A new model was developed to predict head loss in sand media filters. Sand filters with six different media using reclaimed water were used to measure head losses at different flow rates in the laboratory. The parameters influencing head losses were considered to be the uniformity coefficient, the effective diameter, the sand mass, the filtration velocity, the pollution load, and the water viscosity. A dimensional analysis method was used to develop the model. A comparison between the predicted and the measured head losses showed close agreement with a correlation coefficient of 91.7%, reaching a significance level of p < 0.001. The results showed that the model might give satisfactory predictions within the following range of operational and filter structure parameters: uniformity coefficient 1.48–3.31; effective diameter 0.41–2.1 mm; pollution load 0.0169–4.2049 kg, filtration velocity 0.0038–0.0398 m/s.

Quantifying the spatial distribution of nitrogen (N) in the soil under long-term drip fertigation events is essential for the optimal regulation of drip fertigation systems. In this study, a greenhouse soil that had been under drip irrigation for 20 years was selected as the research object, and soil samples were collected from the 0–50 cm soil depth. The concentrations of N in the soil samples were measured and their spatial distribution characteristics were quantified by classical statistical analysis and multifractal analysis. The results showed that long-term drip fertigation and the influence of natural factors resulted in the nitrate N mainly accumulating in the shallow layer of the soil and within a distance from the drip irrigation belt, and the spatial heterogeneity gradually decreased with increasing depth. The content of ammonium N was low, and its distribution was observed in the whole section. Multifractal analysis indicated that the Δα value of nitrate N and inorganic N gradually increased with the increase in the research scale, i.e., the spatial heterogeneity gradually increased, and it did not appreciably change for ammonium N. Meanwhile, the local high value region was the main factor leading to the spatial heterogeneity of N, and this dominant effect gradually increased with increasing depth. Multifractal analysis can effectively reflect the local information of the N spatial distribution in the soil and provide a more detailed description of the spatial heterogeneity of soil properties.

Quantifying the spatial distribution of nitrogen (N) in the soil under long-term drip fertigation events is essential for the optimal regulation of drip fertigation systems. In this study, a greenhouse soil that has been under drip irrigation for 20 years was selected as the research object, and soil samples were collected from 0-50 cm soil depth. The concentrations of N in soil samples were measured and their spatial distribution characteristics were quantified by classical statistical analysis and multifractal analysis. The results showed that long-term drip fertigation and the influence of natural factors resulted in the nitrate N mainly accumulating in the shallow layer of the soil and within a distance from the drip irrigation belt, and the spatial heterogeneity gradually decreased with increasing depth. The content of ammonium N was low and its distribution was observed in the whole section. Multifractal analysis indicated that the Δα value of nitrate N and inorganic N gradually increased with the increase of research scale, i.e., the spatial heterogeneity gradually increased, and it did not appreciably change for ammonium N. Meanwhile, the local high value region was the main factor leading to the spatial heterogeneity of N, and this dominant effect gradually increased with increasing depth. Multifractal analysis can effectively reflect the local information of N spatial distribution in the soil and provide a more detailed description of the spatial heterogeneity of soil properties.