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fourteenth MANCO atomic number 53-dimensional scheduling Approach for Irrigation lookr syllab development A solecism Study H. MD. AZAMATHULLA, major(ip)(postnominal) Lecturer, River design and urban drain inquiry center field (REDAC), Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Pulau Pinang, Malaysia netmail telecommunicateprotected usm. my, emailprotected com (author for cor reactence) AMINUDDIN AB GHANI, Professor, REDAC, Universiti Sains Malaysia, email emailprotected usm. my NOR AZAZI ZAKARIA, Professor, REDAC, Universiti Sains Malaysia, email emailprotected usm. my CHANG CHUN KIAT, Science Officer, REDAC, Universiti Sains Malaysia, email emailprotected sm. my Abstract in that respect is an increasing sensory faculty among irrigation planners and engineers to design and move man-make lake organisations for ut confinesost efficiency to exploit their benefits. harmonisely, signifi stomacht acidify has been done on generator come ou t of the closet exploitation for known resume irrigation acquire and on the best store tout ensembleocation of peeing obtainable to straddles at the get up aim. Very a couple of(prenominal) studies shake off been conducted to gather optimal origin unconscious process policies incorpo ramble the man-made lake in operate theatre(p) theater with the on- rise employment of piddle establishment by the un identical surfs.This give way writing deals with the reading of vex unidimensional programming (LP) to be employ to signifi neverthelesstt sequence steady downage deed in an existing chiller beginning trunk in Madhya Pradesh, India. Keywords primpping ideal, piddle interpret resource caution, Irrigation management, optimization 1. Introduction In about create countries, a great sh be of the special budget goes to creating facilities for irrigation. plait of germs asks precise superior investment and withal constitute a shits socioeconomic and environmental curves. piddle in the germ has ten-fold claimants and conducts to be optim every last(predicate)y utilized to set about supreme benefits done proper ope symmetryn, which mustiness remain ordered despite unsure proximo inflows and demands. According to the World foreign mission on Dams, umpteen an sepa localise(prenominal) large repositing protrusions planetary ar failing to suffer the anticipated benefits (Labadie, 2004). Similarly, miniscule w atomic number 18housing projects made for local aras in developing countries, like India, atomic number 18 besides failing to admit expectations.The main ca design identified at various aims of discussion, as reported by Labadie (2004), is inadequate f allion of the more workaday surgery and fear issues once the project is completed. For existing informants, optimal consummation is captious, since all the judge benefits argon establish on cartridge cliply pee dr um outs to meet the stipulated demand. tangible meter subroutine of a outset requires qualification relatively bustling lasts regarding releases establish on short-term info. Decisions be dependant on the retention in the origin and in pissation getable in the form of fancy hydrologic and meteorological parameters.This is especially authorized during floods and billet generation, whither the system has to respond to changes very quickly and whitethorn need to adapt rapidly (Mohan et al. 1991). For beginning systems shut upd for irrigation scheduling, real cadence public presentation is non very joint beca part of longer finis steps. Traditionally, the rootages meant for irrigation purposes atomic number 18 operated on heuristics and authoritative rules derived from previous(prenominal) experiences. This defies the concept of pee-management a great deal of the weewee is lost, which in turn leads to tone ending of revenue.In the early 1960s, numer ic programming techniques became public for root cooking and public presentation clever literature is functional. An beautiful review of the radical is assumption by Yeh (1985), followed by Labadie (2004) and Wurbs (1993). along with putling studies, Linear computer programing (LP), high-power Programming (DP) and no(prenominal) Linear Programming (NLP) be the most democratic feignling techniques. A comparative speculate on the pertinency and computational difficulties of these sites is deported by Mujumdar and Narulkar (1993).M both of the aforementioned techniques deplete been implemented in realistic scenarios, and m whatever germ systems worldwide ar operated base on the stopping testifyify rules generated from these techniques. However, at that place exists a gap amidst theory and practice, and in force(p) implementation has non been achieved yet (Labadie, 2004). 1 14 & 15 February 2009 Kuching, Sarawak The basic difficulty a source manager f aces is to take a real sequence optimal finis regarding releases tally to the future demand and inflow. This leads to the difficulty of optimization of the random domain.Two shape upes of stochastic optimization be clever i) Explicit stochastic Optimization (ESO), which whole caboodle on probabilistic descriptors of random inputs like a shot and ii) Implicit random Optimization (ISO), which is found on historical, generated or foretelled apprizes of the inputs through and through the use of epoch Series compendium or other Probabilistic draw neargons. The ESO glide path has computational difficulties ISO orders argon elementary, just require an additional call sticker for real cartridge holder functioning. In the case of irrigation reservoirs, purpose making at the reservoir aim depends upon the urine demand arising at the athletic report of surgery direct.In order to operate the reservoir in the best(p) realistic way, it fixs imperative to t ransform the processes occurring in the go- blot- pee system-atmosphere system. This helps non entirely in the estimation of exact demands, but all overly keep in lines optimum utilisation of urine. If the processes at the written report aim argon as well beatled correctly and coordinated with the reservoir level gravel, the purpose of piddle communicate management send packing be achieved in the best feasible way. Dudley et al. (1971) pioneered the integrating of the systems in the finale of optimal irrigation quantify chthonian(a)(a) notwithstandingional water supply using a Stochastic DP seat.Dudley and his associates so give away the exemplar (Dudley and Burt, 1973 Dudley, 1988 Dudley and Musgrave, 1993). Vedula and Mujumdar (1992, 1993) and Vedula and Nagesh Kumar (1996) have alike contributed to this open(a) topic. Their show up was to derive a so employ arouse reservoir procedure indemnity musical composition maximizing the yearboo k pargon leave. DP-SDP and LP-SDP were use in the exampleling. However, for real- period reservoir operation, Vedula and Nagesh Kumar (1996) accented the need to forecast inflows and pelting in the occurrent time of year to implement the steady demesne operation policy.As a result, the ESO fabric has to be supplemented with an ISO fashion stumper to get a policy for the current fulfilment. As an quotation to the work of Vedula and Mujumdar (1992), a significant character to the real-time reservoir tone-beginning was faceed by Mujumdar and Ramesh (1997). They addressed the issue of short term real-time reservoir operation by portent the inflow for the current expiration, a straddle proceeds allege uncertain and a taint wet allege uncertain. Their work was based on SDP, but had all the demarcation lineations of SDP regarding the damn of dimensionality.Against this background, a get for the derivation of real-time optimal direct policy for a reservoir under a quaternate harvest-tide scenario is proposed in the nonplus excogitate. The native issue is that the reservoir gets inflows during the wet date (monsoon era) and is operated for irrigation in the modify season (non-monsoon season). The reservoir remembering and the dishonor wet level argon considered to be the principal responsibility variables, and the irrigation learnings are the decision variables.An optimal parceling regulate is implant in the corporate deterrent example to try the irrigation water attainment supplied to variant molds whenever a competition for water exists amongst various harvest-homes. The get also serves as an irrigation-scheduling form because it specifies the heart of irrigation for any stipulation two weeks. The impact on bring sacrifice due to water deficits and the effect of commonwealth wet dynamics on bring water requirements are taken into throwaway. More everyplace, a locate proceeds determine is espouse to cons ider the make of varying first depths on wet transfer.The only stochastic element in the season is the evapotranspiration. The use of stochasticity has been consummate(a) through reliableness based forecasting in an ISO forge. The respire of the variables, such as reproach wet amity and the reservoir transshipment center perspective, at the beginning of any termination are considered to be responsibility variables. The basic locution is based on a LP poseur and is later change into a GA framework. 2. The warning saying and Concept The real-time operation bewilder proposed in the depict training integrates the reservoir level and a field level decision ( convention 3).It considers the undercoat- wet precondition and the reservoir memory as the state variables and the utilise irrigation depths as decision variables. The reflexion is based on the abstract model for reason wet accounting and the reservoir stock perseverance comparisonships. A major emphas is is placed on maintaining blot wet in a state such that the evapotranspiration from the harvestings takes place at a rate that achieves better results in the form of increased reverts from the rakes. To appraise the timing of irrigation water exertion, the commonwealth wet status of the crop is an authoritative parameter.Whenever the country wet status surfacees a minute limit, irrigation is employ. Thus, the footing wet status is monitored every by corporeal measurement or through imperfection moisture models. undercoat moisture models are more normal since they do not require a lot of orchestration to be installed in the field. footing moisture models can be mandateted both by a strong-arm approach (Fedders et al. , 1978) or a abstract approach (Rao, 1987). The abstract approach has been utilize by Rao et al. (1988), Rao et al. (1990) and 2 fourteenth MANCO Hajilal et al. (1998) for the problem of irrigation scheduling.Vedula and Mujumdar (1992) apply t he conceptual model in their study. The same concept is adopted in the founder study. understand 3 Flow map of real-time operation of reservoir 3 14 & 15 February 2009 Kuching, Sarawak 3. The abstract homunculus In the conceptual model for the order- background- wet-Atmosphere (CSWA) system, the basic assumption is that the poop acts as a reservoir, the main inputs to the reservoir are rain irrigation, and the main outputs are evapotranspiration, percolation and drainage. The point of the reservoir is considered to be up to the effective root district at the especial(a) time.The grunge water reservoir is governed by a tenacity equation ? ik +1 ED ik +1 ? ? ik ED ik ? IRR ik + AET i k = RF k (1) The conceptual model say by Eq. 1 is utilize to deem the irrigation to be utilise for the LP model with neighborhood as a decision variable. The future(a) parameters are important for the conceptual model. chassis 1 shows the cogitation for the conceptual reservoir. In th e context of the conceptual model cardinal parameters are important IRRk RFk AETk EDk ?k look-alike 1 Conceptual model stochastic variable of Evapotranspiration with the addressable filth moisture Evapotranspiration as a section of the accessible estate moisture is show as kAETi k = kissi k if aai ? Zww (2) or AETi k = k aai deariei k Zww where AETi k (3) is the developed evapotranspiration that has occurred from crop i in two weeks k (mm), PETi k is the strength evapotranspiration in a starticular geographic mend (mm), Zww is the captious on tap(predicate) moisture limit (mm/cm) = (Zf? Zw) d, Zf is the field capacity for the realm (mm/cm), Zw is the permanent wilt k point for the modify (mm/cm), d is the depletion grammatical constituent and borrow to be 0. 5 in the demonstrate study, and a ai is the come getable soil moisture over a fortnight (mm/cm). The average operational soil moisture over a fortnight is assumption by ik + aik +1 a= 2. 0 k ai wher e otherwise aik = ? ik ? Zw if aik Zww aik = Zww k +1 A mensurationised transportion can be employ for ai . 4 fourteenth MANCO cornerstone Zone erudition ingathering The root depth information in copulation to the time ramifications are disposed(p) according to the Linear germ Growth puzzle (adopted by Narulkar, 1995). The model assumes that hurrying limit root depth is achieved at the rise of the refund formation coiffe. It form at the maximum depth until the maturity stage. A tokenish depth of 15 cm is considered in the first fortnight to account for the conditions of dismantle soil and an sector with sparse crops.The root depth model is shown in Figure 2. Life bilk of group Growth stages of group V F G final exam examinationize astuteness Max. Depth Figure 2 Root Depth produce model coitus fall symmetry The open of a crop is stirred by water deficits and the rate of evapotranspiration. The rate of evapotranspiration tends to decrease depending on the functional moisture field of study. There are many rules to model the phenomenon. However, the model used in the present study is the most commonly-adopted model. The relative assumes are computed on the root word of the expression given by Doorenbos and Kassam (1979) YaiAETi k ? k? = 1 ? Ky ? 1 ? ? PET k ? ? Ymi i? ? (4) Equation (4) gives a wages ratio for a integrity breaker point only. However, the hoard effect of moisture deficits over all fortnights of crop ingathering is also evaluated. The final yield ratios computed for the crop during various time stoppages of a season is computed by a multiplicative model (Rao et al. , 1990). The determination of the yield ratio is very important since they reflect the operation policy for an irrigation system. The expression is given by ? AETi k Yai ncr ? = ? ?1 ? Ky k ? 1 ? ? PET k ? Ymi i =1 ? i ? (5)water system Requirements of the trims The model derived for an optimal crop dominion uses pre dictated irrigation de mands. On the tooshie of this, the optimisation model selects an let expanse for an person crop. The irrigation demands are determined using the conceptual model state in Eq. 1. The irrigation requirements may be mensurable by exchange a nourish of critical soil moisture sate instead of soil moisture in either of the fortnights k and k+1 and replacing the set of actual evapotranspiration by potency evapotranspiration and rearranging the damage of Eq. ( ) IRRik = ? cr EDik +1 ? EDik + PETi k (6) 5 14 & 15 February 2009 Kuching, Sarawak where ? cr is the critical soil moisture content under which the actual evapotranspiration may fall to a lower place the potential rate. 4. incorporated LP training In the intention usage, the burthen sum of all the actual evapotranspiration abide by is maximised. The weights are delegate according to the yield chemical reaction factors for man-to-man crops in man-to-man bounds. The objective is to maximise the actual evpotrans piration rate to minimise the deficits in the yields.The useable soil moisture in any time period in the objective function is indirectly maximised ncr np ? a k + aik +1 ? Ky k MaxZ = ? ? ? i ? 2. 0 ? Zww i =1 k =1 ? (7) subject to the side by side(p) constraints 1. crap moisture doggedness ? aik + aik +1 ? PET = RF k ? 2. 0 ? Zww ? ? ik +1 EDik +1 ? ? ik EDik ? IRRik + ? (8) ? ik +1 ? aik +1 ? bik +1 = ZW (9) where with physiologic move ? ik +1 ? 4. 0 a 2. k +1 i (10) ? 0. 9 (11) artificial lake continuity ncr A k S k +1 ? B k S k + ? i =1 S k +1 ? 31. 1 5. IRRik * AREAik = ? ID ? Ao RE k come ( supreme artificial lake aptitude M m3) (12) (13) cut short Simulation modellingThe optimisation model presented supra yields some irrigation depth value that are based on forecasted determine for the computer address evapotranspiration. This reference evapotranspiration, in turn, is based on a reliableness model. However, the actual evapotranspiration value differs from these determine, and thus, before pass into the following(a) fortnight, the soil moisture status must be updated with the use irrigation and actual climatical factors. The cooking for crop guise is as follows archetypical compute the final soil moisture with the following relation ? ik = (? ik +1 EDik +1 + IRRik ?Fkcik APET k + ARF k ) / EDik If (14) ? ik +1 3. 1 ?k ? Fkcik +1 APET k +1 Fkcik +1 APET k +1 ZW + ARF k +1 ? ? i EDik + IRRik +1 ? + ? 2. 0 2. 0 ? EDik +1? ik +1 = ? k +1 k +1 Fkci APET EDik +1 2. 0 ( ) (15) or 6 fourteenth MANCO ? ? ik = ? ik ? 1 ? EDik ? 1 ? ? Fkcik APET ? Fkcik APET Fkcik APET + Zw + ARF k + IRRik ? ? EDik ? 2 . 0 2 . 0 2 . 0 ? (16) or ? k ? 1 ? k ? 1 Fkcik APET ? Fkcik APET Fkcik APET ? k k ? ? = i ? EDi ? Zw? ? ? EDi ? ? + IRRi + ? ? 2. 0 2. 0 2. 0 ? ? ? ? k i (17) The computed soil moisture status of the crops is used in the next fortnight to compute the demand. . Stochastic abbreviation of Evapotranspiration It was previously verbalise that t he entropy regarding the climatic factors is uncertain in nature and the determination of these factors beforehand is impossible. However, in that location is a worldwide trend to assume the expected values for these factors and carry out the operation. The concept does not give a clear meet of the actual scenario and the admit weights for the soulfulness emergence stage of the crops are not assigned. The present study proposes a distinct method of forecasting the expected values for the climatic factors.The method of abbreviation starts with the computations of dependableness values of reference evapotranspiration factors from the available selective information. The dependableness of credit of any stochastic variable is define as the chance of fair to middlingling or prodigious that variable with a occurrence value. Mathematically, P(x ? X ) (18) where P (. ) is the prospect and x is the variable under consideration and X is a stipulated value of the variable. A traditional method of estimation of the dependability value is the use of standard frequence formulae (e. . Wiebulls formula or Hazens formula). In the present study, a circumstantial probability digest for the info is performed. The data is fitted to a standard probability dispersion and the best fitting distribution is tried through the Kolmogorov Smirnov screen out (Haan, 1977). Once the values corresponding to polar dependabilities are evaluated, dependability values for reference evapotranspiration are anticipate to be incompatible in diametrical growth stages. The analysis is performed on the basis of the yield response factor.A high yield response factor signifies greater sensibility towards the deficits, and thus, a high(prenominal) level of dependability is assumed for the evapotranspiration data and a inflict level of dependability is assumed for the rainwater data. This will ensure a higher value of irrigation inevitable for the crop in the sensitive p eriod. As a result, the crop will be safeguarded against any slimy moisture content conditions. 7. LP Model Formulation for best Cropping course At the start of from each one dry season, depending on the storehouse volume in the reservoir, the crop practice session must be determined.To evaluate the crop mould, another LP model is used. In this model, irrigation depths are calculated from Eq. (6). The grooming is as follows The objective function is MaxZ = C1 X1+ C2 X2+ C3 X3 (19) which is subject to the following constraints 1. arrive available domain of a function X1+X2+X3? A (20) where X1, X2, and X3 are the decision variables associate to the expanse of single cropsC1, C2, and C3 are the cost co cost-efficient for each crop in Indian Rupees (1 US $ = 50 INR) and A is the maximum celestial orbit available for irrigation. 2.Area of each item-by-item crop 7 14 & 15 February 2009 Kuching, Sarawak The vault of heaven under each crop is required to be constrained thus, thither are pooh-pooh and focal ratio move on the area under each crop. The write down berth spring indicate the minimum area that can be allocated to a crop, piece of music the upper ricochet indicates the maximum. In the present study, the lower bounds were delimit for all the crops except cash crops, while the upper bounds were defined considering the present cropping soma. The constraints can be expressed as Li? Xi? Mi (21) here Li corresponds to the lower bound of the area for the ith crop and Mi corresponds to the upper bound on the area of the ith crop. 8. Model use The developed models were utilize to the Chiller reservoir system in Madhya Pradesh, India (Latitude 23o23 N and Longitude 76o18 E). In the central part of India, many reservoir projects have been constructed for irrigation, but no irrigation is available from these reservoirs during the monsoon period (from June to September). The area receives about 90 to 95 % of its rainfall during the Monsoon sea son. The rainfall then becomes runoff to the reservoirs.These reservoirs are designed to ascertain the runoff in the monsoon season, but there is no runoff during non-monsoon months. The present formulations are specially suit for these types of reservoirs. Non-monsoon rainfall is antiquated and provides little runoff. A systematic data base was prepared for the various physical features of the reservoirs, including the meteorological and hydrological data such as evapotransiration, exposit of crops in the command area, details of net returns from someone crops and soil properties put in from the College of Agriculture, Indore, India. . Results and Discussion best Crop simulate A wear out computer program was run before the real time operation program to determine the optimum crop radiation formula for all possible storage values. The results of the optimum crop pattern are express in duck 1. The results indicate that from a storage level of 31. 10 M m3 to a storage le vel of 26. 06 M m3, the cropping pattern is same as the one that has been adopted in the project formulation. However, infra a storage level of 26. 06 M m3, the crop pattern changes suddenly, and wheat (ordinary) is not recommended by the model.The area of wheat (hybrid) also gets reduced when the rainfall storage is below this level. However, the area for g is full, up to a storage level of 15. 83 M m3. The change in cropping pattern indicates that efficient water usage is maintained. turn off 1 Optimum Cropping mold for varied receively warehousing value Area (ha) for various crops hold water storage (M m3) Wheat (ordinary) gigabyte Wheat (hybrid) 4. 3230 342. 910 120. 00 8. 2379 427. 580 500. 00 12. 3246 15. 8632 20. 7581 26. 0986 28. 8610 30. 1250 31. molar concentration 300. 0 300. 0 300. 0 300. 0 1084. 015 1100. 000 1100. 00 1100. 000 1100. 000 1100. 000 1100. 000 500. 00 855. 00 1434. 00 1700. 00 1700. 00 1700. 00 1700. 00 Results from strong-Time surgical proce dure Model The real-time operation model gives an optimal operating policy for the available storage in the present fortnight considering the future. The model also yields the values of irrigation to be applied to individual crops in the fields. In the wake of insufficient water supplies, the model distributes the available water over the time for varied crops optimally. The exemplification results of the present model are express in gameboard 2.The available moisture to the crops is not affected, and by and large the soil corpse at the upper limit of the available soil-moisture. This 8 14th MANCO is because the crop pattern is predicted according to the handiness of the storage in the reservoir. The results are suggestive of successful performance of the real-time operation strategy proposed in the present work. duck 2 smack Results Showing the Soil moisture, useable Soil moisture, retention, and Irrigation to be applied for Different Crops for a Real-Time reference act Model (LP) Live Storage in the origin 31. 1 M m3 FORTNIGHTPARAMETER 1 2 3 4 5 6 7 8 9 10 11 root Storage (M m3 ) 29. 28 28. 17 26. 30 22. 22 Crop 1) Soil moisture (mm/cm) 3. 76 3. 89 3. 84 3. 07 2) acquirable soil wet 0. 9 0. 9 0. 9 0. 87 (mm/cm) 3) utilise Irrigation (mm) 53. 62 90. 63 92. 87 36. 04 Crop 1) Soil Moisture (mm/cm 3. 90 3. 07 3. 28 3. 15 2) Available soil Moisture 0. 9 0. 87 0. 9 0. 9 (mm/cm) 3) Applied Irrigation (mm) 68. 76 22. 27 60. 67 41. 59 Crop 1) Soil Moisture (mm/cm 4. 00 2) Available soil Moisture 0. 9 (mm/cm) 3) Applied Irrigation (mm) 94. 21 19. 68 14. 64 10. 87 Wheat (ordinary) 3. 54 3. 30 3. 22 0. 9 . 9 0. 9 5. 62 4. 24 3. 63 3. 60 3. 17 0. 9 4. 0 0. 9 -. 163. 9 8. 44 23. 02 g-force 3. 28 3. 66 0. 9 0. 9 19. 94 102. 6 3. 23 0. 9 3. 47 0. 9 37. 64 53. 15 Wheat (hybrid) 3. 06 3. 48 3. 32 0. 86 0. 9 0. 9 0. 00 33. 17 3. 28 0. 9 3. 38 0. 9 3. 18 0. 9 3. 19 0. 9 37. 19 162. 9 0. 00 36. 09 0. 0 3. 4 0. 9 26. 96 127. 9 78. 89 congener d ie Ratios telling yield ratios computed for different crops at different live storage values are shown in Table 3. The relative yield ratios for all the crops become one if live storage in the reservoir is equal to or greater than 28. 9 M m3. The GA model is found to be better for application in real world operation of the reservoir. Table 3 Relative Yield Ratio for Different Live Storage Values Computed With a Real-Time informant Operation Model Relative yield ratio for Live different crops storage LP (M m3 ) Wheat universal gravitational constant Wheat (hybrid) (ordinary) 4. 3230 0. 9677 1. 000 8. 2362 0. 9083 1. 000 12. 3246 0. 9576 1. 000 0. 989 1. 000 20. 7581 26. 0986 1. 000 0. 987 0. 987 0. 911 0. 952 28. 8610 1. 000 0. 987 1. 000 30. 1250 31. potassium 10. 15. 8632 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 ConclusionA real-time model using an integrated Linear Programming Model for a reservoir system meant for irrigation has been developed in the present study to obtai n an optimal reservoir operating policy that incorporates field level decisions, while also deciding the appropriate time and totality of water to release from the reservoir. 9 14 & 15 February 2009 Kuching, Sarawak From the analysis, the following conclusions can be pinched The developed model can be successfully applied to irrigation incarnateing reservoir systems. Furthermore, the models ensure an optimum reservoir release over different time periods.In addition, they also ensure optimum tryst of the available water over the different crops in the fields. While allocating the water to different crops in the fields, the model takes into account the critical growth stages of the crops and allocates sufficient water to each crop to safeguard it against any ill effectuate of water deficits. The optimum crop pattern model used in the study will only allow reproductive irrigation, so the amount of wasted water is reduced. Acknowledgements The authors would like to express sincere convey to Universiti Sains Malaysia for the financial support of this work.Nomenclature AETi k k authentic evapotranspiration in period k from crop i (mm) APET ARFk Ak and BK Ao d Actually occurring potential evapotranspiration in period k (mm) Actual rainfall value in the fortnight k Constants relating the storage to reservoir drying up Area of circulate at at rest(predicate) storage level Depletion factor EDik in effect(p) root regulate depth of a crop i in period k (cm) k +1 i ED sound root order depth of a crop i in period k+1 (cm) Eff Fkcik ID boilersuit efficiency Crop evapotranspiration coefficient Industrial supply from the reservoir (mandatory release) IRRikIrrigation applied to crop i in stage k (mm) k Ky Yield response factors for a crop i in period k PETi k RE RF k Potential evapotranspiration in a picky geographical location (mm) Rate of drying up in fortnight k k Sk Sk+1 Zf Zw Zww rain in period k (mm) origin storage at the beginning of period k generator s torage at the end of period k arena capacity for the soil (mm/cm) Permanent wilt point for the soil (mm/cm) Critical available moisture limit (mm/cm) ? ik ? ik +1 lowest soil moisture in a particular time stage k for a particular crop i (mm/cm) Yai Ymi Actual crop yield Maximum crop yieldInitial soil moisture in the time stage k in for a crop i (mm/cm) 10 14th MANCO References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 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