Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil

Abstract. In this work, a first-order upwind and a high-order flux-limiter schemes for solving the advection–diffusion equation on unstructured grids were evaluated. The numerical schemes were implemented as a module of an unstructured two-dimensional depth-averaged circulation model for shallow lakes (IPH-UnTRIM2D), and they were applied to the Guaíba River in Brazil. Their performances were evaluated by comparing mass conservation balance errors for two scenarios of a passive tracer released into the Guaíba River. The circulation model showed good agreement with observed data collected at four water level stations along the Guaíba River, where correlation coefficients achieved values up to 0.93. In addition, volume conservation errors were lower than 1% of the total volume of the Guaíba River. For all scenarios, the higher order flux-limiter scheme has been shown to be less diffusive than a first-order upwind scheme. Accumulated conservation mass balance errors calculated for the flux limiter reached 8%, whereas for a first-order upwind scheme, they were close to 18% over a 15-day period. Although both schemes have presented mass conservation errors, these errors are assumed negligible compared with kinetic processes such as erosion, sedimentation or decay rates. </jats:p

Rainfall as proxy for evapotranspiration predictions

In this work, we evaluated the relationship between evapotranspiration and precipitation, based on the data recently made available by the Brazilian Meteorological Institute. ETP tend to be lower in rainy periods and vice-versa. This relationship was assessed both in physical and statistical ways, identifying the contribution of each explaining variable of ETP. We derived regression equations between monthly rainfall and ETP, which can be useful in studies where ETP time series are not available, such as reservoir design, irrigation management and flow forecast

Dealing with variability in water availability: the case of the Verde Grande River basin, Brazil

This paper presents a water resources management strategy developed by the Brazilian National Water Agency (ANA) to cope with the conflicts between water users in the Verde Grande River basin, located at the southern border of the Brazilian semi-arid region. The basin is dominated by water-demanding fruit irrigation agriculture, which has grown significantly and without adequate water use control, over the last 30 years. The current water demand for irrigation exceeds water availability (understood as a 95 % percentile of the flow duration curve) in a ratio of three to one, meaning that downstream water users are experiencing more frequent water shortages than upstream ones. The management strategy implemented in 2008 has the objective of equalizing risk for all water users and consists of a set of rules designed to restrict water withdrawals according to current river water level (indicative of water availability) and water demand. Under that rule, larger farmers have proportionally larger reductions in water use, preserving small subsistence irrigators. Moreover, dry season streamflow is forecasted at strategic points by the end of every rainy season, providing evaluation of shortage risk. Thus, water users are informed about the forecasts and corresponding restrictions well in advance, allowing for anticipated planning of irrigated areas and practices. In order to enforce restriction rules, water meters were installed in all larger water users and inefficient farmers were obligated to improve their irrigation systems’ performance. Finally, increases in irrigated area are only allowed in the case of annual crops and during months of higher water availability (November to June). The strategy differs from convectional approached based only on water use priority and has been successful in dealing with natural variability of water availability, allowing more water to be used in wet years and managing risk in an isonomic manner during dry years