Ch3-pre yield analysis - ses.library.usyd.edu.au

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Chapter 3 : Preliminary yield data analysis – quantification and comparisons of yield variation across space and time

3.1 Introduction Comparing a spatial dimension with a temporal dimension is a difficult task. In the context of growing crops, PA and crop growth simulation modelling two important questions are:

- What is the value of managing spatial variation in the light of temporal variation? - How might one judge whether a crop simulation model is predicting appropriate

amounts of spatial and temporal variation in crop yield? In order to answer both these questions, a sound understanding of spatio-temporal yield variation is required. In other words, it is necessary to understand how the structure and magnitude of spatial yield variation compares to the structure and magnitude of temporal yield variation. It is worthwhile briefly reviewing the literature that has approached spatial, temporal and particularly spatio-temporal variation of crop yield. It is apparent that the latter question has not been explicitly addressed in any of the spatio-temporal yield variation literature. In terms of spatial variation alone, quite a lot of research on this topic has been thoroughly documented. Much of this research has had a PA flavour. Fairfield Smith (1938) has been recognised as one of the earliest contributors to documenting spatial variability of crop yields. Smith provided a fractal model of yield variation. Many recent examples of research into spatial crop yield variation using similar analysis tools and including geostatistics can be found in the PA literature. Coefficients of variation (CV) have also been a popular approach to quantifying yield variation. Many examples of this approach exist, one recent example (from many) is Kravchenko et al., (2005). Temporal variability on its own (particularly within a PA context) has not been as popular a research topic. The major thrust of the research has focussed on regional yield averages using a combination of fractal analysis and geostatistical analysis for studies through time. Fractal analysis has been popular for temporal yield variability analysis. Eghball and Power (1995) used fractal analysis to compare temporal yield variability between ten crops in the US over a long term period. They calculated semi-variance for average yearly yields for lags up to 45 years. The fractal dimension for each crop was estimated from log-log plots of the semi-variance versus lag. The fractal dimensions were considered indicators of the importance of short term (or year-to-year) temporal variation.

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Further fractal analysis using a similar methodology was undertaken by Eghball et al. (1995) for a long-term manure and fertilizer experiment. They concluded that short term corn yield variation was mostly influenced by variable environmental conditions and that management practices did not significantly alter these impacts. Valdez-Cepeda and Olivares-Saenz (1998) undertook similar work in Mexico. The question about comparing spatial with temporal yield variation has been directly addressed to different extents in the literature. Some examples include McBratney and Whelan (1999), Eghball and Varvel (1997) and Scherpers et al., (2004). Theory about quantitative spatio-temporal analysis can also be found in the literature. Kyriakidis and Journel (1999) published a review of geostatistical space-time models. They review examples of two different conceptual approaches to modelling spatiotemporal distributions. The first approach is to consider a single random function that can be decomposed into a trend component and a stationary component. The second approach considers multiple random functions of time series. As well, McBratney et al., (1997) provide a summary of the development of space-time models. These authors outline a joint spatial and temporal variogram where semi-variance is a function of a spatial lag and a temporal lag. McBratney et al. (1997) also reports some spatio-temporal analysis. With reference to a couple of long-term Rothamsted experiments variance is calculated for a series of time and a series of spatial lags. These results are directly compared and it is found that temporal variation is large relative to spatial variation. This conclusion is reached also when comparing two years of wheat yield for two fields in NSW, Australia. In this case analysis involved creating yield maps and maps of yield difference between each year. It was noted that on one of the fields the different yield responses on different parts of the fields suggest some basis for spatial management. This work is concluded with the assertion that for successful application of PA, temporal variation in crop yield relative to spatial variation needs to be seriously researched. Eghball and Varvel (1997) reported a study similar in methodology to the fractal analysis of temporal variability described above (eg. Eghball and Power, 1995). In this case the authors also addressed spatial variability by using a randomised complete block design and testing whether the slopes of semi-variance versus lag(year) were different across blocks. They found that no spatial variability was reflected in the grain yields because the temporal variability was completely dominant. This study highlights the importance of this result from the perspective of site specific management practices. Scherpers et al. (2004) delineated some management zones across an irrigated field in NE, USA. They used soil brightness, elevation and ECa to derive the management zones. They found that their management zones reflected the spatial yield patterns for three out of the five years of yield data analysed. This study acknowledges that temporal changes in yield patterns can seriously undermine the value of the management zone approach to spatial management of yield variation even under irrigation.

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A general feeling from these publications is that temporal variation is large and significant and requires further research. This is not necessarily reflected in the volume of literature focussed on quantifying temporal variation of crop yields compared to spatial variation. There are, however, an increasing number of publications focussed on spatio-temporal yield variability. Some of these articles have a PA focus while there are also a significant number without a PA focus. A rough distinction can be made between those studies dominated by qualitative findings and those that provide some quantitative conclusions. Bakhsh et al. (2000) and Jaynes and Colvin (1997) report similar research findings based on different fields in Iowa under corn-soybean rotations. Multiple years of yield data were analysed (three years and six years respectively). They divided the structure of yield variability into large scale deterministic and small scale stochastic. A consistent conclusion from these studies was the instability of yield data between years. It was also noted that an inadequate number of years were studied to enable comprehensive understanding of the yield variability. Additionally, Jaynes and Colvin (1997) reported some relationships between climate and spatial structure. For example, they found significant correlation between variogram sill values and growing season precipitation. Andales et al., (2007) explored the idea that patterns of yield and soil water along a catena are temporally stable. For a semi-arid catena in Colorado, USA, the authors found that relationships between landscape position and yield were temporally stable. However, they reported that it is more difficult to explain the inter-annual yield variation using soil water contents at critical grain filling periods. Lamb et al. (1997) also approach their analysis from a yield stability perspective. The major research question asked by these authors is whether grain yield from more than one year can be used to predict grain yield in following years. Their study site was a field in MN, USA under five years of continuous corn between 1990 and 1995. Yield data from 1991 to 1995 (inclusively) was collected. Rank correlations were used to determine the stability of corn yield. An important assertion made by these authors was that the effect of year on grain yield was approximately 100 times greater than the location effect. The finding of unstable yield culminated in the conclusion that four years of yield data is not enough to determine future yield goals. Joernsgaard and Halmoe (2003) also attempted to use a previous years yield map to predict the next years yield map (pairing points in space). Using 82 fields across the UK and Denmark, the average r2 value was 0.27 suggesting that temporal variation is large. They found that model performance was best for small fields using the same crops and years with similar yield levels. The number of years between crops used did not make any difference. A significant amount of this work has been framed as a search for stability in yield patterns across multiple years. As well there has been a considerable amount of research effort invested in the idea of using previous years of yield maps to predict following years yield patterns. Most of the findings were that yield patterns across two to five years are

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unstable and that inter-seasonal factors impact on the magnitude and structure of spatial variability. A common result has also been that predicting yield from previous yield maps is a problematic task due to temporal variation. It is interesting to note that the research that was undertaken along a catena rather than a whole field reported stability in yield patterns. Explicit quantitative conclusions are sparse, particularly directly comparing temporal and spatial variability. It is apparent that there is room to increase understanding about quantitative spatio-temporal crop yield variation from a PA perspective and also from a crop simulation modelling perspective. Consequently, the primary aim of this chapter is to investigate existing and new approaches quantifying the relationship between spatial and temporal variability in yield. This aim is framed within the discussion about the value of using PA to manage spatial variation in the light of temporal variation. The other important discussion point that this chapter will address is a perspective from which to validate the ability of crop growth simulation models to simulate spatial and temporal yield variation.

3.2 Study sites and data In total seven fields were selected from a number of farms across NSW, Victoria (Riverine) and South Australia where multiple years of wheat yield data exist. For the purposes of this study, three years of yield data was considered the minimum required volume. The farms, the locations and the fields used are outlined in Table 3.1. These seven study fields ensure variety between soil types and climatic conditions (in both space and time). The locations of these fields are also aligned with the three study sites outlined in the preceding chapter. Different volumes of yield data were available from each study site. This is due to different timing in uptake of yield monitoring and also different rotations and management decisions. Wheat yield data formed the focus of the data analysis and interpretation. The yield data that was used in this chapter was cleaned and ‘ready-to-use’ prior to this research as the data collection was a consequence of other research activities. Harvester mounted yield monitors were used to collect the yield data resulting in roughly one to two raw measurements every ten metres. The cleaning process involved removal of zero values and extremely high and low values that were out of place within a field. In some cases the operation of un-calibrated multiple harvesters within a single field meant that some raw yield values required adjustment as well. A detailed description of the cleaning process is outlined in Chapter 2. For the bulk of this research the data was analysed in its ‘clean’ form. However, for some of the fields, the data was also analysed in an interpolated form. The data was interpolated using normal block kriging. Details regarding the kriging process can be found in Chapter 2 as well.

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Table 3.1 The fields used for this study, the farm in which they are located, the location of the farms and the number of years of wheat yield data available for each field is displayed. Farm Location Fields used/no. years of data “BrookPark” South Australia ‘Road/3’; ‘Bills/3’ “Burrendah” North NSW ‘Glens/4’ “Clifton Farm” South Australia ‘Blackflat/6’ “Grandview” Riverine ‘12’/3 “Rayville Park” Riverine ‘41’ “Tarnee” North NSW ‘CometB’

3.3 Methods All of the geostatistical analysis was undertaken on an individual field basis. The decision to analyse fields separately is based on the existence of management differences between fields. The analysis can be separated into three different parts depending on which part of the aim is being addressed. Firstly temporal variation alone is addressed. Following this spatial and comparisons between spatial and temporal variation is addressed. Two approaches for comparison of spatial and temporal variation are outlined.

3.3.1 Quantifying temporal variation The kriged data was used for this part of the data analysis. The kriged data allowed for data values from different years to coincide in space. Making yield maps Using the kriged data, yield maps were created in ArcGIS (ESRI, 2002). These maps were observed with the purpose of making comparison in spatial patterns between years. Calculating temporal semi-variance Temporal semi-variance between pairs of years for individual points within a single field was calculated using Equation 3.1. In this equation, �(t) is the semi-variance for t lag in years and t1 and t2 are yield values at the same point in space from different years. This was done for all possible combinations of lags between years, ie. 2002-wheat with 2003-wheat, 2002-wheat with 2004-wheat, 2003-wheat with 2004-wheat, etc. For each unique lag in terms of years involved, the semivariances from each point were averaged for each field resulting in one mean semi-variance per field per lag in time. Semi-variance maps for each pair of years were created. Maps of mean semi-variance were also created. These mean semi-variance values were calculated irrespective of the number of years of yield data for each field. Equation 3.1 Semi-variance calculation

21 2( )

( )2

t ttγ −=

Rank correlations Yield values for each year were ranked within each field. Correlation coefficients were calculated between years using these ranks. These results were tabulated. These

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correlations for the three most recent years were used to calculate eigenvectors. The first two eigenvectors were plotted for each field. Calculating long term temporal semi- variograms (variograms) Five years of yield data is considered inadequate to fit a temporal variogram. This was the maximum amount of data available for any of the fields studied in this work. Consequently, Agricultural Production Simulator Model (APSIM) (Keating et al., 2003) was used to simulate 100 years of data. For a theoretical point in space, 100 years of continuous wheat was simulated using APSIM. Three different theoretical soil profiles were used to simulate yield data. These profiles were intended to represent grain growing scenarios that might occur in north NSW, north-eastern Victoria (Riverine) and South Australia (the locations of the study sites that are the focus of this PhD thesis). The first theoretical soil profile used was classified using the Australian Soil Classification (ASC) as a Grey Vertosol (Isbell, 1996) and the climate data used corresponds to that of Moree (north NSW) between 1906 and 2006. Secondly, a Red Chromosol (Isbell, 1996) was simulated using climate data that corresponds with Yarrawonga (Riverine). Finally, a Calcarosol (Isbell, 1996) was simulated using climate data that corresponds with Crystal Brook (South Australia). Each of these theoretical soils has been taken from APSoil (APSIM soil data base). The soils within this database are regularly updated and the data is designed to enable simulations within APSIM. On this basis one can assume that these simulations are valid. The program Vesper (Minasny et al., 2005) was used to calculate and fit variograms out to 50 years. 150% lag tolerance and 50 lags were used for the calculations. Exponential models were fit to the semi-variograms. Refer to Chapter 2 for further information about calculating variograms. As well as the temporal yield variograms, temporal variograms were calculated and fit using some cumulative rainfall data. Several rainfall variograms were created. The months included in the cumulative rainfall calculations were different for each theoretical soil profile. This decision was based on timing of predominant rainfall at each of the locations. For example, pre-season rainfall is important for winter cropping in northern NSW as opposed to that in the southern states where in-season rainfall is most important. As well, temporal rainfall variograms were fit out to two years using daily rainfall data. In these instances 70 lags and no lag tolerance was used. These long-term yield variograms were considered an indicator of how real data might behave in the light of longer yield data records.

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3.3.2 Comparing spatial variation with temporal variation Two approaches were explored for the simultaneous visualisation of spatial and temporal variation. Space- time semi-variograms (Approach 1) The first approach involved creating a ‘spatio-temporal’ variogram. Initially, spatial variograms were obtained and then a space-time variogram was explored. Again, the software program Vesper was used to calculate variograms out to 500m. 50 lags were used and 100% lag tolerance. Exponential models were fit to the data. As many spatial semi-variograms as years of data for each field were calculated. Following calculation of these spatial variograms, yield data from all available years was combined (by stacking). A variogram as described above was calculated using the combined yield data such that semi-variance was calculated at different space-time lags. The notable difference between this variogram and the former described variograms is that the lags are a combination of metres and years rather than just metres. This approach does not allow identification of the time component in the lag calculation. However, an attempt was made to extract the temporal component from the spatio-temporal variogram. A mean spatial variogram was calculated from the different years for which spatial variograms were calculated. This mean variogram was then subtracted from the spatio-temporal variogram. This calculated difference was plotted along with the mean spatial variogram and the spatio-temporal variogram. The difference variogram is considered a representation of the ‘temporal component’ contributing to the spatio-temporal variogram. Pseudo cross variograms (approach 2) The second approach involved calculating pseudo (or non-co-located) cross-variograms. The pseudo cross variogram can be described as the expected squared difference between two random variables at two different points (Papritz et al., 1993). A key property of the pseudo cross variogram is that measures of the variables do not have to be at the same point in space (Papritz et al., 1993). Equation 3.2 provides a centred estimator (

,

21

P Pa

γ ) for the pseudo cross variogram (Papritz et al., 1993). In this equation, z1 and z2 are two random processes and h separates two places x and x+h. Applications of the pseudo cross variogram in the literature refer to its use for non-co-located cokriging. Lark (2002) provides an example of estimating temporal change of soil moisture content using cokriging. Equation 3.2 General estimator for the pseudo cross variogram

{ } { }2,1

,

21

2( )

2 2 1 112,1

1( ) ( ) ( )

2 ( )P Pa

N h

i ii

h z x h z z x zN h

γ=

� �= + − − −� ��

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Pseudo cross variograms were calculated using some in-house software. These cross variograms were calculated for each combination of years for each field as described above for the temporal semivariance calculations. The difference between the years from which each cross variogram was calculated was noted and if there were multiple cross variograms for each year difference, these were averaged. Variograms calculated for each year individually were considered to have a corresponding year lag of zero (an average variogram for lag(0) was also calculated). For each field, this meant that each co-variance calculation corresponded with a distance in metres and a distance in years. Contour plots of co-variance were drawn with metres on the x-axis and years on the y-axis.

3.4 Results

3.4.1 Yield maps and temporal semi-variance Maps from two of the seven fields are displayed in these results. These two fields behave quite differently in terms of spatial and temporal yield variation. Figures 3.1 to 3.3 illustrate three years of wheat yield from ‘Bills’ field. Figures 3.4 to 3.6 are the semi-variance maps calculated using the three years of yield data. There is a separate map for each pair of years. Similarly Figures 3.7 to 3.10 illustrates four years of wheat yield from ‘Road’ field and Figures 3.11 to 3.16 demonstrate the semi-variance maps calculated from these years of yield data. Figure 3.17 and Figure 3.18 display mean semi-variance maps calculated using all of the available yield data for ‘Bills’ and ‘Road’ respectively. Table 3.2, 3.3 and 3.4 display the mean temporal semi-variance for fields from northern NSW, South Australia and the Riverine respectively. Different lags in time are displayed for each field as a result of the yield data that was available. Where possible for each field, averages for time lags are also displayed.

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Figure 3.1 Wheat yield from the 2000 season on ‘Bills’ field from “BrookPark”



Figure 3.4 Temporal semivariance between 2000 and 2003 yield from ‘Bills’ field from “BrookPark”



Figure 3.7 Wheat yield from 1999 season on ‘Road’ field from “BrookPark”


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Figure 3.11 Temporal semivariance between 1999 and 2002 yield from ‘Road’ field from “BrookPark”



Figure 3.14 Temporal semivariance between 2002 and 2003 from ‘Road’ field from “BrookPark”



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Figure 3.17 Mean temporal semivariance map for ‘Bills’ field from “BrookPark”

Figure 3.18 Mean temporal semivariance map for ‘Road’ field from “BrookPark”

Table 3.2 Mean temporal semi-variance for wheat from the fields ‘Comet’ and ‘Glens’ located on the farms “Burrendah” and “Tarnee” respectively. Field Years between Lag(years) Semi-variance Comet 1997 and 2000 3 1.21 Comet 1997 and 2003 6 2.35 Comet 1997 and 2004 7 1.72 Comet 2000 and 2003 3 3.52 Comet 2000 and 2004 4 2.84 Comet 2003 and 2004 1 0.53 Comet Mean 3 2.37 Glens 2000 and 2002 2 3.58 Glens 2000 and 2004 4 1.85 Glens 2000 and 2006 6 3.09 Glens 2002 and 2004 2 0.37 Glens 2002 and 2006 4 0.17 Glens 2004 and 2006 2 0.25 Glens Mean 2 1.98 Glens Mean 4 1.01

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Table 3.3 Mean temporal semi-variance for wheat from the fields ‘Bills’ and ‘Road’ located on the farm “BrookPark” and from the fields ‘Blackflat’ located on the farm “Clifton Farm” Field Years between Lag(years) Semi-variance Bills 2000 and 2003 3 0.40 Bills 2000 and 2006 6 0.15 Bills 2003 and 2006 3 0.80 Bills Mean 3 0.60 Road 1999 and 2002 3 0.31 Road 1999 and 2003 4 0.41 Road 1999 and 2005 6 1.61 Road 2002 and 2003 1 1.29 Road 2002 and 2005 3 3.06 Road 2003 and 2005 2 0.46 Road Mean 3 1.64 Black Flat 1998 and 1999 1 0.43 Black Flat 1998 and 2000 2 0.73 Black Flat 1998 and 2001 3 0.42 Black Flat 1998 and 2003 5 0.30 Black Flat 1998 and 2005 7 1.18 Black Flat 1999 and 2000 1 1.57 Black Flat 1999 and 2001 2 0.85 Black Flat 1999 and 2003 4 0.47 Black Flat 1999 and 2005 6 2.29 Black Flat 2000 and 2001 1 0.19 Black Flat 2000 and 2003 3 0.44 Black Flat 2000 and 2005 5 0.17 Black Flat 2001 and 2003 2 0.15 Black Flat 2001 and 2005 4 0.47 Black Flat 2003 and 2005 2 0.81 Black Flat Mean 1 0.73 Black Flat Mean 2 0.63 Black Flat Mean 3 0.43 Black Flat Mean 4 0.47 Black Flat Mean 5 0.23 Table 3.4 Mean temporal semi-variance for wheat from the fields ’12’ and ‘41’ located on the farms “Grandview” and “RayvillePark” respectively. Field Years between Lag(years) Semi-variance 12 2000 and 2002 2 8.26 12 2000 and 2003 3 4.29 12 2002 and 2003 1 1.18 41 1998 and 1999 1 0.39 41 1998 and 2000 2 0.85 41 1998 and 2002 4 0.45 41 1998 and 2005 7 1.35 41 1999 and 2000 1 2.05 41 1999 and 2002 3 0.08 41 1999 and 2005 6 2.72 41 2000 and 2002 2 2.27 41 2000 and 2005 5 0.17 41 2002 and 2005 3 3.02 41 Mean 1 1.22 41 Mean 2 1.56 41 Mean 3 1.55

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3.4.2 Rank correlations and principle component analysis Tables 3.5 to 3.11 are correlation matrices for each of the seven fields based on rankings of each point for each of the years where yield data exists. Figure 3.19 is a plot of the first two eigenvectors calculated from these correlations between three years for each of the fields. It can be seen that field ‘12’ with a negative correlation displayed in Table 3.7 plots negative for the first eigenvector. Table 3.5 Correlation matrix calculated from wheat yield for 'Bills' field from “BrookPark” 2000 2003 2006 2000 1 2003 0.78 1 2006 0.81 0.70 1 Table 3.6 Correlation matrix calculated from wheat yield for ‘Road’ field from “BrookPark” 1999 2002 2003 2005 1999 1 2002 0.69 1 2003 0.49 0.55 1 2005 0.51 0.61 0.40 1 Table 3.7 Correlation matrix calculated from wheat yield for '12' field from “Grandview” 2000 2002 2003 2000 1 2002 0.33 1 2003 0.33 -0.14 1 Table 3.8 Correlation matrix calculated from wheat yield for 'Glens' field from “Burrendah” 2000 2002 2004 2006 2000 1 2002 -0.45 1 2004 -0.03 0.44 1 2006 -0.07 0.49 0.66 1 Table 3.9 Correlation matrix calculated from wheat yield for 'Blackflat' field from “Clifton Farm” 1998 1999 2000 2001 2003 2005 1998 1 1999 0.45 1 2000 0.40 0.05 1 2001 0.13 0.03 0.24 1 2003 0.13 0.35 0.12 0.09 1 2005 0.42 0.25 0.39 0.29 0.33 1 Table 3.10 Correlation matrix calculated from wheat yield for '41' field from “Rayville Park” 1998 1999 2000 2002 2005 1998 1 1999 0.51 1 2000 0.62 0.50 1 2002 0.66 0.53 0.65 1 2005 0.38 0.46 0.51 0.42 1

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Table 3.11 Correlation matrix calculated from wheat yield for 'Comet' field from “Tarnee” 1997 2000 2003 2004 1997 1 2000 0.28 1 2003 0.29 0.67 1 2004 0.27 0.39 0.05 1

eigenvector plot

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Figure 3.19 Eigenvector plot calculated from the correlation matrices displayed in Tables 3.5 to 3.11 Table 3.12 Fitted variogram parameters for simulated wheat yield and annual rainfall for the three theoretical soil types and their corresponding climates

C0 C1 Range C0:C1 C0 C1 Range C0:C1 V e r t o s o l 2.20 2.47 8 0.89 12062 14529 14 0.83 Chromosol 1.40 1.51 9 0.93 10000 10000 10000 1.00

Yield

Calcarosol 1.71 2.24 3 0.76

Rainfall

5501 5795 0 0.95 Table 3.13 Fitted variogram parameters for daily rainfall data for the three representative climates corresponding with the theoretical soil types

C0 C1 Range C0:C1 Vertosol/ Moree 30.4 32.9 41 0.92 Chromosol/ Yarrawonga 18.00 19.6 12 0.92

Daily rainfall

Calcarosol/ CrystalBrook 9. 5 10.3 33 0.92

3.4.3 Long-term temporal variograms Figures 3.20 to 3.25 illustrate the long-term temporal semi-variograms for each of the three theoretical soils. For each location a yield variogram and a rainfall variogram are displayed. Table 3.12 displays the variogram parameters for all the yield and annual rainfall variograms. Table 3.13 displays the variogram parameters for those calculated from the daily rainfall data. It is worth observing the cyclical nature apparent in most of the variograms, particularly the rainfall variograms. The Moree rainfall variogram (Figure 3.21) displays a period of approximately eight years. The Yarrowonga variogram (Figure 3.23) displays a period of approximately 15 years. The Crystal Brook variogram (Figure 3.24) does not appear to be cyclic. In the case of the former two locations, the yield variograms show a similar (however dampened) cyclicity to the corresponding rainfall variograms.

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1.6

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2.12.22.32.42.52.62.72.82.9

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lag (years) Figure 3.25 Temporal rainfall variogram for the Cyrstal Brook climate (May to November cumulative)

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3.4.4 Spatio-temporal variograms (approach 1) Figures 3.26 to 3.32 display the first attempt at spatio-temporal variograms for each of the seven study fields. In each figure the spatial component, the ‘temporal component’ and the ‘spatio-temporal’ variograms are plotted.

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Figure 3.26 Spatio-temporal variograms for 'Road' field from “BrookPark”

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Figure 3.27 Spatio-temporal variograms for 'Bills' field from “BrookPark”

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Figure 3.28 Spatio-temporal variograms for '12' field from “Grandview”

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Figure 3.29 Spatio-temporal variograms for 'Blackflat' field from “Clifton Farm”

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Figure 3.30 Spatio-temporal variograms for 'Glens' field from “Burrendah”

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Figure 3.31 Spatio-temporal variograms for '41' field from “Rayville Park”

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Figure 3.32 Spatio-temporal variograms for 'Comet' field from “Tarnee”

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Figure 3.33 Pseudo cross variograms for 'Road' field from “BrookPark”

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Figure 3.34 Pseudo cross variograms for 'Bills' field from “BrookPark”

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Figure 3.35 Pseudo cross variogram for 'Glens' field from “Burrendah”

3.4.5 Pseudo cross variograms and contour plots (approach 2) Figures 3.33 to 3.35 provide a sample of the cross variograms that were calculated for each of the fields. The labels in these plots identify the space of time between the years for which the cross-variogram has been calculated. These three plots allow some comparison between different fields. Figures 3.36 to 3.39 display contour plots for four of the fields.

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Figure 3.36 Contour plot of space versus time for 'Bills' field from “BrookPark”

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Figure 3.37 Contour plot of space versus time for 'Road' field from “BrookPark”

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Figure 3.38 Contour plot of space versus time for 'Blackflat' field from “Clifton Farm”

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Figure 3.39 Contour plot of space versus time for 'Glens' field from “Burrendah”

3.5 Discussion This discussion will address the main aim of this chapter, which is approaching a quantitative comparison between spatial and temporal yield variation. As well, this discussion will comment on these results in the light of PA management of yield variation. Additionally, the results will be analysed from the perspective of simulation modelling with regards to expectations of the spatial and temporal variation of modelling outcomes.

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From a PA perspective, this discussion is premised upon the ‘null hypothesis’ for Precision Agriculture that was proposed by McBratney and Whelan (1999): “Given the large temporal variation evident in crop yield relative to the scale of a single field, then the optimal risk aversion strategy is uniform management”. A number of prior studies and parts of this analysis where magnitude of spatial and temporal variation is compared point towards acceptance of the null hypothesis for PA mentioned at the beginning of the discussion. However, this is not the only way to compare spatial variation with temporal variation of yield. It is apparent that structure of temporal variation is important and the interaction between spatial and temporal variation requires attention. This chapter offers several additional approaches to compare both the magnitude and structure of spatial and temporal variation. This discussion will attempt to further some understanding about this seriously baffling concept.

3.5.1 Yield maps The yield maps provide some qualitative information about the yield variation across space and time for each of the fields. One of the main interpretations that can be gained from the maps are consistency in spatial patterns from year to year. The two fields where yield maps were displayed (‘Bills’ and ‘Road’) provide an interesting contrast (Figures 3.1 to 3.3 versus Figures 3.7 to 3.10). ‘Bills’ demonstrates consistent yield patterns for the three years that were mapped. This suggests that the spatial variation across this field from year to year might be predictable. ‘Road’ demonstrates greater differences in yield variation from year to year while some consistency in the patterns can be observed. Relative to ‘Bills’, predicting the spatial variation across ‘Road’ might be more difficult. With these maps in mind and from a PA perspective, it appears that there might be more opportunity to manage ‘Bills’ by SSCM. These maps also provide a visual aid from which to interpret and confirm results from some of the further data analysis that will be discussed next.

3.5.2 Rank correlations and eigenvector analysis Rank correlations provide a quantitative way of assessing persistence of yield patterns from year to year. From the seven fields under question in this chapter, the correlations ranged from negative to positive. A management interpretation of these correlations can be made in terms of yield predictability. A high positive correlation could mean that yield is predictable between seasons. A small correlation that is positive or negative could mean that yield is not predictable between seasons. A high negative correlation could mean that the ‘flip-flop’ phenomenon is occurring. For the fields ‘Bills’, ‘Road’ and ‘41’, correlations are consistently high and positive (ie. Greater than or equal to 0.40). This analysis is a quantitative confirmation of what has been observed in the yield maps for individual seasons. For fields ‘Comet’ and ‘Blackflat’ the correlation coefficients range from low and high positive. For ‘Glens’, the correlation between 2000 and 2002 is high and negative. This is fitting as the northern section appears to display the ‘flip-flop’ phenomenon. However, information about cropping in 2001 suggests this is management

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induced. For this field, the correlations between years post 2001 are high and positive. Field ‘12’ displays low correlations that are both positive and negative. The eigenvector analysis simply provided another way of viewing manifestation of the ‘flip-flop’ phenomenon. From a PA management perspective, this approach rests on the idea that spatial patterns may still be significant even if the magnitude of temporal variation is large. If this is the case (as indicated by high positive correlations) then a large temporal variance does not necessarily rule out the possibility of SSCM. If you have a persistent spatial pattern it is not necessarily more risky to manage smaller spatial units accounting for this pattern as the relative high parts of the field are always relatively high etc. regardless of the season. This suggests that ultimately you are really only risking the choice of one average yield goal. In terms of deciding whether or not SSCM is the optimal management strategy, a question about defining acceptable risk is raised. For this analysis, the decision to consider 0.4 and above as a high correlation value was quite arbitrary. The eigenvector analysis distinguishes between fields where the ‘flip-flop’ phenomenon is occurring. For a field with both positive and negative correlations, for example field ‘12’, the eigenvectors plot negative for the first eigenvector. This analysis does not discriminate between the remaining six fields that all plot positive for the first eigenvector. The reason three years of correlations were used rather than all years available is that the magnitude of the eigenvectors are dependent on the number of years used in the matrix.

3.5.3 Semi-variance calculations The magnitudes of these results confirm that there is a great difference in magnitude of temporal variation between fields (refer to Tables 3.2 to 3.4). This result is quantitatively consistent with conclusions that were drawn from observation of the yield maps. As was expected from the prior discussed observations, the mean semi-variances for ‘Bills’ are smaller in magnitude than those for ‘Road’. These results also indicate that there are appreciable differences in magnitude of temporal variation within fields depending on which pair of years are being compared. This result might also be considered normal, particularly if a plot of the lag(years) versus semi-variance culminated in a variogram where the semi-variance increases with greater lag distance. However, this is not the case, instead the temporal variograms appear erratic. A possible reason for this behaviour is an inadequate number of years from which to calculate variograms. While there were a sufficient number of points within each field from which to calculate a mean semi-variance for each unique pair of years, there were insufficient years from which to calculate a mean semi-variance for each lag distance. For most of the lags, one pair of years was used and for some of the lags two pairs of years were averaged.

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The maps of semi-variance for each pair of years demonstrate that within a field, there are appreciable differences in magnitude of semi-variance. These results provide some insight into which parts of the field experience the most yield variability between a pair of years. Average maps were made and these provide information about the stability of yield patterns across a number of years, ie. if parts of the field have consistently high or low temporal variance. For both ‘Bills’ and ‘Road’ there is some spatial structure evident in the mean temporal variance maps. The fields could clearly be divided into parts with consistently low or high temporal semi-variance. There are similarities between these patterns and the yield patterns. From a PA perspective, this analysis provides some insight into how spatial and temporal variation is interacting. These results provide a point to compare the magnitude of temporal variation within different fields. The average semi-variance maps might be particularly useful for this. Manifestation of obvious spatial structure in the average maps would suggest that spatial patterns persist from season to season. It might be possible to identify parts of a field where spatial management through time would be relatively easy by finding patches of low mean semi-variance. These maps could also be potentially valuable for delineating fields into zones for SSCM. This information could potentially aid a decision to prioritise certain fields for SSCM assuming that minimal temporal semi-variance would increase the ease of managing spatial variation. However, it is difficult to make definitive comparisons between fields as the same years of data have not been used and that different field sizes could be impacting the magnitude of the semi-variance calculations.

3.5.4 Long term variograms Firstly it is important to note that the long term yield data used for these variograms was simulated using APSIM. Clearly there are differences between the rainfall variograms and the yield variograms for each of the three scenarios. This indicates that the model is recognising the role of the soil in capturing water for crop growth and the different efficacy of the soil as it performs this role under different amounts and timing of rainfall. The long-term temporal yield variograms demonstrated that temporal semi-variance increases with an increase in time lags. The variogram also illustrates that for short windows of time the variogram cloud is quite erratic while the trend is not apparent until greater periods of time are examined and the semi-variance is allowed to stabilise. This supports the previous explanation that up to five years of yield data is not enough to fit a temporal variogram. The nugget:sill ratios were quite high for each of the yield variograms from the theoretical soils (Figure 3.20, Figure 3.22, and Figure 3.24) (this is equally the case for the rainfall variograms). This demonstrates that a large proportion of the temporal variation is random or unpredictable. These results suggest that the Calcarosol under a South Australian rainfall regime provides the most predictable temporal yield variation.

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In this case 75% of the variation is considered random. This is appreciably small compared to 89% for the Vertosol and 93% for the Chromosol. A noteworthy feature taken from the Moree and Yarrawonga rainfall variograms is the clear cyclicity (Figure 3.21 and Figure 3.23). These variograms indicate that over time there is a regular cyclical pattern of rainfall in these two regions. For the Yarrawonga rainfall, the cycle appears to last 15 years. This is significantly longer than eight years for the Moree rainfall. This same cyclicity can also be seen in the yield variograms however, the clarity has been dampened. It is interesting to note that the Crystal Brook rainfall variogram does not display cyclicity (Figure 3.25) while the yield variogram does to a small extent. It is interesting to note the fitted semi-variance of yield at one year for each of the theoretical soils. The values were 2.2, 1.4 and 1.9 for the Vertosol, Chromosol and Calcarosol respectively. These semi-variances provide a potential comparison point for the spatial variation. Such a question could be asked: “What spatial lag provides an equivalent amount of yield variation as one year of temporal yield variation?” Assuming that the seven study fields represent each of the three grain growing regions (represented by the three theoretical soils), this question can be addressed in the light of some of the above results. All the spatial variograms that are referenced were calculated to 500 metres. For the northern NSW region (Vertosol), two fields provide data for comparison. These are ‘Glens’ and ‘Comet’. The spatial variograms for these fields resulted in maximum semi-variance values ranging from 0.24 to 1.33. These values fall significantly short of 2.2. For the South Australian region (Calcarosol), three fields provide data for comparison. These are ‘Bills’, ‘Road’ and ‘Blackflat’. Again, none of the spatial variograms that were calculated for each of these fields resulted in a semi-variance as large as 1.9. The maximum semi-variances from these three fields ranged from 0.08 to 1.02. For the Riverine region (Chromosol), two fields provide data for comparison. These are ‘12’ and ‘41’. The spatial variograms resulted in maximum semi-variance values ranging from 0.33 to 5.4. More specifically, the variogram calculated and fit for field ‘12’ using yield data from the year 2000 provided semi-variances exceeding 1.4. Based on this particular year of data for this field, a spatial lag of 94 metres results in the equivalent yield variation as does a temporal lag of one year. All of these results, excluding one year of yield data for one field in the Riverine area suggest that the maximum amount of spatial variation within a field is considerably smaller than the temporal variation that occurs between consecutive years. These results demonstrate that temporal variation is large and quite random between most years for most fields. A possible interpretation from a SSCM perspective could be that managing for multiple yield goals within an individual field is likely to be very challenging. The idea that temporal variation is significantly larger than spatial variation has been previously reported in the literature. Eghball and Varvel (1997) assert that year-to-year variation can be as high as two to three orders of magnitude compared with spatial

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variability that is unlikely to exceed one order of magnitude. Similarly, McBratney et al., (1997) reported on results from a long-term experiment where temporal variance peaked at 1.6 while spatial variance peaked at 0.35. Remembering that all the yield results were simulated with APSIM, the ability of the model to account for soil specific variation relative to temporal variation is yet to be validated. There is a possibility that the temporal variation modelled using APSIM has been exaggerated. With reference to the temporal semi-variance calculations made for each field, these few calculations provide semi-variance values for one year lag ranging from 0.53 to 1.29 (Tables 3.2 to 3.4) which is smaller than the simulated range of 1.4 to 2.2. This analysis returns to the ‘null hypothesis for PA’. Further discussion is required to clarify whether these results do in fact suggest that for all but field ‘12’ the null hypothesis should be accepted and uniform management implemented. It is apparent that this issue is also a departure point for further research in terms of analysis of APSIM and collection of more yield data through time.

3.5.5 Spatio-temporal variograms – approach 1 For all the fields the spatio-temporal variogram was flatter and larger in magnitude than the ‘spatial components’ (Figures 3.26 to 3.32). It makes intuitive sense that this variogram would be larger in magnitude as both the spatial and temporal variation is being taken into account. A reason why the variograms appear flatter could be that the erratic nature of the temporal variation (as mentioned above) is coming into play. The most significant difference between each of the fields is the ‘temporal component’ of these spatio-temporal variograms (this was identified in the methods as the difference between the spatio-temporal variogram and the mean of the spatial variograms). The behaviour of the ‘temporal component’ relative to the mean of the spatial variograms might provide some interesting insight such as a way of comparing the amount of spatial and temporal variation within a field. Also it is interesting to examine structure in the ‘temporal component’ of these variograms. For Fields ‘41’ and ‘Road’, the ‘temporal component’ is higher than the spatial mean variogram for all the lags. For ‘Comet’ the ‘temporal component’ declines and meets the spatial mean variogram at the end of the plot. These results might indicate that for these three fields, temporal yield variation is substantially greater than the spatial yield variation. For ‘Blackflat’, ‘Glens’ and ‘Bills’ the ‘temporal component’ declines with greater lags and is below the spatial mean variogram from close to the first calculations onwards. ‘12’ declines and crosses over the spatial mean variogram around the middle of the lags. An interpretation from these results could be that for these four fields, the spatial variation is greater than the temporal variation. It is important to note that this interpretation is quite speculative as there is no way of determining the relative contribution of each year to the ‘temporal component’ of the

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variogram. These results suggest that there is good reason to try a second, more explicitly quantitative approach to spatio-temporal variation comparison.

3.5.6 Pseudo cross variograms and contour plots– approach 2 In most cases the variance through the time axis was fluctuating up and down apparently irrespective of the time lag and the contours rarely intersected both axes (Figures 3.36 to 3.39). This display of erratic behaviour in the time dimension, rather than the variance increasing with time was not expected, however, was demonstrated when temporal semi-variances were calculated above. Again, the significant reason for these results is believed to be the small sample size in the time dimension. The fields that were used for this analysis provided from three to six years of yield data which equates to a small number of lags in time compared to spatial lags. Similar to the prior discussed temporal semi-variance calculations not culminating into variograms, this shortage of data explanation is supported by the long-term temporal variograms. Consequently, this approach to space-time comparison of yield variability is likely to become more useful when more years of yield data are available. It is not suprising that having a ‘lack of data’ has been quite a popular comment in the literature attempting spatio-temporal yield analysis (for example Lamb et al. (1997) and Bakhsh et al. (2000)). However, some preliminary insight into some of these fields can be inferred from the contour plots. ‘Bills’ is a field that may be well suited to SSCM. The contour plot (Figure 3.36) indicates that the spatial structure of yield variation is the same for all the years of data available while there is no structure in the temporal variance. As a result the yield variation is predictable from year to year. For a one year lag, ‘Road’, ‘Blackflat’ and ‘Glens’ each display some space-time variance equivalents. The contours intersecting one year on the temporal axis intersect approximately 300 metres, 200 metres and 50 metres on the spatial axis for the three fields respectively. This information could be used to compare the potential ease of SSCM between fields. It may be that managing spatial variation for ‘Road’ is more difficult than managing spatial variation for ‘Glens’. It is worthwhile discussing what was envisaged for the contour plot results, and what may occur when the temporal dimension is better represented. It was imagined that if you follow the contour from the time to the space axis, the intersection points would indicate some kind of space time variance-equivalent magnitudes. Assuming that more years of yield information were available this approach would allow a new perspective from which to evaluate the magnitude of spatial or temporal variation. Conclusions such as for a certain field, a variance equal to x occurs at both y metres and z years. Consequently for this field, from a management perspective, managing spatial variation that occurs between points y metres apart is equivalent in value to managing the temporal variation that occurs between z years. If y is large relative to z an implication is that SSCM might be a more difficult undertaking. Alternatively, if z is large relative to y, managing spatial variation with SSCM might be more suitable. With reference to the null hypothesis for PA some further discussion about the idea of identifying space time variance-equivalents is necessary. If one year of variance is

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equivalent to variance that occurs at a distance greater than the dimensions of the field does this mean that one should accept the null hypothesis? It is worthwhile briefly discussing how management outcomes are evaluated. Implicit in both SSCM and conventional crop management is the idea that an average yield goal (determined at the beginning of the season) for the chosen spatial unit (field or zone) is strived for. The yield outcome from that particular season is then evaluated with reference to achievement (or not) of the chosen average. To consider temporal variation implies that you are considering more than one year at the same time. From this it might not be outrageous to suggest that spatio-temporal analysis is ill-fated if the spatial component considered is always yield outcome from one year. This poses a problem because the temporal scale financially and socially that is most often used is one year. An option for further analysis might be to observe the spatial variation for some yield accumulated over a number of years.

3.6 Conclusions A number of conclusions can be drawn from this preliminary yield data analysis. This chapter addresses the conceptually difficult question regarding comparison between spatial and temporal variation. In terms of the null hypothesis for PA, there is scope for further research. Some conclusions towards understanding spatio-temporal variation are:

- Yield maps provide some qualitative information about temporal stability of spatial yield patterns. This allows some preliminary conclusions about which fields might be easier to predict spatial yield outcomes from year to year.

- Calculation of temporal semi-variance within fields provides further information

about temporal variation that can contribute to conclusions regarding prioritisation of fields suitable for SSCM. It is apparent that more years of yield data are required to calculate temporal variograms.

- Calculating rank correlations between years for a field provide quantitative

information about the persistence of spatial patterns through time. - Combining yield data for an individual field and calculating a ‘spatio-temporal’

variogram does not provide enough explicitly quantitative information about temporal variability to enable confident conclusions comparing spatial variability with temporal variability.

- Pseudo cross variograms and contour plots provide a promising approach to

quantitatively compare spatial and temporal variation. It can be seen that there is diversity between fields in terms of the relationships between spatial and temporal variation, however, more data is required in the time dimension to validate this approach.

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- Future work to further pursue this aim would be to collect and process greater volumes of yield data from years to come.

Some conclusions from this chapter that are particularly relevant to crop simulation modelling are:

- An advantage of using crop growth simulation models is the ability to create large data sets that would otherwise be unavailable.

- These results provide a clear indication about the amount of spatial variation a

crop growth simulation model should be able to predict. Upon further collection of real yield data, the same indication about temporal variation will be available.

- Temporal variograms constructed from simulated yield data display nugget effects

accounting for between 75% and 93% of the temporal variation.

- With the exception of one field, the simulated temporal yield variability that is due to one year difference exceeds the real spatial yield variability across 500 metres or less.

- Future work highlighted from these results is the need to investigate APSIM’s

ability to realistically simulate temporal variability and spatial variability keeping in mind results from spatio-temporal analysis or real yield data.

References: Andales, A. A., Green, T. R., Ahuja, L. R., Erskine, R. H., and Peterson, G. A. (2007).

Temporally stable patterns in grain yield and soil water on a dryland catena. Agricultural Systems 94, 119-127.

Bakhsh, A., Jaynes, D. B., Colvin, T., and Kanwar, R. S. (2000). Spatio-temporal analysis of yield variability for a corn-soybean field in Iowa. Transactions of the ASAE 43, 31-38.

Eghball, B., Binford, G. D., Power, J. F., Baltensperger, D. D., and Anderson, F. N. (1995). Maize temporal yield variability under long-term manure and fertilizer application: fractal analysis. Soil Science Society of America Journal 59, 1360-1364.

Eghball, B., and Power, J. F. (1995). Fractal description of temporal yield variability of 10 crops in the United States. Agronomy Journal 87, 152-156.

Eghball, B., and Varvel, G. E. (1997). Fractal analysis of temporal yield variability of crop sequences: Implications for site-specific management. Agronomy Journal 89, 851-855.

ESRI (2002). ArcGIS Software. Redlands, California. Fairfield Smith, H. (1938). An empirical law describing heterogeneity in the yield of

agricultural crops Journal of Agricultural Science, Cambridge 28, 1-23. Isaaks, E. H., and Srivastava, R. M. (1989). "An introduction to applied geostatistics,"

Oxford University Press Inc, New York. Isbell, R. F. (1996). "The Australian soil classification," CSIRO Publishing, Victoria.

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Jaynes, D. B., and Colvin, T. S. (1997). Spatiotemporal variability of corn and soybean yield. Agronomy Journal 89, 30-37.

Joernsgaard, B., and Halmoe, S. (2003). Intra-field yield variation over crops and years. European Journal of Agronomy 19, 23-33.

Keating, B. A., Carberry, P. S., Hammer, G. L., Probert, M. E., Robertson, M. J., Holzworth, D., Huth, N. I., Hargreaves, J. N. G., Meinke, H., Hochman, Z., McLean, G., Verburg, K., Snow, V., Dimes, J. P., Silburn, M., Wang, E., Brown, S., Bristow, K. L., Asseng, S., Chapman, S., McCown, R. L., Freebairn, D. M., and Smith, C. J. (2003). An overview of APSIM, a model designed for farming systems simulation. European Journal of Agronomy 18, 267-288.

Kravchenko, A. N., Robertson, G. P., Thelen, K. D., and Harwood, R. R. (2005). Management, topographical and weather effects on spatial variability of crop grain yields. Agronomy Journal 97, 514-523.

Kyriakidis, P. C., and Journel, A. G. (1999). Geostatistical space-time models: A review. Mathematical Geology 31, 651-684.

Lamb, J. A., Dowdy, R. H., Anderson, J. L., and Rehm, G. W. (1997). Spatial and temporal stability of corn grain yields. Journal of Production Agriculture 10, 410-414.

Lark, R. M. (2002). Robust estimation of the pseudo cross-variogram for cokriging soil properties. European Journal of Soil Science 53, 253-270.

McBratney, A. B., and Whelan, B. (1999). The "Null Hypothesis" of Precision Agriculture. In "2nd European conference on Precision Agriculture" (J. Stafford, ed.), pp. 947-957. Sheffield Academic Press, Denmark.

McBratney, A. B., Whelan, B., and Shatar, T. M. (1997). Variability and uncertainty in spatial, temporal and spatiotemporal crop-yield and related data. In "Precision agriculture: Spatial and emporal variability of environmental quality (Ciba Foundation Symposium 210)", pp. 141-160.

Minasny, B., McBratney, A. B., and Whelan, B. (2005). VESPER Version 1.62. Australian Centre for Precision Agriculture, Sydney.

Papritz, A., Kunsch, H. R., and Webster, R. (1993). On the Pseudo Cross-Variogram. Mathematical Geology 25, 1015-1026.

Schepers, A. R., Shanahan, J. F., Liebig, M. A., Schepers, J. S., Johnson, S. H., and Ariovaldo Luchiaria, J. (2004). Appropriateness of Management Zones for Characterizing Spatial Variability of Soil Properties and Irrigated Corn Yields across Years. Agronomy Journal 96, 195-203.

Valdez-Cepeda, R. D., and Olivares-Saenz, E. (1998). Fractal analysis of Mexico's annual mean yields of maize, bean, wheat and rice. Field Crops Research 59, 53-62.

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