INCREASING THE RESULT OF RICE FARMING IN SRI METHOD CASE STUDY: TASIKMALAYA S RICE FIELD ABSTRACT Dian Putri Indah Mardika 1, Adiyanti Firdausi 2, Nicky Ria Azizman 3 Bandung Institute of Technology, Indonesia 1 University of Indonesia, Indonesia 2 Bandung Institute of Technology, Indonesia 3 Rice is Indonesian primary food which always eaten with vegetables or meat. Nowadays conventional rice farming only cultivate 4 ton for each hectare land on average. With the newly found method of rice farming, the System of Rice Intensification for organic farming will improve the result of conventional farming system with less cost. This method can guarantee an increase of the rice harvested, around 7 ton each hectare, this significant result could help our country in maximizing rice produced. This paper will discuss modification in SRI method with mathematical modeling to get the most effective way of farming and produce maximum result even more than 7 ton/ha. Keywords: System of Rice Intensification, Organic Rice, Maximizing SRI Production. PACS: 87.10.Ef, 88.20.df 1. INTRODUCTION The development of the System of Rice Intensification (SRI) began 20 years ago in Madagascar by a Jesuit priest, Fr. Henri de Laulanié, S.J. to improve their rice production without dependence on external inputs resulting in the most remarkable system of rice planting (Uphoff, 2003a). System of Rice Intensification is one of the most remarkable agricultural innovations in the last century, it could be the answer for this planet s problem where increasing number of population for human is not balanced by the area of land that is not increasing at the same pace. SRI could keep all people fed and no one starving, especially in Indonesia where most people are eating rice as their primary food. SRI methods contribute to more grain production and also to a lower percentage of unfilled grains and to higher grain weight compare to the conventional method. With SRI methods, one could see, after the first month a much greater number of tillers, 30-50 per plant, with some plants producing even 80-100 tillers. System of Rice Intensification has evidences that benefits particularly for poor farmers and for the environment: doubling yields or even more without requiring the use of fertilizer or other chemical inputs, and using less water. This benefit makes the cost to maintain SRI rice field cheaper than conventional one, with selling price higher than the conventional rice, SRI rice offers more profit for those who are interested to invest in making rice field. In 1994, CIIFAD, the Cornell International Institute for Food, Agriculture and Development, began working with Tefy Saina to introduce SRI to farmers in the peripheral zone around Ranomafana National Park (Uphoff, 2003a). Farmers around Ranomafana were getting lowland rice yields of only 2 ton/ha from their small areas having irrigation. To feed their families, they needed to practice upland cultivation. Raising lowland yields was thus seen as a requirement for saving the rain forest, as well as for reducing poverty. In 1994-1995, only 38 farmers would try the new methods, which changed four things that had been done from time immemorial in Madagascar, and in most other rice-growing countries such as Indonesia. This new methods are listed below: 1. Instead of planting seedlings 30-60 days old, tiny seedlings less than 15 days old were planted.
2. Instead of planting 3-5 or more seedlings in clumps, single seedlings were planted. 3. Instead of close, dense planting, with seed rates of 50-100 kg/ha, plants were set out carefully and gently in a square pattern (also called Tegel in Bahasa Indonesia) of 25x25cm or wider if the soil was very good. 4. Instead of keeping rice paddies continuously flooded, only a minimum of water was applied daily to keep the soil moist, not always saturated; fields were allowed to dry out several times to the cracking point during the growing period, with much less total use of water. The goal of this paper is to modify two of the methods above (the distance between crops and the plantation system) and calculate the input compositions that can get maximum yield. In Indonesia, the farmers who have been trained to plant paddy with SRI methods are 42,272 farmers in 2011 (increasing from 37,252 farmers in 2009) and the areas of SRI farm are 16,440 hectare in 2011 (increasing from 10,440 hectare in 2009) out of the 11.86 million hectare areas designated for rice field by the government. Figure 1: Indonesian map with SRI farm plot areas of 10,440 Hectare in 2009. (Purwasasmita, 2012a) The increasing trend of SRI adoption from the conventional method of rice farming is an opportunity to seize the farming method in Indonesia and replace the conventional one. The SRI method is the answer to fulfill the food demand by the increasing population, even if the productivity of SRI on average in Indonesia (7.74 dry rice grain adoptee ton/ha) is not the maximum yields that can be achieved with SRI method (Purwasasmita, 2012a). In order to increase the current rice productivity, two variables are chosen to be modified, which are the distance between crops and the plantation system. The different distance between crops and the plantation system can result in various rice yields with the limited area of rice field as its constraints. The goal of this research are to find the best plantation system and distance between crops under the limited farm area to maximize the rice yields with SRI method by using mathematics as a tool to compute and simulate the yields with different inputs of distance between crops in order to improve the overall rice yields. Further details about System of Rice Intensification can be found in some paper related to System of Rice Intensification by Uphoff (2003a) or book about SRI in Bahasa Indonesia by Purwasasmita (2012a).
2. RESEARCH METHODS This research used mathematics optimization formula and derivatives method to project numerous rice yields for certain distances and plantation system without the need of planting trial on the paddy field, this method could save our time to find approximation of the optimum distance between crops to get the maximum harvest result. This research has been done in February 2013 by taking samples of rice that has been planted with various distances between crops and the corresponding rice yields at Mekarwangi village, Tasikmalaya rice field. The sampling strategy was by measuring the arithmetic average amount of stems and the rice yields in ton for each distance between crops that has been planted at Mekarwangi rice field in Tegel Method and then using the samples to simulate the yield for the Jajar Legowo plantation system to compare both systems and find which one can give more yield. Jajar Legowo is a plantation system that arranges the paddy s distance between crops with alternating patterns between two lines and one blank line. This distance between crops arrangement was developed based on the Border Effect that was likely to increase yield than the Tegel system. The distance between crops variable that has been sampled were then be regressed, interpolated, and extrapolated to expand the choices of this independent variable, which represented by rr as the notation, this variable was the main input for the main model to simulate the rice yields for any distance between crops we want to compute. The mathematical models that produced in this paper are based on the assumptions below: 1. The rice was planted using Tegel plantation system / square pattern (see figure 2) 2. For each distance between crops, each seed producing same amount of stems, and each stem producing same amount of panicles. 3. Every seed grow with no harm, virus or bad weather (perfect condition assumption). 4. The area of the farm for computation is 1 hectare with the shape of the land is a square. With this assumption, the rice yields could be approximated for each distance between crops by using the mathematical model that is formed from this paper. The model is modified to calculate the yield for the Legowo plantation system. Figure 2: The Tegel method / square pattern in rice plantation (left figure) and the plantation system Jajar Legowo 3:1 type 2 (right figure) The distance between crops variable that has been sampled from Mekarwangi village, Tasikmalaya (see figure 3) are four different distances with their own corresponding rice yields and amount of stems from one seed on 1 hectare rice field (see table 1). 27 30 50 5-10 27 30 50 5-10 Figure 3: The distance between crops that has been planted in Mekarwangi village, Tasikmalaya rice field (in cm)
Table 1: Sampled data from Mekarwangi village, Tasikmalaya SRI rice field. r (distance between crops) K (amount of stems) D (yield) 27 cm 60 7 ton 30 cm 70 7.3 ton 50 cm 220 7.7 ton The rice that has been planted in Mekarwangi village, Tasikmalaya used the Ciherang rice variety that has the maximum amount of stems of 250, based on all Indonesian SRI planting experiment results recorded by Purwasasmita, 2011. (see figure 4). Figure 4: The Indonesian SRI paddy stems that is planted in a polybag with single seedlings resulting in 147 stems on average (left figure) and the maximum amount of 250 stems from single seedlings that has ever been recorded in Indonesian SRI farming history (right figure). (Purwasasmita, 2011) The rice that has been planted in Mekarwangi village, Tasikmalaya are using the Ciherang rice variety (used in this research) and this variety has the maximum amount of stems of 250, based on all Indonesian SRI planting experiment results that are recorded by Purwasasmita, 2011. (see figure 3). 2.1. Mathematical Models Let the equation that defines the rice harvested from 1 hectare farm as D, this equation is defined as below: D = N I conv K b 0.00027 (1) With N is the number of seedlings that are planted in the rice field (area in m 2 / distance between crops in cm 2 ), I conv is the conversion rate from dry rice grain adoptee to paddy, b is the number of dry rice grain adoptee per each stem, the constant 0.00027 is the conversion rate from amount of paddy grain to ton and the distance between crops from cm to m, adjusting for standard measure of farm field, K is the function of rr that defines the amount of stems for one specific distance between crops. There were some technical assumptions from Tasikmalaya s rice field sample data for the constants: 1. Conversion index from dry rice grain adoptee to dried paddy was 0.8, meaning that 80% of dry rice grain adoptee mass became dried paddy mass. 2. Conversion index from dried paddy to paddy was 0.8, meaning that 80% of dried paddy mass became paddy mass.
3. The variable I conv was the conversion index from dry rice grain adoptee to paddy, which is 0.64. 4. The mean sampled for the number of dry rice grain adoptee from each stem in Tasikmalaya s rice field is 55 The solution or general function for K is needed in order to calculate D towards rr, knowing that the amount of stems are limited to one maximum number for distance approaching infinity is quite similar with the concept of differential equations of population growth. The definition for the differential equation of K for rr is similar with the differential equations models of population growth: dk drr = K(a ck) The ordinary differential equation with respect to rr above is used to find the solution of K, the amount of stems towards the distance between crops. With assumptions of a as the nutrient absorbed by the root and c is the constant to diminish the number of stem that will grow since the root of plant has maximum absorbing capacity. The solution of the differential equation above got the analytical solution as below: K = a/c (2) 1+( a ck 0 ck0 )e αr Equation (2) defines the amount of stems for certain distance between crops. As can be seen from figure 5 below, paddy plant s root has maximum nutrients absorption power hence a seedling that is planted at rr 1 distance to another seedling will only absorb maximum nutrients at rr 2 distance, with rr 2 < rr 1. Thus, the equation (2) is needed in order to find the optimal distance between crops to gain highest productivity at a limited rice field area. rr 2 rr 1 Figure 5: Illustration of maximum absorption power from paddy plant s root. Variable a/c is the maximum amount of stems that one seedling can produce, for rice variety Ciherang (used in this research) the maximum amount of stems are 250. The variable K 0 is the initial value that is set with young seedlings condition K > 0 thus K(0) = K 0 = 1. By using sampled data from the Tasikmalaya s SRI rice field itself (see table 1), constants a and c can be found by substituting the amount of stems with the corresponding distance between crops from table 1 into the equation above to get 3 equations with 3 unknowns that can be solved by Gauss elimination. Thus the solution of the unknowns are a = 136.7439, b = 0.54698, and α = 0.13367. Substituting these solutions back to the equation (2) will get the solution for K with only rr as its independent variable. K = 250 136.7439 0.54698 1 1 + ( 0.54698 1 )e 0.13367r
2.2. Optimization Formula In order to optimize the limited rice field area, let D be the function that define the rice yields in ton at 1 hectare farm. With limited land area and K converge to its maximum value when the value of rr is increasing there will be a lower and upper bound needed for the value of rr as input for equation (1). The formula of D above used as an objective function to maximize the rice yields. Thus, the optimization problem: Maximize D With constraint: 10 rr 100 The constraint condition was set with lower bound for the distance between crops 10 cm as a minimal distance to plant the seedlings, this condition was needed since the seedlings needs a minimum distance to another seedlings to make the root healthy and can be harvested. The upper bound for the distance between crops is 100 cm due to the limited rice field area and the condition of increasing distance between crops more than 100 cm made the rice yields decreasing (see figure 6 and 7). Figure 6: Graphics of function K (amount of stems) towards rr (distance between crops) Figure 7: Graphics of function D (production result / rice yields) towards rr (distance between crops) By using calculus theorem, the function D with domain of [10,100] is a continuous and differentiable function thus the derivative of this function exists and consequently this function will have minimum or maximum extreme value in the domain of the function.
To find which distance between crops gives the maximum harvest result, the initial test was using the first derivative test to find all the critical/ stationary points for the function (1), the stationary point was the point where the slope of the graph D was zero at that point. D rr = 0 By solving the differential equation above, two stationary points can be obtained at: rr 1 = 15.8834 rr 2 = 40.8352 The stationary points tested by using the second derivative test to determine the type of extreme values (relative minimum or maximum value) and the concavity of the function around the stationary points. The rule to get the maximum value from the second derivative test is when the value of the second derivative at a stationary point is negative, thus making the derivative of the function decreasing at that point, and the curve of the graph is concave down at that point. D 2 2 rr < 0 By checking the second derivative for each points that satisfies the above equation, the maximum result for D is when the distance between crops rr = 40 (rounded to nearest integer). The rice harvested for distance between crops 40 cm is 9 ton in 1 hectare land. 2.3. Model Sensitivity The test for model sensitivity for function (1) was by changing the rice field area and rerun the first derivative test to examine the stationary points. The model that is discussed in the chapter 2.2 is using 10,000 m 2 / 1 hectare as the rice field area. The model sensitivity test used the areas of 2,500 m 2 and 50,000 m 2 to run another first derivative test on the model. Thus the stationary points from two different areas are: rr 1 = 15.8834 rr 2 = 40.8352 The stationary points still unchanged, proving that the stationary points are not influenced when the rice field area is changed only the yield that is influenced by the different rice field area (see figure 8). Figure 8: Graphics of D (production result / rice yields) towards rr (distance between crops) with various rice field area.
2.4. Mathematical Model for Legowo Plantation System The models discussed in the previous chapters assumed for Tegel plantation system, the modification for the model to calculate the yield of Legowo plantation system only needs some adjustments in the amount of stems (K) and the number of seedlings functions. The point of comparing both plantation systems was to mathematically prove the advantages of using Legowo are below: 1. Increasing the amount of stems planted which automatically will increase the yield 2. Improving the grain quality by the increasing number of crops that is planted on the border 3. Reducing the rate of pests and plant diseases 4. Use less fertilizer With the same technical assumptions from Tasikmalaya s rice field for the constants, the model to calculate the amount of stems (K) divided into 2 types that corresponded with the types in Legowo (see figure 9). Legowo type 1 and 2 had a blank line that called the border, which divide the repeating pattern of crop plantation, with this border there are 3 variables in Legowo that replaced the distance between crops (rr) in Tegel system, which are JAK (the distance between columns), JAB (distance between rows), JL (the border width). Figure 9: Jajar Legowo 3:1 type 1 plantation system (top left figure), Jajar Legowo 3:1 type 2 plantation system (top right figure), Jajar Legowo 4:1 type 1 plantation system (bottom left figure) and Jajar Legowo 4:1 type 2 plantation system (bottom right figure). The number of seedlings planted in 1 hectare rice field in Legowo plantation system calculated by first subtracting the land area with the border area that dividing one the seedlings group from the next column of the seedlings group. In Legowo type 1 the leftover land divided with the distance between the each seedlings distance, for Legowo type 2 the leftover land divided with the distance between each seedlings took into account the empty spaces inside the seedlings group. Mathematically, the Legowo type 2 had fewer number of seedlings compares to the type 1. The MATLAB code to calculate the number of seedlings in any Legowo type can be seen in appendices. Since the yield is not determined by the number of seedlings alone, the amount of stems from each seedling was the next variable which examined to define the yield of SRI method. The amount of stems was differentiate from the area of rectangle that is surrounding the seedlings, with the border effect in Legowo system the area of rectangle / nutrients that can be absorbed by one
seedlings that planted on the border (border seedlings) widen, thus it increased the amount of stems from the border seedlings. Legowo type 1 had 1 column of border seedlings (taping) at the right side of each seedlings group that produced more amount of stems than the inside seedlings (tandal). Below are the area calculations to absorb nutrients for each seedling: Area of K taping = (JAK + 1 JL) JAB 2 Area of K tandal = JAB 2 The area calculations to absorb nutrients for Legowo type 2 were: Area of K taping = (JAK + 1 JL) JAB 2 Area of K tandal = JAK 3 2 JAB The shaded area in the figure 10 was the illustration of the widen area that can increase the nutrients absorption for the border seedlings thus increasing the amount of stems for the border seedlings. In Legowo type 2 the inside seedlings get the same effect by the increasing area to absorb nutrients from the blank spaces inside the seedlings group, the blue shaded region was the area for the inside seedlings and the red shaded area was the area for the border seedlings). Figure 10: The border effect illustration from Jajar Legowo type 1 (top figure) and the border effect illustration from Jajar Legowo type 2 (bottom figure). The MATLAB codes that compute the amount of stems from border seedlings and inside seedlings can be seen in the appendices.
2.5. Profit and Cost Computation The previous modeling and computation to find the optimal distance between crops were the input for the optimal profit computation by taking into account the operational cost (sampled from the rice field in Mekarwangi village, Tasikmalaya) needed to maintain the rice field with assumptions: 1. The cost and profit calculation using Indonesian Rupiah currency 2. Area of rice field for the computation was 1 hectare 3. Amount of organic fertilizer that is used for any distance between crops is constant 4. The amount of weeding have negative linear correlation with the distance between crops 5. The selling price for rice / kg was set to IDR 8,000. Table 2: Operational costs of 1 hectare SRI rice field using crops 40 cm in IDR. Operational Costs Amount Unit Prices Cost 1. Rice field rent for 1 season (3 months) 1 hectare 3,500,000 3,500,000 2. Maintenance costs - Soil 1 time 800,000 800,000 - Embankment 112 work hours 30,000 480,000 - Organic fertilizer 84 work hours 30,000 360,000 - Pest control with vegetable pesticide 7 work hours 30,000 30,000 - Weeding rice field 35 work hours 30,000 150,000 3. Production medium - Seedlings 2.54 kg 10,000 25,400 - Solid organic fertilizer (compost) 6,000 kg 500,000 3,000,000 4. Seeding and Planting - Seed medium 1 unit 100,000 100,000 - Paddy seeding 7 work hours 30,000 30,000 - Planting 49 work hours 30,000 210,000 5. Harvest 35 work hours 30,000 150,000 6. Milling 9000 kg 300 2,700,000 Total 11,535,400 The number of seedlings to be planted at 1 hectare SRI rice field calculated by dividing the land into n squares with length variable is the distance between crops and then converting them into kilogram by conversion from dry grain adoptee to paddy (see table 3 and 4).
Table 3: Number of Seedlings at 1 hectare rice field for various distances between crops with Tegel system. Distance between Crops (cm) Number of Seedlings Number of Seedlings / 1 m 2 Number of Seedlings / 1 Hectare 25 160.000 16 6.504 kg 27 137.174 13.7 5.57 kg 30 111.111 11 4.47 kg 33 91.827 9.1 3.65 kg 40 62.500 6.25 2.54 kg 43 54.083 5.4 2.199 kg 50 40.000 4 1.62 kg Table 4: Number of Seedlings at 1 hectare rice field with Legowo system. Number of System JAB JAK JL N Seedlings / 1 Hectare Legowo 2:1 12.5 25 50 213,333 8.66 kg Legowo 2:1 15 25 50 177,777 7.19 kg Legowo 3:1 type 1 12.5 25 50 240,000 9.76 kg Legowo 3:1 type 1 15 25 50 200,000 8.13 kg Legowo 3:1 type 2 12.5 25 50 200,000 8.13 kg Legowo 3:1 type 2 15 25 50 173,333 7.03 kg Legowo 4:1 type 1 12.5 25 50 256,000 10.41 kg Legowo 4:1 type 1 15 25 50 213,333 8.66 kg Legowo 4:1 type 2 12.5 25 50 192,000 7.8 kg Legowo 4:1 type 2 15 25 50 170,666 6.95 kg The costs calculation from table 2 is used to simulate the operational costs another distance between crops and plantation system (see table 5). Table 5: Operational costs of 1 hectare SRI rice field with various distances between crops in IDR. No Description Total Cost 1 2 3 4 crops rr = 27 cm crops rr = 30 cm crops rr = 40 cm crops rr = 50 cm 11,625,700 11,494,700 11,535,400 11,016,200
5 6 7 8 9 Jajar Legowo 2:1 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 3:1 type 1 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 3:1 type 2 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 4:1 type 1 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 4:1 type 2 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm 11,699,300 11,783,300 11,421,500 11,833,700 11,255,400 With the assumption that each kilogram of paddy has selling price of IDR 8,000 the revenue from 1 hectare SRI rice field with various distances between crops and plantation systems can be seen in table 6. Table 6: Revenue of 1 hectare SRI rice field with various distances between crops in IDR. No Description Yield Revenue 1 2 3 4 5 6 7 8 9 crops rr = 27 cm crops rr = 30 cm crops rr = 40 cm crops rr = 50 cm Jajar Legowo 2:1 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 3:1 type 1 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 3:1 type 2 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 4:1 type 1 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm Jajar Legowo 4:1 type 2 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm 7000 kg 56,000,000 7300 kg 58,400,000 9000 kg 72,000,000 7700 kg 61,600,000 9290 kg 74,320,000 9540 kg 76,320,000 8370 kg 66,960,000 9690 kg 77,520,000 7820 kg 62,560,000
3. RESULTS The research and calculation in the previous chapter show the optimal distance between crops in SRI farming is 40 cm with Tegel plantation system, and the Legowo 4:1 type 1 is the most optimal plantation system of all Legowo systems. The optimal distance for Tegel system provides the maximum yield of 9 ton/ha and profit of IDR 60,464,600 (see table 8) comparing to the others distance between crops that has been planted in Mekarwangi village, Tasikmalaya SRI farm field that usually yield 7 ton/ha on average. The optimal Legowo system in table 7 provides the maximum yield of 9.69 ton/ha and profit of IDR 65,686,300 comparing to the others Legowo types, even if the number of seedlings planted are fewer than Legowo 3:1 type 1 with the same distance variables. The MATLAB codes that calculate the yield for each legowo types can be seen in the appendices. Table 7: The yield of 1 hectare SRI rice field with Legowo plantation system. System JAB JAK JL N D (yield) Legowo 2:1 12.5 25 50 213,333 8.72 ton Legowo 2:1 15 25 50 177,777 9.29 ton Legowo 3:1 type 1 12.5 25 50 240,000 8.94 ton Legowo 3:1 type 1 15 25 50 200,000 9.54 ton Legowo 3:1 type 2 12.5 25 50 200,000 7.64 ton Legowo 3:1 type 2 15 25 50 173,333 8.37 ton Legowo 4:1 type 1 12.5 25 50 256,000 9.08 ton Legowo 4:1 type 1 15 25 50 213,333 9.69 ton Legowo 4:1 type 2 12.5 25 50 192,000 6.99 ton Legowo 4:1 type 2 15 25 50 170,666 7.82 ton Table 8: The profit of SRI farming at 1 hectare rice field for all plantation systems. Description K (amount of stems) D (yield) Profit crops rr = 27 cm 53 7000 kg 44,374,300 crops rr = 30 cm 72 7300 kg 46,905,300 Tegel system with distance between crops r = 40 cm 151 9000 kg 60,464,600 crops rr = 50 cm 213 7700 kg 50,583,800 Jajar Legowo 2:1 see chapter 2.4 9290 kg 62,620,700 Jajar Legowo 3:1 type 1 see chapter 2.4 9540 kg 64,536,700 Jajar Legowo 3:1 type 2 see chapter 2.4 8370 kg 55,538,500 Jajar Legowo 4:1 type 1 see chapter 2.4 9690 kg 65,686,300 Jajar Legowo 4:1 type 2 see chapter 2.4 7820 kg 51,304,600
The result from this model is an evidence for usual distance between crops that has been used in the Mekarwangi village, Tasikmalaya has not been optimized to get the maximum yield. The planting trial using 40 cm as the optimal distance between crops will be proven after the real plantation on the rice field. 4. DISCUSSION The model discussed in this paper only taking into account the distance between crops as one independent variable that determine the yield, there are other variables that should be added to modify the model into a realistic one. Some of the variables that can determine the yield are the soil condition, the compost input, the water input, the spraying of certain MOL, type of seedlings, and the plantation system. Moreover, when more variables are examined and added to the main model to determine the yield, the function D could become non-linear function instead of the linear model presented in this paper. SRI could achieves higher yields, sometimes over 20 ton/ha in an optimal soil condition. But that is one aspect need to be examined further with different geo-spatial location in one tropical country that planted paddy with SRI methods. Uphoff, 2003a shows the fantastic number. The farmers around Ranomafana who used SRI in 1994 1995 got the result averaged over 8 ton/ha, four times more than their previous yield, and some farmers reached 12 ton/ha and one even got 14 ton/ha. The next year and the following year, the average remained over 8 ton/ha, and a few farmers even reached 16 ton/ha, beyond what scientists considered to be 'the biological maximum' for rice. But these calculations were based on rice plants that had degenerated and truncated root systems. The use of organic fertilizer, water, and compost to nurture the paddy plant has not been done mathematically, to determine what kind of composition of these inputs can maximize the yield in SRI method can be another input variable to the mathematical model discussed in this paper. Another variable that could affect the SRI yield is the effect of MOL spraying to young plant (Local Microorganism made from fermented leftover vegetables, fruits, and foods) (see figure 11). The MOL which made by different ingredients also has different composition of organic substances, so that could influence the paddy plant differently. The research on MOL variable could give an effect to the paddy growth is needed but it has not been done concisely and this variable need to be included with the model from this paper. Figure 11: The Indonesian palm fruit that is sprayed by MOL (left figure) and the palm fruit that is not sprayed MOL (right figure). Source: Purwasasmita, 2012a. Knowing that different type of seedlings, water input, compost input, plantation system, location, and MOL used to spray the plant could provide different yield, one should continue to research the
SRI method and will come to terminal point where one can find the optimal list and composition of all the variables that possibly influence the yield. 5. CONCLUSIONS Based on the mathematical model in this research, Jajar Legowo 4:1 type 1 with JAB = 15 cm, JAK = 25 cm, JL = 50 cm is the optimal plantation system that produce the most yield than all other types from Legowo and Tegel with same distances. This SRI plantation system gained 9.69 ton per hectare from the simulation that could be applied in Mekarwangi village, Tasikmalaya To implement the model in another place in Indonesia, this model will need some adjustment for the conversion rate and variables. By sampling the data from another rice field this model could calculate which distance between crops is optimal for maximizing yield in the corresponding rice field. It can be seen that the projected yield for Tegel system by the mathematical model for sampled distance between crops (see table 9) are not differ too much with the yield gain from the sampled data (see table 1). The simulated yield from the distance between crops by the mathematical model in this research is a good approximation to the sampled data in table 1, knowing that the simulated yield and the sampled yield of the corresponding distance between crops do not differ too much. Table 9: The yield of SRI farming at 1 hectare rice field for various distances between crops and plantation system. Description D (Yield) Tegel system with distance between crops rr = 27 cm 7 ton Tegel system with distance between crops rr = 30 cm 7.3 ton Tegel system with distance between crops rr = 40 cm 9 ton Tegel system with distance between crops rr = 50 cm 7.7 ton Jajar Legowo 2:1 9.29 ton Jajar Legowo 3:1 type 1 Jajar Legowo 3:1 type 2 Jajar Legowo 4:1 type 1 Jajar Legowo 4:1 type 2 9.54 ton 8.37 ton 9.69 ton 7.82 ton
ACKNOWLEDGMENT My work here starts from the topic that I have taken in modeling class in my undergraduate study at Bandung Institute of Technology in 2013. To learn about how to increase the result of rice harvested in SRI that can help farmers, people, thus make less people starving. The chance to implement mathematics in real life problem is better than just learning inside class. All my thanks for Dr. Lili Yan Ing (ERIA) as writer colleague that give insight on how to improve this paper, the coauthor Adiyanti Firdausi (Chemistry Undergrad, University of Indonesia) that has been proof-read this paper, Nicky Ria Azizman (Bandung Institute of Technology) co-author who has help writer to finish this paper, Midun (Microbiology Undergrad, Bandung Institute of Technology) as a friend for discussion who has research project on MOL substances for SRI method, Dr. Novriana Sumarti (Mathematics lecturer, Bandung Institute of Technology) that guide the writer to understand the concept of differential equation, Dr. Mubyar Purwasasmita (Professor of Chemical Engineering, Bandung Institute of Technology) as a guru that help the writer understand the SRI method comprehensively, and the guidance from Muhammad Islahuddin (Mathematics, Bandung Institute of Technology) that give the support and valuable lesson to make this work done. APPENDICES This appendices include MATLAB code for computation of number of seedlings, amount of stems and the yield for the Legowo system (The commentary of the codes are written in Bahasa Indonesia, but the code can be run in any MATLAB software). A. MATLAB Program 1 (Amount of Seedlings for Legowo Type 1): disp ('Masukkan panjang dan lebar sawah') x = 100 ; % panjang sawah bisa diganti-ganti y = 100; % lebar sawah bisa diganti-ganti jak = input('jarak Antar Kolom(cm) = '); jab = input('jarak Antar Baris(cm) = '); jl = 50 ; % jarak lorong kol = input('berapa kolom dalam 1 KL = '); KL = ( (2*jl)+((kol-2)*jak) )/ 100; n1 = kol*(x/kl) ; n2 = 100*(y/jab); n = n1*n2 ; disp(['banyaknya rumpun (N) yang ditanam = ',num2str(n)]);
B. MATLAB Program 2 (Amount of Seedlings for Legowo Type 2): disp ('Masukkan panjang dan lebar sawah') x = input('panjang sawah(m) = '); y = input('lebar sawah(m) = '); jak = input('jarak Antar Kolom(cm) = '); jab_rapat = input('jarak Antar Baris rapat(cm) = '); jab_renggang = input('jarak Antar Baris renggang(cm) = '); jl = input('lebar lorong(cm) = '); kol = input('berapa kolom dalam 1 KL = '); kol_rapat = input('banyak kolom rapat dalam 1 KL = '); kol_renggang = input('banyak kolom renggang dalam 1 KL = '); KL = ( (2*jl)+((kol-2)*jak) )/ 100; n1 = 100*kol_rapat*(x/KL)*(y/jab_rapat) ; % hitung banyak rumpun ditanam di kolom rapat n2 = 100*kol_renggang*(x/KL)*(y/jab_renggang); % hitung banyak rumpun ditanam di kolom renggang n = n1+n2 ; % banyak rumpun yang ditanam disp(['banyaknya rumpun yang ditanam di kolom rapat = ',num2str(n1)]); disp(['banyaknya rumpun yang ditanam di kolom renggang = ',num2str(n2)]); disp(['banyaknya rumpun (N) yang ditanam = ',num2str(n)]); C. MATLAB Program 3 (Amount of Stems from 1 Seedlings for Legowo Type 1): disp ('Masukkan JAK, JAB dan JL ') jak = input('jarak Antar Kolom = '); jab = input('jarak Antar Baris = '); jl = input('jarak Lorong = '); L = (jak+0.5*jl)*jab; r = (L)^0.5; p = (250)/(1+((136.7439-0.54698*1/(0.54698*1))*exp((-0.13367*r)))); q = (250)/(1+((136.7439-0.54698*1/(0.54698*1))*exp((-0.13367*jab)))); disp(['r untuk K = ',num2str(r)]); disp(['aproksimasi banyaknya anakan per rumpun untuk taping = ',num2str(p)]);
disp(['aproksimasi banyaknya anakan per rumpun untuk tanaman dalam = ',num2str(q)]); D. MATLAB Program 4 (Amount of Stems from 1 Seedlings for Legowo Type 2): disp ('Masukkan JAK, JAB dan JL ') jak = input('jarak Antar Kolom = '); jab = input('jarak Antar Baris = '); jl = input('jarak Lorong = '); L1 = (jak+0.5*jl)*jab; r1 = (L1)^0.5; L2 = jak*1.5*jab; r2 = (L2)^0.5; p = (250)/(1+((136.7439-0.54698*1/(0.54698*1))*exp((-0.13367*r1)))); q = (250)/(1+((136.7439-0.54698*1/(0.54698*1))*exp((-0.13367*r2)))); disp(['r untuk K taping = ',num2str(r1)]); disp(['r untuk K tandal = ',num2str(r2)]); disp(['aproksimasi banyaknya anakan per rumpun untuk taping = ',num2str(p)]); disp(['aproksimasi banyaknya anakan per rumpun untuk tanaman dalam = ',num2str(q)]); E. MATLAB Program 5 (Yield Calculation for Legowo Type 1): disp ('Masukkan N dan K ') n1 = input('banyaknya rumpun tanaman pinggir (N legowo 2:1 dengan kriteria sama) = '); n2 = input('banyaknya rumpun tanaman dalam (selisih N dengan legowo 2:1) = '); k1 = input('banyaknya anakan per rumpun untuk taping = '); k2 = input('banyaknya anakan per rumpun untuk tandal = '); D = (n1*k1+n2*k2)*0.64*0.027*55*0.000001; disp(['hasil Panen(ton) = ',num2str(d)]); F. MATLAB Program 6 (Yield Calculation for Legowo Type 2): disp ('Masukkan N dan K ')
n1 = input('banyaknya rumpun di Kolom Rapat = '); n2 = input('banyaknya rumpun di Kolom Renggang = '); K1 = input('banyaknya anakan per rumpun di kolom rapat = '); K2 = input('banyaknya anakan per rumpun di kolom renggang = '); D = (n1*k1+n2*k2)*0.64*0.027*55*0.000001; disp(['hasil Panen(ton) = ',num2str(d)]); REFERENCES Haberman, Richard. (1977). Mathematical Models. New Jersey: Prentice-Hall. Jacob, Bill. (1990). Linear Algebra. New York: Freeman Kolbin, VV. (1984). Systems Optimization Methodology: Part I. St Petersburg: World Scientific. Purwasasmita, M. (2011). Kompos dan Mol. Jakarta: Gramedia. Purwasasmita, M. (2012a). Buku SRI Organik Indonesia - Tani Abad 21. Jakarta: Gramedia. Purwasasmita, M. (2012b). Mikrobioreaktor Tanaman. Jakarta: Gramedia. Rabenandrasanana, J. (1999) Revolution in rice intensification in Madagascar, LEISA Newsletter, 15. Randriamiharisoa, R. and N. Uphoff. (2002). Factorial trials evaluating the separate and combined effects of SRI practices. Ithaca, NY: Cornell International Institute for Food, Agriculture and Development. Rao, SS. (1984). Optimization Theory and Applications. New Delhi: Wiley Eastern Limited. Uphoff, N. (2003a). Development of the System of Rice Intensification (SRI) in Madagascar. Ithaca, New York: Cornell International Institute for Food, Agriculture and Development Uphoff, N. (2003b). Higher yields with fewer external inputs? The System of Rice Intensification and potential contributions to agricultural sustainability. International Journal of Agricultural Sustainability, 1, 38-50.