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At least 181 records · Page 10

Can Simulation Credibility Be Improved Using Sensitivity Analysis to Understand Input Data Effects on Model Outcome?

Model and simulation (MS) credibility is defined as, the quality to elicit belief or trust in MS results. NASA-STD-7009 [1] delineates eight components (Verification, Validation, Input Pedigree, Results Uncertainty, Results Robustness, Use History, MS Management, People Qualifications) that address quantifying model credibility, and provides guidance to the model developers, analysts, and end users for assessing the MS credibility. Of the eight characteristics, input pedigree, or the quality of the data used to develop model input parameters, governing functions, or initial conditions, can vary significantly. These data quality differences have varying consequences across the range of MS application. NASA-STD-7009 requires that the lowest input data quality be used to represent the entire set of input data when scoring the input pedigree credibility of the model. This requirement provides a conservative assessment of model inputs, and maximizes the communication of the potential level of risk of using model outputs. Unfortunately, in practice, this may result in overly pessimistic communication of the MS output, undermining the credibility of simulation predictions to decision makers. This presentation proposes an alternative assessment mechanism, utilizing results parameter robustness, also known as model input sensitivity, to improve the credibility scoring process for specific simulations.

Credibility↗

Towards a Robust Sampling Approach: A Computational Review and Design

As pointed out in several other works, the estimation of the reliability of the electrical grid can not be conducted without the estimation of the stochastic phenomena of electicity demand and electricity production by variable renewable sources. Therefore, sampling procedures have become integral in the design of engineering structures and analysis. Commonly referred to as Monte Carlo uncertainty analysis or integration, the general objective of these procedures is to establish specifics about the uncertainty of an output characteristic of such an engineering system, given uncertainty about its input characteristics. These sampling procedures are applied in a context in which establishing such specifics cannot be performed through other means. Variance-reduction techniques are designed to lessen the variability among estimators to estimate statistics of those output uncertainties. Importance-sampling techniques, on the other hand, are designed to reduce the number of samples needed to estimate a particular statistic—e.g., a tail probability. The combination of these approaches can reduce the computational burden considerably for a particular estimator and statistic. Importance sampling—geared and designed as it is toward improving a particular estimator—suffers, unfortunately, from the unintended consequence of reducing the performance of other estimators in terms of their variance. The objective of this paper is to offer an alternative sampling procedure where this variance does not grow unacceptably large for a suite of estimators. Moreover, it is anticipated that, with additional knowledge of how an engineering output characteristic responds to its input characteristics, tuning parameters of the input’s sampling procedure can be set to improve the output characteristic’s estimation. This work proves the effectiveness of the suggested alternative approach. Such positive outcome will lead to a decrease of the computational burden of performing stochastic optimization of integrated energy systems (e.g., components dispatch, and portfolio composition). In particular, capturing the contribution to the overall system cost of rare and unlikely events and patterns of the electricity demand and production will become less computationally expensive. This is due to the fact that the approach demonstrated here will allow the sampling of those rare occurrences more frequently without misrepresenting their probabilistic impacts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Statistics-Based Material Property Analysis to Support TPS Characterization

Accurate characterization of entry capsule heat shield material properties is a critical component in modeling and simulating Thermal Protection System (TPS) response in a prescribed aerothermal environment. The thermal decomposition of the TPS material during the pyrolysis and charring processes is poorly characterized and typically results in large uncertainties in material properties as inputs for ablation models. These material property uncertainties contribute to large design margins on flight systems and cloud re- construction efforts for data collected during flight and ground testing, making revision to existing models for entry systems more challenging. The analysis presented in this work quantifies how material property uncertainties propagate through an ablation model and guides an experimental test regimen aimed at reducing these uncertainties and characterizing the dependencies between properties in the virgin and charred states for a Phenolic Impregnated Carbon Ablator (PICA) based TPS. A sensitivity analysis identifies how the high-fidelity model behaves in the expected flight environment, while a Monte Carlo based uncertainty propagation strategy is used to quantify the expected spread in the in-depth temperature response of the TPS. An examination of how perturbations to the input probability density functions affect output temperature statistics is accomplished using a Kriging response surface of the high-fidelity model. Simulations are based on capsule configuration and aerothermal environments expected during the Mars Science Laboratory (MSL) entry sequence. We identify and rank primary sources of uncertainty from material properties in a flight-relevant environment, show the dependence on spatial orientation and in-depth location on those uncertainty contributors, and quantify how sensitive the expected results are.

Copeland, Sean R.↗

Computational Workflows for Uncertainty-Quantified Nuclear Reactions: From Nuclear Theory Inputs to Astrophysical Reaction Rates

Reactions on unstable nuclei, particularly those on the neutron-rich side of stability, are important for both fundamental and applied physics. For fundamental science, the most prevalent use case is astrophysi cal nucleosynthesis by rapid neutron capture—the r-process—by which heavy nuclei are formed in extreme astrophysical environments, such as in supernovae and neutron star mergers; see, e.g., Refs. [1–3]. For ap plications, these processes are relevant for the interpretation of radiochemical data from historic nuclear tests, which contribute to our ability to certify the enduring stockpile in the absence of nuclear testing [4]; see Ref. [5] for a broader discussion of applications. However, reaction cross sections involving unsta ble species are generally poorly understood, for the simple reason that useful data become scarce as one moves away from stability. While there are avenues for improving the amount and quality of data for these species [6], one is fundamentally reliant on nuclear theory to make progress on these fields of study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Design of the hybrid automated reliability predictor

The design of the Hybrid Automated Reliability Predictor (HARP), now under development at Duke University, is presented. The HARP approach to reliability prediction is characterized by a decomposition of the overall model into fault-occurrence and fault-handling sub-models. The fault-occurrence model is a non-homogeneous Markov chain which is solved analytically, while the fault-handling model is a Petri Net which is simulated. HARP provides automated analysis of sensitivity to uncertainties in the input parameters and in the initial state specifications. It then produces a predicted reliability band as a function of mission time, as well as estimates of the improvement (narrowing of the band) to be gained by a specified amount of reduction in uncertainty.

Geist, R.↗

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗

Uncertainty Analysis of Consequence Management Data Products

An interlaboratory effort has developed a probabilistic framework to characterize uncertainty in data products that are developed by the US Department of Energy Consequence Management Program in support of the Federal Radiological Monitoring and Assessment Center. The purpose of this paper is to provide an overview of the probability distributions of input variables and the statistical methods used to propagate and quantify the overall uncertainty of the derived response levels that are used as contours on data products due to the uncertainty in input parameters. Uncertainty analysis results are also presented for several study scenarios. This paper includes an example data product to illustrate the potential real-world implications of incorporating uncertainty analysis results into data products that inform protective action decisions. Data product contours that indicate areas where public protection actions may be warranted can be customized to an acceptable level of uncertainty. Finally, the investigators seek feedback from decision makers and the radiological emergency response community to determine how uncertainty information can be used to support the protective action decision-making process and how it can be presented on data products.

61 RADIATION PROTECTION AND DOSIMETRY↗

Role of Forcing Uncertainty and Background Model Error Characterization in Snow Data Assimilation

Accurate specification of the model error covariances in data assimilation systems is a challenging issue. Ensemble land data assimilation methods rely on stochastic perturbations of input forcing and model prognostic fields for developing representations of input model error covariances. This article examines the limitations of using a single forcing dataset for specifying forcing uncertainty inputs for assimilating snow depth retrievals. Using an idealized data assimilation experiment, the article demonstrates that the use of hybrid forcing input strategies (either through the use of an ensemble of forcing products or through the added use of the forcing climatology) provide a better characterization of the background model error, which leads to improved data assimilation results, especially during the snow accumulation and melt-time periods. The use of hybrid forcing ensembles is then employed for assimilating snow depth retrievals from the AMSR2 (Advanced Microwave Scanning Radiometer 2) instrument over two domains in the continental USA with different snow evolution characteristics. Over a region near the Great Lakes, where the snow evolution tends to be ephemeral, the use of hybrid forcing ensembles provides significant improvements relative to the use of a single forcing dataset. Over the Colorado headwaters characterized by large snow accumulation, the impact of using the forcing ensemble is less prominent and is largely limited to the snow transition time periods. The results of the article demonstrate that improving the background model error through the use of a forcing ensemble enables the assimilation system to better incorporate the observational information.

assimilation↗

Modelling Freshwater Resources at the Global Scale: Challenges and Prospects

Quantification of spatially and temporally resolved water flows and water storage variations for all land areas of the globe is required to assess water resources, water scarcity and flood hazards, and to understand the Earth system. This quantification is done with the help of global hydrological models (GHMs). What are the challenges and prospects in the development and application of GHMs? Seven important challenges are presented. (1) Data scarcity makes quantification of human water use difficult even though significant progress has been achieved in the last decade. (2) Uncertainty of meteorological input data strongly affects model outputs. (3) The reaction of vegetation to changing climate and CO2 concentrations is uncertain and not taken into account in most GHMs that serve to estimate climate change impacts. (4) Reasons for discrepant responses of GHMs to changing climate have yet to be identified. (5) More accurate estimates of monthly time series of water availability and use are needed to provide good indicators of water scarcity. (6) Integration of gradient-based groundwater modelling into GHMs is necessary for a better simulation of groundwater-surface water interactions and capillary rise. (7) Detection and attribution of human interference with freshwater systems by using GHMs are constrained by data of insufficient quality but also GHM uncertainty itself. Regarding prospects for progress, we propose to decrease the uncertainty of GHM output by making better use of in situ and remotely sensed observations of output variables such as river discharge or total water storage variations by multi-criteria validation, calibration or data assimilation. Finally, we present an initiative that works towards the vision of hyper resolution global hydrological modelling where GHM outputs would be provided at a 1-km resolution with reasonable accuracy.

Global hydrological model↗

Sources of Uncertainty in the Prediction of LAI / fPAR from MODIS

To explicate the sources of uncertainty in the prediction of biophysical variables over space, consider the general equation: where z is a variable with values on some nominal, ordinal, interval or ratio scale; y is a vector of input variables; u is the spatial support of y and z ; x and u are the spatial locations of y and z , respectively; f is a model and B is the vector of the parameters of this model. Any y or z has a value and a spatial extent which is called its support. Viewed in this way, categories of uncertainty are from variable (e.g. measurement), parameter, positional. support and model (e.g. structural) sources. The prediction of Leaf Area Index (LAI) and the fraction of absorbed photosynthetically active radiation (fPAR) are examples of z variables predicted using model(s) as a function of y variables and spatially constant parameters. The MOD15 algorithm is an example of f, called f(sub 1), with parameters including those defined by one of six biome types and solar and view angles. The Leaf Canopy Model (LCM)2, a nested model that combines leaf radiative transfer with a full canopy reflectance model through the phase function, is a simpler though similar radiative transfer approach to f(sub 1). In a previous study, MOD15 and LCM2 gave similar results for the broadleaf forest biome. Differences between these two models can be used to consider the structural uncertainty in prediction results. In an effort to quantify each of the five sources of uncertainty and rank their relative importance for the LAI/fPAR prediction problem, we used recent data for an EOS Core Validation Site in the broadleaf biome with coincident surface reflectance, vegetation index, fPAR and LAI products from the Moderate Resolution Imaging Spectrometer (MODIS). Uncertainty due to support on the input reflectance variable was characterized using Landsat ETM+ data. Input uncertainties were propagated through the LCM2 model and compared with published uncertainties from the MOD15 algorithm.

Dungan, Jennifer L.↗

Uncertainty and Sensitivity Analyses of a Two-Parameter Impedance Prediction Model

This paper presents comparisons of predicted impedance uncertainty limits derived from Monte-Carlo-type simulations with a Two-Parameter (TP) impedance prediction model and measured impedance uncertainty limits based on multiple tests acquired in NASA Langley test rigs. These predicted and measured impedance uncertainty limits are used to evaluate the effects of simultaneous randomization of each input parameter for the impedance prediction and measurement processes. A sensitivity analysis is then used to further evaluate the TP prediction model by varying its input parameters on an individual basis. The variation imposed on the input parameters is based on measurements conducted with multiple tests in the NASA Langley normal incidence and grazing incidence impedance tubes; thus, the input parameters are assigned uncertainties commensurate with those of the measured data. These same measured data are used with the NASA Langley impedance measurement (eduction) processes to determine the corresponding measured impedance uncertainty limits, such that the predicted and measured impedance uncertainty limits (95% confidence intervals) can be compared. The measured reactance 95% confidence intervals encompass the corresponding predicted reactance confidence intervals over the frequency range of interest. The same is true for the confidence intervals of the measured and predicted resistance at near-resonance frequencies, but the predicted resistance confidence intervals are lower than the measured resistance confidence intervals (no overlap) at frequencies away from resonance. A sensitivity analysis indicates the discharge coefficient uncertainty is the major contributor to uncertainty in the predicted impedances for the perforate-over-honeycomb liner used in this study. This insight regarding the relative importance of each input parameter will be used to guide the design of experiments with test rigs currently being brought on-line at NASA Langley.

Jones, M. G.↗

Determination of Uncertainties for Analytically Derived Material Properties to Be Used in Monte Carlo Based Orion Heatshield Sizing

Ablative materials are often used for spacecraft heatshields to protect underlying structures from the extreme environments associated with atmospheric reentry. NASA's Orion EM-1 capsule has been designed to use a molded Avcoat material system. In order to determine the required heatshield thickness, a Monte Carlo approach to the sizing process was proposed. To perform the Monte Carlo simulation, statistical uncertainties on all material property input parameters were required. Obtaining these values for measured properties is straightforward, however input parameters that are derived analytically have historically used uncertainties based on engineering judgment. A MATLAB program was created to use laboratory generated thermogravimetric analysis (TGA) data to calculate uncertainties on the Arrhenius parameters for molded Avcoat. Uncertainties associated with the normalized ablation rate and pyrolysis gas enthalpy were also generated using a wrapper script and the ACE code. These uncertainties could then be tied directly to measured values of individual elemental constituents. The resulting uncertainty values will allow for a probabilistic sizing approach on molded Avcoat with a higher level of confidence in the input parameters.

material property uncertainties↗

Evaluation of satellite Leaf Area Index in California vineyards for improving water use estimation

Remote sensing estimation of evapotranspiration (ET) directly quantifies plant water consumption and provides essential information for irrigation scheduling, which is a pressing need for California vineyards as extreme droughts become more frequent. Many ET models take satellite-derived Leaf Area Index (LAI) as a major input, but how uncertainties of LAI estimations propagate to ET and the partitioning between evaporation and transpiration is poorly understood. Here we assessed six satellite-based LAI estimation approaches using Landsat and Sentinel-2 images against ground measurements from four vineyards in California and evaluated ET sensitivity to LAI in the thermal-based two-source energy balance (TSEB) model. We found that radiative transfer modeling-based approaches predicted low to medium LAI well, but they significantly underestimated high LAI in highly clumped vine canopies (RMSE ~ 0.97 to 1.27). Cubist regression models trained with ground LAI measurements from all vineyards achieved high accuracy (RMSE ~ 0.3 to 0.48), but these empirical models did not generalize well between sites. Red edge bands and the related vegetation index (VI) from the Sentinel-2 satellite contain complementary information of LAI to VIs based on near-infrared and red bands. TSEB ET was more sensitive to positive LAI biases than negative ones. Positive LAI errors of 50% resulted in up to 50% changes in ET, while negative biases of 50% in LAI caused less than 10% deviations in ET. However, even when ET changes were minimal, negative LAI errors of 50% led to up to a 40% reduction in modeled transpiration, as soil evaporation and plant transpiration responded to LAI change divergently. These findings call for careful consideration of satellite LAI uncertainties for ET modeling, especially for the partitioning of water loss between vine and soil or cover crop for effective vineyard irrigation management.

54 ENVIRONMENTAL SCIENCES↗

Development of a U-19Pu-10Zr fuel performance benchmark case based on the IFR-1 experiment

Metallic nuclear fuels are subject to research and development for use in advanced reactors. Robust, accurate metallic fuel performance models are important for the design, safety analysis, and licensing of these reactors. However, metallic fuel performance models require additional development; they are not as mature as UO 2 fuel performance models. A benchmark case based on the IFR-1 experiment was developed to better gauge the accuracy of existing models, identify models for high-priority development, and potentially quantify any future improvements made by further model development.This work collected publicly available information on the IFR-1 experiment and used it to develop the benchmark case. Fuel behavior during the IFR-1 irradiation was simulated by using the fuel performance code BISON, and the predicted results were compared with postirradiation examination data from the IFR-1 experiment. Furthermore, a sensitivity study and tuning studies were performed as a preliminary investigation into the causes of inaccurate temperature and dimensional change predictions.The benchmark predicted reasonably accurate values for the burnup and fission gas release. There was error in the predicted temperatures, which could be explained by uncertainty in the input parameters and legacy temperatures. BISON over-predicted dimensional changes in the fuel and cladding. The sensitivity study showed that the dimensional changes were most sensitive to the fuel swelling anisotropy and the cladding void swelling model. Future benchmark and model development should focus on cladding swelling behaviors to improve dimensional change predictions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A quantitative risk assessment framework for fault reactivation in underground hydrogen storage: Coupled simulation and deep learning approach

Underground hydrogen storage (UHS) is emerging as a critical solution for large-scale energy storage. However, like all subsurface fluid injection activities, UHS poses the risk of injection-induced fault reactivation. Accurate risk assessment is essential to ensuring the safety and efficiency of UHS operations. This study presents the development of deep-learning surrogate models for fault reactivation prediction in UHS, trained on a comprehensive database of fully coupled fluid flow-geomechanics simulations. Our findings reveal that analytical models often yield unreliable estimates, with errors up to 54% in the allowable injection pressure, potentially leading to a 40% reduction in UHS operational capacity. The developed surrogate models were incorporated into a quantitative risk assessment (QRA) framework, enabling probabilistic evaluation of fault reactivation risk while accounting for uncertainties in the input variables. Site-specific features, such as horizontal stress gradients, fault’s dip and strike angles, and operational parameters like bottom-hole injection pressure and well-fault distance, were identified as the primary drivers of fault reactivation across various stress regimes. Whereas other hydraulic, geological, and poroelastic reservoir properties were found to have a secondary impact. Notably, we observed that the risk of fault reactivation for a critically oriented fault with a static friction coefficient greater than 0.55 remains below 10% in a normal faulting stress regime. However, the risk significantly increases as the stress regime transitions from normal to strike-slip and ultimately to reverse faulting conditions. These findings underscore the importance of rigorous site characterization and comprehensive QRA evaluations to optimize UHS performance and minimize geomechanical risks.

25 ENERGY STORAGE↗

Robust cooperative control strategy for a platoon of connected and autonomous vehicles against sensor errors and control errors simultaneously in a real-world driving environment

In a real-world driving environment, a platoon of connected and autonomous vehicles (CAVs) is subject to many internal and external disturbances, resulting in uncertain vehicle dynamics. In general, the disturbances can be categorized into two types: disturbances due to vehicle sensor errors (e.g., GPS error) and disturbances due to vehicle control errors (e.g., actuator delay). In the literature, many control strategies have been proposed to improve the robustness of the CAV platoon against uncertain vehicle dynamics induced by these disturbances. However, most of these strategies only consider one type of disturbance and cannot tackle both types of disturbances simultaneously. Furthermore, they are designed to maximize the benefits of each vehicle in the platoon independently, which can deteriorate the performance of the platoon. Here, to address these problems, this study proposes a robust cooperative control (RCC) strategy to maneuver the vehicles in the platoon cooperatively to counteract the impacts of both types of disturbances. The RCC strategy is developed based on a minimax problem, where the maximization subproblem seeks to find the worst inputs for the uncertainty terms in the vehicle dynamics equation to minimize the platoon performance, while the minimization subproblem seeks to find the optimal control decisions for all subsequent vehicles to maximize the platoon performance in the worst case. To solve the minimax problem, this study proposes a globally convergent solution algorithm. It can solve the minimax problem very efficiently to enable real time deployment of the RCC strategy. Numerical application indicates that compared to the existing methods, the RCC strategy can dramatically improve the robustness of the CAV platoon against the uncertain vehicle dynamics induced by both vehicle state detection errors and vehicle control errors. Therefore, it can maneuver the CAV platoon safely and efficiently in a real-world driving environment.

33 ADVANCED PROPULSION SYSTEMS↗

Fusion of Multiple Models for Improving Gross Primary Production Estimation With Eddy Covariance Data Based on Machine Learning

Abstract Terrestrial gross primary production (GPP) represents the magnitude of CO 2 uptake through vegetation photosynthesis, and is a key variable for carbon cycles between the biosphere and atmosphere. Light use efficiency (LUE) models have been widely used to estimate GPP for its physiological mechanisms and availability of data acquisition and implementation, yet each individual GPP model has exhibited large uncertainties due to input errors and model structure, and further studies of systematic validation, comparison, and fusion of those models with eddy covariance (EC) site data across diverse ecosystem types are still needed in order to further improve GPP estimation. We here compared and fused five GPP models (VPM, EC‐LUE, GOL‐PEM, CHJ, and C‐Fix) across eight ecosystems based on FLUXNET2015 data set using the ensemble methods of Bayesian Model Averaging (BMA), Support Vector Machine (SVM), and Random Forest (RF) separately. Our results showed that for individual models, EC‐LUE gave a better performance to capture interannual variability of GPP than other models, followed by VPM and GLO‐PEM, while CHJ and C‐Fix were more limited in their estimation performance. We found RF and SVM were superior to BMA on merging individual models at various plant functional types (PFTs) and at the scale of individual sites. On the basis of individual models, the fusion methods of BMA, SVM, and RF were examined by a five‐fold cross validation for each ecosystem type, and each method successfully improved the average accuracy of estimation by 8%, 18%, and 19%, respectively.

Environmental Sciences & Ecology↗

Numerical Investigation of Observational Flux Partitioning Methods for Water Vapor and Carbon Dioxide

Abstract While yearly budgets of CO 2 flux (F c ) and evapotranspiration (ET) above vegetation can be readily obtained from eddy‐covariance measurements, the separate quantification of their soil (respiration and evaporation) and canopy (photosynthesis and transpiration) components remains an elusive yet critical research objective. In this work, we investigate four methods to partition observed total fluxes into soil and plant sources: two new and two existing approaches that are based solely on analysis of conventional high frequency eddy‐covariance (EC) data. The physical validity of the assumptions of all four methods, as well as their performance under different scenarios, are tested with the aid of large‐eddy simulations, which are used to replicate eddy‐covariance field experiments. Our results indicate that canopies with large, exposed soil patches increase the mixing and correlation of scalars; this negatively impacts the performance of the partitioning methods, all of which require some degree of uncorrelatedness between CO 2 and water vapor. In addition, best performances for all partitioning methods were found when all four flux components are non‐negligible, and measurements are collected close to the canopy top. Methods relying on the water‐use efficiency (W) perform better whenWis known a priori, but are shown to be very sensitive to uncertainties in this input variable especially when canopy fluxes dominate. We conclude by showing how the correlation coefficient between CO 2 and water vapor can be used to infer the reliability of differentWparameterizations.

Environmental Sciences & Ecology↗