3.1. Comparison of CMIP5 Climate Modelled Snow-Cover Trends to the Satellite-Derived Rutgers Dataset
Observed Northern Hemisphere snow cover (km2
) for all four seasons (Figure 2
a–d) and the annual average (e) to the equivalent values for each of the 196 CMIP5 runs, averaged over the 50-year period (1967–2016) is shown. The models tended to underestimate the observed values for all four seasons, and a wide range existed for all seasons (although smallest for summer). However, the models did seem to at least capture the general annual cycle in that the snow cover reached a maximum in winter and a minimum in summer, with intermediate values for the spring and autumn/fall. This qualitative replication of the annual cycle was noted by others and suggests that there is at least some realism to the models [11
Because each model run implies a different average snow cover and these values are typically smaller than the observed averages, a direct comparison between the absolute trends can be challenging. Thus, for the rest of the paper, each time-series is converted into an anomaly time-series relative to the 1967–2016 average.
The observed 1967–2016 linear trends were compared to the equivalent trends of each of the 196 CMIP5 runs for each season (Figure 3
). Although the observed annual linear was consistent with that of the models (Figure 3
e), we can see that this was due to the fact that the models significantly underestimated the negative summer trend (Figure 3
c), and to a lesser extent, that of spring (Figure 3
b), while failing to predict the positive trends for winter (Figure 3
a) and autumn (Figure 3
d). In other words, the models poorly described trends for three of the four seasons (winter, summer, and autumn), and fared little better at describing trends in the spring.
As discussed in the introduction, it can be misleading to limit a comparison of climate models and observations to the linear trends over a single time-period, since the observed time-series were not linear in nature. Technically, a linear trend can be nominally computed for any interval, but if the time-series is non-linear in nature, then this can misleadingly imply a “linear” nature to the data which is absent.
To remedy this, the entire time-series was plotted (Figure 4
a) for observed annual snow cover (relative to the 1967–2016 mean). Annual snow cover was lower after the mid-1980s relative to what it was before the mid-1980s. Thus, the linear trend implies
a long-term decrease of −25,000 km2
/year, but this was largely an artefact of the step-like drop in the mid-1980s [25
]. Indeed, the last two years had above-average snow cover.
The multi-model means of all 196 CMIP5 runs (Figure 4
b) showed that unlike the observations, the model-predicted trends were reasonably well described in terms of a decreasing linear trend (−30,000 km2
/year). Qualitatively, this can be seen by visually comparing the two plots. The observations plot (Figure 4
a) showed a considerable amount of yearly variability, while the multi-model mean (Figure 4
b) showed a gradual but almost continuous decline from 1967 to the present.
While the linear fit associated with the multi-model mean had an r2 of 0.93, that associated with the observations was only 0.19. Due to the long time-period, all linear fits were statistically significant (p = 0.0014 for the observations and p = 10−28 for the multi-model mean). Also, the error bars (uncertainty) associated with the linear fits were much greater for the observations (±15,000 km2/year) than that for the multi-model mean (±2000 km2/year).
On this basis, the current climate models appear to be unable to explain the observed trends and are therefore inadequate. However, one might disagree because the multi-model mean is largely determined by the “external forcings” that are input into the models and does not reflect the “internal variability” of individual model runs.
With the current climate models, global snow cover is largely dictated by global temperatures (hence they predict that global snow cover should decrease due to the predicted human-induced global warming from greenhouse gases). If a simulation run is adequately equilibrated and not majorly affected by “drift”, then the global temperatures for a given year are mostly determined by:
External radiative forcing from “anthropogenic factors”. This includes many factors, but atmospheric greenhouse gas and stratospheric aerosol concentrations are the main components.
External radiative forcing from “natural factors”. Currently, models consider only two: changes in total solar irradiance (“solar”) and stratospheric aerosols from volcanic eruptions (“volcanic”).
Internal variability. This is the year-to-year random fluctuations in a given model run. As we will discuss below, some argue that this can be treated as an analogue for natural climatic inter-annual variability.
As Soon et al. [32
] noted, the CMIP5 models only consider a small subset of the available total solar irradiance estimates, and each of the estimates in that particular subset implied that solar output has been relatively constant since the mid-20th century (perhaps with a slight decrease). Meanwhile, the “internal variability” of each model yields different random fluctuations (since they are random). Therefore, the internal variability of the models tends to cancel each other in the multi-model mean.
Thus, the 1967–2018 trends of the multi-model mean are almost entirely determined by the modelled “anthropogenic forcing” (a net “human-induced global warming” from increasing greenhouse gases) and short-term cooling “natural forcing” events from the two stratospheric volcanic eruptions that occurred over that period (i.e., the El Chichón eruption in 1982 and the Mount Pinatubo eruption in 1991). However, clearly, the observed trends in annual snow cover (Figure 4
a) are more complex than that relatively simple explanation.
There seem to be broadly two schools-of-thought within the scientific community on the relevance of the multi-model means. Some researchers argue that the “internal variability” of the climate models is essentially “noise”, and that by averaging together the results of multiple models you can improve the “signal-to-noise” ratio, (e.g., [1
]). Others disagree and argue that this random noise is a “feature” of the models, which can somehow approximate the “internal variability” of nature, (e.g., [15
]). Both camps agree that because the random fluctuations are different for each model run, they cancel each other out in the multi-model ensemble averages. Where they disagree is whether this is relevant for comparing model output to observations.
While we have demonstrated that the multi-model mean cannot fully explain the observed trends in annual snow cover, it is important to also consider the possibility that this is due to the lack of “internal variability” in the multi-model means. There are several methods to address this. For example, when comparing observed and modelled Arctic sea ice trends, Connolly et al. [1
] considered both the multi-model mean and the median model run (in terms of long-term sea ice trends). Rupp et al. [15
], by contrast, used the model output from “pre-industrial simulations” that were run without any “external forcing” to estimate the “internal variability”, and Mudryk et al. [16
] used an ensemble of 40 model runs that all used the same climate model and identical “external forcing”. Other groups have calculated confidence intervals from the entire range of model output (e.g., the upper 5% and lower 5%) [17
Here, we consider the “internal variability” of the models by analyzing three representative model runs. All model runs were ranked according to their 1967–2016 linear annual trend (Figure 2
e). The mean and standard deviation was calculated for all 196 model runs. We then identified (i) the median model run and the model runs whose linear trends were closest to (ii) +1 standard deviation and (iii) −1 standard deviation (Figure 4
Comparing individual model runs to observations yields a more favorable comparison than using the multi-model mean. That is, the individual runs show more year-to-year variability than the multi-model mean. Nonetheless, the individual models still poorly explain the observed trends and all three selected models (i.e., the median and +/− one standard deviation) suggest a fairly continuous long-term decrease in snow cover extent.
If the lack of internal variability in the multi-model mean is proposed as the explanation for the discrepancies between the multi-model mean and the observations, then this does not vindicate the robustness of the climate models. Rather, it merely argues that the models are “not totally inconsistent with” the observations. This argument becomes weaker when the individual seasonal trends are examined.
The above analysis is repeated but for each of the seasonal averages instead of the annual averages—winter (Figure 5
); spring (Figure 6
); summer (Figure 7
); and autumn (Figure 8
). Note that the median, +1 standard deviation, and −1 standard deviation model runs for each of these seasons were not necessarily the same as for the annual averages.
First, consider the modelled winter (DJF) snow cover trends compared to observations (Figure 5
). Climate models predicted a long-term decrease in winter snow cover, but this has not been observed. Indeed, the observations imply a net increase in winter snow cover, although this is not statistically significant. At any rate, since the start of the 21st century, snow cover has mostly been above the 1967–2016 average.
Collectively, climate models predicted a statistically significant decrease in winter snow cover which has not been observed (Figure 5
c), even after more than fifty years of observations. However, for some
of the models (e.g., the +1 standard deviation model), the modelled decrease is not statistically significant.
Results for spring (MAM—Figure 6
) are more encouraging for the climate models, although notable discrepancies still exist between the modelled and observed trends. Perhaps this partially explains why this is the season which has received the most attention, (e.g., [11
Although the trends were all negative, the magnitude of the observed trend was greater than what most of the models had predicted—this can also be seen from Figure 3
b. This has already been noted by others [11
], although the typical implication is that the models performed well but simply “underestimated” the rate of the human-induced global warming to which the decrease is attributed. Derksen and Brown [30
], for example, imply that the discrepancy is “…increasing evidence of an accelerating cryospheric response to global warming” ([30
], p. 5).
Such an explanation is flawed. If the reason the models underestimated the negative trend in snow cover in spring (and summer) was because the models underestimated the effect of human-induced global warming, then their failure to explain winter and autumn is even more significant. Moreover, as previously noted, most of the decrease in spring snow cover occurred as a step-like behavior in the late-1980s [24
], and the two most recent years (2017 and 2018) had values above the 1967–2016 average.
Like spring, modelled trends in summer (JJA—Figure 7
) were negative, commensurate with the observed trends. However, this was where the similarities ended. The observed decrease in summer was greater than for spring, but the modelled decline was much more modest for summer. That is, the discrepancy between the modelled and observed trends was even greater for summer than spring—which was particularly striking (see Figure 3
c). A partial explanation might be that the climate models significantly underestimated the total summer snow cover (see Figure 2
c). However, the models poorly explained the observed summer trends.
Trends for autumn/fall (SON—Figure 8
) were broadly similar to those for winter, but the contrast between the observed and modelled trends was even greater. Although the observed autumn snow cover decreased in the late-1970s, it had mostly been above the 1967–2016 average since the early-1990s (Figure 8
a). As for the other seasons, all models implied an almost continuous decline in autumn snow cover which was not reproduced in the observations.
Brown and Derksen [40
] suggest that the Rutgers dataset overestimated the October snow cover extent for Eurasia in recent years, which could partially explain some of the disagreement among the models [16
]. However, we note that the Rutgers dataset was likely to be reasonably accurate because the weekly satellite-derived charts from which it was constructed, used operationally, and were manually evaluated by a human team for accuracy [27
3.2. Comparison of CMIP5 Climate-Modelled March/April Trends to the Updated Brown and Robinson Time-Series (1922–2018)
Observed spring snow-cover trends for the Northern Hemisphere obtained from the updated Brown and Robinson time-series were compared to those of the climate models (Figure 9
). Since the original time-series covers only the period 1922–2010 [28
], trends for this period were only analyzed for this 88-year period, although all series were plotted to the most recent data point (i.e., 2018).
Results were similar to those of Figure 6
. While all series implied a negative trend, the observations implied a greater decrease in snow cover than the models had predicted. Meanwhile, the pattern of the trends for the models were distinct from the observations. The models implied there should have been a gradual, but almost continuous decrease since the latter half of the 20th century, while the observed trends were more consistent with the step-like decrease in the late-1980s—as has already been noted by others [24
]. The observed annual variability was quite substantial.
The strongly non-linear nature of the observed trends implies that reporting the data in terms of a “linear trend” (over some fixed period) is highly misleading. However, we note that this is essentially what the IPCC did in their 5th Assessment Report:
“There is very high confidence that the extent of Northern Hemisphere snow cover has decreased since the mid-20th century (see Figure SPM.3). Northern Hemisphere snow cover extent decreased 1.6% [0.8 to 2.4%] per decade for March and April, and 11.7% [8.8 to 14.6%] per decade for June, over the 1967 to 2012 period. During this period, snow cover extent in the Northern Hemisphere did not show a statistically significant increase in any month.”.
Their Figure SPM.3 refers to a plot of the Brown and Robinson (2011) [28
] March/April “spring” snow-cover time-series (apparently updated to 2012 using the Rutgers dataset). Based on these data, we agree that the Northern Hemisphere spring snow cover extent decreased over the 1967–2012 period. However, the data before and after that period (1967–2012, Figure 10
) show a general increase
in snow cover. In hindsight, the decision by the IPCC to emphasize the linear trends for such a specific period was unwise and considerably misleading.
We do not wish to read too much into the fact that the linear trends before and after the 1967–2012 are positive—indeed the trends are not statistically significant. Rather, we want to stress that the time-series is strongly non-linear and describing the series in terms of a single linear trend (over any time period) is inappropriate. An example of a more appropriate method of considering the non-linear nature of the time-series is shown in Figure 11
shows the time-frequency wavelet analysis of the spring snow cover from 1922–2018 using the algorithm recently introduced by Velasco et al. [52
] and Soon et al. [53
]. The result mainly illustrates the rich spectral content of the spring snow cover where primary modulation with principal periodicities at 23, 7, 4, and 2.4 years were detected. Such observed oscillations do not appear to be adequately accounted for by the CMIP5 models. We have already mentioned that the CMIP5 models neglected to consider any of the published high-solar variability estimates of total solar irradiance [32
], so this could explain the poor performance of the models. We also note here the importance of considering the changes in short-term orbital forcing which have been of the order of 1–3 W/m2
(depending on season) over the 20th century [54