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At least 163 records · Page 9

A Priori Subgrid Scale Modeling for a Droplet Laden Temporal Mixing Layer

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using a direct numerical simulation (DNS) database. The DNS is for a Reynolds number (based on initial vorticity thickness) of 600, with droplet mass loading of 0.2. The gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. Since Large Eddy Simulation (LES) of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be given by the filtered variables plus a correction based on the filtered standard deviation, which can be computed from the sub-grid scale (SGS) standard deviation. This model predicts unfiltered variables at droplet locations better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: Smagorinsky, gradient and scale-similarity. When properly calibrated, the gradient and scale-similarity methods give results in excellent agreement with the DNS.

Okongo, Nora↗

Initialized Earth system prediction from subseasonal to decadal timescales

Initialized Earth system predictions are made by starting a numerical prediction model in a state as consistent as possible to observations, and running it forward in time for up to ten years. Skillful predictions at time slices from subseasonal to seasonal (S2S), seasonal to interannual (S2I) and seasonal to decadal (S2D) offer information useful for various stakeholders, from agriculture to water resource management, and human and infrastructure safety. In this Review, we examine the processes influencing predictability, and discuss estimates of skill across S2S, S2I and S2D timescales. There are encouraging signs that skillful predictions can be made: at S2S timescales, there has been some skill in predicting the Madden-Julian Oscillation and North Atlantic Oscillation; at S2I in predicting the El Niño-Southern Oscillation; and at S2D, in predicting variability in North Atlantic sea surface temperatures. However, challenges remain, and future work must prioritise reducing model error, more effectively communicating forecasts to users, and increasing process and mechanistic understanding that could increase predictive skill and, in turn, confidence. As numerical models progress towards Earth system models, initialized predictions are expanding to include prediction of sea-ice, air pollution, terrestrial and ocean biochemistry which can bring clear benefit to society and various stakeholders.

climate prediction↗

An Assessment of the Potential Predictability of Interannual and Decadal Variability Based on Climate Model Simulations with Specified SST

The USCLIVAR working group on drought recently initiated a series of global climate model simulations forced with idealized SST anomaly patterns, designed to address a number of uncertainties regarding the impact of SST forcing and the role of land-atmosphere feedbacks on regional drought. The runs were done with several global atmospheric models including NASA/NSIPP-1, NCEP/GFS, GFDL/AM2, and NCAR CCM3 and CAM3.5. Here we focus on the potential predictability associated with the leading patterns of inter-annual and decadal Pacific SST variability. Specific issues addressed include the nature of the seasonality and regionality of the signal, the noise, and the signal-to-noise ratios, as well as the dependence of the results on the models.

Schubert, Siegfried↗

Parametric Studies of Flow Separation using Air Injection

Boundary Layer separation causes the airfoil to stall and therefore imposes dramatic performance degradation on the airfoil. In recent years, flow separation control has been one of the active research areas in the field of aerodynamics due to its promising performance improvements on the lifting device. These active flow separation control techniques include steady and unsteady air injection as well as suction on the airfoil surface etc. This paper will be focusing on the steady and unsteady air injection on the airfoil. Although wind tunnel experiments revealed that the performance improvements on the airfoil using injection techniques, the details of how the key variables such as air injection slot geometry and air injection angle etc impact the effectiveness of flow separation control via air injection has not been studied. A parametric study of both steady and unsteady air injection active flow control will be the main objective for this summer. For steady injection, the key variables include the slot geometry, orientation, spacing, air injection velocity as well as the injection angle. For unsteady injection, the injection frequency will also be investigated. Key metrics such as lift coefficient, drag coefficient, total pressure loss and total injection mass will be used to measure the effectiveness of the control technique. A design of experiments using the Box-Behnken Design is set up in order to determine how each of the variables affects each of the key metrics. Design of experiment is used so that the number of experimental runs will be at minimum and still be able to predict which variables are the key contributors to the responses. The experiments will then be conducted in the 1ft by 1ft wind tunnel according to the design of experiment settings. The data obtained from the experiments will be imported into JMP, statistical software, to generate sets of response surface equations which represent the statistical empirical model for each of the metrics as a function of the key variables. Next, the variables such as the slot geometry can be optimized using the build-in optimizer within JMP. Finally, a wind tunnel testing will be conducted using the optimized slot geometry and other key variables to verify the empirical statistical model. The long term goal for this effort is to assess the impacts of active flow control using air injection at system level as one of the task plan included in the NASAs URETI program with Georgia Institute of Technology.

Zhang, Wei↗

Reconstructing Subgrid Cloud Variability Guided by CloudSat/CALIPSO Observations

Predicting realistic cloud subgrid variability remains a challenge for Global Climate Models (GCMs) even though it can play an important role for proper representation of processes pertaining to cloud microphysics, precipitation, and radiation, but also for comparisons with satellite observations which are of much higher resolution than model grids. The diagnostic approach of subgrid cloud variability is commonly handled by subcolumn cloud generators. For a specific GCM, one ideally wants the subgrid variability used for comparisons with satellite observations to be created by the same generator and with the same rules as the one used for model integration. With this in mind, we have embarked in an effort to test and improve cloud subcolumn generators appropriate for GCMs. For this purpose, we use cloud (hydrometeor) products from active observations by the CloudSat radar (CPR) and the CALIPSO lidar (CALIOP). Cloud products from active sensors while suffering significant sampling and coverage drawbacks have the advantage of resolving both horizontal and vertical variability. The main question is: given a profile of cloud condensate mean and variance, can we create a subgrid cloud field that is statistically similar to the observed subgrid cloud field? By “statistically”, we suggest that we do not aspire to reproduce “well” each individual subgrid cloud field of a GCM-scale region, but that our generator performs well for a large ensemble of cases. We simulate radar, passive imager, and radiation flux fields from the observed 2D cloud fields and create one-point statistics; we use the profiles of cloud condensate mean and variance as input to the generator to create subgrid cloud fields; we compare the statistics; we adjust the rules of the generator to create the best possible agreement between the radar, imager and radiation field statistics. In this process, the active observations have actually a dual role: they provide the actual subgrid cloud field which can be reduced to a profile of mean and variance used by the subcolumn generator, but they also provide the rules needed by the generator, such as measures (e.g, decorrelation length) of the vertical overlap of cloud fraction and of the condensate horizontal variability. This presentation will show our progress using Cloudsat and CALIPSO products in this dual fashion.

cloud↗

Reconstructing Subgrid Cloud Variability Guided by CloudSat/CALIPSO Observations

Predicting realistic cloud subgrid variability remains a challenge for Global Climate Models (GCMs) even though it can play an important role for proper representation of processes pertaining to cloud microphysics, precipitation, and radiation, but also for comparisons with satellite observations which are of much higher resolution than model grids. The diagnostic approach of subgrid cloud variability is commonly handled by subcolumn cloud generators. For a specific GCM, one ideally wants the subgrid variability used for comparisons with satellite observations to be created by the same generator and with the same rules as the one used for model integration. With this in mind, we have embarked in an effort to test and improve cloud subcolumn generators appropriate for GCMs. For this purpose, we use cloud (hydrometeor) products from active observations by the CloudSat radar (CPR) and the CALIPSO lidar (CALIOP). Cloud products from active sensors while suffering signi􀂦cant sampling and coverage drawbacks have the advantage of resolving both horizontal and vertical variability. The main question is: given a profile of cloud condensate mean and variance, can we create a subgrid cloud field that is statistically similar to the observed subgrid cloud field? By “statistically”, we suggest that we do not aspire to reproduce “well” each individual subgrid cloud field of a GCM-scale region, but that our generator performs well for a large ensemble of cases. We simulate radar, passive imager, and radiation flux fields from the observed 2D cloud fields and create one-point statistics; we use the profiles of cloud condensate mean and variance as input to the generator to create subgrid cloud fields; we compare the statistics; we adjust the rules of the generator to create the best possible agreement between the radar, imager and radiation field statistics. In this process, the active observations have actually a dual role: they provide the actual subgrid cloud field which can be reduced to a profile of mean and variance used by the subcolumn generator, but they also provide the rules needed by the generator, such as measures (e.g, decorrelation length) of the vertical overlap of cloud fraction and of the condensate horizontal variability. This presentation will show our progress using Cloudsat and CALIPSO products in this dual fashion.

clouds↗

An Exploratory Approach Using Regression and Machine Learning in the Analysis of Mass Absorption Cross Section of Black Carbon Aerosols: Model Development and Evaluation

Mass absorption cross-section of black carbon (MAC BC ) describes the absorptive cross-section per unit mass of black carbon, and is, thus, an essential parameter to estimate the radiative forcing of black carbon. Many studies have sought to estimate MAC BC from a theoretical perspective, but these studies require the knowledge of a set of aerosol properties, which are difficult and/or labor-intensive to measure. We therefore investigate the ability of seven data analytical approaches (including different multivariate regressions, support vector machine, and neural networks) in predicting MAC BC for both ambient and biomass burning measurements. Our model utilizes multi-wavelength light absorption and scattering as well as the aerosol size distributions as input variables to predict MAC BC across different wavelengths. We assessed the applicability of the proposed approaches in estimating MAC BC using different statistical metrics (such as coefficient of determination (R 2 ), mean square error (MSE), fractional error, and fractional bias). Overall, the approaches used in this study can estimate MAC BC appropriately, but the prediction performance varies across approaches and atmospheric environments. Based on an uncertainty evaluation of our models and the empirical and theoretical approaches to predict MAC BC , we preliminarily put forth support vector machine (SVM) as a recommended data analytical technique for use. We provide an operational tool built with the approaches presented in this paper to facilitate this procedure for future users.

54 ENVIRONMENTAL SCIENCES↗

Identifying Key Drivers of Wildfires in the Contiguous US Using Machine Learning and Game Theory Interpretation

Abstract Understanding the complex interrelationships between wildfire and its environmental and anthropogenic controls is crucial for wildfire modeling and management. Although machine learning (ML) models have yielded significant improvements in wildfire predictions, their limited interpretability has been an obstacle for their use in advancing understanding of wildfires. This study builds an ML model incorporating predictors of local meteorology, land‐surface characteristics, and socioeconomic variables to predict monthly burned area at grid cells of 0.25° × 0.25° resolution over the contiguous United States. Besides these predictors, we construct and include predictors representing the large‐scale circulation patterns conducive to wildfires, which largely improves the temporal correlations in several regions by 14%–44%. The Shapley additive explanation is introduced to quantify the contributions of the predictors to burned area. Results show a key role of longitude and latitude in delineating fire regimes with different temporal patterns of burned area. The model captures the physical relationship between burned area and vapor pressure deficit, relative humidity (RH), and energy release component (ERC), in agreement with the prior findings. Aggregating the contribution of predictor variables of all the grids by region, analyses show that ERC is the major contributor accounting for 14%–27% to large burned areas in the western US. In contrast, there is no leading factor contributing to large burned areas in the eastern US, although large‐scale circulation patterns featuring less active upper‐level ridge‐trough and low RH two months earlier in winter contribute relatively more to large burned areas in spring in the southeastern US.

54 ENVIRONMENTAL SCIENCES↗

Predicting soil carbon changes in switchgrass grown on marginal lands under climate change and adaptation strategies

Abstract The United States Great Lakes Region (USGLR) is a critical geographic area for future bioenergy production. Switchgrass ( Panicum virgatum ) is widely considered a carbon (C)‐neutral or C‐negative bioenergy production system, but projected increases in air temperature and precipitation due to climate change might substantially alter soil organic C (SOC) dynamics and storage in soils. This study examined long‐term SOC changes in switchgrass grown on marginal land in the USGLR under current and projected climate, predicted using a process‐based model (Systems Approach to Land‐Use Sustainability) extensively calibrated with a wealth of plant and soil measurements at nine experimental sites. Simulations indicate that these soils are likely a net C sink under switchgrass (average gain 0.87 Mg C ha −1 year −1 ), although substantial variation in the rate of SOC accumulation was predicted (range: 0.2–1.3 Mg C ha −1 year −1 ). Principal component analysis revealed that the predicted intersite variability in SOC sequestration was related in part to differences in climatic characteristics, and to a lesser extent, to heterogeneous soils. Although climate change impacts on switchgrass plant growth were predicted to be small (4%–6% decrease on average), the increased soil respiration was predicted to partially negate SOC accumulations down to 70% below historical rates in the most extreme scenarios. Increasing N fertilizer rate and decreasing harvest intensity both had modest SOC sequestration benefits under projected climate, whereas introducing genotypes better adapted to the longer growing seasons was a much more effective strategy. Best‐performing adaptation scenarios were able to offset >60% of the climate change impacts, leading to SOC sequestration 0.7 Mg C ha −1 year −1 under projected climate. On average, this was 0.3 Mg C ha −1 year −1 more C sequestered than the no adaptation baseline. These findings provide crucial knowledge needed to guide policy and operational management for maximizing SOC sequestration of future bioenergy production on marginal lands in the USGLR.

09 BIOMASS FUELS↗

Measurement of charged-current $\nu_\mu$ and $\bar{\nu}_\mu$ cross sections on hydrocarbon in a shallow inelastic scattering region

This MINERvA analysis is the first neutrino and antineutrino study of a shallow inelastic scattering region, which is the transition region between resonant production and deep inelastic scattering processes. This transition is explicitly included in this study by expanding the scope of shallow inelastic scattering to include not only the mainly lower-$Q^2$ nonresonant pion production but also the kinematic region where pion production off quarks within the nucleon becomes significant with $Q^2$ below the onset of the deep-inelastic scattering region defined in this analysis. To reduce the resonance background the kinematic region 1.5 $<$$W$$<$ 2 GeV/$c^2$ was chosen. In addition to the inclusive differential cross section measurements, to emphasize SIS interactions off quarks within the nucleon a sample with $Q^2$$\geq$ 1 GeV/$c^2$ was also analyzed. The measurements of one-dimensional cross sections at $\left\langle E_\nu \right\rangle \sim 6$ GeV on hydrocarbon of $Q^2$, Bjorken x and muon momentum variables are compared with modified predictions from the GENIE 2 neutrino generator as well as predictions of other neutrino simulators GiBUU, NEUT, NuWro and an alternative GENIE 3 version. Significant discrepancies both in shape and magnitude between measurements and neutrino simulator predictions of all variables have been observed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The predictive information obtained by testing multiple software versions

Multiversion programming is a redundancy approach to developing highly reliable software. In applications of this method, two or more versions of a program are developed independently by different programmers and the versions are combined to form a redundant system. One variation of this approach consists of developing a set of n program versions and testing the versions to predict the failure probability of a particular program or a system formed from a subset of the programs. The precision that might be obtained, and also the effect of programmer variability if predictions are made over repetitions of the process of generating different program versions, are examined.

Lee, Larry D.↗

Variance and Predictability of Precipitation at Seasonal-to-Interannual Timescales

A series of atmospheric general circulation model (AGCM) simulations, spanning a total of several thousand years, is used to assess the impact of land-surface and ocean boundary conditions on the seasonal-to-interannual variability and predictability of precipitation in a coupled modeling system. In the first half of the analysis, which focuses on precipitation variance, we show that the contributions of ocean, atmosphere, and land processes to this variance can be characterized, to first order, with a simple linear model. This allows a clean separation of the contributions, from which we find: (1) land and ocean processes have essentially different domains of influence, i.e., the amplification of precipitation variance by land-atmosphere feedback is most important outside of the regions (mainly in the tropics) that are most affected by sea surface temperatures; and (2) the strength of land-atmosphere feedback in a given region is largely controlled by the relative availability of energy and water there. In the second half of the analysis, the potential for seasonal-to-interannual predictability of precipitation is quantified under the assumption that all relevant surface boundary conditions (in the ocean and on land) are known perfectly into the future. We find that the chaotic nature of the atmospheric circulation imposes fundamental limits on predictability in many extratropical regions. Associated with this result is an indication that soil moisture initialization or assimilation in a seasonal-to-interannual forecasting system would be beneficial mainly in transition zones between dry and humid regions.

Koster, Randal D.↗

Modeling Spatial Distribution of Snow Water Equivalent by Combining Meteorological and Satellite Data with Lidar Maps

Abstract An accurate characterization of the water content of snowpack, or snow water equivalent (SWE), is necessary to quantify water availability and constrain hydrologic and land surface models. Recently, airborne observations (e.g., lidar) have emerged as a promising method to accurately quantify SWE at high resolutions (scales of ∼100 m and finer). However, the frequency of these observations is very low, typically once or twice per season in the Rocky Mountains of Colorado. Here, we present a machine learning framework that is based on random forests to model temporally sparse lidar-derived SWE, enabling estimation of SWE at unmapped time points. We approximated the physical processes governing snow accumulation and melt as well as snow characteristics by obtaining 15 different variables from gridded estimates of precipitation, temperature, surface reflectance, elevation, and canopy. Results showed that, in the Rocky Mountains of Colorado, our framework is capable of modeling SWE with a higher accuracy when compared with estimates generated by the Snow Data Assimilation System (SNODAS). The mean value of the coefficient of determination R 2 using our approach was 0.57, and the root-mean-square error (RMSE) was 13 cm, which was a significant improvement over SNODAS (mean R 2 = 0.13; RMSE = 20 cm). We explored the relative importance of the input variables and observed that, at the spatial resolution of 800 m, meteorological variables are more important drivers of predictive accuracy than surface variables that characterize the properties of snow on the ground. This research provides a framework to expand the applicability of lidar-derived SWE to unmapped time points. Significance Statement Snowpack is the main source of freshwater for close to 2 billion people globally and needs to be estimated accurately. Mountainous snowpack is highly variable and is challenging to quantify. Recently, lidar technology has been employed to observe snow in great detail, but it is costly and can only be used sparingly. To counter that, we use machine learning to estimate snowpack when lidar data are not available. We approximate the processes that govern snowpack by incorporating meteorological and satellite data. We found that variables associated with precipitation and temperature have more predictive power than variables that characterize snowpack properties. Our work helps to improve snowpack estimation, which is critical for sustainable management of water resources.

54 ENVIRONMENTAL SCIENCES↗

Ellicott City Disasters II - Building a Real-Time Predictive Flood Model for Improving Early Warning Systems in Ellicott City, Maryland

As flood events in the United States grow in frequency and intensity, the uses of applied remote sensing analyses are increasingly necessary for effective flood monitoring and warning systems. The NASA DEVELOP Ellicott City Disasters III project investigated the use of machine learning for applications in flood risk detection to support the improvement of early warning systems in Ellicott City, Maryland. To strengthen the efforts of the Howard County Office of Emergency Management (OEM) in building a more robust flood monitoring system, this term built on the predictive capability of the long-short term memory (LSTM) model created by the second term of this DEVELOP project to create a Sequentially Trained Real-time EstimAted Model (STREAM). Enhancements to the model included the integration of both real-time and predicted weather products from the National Weather Service to increase predictive capacity. These weather products were supplemented by stream gauge data from the OEM as well as real-time radar products. The resultant flood risk model was trained to evaluate input variables and predict stage height in Ellicott City in real time. The model, upgraded to predict stage height up to 8 hours in advance, was incorporated into an online dashboard in a user-friendly interface. The project demonstrated the potential for integration of open data and NASA Earth observations into a flood risk forecasting tool capable of informing real-time decision-making.

Erika Munshi↗

Ellicott City Disasters III: Building a Real-Time Statistical Flood Model for Improving Early Warning Systems in Ellicott City, Maryland

As flood events in the United States grow in frequency and intensity, the uses of applied remote sensing analyses are increasingly necessary for effective flood monitoring and warning systems. The NASA DEVELOP Ellicott City Disasters III project investigated the use of machine learning for applications in flood risk detection to support the improvement of early warning systems in Ellicott City, Maryland. To strengthen the efforts of the Howard County Office of Emergency Management (OEM) in building a more robust flood monitoring system, this term built on the predictive capability of the long-short term memory (LSTM) model created by the second term of this DEVELOP project to create a Sequentially Trained Real-time EstimAted Model (STREAM). Enhancements to the model included the integration of both real-time and predicted weather products from the National Weather Service to increase predictive capacity. These weather products were supplemented by stream gauge data from the OEM as well as real-time radar products. The resultant flood risk model was trained to evaluate input variables and predict stage height in Ellicott City in real time. The model, upgraded to predict stage height up to 8 hours in advance, was incorporated into an online dashboard in a user-friendly interface. The project demonstrated the potential for integration of open data and NASA Earth observations into a flood risk forecasting tool capable of informing real-time decision-making.

Erika Munshi↗

Ellicott City Disasters II: Enhancing a Statistical Flood Risk Model to Continue Improving Early Warning Systems and Public Safety in Ellicott City, Maryland

As flooding events in the United States grow in frequency and intensity, the use of technological advancements and applied science are increasingly necessary for effective flood monitoring and warning systems. The NASA DEVELOP Ellicott City Disasters II project investigated the use of machine learning for applications in flood risk detection to support the improvement of early warning systems. To strengthen the efforts of the Howard County Office of Emergency Management (OEM) in building a more robust flood monitoring system, the project improved the original statistical flood risk model, FLuME (Flood Learning Model Environment), programmed by the first DEVELOP term. The enhancements incorporated an additional six years of precipitation and soil moisture data from the North American Land Data Assimilation System (NLDAS), modeled using Aqua Advanced Microwave Scanning Radiometer for EOS and Tropical Rainfall Measuring Mission (TRMM) Microwave Imager. These Earth observations were supplemented by stream gauge data from the OEM and the US Geological Survey. The resultant flood risk model FLASH (Flood Learning Environment and Severity Assessment Hub) was trained to evaluate input variables and predict stage height in Ellicott City in real time. The addition of an advanced deep learning framework known as long short-term memory improved the model’s ability to capture relationships between variables. To assess the effectiveness of the new model, FLASH produced a model efficiency metric of 0.99, a significant improvement over the 0.85 value produced by the previous model. The project assisted the OEM in pursuing the integration of open data and NASA Earth observations into a threat matrix capable of informing near real-time decision making.

Disasters↗

Ellicott City Disasters II: Enhancing a Statistical Flood Risk Model to Continue Improving Early Warning Systems and Public Safety in Ellicott City, Maryland

As flooding events in the United States grow in frequency and intensity, the use of technological advancements and applied science are increasingly necessary for effective flood monitoring and warning systems. The NASA DEVELOP Ellicott City Disasters II project investigated the use of machine learning for applications in flood risk detection to support the improvement of early warning systems. To strengthen the efforts of the Howard County Office of Emergency Management (OEM) in building a more robust flood monitoring system, the project improved the original statistical flood risk model, FLuME (Flood Learning Model Environment), programmed by the first DEVELOP term The enhancements incorporated an additional six years of precipitation and soil moisture data from the North American Land Data Assimilation System (NLDAS), modeled using Aqua Advanced Microwave Scanning Radiometer for EOS and Tropical Rainfall Measuring Mission TRMM Microwave Imager. These Earth observations were supplemented by stream gauge data from the OEM and the US Geological Survey. The resultant flood risk model FLASH (Flood Learning Environment and Severity Assessment Hub) was trained to evaluate input variables and predict stage height in Ellicott City in real time. The addition of an advanced deep learning framework known as long short-term memory improved the model’s ability to capture relationships between variables. To assess the effectiveness of the new model, FLASH produced a model efficiency metric of 0.99, a significant improvement over the 0.85 value produced by the previous model. The project assisted the OEM in pursuing the integration of open data and NASA Earth observations into a threat matrix capable of informing near real-time decision making.

Disasters↗

A predictability study of Lorenz's 28-variable model as a dynamical system

The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.

Krishnamurthy, V.↗