The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

A Large-Eddy Simulation Study of Water Vapour and Carbon Dioxide Isotopes in the Atmospheric Boundary Layer

A large-eddy simulation model developed at the National Center for Atmospheric Research (NCAR) is extended to simulate the transport and diffusion of C¹⁸OO, H₂¹⁸O and ¹³CO₂ in the atmospheric boundary layer (ABL). The simulation results show that the ¹⁸O compositions of leaf water and the ABL CO₂ are moderately sensitive to wind speed. The variations in the ¹⁸O composition of water vapour are an order of magnitude greater than those in the ¹³C and ¹⁸O compositions of CO₂ both at turbulent eddy scales and across the capping inversion. In a fully-developed convective ABL, these isotopic compositions are well mixed as with other conserved atmospheric quantities. The Keeling intercepts determined with the simulated high-frequency turbulence time series do not give a reliable estimate of the ¹⁸O composition of the surface water vapour flux and may be a reasonable approximation to the ¹³C and ¹⁸O compositions of the surface CO₂ flux in the late afternoon only after a deep convective ABL has developed. We suggest that our isotopic large-eddy simulation (ISOLES) model should be a useful tool for testing and formulating research hypotheses on land–air isotopic exchanges.     

Assessment of the changes in extreme vulnerability over East Asia due to global warming

A number of indices have been employed to describe weather extremes on the basis of climate regimes and public concerns. In this study, we combined these traditional indices into four groups according to whether they relate to warm (T_warm), cold (T_cold), wet (P_wet), or dry (P_dry) extremes. Analysis of the combined indices calculated for the daily temperatures and precipitation at 750 meteorological stations in Korea, China, and Japan for 1960s?C2000s shows increasing trends in T_warm and P_dry events and decreasing trends in T_cold events in recent decades, particularly in the northern part of East Asia. A notable regional variation is an increase in the P_wet events in the Korean Peninsula. We applied the same analysis to a 200-year global climate model simulation for 1900?C2099 using the National Center for Atmospheric Research-Community Climate System Model 3. During the 20th century, the changes in T_warm and T_cold calculated from the model data are largely consistent with those calculated from the observations, especially in northern East Asia. The model projections for the 21st century indicate statistically significant increasing T_warm and decreasing T_cold trends in extreme events over the region. Results obtained from historical archives and model simulations using our combined weather extreme indices suggest that northern East Asia will be subject to increased warm and dry extremes and the Korea Peninsula will experience more wet extremes.     

The influences of interannual stratification variability and wind stress forcing on ENSO before and after the 1976 climate shift

In order to understand the change in oceanic variability associated with the climate shift of the mid-1970s, we analyze the contribution of momentum forcing to the leading baroclinic modes over the tropical Pacific using Simple Ocean Data Assimilation (SODA, version 2.0.2) for the period of 1958–1997. Specifically, we look at the statistical relationship between the wind projection coefficients and climate indices and attempt to provide a physical explanation for the observed changes. It is found that the wind stress projection coefficients according to the oceanic baroclinic modes are different in terms of their magnitude and phase in the tropical Pacific, reflecting a specific forcing associated with each mode before and after the 1976 climate shift. Compared to that before the 1970s, the first baroclinic mode is had a greater effect on the interannual sea surface temperature due to equatorial wave dynamics, and there was an increased delayed response of the second baroclinic mode variability to the interannual atmospheric forcing after the late 1970s. This reflects changes in ENSO feedback processes associated with the climate shift. Our analysis further indicates that, after the late 1970s, there was a decrease in the wind stress forcing projecting onto the Ekman layer, which is associated with increased mixed-layer depth. This result suggests that the changes in the ENSO properties before and after the late 1970s are largely associated with the changes in the way in which the wind stress forcing is dynamically projected onto the surface layer of the tropical Pacific Ocean over interannual timescales.     

Effects of high-resolution land cover and topography on local circulations in two different coastal regions of Korea: a numerical modeling study

The effects of high-resolution land cover (LC) and topography (TP) on coastal wind circulations were evaluated in two different coastal regions of Korea (i.e. a southwestern coast (SWC), including a fairly complex coastline and a number of islands, and an eastern coast (EC), including a simple coastline with high mountains) during spring 2007. These analyses were performed based on a numerical modeling approach, using data sets with different resolutions, such as the LC and TP from the U.S. Geological Survey (USGS-LC and USGS-TP: a 900-m resolution), the LC from the Environmental Geographic Information System (EGIS-LC: a 90-m), and the TP from the Shuttle Radar Topography Mission (SRTM-TP: a 90-m). The combined effects of the LC and TP on the spatial distributions of the coastal winds in the SWC region during the day were somewhat higher than those of the EC region, mainly due to the daytime land surface warming or the extension of the coastal area resulting from changes in the LC. At night, the effects of the EC region were more apparent along the coastline and adjacent sea. From the correlation analyses, the effect of the LC on the vertical wind distributions on land during the day was higher in the SWC region than in the EC region and vice versa for the effect of the TP. In particular, large effects of the LC and TP occurred in the EC region at night and at sea due to the differences in the surface conditions and elevations resulting from the changes in the LC and TP, respectively. In addition, the circulation of coastal winds from the near surface to the upper levels occurred at a relatively high elevation in the EC region (about 1,500?m) relative to the SWC region (about 600?m).     

A proposal for a new scenario framework to support research and assessment in different climate research communities

In this paper, we propose a scenario framework that could provide a scenario “thread” through the different climate research communities (climate change – vulnerability, impact, and adaptation - and mitigation) in order to support assessment of mitigation and adaptation strategies and climate impacts. The scenario framework is organized around a matrix with two main axes: radiative forcing levels and socio-economic conditions. The radiative forcing levels (and the associated climate signal) are described by the new Representative Concentration Pathways. The second axis, socio-economic developments comprises elements that affect the capacity for mitigation and adaptation, as well as the exposure to climate impacts. The proposed scenarios derived from this framework are limited in number, allow for comparison across various mitigation and adaptation levels, address a range of vulnerability characteristics, provide information across climate forcing and vulnerability states and span a full century time scale. Assessments based on the proposed scenario framework would strengthen cooperation between integrated-assessment modelers, climate modelers and vulnerability, impact and adaptation researchers, and most importantly, facilitate the development of more consistent and comparable research within and across these research communities.     

Advance and prospectus of seasonal prediction: assessment of the APCC/CliPAS 14-model ensemble retrospective seasonal prediction (1980–2004)

We assessed current status of multi-model ensemble (MME) deterministic and probabilistic seasonal prediction based on 25-year (1980–2004) retrospective forecasts performed by 14 climate model systems (7 one-tier and 7 two-tier systems) that participate in the Climate Prediction and its Application to Society (CliPAS) project sponsored by the Asian-Pacific Economic Cooperation Climate Center (APCC). We also evaluated seven DEMETER models’ MME for the period of 1981–2001 for comparison. Based on the assessment, future direction for improvement of seasonal prediction is discussed. We found that two measures of probabilistic forecast skill, the Brier Skill Score (BSS) and Area under the Relative Operating Characteristic curve (AROC), display similar spatial patterns as those represented by temporal correlation coefficient (TCC) score of deterministic MME forecast. A TCC score of 0.6 corresponds approximately to a BSS of 0.1 and an AROC of 0.7 and beyond these critical threshold values, they are almost linearly correlated. The MME method is demonstrated to be a valuable approach for reducing errors and quantifying forecast uncertainty due to model formulation. The MME prediction skill is substantially better than the averaged skill of all individual models. For instance, the TCC score of CliPAS one-tier MME forecast of Niño 3.4 index at a 6-month lead initiated from 1 May is 0.77, which is significantly higher than the corresponding averaged skill of seven individual coupled models (0.63). The MME made by using 14 coupled models from both DEMETER and CliPAS shows an even higher TCC score of 0.87. Effectiveness of MME depends on the averaged skill of individual models and their mutual independency. For probabilistic forecast the CliPAS MME gains considerable skill from increased forecast reliability as the number of model being used increases; the forecast resolution also increases for 2 m temperature but slightly decreases for precipitation. Equatorial Sea Surface Temperature (SST) anomalies are primary sources of atmospheric climate variability worldwide. The MME 1-month lead hindcast can predict, with high fidelity, the spatial–temporal structures of the first two leading empirical orthogonal modes of the equatorial SST anomalies for both boreal summer (JJA) and winter (DJF), which account for about 80–90% of the total variance. The major bias is a westward shift of SST anomaly between the dateline and 120°E, which may potentially degrade global teleconnection associated with it. The TCC score for SST predictions over the equatorial eastern Indian Ocean reaches about 0.68 with a 6-month lead forecast. However, the TCC score for Indian Ocean Dipole (IOD) index drops below 0.40 at a 3-month lead for both the May and November initial conditions due to the prediction barriers across July, and January, respectively. The MME prediction skills are well correlated with the amplitude of Niño 3.4 SST variation. The forecasts for 2 m air temperature are better in El Niño years than in La Niña years. The precipitation and circulation are predicted better in ENSO-decaying JJA than in ENSO-developing JJA. There is virtually no skill in ENSO-neutral years. Continuing improvement of the one-tier climate model’s slow coupled dynamics in reproducing realistic amplitude, spatial patterns, and temporal evolution of ENSO cycle is a key for long-lead seasonal forecast. Forecast of monsoon precipitation remains a major challenge. The seasonal rainfall predictions over land and during local summer have little skill, especially over tropical Africa. The differences in forecast skills over land areas between the CliPAS and DEMETER MMEs indicate potentials for further improvement of prediction over land. There is an urgent need to assess impacts of land surface initialization on the skill of seasonal and monthly forecast using a multi-model framework.     

The Asian Dust Aerosol Model 2 (ADAM2) with the use of Normalized Difference Vegetation Index (NDVI) obtained from the Spot4/vegetation data

The operational Asian Dust Aerosol Model (ADAM)1 in Korea Meteorological Administration has been modified to the ADAM2 model to be used as an operational forecasting model all year round not only in Korea but also in the whole Asian domain (70-160°E and 5-60°N) using the routinely available World Meteorological Organization (WMO) surface reporting data and the Spot/vegetation Normalized Difference Vegetation Index (NDVI) data for the period of 9 years from 1998 to 2006. The 3-hourly reporting WMO surface data in the Asian domain have been used to re-delineate the Asian dust source region and to determine the temporal variation of the threshold wind speed for the dust rise. The dust emission reduction factor due to vegetation in different surface soil-type regions (Gobi, sand, loess, and mixed soil) has been determined with the use of NDVI data. It is found that the threshold wind speed for the dust rise varies significantly with time (minimum in summer and maximum in winter) and surface soil types with the highest threshold wind speed of 8.0 m?s^?1 in the Gobi region and the lowest value of 6.0 m?s^?1 in the loess region. The statistical analysis of the spot/vegetation NDVI data enables to determine the emission reduction factor due to vegetation with the free NDVI value that is the NDVI value without the effect of vegetation and the upper limit value of NDVI for the dust rise in different soil-type regions. The modified ADAM2 model has been implemented to simulate two Asian dust events observed in Korea for the periods from 31 March to 2 April 2007 (a spring dust event) and from 29 to 31 December 2007 (a winter dust event) when the observed PM₁₀ concentration at some monitoring sites in the source region exceeds 9,000 μg m^?3. It is found that ADAM2 model successfully simulates the observed high dust concentrations of more than 8,000 μg m^?3 in the dust source region and 600 μg m^?3 in the downstream region of Korea. This suggests that ADAM2 has a great potential for the use of an operational Asian dust forecast model in the Asian domain.     

Evaluation of proxy-based millennial reconstruction methods

A range of existing statistical approaches for reconstructing historical temperature variations from proxy data are compared using both climate model data and real-world paleoclimate proxy data. We also propose a new method for reconstruction that is based on a state-space time series model and Kalman filter algorithm. The state-space modelling approach and the recently developed RegEM method generally perform better than their competitors when reconstructing interannual variations in Northern Hemispheric mean surface air temperature. On the other hand, a variety of methods are seen to perform well when reconstructing surface air temperature variability on decadal time scales. An advantage of the new method is that it can incorporate additional, non-temperature, information into the reconstruction, such as the estimated response to external forcing, thereby permitting a simultaneous reconstruction and detection analysis as well as future projection. An application of these extensions is also demonstrated in the paper.