Modelling and mapping agricultural opportunity costs to guide landscape planning for natural resource management

Ecological Indicators 11 (2011) 199–208

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Modelling and mapping agricultural opportunity costs to guide landscape planning for natural resource management B.A. Bryan *, D. King, J.R. Ward Policy and Economic Research Unit, CSIRO Sustainable Ecosystems, PMB 2 Glen Osmond, South Australia, 5064, Australia

A R T I C L E I N F O

A B S T R A C T

Article history: Received 7 February 2008 Received in revised form 17 January 2009 Accepted 17 February 2009

On-farm actions to better manage natural resources often involve an opportunity cost associated with foregone agricultural production. Spatial information on agricultural opportunity costs is a key indicator that has been demonstrated to increase the cost-effectiveness of environmental investment through spatial targeting. In this paper we develop a method for calculating expected profit as a more robust spatial measure of economic rent accruing from agricultural land and indicator of opportunity cost for use in landscape and planning for natural resource management. We apply this method to the Lower Murray region in southern Australia. Agricultural profit is calculated for three farming system phases (cereals, legumes, and grazing) by census zones based on agricultural statistics and cost of production information within a GIS environment. Zonal profit layers are smoothed using pycnophylactic (mass preserving) interpolation. Farming system rotations are quantified as a set of continuous spatial probability layers for each phase using a moving window kernel density technique based on existing land use data and these probability layers are used in a weighted allocation of expected profit across the landscape. The expected profit layer provides a high spatial resolution description of opportunity costs associated with natural resource management over the Lower Murray region suitable for input into systematic landscape planning analyses. Validation of the opportunity cost layer by field survey identified both random and systematic error. Interpretation of systematic error highlighted the need to augment pycnophylactic interpolation techniques with consideration of covariates of profit such as rainfall for better estimation in areas with high profit gradients. ß 2009 Elsevier Ltd. All rights reserved.

Keywords: GIS Landscape planning Conservation Agriculture Economics Modelling

1. Introduction In productive agricultural landscapes, natural resource management on private lands inevitably involves some change in land use and/or management. The nature of this change may range from a relatively minor shift in management (e.g. minimum tillage, Thomas et al., 2007) to total conversion to an alternative land use (e.g. ecological restoration, Saunders and Hobbs, 1995). Natural resource management often involves an opportunity cost to landholders resulting from foregone agricultural production from the land (Naidoo et al., 2006; House et al., 2008). Together with upfront establishment costs, the opportunity costs associated with foregone agricultural production are one of the major economic barriers to the adoption of natural resource management by landholders (Guerin and Guerin, 1994; Ridley, 2005; Pannell et al., 2006; Mendham et al., 2007). In systematic landscape and regional planning for natural resource management, spatial information on the distribution of opportunity costs

* Corresponding author. Tel.: +61 402 881 598. E-mail address: [email protected] (B.A. Bryan). 1470-160X/$ – see front matter ß 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ecolind.2009.02.005

can be integrated with layers describing environmental benefits (Bryan and Crossman, 2008). Through targeting hotspots of both low economic cost and high environmental benefit, natural resource management adoption rates may be increased and the cost-effectiveness of public investment in achieving environmental objectives in agricultural landscapes may be enhanced (Ando et al., 1998; Drechsler and Wa¨tzold, 2001; Schou and BirrPedersen, 2001; Naidoo et al., 2006; Naidoo and Iwamura, 2007; Crossman et al., 2007; Gimona and van der Horst, 2007; Groot et al., 2007; Holzka¨mper and Seppelt, 2007; Polasky et al., 2008; Crossman and Bryan, 2009). Quantitative spatial information is required to characterise the distribution of agricultural opportunity costs in order to achieve joint economic and environmental benefits of natural resource management actions. For maximum utility in informing systematic landscape and regional planning for natural resource management, spatial layers of agricultural opportunity costs need to cover a spatial extent meaningful in planning analyses such as a landscape, catchment, or region. In addition, these layers need to be of a spatial resolution to capture landscape-scale heterogeneity in both agricultural opportunity costs and the biophysical processes influential on both natural and agricultural systems (e.g.

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the topographic redistribution of water, soil properties, solar radiation, and biological habitat). In the context of global scale conservation planning, Naidoo and Iwamura (2007) state that whilst spatial layers describing biophysical indicators such as biodiversity are becoming increasingly available, parallel economic indicators are not nearly so well developed. The same is true at the landscape level. Whilst spatial layers of appropriate resolution and extent are readily available for biophysical processes operating in agricultural landscapes, similarly detailed data on the spatial distribution of economic indicators in the landscape such as opportunity cost are rarely available. In this paper we present a method for modelling the spatial distribution of agricultural opportunity costs associated with undertaking natural resource management at an appropriate spatial resolution and extent for systematic landscape and regional planning. This is demonstrated for a case study area in the Lower Murray region of southern Australia. To create a layer of opportunity cost the spatial distribution of farming system rotations across the study area is first characterised as the frequency of rotation of different farming system phases as derived from agricultural census and catchment scale land use mapping. The spatial distribution of annualised profit for each farming system phase is calculated using a profit function based on agricultural census and economic data from the year 2000/01 and spatially smoothed across census zones using pycnophylactic interpolation. An annualised expected profit layer is created as a function of the profit and relative rotation frequency of each farming system phase. Expected profit is designed to be a robust indicator of the opportunity cost of foregone agricultural production over the longer term given the dynamic nature of farming system rotations in the Lower Murray study area. The expected profit layer is validated against a survey of dryland farmers in the study area and the error is assessed using a Wilcoxon signed rank test, a graphical analysis, and an assessment of global and local spatial autocorrelation. The implications of opportunity cost mapping in systematic regional planning are discussed. 2. Mapping indicators of opportunity costs A number of different indicators have been used to represent the costs of natural resource management options in landscape scale planning. Land sales price has been used as an indicator of cost both with respect to reserve selection (Ando et al., 1998; Sinden, 2004; Naidoo and Adamowicz, 2005) and habitat restoration in an agricultural landscape (Westphal et al., 2007). Land sales price provides a suitable indicator of cost and is useful in cases where management involves the loss of all returns or the sale of land (e.g. Newburn et al., 2005; Murdoch et al., 2007). However, undertaking natural resource management often involves more subtle changes in land use and management that result in lower net returns. In this case alternative indicators based on economic rent are required for quantifying the spatial distribution of opportunity costs as the change in profit associated with undertaking natural resource management actions in agricultural landscapes. Agricultural profitability is a useful measure of the financial opportunity cost associated with the adoption of natural resource management on agricultural land as it represents the surplus economic rent accruing to the farmer from the use of natural land and water resources (Perman et al., 2003; Hajkowicz and Young, 2005). The profitability of agricultural land (and therefore the opportunity costs of natural resource management) varies continuously across the farm at a within-paddock scale (Cook and Bramley, 1998). High spatial resolution mapping of agricultural profitability has been developed in the field of precision agriculture

(Cook and Bramley, 1998; Khosla et al., 2002) but only applied over small areas. Whilst precision agriculture techniques display substantial promise for the mapping of agricultural profits over geographic extents meaningful for systematic landscape planning, challenges remain in demonstrating the applicability of these techniques over larger areas, especially in the context of dryland agriculture (Jochinke et al., 2007). Agricultural and farm statistics acquired through census and survey techniques have been used as a basis for mapping the profitability of agricultural land over landscapes, catchments and regions (Skop and Schou, 1999; Schou and Birr-Pedersen, 2001). However, agricultural statistical information is usually subject to spatial aggregation by coarse scale statistical zones to achieve sufficient statistical explanatory power. For application in regional and landscape planning, higher spatial resolution information is required on the distribution of agricultural profits. Several studies have developed simple spatial layers of agricultural opportunity cost at spatial resolution suitable for use in landscape-scale planning for conservation and natural resource management (Norton-Griffiths and Southey, 1995; Meyer-Aurich et al., 1998; Munier et al., 2004; Naidoo and Ricketts, 2006; Prato and Hey, 2006; Messer, 2006; Crossman et al., 2007; Groot et al., 2007). Typically, these studies have calculated the economic returns from each land use in the region of interest based on published commodity price, cost and production figures. Opportunity costs for each land use are then spatially allocated using land use maps to create spatial layers. However, this technique does not capture the spatial heterogeneity in opportunity costs within agricultural land uses critical in cost-effective regional planning for natural resource management. A few studies have attempted to capture the spatial heterogeneity of opportunity costs at a spatial resolution and extent suitable for planning for conservation and natural resource management. On a global scale, Naidoo and Iwamura (2007) assessed agricultural opportunity costs by calculating gross rents based on spatially varying estimates of production of selected crops and livestock. Polasky et al. (2005) developed a landscapescale model of agricultural opportunity costs using spatially varying yields and demonstrated the application in a stylised 14  14 grid cell simulation. Polasky et al. (2008) subsequently applied these methods in modelling the spatially explicit returns for agricultural land uses in the Willamette Basin, Oregon. Naidoo and Adamowicz (2006) modelled the potential agricultural opportunity costs of conserving forest areas in Paraguay by regressing a number of spatial and landscape variables against the expected annual returns from agriculture in the region. Bryan and Crossman (2008) calculated the spatial distribution of agricultural opportunity costs by modifying typical gross margin values by rainfall. Bateman et al. (1999, 2005) combined a range of data on productivity-influencing biophysical factors with agricultural statistics to disaggregate the opportunity costs of foregone agricultural production in terms of net farm income in the UK at a 1 km grid cell resolution. Similarly, as part of the National Land and Water Resources Audit (NLWRA, 2002), Hajkowicz and Young (2005) mapped the spatial distribution of agricultural profits at a 1.1 km resolution over the entire Australian continent for the year 1996/97. This work integrated spatial information on productivity, price, and costs from several disparate data sources including agricultural statistics, field data, and remote sensing using a profit function within a GIS. Bryan et al. (in press) extended this methodology in mapping agricultural profits in the MurrayDarling Basin, Australia for the years 1996/97 and 2000/01. The above studies make significant progress in mapping the distribution of agricultural profits as opportunity costs at a spatial resolution and a geographic extent useful for implementation in landscape planning. However, many farming systems in Australia

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and around the world are dynamic insofar as they rotate cropping and grazing phases, and the types of crops and pastures used (Connor, 2004). Farming systems vary over the landscape with variation in biophysical characteristics and with the management styles of farmers themselves (Cary et al., 2002). Profit layers are generally constructed from single-year snapshot land use maps developed from remote sensing and/or agricultural census data. Land use maps appear as a mosaic of rotational phases (e.g. cropping or grazing) and subsequent spatial layers of agricultural profitability exhibit a discontinuous distribution reflecting the profits from the farming system rotation phase occurring in the snapshot year of land use mapping (Hajkowicz and Young, 2005). When used as a basis for cost-effective spatial planning, spurious targeting of natural resource management actions for land parcels mapped as the lower profit fallow or grazing phase of the farming system rotation can occur (e.g. Bryan and Crossman, 2008). Other indicators of the opportunity cost of natural resource management do incorporate the dynamic economic returns to agricultural land across the farm and landscape associated with farming system rotations. Land sales price indicators of opportunity cost inherently include the effect of dynamic farming system rotations as they build in the expectations of future returns. However, economic rent-based agricultural profitability mapping studies have rarely attempted to capture this spatio-temporal dynamism. In this study, we calculate the spatial distribution of a more robust spatial indicator of the long term annual opportunity costs of agricultural production for use in landscape-scale planning for natural resource management based on the concept of expected profit. 3. Study area description The Lower Murray study area (Fig. 1) includes covers an area of 118,713 km2 including the South Australian Murray-Darling Basin, and the Victorian Mallee and Wimmera catchment regions. Topography is mostly flat and the climate ranging from Mediterranean in the south to semi-arid in the north. Land cover in the study area is dominated by remnant vegetation and dryland farming systems (Fig. 1). Dryland farming areas incorporate a diverse range of different land uses including different crop types, fallow periods, stock types and densities, and rotation frequencies. Generally, farming systems in the Lower Murray involve some sort of cropping/ grazing rotation ranging between continuous cropping right through to continuous livestock grazing. The cropping phase in the Lower Murray is dominated by cereals and oilseeds including barley, oats, cereal rye, buckwheat, triticale, wheat, and canola. Legume crops are also used in rotation such as lupins, chick peas, faba beans, field peas, lentils, mung beans, soybeans, and vetches. Land may also be routinely left fallow and the pasture grazed predominantly by sheep but some beef cattle also occur in the SAMDB (Bryan and Marvanek, 2004). Farming system rotations are employed for a variety of reasons including opportunistic response to markets, protection against pests and diseases, and the maintenance of soil health. Farming systems in the Lower Murray also vary greatly across the landscape according to environmental conditions (e.g. climate and soils) and a range of other factors. 4. Methods 4.1. Calculating agricultural profit of individual land uses In this study, profit at full equity is used to represent agricultural opportunity costs after Hajkowicz and Young (2005). Profit at full equity is a measure of the net annual returns

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to land from agricultural production under the control of private individuals. It is calculated as the gross revenue received in a year less all variable and fixed costs of production. It does not consider interest payments on loans, nor off-farm income (Hajkowicz and Young, 2005). The spatial distribution of agricultural profit at full equity was calculated for each hectare of land in the Lower Murray study area using a profit function within a Geographic Information System (GIS). The profit function integrates a variety of production, price, and cost data in calculating agricultural profit at full equity (PFE) in $/ ha (NLWRA, 2002; Bryan and Marvanek, 2004; Hajkowicz and Young, 2005; Bryan et al., in press). Profit at full equity was calculated for each agricultural land use i as: PFEi ¼ ððP1i  Q 1i  TRN i Þ þ ðP2i  Q 2i  Q 1i ÞÞ  ððQC i  Q 1i Þ þ AC i þ FDC i þ FOC i þ FLC i Þ

(1)

where P1i ($/tonne or $/DSE1) is the farm gate price of the primary product; P2i ($/kg of wool) is the farm gate price of the secondary product; Q1i (tonnes/ha or DSE/ha) is the yield of the primary product; Q2i (kg of wool, sheep only) is the yield of the secondary product; TRNi is the turn-off rate or proportion of the herd sold (sheep only); QCi ($/tonne or $/DSE) is quantity dependant costs such as harvest, storage, handling, and product treatment costs; ACi ($/ha) is area dependant costs such as the cost of seeding, fertiliser and pesticide treatment; FOCi ($/ha) is fixed operating costs such as accountant fees and costs for energy, waste disposal, maintenance, insurance and administrative overheads; FDCi ($/ha) is fixed depreciation costs on farm machinery and infrastructure, and; FLCi ($/ha) is fixed costs of labour required in production including the payment of a wage to the farmer. Profit at full equity was calculated for each statistical zone (Statistical Local Area or SLA, see Fig. 1) in the study area for each land use i where i 2 {cereals (C), legumes (L), and grazing (G)}. Parameter values for wheat, lupins, and sheep were used to represent cereals, legumes, and grazing land uses, respectively. ABS (2001) agricultural census data the year 2000/01 was used to quantify the quantity, price and turn-off rate parameters. Yield data for sheep was sourced from Bryan and Marvanek (2004) by SLA. Data for the cost parameters was sourced primarily from state government Gross Margin Handbooks and other similar publications. 4.2. Pycnophylactic interpolation SLA-based (Fig. 1) zonal layers of profit at full equity were regionalised or blocky and not representative of the more continuous nature of the spatial distribution of agricultural profit in the region. To better capture the continuous transition of agricultural profit over the landscape, the homogeneous SLA-based values were smoothed using pycnophylactic (mass preserving) interpolation in a raster GIS. Pycnophylactic interpolation is a mass preserving reallocation interpolator developed by Tobler (1979). Pycnophylactic interpolation adjusts the value of all grid cells in a homogenous region according to the values of surrounding regions whilst preserving the aggregated value of the region. Hence, recalculating the mean grid cell value of any given region after pycnophylactic interpolation will result in the same value as the original zone prior to interpolation (Tobler, 1979). Pycnophylactic interpolation was implemented using a moving window spatial averaging kernel in a GIS and applied to smooth the spatial distribution of profit for cereals, legumes, grazing. 1 Note that sheep production is measured in Dry Sheep Equivalent (DSE) terms respectively after McLaren (1997), to standardise for the energy requirements of the animals where 1 head of sheep = 1.5 DSE.

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Fig. 1. Location map of the Lower Murray study area including Statistical Local Area boundaries.

4.3. Quantifying farming system rotations In any given year each parcel of dryland agricultural land could be cropped with cereals, legumes, or in fallow and grazed by sheep. The spatial distribution of farming system rotations was quantified as a series of three probability layers in two steps. Firstly, the probabilities of grazing versus cropping were quantified. Secondly, the cropping probability was split up into cereals and legumes components. To quantify the probabilities of grazing versus cropping for dryland agricultural areas of the Lower Murray, smooth surfaces were created characterising the density of cropping and grazing land uses within a neighbourhood. A moving window kernel density function (Silverman, 1986) was used within a GIS to calculate the spatial density of grazing and cropping land use

within a 30 km radius based on catchment scale land use mapping. The probability of grazing P(G) was then calculated for each grid cell by dividing the grazing density layer (dG) by the sum of the grazing density and cropping density (dCr) layers: PðGÞ ¼

dG dG þ dCr

(2)

A probability of cropping P(Cr) layer was calculated as one minus the probability of grazing: PðCrÞ ¼ 1  PðGÞ

(3)

Deconstructing the probability of cropping layer into cereals P(C) versus legumes P(L) was done in a similar way but instead

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based on the agricultural production mapping by Bryan and Marvanek (2004). The source data is of a coarser spatial resolution (1.1 km) than the catchment scale land use mapping but captures a higher level of detail in mapping individual agricultural commodities, making it suitable for distinguishing between crop types. Density surfaces were calculated using the same moving window function for both cereals (dC) and legumes (dL) using a 100 km radius to cover differences in the focus areas of the two studies in the south western Wimmera. The probability of cereal crops layer was calculated for each cell by multiplying the probability of cropping by the ratio of cereal and legume density layers: PðCÞ ¼

dC  PðCrÞ dL þ dC

(4)

The probability of legume cropping (P(L)) layer was calculated by subtracting the probability of cereal cropping layer from the probability of cropping layer: PðLÞ ¼ PðCrÞ  PðCÞ

(5)

The result of this modelling is three layers displaying the probability of cereal cropping, legume cropping, and sheep grazing such that P(C) + P(L) + P(G) = 1 for each grid cell. Together these three surfaces quantify the farming systems rotation frequencies of cereal, legumes, and grazing operating across the Lower Murray according to the probability that these land uses occur in any given year. 4.4. Spatial allocation of expected profit To calculate the expected profit from agricultural land the profit from individual land uses of cereals (PFEC), legumes (PFEL), and grazing (PFEG) are combined using the farming system rotation frequencies. An expected profit layer (PE) was calculated as: P E ¼ PðCÞPFEC þ PðLÞPFEL þ PðGÞPFEG

(6)

The change in land management and/or land use associated with natural resource management actions have an opportunity cost in the form of foregone income from agricultural production. Expected profit can be thought of as the annualised returns from agricultural land and the expected profit layer provides a baseline for calculating the opportunity costs of undertaking natural resource management actions on privately owned productive agricultural land. 4.5. Validation 4.5.1. Survey A mail-out survey was used to elicit empirical data to validate the mapped opportunity cost surface. A census approach was used in sending a pre-tested questionnaire to all 1,142 dryland farmers (with properties >10 ha) in the SAMDB (Fig. 1) following the Total Design Method of Dillman (1978). The survey included 54 questions covering the demographic characteristics of landholders, attitudes and behaviours in regard to environmental management, and details about various aspects of farm economics and management. In particular, the survey included questions about farm size and annual farm profits for the year 2004/05 which have been used to validate the modelled results. The question on farm financial performance was optional in the survey and asked respondents to indicate their farm profit in $10,000 classes thereby maintaining some level of privacy and enhancing the response rate:

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Please indicate the before-tax profit of your on-farm business activities:

4.5.2. Analysis of profit mapping error A total of 583 (54%) landholders responded to the survey. Of these, 385 (66%) answered the question on farm profit. The response data was filtered to remove outliers. The 58 respondents that reported a loss for the year 2004/05 were removed from further analysis. A total of 37 respondents reported an area less than 300 ha which were also removed as it is unlikely that these properties are large enough to be profitable dryland farming enterprises and the low area had the effect of increasing the profit calculation in $/ha. Finally, three remaining outliers were also removed leaving 287 properties for comparison. Analytical validation of the mapped expected profit data against the surveyed responses was performed in three stages. First, the mapped profit surface values were directly compared to the surveyed profit responses (PS) in terms of profit mapping error in $/ha. For the survey respondents, profit in $/ha was calculated based on the median of the reported profit range and area farmed.2 This was compared with the mean of the profit surface in $/ha calculated for the corresponding farm property identified in the cadastral database. Profit mapping error was calculated for each property as:

eP ¼ PE  PS

(7)

A Wilcoxon signed rank test was then used as a non-parametric paired samples test to assess whether the median profit mapping error is significantly different to zero. Second, analysis of the level of agreement of the profit mapping with the reported profit class in the survey was undertaken for each of the 287 survey respondent properties. The mapped values were converted to total farm profit to match the survey question by converting of the mapped profit into total annual expected profit for each of the 287 properties by multiplying expected profit ($/ha) by the property area as recorded in the cadastral database. A graph analysis was then conducted to assess the agreement of mapped profit to reported survey profit classes for each property. Finally, the spatial distribution in error between mapped and surveyed profit values was assessed. Spatial autocorrelation was quantified by calculating the global Moran’s I (Moran, 1950; Goodchild, 1986) and local Moran’s I statistics (Anselin, 1995). Global Moran’s I tests the spatial autocorrelation of the entire area of analysis (i.e. whole of SAMDB). Values for I approaching +1 indicate clustering while values approaching 1 indicate dispersed data. Local Moran’s I provides mapped Z-scores which indicate the statistically significant localised spatial autocorrelation. Local clusters of agreement and divergence between the mapped and surveyed profit values are interpreted and discussed. Ideally, there should be no spatial autocorrelation of profit mapping error. Error should be normally distributed around a mean of zero and randomly distributed over the landscape. Spatial 2 Note that often the reported area farmed did not correspond to the cadastral area of the farm property due to commonplace share-farming and leasing arrangements. However, the comparison based on mean profit was robust to this disparity.

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Table 1 Summary of long term average annual profit at full equity ($/ha) of agricultural land uses by region. Region

Farming system component

PFE ($/ha)

SAMDB

Sheep grazing Cereal crops Legumes

9.03 202.55 83.86

Mallee

Sheep grazing Cereal crops Legumes

16.44 412.60 79.91

Wimmera

Sheep grazing Cereal crops Legumes

55.38 467.71 139.77

correlation indicates systematic error and the identification and mapping of systematic error can provide insight into the causality which can be used to improve the mapping technique. 5. Results 5.1. Opportunity costs of foregone agricultural production Table 1 provides information about the economic returns from the three farming system phases—cereals, legumes, and grazing. Profit to sheep grazing was lowest, followed by legumes, with cereals returning the highest profit per hectare. All three components return substantially higher profits in the Mallee and Wimmera regions, compared to the SAMDB (Table 1). Although there is inevitably some localised random variation between landholders, the broad pattern of farming system rotations was found to change continuously across the study area. The layers displaying the probability of cereal cropping, legume cropping, and sheep grazing (Fig. 2) represent the relative temporal frequency of rotation of these phases in farming systems across the Lower Murray. The SAMDB region has a higher frequency of grazing with some cereal cropping. The Mallee region is more heterogeneous with some areas having a higher grazing frequency and lower cereal cropping frequency following the distribution of poorer soils. The southern Mallee and Wimmera regions tend to have low grazing frequencies and high cereal cropping frequency with some inclusion of legumes in the rotation (Fig. 2). This broad spatial pattern generally follows the suitability of climate and soil for dryland agriculture in the study area. However, there is a notable discontinuity in farming system rotation between the SAMDB and Mallee regions despite very similar climate and soil conditions. It is not clear why this should

Fig. 3. Annual opportunity cost of undertaking natural resource management actions calculated as annual expected profit to agriculture in the Lower Murray.

occur but may be related to the differences in tradition, knowledge, and landholder access to information and support across the state border. Farming systems in the SAMDB were found to have substantially lower total annual expected profits to agriculture ($143 M/ yr) than both the Mallee ($468 M/yr) and Wimmera ($485 M/yr) regions. Similarly, on average, annual profits in the SAMDB were around $60/ha/yr compared to around $235/ha/yr in the Mallee and $270/ha/yr in the Wimmera. Geographically, returns to traditional agriculture are heterogeneous within each catchment region and generally follow the distribution of rainfall (Fig. 3). In the SAMDB, economic returns are higher in the wetter areas of the eastern Mt. Lofty Ranges and in the southern parts of the region. These areas tend to have a higher cropping rotation frequency and more productive pastures. Similarly, in the Mallee, higher returns are found in the southern parts, particularly the higher rainfall areas in the south-east (Fig. 3)

Fig. 2. Quantification of farming systems of the Lower Murray study area in terms of the rotation probabilities of cereal crops, legume crops, and sheep grazing.

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Fig. 4. Distribution of profit mapping error and summary of profit mapping error statistics (mapped profit  surveyed profit).

representing some of the most profitable dryland agricultural land in the Lower Murray region. In the Wimmera, the higher rainfall areas in the upper Wimmera are too wet for cereal cropping and grazing is the dominant land use which returns lower profits per hectare. In contrast, higher returns are found in the cropping areas of the central Wimmera (Fig. 3). 5.2. Validation In assessing the profit mapping error across all 287 properties, the modelled profit values were on average $34.73/ha higher than the profit values reported in the survey (std. dev. = $43.89/ha) with survey profit values calculated on the median reported profit class value (Fig. 4). Profit mapping error was also positively skewed (Fig. 4) towards an over estimation of the mapped farm profits when compared with the survey results. The Wilcoxon signed rank test found a significant difference between the median mapped and surveyed profit values for the 287 properties assessed. A substantial number of properties displayed a higher mapped profit than that reported in the survey, thereby supporting the results the descriptive analysis above (Table 2). Analysis of the level of agreement of the profit mapping with the reported profit class in the survey for each landholder uncovers more detail about the areas of similarities and disparities between mapped profit and surveyed profit. Mapped profit fell into the same survey profit category for 81 properties (28%, Fig. 5). Mapped profit was one class higher for 40 properties and 1 class lower for 15 properties. Thus, mapped profit was within one class of reported profit for 47% of all properties. A major area of disagreement was that for 89 properties (31%) the mapped profit was more than four classes higher than the reported farm profit class (Fig. 5). Assessment of the spatial autocorrelation returned a global Moran’s I value of 0.22 which indicates mild clustering of profit mapping error (significant at p < 0.01). Analysis of local spatial autocorrelation reveals five main clusters of error (Fig. 6). Clusters

Table 2 Outputs of the Wilcoxon signed rank test of mapped versus surveyed profit values. N Mapped profit  survey profit

Negative ranks Positive ranks Ties Total

a b c

Mapped profit < survey profit. Mapped profit > survey profit. Mapped profit = survey profit.

Mean rank

Sum of ranks

52a

88.92

4,624

235b 0c

156.19

36,704

287

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Fig. 5. Level of agreement between mapped profit and surveyed profit presented as the difference in the number of profit classes (mapped profit class #  surveyed profit class #).

A, B, and E reflect the overestimation of profit mapping compared to the reported profit class whilst Cluster D reflects good agreement and Cluster C, an underestimation of mapped profit. The clusters of substantially overestimated mapped profit are represented in the 89 properties where mapped profit is more than 4 profit classes higher than the surveyed profit (Fig. 5). The rest of the SAMDB region displays no systematic or autocorrelated error in profit mapping. An interpretation of the spatial distribution of profit mapping error clusters is provided below. 6. Discussion 6.1. Landscape scale profit mapping Natural resource management actions involve changes in land use and land management that require the landholder to forego income formerly derived from agricultural production. The concept of profit at full equity is an established measure of economic rent from the agricultural use of natural, built, and human capital (Trewin, 2006; ABARE, 2007; Environmental Protection Authority, 2007). Agricultural profit at full equity in this study has proven to be a useful spatial indicator providing a baseline for calculating the opportunity costs associated with undertaking natural resource management capturing heterogeneity across the landscape. Agricultural statistics and government publications similar to that used in this study have been used to calculate economic returns to agriculture before (Skop and Schou, 1999; Schou and Birr-Pedersen, 2001). Simple mapping of agricultural opportunity costs has been done by allocating representative, land-use-specific profit values calculated using the above data sources to individual land parcels based on land use mapping. Further, these data sources have also been augmented with other biophysical data to disaggregate and model the spatial heterogeneity of agricultural profits across the landscape (Bateman et al., 1999, 2005; Hajkowicz and Young, 2005; Bryan et al., in press). This study adds to this knowledge in three ways. Firstly, we demonstrate the combined use of pycnophylactic interpolation and farming system rotation data in spatially disaggregating zonal profit calculations. Secondly, we create a more robust, temporally stable, and spatially continuous economic rent-based indicator of agricultural profit and hence, opportunity cost of undertaking natural resource management through the use of farming system rotation data. Thirdly, we assess the accuracy of the mapped opportunity cost layer and interpret error sources and their implications for systematic landscape and regional planning. Mapping the distribution of expected profit as a longer term indicator of agricultural rent to the natural resource base over a

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Fig. 6. Spatial distribution of profit mapping error (mapped profit ($/ha)  surveyed profit ($/ha)) and local spatial autocorrelation.

spatial extent and at a spatial resolution useful for landscape and regional planning in this study is an advance on previous work. The use of a moving window kernel density approach to calculate the relative spatial densities of three different farming system components and the transformation into probability layers enabled the characterisation of dynamic farming systems over time. Data requirements for this approach were no greater than that required in snapshot approaches to opportunity cost mapping. Expected profit captures the longer term economic rent from agricultural use of land and water resources which likely varies more continuously over the landscape with variation in soil and climatic properties than has been represented in previous studies (NLWRA, 2002; Hajkowicz and Young, 2005; Bryan et al., in press). The technique is also amenable to analysis of the impact of varying production, price, and costs on expected profit and the assessment of the economic resilience of farming systems under future scenarios. However, this is beyond the scope of this study. 6.2. Error sources and implications for mapping opportunity costs There are many potential sources of uncertainty and error in the mapping of agricultural opportunity costs. Due to the nature of the data used in this study, the greatest potential for error comes in the estimation of the spatial distribution of costs of production as these vary with the management techniques of individual farmers, crop type, seasonal vagaries, climate, and soil properties. There is also significant uncertainty generated during from the process of downscaling of zone-based census data to expected profit on a 1-ha grid cell resolution based on pycnophylactic interpolation and farming system rotation probabilities. Both random and systematic errors were found between the mapped and surveyed profit values.

Much of the random error results from variation in the characteristics of individual landholders such as management style and skill, level of innovation, attitude to risk, and other differences between landholders. In the analysis of profit mapping error based on a survey of landholders the necessarily imprecise nature of survey questions concerning farming profits is another source of random error. Many people are unlikely to respond accurately, if at all, to questions regarding their private economic affairs, thereby introducing a non-response bias. This is evidenced by one third of survey respondents who elected not to answer the questions on income. The $10,000 income ranges used in this survey were designed to strike a balance between response rates and the accuracy of the reported figures but they also introduce additional random error into the validation of mapped profit. Further, the inter-annual variability of economic returns is also a likely source of error given that the profit mapping and survey were undertaken in different, albeit average years. Ideally, the error as assessed in this study should be normally distributed with a mean of zero and a Kurtosis determined by the influence of the factors discussed above on profit. Fig. 5 provides insights into the influence of these factors on profit mapping error. However, several sources of systematic error were also found. Assessment of systematic error between the profit mapping surface and the survey identifies several areas for attention in the techniques used in this study. First, major source of systematic error was generated through the pycnophylactic interpolation process. Pycnophylactic interpolation worked well in the parts of the SAMDB with gentle topographic and climatic gradients where changes in agricultural profits are fairly continuous over the landscape. This was captured successfully by the interpolation process as reflected in cluster

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D—an area of good agreement between the mapped profit and the surveyed profit (Fig. 6). However, systematic and autocorrelated error occurs in other areas (clusters A, B, and E, Fig. 6) where sharper gradients in the interpolation variable occur between neighbouring census zones. Clusters A and B result from a geographical quirk in agricultural census boundaries, topography, and rainfall in this area. A steep rainfall gradient occurs in this eastern scarp of the Mt. Lofty Ranges—a key driver of agricultural production and profits. Clusters A and B occur within the same large SLA (Goyder) which stretches to the less productive northern part of the study area but which border several SLAs which cover the high rainfall areas of the Mt. Lofty Ranges (Fig. 1). The pycnophylactic interpolation process is likely to have attributed an artificially high profit value in attempting to smooth the sharp profit gradient at the interface of these statistical zones. The overestimation of profit mapping in Cluster E is similarly a result of the pycnophylactic smoothing of a high profit gradient between statistical zones. However, the gradient evident at the state border is generated by variation in agricultural profits resulting from different farming system rotations rather than topographical or climatic variation (Fig. 3). The pycnophylactic technique smoothes gradients geographically without any intelligence on the spatial distribution of the underlying processes driving the change in profit. This technique has met with some success in our study area due to the lack of sharp discontinuities in topography, climate, soils, and hence, profit. The pycnophylactic interpolation technique for downscaling zonal profit data could be enhanced through the incorporation of spatial data on the biophysical and geographic processes driving the agricultural profits. A technique that combines the mass preserving and zonal smoothing properties of pycnophylactic interpolation with the consideration of spatial covariates (e.g. Bateman et al., 1999, 2005; Naidoo and Adamowicz, 2006) needs to be investigated. In this case, information on rainfall (a key driver of crop yield and livestock carrying capacity) or more sophisticated crop/pasture productivity simulation models could be used to downscale yield data prior to incorporation into the profit calculation. Second, a lack of survey specificity in identifying the sampling frame of dryland farmers only may have contributed to error cluster C (Fig. 6). Inspection of recent satellite imagery revealed that irrigation is common in this area. We suspect that dryland farmers in this area may also engage in irrigated agricultural production, particularly pastures. This may have caused the inflated survey profit responses in cluster C. This is a problem with the validation data rather than the profit mapping technique. A third source of error is the use of two different dates for assessing profit. For the profit mapping agricultural survey data was sourced from agricultural census data for the year 2000/01. The farmer survey was conducted late in 2006 and questions were asked about the year 2005/06. Although the annual rainfall for both years was close to the average for the Lower Murray region, variation in both costs of production and commodity prices may have contributed to the assessed error. 6.3. Application of opportunity cost layers in landscape planning Quantification of spatially variable economic rent from each pixel of land to represent the agricultural opportunity cost of natural resource management actions has both ex ante and ex post application in systematic landscape and regional planning studies. Ex ante, cost layers have been used to inform spatial targeting of nature conservation and protected area selection (Naidoo et al., 2006). Strategies may include meeting environmental goals at minimum cost, or maximising environmental benefits within a constrained budget (Ando et al., 1998; Newburn et al., 2005). Opportunity cost layers are also becoming widely applied in

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landscape planning for natural resource management in agricultural regions. Opportunity cost layers have been combined with biophysical benefit layers to identify hotspots for achieving multiple environmental and economic objectives (Gimona and van der Horst, 2007). Opportunity cost layers have also had application in spatially targeting nitrate management (Skop and Schou, 1999), ecological restoration (Crossman and Bryan, 2006) and reafforestation (Bateman et al., 1999; Schou and Birr-Pedersen, 2001), and agricultural extensification (Munier et al., 2004). Agricultural opportunity cost layers have also been used as an indicator of priority areas for restoring natural capital and ecosystem services, and for enhancing the multifunctionality of agricultural landscapes (Crossman and Bryan, 2009). Incorporating spatially explicit indicators of cost into planning can routinely multiply the amount of benefits achieved in constrained budgets for environmental management (Ando et al., 1998; Schou and BirrPedersen, 2001; Naidoo et al., 2006). The spatial layer of opportunity costs developed in this study has already been used ex ante to inform the spatial priority setting and site selection processes in landscape planning and futures models in the context of natural resource management (Bryan et al., 2008). Ex post, opportunity costs have also been used as a key indicator of the economic performance of natural resource management planning. In assessing different planning options and scenarios, the economic impacts can be calculated as the aggregate net opportunity cost of foregone production for the region resulting from the uptake of natural resource management actions and associated land use change. Cost layers can be used as a basis for the audit of costeffectiveness of public investment in the environment (e.g. ANAO, 2008) and justification of future programs. 7. Conclusion This study developed an expected profit layer as an indicator of the landscape-scale spatial distribution of agricultural opportunity costs using spatial information that characterises farming system rotations. The expected profit layer is more robust to the inherently dynamic nature of farming system rotations and a more spatially continuous indicator of agricultural opportunity costs than indicators derived from a single year land use snapshot. Validation of the opportunity cost layer using empirical survey data revealed significant error between the mapped profit surface and profit levels reported by landholders in a survey. This was found to be spatially autocorrelated and related to both artefacts of the profit mapping process and a lack of specificity in the targeting of the validation survey to dryland farmers. We conclude that the pycnophylactic interpolation of zone-based economic data and profit calculations is useful in more geographically homogeneous areas but may over- or under-estimate profit in heterogeneous regions. In heterogeneous regions information on the spatial distribution of other covariates should be used to enhance the spatial reallocation of yield data prior to profit calculations. The spatial indicator of expected profit produced in this study is useful for quantifying the opportunity costs of undertaking natural resource management actions such as ecological restoration. The opportunity cost layer can be integrated with environmental benefit layers and used to target sites for cost-effective natural resource management actions in the landscape. Acknowledgements The authors gratefully acknowledge funding from the National Action Plan for Salinity and Water Quality and CSIRO’s Water for a Healthy Country Flagship program through the Lower Murray Landscape Futures project. We are also grateful to our project stakeholders including many individuals from CSIRO, the

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