Simple Average Model Research Articles

Bayesian multi-model projection of irrigation requirement and water use efficiency in three typical rice plantation region of China based on CMIP5

Rice growth is significantly influenced by the ongoing climatic change and subjected to water shortages. Projection on the changes of rice productivity growth and water resources utilization under future climates is of great importance for food security and water resources sustainable management. Climate model outputs in combination with physical-based crop model is an effective way to modeling the crop productivity and water consumption response, but uncertainties associated with climate models remain a major challenge. In this study, we introduce a Bayesian model averaging (BMA) method to provide the multi-model ensemble projections by merging 4 climate models under four emissions scenarios (RCP2.6, RCP4.5, RCP6.0 and RCP8.5) from phase five of the Coupled Model Intercomparsion Project (CMIP5). The comprehensive investigation on how the rice yield, water consumption (ET), irrigation water requirement (IR), water use efficiency (WUE) and irrigation water use efficiency (IWUE) response to future climate scenarios with taking account of CO2 concentration enrichment in three typical sites (Kunshan and Nanjing in the Yangtze River Basin, and Kaifeng in the Yellow River Basin) in rice plantation region of China was conducted by driving a well-validated rice crop model ORYAZ2000 with merging multi-model ensemble projected climate outputs. There are some obvious uncertainties for climate models projections in climatic variables with wide model spread, especially for solar radiation and wind speed. The BMA method is most competent to produce the ensemble with the lowest bias in comparison with simple model averaging (SA) method and individual climate model. In despite of the distinct response of the growth duration to future climate change for the three stations, the rice yield would be reduced significantly under the climate warming. IR would present more remarkable increase compared with the ET, especially for Nanjing and Kunshan stations, due to the decrease in precipitation during the rice growth period. The significant reduction in rice production together with enlargement in ET and IR, resulted in the generally depressed the WUE and IWUE. In addition, despite that the CO2 fertilization effect cannot compensate the negative effect of temperature increase, the increase of CO2 concentration can promote the overall level of yield and consequently improve the water use efficiencies of rice.

Assessment and simulation of global terrestrial latent heat flux by synthesis of CMIP5 climate models and surface eddy covariance observations

The latent heat flux (LE) between the terrestrial biosphere and atmosphere is a major driver of the global hydrological cycle. In this study, we evaluated LE simulations by 45 general circulation models (GCMs) in the Coupled Model Intercomparison Project Phase 5 (CMIP5) by a comparison with eddy covariance (EC) observations from 240 globally distributed sites from 2000 to 2009. In addition, we improved global terrestrial LE estimates for different land cover types by synthesis of seven best CMIP5 models and EC observations based on a Bayesian model averaging (BMA) method. The comparison results showed substantial differences in monthly LE among all GCMs. The model CESM1-CAM5 has the best performance with the highest predictive skill and a Taylor skill score (S) from 0.51–0.75 for different land cover types. The cross-validation results illustrate that the BMA method has improved the accuracy of the CMIP5 GCM’s LE simulation with a decrease in the averaged root-mean-square error (RMSE) by more than 3 W/m2 when compared to the simple model averaging (SMA) method and individual GCMs. We found an increasing trend in the BMA-based global terrestrial LE (slope of 0.018 W/m2 yr−1, p < 0.05) during the period 1970–2005. This variation may be attributed directly to the inter-annual variations in air temperature (Ta), surface incident solar radiation (Rs) and precipitation (P). However, our study highlights a large difference from previous studies in a continuous increasing trend after 1998, which may be caused by the combined effects of the variations of Rs, Ta, and P on LE for different models on these time scales. This study provides corrected-modeling evidence for an accelerated global water cycle with climate change.

Multi-model ensemble prediction of terrestrial evapotranspiration across north China using Bayesian model averaging

Using high-quality dataset from 12 flux towers in north China, the performance of four evapotranspiration (ET) models and the multi-model ensemble approaches including the simple averaging (SA) and Bayesian model average (BMA) were systematically evaluated in this study. The four models were the single-layer Penman–Monteith (P–M) model, the two-layer Shuttleworthe–Wallace (S–W) model, the advection–aridity (A–A) model, and a modified Priestley–Taylor (PT-JPL). Based on the mean value of Taylor skill (S) and the regression slope between measured and simulated ET values across all sites, the order of overall performance of the individual models from the best to the worst were: S–W (0.88, 0.87), PT-JPL (0.80, 1.17), P–M (0.63, 1.73) and A–A (0.60, 1.68) [statistics stated as (Taylor skill, regression slope)]. Here, all models used the same values of parameters, LAI and fractional vegetation cover as well as the forcing meteorological data. Thus, the differences in model performance were mainly attributed to errors in model structure. To the ensemble approach, the BMA method has the advantage of generating more skillful and reliable predictions than the SA scheme. However, successful implementation of BMA requires accurate estimates of its parameters, and some degradation in performance were observed when the BMA parameters generated from the training period were used for the validation period. Thus, it is necessary to explore the seasonal variations of the BMA parameters according the different growth stages. Finally, the optimal conditional density function of half-hourly ET approximated well by the double-exponential distribution. Copyright © 2016 John Wiley & Sons, Ltd.

Parameter Estimation of a Distributed Hydrological Model Using a Genetic Algorithm

Water is a vital resource, and can also sometimes be a destructive force. As such, it is important to manage this resource. The prediction of stream flows is an important component of this management. Hydrological models are very useful in accomplishing this task. The objective of this study is to develop and apply an optimization method useful for calibrating a deterministic model of the daily flows of the Miramichi River watershed (New Brunswick). The model used is the CEQUEAU model. The model is calibrated by applying a genetic algorithm. The Nash-Sutcliffe efficiency criterion, modified to penalize physically unrealistic results, was used as the objective function. The model was calibrated using flow data (1975-2000) from a gauging station on the Southwest Miramichi River (catchment area of 5050 km2), obtaining a Nash-Sutcliffe criterion of 0.83. Model validation was performed using flow data (2001-2009) from the same station (Nash-Sutcliffe criterion value of 0.80). This suggests that the model calibration is sufficiently robust to be used for future predictions. A second model validation was performed using data from three other measuring stations on the same watershed. The model performed well in all three additional locations (Nash-Sutcliffe criterion values of 0.77, 0.76 and 0.74), but was performing less well when applied to smaller sub-basins. Nonetheless, the relatively strong performance of the model suggests that it could be used to predict flows anywhere in the watershed, but caution is suggested for applications in small sub-basins. The performance of the CEQUEAU model was also compared to a simple benchmark model (average of each calendar day). A sensitivity analysis was also performed.

Evaluating the skill of NMME seasonal precipitation ensemble predictions for 17 hydroclimatic regions in continental China

There is an increasing focus on the usefulness of climate model–based seasonal precipitation forecasts as inputs for hydrological applications. This study reveals that most models from the North American Multi-Model Ensemble (NMME) have potential to forecast seasonal precipitation over 17 hydroclimatic regions in continental China. In this paper, we evaluated the NMME precipitation forecast against observations. The evaluation indices included the correlation coefficient (R), relative root-mean-square error (RRMSE), rank histogram (RH), and continuous ranked probability skill score (CRPSS). We presented the RRMSE-R diagram to distinguish differences between the performances of individual models. We find that the predictive skill is seasonally and regionally dependent, exhibiting higher values in autumn and spring and lower values in summer. Higher predictive skill is observed over most regions except the southeastern monsoon regions, which may be attributable to local climatology and variability. Among the 11 NMME models, CFS, especially CFSv2, exhibits the best predictive skill. The GFDL and NASA models, which are followed by CMC, perform worse than CFS. The performances of IRI and CCSM3 are relatively worse than that of the other models. The forecast skills are significantly improved in multi-model mean forecasts based on simple model averaging (SMA). The improvement is more obvious for Bayesian model averaging (BMA), which is employed to further improve the forecast skill and address model uncertainty using multiple model outputs, than individual model and SMA.

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.

Future Climate Impact on the Desertification in the Dry Land Asia Using AVHRR GIMMS NDVI3g Data

Dry Land Asia is the largest arid and semi-arid region in the northern hemisphere that suffers from land desertification. Over the period 1982–2011, there were both overall improvement and regional degeneration in the vegetation NDVI. We analyze future climate changes in these area using two ensemble-average methods from CMIP5 data. Bayesian Model Averaging shows a better capability to represent the future climate and less uncertainty represented by the 22-model ensemble than does the Simple Model Average. From 2006 to 2100, the average growing season temperature value will increase by 2.9 °C, from 14.4 °C to 17.3 °C under three climate scenarios (RCP 26, RCP 45 and RCP 85). We then conduct multiple regression analysis between climate changes compiled from the Climate Research Unit database and vegetation greenness from the GIMMS NDVI3g dataset. There is a general acceleration in the desertification trend under the RCP 85 scenario in middle and northern part of Middle Asia, northwestern China except Xinjiang and the Mongolian Plateau (except the middle part). The RCP 85 scenario shows a more severe desertification trend than does RCP 26. Desertification in dry land Asia, particularly in the regions highlighted in this study, calls for further investigation into climate change impacts and adaptations.

High resolution modelling and forecasting of soil sealing density at the regional scale

The on-going growth of urban areas results in increased sealed surface cover, affecting the environment through fragmentation of the landscape, increased surface runoff and obstruction of water infiltration. Within Flanders (Belgium), which is characterized by a highly sprawled urban network and a sealed surface density much higher than in many other European metropolitan regions, there is a strong need for more accurate high-resolution forecasting of soil sealing densities. This study attempts to meet this need by developing a spatial explanatory model for soil sealing density that is applicable at the regional scale and that can be applied in combination with the Flanders cellular automata land-use change model for evaluating the impact of future land-use scenarios on soil sealing. In the modelling, neighbourhood characteristics such as land-use composition and positioning with respect to the urban network and its major transport axes are considered as attraction/repulsion factors for soil sealing. Global multiple regression and regression tree models are compared with a simple average model. The regression models yield clear improvements in overall estimation accuracy and a favourable distribution of the remaining error. Applying a two-rule partitioning model on a future land-use map, produced by the Flanders land-use change model, shows an increase of 23.6% and 44.6% of sealed surface cover within residential/mixed areas in the study area by 2030 and 2050, respectively.

Instantaneous-to-daily GPP upscaling schemes based on a coupled photosynthesis-stomatal conductance model: correcting the overestimation of GPP by directly using daily average meteorological inputs.

Daily canopy photosynthesis is usually temporally upscaled from instantaneous (i.e., seconds) photosynthesis rate. The nonlinear response of photosynthesis to meteorological variables makes the temporal scaling a significant challenge. In this study, two temporal upscaling schemes of daily photosynthesis, the integrated daily model (IDM) and the segmented daily model (SDM), are presented by considering the diurnal variations of meteorological variables based on a coupled photosynthesis-stomatal conductance model. The two models, as well as a simple average daily model (SADM) with daily average meteorological inputs, were validated using the tower-derived gross primary production (GPP) to assess their abilities in simulating daily photosynthesis. The results showed IDM closely followed the seasonal trend of the tower-derived GPP with an average RMSE of 1.63 g C m(-2) day(-1), and an average Nash-Sutcliffe model efficiency coefficient (E) of 0.87. SDM performed similarly to IDM in GPP simulation but decreased the computation time by >66%. SADM overestimated daily GPP by about 15% during the growing season compared to IDM. Both IDM and SDM greatly decreased the overestimation by SADM, and improved the simulation of daily GPP by reducing the RMSE by 34 and 30%, respectively. The results indicated that IDM and SDM are useful temporal upscaling approaches, and both are superior to SADM in daily GPP simulation because they take into account the diurnally varying responses of photosynthesis to meteorological variables. SDM is computationally more efficient, and therefore more suitable for long-term and large-scale GPP simulations.

Assessment of CMIP5 climate models and projected temperature changes over Northern Eurasia

Assessing the performance of climate models in surface air temperature (SAT) simulation and projection have received increasing attention during the recent decades. This paper assesses the performance of the Coupled Model Intercomparison Project phase 5 (CMIP5) in simulating intra-annual, annual and decadal temperature over Northern Eurasia from 1901 to 2005. We evaluate the skill of different multi-model ensemble techniques and use the best technique to project the future SAT changes under different emission scenarios. The results show that most of the general circulation models (GCMs) overestimate the annual mean SAT in Northern Eurasia and the difference between the observation and the simulations primarily comes from the winter season. Most of the GCMs can approximately capture the decadal SAT trend; however, the accuracy of annual SAT simulation is relatively low. The correlation coefficient R between each GCM simulation and the annual observation is in the range of 0.20 to 0.56. The Taylor diagram shows that the ensemble results generated by the simple model averaging (SMA), reliability ensemble averaging (REA) and Bayesian model averaging (BMA) methods are superior to any single GCM output; and the decadal SAT change generated by SMA, REA and BMA are almost identical during 1901–2005. Heuristically, the uncertainty of BMA simulation is the smallest among the three multi-model ensemble simulations. The future SAT projection generated by the BMA shows that the SAT in Northern Eurasia will increase in the 21st century by around 1.03 °C/100 yr, 3.11 °C/100 yr and 7.14 °C/100 yr under the RCP 2.6, RCP 4.5 and RCP 8.5 scenarios, respectively; and the warming accelerates with the increasing latitude. In addition, the spring season contributes most to the decadal warming occurring under the RCP 2.6 and RCP 4.5 scenarios, while the winter season contributes most to the decadal warming occurring under the RCP 8.5 scenario. Generally, the uncertainty of the SAT projections increases with time in the 21st century.

Using different multimodel ensemble approaches to simulate soil moisture in a forest site with six traditional pedotransfer functions

Pedotransfer functions (PTFs) have routinely been used to estimate the soil hydraulic properties (SHPs) from easily measurable soil properties, such as particle-size distribution, organic matter content and bulk density. However, different PTFs often yielded different prediction results. In order to deal with the PTF selection problem, this study used multimodel ensemble approaches to simulate forest soil moisture based on the modelling results of different PTFs. A total of 300 days of observed soil moisture data at four depths (10-, 20-, 40- and 60-cm) were adopted to calibrate the Richards equation and obtain the SHPs by using the inverse option in HYDRUS-1D. Six published PTFs were selected to predict the SHPs, which were used to predict soil moisture temporal variations at these four different depths. Two multimodel ensemble methods, including the simple model average (SMA) and the multiple linear regression (MLR)-based superensemble, were used in this study. Under different selections of training periods (i.e. 50, 100 and 150 days), performances of these multimodel ensemble approaches were compared with those of the best single PTF model. The SMA always had worse performance than the best single model. However, the performances of the superensemble approach were better than those of the best single model, and even comparable to those of the calibrated soil water flow model. Results show that given the relatively long training period (>50 days), it is worthwhile to consider the superensemble method to simulate soil moisture contents in forestland.

Bayesian multimodel estimation of global terrestrial latent heat flux from eddy covariance, meteorological, and satellite observations

AbstractAccurate estimation of the satellite‐based global terrestrial latent heat flux (LE) at high spatial and temporal scales remains a major challenge. In this study, we introduce a Bayesian model averaging (BMA) method to improve satellite‐based global terrestrial LE estimation by merging five process‐based algorithms. These are the Moderate Resolution Imaging Spectroradiometer (MODIS) LE product algorithm, the revised remote‐sensing‐based Penman‐Monteith LE algorithm, the Priestley‐Taylor‐based LE algorithm, the modified satellite‐based Priestley‐Taylor LE algorithm, and the semi‐empirical Penman LE algorithm. We validated the BMA method using data for 2000–2009 and by comparison with a simple model averaging (SA) method and five process‐based algorithms. Validation data were collected for 240 globally distributed eddy covariance tower sites provided by FLUXNET projects. The validation results demonstrate that the five process‐based algorithms used have variable uncertainty and the BMA method enhances the daily LE estimates, with smaller root mean square errors (RMSEs) than the SA method and the individual algorithms driven by tower‐specific meteorology and Modern Era Retrospective Analysis for Research and Applications (MERRA) meteorological data provided by the NASA Global Modeling and Assimilation Office (GMAO), respectively. The average RMSE for the BMA method driven by daily tower‐specific meteorology decreased by more than 5 W/m2 for crop and grass sites, and by more than 6 W/m2 for forest, shrub, and savanna sites. The average coefficients of determination (R2) increased by approximately 0.05 for most sites. To test the BMA method for regional mapping, we applied it for MODIS data and GMAO‐MERRA meteorology to map annual global terrestrial LE averaged over 2001–2004 for spatial resolution of 0.05°. The BMA method provides a basis for generating a long‐term global terrestrial LE product for characterizing global energy, hydrological, and carbon cycles.

Anisotropy of the piezoelectric properties of the domain-engineered pseudotetragonal ferroelectric relaxor-PbTiO3 single crystals

In the frame of thermodynamic approach the areas of the admissible values of longitudinal (d33) and transverse (d31) piezoelectric moduli have been determined for 12 domain-engineered pseudotetragonal ferroelectric relaxor-PbTiO3 single crystals’ compositions belonging to so-called first, second and third generations. The parameters characterizing the piezoelectric anisotropy are shown to be practically the same for all the crystals considered, independently of their composition. Such behavior is explained in the frame of a simple averaging model.

Improving simulation of soil moisture in China using a multiple meteorological forcing ensemble approach

Abstract. The quality of soil-moisture simulation using land surface models depends largely on the accuracy of the meteorological forcing data. We investigated how to reduce the uncertainty arising from meteorological forcings in a simulation by adopting a multiple meteorological forcing ensemble approach. Simulations by the Community Land Model version 3.5 (CLM3.5) over mainland China were conducted using four different meteorological forcings, and the four sets of soil-moisture data related to the simulations were then merged using simple arithmetical averaging and Bayesian model averaging (BMA) ensemble approaches. BMA is a statistical post-processing procedure for producing calibrated and sharp predictive probability density functions (PDFs), which is a weighted average of PDFs centered on the bias-corrected forecasts from a set of individual ensemble members based on their probabilistic likelihood measures. Compared to in situ observations, the four simulations captured the spatial and seasonal variations of soil moisture in most cases with some mean bias. They performed differently when simulating the seasonal phases in the annual cycle, the interannual variation and the magnitude of observed soil moisture over different subregions of mainland China, but no individual meteorological forcing performed best for all subregions. The simple arithmetical average ensemble product outperformed most, but not all, individual members over most of the subregions. The BMA ensemble product performed better than simple arithmetical averaging, and performed best for all fields over most of the subregions. The BMA ensemble approach applied to the ensemble simulation reproduced anomalies and seasonal variations in observed soil-moisture values, and simulated the mean soil moisture. It is presented here as a promising way for reproducing long-term, high-resolution spatial and temporal soil-moisture data.

Evaluation and application of Bayesian multi-model estimation in temperature simulations

Use of multi-model ensembles from global climate models to simulate the current and future climate change has flourished as a research topic during recent decades. This paper assesses the performance of multi-model ensembles in simulating global land temperature from 1960 to 1999, using Nash-Sutcliffe model efficiency and Taylor diagrams. The future trends of temperature for different scales and emission scenarios are projected based on the posterior model probabilities estimated by Bayesian methods. The results show that ensemble prediction can improve the accuracy of simulations of the spatiotemporal distribution of global temperature. The performance of Bayesian model averaging (BMA) at simulating the annual temperature dynamic is significantly better than single climate models and their simple model averaging (SMA). However, BMA simulation can demonstrate the temperature trend on the decadal scale, but its annual assessment of accuracy is relatively weak. The ensemble prediction presents dissimilarly accurate descriptions in different regions, and the best performance appears in Australia. The results also indicate that future temperatures in northern Asia rise with the greatest speed in some scenarios, and Australia is the most sensitive region for the effects of greenhouse gas emissions. In addition to the uncertainty of ensemble prediction, the impacts of climate change on agriculture production and water resources are discussed as an extension of this research.

A new approach of power electronic design using a nonlinear average model

PurposeThe present work aims to explain how the nonlinear average model can be used in power electronic integration design as a behavioral model.Design/methodology/approachThe nonlinear average model is used in power electronic integration design as a behavioral model, where it is applied to a voltage source inverter based on IGBTs. This model was chosen because it takes into account the nonlinearity of the power semiconductor components and the wiring circuit effects, which can be formalized by the virtual delay concept. In addition, the nonlinear average model cannot distinguish between slow and quick variables and this is an important feature of the model convergence.FindingsThe paper studies extensively the construction of the nonlinear average model algorithm theoretically. Detailed explanations of the application of this model to voltage source inverter design are provided. The study demonstrates how this model illustrates the effect of the nonlinearity of the power semiconductor components' characteristics on dynamic electrical quantities. It also predicts the effects due to wiring in the inverter circuit.Research limitations/implicationsMore simulations and experimental analysis are still necessary to improve the model's accuracy, by using other static characteristic approaches, and to validate the applicability of the model to different converter topologies.Practical implicationsThe paper formulates a simple nonlinear average model algorithm, discussing each step. This model was described by VHDL‐AMS. On the one hand, it will assist theoretical and practical research on different topologies of power electronic converters, particularly in power integration systems design such as the integrated power electronics modules (IPEM). On the other hand, it will give designers a more precise behavioral model with a simpler design process.Originality/valueThe nonlinear average model used in power electronic integration design as behavioral model is a novel approach. This model reduces computational costs significantly, takes physical effects into account and is easy to implement.

Estimation of oil firm's systematic risk via composite time-varying models

This paper examines the performance of alternative models in estimating systematic risk in the oil industry, considering the traditional market model, three time-varying models, and some combination methods of individual models. This study uses the world's top 10 oil firms’ data series to find that the combination method outperforms other individual models in out-of-sample forecasting of returns. The results indicate that the forecasting performance of the regression method is superior to individual and simple average models.

Using spacecraft measurements ahead of Earth in the Parker spiral to improve terrestrial space weather forecasts

Space weather forecasting is important for mitigating the risks that the effects of the near‐Earth space environment have on man‐made systems. Here we investigate an innovative technique for extending the temporal range of solar wind–based forecast models by using solar wind measurements made azimuthally ahead of Earth in the Parker spiral near 1 AU. Cross correlations between STEREO (near 1 AU) and ACE (at L1) solar wind quantities are examined for a 1 year period during the most recent solar minimum, and we show that data from STEREO‐B, which is azimuthally behind Earth in its orbit but ahead of Earth in the Parker spiral, can be used as an input to a relativistic electron forecast model to extend its capability to +6 days from its original range of +2 days. We show that this extended forecast performs better than simple persistence or average models for all 6 forecast days. We also compare +1 day solar wind speed forecasts using offset STEREO‐B data and the Wang‐Sheeley‐Arge model, and we find that the offset STEREO‐B data performs significantly better for estimating the future solar wind at Earth during the investigation period. We conclude that this technique could be particularly beneficial to space weather forecasting and argue for a permanent solar wind monitor at the fifth Lagrange point in the Sun‐Earth system.

A multimodel ensemble-based Kalman filter for the retrieval of soil moisture profiles

With the combination of three land surface models (LSMs) and the ensemble Kalman filter (EnKF), a multimodel EnKF is proposed in which the multimodel background superensemble error covariance matrix is estimated by two different algorithms: the Simple Model Average (SMA) and the Weighted Average Method (WAM). The two algorithms are tested and compared in terms of their abilities to retrieve the true soil moisture profile by respectively assimilating both synthetically-generated and actual near-surface soil moisture measurements. The results from the synthetic experiment show that the performances of the SMA and WAM algorithms were quite different. The SMA algorithm did not help to improve the estimates of soil moisture at the deep layers, although its performance was not the worst when compared with the results from the single-model EnKF. On the contrary, the results from the WAM algorithm were better than those from any single-model EnKF. The tested results from assimilating the field measurements show that the performance of the two multimodel EnKF algorithms was very stable compared with the single-model EnKF. Although comparisons could only be made at three shallow layers, on average, the performance of the WAM algorithm was still slightly better than that of the SMA algorithm. As a result, the WAM algorithm should be adopted to approximate the multimodel background superensemble error covariance and hence used to estimate soil moisture states at the relatively deep layers.

Seasonal Hydrologic Forecasting: Do Multimodel Ensemble Averages Always Yield Improvements in Forecast Skill?

Abstract Multimodel techniques have proven useful in improving forecast skill in many applications, including hydrology. Seasonal hydrologic forecasting in large basins represents a special case of hydrologic modeling, in which postprocessing techniques such as temporal aggregation and time-varying bias correction are often employed to improve forecast skill. To investigate the effects that these techniques have on the performance of multimodel averaging, the performance of three hydrological models [Variable Infiltration Capacity, Sacramento/Snow-17, and the Noah land surface model] and two multimodel averages [simple model average (SMA) and multiple linear regression (MLR) with monthly varying model weights] are examined in three snowmelt-dominated basins in the western United States. These evaluations were performed for both simulating and forecasting [using the Ensemble Streamflow Prediction (ESP) method] monthly discharge, with and without monthly bias corrections. The single best bias-corrected model outperformed the multimodel averages of raw models in both retrospective simulations and ensemble mean forecasts in terms of RMSE. Forming an MLR multimodel average from bias-corrected models added only slight improvements over the best bias-corrected model. Differences in performance among all bias-corrected models and multimodel averages were small. For ESP forecasts, both bias correction and multimodel averaging generally reduced the RMSE of the ESP ensemble means at lead times of up to 6 months in months when flow is dominated by snowmelt, with the reduction increasing as lead time decreased. The primary reason for this is that aggregating simulated streamflows from daily to monthly time scales increases model cross correlation, which in turn reduces the effectiveness of multimodel averaging in reducing those components of model error that bias correction cannot address. This effect may be stronger in snowmelt-dominated basins because the interannual variability of winter precipitation is a common input to all models. It was also found that both bias correcting and multimodel averaging using monthly varying parameters yielded much greater error reductions than methods using time-invariant parameters.