Optimizlng the Management of Soil Erosion

OPTIMIZING THE MANAGEMENT OF SOIL EROSION USING GIS Davood Nikkami A Thesis in the Department of Building, Civil, and Environmental Engineering Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy at Concordia University Montreal, Quekc, Canada August 1999 @ Davood Nikkami, 1999 National Library Bibliothèque nationale du Canada Acquisitions and Bibliogisphic Services Acquisitions et services bibliographiques 395 WeUington Street Ottawa ON K1A ON4 Canada 395, rue Wellington Ottawa ON K1A ON4 Canada The author has granted a nonexclusive licence allowing the National Library of Canada to reproduce, loan, distnbute or sel1 copies of this thesis in microform, paper or electronic fonnats. L'auteur a accordé une Licence non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/film, de reproduction sur papier ou sur format électronique. The author retains ownership of the copyright in this thesis. Neither the thesis nor substantial extracts tiom it may be printed or othenvise reproduced without the author's permission. L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation. ABSTRACT OPTIMIZLNG THE MANAGEMENT OF SOIL EROSION USING GIS Dxood Nikkami, Ph.D. Concordia University, 1999 The dynamic nature of erosion and associated processes and their dependence on climatic, pedological, land cover, land use, and management factors result in spatial and temporal variability. Computing and mapping this variability will produce information w hich is essential for designing dams, reservoin, channels, soi 1 conservation management pians, and the evaluation of on-site and off-site damages by soi1 erosion. land use projects, and transport of pollutanrs. This thesis presents the Modified Universal Soi1 Loss Equation (MUSLE)as a promising tool for the spatial rnodelin_o of soil erosion by water integrated with the SPatid ANalysis System (SPANS)-GIS. The information that resulted from this integraiion was used for land-use optirnization to rninimize sediment yield and maximize watershel fm income by a multi-objective linear progamming model. These models were applied to Syahrood, one of the sub-basins cf Damavûnd watershed in Iran, where soil erosion by water is one of the major land-related problems. Runoff erosivity, soil erodibility, dope len~th,slope steepness, cover management, and erosion control practice factors were computed and included in the digitized and iii computed Thiessen polygon, land component, slope and land-use maps of the watenhed. The sediment yield of each land use was computed by overlaying these maps with the appropriate models in the SPANS-GIS. The optimization process allocmed drylandfarming areas to rangelands if no changes are made to the current supporting practice system. The expected annual sediment yield from the entire sub-basin was reduced by 2420 t/y (or by 5%) and the annual net farm income was increased by 3.99 billion banian RiaVy (or by 134%). Results demonstrated that interfacing MUSLE with a GIS is an effective method for the prediction of soi1 erosion in luge watersheds with limited data sets. Overlay opentions enable the Imd manager to obtain higher quality results in a shoner period of tirne compmed to manual calculations. A GIS simplifies the extracting of necessary factors from the databases. However the SPANS-GIS6.0 was weak in preparing a slope map from the digital elevation database for such mountainous areas. The results indicate that application of land-use optimization methods to reduce sediment yields has great potentiûl in the study area and in othrr watersheds. The methodology developed in this study can provide a useful tool for watershed managers to reduce sediment yield (soi1 conservation) while increasing the income of the local inhabitnnts. Acknowledgrnents The author is profoundly grateful to his supervisors Dr. M. Elekorowicz of Concordia University and Dr. G.R. Mehuys of McGill University, for their valuable guidance. patience, suggestions, and corrections. Their COnsmctive guidance. fruitful discussions, engineering jud,ment, and conscientious rupervision ensured the completion of the present work. Acknowled~ments are due to the Deputment of Building, Civil, and Environmental Engineering for the supply of excellent computer facilities. The author also gratefully acknowledges the Department of Education and Research in the Ministry of Construction of Iran, especially Mr. S. Yousof-Kalafi for supplyinp valuable information on the study aren. The authot also wishes to express his h e d e l t thanks to his whole family for their mord support and encouragement. Finally, the author extends his special thûnks to his wife, F. Kargahi, for her support. encouragement and understanding. To M y Family TABLE OF CONTENTS Content- Paoe - LIST OF FIGURES xi LIST OF TABLES xiii LIST OF SYMBOLS xv CHAPTER 1 INTRODUCTION 1.1 Background and statement of the problem 1.2 Objectives 1.3 Thesis organization CHAPTER 2 LITERATURE REVEW S 2.1 Soi1 erosion 8 2.1.1 Introduction S 2.1.2 Soi1 erosion prediction 10 2.1.3.1 Before Univend Soi1 Loss Equation (USLE) 10 2.1.2.2 Universal Soi1 Loss Equation (USLE) 13 2.1.2.3 Modified Universal Soil Loss Equotion (MUSLE) 15 2.1.3 Conclusion 16 2.2 Geographic Information Systems (GIS) 17 2.2.1 Introduction 17 2.2.2 ~ e 0 g r a ~ hdata .k 19 vii 3.2.3 GIS software 2.2.4 GIS and modeling soi1 erosion 2.2.5 Conclusion 2.3 Optimization 2.3.1 Optimization techniques 2.3.2 Multi-objective programming 2.3.3 Conclusion CHAPTER 3 STUI)Y AREA AND DATABASE 3.1 Study area 3.2 Development of database 3.2.1 Digitking hardcopy maps by SPrtUS-TYDK 3.2.2 Development of digitized maps in SPANS-GIS CHAPTER 4 MODELING S O L EROSION IN A GIS 4.1 Soi1 erodibility factor (K) 4.2 Slope length and steepness factors (L and S) 4.3 Cropping system factor (C) 4.3.1 Cropping system factor (C)for rangelands 4.3.2 Cropping system fiictor (C) for croplands 4.3.2.1 Cropping system factor (C) for drylûnds 4.3.1.2 Cropping system factor (C) for imgated lands 4.3.2.3 Cropping system factor (C) for orchards 4.4 S upporting practices factor (P) 61 4.5 Computing mnoff peak flow (Q) 62 4.6 Cornputing the volume of runoff water (V) ûpplied to each polygo:: 63 4.7 Cornputing sediment yield 70 CHAPTER 5 G-0 THE MANAGElMELCT OF S O L EROSION 73 5.1 Formulation of the problem 73 5.2 Estimation of constants 76 5.2.1 Estimation of each land use area ( B , ,B2,B,, B,, B,, B,, B,) . . 5.2.2 Estimation of soi1 erosion in each land use (C,C-.C, C,) 5.2.3 Estimation of benefit and cost in orchards (4,&) 76 75 7s 5.2.4 Estimation of benefir and cost in ranp_eliinds (Af- ,k- ) 79 5.2.5 Estimation of benefit and cost in imgared lands ( A : , $ ) 81 5.2.6 Estimation of benefit and cost in drylands (A:,A:) 81 5.2.7 Estimation of erosion cost in each land use (43, 4,& A:) 5.3 Solution of the problem C H M E R 6 DISCUSSION, CONCLUSIONS, AND SUGGESTIONS 6.1 Accuracy of sediment yield modeling within SPANS-GIS 82 83 85 89 6.1.1 Accuracy of soi1 erosion model 92 6.1.2 Accuracy of modeling in GIS environment 92 6.2 Sensitivity analysis of the optimization mode1 94 6.3 Conclusion 6.4Suggestions for future work LIST OF FIGURES Fi oure Page Typicûl form of interrill and riIl erosion Typicd form of gully erosion Dia-m of the multi-objective propunmine methods Study area (Syahrood sub-basin) on the Iran map Study area (Syahrood) in the Damavand watershed Typical fonn of good quality rangelands in Syahrood sub-basin Typical form of improper degraded drylands in Syahrood sub-basin Digitized elevation and hydrologic soil group maps of Syahrood Digitized land-component and land-use maps of Syahrood Elevlition rnap of Syahrood sub-basin Hydrologie soil group rnap of Syahrood sub-basin Land-component map of Syahrood sub-basin Land-use map of Syahrood sub-basin Overlay opention in the GIS environment Nomopph of Wischmeier and Smith (1978) Slope map of Syahrood sub-basin Thiessen polygon map of Dmavand watenhed Thiessen polygon rnap of Syahrood sub-basin Consistency andysis of Ardineh station Consistency analysis of Cheshmeh station Consistency analysis of Gol Khandan station Consistency anaiysis of Lavasan Bozorg station Consistency analysis of Mani00 station Consistency analysis of Maara station Overlaid land-use and slope maps of Syahrood sub-basin Sediment yield in each (and use of Syahrood sub-basin Land use area in Syahrood before and after optirnization Annunl sediment yield in Syahrood before and after optimization Annual net income in Syahrood before and after optirnization xii LIST OF TABLES Table Paoe A multi-objective sirnplex tableau 30 Land use classes in Syahrcod sub-basin 35 Land component classes in Syûhrood sub-basin 36 Slope classes of Syd~roodsub-basin 38 Characteristics of hydrologie soi1 groups in Syahrood sub-basin 39 Soi1 fractions and K factors on each land component of Syahrood 50 L and S factors of each slope class in Syahrood sub-basin 52 C factor for rangelands in Syahrood sub-basin 53 Cumulative percentage of the average annual El extracted from sin raingauges in Dmüvand watershed 55 C factor for drylands (alfalfa and small grains) in Syahrood sub-basin 57 C factor for drylands (pea) in Synhrood sub-basin 5s C factor for imgated lands (smali grains) in Syahrood sub-basin 59 C factor for imgated lands (grains) in Syahrood sub-basin 60 C factor for imgated lands (alfiilfa) in Syahrood sub-basin 60 C factor for imgated lm& (potato and vegetable) in Syahrood sub-basin 6 1 CP factors for each land use in Syahrood sub-basin 62 c, for each dope class of Syahrood sub-basin 63 Computing Q for Syahrood sub-basin 63 Sr for each combination of land-use and hydrologie soi1 poup 69 xiii Sr for each Thiessen polygon area in Syahrood sub-basin LS.CP for each land use in Syahrood sub-bain K.LS.CP for each land use of Syahrood sub-basin Sediment jield in each land use of Syahrood sub-basin Distribution of land use activities in different slope classes of Syahrood Major orchud crops and their costhenefit information in Syahrood Differentiation of rangelands by type, area. and production in Syahrood Major imgated land crops and their cosVbenefit information in Syahrood Major dryland crops and their cosdbenefir information in Syahrood Estimated economical losses due to sediment yield in Syahrood Current land uses and production of Syahrood sub-bûsin Linear multi-objective simplex tableau of Syahrood sub-basin problem Land-use optirnization output of Syahrood sub-basin Sensitivity analysis of land resources (Bi) in Syahrood Sensitivity ûnalysis of A{ in optirnizing land use activities in Syahrood Sensitivity analysis of C,in optimizing land use activities in Syahrood LIST OF SYMBOLS Svrnbol A Description Unit Average annud soi1 loss A v e n p annual rninfall erosivity factor Soi1 erodibility factor ha.lMJ.mrn Slope length factor dimensionless Slope steepness factor dimensionless Cropping system factor dimensionless Supporting practices factor dimensionless Sediment yield t Peak flow Volume of water applied to the area Daily rainfall Retention parmeter mm Runoff curve number dimensionless Drainage areo ha Time to peak of the unit hydropph h Coefficient on type of land Length of the watenhed dimensionless Distance from the outlet to the center of the watershed m Objective function coefficient Decision v-iable Technological coefficient Right-hand side coefficient Number of constrriints or slack variables Number of decision variables Number of objective functions Reduced cost Hydrologic soil group with minimum infiltration of 7.67-1 1.43 mm/h Hydrologic soi1 goup with minimum infiltration of 3.8 1-7.62 m d h Hydrologic soi1 group with minimum infiltration of L .Y-3.8 1 mm/h Hydrologic soil group with minimum infiltration of 0.5- 1.27 mmlh Annud net fm income of whole watershed 1o6 Rially Annual sediment yield of whole watenhed VY Surface are3 of erich land use ha Annual sediment yield per unit area in e x h land use t/hri.y Amount of net fm income per unit area of each land use 106RiaIlha Production cost per unit area of each land use 106Riaiha Cost due to soi1 loss per unit area of each lmd use 1o6RiaVha Surface areo of each land use ha xvi Area allocated to orchard Area allocated to rangeland Area allocated to imgated land Area allocated to dryland Amount of net f m income per unit area of orchard Production cost per unit area of orchard Erosion cost per unit area of orchard Amount of net fann income per unit area of rangeland Production cost per unit area of rangeland Erosion cost per unit area of rangeland Amount OF net fm income per unit area of imzated land Production cost per unit area of irrignted land Eïusion cos: per unit ûrea of imgated land Amount of net farm income per unit area of dryland Production cost per unit ûrea of dry land Erosion cost per unit area of dryland Annual sediment yield per unit area of orchard Annual sediment yield per unit area of rangeland Annud sediment yield per unit area of imgated land Annud sediment yield per unit areû of dryland Maximum limit of orchard surface area Surface area of imgated land Surface are? of dryland Surface area of orchard plus imgated land ha Total area ha Minimum Iimit of orchard surface area ha Surface area of rangeland ha Shadow price for resource i t xviii or 106 Rial CHAPTER 1 INTRODUCTION 1.1 Background and statement of the problem Soi1 is produced as a result of the decomposition of rocks by chernicai, physical, biological. and climatological processes. Tens of thousands of years may be required in the formation of differentiated layers of soil. The process is slow enough that soil can be considered a nonrenewable resource. Climate. overland cover, geology, topography and land uses promote a combinntion of events that control the amount of soil removal and transport, either by water or by wind. The woodcutting, o v e r p i n g , and destructive cultivation thnt caused devastation in the Middle East thousands of yean ago (Lowdermilk, 194s) has continued in the intervening years until there is little land left that has not suffered man-made degradation. Peme (1970) contends that rangeland deterioration (and erosion) has acceleratrd since 1950, primarily due to a doubling or tripling of livestock numbers, extensive plowing of rangeiands, fmwood cutting, expansion of well drilling into fomerly inaccessible areas. and better transportation facilities. Destruction of vegtative cover o n snndy soils in Inn has led tu increased wind erosion and required strenuous efforts to stabilize the dunes that have formed (Niloiam and Ahrimjani, 1976). The area of abmdoned arable land in !nn has doubled in recent y e m and the number of livestock on grazing lands is estimated to be two to three times the canying capacity. Accelerated erosion is the result of two factors: improper management of productive soils and exploitation of marginal lands @regne, 1983); both mean using lands without considering their suitability . The primary energy causing erosion by water is gavity, through Mling precipitation and flow down the terrain slope. Raindrop splnsh and overland flow detach soil particles which are then transported down-slope by the kinetic energy transferred from the water flow to the sediment (Crinali, 1992). The sorting action by erosion agents causes removd of a high proportion of the c h y ' and humus' from the soil and leaves the coasse sand3 and rock fragmentsJ behind. Most of the soil fertility is associated with clay and humus. These components also are important in microbiûl activity, soil structure, permeability, and water storase. Thus, an eroded soil is d e p d e d chemically, physically and biolog~cally. The eroded soil becomes sediment that covers bottomlmds and man-made structures. Gullies, sand dunes. and other obvious signs of erosion are examples of using the lands without proper management. Proper management implies long-term usefulness as well as satisfying current needs. The cost of erosion in ternis of yield reduction is difficult to determine. Based on data relating topsoil loss to yield reductions, just 3.5 cm of topsoil loss is enough to reduce U.S.wheat yields an average of 60 million bushels (bushel = 35.2 1 liter) every year (Drege, 1952). l A soil sepuate consisting of pyticles c0.001 mm in equivdent diameter (S.S.S.A., 1998). 'Toul of the o r p i c cornpounds in soil exclusive of undeciyed plant and animal tissues, their "partial decomposition"products, and the soil biomass. The term is oftcn used synonymously with soi1 organic matter. (S.S.S.A., 1998). A soil pyticle between 1.0 to 0 5 mm in diameter (S.S.S.A., 1998). 4 Unattached piccer of rock 2.0 mm in duneter or lvger that are strongly cemented or more resisunt to rupture. (S.S.S.A., 1998). Deterioration in the quality of cropping and gazing land as a result of erosion reduces productivity and increases expenditure on fertilizen to maintain fertility. In extreme cases yields becorne so poor that land has to be taken out of cultivation (Morgan. 1956). Many researchen have observed declining crop yields with decreasing topsoil depth (Segrna, 1993). Erosion adds to the cost of producing food and other soil products and thereby increlises the cost of living. Taking ruined land out of production places a greeater load on the remaining land and drives up production costs. Implementing expensive erosion control practices dso adds to production costs. Perhaps the most costly result of soi1 erosion is related to damage done by the soil particles that are dislodged and moved downwind or downstrem. ~edirnentation'raises streambeds, reducing the depth and capacity of the channels. This causes navigation problems and can lead to severe flooding. Sedimentation of lakes and reservoirs reduces their capacity, value, and life expectancy (Frederick et al., 1991). Erosion has become an environmental problem that must be remedied for the sake of clenn air and warer. Soi1 particles dsorb pollutants such as pesticides. fertilizen. and different industrial and municipal chernicals that are best kept out of water by keeping the soil on the land (Glymph. 1971; Foster, 198s; Singh. 1997; Wanielistn and Yousef, 1993). Keepin: sediment out of water lowen the supply of plant nutrients in the water and thereby reduces unwanted growth of algae and other vegetation, which is an important problem in most riven, reservoirs and lakes. Changing the aquatic environment of streams and lakes reduces their value for home and industriai use, recreation, and fish and wildlife (Frederick et ai., 1991). Controlling soil erosion keeps streams. ponds, and lakes from ' Deposition of soi1 puticles dter the processes of detachment and anspomtion (Renard et al., 1989). filling as rapidly with sediment. Reservoir capacities are thus maintained for recreation, flood control, power generation. and imgation. Regarding the time needed for soil formation under different climatic, topogmphic, and biological conditions, Birkeland (1974) concluded thot lo5 to 106 yexs are required to develop weathered surfaces on granite rocks, and longer periods are required for non-granite rocks. The development of a mollic horizon' requires from 200 to 3000 yevs (Birkeland, 1974). The prevention of soil erosion, which means reducing the rate of soil erosion to approxirnately that which would occur under nûtural conditions, relies on selecting appropriate strattegies for soil conservation (Morgan, 1979). Although it is impossible to stop soil erosion completely under natural conditions. there is a great need to control erosion for proper land and water use planning. This requires awareness of sediment yield' acd foreseeing changes such as in land use. Therefore, sediment yield determination as a base for proper land and water use planning is of greot importance. Since most watersheds, p;irticularly smÿll watersheds, are o f t a un-gauged, sediment yield determination cannot be made due to lack of dma. Predicting sediment yield for such watenheds is imperative. Estimates of watershed sediment yield are required for solution of a number of problems. Design of dams and reservoin, transport of pollutants, design of soi1 conservation practices, design of stable channels, determination of the effects of basin - . A surface horizon of minera1 soil that is duk colored and rclatively thick contains at lest 5.8 @g organic carbon, is not massive and hard or very hard when dry, and has a brise saturation of >SOS when mesurcd at pH 7 (SSSA, 1998). The mount of emded mil that is delivered to a point in the wstenhed that is remoce fiom the ongin of the demched soil prinicles (Renard et al., 1989). I management, off-site damage evaluation, and cost evaluation of a water-resources project are some of the example problems (Singh, 1992). A major problem in the area of spatial data rnodeling has been the complexity of handling, manipulating, and mmaging large volumes of input panmeters and data. In recent years, modeling in a Geographic Information System (GIS)environment, which refers to creation of digital databases interacting airh a mathematical model, has been developed. GIS is now ~rovidingthe opponunity and tools to spatially orgmize and effectively manage huge quantities of data for modeling. Land-use optimization, on the other hand, is one of the appropriate strategies for soil conservation. It can empower the decision-maker or watenhed manager to choose from different land-use scenarios to rerich the best decision between the different combinations of variables. Development of a methodolo_gy and associared tools for rnodeling the management of soil erosion could be one of the research components. Integration of a soil erosion model with a GIS should provide an effective method for the prediction of soi1 erosion in a vast area. To reduce the environmental and economical impact of soi1 erosion resulting from improper management of land-use activities, a study was inirioted by Iranian Ministry of Construction on Syahrood, one of the sub-bassins of Dmavand watershed in han. 1.2 Objectives The main objective of present study was to develop a new methodolo=y and associated tools to predict the sediment yield with grenter reliability in watersheds with deficiency of recorded rain gauge data. A subsequent objective was to optirnize land-use activities of a watershed in such a way that soil erosion is minimized while mwimizing the agicultural econornic income. Integrating a soil erosion model with a GIS would serve to handle the complexity of modeling huge volumes of input parameters and overlayinp data themes containing spatially distributed factors. Combination of the results would proiide a guideline for decision-rnakers or watershed managers to optimize the use of water and soil resources for long-tenn sustainability. 1.3 Thesis organization The work presented in this thesis consists of six chapters: Chapter 1 introduces general information about soil ero sio on, its on-site and offsite problems, and the need for its prediction. Objectives of this study are also part of this c hapter. Chiipter 2 gives some background information about predicting soil erosion. GIS, and optimization. USLE. RUSLE. MUSLE, and WEPP are introduced as available soil erosion prediction models. ARC/INFû, ArcView, IDRISI, GRA4SS,and SPr\Er'S are introduced as the most popular GIS packages for spatial data modeling. Multi-objective linear progamming is also introduced as a powerful model in optimization. Chnpter 3 introduces Syahrood one of the sub-basins of D m a v m d warenbed in irm as the study area. This chapter also, presents the procedure of developing spatial dmbase for modeling soil erosion in a GIS environment. - Chapter 4 explains the first part of technical approach, containing the inte_ption of EIIUSLE with SPANS-GIS for modeling soi1 erosion under different land uses of Syahrood sub-basin. Chapters 5 presents the second part of technical approach, rninimizing soi1 erosion agricultural economic income by utilizing the simplex method of while m~~irnizing multi-objective Iinear p r o g m n g . Discussion and conclusions of the results and necessary future work relaicd to the area of this reseûrch are covered in Chapter 6. CHAPTER 2 LITERATURE REVIEW This chapter is divided into three sections. Section 2.1 presents background on soi1 erosion and sediment yicld prediction. A brief discussion of the most farnous soi! erosion inodels such as the Universal Soil Loss Equation (CSLE). Re\ ised Vniversal Soil Loss Equation (RUSLE), Modified Universal Soil Loss Equation (MUSLE), and Water Erosion Prediction Project (WEPP), is the subject of this section. In Section 2.2. Geographic Information Systems (GIS), their organizûtion. fundamental components of geographically referenced data. and modeling in GIS envirocments are presented. Finally, operational research, opt imizat ion techniques, and mu1ti-objective programming are discussed in Section 2.3. 2.1 Soil erosion 2.1.1 Introduction Water erosion is a serious problem in subhumid, semiarid, and arid regions. [nadequate rnoisture and periodic droughts reduce the periods when growing plants provide good soil cover and limit the quantities of plant residue produced. Erosive rainstorrns are not uncommon and they are usu~llyconcentrated within the season-when cropland is least protected (Wischmeier and Smith, 1978). Ellison (1946) has dehed soil erosion as a process of detachment and transportation of soil materials by erosive agents, such as water and wind. Water, as rainfall and runo& is the active agent for die basic process of water erosion (Cook, 1936). The third soü erosion process is deposition (Ekem, 1950), and it happens when suEcient energy is no longer available to transport the soil particles any further (Morgaa 1986). The energy available for erosion takes two forms: potential and kinetic (Morgan, 1979). Potenthl energy results fkom the difference in height of one body with respect to another. This energy in the form of rainfall causes splash erosion The potential energy for erosion is converted into kinetic energy, the energy of motion of the running water. This kind of energy in running water causes interrill, ri& gully, and riverbnnk erosion. Figures 2.1 and 2.2 represent typical forms of interrill, rill and gully erosion. Figure 2.1 Typical form of interrill and riN erosion One of the needs in the area of soil erosion control as in al1 areas of science, has been to develop quantitative relationships among many factors, such as dope, rainfali, runo& soil physical properties (texture, structure, permeability, etc.), and crop cover, that influence erosion (Pratt, 1979). Erosion prediction is the most widely used and most effective tool for use, management, assessrnent of land, soi1 conservation planning and design in wateaheds (Lden et al., 1 99 1). 2.1.2 Soi1 erosion prediction 2.1.2.1 Before Universal Soü los^ Equation (USLE) The fira cornprehensive e.8ort to quant* some of the nctors affecthg soil erosion began with the establishment of the erosion plots in 1914 by M.F.Miller, at the University of Missouri. The ïunoff that accumulated in the concrete tanks at the end of the plots was xooped, weighed, q d sampled. H.H.Bennett, a soii surveyor in the Bureau of Soils in Washington D.C.,obsmed th resuhs fiom the control plots of Miller. He recognized the need for similar studies in other areas of the U.S. where soils, rainfall, and cropping practices differed widely from those at the Missouri control plots (Browning, 1979). Development of &pations for calculating field soil loss began in about 1940 in the Corn Belt States. In 1940 Zingg published an equation relating soil-loss rate to leneth and percentage of slope. In the following year, Smith d d e d crop and conservationpractice factors and the concept of a specified soil-loss limit, to develop a graphical method for selecting conservation practices needed on specific soi1 conditions of the Midwest U.S.(Wischmeier and Smith, 1965). Progress in developing an equation to predict soil loss was made afier World War II (Sukresno, 1991). Browning and coworkers in 1947 added soil erodibility and management factors and prepared a set of tables to sirnplij. field use of the equation in Iowa (Wischmeier and Srnidi, 1965). Further equations and methods were developed over the next ten yeus. Smith and Whin in 1947 presented a method for estimating soil losses for claypan soils'. Soi1 loss ratios at different slopes were given for contour farming2, strip-croppin$, and terracing4. They developed tables and curves to cdculate soil loss from a field including tables for tolerable soil loss. The following year, Smith and Whin presented - - -- ' ;in equation for - A dense, compact, slowly permeable Iayer in the subsoil having a much hi&w clay content thm the ovalying material, Corn which it is sepanted by a sharply defmed bounduy. Claypms are usually hard when dry, and plastic and sticky when wet (S.S.S.A., 1998). This p n d c e is that of perfoming field operatioru, such as plowing, planting, cultivating, and harvesting approximately on the contour. tt reduces surface runoff by impowidmg water in srnail depressions and decreases the developent of dis, in which the Mgh water velocity results in destructive emsion (Schwab et al,, 198 1). ï h e practice of growing two or more cmps in alternathg strips along contours, often perpendiculûr to the ~ r e v a i h gdinetion of wind or d c e water flow (S.S.S.A., 1998). To deçreasc the lm@ of the hiiiside slope, thacby nducing shea and 81erosion, and retaining runoff in arcas of hadequate pmipitation, tenaces are constructed in these regions (Schwaù et ai., 1981). ' predicting soil loss based on slope gradient, slope lengthl, soil erodibilig, and supporting practices (Sukresno, 1991). biusgrave in 1947 showed that the pnmary factors infiuencing the rate of erosion are intensity and amount of ninfall, flow characteristics of surface runoff, soil erodibility, and p ~ ~ t e c t i veffects e of vegetation cover. This, in tum, was calied the Musgrave equation. Lloyd and Eley in 1952 M e r developed the Musgrave equation to estimate soil loss from large watersheds and to estimate sheet erosion3 rates in an attempt to determine sediment delivery rates fiom watersheds. Graphics were used for this solution (Sukresno, 199 1). An equation for estimating soil loss under different management and conservation practices on various soils in Illinois was presented by Van Doren and Bartelli in 1956. Nine factors were used in their equation. Where soil loss (A) was a f i c t i o n of dope gradient (S), slope length ((L) , conservation practices (P) , soil erodibility ( E l ) , intensity and frequency of 30-minute rainfâil ( I ) , previous erosion ( E ) , mana, dement ( M ) , and rotation (R). The equation is based on the evaluation of different factors influencing the amount of soil movement. The soi1 iuss factor, as measured on standard reseuch plots, was adjusted to site conditions based on data from previous researchers and factors for prior erosion and management levels (Sukresno, 1991). ' The horizontal dimince from the origin of overland flow to the point where either (i) the slope gradient decreases enough chat deposition begins or (ii) runoff becomcs concentrated in a defîed channel (Renard et al., 1989). A measun of the soil's susceptibility to detachment and transport by the agents of erosion (Lai, 1988). The removal of a relatively uniform thin layer of soil from the land surface by ninfall and largely unchanneled surface nmoff (S.S.S.A., 1998). * ' 2.1.2.2 Universol Soil Loss Equrtion (USLE) The National Runoff and Erosion Data Center of the United States was established by the United States Department of Agiculhue-Agricultural Research Service (USDA-ARS) ai Purdue University in 1954 to develop the USLE. The Data Center was given the responsibility for locating, assembling, and consolidating al1 available data on nuioff and erosion studies throughout the United States. More than 8000 plot-years of basic runoff and erosion data from more than 49 locations were assembled. These data were edited, coded, and recorded on punch cards at the Data Center for summarizing and overall statistical analysis. Wischmeier and Smith (1965) developed the Universal Soil Loss Equation (USLE) which was first published in Agriculture Handbook 282. The USLE has been continuously refined through research and g a t h e ~ of g additional data. Wischrneier and Smith (1 978) developed the new USLE for predicting rainfall erosion losses. This mode1 and its guide were published in Agriculture Handbook 537. Predicting soil loss (A) by this method, requires the assessrnent of six factors (Wischrneier, 1976 and Wischmeier and Smith, 1978): where A = RKLSCP A = Average annuai soi1 loss' ( metric ton t )or(-) ha.y hectare.year R = Average m u a i rainfall erosivig factor, which is the sum of individuai stonn erosivity values, EI (E is the total eneru for a storm and I is the storm's ' Convmion âom US. to SI Units by Foster et ai. (1981). 'An expression of the abiüty of erosive agents to cause soil detachment and its adnspon&al, 1988). m-um 30-minute intensity), for q u d i w g storms over a time penod K = Soi1 erodibility factor ( metric ton.hect;ire.hour t.ha.h )or( 1 hectare.megajoule.millimeter ha.MJ.mm L and S = Slope length and steepness, respectively (dimensioniess). C and P = Cropping system and supporting practices. respectively (dimensionless). The USLE estimates long-term average annual or seasonal soi1 erosion for specific combinations of p hysical and management conditions (Wischmeier, 1976 and Wischmeier and Smith, 1978). Estimates of soi1 loss using the USLE were compared with measured values on 208 naturd runoff plots, representing more than 1700 plot-years of data, to assess the error associated with the USLE predictions. The USLE is used in models such as Areal Nonpoint Source Watershed Environment Response Simulation, ANSWERS (Beasley and Huggins, 1982) and Problem-Oriented Computer Language for Hydrologie Modeling, HYMO (Williams and Hann, 1973). Many researchers have used it. Hayes, (1976),Farmer and Fletcher, (1976), Brooks, (1976), Evans and Kaikanis, (1976), Robinson, (1979), Batista, (1989), Sukresno, (1991), Osbom et ai., (1976), McCool et al., (1976), Roose, (1976), Aina et al., (1 W6), Foster, (1 979), Moldenhauer, (1979), Kirby and Mehuys (1986, 1987), and Montas and Madramootoo (1 99 1) are just a few. 2.1.2.3 Modified Universrl Soil Loss Equation (MUSLE) In many watersheds, only daily precipitation data are available which is insufficient for determininp the rainfall intensity and estimatirig the rainfall erosivity factor (R). Williams (19%) replaced the R factor with a terni that includes both the p e L discharge and total amount of water applied to the field during a storm. His Modified Universal Soil Loss Equation (MUSLE) is given by: S, = 1 1.8@v)OJ6 KLSCP where Sv= Sediment yield (t) Q= The peak flow (m3/s) V = The volume of water ( m' ) applied to the area Q = 0.042DAlrp with t, = C,(L L y . 0 3 2 W V= (4 - 0.2s,y + 0.8Sr with Sr = 25.4(- b- 1O00 - 10) CfV where = Daily rainfall (mm) Sr = Retention parameter (mm) CN= RunofT curve number which depends on land use and management, hydrologic conditions, hydrologic soi1 group DA = Drainage area (ha) t,, = T h e fiom the onset of excess rainfdl to peak of the unit hydrograph (h) c, = Coefficient based on type of land (1.82.2) Lw = Length of the watershed (m) L, = Distance from the outlet to the center of the watershed (m) K, L , S, C, and P are as defined in the USLE Williams (1975) found that MUSLE can be applied to large watersheds if sediment sources are unifomly distributed over the wateshed and if major watenhed tributaries are hydraulicdy similar. Fogel et al. (1976) used this model to present a method of forecasting watershed sediment yield. Bashier (1985) successfùlly used the MUSLE to mode1 the sedirnent yield on Siran watershed in Pakistan. Krishna et al. (1988) used this model in the SWRRB mode1 (Sirnulator for Water Resources in R d Basins) for agriculture and grassland on a watershed near Riesel, Texas. Renard et al. (1989) updated the USLE (Wischrneier and Smith, 1978) as the Revised Universal Soi1 Loss Equation (RUSLE),by revising the R , K, C, and P factors. The United States Department of A g k u l w e (USDA)-Water Erosion Prediction Project (WEPP) is another effort by the National Soi1 Erosion Research Laboratory to develop an erosion prediction model (Agassi, 1996). The first phase of developing the WEPP project lasted from 1985 until 1939 (Laflen et al., 1991). This model is able to deal with deposition of eroded soil and practices that dnstically change the hydrology of the field. 2.13 Conclusion Sediment yield determination as a base for proper land and water use planning is of great importance. It is required for solution of a number of problems. Design of dams, reservoirs, charnels, and soil conservation practices, detemination of the effects of basin management, off-site damage evduatioa, transport of pollutants, and cost evaluation of a water-resources project are some of the example problems. Since most watersheds, particularly smdl oncs, are often un-gauged, sediment yield determination cannot be made due to lack of data. Among the models, MUSLE as a soil erosion predicüon mode1 is the only one that can handle lack of recording min gauges. 2.2 Geographic Information Systems (GIS) 2.2.1 Introduction A major problem in the area of modeling, and soil erosion modeling as well, has been the inability to eficiently handle, manipulate, and manage large volumes of input data. The collection of data about the spatial distribution of significant properties of the euth's surface, people, animais, and plants has long been an important pan of the activities of organized societies. Until relatively recently, however, most of these data were kept in the form of paper documents and maps. They could be read off easily, but oniy mith difficulty could they be used to analyze the patterns of distribution of anributes over the earth's surface and the processes that had given rise to them. Developments in both compter technology and mathematical tools for spatial analysis that have taken place in the second h d f of the 20th century have made many things possible, among them the ability to store, retrieve, and display data about al1 aspects of the earth's surface (Huxhold, 199 1). Developments in Geopphic Wonnation Systems (GIS) as a unique computational too1 provide the opportwiity to spatiaily organize and effectively manage input data for andyùng and modeling and eventually visualizhg mode1 outputs. GIS is becoming a basic tool for a wide variety of evth science and land-use applications (Chuvieco, 1993). It can be used to reduce data collection demands by extracting valuable information from existing databases. For example, one important application is in estimating dope steepness fiom elevation data, which is a critical factor in estimating soi1 loss (Srhivasan and Engel, 1991). A simple definition of GIS is that it is m organized collection of cornputer hardware, software, and geographic data designed to effciently capture, update, manipulate, analyze, and display al1 forms of geographicdly referenced information (Dangemond, 1992). Aronoff (1991) defined a GIS as any manuai or cornputer-based system that provides the following four sets of capabilities to handle geo-referenced data: input, data management (data stonge and retrieval), manipulation and analysis, and output. Star and Estes (1990) defined the GIS as an information system that is designed to work with data referenced by spatial or geo*mphic coordinates. This developing technology offers an extraordinary oppomuiity to empower and transform the practice of planning (Innes and Simpson, 1992). GIS and closely related technologies are now being applied to many different disciplines and fields of work. Among the rnost important are watershed monitoring, naturd resource management, agriculture, land-use planning, wildlife management, automated mapping, urban planning, geology, ecology, hydrology, geotechnics, archaeology, coastal-zone planning, maaaghg naturd and technological hazards', and military exercises (Dangermond, 1992). ' A physical situation with a potential for human injury, damage to propny, damage to the environment, or sorne combination of these (Hedth and Safcty Exccutivc, 1989). In the 1960s, GISs were supported by mainframe computers, which are now found typically in large computer centen. From the mid-1970s to the early 1980s, the dominant type of computers supporting GIS were minicornputers running in a tirnesharing mode. In the early and middle 1980s there was an explosive growth in the use of peaond computers, and by the middle of the decde GIS software became avivailable on these machines. The second fastest growing segment of the GIS hardwre has been in the last few years, when 32-bit machines with great computing power and exceptionai graphics performance were introduced. Perhaps the most recent hardware developrnent supporting GIS is the interconnection of various hardware devices (cornputen, storage devices, output devices, etc.) to form a computing network. In addition to the computers, some other kinds of hardware devices are quite important to GIS. Many of these are general-purpose computing devices, such as display terminais, plotters, scanners, and digitizers (Dangermond, 1992). 2.2.2 Geographic data Geographic information or geographic data usuaily have three fundamental components which are the phenornenon (like physical dimension or class), the spatial location of the phenornenon, and findly time. Thus, geographic data describe a phenornenon at a location at a specific time. Geographic data may be represented either on a map or in a GIS environment as different features, such as points, lines, and ares. Ml spatial data are of limited accuracy. The accuracy of spatial data is ofien descnbed in terms of positional and amibutes accuracy as if these were separable. For example, a spot elevation at a benchmark has a vertical accuracy, which may be quite independent of the accuracy of its position, as different Uistnunents were likely used to determine them. Error is introduced at every step in the process of generating and using geographic information, from collection of the source data to the interpretation of the results of P completed &dysis (Aronoff, 1991). Usually, operator, equipment, and geographic feature (such as edges) cause the cornmon sources of error in every step. Ihe objective in dealing with error shouid not be to eliminate it but to manzge it. Achieving the lowest possible level of error may not be the most cost-effective approach. There is a trade-off between reducing the level of error in the database and the cost to create and maintain the database. The level of error in a GIS needs to be managed so that data errors will not invalidate the information that the system is used to provide (Aronoff, 1991). There are nvo fundmentally different ways to organize the geographical data inside any information system: the raster model and the vector modcl. In the raster data stnicture, the space is regularly subdivided into cells, each grid ce11 of the array can be referenced by a row and column number and contains a value for die type of annbute bcing represented. The value stored for each ce11 indicates the type of object or the value of the attribute it represents. Many of the cells may contain the same value as neighboring cells. There are various methods of data compression for reducing the size of the rasrer file such as runlen,& encoding and quadtrees. In the vector data structure, points, lines, and areas represent the features. ïhe position of each object is defmed by its placement in a map space that is orgmized by a coordinate reference system. Each approach tends to work best in situations where the spatiai information is to be treated in a rnanner that closely matches the data model. High spatial variability is efficientiy represented in a raster format. It has a simple data structure, and overlay operations are easiiy and efficiedy implernented. But less compactness of its data structure and blocky appearance on its graphies are disadvantages of this model. On the other ha&, the vector data mode1 provides a more compact data structure, efficient encoding of topoloml, and the appeannce of graphitai outputs is close to that of hand-drawn maps. But its complex data structure, difficult irnplementation in overlay operations, and inefficiency in representztion of high spatial variability are disadvantages of this model (Aronoff, 1991). 2.2.3 GIS software Many cornpanies and universities are developing GIS packages with different level of functionality. Among them, ARCrmFO and ArcView developed by ESRI, IDNSI by Clark University, GRASS by USACERL, and SPANS by TYDAC are the most popular and widely used GIS packages. ARClINFO developed by Envuonmental Systems Research Institute (ESRI), Redlands, CA, manages spatial data in ARC and non-spatial data in M O .This package commenced by utilizing a vector-based spatial data structure approach (ESRI, 1995). A R C N O Version 8 and SDE Version 4 are products built from ESRIts next generation ArcGIS component-based GIS technoiogy. Both s o h e products continue to operate independently, but at version 8, they are d s o inte=nted (ESRI, 1999). ArcView is dso made by ESRI and uses g e o p p h i c data fiom a vmiety of sources such as spatial data, image data, and tabular data. ArcView 3.1 is the latest version of desktop GIS package fiom ESRI (ESRI, 1999). ' î h e mathematical m e W used to define spatial nlationship, iikc arcsode data model (Burke, 3997). Ron Eastman developed the raster-based IDRISI geographic information and image-processing package at Clark University in 1988. S ince that time, its development was partially supported by the United Nations Environment Program Global Resource Information Database ( ~ E P G R Ithe D )United , Nations Institute for Training and Research (UNITER), and the United States Agency for International Developrnent (USAID). Now, it is only supported by software sales. The latest version of IDRISI for Windows (version 2) couples the extensive analytical capabilities of the IDRISI GIS and Image Processing System with the highly interactive graphical user interface of Microsofi Windows (Clark, 1999). Geographical Resources Analysis Support System (GRASS) is a GIS package developed by the United States Army Construction Engineering Research Laboratory in the 1980s. The technology was transferred to LASy Inc. (now Global Geomatics) for commerciaiization in 1995 and to Baylor University in 1997 to sumain the public domain software venions. Bglor has just released GRASS 5.0, the first major upgrade of public domain GRASS. It hûs a raster, topological vector, image processing, and graphics production functionaiity that operates in the üNIX environment through a graphical user interface and shell in X-Windows and is available as source code on the GRASS internet site (GRASS, i999). SPANS was developed by TYDAC Technologies, Ottawa, Ontano. It is unique in its adoption of a quadtree spatiai data structure. This provides compact raster representation by ushg a variable-sized grid cel1, useful for ha* a small file size when the data are relatively homogeneous and do not require fiequent updating. It provides a wide variety of modules for dipitizhg, desktop mapping, data Mporthg and exporting (data translation), and image processing. Its modeling language provides the ability of combining multiple layers of spatial data to create desired maps, charts, and tables (Burke, 1997). 2.2.4 GIS and modeling soil erosion GIS software capabilities are useh! in them selves, but they becorne much more important when they are combined into various kinds of analytical models. These include resource allocation, population forecasting and spatial distribution, land-use forecasting, transportation, and site selection models (Dangermond, 1992). Modeling in a GIS environment refers to creation of a digital database that cm intenct with a mathematical model. For example with the use of a GIS, planners c m correlate land cover and topographie data with a variety of environmental parameters relating to such indicators as surface mnoff, drainage basin area, and terrain configuration. Cornputer-based information cm also be used to refine such models as the USLE. The result is reasonable predictions of agricultunl poilutant loads and the poteniial transport of nonpoint source pollutuits based on wateahed parameters, such as soil, slope, vegetative cover, and area (Walsh, 1983). The process of obtaining the terrain (LS) factor from digital elevation models (DEMs) permits quick calculation of soil loss potential for large areas (Blaszcqnski, 1992). Logan et ai. (1982) used the USLE wvith the U.S. Army Corps of Engineen Land Resources Information System (LRIS) to estimate soil loss in the U.S.portion of the Lake Erie drainage basin. Blaszczynski (1991), used the RUSLE for regional soil loss prediction utilking the raster processing capabilities of the Map Analysis and Processing System (MAPS). Montas and Madramootoo (1991) descnbed and applied a Decision Support System @SS) for the planning of soi1 conservation systems on an agiculhird watershed in southwestem Quebec. This system consists of a raster-based GIS, the ANSWER model, and Ëxpert System (ES) technologies. Younos et al. (1993) used the USLE with a sedirnentyield component to evaluate the cornpantive effects of alternative reclamation stntegies in abandoned mined land located in soudiwest Virginia. n e rater- based Virginia GIS was used to create digital data layers, store, analyze, and display information. Kertesz (1993) used the USLE interfaced with the ARCANFO GIS for soi1 loss assessrnent in Hungary. Rewerts (1992) deveioped a method to simplify the preparation of information n o m the GRASS-GIS for use in modeling erosion in the ANSWERS model. Engel et d. (1993) integrated ANSWER with the GRASS GIS to simulate a watershed response to a series of rainfall events. Then the sirnulated responses were compared with obsewed runoff and sediment data. The simulated results matched the observed results reasonably well considering model inputs were estimated from base GIS data. Chairat (1993) used the GRASS-GISto simdate the w o f f produced bp shortterni rainfall events by the physically based, variable source area model. SPANS is used in difTerent countries around the world mostly for managing and planing in the areas of agriculture, naturai resources, water resources, and environment. A smdlrr but growing nurnber of usea are those in the areas of business who perfom economic analysis (Tomlinson and Toomey, 1995). Using SPANS, Stempvooa et al. (1993) produced maps by comparing and mer& with other GIS spatial data to determine contiuninated groundwater dong the Saskatchewan-Alberta boundary. Bajaii and Daneshfar (1995) used fuPy logic modeling in SPANS to investigate the suitabiiity of groundwater resources for dnnking purposes in North Jordan. Luo (1995) developed a methodology in the analysis of erosion risk in Snowdonia National Park, U.K. by utilizing the SPANS. 2.2.5 Conciusion SPANS-GIS is unique in funy logical modeiing and is a powerful anaiyticd mapping tool. Its modeling uses custornized equations written in the SPANS modeling language to evaiuate tables and maps and to creûte new tables and maps from the resulting data. It is unique in its adoption of a quadtree spatial data structure too. This provides compact raster representation by using a variable-sized grid cell, useful for having a smdl file size. Before starting this research, a few PC versions of SPANS were prepared by Civil Engineering Department of Concordia University. 2.3 Optimizrtion 23.1 Optimizrtion techniques Optimization theory develops methods for optimal choices of the decision variables. Based on the nature of the problem, one of the mathematical progranunhg techniques such as Lines Programming (LP), Dynamic Progamming @P), and Noniinear Programming (NLP)could be used to find the best possible solution. LP models have been applied extensively to optimize resource allocation problems. They defme a class of problems with the following chancteristics (Lau, 1988): 1. Al1 the decision variables are nomegative. 2. The objective fiinction is a linear fuaction of the decision variables. 3. The smcturai constnints are linear inequalities (or equations) in the decision variables. n i e standard form of an LP mode1 cm be expressed as (Mays and Tung, 1992): Màx(orMin).r, = j=l c, x, Subject to: &,xi = b, , for i = 1)2) ..., rn x, 20,for j = 1,2,...,n where x, = The objective The objective function coeficient Decision variable The technological coefficient bi = n i e right-hand side coefficient DP is a mathematical technique that can be used to make a sequence of interrelated decisions in order to optimize a given objective. It transfomis a sequential or multistage decision problem that may contain many interrelated decision variables+into a series of single-stage problems, each containing only one or a few variables. Unlike linev programrning, there is no standard f o m for a DP problem and thus there is no standard algorithm that can be used for solving al1 such problems. Examples that can describe the general philosophy of the DP technique, are resource docation problems (such as fund allocation to dEennt projects and water allocation to dinerent demands) and the stagecoach problems (such as fmding the shortest route nom the ori@ to the destination in a network path). Although DP possesses several advantages in solving water resources problems. especidly for those involviq the analysis of rnultistage processes, it has two disadvantages, which are large cornputer memory and time requirements (Mays and Tung, 1992). NLP deals with problems, which have some degree of nodinewity. These problems corne in many different shapes and forms, and no single algorithm that will solve al1 of these different types of problems exists. Instead, aigorithms have been developed for various individual classes of nonlineu progranunhg problems. 23.2 Multisbjective progrnmming Multi-objective programming is concemed with decision-making problems in which there are several conflicting objectives. Multi-objective problems arise in the design, modeling, and planning of many complex resource allocation systems in the areas of industrial production, urban transportation, agricultural and livestock production, and water resources management (Goicoechea et al., 1982). Multi-objective analysis has been developed in explicit fonn largely through the work of the Harvard Water Program, a resevch enterprise supported by the Rockefeller Foundation, the U.S.A m y Corps of Engineen, and the Bureau of Land Reclarnation. Much of the methodolo~and research findings were published by Mass et al. in 1962 (cited by Goicoechea et al., 1982). Since that tirne, muiti-objective planning has awakened widespread interest and acceptance, and contributions to its application are being made in many agencies and reseorch centers (Major, 1977). The general rnuiti-objective optimintion problern with n decision variables. m constnints and p objectives is: M ~ Z ( X,-y2, ,...,xn) = [z,(x, ,-y2,* .,-y. ... ),z2 (x, ,-Y?,...,x,, 1,. ..,zp(x, ,x2 ,x, )] (Ma) Subject to: g,(~,,x?,..., .rn)s O for i = f, 2, ..., m .yj 2 0 for j = 1,2,...,n where Z(x, , x, , ..., x,) = objective function 2,(. ..), & (...), 2, (...) = p individual objective functions x, = Decision variable The characteristics of the decision-making process that will be used to categorize multi-objective progamming methods are the information flows in the process and the decision-making conte*. The diagram in Figure 2.3 shows the relationships of the dif3erent methods, based on the information flows (Cohon, 1978). Genrrating techniques emphasize the development of information about a multi- objective problem that is presented to a decision maker in a m m e r that ailows the range of choice and the tradesff among objectives and does not allow preferences ta be incorporated into the solution process. Several generating techniques, which are reviewed in the Literature, are the Weighting method, Constraint method, and Muiti-objective Simplex method. The first two methods transform the rnuiti-objective problem h t o a single-objective programming format. Then, by parametric variation of the parameters used to effect the transformation, a noninferior set of solutions can be generated. Dec3ion-rnaking context 1 Singie decision maker or decision group information tlow Genenting techniques Figure 2.3 Dia- Multiple-decision-maker methods information flow Techniques that incorponte preferences of the mdti-objective prognmming methods An active research area among mathematical programmers is the development of generating techniques that do not depend on the conversion of a muiti-objective optimization problem into a single-objective optimization problem. Those approaches that have bern suggested by Philip in 1972. Zeleny (1974), and Steuer (1995) are based on the use of the simplex method for linear propmming problems. A multi-objective simplex tableau for a problem with n + m decision variables ( nz of hem slack variables). m coIlStraints, and p objectives is shown in Table 2.1. Table 2.1 A multi-objective simplex tableau In this table, the symbol c: stands for the coefficient on the decision variable i in objective k . The symbol f : stands for the reduced cost for objective k , and column j . For each variable we now have a set of reduced costs that will be cailedx, Le., f, = [flifi2,...,1)r (2.6) Chung (198 1) used the multi-objective linear propmming to trace out a partial tnde-off relationship between a soil-loss control policy and an energy-use reduction policy. Batista (1989) used LP and the USLE ro minimize the amount of soi1 loss in a watershed. Chuvieco (1993) presented LP as a promising tool for spatial modeling within an IDRISI-GIS.He used LP in land-use planning with the aim of rninimizing rural unemployment. Jacovkis et al. (1989) described a linear programmhg mode1 for use in adalysis and planning of multi-objective water resources systems consisting of reservoirs, hydropower stations, irrigated land, artincial and navigation channeis in Argenth Benabdailah (1990) applied multi-objective linear programming to the shape of regions allocated to different land uses in a watershed. 2.3.3 Condusion As is shown in the technical approach, both objective functions and ail constrahts of this project are linearly related to decision variables. So the multi-objective linear programming is chosen as solution algorithm. The multi-objective linear programrning of Steuer (1995j can be used for al1 efficient extreme points by moving mathematicdly from one noninfenor extreme point to adjacent points until al1 noninfenor extreme points have been found. CHAPTER 3 STUDY AREA AND DATABASE 3.1 Shidy area Syahrood one of the subbasins of Damnvand watershed in the north-central part of Iran between 35'37' to 35'46' N latitude and 5 1'50' to 52'02' E longitude is chosen as study area. It covers an area of 10 820 ha with average yearly precipitation of 423 mm and temperature of 10 'C . Compared to other sub-basins of the watershed, Syahrood covers rnany different f o m of land type, land use, and dope classes, which will be discussed in Section 3.2. Figures 3.1 and 3.2 present the location of the study area on the Iran rnap and Damavand watershed, respectively. Figure 3.1 Study area (SyBhrood subbasui) on the lran map ( m ) Figure 3.2 Study area (Syahrood) in the Damavand watenhed 3.2 Development of dotabase Most of the nnecssary field data for modehg soit erosion in a GIS environment are extracted fiom the "Watershed Manasement Studies of Damavand". These studies were done by Natunl Resources Consulting Engineea (NRCE) for the Construction Ministry of Iran in 1992. The Power Ministry of Iran prepared precipitation data and their consistency are tested in this research. A h , economic data were gathered for this research through the Agicultural and Construction Ministries of Iran, and agicultural offices in the Damavand watershed. Usually, most of the precipitation in Syabrood subbasin occurs in Febniery, March, and April with high intensity and in short periods. Based on climatological d i e s at Homand Absard (an area located 20 km east of Syahrood sub-basin), an 18 mmh r a h intensity has k e n calculated for a hvo-year r e m period and 15 minutes intend (MZCE,1992). Based on the same source, the area belongs to a cold semi-arid zone. There are no recordhg rain gauges in the entire region. Instead there are six nonrecording min gauges in Damavand watershed and one of them lays in Syahrood nib- basin. Double-mass analy'sis was used to test the consistency of eight yean precipitation record of six rain gauge stations, Le., Ardineh, Cheshmeh, Go1 Khandan, Lavasan Bozorg, M d o o , and Maara. The major land uses in Syahrood are orchard, imgated land, dryland fyming, and rangeland. Wheat, barley, alldfa, clover, potato, tomato, grape, cucurnber, squash, apple, apricot, and fig are the main @cultural products. Figures 3.3 and 3.4 show typical f o m of good quality rangelands and degraded drylands in the study area. (The snow-covered crest is not located in the sub-besin) U~ûlly,drylands are located on steep dopes and are cultivated by many famers in the slope direction, which causes the concentrationof d a c e w o f f and the movement of soi1 particles. Table 3.1 presents land use classification in Syahrood sub-basin. Table 3.1 Land use classes in Syahrood nib-basin L 1 Orcbard Imgated Dryland % of total area 1.5 14 15 65 Area (ha) 160 1540 1620 6990 Land use Rangland Municipal - Total 4.5 100 510 10820 There are three kinds of land type in the study area: mountains 43%, hills 43%, and plateaus and terraces 14% of total area. A h , there are 16 different land components (iandform classes) in these land types. Table 3.2 presents different iand coniponents of the study anxi (NRCE, 1992). Table 3.2 Land component classes in Syahrood sub-basin Land Land wpe unit Land component 1.1.2 f 1 1.1.5 1.2.1 I Description Sharp crests; undeveloped soi1 profile, veiy shallow, with gravel, heavy; low vegetation density; used as 1 low prodiiction rangelands Round crests; undeveloped soi1 profile, shallow in higlis, deeper in low lands, with gravel, Iieavy; low to 1 medium vegetation density; used as rangelands . Round crests; undeveloped soi1 profile, shallow, ligl~tto medium with giavel; medium vegetation density; used as medium production ranplands and drylands 2 1.2.2 Round crests; undeveloped soi1 profile, slightly deep, heavy; good vegetation cover; used as medium production rangelands and as irrigated lands and orchards 1.2.3 Roiind crests; soils sligliily deep in liiglis and deep witli grave1 in low lands; niediuni vegeiatinn cover; used as medium to good production ranplands, and as orchards and irrigated lands 2.1.2 High hills, round and flat crests; undeveloped soil profile, shallow to slightly deep, heavy to very heavy; low to medium vegetation cover; used as medium to good production rangelands 1 2.2.1 2 Iligli liills, rniind crests; iindeveloped soil profile, sligiitly deep, henvy witli gravel; medium vegetation cover; used as medium productivity rangelands, also drylands in the slopes 2.2.2 Low height to high hills, flat crests; iindeveloped soi1 profile, slightly deep to deep, Iieavy; good 1 vegetation cover; used as rangetonds, some parts drylands, irrigated lands, and orchards Table 3.2 Land component classes in Syalirood siib-basin (continue) Land Land Land @P unit component Descript ion Low heiglit hills, round plateaus, too many cuts; undeveloped soif profile, shallow to slightly deep, lieavy; 3 good vegetation cover; used as good production ranplands and drylands Low heiglit hills and upper plateaiis; undeveloped soil profile, slightly deep, heavy; good vegetation cover; used as good production rangelands, drylands, and irrigated lands I-ligli liills with many ciits; developed soil, deep, heavy; medium vegetat ion cover; iised as low production rangelands, and drylands 1-ligli liills; developed soil, deep, Iieavy; medium to good vegetation cover; iised as medium production ranplands, drylands, and irrigated lands Round platenus witli higli topograpliy; imdcveloped soil profile, deep, Iieavy; medium vegetation cover; used as low production rangelands and drylands Round plateaiis witli low topography; developed soil, deep, heajy; medium vegetation cover; used as low to medium production rangelands and drylands Uppeir round plateaiis witli medium to high topography; iindeveloped soi1 profile, deep, Iieavy; medium to good vegetation cover; used as good production rangelands and drylands Medium height plateaus, sedimentary terraces; undeveloped soil profile, medium to deep with gravel, medium to Leavy; used as orcliards and irrigated lands Syahrood is a mountainous area with a divenity of dope classes. The elevation on the wateahed ranges from 1400 m in the southwest to above 2800 m in the northeast. Table 3.3 shows the existing different slope classes with the area of ench class. The method of preparing the slope map and its classification is presented in Chapter 4. Table 3.3 Slope classes of Syahrood sub-basin Slope class ( G k ) 0-5 5-10 10-20 20-40 40-60 >60 Total 5% of total area 0.0 43.1 25.1 17.2 11.1 0.5 100 Areri (ha) 0.0 4668 3045 1859 1195 53 los20 Because of cold weather, high steepness, and hi& erosion, the soils in the mountainous areas are shnllow, but in the lowlands they are very deep. By the Soi1 Conservation Service (SCS) method, there are four hydrologie soi1 groups (Singh, 1992). Group A: Soils in this group have a low-ninoff potential (high-infiltration rates) even when thoroughly wetted. They consist of deep, well to excessively well-drnined sands or gravels. These soils have a high rate of water transmission. Group B: Soils in this group have moderate infiltration rates when thoroughly wetted and consist chiefly of moderately deep to deep, well-drained to moderately welldnined soils with moderately fine to moderately corne texnires. These soils have a moderate rate of water transmission. Group C: Soils have slow infiltration rates when thoroughly wetted and consist chiefly of soils with a layer that impedes the downwvd movement of water, or soils with modentely fine to fine texture. These soils have a slow rate of water transmission. Group D: Soils have a high-runoff potential (very slow infiltration rates) when thoroughly wetted. These soils consist chiefly of clay soils with hi@ sweiling potential, soils with a permanent hi@-water table, soils with a clay pan or clay layer near the surface, and shailow soils over nearly irnpervious material. These soils have a very slow rate of water transmission. Table 3.4 shows the potential runoff. minimum infiltration rate. percent and area covered by each soil group (NRCE. 1992). Table 3.4 Characteristics of hydrologic soil groups in Syahrood sub-basin Soil group Potential runoff Min. infiltration Area % of total area (ha) 1 A ~OW 7.62- 11.43 943 8.7 1 B mediurn 3.8 1-7.62 5818 53.8 C medium-high 1.27-3.81 3724 34.3 . The process of digitizing and developing the necessary database for modeling soil erosion in SPANSGIS is mentioned later in Sections 3.2.1 and 3.2.2. The following maps were chosen to be digitized and imported to the SPANS-GISenvironment. 1. Damavand watenhed rnap showing sub-basins, nvers, and rain gauge stations 2. Elevation map showing contours with 100-mintervals 3. Hydrologie soil group map showing soi1 classes differentiated by antecedent soil moisture, soil texture, and soi1 permeability 4. Land-component map defining landform classes 5. Land-use map showing different land uses These maps were prepared by NRCE at the 150 000 scale in 1992. In the fint phase al1 hardcopy maps were digitized by SPANS-TYDIG. In the next phase. digital information was used to provide the necessary loyers at the 15" quad level. The SPANS- GIS environment provides a finest grid size of 1.375 m at this level. 3.3.1 Digitizing hardcopy mrps by SPANS-TYDIG SPANS-TYDIG is a digitizing and editing tool designed by iNTERA TYDAC Technologies Inc. for manipulation of spatial data. It provides data in digital form from hardcopy maps by using a digitizing table. A digitizing table with a 16-button cursor supponing serial communications and Stream mode is needed. Points, lines (arcs) and areas (whole polygons) are three kinds of spatial data on a hardcopy map, which had to be digitized to deveiop the databûse. Every type of geopphical feature on a map should be digitized separately and stored in a sepmte file CO build a different layer. Rain gauge locations were digtized as points, while land-use, land-component, elevation, and hydrologic soi1 group maps were digitized in arc-node polygons. Polygon attributes were assigned to a point digitized inside of each polygon. Digitized files were exponed in the TYDIG environment to create appropriate ".velr/.vec" file pairs. These two files are used to build different layen when imported in the SPiWS environment. Figures 3.5 and 3.6 show digitized elevation, hydrologic soi1 group, landcomponent, and land-use mûps within the SPANS-TYDIG. CZEl Hydrologie soil group Figure 3.5 Digitized elevation and hydrologie soil group maps of Syahrood l Land component I Figure 3.6 Digitized land-component and land-use mips -of Syahmod 32.2 Development of digitized maps in SPANS-GIS Exporting digitized files in SPANS-TYDIG successfully created appropnate ".veldvec" file pairs. These file pais were imported into the study area, narnely Syahrood, to creûte different data layers within the SPANS-GIS environment. Setting up a study area in SPANS requires the following steps: 1. Creating the study m a : Identifying a directory that contains a cornpletc set of files pertaining to o specific, pographic area. imponed ".velJ.vec" file pairs, al1 developing and modeling results will be stored in this directory. 2. Establishing the projection: A pr~jectionis a mûthematical formula, which is used to reduce the amount of distonion appearing when the three-dimensional, curved surface of the euth is projected ont0 a flat. two-dimensional surface as a piece of paper or a computer screen. According to these formulas, the geographic coordinates of displayinp data are adjusted. The Universd Transverse Mercator (UTM)projection was selected for Syahrood sub-basin. 3. Setting the extents of the study area: The extents define the physical iimits (size, position. and rotation angle) of the region to be included in the study Once the study area had been set up, al1 irnporting and developing operations were done in the same study area. Digitized arc-node polygons such as elevation, land- use, land-component, and hydrologie soi1 group were imponed as line or vector data. While the attribute data assigned to the points digitized inside each polygon, were imported as point data. Aiso, digitized rain gauge locations and their attributes were imported as point data. Developing a map in SPANS requires the following steps: 1. Importing the vector data: Geographical data must always be imported prior to importing and appending the attribute data. 2. Transforming the vector or line data into polypn or area data 3. Transforming polygon data into a map or quadtree. 4. Importing the point data or attribute data. Appending classes to points, reclassifcations, and map annotations such as title, legend, scale, North arrow, and labels are additional map developing tools in SPANSGIS. Figures 3.7 through 3.10 show developed maps as databases used for overhy operations in modelulg soi1 erosion in a GIS environment. Slope and Thiessen polygon maps are two other spatial databases, whifh are to be created by existirig databases within the SPANS environment. Therefore, the procedure for developing these two maps will be discussed in the Chapter 4. Elwatian (m) 1300-1500 1501- 1700 1700- 1900 1900-2100 2500-2700 Figure 3.7: Elevation map of Syahrood sub-basin Hyârologic soi1 gmup Ama ma) Total 10820 Figure 3.8 Hydrologie soil group map of Syahrood sub-basin. For the meaning of legend see "3.2 Development of database". Land componmt E2.2.1 3.2.3 Figure 3.9 Land-component map of Syahrood sub-basin. For the m e d g of iegend set "3.2 Development of database". Land ma Arer (ha] Otchard 16U Rangeland 6!RHi Inigated land 1510 Dylrnd 16a) Municipal 510 1 - - - Figure 3.10 Land-use map of Syahrood sub-basin CHAPTER 4 MODELING SOIL EROSION IN A GIS The main objective of the study was to examine the effect of different land uses on the sediment yield rate. Two years of data on sediment yield were available for the area, which proved the usefulness of the sediment yield model. As was discussed in Chapter 2, MUSLE was chosen to interface with SPANS-GIS for spatial modeling of sediment yield in the semi-arid zone of Syahrood sub-basin. The selection of the model was based on its simplicity, and its independence from recording rain-gauge data. Equation (4.1 a) shows that this model requires seven main variables to be assessed before and during modeling in a GIS environment. s, = 1 ~ . ~ @ v ) O . ~ ~ K L K L P where S, =Sediment yield (t) Q=The peak flow ( m3/s ) Y =The volume of water ( m3) applied to the area S, =Retention parameter (mm) CN =Runoff curve number depends on land use and management, hydrologic conditions, hydrologic mil group DA =Drainage area (ha) t , =Tirne fiom the onset of excess d a 1 1 to peak of the unit hydrograph (h) c, =Coefficient based on type of land (1.8-3.2) Lw =Length of the watershed (rn) L,=Distance f?om the outlet to the center of the watershed (m) K=Soil erodibility factor ( metric ton.hectare.hour t.ha.h )or( 1 ha.MJ.mm hectare.megajoule.miW t e r L andS =Slope length and steepness (dimensionless). C and P =Cr0pping system and supporting practices (dimensionless). Figure 4.1 illustrates the concept of overlay operation in the GIS environment. L & S factors Figure 4.1 Owrlay operation in the GIS environment Sections 4.1 through 4.5 explain the procedure of computing K. L, S, C,and P factors in the MUSLE. 4.1 Soil erodibifity factor (X) Soil fractions' such as silt plus veiy fine sand, sand (except very fine portion), and oreanic matter as well as soi1 stnicture' and soi1 pemeability3 classes were estracted Cr from the existing 26 soil profile data (NRCE, 1992). These data were used on the nomograph (Figure 4.2 ) of Wischmeier and Smith (1978) to compute K factors. Calculated K factors were assigned to related class of the land-component rnap (Figure 3.9). Table 4.1 presents the result of soil profile analysis as well as K factors for each land component. ' USDA grain sizes (mm) for differentiating soi1 hciions. - 1 3 Sand Coarse Very coarse Fine Medium 0.5 035 Silt Very €me 0.1 0.002 0.05 'USDA soil structure classes. Code 1 Clss Very fine or very thin Fine or thin Medium Corne or thick Very coarse or very thick 2 3 4 5 ' USDA soi1 penneability classes. L Class Code 1 2 Verv sIow ---- 3 4 5 6 7 I Slow Moderately slow Modcrate Moderateh * rabid ' Rapid Very rapid - 1 1 I 1 Permeability (mm/h) 1.524 1,524-5.08 5.08-1 534 15 34- 50.8 50.8- 152.4 152.4 508 > 508 Clay 1 0.001 - - -- -- - Figure 4.2 Nomograph of Wischmeier and Smith (1978) Table 4.1 Soi1 hctions and K factors on each land component of Syahrood 1 Silt + very 1 1 Land component Permeability code 1 K ( t.ha.h 1 haMJ.mm 4.2 Slope length and steepness factors (L and S) Computation of L and S factors required preparation of a slope map. SPANS was supposed to compute dope h m the elevation map using equation (4.2) and a 3 x 3 neighborhood about each ce11 location (Burke, 1997). slope = ((&/&/8 *ceil size)' + (kldyl8 *ce11 where the ce11 size is determined by the quad level of the input map. The templates used to compute x and y partial derivatives are: By testing many points, it was found that this software was not able to produce an accurate slope map for mountainous areas neither fiom the elevation map nor directly fiom the digital devation points. Therefore, a preliminxy dope map for the entire area was computed by hand (NRCE, 1992) using equation (4.3) and then slopes were classified in groups of 5-10, 10-20, 20-40,40-60, and >60 %. As can be noticed, there is no dope class of 0-5 percent in the study area. where s,, s,, s,, s,, and s, are the slopes of the corners and center and S, is the average slope of each 1 x 1 km grid on the elevation map. Figure 4.3 shows the computed dope map of the study area. According to the dope classes and using equations (4.4) to (4.6) fiom Wischmeier and Smith (1978) the L factors were calculated (Table 4.2). p = (sin 8/ 0.0896)/[3.0(sin where A =siope length (m) B =the angle of dope (degree). i 0.561 Total 1OB#I Figure 4.3 Slope map of Syahrood sub-basin Table 4.2 L and S factors of each dope class in Syahrood sub-basin +l Slope For computing the dope length ( A ) a few sample areas were randomly chosen on each class of slope map and measured on the field. The masurement startesi fiom the point of origin of overland flow to either the point where the slope gradient decreases to the extent that deposition begins or the point where riuroff enters a channeL Using equations (4.7) and (4.8), the S facton were calculated according to the same procedure (Table 4.2). S = 10.8sin0 + 0.03 for 8 < 9 percent (4.7) S = 16.8 sin 0 - 0.50 for 0 2 9 percent (4.8) Fhally, resulting LS factors were assigned to appropriate slope classes on the slope map of Figure 4.3. 4.3 Cropping system factor (C) The C factor is the ratio of soi1 loss from land cropped under specific conditions to the corresponding loss fiom clean-tilled, continuous fallow. This factor measures the combined effect of al1 the interrelated cover and management variables. The C factor was computed for each crop and crop nage and supporting practice information in each Land use, using agicultural studies (NRCE,1992) and Wischmeier and Smith (1978). 4.3.1 Croppiag system factor (C) for rangelinds Field studies have indicated different canopy covers in rangelands of Damavand watershed (NRCE,1992). The results of this study are presented in the first two columns of Table 4.3. Using these data and Table 10 of Handbook 537 (Wischmeier and Smith, 1978), the C factors were calculated for cach C!SS of canopy cover and the results are given in the last column of Table 4.3. The weighted average of the C factor was calculated to be 0.0833 for the entire rangelands. Table 4.3 C factor for rangelands in Syahrood nib-basin % of rangeland (NRCE, 1992) 13.72 Canopy cover (%) (NRCE,1992) 70-1O0 1 Weighted average C 0.0780 0.0833 1.3.2 Cropping system factor (C)for croplands The three main croplands in the Syahrood sub-basin are drylands, irrigated lands, and orchards. In the following sub-sections the C factor will be calculated for each kind of crop in each cropland. The rainfall factor does not completely describe the effects of local differences in rainfall pattern on soi1 erosion. The erosion control effectiveness of a cropping synem on a particular field depends, in part, on how the year's erosive rainfall is distributed among the six crop-stage periods of each crop included in the system. Therefore, expected monthly distribution of erosive rainfall (El) at a particular location is an element in deriving the applicable value of cover and management factor (C). Table 4.4 shows the cumulative percentage of the average annual EI that nomally occun between January 1%and indicated dates in existing min gauges of Damavand watershed. This table is exnacted fiom precipitation data of Damavand watershed, which will be discussed later in this chapter. In general, there are six different crop-stage periods for each kind of crop. 1. Period F (rough fallow), starts fiom inversion plowing ta secondary tillage. Table 4.4 Cumulative percentage of the average annuai EI extracted from six rain gauges in Damavand watershed D Month 1 Jan. Feb. Mar. Apr. Aug. Sep. Ott. Nov. Dec. - Ardineh Cheshmeh Khandan 5.6 4.0 4.9 Lavasan 1 4.3 Maara Mamloo Average 6.2 5.1 5 .O 2. Penod SB (seedbed), secondary tillage for seedbed preparation until the crop has developed 10 % of canopy cover. 3. Period 1 (establishment), starts fiom the end of SB until crop has developed 50 % of canopy cover. 4. Period 2 (development), starts frorn the end of Penod 1 until canopy cover reaches 75 %. 5. Penod 3 (maturing crop), the time fiorn the end of Period 2 until the crop is harvested. 6. Penod 4 (residue or stubble), covers the time penod of harvesting to plowing or new seeding. 1.3.2.1 Cropping system factor (C) for drylands There are 1620 ha of drylands in Syahrood sub-basin with 8 10 ha under fallow every year. Small grains (wheat and barley), alfdfa, and pea are the most cornmonly planted crops, which are planted on 758, 37, and 15 ha, respectively. Small grains that cover 46.7 % of drylands and need 270 days to mature are rotationally planted with aifdfa. Table 4.5 shows the calculation of the C factor for areas covered by alfalfa and small grains. Agriculniral information about cultivation of the different crops was obtained fiom NRCE, (1992) and illustrated in table format. Setting up this table is as follow: Column 1. Chronological sequence of al1 the land-cover changes bat begin a new cropstage period. Column 2. List of the dates on which each cropstage period begins. Column 3. The cumulative percentage of EI for each date fiom Table 4.4. The EI percentage of the dates not available in this table was obtained by interpolating between available dates. Table 4.5 C factor for drylands (aifiilfa and small grains) in Syahrood sub-basin Event Cumulative CropPercentage stage EI period Sep. 23 68.6 F El in period Planting (alfalfa) Apt. 4 45.1 10% canopy cover Apr. 20 50% canopy cover 0.765 Soi1 loss ratio 0.68 Cropstage C value 0.520 SB 0.055 0.70 0.039 50.6 1 0.083 0.55 0.046 May 20 58.9 2 0.01 0.43 0.004 75% canopy cover Jun. 22 59.9 3 0.852 0.11 0.094 Plowing Apr. 4 35.1 0.235 0.68 0.160 Sep. 23 68.6 F SB 0.053 0.70 0.037 10% canopy cover Oct. 9 73.9 1 0.116 0.55 0.064 50% canopy cover I Nov. 9 I 85.5 Date Plowing Planting (small @s) 75% canopy cover Harvest Plowing Surn of 3 years 2 1 0.654 I 0.43 1 0.281 I Apr. 21 50.9 3 0.09 0.11 0.009 Jun. 22 59.9 4 0.087 0.34 0.029 - - 1 Sep. 23 1 1 Yearly average - F 68.6 1 1 1 1 1.283 0.428 Column 4. The cropstage periods. Column 5. E l in period. These values are obtained by subtracting the number in Column 3 from the number in the next lower liae in Column 3. If the cropstage period includes a year-end, the value in Column 3 is nrst subtracted fiom 100 and then added to the number in the next lower line. The EI in period values are presented as ratios by dividing them by 100. Column 6. Soi1 loss ratios is the ratios of soi1 losses fiom the cropped plots to corresponding losses fiom continuous failow. This ratios were computed for each cropstage period, for each particular crop, in various combinations of crop sequence and productivity level and grtthered in fôble 5 of Huidbook 537 (Wischmcier and Smith, 1978). Column 7. The product of values in Columns 5 and 6. The sum of these products is the value of C for the entire event penod. Because C is usually desired as an average annuai value, this sum is divided by the number of years in the event periods. Table 1.6 presents the same calculations for pea. Table 4.6 C factor for drylands @ea) in Syahrood sub-basin Crop- EI in stage period period F 0.803 Soi1 loss ratio 0.68 Plowing Oct. 13 Cumulative percentage El 78.7 Planting May 22 59.0 SB 0.006 0.70 0.004 10% canopy cover Jun. 7 59.6 1 0.013 0.55 0.007 50% canopy cover Jul. 7 60.9 2 0.025 0.43 0.011 75% canopy cover Aug. 7 63.4 3 0.052 0.1 1 0.006 Harvest Sep. 23 68.6 4 0.101 0.34 0.034 Plowing Oct. 23 78.7 F - - - Event Sum Date Cropstage C vaiue 0.546 0.608 The calculated C factors for alfalfa and small grains, pea, and fallow are 0.428, 0.608, and 0.50,respectively. By weighting the areas planted to each crop, the average C factor for drylands is 0.47. 43.2.2 Cropping system factor (C)for irrigated lands There are 1540 ha of imgated croplands in Syahrood sub-basin of which 460 ha are under fallow every year, 581 ha are in small gains (wheat and barely), 225 ha in alfalfa and other forages, 168 ha in potato and vegetables, and 106 ha in legumes (pea and bean). Using the same procedure explained for drylands, Tables 4.7 through 4.10 show the calculations of the C factor for different crops. Weighting for the areas planted to each crop, the average C factor for imgated lands is 0.26. Table 4.7 C factor for imgated lands (srnall grains) in Syahrood sub-basin EI in period El Cropstage period Cumulative percentage Cropstage C value 0.0 1O Plowing Aug. 23 63.6 F 0.040 Soi1 loss ratio 0.25 Planting Sep. 23 68.6 SB 0.053 0.20 0.0 1 1 10% canopy cover Oct. 9 73.9 0.116 0.019 50% canopy cover Nov. 9 85.5 I I 0.654 0.16 2 0.12 0.078 75% canopy cover Apr. 2 1 50.9 3 0.090 0.05 0.005 Harvest Jun. 22 59.9 4 0.047 0.15 O .O07 Plowing Aug. 23 64.6 F - - - Event Sum Date - l 0J30 Table 4.8 C factor for imgated lands (grains) in Syahrood sub-basin Plowing Sep. 23 Cumulative percentage EI 68.6 Planting May. 22 59.0 SB 10%canopy covcr Jun. 7 59.6 1 Event 50% canopy cover 75% canopy cover l ~ Date I JuL7 Aug. 7 Harvest Sep. 23 Plowing Sep. 23 ratio value F 1 1 Cropstage penod 2 1 I I 60*9 63.4 3 68.6 4 68.6 1 1 F 1 Table 4.9 C factor for imgated lands (aifalfa) in Syahrood sub-basin Date Event Cumulative Crop- Elin Soil loss Crop- percentage stage period ratio stage C EI period 0.040 0.25 0.0 10 0.053 0.20 0.01 1 value Plowing Aug. 23 64.6 Planting Sep. 23 68.6 F SB 10% canopy cover Oct. 9 73 -9 1 0.116 50%canopy cover Nov. 9 85.5 2 0.654 75% canopy cover Apr. 2 1 50.9 3 0.090 1 - Harvest (first) Jun. 22 Plowing Aug. 23 _ Wer 4 YQ I I 11 59.9 4 64.6 F 2 (3 yr) rable 4.10 C factor for irrigated lands (potato and vegetable) in Syahrood sub-basin Event Date Cumulative Crop- EI in Soil loss percentage stage period ratio El period Cropstage C value Plowing Sep. 23 68.6 F 0.864 0.25 0.216 Planting May 5 55.0 Si3 0.040 0.20 0.008 10% canopy cover May 2 1 59.0 I 0.009 0.16 0.001 50% canopy cover Jun. 21 59.9 2 0.036 0.12 0.006 75% canopy cover Aug. 21 63.5 3 0.197 0.05 0.009 Harvest Nov. 6 83.2 4 0.844 0.15 O.127 Plowing Sep. 23 68.6 F - - Sum O 0.367 4.3.2.3 Cropping system factor (C)for orchards There are 160 ha of orchards in Syahrood sub-basin. Using agricultural studies (NRCE,1992) and Table 12 of Handbook 537 (Wischmeier and Smith, 1978) with fair soil condition, no live ground vegetation, and 40% mulch cover, the C factor for orchards is 0.17. 4.4 Supporting prrictices factor (P) The P factor is the ratio of soil loss with a specific support practice to the correspondhg loss with up-and dom-dope culture. The P factor was computed for each supporting practice information ip each land use, ushg agricuin~aistudies (NRCE,1992) and Wischmeier and Smith (1978). In the study area irrigated lands and orchards are terraced and contoured by f m e a . These kinds of supporting practices are used partidly in drylands and rangelands. Due to heavy grazing on the rangelands, narrow terraces built by animal movement are plainly visible. Therefore, using Tables 13 and 15 of Handbook 537 (Wischmeier and Smith, 1978), the P factors were cdculated for orchards, rangelands, Urigated lands, and drylands (Table 4.1 1). This table summarizes C, P, and consequently CP factors for each land use. Table 4.1 1 CP factors for each land use in Syahrood sub-basin Land use C P CP Orchard 0.17 0.50 0.085 Rangeland 0.08 0.40 0.048 Irrigated land 0.26 0.50 0.130 Dry land 0.47 0.70 0.329 4.5 Computing runoff peak flow ( Q) Calculation of tirne fiom the onset of excess rainfall to peak of the unit hydropph, t, , in Snyder's method (equation 4.1 b) is necessary for computing Q. For this purpose Handbook 537 (Wischmeier and Smith, 1978) is used to determine the coefficient based on type of land, c, , for each dope class. Table 4.12 shows the amount of c, for each dope class as well as its weighted average for Syahrood sub-basin. The length of the watershed, Lw, and the distance from the outlet to the center of the watershed, L,, were measured on Syahrood sub-basin by tracing the main river and Stream on the 150 000 topographie map of the area Table 4.13 shows the procedure for 62 calculating runoff peak flow (Q) for the Syahrood sub-basin by Snyder's method (equation 4.1 b). Table 4.12 c, for each dope class of Syahrood sub-basin Slope (%) 5-10 10-20 2040 40-60 >60 Area (ha) 4668 3045 1859 1195 53 c, 2.14 2.08 2.00 1.92 1.80 2.07 Weighted average c, Table 4.13 Computing Q for Syahrood sub-basin Area (ha) Cl 10820 2.07 Lw Lc 1P (m) (m) 0) 16016 12109 9.39 P (m3/s ) 48.43 L. J 1.6 Computing the volume of runoff water ( V ) applied to ench polygon Distribution of precipitation data due to distribution of rain gauge stations in any watershed obliges consideration of the zones affected by each rain gauge. For this reason it is necessary to coinpute V factor for such influenced areas. A Thiessen polygon, aiso known as a Voronoi diagram, defines an area about a point (rab gauge station) such that al1 locations within that area are closer to that point than to any other point. SPANS-GIS can analyze the point location of such rain gauges and produce the Thiessen polygon map. The point attribute data of Figure 3.2 was used to produce Thiessen polygon map for Damavanci watershed (Figure 4.4). For soi1 erosion modeling there was no need tomuse other sub-bah of Damavand watershed except Syahrood. Figure 4.5 present.the Thiessen polygon map of Syahrood sub-basin. I Figure 4.4 Thiessen polygon map of Damavand watershed Figure 4.5 Thiessen polygon map of Syahrood sub-basin Before computation of the volume of m o f f water (V) applied to each Thiessen polygon area, the consistency of precipitation data for dl rab gauge stations was tested. In double-mass analysis method, the accumulated annual precipitation record at a given station is compared with that of the accumulated annuai precipitation mean values of other nearby stations. When a change greater than 10% in the dope of the relationship occurs, it indicates that the gauge was moved or some other occurrence caused the gauge to receive a different amount of precipitation. In this case it is necessary to adjust the record by the ratio of the slope to rnake the record consistent (Singh, 1992). Figures 4.6.a through 4.6.f show no significant change in the slope of the regression lines. Based on these tests, the precipitation data of al1 stations are acceptable. O 1000 2000 Ardineh (mm) -300O 4000 Cheshmeh (mm) e" 4.6.b Consistency analysis of Cheshneh station O 500 100O 1500 2000 Gol Khandan (mm) Figrire 4.6.c Consîstency snalysis of Go1Hhandan station 250 0 3000 O 200 0 300O 4000 Lavas an Bm org (mm) Figure 4.6. d Consistency analysis of Lavasw Bozorg station Figure 4.6.e Comistency anaiysis ofMamioo station 5000 600 O Maara (mm) Figure 4.6.f Consistency analyas of Maara station Computation of the volume of runoff water (Y) applied to each Thiessen polygon area requires the following steps: 1. Calculation of the retention parameter ( S r ) in each Thiessen polygon area: Fint, hydrologic soi1 group and land-use maps were overlaid and using equation (4.lc), S, is calculated for each combination of the above overlay results (Table 4.14). In this table, Curve Numben (CN)are calculated based on the cropland condition fiom the CN table of SCS (Singh,1992). Second, the Thiessen polygon map is overlaid with the resuit of the last overiay (hydrologic soil group and land-use). The results are given in Table 4.15 showing S, for each Thiessen polygon. Table 4.14 S, for each combination of land-use and hydrologic soil group Land-use and "v sr Area hydrologie soi1 group @a) CN (mm) Rangeland-A 147 62 156 Municipal-A 225 59 177 Orchard-B 140 66 131 Rangeland-B 3694 76 80 Imgated land-B 865 76 80 Dryland-B 1017 81 60 103 74 89 20 77 76 Rangeland-C 2823 84 48 Imgated land-C 323 84 48 Municipal-C 173 82 56 Rangeland-D 330 87 38 Imgated land-D 1 88 35 Municipal-D 5 86 41 10830 - - Municipal-B I Orchard-C Total Table 4.15 Sr for each Thiessen polygon area in Syahrood sub-basin - - . sr Thiessen polygon Ardineh 1 . (mm) 58.89 1 Cheshmeh 1 72.77 2. Computing V for each rainfall event: Neglecting precipitation less than 0.2 Sr in the record to avoid negative values of P, -0.2Sr in equation ( 4 . 1 ~ )the ~ amount of V for each rainfall event and in each Thiessen polygon is calculated and stored 3. Finally, the results are multiplied by the related Q factors in Table 4.13 and then raised to the power 0.56. 4 7 Computing sedimeat yield 1. Overlaying land-use and dope maps: To compute the LS.CP products land- use and slope maps are overlaid. Figure 4.7 and Table 4.16 present the results of this overlaying. Figure 4.7 Overiaid land-useand slope maps of Syahrood subbasin Table 4.16 LS CP for each land use in Syahrood sub-basin . Slope classes (%) 10-20 Land use 20-40 40-60 Tota1 >60 land use Weighted 0 1 LS.CP area Orchard Rangeland Irrigated Dry land 2. Overlaying land-use and land-component maps: To compute the KLS-CP combination, the land-use map with new values of LS.CP is overlaid on the landcomponent map with 16 classes. The result is presented in Table 4.17. Table 4.17 KLS.CP for each land use of Syahrood sub-basin Land use K.LS.CP Orchard 0.01991 Rangeland 0,0231 Imgated land 0.0493 Dryland 0.1041 3. Computing the amount of sediment yield in each land use: As was noted in Figure 3.2, the locations of eight min gauge stations are distributed u n i f o d y in the area. Therefore, to cornpute the amcunt of sedirnent yield in each land use, Thiessen polygon and land-use rnaps are overlaid. In this overlaying, the result of part 3 in Section 4.6 is multiplied by a constant (1 1.8) and by the appropriate value of KLSCP in Table 4.17. Figure 4.8 presents the amount of sediment yield in each h d use. The average sediment yield based on the mode1 was 4.75 t/ha.y over the entire Syahrood sub-basin. The higher sediment yields are in the drylands, which are wualiy found on steep slopes and are cultivated in rows parallel to the slope direction. This causes higher concentration of runoffthat removes soi1particles. land use Ordiard Rangeland lnigated land Diy(and Munidprl w - - -- -- -- - - Figure 4.8 Sediment yield in each land use of Syahrood subbasin t/ha.v 1.41 499 241 624 CHAPTER 5 OPTIMIZING THE MANAGEMENT OF S O L EROSION n i e second important objective of the study was to optimize the management of soi1 erosion. In other words, minimize the sediment yield and maximize the f m income in the watershed. 5.1 Formulation of the problem As was described in Chapter 2, based on linearity of objective functions in the study area problem, multisbjective linear programming is chosen. Also, the simplex method does not depend on the conversion of a multi-objective optimization into a single-objective one. Therefore, this method was chosen to solve the rnulti-objective linear programming problem of the Syahrood sub-basin. The general multi-objective optimization problem with n decision variables, rn conmaints and p objectives is as given in equation (3.5a) through ( 2 . 5 ~ ) Using . these equations, the generai form of the existing problem in Syahrood sub-basin can be written as: Subject to: (5. lc) (5. ld) where 2,= Annual net farm incorne of whole watershed (106Rial/y) 2,= Annual sediment yield of whole watershed .y) Xi = Surface area of each land use (ha) C,= Annual sediment yield per unit area in each land use (t/ha.y) A ( = Amount of net fwincorne per unit area of each land use (106Riaha) A: = Production coa per unit area of each land use (106Rialha) A: = Cost due to soi1 loss per unit area of each land use (Io6 Rialha) B = Total land area (ha) The problem cm be written in detail in the following form: Subject to: X,IB, X,S B , X, IB, X1+X,5 B, XI + X 2+X,+X4= Bs XI 1 B6 X, 2 B, xz,*y3, XI> x 4 20 where X , = Area allocated to orchard (ha) X, = Area allocated to rangeland (ha) X , = Area allocated to imgated land (ha) X,= Area allocated to dryland (ha) A: = Amount of net farm income per unit area of orchard (106 Rima) A: = Production cost per unit area of orchard (1 o6 Rialha) A: = Erosion cost per unit area of orchard (106 Riaiha) A;= Amount of net farm hcorne per unit area of rangeland (106 Riaha) A: = Production cost per unit area of rangeland (106 Rialha) A: = Erosion cost per unit area of rangeland (106 Riaiha) A: = Amount of net f m income per unit area o f imgate'd land (106 RiaYha) A: = Production cost per unit area of irrigated land (lo6 R i m a ) A: = Erosion cost per unit area of irrigated land (106 RiaVha) A: = Amount of net f m income per unit area of dryland (1 o6 R i m a ) A: = Production cost per unit area of dryland (106 RiaVha) A: = Erosion cost per unit area of dryland (106 RiaVha) C,= h u a i sediment yield per unit area of orchard (fia-y) C,= Annual sedirnent yield per unit area of rangeland (tlhay) C,= Annual sediment yield per unit area of irrigated land (r/ha.y) C,= Annual sediment yield per unit area of dryland (t/ha.y) B, = Maximum limit of orchard surface area (ha) B, = Surface area of imgated land (ha) B, = Suface area of dryland (ha) B, = Surface area of orchard plus irrigated land (ha) B, = Total area (ha) B, = Minimum limit of orchard surface area (ha) B, = Surface area of rangeland (ha) 5.2 Estimation of constants Estimation of the A,', B,, and C, constants is necessary to be able to solve equations (5.2~1)ihrough (5.2j). The procedure for estimating these constants is described in the following sub-sections. 5.2.1 Estimation of each land use area ( B , , B,, B,, B,, B,, B,, B , ) Due to not being able to make any changes in the use of municipal lands, these areas were excluded fiom land-use optimization. Therefore, municipal lands are subtracted fiom the total area in Table 5.1 and the remaining of 10310 ha is considered as B5 or the total area of the Syahrood sub-basin in equation (5.2g). hble 5.1 Sediment yield in each land use of Syahrood sub-basin (ha) Sediment yield @/ha-Y ) 160 1.41 226 Rangeland 6990 4.99 33880 Irrigated land 1540 2.41 371 1 Dry land 1620 6.34 10109 Total 10310 4.75 48926 Area Land use Orchard r Sediment yield WY According to the results of the overlay operation of land-use and dope maps within the GIS environment, the distribution of land use activities in different dope classes is illustrated in Table 5.2. For proper management of agriculturai lands, it is not wise to have dryland faxming on slopes greater than 20% and imgated f m s on slopes greater than 10%. Actual recommended slopes are less than these numbers in order to avoiding soi1 erosion and reduction of crop yield. nierefore, irrigated f m s on more than 10% siopes and drylands on more than 20% slopes were deducted in the optimizing formulations. According to Table 5.2, the values of B, through B, in equations (5.2~)through (5.2i), were 55 7, 1143, 1577, 1700, 103 10,164 and 6990 ha, respectively. Table 5.2 Distribution of land use activities in different slope classes of Syahrood Orchard Rangeland Inigated land Dryland Total Ois) fia) (ha) Ois) Ois) 5-10 134 1810 1143 1254 4341 10-20 1 2390 178 323 3892 20-40 25 1556 214 33 1828 40-60 - 1180 5 10 1195 >60 - 54 - - 53 Tota1 160 6990 1540 1620 10310 Slope (W 1 5.2.2 Estimation of soil erosion in each land use (C,,C,,C,,C, ) From the GIS results in Chapter 4, and from Figure 4.8, soil erosion in orchard, rangeland, imgated, and dryland areas (C, through C, ) in equation ( W b ) was 1.4 1, 4.99,2.4 1, and 6.24 t/ha.y, respectively. 5.2.3 Estimation of benefit nnd cost in orchards ( A : ,A: ) There are 160 ha of orchards in Syahrood sub-basin. The major crops that are included in this mode1 are given in Table 5.3. The area of each crop, yield, net benefit and cost from farm crop production were detailed in studies by NRCE (1992). By talcng the municipal area into account, and dividing the total cost and benefit values in the last row of Table 5.3, the weighted average of benefit ( A : ) and cost (A:) of orchard crops are 11A44 and 0,899 million Riaiha. In 1997, 1 $US was equal to 70 and 1500 Rial (Iranian cunency) in the Centrai Bank of Iran and in the open market, respectively. At the time of writing this thesis, conversions changed to 4950 and 9100 Rial per US 0, respectively. Table 5.3 Major orchard crops and their costhenefit information in Syahrood Area Y ield Cost Benefit Total cost Total benefit (ha) @/ha) (Ridt) (RiaVt) (1o6 R i d y ) (1 o6 RiaVy) 19.00 47,370 500,000 70.38 742.90 30.25 8.50 105,880 750,000 27.22 192.84 Fig 1.O0 5 50 163,640 450,000 0.90 2.47 Grape 6.25 6.00 150,000 430,000 5.62 16.12 Pineapple 3 1.50 13 .O0 69,230 500,000 28.3 5 204.75 Wainut 12.80 7.50 120,000 7000,000 1I .52 672.00 1 - I I - Crop A P P ~ ~ 78.20 Cherry l I I 143.99 I 183 1.O8 5.2.1 Estimation of benefit and cost in nngelrnds ( A : , A: ) Through range management studies (NRCE,1992), three types of condition' were studied in 6990 ha of rangelands in Syahrood sub-basin. These conditions were classified by cornparhg the rangelands at the time of study with its potential situation regarding vegetation canopy cover, vegetation combination, soi1 conservation, and residue Range condition is an ecological meanve to compare cumnt plant species composition of a mgeland to its potential (often callcd "climax") and is determmcd by totaling the condition scons for al1 present species. Poor, fair, good, and excellent conditions have O to 25%, 26 to 50% 5 1 to 75%, and 76 to 100%of the c h a x comunity, rcspectively (McGinty and White, 1996). condition. Table 5.4 differentiates these rangelands by condition types, are% and production. Using Table 5.4, the weighted average dry-forage1 production in Syahrood subbasin is calculated as 0.14 tha. Assuming 55% of produced forage is Totd Digestible Nutrients (TDN), the total produced TDN is 0.08 tha. Considering that 230 kg/y TDN is required for each animal unit (sheep). 0.35 animal units per hectare are fed by rangelands every year. Also, the average weight of each animal unit in the area is 32 kg (NRCE, 1992). Therefore, the total weight of live animal units is 1 1.3 kgha. Table 5.4 Differentiation of rangelands by type, area, and production in Syahrnod m Area L Average dry-forage Total dry-forage (t/ha) 0) 0.340 550 ha Yi0 2290 33.7 Poor 3300 48.7 O. 103 350 Very poor 1300 18.6 0.085 110 Total 6990 100 - 1010 Rangeland condition Medium Considering the price of live sheep in 1992, which was 4,230 Rialkg, the total economic production of rangelands ( A : ) amounts to 0.047 million RiaVha. On the other hand, due to governmental ownership of rangelands in the study area, there is no cost ( A : ) for meat production. Also, other animai productions such as milk,wool, and animal fertilizer are not taken into account. ' Al1 browsed and hcrbaccous foods that arc avaiiable to g d n g animals. Forages are cut and dticd in the field for later use (Trottier, f 992). 5.2.5 Estimation of benefit and cost in irrigated lands (A:, A: ) From the total 1540 ha of irrigated croplands in Syahrood sub-basin, 458 ha is under fallow condition every year. Table 5.5 gives crop production data in imgated lands. By taking the fallow area into account, and dividing the total cost and benefit values in the last row of Table 5.5, the weighted average of benefit ( A : ) and cost ( A:) in imgated lands are 1.523 and 0.926 million Riaiha, respectively. Table 5.5 Major irrigated land crops and their costhenefit information in Syahrood 1 Crop Alfalfa 1 Area 1 Yield 1 Cost 1 Benefit 1 Total cost 1 Total benefit (Ridt) (10' RiaYy) (Ridt) (106 RiaVy) 130,000 146.25 300,000 3 3 7.50 (ha) ( 225 15.00 Barley 175 2.00 267,000 296,000 93.45 103.O0 Onion 52 7.00 325,000 350,000 1 18.30 127.40 Pea 106 12 0 3,142,000 2,630,000 272.46 334.54 Potato 116 18.00 225,000 500,000 469.80 1044.00 Wheat 408 3.O0 266,000 326,000 325.58 399.02 Failow 458 - - - Total 1540 - 1425.84 2346.06 @/ha) O O - 5.2.6 Estimation of benefit and cost in drylnnds ( A : , A:) There are 1620 ha drylands in Syahrood sub-basin with 812 ha under fdlow con4ition every year. Small grains (wheat and barley), dfdfa, and pea are the most popular crops. Table 5.6 indicates crops, area, yield, and benefitlcost data of each crop in drylands. By taking the fallow area into account, and dividing the total cost and beneft values in the last row of Table 5.6, the total benefit (A:) and cost (A,') in drylands are 0.095 and 0.073 million R i a h , respectively. Table 5.6 Major dryland crops and their costmenefit information in Syahrood r 36 Yield Cost (RiaVt) ( t h ) 1 .50 130,000 Benefit (lüdt) 300,000 214 0.50 256,000 296,000 Pea 16 0.40 Wheat 544 0.50 252,000 Fallow 810 Total 1620 - - Crop Alfdfà Barley Area @a) 28.67 33-15 13.71 16.83 326,000 68.54 88.67 - - 2,142,000 2,630,000 1 Total cost Total benefit (106RidY) (106RiaVy) 7.02 16.20 O 1 17.94 O 1 54.85 3.2.7 Estimation of erosion cost in different land uses ( A:, A: ,A: ,A: ) There is no research on the evaluation of economic losses due to sediment yield in the study area. 'Iherefore, it is difficult to evaluate it directiy. However, these losses can be estimated indirectly by the evaluation of fertile soil loss. For example, based on data relating topsoil loss to yield reductions, just 2.5 cm of topsoil loss is enough to reduce U.S.wheat yields an average of 60 million bushels (bushel = 35.21 liter)/year (Dregne, 1982). Another way to estimate economical Iosses due to sediment yield is to apply lost soil to the eroded area based on the depth of root zone in each land use (NRCE,1992). The depth of the lost soil in each land use is cdculated by considering the amount of sediment yield in that land use, the appropriate rooting depth of vegetation (root zone), and soil bulk density (NRCE, 1992). Table 5.7 presents the land use, the amount of sedirnent yield, root zone, soil bulk density, total area lost due to erosion, and the estimated cost due to soil erosion in each land use. Estimated lost areas in this table (column 5) were muitiplied by the economic net income of each land use to estimate economic cost due to sediment yield (column 6 ) in each land use. Table 5.7 Estimated economical losses due to sediment yield in Syahrood Soi1 bulk Root zone density (g/cm3) (cm) 1O0 1.4 Lost area (m2/ha) 1.01 Cost (Riaiha) 1062 Land use Orchard Erosion (t/ha.y) 1 .41 Rangeland 4.99 15 1.6 20.79 98 Imgated land 2.41 50 1.4 3.44 205 i~rylmd 1 6.24 1 15 1 1.5 1 27.73 1- Table 5.8 sumrnarizes the production of each land use activity in the study area. The annual average of net farm incorne in the area is 0.288 million Riaha. Table 5.8 Cumnt land uses and production of Syahrood sub-basin b Area (ha) Land use Orchard Production Cost Net incorne (106Rial/ha) (106RiaVha) (106Rial/ha) 160 Rangeland 6990 1 Imgated land ( 1 Dry land 1 1620 1 0.095 0,936 0.073 1 1 I Total 10310 0.453 1 O. 164 0.597 I 328.53 0.047 1 1 1.523 10.545 - 0.047 1 1540 O. 899 11.444 Total net incorne (106 Rial) 1657.20 1 919.38 0.022 35.64 0,288 2969.28 1 5.3 Solution to the problem According to the computations in the last few sections, the general form of the optimization problem c m be written as follow. Mm(Z,)= [(Il .444X,-(O.899Xt + 0.00 1O6X,)) + (0.047(1S23X, - (OX, + 0.000 1O-)) + - (0.926X3+ 0.00021XJ) + (0.095X4- (0.073X4 + 0.00006X4))] (5.3a) (5.3b) By simplifying the fist objective function, and changing the minimization to maximization form in the second objective, these equations change to the followiag simpler forms. Objective 1. Mar(Z,) = 10.544X, + O.OUX, + O . W X , + O.OZX, Objective 2. h ( - 2 , ) = -1.41XI - 4.99- - 2.4 lx, - 6.24X4 There are seven constraints of the land-use optimization model. The constraints and their justifications are discussed below. Constraint 1. X, 1 557 nie first constraint indicates that the present area under orchard, which is 160 ha could be increased up to 557 ha. The reason for these constraints is that the areas of irrigated lands with slope classes of 10-20, 20-40,and 40-60 % are not suitable for imgating cropland. These lands could be changed to other land uses especially orchards, by terraciag, if necessary, and planting permanent vegetrition. Constraint 2. X,5 1143 The second consaint is that the area under irrigated lands, which is 1540 ha, after subtracting high dope classes, as described in constraint 1, should not be more than 1 143 ha. Constraint 3. X , < 1577 Slopes more than 20% are not suitable for dryland famiing. The third constraint indicates that the area under dryland farming, which is 1620 h, afier subtracting high slope classes, should not be more than 1577 ha. Other reasons for this constraint are as follows. A. The government owns the rangelands and people cannot change their use of these lands. B. Due to lack of sufficient rainfall in the area, dryland farming is not suitable for most areas in this watershed. C. People seldom use supporthg practice systems in drylands, which causes large arnounts of soi1 erosion in this f o m of land use. Constraint 4. X , + X , < 1700 Based on the limitation of irrigation water, the forth coIlstra.int implies that the area under orchard and imgated croplands could not be more than 1700 ha. Constraint5. X , + X , + X , + X , =IO310 The fifth constraint is simple and it is the area limitation of the Syahrood subbasin after subtracting the municipal lands. The sum of the areas under the four land uses can be neither increased nor decreased fiom the 10310 ha of the available lands in the watershed. constra.int 6. X,2 160 Base on the reasons in Constraint 1, the sixth constraint shows the present area under orchards. Constraint 7. X, 2 6990 The seventh constraint indicates that the area under rangeland should be at l e m 6990 ha. The reason for this constraint is that the govemment owns the rangelands and people cannot change their fom of !and use. Many -rangelands have been illegally converted to improper drylands, which could be changed back to rangelands coamainta. x,,x , , x , , x , ~ ~ The l a s constraint is the non-negative variable declaration, i.e., the areas allocated to each land use must be positive. Socioeconornic conditions in the study area do not allow converting al1 the imgated lands to orchards. Also, limited detail data on suitability of croplands to different crops or combination of crops as well as the lack cf costhenefit information Iimits the objectives and constraints to those explained. Simplified objective fùnctions and their constnints discussed above are entered in Table 5.9 as a revised linear multi-objective simplex tableau. In this table. variables and their units are as folIows: Table 5.9 Linear multisbjective simplex tableau of Syahrood sub-basin problem (1) Equation (2) (3) (4) (5) -YI .Y2 x 3 Objective 1 10.544 0,047 Objective 2 -1.41 Constraint 1 (6) (7) ~b TYPc RHS 0.597 0.022 Max O -4.99 -2.4 1 -6.24 Mau O 1 O O O -c 557 Constraint 2 O 1 O O O 1 -c -c 1143 Constraint 3 Constraint 4 1 O O O 1 O c 1700 constm.int 5 1 1 1 1 - - 10310 Constraint 6 1 O O O >, 160 Constra.int 7 O 1 O O >, 6990 1 1577 Columns 2 through 5 in this table present decision variables, which in rows 2 and 3 have currency and sedhtnt yield units, respectively. Numbers 1 and O in the remaining rows show the prescnce or absence of the decision variables in constraints, respectively. Rows 2 and 3 of column 6 indicate the maxirnization or minimization fonn of the objective fiurctions while reniainhg rows indicate the cquality or inequality fom of the consuaints. The last column gives the kight Hand Side ( ' S ) value of each consaaint, which reprcscnt land availability in h a After solution of the revised simplex tableau in Table 5.9 by the cornputer program of Steuer (1995), the proposed areas for orchards (Xl),rangelands (X?),irrigated lands (X3),and drylands (X')are revealed in Table 5.10. Using the proposed land-use values, the annual net income (ZI) and sediment yield (&) are calculated as 6.96 billion R i d y and 46504 t/y, respectively. Table 5.10 Land-use optimization output of Syahrood sub-basin Sediment yield (tfy) Net income (1 o6 RiaVha.y) 1.41 785 10.545 Total net income (1 o6 maly) 5873 .56 8610 4.99 42964 0.047 404.67 Irrigated land 1 143 2.4 1 2755 0.597 683.37 Dryland - 6.24 - 0.022 - Total 10310 46504 0.675 6960.6 Land use Allocated area (ha) Orchard 557 Rangeland Sediment yield wa.~) CHAPTER 6 DISCUSSION, CONCLUSIONS, AND SUGGESTIONS The main objective of present study was to develop a new methodology and associated tools to predict the sediment yield with greater reliabiiity in watersheds with deficiency of recorded min gauge data. A subsequent objective was to optimize land-use activities of a watershed in such a way that soi1 erosion is minirnized while maximizing the agricultural economic income for the Syahrood sub-basin which drains directiy into the Damavand river in Northeastem Tehran, the capital city of Iran. The high sediment yield and serious fiooding due to faulty land practices in the area provided the initiative for using that area as a study site. It was hoped that the results of the study would have the potential for application in other watersheds. The study describes the development of two models, the integration of a sedirnent yield model with a GIS and a land-use optimization model. The sediment yields are predicted by Modified Universal Soi1 Loss Equation using daily precipitation as input. Seven factors were computed and assigned to related land-component, dope, land-use, and Thiessen polygon m q s . SPANS-GISmodeling tools were used to provide necessary database and assist soi1 loss estimation. The output results of the sediment yield model dong with the net income of each land-use were used as input in the land-use optimization model foi khhizing the sediment yield and maximiPng f m production of each land-use. The multi-objective linear programming simplex method was used to solve the problem. This method can be used to generate an exact representation of the noninferior set by moving mathematically fiom one nonhferior extreme point to adjacent points until al1 noninferior extreme points have k e n fouad. Figures 6.1 through 6.3 compare the area, sediment yield, and total net f m income of diflierent land uses of Syahrood sub-basin before and after optimization. 6.1 Accuracy of sediment yield modeüng within SPANS-GIS For estimation of sediment yield the Modified Universal Soi1 Loss Equation was integrated by a GIS. The selection of the MUSLE was due to its advantage of easy estimation of the ninoff factor fkom the peak flow volume and total flow volume. Also, the estimation of the rainfall erosivity factor for the original USLE requires the intensity of rainfall, which is impossible to obtain kom the daiiy precipitation record. - O,'0 1 Before optirniration Ader optimizltion 10310 10310 I Figure 6.1 Land use area in Syahrood before and after optimization mi Belbre optirniration Orchard Rangdand i M e r aptniization lnigled land Dryland Tdd a m Figue 6.2 Annual sediment yield in Syahrood before and afler optimization Figure 6.3 A ~ u anet l incorne in Syahrood before and after optimiPition In addition, the nuioff erositivity factor gives more accurate estimates of sediment yield as compared to the rainfall erosivity factor, because ninoff is more closely related to erosion than is rainfdl. Accuracy is the degree of likelihood that the information provided is correct. This defmition focuses on two components of accuracy. The first and more familiar aspect of accuracy is that it predicts the proportion of infcrmation that is expected to be correct or the magnitude of error to be expected. The second and ofien ignored aspect of accuracy is that it involves a probability. When a map or other data set is asserted to be 80% accurate it means that when the data set is used, it cm be expected that on average 80% of the information will be correct. The measure of this probability of having a higher or lower accuracy than expected is termed the level of confidence. So, when a map is rated 80% accurate with a 90% level of confidence it means that if a large nurnber of accuracy tests were done on the map, then 80% or more of the test points would be correct in 9 out of every 10 tests. The level of accuracy depends on the information to be provided and the level of detail required. For example a road map with an accuracy of one km may be suitable to estimate the driving time between cities. However engineering drawings of a city street are required to have accuracy on the order of centimeters. Accuracy cm usually be improved by expending more resources. More money c m be spent on the field investigations, more time can be spent on analysis, and more quality control can be exercised in assembling the data. An acceptable level of accuracy is that level where the costs of making the wrong decision are equal to the costs of acquiring more accurate The accuracy of predicted sediment yield in the study area depends on two major resources. Fust, the soil erosion prediction model (MUSLE) and the parameters used with it. Second, the GIS environment and the components used to model soil erosion with it. 6.1.1 Accuracy of soil erosion model The MUSLE model is an experimental model whose parameters are gathered by field studies at a proposed scale. The accuncy of a model in an expected scaie depends on the precision of the model parameters and the ski11 of the people working on the project. If assurning d l the p m e t e r s gathered to model soil erosion are precise, still the model should be calibrated in the study area before using it. The MUSLE model was used to predict sediment yield in many similar wateaheds by the Forests and Range Research Institute of Iran. Two years of sedimentary data were collected fiom the rivers of Damavand wateshed (NRCE, 1992). Based on these data, sediment load caused by channel erosion was cdculated on non-rainy days and subtracted fiom the sediment data. According to this study, 4.73 t/ha.y of sediment yield was reported for Syahrood sub- basin. Cornparing the estimated sediment yield (4.75 t/ha.y) with this later value shows that the present research goals were achieved. 6.1.2 Accuracy of modeling in GIS environment In the GIS environment, map accuracy depends on many factors. At the micro level, there are components such as positional accuncy, attribute accuracy, logical consistency, and resolution. At the macro level, there are components such as compIeteness. tirne, and lineage. Finally. usage components are accessibility and direct or indirect costs. There are also different sources of enors associated with al1 geographic information. Some of the more comrnon errors are related to data collection, data input, data storage, data manipulation, data output, and the way of using and understanding results. Paper data such as different maps and associated geographic attributes and data are used as one of the sources of input data to the GIS environment. In this process the paper data are converted to digital data. The level of accuracy of the digital data will be the same as paper data if they are correctly converted to the digital fomi with a suitable package in an acceptable resolution. Once the data are converted, the accuracy of the output data resulting fkom different manipulations depends on the resolution power of the software dong with the ski11 of the operator. SPANS-GIS utilizes a quadtree data structure, which provides a more compact raster representation by using a variable-sized grid cell. Instead of dividing an area into cells of one size, fmer subdivisions are used in those areas with finer details. In this way, a higher level of resolution is provided only where it is needed. For a thematic map, the fine grid is only needed in the vicinity of Iines, points, and polygon boundaries. A large area of a single class would be just as accurately encoded with one large ce11 as with many small cells because they al1 have the same attribute value. At the quad level of 15, the finest grid size is 1.375 m for 150 000 scale maps of the study area It means that the output rnaps have a resolution of 1.375 m, which is a very good resolution for this scaie. For positional and attribute accuracy tests of the prepared maps with TYDIG and SPANS-GIS, 25 points were selected on each of four digitized elevatioq-land-use, landcomponent, and hydrologie soi1 group maps of Syahrood sub-basin. Their longitude, latitude, and class attributes were compared with the ones on paper maps by the query tool in SPANS.Ail tested points had exactiy the same positional and attribute data as the paper maps. 6.2 Sensitivity analysis of the optimization model Post-optimaiity analysis involves conducting sensitivity analysis to determine which parameten of the model are the most citical in determinhg the solution. Some or al1 of the parameters generally are an estimate of some quantity whose exact value will become known only afier the solution has been implemented. Therefore, after identieing the sensitive parameters, special attention is given to estimating each one more closely, or at lest its range of likely values. Sensitivity analysis ofien begins with the investigation of the effect of changes in the Br, the amount of resource i being made available for the activities under consideration. The reason is that there generally is more flexibility in setting and adjusting these values than there is for the other parameters of the model. The economic interpretation of the dual variables as shadow pnces is extrernely useful for deciding which changes should be considered. The shadow price (Y,') for resource i measures the marginal value of this resource, that is, the rate at which Z could be increased by slightly increasing the amount of this resource being made available. In pariicular, if y; > O, then the optimal solution changes if Bi is changed, so Bi is a sensitive parameter. The sensitivity analysis for checkuig al1 sensitive parameters of the problem started with B i . Then the investigation coatinued on 4 and Ci parameters. It was found that B,, which refers to the restriction of area under orchard was the most sensitive parameter. Increasing the area in orchards by 1 ha increases y; by 10 million RiaUy and decreases y; by 1 t/y, which meam the most attention should be toward allocating ares to orchard under the present conditions. Tables 5.1 1 through 5.13 show the results of sensitivity analysis for al1 problem parameters. 6.3 Conclusion Mrasures are being taken to improve the watershed conditions to reduce the sediment yield while mavimizing production. To achieve these goals, the objective functions for maximizing watershed production were designed in such a way that the cost of sediment yield fiom each land-use practice w u counted towards its cost of production. A multi-objective linear program was used for land-use optimization for maximizing watershed production and minimizing sediment yield. AAer taking dlocated areas into account, average m u a l sediment yield and average annuai income for the entire study area were 46304 t/y and 6.96 billion RiaVy, respectively. Compared with the values before optimization, the annual sediment yield would have decreased by 2422 t/y (or by 5%) and the annual net income increased by 3.99 billion RiaYy (or by 134%). The results indicate that the objectives of the snidy were achieved. The models used for prediction of sediment yield and optimization of land use in the Syahrood sub- basin gave reawnable results. The encouraging results of these models allow the scope of their applicability to extend to other wateaheds. The watershed manager or planner can use land-use optimization for m a h g decision in allocating watershed area for dinerent land uses to xhieve specific objectives. Table 6.2 Sensitivity analysis of A,! in optimizing land ilse activities in Syalirood A: (1 o6 Rialha) 0.022 0.022 0.022 XI (ha) 557 557 557 x 2 (ha) Table 6.3 Sensitivity analysis of C,in optimizing land use activities in Syahrood c, (1) 1.41 2.41 3.41 1 -41 1 .41 1.41 1.41 1 .41 1.41 ' c* (0 c 3 (0 4.99 4.99 4.99 5.99 6.99 4.99 4.99 4.99 4.99 1 2.4 1 2.4 1 2.41 2.4 1 2.4 1 3.4 1 4.4 1 2.4 1 2.4 1 c4 4 4 4 (1) (114 557 (lia) 8610 (lia) 1143 (lia) O 557 557 557 557 557 557 8610 1143 1143 1143 1143 1143 1143 O O 6.24 6.24 6.24 6.24 6.24 6.24 6.24 7.24 8.24 8610 8610 8610 8610 8610 4 O 4 WY 6960 6960 6960 6960 46504 4706 1 476 1 8 551 14 63724 47647 48790 46504 46504 6960 O 6960 6960 6960 O 6960 O 2 2 (1o6 Rially) The study also recognizes that before making any decision for Unplementing land- use optimization, the objectives and the constraints should be clearly recognized and realistic estimates of constants of the objective function made. The estimated sediment yield from orchards, rangelands, imgated lands, and drylands in the Syahrood sub-basin was 1A l , 4.99, 2.41, and 6.24 tlha.y, respectively. h m a i weighted average of sediment yield for the entire area amounts to 4.75 t/ha.y. Compared with Europe, Australia, North Arnerica, and Asia with 0.84, 2.73, 4.91, 6.10 t1ha.y of soi! erosion, respectively (NRCE, !992), it is clear that the lands are improperly managed in the study area. In generai, the high erosion rate in the Syahrood sub-basin is related to the following reasons. 1. 244 400 animal units (sheep) are grazing on the rangelands of Damavand watershed, which need 29 100 t of dry forage (NRCE,1992). The produced cùy forage in the area is 8 610 t, which provides 113 of the needs. Therefore, decreasing vegetation cover of rangelands by heavy graPng causes lower soil fertility, greater soi1 compaction, and evennially more surface runoff, which easily removes soil particles. 2. Table 5.2 indicates that 313 ha of drylands are on the 10-20% slopes and 43 ha on slopes greater than 20%. Based on steep slopes and low precipitation (123 mrnly), crop yield of these drylands is often so low that the farmers do not attempt to harvest. They leave these lands for one or two years fallow without any vegetation cover, which causes more erosion in these .periods. As it can be noticed (~igures3.3 and 3.4), rangelands with permanent vegetation cover on steep slopes are converted to drylands with seasonal vegetation cover and cultivated in rows parallel to the dope direction. Converting these lands back to rangeland, reduces annual sediment yield fiom 6.24 to 4.99 t/hay and increases the annud net income fiom 0.022 to 0.047 million Riai/ha.y . 3. Lack of proper erosion control practices cause high values of the supporting practices factor (P) in many lands. Utilizing proper supporthg practice systems such as contour furrowing, stnp cropping, terracing, and pitting accompanied with pianting permanent or annual plants will further decrease the value of P and subsequently annuai erosion and increase annual net income. 4. Cutting trees and shrubs from the rangelands by farrnea to use as fuel causes the same problems discussed above, in parts 1 and 2. 6.1 Suggestions for future work The present work could be M e r developed in the following aspects: SPANS-GIS is not capable of producing an accurate slope map for mo arem. The dope module of this package needs to be improved in new versions. In addition work is necessary to make the modeling environment more user fiiendly. MUSLE does not take gully and channel erosion hto account. Further investigations are recommended in this area. benefits fiom the the combination should be considered in the optimization procedure. different crops 4. Taking other animal products such as wool, miik, and fertilizer into account increaes the precision of the optimization problem. This information was not available for this research. 5 . There are some costs associated with transfonning land uses (like seeding in drylands to convert them to rangelands). They should be computed and taken into account. Further investigations are necessary in this matter. 6. Continued monitoring and gathering of precipitation and sedimentary data are the essentid tools for vaiidating proposed rnodels. In Syahrood sub-basin, there were just two years of sedimentary data available to this research. 7. The relationship between erosion and crop yield in different croplands is another topic, which needs to be investigated m e r . This later suggestion is valid for dl areas of the world and is not specific to the Sydxood sub-basin. 8. Investigation on water availability, supply, and quality, is also recommended. 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