturbances was used for each scenario. • W is an n x n matrix defining a neighborhoods of observations.• Two levels of ρ were used to induce correlation between grid cells: 0.5 and 0.9.

Monte Carlo experimental design: detail


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Returns above fertilizer cost ($ ha-1) = NPNNP Niioici

i

221

4

1

where: Pc = Price of corn ($6.85 q-1); i = Topography zone (1=Low E, 2= Slope E, 3=Hilltop, 4=Slope W); N = N rate (profit max N* rate for VRT computations); PN = Price of N fertilizer ($0.435 kg-1), plus interest for 6 months at

15% annual interest rate; ωi = % of landscape represented by topography zone i.

Partial Budgeting for the experiment

Profit is maximized when the value of the increased yield from added N equals the cost of applying an additional unit; or when the marginal value product equals the marginal factor cost.


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Spatial error model (SAR*)

1. Obtain OLS residuals, e2. Given e, estimate ρ that

maximizes the SAR Log likelihood function

3. Given ρ, find the GLS estimates4. Compute a new set of residuals

until convergence5. Given ρ* and e*, compute

variance for inferential statistics

0 1 0 1 1 0 0 0 01 0 1 1 1 1 0 0 00 1 0 0 1 1 0 0 01 1 0 0 1 0 1 1 01 1 1 1 0 1 1 1 10 1 1 0 1 0 0 1 10 0 0 1 1 0 0 1 00 0 0 1 1 1 1 0 10 0 0 0 1 1 0 1 0

1 2 3

4 5 6

7 8 9

W =

Queen weighty = Xβ + e with e = ρW e + u

*Anselin, 1988.


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Results of Pilot Simulations

Neither the single plot or the repetitions were very successful in correctly identifying spatial variability

Identifying Spatial Variabilty in N Response

48%

8%

25%

36%

0%

10%

20%

30%

40%

50%

60%

Single Plot Repetitions

Per

cent

Cor

rect

OLS

SAR

High Spatial Correlation (rho=0.9)


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Spatial analysis and repetitions

increase reliability

Net Returns to N Variable Rate NHigh Spatial Correlation (rho = 0.90)

0

100

200

300

400

500

OLS - Singleplot

SAR - Singleplot

OLS -Repetitions

SAR -Repetitions

$ ha

-1 +/

- 2 S

TD

Single plot data and non-spatial analysis are least reliable.

Single plot data with spatial analysis is as reliable as OLS with three repetitions.

Results of Pilot Simulation Study

Repetitions and spatial analysis most reliable


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Results from Pilot Simulations:

Neither experimental design is particularly successful in identifying spatially variable response to nitrogen

Single plot design was often as successful at identifying spatial variability of response as the traditional randomised block design

Traditional design usually results in a more reliable decision than the single plot design, in the sense that the range and standard deviation of returns is smaller


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Summary With rapid technology change farmers need

more on-farm information to make good decisions

Farmers often shy away from rigorous on-farm comparisons because of logistical problems

Precision Ag technology facilitates data gathering, but classic on-farm trial designs are still often too time consuming

Simulation provides a practical way to narrow the range of alternative designs before on-farm testing


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Further research

Alternative statistical models (e.g. Nearest Neighbor, Cressie’s REML-geostatistic approach)

Continuous spatial process assumption vs. discrete approach

More Monte Carlo trials: the unexpectedly small success rate (large Type II error rate) in correctly identifying spatial variation of N response may in part be due to too few simulation runs

Different designs: this preliminary run looked at only a single plot and five blocks


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Questions or Comments?

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