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Seth Westra and Ashish Sharma

Abstract

A statistical estimation approach is presented and applied to multiple reservoir inflow series that form part of Sydney’s water supply system. The approach involves first identifying sources of interannual and interdecadal climate variability using a combination of correlation- and wavelet-based methods, then using this information to construct probabilistic, multivariate seasonal estimates using a method based on independent component analysis (ICA). The attraction of the ICA-based approach is that, by transforming the multivariate dataset into a set of independent time series, it is possible to maintain the parsimony of univariate statistical methods while ensuring that both the spatial and temporal dependencies are accurately captured.

Based on a correlation analysis of the reservoir inflows with the original sea surface temperature anomaly data, the principal sources of variability in Sydney’s reservoir inflows appears to be a combination of the El Niño–Southern Oscillation (ENSO) phenomenon and the Pacific decadal oscillation (PDO). A multivariate ICA-based estimation model was then used to capture this variability, and it was shown that this approach performed well in maintaining the temporal dependence while also accurately maintaining the spatial dependencies that exist in the 11-dimensional historical reservoir inflow dataset.

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Seth Westra and Ashish Sharma

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The asymptotic predictability of global land surface precipitation is estimated empirically at the seasonal time scale with lead times from 0 to 12 months. Predictability is defined as the unbiased estimate of predictive skill using a given model structure assuming that all relevant predictors are included, thus representing an upper bound to the predictive skill for seasonal forecasting applications. To estimate predictability, a simple linear regression model is formulated based on the assumption that land surface precipitation variability can be divided into a component forced by low-frequency variability in the global sea surface temperature anomaly (SSTA) field and that can theoretically be predicted one or more seasons into the future, and a “weather noise” component that originates from nonlinear dynamical instabilities in the atmosphere and is not predictable beyond ~10 days.

Asymptotic predictability of global precipitation was found to be 14.7% of total precipitation variance using 1900–2007 data, with only minor increases in predictability using shorter and presumably less error-prone records. This estimate was derived based on concurrent SSTA–precipitation relationships and therefore constitutes the maximum skill achievable assuming perfect forecasts of the evolution of the SSTA field. Imparting lags on the SSTA–precipitation relationship, the 3-, 6-, 9-, and 12-month predictability of global precipitation was estimated to be 7.3%, 5.4%, 4.2%, and 3.7%, respectively, demonstrating the comparative gains that can be achieved by developing improved SSTA forecasts compared to developing improved SSTA–precipitation relationships. Finally, the actual average cross-validated predictive skill was found to be 2.1% of the total precipitation variance using the full 1900–2007 dataset and was dominated by the El Niño–Southern Oscillation (ENSO) phenomenon. This indicates that there is still significant potential for increases in predictive skill through improved parameter estimates, the use of longer and/or more reliable datasets, and the use of larger spatial fields to substitute for limited temporal records.

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Shahadat Chowdhury and Ashish Sharma

Abstract

The interest in climate prediction has seen a rise in the number of modeling alternatives in recent years. One way to reduce the predictive uncertainty from any such modeling procedure is to combine or average the modeled outputs. Multiple model results can be combined such that the combination weights may either be static or vary over time. This research develops a methodology for combining forecasts from multiple models in a dynamic setting. The authors mix models on a pairwise basis using importance weights that vary in time, reflecting the persistence of individual model skills. Such an approach is referred to here as a dynamic pairwise combination tree and is presented as an improvement over the case where the importance weights are static or constant over time. The pairwise importance weight is modeled as a product of a “mixture ratio” and a “bias direction,” the former representing the fraction of the absolute residual error associated with each of the paired models, and the latter representing an indicator of the sign of the two residual errors. The mixture ratio is modeled using a generalized autoregressive model and the bias direction using ordered logistic regression.

The method is applied to combine three climate models, the variables of interest being the monthly sea surface temperature anomalies averaged over the Niño-3.4 region from 1956 to 2001. The authors test the combined model skill using a “leave ± 6 months out cross-validation” approach along with validation in 10-yr blocks. This study attained a small but consistent improvement of the predictive skill of the dynamically combined models compared to the existing practice of static weight combination.

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Fiona Johnson and Ashish Sharma

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Trends of decreasing pan evaporation around the world have renewed interest in evaporation and its behavior in a warming world. Observed pan evaporation around Australia has been modeled to attribute changes in its constituent variables. It is found that wind speed decreases have generally led to decreases in pan evaporation. Trends were also calculated from reanalysis and general circulation model (GCM) outputs. The reanalysis reflected the general pattern and magnitude of the observed station trends across Australia. However, unlike the station trends, the reanalysis trends are mainly driven by vapor pressure deficit changes than wind speed changes. Some of the GCMs modeled the trends well, but most showed an average positive trend for Australia. Half the GCMs analyzed show increasing wind speed trends, and most show larger changes in vapor pressure deficit than would be expected based on the station data. Future changes to open water body evaporation have also been assessed using projections for two emission scenarios. Averaged across Australia, the models show a 5% increase in open water body evaporation by 2070 compared to 1990 levels. There is considerable variability in the model projections, particularly for the aerodynamic component of evaporation. Assumptions of increases in evaporation in a warming world need to be considered in light of the variability in the parameters that affect evaporation.

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Rajeshwar Mehrotra and Ashish Sharma

Abstract

A novel multivariate quantile-matching nesting bias correction approach is developed to remove systematic biases in general circulation model (GCM) outputs over multiple time scales. This is a significant advancement over typical quantile-matching alternatives available for bias correction, as they implicitly assume that correction of individual variable attributes will lead to correction of dependence biases between multiple variables. Furthermore, existing approaches perform bias correction at a given time scale (e.g., daily), whereas applications often require biases to be addressed at more than one time scale (such as annual in the case of most water resources planning projects). The proposed approach addresses all these issues, and additionally attempts to correct for lag-1 dependence (and cross-dependence) attributes across multiple time scales. The approach is called multivariate recursive quantile nesting bias correction (MRQNBC). The fidelity of the approach is demonstrated by applying it to a vector of CSIRO Mk3 GCM atmospheric variables and comparing the results with the commonly used quantile-matching approach. Following this, the implications of the approach in hydrology- and water resources–related applications are demonstrated by feeding the bias-corrected data to a rainfall downscaling model and comparing the downscaled rainfall attributes for current and future climate. The proposed approach is shown to represent the variability and persistence related attributes better and can thus be expected to have important consequences for the simulation of occurrence and intensity of extreme events such as floods and droughts in downscaled simulations, of importance in various climate impact assessment applications.

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Shahadat Chowdhury and Ashish Sharma

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This paper dynamically combined three multivariate forecasts where spatially and temporally variant combination weights are estimated using a nearest-neighbor approach. The case study presented combines forecasts from three climate models for the period 1958–2001. The variables of interest here are the monthly global sea surface temperature anomalies (SSTA) at a 5° × 5° latitude–longitude grid, predicted 3 months in advance. The forecast from the static weight combination is used as the base case for comparison. The forecasted sea surface temperature using the dynamic combination algorithm offers consistent improvements over the static combination approach for all seasons. This improved skill is achieved over at least 93% of the global grid cells, in four 10-yr independent validation segments. Dynamically combined forecasts reduce the mean-square error of the SSTA by at least 25% for 72% of the global grid cells when compared against the best-performing single forecast among the three climate models considered.

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Fiona Johnson and Ashish Sharma

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Simulations from general circulation models are now being used for a variety of studies and purposes. With up to 23 different GCMs now available, it is desirable to determine whether a specific variable from a particular model is representative of the ensemble mean, which is often assumed to indicate the likely state of that variable in the future. The answers are important for decision makers and researchers using selective model outputs for follow-on studies such as statistical downscaling, which currently assume all model outputs are simulated with equal reliability.

A skill score, termed the variable convergence score (VCS), has been derived that can be used to rank variables based on the coefficient of variation of the ensemble. The key benefit is the development of a simple methodology that allows for a quantitative assessment between different hydroclimatic variables.

The VCS methodology has been applied to the outputs of nine GCMs for eight different variables and two emission scenarios to provide a relative ranking of the variables averaged across Australia and over different climatic regions of the country. The methodology, however, would be applicable for any region or any variable of interest from GCMs.

It was found that the surface variables with the highest scores are pressure, temperature, and humidity. Regionally in Australia, models again show the best agreement in the surface pressure projections. The tropical and southwestern temperate zones show the overall highest variable convergence when all variables are considered. The desert zone shows relatively low model agreement, particularly in the projections of precipitation and specific humidity.

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Seokhyeon Kim, Alfonso Anabalón, and Ashish Sharma

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While broad consensus exists that temperatures are increasing, there is uncertainty surrounding the direction of change manifested in actual evapotranspiration (ET) worldwide. This study assessed trends in ET across the land surface using 11 widely used global datasets for a 32-yr study period. To demonstrate the agreement and disagreement of trends, the spatial distribution, concurrence, correlation, and similitude were estimated. The results showed that while the global average trend in ET is −0.072 mm month−1 yr−1, the trends from individual datasets show a wide range of differences in magnitudes and directions. The considerable differences in the trends in each dataset were found to be weakly correlated with each other and highly divergent in their distribution and direction. No single dataset was sufficiently similar to another to offer a fair representation of trends. In a dynamic trend analysis using a 10-yr moving window over the study period, high concurrence in the significant trends throughout the datasets was found to be rare for each time period. In general, the global data concurrence became negative by 1997 but rebounded to positive toward the end of the study period. In terms of spatial tendency, some regions were more prone to change the direction of their significant trends within the study period. This result shows a high inconsistency in the location and direction of significant ET trends, implying that selection of an ET dataset should consider its spatiotemporal uncertainty before use for any water balance study aiming to infer hydrological change over time.

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Siriluk Chumchean, Alan Seed, and Ashish Sharma

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This paper presents a method to correct for the range-dependent bias in radar reflectivity that is a result of partial beam filling and of the increase in observation volume with range. The scaling behavior of reflectivity fields as a function of range from the radar was explored in this study. It was found that a simple scaling paradigm was applicable, and a scale transformation function was proposed to ensure uniformity in the probability distributions of reflectivity at both near and far range. The scaling exponents of the power-law transformation function were estimated using a 6-month sequence of reflectivity maps in a Cartesian grid and two sets of instantaneous reflectivity maps in polar coordinates from 1° C-band and 1.6° S-band radars at Sydney, Australia. The averaging process that transforms the instantaneous polar reflectivity into the hourly Cartesian grid data leads to a lower scaling exponent of the hourly Cartesian reflectivity data compared with the instantaneous plan precipitation indicator (PPI) polar data. The scaling exponents for the hourly Cartesian case, the instantaneous polar case using the 1° C-band radar, and the instantaneous polar case using the 1.6° S-band radar data were estimated as 0.024, 0.10, and 0.22, respectively.

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Eytan Rocheta, Jason P. Evans, and Ashish Sharma

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Global climate model simulations inherently contain multiple biases that, when used as boundary conditions for regional climate models, have the potential to produce poor downscaled simulations. Removing these biases before downscaling can potentially improve regional climate change impact assessment. In particular, reducing the low-frequency variability biases in atmospheric variables as well as modeled rainfall is important for hydrological impact assessment, predominantly for the improved simulation of floods and droughts. The impact of this bias in the lateral boundary conditions driving the dynamical downscaling has not been explored before. Here the use of three approaches for correcting the lateral boundary biases including mean, variance, and modification of sample moments through the use of a nested bias correction (NBC) method that corrects for low-frequency variability bias is investigated. These corrections are implemented at the 6-hourly time scale on the global climate model simulations to drive a regional climate model over the Australian Coordinated Regional Climate Downscaling Experiment (CORDEX) domain. The results show that the most substantial improvement in low-frequency variability after bias correction is obtained from modifying the mean field, with smaller changes attributed to the variance. Explicitly modifying monthly and annual lag-1 autocorrelations through NBC does not substantially improve low-frequency variability attributes of simulated precipitation in the regional model over a simpler mean bias correction. These results raise questions about the nature of bias correction techniques that are required to successfully gain improvement in regional climate model simulations and show that more complicated techniques do not necessarily lead to more skillful simulation.

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