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.
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.
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.
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.
As in Fig. 1 but using CMIP3 historical simulations.
As in Fig. 2 but using CMIP3 historical simulations.
As in Fig. 3 but using CMIP3 historical simulations.
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.
As in Fig. 2 but using CMIP3 "A2" scenario future projections (AD 2074-99).
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.