Correcció del biaix en la relació estadística entre cabal i càrrega de fons en un riu Mediterrani amb llit de sorres

Abstract

Stream loads often have to be calculated from continuous records of discharge and discontinuous or infrequent sampling of sediment or dissolved load. Several statistical analyses indicate that sediment loads estimated from log-log rating curves between discharge and concentration underestimate real loads. Underestimate increases with the degree of scatter about the rating curve. Main purposes of this work are: 'a) to illustrate the statistical bias entered during the calculation of least square regression between discharge and concentration and, b) to show how it can be removed by using a simple correction factor developed by Ferguson (1986). This procedure is tested through a real case of bedload transport in a sandy gravel-bed never (Arbúcies, Catalan Coastal Ranges). The residual analysis of the statistical relation between bedload transport rates and discharge of the Arbúcies river shows a non-linearity trend between both variables. Thus, in order to a better adjustment between those variables a simple log transformation of the parameters was achieved. The statistical bias during he back-transformed procedure was calculated to be 60%, and it was removed by applying the correction factor previously mentioned. The marked statistical bias can be attributed to the scattered nature of the data. The scatter can be related to spatial and temporal variations of sand transport partly associated to the development and migration of bedforms, especially during floods.