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Soil nutrient mapping implications using GPS
Computers and electronics in agriculture Computers and Electronics in Agriculture 11 (1994) 37-51
ELSEVIER
Soil nutrient mapping implications using GPS Hans Delcourt *, Josse De B a e r d e m a e k e r Agricultural Engineering Department, Katholieke Universiteit Leuven, Kardinaal Mercierlaan 92, B-3001 Leuven, Belgium Accepted 3 May 1994
Abstract
The application of site-specific crop production systems involves a detailed knowledge of the soil as the main production resource. A detailed soil survey at two experimental fields of 5 ha and 13 ha revealed a considerable spatial variation of the nutrient levels. Three different approaches to define management areas in the field are discussed. The "land register approach", which partitioned the field based on a priori knowledge resulted in a minimal number of soil samples. In the "yield map" approach, it was attempted to define the management areas starting from yield maps of wheat over two seasons. It was concluded that no clear-cut partitioning of the field was possible in this way. A last method, "the detailed soil survey approach", was based on the geographically detailed knowledge of the topsoil nutrient status for the entire field. These approaches were used for the phosphorus management for the two experimental fields. The pattern of P-levels seemed to stay very constant during three years, indicating that an intensive soil survey can be used to define P-management areas valid for several years. The effect of positioning errors during the sampling campaign on the estimation variance of the P-level was simulated. For the first and third case, respectively, the geometry of the a priori defined management areas and the geographical variability of soil nutrients were used to estimate positioning accuracy requirements for the soil samples. Under the assumptions made a position accuracy requirement of 1 m in 95% of the measurements was derived in both approaches. Key words." Soil variability; Yield maps; Geostatistics; Nutrient maps
1. I n t r o d u c t i o n
T h e r e is a m o r e a n d m o r e c o n c e r n that in applying a u n i f o r m prescribed doses of agrochemicals to a whole field, farmers u n d e r - a n d oversupply fertilizer to specific parts in the field. T h e last decade however, new technologies have b e e n * Corresponding author. Fax: 32 (16) 22 74 79. 0168-1699/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved. SSDI 0 1 6 8 - 1 6 9 9 ( 9 4 ) 0 0 0 1 4 - H
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14. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
under development to take into account the spatial variability within fields to finetune field activities to the specific needs of soil and plants at any location in the field. These technologies include sensing of soil properties and crop growth, yield mapping, varying fertilizer application rate and pesticide concentrations on-the-go, information systems at field scale and positioning systems. An intensive field management where the local needs of the crop-soil system are taken into account must rely on a field information system, named in analogy with a geographical information system, in which the collected field specific data are stored and processed as a set of layered data. An important point in the whole system is the geographical reference of all the data to make the superposition of data layers possible. Apart from the data as grain yield and the applied fertilizer doses, which can be measured continuously over the field area during the normal crop production activities, other information such as soil data are collected at discrete points in the field. In the latter case, techniques are needed for the determination of the most appropriate sampling spots in the field and for deriving the soil information at non-sampled locations. The necessity of geographical referenced data involves a positioning system which gives (x, y) coordinates of the field specific data at the time they are collected. Amongst other systems, the Global Positioning System (GPS) which provides a continuous world covering data stream originating from satellites and which can be captured by receivers, is a promising, powerful positioning tool with a wide application range. According to the system configuration a positioning accuracy can be obtained from 1 mm to 100 m, with an exponential relation between the price and the accuracy (Jahns and K6gl, 1992). However, 4-1 mm can only be achieved in static measurements like surveying or geodetic investigations. In the selection of the most appropriate GPS receivers for agricultural purposes, the question of the maximal acceptable positioning error during the different data collection and crop production activities should be answered. Starting from knowledge about the spatial variability of the soil profile development, the top soil nutrients and the yield of winter wheat in these experimental fields, some implications towards the accuracy requirements of a positioning system (e.g. GPS) for making a detailed soil nutrient map of the field will be derived. These nutrient maps should be used for the implementation of the optimal application rate of fertilizing. It is also desired to know if these patterns are the same in different growing seasons and for different observed characteristics. 2. Soil nutrient variability
The variability of soil properties in a field is recognized since a long time by soil scientists and agronomists. Up to now, extension services dealt with field heterogeneity by advising farmers to take composite soil samples consisting of a number of soil cores which were taken from visually uniform looking areas. The analysis of these soil samples yields a mean nutrient level for the field or the area in the field from which the soil sample was taken. In sampling fields this way, micro-variability was removed and a mean fertilizer advise could be formulated.
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
39
Table 1 Coefficients of variation (C.V.) for different soil properties calculated from samples from one field Variable
Number of samples
C.V. (%)
Reference
K+ K+ Na' C.E.C. ~ O.M. b pH pH pH P K+
161 25 25 25 25 25 68 256 256 256
12.6 8-35 10-26 2-6 2-6 1 7.7 7 49/76 18/10
Ndiaye and Yost (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Borgelt et al. (1989) Peck and Melsted (1973) Peck and Melsted (1973) Peck and Melsted (1973)
a C.E.C = cation exchange capacity; b O.M. = organic matter. In a review of soil variability, Beckett and Webster (1971) analysed the variance of measured soil properties and made some conclusions towards the surface area for samples. Table 1 shows coefficients of variation mentioned in the literature by authors whose interests are in the spatial distribution of chemical soil characteristics in cultivated fields. These data are an illustration of what was known since a long time. For spatially variable crop production the interest is not only in the variability itself, but in how these highly variable quantities are distributed over the whole field. The question is if the presence of some spatial pattern in the measured values of soil nutrients and soil properties can be detected and described. Geostatistics are developed for handling in a statistic way observations that are spatially dependent. Geostatistical techniques to describe the spatial structure of nutrients in the topsoil are applied by a rapidly increasing n u m b e r of authors (Burgess and Webster, 1980; Webster and Nortcliff, 1984; Borgelt et al., 1989; Goovaerts et al., 1989; Goovaerts, 1991). Kriging, a spatial interpolation algorithm, is used for generating the data to make contour maps for visualizing the spatial patterns of the considered variable. 3. Materials and methods
During two seasons, data on the spatial variability of soil profiles, topsoil nutrients and the yield of winter wheat were collected from two experimental fields of 13 ha and 5 ha, situated in the loamy and the sandy loamy region of Belgium. The soil profile description and the topsoil sampling were carried out on a 20 m square grid during the winter of 1990. A second sampling campaign was organised during the winter of 1992. From the 20 m sampling grid, five grid cells were then also sampled in a m o r e intensive way on a 5 x 5 m grid. The composite topsoil samples (12 cores of 25 cm length and 10 m m radius taken in a circle of about 2 m radius around each grid node) were analysed for pH, carbon content, phosphorus, potassium, sodium, magnesium and calcium by the Soil Service of Belgium in Heverlee.
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H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
A
I
//
/
///
i 1
i sill (C1)
~n-ge--(a) ~nugget(~) (0,0)
lag
"~
Fig. 1. The semivariogramand its main characteristics.
During the harvest in the summers of 1990 and 1992, yields of winter wheat were measured in a continuous way on a combine harvester equipped with a speed radar, a cutting-width sensor and a grain flow sensor (Vansichen and De Baerdemaeker, 1991). Yields were calculated and averaged over a square area of 100 m 2 around each grid node. Geostatistical concepts were applied for characterizing the spatial structure of the soil nutrients. This can be done by calculating semivariograms for the spatially distributed variables (Journel and Huijbregts, 1989). The semivariance F (h) is defined as the expected value of the squared difference of two observations separated by a distance vector h, called lag: 2y(h) = E {[z(xi) - z(xi + h)] 2 }
(1)
where xi = coordinate vector (x, y) of position i, and z(xi) = value of variable Z ( x ) at xi. Fig. 1 illustrates a typical semivariogram with its main characteristics. The nugget effect characterizes the residual variance that occurs at distances much smaller than the sampling distance. Two observations become spatially independent when they are separated by a lag greater than the range. The semivariance at lags greater than this range levels out to the sill value which equals the a priori variance of Z(x). For a limited number of observations the semivariance can be estimated by: n(h) 1
~_,[z(xi) -z(xi s ( h ) -- 2n(h) i=l
+h)] 2
(2)
where n (h) is the number of observations separated by lag h. In this work the suggestions of Journel and Huijbregts (1989) were followed to visually fit models on the experimental variograms using the GEO-EAS software (England and Sparks, 1987).
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
41
4. Accuracy requirements for positioning the soil samples There is no simple or direct answer to the question of the maximal tolerable error for the positioning of the soil samples. Therefore a distinction is made between different approaches of the site-specific field management. Whatever the proposed approach, management units have to be defined. Such a management unit can be defined as the smallest area in the field which can be managed (fertilized, limed, treated with pesticides, etc.) separately. The minimal length (size along the driving direction) of a management unit will be determined by machinery response characteristics. The minimal width (size perpendicular to the driving direction) is dependent on the minimal working resolution or width of the agricultural machinery. Han and Goering (1992) proposed that the optimum cell size should vary somewhere between an upper limit, equal to the mean correlation distance which is derived from the correlogram and a lower limit mainly determined by the sensor and/or the applicator response time. Several of these management units can be grouped together for a specific treatment. This results in management areas for which the treatment is not changed. Management areas are assumed to be uniform and need at least one composite soil sample for every area defined. The most simple or limiting case of spatially variable field management is that where the whole field is considered as one management area based on its uniformity. at first glance. Positioning accuracy requirements hardly exists and the only demand will be that the composite soil sample is taken somewhere distributed over the field. In this case one can hardly speak about site-specific crop production. In the next section three different approaches to arrive to a division of the field in management areas are discussed and illustrated with the experiences from the measurements described above. Positioning accuracy requirements are estimated. It is assumed that the probability distribution of the location vector given by a positioning system has any bivariate radial symmetric form. The positioning error exy is defined as the 95% probability interval around the real position (x, y). The probability that the real position vector (x, y) will be situated in the interval (x, Y)measured 4- exy is 95%.
4.1. Approach 1: Land register approach Suppose that from a priori knowledge of the field history a certain partitioning in smaller parts is desirable. While taking soil samples the positioning system should offer the certainty to operate into the designated part of the field. The value of exy should guarantee that a sufficient number of soil cores can be taken to result in composite sample representative for the nutrient status of the different parts of the field. Fig. 2 illustrates what an acceptable exy value could be for the field in Assent if it is split up in five management areas as shown. The areas were obtained from historic land register records. For purposes of representativeness soil cores should be taken more or less uniformly over the whole management area. One can state arbitrarily that the
42
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 3 7 - 5 1
Exy I
I
I J
! 0 0m
Fig. 2. Visualisation of the acceptable positioning error in the Assent field split up in four parts. Soil cores should be taken when the position indication is in the shaded area.
accuracy of the used positioning system must allow to move over 90% of the total area for taking the cores. The e r r o r 8xy can than be calculated such that even for the smallest a priori management area within the field there is a 95% confidence that the cores are located in this area. For each management area i this condition is:
0.9Ai = (Li - 2eixy)(Bi - 2eiy)
(3)
where Ai is the area (m2), Bi is the width (m) and Li is the length (m) of area i. The required accuracy for the positioning system is given by min (elxy, eZy . . . . . n E xi y , • . . , E x y ) .
When applied on the 5-ha experimental field at Assent, the above procedure leads to a required accuracy of 88 cm.
4.2. Approach 2: Yield map approach In a second approach, yield maps can be used to define management areas. Schnug et al. (1992) introduced deductive equifertiles as lines which connect points that have an identical or similar productive capacity derived from a yield map. From a yield map in one season, different production areas might be delineated. These yield variations only reflect variations in one year. Low-yielding spots may be sampled and analysed to decide on whether a shortage of nutrients or other factors were limiting for crop yield. On the other hand, higher-yielding spots only indicate that growing conditions were fulfilled during the past season, but they may hide differences in nutrient levels of the soil and the amount of chemical surpluses in the soil. Parts of these spots may have a considerable amount of some nutrients in reserve, where as other parts may need an new dose of fertilizer to satisfy the production requirements for the next season. Combining yield maps over several seasons may reveal areas in the field with a consistent lower or higher yield, indicating a persistent fertility level of the soil. At cereal yield maps of a 16.6 ha field for three consecutive years, made by Demmel et al. (1992) and H. Auernhammer (pers. commun., 1993), similar patterns were vaguely recognizable on the three maps. The authors preferred a cell size of 24 x 24 m for the presentation of the yield maps. This cell size matched the working width
H. Delcourt, 3. De Baerdemaeker/ Computers and Electronics in Agriculture 11 (1994) 37-51
43
Table 2 Yield-correlated variables in blocks from the two experimental fields where the local correlation between the yields of two seasons was greater than 70% Block
Area (m 2)
,Oy90,y92 (%)
Number of observations
Leefdaal 1 2 3 4
3300 2900 2000 4000
61 56 76 66
Assent 1 2 3 4
2000 3900 5500 3200
83 72 66 74
Yield correlated variables Y90
Y92
8 7 6 10
X**, azi** X, Y, pH X*, azi X**, Y, C*
azi* Y, P**, azi, prof X, Na Y*, Z**, slope*
8 16 23 10
X**, P**, K**, Na X**, Y** X**, P*, K* X**, P
X, P**, K, Mg* X** pH**, P*, Ca Y**, Na
X, Y = geographical coordinates, Z = elevation, azi = azimuth, prof = profile, C = carbon content, pH = acidity (KCI), K, Na, P = potassium, sodium, phosphorus level, respectively. The significance level of the correlations with the indicated variables exceeds respectively 10%, 5% (*) or 1% (**).
of large-scaled agricultural machinery and reduced nearly completely the gaps of the maps based on smaller cells, which were caused by a lack of satellite data for the positioning of some locations. However, no management areas were derived from these yield maps. The experience in trying to define management areas based on a sequence of yield maps is summarized below. For both of the described experimental fields, yield maps of winter wheat were made for two non-consecutive seasons which were separated by one year of growing other crops. The yield figures were averaged over 10 x 10 m cells. Pearson's correlation coefficients, p (SAS, 1990), between the yields in 1990 and 1992 per squares of, respectively, 9, 25 and 49 grid cells were calculated after superposition of the two yield maps to detect spots with a similar production pattern during the two years. The calculated correlation coefficients were assigned to the central grid cell of each square area. The correlations for which IPl > 70% were retained for visualisation on the maps in Figs. 3 and 4. These reveal that 37% and 52% of the total area was locally correlated at respectively Leefdaal and Assent. Joining the adjacent grid cells with IPl > 70% some larger blocks were defined (Table 2). Within each of these blocks correlations between the yield of the two seasons and other measured field characteristics were calculated. From Table 2 it can be concluded that in Leefdaal common yield correlated characteristics (printed in bold) were limited to geographical attributes. These observations did not explain yield variations. Probably there exists some yield limiting factors correlated with the same geographical parameters but which were not measured. The phosphorus and the potassium level seemed to be correlated with yield during the two seasons in Assent only. In this case it was clear that for two blocks (1 and 3), the phosphorus status was related to the yield in 1990 and 1992. This conclusion could already be made after the calculation of the correlation
44
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
E
0
0
8
t--t-V A
~= .~
~
.o
xa
i
oo
h.~
Oo
.~
~
~m
>.
X
~.=-
.~
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
45
(a)
(b)
~ ~55~
Yield (kg/m 2)
.-~
_
J
l
-
r
-
-
0.50 0.80 ~
~ff~_z~0 . 6 0 ~ 0.85 .
.
.
.
.
.
__
F [ ~ ; ~ 0.75
_
-
.
i
(c)
1 block 4
p[°n]
block 2
~
<-70
0
~
50 m
> 70
Fig. 4. Maps from the Assent field of the yield of winter wheat in 1990 (top), the yield in 1992 (middle) and the regions in the Assent field where the correlation between the yield in 1990 and 1992 for 3 x 3 grid cells was higher than 70% (bottom).
between the yield and the phosphorus status of the whole field for the 1990 data (p = 66%). The same correlation calculated for 1992 was statistically not significant. In the case of the Leefdaal field no direct conclusions towards the specific m a n a g e m e n t units could be made based on the yield correlation maps.
46
H. Delcourt, J. De Baerdemaeker/ Computers and Electronics in Agriculture 11 (1994) 37-51
For the Assent field one can conclude that the availability of phosphorus for the crop should be taken into account in a site-specific management. Based on the correlation analysis of the 1990 data, management areas could not be clearly delineated. More useful information was derived from a one way analysis of variance model where the partitioning according to the land register parcels was introduced as the explanatory variable in the model. For the 1990 season similar significant differences between the parcels could be recognized for the yield model as well as for the phosphorus model. There seems to exist a close relationship between these variables. In the second season there was a correlation between the yield and the phosphorus level only in blocks 1 and 3 and not over the whole field. However the correlation between P levels in 1990 and 1992 was 83%. Thus, the yield figures in 1992 were at least at some parts in the field limited by other factors than phosphorus. This illustrates the difficulty of making the right management decisions and the need for data over several seasons in a site-specific crop production system. 4.3. A p p r o a c h 3: Detailed soil survey approach
In the previously mentioned approaches, only indirect information was used to define management areas. If a more complete knowledge about the spatial variability of the fertility levels is preferred, the soil samples must be taken in a systematic way over the entire field. Management areas can then immediately be derived from the detailed soil nutrient maps. Burgess et al. (1981) indicated that a rectangular grid is the most convenient and also preferred for practical purposes. The sampling density can be derived from the application of geostatistical techniques after the minimal accuracy of the estimated nutrient level at non-sampled points is predefined. On this basis, first a spherical semivariogram model was calculated in the form y ( h ) = co + c [ 3 h / 2 a - 1 / 2 ( h / a ) 3]
for 0 < h < a
y(h) = co + c
for h > a
(4)
with nugget co = 1.5 (mg/100 g dry soil) 2, sill c = 10 (mg/100 g dry soil) 2 and range a = 45 m. The lag is symbolized by h (m). From this semivariogram the estimation variance of any point can be derived through the application of kriging. This is well described by Journel and Huijbregts (1989). The kriging process results in unbiased estimates of a spatial variable with a minimal and known estimation variance, the kriging-variance 0-2. The estimation variances are maximal at the points which are more distant from their nearest neighbour than any other point. In a rectangular grid, this point coincides with the centre of each cell of a grid. According to Burgess et al. (1981) a graph can be constructed where the maximum estimation variance for punctual kriging, given a square sampling grid, is given as a function of the sample grid spacing. Such a graph is given in Fig. 5 for the phosphorus content in the topsoil of the Leefdaal field. It can be seen that the estimation variance of the central point in a grid cell never decreases below 1.5, the equivalent of a standard error of 1.22 mg P/100 g dry soil.
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture I1 (1994) 37-51
Estimation vanance [(meCloog)]
14
47
i~ -
12
//
10
~
i i
/<
J
2 iJ / 0 I 0
20
40
60
80
100
Gridspacing [m]
Fig. 5. The kriging variance of an estimate of the phosphorus content at the centre of a grid cell in function of the spacing of a square sample grid. Only the four nearest neighbours were used for kriging.
Table 3 Assessment of the topsoil phosphorus level in cropped fields P level (mg/100 g dry soil)
Assessment
<5 5-8 9-11 12-18 19-30 31-50 >50
very low low fairly low normal fairly high high very high
This value is determined by the nugget value co of the semivariogram (Eq. 4) which embraces the variance occurring at distances much less than the sampling interval. Suppose that an acceptable mean estimation error of the phosphorus level is 2 mg/100 g dry soil. This estimation is somehow arbitrarily based on soil fertility levels used by the Soil Service of Belgium (Table 3). From Fig. 5 it can then be derived that a sampling grid of 14 m will be necessary to fulfil this condition. Relative to the accuracy requirements for positioning the soil samples on this 14 m grid, it will be interesting to quantify the penalty of a deteriorated estimation variance related to a position error of a known magnitude. The distribution of the estimation variance of the P level at the central point of a grid cell was calculated for this example through a Monte Carlo simulation where a position error exy was imposed on the coordinates of the four nodes used in the kriging process (Fig. 6). The simulated position of the samples was somewhere within the circles indicated in Fig. 7. Figs. 8 and 9 show how the mean and the standard error of the estimation variance change with increasing position errors for variograms with varying nugget values and ranges. The negligible effect of the position error on the m e a n estimation
48
H. Delcourt, J. De Baerdemaeker I Computers and Electronics in Agriculture 11 (1994) 37-51
frequency
WI
16 14 12 10 8 6 4 2 0
0
2
4
6
8
kriging variance [(mg/lOO g soil)] Fig. 6. The evolution of the frequency distribution of the kriging variance at the centre of a 14 m grid cell when positioning systems with an increasing position error are used. From the outermost distribution to the inner one, position errors are equal to respectively 5 m, 3 m, 2 m, 1 m and 0.5 m.
q
Fig. 7. Simulated positioning error.
position
of the samples
around
the grid
nodes
using
a positioning
system
with
variance seems normal for this simulation. However the uncertainty of the estimated values increases rapidly with an increasing position error, especially for variograms with a small range. In our example a position error equal to 1 m results in a maximum estimation error varying between 1.95 and 2.13 mg/(lOO g dry soil) when samples are taken on a grid of 14 m. In spite of the dense sampling in this example, the estimates are still rather erroneous. Thus, the classification of the sampled points according to the nutrient level classes as they are defined by the Soil Service of Belgium also will inevitably result in misclassified spots. This is especially so in the low P-level regions of the field. As a consequence, some parts of the field will not receive the appropriate fertilizer dose. This error will however be limited to one class used in the fertilizer recommendation. At the Leefdaal field a correlation between the topsoil phosphorus level of 1990 and 1992 was as high as 88%, indicating that the main patterns of phosphorus levels did not change much after two years. A P-availability map can be generated by the
H. Delcourt, J. De Baerdemaeker/ Computers and Electronics in Agriculture 11 (1994) 37-51 mean est.var
10
.
.
.
.
49
.
co =O 8
-
-
-
6
a
=
2 0 m
Co = 3 a=45m Co = 1.5 a=45m
4 .
.
.
.
.
2 0
~_ : : co = 0 a =45m
.......
I /
1
c o = 1.5 a =90m
2 4 position error [m]
J I
6
Fig. 8. E v o l u t i o n o f t h e m e a n v a l u e o f t h e k r i g i n g v a r i a n c e as f u n c t i o n o f t h e p o s i t i o n e r r o r f o r s e m i v a r i o g r a m s w i t h d i f f e r e n t r a n g e s ( a ) a n d n u g g e t v a r i a n c e s (co).
std.error of est vat.
a =20m
1.5
CO=0 Co = 1.5 /~
j j/
"
C0 = 3
a = 45m c o
0.5
-~
a
=
1.5
= 90 inli 1 -
i
0
0
2
4
6
position error [m] Fig. 9. E v o l u t i o n o f t h e s t a n d a r d d e v i a t i o n o f t h e k r i g i n g v a r i a n c e as f u n c t i o n o f t h e p o s i t i o n e r r o r f o r s e m i v a r i o g r a m s w i t h d i f f e r e n t r a n g e s ( a ) a n d n u g g e t v a r i a n c e s (co).
application of kriging. The class boundaries proposed by the Soil Service of Belgium can be used as contour levels. After adjusting the P-level map of the field in function of the machinery restrictions (i.e. the working resolution along the driving direction and perpendicular to it), it can be used as an input for the site-specific P fertilization of this field. Fig. 10 shows a site specific P-fertilization map of the Leefdaal field. In this example, the advised phosphorus doses for every grid node are assigned to cells of 20 × 20 m. S. Conclusions
The introduction of site-specific crop production systems assumes a detailed knowledge of the soil as the main production resource. A detailed soil survey at two experimental fields of 5 ha and 13 ha revealed a considerable spatial variation of the nutrient levels.
50
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51 Y (m) 0
-70
-140
-210
-280 -240
-120
0
120
240
x (m) P-advise [kg P/hal
-
~
45
~
65
105
~
125
~
85
Fig. 10. Site-specific P - f e r t i l i z a t i o n m a p of the s o u t h e r n p a r t o f the L e e f d a a l field.
As a site-specific crop production system is based on dividing the field into different management areas, three different approaches involving increasing efforts for defining them are discussed. The land register approach, which partitioned the field based on a priori knowledge resulted in a minimal number of soil samples. In a second approach, it was attempted to define the management areas starting from wheat yield maps over two seasons. It was concluded that no clear-cut partitioning of the field was possible in this way. Probably yield maps over more seasons will reveal more consistent yield patterns that can be used for soil sampling and partitioning the field. A last method was based on the geographically detailed knowledge of the topsoil nutrient status for the entire field. The pattern of P levels seemed to stay very constant during three years, indicating that an intensive soil survey can be used to define P-management areas valid for several years. The effect of positioning errors during the sampling campaign on the estimation variance of the P level was simulated. For the first and third case respectively the geometry of the a priori defined management areas and the geographical variability of s0il nutrients were used to estimate positioning accuracy requirements for the soil samples. Under the assumptions made here an accuracy requirement of 1 m in 95% of the measurements was derived in both approaches. It should be stated that accuracy requirements may be different for other fields or regions depending on the size and the geometry of the field and the within field variability.
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
51
Acknowledgements W e t h a n k t h e Soil S e r v i c e o f B e l g i u m at H e v e r l e e for t h e analysis o f t h e t o p s o i l samples.
References Beckett, EH.T. and Webster, R., 1971. Soil variability: a review. Soils and Fert., 34: 1-15. Borgelt, S.C., Searcy, S.W., Stout, B.A. and Mulla, D.J., 1989. A method for determining spatially variable liming rates. ASAE paper No. 89-1034, ASAE, MI 49085, USA, 22 pp. Burgess, T.M. and Webster, R., 1980. Optimal interpolation and isarithmic mapping of soil properties, 1. The semi-variogram and punctual kriging. J. Soil Sci., 31: 315-331. Burgess, TM., Webster, R. and McBratney, A.B., 1981. Optimal interpolation and isarithmic mapping of soil properties, IV. Sampling strategy. J. Soil Sci., 32: 643-659. Demmel, M., Muhr, T., Rottmeier, J., v. Perger, E and Auernhammer, H., 1992. Ortung und Ertragsermittlung beim M/ihdrusch in den Erntejahren 1990 und 1991. Tagungsband VDI/MEG Kolloquium Ortung und Navigation landwirtschaftlicher Fahrzeuge, Weihenstephan (D), 5-6 M~irz 1992. Heft 14, pp. 107-122. England, E. and Sparks, A., 1987. Geostatistical environmental assessment software user's guide. EPA 600/4-88/033. US Environmental Protection Agency. Environmental Metering Systems Laboratory, Las Vegas, Nev., 89193-3478. Goovaerts, E, 1991. Etude des relations entre propri6t6s physico-chimiques du sol par la g6ostatistique multivariable. Cahiers de G6ostatistique, Fascicule 1, Compte-rendu des Journ6es de G6ostatistiques 6-7 Juin 199l, Fontainebleau, pp. 247-261. Goovaerts, E, Gerard, G. and Frankart, R., 1989. Etude de la variabilit6 spatiale de quelques propri6t6s chimiques du sol en Fagne de Chimay, Belgique. P6dologie, 39(2): 191-207. Han, S. and Goering, C.E., 1992. A field information system for site-specific crop management. ASAE-Paper No. 923608, 26 pp. Jahns, G. and K6gl, H., 1992. Nutzung der Ortung und Navigation landwirtschaftlicher Fahrzeuge zur Reduzierung des Betriebsmitteleinsatzes - wirtschaftliche Grundsfitze und praktische Anwendung. Tagungsband VDI/MEG Kolloquium Ortung und Navigation landwirtschaftlicher Fahrzeuge, Weihenstephan (D), 5-6 M~irz, Heft 14, pp 17-33. Journel, A.G. and Huijbregts, Ch.J. (1989) Mining Geostatistics. Academic Press, London, 600 pp. Ndiaye, J.P. and Yost, R.S. (1989) Influence of fertilizer application nonuniformity on crop response. Soil Sci. Soc. Am. J., 53: 1872-1878. Peck, TR. and Melsted, W.S. (1974) Field sampling for soil testing. In: L.M. Walsh and J.D. Beaton (Editors), Soil Testing and Plant Analysis. Soil Science Society of America, Madison, Wise., pp. 67-76. Schnug, E., Murphy, D. and Haneklaus, S. (1992) Importance, evaluation and application of equifertiles to CAF (Computer aided farming). Presented VDI/MEG Colloquium Ortung und Navigation Iandwirtschaftlicher Fahrzeuge, Weihenstephan, March 5-6, 1992, 9 pp. Vansichen, R. and De Baerdemaeker, J., 1991. Continuous wheat yield measurement on a combine. Proc. 1991 Symp. on Automated Agriculture for the 21st Century, December 16-17, 1991, Chicago, Ill., pp. 346-355. Webster, R. and Nortcliff, S., 1984. Improved estimation of micro nutrients in hectare plots of the Sonning Series. J. Soil Sci., 35: 667-672.
ELSEVIER
Soil nutrient mapping implications using GPS Hans Delcourt *, Josse De B a e r d e m a e k e r Agricultural Engineering Department, Katholieke Universiteit Leuven, Kardinaal Mercierlaan 92, B-3001 Leuven, Belgium Accepted 3 May 1994
Abstract
The application of site-specific crop production systems involves a detailed knowledge of the soil as the main production resource. A detailed soil survey at two experimental fields of 5 ha and 13 ha revealed a considerable spatial variation of the nutrient levels. Three different approaches to define management areas in the field are discussed. The "land register approach", which partitioned the field based on a priori knowledge resulted in a minimal number of soil samples. In the "yield map" approach, it was attempted to define the management areas starting from yield maps of wheat over two seasons. It was concluded that no clear-cut partitioning of the field was possible in this way. A last method, "the detailed soil survey approach", was based on the geographically detailed knowledge of the topsoil nutrient status for the entire field. These approaches were used for the phosphorus management for the two experimental fields. The pattern of P-levels seemed to stay very constant during three years, indicating that an intensive soil survey can be used to define P-management areas valid for several years. The effect of positioning errors during the sampling campaign on the estimation variance of the P-level was simulated. For the first and third case, respectively, the geometry of the a priori defined management areas and the geographical variability of soil nutrients were used to estimate positioning accuracy requirements for the soil samples. Under the assumptions made a position accuracy requirement of 1 m in 95% of the measurements was derived in both approaches. Key words." Soil variability; Yield maps; Geostatistics; Nutrient maps
1. I n t r o d u c t i o n
T h e r e is a m o r e a n d m o r e c o n c e r n that in applying a u n i f o r m prescribed doses of agrochemicals to a whole field, farmers u n d e r - a n d oversupply fertilizer to specific parts in the field. T h e last decade however, new technologies have b e e n * Corresponding author. Fax: 32 (16) 22 74 79. 0168-1699/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved. SSDI 0 1 6 8 - 1 6 9 9 ( 9 4 ) 0 0 0 1 4 - H
38
14. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
under development to take into account the spatial variability within fields to finetune field activities to the specific needs of soil and plants at any location in the field. These technologies include sensing of soil properties and crop growth, yield mapping, varying fertilizer application rate and pesticide concentrations on-the-go, information systems at field scale and positioning systems. An intensive field management where the local needs of the crop-soil system are taken into account must rely on a field information system, named in analogy with a geographical information system, in which the collected field specific data are stored and processed as a set of layered data. An important point in the whole system is the geographical reference of all the data to make the superposition of data layers possible. Apart from the data as grain yield and the applied fertilizer doses, which can be measured continuously over the field area during the normal crop production activities, other information such as soil data are collected at discrete points in the field. In the latter case, techniques are needed for the determination of the most appropriate sampling spots in the field and for deriving the soil information at non-sampled locations. The necessity of geographical referenced data involves a positioning system which gives (x, y) coordinates of the field specific data at the time they are collected. Amongst other systems, the Global Positioning System (GPS) which provides a continuous world covering data stream originating from satellites and which can be captured by receivers, is a promising, powerful positioning tool with a wide application range. According to the system configuration a positioning accuracy can be obtained from 1 mm to 100 m, with an exponential relation between the price and the accuracy (Jahns and K6gl, 1992). However, 4-1 mm can only be achieved in static measurements like surveying or geodetic investigations. In the selection of the most appropriate GPS receivers for agricultural purposes, the question of the maximal acceptable positioning error during the different data collection and crop production activities should be answered. Starting from knowledge about the spatial variability of the soil profile development, the top soil nutrients and the yield of winter wheat in these experimental fields, some implications towards the accuracy requirements of a positioning system (e.g. GPS) for making a detailed soil nutrient map of the field will be derived. These nutrient maps should be used for the implementation of the optimal application rate of fertilizing. It is also desired to know if these patterns are the same in different growing seasons and for different observed characteristics. 2. Soil nutrient variability
The variability of soil properties in a field is recognized since a long time by soil scientists and agronomists. Up to now, extension services dealt with field heterogeneity by advising farmers to take composite soil samples consisting of a number of soil cores which were taken from visually uniform looking areas. The analysis of these soil samples yields a mean nutrient level for the field or the area in the field from which the soil sample was taken. In sampling fields this way, micro-variability was removed and a mean fertilizer advise could be formulated.
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
39
Table 1 Coefficients of variation (C.V.) for different soil properties calculated from samples from one field Variable
Number of samples
C.V. (%)
Reference
K+ K+ Na' C.E.C. ~ O.M. b pH pH pH P K+
161 25 25 25 25 25 68 256 256 256
12.6 8-35 10-26 2-6 2-6 1 7.7 7 49/76 18/10
Ndiaye and Yost (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Goovaerts et al. (1989) Borgelt et al. (1989) Peck and Melsted (1973) Peck and Melsted (1973) Peck and Melsted (1973)
a C.E.C = cation exchange capacity; b O.M. = organic matter. In a review of soil variability, Beckett and Webster (1971) analysed the variance of measured soil properties and made some conclusions towards the surface area for samples. Table 1 shows coefficients of variation mentioned in the literature by authors whose interests are in the spatial distribution of chemical soil characteristics in cultivated fields. These data are an illustration of what was known since a long time. For spatially variable crop production the interest is not only in the variability itself, but in how these highly variable quantities are distributed over the whole field. The question is if the presence of some spatial pattern in the measured values of soil nutrients and soil properties can be detected and described. Geostatistics are developed for handling in a statistic way observations that are spatially dependent. Geostatistical techniques to describe the spatial structure of nutrients in the topsoil are applied by a rapidly increasing n u m b e r of authors (Burgess and Webster, 1980; Webster and Nortcliff, 1984; Borgelt et al., 1989; Goovaerts et al., 1989; Goovaerts, 1991). Kriging, a spatial interpolation algorithm, is used for generating the data to make contour maps for visualizing the spatial patterns of the considered variable. 3. Materials and methods
During two seasons, data on the spatial variability of soil profiles, topsoil nutrients and the yield of winter wheat were collected from two experimental fields of 13 ha and 5 ha, situated in the loamy and the sandy loamy region of Belgium. The soil profile description and the topsoil sampling were carried out on a 20 m square grid during the winter of 1990. A second sampling campaign was organised during the winter of 1992. From the 20 m sampling grid, five grid cells were then also sampled in a m o r e intensive way on a 5 x 5 m grid. The composite topsoil samples (12 cores of 25 cm length and 10 m m radius taken in a circle of about 2 m radius around each grid node) were analysed for pH, carbon content, phosphorus, potassium, sodium, magnesium and calcium by the Soil Service of Belgium in Heverlee.
40
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
A
I
//
/
///
i 1
i sill (C1)
~n-ge--(a) ~nugget(~) (0,0)
lag
"~
Fig. 1. The semivariogramand its main characteristics.
During the harvest in the summers of 1990 and 1992, yields of winter wheat were measured in a continuous way on a combine harvester equipped with a speed radar, a cutting-width sensor and a grain flow sensor (Vansichen and De Baerdemaeker, 1991). Yields were calculated and averaged over a square area of 100 m 2 around each grid node. Geostatistical concepts were applied for characterizing the spatial structure of the soil nutrients. This can be done by calculating semivariograms for the spatially distributed variables (Journel and Huijbregts, 1989). The semivariance F (h) is defined as the expected value of the squared difference of two observations separated by a distance vector h, called lag: 2y(h) = E {[z(xi) - z(xi + h)] 2 }
(1)
where xi = coordinate vector (x, y) of position i, and z(xi) = value of variable Z ( x ) at xi. Fig. 1 illustrates a typical semivariogram with its main characteristics. The nugget effect characterizes the residual variance that occurs at distances much smaller than the sampling distance. Two observations become spatially independent when they are separated by a lag greater than the range. The semivariance at lags greater than this range levels out to the sill value which equals the a priori variance of Z(x). For a limited number of observations the semivariance can be estimated by: n(h) 1
~_,[z(xi) -z(xi s ( h ) -- 2n(h) i=l
+h)] 2
(2)
where n (h) is the number of observations separated by lag h. In this work the suggestions of Journel and Huijbregts (1989) were followed to visually fit models on the experimental variograms using the GEO-EAS software (England and Sparks, 1987).
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
41
4. Accuracy requirements for positioning the soil samples There is no simple or direct answer to the question of the maximal tolerable error for the positioning of the soil samples. Therefore a distinction is made between different approaches of the site-specific field management. Whatever the proposed approach, management units have to be defined. Such a management unit can be defined as the smallest area in the field which can be managed (fertilized, limed, treated with pesticides, etc.) separately. The minimal length (size along the driving direction) of a management unit will be determined by machinery response characteristics. The minimal width (size perpendicular to the driving direction) is dependent on the minimal working resolution or width of the agricultural machinery. Han and Goering (1992) proposed that the optimum cell size should vary somewhere between an upper limit, equal to the mean correlation distance which is derived from the correlogram and a lower limit mainly determined by the sensor and/or the applicator response time. Several of these management units can be grouped together for a specific treatment. This results in management areas for which the treatment is not changed. Management areas are assumed to be uniform and need at least one composite soil sample for every area defined. The most simple or limiting case of spatially variable field management is that where the whole field is considered as one management area based on its uniformity. at first glance. Positioning accuracy requirements hardly exists and the only demand will be that the composite soil sample is taken somewhere distributed over the field. In this case one can hardly speak about site-specific crop production. In the next section three different approaches to arrive to a division of the field in management areas are discussed and illustrated with the experiences from the measurements described above. Positioning accuracy requirements are estimated. It is assumed that the probability distribution of the location vector given by a positioning system has any bivariate radial symmetric form. The positioning error exy is defined as the 95% probability interval around the real position (x, y). The probability that the real position vector (x, y) will be situated in the interval (x, Y)measured 4- exy is 95%.
4.1. Approach 1: Land register approach Suppose that from a priori knowledge of the field history a certain partitioning in smaller parts is desirable. While taking soil samples the positioning system should offer the certainty to operate into the designated part of the field. The value of exy should guarantee that a sufficient number of soil cores can be taken to result in composite sample representative for the nutrient status of the different parts of the field. Fig. 2 illustrates what an acceptable exy value could be for the field in Assent if it is split up in five management areas as shown. The areas were obtained from historic land register records. For purposes of representativeness soil cores should be taken more or less uniformly over the whole management area. One can state arbitrarily that the
42
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 3 7 - 5 1
Exy I
I
I J
! 0 0m
Fig. 2. Visualisation of the acceptable positioning error in the Assent field split up in four parts. Soil cores should be taken when the position indication is in the shaded area.
accuracy of the used positioning system must allow to move over 90% of the total area for taking the cores. The e r r o r 8xy can than be calculated such that even for the smallest a priori management area within the field there is a 95% confidence that the cores are located in this area. For each management area i this condition is:
0.9Ai = (Li - 2eixy)(Bi - 2eiy)
(3)
where Ai is the area (m2), Bi is the width (m) and Li is the length (m) of area i. The required accuracy for the positioning system is given by min (elxy, eZy . . . . . n E xi y , • . . , E x y ) .
When applied on the 5-ha experimental field at Assent, the above procedure leads to a required accuracy of 88 cm.
4.2. Approach 2: Yield map approach In a second approach, yield maps can be used to define management areas. Schnug et al. (1992) introduced deductive equifertiles as lines which connect points that have an identical or similar productive capacity derived from a yield map. From a yield map in one season, different production areas might be delineated. These yield variations only reflect variations in one year. Low-yielding spots may be sampled and analysed to decide on whether a shortage of nutrients or other factors were limiting for crop yield. On the other hand, higher-yielding spots only indicate that growing conditions were fulfilled during the past season, but they may hide differences in nutrient levels of the soil and the amount of chemical surpluses in the soil. Parts of these spots may have a considerable amount of some nutrients in reserve, where as other parts may need an new dose of fertilizer to satisfy the production requirements for the next season. Combining yield maps over several seasons may reveal areas in the field with a consistent lower or higher yield, indicating a persistent fertility level of the soil. At cereal yield maps of a 16.6 ha field for three consecutive years, made by Demmel et al. (1992) and H. Auernhammer (pers. commun., 1993), similar patterns were vaguely recognizable on the three maps. The authors preferred a cell size of 24 x 24 m for the presentation of the yield maps. This cell size matched the working width
H. Delcourt, 3. De Baerdemaeker/ Computers and Electronics in Agriculture 11 (1994) 37-51
43
Table 2 Yield-correlated variables in blocks from the two experimental fields where the local correlation between the yields of two seasons was greater than 70% Block
Area (m 2)
,Oy90,y92 (%)
Number of observations
Leefdaal 1 2 3 4
3300 2900 2000 4000
61 56 76 66
Assent 1 2 3 4
2000 3900 5500 3200
83 72 66 74
Yield correlated variables Y90
Y92
8 7 6 10
X**, azi** X, Y, pH X*, azi X**, Y, C*
azi* Y, P**, azi, prof X, Na Y*, Z**, slope*
8 16 23 10
X**, P**, K**, Na X**, Y** X**, P*, K* X**, P
X, P**, K, Mg* X** pH**, P*, Ca Y**, Na
X, Y = geographical coordinates, Z = elevation, azi = azimuth, prof = profile, C = carbon content, pH = acidity (KCI), K, Na, P = potassium, sodium, phosphorus level, respectively. The significance level of the correlations with the indicated variables exceeds respectively 10%, 5% (*) or 1% (**).
of large-scaled agricultural machinery and reduced nearly completely the gaps of the maps based on smaller cells, which were caused by a lack of satellite data for the positioning of some locations. However, no management areas were derived from these yield maps. The experience in trying to define management areas based on a sequence of yield maps is summarized below. For both of the described experimental fields, yield maps of winter wheat were made for two non-consecutive seasons which were separated by one year of growing other crops. The yield figures were averaged over 10 x 10 m cells. Pearson's correlation coefficients, p (SAS, 1990), between the yields in 1990 and 1992 per squares of, respectively, 9, 25 and 49 grid cells were calculated after superposition of the two yield maps to detect spots with a similar production pattern during the two years. The calculated correlation coefficients were assigned to the central grid cell of each square area. The correlations for which IPl > 70% were retained for visualisation on the maps in Figs. 3 and 4. These reveal that 37% and 52% of the total area was locally correlated at respectively Leefdaal and Assent. Joining the adjacent grid cells with IPl > 70% some larger blocks were defined (Table 2). Within each of these blocks correlations between the yield of the two seasons and other measured field characteristics were calculated. From Table 2 it can be concluded that in Leefdaal common yield correlated characteristics (printed in bold) were limited to geographical attributes. These observations did not explain yield variations. Probably there exists some yield limiting factors correlated with the same geographical parameters but which were not measured. The phosphorus and the potassium level seemed to be correlated with yield during the two seasons in Assent only. In this case it was clear that for two blocks (1 and 3), the phosphorus status was related to the yield in 1990 and 1992. This conclusion could already be made after the calculation of the correlation
44
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
E
0
0
8
t--t-V A
~= .~
~
.o
xa
i
oo
h.~
Oo
.~
~
~m
>.
X
~.=-
.~
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
45
(a)
(b)
~ ~55~
Yield (kg/m 2)
.-~
_
J
l
-
r
-
-
0.50 0.80 ~
~ff~_z~0 . 6 0 ~ 0.85 .
.
.
.
.
.
__
F [ ~ ; ~ 0.75
_
-
.
i
(c)
1 block 4
p[°n]
block 2
~
<-70
0
~
50 m
> 70
Fig. 4. Maps from the Assent field of the yield of winter wheat in 1990 (top), the yield in 1992 (middle) and the regions in the Assent field where the correlation between the yield in 1990 and 1992 for 3 x 3 grid cells was higher than 70% (bottom).
between the yield and the phosphorus status of the whole field for the 1990 data (p = 66%). The same correlation calculated for 1992 was statistically not significant. In the case of the Leefdaal field no direct conclusions towards the specific m a n a g e m e n t units could be made based on the yield correlation maps.
46
H. Delcourt, J. De Baerdemaeker/ Computers and Electronics in Agriculture 11 (1994) 37-51
For the Assent field one can conclude that the availability of phosphorus for the crop should be taken into account in a site-specific management. Based on the correlation analysis of the 1990 data, management areas could not be clearly delineated. More useful information was derived from a one way analysis of variance model where the partitioning according to the land register parcels was introduced as the explanatory variable in the model. For the 1990 season similar significant differences between the parcels could be recognized for the yield model as well as for the phosphorus model. There seems to exist a close relationship between these variables. In the second season there was a correlation between the yield and the phosphorus level only in blocks 1 and 3 and not over the whole field. However the correlation between P levels in 1990 and 1992 was 83%. Thus, the yield figures in 1992 were at least at some parts in the field limited by other factors than phosphorus. This illustrates the difficulty of making the right management decisions and the need for data over several seasons in a site-specific crop production system. 4.3. A p p r o a c h 3: Detailed soil survey approach
In the previously mentioned approaches, only indirect information was used to define management areas. If a more complete knowledge about the spatial variability of the fertility levels is preferred, the soil samples must be taken in a systematic way over the entire field. Management areas can then immediately be derived from the detailed soil nutrient maps. Burgess et al. (1981) indicated that a rectangular grid is the most convenient and also preferred for practical purposes. The sampling density can be derived from the application of geostatistical techniques after the minimal accuracy of the estimated nutrient level at non-sampled points is predefined. On this basis, first a spherical semivariogram model was calculated in the form y ( h ) = co + c [ 3 h / 2 a - 1 / 2 ( h / a ) 3]
for 0 < h < a
y(h) = co + c
for h > a
(4)
with nugget co = 1.5 (mg/100 g dry soil) 2, sill c = 10 (mg/100 g dry soil) 2 and range a = 45 m. The lag is symbolized by h (m). From this semivariogram the estimation variance of any point can be derived through the application of kriging. This is well described by Journel and Huijbregts (1989). The kriging process results in unbiased estimates of a spatial variable with a minimal and known estimation variance, the kriging-variance 0-2. The estimation variances are maximal at the points which are more distant from their nearest neighbour than any other point. In a rectangular grid, this point coincides with the centre of each cell of a grid. According to Burgess et al. (1981) a graph can be constructed where the maximum estimation variance for punctual kriging, given a square sampling grid, is given as a function of the sample grid spacing. Such a graph is given in Fig. 5 for the phosphorus content in the topsoil of the Leefdaal field. It can be seen that the estimation variance of the central point in a grid cell never decreases below 1.5, the equivalent of a standard error of 1.22 mg P/100 g dry soil.
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture I1 (1994) 37-51
Estimation vanance [(meCloog)]
14
47
i~ -
12
//
10
~
i i
/<
J
2 iJ / 0 I 0
20
40
60
80
100
Gridspacing [m]
Fig. 5. The kriging variance of an estimate of the phosphorus content at the centre of a grid cell in function of the spacing of a square sample grid. Only the four nearest neighbours were used for kriging.
Table 3 Assessment of the topsoil phosphorus level in cropped fields P level (mg/100 g dry soil)
Assessment
<5 5-8 9-11 12-18 19-30 31-50 >50
very low low fairly low normal fairly high high very high
This value is determined by the nugget value co of the semivariogram (Eq. 4) which embraces the variance occurring at distances much less than the sampling interval. Suppose that an acceptable mean estimation error of the phosphorus level is 2 mg/100 g dry soil. This estimation is somehow arbitrarily based on soil fertility levels used by the Soil Service of Belgium (Table 3). From Fig. 5 it can then be derived that a sampling grid of 14 m will be necessary to fulfil this condition. Relative to the accuracy requirements for positioning the soil samples on this 14 m grid, it will be interesting to quantify the penalty of a deteriorated estimation variance related to a position error of a known magnitude. The distribution of the estimation variance of the P level at the central point of a grid cell was calculated for this example through a Monte Carlo simulation where a position error exy was imposed on the coordinates of the four nodes used in the kriging process (Fig. 6). The simulated position of the samples was somewhere within the circles indicated in Fig. 7. Figs. 8 and 9 show how the mean and the standard error of the estimation variance change with increasing position errors for variograms with varying nugget values and ranges. The negligible effect of the position error on the m e a n estimation
48
H. Delcourt, J. De Baerdemaeker I Computers and Electronics in Agriculture 11 (1994) 37-51
frequency
WI
16 14 12 10 8 6 4 2 0
0
2
4
6
8
kriging variance [(mg/lOO g soil)] Fig. 6. The evolution of the frequency distribution of the kriging variance at the centre of a 14 m grid cell when positioning systems with an increasing position error are used. From the outermost distribution to the inner one, position errors are equal to respectively 5 m, 3 m, 2 m, 1 m and 0.5 m.
q
Fig. 7. Simulated positioning error.
position
of the samples
around
the grid
nodes
using
a positioning
system
with
variance seems normal for this simulation. However the uncertainty of the estimated values increases rapidly with an increasing position error, especially for variograms with a small range. In our example a position error equal to 1 m results in a maximum estimation error varying between 1.95 and 2.13 mg/(lOO g dry soil) when samples are taken on a grid of 14 m. In spite of the dense sampling in this example, the estimates are still rather erroneous. Thus, the classification of the sampled points according to the nutrient level classes as they are defined by the Soil Service of Belgium also will inevitably result in misclassified spots. This is especially so in the low P-level regions of the field. As a consequence, some parts of the field will not receive the appropriate fertilizer dose. This error will however be limited to one class used in the fertilizer recommendation. At the Leefdaal field a correlation between the topsoil phosphorus level of 1990 and 1992 was as high as 88%, indicating that the main patterns of phosphorus levels did not change much after two years. A P-availability map can be generated by the
H. Delcourt, J. De Baerdemaeker/ Computers and Electronics in Agriculture 11 (1994) 37-51 mean est.var
10
.
.
.
.
49
.
co =O 8
-
-
-
6
a
=
2 0 m
Co = 3 a=45m Co = 1.5 a=45m
4 .
.
.
.
.
2 0
~_ : : co = 0 a =45m
.......
I /
1
c o = 1.5 a =90m
2 4 position error [m]
J I
6
Fig. 8. E v o l u t i o n o f t h e m e a n v a l u e o f t h e k r i g i n g v a r i a n c e as f u n c t i o n o f t h e p o s i t i o n e r r o r f o r s e m i v a r i o g r a m s w i t h d i f f e r e n t r a n g e s ( a ) a n d n u g g e t v a r i a n c e s (co).
std.error of est vat.
a =20m
1.5
CO=0 Co = 1.5 /~
j j/
"
C0 = 3
a = 45m c o
0.5
-~
a
=
1.5
= 90 inli 1 -
i
0
0
2
4
6
position error [m] Fig. 9. E v o l u t i o n o f t h e s t a n d a r d d e v i a t i o n o f t h e k r i g i n g v a r i a n c e as f u n c t i o n o f t h e p o s i t i o n e r r o r f o r s e m i v a r i o g r a m s w i t h d i f f e r e n t r a n g e s ( a ) a n d n u g g e t v a r i a n c e s (co).
application of kriging. The class boundaries proposed by the Soil Service of Belgium can be used as contour levels. After adjusting the P-level map of the field in function of the machinery restrictions (i.e. the working resolution along the driving direction and perpendicular to it), it can be used as an input for the site-specific P fertilization of this field. Fig. 10 shows a site specific P-fertilization map of the Leefdaal field. In this example, the advised phosphorus doses for every grid node are assigned to cells of 20 × 20 m. S. Conclusions
The introduction of site-specific crop production systems assumes a detailed knowledge of the soil as the main production resource. A detailed soil survey at two experimental fields of 5 ha and 13 ha revealed a considerable spatial variation of the nutrient levels.
50
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51 Y (m) 0
-70
-140
-210
-280 -240
-120
0
120
240
x (m) P-advise [kg P/hal
-
~
45
~
65
105
~
125
~
85
Fig. 10. Site-specific P - f e r t i l i z a t i o n m a p of the s o u t h e r n p a r t o f the L e e f d a a l field.
As a site-specific crop production system is based on dividing the field into different management areas, three different approaches involving increasing efforts for defining them are discussed. The land register approach, which partitioned the field based on a priori knowledge resulted in a minimal number of soil samples. In a second approach, it was attempted to define the management areas starting from wheat yield maps over two seasons. It was concluded that no clear-cut partitioning of the field was possible in this way. Probably yield maps over more seasons will reveal more consistent yield patterns that can be used for soil sampling and partitioning the field. A last method was based on the geographically detailed knowledge of the topsoil nutrient status for the entire field. The pattern of P levels seemed to stay very constant during three years, indicating that an intensive soil survey can be used to define P-management areas valid for several years. The effect of positioning errors during the sampling campaign on the estimation variance of the P level was simulated. For the first and third case respectively the geometry of the a priori defined management areas and the geographical variability of s0il nutrients were used to estimate positioning accuracy requirements for the soil samples. Under the assumptions made here an accuracy requirement of 1 m in 95% of the measurements was derived in both approaches. It should be stated that accuracy requirements may be different for other fields or regions depending on the size and the geometry of the field and the within field variability.
H. Delcourt, J. De Baerdemaeker / Computers and Electronics in Agriculture 11 (1994) 37-51
51
Acknowledgements W e t h a n k t h e Soil S e r v i c e o f B e l g i u m at H e v e r l e e for t h e analysis o f t h e t o p s o i l samples.
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