Simulating the effects of mapping and spraying resolution and threshold level on accuracy of patch spraying decisions and herbicide use based on mapped weed data

Figures & data

Figure 1.  Experimental design with an example of spraying decisions in ‘ground truth’: open (□) and filled squares (▪) are quadrats (0.25 m²) with weed densities below and above the threshold, respectively. Rectangles (- - -) delimit sprayed patches by a 14.5 m wide boom travelling in direction 1 and images taken every 1.5 m (3 m) along the line indicated by the arrow on the left. Further details in text (Material and methods).

Table I. Definition and weed threshold densities (plants m⁻²) of threshold model, after Fykse (1991). Decision is ‘spray’ if criterion xx is met.

		Threshold level
	Definition	−25%^1	Original	+25%^1
A	Total density of seed-propagated broad-leaved weeds	131	175	219
B	Density of Galeopsis spp. L.	19	25	31
C	Density of Chenopodium album L.	34	45	56
D	Density of Brassica rapa ssp. oleifera (DC.) Metzger	15	20	25
E	Density of Stellaria media (L.) Vill.	34	45	56
F	Density of Galium aparine L.	1	1	1
x	Density of at least two of the species B-F higher than the threshold for the species with the highest value
xx	‘Full model’, one of the criteria A-x fulfilled
^1For G. aparine not relevant, explained in text.

Table II. Summary statistics of total weed density per trial and as mean of all trials (last column).

	Trial No.
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	All trials
Mean (weeds m^−2)	302	4	161	369	246	119	377	75	18	152	28	126	40	6	80	126	13	323	308	151
Minimum (weeds m^−2)	120	0	64	80	16	48	60	20	0	64	0	28	4	0	20	28	0	92	44	0
Maximum (weeds m^−2)	552	24	388	1296	704	436	1480	168	176	340	84	328	152	36	212	272	60	968	748	1480
SD (weeds m^−2)	79	4	55	179	142	50	287	27	21	56	14	51	33	7	35	56	9	130	113	161
Coef. var. (%)	26	97	34	49	58	42	76	36	114	37	49	41	83	117	44	45	75	40	37	107
SD, standard deviation; Coef.var., coefficient of variations.

Table III. Mean total weed density and mean density (weeds m⁻²) of the five criteria species in the threshold model (cf. Table I), per trial and as mean of all trials (last column). Rows denoted by letters (a,b,c) are proportions of quadrats (%) above the actual criterion in ‘ground truth’ when threshold values were either reduced by 25% (a), original (b) or increased by 25% (c). Empty cells = species not present.

	Trial No.
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	All trials
All weeds, mean density	302	4	161	369	246	119	377	75	18	152	28	126	40	6	80	126	13	323	308	151
a	100	0.0	68	96	75	33	88	5	1	56	0.0	42	3	0.0	7	39	0.0	98	96	42
b	97	0.0	34	91	62	5	74	0.0	0.5	27	0.0	16	0.0	0.0	2	19	0.0	94	90	32
c	86	0.0	12	82	51	4	65	0.0	0.0	15	0.0	6	0.0	0.0	0.0	10	0.0	81	80	26
Galeopsis spp., mean density	0.1	0.3	3	0.4	0.0	0.0	6	22	2	0.9	0.1	1				9	0.1	6	6	3
a	0.0	0.0	1	0.5	0.0	0.0	5	59	0.0	0.0	0.0	0.0				12	0.0	4	4	5
b	0.0	0.0	0.0	0.0	0.0	0.0	0.5	31	0.0	0.0	0.0	0.0				5	0.0	2	0.5	2
c	0.0	0.0	0.0	0.0	0.0	0.0	0.5	21	0.0	0.0	0.0	0.0				4	0.0	1	0.0	1
C. album, mean density		2	23	0.7	1	0.8	189	3	2	4	0.7	0.1	0.0	0.1	74	18	1	5	65	20
a		0.0	13	0.0	0.0	0.0	95	0.0	0.0	0.0	0.0	0.0	0.0	0.0	89	18	0.0	3	83	16
b		0.0	7	0.0	0.0	0.0	90	0.0	0.0	0.0	0.0	0.0	0.0	0.0	75	12	0.0	1	66	13
c		0.0	2	0.0	0.0	0.0	82	0.0	0.0	0.0	0.0	0.0	0.0	0.0	65	8	0.0	0.5	45	11
B. rapa, mean density	0.0		0.5		0.0	0.4			0.4				0.0				0.1	17		1
a	0.0		0.0		0.0	0.0			0.0				0.0				0.0	44		2
b	0.0		0.0		0.0	0.0			0.0				0.0				0.0	20		1
c	0.0		0.0		0.0	0.0			0.0				0.0				0.0	14		0.7
S. media, mean density	198		29	158	24	36	35	30	13	24	1	4	15	0.7	0.2	27	3	31	33	35
a	100		35	93	23	37	37	37	8	19	0.0	0.5	15	0.0	0.0	32	0.0	25	41	24
b	100		21	87	13	24	30	14	4	12	0.0	0.0	10	0.0	0.0	12	0.0	24	26	19
c	100		10	80	5	16	21	6	3	7	0.0	0.0	6	0.0	0.0	6	0.0	21	12	15
G. aparine, mean density			0.1	0.3			0.0				0.0	0.0			4				0.0	0.3
a,b,c^1			2	6			0.5				0.5	1			52				0.5	9
^1Threshold 1 plant m^−2, irrespective of threshold level, explained in text (Materials and methods).

Figure 2.  Mean total error (TOE) with 95% confidence interval bars of mean versus boom width and image distance, original threshold level. Black bold lines: connected means of equal boom width.

Figure 3.  Total error (TOE) per trial at three threshold levels and two spraying resolutions: (A) boom width 2 m and image distance 2 m, and (B) boom width 14.5 m and image distance 4.5 m, versus proportion of quadrats with weed infestation below the threshold (WBT) per trial at the original threshold level. Figures above bars are trial numbers.

Figure 4.  Predicted total error (TOE) as a function of boom width and image distance from non-linear regression model (see equation 6) with parameter coefficients for original threshold (Table IV).

Table IV. Regression model parameter estimates for prediction of mean mapping error (MAE), spraying error (SPE) and total error (TOE) from boom width and image distance. SE = standard error, R ²=coefficient of determination, MSE = mean square error. See equation 6 for model.

		Model parameter values
Threshold Level		C 0	SE	C 1	SE	C 2	SE	R ^2,%	MSE
Reduced	MAE	7.5848	0.3600	−0.0884	0.0207	−0.1297	0.0285	71	0.816
	SPE	7.9396	0.2254	−0.1001	0.0147	−0.1284	0.0182	87	0.352
	TOE	15.5179	0.3570	−0.0947	0.0110	−0.1288	0.0143	91	0.846
Original	MAE	8.5722	0.2132	−0.1108	0.0141	−0.1171	0.0150	90	0.322
	SPE	9.1319	0.2410	−0.0927	0.0116	−0.1184	0.0143	90	0.354
	TOE	17.6806	0.3163	−0.1020	0.0090	−0.1178	0.0103	95	0.663
Increased	MAE	9.0765	0.4121	−0.1154	0.0263	−0.1084	0.0253	72	1.189
	SPE	9.6352	0.4016	−0.0816	0.0134	−0.0936	0.0148	84	0.722
	TOE	18.6585	0.5529	−0.0956	0.0126	−0.1026	0.0134	89	1.730

Figure 5.  Mean simulated herbicide reduction (SHR) versus potential herbicide reduction (PHR) per trial at two selected spraying resolutions: • = boom width 2.0 m and image distance 2.0 m, ○ = boom width 39.5 m and image distance 16.0 m. Original threshold level. Data point labels are trial ID numbers.

Figure 6.  Mean simulated herbicide reductions (SHR) with 95% confidence interval bars of mean versus spraying resolution (boom width and image distance), for original threshold level (

, mean SHR 52%), increased threshold level (♦, mean SHR 59%) and reduced threshold level (⊕, mean SHR 42%). Black bold lines: connected means of equal boom width.

Figure 7.  Illustration of the influence of threshold level on simulated herbicide reduction (SHR) per trial at two selected spraying resolutions: ○ = boom width 14.5 m and image distance 4.5 m. • = boom width 2 m and image distance 2 m. ‘SHR range’ is the absolute difference in SHR between the two threshold levels giving the lowest and highest SHR in the actual trial. Each trial is plotted according to its proportion of quadrats with weed infestation below the original threshold level (WBT).