Comparison of maximum pointwise errors in the numerical solution of the KSe on an adaptive mesh at different times with \n
\r\n\tThe aim of this book will be to describe the most common forms of dermatitis putting emphasis on the pathophysiology, clinical appearance and diagnostic of each disease. We also will aim to describe the therapeutic management and new therapeutic approaches of each condition that are currently being studied and are supposed to be used in the near future.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"278931ae110500350d8b64805c70f193",bookSignature:"Dr. Eleni Papakonstantinou",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/7934.jpg",keywords:"Atopic eczema, Interleukin, Topical corticosteroids, Hand eczema, Blisters, Pruritus, Irritant contact dermatitis, Allergic contact dermatitis, Discoid eczema, Sebaceous glands, Inflammatory dermatitis, Facial rash",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 5th 2019",dateEndSecondStepPublish:"March 19th 2019",dateEndThirdStepPublish:"May 18th 2019",dateEndFourthStepPublish:"August 6th 2019",dateEndFifthStepPublish:"October 5th 2019",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"203520",title:"Dr.",name:"Eleni",middleName:null,surname:"Papakonstantinou",slug:"eleni-papakonstantinou",fullName:"Eleni Papakonstantinou",profilePictureURL:"https://mts.intechopen.com/storage/users/203520/images/system/203520.jpg",biography:"Dr. med. Eleni Papakonstantinou is a Doctor of Medicine graduate and board certified Dermatologist-Venereologist. She studied medicine at the Aristotle University of Thessaloniki, in Greece and she continued with her dermatology specialty in Germany (2012-2017) at the University of Magdeburg and Hannover Medical School, where she completed her dissertation in 2016 with research work on atopic dermatitis in children. During this time she gained wide experience in the whole dermatological field with special focus on the diagnosis and treatment of chronic inflammatory skin diseases and also the prevention and treatment of melanocytic and non-melanocytic skin tumors. Her research interests were beside atopic dermatitis and pruritus also the pathophysiology of blistering dermatoses. In addition to lectures at german and international congresses, she has published several articles in german and international journals and her work has been awarded with various prizes (poster prize of the German Dermatological Society for the project: 'Bullous pemphigoid and comorbidities' (DDG Leipzig 2016), 'Michael Hornstein Memorial Scholarship' (EADV Athens 2016), travel grant (EAACI Vienna 2016). Since 2017, she works as a specialist dermatologist in private practice in Dortmund, in Germany. Parallel she co-administrates an international dermatologic network, Wikiderm International and she writes a dermatology public guide for patients, as she is convinced that evidence-based knowledge has to be shared not only with colleagues but also with patients.",institutionString:"Private Practice, Dermatology and Venereology",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"16",title:"Medicine",slug:"medicine"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"270941",firstName:"Sandra",lastName:"Maljavac",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/270941/images/7824_n.jpg",email:"sandra.m@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"6550",title:"Cohort Studies in Health Sciences",subtitle:null,isOpenForSubmission:!1,hash:"01df5aba4fff1a84b37a2fdafa809660",slug:"cohort-studies-in-health-sciences",bookSignature:"R. Mauricio Barría",coverURL:"https://cdn.intechopen.com/books/images_new/6550.jpg",editedByType:"Edited by",editors:[{id:"88861",title:"Dr.",name:"R. Mauricio",surname:"Barría",slug:"r.-mauricio-barria",fullName:"R. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"57654",title:"Numerical Simulation of Wave (Shock Profile) Propagation of the Kuramoto-Sivashinsky Equation Using an Adaptive Mesh Method",doi:"10.5772/intechopen.71875",slug:"numerical-simulation-of-wave-shock-profile-propagation-of-the-kuramoto-sivashinsky-equation-using-an",body:'\nThe Kuramoto-Sivashinsky equation (KSe) is a non-linear fourth order partial differential equation (PDE) discovered separately by Kuramoto and Sivashinsky in the study of non-linear stability of travelling waves. Sivashinsky [1] came up with the equation while modelling small thermal diffusive instabilities in laminar flame fronts. Kuramoto [2, 3, 4, 5] derived the equation in the study of the Belousov-Zhabotinsky reaction as a model of diffusion induced chaos. The KSe is of interest to many researchers because of its ability to describe several physical contexts such as long waves on thin films or on the interface between two viscous fluids [6] and unstable drift waves in plasmas. The equation is also used as a model to describe spatially uniform oscillating chemical reaction in a homogeneous medium and fluctuations in fluid films on inclines [7]. In one dimension, consider the KSe of the form
\nThe second derivative term is an energy source and thus has a distributing effect. The non-linear term is a correction to the phase speed and responsible for transferring energy. The fourth derivative term is the dominating term and is responsible for stabilising the equation. Several methods have been used to solve the KSe numerically and these include Chebyshev spectral collocation method [8], Quintic B-spline collocation method [9], Lattice Boltzmann method [10], meshless method of lines [11], Fourier spectral method [12] and septic B-spline collocation method [13].
\nGeneration of an adaptive mesh in the spatial domain is based on the r-refinement technique [14] which relocates a fixed number of nodal points to regions which need high spatial resolution in order to capture important characteristics in the solution. This has the benefit of improving computational effort in those regions of interest whilst using a fixed number of mesh points. The relocation of the fixed number of nodal points at any given time is achieved by solving Moving Mesh Partial Differential Equations (MMPDEs) [15, 16] derived from the Equidistribution Principle (EP). The EP [17] makes use of a measure of the solution error called a monitor function, denoted by M which is a positive definite and user defined function of the solution and/or its derivatives. Mesh points are then chosen by equally distributing the error in each subinterval. In this paper, MMPDE4 [15] is chosen to generate the adaptive mesh because of its ability to stabilise mesh trajectories and ability to give unique solutions for the mesh velocities with Dirichlet boundary conditions. MMPDE4 is given by
\nwhere \n
where
\nThe modified monitor function given by
\nis used. It is composed of the standard arc-length monitor and the curvature monitor functions. Smoothing on the monitor function is done as described in [15]. Values of the smoothed monitor function \n
where the parameter \n
The Crank-Nicolson scheme for the KSe is
\nwhere \n
for the linearization of the non-linear term \n
Consider the mesh on the domain \n
The variable spatial length of each interval is given by \n
such that \n
For \n
where \n
Where \n
for \n
which are given by
\nOne regards these points as the collocation points in each subinterval of the mesh (11). Scaling of the Gauss-Legendre points into subsequent intervals is done by defining the collocation points as
\nand redefining the local variable \n
for \n
where
\nand
\nFrom the boundary conditions (28) and (29), one gets
\nwhich results in a consistent system of \n
The PDE system is solved using the rezoning approach which works best with the decoupled solution procedure [20]. The rezoning approach allow varying criteria of convergence for the mesh and physical equation since in practice the mesh does not require the same level of accuracy to compute as compared to the physical solution. The algorithm for the rezoning approach is as follows:
Solve the given physical PDE on the current mesh.
Use the PDE solution obtained to calculate the monitor function.
Find the new mesh by solving a MMPDE.
Adjust the current PDE solution to suite the new mesh by interpolation.
Solve the physical PDE on the new mesh for the solution in the next time.
Discretization of the time domain \n
At each time \n
where \n
where the \n
Given the partition (23) and approximations \n
\n\n
for \n
Consider the KSe
\nin the domain \n
Where \n
With \n
Figures 1 and 2 show the behaviour of the numerical solution and the absolute error, respectively of the KSe equation on a stationary mesh using Hermite collocation method at \n
Hermite collocation method, uniform mesh, numerical solution behaviour of KSe at \n\nt\n=\n4\n\n with \n\nN\n=\n100\n\n and \n\nδt\n=\n0.001\n\n.
Hermite collocation method, uniform mesh, absolute error in numerical solution of KSe at \n\nt\n=\n4\n,\nN\n=\n100\n\n and \n\nδt\n=\n0.001\n\n.
Figure 3 shows the solution obtained by the collocation method on a stationary mesh for time \n
Hermite collocation method, stationary mesh, numerical solution behaviour of KSe problem with \n\nN\n=\n100\n,\nδt\n=\n0.001\n\n up to final time \n\nT\n=\n4\n.\n\n
Figures 4 and 5 show the numerical solution profile and the behaviour of the maximum absolute error, respectively at \n
Hermite collocation method, non-uniform mesh, numerical solution behaviour of KSe problem at \n\nt\n=\n4\n\n with \n\nN\n=\n100\n,\nδt\n=\n0.001\n,\nτ\n=\n2\n×\n\n10\n\n−\n2\n\n\n\n and \n\nα\n=\n8\n\n.
Hermite collocation method, non-uniform mesh, absolute error in numerical solution of KSe at \n\nt\n=\n100\n,\nδt\n=\n0.001\n,\nτ\n=\n2\n×\n\n10\n\n−\n2\n\n\n\n and \n\nα\n=\n8\n\n.
Figure 6 shows the numerical solution profiles produced by the adaptive collocation method for time \n
Hermite collocation method, adaptive mesh, numerical solution behaviour of KSe up to final time \n\nT\n=\n4\n\n for \n\nN\n=\n100\n,\nδt\n=\n0.001\n,\nτ\n=\n2\n×\n\n10\n\n−\n2\n\n\n\n and \n\nα\n=\n8\n\n.
Hermite collocation method, mesh trajectories of KSe equation up to final time \n\nT\n=\n4\n\n with \n\nN\n=\n100\n,\nδt\n=\n0.001\n,\nτ\n=\n2\n×\n\n10\n\n−\n2\n\n\n\n and \n\nα\n=\n8\n\n.
Time | \nHermite collocation | \nMethod in [19] | \n
---|---|---|
0.5 | \n\n\n | \n\n\n | \n
1 | \n\n\n | \n\n\n | \n
1.5 | \n\n\n | \n\n\n | \n
2 | \n\n\n | \n\n\n | \n
2.5 | \n\n\n | \n\n\n | \n
3 | \n\n\n | \n\n\n | \n
3.5 | \n\n\n | \n\n\n | \n
4 | \n\n\n | \n\n\n | \n
Comparison of maximum pointwise errors in the numerical solution of the KSe on an adaptive mesh at different times with \n
The KSe is solved using an adaptive mesh method with discretization in the spatial domain done using seventh order Hermite basis functions. Numerical results show that Hermite collocation method on a non-uniform adaptive mesh is able to improve the accuracy of the numerical solution of the KSe. The method is able to keep track of the region of rapid solution variation in the KSe, which is one of the desired properties of an adaptive mesh method.
\nIn the coming years, agricultural production will have to face a double challenge, meeting the growing needs of the world’s population while preserving the environment and natural resources. According to [1], the world’s current population of about 6.3 billion people will reach nearly 8.6 billion in 2030. Agricultural production will then have to be significantly higher. This will be achieved by increasing yields. This has been achieved mainly through varietal improvement and associated cultivation techniques, including nitrogen fertilization.
In Algeria, 20% of the agricultural potential is located in the north of the country, which is characterized by poorly fertile soils. These soils are low in nutrients and have a very low rate of organic matter. Fertilization has remained archaic in the country. According to [2], in Algeria, the use of fertilizers in agriculture is not under control, despite the efforts made by farmers in charge of the cereal intensification program and potato farmers.
According to [3], fertilizers are applied in the absence of technical standards, neglecting the initial soil content; consequently, inputs are often poorly fractioned, leading to waste, which is a source of soil and water pollution. As several researchers have shown in their work on Algerian soils. In this context, [4, 5] conducted trials in the same semi-arid climate, respectively, on durum wheat and barley seed production, obtained maximum yields with similar rates (150 kg N/ha). These yields reached the respective values of 33.82 and 33.25 q/ha, i.e. gains of 11.52 and 9.76 q/ha. [6] showed that the interaction of potassium (P) and nitrogen (N) fertilization significantly affects wheat grain yield in the Saharan zone. The maximum yield reached 6.780 Mt./ha with the N250 P180 dose. With regard to nitrogenous fertilization, the observation highlights the need to promote adapted and balanced fertilization. Since urea is the most widely used nitrogen fertilizer in the world [7], it is crucial to assess the nitrogen use efficiency (NUE) by crops, since it is always aimed at achieving higher yields with a minimum application of fertilizer. This indicator (NUE) has been widely studied by several researchers around the world on various crops, including cereals, e.g. rice [8], maize [9], durum wheat [10, 11]; leafy vegetables, e.g. lettuce [12, 13, 14], spinach [15], cabbage [16] and vegetable crops, e.g. Potato [17, 18]; beans [19], tomato [20, 21].
In this perspective, this study uses the isotope approach 15 N to evaluate the nitrogen use efficiency. This new method, used by [22], highlights 15 N isotopic nitrogen, which is the most commonly used stable isotope in agriculture-related studies. It is the direct way to measure nitrogen uptake by applied fertilizer, and the most reliable way to monitor the flow and fate of nitrogen in the soil–plant system [23, 24]. To highlight the monitoring of this system, the chosen plant material is lettuce (Lactuca sativa L.), due to its short growing cycle. But also, because of the socio-economic impact that is beginning to dominate, at the national level. It is a source of wealth and income for producers. The search for decision support tools is essential in order to master agricultural practices and to plan for a sustainable agriculture that respects the environment. In this respect, the AquaCrop model, designed by the FAO, has been chosen as a decision support tool. The objective of this study is essentially oriented toward the search for optimum doses of nitrogenous fertilizers with the aim of contributing to the production of technical references for the efficient use of fertilizers.
The study was conducted at the National Institute of Agronomic Research of Algiers (36°68′ N and 3°1′ E, at an altitude of 18 m), located south-west of Algiers in the eastern part of the Mitidja (Figure 1).
Location of the study area.
Climatic conditions in the study area are characterized by pronounced seasonal variations with mild, wet winters and hot, dry summers. The meteorological data used are from the automatic weather station installed in the field. The measurements taken at daily time steps are: minimum and maximum temperatures (°C), rainfall (mm), wind speed (m/s) at 2 m above ground level, solar radiation (W/m2) and relative humidity (%). The reference evapotranspiration (ET0) was calculated according to the FAO Penman-Monteith method [25]. A soil profile was carried out over a depth of one meter, comprising three horizons. Soil samples were taken from each horizon with an auger for analysis physico-chemical.
The crop taken into consideration is variety lettuce, stubborn from Nîmes, belonging to the lettuce to be applesauce class, which is eaten young, before it goes to seed. Lettuce seeds were sown in the honeycomb plates for 19–25 days in the nursery before being transplanted. The young lettuce plants were transplanted at the 3–4 leaf stage onto well plowed soil in the field.
The experiment was carried out in the open field using a complete randomized block experimental design with four levels of nitrogen, namely: T1 (0 N kg/ha), T2 (60 N kg/ha), T3 (120 N kg/ha) and T4 (180 N kg/ha) arranged in four blocks. Each block has four sub-plots. Each micro plot is 6 m long and 3 m wide, giving a total area of 18 m2, of which 4.5 m2 was used for the 15 N. The trial was repeated for two consecutive years (2014–2015) and (2015–2016). Isotopic nitrogen was used only in the first year because of its high cost. The amounts of nitrogen used were distributed along the crop development cycle, namely: 10% at 15 days after transplanting (DAT), 30% at 40 DAT, 40% at 60 DAT and 20% at 75 DAT. The growing season is from January to April for both companions, coinciding with the winter season, during which irrigation is not necessary.
The parameters measured in the field are essentially the above-ground biomass (B), which represents a parameter that best allows verification of fertilizer efficiency in lettuce where the growth of the above-ground part is a determining factor in agricultural value [26]. Every 10 days, samples of 6 plants/subplot are taken and brought back to the laboratory where they are dried in the open air for 24 h and then in an oven for 48 h at 70 C°. In addition to this, the evolution of the green canopy (CC) cover is monitored by reference to photos taken vertically at a height of 1.8 m above the crop, using a photometric device. The photos were analyzed using ARCgis 10.1 software using the supervised classification by maximum likelihood method (Figure 2). Harvesting was done when the apples were tightly packed and full for each subplot of 1 m × 1 m.
Analyses of the fraction of the green canopy for the growth stage.
To determine the isotopic composition of lettuce plants, lettuce heads receivingan15N were divided into two parts (roots and leaves). Fresh weight was assessed for all parts of the crop. The samples were dried at 70°C for 24 hours, weighed for dry weight determination, ground into a fine powder using a 0.3 mm sieve and homogenized for total nitrogen and excess N15. The isotopic analysis of the lettuce culture samples was carried out at the National Centre for Energy, Science and Nuclear Techniques (CNESTEN-Morocco).
The quantification of fertilizer nitrogen was measured on the basis of the isotope dilution method from fertilizer nitrogen and the rate of nitrogen fertilizer applied, according to the following equation defined by [22]:
AquaCrop requires five important components to be functional: climate, with its thermal regime, rainfall, evaporative demand (ETP) and carbon dioxide concentration; then crop characteristics, including development, growth and yield formation processes (Table 1); then soil, with its hydraulic characteristics (hydraulic conductivity at saturation, moisture at saturation, field capacity and permanent wilting point); and finally management practices, which are divided into two categories: plot management and irrigation practice management; and finally initial conditions.
Description | Units | 2015–16 | Source |
---|---|---|---|
Conservative crop parameters | |||
Base temperature | C° | 7 | Calibrated |
Upper temperature | C° | 30 | Calibrated |
Upper threshold for canopy expansion, Pexp,upper | — | 0.25 | Simulated |
Lower threshold for canopy expansion, Pexp,lower | — | 0.55 | Simulated |
Shape factor for the stress coefficient for canopy expansion | — | 3 | Calibrated |
Upper threshold for stomatal closure, Psto,upper | - | 0.50 | Calibrated |
Shape factor for the stress coefficient for stomatal closure | — | 3 | Calibrated |
Water productivity (WP) | g m−2 | 19 | Calibrated |
Reference harvest index (HIo) | % | 95 | Measured |
Crop coefficient when canopy is complete | — | 0.85 | Simulated |
Non conservative parameters | 2015–16 | ||
Number of plants per m2 | Plant m−2 | 15 | Measured |
CC0 | % | 2.25 | Simulated |
Maximum canopy cover CCx | % | 81 | Measured |
Canopy size of the transplanted seedling | cm2 plant−1 | 15 | Measured |
Time from transplantation to emergence | Days | 7 | Observed |
Time from transplantation to senescence | Days | 80 | Observed |
Time from transplantation to maximum (CCx) | Days | 50 | Observed |
Time from transplantation to maturity | Days | 95 | Observed |
Minimum effective rooting depth | m | 0.20 | Measured |
Maximum effective rooting depth | m | 0.40 | Measured |
Transplantation time at maximum depth of rooting | Days | 55 | Observed |
Date of transplantation | 11/01/16 | ||
Harvest date | 14/04/2016 | ||
Canopy growth coefficient (CGC) | % days−1 | 14.30 | Simulated |
Canopy decline coefficient (CDC) | % days−1 | 8.0 | Simulated |
Input culture parameters to calibrate the AquaCrop model.
Calibration of the model to fertility stress requires coverage of the green canopy (CC) and biomass production (B), recorded on the fertility stressed plot ‘stressed plot’ and the unstressed plot ‘reference plot’ (Table 2). The soil fertility stress in the AquaCrop model is given as follows:
Treatments | Brel (%) | CCx under fertility level (%) | Canopy Decline (-) |
---|---|---|---|
T1 | 51 | 51 | Strong |
T2 | 73 | 55 | Medium |
T3 | 100 | 61 | Little |
T4 | 100 | 58 | Little |
Input data to calibrate the AquaCrop model for soil fertility stress.
Where: Brel is the ratio of total dry above-ground biomass at the end of the growing season in the reference plot (Bref) to that under stress (Bstress). Soil fertility affects water productivity (WP), canopy growth coefficient (CGC), maximum cover (CCx) and canopy senescence.
The evolution of canopy cover, dry above-ground biomass and yield were taken into account in the evaluation of the AquaCrop model, while using the following statistical indicators: the coefficient of determination (R2) of the linear fit, the square root of the normalized root mean square error (nRMSE) and the Willmott’s agreement index (d).
Variations in rainfall and ETP are shown in Figure 3, which illustrates the rainfall distribution during the two years of experience 2014–2015 and 2015–2016.The cumulative rainfall received between September and August is, respectively, of the order of 552 and 551 mm. Those corresponding to the experimental seasons (January to April), they are close to the averages of 211.4 and 303.4 mm. The corresponding potential annual evapotranspiration is of the order of 744.3 and 782.6 mm. Those corresponding to the growing seasons are, respectively, 195.4 and 196.5 mm.
Precipitation, potential evapotranspiration (ETP) on a monthly scale for test years 2014–2015 and 2015–2016.
The study site is characterized by deep and heavy soils with high clay content. Soil analysis revealed the existence of 3 horizons with a silty-clay texture with high clay rates increasing with soil depth. At profiles of 0–25 cm, 25–55 cm and beyond 55 cm depth, these rates are 43, 49, and 52%, respectively. The pH of the station soils is generally slightly basic at 7.8, CEC varies between 17.9 and 15 meq/100 g and total limestone has a rate between 7.9 and 7.8%. The organic matter rate is 1.57% on the surface and 0.49% at depth.
Figure 4 shows the evolution of the nitrogen doses applied at different phenological stages of the plant. This evolution is supported by the analysis of variance, which showed a very highly significant effect (p < 0.001), of the dry biomass, in relation to the increase in the doses of nitrogen supplied. A maximum of dry biomass is reached at the dose of 120 kg N/ha. Above this level, the increase in nitrogen rate is not significant. This result is consistent with that of [27], which showed that fertilization at high doses leads to a decrease in above-ground biomass. This is the case in the first year (2014–2015).
Effect of different levels of fertilization on the evolution of dry above-ground biomass for the two growing seasons.
Figure 5 shows lettuce yields as a function of applied nitrogen rates. In fact, the graph shows that, during the two experimental campaigns, the highest lettuce yields (55.24 and 57.96 t/ha) were obtained by applying the 120 and 180 kg/ha rates. These doses are very highly significant (p < 0.001) compared to those obtained (30.19 and 45.49 t/ha) by applying the minimum doses of less than 60 kg/ha. This result is consistent with those of [28, 29, 30], who reported that increasing the N level from 0 to 120 kg N/ha had a positive effect on lettuce production. Nevertheless, in detail, the T4 treatment from the 2014–2015 trial shows a relatively lower yield of 50.25 t/ha compared to the T3 treatment (54.25 t/ha) from the same year. The difference, evaluated at 3.08 t/ha, can be explained by the toxicity of the plants or by the nonattraction of nitrogen by the plants resulting from the consumption of excess nitrogen fertilizer, as pointed out by [31]. The response of lettuce for yields is considerably higher in 2016 than in 2015. This result is related to the higher rainfall amounts.
Effect of different levels of fertilization on yield for the two growing seasons.
Nitrogen Use Efficiency (NUE) is an important indicator in the application of nitrogen fertilizers. Achieving a higher NUE always becomes a priority in agriculture [8]. In this context, Figure 6 illustrates the variation in the percentage of NUE as a function of defined thresholds. For rates ranging from 60, 120 to 180 kg N/ha, the NUE varies from 65.42, 74.49 to 68.38%, respectively. The NUE decreased from 74.49% to 68.38% by increasing the rate from 120 to 180 kg N/ha. These results are similar to those reported by [32, 33]. The 120 kg N/ha rate provides the best efficiencies. This means that 74.48% of the fertilizer applied is consumed by the lettuce crop. The remaining 25.52% of N is either in the soil or lost through leaching. Lettuce is a short-cycle crop, making the best use of available nitrogen, as reported by [34].
Variation in nitrogen use efficiency by lettuce, expressed as a percentage (%).
Figure 7 shows the variation in water productivity (WP), soil evaporation (Es) and transpiration (Tr) of the lettuce crop under different levels of fertilization. This variation is supported by the analysis of variance, which showed a very highly significant effect (p < 0.001) of these parameters (WP, Es and Tr), in relation to the increase in the doses of nitrogen applied. The maximum values of WP and Tr are reached at the dose of 120 kg N/ha, for the two companions 2014–2015 (WP = 8.95 kg/m3; Tr =51.4 mm) and 2015–2016 (9.57 kg/m3; Tr = 55.80 mm). Above this level, the increase in the nitrogen rate is not significant.
Variation in water productivity of lettuce under different levels of fertilization.
Experimental results of yield, canopy cover and dry above-ground biomass under different levels of fertilization are presented in Table 3. The AquaCrop model (V. 6.1) was calibrated using the crop data set obtained from the T3 treatment (120 kg N/ha). The lowest dry yield and dry aboveground biomass observed were 4.021 t/ha and 4.125 t/ha under the T1 treatment (0 kg N/ha), and the highest were 8.854 t/ha and 9.320 t/ha under the T3 treatment (120 kg N/ha), respectively.
Treatments | Biomass (t/ha) | Dry yield (t/ha) | CCx (%) | |||||
---|---|---|---|---|---|---|---|---|
Obs | Sim | Obs | Sim | SD (±%) | Obs | Sim | SD (±%) | |
T1 | 4.125 | 4.785 | 4.021 | 4.546 | (6.70) | 51 | 44.80 | (1.68) |
T2 | 5.872 | 6.806 | 5.234 | 5.785 | (11.68) | 55 | 54.10 | (5.76 |
T3 | 7.969 | 9.320 | 7.834 | 8.854 | (8.27) | 61 | 63.90 | (2.67) |
T4 | 7.788 | 9.100 | 7.626 | 8.645 | (8.40) | 58 | 63.70 | (3.55) |
Biomass calibration results, yield, and maximum canopy cover under different levels of fertilization in 2015–2016.
The AquaCrop model is capable of simulating these parameters. Overall, the agreement between simulated and observed vegetation cover and biomass is satisfactory with 0.64 < R2 < 0.81, 18 < nRMSE > 46.3 and 0.78 < d < 0.94; 0.92 < R2 < 0.94, 21.6 < nRMSE <34.5, 0.91 < d < 0.96 (Table 4).
Indicators | CC (%) | Dry biomass (t/ha) | ||||||
---|---|---|---|---|---|---|---|---|
T1 | T2 | T3 | T4 | T1 | T2 | T3 | T4 | |
R2 | 0.81 | 0.71 | 0.66 | 0.64 | 0.92 | 0.98 | 0.94 | 0.94 |
NRMSE | 18 | 35.5 | 41.4 | 46.3 | 34.5 | 21.6 | 25.6 | 25 |
EF | 0.79 | 0.03 | −0.13 | −0.06 | 0.55 | 0.85 | 0.82 | 0.82 |
d | 0.94 | 0.81 | 0.78 | 0.80 | 0.91 | 0.96 | 0.96 | 0.96 |
Indicators of goodness of fit in estimating canopy cover and dry biomass.
Figure 8 shows the comparison between simulated and observed canopy cover (CC) and dry above-ground biomass (B) for the calibration period (2015–2016). This figure shows that there is a close correspondence between observed and simulated CC and B. It is also important to note that the AquaCrop model correctly simulates CC from seeding to the maximum growth phase at which CCx is reached. This observation has been reported in several studies [35, 36, 37]. From Figure 8, it is clear that both parameters (CC) and B were overestimated by the AquaCrop model. In a recent study [38], it was shown that the AquaCrop model overestimated the cabbage canopy under different irrigation regimes. [39] also noted a slight (10%) but systematic overestimation of the amount of rice biomass conducted under different levels of irrigation and fertilization.
Canopy coverage (a) and dry biomass (b) simulated and measured for the calibration period (2015–2016) under different fertilization levels (T1, T2, T3, and T4).
Observed and simulated lettuce yields are shown in Figure 9. The observed yields for treatments T1, T2, T3 and T4 are, respectively, 4.214; 5.187; 6.942 and 6.214 t/ha, while the simulated yields are 4.897; 5.981; 7.414 and 6.987 for the trial period (2014–2015), with a correlation coefficient R2 = 0.92. On the other hand, the yields observed and simulated under the four treatments for the trial period (2015–2016) are of the order of 4.021; 5.234; 7834 and 7.626 t/ha, while those simulated are of the order of 4.546; 5.785; 8.854 and 8.645, with a correlation coefficient R2 = 0.99. Analysis of statistical tests and linear regression indicated that the values simulated by the AquaCrop model are in good agreement with those observed. [40] reported R2 values >0.80 when simulating above-ground biomass and barley grain yield using AquaCrop.
Simulated and observed lettuce yields under different levels of fertilization.
The management of nitrogen fertilization is a major issue for agricultural production while contributing to water and soil pollution. In this situation, the adoption of fertilization management strategies aimed at using efficient doses and increasing the effectiveness of their use becomes necessary. Crop models simulating yield under such conditions could be important tools for fertilizer management planning. To this end, the parameterization of the AquaCrop model to estimate the effect of fertility constraints on lettuce yield under different levels of fertilization was investigated. The model tended to overestimate canopy coverage for T3 (120 kg N/ha) and T4 (180 kg N/ha) treatments, but with reasonable statistical indices (nRMSE: 14.80 for T3 and 12.50 for T4). AquaCrop has confirmed that it is a very useful tool that can be used to optimize the N rates applied to the crops, to play on the management of the plot in order to maximize yields.
IntechOpen publishes different types of publications
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