Revisiting the Solid Flux Theory

Several variations of the basic activated sludge process and of the related design procedures for final clarifiers have been developed, which are frequently based on the well-known solid flux theory (SFT). In this paper, by using the Lambert W function and a “virtual” solid flux corresponding to the Vesilind parameters’ ratio, the SFT is reformulated, and dimensionless groups are detected, which highly reduce the number of parameters that are involved in the final clarifiers’ design procedure. The derived dimensionless relationships and the corresponding plots have general validity since they can be applied to all the possible design/verification parameter combinations. Moreover, it is shown that for any input dataset, the suitable domains of the SS concentration and of the solid flux can be simply expressed by the two branches of the Lambert W function. By using data retrieved from the literature, several numerical applications and validations of the dimensionless relationships are performed. Finally, it is shown that by introducing in the SFT a new reduction hydrodynamic factor, rhoR, to be applied to the modified return flow formula rather than to the limiting solid flux as in the past, a significant improvement in the comparison between the results by theory and by experiments can be obtained

Simplified Interception/Evaporation Model

It is known that at the event scale, evaporation losses of rainfall intercepted by canopy are a few millimeters, which is often not much in comparison to other stocks in the water balance. Nevertheless, at yearly scale, the number of times that the canopy is filled by rainfall and then depleted can be so large that the interception flux may become an important fraction of rainfall. Many accurate interception models and models that describe evaporation by wet canopy have been proposed. However, they often require parameters that are difficult to obtain, especially for large-scale applications. In this paper, a simplified interception/evaporation model is proposed, which considers a modified Merrian model to compute interception during wet spells, and a simple power-law equation to model evaporation by wet canopy during dry spells. Thus, the model can be applied for continuous simulation, according to the sub hourly rainfall data that is appropriate to study both processes. It is shown that the Merrian model can be derived according to a simple linear storage model, also accounting for the antecedent intercepted stored volume, which is useful to consider for the suggested simplified approach. For faba bean cover crop, an application of the suggested procedure, providing reasonable results, is performed and discussed

Applying the Hardy Cross method to assess the energy-saving associated with closed circuits in drip irrigation systems compared to open circuits

The analysis of a looped water distribution system, usually employed in subsurface drip irrigation (SDI), under pressure and steady-state conditions, can be successfully performed if the topology of the network, the structure pipes, and the discharges at the nodes are known (Wang et al., 2021). Solving these complex networks usually requires an iterative approach. The Hardy Cross method (HCM), which was originally developed in 1936 (Cross, 1936) for manual calculations in civil engineering, can also be applied in lopped drip irrigation systems. This approach relies on the successive addition of flow-rate adjustments in each pipe to achieve the energy balance in each network segment, although limited by the Darcy-Weisbach resistance equation where the discharge exponent is set to 2. In this work, a reformulated HCM was applied to looped drip irrigation systems, considering both local losses due to emitters’ insertion and the Hazen-Williams resistance equation (discharge exponent = 1.852), which is better suited to describe friction losses in the commonly used polyethylene pipes. The hydraulic performance of closed circuits calculated by HCM was analysed and compared with that of open circuits designed by IRRILAB software application (Baiamonte, 2018). In particular, the final objective is to assess the energy-saving provided by the closed circuits (cc) in drip irrigation systems with respect to open circuits (oc). The energy-saving amount is expressed as the ratio (hratio < 1), between the inlet pressure head, hin, of the closed circuit and that of the open circuit. A predictive relationship of hratio was calibrated for 3000 simulations carried out for rectangular irrigation units characterized by different geometry, pipe diameters, emitters’ spacing and flow rate, providing relative errors RE < 0.25%. The results show that hratio depends on the pressure head tolerance of the manifold, δM, associated with the open circuits, which IRRILAB requires as an input parameter. This is very reasonable since, for high δM, the discharge circulating in the manifold is also high and closing the circuits provides low hratio (hin cc << hin oc). The vice versa occurs for low δM. Contrarily, the number of drip laterals, Nrows, has only a marginal effect on hratio. Of course, the energy-saving benefit should also consider the higher investment costs of cc than oc. However, this issue is beyond the scope of this study

A model of dunnian flow at hillslope scale

The development of a thin stream above the soil surface (overland flow) is associated to two mechanism of runoff generation on the hillslope: the infiltration excess (hortonian flow) and saturation excess (dunnian flow) mechanism. The first one is typical of arid and semi-arid regions, usually characterised by high rainfall intensities on soil exhibiting low permeability. The second one, firstly introduced by Hewlett and Hibbert, constitutes the main mechanism of runoff generation in humid regions, characterised by high groundwater table. In the last mechanism runoff is produced by contributing areas of restricted extent that expands with time, where near to the bottom of the hillslope a high value initial soil water content occurs and gradually decreases versus upstream of the hillslope. Following this sketch, under the hypothesis of constant depth of the permeable layer, for stationary rainfall of indefinite duration, this work aims to investigate on the implications of temporal variability of active hillslope length on the hydrologic response for the dunnian mechanism of runoff generation. The flow in the unsaturated zone is modelled by the piston displacement model of Beven (1982a, 1982b). Once the wetting front reaches the impermeable layer (with different times along the hillslope), the transportation process, over and under the hillslope, is represented as the envelope of the infinite sequence of hydrographs, corresponding to the progressive lengths activated by the infiltration process and Ta - shifted from the beginning of the rainfall, where Ta is the starting up time associated to the active length. The overland hydrographs are modelled with the analytical solution of Agnese et al. (2001) over a plan hillslope, recently introduced. The subsurface stormflow hydrographs is modelled by using the classical linear storage model

Impact of solar panels on runoff generation process

Because of the benefits of solar energy, solar photovoltaic (PV) technology is being deployed at an unprecedented rate and the number of photovoltaic panels is sharply increasing. Agrophotovoltaic systems (solar farms) seem to be the most sustainable tools to create renewable energy without compromising agricultural production. However, utility-scale solar energy development is land intensive and its large-scale installation can have negative impacts on the environment. Moreover, its impacts on soil and on relative hydrological processes have been poorly studied. This article aims to evaluate the impact of solar panels on the runoff generation process, which is directly linked to the soil erosion process. Using a rainfall simulator, runoff measurements for a rainfall intensity equal to 56 mm/h were carried out by assuming different panel arrangements with respect to the maximum slope direction of the field (cross slope and aligned slope). Results were compared to a control reference of the same plot, with no panels (bare soil). Physical models found in the literature were then applied and calibrated, to upscale the models to a much higher hillslope length. Results showed that solar panels increase the peak discharge by about 11 times compared to the reference hillslope. A moderate effect of PV panel arrangement was observed on the peak discharges (11.7 and 11.5 times higher, for cross slope and aligned slope panels, respectively), whereas the time to runoff was the lowest for aligned slope panels (0.3 h), higher for cross slope panels (0.62 h), and the highest (1.2 h), for the bare soil hillslope. As it would be expected, upscaling the models to longer hillslopes resulted in increases in outlet discharges, and in the time to runoff, with an exception for aligned slope panels

Comparing Hydrus-2D/3D and Philip (1984)’s model to assess wetting bulb expansion from buried and surface point sources

In surface and subsurface drip irrigation systems, predicting the size expansion of the wetting bulb and the irrigation time are mandatory for water saving, and help drive their design and scheduling. At this aim, different hydrological models have been suggested to predict the wetting bulb expansion from buried and surface point sources. In this work, we compare the results obtained by the application of Hydrus-2D/3D and Philip (1984) model. The Philip (1984) model accounts for the Gardner conductivity function, which is not implemented in Hydrus 2D/3D. Moreover, in the Philip (1984) model, a certain approximation in the choice of the water contents to be used for calculating the average volumetric water content behind the wetting front, θav, is necessary, also considering that definitions do not seem univocal. For example, the water content at the wetting front was assumed as the θav, value when soil hydraulic conductivity, K, was equal to 1 mm/day by Cook et al. (2003) and 1 mm/h by Thorburn et al. (2003). For the purpose of the comparison, an extended analysis aiming at detecting the parameter ranges of the van Genuchten-Mualem model (van Genuchten 1980), which provide hydraulic conductivity functions matching those of Gardner, was preliminary conducted. Then, for van Genuchten-Mualem parameters falling in such parameters’ ranges, the average volumetric water content that is required in the Philip (1984) model was calculated in Hydrus-2D/3D. For sandy-loam soil, results showed a quite good agreement between the simplified Philip (1984) model and the more accurate but numerically demanding Hydrus 2D/3D, suggesting that Philip (1984)’s model can be successfully applied to predict the wetting bulb expansion from buried and surface point sources, provided the average volumetric water content in the soil behind the wetting front and the saturated hydraulic conductivity are appropriately considered

Verification of IRRILAB Software Application for the Hydraulic Design of a Micro-Irrigation System by Using IRRIPRO for an Apple Farm in Sicily

In recent years, many studies have been performed to develop simple and accurate methods to design micro\u2010irrigation systems. However, most of these studies are based on numerical solutions that require a high number of iterations and attempts, without ensuring to maximize water use efficiency and energy\u2010saving. Recently, the IRRILAB software, which is based on an analytical approach to optimally design rectangular micro\u2010irrigation units, has been developed, providing the solution corresponding to the maximum energy\u2010saving condition, for any slope of the laterals and of the manifold. One IRRILAB limitation is that, according to its theoretical basis, the rectangular planform geometry and uniform slope of the laterals and of the manifold are required. On the contrary, IRRIPRO software, which is based on the traditional numerical solution, does not have the aforementioned limitations, but requires an important number of attempts, especially when common emitters are used. In this study, the results of a joint use of IRRILAB and IRRIPRO software applications are illustrated, towards the aim to verify the IRRILAB performance in a large number of micro\u2010irrigation sectors belonging to a Sicilian apple farm, which is characterized by a high irregular topography, thus it is suitable for the purpose of this study. First, only five irrigation sectors, for the actual subdivisions of the farm, were considered, showing limited reasonable IRRILAB results. Dividing the farm into a higher number of sectors so as to provide a better uniformity in planform geometry and slope revealed that IRRILAB results improved in terms of emission uniformity and energy consumption, as verified by IRRIPRO applications. The energy-saving provided by IRRILAB (in one step) with respect to that by IRRIPRO (by attempts) resulted higher for common emitters (CEs) ( 1215% for five sectors and 129% for nine sectors) than for pressure compensating emitters (PCEs) ( 127% for five sectors and 126% for nine sectors). In absolute terms, the energy is greater for five\u2010sector subdivision than for nine\u2010sector subdivision. For both software, the use of PCEs always required less energy than CEs, because of the higher range of pressure compensating of PCEs than CEs. However, PCEs are characterized by less durability and by a higher manufacturing variation coefficient, thus they should not be the first choice. In conclusion, IRRILAB software could be recommended because it is easy to use, making it possible to save energy, especially when sectors are almost rectangular and uniform in slopes

Improvement of FAO-56 Model to Estimate Transpiration Fluxes of Drought Tolerant Crops under Soil Water Deficit: Application for Olive Groves

[EN] Agro-hydrological models are considered an economic and simple tool for quantifying crop water requirements. In the last two decades, agro-hydrological physically based models have been developed to simulate mass and energy exchange processes in the soil-plant-atmosphere system. Although very reliable, because of the high number of required variables, simplified models have been proposed to quantify crop water consumes. The main aim of this paper is to propose an amendment of the Food and Agricultural Organization (FAO) of the United Nations FAO-56 spreadsheet program to introduce a more realistic shape of the stress function, valid for mature olive orchards (Olea europaea L.). The modified model is successively validated by means of the comparison between measured and simulated soil water contents and actual transpiration fluxes. These outputs are finally compared with those obtained with the original version of the model. Experiments also allowed assessing the ability of simulated crop water stress coefficients to explain the actual water stress conditions evaluated on the basis of measured relative transpirations and midday stem water potentials. The results show that the modified model significantly improves the estimation of actual crop transpiration fluxes and soil water contents under soil water deficit conditions, according to the RMSEs associated with the revised model, resulting in significantly higher than the corresponding values obtained with the original version. (C) 2014 American Society of Civil Engineers.Rallo, G.; Baiamonte, G.; Manzano Juarez, J.; Provenzano, G. (2014). Improvement of FAO-56 Model to Estimate Transpiration Fluxes of Drought Tolerant Crops under Soil Water Deficit: Application for Olive Groves. Journal of Irrigation and Drainage Engineering. 140(9):1-8. doi:10.1061/(ASCE)IR.1943-4774.0000693S18140