The objective of the present study is to demonstrate the informative capacity of the longitudinal anomaly of potential energy (LAPE) in the analysis of the magnitude and spatiotemporal variability of estuarine processes. For this purpose, a LAPE balance equation is formulated. The LAPE integrates and varies with the vertical and longitudinal density distribution. The formulation is applied on a subtidal scale to each box or stretch of the Guadalquivir River estuary, a narrow, highly turbid, weakly stratified, and strongly anthropized estuary. Data recorded by a large network of monitoring stations in 2008 and 2009 are used to quantify advective transports as well as the transports associated with longitudinal dispersion and vertical turbulent mixing in different hydraulic regimes. In low‐river flow conditions, (river flows Q400 m³s⁻¹), this convergence disappears and the maximum longitudinal density gradient moves towards the mouth. More specifically, tidal pumping ‐induced LAPE governs during these conditions and manages to compensate the sum of the mean nontidal and dispersive and differential advective LAPE transports. However, during the post‐riverflood period, the mechanisms controlling recovery downstream from the mouth are the longitudinal dispersive and differential advective LAPE transports. Furthermore, the convergence zone reappears with a longitudinal gradient of the net LAPE transport that is even greater than in low‐river flow conditions.

Hydrological studies depend heavily on environmental variables, such as precipitation and resulting runoff, which exhibit highly seasonal and intermittent behaviour in semiarid basins. In these basins, the use of traditional methods to adjust biases in time series projections can lead to inaccurate results regarding the impacts of climate change. This study introduces a non-stationary bias adjustment methodology (NS) specifically designed for environmental variables characterized by sporadic events and substantial intensity variability, such as precipitation. The methodology involves establishing a probability threshold to adapt the occurrence of precipitation events and utilizes a quantile mapping method based on a non-stationary theoretical and parametric distribution to adjust biases associated with precipitation intensity. The NS method is applied to daily precipitation projections from seven regional climatic models under the RCP 8.5 scenario spanning 2006–2100, alongside historical concurrent data from 1970 to 2005. The present method is compared to the widely used quantile delta mapping approach (QDM), revealing significant differences in performance related to the distribution of precipitation events throughout the year and the behaviour of mean and extreme intensity values. Both approaches show reliable performance, with root mean square errors between the empirical distribution functions of the corrected hindcast time series and the observations being lower than or close to 1 mm for the percentiles smaller than 50th. The error increases with the percentiles, particularly at stations located at higher altitudes. In these locations, QDM doubles or triples the error obtained with the non-stationary approach for percentiles higher than 75th, reaching up to 34 mm. The proposed methodology demonstrates promising potential in reducing uncertainties associated with systematic errors in inter-annual precipitation variability. It is a first step to jointly apply a similar approach to all involved driving variables. Such methods are key to assessing hydrological responses and associated impacts in semi-arid mountainous basins all around the Globe.

We propose a general methodology to characterize a non-stationary random process that can be used for simulating random realizations that keep the probabilistic behavior of the original time series. The probability distribution of the process is assumed to be a piecewise function defined by several weighted parametric probability models. The weights are obtained analytically by ensuring that the probability density function is well defined and that it is continuous at the common endpoints. Any number of subintervals and continuous probability models can be chosen. The distribution is assumed to vary periodically in time over a predefined time interval by defining the model parameters and the common endpoints as truncated generalized Fourier series. The coefficients of the expansions are obtained with the maximum likelihood method. Different sets of orthogonal basis functions are tested. The method is applied to three time series with different particularities. Firstly, it is shown its good behavior to capture the high variability of the precipitation projected at a semiarid location of Spain for the present century. Secondly, for the Wolf sunspot number time series, the Schwabe cycle and time variations close to the 7.5 and 17 years are analyzed along a 22-year cycle. Finally, the method is applied to a bivariate time series that contains (1) freshwater discharges at the last regulation point of a dam located in a semiarid zone in Andalucía (Spain) which is influenced not only by the climate variability but also by management decisions and (2) the salinity at the mouth of the river. For this case, the analysis, that was combined with a vectorial autoregressive model, focus on the assessment of the goodness of the methodology to replicate the statistical features of the original series. In particular, it is found that it reproduces the marginal and joint distributions and the duration of sojourns above/below given thresholds.