The Analysis of Spatial and Temporal Trends in Yield Map Data over Six Years

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Biosystems Engineering (2003) 84 (4), 455–466 doi:10.1016/S1537-5110(03)00038-2 PA}Precision Agriculture

The Analysis of Spatial and Temporal Trends in Yield Map Data over Six Years Simon Blackmore1; Richard J. Godwin2; Spyros Fountas1 1

AgroTechnology, The Royal Veterinary and Agricultural University, Agrovej 10 Bulding 8-51, Taastrup 2630 Denmark; e-mail address of corresponding author: [email protected] 2 National Soils Resources Institute, Cranfield University at Silsoe, UK; r.godwin@cranfield.ac.uk (Received 26 October 2002; accepted in revised form 20 February 2003)

A quantitative analysis of yield data from four fields over 6 years was carried out to identify the spatial and temporal trends. The methodology was modified from previous work to separate the temporal effects into two parts; the inter-year offset and the temporal variance. The inter-year offset quantifies the overall differences in yield between 1 year and the next, whereas the temporal variance indicates the amount of change at a particular point over time. Results from these fields show that the significant spatial variability found within each individual yield map cancelled out over time, leaving a relatively homogenous spatial trend map. The implications of these findings are that each field should be managed according to the current years’ conditions. # 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd

1. Introduction When commercial yield mapping started in the early 1990s, it was expected that parts of a field would constantly yield well, while other parts would produce poor results. This was due to the assumption that permanent soil characteristics would always behave in the same way each year. A number of researchers have developed methods to analyse these trends. Larscheid and Blackmore (1996) developed a technique to normalise successive years yield data and produce trend maps. Swindell (1997) analysed spatial trends over time using a geographical information system (GIS) and summed the annual classes into a harvest score. Lark and Stafford (1996a; 1996b) developed an unsupervised fuzzy clustering technique that identified homogenous areas of the field without using any agronomic background. Panneton et al. (2001) and Panneton and Brouillard (2002) used a similar technique to identify where yields were stable in time (SIT) and unstable in time (UNSIT). Fraisse et al. (1999) went further by including topographical features and soil electrical conductivity in their analysis. In this study, yield map data were collected between 1995 and 2000 inclusively, as part of a precision farming research programme at four sites in England (Earl et al., 2003; Taylor et al., 2003; Welsh et al., 2003a, 2003b; 1537-5110/03/$30.00

Wood et al., 2003). The data were processed to remove identifiable errors such as narrow finishes, fill-mode errors and outliers, using the methodology described by Blackmore and Moore (1999) and to extract the spatial and temporal trends using techniques described by Blackmore (2000). These techniques are further developed here to improve the trend analysis. Both the spatial trend and temporal stability maps were brought together to form the spatial and temporal trend map. Furthermore, during the analysis, the temporal stability was seen to take two forms. Firstly, there was the inter-year offset where the whole field yielded higher or lower. This could be attributed to a major systemic factor such as good or bad weather, a major pest or disease attack. The other type of temporal trend was seen to vary in a particular part of the field over time. This effect, defined as the temporal variance, is calculated from a modified standard deviation function. If these yield patterns were temporally stable, the resulting trend maps would have been a very useful management tool as they could have predicted the spatial yield patterns in the following years. To test the magnitude of this temporal stability, a simple prediction analysis was carried out to compare the previous trend with the actual yield in the following year. 455

# 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Science Ltd

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Difficulty was experienced in assigning a threshold value between temporal stability and instability. Therefore, an attempt was made to understand the sensitivity of a range of values by comparing them with the area of the field that was then considered unstable and arriving at suggested threshold.

2. Methods 2.1. Data collection and processing Yield map data were collected between 1995 and 2000 inclusive. The variation in crop yields were recorded using a combine harvester equipped with a radiometric yield sensor, with a mean instantaneous grain flow error of 0
05 kg s1 and a standard deviation of 0
15 kg sl, both of which are effectively independent of grain flow rate as shown in Fig. 1. When harvesting an 8 t ha1 crop with a 5 m wide cutter bar at 1
25 m s1 (4
5 km h1) this is equivalent to an instantaneous grain flow error of 1%. The data for each field over all the years were standardised on a 20 m grid that used a 20 m search radius, to ensure that each area had at least three harvester tracks of data and to span the voids left by the removal of field trial data. Larger grid sizes tended to smooth the data more and loose details from the resulting maps, whereas smaller grids became too reliant on low numbers of data points or even have data voids. Individual yield maps have not been presented here due to lack of space.

2.2. Spatial trend map Up until recently, it was expected that parts of a field would always produce well while other parts would always have lower yields. This was due to the assumption that the permanent soil characteristics would affect the crop yield in the same way each year. This assumption is valid if the characteristic introduces a permanent limiting factor. When these conditions occur, the spatial yield pattern should be the same each year. The spatial trend map was designed to show this trend by calculating the arithmetic temporal mean yield at the same point over a number of years. As the yield data comprised the complete population, the arithmetic mean was used. The mean yield from each grid point over the 6 year produced the data for the spatial trend map, which was then divided into 1 t ha1 classes. 2.3. Temporal stability: inter-year offset During the analysis, it was noted that there was a large difference between yields from year to year, probably due to ‘good’ or ‘bad’ overall weather conditions in each year, which was quite different from how each part of the field behaved from year to year. It was felt important to separate these very large inter-year offsets from the smaller spatio-temporal effects. In the case of the inter-year offset, where the temporal effects between the years are important, multiple histograms can be used and the temporal effects can be judged by the offsets between the yearly curves. This inter-year offset, can be defined as the difference between the mean yield values between 2 years in the same field.

20 15 10

Error, %

5 0 2

3

4

5

6

7

8

9

10

12

0.5 0.10

Gain flow, kg s-1

0.15 0.20 0.25

Fig. 1. Yield monitor calibration showing percentage error between actual and measured grain flow: , average error; , standard deviation; , maximum; , minimum; log. (average error); log. (standard deviation); log. (maximum); } log. (minimum); ordinate, %; abscissa grainflow, Kg/s (Moore, 1998)

SPATIAL AND TEMPORAL TRENDS IN YIELD MAP DATA

2.4. Temporal stability: temporal variance map The second temporal effect that has been identified in this research is where one part of the field yields relatively high in 1 year and relatively low in another when compared to the mean. This can be defined as the temporal variance at a point. An approach to quantify the temporal variance has been suggested previously, (McBratney & Whelan, 1999) where the variance was measured between 2 years over all points in the field: 2 Pn 1 Y2;i  Y1;i i5l 2 s2t 5 ð1Þ n where: s2t is the temporal variance in year t, Y is the yield at grid point i in year 1 and 2 and n is the number of points in the field. This technique gives a single number to quantify the temporal variance across the whole field and hence cannot be mapped. As it includes the gross offsets that are the same over the whole field, they dominate the smaller spatial responses. It also only quantifies the variance between 2 years. As the inter-year offsets have already defined as the distribution mean, they can be removed by establishing a method to quantify the variance relative to the mean. To achieve this, the authors propose a new definition of temporal variance, which shows the variance from the mean (point yield minus the field mean) over time (1995–2000): 2 Pt 5 00  t 5 95 Yt;i  Yt 2 si 5 ð2Þ 6 where: s2i is the temporal variance at grid point i, t is the time in years between 1995 and 2000, Y is the yield in years t at point i, and Y% t is the mean of the yield for the whole field in years t. In a similar manner, to conventional statistics the temporal variance is the square of the standard temporal deviation. This may sometimes be a more useful term, as the units are tonnes per hectare. This definition of temporal variance indicates a low value if an area of the field were to always yield close to the mean. This could be considered as SIT as it would have a low temporal variance. If another area were to yield sometimes high and sometimes low, relative to the mean, it to be temporally unstable and it would give a high value of temporal variance. 2.5. Sensitivity of temporal stability The temporal variance map can be classified into areas that are SIT and areas considered UNSIT, by

457

setting a particular threshold in the temporal standard deviation data. Previously, a value for the coefficient of variation (CV) of 30% was used (Blackmore, 2000) but this is probably too high as no significant areas were then designated as unstable in all the fields over all the years. As yet, no conclusive method has been defined to set this level, so it was decided to look at the sensitivity of the areas within the map that were deemed to be UNSIT at a number of levels. The temporal standard deviation at each of the grid points was calculated and the areas of each class were then shown in a map. To be able to compare the fields together (as they are of different sizes) the affected areas were then summated and divided by the total to give the cumulative percentage. All fields could then be compared to see which ones were more sensitive to temporal instability. 2.6. Spatial and temporal trend map The spatial trend and temporal variance maps uniquely quantify their respective trends, but these data can be brought together to give a single overview of the field by further classifying each part of the field into four homogenous classes. These are: (1) high yielding area}above the grand mean (for all years) for the field; (2) low yielding area}below the grand mean (for all years) for the field; (3) stable area}low inter-year spatial variance (arbitrary threshold) and (4) unstable area}high inter-year spatial variance (arbitrary threshold). As yield and stability are non-mutually exclusive, this gives four possible combinations: high and stable (HS); high and unstable (HU); low and stable (LS) and low and unstable (LU). The method presented here is slightly different from that described by Blackmore (2000) as it can now have any combination of independent adjacent classes shown as a grid, whereas before it could only have a continuum between the classes, shown as contours, which are not so realistic. 2.7. Prediction If a particular spatial pattern was seen to be stable within a field then it is reasonable to suppose that it should be relatively good predictor of the pattern in the following year. This would assume that the prevailing conditions and limiting factors are the same in each

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winter wheat (1993, 1995, 1996, 1998 and 2000) and oil seed rape (1994 and 1997). Due to the previous wet autumn, it was planted with spring wheat in 1999. (All years here, denote the year of harvest.) Therefore, yield data from 1993 was included to replace 1997. Twelve Acres field was planted with winter wheat but the yield data for 1997 was lost so is not included. All fields had cropping trials during 1998–2000 but significantly different data were removed before this analysis. (Some trials showed no discernable difference from the surrounding crop so their data were included in this analysis.)

year. To test this hypothesis, a simple correlation analysis was carried out between the spatial trend data from a varying number of years and the following year’s actual yield. Yield data from the four fields in 1995, 1996 and 1997 were gridded, averaged and correlated with the yield from the same points in 1998. Similarly data between 1995, 1996, 1997 and 1998 were correlated with yield from 1999, as was data between 1995 and 1999 correlated with yield from 2000.

3. Results 3.1. Spatial trend map

Yield data and the results of the analysis are presented here for four fields (Trent, Onion, Far Sweetbrier and Twelve Acres) using 6 year harvest data. Trent Field was planted with winter malting barley in each year between 1995 and 2000. Onion Field grew winter wheat each year. Far Sweetbrier was managed in a rotation of 140 600

The spatial trend maps are presented in Figs 2 and 3. Fig. 2 shows the spatial trend after 3 years and Fig. 3 after 6 years. The spatial trends identified in Fig. 2, were used as a basis for spatially variable fertiliser treatment

Trent Field 242 800

Mean yield contour, 5.7 t ha-1 140 500

Onion Field

242 700

242 600

140 400

242 500 140 300 242 400 140 200 436 900 437 000 437 100

437 200

437 300

437 400 242 300

Far Sweetbrier field

245 350

Mean yield contour, 7.8 t ha-1

242 200

245 450 Yield, t ha-1 11

Mean yield contour, 8.4 t ha-1

10 9

505 500 505 600 505 700 505 800 505 900 506 900 Twelve Acres field

206 300

8 245 250

7

206 200

6 5

245 150

206 100 4 3

245 050 511 950

512 050

512 150

512 250

512 350

2

206 000 416 750 416 850 416 950

Mean yield contour, 6.7 t ha-1 417 050 417 150

417 250

Fig. 2. The spatial yield trend maps, based on a 20 m grid, for the four fields after 3 years: ordinate}Northings, m; abscissa}Eastings, m.

459

SPATIAL AND TEMPORAL TRENDS IN YIELD MAP DATA

140 600

Trent Field

242 800

Onion Field

Mean yield contour, 6.1 t ha-1 140 500

242 700

242 600

140 400

242 500 140 300 242 400 140 200 436 900 437 000 437 100

437 200

437 300 437 400

242 300

Far Sweetbrier field

245 350

Mean yield contour, 6.9 t ha-1

242 200

245 450 Yield, t ha-1 11

Mean yield contour, 7.5 t ha-1

10 9

505 500 505 600 505 700 505 800 505 900 506 900 Twelve Acres field

206 300

8 245 250

7

206 200

6 5

245 150

206 100 4 3

245 050 511 950

512 050

512 150

512 250

512 350

2

206 000 416 750 416 850 416 950

Mean yield contour, 6.5 t ha-1 417 050 417 150

417 250

Fig. 3. The spatial yield trend maps, based on a 20 m grid, for the four fields after 6 years: ordinate}Northings, m; abscissa}Eastings, m

trials in 1998 (Welsh et al., 2003a, 2003b). Note the addition of the mean contour, which is the overall mean of this field over this time period. All coordinates are in metres [Ordnance Survey of Great Britain (OSGB)]. It is interesting to note that although there is significant spatial variability in most individual years (not shown), the effects from each year appear to cancel out and the spatial trend map flattens out over time. The maps in Fig. 3 show only a 1 t ha1 yield range about the mean after 6 years.

3.2. Temporal stability: inter-year offset The inter-year offset only needs to be defined by the differences between the yearly mean of the yield but other inferences can be drawn from the data when a histogram is used. Most histograms are skewed towards the high-yielding end of their distribution but the lower kurtosis indicates higher spatial variability. The inter-

year offsets for the four fields can be seen in the histograms of Fig. 4 and the mean yield values in Table 1. All fields seem to be high yielding in 1996, while 1997 was a particularly poor year for Trent Field. The inter-year offsets can be calculated by taking the difference between the arithmetic mean of the years in question. The greatest inter-year offsets were 3
2 t ha1 for Trent Field between 1997 and 1998, 3
4 t ha1 for Onion Field between 1996 and 1998, Sweetbrier between 1996 and 1999 and Twelve Acres between 1995 and 1996 respectively. To validate the assumption of independence between the spatial mean of yield and the spatial variance of yield, both factors were plotted together in Fig. 5 for each field and each year. The spatial variance and mean were calculated from the original yield data and showed little correlation apart from Far Sweetbriar, which showed smaller variance with higher mean yields, this is as might be expected to achieve the higher means.

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40

30

1995 1996

1997

1998

20 1999

10 0

2000 0

1

3

2

4

(a)

2000 0

2

1

3

4

(b)

5 6 7 8 Yield, t ha-1

9 10 11 12

40 1995

30 1998 20

1995 Frequency, %

Frequency, %

1999 10

9 10 11 12

40 1996

1993 1999

10

30

1998

0

1

2

3

4

(c)

5 6 7 8 Yield, t ha-1

1999

20 1996

10 2000

2000 0

1995

1998

20

0

5 6 7 8 Yield, t ha-1

1996

1997

30

Frequency, %

Frequency, %

40

0

9 10 11 12

0

2

1

3

4

(d)

5 6 7 8 Yield, t ha-1

9 10 11 12

Fig. 4. Six-year yield histograms for the four fields: (a) Trent Field; (b) Onion Field; (c) Far Sweetbrier field; (d) Twelve Acres field

Table 1 Mean yield values for the four fields over the 6 years Mean yield, t ha1 1993 *

Trent Field Onion Field Far Sweetbrier field Twelve Acres field

7
5 *

1996

5
8 8
2 8
8 4.9

7
2 9
1 9
5 8.3

1997

1998

1999

2000

4
2 6
3

7.4 5.7 7
7 7
1

5
8 6
1 6.1 7
3

7
0 6
3 6
3 5
4

* *

Not available.

Spatial variance of yield per field, t ha-1 squared

*

*

1995

3.3. Temporal stability: temporal variance map

5 2000

4

3 1999 1997 2000

2

2000 19991999 1

1997

20001998 1995

1995

0

4

19 93 1996 19961998 1998 199519951996 1996 1999 1998

7 5 6 9 8 Spatial mean of yield per field, t ha-1

10

Fig. 5. Relationship between spatial variance and spatial mean of yield per field from 1995 to 2000: , Trent Field; , Onion Field; , Far Sweetbrier; , Twelve Acres

The temporal standard deviation was calculated at each grid point over the 6 years and is presented as the temporal variance maps for the four fields in Fig. 6. The temporal variance is equal to the square of the standard temporal deviation. The range was divided into quartiles and used as classes in the figure. The relationship between the temporal standard deviation and the temporal mean is shown in Fig. 7. Each grid point in the field is represented by the temporal mean yield and the temporal standard deviation over the 6 years. Each graph is subdivided into four classes using two orthogonal thresholds. The X-axis is divided by the grand mean yield (for all grid points over all years) for each field and the Y-axis is divided at the 1 t temporal stability threshold. As the grand mean is made up of the inter-year offsets, it is better to use the

461

SPATIAL AND TEMPORAL TRENDS IN YIELD MAP DATA

Trent Field

140 600

242 800 Onion Field

242 700

140 500

242 600

140 400

242 500 140 300 242 400 140 200 436 900 437 000 437 100 437 200 437 300 437 400

242 300

Far Sweetbrier field 242 200

245 450

505 500 505 600 505 700 505 800 505 900 506 900 Maximum 245 350

Twelve Acres field Upper quartile

245 250 Median Lower quartile

245 150

Minimum 245 050 511 950

512 050

512 150

512 250

512 350

416 750 416 850 416 950 417 050 417 150

417 250

Fig. 6. Temporal variance maps of yield, based on a 20 m grid, for the four fields: ordinate}Northings, m; abscissa}Eastings, m

annual field mean for classifying the temporal variance and temporal standard deviation.

3.4. Sensitivity of temporal stability The frequency histograms for each class of stability are shown in Fig. 8. The columns indicate the actual area of the field in each class (left-axis) and the lines shows the cumulative percentage of the field considered to be stable at that level (right-axis). The bottom axis shows the temporal standard deviation divided into 11 yield classes between 0 and 2 t ha1. The sensitivity between a level of temporal standard deviation and the area it affects in the four fields are shown in Fig. 9. In this family of curves, it can be seen that Twelve Acres has the least area affected by temporal variability (i.e. it is more stable) while Far Sweetbrier has the most variability compared to the year’s mean. Note that this is after the inter-year offset

has been removed. The curves have been reversed from the cumulative percentage stability curves shown in Fig. 8, as the cumulative area of the field affected by instability is now of interest. If a level of temporal instability that could be managed practically by a farmer was estimated, then a figure of about one tonne per hectare seems reasonable. At this level, Trent Field has 7% (0
6 ha) of its area considered as unstable. Similarly Onion, Far Sweetbrier and Twelve Acres fields have 7% (1
2 ha), 22% (1
4 ha) and 8% (0
6 ha), respectively. If this threshold was dropped to 0
8 t ha1 then a much larger area of the fields would be considered unstable with Far Sweetbrier reaching 50%.

3.5. Spatial and temporal trend map Figure 10 shows the spatial and temporal trend maps where the data from the spatial trend and the temporal

5 4 3 2 (e)

(f)

1

(h)

(g) 0

0

1

2

3

Temporal standard deviation of yield, t ha-1

(a)

4

5

6

Temporal mean yield, t

7

8

9

10

ha-1

4 3 2 (e)

(f)

1

(h)

(g) 0

1

2

3

4

5

6

7

Temporal mean yield, t ha

(c)

5 4 3 2 (e)

(f)

(g)

(h)

1 0

0

1

2

3

8

9

10

-1

4

5

6

8

7

Temporal mean yield, t

(b)

5

0

Temporal standard deviation of yield, t ha-1

S. BLACKMORE ET AL.

Temporal standard deviation of yield, t ha-1

Temporal standard deviation of yield, t ha-1

462

9

10

ha-1

5 4 3 2 (e)

(f)

(g)

(h)

1 0

0

1

2

3

4

5

6

Temporal mean yield, t

(d)

8

7

9

10

ha-1

0 (a)

Area of field, ha

2.5

(c)

20 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 More Temporal standard deviation, t ha-1 100

2

80

1.5

60

1

40

0.5

20

0

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 More -1 Temporal standard deviation, t ha

80

4

60 40

2

20

0

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 More (b) Temporal standard deviation, t ha-1 100 3

80

2

60 40

1 0

20

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 More (d) Temporal standard deviation, t ha-1

Percentage of the field, %

40 1

6

Percentage of the field, %

60

Area of field, ha

2

100

Area of field, ha

80

Percentage of the field, %

Area of field, ha

100 3

Percentage of the field, %

Fig. 7. Relationship between temporal standard deviation (TSD) and temporal mean yield (spatial trend) on 20 m grid from 1995 to 2000: (a) Trent Field (grand mean of 6
1 t ha1); (b) Onion Field (grand mean of 6
9 t ha1); (c)Far Sweetbrier (grand mean of 7
5 t ha1); (d) Twelve Acres (grand mean of 6
5 t ha1); (e) low yielding, unstable (at 1 t ha1 TSD); (f) high yielding, unstable (at 1 t ha1 TSD); (g) low yielding, stable (at 1 t ha1 TSD); (h) high yielding, stable (at 1 t ha1 TSD)

Fig. 8. Frequency distribution of temporal standard deviation of yield for the four fields: (a) Trent Field; (b) Onion Field; (c) Far Sweetbrier field; (d) Twelve Acres field: , area; , cumulative percentage

SPATIAL AND TEMPORAL TRENDS IN YIELD MAP DATA

Percentage of the field, %

variability maps have been combined into four classes. The spatial trend data was classed into high and low according to whether it was above or below the mean and the temporal variance data was classed as SIT and

100 90 80 70 60 50 40 30 20 10 0

Less stable

More stable

0

0.2

0.6

0.4

0.8

1

1.2

1.4

Temporal standard deviation, t

1.6

1.8

2.0

ha-1

Fig. 9. Percentage of field area affected by temporal instability of yield: }^}, Trent Field; }&}, Onion Field; }m}, Far Sweetbrier field; }*}, Twelve Acres field.

140 600

Trent Field

463

unstable in time according to whether it was above or below the arbitrary one tonne stability threshold. These four elemental classes are combined into four composite classes of high yielding and SIT (HS), high yielding and unstable in time (HU), low yielding and SIT (LS) and finally low yielding and UNSIT (LU). In Trent Field, it can be seen that the temporal instability at 1 t ha1 is not pronounced but it does seem to occur around the outside of the field and in the corners. The remaining stable area is divided equally into high and low-yielding area, as would be expected by using the mean as the threshold. More significantly, the western side is always higher yielding but the eastern side seems always to be lower yielding. Onion Field exhibits similar behaviour but the spatial trend shows that lower yields are always around the field boundary. Note that the field is bounded by hedgerows and ditches except for the southeastern boundary where it is just a footpath. (Another field extends on the other side) Another feature is the generally low and stable area

Onion Field

242 800

140 500

242 700

140 400

242 600

242 500

140 300

140 200 436 900 437 000 437 100 437 200 437 300 437 400

242 400

242 300 Far Sweetbrier field 242 200 245 450 505 500 505 600 505 700 505 800 505 900 506 900 Twelve Acres field

245 350 206 300

245 250

206 200

245 150

245 050 511 950

206 100

512 050

512 150

512 250

512 350 1

206 000 416 750 416 850

416 950 417 050 417 150 417 250

Fig. 10. The spatial and temporal trend maps with a 1 t ha yield stability threshold: &, high and stable; , high and unstable; , low and stable; &, low and unstable; ordinate}Northings, m; abscissa}Eastings, m.

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S. BLACKMORE ET AL.

140 600

Trent TrentField Field

242 800 Onion Field

140 500

242 700

140 400

242 600

140 300

242 500

140 200 436 900 437 000 437 100 437 200 437 300 437 400

242 400 242 300

Far Sweetbrier field

242 200

245 450 505 500 505 600 505 700 505 800 505 900 506 000 Twelve Acres field

245 350 206 300

245 250

206 200

245 150

245 050 511 950 512 050 512 150

206 100

512 250

512 350

206 000 416 750 416 850

416 950 417 050 417 150 417 250

Fig. 11. The spatial and temporal trend maps with a 0.8 t ha1 yield stability threshold: &, high and stable; , high and unstable, , low and stable; &, low and unstable; ordinate}Northings, m; abscissa}Easting, m.

with a low and unstable centre. This area has a slight depression and often collects ponded water. This gave higher yields in dry years and lower yields in wet years. Far Sweetbrier field also shows lower yields around the field boundary and in the corners but has a much larger unstable area in the high yielding part of the field. The low yielding area in the northern part of the field may be due to the high conifer plantation to the northeast. Twelve Acres field has very small areas of low unstable yield but also shows instability along the relatively high yielding northeastern boundary. This area has produced some of the highest yields of all. It is a low-lying deep soil area next to an open drain. The rest of the field has a distinctive north–south divide between high and low-yielding areas. Figure 10 has been presented in this grid pattern to show the original classification from the data. It may now be sensible to interpret these into areas of similar characteristics depending on the use the maps will be put to.

If the temporal variance threshold is reduced from 1 to 0
8 t ha1 then a much larger area of all the fields would be considered to be unstable; see Figs 9 and 11.

3.6. Predicted results The predicted yield patterns based on the previous spatial trends were compared with the following years actual yield pattern for each grid point in the field and the results are presented in Table 2. The years used in the prediction are shown, together with the coefficient of determination R2 for their respective yield patterns.

4. Discussion The spatial trends that were expected to become more stable over time did not materialise. Instead, the spatial trends over 6 years in all the fields became less

SPATIAL AND TEMPORAL TRENDS IN YIELD MAP DATA

Table 2 Correlation results between predicted and actual yield map patterns Field name

Prediction based on spatial trend years

Actual year

R2

Twelve Acres

1995,96,98

1999

0
4304

1995,96,98,99 1995,96,97 1995,96,97,98

2000 1998 1999

0
2225 0
0294 0
0951

1995,96,97,98,99 1993,95,96 1993,95,96,98

2000 1998 1999

0
3484 0
1631 0
1955

1993,95,96,98,99 1995,96,97 1995,96,97,98

2000 1998 1999

0
3098 0
2613 0
0202

1995,96,97,98,99

2000

0
0765

Onion Field Far Sweetbrier Trent Field 2

R , coefficient of determination.

pronounced than the variability found in individual years. This is a significant reversal of current wisdom and has profound implications on how spatial and temporal variability should be managed. Each year, individual yield maps often show significant spatial variability but they appear to cancel out each other over time. Firstly, this means historical yield map trends cannot be used to extrapolate yield patterns into the future. The best correlation gave a value for R2 of 0
4 but a value of around 0
2 was more normal indicating very little conformity. Secondly, the treatment of fields based entirely on historical yield trends can no longer be supported. The corollary of this is that management should now concentrate more on managing the variability within 1 year. This is supported by the findings of (Geesung et al., 2001) who identified the importance of managing nitrogen, based on available soil moisture and Wood et al. (2003), who proposed the adoption of a canopy management technique that adjusts the nitrogen input to influence the growing crop to achieve a pre-defined optimum canopy at each growth stage. Another implication of these flat trend maps is the explanation of how a part of the field can be high yielding in 1 year and low yielding in another (to cancel out over time). One explanation could be that the soil moisture-holding capacity is in balance with the average rainfall. A particular soil type may have a high moisture-holding capacity. In a dry year, this will be good for the crop and promote a high yield but the opposite could be true in a wet year. This hypothesis could be explored further by correlating yield within a

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selected soil type with the temporal rainfall pattern and the crop growth stage. The assessment of temporal effects has now changed by differentiating between the inter-year offset and the temporal variance map. The first quantifies the major systemic effects on yield (weather, pest diseases); the second shows how the spatial conditions affect the crop differently from year to year. In this way, these two temporal effects are mutually exclusive and can be managed differently. In order to simplify this complex data, the spatial and temporal trend map should be used with the yield histograms. With these two graphs, all of the spatial and temporal effects appear to be defined. Different class boundaries could be chosen according to the user needs. Of all of the variability measured and analysed in this paper, the most significant is the inter-year offset and the spatial variability in the individual yield map, both factors point to managing the variability within each growing season. 5. Conclusions Assessment of temporal stability has two components. The first one being the inter-year offset characterised by the median of the yield, and the second being the temporal variance map, showing the spatial changes over time. A suggested modified standard deviation formula is proposed called the temporal standard deviation. Significant spatial variability is evident in most individual yield maps, which were expected to stabilise into areas of consistent trends after a few years. This can now be seen as untrue as the trend maps become more homogenous over time. If this is correct, as it appears to be, then the implications are far reaching. (1) Inter-year variability can have the greatest impact on overall yield. (2) Spatial variability within each year is significant. (3) Most spatial variability cancels out over time. (4) Yield map trends cannot predict the following year’s yield. (5) The growing crop should therefore be managed according to its current needs. (6) The spatial and temporal trend map can help identify homogenous management zones.

Acknowledgements We would like to thank the Home Grown Cereals Authority for their support in this work as well as ‘The Nordic Rector’s Conference’ for the travel award to Spyros Fountas to travel to Denmark.

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References Blackmore B S (2000). The interpretation of trends from multiple yield maps. Computers and Electronics in Agriculture, 26(1), 37–51 Blackmore B S; Moore M R (1999). Remedial correction of yield map data. Precision Agriculture Journal, 1, 53–66 Earl R; Taylor J C; Wood G A; Bradley I; James I T; Waine T; Welsh J P; Godwin R J; Knight S M (2003). Soil factors and their influence on within-field crop variability part I: field observation of soil variation. Biosystems Engineering (Special Issue on Precision Agriculture), 84(4), doi: 10.1016/S1537-5110(03)00004-7, this issue Fraisse C W; Sudduth K; Kitchen N R; Fridgen J J (1999). Use of unsupervised clustering algorithms for delineating withinfield management zones. ASAE, St. Joseph, MI, USA Geesung D; Gutser R; Schmidhalter U (2001). Importance of spatial and temporal soil water variability for nitrogen management decisions. In: 3rd European Conference on Precision Agriculture (Grenier G; Blackmore B S, eds), pp 659–664. Agro Montpellier, Montpellier Lark R M; Stafford J V (1996a). Classification as a first step in the interpretation of temporal and spatial variability of crop yield. Aspects of Applied Biology, 46, 139–142 Lark R M; Stafford J V (1996b). Consistency and change in spatial variability of crop yield over successive seasons: methods of data analysis.In: 3rd International Conference on Precision Agriculture (Robert PC; Rust RH; Larson W E, eds), pp 141–150. ASA, CSSA, SSSA & ASAE, Madison, Wisconsin, USA Larscheid G; Blackmore B S (1996). Interactions between farm managers and information systems with respect to yield mapping. In: 3rd International Conference on Precision Agriculture (Robert P C; Rust R H; Larson W E, eds), pp 1153–1163. ASA, CSSA, SSSA & ASAE McBratney A B; Whelan B M (1999). The null hypothesis of precision agriculture. In: 2nd European Conference on Precision Agriculture (Stafford J V, ed), pp 947–956. Sheffield Academic Press, Sheffield, UK

Moore M R (1998). An investigation into the accuracy of yield maps and their subsequent use in crop management. Unpublished Ph.D. Thesis, Cranfield University at Silsoe Panneton B; Brouillard M (2002). Use of fuzzy mapping to extract management zones from yield maps. AIC 2002. CSAE/SCGR, Mansonville, QC, Canada Panneton B; Brouillard M; Piekutowski T (2001). Integration of yield data from several years into a single map. In: 3rd European Conference on Precision Agriculture (Grenier G; Blackmore B S, eds), pp 73–78. Agro Montpellier, Montpellier Swindell J (1997). Mapping the spatial variability in the yield potential of arable land through GIS analysis of sequential yield maps. In: 1st European Conference on Precision Agriculture (Stafford J V, ed), pp 827–834. BIOS Scientific publishers, Warwick, UK Taylor J C; Wood G A; Earl R; Godwin R J (2003). Soil factors and their influence on within-field crop variability part II: spatial analysis and determination of management zones. Biosystems Engineering (Special Issue on Precision Agriculture), 84(4), doi: 10.1016/S1537-5110(03)00005-9, this issue Welsh J P; Wood G A; Godwin R J; Taylor J C; Earl R; Blackmore B S; Knight S M (2003a). Developing strategies for spatially variable nitrogen application in cereals part I: winter barley. Biosystems Engineering (Special Issue on Precision Agriculture), 84(4), doi: 10.1016/S15375110(03)00002-3, this issue Welsh J P; Wood G A; Godwin R J; Taylor J C; Earl R; Blackmore B S; Knight S M (2003b). Developing strategies for spatially variable nitrogen application in cereals part II: wheat. Biosystems Engineering (Special Issue on Precision Agriculture), 84(4), doi: 10.1016/S1537-5110(03)00003-5, this issue Wood G A; Welsh J P; Godwin R J; Taylor J C; Earl R; Knight S M (2003). Real time measures of canopy size as a basis for spatially varying nitrogen at different seed rates in winter wheat. Biosystems Engineering (Special Issue on Precision Agriculture), 84(4), doi: 10.1016/S1537-5110(03)00006-0, this issue