Discussion of: A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?

McShane and Wyner [(2011); hereinafter MW11] reiterate a well-known and central challenge of paleoclimatology: it is fraught with uncertainties and based on noisy observations. Decades of research have aimed at characterizing these uncertainties and interpreting proxies through laboratory experiments, field observations, theory, process-based modeling, cross-record comparisons, and indeed through statistical modeling and hypothesis testing. It is against this larger backdrop that the problem addressed by MW11 must be considered. Attempts to reconstruct global or hemispheric temperature indices and fields using multi-proxy networks are an outgrowth of many efforts in paleoclimatology, but represent relatively recent pursuits in the field. They provide neither the principal scientific evidence supporting climate-proxy connections, nor the most compelling, and the inference by MW11 that their own findings demonstrate a widespread failure in the predictive capacity of climate proxies is at odds with most other independent lines of proxy research

Simulating heat transport of harmonic temperature signals in the Earth's shallow subsurface: Lower-boundary sensitivities

We assess the sensitivity of a subsurface thermodynamic model to the depth of its lower-boundary condition. Analytic solutions to the one-dimensional thermal diffusion equation demonstrate that boundary conditions imposed at shallow depths (2-20 m) corrupt the amplitudes and phases of propagating temperature signals. The presented solutions are for: 1) a homogeneous infinite half-space driven by a harmonic surface-temperature boundary condition, and 2) a homogeneous slab with a harmonic surface-temperature boundary condition and zero-flux lower-boundary condition. Differences between the amplitudes and phases of the two solutions range from 0 to almost 100%, depending on depth, frequency and subsurface thermophysical properties. The implications of our results are straightforward: the corruption of subsurface temperatures can affect model assessments of soil microbial activity, vegetation changes, freeze-thaw cycles, and hydrologic dynamics. It is uncertain, however, whether the reported effects will have large enough impacts on land-atmosphere fluxes of water and energy to affect atmospheric simulations

Characterizing Land–Atmosphere Coupling and the Implications for Subsurface Thermodynamics

The objective of this work is to develop a Simple Land-Interface Model (SLIM) that captures the seasonal and interannual behavior of land–atmosphere coupling, as well as the subsequent subsurface temperature evolution. The model employs the one-dimensional thermal diffusion equation driven by a surface flux boundary condition. While the underlying physics is straightforward, the SLIM framework allows a qualitative understanding of the first-order controls that govern the seasonal coupling between the land and atmosphere by implicitly representing the dominant processes at the land surface. The model is used to perform a suite of experiments that demonstrate how changes in surface air temperature and coupling conditions control subsurface temperature evolution. The work presented here suggests that a collective approach employing both complex and simple models, when joined with analyses of observational data, has the potential to increase understanding of land–atmosphere coupling and the subsequent evolution of subsurface temperatures

Defining spatial comparison metrics for evaluation of paleoclimatic field reconstructions of the Common Era

Climate field reconstructions (CFR) of the Common Era (the last two millennia) provide important insights into the dynamics of past climate change that, in turn, have implications for the future. Multiple CFR methods have emerged in the literature, and comparisons between these methods using pseudoproxy experiments have been performed. These experiments, however, have not fully quantified the spatial skill of the CFRs, particularly with regard to the relative performance of each. Toward such ends, a formal statistical hypothesis test is proposed as a means of evaluating the differences between two random fields that integrate the differences in both the mean and the dependence structure. This involves a careful selection of the statistical model for the CFR residual process and systematic comparisons over different spatial scales. Application of this method yields a systematic assessment of the spatial character of five widely applied CFRs in a pseudoproxy experiment context. The analyses indicate that spatial differences among the five CFRs are not statistically significant. Further rigorous statistical assessments will help elucidate the strength and weakness of each CFR method, while quantifying the degree to which their spatial dissimilarities can be ascribed to methodological choices

Comparative performance of paleoclimate field and index reconstructions derived from climate proxies and noise-only predictors

The performance of climate field reconstruction (CFR) and index reconstruction methods is evaluated using proxy and non-informative predictor experiments. The skill of both reconstruction methods is determined using proxy data targeting the western region of North America. The results are compared to those targeting the same region, but derived from non-informative predictors comprising red-noise time series reflecting the full temporal autoregressive structure of the proxy network. All experiments are performed as probabilistic ensembles, providing estimated Monte Carlo distributions of reconstruction skill. Results demonstrate that the CFR skill distributions from proxy data are statistically distinct from and outperform the corresponding skill distributions generated from non-informative predictors; similar relative performance is demonstrated for the index reconstructions. In comparison to the CFR results using proxy information, the index reconstructions exhibit similar skill in calibration, but somewhat less skill in validation and a tendency to underestimate the amplitude of the validation period mean

Tropical climate influences on drought variability over Java, Indonesia

We investigate relationships between Indonesian drought, the state of the equatorial Indian Ocean, and ENSO using three instrumental indices spanning 1884-1997 A.D.: 1. EQWIN, a zonal wind index for the equatorial Indian Ocean; 2. the Dipole Mode Index (DMI), an indicator of the Indian Ocean SST gradient; and 3. tropical Pacific Niño-3.4 SSTs. A regression model of the Java Sep-Dec Palmer Drought Severity Index (PDSI) using a combination of these indices provides significant predictive skill (ar^2 = 0.50). Both the DMI and EQWIN correlate strongly with Java droughts (r = 0.71 and 0.66, respectively), but weakly with wet events (r = 0.21 and 0.18, respectively), while the Niño SST index correlates moderately with both dry and wet events (r = 0.31 and 0.36, respectively). Our findings indicate that Java droughts are intensified during El Niños that coincide with negative EQWIN conditions, which are also linked to a strengthened Indian monsoon

Erroneous Model Field Representations in Multiple Pseudoproxy Studies: Corrections and Implications

Pseudoproxy experiments evaluate statistical methods used to reconstruct climate fields from paleoclimatic proxies during the Common Era. These experiments typically employ output from millennial simulations by general circulation models (GCMs). It is demonstrated that multiple published pseudoproxy studies have used erroneously processed GCM surface temperature fields: the NCAR Community Climate System Model (CCSM), version 1.4, field was incorrectly oriented geographically and the GKSS ECHO-g FOR1 field was corrupted by a hemispheric-scale smoothing in the Western Hemisphere. These problems are not associated with the original model simulations; they instead arose because of incorrect processing of the model data for the pseudoproxy experiments. The consequences of these problems are evaluated for the studies in which the incorrect fields were used. Some quantitative results are invalidated by the findings: these include all experiments that used the corrupted ECHO-g field and those aspects of previous CCSM experiments that focused on Niño-3 reconstructions. Other results derived from the CCSM field can be reinterpreted based on the information provided herein and their qualitative characteristics remain similar

Continental-scale temperature variability in PMIP3 simulations and PAGES 2k regional temperature reconstructions over the past millennium

Estimated external radiative forcings, model results, and proxy-based climate reconstructions have been used over the past several decades to improve our understanding of the mechanisms underlying observed climate variability and change over the past millennium. Here, the recent set of temperature reconstructions at the continental-scale generated by the PAGES 2k project and a collection of state-of-the-art model simulations driven by realistic external forcings are jointly analysed. The first aim is to estimate the consistency between model results and reconstructions for each continental-scale region over the time and frequency domains. Secondly, the links between regions are investigated to determine whether reconstructed global-scale covariability patterns are similar to those identified in model simulations. The third aim is to assess the role of external forcings in the observed temperature variations. From a large set of analyses, we conclude that models are in relatively good agreement with temperature reconstructions for Northern Hemisphere regions, particularly in the Arctic. This is likely due to the relatively large amplitude of the externally forced response across northern and high-latitude regions, which results in a clearly detectable signature in both reconstructions and simulations. Conversely, models disagree strongly with the reconstructions in the Southern Hemisphere. Furthermore, the simulations are more regionally coherent than the reconstructions, perhaps due to an underestimation of the magnitude of internal variability in models or to an overestimation of the response to the external forcing in the Southern Hemisphere. Part of the disagreement might also reflect large uncertainties in the reconstructions, specifically in some Southern Hemisphere regions, which are based on fewer palaeoclimate records than in the Northern Hemisphere

Comparison between spatio-temporal random processes and application to climate model data

Comparing two spatio-temporal processes are often a desirable exercise. For example, assessments of the difference between various climate models may involve the comparisons of the synthetic climate random fields generated as simulations from each model. We develop rigorous methods to compare two spatio-temporal random processes both in terms of moments and in terms of temporal trend, using the functional data analysis approach. A highlight of our method is that we can compare the trend surfaces between two random processes, which are motivated by evaluating the skill of synthetic climate from climate models in terms of capturing the pronounced upward trend of real-observational data. We perform simulations to evaluate our methods and then apply the methods to compare different climate models as well as to evaluate the synthetic temperature fields from model simulations, with respect to observed temperature fields

Propagation of linear surface air temperature trends into the terrestrial subsurface

Previous studies have tested the long-term coupling between air and terrestrial subsurface temperatures working under the assumption that linear trends in surface air temperature should be equal to those measured at depth within the subsurface. A one-dimensional model of heat conduction is used to show that surface trends are attenuated as a function of depth within conductive media on time scales of decades to centuries, therefore invalidating the above assumption given practical observational constraints. The model is forced with synthetic linear temperature trends as the time-varying upper boundary condition; synthetic trends are either noise free or include additions of Gaussian noise at the annual time scale. It is shown that over a 1000 year period, propagating surface trends are progressively damped with depth in both noise-free and noise-added scenarios. Over shorter intervals, the relationship between surface and subsurface trends is more variable and is strongly impacted by annual variability (i.e., noise). Using output from the FOR1 millennial simulation of the GKSS ECHO-G General Circulation Model as a more realistic surface forcing function for the conductive model, it is again demonstrated that surface trends are damped as a function of depth within the subsurface. Observational air and subsurface temperature data collected over 100 years in Armagh, Ireland, and 29 years in Fargo, North Dakota, are also analyzed and shown to have subsurface temperature trends that are not equal to the surface trend. While these conductive effects are correctly accounted for in inversions of borehole temperature profiles in paleoclimatic studies, they have not been considered in studies seeking to evaluate the long-term coupling between air and subsurface temperatures by comparing trends in their measured time series. The presented results suggest that these effects must be considered and that a demonstrated trend equivalency in air and subsurface temperatures is inconclusive regarding their long-term tracking