A Bayesian ANOVA Scheme for Calculating Climate Anomalies ----------------------------------------------------------------------- World Data Center for Paleoclimatology, Boulder and NOAA Paleoclimatology Program ----------------------------------------------------------------------- NOTE: Please cite original reference when using these data, plus the data file URL and date accessed. NAME OF DATA SET: A Bayesian ANOVA Scheme for Calculating Climate Anomalies LAST UPDATE: 1/2012 (Original receipt by WDC Paleo) CONTRIBUTOR: Tingley, M.P. IGBP PAGES/WDCA CONTRIBUTION SERIES NUMBER: 2012-005 WDC PALEO CONTRIBUTION SERIES CITATION: Tingley, M.P. 2012. A Bayesian ANOVA Scheme for Calculating Climate Anomalies. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2012-005. NOAA/NCDC Paleoclimatology Program, Boulder CO, USA. ORIGINAL REFERENCE: Tingley, M.P. 2012. A Bayesian ANOVA Scheme for Calculating Climate Anomalies, with Applications to the Instrumental Temperature Record. Journal of Climate, Vol. 25, Issue 2, January 2012, pp. 777-791. doi: http://dx.doi.org/10.1175/JCLI-D-11-00008.1 ABSTRACT: Climate datasets with both spatial and temporal components are often studied after removing from each time series a temporal mean calculated over a common reference interval, which is generally shorter than the overall length of the dataset. The use of a short reference interval affects the temporal properties of the variability across the records, by reducing the standard deviation within the reference interval and inflating it elsewhere. For an annually averaged version of the Climate Research Unit's (CRU) temperature anomaly product, the mean standard deviation is 0.67°C within the 1961-90 reference interval, and 0.81°C elsewhere. The calculation of anomalies can be interpreted in terms of a two-factor analysis of variance model. Within a Bayesian inference framework, any missing values are viewed as additional parameters, and the reference interval is specified as the full length of the dataset. This Bayesian scheme is used to re-express the CRU dataset as anomalies with respect to means calculated over the entire 1850-2009 interval spanned by the dataset. The mean standard deviation is increased to 0.69°C within the original 1961-90 reference interval, and reduced to 0.76°C elsewhere. The choice of reference interval thus has a predictable and demonstrable effect on the second spatial moment time series of the CRU dataset. The spatial mean time series is in this case largely unaffected: the amplitude of spatial mean temperature change is reduced by 0.1°C when using the 1850-2009 reference interval, while the 90% uncertainty interval of (-0.03, 0.23) indicates that the reduction is not statistically significant. GEOGRAPHIC REGION: N/A PERIOD OF RECORD: N/A FUNDING SOURCES: DATA FILE URLS: ftp://ftp.ncdc.noaa.gov/pub/data/paleo/softlib/anova/ DESCRIPTION: Matlab code for two-factor (location and year) analysis-of-variance model for the calculation of climate anomalies, in which the reference interval is specified as the full length of the dataset. This scheme avoids the affects of shorter (e.g. 1961-1990) reference intervals on the temporal evolution of the spatial standard deviation of climate anomalies. Data and code associated with M.P. Tingley Journal of Climate 25:777 File and folders are as follows: Demo_code_package Matlab files to implement the Bayesian model. See associated ReadMe.rtf file for details. Generate_Figures_2_and_3.m Generate_Figure_4.m Matlab files to generate Figures 2, 3 and 4 from the paper. CRU_Anomalies CRU_Lats_Lons CRU_Years Initial data files. Each entry of CRU_Anomalies corresponds to the average of the CRU monthly anomalies (from 1961-199) at a particular year and location. The rows are years, given by CRU_Years, and the columns locations, given by CRU_Lats_Lons. Location_effects_delta_5_50_95 Year_effects_mu_5_50_95 The 5th, 50th, and 95th percentiles of the posterior draws of the Location and Year effects. The locations corresponding to the rows of Location_effects_delta_5_50_95 are given by the rows of CRU_Lats_Lons, while the years corresponding to the rows of Year_effects_mu_5_50_95 are given by CRU_Years. The three percentiles of the year and location effects are used to create Figure 6. Scalar_Draws 5000 draws of the scalar parameters. Columns are (gamma, sigma^2, sigma^2_mu, sigma^2_delta). Histograms of these draws will produce Figure 7. Means_Original_Post_5_50_95 StandDevs_Orignal_Post_5_50_95 Left column is the mean (standard deviation) time series of the original data (X from the paper). Second through fourth columns are the 5th, 50th, and 95th percentiles of the mean (standard deviation) time series of the adjusted data (Y from the paper). These data sets are used to create Figures 8&9. Spatial_Mean_1961_1990_5_50_95 Spatial_Mean_1850_2009_5_50_95 Spatial_Mean_1961_1990_Smoothed_5_50_95 Spatial_Mean_1850_2009_Smoothed_5_50_95 The 5th, 50th, and 95th percentiles of the posterior draws of the spatial mean time series estimated from BARCAST. The years indicate the reference interval used to calculate the anomalies, with 1961-1990 being the original CRU data set. 'Smoothed' indicates that each draw has been temporally smoothed prior to calculating percentiles. Note that temporal means of the draws were removed prior to forming percentiles (see text). These data sets are used to create the panels (a) and (b) of Figure 10. Spatial_Mean_Smoothed_difference_5_50_95 The 5th, 50th, and 95th percentiles of the difference between the posterior draws of the spatial mean time series estimated from BARCAST, using the anomalies from each of the two reference intervals. Note that the 90% uncertainty interval for the effect of the reference interval on the spatial mean temperature change over the last 160 years is calculated from the actual draws of the difference, not the percentiles. For each draw of the time series of difference, the difference between year 2005 and 1866 is calculated, and percentiles calculated from the resulting distribution. Anomalies_1850_2009_5th Anomalies_1850_2009_50th Anomalies_1850_2009_95th The 5th, 50th, and 95th percentiles of the anomalies with respect to 1850--2009. These matrices have the same missing data pattern as CRU_Anomalies. Please contact the author if your application requires the actual posterior draws of the anomaly field, rather then the percentiles.