Implicit yield function formulation for granular and rock-like materials

The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or false elastic domains) preventing the use of efficient return-mapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a return-mapping integration scheme is implemented and tested for elastic-plastic (or -damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately.Comment: 19 page

Assessment of “Carbopeaking” in a hydropeaking-impacted river in the Italian Alpine area

Hydropeaking (i.e., rapid and frequent artificial flow fluctuations caused by reservoir-operated hydropower production) is a much-investigated river stressor, and has been associated, among others, to sudden changes in temperature (“thermopeaking”), underwater soundscape (“soundpeaking”), total dissolved gas saturation (“saturopeaking”). We have recently started investigating the “carbopeaking”, i.e., variations of greenhouse gas (mainly CO2) concentrations and evasion fluxes through the water-air interface associated with hydropeaks. Here we report on the methodology and preliminary results from a field-measurement campaign conducted in a single-thread Alpine river (River Noce, Italy) during multiple hydropeaking events. The analysis of water samples collected in the upstream reservoir showed CO2 oversaturation in the hypolimnion, around the depth of the hydropower intake system. In the Noce reach upstream of the hydropower plant outlet (i.e., in a residual flow stretch), the CO2 concentrations displayed diel fluctuations around the atmospheric equilibrium concentration, likely driven by diurnal primary production. Conversely, water released at the hydropower outlet during hydropeaking were consistently oversaturated in CO2 relative to the atmosphere, in agreement with the concentrations in the reservoir’s hypolimnetic water. As a result, hydropeaking events were associated with an alteration of the sub-daily patterns of CO2 concentration downstream of the hydropower outlet which, combined with higher gas exchange velocities occurring during higher flow rates, can cause periods of enhanced CO2 emissions. The results highlight the potential impact of hydropeaking on greenhouse gas emissions, demonstrating the need to account for sub-daily variations of flow and gas concentration to accurately quantify carbon balances in rivers impacted by hydropower

Changing nutrient cycling in Lake Baikal, the world's oldest lake

Lake Baikal, lying in a rift zone in southeastern Siberia, is the world's oldest, deepest, and most voluminous lake that began to form over 30 million years ago. Cited as the "most outstanding example of a freshwater ecosystem" and designated a World Heritage Site in 1996 due to its high level of endemicity, the lake and its ecosystem have become increasingly threatened by both climate change and anthropogenic disturbance. Here, we present a record of nutrient cycling in the lake, derived from the silicon isotope composition of diatoms, which dominate aquatic primary productivity. Using historical records from the region, we assess the extent to which natural and anthropogenic factors have altered biogeochemical cycling in the lake over the last 2,000 y. We show that rates of nutrient supply from deep waters to the photic zone have dramatically increased since the mid-19th century in response to changing wind dynamics, reduced ice cover, and their associated impact on limnological processes in the lake. With stressors linked to untreated sewage and catchment development also now impacting the near-shore region of Lake Baikal, the resilience of the lake's highly endemic ecosystem to ongoing and future disturbance is increasingly uncertain

Warming of Central European lakes and their response to the 1980s climate regime shift

Lake surface water temperatures (LSWTs) are sensitive to atmospheric warming and have previously been shown to respond to regional changes in the climate. Using a combination of in situ and simulated surface temperatures from 20 Central European lakes, with data spanning between 50 and ∼100 years, we investigate the long-term increase in annually averaged LSWT. We demonstrate that Central European lakes are warming most in spring and experience a seasonal variation in LSWT trends. We calculate significant LSWT warming during the past few decades and illustrate, using a sequential t test analysis of regime shifts, a substantial increase in annually averaged LSWT during the late 1980s, in response to an abrupt shift in the climate. Surface air temperature measurements from 122 meteorological stations situated throughout Central Europe demonstrate similar increases at this time. Climatic modification of LSWT has numerous consequences for water quality and lake ecosystems. Quantifying the response of LSWT increase to large-scale and abrupt climatic shifts is essential to understand how lakes will respond in the future

Amplified surface temperature response of cold, deep lakes to inter-annual air temperature variability

Summer lake surface water temperatures (LSWTs) have previously been shown to respond more rapidly to climatic warming compared to local summer surface air temperatures (SATs). In a global- scale analysis, we explore the factors underpinning the observation of an amplified response of summer LSWT to SAT variability using 20 years of satellite-derived temperatures from 144 lakes. We demonstrate that the degree of amplification in inter-annual summer LSWT is variable, and is greater for cold lakes (e.g. high latitude and high altitude), which are characterised by a short warming season, and deep lakes, that exhibit long correlation timescales of temperature anomalies due to increased thermal inertia. Such lakes are more likely to display responses in excess of local inter-annual summer SAT variability. Climatic modification of LSWT has numerous consequences for water quality and lake ecosystems, so quantifying this amplified response at a global scale is important

Ice cover and extreme events determine dissolved oxygen in a placid mountain lake

A decrease in hypolimnetic dissolved oxygen (DO) is a commonly seen effect of climate change. However, in oligotrophic Lake Tovel (Italy), a deep mountain lake, annual mean DO (% saturation) has increased from near anoxia to >20% in the bottom layer (35–39 m). We analyzed long‐term patterns of DO (1937–2019) using different methods (correlation and trend analysis, identification of extreme events) to link DO to drivers and indices of mixing. While spring mixing remained temporally limited, later ice‐in (5.1 days decade−1) and the positive relationship between ice‐in and DO the following year evidenced autumn mixing as the main driver for hypolimnetic DO increase. Extreme meteorological events also replenished hypolimnetic DO. Using DO and conductivity (1995–2019), we identified 14 deep mixing events with hypolimnetic DO > 40%. Density‐based indices (Schmidt stability, relative thermal resistance, Lake Number, and Wedderburn Number) only partially captured these events that were related to snowmelt, flooding, and cold spells during spring and autumn, with a carryover effect sometimes lasting >1 year. Recently, annual mean DO in the upper layer decreased beyond temperature‐dependent solubility. This decrease was not comprehensively confirmed by statistical tests but was possibly linked to atmospheric stilling. We suggest that Lake Tovel's shift from meromixis to dimixis was driven by climate warming (i.e., increasing air temperature 0.6°C decade−1) that delayed ice‐in and increased autumn mixing. Our work underlines the vulnerability of mountain lakes and their different response to climate change with respect to more studied lowland lake