Journal of Irrigation and Drainage Engineering

An inclined rectangular overflow structure, also called a pivot weir, consists of a rectangular plate, angled downstream from the vertical, that can be used as an upstream water level control device. A pivot weir is submerged when the upstream water level is influenced by the downstream flow depth. In this paper, to investigate factors influencing submerged flow conditions, an extensive experimental program including 251 experimental trials was carried out using weir inclination angles of 39.6°, 53°, 85°, and 90° and weir heights ranging from 0.263 to 0.312 m. A formula to distinguish between free and submerged flow conditions was developed using the $\mathrm{\Pi }$ theorem of dimensional analysis and the incomplete self-similarity (ISS) theory, and the submergence threshold curve was calibrated by the measurements carried out in this study. Employing a similar theoretical procedure (dimensional analysis and ISS theory), the tailwater depth for which a downstream standing wave starts and a stage-discharge relationship for submerged conditions also were developed. A comparison with the submerged stage-discharge formula proposed by the United States Bureau of Reclamation revealed that the proposed method could be more accurate for the entire operating range and conditions evaluated.

Climatological data for 101 stations in Catalonia and Navarre in northeastern Spain were used for comparing estimates of daily reference evapotranspiration (${\mathrm{ET}}_o$) by several temperature-based methods against daily estimates provided by the FAO-56 Penman–Monteith equation. Improved versions of both the Hargreaves–Samani (HS) and the Penman–Monteith temperature (PMT) equations were achieved. Specifically, the Hargreaves coefficient (in the case of the HS) and the empirical coefficient for the estimation of solar radiation (in the case of the PMT) were calibrated for each station and then regionalized by means of quadratic regressions based on the average daily temperature range. The results showed that both the calibrated and regionalized versions of the HS model performed better than the corresponding PMT model versions, with average mean absolute error (MAE) of $0.53\pm 0.16$ and $0.58\pm 0.18\mathrm{mm}·{\mathrm{d}\mathrm{ay}}^{-1}$, for the calibrated and regionalized HS, respectively, versus $0.63\pm 0.17$ and $0.64\pm 0.18\mathrm{mm}·{\mathrm{d}\mathrm{ay}}^{-1}$ for the calibrated and regionalized PMT, respectively. Furthermore, a regionalization approach for the Hargreaves coefficient based on a climate classification led to even better results for the regionalized HS model ($\mathrm{MAE}=0.56\pm 0.17\mathrm{mm}·{\mathrm{d}\mathrm{ay}}^{-1}$). This study highlighted the potential of the calibrated Hargreaves coefficient and its high correlation with the average daily temperature range, allowing reliable regionalization equations, especially over homogeneous climatic regions.