Sources Of Uncertainty In Models Research Articles

Optimal robust reinsurance with multiple insurers*

We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to n insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the reinsurer is uncertain about the insurers' claim severity distributions and frequencies, they design reinsurance contracts that maximise their expected wealth subject to an entropy penalty. Insurers meanwhile seek to maximise their expected utility without ambiguity. We solve this continuous-time Stackelberg game for general reinsurance contracts and find that the reinsurer prices under a distortion of the barycentre of the insurers' models. We apply our results to proportional reinsurance and excess-of-loss reinsurance contracts, and illustrate the solutions numerically. Furthermore, we solve the related problem where the reinsurer maximises, still under ambiguity, their expected utility and compare the solutions.

Sensitivity of a carbon-based primary production model on satellite ocean color products

Satellite remote sensing plays a crucial role in estimating global primary production. One well-known model is the carbon-based production model (CbPM), which focuses on the estimation of carbon biomass (Cph) via particulate backscattering coefficient at 443 nm (bbp(443)) and emphasizes the physiological characteristics of phytoplankton. However, as there are various remote sensing algorithms for the estimation of bbp(443) and chlorophyll-a concentration (Chl), the impacts introduced by different bbp(443) and Chl products on the estimated water-column integrated primary production (PPeu) by CbPM are unknown, especially with the new CbPM version (CbPM08) (Westberry et al., 2008). In this study, we conducted analyses to examine the impact of Chl, bbp(443), and Kd(490) (the diffuse attenuation coefficient at 490 nm) that were derived from ocean color remote sensing on PPeu estimated by CbPM08. Our results revealed that Chl constitutes the primary source of model uncertainty, followed by Kd(490), while variations of bbp(443) exhibit negligible impact on the estimation of PPeu. Especially, between Chl and Cph, sensitivity studies indicate that the PPeu values estimated by CbPM08 are fundamentally driven by Chl, rather than by Cph (or bbp(443)). These results provide important insights on understanding the uncertainties associated with CbPM08-estimated PPeu and future directions for further improvement for the estimation of PPeu via this model, as well as its applications on estimating water-column primary production.

High-resolution LGM climate of Europe and the Alpine region using the regional climate model WRF

Abstract. In this study we present a series of sensitivity experiments conducted for the Last Glacial Maximum (LGM, ∼21 ka) over Europe using the regional climate Weather Research and Forecasting model (WRF). Using a four-step two-way nesting approach, we are able to reach a convection-permitting horizontal resolution over the inner part of the study area, covering central Europe and the Alpine region. The main objective of the paper is to evaluate a model version including a series of new developments better suitable for the simulation of paleo-glacial time slices with respect to the ones employed in former studies. The evaluation of the model is conducted against newly available pollen-based reconstructions of the LGM European climate and takes into account the effect of two main sources of model uncertainty: a different height of continental glaciers at higher latitudes of the Northern Hemisphere and different land cover. Model results are in good agreement with evidence from the proxies, in particular for temperatures. Importantly, the consideration of different ensemble members for characterizing model uncertainty allows for increasing the agreement of the model against the proxy reconstructions that would be obtained when considering a single model realization. The spread of the produced ensemble is relatively small for temperature, besides areas surrounding glaciers in summer. On the other hand, differences between the different ensemble members are very pronounced for precipitation, in particular in winter over areas highly affected by moisture advection from the Atlantic. This highlights the importance of the considered sources of uncertainty for the study of European LGM climate and allows for determining where the results of a regional climate model (RCM) are more likely to be uncertain for the considered case study. Finally, the results are also used to assess the effect of convection-permitting resolutions, at both local and regional scales, under glacial conditions.

Role of data uncertainty when identifying important areas for biodiversity and carbon in boreal forests

Forest conservation plays a central role in meeting national and international biodiversity and climate targets. Biodiversity and carbon values within forests are often estimated with models, introducing uncertainty to decision making on which forest stands to protect. Here, we explore how uncertainties in forest variable estimates affect modelled biodiversity and carbon patterns, and how this in turn introduces variability in the selection of new protected areas. We find that both biodiversity and carbon patterns were sensitive to alterations in forest attributes. Uncertainty in features that were rare and/or had dissimilar distributions with other features introduced most variation to conservation plans. The most critical data uncertainty also depended on what fraction of the landscape was being protected. Forests of highest conservation value were more robust to data uncertainties than forests of lesser conservation value. Identifying critical sources of model uncertainty helps to effectively reduce errors in conservation decisions.

Reducing uncertainty of high-latitude ecosystem models through identification of key parameters

Climate change is having significant impacts on Earth’s ecosystems and carbon budgets, and in the Arctic may drive a shift from an historic carbon sink to a source. Large uncertainties in terrestrial biosphere models (TBMs) used to forecast Arctic changes demonstrate the challenges of determining the timing and extent of this possible switch. This spread in model predictions can limit the ability of TBMs to guide management and policy decisions. One of the most influential sources of model uncertainty is model parameterization. Parameter uncertainty results in part from a mismatch between available data in databases and model needs. We identify that mismatch for three TBMs, DVM-DOS-TEM, SIPNET and ED2, and four databases with information on Arctic and boreal above- and belowground traits that may be applied to model parametrization. However, focusing solely on such data gaps can introduce biases towards simple models and ignores structural model uncertainty, another main source for model uncertainty. Therefore, we develop a causal loop diagram (CLD) of the Arctic and boreal ecosystem that includes unquantified, and thus unmodeled, processes. We map model parameters to processes in the CLD and assess parameter vulnerability via the internal network structure. One important substructure, feed forward loops (FFLs), describe processes that are linked both directly and indirectly. When the model parameters are data-informed, these indirect processes might be implicitly included in the model, but if not, they have the potential to introduce significant model uncertainty. We find that the parameters describing the impact of local temperature on microbial activity are associated with a particularly high number of FFLs but are not constrained well by existing data. By employing ecological models of varying complexity, databases, and network methods, we identify the key parameters responsible for limited model accuracy. They should be prioritized for future data sampling to reduce model uncertainty.

Uncertainty quantification analysis of Reynolds-averaged Navier–Stokes simulation of spray swirling jets undergoing vortex breakdown

The computational fluid dynamics-based design of next-generation aeronautical combustion chambers is challenging due to many geometrical and operational parameters to be optimized and several sources of uncertainty that arise from numerical modeling. The present work highlights the potential benefits of exploiting Bayesian uncertainty quantification at the preliminary design stage. A prototypical configuration of an acetone/air spray swirling jet is investigated through an Eulerian–Lagrangian method under non-reactive conditions. Two direct numerical simulations (DNSs) provide reference data, coping with different vortex breakdown states. Consequently, a set of Reynolds-averaged Navier–Stokes simulations is conducted. Polynomial chaos expansion (PCE) is adopted to propagate the uncertainty associated with the spray dispersion model and the turbulent Schmidt number, delivering confidence intervals and the sensitivity of the output variance to each uncertain input. Consequently, the most significant sources of modeling uncertainty may be identified and eventually removed via a calibration procedure, thus making it possible to carry out a combustion chamber optimization process that is no longer affected by numerical biases. The uncertainty quantification analysis in the current study demonstrates that the spray dispersion model slightly affects the fuel vapor spatial distribution under vortex breakdown flow conditions, compared with the output variance induced by the selection of the turbulent Schmidt number. As a result, additional high-fidelity experimental and numerical campaigns should exclusively address the development of an ad hoc model characterizing the spatial distribution of the latter in the presence of vortex breakdown phenomenology, discarding any effort to improve the spray dispersion formulation.

Oblique Propagation and Refraction of Gravity Waves Over the Andes Observed by GLORIA and ALIMA During the SouthTRAC Campaign

AbstractGravity waves (GW) carry energy and momentum from the troposphere to the middle atmosphere and have a strong influence on the circulation there. Global atmospheric models cannot fully resolve GWs, and therefore rely on highly simplified GW parametrizations that, among other limitations, account for vertical wave propagation only and neglect refraction. This is a major source of uncertainty in models, and leads to well‐known problems, such as the late break‐up of polar vortex due to the “missing” GW drag around 60°S. To investigate these phenomena, GW observations over Southern Andes were performed during SouthTRAC aircraft campaign. This paper presents measurements from a SouthTRAC flight on 21 September 2019, including 3‐D tomographic temperature data of the infrared limb imager GLORIA (8–15 km altitude) and temperature profiles of the ALIMA lidar (20–80 km altitude). GLORIA observations revealed multiple overlapping waves of different wavelengths. 3‐D wave vectors were determined from the GLORIA data and used to initialize a GW ray‐tracer. The ray‐traced GW parameters were compared with ALIMA observations, showing good agreement between the instruments and direct evidence of oblique (partly meridional) GW propagation. ALIMA data analysis confirmed that most waves at 25–40 km altitudes were indeed orographic GWs, including waves seemingly upstream of the Andes. We directly observed horizontal GW refraction, which has not been achieved before SouthTRAC. Refraction and oblique propagation caused significant meridional transport of horizontal momentum as well as horizontal momentum exchange between waves and the background flow all along the wave paths, not just in wave excitation and breaking regions.

Model behavior regarding in- and below-cloud 137Cs wet scavenging following the Fukushima accident using 1-km-resolution meteorological field data

Wet deposition remains an important source of uncertainty in modeling of the atmospheric transport of 137Cs following the Fukushima Daiichi Nuclear Power Plant accident. Its behavior is often difficult to investigate owing to the limited resolution of meteorological field data and inconsistent model implementations. This study investigated the detailed behavior of 25 combinations of in- and below-cloud wet scavenging models using high-resolution (1 km × 1 km) meteorological input. These combinations were all implemented in the Weather Research and Forecasting-Chemistry model, thereby enabling consistent evaluation. The 1-km-resolution simulations were compared with simulations obtained previously using 3-km-resolution meteorological field data. Results revealed that rainfall of <1 mm/h is critical for simulation accuracy. The 1-km results revealed better representation of rainfall than that revealed by the 3-km results, but with spatiotemporal variability in accuracy. Owing to their sensitivity to rainfall, single-parameter wet deposition models showed improvements in performance in the 1-km simulations relative to that in the 3-km simulations. The multiparameter models showed more robust performance in terms of both simulations, and the Roselle–Mircea model presented the best performance among the 25 models considered. Wind transport showed substantial influence on the removal of atmospheric 137Cs, and it was nonnegligible even during periods in which wet deposition was dominant. The 1-km-resolution simulations effectively reproduced local-scale 137Cs concentrations but with deviations in timing, mainly because of biased wind direction. These findings indicate the necessity for a refined wind and dispersion model for local-scale simulation of 137Cs concentration.

Stochastic simulation uncertainty analysis to accelerate flexible biomanufacturing process development

Motivated by critical challenges and needs from biopharmaceuticals manufacturing, we propose a general metamodel-assisted stochastic simulation uncertainty analysis framework to accelerate the development of a simulation model with modular design for flexible production processes. There are often very limited process observations. Thus, there exist both simulation and model uncertainties in the system performance estimates. In biopharmaceutical manufacturing, model uncertainty often dominates. The proposed framework can produce a confidence interval that accounts for simulation and model uncertainties by using a metamodel-assisted bootstrapping approach. Furthermore, a variance decomposition is utilized to estimate the relative contributions from each source of model uncertainty, as well as simulation uncertainty. This information can be used to improve the system mean performance estimation. Asymptotic analysis provides theoretical support for our approach, while the empirical study demonstrates that it has good finite-sample performance.

Model Uncertainty and Correctability for Directed Graphical Models

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to quantities of interest. These methods allow us to rank the different sources of uncertainty and correct the graphical model by targeting its most impactful components with respect to the quantities of interest. Thus, from a machine learning perspective, we provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate our methods in two physico-chemical examples, namely quantum scale-informed chemical kinetics and materials screening to improve the efficiency of fuel cells.

Evaluating soil organic carbon changes after 16 years of soil relocation in Chinese Mollisols by optimizing the input data of the RothC model

Long-term intensive cultivation leads to the loss of soil organic carbon (SOC) in agricultural lands, which inevitably threatens food security and exacerbates greenhouse gas (GHG) emissions. The RothC model (Ver. 26.3win) is generally used to evaluate the changes in SOC and its responses to agricultural practices and climate change. However, previous calibrations of the RothC model emphasize the parameterization of C decomposition and neglect the effect of input data on the model accuracy. In this study, a long-term soil relocation experiment (1 m depth) in Chinese Mollisols was used to determine the effect of input parameters on the performance of the RothC model, and the optimal combination was filtered to evaluate the changes in SOC after 16 years of soil relocation. The results showed that the estimated C input from crop residues ranged from 1.22 to 2.53 t C ha−1 yr−1, and these inputs were insufficient to maintain the equilibrium state of the SOC. We also found a non-linear relationship between the initial SOC and C input, i.e., the largest C input amount was obtained under 3.24 % SOC rather than 6.31 % SOC. The difference in C input derived from estimation algorithms was the main source of model uncertainty. The simulation results indicated that from 2005 to 2020, the loss of SOC in Mollisols ranged from 2.54 to 13.90 t ha−1 when the initial SOC stocks were greater than 60 t ha−1, while the rate of SOC sequestration was 0.15 t ha−1 yr−1 when the SOC stocks was 33.03 t ha−1. Meanwhile, warming accelerated the loss and delayed the recovery of SOC in Mollisols. We suggested the equilibrium point of SOC in Mollisols under current agricultural practices was approximately 45 t ha−1. These results highlighted that Mollisols were an important C source of GHG and that a substantial capacity exists in SOC sequestration under conventional agricultural practices.

Evaluating the contribution of the unexplored photochemistry of aldehydes on the tropospheric levels of molecular hydrogen (H2)

Abstract. Molecular hydrogen, H2, is one of the most abundant trace gases in the atmosphere. The main known chemical source of H2 in the atmosphere is the photolysis of formaldehyde and glyoxal. Recent laboratory measurements and ground-state photochemistry calculations have shown other aldehydes photodissociate to yield H2 as well. This aldehyde photochemistry has not been previously accounted for in atmospheric H2 models. Here, we used two atmospheric models to test the implications of the previously unexplored aldehyde photochemistry on the H2 tropospheric budget. We used the AtChem box model implementing the nearly chemically explicit Master Chemical Mechanism at three sites selected to represent variable atmospheric environments: London, Cabo Verde and Borneo. We conducted five box model simulations per site using varying quantum yields for the photolysis of 16 aldehydes and compared the results against a baseline. The box model simulations showed that the photolysis of acetaldehyde, propanal, methylglyoxal, glycolaldehyde and methacrolein yields the highest chemical production of H2. We also used the GEOS-Chem 3-D atmospheric chemical transport model to test the impacts of the new photolytic H2 source on the global scale. A new H2 simulation capability was developed in GEOS-Chem and evaluated for 2015 and 2016. We then performed a sensitivity simulation in which the photolysis reactions of six aldehyde species were modified to include a 1 % yield of H2. We found an increase in the chemical production of H2 over tropical regions where high abundance of isoprene results in the secondary generation of methylglyoxal, glycolaldehyde and methacrolein, ultimately yielding H2. We calculated a final increase of 0.4 Tg yr−1 in the global chemical production budget, compared to a baseline production of ∼41 Tg yr−1. Ultimately, both models showed that H2 production from the newly discovered photolysis of aldehydes leads to only minor changes in the atmospheric mixing ratios of H2, at least for the aldehydes tested here when assuming a 1 % quantum yield across all wavelengths. Our results imply that the previously missing photochemical source is a less significant source of model uncertainty than other components of the H2 budget, including emissions and soil uptake.

Matrix Approach to Land Carbon Cycle Modeling

AbstractLand ecosystems contribute to climate change mitigation by taking up approximately 30% of anthropogenically emitted carbon. However, estimates of the amount and distribution of carbon uptake across the world's ecosystems or biomes display great uncertainty. The latter hinders a full understanding of the mechanisms and drivers of land carbon uptake, and predictions of the future fate of the land carbon sink. The latter is needed as evidence to inform climate mitigation strategies such as afforestation schemes. To advance land carbon cycle modeling, we have developed a matrix approach. Land carbon cycle models use carbon balance equations to represent carbon exchanges among pools. Our approach organizes this set of equations into a single matrix equation without altering any processes of the original model. The matrix equation enables the development of a theoretical framework for understanding the general, transient behavior of the land carbon cycle. While carbon input and residence time are used to quantify carbon storage capacity at steady state, a third quantity, carbon storage potential, integrates fluxes with time to define dynamic disequilibrium of the carbon cycle under global change. The matrix approach can help address critical contemporary issues in modeling, including pinpointing sources of model uncertainty and accelerating spin‐up of land carbon cycle models by tens of times. The accelerated spin‐up liberates models from the computational burden that hinders comprehensive parameter sensitivity analysis and assimilation of observational data to improve model accuracy. Such computational efficiency offered by the matrix approach enables substantial improvement of model predictions using ever‐increasing data availability. Overall, the matrix approach offers a step change forward for understanding and modeling the land carbon cycle.

Diagnosing Discrepancies between Observations and Models of Surface Energy Fluxes in a Midlatitude Lake

Abstract The physical processes of heat exchange between lakes and the surrounding atmosphere are important in simulating and predicting terrestrial surface energy balance. Latent and sensible heat fluxes are the dominant physical process controlling ice growth and decay on the lake surface, as well as having influence on regional climate. While one-dimensional lake models have been used in simulating environmental changes in ice dynamics and water temperature, understanding the seasonal to daily cycles of lake surface energy balance and its relationship to lake thermal properties, atmospheric conditions, and how those are represented in models is still an open area of research. We evaluated a pair of one-dimensional lake models, Freshwater Lake (FLake) and the General Lake Model (GLM), to compare modeled latent and sensible heat fluxes against observed data collected by an eddy covariance tower during a 1-yr period in 2017, using Lake Mendota in Madison, Wisconsin, as our study site. We hypothesized transitional periods of ice cover as a leading source of model uncertainty, and we instead found that the models failed to simulate accurate values for large positive heat fluxes that occurred from late August into late December. Our results ultimately showed that one-dimensional models are effective in simulating sensible heat fluxes but are considerably less sensitive to latent heat fluxes than the observed relationships of latent heat flux to environmental drivers. These results can be used to focus future improvement of these lake models especially if they are to be used for surface boundary conditions in regional numerical weather models. Significance Statement While lakes consist of a small amount of Earth’s surface, they have a large impact on local climate and weather. A large amount of energy is stored in lakes during the spring and summer, and then removed from lakes before winter. The effect is particularly noticeable in high latitudes, when the seasonal temperature difference is larger. Modeling this lake energy exchange is important for weather models and measuring this energy exchange is challenging. Here we compare modeled and observed energy exchange, and we show there are large amounts of energy exchange happening in the fall, which models struggle to capture well. During periods of partial ice coverage in early winter, lake behavior can change rapidly.

Conclusion or Illusion: Quantifying Uncertainty in Inverse Analyses From Marker-Based Motion Capture due to Errors in Marker Registration and Model Scaling.

Estimating kinematics from optical motion capture with skin-mounted markers, referred to as an inverse kinematic (IK) calculation, is the most common experimental technique in human motion analysis. Kinematics are often used to diagnose movement disorders and plan treatment strategies. In many such applications, small differences in joint angles can be clinically significant. Kinematics are also used to estimate joint powers, muscle forces, and other quantities of interest that cannot typically be measured directly. Thus, the accuracy and reproducibility of IK calculations are critical. In this work, we isolate and quantify the uncertainty in joint angles, moments, and powers due to two sources of error during IK analyses: errors in the placement of markers on the model (marker registration) and errors in the dimensions of the model’s body segments (model scaling). We demonstrate that IK solutions are best presented as a distribution of equally probable trajectories when these sources of modeling uncertainty are considered. Notably, a substantial amount of uncertainty exists in the computed kinematics and kinetics even if low marker tracking errors are achieved. For example, considering only 2 cm of marker registration uncertainty, peak ankle plantarflexion angle varied by 15.9°, peak ankle plantarflexion moment varied by 26.6 N⋅m, and peak ankle power at push off varied by 75.9 W during healthy gait. This uncertainty can directly impact the classification of patient movements and the evaluation of training or device effectiveness, such as calculations of push-off power. We provide scripts in OpenSim so that others can reproduce our results and quantify the effect of modeling uncertainty in their own studies.

Decomposing crop model uncertainty: A systematic review

Crop models are essential tools for analysing the effects of climate variability, change on crop growth and development and the potential impact of adaptation strategies. Despite their increasing usage, crop model estimations have implicit uncertainties which are difficult to classify and quantify. Failure to address these uncertainties may result in poor advice to policymakers and stakeholders for the development of adaptation strategies. Since the 1990s, the number of crop model uncertainty assessments that consider different sources of model uncertainty (model structure, model parameters and model inputs such as climate, soil, and crop management practices) has increased significantly. We present the outcomes of a systematic review focused on uncertainty assessments of crop model outputs (mainly grain yield) and crop model uncertainty decomposition. We reviewed 277 articles from 1991 to 2019 which included studies conducted in 82 countries (460 locations) across all continents. 57% of the articles have been published between 2015 and 2019. 52% of the studies focus on input uncertainty assessments with climate change projections as the most frequently considered source of input uncertainty. Only 28% and 20% of the studies, respectively, dealt with uncertainties related to model parameters and model structure. The latter was mainly quantified using multi-model ensembles. Over half the studies were carried out in European and Asian countries, 34% and 23%, respectively. Most articles estimated model uncertainty focusing on the grain yield of major cereal crops (wheat > maize > rice) using the Decision Support System for Agrotechnology Transfer (DSSAT) model. Sensitivity analysis was the most used technique to quantify the contribution of different sources of uncertainty although the range of approaches for uncertainty quantification was wide. There is a need for standard procedures to estimate crop model uncertainty and evaluate estimates. We discuss the challenges of quantifying the components of uncertainty within crop models and identify research needs to better understand sources of uncertainty and thus improve the accuracy of crop models.

Risk-based flood adaptation assessment for large-scale buildings in coastal cities using cloud computing

• A risk-based flood adaptation model was developed and investigated in the cloud computing system • Both global and local sensitivity analysis were conducted to show sensitivity of model parameters • Adaptation scenarios were designed to incorporate life-cycle cost and benefits of adaptation, social vulnerability, and public adaptation policies • Public adaptation with seawall and enforced building elevation policy within flood zones could substantially reduce building damages Flood risk management (FRM) in coastal cities is a challenging task due to uncertain climate hazards under sea-level rise (SLR) and large-scale vulnerable buildings within in the floodplain. This study presents a building-level adaptation framework to evaluate alternative community adaptation strategies relying on cloud computing. We incorporated multiple sources of model uncertainties and randomly generated storm surges in each year of simulation using the extreme value distribution (GEV) theory. Based on a case study in Miami-Dade County, Florida, four adaptation scenarios were designed to evaluate their effectiveness in adaptation. Our sensitivity analysis suggested a positive linear relationship between community flood risk reduction and total community adaptation costs in the life-cycle cost-benefit (LCCB) model. Our results showed that uncertainties of the total community damage based on the LCCB model ranges from $ 221 million to $ 2.75 billion. However, when considering social vulnerability, the total community damage increased substantially, ranging from $ 244 million to $ 3.44 billion. Nevertheless, a 6ft public seawall based on the upper bound of the GEV distribution with the enforced building elevation policy in flood zones could substantially reduce community flood damage under uncertain sea-level rises.

Assessing the importance of bi-directional melting when modeling boreal peatland freeze/thaw dynamics

The modeling of seasonal ground ice (SGI) freeze/thaw a common feature in boreal peatlands, has often been completed using a unidirectional approach, where melting is driven by energy inputs from the surface. However, bi-directional melt is known to occur, and can potentially increase the spring melt rate. Accurate modelling of the timing of ice-free conditions in peatlands is important because SGI can impede spring infiltration and lead to substantial spring snowmelt runoff from peatlands. However, when modelling melt only from above, erroneous results in the model estimation of ice-free conditions can occur, which can lead to knock on-effects for modelling peatland hydrological function. Furthermore, as the climate warms, it is unclear how this role of SGI may change in the future. This study used the Stefan Equation to model unidirectional and bi-directional melt to assess which performed better in modelling the timing of ice-free conditions compared to observed values (BI: 3.9 ± 2.1 days, UNI: 9.0 ± 4.7). Including bi-directional melt improved model performance by reducing this difference by approximately 5 days. Model performance for SGI freeze/thaw cycles were similar, with BI being slightly more accurate in freezing (RMSE:2.7 cm versus 3.3 cm) and melting (RMSE: 2.6 cm vs 3.7 cm) compared to the unidirectional approach. While the model improvement in the timing of ice-free conditions was substantial, careful consideration is needed in determining when a peatland is functionally ice free in future modelling studies. The Stefan Equation was found to be most sensitive to changes in soil moisture, compared to ground surface temperature and peat porosity, likely due to the relationship between thermal conductivity and frozen and liquid water content. Comparisons with future climate change projections suggest that the timing of ice-free conditions could shift by as much as 2 weeks earlier in the 2050′s and by almost a month earlier in the 2080′s. However, the timing of snowfall, and rain on snow events continues to be a source of model uncertainty. Future studies should work to investigate the potential positive feedbacks this could create. In conclusion, the Stefan Equation presents a relatively easy path for incorporating bi-directional melt into peatland models. This process should be included in peatland ecohydrological models in order to properly model the timing of melt and ice-free conditions.

Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models: a case study for biogenic emissions from EURAD-IM version 5

Abstract. Atmospheric chemical forecasts heavily rely on various model parameters, which are often insufficiently known, such as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties with an ensemble of forecasts is impaired by the high dimensionality of the system. This study presents a novel approach, which substitutes the problem into a low-dimensional subspace spanned by the leading uncertainties. It is based on the idea that the forecast model acts as a dynamical system inducing multivariate correlations of model uncertainties. This enables an efficient perturbation of high-dimensional model parameters according to their leading coupled uncertainties. The specific algorithm presented in this study is designed for parameters that depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen–Loéve expansion. Due to their perceived simulation challenge, the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state that highly correlated uncertainties of regional biogenic emissions can be represented by a low number of dominant components. Depending on the required level of detail, leading parameter uncertainties with dimensions of 𝒪(106) can be represented by a low number of about 10 ensemble members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

Assessing errors during simulation configuration in crop models – A global case study using APSIM-Potato

Crop models are usually developed using a test set of data and simulations representing a range of environment, soil, management and genotype combinations. Previous studies demonstrated that errors in the configuration of test simulations and aggregation of observed data sets are common and can cause major problems for model development. However, the extent and effect of such errors using Agricultural Production system SIMulator Next Generation (APSIM) crop models are not usually considered as a source of model uncertainty. This is a methodological paper describing several approaches for testing the APSIM simulation configuration to detect anomalies in the input and observed data. In this study, we assess the simulation configuration process through (i) quality control analysis based on a standardised climate dataset (ii) outlier identification and (iii) a palette of visualization tools. A crop model – APSIM-Potato is described to demonstrate the main sources of error during the simulation configuration and data collation processes. Input data from 426 experiments conducted from 1970 to 2019 in 19 countries were collected and configured to run a model simulation. Plots were made comparing simulation configuration data and observed data across the entire test set so these values could be checked relative to others in the test set and with independent datasets. Errors were found in all steps of the simulation configuration process (climate, soil, crop management and observed data). We identified a surprising number of errors and inappropriate assumptions that had been made which could influence model predictions. The approach presented here moved the bulk of the effort from fitting model processes to setting up broad simulation configuration testing and detailed interrogation to identify current gaps for further model development.