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Alex J. Cannon
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Alex J. Cannon

Abstract

A nonlinear, probabilistic synoptic downscaling algorithm for daily precipitation series at multiple sites is presented. The expanded Bernoulli–gamma density network (EBDN) represents the conditional density of multisite precipitation, conditioned on synoptic-scale climate predictors, using an artificial neural network (ANN) whose outputs are parameters of the Bernoulli–gamma distribution. Following the methodology used in expanded downscaling, predicted covariances between sites are forced to match observed covariances through the addition of a constraint to the ANN cost function. The resulting model can be thought of as a regression-based downscaling model with a stochastic weather generator component. Parameters of the Bernoulli–gamma distribution are downscaled from the synoptic-scale circulation, and unresolved temporal variability is generated via an autoregressive noise model. Demonstrated on a multisite precipitation dataset from coastal British Columbia, Canada, the EBDN is capable of specifying the conditional distribution of precipitation at each site, modeling the occurrence and the amount of precipitation simultaneously, reproducing observed spatial relationships between sites, randomly generating realistic synthetic precipitation series, and predicting precipitation amounts in excess of those in the observational record.

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Alex J. Cannon

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Univariate bias correction algorithms, such as quantile mapping, are used to address systematic biases in climate model output. Intervariable dependence structure (e.g., between different quantities like temperature and precipitation or between sites) is typically ignored, which can have an impact on subsequent calculations that depend on multiple climate variables. A novel multivariate bias correction (MBC) algorithm is introduced as a multidimensional analog of univariate quantile mapping. Two variants are presented. MBCp and MBCr respectively correct Pearson correlation and Spearman rank correlation dependence structure, with marginal distributions in both constrained to match observed distributions via quantile mapping. MBC is demonstrated on two case studies: 1) bivariate bias correction of monthly temperature and precipitation output from a large ensemble of climate models and 2) multivariate correction of vertical humidity and wind profiles, including subsequent calculation of vertically integrated water vapor transport and detection of atmospheric rivers. The energy distance is recommended as an omnibus measure of performance for model selection. As expected, substantial improvements in performance relative to quantile mapping are found in each case. For reference, characteristics of the MBC algorithm are compared against existing bivariate and multivariate bias correction techniques. MBC performs competitively and fills a role as a flexible, general purpose multivariate bias correction algorithm.

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Alex J. Cannon

Abstract

Logistical constraints can limit the number of global climate model (GCM) simulations considered in a climate change impact assessment. When dealing with annual or seasonal variables, one can visualize and manually select GCM scenarios to cover as much of the ensemble’s range of changes as possible. Most environmental systems are sensitive to climate conditions (e.g., extremes) that cannot be described by a small number of variables. Instead, algorithms like k-means clustering have been used to select representative ensemble members. Clustering algorithms are, however, biased toward high-density regions of climate variable space and tend to select scenarios that describe the central tendency rather than the full spread of an ensemble. Also, scenarios selected via clustering may not be ordered: that is, scenarios in the five-cluster solution may not appear in the six-cluster solution, which makes recommending a consistent set of scenarios to researchers with different needs difficult. Alternatively, an automated procedure based on a cluster initialization algorithm is proposed and applied to changes in 27 climate extremes indices between 1986–2005 and 2081–2100 from a large ensemble of phase 5 of the Coupled Model Intercomparison Project (CMIP5) simulations. Selections by the method are ordered and are designed to span the overall range of the ensemble. The number of scenarios required to account for changes spanned by at least 90% of the CMIP5 ensemble members is reported for 21 regions of the globe and compared with k-means clustering. On average, the proposed method requires 40% fewer scenarios to meet this threshold than k-means clustering does.

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Alex J. Cannon

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Principal predictor analysis is a multivariate linear technique that fits between regression and canonical correlation analysis in terms of the complexity of its architecture. This study introduces a new neural network approach for performing nonlinear principal predictor analysis (NLPPA). NLPPA is applied to the Lorenz system of equations and is compared with nonlinear canonical correlation analysis (NLCCA) and linear multivariate models. Results suggest that NLPPA is capable of performing better than NLCCA when datasets are corrupted with noise. Also, NLPPA modes may be extracted in less time than NLCCA modes. NLPPA is recommended for prediction problems where a clear set of predictors and a clear set of predictands can be easily defined.

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Alex J. Cannon

Abstract

Regression-guided clustering is introduced as a means of constructing circulation-to-environment synoptic climatological classifications. Rather than applying an unsupervised clustering algorithm to synoptic-scale atmospheric circulation data, one instead augments the atmospheric circulation dataset with predictions from a supervised regression model linking circulation to environment. The combined dataset is then entered into the clustering algorithm. The level of influence of the environmental dataset can be controlled by a simple weighting factor. The method is generic in that the choice of regression model and clustering algorithm is left to the user. Examples are given using standard multivariate linear regression models and the k-means clustering algorithm, both established methods in synoptic climatology. Results for southern British Columbia, Canada, indicate that model performance can be made to range between that of a fully unsupervised algorithm and a fully supervised algorithm.

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Alex J. Cannon, Stephen R. Sobie, and Trevor Q. Murdock

Abstract

Quantile mapping bias correction algorithms are commonly used to correct systematic distributional biases in precipitation outputs from climate models. Although they are effective at removing historical biases relative to observations, it has been found that quantile mapping can artificially corrupt future model-projected trends. Previous studies on the modification of precipitation trends by quantile mapping have focused on mean quantities, with less attention paid to extremes. This article investigates the extent to which quantile mapping algorithms modify global climate model (GCM) trends in mean precipitation and precipitation extremes indices. First, a bias correction algorithm, quantile delta mapping (QDM), that explicitly preserves relative changes in precipitation quantiles is presented. QDM is compared on synthetic data with detrended quantile mapping (DQM), which is designed to preserve trends in the mean, and with standard quantile mapping (QM). Next, methods are applied to phase 5 of the Coupled Model Intercomparison Project (CMIP5) daily precipitation projections over Canada. Performance is assessed based on precipitation extremes indices and results from a generalized extreme value analysis applied to annual precipitation maxima. QM can inflate the magnitude of relative trends in precipitation extremes with respect to the raw GCM, often substantially, as compared to DQM and especially QDM. The degree of corruption in the GCM trends by QM is particularly large for changes in long period return values. By the 2080s, relative changes in excess of +500% with respect to historical conditions are noted at some locations for 20-yr return values, with maximum changes by DQM and QDM nearing +240% and +140%, respectively, whereas raw GCM changes are never projected to exceed +120%.

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Rajesh R. Shrestha, Markus A. Schnorbus, and Alex J. Cannon

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Recent improvements in forecast skill of the climate system by dynamical climate models could lead to improvements in seasonal streamflow predictions. This study evaluates the hydrologic prediction skill of a dynamical climate model–driven hydrologic prediction system (CM-HPS), based on an ensemble of statistically downscaled outputs from the Canadian Seasonal to Interannual Prediction System (CanSIPS). For comparison, historical and future climate traces–driven ensemble streamflow prediction (ESP) was employed. The Variable Infiltration Capacity model (VIC) hydrologic model setup for the Fraser River basin, British Columbia, Canada, was used as a test bed for the two systems. In both cases, results revealed limited precipitation prediction skill. For streamflow prediction, the ESP approach has very limited or no correlation skill beyond the months influenced by initial hydrologic conditions, while the CM-HPS has moderately better correlation skill, attributable to the enhanced temperature prediction skill that results from CanSIPS’s ability to predict El Niño–Southern Oscillation (ENSO) and its teleconnections. The root-mean-square error, bias, and categorical skills for the two methods are mostly similar. Hydrologic modeling uncertainty also affects the prediction skill, and in some cases prediction skill is constrained by hydrologic model skill. Overall, the CM-HPS shows potential for seasonal streamflow prediction, and further enhancements in climate models could potentially to lead to more skillful hydrologic predictions.

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Johannes Jenkner, William W. Hsieh, and Alex J. Cannon

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A novel methodology is presented for the identification of the mean cycle of the Madden–Julian oscillation (MJO) along the equator. The methodology is based on a nonlinear principal component (NLPC) computed with a neural network model. The bandpass-filtered input data encompass 30 yr with zonal winds at 850 and 200 hPa plus outgoing longwave radiation (OLR). The NLPC is conditioned on a sufficiently strong MJO activity and is computed both for the pooled dataset and for the dataset stratified into seasons. The NLPC for all data depicts a circular mode formed by the first two linear principal components (LPCs) with marginal contributions by the higher-order LPCs. Hence, the mean MJO cycle throughout the year is effectively captured by the amplitude of the leading two LPCs varying in quadrature. The NLPC for individual seasons shows additional variability, which mainly arises from a subordinate oscillation of the second pair of LPCs superimposed on the annual MJO signal. In reference to the all-year solution, the difference in resolved variability approximately accounts for 9% in solstitial seasons and 3% in equinoctial seasons. The phasing of the third LPC is such that convective activity oscillations over the Maritime Continent as well as wind oscillations over the Indian Ocean appear enhanced (suppressed) during boreal winter (summer). Also, convective activity oscillations appear more pronounced at the date line during both winter and summer. The phasing of the fourth LPC is such that upper-level westerlies over the Atlantic region are more persistent during boreal spring than during other seasons.

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Alex J. Cannon, Paul H. Whitfield, and Edward R. Lord

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A method for classifying synoptic-scale maps into discrete groups is introduced. Tree-based recursive partitioning models are used to develop mappings between synoptic-scale circulation fields and the leading linear and nonlinear principal components (PCs) of weather elements observed at a surface station. Statistically unique but climatically insignificant patterns are avoided by identifying map patterns based on their association with indices related to local weather conditions. The method requires few user-adjustable parameters and includes an algorithm that provides objective guidance for determining the appropriate number of map patterns to retain. The classification method is demonstrated using daily sea level pressure and 500-hPa geopotential height maps from a domain covering British Columbia and the northeastern Pacific Ocean. The linear and nonlinear weather element PCs are derived from daily measurements of surface temperature, dewpoint temperature, cloud opacity, and u and υ wind components taken at Vancouver, British Columbia.

Classification performance is tested by applying the method to precipitation and air quality scenarios. Results are compared with those from unsupervised map-pattern classifications based on the k-means clustering algorithm. Results from recursive partitioning models using linear weather element PCs as targets were better than those from the k-means algorithm. Recursive partitioning trees using nonlinear PCs as targets performed slightly worse than those using linear PCs as targets. Interestingly, trees using gridpoint circulation data as inputs outperformed models that used truncated PCs of the circulation data as inputs. Poorer results were found not to result from loss of information due to truncation of the PCs. Instead, the way information is encoded in principal component analysis (PCA) may be responsible for the poor classification performance in the recursive partitioning models using circulation PCs as inputs.

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