Appropriate On-Farm Trial Designs for Precision Farming J.
Appropriate On-Farm Trial Designs for Precision Farming J. Lowenberg-DeBoer1, D. Lambert1, R. Bongiovanni2 1Purdue University, Site-Specific Management Center, Department of Agricultural Economics, Purdue University, West Lafayette, Indiana 2Precision Agriculture Project, National Institute for Agricultural Technology (INTA), Manfredi, Crdoba, Argentina [email protected] Lowenberg-DeBoer, Lambert, Bongi ovanni 1 Motivation Objective of on-farm trials is different from research trials Farmers want to make the best economic decisions for their operation Most farmers do not care about underlying mechanisms or whether results are generalizable For on-farm trials we need to shift focus away from research to farm management decision making Lowenberg-DeBoer, Lambert, Bongi ovanni 2 Photo: Farmphotos.com Feedback from US Farmers For hybrid and variety trials, filling planters with small quantities of seed and cleaning boxes for the next hybrid or variety takes too much time. In larger operations, seed is often purchased in bulk. This makes it difficult to fill the planter with small quantities. Hybrid and variety strip trials work better with seed in bags. Split planter trials are convenient only if your combine head is exactly half the width of the planter. That is not always the case. For narrow row soybeans, many producers prefer to harvest at a diagonal to the rows. This makes it impossible to detect narrow strips on the yield maps. Lowenberg-DeBoer, Lambert, Bongi ovanni 3 Farmers prefer large block designs Telephone
pole 96.4' Road Sleepy Eye Christensen Farms 1999 Brown County 10.7 acre Hub 63.9" 120ft 24ft North 135.0' 360 ft 1 0 2 1 0 3 1 0 4 1 0 5 2 0 1 2 0 2 2 0 3 2 0 4
4. 6000 gals/acre 5. 8000 gals/acre 900 feet Hub add ons 5 tr. see back for tr. 109.0 Flags Flags Lath-pole 92.0' 83.9' Hub 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? SOURCE: Malzer et al., 2000. University of Minnesota Dept. of Soil Sciences Lowenberg-DeBoer, Lambert, Bongi ovanni 4 Soil Density Trials, LeRoy, IL, USA, are an example Lowenberg-DeBoer, Lambert, Bongi ovanni 5 Photo: Russ Munn Field were split into large blocks (>10 ha) and yield data averaged by soil type polygon
On-farm trials provide experience with different designs, but do not tell us which is best. Lowenberg-DeBoer, Lambert, Bongi ovanni 8 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 Lowenberg-DeBoer, Lambert, Bongi ovanni 9 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 Lowenberg-DeBoer, Lambert, Bongi ovanni 10 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 Slope W (4) Hilltop (3) Slope E (2) Low E (1) 132 kg/ha Lowenberg-DeBoer, Lambert, Bongi ovanni 11 Two Experimental Designs Simulated TOP4 0 TOP2 TOP1 TOP3 TOP4 TOP3 TOP2 TOP1 150 75 3 blocks with 3 N treatments in each block 0 75 150 150 0 75 0 75
150 75 150 0 0 150 75 5 blocks with 3 N treatments in each block Lowenberg-DeBoer, Lambert, Bongi ovanni 12 Monte Carlo experimental design: detail Treatments were randomly assigned in blocks; Blocks were randomly assigned over the grid Quadratic model to generate yields (with Las Rosas OLS coefficients): y* = o + 1N + 2N2 + i + interaction terms + u Spatial model to induce correlation: y* = X + (I W)-1u* u*; a randomly drawn i.i.d. innovation~N(0, 2); 2 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 were used to induce correlation between grid cells: 0.5 and 0.9. Lowenberg-DeBoer, Lambert, Bongi ovanni 13 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. -1 4
Returns above fertilizer cost ($ ha ) = i Pc oi 1i N 2 i N 2 PN N i 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; i = % of landscape represented by topography zone i. Lowenberg-DeBoer, Lambert, Bongi ovanni 14 Spatial error model (SAR*) y = X + e with e = W e + u 1. 2. 3. 4. 5. Obtain OLS residuals, e Given e, estimate that maximizes the SAR Log likelihood function Given , find the GLS estimates Compute a new set of residuals until convergence Given * and e*, compute variance for inferential statistics Queen weight 1 2 3 4 5 6 7
Identifying Spatial Variabilty in N Response High Spatial Correlation (rho=0.9) 60% Percent Correct Neither the single plot or the repetitions were very successful in correctly identifying spatial variability 50% 48% 36% 40% 30% 25% 20% OLS SAR 8% 10% 0% Single Plot Lowenberg-DeBoer, Lambert, Bongi ovanni Repetitions 16 Results of Pilot Simulation Study Net Returns to N Variable Rate N High Spatial Correlation (rho = 0.90) -1 +/- 2 STD
500 $ ha Spatial analysis and repetitions increase reliability 400 300 Single plot data and non-spatial analysis are least reliable. Single plot data with spatial analysis is as reliable as OLS with three repetitions. 200 100 0 OLS - Single SAR - Single OLS SAR plot plot Repetitions Repetitions Lowenberg-DeBoer, Lambert, Bongi ovanni Repetitions and spatial analysis most reliable 17 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 Lowenberg-DeBoer, Lambert, Bongi ovanni 18
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 Lowenberg-DeBoer, Lambert, Bongi ovanni 19 Further research Alternative statistical models (e.g. Nearest Neighbor, Cressies 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 Lowenberg-DeBoer, Lambert, Bongi ovanni 20 Questions or Comments? Lowenberg-DeBoer, Lambert, Bongi ovanni 21
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