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Building energy performance (BEP) is an ongoing point of reflection among researchers and practitioners. The importance of buildings as one of the largest activators in climate change mitigation was illustrated recently at the United Nations Framework Convention on Climate Change 21st Conference of the Parties (COP21). Continuous technological improvements make it necessary to revise the methodology for energy calculations in buildings, as has recently happened with the new international standard ISO 52016-1 on Energy Performance of Buildings. In this area, there is a growing need for advanced tools like building energy models (BEMs). BEMs should play an important role in this process, but until now there has no been international consensus on how these models should reconcile the gap between measurement and simulated data in order to make them more reliable and affordable. Our proposal is a new generation of models that reconcile the traditional data-driven (inverse) modelling and law-driven (forward) modelling in a single type that we have called law-data-driven models. This achievement has greatly simplified past methodologies, and is a step forward in the search for a standard in the process of calibrating a building energy model.

The continental margin of southeast Brazil is elevated. Onshore Tertiary basins and Late Cretaceous/Paleogene intrusions are good evidence for post breakup tectono‐magmatic activity. To constrain the impact of post‐rift reactivation on the geological history of the area, we carried out a new thermochronological study. Apatite fission track ages range from 60.7 ± 1.9 Ma to 129.3 ± 4.3 Ma, mean track lengths from 11.41 ± 0.23 μm to 14.31 ± 0.24 μm and a subset of the (U‐Th)/He ages range from 45.1 ± 1.5 to 122.4 ± 2.5 Ma. Results of inverse thermal history modeling generally support the conclusions from an earlier study for a Late Cretaceous phase of cooling. Around the onshore Taubaté Basin, for a limited number of samples, the first detectable period of cooling occurred during the Early Tertiary. The inferred thermal histories for many samples also imply subsequent reheating followed by Neogene cooling. Given the uncertainty of the inversion results, we did deterministic forward modeling to assess the range of possibilities of this Tertiary part of the thermal history. The evidence for reheating seems to be robust around the Taubaté Basin, but elsewhere the data cannot discriminate between this and a less complex thermal history. However, forward modeling results and geological information support the conclusion that the whole area underwent cooling during the Neogene. The synchronicity of the cooling phases with Andean tectonics and those in NE Brazil leads us to assume a plate‐wide compressional stress that reactivated inherited structures. The present‐day topographic relief of the margin reflects a contribution from post‐breakup reactivation and uplift. Key Points New (U‐Th)/He and AFT data from southeast Brazil Results imply polyphased post‐rift tectonic reactivation Passive margins are not passive

Simulation of pyrolysis involves the knowledge of reaction kinetics and thermo-physical parameters, which are in general not directly measurable. Inverse modelling provides means to deduce the needed parameters from experimental data. This complex process involves the coupling of a simulation model with an optimisation method as well as the handling of a large amount of data. All of these processes are prone to errors and therefore a unified and automated implementation is beneficial for the whole community. In this contribution, a software to carry out this process is proposed. PROPTI is an open source tool written in Python, that is meant to provide a framework for inverse modelling of parameters in computer simulation, with emphasis on pyrolysis modelling in fire simulation. Its generalised formulation allows the usage of any simulation model in combination with various experimental data. The underlying optimisation library allows the utilisation of HPC systems. After presenting the concept of this framework, two examples are shown to illustrate the process and demonstrate the capabilities.

A new approach for inverse thermal history modeling is presented. The method uses Bayesian transdimensional Markov Chain Monte Carlo and allows us to specify a wide range of possible thermal history models to be considered as general prior information on time, temperature (and temperature offset for multiple samples in a vertical profile). We can also incorporate more focused geological constraints in terms of more specific priors. The Bayesian approach naturally prefers simpler thermal history models (which provide an adequate fit to the observations), and so reduces the problems associated with over interpretation of inferred thermal histories. The output of the method is a collection or ensemble of thermal histories, which quantifies the range of accepted models in terms a (posterior) probability distribution. Individual models, such as the best data fitting (maximum likelihood) model or the expected model (effectively the weighted mean from the posterior distribution) can be examined. Different data types (e.g., fission track, U‐Th/He, 40Ar/39Ar) can be combined, requiring just a data‐specific predictive forward model and data fit (likelihood) function. To demonstrate the main features and implementation of the approach, examples are presented using both synthetic and real data. Key Points New method for quantifying thermal histories from multiple samples Transdimensional approach naturally prefers simpler models to explain the data Outputs are probability distributions on unknowns and fully characterise model

Surface observations have recorded large and incompletely understood changes to atmospheric methane (CH 4 ) this century. However, their ability to reveal the responsible surface sources and sinks is limited by their geographical distribution, which is biased towards the northern midlatitudes. Data from Earth-orbiting satellites designed specifically to measure atmospheric CH 4 have been available since 2009 with the launch of the Japanese Greenhouse gases Observing SATellite (GOSAT). We assess the added value of GOSAT to data collected by the US National Oceanic and Atmospheric Administration (NOAA), which have been the lynchpin for knowledge about atmospheric CH 4 since the 1980s. To achieve that we use the GEOS-Chem atmospheric chemistry transport model and an inverse method to infer a posteriori flux estimates from the NOAA and GOSAT data using common a priori emission inventories. We find the main benefit of GOSAT data is from its additional coverage over the tropics where we report large increases since the 2014/2016 El Niño, driven by biomass burning, biogenic emissions and energy production. We use data from the European TROPOspheric Monitoring Instrument to show how better spatial coverage and resolution measurements allow us to quantify previously unattainable diffuse sources of CH 4 , thereby opening up a new research frontier. This article is part of a discussion meeting issue ‘Rising methane: is warming feeding warming? (part 1)’.

Arsenic (As) contamination in groundwater is a worldwide concern for drinking water safety. Environmental changes and anthropogenic activities are making groundwater vulnerable in Pakistan, especially in Southern Punjab. This study explores the distribution, hydrogeochemical behavior, and pathways of As enrichment in groundwater and discusses the corresponding evolution mechanism, mobilization capability, and health risks. In total, 510 groundwater samples were collected from three tehsils in the Punjab province of Pakistan to analyze As and other physiochemical parameters. Arsenic concentration averaged 14.0 μg/L in Vehari, 11.0 μg/L in Burewala, and 13.0 μg/L in Mailsi. Piper-plots indicated the dominance of Na+, SO42−, Ca2+, and Mg2+ ions in the groundwater and the geochemical modeling showed negative saturation indices with calcium carbonate and salt minerals, including aragonite (CaCO3), calcite (CaCO3), dolomite (CaMg(CO3)2), and halite (NaCl). The dissolution process hinted at their potential roles in As mobilization in groundwater. These results were further validated with an inverse model of the dissolution of calcium-bearing mineral, and the exchange of cations between Ca2+ and Na+ in the studied area. Risk assessment suggested potential carcinogenic risks (CR > 10−4) for both children and adults, whereas children had a significant non-carcinogenic risk hazard quotient (HQ > 1). Accordingly, children had higher overall health risks than adults. Groundwater in Vehari and Mailsi was at higher risk than in Burewala. Our findings provide important and baseline information for groundwater As assessment at a provincial level, which is essential for initiating As health risk reduction. The current study also recommends efficient management strategies for As-contaminated groundwater.

Accurate correction of radial lens distortion is a fundamental requirement in computer vision and photogrammetry, as geometric inaccuracies directly affect 3D reconstruction, mapping, and geospatial measurements, particularly in high-precision imaging systems. In this study, we propose a fully analytical, non-iterative method for truncated inverse modeling of radial lens distortion, applicable to general radial distortion polynomials that contain constant terms. Unlike classical truncated Lagrange series reversion, which relies on recursive expansion and combinatorial series construction, the proposed formulation determines inverse distortion coefficients directly through a system of constrained algebraic inverse polynomials. This enables deterministic computation of inverse parameters without iterative refinement, numerical root finding, or combinatorial complexity. The method was evaluated using ultra-wide-angle smartphone camera imagery exhibiting severe barrel distortion modeled by an eighth-degree depressed radial distortion polynomial. Its performance was compared with a commonly used iterative inverse modeling approach. The analytical formulation demonstrated improved numerical stability and substantially reduced reprojection errors when correcting highly nonlinear distortion profiles, achieving sub-pixel accuracy in image rectification. In contrast, the iterative approach exhibited instability and significantly larger reprojection errors under identical conditions. These results demonstrate that the proposed framework provides a general, robust, and repeatable solution for inverse radial distortion modeling, particularly for high-order polynomial models. The method offers clear practical advantages for camera calibration pipelines in photogrammetry, remote sensing, robotics, and other applications requiring high-fidelity imaging.

The temperature sensitivity of the U-Pb apatite system (350–570 °C) makes it a powerful tool to study thermal histories in the deeper crust. Recent studies have exploited diffusive Pb loss from apatite crystals to generate t-T paths between ~350–570 °C, by comparing apatite U-Pb ID-TIMS (isotope dilution-thermal ionisation mass spectrometry) dates with grain size or by LA-MC-ICP-MS (laser ablation-multicollector-inductively coupled plasma-mass spectrometry) age depth profiling/traverses of apatite crystals, and assuming the effective diffusion domain is the entire crystal. The key assumptions of apatite U-Pb thermochronology are discussed including (i) that Pb has been lost by Fickian diffusion, (ii) can experimental apatite Pb diffusion parameters be extrapolated down temperature to geological settings and (iii) are apatite grain boundaries open (i.e., is Pb lost to an infinite reservoir). Particular emphasis is placed on detecting fluid-mediated remobilisation of Pb, which invalidates assumption (i). The highly diverse and rock-type specific nature of apatite trace-element chemistry is very useful in this regard—metasomatic and low-grade metamorphic apatite can be easily distinguished from sub-categories of igneous rocks and high-grade metamorphic apatite. This enables reprecipitated domains to be identified geochemically and linked with petrographic observations. Other challenges in apatite U-Pb thermochronology are also discussed. An appropriate choice of initial Pb composition is critical, while U zoning remains an issue for inverse modelling of single crystal ID-TIMS dates, and LA-ICP-MS age traverses need to be integrated with U zoning information. A recommended apatite U-Pb thermochronology protocol for LA-MC-ICP-MS age depth profiling/traverses of apatite crystals and linked to petrographic and trace element information is presented.

Dynamic vegetation models provide process-based explanations of the dynamics and the distribution of plant ecosystems. They offer significant advantages over static, correlative modelling approaches, particularly for ecosystems that are outside their equilibrium due to global change or climate change. A persistent problem, however, is their parameterization. Parameters and processes of dynamic vegetation models (DVMs) are traditionally determined independently of the model, while model outputs are compared to empirical data for validation and informal model comparison only. But field data for such independent estimates of parameters and processes are often difficult to obtain, and the desire to include better descriptions of processes such as biotic interactions, dispersal, phenotypic plasticity and evolution in future vegetation models aggravates limitations related to the current parameterization paradigm. In this paper, we discuss the use of Bayesian methods to bridge this gap. We explain how Bayesian methods allow direct estimates of parameters and processes, encoded in prior distributions, to be combined with inverse estimates, encoded in likelihood functions. The combination of direct and inverse estimation of parameters and processes allows a much wider range of vegetation data to be used simultaneously, including vegetation inventories, species traits, species distributions, remote sensing, eddy flux measurements and palaeorecords. The possible reduction of uncertainty regarding structure, parameters and predictions of DVMs may not only foster scientific progress, but will also increase the relevance of these models for policy advice.

Lagrangian particle dispersion models (LPDMs) are frequently used for regional-scale inversions of greenhouse gas emissions. However, the turbulence parameterizations used in these models were developed for coarse resolution grids, hence, when moving to the kilometre-scale the validity of these descriptions should be questioned. Here, we analyze the influence of the turbulence parameterization employed in the LPDM FLEXPART-COSMO model. Comparisons of the turbulence kinetic energy between the turbulence schemes of FLEXPART-COSMO and the underlying Eulerian model COSMO suggest that the dispersion in FLEXPART-COSMO suffers from a double-counting of turbulent elements when run at a high resolution of 1×1km2. Such turbulent elements are represented in both COSMO, by the resolved grid-scale winds, and FLEXPART, by its stochastic parameterizations. Therefore, we developed a new parametrization for the variations of the winds and the Lagrangian time scales in FLEXPART in order to harmonize the amount of turbulence present in both models. In a case study for a power plant plume, the new scheme results in improved plume representation when compared with in situ flight observations and with a tracer transported in COSMO. Further in-depth validation of the LPDM against methane observations at a tall tower site in Switzerland shows that the model’s ability to predict the observed tracer variability and concentration at different heights above ground is considerably enhanced using the updated turbulence description. The high-resolution simulations result in a more realistic and pronounced diurnal cycle of the tracer concentration peaks and overall improved correlation with observations when compared to previously used coarser resolution simulations (at 7 km × 7 km). Our results indicate that the stochastic turbulence schemes of LPDMs, developed in the past for coarse resolution models, should be revisited to include a resolution dependency and resolve only the part of the turbulence spectrum that is a subgrid process at each different mesh size. Although our new scheme is specific to COSMO simulations at 1×1km2 resolution, the methodology for deriving the scheme can easily be applied to different resolutions and other regional models.