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Scale-dependent Regional Climate Predictability over North America Inferred from CMIP3 and CMIP5 Ensemble Simulations

doi: 10.1007/s00376-016-6013-2

  • Through the analysis of ensembles of coupled model simulations and projections collected from CMIP3 and CMIP5, we demonstrate that a fundamental spatial scale limit might exist below which useful additional refinement of climate model predictions and projections may not be possible. That limit varies among climate variables and from region to region. We show that the uncertainty (noise) in surface temperature predictions (represented by the spread among an ensemble of global climate model simulations) generally exceeds the ensemble mean (signal) at horizontal scales below 1000 km throughout North America, implying poor predictability at those scales. More limited skill is shown for the predictability of regional precipitation. The ensemble spread in this case tends to exceed or equal the ensemble mean for scales below 2000 km. These findings highlight the challenges in predicting regionally specific future climate anomalies, especially for hydroclimatic impacts such as drought and wetness.
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  • Bei N., F. Q. Zhang, 2007: Impacts of initial condition errors on mesoscale predictability of heavy precipitation along the Mei-Yu front of China. Quart. J. Roy. Meteor. Soc., 133, 83- 99.10.1002/ Summertime heavy precipitation associated with the quasi-stationary Mei-Yu front often causes severe flooding along the Yangtze river basin in China. This study explores the mesoscale predictability of one such event near Wuhan, the capital city of Hubei Province. The 20-21 July rainfall event contributed to making the 1998 flood season the worst in this region since 1954. Various sensitivity experiments were performed to examine the impact of both realistic and idealized initial condition uncertainties of different scales and amplitudes on the prediction of the mesoscale precipitation systems along the Mei-Yu front. While it is found that mesoscale model simulations initialized with global analyses at a 36-h lead time can depict the evolution of the synoptic environment reasonably well, there are large variations between different experiments in the prediction of the mesoscale details and heavy precipitation of this event. It was also found that larger-scale, larger-amplitude initial uncertainties generally led to larger forecast divergence than did uncertainties of smaller scales and small amplitudes. However, the forecast errors induced by perturbations of the same amplitude but at different scales are very similar if the initial error is sufficiently small. Error growth is strongly nonlinear and small-amplitude initial errors, which are far smaller than those of current observational networks, may grow rapidly and quickly saturate at smaller scales. They subsequently grow upscale, leading to significant forecast uncertainties at increasingly larger scales. In agreement with previous studies, moist convection is found to be the key to the rapid error growth leading to limited mesoscale predictability. These findings further suggest that, while there is significant scope for improving forecast skill by improving forecast models and initial conditions, mesoscale predictability of such a heavy precipitation event is inherently limited. Copyright 漏 2007 Royal Meteorological Society
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    Mearns L. O., I. Bogardi, F. Giorgi, I. Matyasovszky, and M. Palecki, 1999: Comparison of climate change scenarios generated from regional climate model experiments and statistical downscaling. J. Geophys. Res., 104, 6603- 6621.10.1029/ compare regional climate change scenarios (temperature and precipitation) over eastern Nebraska produced by a semiempirical statistical downscaling (SDS) technique and regional climate model (RegCM2) experiments, both using large scale information from the same coarse resolution general circulation model (GCM) control and 2 脳 COsimulations. The SDS method is based on the circulation pattern classification technique in combination with stochastic generation of daily time series of temperature and precipitation. It uses daily values of 700 mbar geopotential heights as the large-scale circulation variable. The regional climate model is driven by initial and lateral boundary conditions from the GCM. The RegCM2 exhibited greater spatial variability than the SDS method for change in both temperature and precipitation. The SDS method produced a seasonal cycle of temperature change with a much larger amplitude than that of the RegCM2 or the GCM. Daily variability of temperature mainly decreased for both downscaling methods and the GCM. Changes in mean daily precipitation varied between SDS and RegCM2. The RegCM2 simulated both increases and decreases in the probability of precipitation, while the SDS method produced only increases. We explore possible dynamical and physical reasons for the differences in the scenarios produced by the two methods and the GCM.
    Meehl, G. A., Coauthors, 2007: The WCRP CMIP3 multimodel dataset: A new era in climate change research. Bull. Amer. Meteor. Soc., 88, 1383- 1394.10.1175/ article discusses the use of global coupled climate models for conducting climatic research. It focuses on the rapid climate changes facing the Earth, and the experiments that are being conducted by a World Climate Research Programme (WCRP) committee. It is stated that open access to climate simulation data has helped students and scientists from around the globe to analyze model data on weather changes. It is stated that significant contributions have recently been made not only to the Intergovernmental Panel on Climate Change (IPCC), but also to the human knowledge of climate variability and forecasting.
    Murphy J. M., D. M. H. Sexton, D. N. Barnett, G. S. Jones, M. J. Webb, M. Collins, and D. A. Stainforth, 2004: Quantification of modelling uncertainties in a large ensemble of climate change simulations. Nature, 430, 768- 772.10.1038/ global climate models are the only tools that account for the complex set of processes which will determine future climate change at both a global and regional level. Planners are typically faced with a wide range of predicted changes from different models of unknown relative quality, owing to large but unquantified uncertainties in the modelling process. Here we report a systematic attempt to determine the range of climate changes consistent with these uncertainties, based on a 53-member ensemble of model versions constructed by varying model parameters. We estimate a probability density function for the sensitivity of climate to a doubling of atmospheric carbon dioxide levels, and obtain a 5-95 per cent probability range of 2.4-5.4 degrees C. Our probability density function is constrained by objective estimates of the relative reliability of different model versions, the choice of model parameters that are varied and their uncertainty ranges, specified on the basis of expert advice. Our ensemble produces a range of regional changes much wider than indicated by traditional methods based on scaling the response patterns of an individual simulation.
    Separovic L., R. de Ela, and R. Laprise, 2008: Reproducible and irreproducible components in ensemble simulations with a Regional Climate Model. Mon. Wea. Rev. 136, 4942- 4961.10.1175/ High-resolution limited-area models (LAMs) have been widely employed to downscale coarse-resolution climate simulations or objective analyses. The growing evidence that LAM climate statistics can be sensitive to initial conditions suggests that a deterministic verification of LAM solutions in terms of finescale atmospheric features might be misguided. In this study a 20-member ensemble of LAM integrations with perturbed initial conditions, driven by NCEP-揘CAR reanalyses, is conducted for a summer season over a midlatitude domain. Ensemble simulations allow for the separation of the downscaled information in two parts: a unique, reproducible component associated with lateral-boundary and surface forcing, and an irreproducible component associated with internal variability. The partition in the reproducible and irreproducible components and their seasonal statistics is examined as a function of horizontal length scale, geographical position within the domain, height, and weather episodes during the season. The scale analysis of time-dependent model variables shows that, at scales smaller than a few hundred kilometers, the irreproducible component dominates, on average, the model solution, implying that the downscaled information at these scales is mainly in stochastic form. The constraint exerted by the surface forcing on the internal variability is weak. For seasonal averages, the reproducible component dominates at all scales, although for precipitation the reproducible and irreproducible components are of the same order of magnitude at scales smaller than 150 km. These results imply a need for a probabilistic approach to LAM climate simulations and their verification, especially for shorter integration times, from months to seasons.
    Taylor K. E., R. J. Stouffer, and G. A. Meehl, 2012: An overview of CMIP5 and the experiment design. Bull. Amer. Meteor. Soc., 93, 485-
    Tebaldi C., R. L. Smith, D. Nychka, and L. O. Mearns, 2005: Quantifying uncertainty in projections of regional climate change: A Bayesian approach to the analysis of multimodel ensembles. J. Climate., 18, 1524- 1540.10.1175/ Bayesian statistical model is proposed that combines information from a multimodel ensemble of atmosphere-ocean general circulation models (AOGCMs) and observations to determine probability distributions of future temperature change on a regional scale. The posterior distributions derived from the statistical assumptions incorporate the criteria of bias and convergence in the relative weights implicitly assigned to the ensemble members. This approach can be considered an extension and elaboration of the reliability ensemble averaging method. For illustration, the authors consider the output of mean surface temperature from nine AOGCMs, run under the A2 emission scenario from the Synthesis Report on Emission Scenarios (SRES), for boreal winter and summer, aggregated over 22 land regions and into two 30-yr averages representative of current and future climate conditions. The shapes of the final probability density functions of temperature change vary widely, from unimodal curves for regions where model results agree (or outlying projections are discounted) to multimodal curves where models that cannot be discounted on the basis of bias give diverging projections. Besides the basic statistical model, the authors consider including correlation between present and future temperature responses, and test alternative forms of probability distributions for the model error terms. It is suggested that a probabilistic approach, particularly in the form of a Bayesian model, is a useful platform from which to synthesize the information from an ensemble of simulations. The probability distributions of temperature change reveal features such as multimodality and long tails that could not otherwise be easily discerned. Furthermore, the Bayesian model can serve as an interdisciplinary tool through which climate modelers, climatologists, and statisticians can work more closely. For example, climate modelers, through their expert judgment, could contribute to the formulations of prior distributions in the statistical model.
    Timm O., H. F. Diaz, 2009: Synoptic-statistical approach to regional downscaling of IPCC twenty-first-century climate projections: Seasonal rainfall over the Hawaiian Islands. J.Climate, 22, 4261-
    von Storch, H., E. Zorita, U. Cubasch, 1993: Downscaling of global climate change estimates to regional scales: An application to Iberian rainfall in wintertime. J.Climate, 6, 1161-
    Watterson I. G., P. H. Whetton, 2011: Distributions of decadal means of temperature and precipitation change under global warming. J. Geophys. Res., 116, D07101.10.1029/ remains uncertainty in the projected climate change over the 21st century, in part because of the range of responses forced by rising greenhouse gas concentrations among global climate models. This paper applies a method of estimating distributions and "probability density functions" (PDFs) for forced change, based on the pattern scaling technique and previously used for Australia, to generate changes in temperature and precipitation at locations over the globe, from simulations of 23 CMIP3 models. Changes for 2030 and 2100, under the A1B scenario for concentrations, for both seasonal and annual cases are presented. The PDFs for temperature have a standard deviation that averages 31% of the mean change, and they tend to be positively skewed. The standard deviation for precipitation averages 15% of the base climate mean, leading to five and 95 percentile estimates that are of opposite sign for most of the globe. A further source of uncertainty of change for a particular period of time, such as a decadal average, is the unforced or internal variability of climate. A joint probability distribution approach is used to produce PDFs for decadal means by adding in an estimate of internal variability. In the decade centered on 2030, this broadens the PDFs substantially. The results are related to time series of observations and projections over 1900-2100 for the agricultural regions of Iowa and the Murray-Darling Basin. For most land areas, warming becomes clearly discernable, allowing for both uncertainties, in the next few decades. Data files of the key results are provided.
    Watterson I. G., J. Bathols, and C. Heady, 2014: What influences the skill of climate models over the continents? Bull. Amer. Meteor. Soc., 95, 689- 700.10.1175/ modeling groups from four continents have submitted simulations as part of phase 5 of the Coupled Model Intercomparison Project (CMIP5). With climate impact assessment in mind, we test the accuracy of the seasonal averages of temperature, precipitation, and mean sea level pressure, compared to two observational datasets. Nondimensional skill scores have been generated for the global land and six continental domains. For most cases the 25 models analyzed perform well, particularly the models from Europe. Overall, this CMIP5 ensemble shows improved skill over the earlier (ca. 2005) CMIP3 ensemble of 24 models. This improvement is seen for each variable and continent, and in each case it is largely consistent with the increased resolution on average of CMIP5, given the correlation between scores and grid length found across the combined ensemble. From this apparent influence on skill, the smaller average score for the 13 Earth system models in CMIP5 is consistent with their mostly lower resolution. There is some variation in the ranking of models by skill score for the global, versus continental, measures of skill, and this prompts consideration of the potential influence of a regional focus that model developers might have. While some models rank considerably better in their 'home' continent than globally, most have similar ranks in the two domains. Averaging over each ensemble, the home rank is better by only one or two ranks, indicating that the location of development is only a minor influence.
    Whetton P., I. Macadam, J. Bathols, and J. O'Grady, 2007: Assessment of the use of current climate patterns to evaluate regional enhanced greenhouse response patterns of climate models. Geophys. Res. Lett., 34, L14701.10.1029/ of multiple global climate models is often considered in the generation of regional climate change projections. The reliability of the regional responses of models to enhanced greenhouse forcing is often assessed by comparing their current climate simulation against observations. The rationale for this assessment is that a model should be able to reproduce key aspects of the present climate if it is to be used to provide guidance for future changes in climate. However, the best way to assess the current climate of a model is unresolved. One can assess regional average or grid point model biases for the variable and season for which projections are to be prepared. However, a model that performs well for a target variable, season and location, may perform poorly for another variable, season or location, in which case model processes would be suspect. Other approaches consider spatial patterns and multiple variables, but this then raises the issue of how large an area the patterns should cover and what set of variables should be considered. We demonstrate how such a pattern-based approach can be evaluated by investigating the relationship between inter-model similarity in patterns of current regional climate and inter-model similarity in patterns of regional enhanced greenhouse response using data from the CMIP3 multi-model database. By making the assumption that the real world behaves like a typical climate model, we can use these results to assess whether the testing of the current climate patterns of the models against observations can be used to discriminate amongst enhanced greenhouse results of the models. Correlations of moderate magnitude are common in our results, indicating the value of testing the current regional climate simulation of models. Notably, relationships vary significantly regionally (e.g. are weakest in the tropics), cross variables (e.g. current climate mean sea level pressure is related to temperature and precipitation change in some extra-tropical regions) and can be insensitive to whether the current climate is assessed in the region concerned or globally. The presentation will also consider how the approach may be applied to performance-weighting of models in the generation of regional climate projections and in the assessment of the independence of output from different models.
    Zhou T.-J., R. C. Yu, 2006: Twentieth-century surface air temperature over china and the globe simulated by coupled climate models. J.Climate, 19( 22), 5843- 5858.10.1175/ Available
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Manuscript received: 19 January 2016
Manuscript revised: 16 March 2016
Manuscript accepted: 11 April 2016
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Scale-dependent Regional Climate Predictability over North America Inferred from CMIP3 and CMIP5 Ensemble Simulations

  • 1. Department of Meteorology and Center for Advanced Data Assimilation and Predictability Techniques, The Pennsylvania State University, University Park, PA 16802, USA
  • 2. IMSG at NOAA/NWS/NCEP/Environmental Modeling Center, College Park, MD 20740, USA

Abstract: Through the analysis of ensembles of coupled model simulations and projections collected from CMIP3 and CMIP5, we demonstrate that a fundamental spatial scale limit might exist below which useful additional refinement of climate model predictions and projections may not be possible. That limit varies among climate variables and from region to region. We show that the uncertainty (noise) in surface temperature predictions (represented by the spread among an ensemble of global climate model simulations) generally exceeds the ensemble mean (signal) at horizontal scales below 1000 km throughout North America, implying poor predictability at those scales. More limited skill is shown for the predictability of regional precipitation. The ensemble spread in this case tends to exceed or equal the ensemble mean for scales below 2000 km. These findings highlight the challenges in predicting regionally specific future climate anomalies, especially for hydroclimatic impacts such as drought and wetness.

1. Introduction
  • There is widespread scientific consensus that the accumulation of greenhouse concentrations from fossil fuel burning and other human activities is leading to a warming of the globe and other associated changes in large-scale climate (IPCC, 2013). Most assessments indicate that the cost of the resulting damage from climate change will rise to several percent of the global economy in the decades ahead if left unchecked. Yet, our ability to assess the regional impacts of climate change, which are critical both to assessing the damage caused by climate change and the implementation of adaptive strategies, remains hampered by the remaining substantial uncertainties associated with regional climate projections (Murphy et al., 2004; Tebaldi et al., 2005; Hawkins and Sutton, 2009; Deser et al., 2012; Watterson et al., 2014).

    Regional climate projections are typically derived by one of two methods: statistical downscaling or dynamical downscaling (IPCC, 2013). In the former case, statistical relationships between coarse and fine scales derived from modern climate data are used to take coarse-scale climate model predictions/projections and estimate the likely impact on climate statistics at finer spatial and temporal scales. In the latter case, information from coarse climate models is used as boundary constraints on a finer resolution model (a regional climate model) that resolves the smaller spatiotemporal scales of interest. In either case, there is an assumption of a predictable relationship between the large scales captured in the coarse climate model projection and the local scales sought by the downscaling method.

    Downscaled climate model projections have increasingly been used as guidance for policymakers and stakeholders at the local, national, and international level in assessing potential impacts and risks associated with human-caused climate change (von Storch et al., 1993; Mearns et al., 1999; Jones et al., 2011). However, the reliability of these projections continues to be debated. There is clearly skill in the largest-scale quantities; for example, the observed increase in global mean temperature (and even continental mean temperatures) can be detected and attributed to anthropogenic climate change (IPCC, 2007). However, confidence in regional-scale projections of surface temperature and precipitation is considerably lower (Whetton et al., 2007; Separovic et al., 2008; Watterson and Whetton, 2011; Deser et al., 2012; Li et al., 2012).

    In the current study, we seek to quantify the predictability of regional-scale climate change, with an emphasis on surface temperature and precipitation, across the coterminous United States and surrounding areas, through analysis of the multimodel ensembles of coupled model simulations collected from both CMIP3 and CMIP5. In section 2 we describe the data and methods used in the study. In section 3 we present an analysis of regional climate predictability based on CMIP5 multimodel historical simulations. In section 4 we provide a complementary analysis of CMIP3 multimodel simulations, analyzing both historical simulations and future projections. Conclusions are presented in section 5.

2. Data and methodology
  • We analyze surface temperature and precipitation fields across the coterminous United States and neighboring oceanic regions (15°-60°N, 70°-130°W), as derived from both observational data and an ensemble of climate model simulations.

    Observational data analyzed include monthly mean 5° latitude × 5° longitude grid-box near-surface temperature anomalies over 1850-2014 from HadCRUT4. We add the reference period climatology over 1961-90 to yield absolute surface temperatures. Precipitation data are taken from the 1° latitude × 1° longitude GPCC dataset over the period 1979-2004.

    For the climate model simulations, monthly mean surface (2 m) air temperature and precipitation spanning the period 1979-2004 are available for 38 climate models in the historical late 19th to early 21st century 20C3M CMIP5 simulation archives, and 18 for CMIP3 (Taylor et al., 2012) (Table 1). Where multiple simulations are available for a given model, a single ensemble mean is calculated to ensure that each distinct model is represented equally in the ensuing analysis.

    We focus our analysis on the boreal summer (June-August) climatological period during the 1979-2004 period of overlap between observations and model simulations. Both observational and model data are interpolated to a common (T85, 1.4° latitude × 1.4° longitude) spatial resolution prior to analysis. For the purpose of the ensuing analyses, we define the following terms:

    (1) Ensemble mean: the uniform arithmetic mean of all ensemble members;

    (2) Ensemble spread: the uniform arithmetic mean of the absolute difference between any two members across all ensemble members;

    (3) Ensemble mean error or bias: the (signed) difference between the model ensemble mean and the observational analysis.

    In addition to evaluating the ensemble mean, ensemble spread, and error for the observational and model fields themselves, we perform a power spectral analysis (using the Fast Fourier transform) of the fields to evaluate the power spectral density (PSD) characteristics of the various quantities in wavenumber space. In these analyses:

    (1) The ensemble mean power spectrum (P) is defined as the PSD of the non-weighted arithmetic mean (V m) for all ensemble members (M=38):

    P= PSD(V m),V m=(1/M)∑iVi,M=38;

    (2) The PSD of the ensemble spread is defined as:

    ∆ P=(1/N)∑k=1NP d,P d= PSD(Vi-Vj), where i and j are any pair of ensemble members and N=703.

    (3) The PSD of the ensemble mean error or bias is defined as the power spectra of the difference between the ensemble mean and the observation, i.e.,

    P'= PSD(V m-V o), where V m and V o refer to the ensemble mean and observational variables, respectively.

    The ratio of the PSD ensemble mean (signal) and ensemble spread (noise) as a function of wavenumber defines a scale-dependent SNR measure (Bei and Zhang, 2007). A ratio smaller than unity indicates that the noise amplitude is greater than the signal amplitude, and implies that model estimates of mean changes are unreliable at that spatial scale. Wavenumber 1 corresponds to a single sinusoidal fluctuation over the entire circle of latitude, i.e., it is the coarsest possible measure of zonal variability (wavenumber 0 represents the zonal mean). Since the selected U.S. domain is precisely 1/6 of a circle of latitude, the lowest resolvable wavenumber for that domain is global wavenumber 6. The horizontal scale (wavelength) for a given wavenumber is the length of the circle of latitude divided by the wavenumber, e.g., the length scale corresponding to wavenumbers 1, 2, 3, 4, 5, 6 and 9 are 36 000, 18 000, 12 000, 9000, 7200, 6000 and 4000 km, respectively.

3. CMIP5 multimodel historical experiments
  • We form estimates of the internal variability in the climate means of summertime precipitation and surface air temperature during the period 1979-2004 using the multimodel ensemble of 38 CMIP5 historical simulations (Fig. S1 in electronic supplementary material). The mean difference between any two models within the 38-model ensemble is defined as the ensemble spread; a measure of uncertainty of any deterministic prediction assuming the truth (as well as any single deterministic prediction) is a random draw out of the multimodel ensemble. The ensemble spread can be regarded as a lower bound on the model uncertainty, since it neither accounts for the potential bias due to deficiencies in model physics that are common among models, nor uncertainties in forcing (both anthropogenic and natural).

    Figures 1a and b show the resulting mean and ensemble spread of surface temperature and monthly precipitation over the U.S. domain. The largest uncertainty for the surface temperature field is found over the western U.S., with the ensemble spread as high as 5°C-6°C; followed by the central U.S., with a spread of 3°C-5°C; and the eastern U.S., with a spread of 1.5°C-3°C (all higher than the surrounding oceans, at 0.5°C-1.5°C). It is worth noting that the warming trend over the U.S. during the past century is on the order of 1°C (Ji et al., 2014), though it is beyond the scope of this study to examine the scale-, variable- and location-dependent predictability of the climate trend.

    Figure 1.  Ensemble mean and spread/error for CMIP5 historical simulations and observations of summer (June-August) surface air temperature and precipitation over the U.S. during 1979-2004. Top: ensemble mean (contours) and ensemble spread (color-shaded) for (a) surface air temperature and (b) precipitation. Bottom: observational mean (contours) and error (color-shaded) for (c) surface air temperature and (d) precipitation. The corresponding domain-mean spreads are $2.09^\circ$C for (a), 0.97 mm d$^-1$ for (b), $1.16^\circ$C for (c), and 0.58 mm d$^-1$ for (d).

    The large uncertainty in the mean surface temperature field (Fig. 1a) can be interpreted through a parallel assessment using the observational (HadCRUT4) surface temperature during the overlapping time period (Fig. 1c). The error/bias can be estimated as the model ensemble mean minus the observations. The domain-averaged ensemble spread (2.1°C) is found to be larger but grossly comparable to the domain-averaged root-mean-square of this estimate of error/bias (1.2°C). Moreover, the spatial pattern of the error/bias is similar to that of the ensemble spread, with the western U.S. displaying the largest mean error, followed by the Great Plains in the central U.S., and finally the eastern U.S. There are, however, some notable differences as well. Of particular interest is the relatively low spread over the North American west and east coasts and neighboring ocean regions (Fig. 1a), which contrasts with the large error/bias estimates over these same regions (Fig. 1c). This suggests the presence of a systematic bias that is common to most or all of the climate models, perhaps associated with deficiencies in the models' representations of land-sea contrast or continental sea-breeze circulations.

    The region of maximum uncertainty (ensemble spread) for precipitation (Fig. 1b) is found over lower latitudes (the south central U.S. and Latin America), with an ensemble spread exceeding 2.5 mm d-1——roughly half the amplitude of the observed mean (signal). A second uncertainty maximum in precipitation is located over the northern Great Plains in the lee of the Rockies, with an ensemble spread exceeding 1.5 mm d-1. The spatial pattern of the ensemble mean error (Fig. 1d) is once again grossly consistent with that for the ensemble spread (uncertainty), in that regions of peak amplitude are similar (e.g., common maxima along the southern edge of the domain and northern Great Plains), though the ensemble mean errors of approximately -2.5 mm d-1 are considerably larger than the ensemble spread for the Gulf Coast and Florida Peninsula. In addition, the North American domain-mean absolute ensemble mean error and spread are also comparable in magnitude (0.58 mm d-1 and 0.97 mm d-1, respectively).

    Unlike surface temperature, which is primarily determined by large-scale processes, precipitation is heavily influenced by smaller-scale processes including moist convection, land-sea contrast, and orographic lifting. This distinction is exemplified by the local maxima for both ensemble mean error and spread over the Gulf of Mexico (hot spot of convection) and the mountainous areas of the western U.S. (where orographic effects are important). Comparing Figs. 1b and d suggests that, for the CMIP5 simulations of climatological mean precipitation, the ensemble spread can be used qualitatively to assess the uncertainty in the ensemble mean estimate. To place the U.S. results in a broader perspective, we also compare the ensemble mean, spread, and error for the global domain (not shown). The basic results discussed above appear to apply at this larger scale as well (though a detailed analysis of the global domain is beyond the scope of the current study).

    The spatial scale-dependence of the predictability of surface temperature and precipitation is quantified by evaluating the PSD along both global circles of latitude and a latitudinal/longitudinal sub-region containing the coterminous U.S. (15°-60° N, 70°-130°W). Figure 2 shows the ensemble mean (left) and ensemble spread (middle) PSD for the CMIP5 surface temperature and precipitation fields, along with the ratio of the ensemble mean to the ensemble spread, i.e., the SNR (right) as a function of global wavenumber. For the global circle of latitude ensemble mean temperature (Fig. 2a), the PSD exhibits a peak at lower wavenumbers (1-3) for the midlatitudes (40°-60°N); while for the subtropics (20°-40°N), three distinct spectral peaks are observed (wavenumbers 1, 3 and 5). By contrast, for the ensemble spread, the PSD (Fig. 2b) decreases quite gradually in both the midlatitudes and the subtropics, though greater amplitudes are found across all wavenumbers for the former. The SNR (Fig. 2c) exceeds unity at all latitude and wavenumber ranges, with the exception of (1) wavenumber 4 between 40°-60°N, (2) wavenumber 6 poleward of 50°N, and (3) wavenumber 9 between 45°-55°N. Given the SNRs, surface temperature projections can be considered most reliable for wavenumbers 1-2 in the midlatitudes, and wavenumbers 1, 3 and 5 within the subtropics. Therefore, meaningful surface temperature predictions (SNR>1) appear possible over a somewhat broad range of latitudes and wavenumbers.

    Figure 2.  Wavenumber-latitude distribution of the PSD of (a-f) surface air temperature and (g-l) precipitation over the global (0$^\circ$-360$^\circ$) and U.S. regional (70$^\circ$-130$^\circ$W) sub-domain. Shown are the PSDs for the ensemble mean, i.e., signal (left); ensemble spread, i.e., noise (middle); and ratio of the former to the latter, i.e., the SNR (right). The PSD amplitude scale is logarithmic.

    For the more limited U.S. sub-region, the ensemble mean (Fig. 2d) and spread (Fig. 2e) are both larger at lower wavenumbers than for their global counterparts, but the SNR (Fig. 2f) falls below unity for global wavenumber 12 (horizontal scale of 30° longitudinal variation, i.e., distances of 3000 km) over the central latitudes of the U.S. (35°-45°N), and for nearly all wavenumbers greater than 36 (scales less than 10° in longitudinal distance, i.e., distances less than 1000 km). This observation implies that state-of-the-art (i.e., CMIP5) climate model projections are likely to exhibit very limited skill in predicting regional variations in surface temperature at scales below 1000 km. It is noteworthy that wavenumber 18 (20° or 2000 km in longitudinal distance) exhibits the maximum SNR at nearly all latitudes for the U.S. domain. We interpret this observation as indicative of the influence of topographical features in the U.S. that induce enhanced predictability at this characteristic spatial scale.

    The findings for precipitation (Figs. 2g and h) are quite different from those for surface temperature (Figs. 2a and b). Precipitation exhibits greater spectral amplitude in the subtropics relative to the midlatitudes, especially for lower (1-2) wavenumbers. SNRs at the global scale (Fig. 2i) are generally lower, substantially exceeding unity only for wavenumbers 1-2 between 20°N and 50°N, and wavenumber 4 between 40°N and 60°N. Low predictability (SNR<1) is observed even at wavenumbers 1-2 poleward of 50°N, implying considerable challenges in predicting regional-scale variations in precipitation at high latitudes. Interestingly, however, for the U.S. regional sub-domain (Figs. 2j-l), there are apparently predictable signals (SNR>1) for global wavenumbers 6-12 at nearly all latitudes, and for even higher wavenumbers (24-60, i.e., scales as small as 600 km) in the central U.S. latitudes (35°-45°N). The larger signals over these latitudes in the North American domain may be related to regional-scale terrain effects and land-ocean contrasts, although some models may still have deficiencies in simulating these effects.

    To further assess the scale and latitude dependence of surface temperature and precipitation predictability over the U.S. sub-domain, we average the fields over three representative latitude ranges (low latitude, 15°-30°N; midlatitude, 30°-45°N; and high latitude, 45°-60°N; see Fig. 3). Given that the observations represent a single realization drawn from a larger distribution of possible climate histories, if the model ensemble accurately reflects the true climate, the PSD of the observations should be similar to that of individual ensemble members, and the ensemble mean should reflect the approximate mode of the distribution. On the other hand, the PSD of the ensemble spread (representing the uncertainty) should closely resemble that of the difference between the ensemble mean and observations (error/bias) across wavenumbers.

    Figure 3.  PSD of the observations (black), ensemble mean (red), ensemble error (blue) and ensemble spread (green) for summer (June-August) (a-f) surface air temperature and (g-l) precipitation over the global (0$^\circ$-360$^\circ$E) and U.S. regional (70$^\circ$-130$^\circ$W) sub-domain averaged over three different latitude bands (left, 15$^\circ$-30$^\circ$N; middle, 30$^\circ$-45$^\circ$N; right, 45$^\circ$-60$^\circ$N). Scales for both axes are logarithmic.

    Figure 4.  As in Fig. 1 but using CMIP3 historical simulations.

    Figure 5.  As in Fig. 2 but using CMIP3 historical simulations.

    Figure 6.  As in Fig. 3 but using CMIP3 historical simulations.

    Figure 7.  Ensemble mean (contours) and ensemble spread (color-shaded) for CMIP3 "A2" scenario future projections (AD 2074-99) for (a) averaged summer (June-August) surface air temperature and (b) precipitation over the U.S.

    Figure 8.  As in Fig. 2 but using CMIP3 "A2" scenario future projections (AD 2074-99).

    Figure 9.  As in Fig. 3 but using CMIP3 "A2" scenario future projections (AD 2074-2099).

    For the global domain, the PSD of the ensemble mean and observational mean are indeed similar for all latitude ranges for both surface temperature and precipitation. An exception is the anomalously low PSD values for surface temperature at wavenumber 2 and those exceeding 50, the latter of which we attribute to the low spatial density of surface temperature observations over the open ocean. The PSD for the ensemble spread generally exceeds that of the ensemble error/bias at most wavenumbers, and especially at lower wavenumbers (<10) and for surface temperature. Consistent with our earlier findings (Fig. 2), the PSD for both the ensemble mean and observations (i.e., the signals) exceed those for the ensemble spread and error (noise or uncertainties) for wavenumbers 1-20 for all three latitude ranges for surface temperature (Figs. 3a-c), implying predictability across the associated spatial scales. For precipitation, by contrast, predictability is only evident (Figs. 3g-i) for wavenumbers 1-3 for the low-latitude (15°-30°N) and midlatitude (30°-45°N) zone, and for almost no wavenumbers for the high-latitude (45°-60° N) zone.

    For the U.S. regional sub-domain, the PSD for the ensemble mean is generally consistent with that for the observations for both surface temperature and precipitation, and low and intermediate wavenumbers. However, for the high-latitude zone (45°-60°N) the ensemble-mean PSD considerably exceeds that of the observations for higher (> 24 for surface temperature and > 12 for precipitation) wavenumbers. The discrepancy between the ensemble spread and the ensemble mean error/bias is considerably greater for the U.S. regional domain than for the global domain as well.

    The inferred predictability of surface temperature and precipitation for the U.S. regional domain varies considerably between the two variables and three latitude ranges (Figs. 3d-f, j-l). For example, the SNR for surface temperature exceeds unity for all wavenumbers lower than 36 (spatial scales as small as 1000 km) for the low-latitude (15°-30°N) zone, but the SNR is close to the "no predictability" value of unity for nearly all wavenumbers for the midlatitude (30°-45°N) and high-latitude (45°-60°N) zones. For precipitation, only for the midlatitude zone (30°-45°N) is there evidence of predictability, and at fairly low (6-12) global wavenumbers (i.e., spatial scales no less than 6000 km). These examples highlight the challenge for regional-scale climate predictability in North America with existing state-of-the-art global climate models.

4. CMIP3 historical experiments and future projections
  • To further investigate the robustness of our findings based on the CMIP5 historical simulations (Figs. 1-3) we perform parallel analyses using the CMIP3 (Meehl et al., 2007; Watterson et al., 2014) (Table 2) multimodel ensemble simulations using both (1) the same historical period (1979-2004) (Zhou and Yu, 2006; Timm and Diaz, 2009) and (2) the CMIP3 ("A2" scenario) 21st century climate change projections.

    Our conclusions regarding the predictability of regional-scale climate over North America with the CMIP5 historical simulations (Figs. 1-3) are similar to those obtained with the CMIP3 historical multimodel simulations (Figs. 4-6), with only one minor discrepancy: slightly lower SNR values are found for both the global surface temperature and precipitation fields over the midlatitudes of North America for global wave numbers 6-12. The fact that little-to-no improvement in regional predictability is found to result from the substantial model development and improvement reflected by the 5-year period between CMIP3 and CMIP5 suggests that, even with increasingly refined and detailed climate models, our conclusions regarding an apparent scale limit for regional-scale climate predictability are likely to remain true.

    Similar conclusions are also obtained for the 21st century projections using the "A2" emissions scenario for the period 2074-99 using the CMIP3 multimodel ensemble simulations (Figs. 7-9). Even though obviously we do not have observations to verify these simulations, our conclusions again remain mostly unchanged: there is an apparent scale limit by which the uncertainty in the prediction (noise) becomes greater than the ensemble mean prediction (signal). This further highlights the limited predictability of climate models, especially at regional scales for different climate scenarios.

5. Concluding remarks
  • In summary, through an analysis of surface temperature and precipitation variability in the CMIP5 historical simulations and comparisons with observational data during the overlapping (1979-2014) interval of the late 20th/early 21st century, we have found that there appears to be a fundamental scale limit below which refinement of climate model predictions may not be possible. While the predictability limit depends on the variables and regions analyzed, the averaging period and/or season, a seemingly robust result is that, for North America, the uncertainty due to intrinsic noise approaches in magnitude the amplitude of the climate change signal at horizontal scales below about 1000 km for surface temperature, and 2000 km for precipitation.

    Our findings generalize beyond the specifics of the CMIP5 historical simulation ensemble. Parallel analyses of both (i) the earlier generation CMIP3 historical simulation ensemble and (ii) 21st century climate projections based on the CMIP3 "A2" emissions scenario, yield qualitatively very similar conclusions. Given that downscaling methods (whether based on statistical or dynamical approaches) require information from large-scale climate model simulations as boundary conditions and/or reference states, the lack of predictability at these larger scales likely translates to a lack of predictability at local scales. One apparent exception, based on our findings, are cases where smaller-scale orographic forcing or land-sea contrasts provide additional predictability at smaller scales.

    Given the importance of future projections of surface temperature and precipitation for assessing climate change impacts such as heat stress, flooding potential and drought magnitude, duration and extent, our findings suggest great challenges in assessing climate change risk and damage at regional scales most important to stakeholders and policymakers. One potential implication of our findings is that regional adaptation efforts might, in some circumstances, be better focused on reducing vulnerability to climate change in general, rather than planned adaptation to specific projected climate changes.




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