However, because Richards is a nonlinear second order partial differential equation, the analytical solutions are obtained mainly from simplifications of the hydraulic properties of the soil. Therefore, the objective of the present study was to develop a numerical model capable of simulating the water distribution and the shape of the wetted soil from the irrigation by a point source in the soil surface dripper , using the hydraulic properties of the soil and the soil irrigation system as input variables. The computational program was structured to allow the user to enter information such as: a soil profile data, with regard to their physical-hydric properties, b information about the irrigation system, c boundary conditions, d simulation time and e water application time through irrigation.
The model presents some simplifications in the solution of Richards' equation, such as, not considering the environment as isotropic and isothermal, the flow in macropores and the flow of steam in the soil. These simplifications were performed with the intention of leaving the model with a smaller number of input parameters.
The Richards' equation which describes the movement of water in an isothermal porous medium, two-dimensional, with the positive vertical coordinate downwards, and under unsaturated conditions, can be described by [ eq. In this expression, partial derivatives of h appear with respect to space and time, which can be replaced by finite differences.
The coefficients are function of the dependent variable h, having their values estimated for the different situations of time and space. The finite differences approximation implies that the calculation domain and the time are discretized. Among several possible forms of resolution by finite differences, an implicit scheme was chosen. In the present model, we used the modification in the solution of [ eq. Substituting [ eq. For the convergence analysis of the iterative solution of the [ eq. The value of the function K h is explicitly linearized in [ eq.
In this model the arithmetic mean was used. The model used to describe the water retention curve in the soil was the van Genuchten model. For the calculation of the hydraulic conductivity, the model developed by Mualem was used further details of the van Genuchten and Mualem equation can be checked in Li et al.
Contrary to the great majority of the models of water movement simulation in two dimensions, we opted for a more realistic way, by the hypothesis of a non-uniform initial water profile. For the first irrigation, it was assumed that the initial matric potential h o depended only on the depth, while at the beginning of the subsequent irrigations, a variation along the horizontal axis was also considered. In this way, a Cartesian coordinate system was considered in which flow directions X and Z were established. The following boundary conditions were adopted:.
Because it is a Boundary of the domain where its neighboring cells in the negative direction of the X axis belong to one of the quadrants of the total soil volume, given the symmetry, we are faced with a situation equivalent to a null flow or Neumann condition , which is:. Once the hypothesis of insulation of the bulbs or wetting front has been established, and as this boundary is defined so that the wetting front does not reach the boundary, there is also a null flow condition Neumann condition.
The lower boundary was displaced in such a way that the influence of the irrigation water in this zone was null Dirichlet condition. For validation of the model, the data obtained by Rivera were used in an experiment conducted in the Department of Biosystems Engineering of the Luiz de Queiroz College of Agriculture. Table 1 shows the physical-water characteristics of the soil and Table 2 shows the parameters of the retention curve. This dispenser was located in the center of the polyethylene carton containing the soil and was coupled to a liter capacity Mariotte flask by means of capillary tube, keeping the hydraulic charge constant in the flask.
The application time was two hours, and a solution volume of 6 liters was therefore applied. Soil moisture, after the test, was determined using the gravimetric method. The sampling points were located along a mesh, taking as the central axis the point where the emitter was located; from that point it was shown every 10 cm in the horizontal direction and 10 cm in the vertical along two rays, so that every schematized ring was sampled twice.
The total sampled rays were six two replicates for each time , arranged to form on the surface of the soil angles of 60 degrees, that is, the bulb was divided into six slices of equal sizes. In both radial and vertical directions, 5 samples were taken, totaling 25 samples per radius. The sampling times were: before irrigation; 24; 48; and 72 hours after the end of irrigation. These indices are defined by eqs. Therefore, for the points located farthest from the emitter, the soil moisture values would still be close to the initial simulation condition.
It can be observed that soil moisture, both observed as simulated, ranged about 0. According to Figure 3 , it can be seen that the soil moisture values obtained by Rivera varied in the range of 0. This same behavior was simulated with great precision by the proposed model. From the observation of the isolines shown in Figure 3 , in general, the water distribution in the simulated soil showed good agreement when compared to that observed in both depth and width of the wet zone. These indices can be checked by Table 3 ; the value of the id was 0.
This index, therefore, presents a superiority in relation to the Willmott index in terms of interpretation. The simulation of water redistribution in the soil after 24 hours from the beginning by the finite difference method showed RMSE values equal to 0. From Figure 4 , it is possible to observe a comparison between the soil water content vertically, at different distance positions from the emitter, for the redistribution time of 48 hours after irrigation.
A significant agreement can be noted between the values simulated by the proposed model and the observed values.
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The largest differences between the observed and simulated values were for the distance of 35 cm Figure 4C and for the distance of 55 cm Figure 4D. It can be observed from Figure 4C that the model underestimated the values at the lowest depths and overestimated them to greater depths.
In other words, the model was not able to predict lower percolation at the most superficial depths and most percolation in the deeper layers of the soil. For the distance of 55 cm the model estimated a greater percolation than it was observed by the data. The comparison of the water distribution in the soil obtained by the experimental Rivera, and simulated values, evidenced a similar water distribution pattern Figure 5.
It was observed that the dimensions of the bulb remained statistically constant when compared with the time of 24 hours of redistribution. According to Lewis and Nyakatawa et al.
Modelling Impact of Adjusted Agricultural Practices on Nitrogen Leaching to Groundwater
This reduces soil fertility, thereby resulting in land degradation and environmental problems Sutherst and Bourne, The average predicted soil erosion rate in South Africa based on the general pattern of relative differences is Similarly, Australia has an average soil erosion rate of 4. The USA has an average soil erosion rate of However, the concept of an average erosion rate on a continental scale is illogical because of temporal and spatial variability in erosion rates Boardman, Unsustainable soil loss from a field results in a reduction in the capacity of the field to sustain crop yield Russell, b.
Research on soil erosion only started in in the USA, which has continued to lead the world in this field Matthee and Van Schalkwyk, According to Haylett , research to determine the effects of soil cover on runoff and erosion was started in in South Africa. Many studies have since then tried to estimate the historical and current soil and subsequent soil water-holding capacity losses in the country due to soil erosion Matthee and Van Schalkwyk, For example, Platford conducted research focusing on soil and water losses from sugarcane fields in South Africa to produce recommendations for protective practices.
Various studies in the area of soil and water losses in South Africa are also documented in literature e. Schulze and Arnold, ; McPhee et al. According to Platford , sugarcane in South Africa is regularly grown in adverse climatic and topographic conditions and on a range of soils. Soils in sugarcane growing areas are predominantly granular, leached and are characterised by high rates of erosion after the removal of the natural vegetation.
Protection of cropped land in areas experiencing high rainfall has traditionally been provided by water-carrying terrace banks built across the hillside at gentle slopes, but sugarcane is not always grown on the relatively gentle slopes for which this control system was designed Platford, Therefore, strip planting, rotational crops, reduced tillage and other management practices which provide sufficient protection should be used in place of, or in addition to, terrace banks. SASA developed guidelines and norms for the design of land-use plans in the sugar industry, which includes soil conservation structures e.
The nomograph included for the design of soil and water conservation structures as shown in Fig. The USLE is a model widely used in the estimation of soil erosion and supporting soil conservation measures Song et al. The sugar industry design nomograph does not Smithers, :. It is not clear as to why an unsustainable soil loss was used by Platford , but it is suspected that it was considered more economic to implement wider spaced structures which result from design rules with the higher acceptable loss.
The main aim of this article is to review the design norms for soil and water conservation structures in the South African sugar industry, compare and contrast the norms with national norms and international practices and to identify research gaps required to update the current design norms. Sugarcane production systems in South Africa involve activities ranging from land preparation to the transportation of the harvested crop to the mill SASRI, A typical production cycle lasts for about 10 years which is the time frame that allows a farmer to maintain the economic viability of sugarcane Platford, ; SASA, ; SASRI, The agronomic practices which constitute production systems in the sugar industry include land preparation, planting, weed, pest and disease control, and harvesting of sugarcane SASA, According to Meyer , the goal of land preparation is to produce a tilth which results in good bud germination and subsequent root development of the new crop.
Land preparation includes conventional tillage and minimum tillage practices.
On the other hand, conventional tillage is acceptable on slopes with smaller gradients as long as ploughing is conducted across the slope and not up and down the slope SASA, Planting of sugarcane can be done either by hand manually or mechanically Meyer, SASEX advocated for sugarcane strip planting and harvesting across all steep slopes other than short run slopes which are in, and adjacent to, valley bottoms. However, where strip planting is not practiced, dimensions and location of conservation structures have been adjusted in conformity with the SASA nomograph.
According to SASA and SASRI , the strip widths at right angles to the contour should not exceed thrice the maximum distance between contour banks as long as the alternate strips have a difference in age which is not less than 6 months. Weed, pest and disease control. Weed control is achieved either by mechanical means or via spraying of chemicals while pest and disease control is achieved through manual and mechanical application of chemicals. Both conventional tillage and conservation tillage practices are vital in the control of weeds but it is conservation tillage which ensures soil and water conservation through maintaining as much crop residue as possible on the soil surface Russell, a.
The crop residues reduce the impact of raindrop splash on the soil surface, reduce the velocity of surface runoff and protect the soils from erosion. Crop rotation is a practice which is required for the control of pests and diseases Sustainet, According to SASRI , land should be used in accordance with a crop rotation system so as to promote addition of organic matter to soils, soil fertility, reduction of pests and diseases, and erosion control.
Crop rotation is achieved through growing secondary crops that enhance soil health.
Modeling Methods and Practices in Soil and Water Engineering
Generally, after 5 to 6 harvests, sugarcane yield might have been decreased significantly thus calling for rejuvenation of the field Zuurbier and Van de Vooren, Rejuvenation of a sugarcane field is usually performed by planting an annual leguminous food crop. The legumes improve soil quality, prevent soil erosion and contribute to food production Zuurbier and Van de Vooren, Harvesting of sugarcane should be planned so as to minimise negative environmental impacts, and equipment having the least impact on the environment should be used SASA, The burning of sugarcane prior to harvesting is a widespread practice in South Africa and the main reason is to eliminate excess residue so as to improve harvesting, handling and milling of the cane SASRI, According to SASRI , accidental and runaway fires are common occurrences and often spread over entire hillsides, thereby exposing the land to potential erosion.
Serious erosion can be experienced if heavy rains follow soon after burning, thus making it necessary to leave the tops and residues scattered over the soil surface so as to protect the soil and reduce the velocity of runoff SASRI, In addition, codes of practice on burning which provide acceptable ways of complying with legislation and minimising negative impacts on the environment while aiding crop production are in place SASRI, Soil and water conservation and yield improvement are some of the benefits associated with green cane harvesting, among others SASRI, SASA and SASRI advocate for mulching wherever possible for maximum conservation of soil and water, particularly on steep slopes and erodible soils.
In summary, the agronomic practices in the sugarcane production systems discussed above play a role in soil and water conservation and they should be considered when updating design norms for soil and water conservation structures in the sugar industry. Design norms are guidelines applied in the design of structures. The commonly used structures in soil and water conservation are waterways and contour banks and their designs entail both hydrologic and hydraulic designs.
Hydrologic design entails estimation of design floods which is important in the sizing of hydraulic structures and thus to quantify and limit the risk of failure of the structures Reinders et al. The risk of failure is related to the return period and it is quantified as a probability of exceedance, as shown in Eq. ASABE recommended a yr return period, h storm for the design of contour banks but stresses the need for the selection of larger design storms appropriate to the level of risk of failure.
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A yr return period is also recommended for the design of soil conservation structures in Australia and in situations where failure would threaten public safety or lead to severe damage, larger return periods are recommended Carey et al. Matthee and Van Schalkwyk recommended that soil conservation structures should be designed so as to cope with year return period floods while SASA specifies a yr return period for the design of soil and water conservation structures in the South African sugar industry.
According to Russell , the Soil Conservation Service SCS method SCS, of runoff estimation should be used for the design of structures on cultivated land while the Rational Method Kuichling, is to be used for storage dam and gulley stabilization design in natural catchments. The SCS method Eq. Schmidt et al. The peak discharge estimated using the SCS-SA approach depends on storm flow depth, catchment area, catchment lag time, and the effective storm duration shown in Eq. The Rational Method is extensively used worldwide for both small rural and urban catchments Alexander, Parak and Pegram reported that the Rational Method is the most widely used method for estimating design peak discharges from rainfall events and is easy to understand and simple to use.
The method, which only computes flood peaks, is sensitive to the input design rainfall intensity and the runoff coefficient, whose selection is based on the experience of the user Smithers, The algorithm for the Rational Method is shown in Eq.
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The hydraulic design of soil and water conservation structures entails selecting the placement, size, shape and slope of physical protection works, namely contour banks and waterways. According to SASA , contour banks are defined as structures designed hydraulically and placed in the field to protect the land situated immediately below. Design of contour banks involves the selection of vertical and horizontal spacing between contour banks, and the sizing of the contour to safely convey the design discharge Reinders et al.
Two methods, namely, vertical interval method and sustainable soil loss method, are employed in the determination of contour bank spacing ASABE, The vertical interval method is an empirical method developed by the SCS in the s and is not soil, cropping system, or rainfall specific ASABE, The existing land slope is the slope used in the equation and thus the method does not account for the effect of terrace shape on the constructed land slope.
Frequently the maximum terrace spacing computed by use of the vertical interval method is more conservative than that obtained using the sustainable soil loss method ASABE, The vertical interval equation is shown in Eq.