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On the future reduction of snowfall in western and central Europe


Large parts of western and central Europe face a 20–50 % future reduction in snowfall on Hellmann days (days with daily-mean temperatures below freezing). This strong reduction occurs in addition to the expected 75 % decrease of the number of Hellmann days near the end of the twenty first century. The result is insensitive to the exact freezing-level threshold, but is in sharp contrast with the winter daily precipitation, which increases under most global warming scenarios. Not only climate model simulations show this. Observational records also reveal that probabilities for precipitation on Hellmann days have been larger in the past. The future reduction is a consequence of the freezing-level threshold becoming a more extreme quantile of the temperature distribution in the future. Only certain circulation types permit these quantiles to be reached, and it is shown that these have intrinsically low precipitation probability.

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The paper has benefited from comments by the reviewers. Furthermore, we acknowledge the E-OBS dataset from the EU-FP6 project ENSEMBLES ( and the data providers in the ECA&D project ( The research undertaken in this study has been made possible by GasTerra and NAM.

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Correspondence to Hylke de Vries.

Appendix: Projecting onto target patterns

Appendix: Projecting onto target patterns

Here we elaborate on the method how to project the large-scale flow on to target patterns, and how future changes can be attributed to several change mechanisms. The approach is based on Cattiaux et al. (2012).

Basic steps

First, the target patterns (TP) have to be determined. In this study we use Ward clustering of a reference set of Z500-anomaly maps. The TP-structure is denoted as e k . Next, the objective fields a i (the Z500-anomaly fields) are assigned to the TP with which they have the highest correlation cor(e k a i ). A map is not assigned if cor(e k ,a i ) <0.5 for all e k . After the assigning process, the mean of all a i can be written as

$$ \bar{A} = \frac{1}{n}\sum_{i=1}^n a_i=\sum_k f_k d_k \equiv \sum_k\lfloor f d\rfloor_k $$

where \(\lfloor\rfloor_k\) is shorthand notation, n is the number of fields in the dataset, f k  = n k /n is the relative frequency of the fields assigned to TP-k, and

$$ d_k = \frac{1}{n_k}\sum_{i=1}^{n_k} a_{i} $$

is called the response pattern (RP), the centroid of all a i assigned to TP-k. Residual maps, that could not be assigned to any TP, are included in (3) and form the “garbage-bin”, RP-X.

Analyzing changes

In the main text, we use 30-winter sliding windows of data and project each of these on to the TPs. As a result, both the frequencies f k and the RPs become functions of the period, which is indicated by t. The first 30 winters are used as a reference period t ref . \(\bar{A}(t)\) can be written as:

$$ \bar{A}(t)=\sum_k f_k(t) d_k(t)\equiv \bar{A}(t_{ref}) + \sum_k\lfloor f(t)\delta(t)\rfloor_k $$

which defines \(\delta_k(t)=d_k(t)-\bar{A}(t_{ref})\) as the anomaly with respect to the mean field of the reference period. The second step follows by noting that ∑ k f k (t) = 1 for all periods (by definition). Note that according to this definition ∑ k f k (t ref )δ(t ref ) = 0. To simplify notation we now focus on two periods which will be labeled with superscripts PF (“present” and “future”) e.g., \(\bar{A}^{F,P}=\bar{A}(t^{F,P}), \delta_k^P=\delta_k(t^P), f_k^F=f_k(t^F). \) Then we can write for the difference of mean \(\Updelta\bar{A}=\bar{A}(t^F)-\bar{A}(t^P)\)

$$ \Updelta\bar{A} =\sum_k\left\lfloor(f+f')(\delta+\delta')-f\delta\right\rfloor_k=\sum_k\left\lfloor f'\delta+f\delta' + f'\delta'\right\rfloor_k $$

where we suppressed all labels by using the notation f = f P and f′ = f F − f P (similar notation for δ).

Other fields: transfer functions

The next step is to consider the change of a variable x, related to the circulation a by means of a transfer function \(\Upphi, \) such that \(x=\Upphi[a].\) This transfer function selects for example the local temperature/precipitation in the Netherlands, associated with a specific large-scale circulation a. Using the same approach as before we get [cf., (5)]:

$$ \bar{X}(t) = \sum_k f_k(t)x_k(t) \equiv \bar{X}(t_{ref}) + \sum_k\lfloor f(t)\xi(t)\rfloor_k, $$

with \(x_k(t)=\Upphi[d_k(t),t]\) and \(\xi_k(t)=x_k(t)-\bar{X}(t_{ref})\). Note that \(\Upphi\) generally depends both explicitly and implicitly on time. The change of mean \(\Updelta \bar{X}=\bar{X}^F-\bar{X}^P\) can be written as [cf., (6)]

$$ \Updelta \bar{X} =\sum_k\left\lfloor f'\xi+f\xi' + f'\xi'\right\rfloor_k = \hbox{BeC-CC}+\hbox{WiC}+\hbox{N.L.}, $$

where we have suppressed labels by writing ξ = ξP and ξ′ = ξF − ξP (similar notation for f).

Term BeC-CC denotes the Between-Cluster Circulation Change, the contribution to \(\Updelta X\) from cluster frequency changes; term WiC denotes the Within-Cluster Changes; N.L is the nonlinear term. Cattiaux et al. (2012) suggest to decompose term WiC into a Within-Cluster Circulation Change (WiC-CC) and a Within-Cluster Response Change (WiC-RC):

$$ \begin{aligned} \hbox{WiC-CC}'=&\sum_k\left\lfloor f^P\big(\Upphi^P[d^F]-\Upphi^P[d^P]\big)\right\rfloor_k,\\ \hbox{WiC-RC}'=&\sum_k\left\lfloor f^P\big(\Upphi^F[d^F]-\Upphi^P[d^F]\big)\right\rfloor_k, \end{aligned} $$

where \(\Upphi^i[d^j]=\Upphi[d(t_j),t_i]\) with ij = (PF). However, it is easily shown that an equally valid decomposition is:

$$ \begin{aligned} \hbox{WiC-CC}''&=\sum_k\left\lfloor f^P\big(\Upphi^F[d^F]-\Upphi^F[d^P]\big)\right\rfloor_k,\cr \hbox{WiC-RC}''&=\sum_k\left\lfloor f^P\big(\Upphi^F[d^P]-\Upphi^P[d^P]\big)\right\rfloor_k. \cr \end{aligned} $$

The simplest way to take the ambiguity of the decomposition into account is by writing

$${\text{WiC-CC}} = (\varepsilon ){\text{WiC-CC}}^{\prime } + (1 - \varepsilon ){\text{WiC-CC}}^{{\prime \prime }} , $$

where \(\varepsilon \in (0,1), \) and similar for WiC-RC. Two terms require further explanation: \(\Upphi^P[d^F]\) is the present-day response x to future circulations. As in Cattiaux et al. (2012) this term is estimated by searching for the present-day analogues of the future circulations and taking the accompanying present-day x values. The future response to present-day circulations \((\Upphi^F[d^P])\) is evaluated in the same way.

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de Vries, H., Haarsma, R.J. & Hazeleger, W. On the future reduction of snowfall in western and central Europe. Clim Dyn 41, 2319–2330 (2013).

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  • Snowfall
  • Climate change
  • Circulation patterns
  • Attribution