a remote sensing and fuzzy multi-objective linear

A REMOTE SENSING AND FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING APPROACH TO MODEL IMPACT OF LAND MANAGEMENT DECISIONS ON ECOSYSTEM SERVICES OF RANGELANDS P.D. Blanco1*, G.I. Metternicht2, H.F. del Valle1, P. Laterra3, L.A. Hardtke1, P.J. Bouza1 1 Centro Nacional Patagónico (CENPAT), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Puerto Madryn, Chubut, Argentina 2 Institute of Environmental Studies (IES), University of New South Wales (UNSW), Sydney, Australia 3 GEAP, Grupo de Estudios en Agroecología y Ecología de Paisajes, Unidad Integrada Balcarce, EEA INTA Balcarce, Fac. Cs. Agrarias, UNMdP, Balcarce, Argentina ABSTRACT

This paper presents an approach to explicitly determinate optimal stocking rates based on trade-offs between guanaco density and livestock grazing intensity on rangelands of Patagonia, Argentina. As sheep farming becomes less profitable in this region, farmers and ranchers need to focus on sustainable wildlife harvesting as alternative income generation. We developed a methodology for spatially-explicit assessment and mapping of stocking rates based on tradeoffs and synergies between ecosystem services and livestock grazing intensity on rangelands. Forage use for livestock production, carbon sequestration, wildlife conservation and soil erosion are the ecosystem services and disservices evaluated over a gradient of grazing intensity. We show how rangelands stocking rate determination can be converted into a multi-objective optimization problem that can be solved using a Fuzzy Multi-Objective Linear Programing (MOLP). Index Terms— ecosystem services, fuzzy, GIS, modelling 1.

INTRODUCTION

Rangelands contribute to the productivity and biodiversity of the biosphere, and provide several ecosystem services (ESs) including raw materials and food, as well as wildlife habitat, greenhouse gas mitigation, lifestyle, water quality and quantity, soil health, carbon sequestration and storage [1]. The supply of these services is highly dependent on rangelands’ natural productivity and management; with latter determining intensity of grazing as a function of stocking rate and paddocks’ potential carrying capacity. Sustainable management of rangelands requires determining trade-offs and synergies between grazing intensities,

stocking rates and ecosystem services to avoid mismanagement that ends up in accelerated disservices like soil erosion [2]. Spatially explicit assessments of management-related trade-offs and synergies between livestock rates, ESs and disservices are essential to support sustainable decision-making. Remote sensing and GIS have shown potential for quantitative assessment and mapping of ESs related to land cover, biodiversity, soil carbon and water [3]. This study proposes a new approach for spatially-explicit assessment and mapping of stocking rates based on tradeoffs and synergies between ecosystem services and livestock grazing intensity on rangelands. Forage utilization for livestock production, carbon sequestration, wildlife conservation and soil erosion are the ecosystem services and disservices evaluated over a gradient of grazing intensity. The main objective relies on finding optimal stocking rate at paddock level, to deliver the highest production output, while meeting pre-requisites of maximizing soil carbon sequestration and wildlife conservation, and minimizing soil erosion. This means converting rangelands stocking rate determination into a multi-objective optimization problem that can be solved using a Fuzzy Multi-Objective Linear Programing (MOLP) [4] approach. Through introducing a set of objective weights MOLP transforms multi-objective problems into single objective optimization, applying fuzzy logic through membership functions so that each objective function is mapped on interval [0,1]. The significance of using fuzzy logic in this context resides on the fact that most modes of human reasoning are approximate in nature, and that in most management decisions it is not possible to have all constraints and resources in exact form, rather they are in ‘expected’ or vague form. Thus, in our model, each objective function indicates decision-makers (DMs) satisfaction towards a specific objective.

2.

CONCEPTUAL FRAMEWORK

The inclusion of ecosystem services and disservices in land management decision making of rangelands, with support of remote sensing, GIS and Fuzzy MOLP, can be realised through the following framework and steps: 1) Multi- and hyper-spectral data acquisition and image processing to map ecosystems services and disservices. 2) Setting the objectives, and the minimum (in the case of the objectives to maximize) and maximum (in the case of the objectives to minimize) acceptable values, as well as number of constraints. 3) Formulate a multi-objective linear programming model as follows: The objective function: MAX (MIN) Z(x) = (Z1(x), Z2(x), ….Zk(x))T in Subject to: 𝑥 ∈ 𝐷 = {𝑥 ∈ 𝑅𝑛 |𝐴𝑥 ≤ 𝐵, 𝑥 ≥ 0}, which: Zi(x) are objectives, Zi(x) = Cix ; Ci = (Ci1, Ci2,…, Cin)T, i=1,2,….,k; A is a matrix m x n; B is a matrix 1 x m; D is a set of constraints, and X are decision variables 4) Solve the MOLP model in a fuzzy environment as follows: (i) Solve individual objective functions under the given constraints D, to determine their upper/lower limits. (ii) Set membership functions with these limits for each of the objective functions (µ1(Z1), µ2(Z2),….., µk(Zk)). (iii) Develop an aggregated objective function: U = w1 µ1(Z1) + w2 µ2(Z2) +…..+ wk µk(Zk)→max (iv) Set scenarios based on the exploration of trade-off and synergies amongst two or more objectives, determining respective priorities of objectives functions (a set of weight [w1, w2,….wk]). (v) Solve the linear programming U under given constraints D; evaluate optimization results, and export the outputs tables resulting from the fuzzy MOLP analysis to a GIS software for visualizing the spatial distribution of the results. 3. APPLICATION OF THE PROPOSED APPROACH TO A SEMIARID RANGELAND The conceptual framework was tested on 21 paddocks comprising about 40,000 ha, in the semiarid Patagonian rangelands. Extensive, continuous sheep grazing for wool production is the main land use of these rangelands. 3.1 Mapping ecosystem services and disservices Carbon sequestration is a regulating ES that was estimated using topsoil Organic carbon (OC) as a proxy; the OC map was derived from an ecological site classification that integrates Landsat TM and Hyperion remote sensing data, using a subpixel classification technique [5].

Wildlife conservation: Guanaco (Lama guanicoe) the largest Patagonian ungulate density was used as a proxy of wildlife conservation. Density was estimated by ground surveys using the line transect method in the different physiographic systems of the study area, delineated on Landsat multispectral data. Forage production (provisioning ES): Forage availability was estimated at field using the Pastoral Value Method [6]. Regression models based on NDVI and field forage availability data were used to mapping the carrying capacity on the study area. Actual stocking rates were obtained from ranchers interviews. Disservice of Soil erosion: soil loss was estimated using EROSAR, an erosion model for semi-arid rangelands, that sources panchromatic, multispectral, and hyperspectral data, and digital elevation models (DEMs) [7]. 3.2 Setting the objectives, acceptable values, and constraints: We pursue four objectives: 1. Maximize livestock production (Z1): ∑21 𝑖=1 𝑆𝑅𝑖𝑗 𝐴𝑖𝑗 → 𝑚𝑎𝑥 2. Minimize soil erosion loss (Z2): ∑21 𝑖=1 𝐸𝐿𝑖𝑗 𝐴𝑖𝑗 𝑆𝑅𝑖𝑗 → 𝑚𝑖𝑛 3. Maximize soil organic carbon sequestration (Z3): ∑21 𝑖=1 𝑂𝐶𝑖𝑗 𝐴𝑖𝑗 /𝑆𝑅𝑖𝑗 → 𝑚𝑎𝑥 4. Maximize guanaco’s number (Z4): ∑21 𝑖=1 𝐺𝑁𝑖𝑗 𝐴𝑖𝑗 /𝑆𝑅𝑖𝑗 → 𝑚𝑎𝑥 Considering that: 𝑆𝑅𝑖𝑗 is the stocking rate in UGOs (Spanish acronym for sheep livestock units) per hectare at paddock i, 𝐸𝐿𝑖𝑗 is soil erosion rate in Mg.ha.year at paddock i, 𝑂𝐶𝑖𝑗 is the soil organic carbon sequestration in tons C per ha at paddock i, 𝐺𝑁𝑖𝑗 is the number of guanacos at paddock i, 𝐴𝑖𝑗 is the area of paddock i. Acceptable values are: a) the minimum livestock production was setting in 0.18 UGOs.ha-1, that is the minimum economic unit for a sheep enterprise in Patagonia [8]; b) Soil loss tolerance was set at 5 Mg ha-1 year-1 (USDA); c) Reference value of SOC at 4.9 cm was set to 9.6 t C ha-1 [9]; and d) Guanaco density was set at 5000 individuals, the minimum viable population for wild animals [10]. The constraints for the paddock stocking number were based on the forage availability in each paddock. 3.3 Linear programming for each objective function to determine fuzzy membership function: LINGO application software was used to this end. In the fuzzy environment; the objective functions express the degree of satisfaction of the DMs; hereafter is an example of such functions: 𝜇1 (Z1 ) =

Z1 − 9014.37 Z1 − 9014.37 = 11135.40 − 9014.37 2121.02

𝜇2 (Z2 ) =

Z2 − 14348,76 Z2 − 14348,76 = 115373.36 − 14348,76 101024.60

3.4 Establish an aggregated objective function: 𝑈 = 𝑤1 𝜇1 (Z1 ) + 𝑤2 𝜇2 (Z2 ) + 𝑤3 𝜇3 (Z3 ) + 𝑤4 𝜇4 (Z4 ) → max In which, w1, w2, w3, w4 are weights of objectives Z1, Z2, Z3, Z4 respectively. 3.5 Scenario development: this phase was based on the exploration of trade-offs and synergies among two or more objectives. We considered, for instance: maximize production (Scenario 1); b) Sheep production having the same weight as provision of ESs while avoiding disservices, etc. A total of 6 scenarios were defined (see Table 1, with outputs). 3.6 Geo-visualisation of scenario outputs: Results for the spatially explicitly stocking rates determination, based on trade-offs and synergies between ESs and livestock grazing intensity on rangelands. Visual display of scenario modelling (Figure 1) shows that highest livestock production is attained in Scenario 1, with ESs having the lowest values and soil erosion being at its highest. On the other hand, prioritising ESs is conducive to the lowest values of livestock production. A table of quantitative estimates (Table 1) complements the spatial display.

Fig. 1: Example of stocking rate at paddock level for scenarios 1 and 2. UGO: sheep livestock units (Spanish acronym for Unidad Ganadera Ovina)

4. CONCLUSIONS MOLP in a fuzzy environment for spatially-explicit determination and mapping of stocking rates in rangelands based on trade-offs and synergies between ecosystem services and livestock grazing intensity on rangelands has been presented and applied, providing six alternative scenarios for DMs. Remote sensing provided efficient data for spatial analysis and modeling of ESs and disservices, which in turn were input data for a fuzzy MOLP. Fuzzy

logic furnishes a tool to deal (and accommodate for) expectations of DMs, in the process of determining the best desirable set of relative weights, which determine alternative outputs of the objectives considered.

5. REFERENCES [1] K.M. Havstad, D. Peters, R. Skaggs, J. Brown, B. Bestelmeyer, E. Frederickson, J. Herrick, and J. Wright. Ecological services to and from rangelands of the United States. Ecological Economics 64:261-268. 2007. [2] K. Petz, R Alkemade, M. Bakkenes, C.J. Schulp M. van der Velde, R. Leemans. Mapping and modelling trade-offs and synergies between grazing intensity and ecosystem services in rangelands using global-scale datasets and models. Global Environmental Change 29:223-234, 2014. [3] Y.Z. Ayanu, C. Conrad, T. Nauss, M. Wegmann, T. Koellner. Quantifying and Mapping Ecosystem Services Supplies and Demands: A Review of Remote Sensing Applications. Environ. Sci. Technol. 46 (16), pp 8529–8541. 2012. [4] D.L. Canh, D.T. Trong. The integration of GIS and fuzzy multiobjective linear programming - An interactive decision making tool in sustainable use of agricultural land. 7th FIG Regional Conference Spatial Data Serving People: Land Governance and the Environment – Building the Capacity Hanoi, Vietnam, 19-22 October 2009. [5] P.D. Blanco, H. del Valle, P. Bouza, G. Metternicht, L. Hardtke. Ecological site classification of semiarid rangelands: Synergistic use of Landsat and Hyperion imagery. International Journal of Applied Earth Observation and Geoinformation 29: 11– 21. 2014. [6] P.D. Blanco, H.F. del Valle, P. Bouza, G.I. Metternicht, L.A. Hardtke. Using the distributed model EROSAR and remotely sensed data to regional assessment of soil water erosion in semiarid rangelands. UNCCD 3rd Scientific Conference-Combating drought, land degradation and desertification for poverty reduction and sustainable development, Cancun, Mexico, 9-12 March 2015. [7] N. Elissalde, J. Escobar, V. Nakamatsu. Inventario y evaluación de pastizales naturales de la zona árida y semiárida de la Patagonia. Programa de acción nacional de lucha contra la desertificación. Convenio SA y DS- INTA- GTZ. 2002. [8] A De Caro, J. Peláez, M. Román, D.H. Álvarez Ugarte, A. Frey. Determinación de la unidad económica en la provincia del chubut como herramienta para la toma de decisions sobre la producción ovina. Revista Facultad de Agronomía UBA 29(1): 4154, 2009. [9] IPCC Guidelines for National Greenhouse Gas Inventories (eds H.S. Eggleston, L. Buendia, K. Miwa et al.). Prepared by the National Greenhouse Gas Inventories Programme, IGES, Japan. 2006. [10] R. Lande. Mutation and conservation. Conservation Biology 9: 782-791.1995.

Table 1: Ecosystem services and disservice (soil erosion) modelled values for each scenario Livestock prod. Soil erosion C seq. Scenarios (UGOs) (Mg ha-1 year-1) (t C ha-1) 1) Maximize Production 11655,97 11.90 7.44

Wildlife conservation (guanacos number) 5231.68

2) 3) 4) 5) 6)

Production=ESs=Disservice Production>ESs>Disservice Production>Disservice >ESs Production> ESs and Disservice ESs and Disservice>Production

10178,47 10735,76 10541,40 11064,97 9882,97

10.38 10.95 10.75 11.29 10.07

8.55 8.08 8.23 7.83 8.84

5954.01 5658.19 5736.62 5489.88 6136.36