Multi-model Combination Research Articles

Towards Bayesian hierarchical inference of equilibrium climate sensitivity from a combination of CMIP5 climate models and observational data

Despite decades of research, large multi-model uncertainty remains about the Earth’s equilibrium climate sensitivity to carbon dioxide forcing as inferred from state-of-the-art Earth system models (ESMs). Statistical treatments of multi-model uncertainties are often limited to simple ESM averaging approaches. Sometimes models are weighted by how well they reproduce historical climate observations. Here, we propose a novel approach to multi-model combination and uncertainty quantification. Rather than averaging a discrete set of models, our approach samples from a continuous distribution over a reduced space of simple model parameters. We fit the free parameters of a reduced-order climate model to the output of each member of the multi-model ensemble. The reduced-order parameter estimates are then combined using a hierarchical Bayesian statistical model. The result is a multi-model distribution of reduced-model parameters, including climate sensitivity. In effect, the multi-model uncertainty problem within an ensemble of ESMs is converted to a parametric uncertainty problem within a reduced model. The multi-model distribution can then be updated with observational data, combining two independent lines of evidence. We apply this approach to 24 model simulations of global surface temperature and net top-of-atmosphere radiation response to abrupt quadrupling of carbon dioxide, and four historical temperature data sets. Our reduced order model is a 2-layer energy balance model. We present probability distributions of climate sensitivity based on (1) the multi-model ensemble alone and (2) the multi-model ensemble and observations.

Recent Advances in Functional Polymer Decorated Two-Dimensional Transition-Metal Dichalcogenides Nanomaterials for Chemo-Photothermal Therapy.

Novel nanomaterials and advanced nanotechnologies continue to promote the fast development of new approaches for efficient tumor therapy. As an alternative choice to various traditional therapies, non-invasive photothermal therapy (PTT) has attracted significant attention mainly due to its low cost, highly localizing, specific tumor treatment and minimal side effects on healthy tissues. PTT induced by photo-absorbing agents which can absorb and convert the external NIR laser into heat to ablate tumors. Plenty of studies have shown the significant potential of PTT to treat tumors in future practical applications. However, PTT alone usually could not eradicate tumors considering the intensity of laser gradual attenuates in biological tissues and the heat generated tends to distribute inhomogeneous within tumors tissues. Combination of chemotherapy with photothermal therapy into one system for tumor therapy is an effective strategy to further improve the therapy efficiency. In this Minireview, we focus on the recent advances in constructing PTT therapeutic and multi-model combination therapeutic via integrating nanomaterials and functional polymers.

Reducing Model Structural Uncertainty in Climate Model Projections—A Rank-Based Model Combination Approach

Future changes in monthly precipitation are typically evaluated by estimating the shift in the long-term mean/variability or based on the change in the marginal distribution. General circulation model (GCM) precipitation projections deviate across various models and emission scenarios and hence provide no consensus on the expected future change. The current study proposes a rank/percentile-based multimodel combination approach to account for the fact that alternate model projections do not share a common time indexing. The approach is evaluated using 10 GCM historical runs for the current period and is validated by comparing with two approaches: equal weighting and a non-percentile-based optimal weighting. The percentile-based optimal combination exhibits lower values of RMSE in estimating precipitation terciles. Future (2000–49) multimodel projections show that January and July precipitation exhibit an increase in simulated monthly extremes (25th and 75th percentiles) over many climate regions of the conterminous United States.

Multi-model Combination Housing Price Forecasting Based on Web Search Data

In the background of large data, taking the housing price in Xi'an as an example, this paper extracts the relevant search words data from Baidu Index and builds the neural network, support vector machine and random forests model, according to the purchase information inquired by the consumers in Baidu. The gradient boosting decision tree model is established by forecast results of the three single model to achieve a combination of housing prices forecast to determine the final residential sales price index forecast. The result shows that the fitting degree of the combined model is 0.995, and the prediction accuracy is 10.4% higher than the optimal single forecasting model. This method can calculate the new commodity housing price index two weeks in advance than the National Bureau of Statistics. In future studies, this approach will be applied to many types of market forecasts to help companies and consumers make the best decisions.

Grand European and Asian-Pacific multi-model seasonal forecasts: maximization of skill and of potential economical value to end-users

Multi-model ensembles (MMEs) are powerful tools in dynamical climate prediction as they account for the overconfidence and the uncertainties related to single-model ensembles. Previous works suggested that the potential benefit that can be expected by using a MME amplifies with the increase of the independence of the contributing Seasonal Prediction Systems. In this work we combine the two MME Seasonal Prediction Systems (SPSs) independently developed by the European (ENSEMBLES) and by the Asian-Pacific (APCC/CliPAS) communities. To this aim, all the possible multi-model combinations obtained by putting together the 5 models from ENSEMBLES and the 11 models from APCC/CliPAS have been evaluated. The grand ENSEMBLES-APCC/CliPAS MME enhances significantly the skill in predicting 2m temperature and precipitation compared to previous estimates from the contributing MMEs. Our results show that, in general, the better combinations of SPSs are obtained by mixing ENSEMBLES and APCC/CliPAS models and that only a limited number of SPSs is required to obtain the maximum performance. The number and selection of models that perform better is usually different depending on the region/phenomenon under consideration so that all models are useful in some cases. It is shown that the incremental performance contribution tends to be higher when adding one model from ENSEMBLES to APCC/CliPAS MMEs and vice versa, confirming that the benefit of using MMEs amplifies with the increase of the independence the contributing models. To verify the above results for a real world application, the Grand ENSEMBLES-APCC/CliPAS MME is used to predict retrospective energy demand over Italy as provided by TERNA (Italian Transmission System Operator) for the period 1990–2007. The results demonstrate the useful application of MME seasonal predictions for energy demand forecasting over Italy. It is shown a significant enhancement of the potential economic value of forecasting energy demand when using the better combinations from the Grand MME by comparison to the maximum value obtained from the better combinations of each of the two contributing MMEs. The above results demonstrate for the first time the potential of the Grand MME to significantly contribute in obtaining useful predictions at the seasonal time-scale.

Evaluating the contribution of multi-model combination to streamflow hindcasting by empirical and conceptual models

ABSTRACTThe contribution of multi-model combination to daily streamflow hindcasting was evaluated through the HBV (Hydrologiska Byråns Vattenbalansavdelning) and RNN (recurrent neural networks) models with 100 ensemble members generated with different initial conditions for both. In the calibration phase, the analysis showed that the HBV and RNN models with 20 members have better accuracy and require less calibration time. The combination of two models, however, did not provide significant improvements when 80 more members were added in the combination. In the validation phase, the results indicated that both HBV and RNN models with 20 members not only accurately produce reliable and stable streamflow hindcasting, but also effectively simulate the timing and the value of peak flows. From the consistency of calibration and validation results, the study provides an important contribution, namely, that ensemble size is not sensitive to the type of hydrological model in terms of streamflow hindcasting.

The Subseasonal to Seasonal (S2S) Prediction Project Database

Abstract Demands are growing rapidly in the operational prediction and applications communities for forecasts that fill the gap between medium-range weather and long-range or seasonal forecasts. Based on the potential for improved forecast skill at the subseasonal to seasonal time range, the Subseasonal to Seasonal (S2S) Prediction research project has been established by the World Weather Research Programme/World Climate Research Programme. A main deliverable of this project is the establishment of an extensive database containing subseasonal (up to 60 days) forecasts, 3 weeks behind real time, and reforecasts from 11 operational centers, modeled in part on the The Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE) database for medium-range forecasts (up to 15 days). The S2S database, available to the research community since May 2015, represents an important tool to advance our understanding of the subseasonal to seasonal time range that has been considered for a long time as a “desert of predictability.” In particular, this database will help identify common successes and shortcomings in the model simulation and prediction of sources of subseasonal to seasonal predictability. For instance, a preliminary study suggests that the S2S models significantly underestimate the amplitude of the Madden–Julian oscillation (MJO) teleconnections over the Euro-Atlantic sector. The S2S database also represents an important tool for case studies of extreme events. For instance, a multimodel combination of S2S models displays higher probability of a landfall over the islands of Vanuatu 2–3 weeks before Tropical Cyclone Pam devastated the islands in March 2015.

Assessment of models predicting anthropogenic interventions and climate variability on surface runoff of the Lower Zab River

Multi-regression, hydrologic sensitivity and hydrologic model simulations were applied to quantify the climate change and anthropogenic intervention impacts on the Lower Zab River basin (LZRB). The Pettitt, precipitation-runoff double cumulative curve (PR-DCC) and Mann–Kendall methods were used for the change points and significant trend analyses in the annual streamflow. The long-term runoff series from 1979 to 2013 was first divided into two main periods: a baseline (1979–1997) and an anthropogenic intervention period (1998–2013). The findings show that the mean annual streamflow changes were consistent using the three methods. In addition, climate variability was the main driver, which led to streamflow reduction with contributions of 66–97% during 2003–2013, whereas anthropogenic interventions caused reductions of 4–34%. Moreover, to enhance the multi-model combination concept and explore the simple average method (SAM), Hydrologiska Byrans Vattenbalansavdelning (HBV), Génie Rural a Daily 4 parameters (GR4J) and Medbasin models have been successfully applied.

A wavelet based approach for combining the outputs of different rainfall–runoff models

The rainfall–runoff modelling being a stochastic process in nature is dependent on various climatological variables and catchment characteristics and therefore numerous hydrological models have been developed to simulate this complex process. One approach to modelling this complex non-linear rainfall–runoff process is to combine the outputs of various models to get more accurate and reliable results. This multi-model combination approach relies on the fact that various models capture different features of the data, and hence combination of these features would yield better result. This study for the first time presented a novel wavelet based combination approach for estimating combined runoff The simulated daily output (Runoff) of five selected conventional rainfall–runoff models from seven different catchments located in different parts of the world was used in current study for estimating combined runoff for each time period. Five selected rainfall–runoff models used in this study included four data driven models, namely, the simple linear model, the linear perturbation model, the linearly varying variable gain factor model, the constrained linear systems with a single threshold and one conceptual model, namely, the soil moisture accounting and routing model. The multilayer perceptron neural network method was used to develop combined wavelet coupled models to evaluate the effect of wavelet transformation (WT). The performance of the developed wavelet coupled combination models was compared with their counterpart simple combination models developed without WT. It was concluded that the presented wavelet coupled combination approach outperformed the existing approaches of combining different models without applying input WT. The study also recommended that different models in a combination approach should be selected on the basis of their individual performance.

Building a Multimodel Flood Prediction System with the TIGGE Archive

Abstract In the last decade operational probabilistic ensemble flood forecasts have become common in supporting decision-making processes leading to risk reduction. Ensemble forecasts can assess uncertainty, but they are limited to the uncertainty in a specific modeling system. Many of the current operational flood prediction systems use a multimodel approach to better represent the uncertainty arising from insufficient model structure. This study presents a multimodel approach to building a global flood prediction system using multiple atmospheric reanalysis datasets for river initial conditions and multiple TIGGE forcing inputs to the ECMWF land surface model. A sensitivity study is carried out to clarify the effect of using archive ensemble meteorological predictions and uncoupled land surface models. The probabilistic discharge forecasts derived from the different atmospheric models are compared with those from the multimodel combination. The potential for further improving forecast skill by bias correction and Bayesian model averaging is examined. The results show that the impact of the different TIGGE input variables in the HTESSEL/Catchment-Based Macroscale Floodplain model (CaMa-Flood) setup is rather limited other than for precipitation. This provides a sufficient basis for evaluation of the multimodel discharge predictions. The results also highlight that the three applied reanalysis datasets have different error characteristics that allow for large potential gains with a multimodel combination. It is shown that large improvements to the forecast performance for all models can be achieved through appropriate statistical postprocessing (bias and spread correction). A simple multimodel combination generally improves the forecasts, while a more advanced combination using Bayesian model averaging provides further benefits.

Improvements in precipitation simulation over South America for past and future climates via multi-model combination

Combining individual forecasts is one of the practices used to improve weather prediction results. Identifying which combination of techniques results in a more accurate forecast is the subject of many comparative studies as well proposals for combined methods. Here we compare three combination techniques: (1) principal component regression (PCR), (2) convex combination by mean squared errors (MSE) and (3) ensemble average to combine six regional climate models of the Regional Climate Change Assessment for the La Plata Basin Project (CLARIS-LPB) for variable rainfall in three regions: Amazon (AMZ), Northeastern Brazil (NEB) and La Plata Basin (LPB), for the past (1961–1990) and future (2071–2100) climates. The results indicate that the average RMSE values showed improved representation of climate for LPB in some months, which is an important advance in climate studies. On the other hand, PCR presented greater accuracy (lower RMSE) than MSE in the AMZ and NEB regions. In winter months, both combinations presented lower RMSE results, mainly PCR in the three study regions. The correlation coefficient supports the results already found, namely, PCR obtained moderate to strong correlations, which were statistically significant at 5 % in both regions for all months, while MSE presented low to moderate correlations, which were statically significant at 5 % only in some months. Based on that, PCR achieved the best corrected forecast, as it was superior in forecasting precipitation due to the lower RMSE value. It is noteworthy that the PCR data were first subjected to principal component analysis (PCA) and the scores were used to perform the prediction.

Multimodel Approach Using Neural Networks and Symbolic Regression to Combine the Estimated Discharges of Rainfall-Runoff Models

The aim of this study is to compare the performance of a symbolic regression combination method based on gene expression programming (GEP) with different neural network combination methods when used in the development of multimodel systems. The two different neural network combination methods used in this study are the multilayer perceptron neural network (MLPNN) and the radial basis function neural network (RBFNN). The methods were used to combine the results from different types of rainfall-runoff models to test the multimodel combination system in catchments located in Thailand and New Zealand. Comparison of the results revealed that the GEP performed better than neural network methods in the case of the catchment located in New Zealand. Nevertheless, the RBFNN method outperformed the GEP and the MLPNN combination method in the case of the catchment located in Thailand. However, which combination method produces better results in the multimodel combination is not conclusive. The results suggest that the selection of the best combination method to be used in conjunction with the multimodel approach may depend on the catchment type.

Role of multimodel combination and data assimilation in improving streamflow prediction over multiple time scales

In hydrologic modeling, various uncertainty sources may arise due to simplification/representation of real-world spatially distributed processes into the modeling framework, such as uncertainty due to model structure, initial conditions and input errors. One approach that is currently gaining attention to reduce model uncertainty is by optimally combining multiple models. The rationale behind this approach is that optimal weights could be derived for each model during the model combination process so that the developed multimodel predictions will result in improved predictability. Another approach—data assimilation—is gaining popularity in reducing uncertainty by deriving updated initial conditions recursively from the current available observations to reduce overall uncertainty by minimizing the error covariance matrix of state variables. In this paper, an experimental design is proposed to test the performance of both approaches, multimodel combination and data assimilation, in improving the hydrologic prediction at daily and monthly time scales. The experimental design is constructed on a synthetic basis such that the ‘true’ model structure and streamflow values are known. We evaluated the performance of multimodel combination and data assimilation through the experimental design at monthly and daily time scales, then compare how uncertainty due to initial conditions and hydrologic model can be dominant at the respective time scales. For the multimodel combination, we combined the models by evaluating the model performance conditioned on the predictor state. For data assimilation, the Ensemble Kalman Filter (EnKF) was adopted to test its usefulness through the same experimental design. Results from the synthetic study showed that under increased model uncertainty, the multimodel algorithm consistently performed better than the single model predictions and the EnKF algorithm in terms of all performance measures at monthly time scale. However, under daily time scale, the multimodel algorithm did not performing better than the EnKF algorithm in most of the model uncertainty cases. Findings from the synthetic study was also consistent upon application in predicting streamflow at daily and monthly time scales for a watershed in North Carolina.

Ensemble Combination of Seasonal Streamflow Forecasts

Various hydrologic models with different complexities have been developed to represent the characteristics of river basins, improve streamflow forecasts such as seasonal volumetric flow predictions, and meet other demands from different stakeholders. Because no single hydrologic model is able to perfectly simulate the observed flow, multimodel combination techniques are developed to combine forecasts obtained from different models and to quantify the uncertainties with the goal of improving upon single-model performance. In this study, a comprehensive set of multimodel ensemble averaging techniques with varying complexities are investigated for operational forecasting over four river basins in the Western United States. Ensemble merging models are divided into three categories of simple, intermediate, and complex, and comparison is made between each class by using a bootstrap approach. Analysis suggests that model combination effectively improves most of the individual seasonal forecasts and can outperform the best forecast model. Simple average, median, Bates-Granger, constrained linear regression, and Bayesian model averaging optimized by expectation maximization showed better results compared with other methods over three basins. For the Rogue River basin, the intermediate and complex models outperformed most of the individual forecasts and the simple methods. Multimodeling techniques based on information criteria showed similar performances.

Attributing runoff changes to climate variability and human activities: uncertainty analysis using four monthly water balance models

Hydrological simulations to delineate the impacts of climate variability and human activities are subjected to uncertainties related to both parameter and structure of the hydrological models. To analyze the impact of these uncertainties on the model performance and to yield more reliable simulation results, a global calibration and multimodel combination method that integrates the Shuffled Complex Evolution Metropolis (SCEM) and Bayesian Model Averaging of four monthly water balance models was proposed. The method was applied to the Weihe River Basin, the largest tributary of the Yellow River, to determine the contribution of climate variability and human activities to runoff changes. The change point, which was used to determine the baseline period (1956–1990) and human-impacted period (1991–2009), was derived using both cumulative curve and Pettitt’s test. Results show that the combination method from SCEM provides more skillful deterministic predictions than the best calibrated individual model, resulting in the smallest uncertainty interval of runoff changes attributed to climate variability and human activities. This combination methodology provides a practical and flexible tool for attribution of runoff changes to climate variability and human activities by hydrological models.

Does improved SSTA prediction ensure better seasonal rainfall forecasts?

AbstractSeasonal rainfall forecasts in Australia are issued based on concurrent sea surface temperature anomalies (SSTAs) using a Bayesian model averaging (BMA) approach. The SSTA fields are derived from the Predictive Ocean‐Atmosphere Model for Australia (POAMA) initialized in the preceding season. This study investigates the merits of the rainfall forecasted using POAMA SSTAs in contrast to that forecasted using a multimodel combination of SSTAs derived using five existing models. In addition, seasonal rainfall forecasts derived from multimodel and POAMA SSTA fields are subsequently combined to obtain a single weighted forecast over Australia. These three forecasts are compared against “idealized” forecasts where observed SSTAs are used instead of those predicted. The results indicate that while seasonal rainfall forecasts derived using multimodel‐based SSTA indices offer improvements in selected seasons over a majority of grid cells in comparison to the case where a single SSTA model is used in two seasons, these improvements are not as significant as the improvements in the SSTA field that drive the rainfall forecasting model. The forecasts derived from the combination of multimodel and POAMA SSTA indices forecasts are found to offer greater improvements over the multimodel or the POAMA forecasts for a majority of grid cells in all seasons. It is also observed that these combined forecasts are touching the upper limits of forecastability, which are reached when observed SSTAs are used to forecast the rainfall. This suggests that further improvements in rainfall forecasting are only possible through the use of an improved forecasting algorithm, and not the driver (SSTA) information used in the current study.

Multi-model ensemble analysis of runoff extremes for climate change impact assessments

Summary In this study multi-model ensemble analysis of extreme runoff is performed based on eight regional climate models (RCMs) provided by the North American Regional Climate Change Assessment Program (NARCCAP). Hydrologic simulation is performed by driving the Variable Infiltration Capacity (VIC) model over the Pacific Northwest region, for historical and future time periods. Extreme event analysis is then conducted using spatial hierarchical Bayesian modeling (SHB). Ensemble merging of extreme runoff is carried out using Bayesian Model Averaging (BMA) in which spatially distributed weights corresponding to each regional climate model are obtained. Comparison of the residuals before and after the multi-model combination shows that the merged signal generally outperforms the best individual signal. The climate model simulations show close performance regarding maximum and minimum temperature and wind speed, however, the differences are more pronounced for precipitation and runoff. Between-model variances increase for the future time series compared to the historical ones indicating larger uncertainties in climate change projections. The combined model is then used to predict projected seasonal runoff extremes and compare them with historical simulations. Ensemble average results suggest that seasonal extreme runoff will increase in most regions in particular the Rockies and west of the Cascades.

Identification of the best multi-model combination for simulating river discharge

This paper focuses on the selection of the best multi-model ensemble method that is subsequently used to create an ensemble for the discharge estimation in a catchment of the Mahanadi river basin in India. Ten different multi-model ensemble methods, viz., mean, median, trimmed mean, unconstrained and constrained multiple linear regression, weighted mean based on calibration performance (two variants), linear programming, simple model average and multi model super ensemble, are compared using calibrated and validated data of eight popular hydrological models, MIKE SHE, SWAT, HEC-HMS, AWBM, SIMHYD, SACRAMENTO, SMAR and TANK. Constrained multiple linear regression (MLR_C) method is found to be the most suitable multi-model ensemble method for the study area. MLR_C method is subsequently used to develop 189 possible multi-model ensembles. These ensembles are evaluated for categorical and temporal accuracy, using a proposed SCORE that includes normalized relative operating characteristic (ROC) area and normalized number of skillful days. The results show that an ensemble having five models, one physically based (SWAT) and four conceptual (AWBM, SIMHYD, SACRAMENTO and SMAR), performs the best for the chosen catchment. The best performing ensemble also outperforms all eight individual models in simulating the observed discharge and flow volume. Furthermore, uncertainty in simulating river discharge due to all sources collectively is analyzed through uncertainty analysis.

A robust multimodel framework for ensemble seasonal hydroclimatic forecasts

AbstractWe provide a framework for careful analysis of the different methodological choices we make when constructing multimodel ensemble seasonal forecasts of hydroclimatic variables. Specifically, we focus on three common modeling decisions: (i) number of models, (ii) multimodel combination approach, and (iii) lead time for prediction. The analysis scheme includes a multimodel ensemble forecasting algorithm based on nonparametric regression, a set of alternatives for the options previously pointed, and a selection of probabilistic verification methods for ensemble forecast evaluation. The usefulness of this framework is tested through an example application aimed to generate spring/summer streamflow forecasts at multiple locations in Central Chile. Results demonstrate the high impact that subjectivity in decision‐making may have on the quality of ensemble seasonal hydroclimatic forecasts. In particular, we note that the probabilistic verification criteria may lead to different choices regarding the number of models or the multimodel combination method. We also illustrate how this objective analysis scheme may lead to results that are extremely relevant for the case study presented here, such as skillful seasonal streamflow predictions for very dry conditions.

Integrated Multimodel Control of Nonlinear Systems Based on Gap Metric and Stability Margin

To avoid linear model redundancy and simplify the structure of a multimodel controller, two general integrated multimodel control design frameworks, which integrate the multimodel decomposition and the multimodel combination of a nonlinear system, are proposed based on the gap metric and stability margin criteria. One method uses the maximum stability margin (which is comparatively controller-independent) while the other uses the actual stability margin of a given controller design. For a prescribed linear control algorithm for local controller design, a smaller and better linear model bank that provides necessary information for multimodel controller design is obtained systematically without model redundancy. Besides, the local robust stability and performance of the system in each subregion can be achieved by the corresponding local controller. Many linear control techniques can be used in the proposed design frameworks, and H∞ control algorithm is employed as an example and applied to two benchmark nonlinear chemical processes for set point tracking and disturbance rejection control. Closed-loop simulations demonstrate that the proposed approaches are both systematic and effective and are better than the traditional multimodel control methods in terms of robust performance.