Application of Mathematical Modelling to Development Issues: An Illustrative Model on Agricultural Systems 1 Shahid Ahmad 2 Abstract Agricultural systems are diverse in nature depending upon the agro-ecology, market-economics and farmers preferences. Commonly practiced agricultural systems in the country include plant and/or livestock production. The integration makes these systems complex to model. Therefore, integrated systems can be modeled once the basic framework of individual systems is in place. The resource base for agriculture, unless husbanded carefully and replenished continuously, will dwindle in its capacity to produce at levels of global demand. The overuse of favoured environments, exploitation of under-utilized areas and excessive irrigation or chemical usage will lead to the same un-intended results: a narrower base for future production. Therefore, systems approach is essential, which takes the guesswork out of developing and managing agricultural resources for farming. The approach is based on the premise that a given commodity (crop, plant, animal, etc.) responds in a practicable way to its environment. The equation simply says that commodity response is dependent upon the commodity material selected as well as the environment and the manner in which this environment is modified through different commodity husbandry practices such as irrigation, drainage, pest control, etc. The basic elements of an agricultural system are included in the local climate, land and water resources. Also included here is human and socio-economic element. This is an extremely important part of the complex that many people forget in agricultural research and development. The basic elements provide the resources for growing a crop. Not one of the basic elements can be ignored in the system development if optimum production is expected. The development of an efficient database facilitates informed decision making for management of irrigated agriculture. The advantage of well established database is to access specific information in an organized and standardized format. The advent of IT has altered the scope of information processing. Computers are now able to process maps (spatial data) and tabular data (nonspatial data) and merge them together to give an added value. Using GIS tools, a user interface can be developed based on data available in different forms. The GIS based database is particularly useful for multi-sectoral analysis and planning strategies. The user interface provides the information in friendly and easy format in the form of maps, tables, and charts. Thus reliable and accurate information is a key for sustainable management of natural resources. This can be achieved by applying technologies such as geo-information technologies and mathematical modelling. Complex analyses require digital spatial data that define the characteristics of geographic space. In summary, mathematical modeling coupled with integrated databases and spatial analysis softwares can provide options for the application of systems approach to agriculture. 1. Agricultural Systems and Challenges 1.1. Agricultural Systems Agricultural systems are diverse in nature depending upon the agro-ecology and the farming systems practiced by the farming communities. The commonly practiced agricultural systems in the country are listed as under: q Plant production systems include crops, fruit/forest plants, forages, etc. These systems can be found under irrigated basin, Barani farming, rangelands, farm forestry systems, etc.; q Livestock production systems include poultry, small- and large-ruminants, freshwater aquaculture, etc. These systems can be found under irrigated agriculture and Barani farming; 1 Paper Presented in the Introductory Workshop on Mathematical Modelling and its Application to Development Issues, October 29 th to November 2 nd, 2002, COMSATS, Islamabad. 2 Chief Scientific Officer/Senior Director (Water Resources), Natural Resources Division, Pakistan Agricultural Research Council, Islamabad. 1
q Integrated systems, where integration is based on preferences of farmers i.e. crops, livestock, aquaculture and forestry. In Pakistan, majority of farmers especially the small- and mediumholders are engaged in integrated farming mainly due to the involvement of the family labour. The integration makes the systems complex to model. Therefore, initially the individual systems may be modeled separately and then integrated systems can be modeled once the basic framework of individual systems is in place. Design and management of innovative and sustainable agricultural systems should be based on ecological principles. With this approach, interactions among agro-ecosystems components and processes are the central theme, as opposed to the more singular approach of trying to maximize anyone parameter, such as grain yields or milk production. Perhaps the most important barriers to adoption of sustainable agricultural systems are not biological or technological, but managerial, sociological and political (Ahmad and Sandhu 1988). 1.2. Challenges of Agricultural Development The agricultural development community is facing four challenges to have development of sustainable agricultural systems in Pakistan (Ahmad 1993). First is the challenge to better understand the true nature of agricultural sustainability in the country. There are serious weaknesses in the notion that we can simply transfer to the farming communities of varying ecosystems the technologies and systems developed at the experimental stations. Practices and policies that have found successful for mechanized agriculture often fail miserably on smallholder s farms where integrated land use is in practice with family labour. Likewise, trying to handle environmental problems by merely passing laws against degradation simply will not work. We must better educate ourselves as to the biological, technological, managerial, social, economic and political environments of the country. The second challenge is to work with the farming communities in creating and testing improved technologies and systems that will help them increase rural income, alleviate hunger, and conserve natural resources. Once again, there are limitations as to what can be transferred to the farming communities considering their socio-economic conditions. Technologies and systems must be adapted for the needs and environments of the country using the most modern scientific tools. Third is the challenge to create an economic and social environment that will encourage the adoption of the new technologies and systems. Policies must encourage this adoption, and needed outputs must be available. Universities and private voluntary organizations have key roles to play in helping to identify needed policy changes and to encourage their implementation. Fourth is the challenge to establish linkages between scientists and institutions to expedite cooperation between Pakistan and developed countries like USA. Such linkages will further the concept that sustainability is an international problem and opportunity. The struggle to further the sustainability of agriculture in Pakistan has just begun. 1.3. Challenges of Agricultural Research The resource base for agriculture, unless husbanded carefully and replenished continuously, will dwindle in its capacity to produce at levels of global demand. While the initial challenges of averting Malthusian famine has been met, at least for the present, new ones have emerged. q Globally, can yields be increased to and maintained at their technical and economic potential; 2
q Can productivity be improved in less-favoured areas that have become the last frontier of agricultural expansion; q Will production technologies maintain soil fertility and other vital resources upon which production depends? The overuse of favoured environments, exploitation of under-utilized areas and excessive irrigation or chemical usage will lead to the same un-intended results: a narrower base for future production. 2. Systems Approach in Agriculture 2.1. Systems Approach and Components The systems approach to agricultural development takes the guesswork out of developing and managing agricultural resources for farming. The approach is based on the premise that a given commodity (crop, plant, animal, etc.) responds in a practicable way to its environment. Agricultural system components for commodities are presented in Figure 1 (Ahmad and Sandhu 1988). The equation simply says that commodity response is dependent upon the commodity material selected as well as the environment and the manner in which this environment is modified through different commodity husbandry practices such as irrigation, drainage, pest control, etc. The basic elements of an agricultural system are included in the local climate, land and water resources. Also included here is human and socio-economic element. This is an extremely important part of the complex that many people forget in agricultural research and development. The basic elements provide the resources for growing a crop. Not one of the basic elements can be ignored in the system development if optimum production is expected (Ahmad et al. 2002). Commodity Material Complex (crop, plant, animal, etc.) Local Climate, Land, Water, Human, Economics. Modified by Husbandry Complex (crop, plant, animal, etc.) Commodity Response (crop, plant, animal, etc.) Figure 1. System Components for Agricultural Commodities 2.2. Crop Production System In Agricultural system development, the manner in which the variables, crop selection and plant husbandry practices are applied to the basic elements determines the success of the system. Table 1 is a simplified outline of the possible interaction of the variables with each of the basic elements. The interaction is actually much more complicated than this, but the importance of careful consideration of all the elements in the design or selection of any one element is evident even in this simplified example. For 3
instance, crop selection is dependent upon all of the basic elements, crops normally un-suited to the conditions may not be considered (Ahmad 1988). Table 1. Interaction of the Elements of an Agricultural System for Crop Production Basic Elements Climate Land Water Human Economics Variables or Modifying Elements Crop selection Irrigation Temperature Modification (Frost control or cooling) Crop selection Drainage Fertility Irrigation Soil amendment Tillage Crop selection Drainage Irrigation Water Treatment Crop selection Motivation Training Management Crop selection Irrigation Drainage Fertility Soil management Tillage Pest management 2.3. Sub-systems of Crop Production System For a given location, the basic elements are essentially fixed. The agricultural system for that area is a composite of the various modifiers as they act upon the basic elements. These interactions can be thought of sub-systems, each requiring design process that considers the relationship of the sub-system to the total agricultural system. When all the sub-systems are developed together, the basic elements of the system are tied together to give the desired result of optimum crop production. This results in a complete agricultural system for crop production as depicted in Figure 2 (Ahmad 1988). To make the agricultural system function at an optimum level, a project must be treated as a total system from its very inception. This system approach to agricultural developments is applicable to all types of projects but is essential in the successful development of agricultural resource management research. Agricultural resources management, as it is understood today, is a relatively new concept in agriculture and requires modification of many farming practices used in agriculture today. 4
Crop Selection and Management Subsystem Water Management Sub-system Soil Nutrient Management Sub-system OPTIMUM CROP PRODUCTION SYSTEM Tillage Sub-system Pest Management Sub-system Socio-economic Sub-system Figure 2. Sub-systems of the Crop Production System 2.4. Soil Nutrient Management Sub-System Nutrient cycling is the key to nutrient management in sustainable agricultural systems. Cycling can be viewed at several levels. On a field level in a natural system nutrients move from soil into plants and are returned to the soil via residue as plants die (Figure 3). Most of the nutrients are conserved in the cycle, but inputs from the atmosphere and losses due to erosion, leaching, de-nitrification, and ammonia volatilization must be considered. Agricultural systems differ from natural systems because nutrients are removed from the cycle in the harvested product (Figure 4). If the agricultural system is to continue, these nutrients must be replaced. In conventional agricultural systems nutrients are replenished with commercial fertilizers. The nutrient cycle can be expanded to include an entire farm (Figure 5). On a crop/livestock farm nutrients are removed from the fields and leave the farm either in harvested crops or in animal products. A large fraction of the nutrients consumed by animals do not leave the cycle because they are returned to the soil in manure. Nutrients lost from the system are replenished with fertilizer and purchased feed. The cycle can be expanded further to include nutrient cycling in a region (Figure 6). Harvested crops, animals and animals products leave the farm and are processed before being sold to consumers in the city. Most of the nutrients in these products end up in landfills or in surface water rather than being cycled back to the farm. In a few cases by-products from food processing may be returned to farms near the processor. More prevalent is the recycling of nutrients in sewage sludge. However, although many cities apply sludge to agricultural land and some apply sewage effluent to land, only a small fraction of the total cropland in a region is affected. The other example of using the agro-based processing industry is the sugar industry where press-mud is used to reclaim sodic soils but provides nutrients (NPK and micro-nutrients 7-8%). Similarly, now molasses are also being used for the 5
propagation of the microorganisms and some farmers do apply these as fertigation to manage the sodic soils, as the ph of molasses is around 4.5. Consequently, nutrients lost from the cycle are replaced mainly with commercial fertilizer. To make an agricultural system more sustainable, losses from leaching, erosion, de-nitrification, and ammonia volatilization must be minimized while maximizing nitrogen input via biological nitrogen fixation; utilization of nutrients currently present in the soil; and, where practical, recycling of nutrients from off-farm sources. PLANT RESIDUE ATMOSPHERE (N fixation, nitrate, sulfate) SOIL LOSSES: leaching, erosion, de-nitrification, NH 3 Figure 3. Nutrient Cycling in Natural Systems. PLANT HARVEST RESIDUE ATMOSPHERE SOIL FERTILIZER LOSSES Figure 4. Nutrient Cycling in an Agricultural System 6
Milk ATMOSPHERE Meat RESIDUE PLANT ANIMAL Feed SOIL Fertilizer LOSSES: erosion, leaching, denitification, NH 3 Figure 5. Nutrients Cycling on a Farm. Feed, Fertilizer FARM1 PROCESSING PLANT By-products sludge CITY effluent Erosion Leaching De-nitrification LANDFILL & RIVER Figure 6. Nutrient Cycling in a Region 7
2.5. Water Management Sub-system The Water management sub-system is one of the essential elements of the agricultural system, where water is the crucial input in agricultural system. The first-most important component of the water management sub-system is adjusting crops with water availability. As water is always a scarce commodity, therefore farmers have to make adjustments prior to a cropping season i.e. Rabi and Kharif. The decision making at this stage is important to decide what crops to be grown and area under each crop so that productivity and profitability can be optimized (Figure 7). Water Availability at the Farm Level (surface and groundwater) Farm Area, Number of Fields, Field Sizes, Watercourse Layout Adjusting Crops, Cropping Pattern and Cropping Intensity with Water Availability Soils (type, texture, infiltration rate, moisture retention characteristics, bulk density, etc.) Crops Selection, Cropping Pattern, Cropping Intensity, Crop Profitability Figure 7. Adjusting Crops with Water Availability The second important aspect of the water management sub-system is to compute the net irrigation water requirement considering the crop evapotranspiration, irrigation systems, soil, field layout, etc. The details are given in Figure 8. Computation of Reference Crop Evapotranspiration using the Daily Climatic Data and Equations Calibrated for Pakistan Selection of Crops, Crop Coefficients, Planting and Harvesting Dates, Growing Season Length, etc. Estimation of Daily Actual Crop Evapotranspiration and Seasonal Crop Water Requirement of Selected Crops 8
Irrigation Scheduling for Selected Crops, Field and farm Level Considering Irrigation Practices, Rooting Depth, Management Allowed Deficit, Crop Management Strategies considering Phenological Requirement Estimate Gross Irrigation Water Requirement and Adjusting the Irrigation Depth by imposing Criteria for D min and D max Considering the Irrigation System used and the Surface Irrigation Hydraulics Estimate Leaching Fraction considering the Soil and Water Quality and Water Table Depth to Maintain the Basin Health and Adjust the Gross Irrigation Water Requirement. Also Compute Drainable Surplus Figure 8. Scheduling for Irrigation of Crops and Salt Balance at the Farm Level 3. Integrated Database Development and Decision Support System 3.1. Conceptual Framework The development of an efficient database facilitates informed decision making for management of irrigated agriculture. The advantage of well established database is to access specific information in an organized and standardized format. The advent of IT has altered the scope of information processing. Computers are now able to process maps (spatial data) and tabular data (non-spatial data) and merge them together to give an added value. Using GIS tools, a user interface can be developed based on data available in different forms. The GIS based database is particularly useful for multi-sectoral analysis and planning strategies. The user interface provides the information in friendly and easy format in the form of maps, tables, and charts. The conceptual framework for the development of Integrated Database and Decision Support System is presented in Figure 9 (Ahmad et al. 2002). 3.2. Tools for Integrated Database Presently, various state-of-the-art tools like GIS/RS, EXCEL and other software like Visual Basic are available to establish better and efficient database. Institutions like IWMI and WRRI-NARC, in collaboration with partners, intend to establish integrated databases that can be used by various government agencies, research institutes and universities involved in management of irrigated agriculture. Use of GIS is gradually replacing the conventional approach to spatial information handling. Current handling of spatial information among line agencies is neither efficient nor effective. Spatial data are generally not available or are poorly maintained, out of date, and often inaccurate. Maps are on varying scales and have different coordinate systems, making it difficult to make overlays and integrate 9
them. Moreover, spatial information is often not defined in a consistent and natural manner (Ahmad et al. 2002). 3.3. Case Studies from Pakistan 3.3.1. Integrated Database Development for the Rechna Doab of the Indus Basin The Rechna Doab was selected by the International Water Management Institute (IWMI), Pakistan as a benchmark basin to develop integrated database. The Rechna Doab is the interfluvial area between the rivers of Chenab and Ravi. The gross area of Rechna Doab is 2.97 million hectares out of which 2.3 million hectares are cultivable. It is one of the oldest and most intensively developed irrigated areas of the Punjab, Pakistan. The area falls in the rice-wheat and sugarcane-wheat agro-ecological zones. Rice, cotton and fodders are dominating crops in the Kharif season, and wheat and fodders in the Rabi season. In some parts of the Doab, sugarcane is also cultivated which is an annual crop (IWMI 2000). The main purpose of the basin case studies being conducted by the IWMI is to facilitate in integrated water resource management challenges by information and knowledge. Reliable and accurate information is the key for development and equitable distribution of water resources. This can be achieved by applying technologies such as geo-information technologies. The details of inputs, analysis and output are presented in Figure 10 (IWMI 2000). 3.3.2. Integrated Database Development for the HKH Region of Pakistan The Himalaya, Karakuram and Hindukush (HKH) region of Pakistan covers an extensive area of Pakistan comprising northern, northwestern and western and southwestern parts of the country. The major areas excluded are Indus basin, deserts and coastal areas of the Sindh province. It covers all the mountainous and sub-mountainous tract of Pakistan. The WRRI-NARC started the development of integrated database for the HKH region of Pakistan. The base map was digitized using the scale of 1:250,000. Initially the work was started for the Balochistan part of the HKH region, which has been completed and now work of digitization is underway for the other parts of the HKH region. The main purpose of the catchments case studies being conducted by the WRRI-NARC is to contribute to address Integrated Natural Resources Management (INRM) by generating, synthesizing and disseminating information and knowledge for use by the people concerned (WRRI and IUCN 1999a,b; WRRI 2000 a,b; WRRI 2001). Reliable and accurate information is a key for sustainable management of natural resources. This can be achieved by applying technologies such as geo-information technologies (Ahmad et al. 1999). Complex analyses require digital spatial data that define the characteristics of geographic space. The details of inputs, analysis and output are presented in Figure 11. 10
Line Agencies WAPDA Irrigation Department Agriculture Department Soil Survey of Pakistan Survey of Pakistan Meteorological Department Water & Sanitation Health Department Others GIS Integrated Database Feedback DSS Beneficiaries Policy Maker Planner Manager Scientist Student Figure 9. Conceptual framework for Integrated Database and Decision Support System (DSS) GIS/RS Map Data Satellite Data Tabular Data Data Collection Database Development GIS/RS Analysis Spatial Modeling Water Productivity Environmental Impact Irrigated area Mapping Information for Decision Making Figure 10. Input, analysis and output of the integrated database for Rechna Doab. 11
GIS/RS GIS/RS M ap Data Satellite Data Tabular Data Data Collection Database Development Topography Hydrology Groundwater Surface W ater Land Cover Vegetation Type Agroclimate Communication Agriculture Population Agriculture Population Others Othe rs GIS/RS Analysis Information for Decision Making Resource Sustainability Spatial Modeling Environmental Impact Catchment area Mapping Figure 11. Input, analysis and output of the integrated database for the HKH Region of Pakistan. References 1. Ahmad, S. and G.R. Sandhu. 1988. Agricultural modelling: Computer assisted system's approach. Progressive Farming, 8(2):26-31. 2. Ahmad, S. 1993. Viability of Agricultural Resource base: A critical appraisal. In: Agricultural Strategies in the 1990s: Issues and Policies. ED. A.S. Haider; Z. Hussain, R. McConnen and S. J. Malik. Pakistan Association of Agricultural Social Sciences. Islamabad. p.436-448. 3. Ahmad, S., R. Roohi and A. Kohlown. 1999. Application of GIS for the evaluation of agroenvironment in the semi-arid areas of Pakistan. Proceedings of the 6 th JIRCAS International Symposium on GIS Applications for Agro-Environmental Issues in Developing Regions. Ed. M. Kokubun, S. Uchida and K. Tsurumi. JIRCAS. Ministry of Agriculture, Forestry and Fisheries. p. 85-104. 4. Ahmad, S., N.A. Bhatti and R. Majeed. 2002. Water Informatics. In. Water and New Technologies. Edited by Dr. Ishfaq Ahmad, Global Change Impact Study Centre, Islamabad. p.135-158. 5. IWMI. 2000. A Framework for River Basin Management. Integrated Database Development for Rechna Doab. International Water Management Institute, Pakistan. 6. WRRI and IUCN. 1999a. Landcover map of Pakistan. Water Resources Research Institute, National Agricultural Research Institute, Islamabad. Map Series. 7. WRRI and IUCN. 1999b. Vegetation types map of Pakistan. Water Resource Research Institute, National Agriculture Research Centre, Islamabad. 12
8. WRRI. 2000a. Spatial and temporal analysis of groundwater in MONA SCARP area. Methodology Report-I. Water Resources Research Institute, National Agricultural Research center, Islamabad. 32 p. 9. WRRI. 2000b. Effect of Kalabagh dam reservoir on Salt Range and associated environmental concerns. Water Resources Research Institute, National Agricultural Research center, Islamabad. 10 p. 10. WRRI. 2001. Assessment of hydrological potential for installation of dugwells: Development of practical methodology. Water Resource Research Institute, National Agriculture Research Centre, Islamabad. 16 p. 13