Mikyoung Jun

Spatial Analysis to Quantify Numerical Model Bias and Dependence : How Many Climate Models Are There?

A limited number of complex numerical models that simulate the Earths atmosphere, ocean, and land processes are the primary tool to study how climate may change over the next century due to anthropogenic emissions of greenhouse gases. A standard assumption is that these climate models are random samples from a distribution of possible models centered around the true climate. This implies that agreement with observations and the predictive skill of climate models will improve as more models are added to an average of the models. In this article we present a statistical methodology to quantify whether climate models are indeed unbiased and whether and where model biases are correlated across models. We consider the simulated mean state and the simulated trend over the period 1970–1999 for Northern Hemisphere summer and winter temperature. The key to the statistical analysis is a spatial model for the bias of each climate model and the use of kernel smoothing to estimate the correlations of biases across different climate models. The spatial model is particularly important to determine statistical significance of the estimated correlations under the hypothesis of independent climate models. Our results suggest that most of the climate model bias patterns are indeed correlated. In particular, climate models developed by the same institution have highly correlated biases. Also, somewhat surprisingly, we find evidence that the model skills for simulating the mean climate and simulating the warming trends are not strongly related.

NONSTATIONARY COVARIANCE MODELS FOR GLOBAL DATA

With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of parametric covariance models that can capture the nonstationarity in global data, especially strong dependency of covariance structure on latitudes. We apply the Discrete Fourier Transform to data on regular grids, which enables us to calculate the exact likelihood for large data sets. Our covariance model is applied to global total column ozone level data on a given day. We discuss how our covariance model compares with some existing models.

An approach to producing space-time covariance functions on spheres

For space–time processes on global or large scales, it is critical to use models that respect the Earths spherical shape. The covariance functions of such processes should be not only positive definite on sphere × time, but also capable of capturing the dynamics of the processes well. We develop space–time covariance functions on sphere × time that are flexible in producing space–time interactions, especially space–time asymmetries. Our idea is to consider a sum of independent processes in which each process is obtained by applying a first-order differential operator to a fully symmetric process on sphere × time. The resulting covariance functions can produce various types of space–time interactions and give different covariance structures along different latitudes. Our approach yields explicit expressions for the covariance functions, which has great advantages in computation. Moreover, it applies equally well to generating asymmetric space–time covariance functions on flat or other spatial domains. We study various characteristics of our new covariance functions, focusing on their space–time interactions. We apply our model to a dataset of total column ozone levels in the Northern hemisphere.

Local eigenvalue analysis of CMIP3 climate model errors

A B S T R A C T Of the two dozen or so global atmosphere–ocean general circulation models (AOGCMs), many share parameterizations, components or numerical schemes, and several are developed by the same institutions. Thus it is natural to suspect that some of the AOGCMs have correlated error patterns. Here we present a local eigenvalue analysis for the AOGCM errors based on statistically quantified correlation matrices for these errors. Our statistical method enables us to assess the significance of the result based on the simulated data under the assumption that all AOGCMs are independent. The result reveals interesting local features of the dependence structure of AOGCM errors. At least for the variable and the timescale considered here, the Coupled Model Intercomparison Project phase 3 (CMIP3) model archive cannot be treated as a collection of independent models. We use multidimensional scaling to visualize the similarity of AOGCMs and all-subsets regression to provide subsets of AOGCMs that are the best approximation to the variation among the full set of models.

Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors.

Farm Management, Environment, and Weather Factors Jointly Affect the Probability of Spinach Contamination by Generic Escherichia coli at the Preharvest Stage

ABSTRACT The National Resources Information (NRI) databases provide underutilized information on the local farm conditions that may predict microbial contamination of leafy greens at preharvest. Our objective was to identify NRI weather and landscape factors affecting spinach contamination with generic Escherichia coli individually and jointly with farm management and environmental factors. For each of the 955 georeferenced spinach samples (including 63 positive samples) collected between 2010 and 2012 on 12 farms in Colorado and Texas, we extracted variables describing the local weather (ambient temperature, precipitation, and wind speed) and landscape (soil characteristics and proximity to roads and water bodies) from NRI databases. Variables describing farm management and environment were obtained from a survey of the enrolled farms. The variables were evaluated using a mixed-effect logistic regression model with random effects for farm and date. The model identified precipitation as a single NRI predictor of spinach contamination with generic E. coli, indicating that the contamination probability increases with an increasing mean amount of rain (mm) in the past 29 days (odds ratio [OR] = 3.5). The model also identified the farms hygiene practices as a protective factor (OR = 0.06) and manure application (OR = 52.2) and state (OR = 108.1) as risk factors. In cross-validation, the model showed a solid predictive performance, with an area under the receiver operating characteristic (ROC) curve of 81%. Overall, the findings highlighted the utility of NRI precipitation data in predicting contamination and demonstrated that farm management, environment, and weather factors should be considered jointly in development of good agricultural practices and measures to reduce produce contamination.

Multifactorial effects of ambient temperature, precipitation, farm management, and environmental factors determine the level of generic Escherichia coli contamination on preharvested spinach.

ABSTRACT A repeated cross-sectional study was conducted to identify farm management, environment, weather, and landscape factors that predict the count of generic Escherichia coli on spinach at the preharvest level. E. coli was enumerated for 955 spinach samples collected on 12 farms in Texas and Colorado between 2010 and 2012. Farm management and environmental characteristics were surveyed using a questionnaire. Weather and landscape data were obtained from National Resources Information databases. A two-part mixed-effect negative binomial hurdle model, consisting of a logistic and zero-truncated negative binomial part with farm and date as random effects, was used to identify factors affecting E. coli counts on spinach. Results indicated that the odds of a contamination event (non-zero versus zero counts) vary by state (odds ratio [OR] = 108.1). Odds of contamination decreased with implementation of hygiene practices (OR = 0.06) and increased with an increasing average precipitation amount (mm) in the past 29 days (OR = 3.5) and the application of manure (OR = 52.2). On contaminated spinach, E. coli counts increased with the average precipitation amount over the past 29 days. The relationship between E. coli count and the average maximum daily temperature over the 9 days prior to sampling followed a quadratic function with the highest bacterial count at around 24°C. These findings indicate that the odds of a contamination event in spinach are determined by farm management, environment, and weather factors. However, once the contamination event has occurred, the count of E. coli on spinach is determined by weather only.

A Statistical Investigation of the Sensitivity of Ensemble-Based Kalman Filters to Covariance Filtering

This paper investigates the effects of spatial filtering on the ensemble-based estimate of the background error covariance matrix in an ensemble-based Kalman filter (EnKF). In particular, a novel kernel smoothing method with variable bandwidth is introduced and its performance is compared to that of the widely used Gaspari‐Cohn filter, which uses a fifth-order kernel function with a fixed localization length. Numerical experiments are carried out with the 40-variable Lorenz-96 model. The results of the experiments show that the nonparametric approach provides a more accurate estimate of the background error covariance matrix than the Gaspari‐Cohn filter with any localization length. It is also shown that the Gaspari‐Cohn filter tends to provide more accurate estimates of the covariance with shorter localization lengths. However, the analyses obtained by using longer localization lengths tend to be more accurate than those produced by using short localization lengths or the nonparametric approach. This seemingly paradoxical result is explained by showing that localization with longer localization lengths produces filtered estimates whose time mean is the most similar to the time meanof both the unfilteredestimate and the true covariance. This result suggeststhat a better metric of covariance filtering skill would be one that combined a measure of closeness to the sample covariance matrix for a very large ensemble with a measure of similarity between the climatological averages of the filtered and sample covariance.

Matérn-based nonstationary cross-covariance models for global processes

Many spatial processes in environmental applications, such as climate variables and climate model errors on a global scale, exhibit complex nonstationary dependence structure, in not only their marginal covariance but also their cross-covariance. Flexible cross-covariance models for processes on a global scale are critical for an accurate description of each spatial process as well as the cross-dependences between them and also for improved predictions. We propose various ways to produce cross-covariance models, based on the Matern covariance model class, that are suitable for describing prominent nonstationary characteristics of the global processes. In particular, we seek nonstationary versions of Matern covariance models whose smoothness parameters vary over space, coupled with a differential operators approach for modeling large-scale nonstationarity. We compare their performance to the performance of some existing models in terms of the aic and spatial predictions in two applications: joint modeling of surface temperature and precipitation, and joint modeling of errors in climate model ensembles.

Observation Quality Control with a Robust Ensemble Kalman Filter

AbstractCurrent ensemble-based Kalman filter (EnKF) algorithms are not robust to gross observation errors caused by technical or human errors during the data collection process. In this paper, the authors consider two types of gross observational errors, additive statistical outliers and innovation outliers, and introduce a method to make EnKF robust to gross observation errors. Using both a one-dimensional linear system of dynamics and a 40-variable Lorenz model, the performance of the proposed robust ensemble Kalman filter (REnKF) was tested and it was found that the new approach greatly improves the performance of the filter in the presence of gross observation errors and leads to only a modest loss of accuracy with clean, outlier-free, observations.