Aplicação da estatística à modelagem hidrológica e à previsão de uso e ocupação do solo para o desenvolvimento de novas métricas de desempenho

Abstract

The application of statistical elements to hydrology is recurrent, and it is very common to use statistical tests or trend analyses on time series of hydrological data, such as flows. However, there is a lack in the literature of the application of statistics to the development of efficiency metrics to be used in the evaluation of hydrological simulations, which generates a demand for functions that can complement those that already exist, such as the Nash-Sutcliffe coefficient (NASH), the Nash-Sutcliffe coefficient with logarithms (NASHLOG) and the percentage of bias (PBIAS).

Therefore, this research was involved not only in the development of new metrics, but also in the construction of a composite objective function based on the metrics developed. Initially, the metrics developed were tested separately in uncalibrated flow simulations made using the Large Basin Model (MGB) for the Rio Grande River Basin (BHRG), representing the period from 01/01/1990 to 29/06/2015. Next, the composition of the objective function was elaborated, and the resulting function was applied to the calibration of the Hydrologiska Byråns Vattenbalansavdelning (HBV) model for random precipitation, evapotranspiration and flow data provided by the Polytechnic University of Valencia (UPV) for the period from April 1996 to September 2004.

Individual testing with the MGB revealed that the metrics developed were able to satisfactorily demonstrate the following factors: the position of the 90% permanence flow calculation error in relation to the average of the errors determined for all the flows in the hydrograph; the tendency to underestimate or overestimate the simulation, based on the areas of the calculated and observed hydrographs and also on the percentages of underestimation, overestimation and success; the compatibility between the lengths of the calculated and observed hydrographs; the compatibility between the paths of these hydrographs.

At the same time, the application of the composition of metrics as an objective function revealed that the calibration of the HBV model tended to considerably reduce the peak and trough variations in flows. Comparative calibrations were carried out using NASH, NASHLOG and PBIAS as objective functions, and the dispersion conditions of the observed and calculated flow data without HBV calibration were also analyzed. Trend lines were plotted for all the hydrographs produced, and R2 values were determined for these lines, obtaining 0.65 in the case of the calibration made with the composition of metrics, 0.23 for the calibration with NASHLOG, 0.17 for the calibration with NASH, 0.13 for the calibration with PBIAS, 0.10 for the data calculated by HBV without calibration and 0.06 for the observed data. Remarkably, the effect of using composition as an objective function was very different from using the other efficiency metrics.

Other applications of statistics were also carried out in the research. Simple moving averages (SMA), power moving averages (PMA) and exponential moving averages (EMA) were used to perform flow estimates in the BHRG for the period from June 30, 2015 to June 29, 2016. Markov chains were applied to obtain the chances of the estimates occurring. None of the moving averages were considered satisfactory when comparing the calculated hydrographs with the observed hydrographs, although the mathematical check for bias pointed to reasonably reliable results generated with EMA.

The Mann-Kendall, Pettit and Student's t statistical tests were also used, respectively, to assess the presence of trends, breakpoints in behavior and differences between the flow averages in the first and second halves of the period analyzed (01/01/1990 to 29/06/2015). None of the tests led to the conclusion that there were significant trends or changes in the BHRG's flow regime during this period. An analysis was also carried out using basic statistical parameters, in this case quartiles, mean and standard deviation, which also did not lead to any finding of prevalent trends.

Finally, land use and occupation maps were created in QGIS for three regions of the BHRG, for the years 1995, 2005 and 2015, using Landsat images. In the TerrSet program, land use forecasts were obtained for 2025 and 2035 in two regions of the basin. This showed a tendency for farming to prevail on the BHRG's land, especially in the regions with the lowest slopes.