SELF v1.0: a minimal physical model for predicting time of freeze-up in lakes

Predicting the freezing time in lakes is achieved by means of complex mechanistic models or by simplified statistical regressions considering integral quantities. Here, we propose a minimal model (SELF) built on sound physical grounds that focuses on the pre-freezing period that goes from mixed conditions (lake temperature at 4 ∘C) to the formation of ice (0 ∘C at the surface) in dimictic lakes. The model is based on the energy balance involving the two main processes governing the inverse stratification dynamics: cooling of water due to heat loss and wind-driven mixing of the surface layer. They play opposite roles in determining the time required for ice formation and contribute to the large interannual variability observed in ice phenology. More intense cooling does indeed accelerate the rate of decrease of lake surface water temperature (LSWT), while stronger wind deepens the surface layer, increasing the heat capacity and thus reducing the rate of decrease of LSWT. A statistical characterization of the process is obtained with a Monte Carlo simulation considering random sequences of the energy fluxes. The results, interpreted through an approximate analytical solution of the minimal model, elucidate the general tendency of the system, suggesting a power law dependence of the pre-freezing duration on the energy fluxes. This simple yet physically based model is characterized by a single calibration parameter, the efficiency of the wind energy transfer to the change of potential energy in the lake. Thus, SELF can be used as a prognostic tool for the phenology of lake freezing.

Sediment load determines the shape of rivers

Understanding how rivers adjust to the sediment load they carry is critical to predicting the evolution of landscapes. Presently, however, no physically based model reliably captures the dependence of basic river properties, such as its shape or slope, on the discharge of sediment, even in the simple case of laboratory rivers. Here, we show how the balance between fluid stress and gravity acting on the sediment grains, along with cross-stream diffusion of sediment, determines the shape and sediment flux profile of laminar laboratory rivers that carry sediment as bedload. Using this model, which reliably reproduces the experiments without any tuning, we confirm the hypothesis, originally proposed by Parker [G. Parker, J. Fluid Mech. 89, 127–146 (1978)], that rivers are restricted to exist close to the threshold of sediment motion (within about 20%). This limit is set by the fluid–sediment interaction and is independent of the water and sediment load carried by the river. Thus, as the total sediment discharge increases, the intensity of sediment flux (sediment discharge per unit width) in a river saturates, and the river can transport more sediment only by widening. In this large discharge regime, the cross-stream diffusion of momentum in the flow permits sediment transport. Conversely, in the weak transport regime, the transported sediment concentrates around the river center without significantly altering the river shape. If this theory holds for natural rivers, the aspect ratio of a river could become a proxy for sediment discharge—a quantity notoriously difficult to measure in the field.

Application of the KINEROS 2 Model to Natural Basin for Estimation of Erosion

This study compares different methods to calculate erosion and sedimentation processes in the Aviar Basin, a natural peri-urban basin located in Comúd’Encamp (Andorra).The basin area is small, covering less than one square kilometer. Currently, increased densities of houses and buildings under natural basins can cause drainage problems. This is due to the heavy accumulation of eroded solid material in the sewer systems. Therefore, for a given basin condition, accurate estimation of erosion and sedimentation amounts is important. The development of erosion models aims to facilitate the estimation of eroded solid material and the design of possible protective measures to prevent soil losses. Both empirical and physically based erosion models were used to study the Aviar Basin for these purposes. Empirical models include USLE (Universal Soil Loss Equation), RUSLE (Revised USLE) and MUSLE (Modified USLE), while one physically based model, KINEROS 2, was used. The volumes of solid materials produced in the Aviar Basin during the year 2012 were determined using these four different erosion models and then compared between them. The results of this study show that the estimation of soil loss using KINEROS 2 is useful in practice because the results obtained are close to those obtained from the empirical models.

SELF v1.0: A minimal physical model for predicting time of freeze-up in lakes

Predicting the freezing time in lakes is pursued by means of complex mechanistic models or by simplified statistical regressions considering integral quantities. Here, we propose a minimal model (SELF) built on sound physical grounds, which focuses on the pre-freezing period that, in dimictic lakes, goes from mixed conditions (lake temperature at 4 °C) to the formation of ice (0 °C at the surface). The model is based on the energy balance involving the two main processes governing the inverse stratification dynamics: cooling of water due to heat loss and wind-driven mixing of the surface layer. They play an opposite role in determining the time required for ice formation and contribute to the large inter-annual variability observed in ice phenology. More intense cooling, indeed, accelerates the rate of decrease of lake surface water temperature (LSWT), while stronger wind deepens the surface layer, increasing the heat capacity, and thus reduces the rate of decrease of LSWT. A statistical characterization of the process is obtained with a Monte Carlo simulation considering random sequences of the energy fluxes. The results, interpreted through an approximate analytical solution of the minimal model, elucidate the general tendency of the system, suggesting a power-law dependence of the pre-freezing duration on the energy fluxes. This simple, yet physically based model is characterized by a single calibration parameter, the efficiency of the wind energy transfer to the change of potential energy in the lake. Thus, SELF can be used as a prognostic tool for the phenology of lake freezing.