These criteria include: o Accuracy of Calculations being aware of accuracy requi
ID: 3141558 • Letter: T
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These criteria include: o Accuracy of Calculations being aware of accuracy required and applying accurately and consistently. o Problem solving evidence of problem solving is shown and methods and assumptions are clearly explained o Use of Technology-this needs to be clearly shown and used appropriately. o Quality of Analysis and Conclusions results of calculations are to analysed and conclusions drawn o Presentation of the Report the report should be presented clearly as for a major project. Introduction/Conclusion/Headings/subheadings/graphs/bibliography etc.Explanation / Answer
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In sprinkler irrigation water is applied from the sprinkler nozzle, which produces a jet breaking up in thousands of drops of different diameters. Drops travel for a distance of 2 to 15 m (depending on their diameter) before reaching the soil surface. In the dry, hot and windy conditions of the Ebro Valley, transporting water drops through the air results complicated. The wind modifies the landing place of individual drops, concentrating water application in certain areas. Additionally, wind speed is the most explanatory variable for wind drift and evaporation losses. Despite the use of the best available technology, sprinkler irrigation performance is not always excellent [7]. 155 Irrigation performance is measured using a number of performance indicators [2]. In the case of sprinkler irrigation, the Coefficient of Uniformity (CU, %), proposed by Christiansen [5], is very important. This coefficient expresses numerically the uniformity of water application in the field, so that 100% would be a perfect, unreal uniformity case, in which all parts in the field would receive exactly the same amount of irrigation water. CU can be determined as: CU = 1 1 nx Xn i=1 (xi x) ! 100%, (1) where: n is the number of pluviometers evenly distributed in the irrigated area; xi is the irrigation water depth received in an individual pluviometer (mm); and x is the average irrigation water depth received in the pluviometers (mm). Another indicator commonly used in sprinkler irrigation is the Potential Application Efficiency of the Low Quarter (P AElq, %), as defined by Merriam and Keller [18] and revised by Burt et al. [2]. P AElq applies to an irrigation event, and can be expressed as: P AElq = average depth of irrigation water contributing to the target average depth of irrigation water applied such that dlq = target 100%. (2) 0 6 12 18 24 30 36 0 5 10 15 0 10 20 30 40 50 0 5 10 15 mm Wind: 5.2 m s-1 (CU = 55 %) Wind: 1.2 m s-1 (CU = 98 %) Figure 2.— Maps of water distribution in a triangular 18 x 15 m sprinkler irrigation solid-set operating at two wind speeds The problems resulting from sprinkler irrigation under strong wind in the Ebro Valley are evident in Fig. 1 extracted from SigPac, a tool for the control of the Common Agricultural Policy elaborated by the Government of Spain (http://sigpac.mapa.es/fega/visor/). 156 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Enero Febrero Marzo Abril Mayo Junio Julio Agosto Septiembre Octubre Noviembre Diciembre MES FRECUENCIA RELATIVA, % Calma Flojo Moderado débil Moderado fuerte Fuerte 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Enero Febrero Marzo Abril Mayo Junio Julio Agosto Septiembre Octubre Noviembre Diciembre MES FRECUENCIA RELATIVA, % Calma Flojo Moderado débil Moderado fuerte Fuerte Day Night Relative Frequency Relative Frequency J F M A M J J A S O N D <1 m s-1 1-2 m s-1 2-3.5 m s-1 3.5-5 m s-1 >5.0 m s-1 Figure 3.— Analysis of wind intensity in Zaragoza during day and night time. Figures present the relative frequency of wind classes in different months. Data were obtained at the CITA experimental farm automated station in the period 1995-2002. Daytime was assumed as 7:00-19:00 GMT The aerial photograph shows the results of sprinkler irrigation, with water accumulating in certain areas of the field and being applied in very small amounts in other areas. Consequently, crop growth is intense in certain areas, while in other areas water stress decreases crop growth and results in yield losses. This problem is further illustrated by Fig. 2 [6], developed under experimental conditions. In the Figure, maps of irrigation water depth isolines corresponding to two irrigation events differing in wind speed are compared. In the high wind speed irrigation event (5.2 m s1 ), water accumulated in parts of the field downstream from the sprinkler, and CU only reached 55%. In the low wind speed irrigation event (1.2 m s1 ), water application was more uniform and CU reached 98%. In order to minimize these problems, farmers can adapt the design of the irrigation system (narrow sprinkler spacing, sprinklers located at lower height from the soil surface, avoid high operating pressures?). They can also adapt irrigation management by selecting the irrigation time, looking for periods of low wind. Fig. 3 shows that even under the prevailing windy conditions of the Ebro Valley low wind speed periods can be effectively selected. The Figure presents an analysis of monthly wind intensity in Zaragoza separating day and night time. Subfigures present the relative frequency of wind classes in different months. Daytime was assumed to last from 7:00 to 19:00 GMT (Greenwich Mean Time). The two low-wind classes (0–2 m s1 ) represent the prime time for irrigation, according to the wind speed thresholds proposed by Faci and Bercero [10] for adequate sprinkler irrigation. These two wind classes represent 40–50% of the day time and about 70% of the night time in Zaragoza. Night time irrigation thus 157 0 5 10 15 Solid Set Pivot Ranger Wind Drift and Evaporation Losses (%) Day Night 0 5 10 15 Solid Set Pivot Ranger Wind Drift and Evaporation Losses (%) Day Night Figure 4.— Average wind drift and evaporation losses resulting from solid-set and pivot (or ranger, a linear-move machine) irrigation, operating during day and night conditions represents a clear advantage to obtain high irrigation uniformity. Night irrigation can be easily performed by means of automated irrigation programmers. The effect of irrigation technology and day/night irrigation on wind drift and evaporation losses is illustrated in Fig. 4, which presents the percentage of water emitted by the sprinkler and not reaching the soil surface under different conditions [22]. Night time irrigation reduces these water losses to roughly one-third as compared to day time irrigation, while pivot irrigation and linear move irrigation systems (ranger) reduce losses to about two-thirds, when compared to solid-set sprinkler irrigation. Once an irrigation system is in place, farmers can only modify the time of irrigation to maximize uniformity and to minimize water losses. The selection of appropriate irrigation time is hampered by the generalised use of irrigation programmers executing rigid, wind-insensitive irrigation orders. This paper presents the problematic of sprinkler irrigation from a mathematical point of view, and provides mathematical solutions to these problems. The goal is to illustrate the relationship between mathematics and agricultural water management in the specific field of sprinkler irrigation. The addressed problems include: • characterization of sprinkler drops using photography; • a disdrometer for drop characterization: minimizing measurement errors; • a ballistic model of sprinkler irrigation based on drop diameter distribution; • optimizing the ballistic model for computational speed: Runge-Kutta pairs; and • collective irrigation scheduling: optimising daily irrigation operation. 158 2 Characterization of sprinkler drops using photography Different methodologies have been reported in the literature to manually determine drop diameters resulting from precipitation, sprinkler irrigation or pesticide application. Montero et al. [20] discussed a series of manual methods based on impression, photography, immersion in viscous fluids and impact on a layer of flour. Figure 5.— Photograph of water drops resulting from outdoor sprinkler irrigation. The camera was set at a shutter speed of 1/100 s. Drops in focus were numbered (left) and prepared for the measurement of drop diameter, drop angle and length (right) This section describes a new, reliable, methodology aiming at describing the diameter and velocity of sprinkler irrigation generated drops. A VYR35 impact sprinkler (VYRSA, Burgos, Spain) was used in this experiment. This sprinkler model is commonly used in solid-set systems in Spain. The sprinkler was equipped with a 4.8 mm nozzle (including a straightening vane). An isolated sprinkler was installed at an elevation of 2.15 m and operated at a nozzle pressure of 200 kPa. A digital photographic camera (Nikon D80) equipped with a 18–70 mm lens was installed at an elevation of 0.80 m, and adjusted to a shutter speed of 100 (1/100 s) and F11. A black cloth screen was installed at a distance of 1.0 m. The screen had a millimetric ruler located at a distance of 0.25 m towards the camera. The camera was focused at the ruler. Photo quality “L” (3872×2592 pixels) was selected because this was the highest available image resolution in JPEG format, and the picture taking speed was acceptable (9 photos in the first 3.1 seconds, one photo each 1.13 seconds later on). The combination of photo quality, zoom regulation and distance to the target resulted in a linear density of 14–15 pixels mm1 . More details on the experiments and its results can be found in Salvador et al. [25]. The camera was located at different distances from the sprinkler and operated on continuous shooting mode (2.9 photos s1 ) whenever the sprinkler water reached it. 159 After digital treatment of the resulting images, drops appeared as transparent cylinders (Fig. 5). The Figure presents a set of drops and the ruler (left), and an individual drop (right). Drop diameter, length and angle were individually measured. Drop velocity was derived from drop length and shutter speed. For each distance to the sprinkler, a set of drop diameters and velocities was obtained. Fig. 6 presents histograms of these two variables, which show very important changes along the distance irrigated by a sprinkler. Proximal drops have diameters below 1 mm (with a few exceptions), and velocities lower than 3 m s1 . Distal drops show very different features, with well-graded diameters with modal values in the 3–4 mm range and most drops in the velocity range of 5–6 m s1 . These data permit to gain knowledge on drop diameter and velocity distributions measured individually in a series of experiments. The method is very time consuming, but permits individual drop characterization, very well suited for comparison with automated drop characterization methods, such as the disdrometer.
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