Natural risk studies such as flood risk assessments require long series of weather variables. As an alternative to observed series, which have a limited length, these data can be provided by weather generators. Among the large variety of existing ones, resampling methods based on analogues have the advantage of guaranteeing the physical consistency between local weather variables at each time step. However, they cannot generate values of predictands exceeding the range of observed values. Moreover, the length of the simulated series is typically limited to the length of the synoptic meteorological records used to characterize the large-scale atmospheric configuration of the generation day. To overcome these limitations, the stochastic weather generator proposed in this study combines two sampling approaches based on atmospheric analogues: (1) a synoptic weather generator in a first step, which recombines days of the 20th century to generate a 1000-year sequence of new atmospheric trajectories, and (2) a stochastic downscaling model in a second step applied to these atmospheric trajectories, in order to simulate long time series of daily regional precipitation and temperature. The method is applied to daily time series of mean areal precipitation and temperature in Switzerland. It is shown that the climatological characteristics of observed precipitation and temperature are adequately reproduced. It also improves the reproduction of extreme precipitation values, overcoming previous limitations of standard analogue-based weather generators.
Increasing the resilience of socio-economic systems to natural hazards and identifying the required adaptations is one of today's challenges. To achieve such a goal, one must have an accurate description of both past and current climate conditions. The climate system is a complex machine which is known to fluctuate at very small timescales but also at large ones over multiple decades or centuries (Beck et al., 2007). It is necessary to study meteorological series as long as possible in order to catch all sources of variability and fully cover the large panel of possible meteorological situations. Regarding weather extremes, the same need arises, as estimating return levels associated with large return periods cannot be successfully done without long climatic records (e.g. Moberg et al., 2006; Van den Besserlaar et al., 2013). This comment also applies to all statistical analyses on any derived variable, such as river discharge, for which multiple meteorological drivers come into play and for which extreme events correspond to the combination of very specific and atypical hydro-meteorological conditions.
Using weather generators, long simulations of weather variables provide accurate descriptions of the climate system and can be used for natural hazard assessments. Among the large panel of existing weather generators, stochastic ones are used to construct, via a stochastic generation process, single or multi-site time series of predictands (e.g. precipitation and temperature) based on the distributional properties of observed data. These characteristics, and consequently the weather generator parametrization, are usually determined on a monthly or seasonal basis to take seasonality into account. They can also be estimated for different families of atmospheric circulation, often referred to as weather types. The state of the art of the most common methods which have been used for the downscaling of precipitation (single or multi-site) is presented in Wilks and Wilby (1999) and in Maraun et al. (2010). More recent publications gather detailed reviews of some sub-categories of weather generators (e.g. Ailliot et al., 2015, for hierarchical models). An increasing number of studies focus on the generation of multi-variate and/or multi-site series of predictands (e.g. Steinschneider and Brown, 2013; Srivastav and Simonovic, 2015; Evin et al., 2018a, b). Stochastic weather generators are able to produce large ensembles of weather time series presenting a wide diversity of multi-scale weather events. For all these reasons, they have been used for a long time to enlighten the sensitivity and possible vulnerabilities of socio-ecosystems to the climate variability (Orlowsky and Seneviratne, 2010) and to weather extremes.
Other models used for the generation of weather sequences are based on the analogue method. Since the description of the concept of analogy by Lorenz (1969), the analogue method has gained popularity over time for climate or weather downscaling. This analogue-model strategy has been applied in many studies (Boé et al., 2007; Abatzoglou and Brown, 2012; Steinschneider and Brown, 2013) and has been used to address a wide range of questions from past hydro-climatic variability (e.g. Kuentz et al., 2015; Caillouet et al., 2016) to future hydro-meteorological scenarios (e.g. Lafaysse et al., 2014; Dayon et al., 2015). The standard analogue-approach hypothesizes that local weather parameters are steered by synoptic meteorology. A set of relevant large-scale atmospheric predictors is used to describe synoptic weather conditions. From the atmospheric state vector, characterizing the synoptic weather of the target simulation day, atmospheric analogues of the current simulation day are identified in the available climate archive. Then, the analogue method makes the assumption that similar large-scale atmospheric conditions have the same effects on local weather. The local or regional weather configuration of one of the analogue days is then used as a weather scenario for the current simulation day. The key element of the analogue method is that it does not require any assumption on the probability distributions of predictands. This is a noteworthy advantage for predictands, such as precipitation, which have a non-normal distribution with a mass in zero. Most of the studies using analogues focused on precipitation and temperature either for meteorological analysis (Chardon, 2014; Ben Daoud et al., 2016) or as inputs for hydrological simulations (Marty et al., 2013; Surmaini et al., 2015). Nevertheless, analogues are increasingly used for other local variables such as wind, humidity (Casanueva et al., 2014) or even more complex indices (e.g. for wild fire; Abatzoglou and Brown, 2012). When multiple variables are to be downscaled simultaneously, another major advantage of the analogue method is that the different predictands scenarios are physically consistent and the simulated weather variables are bound to reproduce the correlations between the variables (e.g. Raynaud et al., 2017) and sites (Chardon et al., 2014). Indeed, when analogue models use the same set of predictors (atmospheric variables and analogy domains) for all predictands, all surface weather variables and sites are sampled simultaneously from the historical records, thus preserving inter-site and inter-variable dependency.
The two simulation approaches (stochastic weather generators and analogue methods) described above present some important advantages for the generation of long weather series but also some sizable drawbacks. Indeed, stochastic weather generators rely on strong assumptions about the statistical distributions of predictands. Identifying the relevant mathematical representations of the processes and achieving a robust estimation of their parameters can be difficult, especially if the length of the meteorological records is short. Modelling the spatial–temporal dependency between variables and sites is often another challenge. Conversely, for the analogue-based approaches, the identification of relevant atmospheric variables providing good prediction skills is not straightforward. The limited length of local weather records is also a critical issue, since resampling past observations restricts the range of predicted values. In particular, the simulation of unobserved values of predictands is not possible. This can be problematic if one is interested in estimating possible extreme values of the considered variable. Furthermore, the information on synoptic atmospheric conditions required by analogue methods are generally coming from atmospheric reanalyses, which also have a limited temporal coverage (e.g. from the beginning of the 20th century for ERA-20C – EMCWF Reanalysis; Poli et al., 2016) and from the mid-19th century for 20CR (Twentieth Century Reanalysis; Compo et al., 2011). The length of the generated time series is thus typically bounded by the length of the reanalyses.
In this study we propose a weather generator (hereafter SCAMP
These developments are carried out for the exploration of hydrological
extremes (extreme floods) of the Aare River basin in Switzerland (Andres et
al., 2019a, b). Meteorological forcings, i.e. temperature and precipitation,
are thus simulated to be used as inputs of a hydrological model, for
different sub-basins of the Aare River basin. Meteorological simulations
from SCAMP
This study is carried out on the Aare River basin, which covers almost half
of Switzerland (17 700 km
The application of the analogue method requires a long archive providing an
accurate description of both past synoptic weather patterns and local
atmospheric conditions. Indeed, a wide panel of meteorological situations
available for resampling is necessary in order to identify the best
analogues for the simulation (e.g. Van Den Dool et al., 1994; Horton et al.,
2017). In most studies, synoptic situations are provided by atmospheric
reanalyses. Here, we use the ERA-20C atmospheric reanalysis (Poli et al.,
2013), which provides information on large-scale atmospheric patterns on a 6 h
basis from 1900 to 2010. Data are available at a 1.25
The local and surface weather parameters of interest are retrieved from 105 weather stations for precipitation and 26 weather stations for temperature, which are spread out homogeneously over our target region, as presented in Fig. 1. These data are available at a daily time step from 1930 to 2014. They have been spatially aggregated in order to obtain daily time series of mean areal precipitation (MAP) and temperature (MAT) for the Aare region. The three weather generators considered in this study aim at producing scenarios of daily time series of MAP and MAT. In this study, a scenario is defined as a possible realization of the climate system under current climate conditions (i.e. the climate observed for the past few decades). It can be noticed that many applications of analogue-based approaches produce simulations at specific weather stations. However, as shown by Chardon et al. (2016) for France, the prediction skill is significantly improved when the prediction is produced for areal averages, which motivates the generation of MAP and MAT values in this study.
The Aare River basin (red) and locations of the different precipitation (dots) and temperature (triangles) stations.
This section presents the three different models considered and evaluated in this study.
The most basic model evaluated in this study, hereafter referred to as ANALOGUE, relies on a standard two-level analogue method. For each day of the simulation period (1900–2010), analogue days are identified from candidate days. The candidate days extracted from the archive period, i.e. the period during which both predictors and local observations are available (1930–2010), are all days of the archive located within a 61 d calendar window centred on the target day. This calendar filter is expected to account for the possible seasonality of the large-scale–small-scale downscaling relationship. For instance, candidate days for 15 May 2000 are selected within the pool of days ranging from 15 April to 14 June of each year of the archive.
The predictors used for the analogue selection were chosen based on Raynaud
et al. (2017). They have been shown to guarantee both inter-variable
physical consistency and good predictive skills according to the Continuous
Ranked Probability Skill Score (CRPSS) for four predictands (precipitation,
temperature, solar radiation and wind). In the present work, the predictors
considered for each level for the two-level analogy are as follows:
The first level of analogy is based on daily geopotential heights at 1000 and 500 hPa (HGT1000 and HGT500) as proposed by Horton et al. (2012) and Raynaud et al. (2017). The analogy criterion used here is the Teweles–Wobus score (TWS) proposed by Teweles and Wobus (1954). This score has been found to lead to higher performance than a more classical Euclidian or Mahalanobis distance (Kendall et al., 1983; Guilbaud and Obled, 1998; Wetterhall et al., 2005). It quantifies the similarity between two geopotential fields by comparing their spatial gradients. It allows for selecting dates that have the most similar spatial patterns in terms of atmospheric circulation. From September to May, the analogy is based on the geopotential fields on both the current day The second analogy level makes a sub-selection of 30 analogues within the 100 analogues identified in the first analogy level. The analogy score used for the selection is the root mean square error (RMSE). From September to May, the predictors are the vertical velocities at 600 hPa and the large-scale temperature at 2 m. In summer, not only the vertical velocities but also other predictors such as the convective available potential energy (CAPE) led to a rather poor prediction of precipitation due to the coarse resolution of the atmospheric reanalysis, which prevents it from providing an accurate simulation of convective processes. Consequently, large-scale precipitation from the reanalysis has been used as a predictor instead, resulting in predictive skills similar to the ones obtained for the rest of the year. The different predictor sets retained for summer and the rest of the year illustrate the differences typically observed between seasons for the main meteorological conditions and processes.
The dimensions and position of the different analogy windows used to compute
the analogy measures are presented in Fig. 2. They follow the recommendations for the analogy windows optimization presented in Raynaud et al. (2017) for all predictors.
Positions and dimensions of the analogy windows in the analogue model at both analogy levels. Z500: geopotential at 500 hPa; Z1000: geopotential at 1000 hPa; VV600: vertical velocities at 600 hPa;
With this two-step analogy, 30 scenarios of daily MAP and daily MAT are obtained for each day of the simulation period (1900–2010). Combined with the Schaake shuffle method described in Sect. 3.3.4, the application of the ANALOGUE model leads to 30 scenarios of 110-year time series of daily MAP and MAT.
The SCAMP model enhances the previous ANALOGUE approach, which is not able to generate daily values exceeding the range of observed precipitation and temperature. SCAMP combines the analogue method with a day-to-day adaptive and tailored downscaling method using daily distribution adjustment (Chardon et al., 2018).
For each prediction day, the following discrete–continuous probability
distribution proposed by Stern and Coe (1984) is fitted to the 30 MAP values
obtained from the atmospheric analogues of this day:
Similarly, for each prediction day, a Gaussian distribution
As for the ANALOGUE approach, the Schaake shuffle reordering method is applied to the daily scenarios obtained from SCAMP. A total of 30 scenarios of 110-year time series of daily MAP and MAT are produced.
As mentioned previously, the first limitation of the analogue method is related to the length of the synoptic weather information that is used to generate local predictand time series. In the present case, the length of time series that can be produced with the models ANALOGUE and SCAMP is limited to 110-year-long weather scenarios.
In SCAMP
The principle of a random atmospheric-trajectory generation is sketched on
Fig. 3. In the present work, the only predictor involved with comparing the
synoptic atmospheric configuration between 2 different days is the
geopotential height field at 1000 hPa, for both the present day and its
followers. The spatial analogy domain is the one used in Philipp et al. (2010) for the identification of Swiss weather types. The first line of
Fig. 3 presents an observed atmospheric trajectory in HGT1000 from
8–12 February 1934. On 9 February, we look for analogues of the current day and its following day
Construction of a new 5 d atmospheric trajectory from an observed synoptic weather sequence. Each panel presents the geopotential at 1000 hPa on the domain of interest. The black squares and arrows give the new atmospheric trajectory, and the blue shading highlights the 2 d analogue that helps the “changing of atmospheric direction”.
Practically, the five best analogues of the current atmospheric 2 d
sequence are identified, and one of those sequences is then selected with a
probability
To ensure that 2 consecutive days of the generated sequences belong to the
appropriate season, the five 2 d analogue sequences are identified within
a
The transition probability
Mean persistency (in days) of each of the nine weather types (indicated by the
different circles in each panel), as defined by Philipp et al. (2010), in
the observed time series and in the simulated ones for transition
probabilities ranging from 1 to
The long time series of synoptic weather generated with the above approach
is further used as inputs to the SCAMP generator described in the previous
section. The SCAMP
For each model (ANALOGUE, SCAMP and SCAMP
The different components of the models ANALOGUE, SCAMP and SCAMP
Illustration of the different steps applied (grey boxes) with models
ANALOGUE, SCAMP and SCAMP
This section presents different statistical properties of the scenarios
obtained with the three models and discusses the performances of each model by
comparison with observed statistical properties. For the sake of consistency
between the outputs, we compare the 30 scenarios of 111 years obtained from
ANALOGUE and SCAMP to 300 scenarios of 100 years from SCAMP
For both temperature and precipitation, the three models lead to an accurate
simulation of their seasonal fluctuations (Fig. 6). However, one can
notice the slight overestimation of winter temperature and an
underestimation of July and August precipitation. SCAMP also tends to have a
smaller inter-annual variability compared to ANALOGUE and SCAMP
Observed and simulated seasonal cycles of temperature and
precipitation for ANALOGUE, SCAMP and SCAMP
The distributions of seasonal precipitation amounts and seasonal temperature
averages are presented in Fig. 7. Whatever the season, the three models
are able to generate drier and wetter seasons than the observed ones (Fig. 7a). The very similar results obtained for ANALOGUE and SCAMP suggest that the daily distribution adjustments used in SCAMP do not introduce more
variability at the seasonal scale. SCAMP
The same comments can be made for spring and autumn temperatures (Fig. 7b). For those variables however, SCAMP
As mentioned in Sect. 1, simple analogue methods cannot simulate unobserved precipitation extremes at the temporal resolution of the simulation (here daily). Moreover, for higher aggregation durations, they also tend to underestimate observed precipitation extremes. Figure 8 presents the precipitation values obtained with the three models for different return periods (from 2 to 200 years) and different aggregation durations (from 1 to 5 d).
Return level analysis of extreme precipitation values associated with
models ANALOGUE, SCAMP and SCAMP
Considering 1 d extreme events, ANALOGUE is obviously not able to generate
precipitation accumulations that exceed the maximum observed one. Combining
the analogue method with daily distribution adjustments (SCAMP) overcomes
this issue with maximum values reaching 115 mm. SCAMP
The large underestimation of daily extremes obtained with ANALOGUE leads to
an important underestimation of 3 and 5 d extremes. Despite a better
simulation of daily values, SCAMP does not improve significantly the
reproduction of 3 and 5 d extremes. SCAMP
Figure 9a and b presents examples of simulated time series of annual MAP
and MAT obtained with ANALOGUE and SCAMP models. Concerning SCAMP
For ANALOGUE and SCAMP, the simulated year-to-year variations of annual precipitation and temperature are in agreement with the observed ones. The successions of dry and wet or cold and warm years are well simulated in both temporality and amplitude, and the positive trend in temperature starting in 1980 is also adequately reproduced. Similar results are obtained for seasonal precipitation and temperature (not shown). These results illustrate the determinant influence of the large-scale conditions on local weather in this region and the relevance of a generation process based on atmospheric analogues.
In contrast, the chronological year-to-year variations produced by the
different runs of SCAMP
The different extensions of the classical analogue method introduced in this
study aim at generating long regional weather time series without suffering
from the main limitations of analogue models. Indeed, due to the limited
extent of the observed time series and the impossibility to simulate
unobserved daily scenarios, analogue models usually underestimate observed
precipitation extremes. These limitations are relaxed by SCAMP
SCAMP
SCAMP
As highlighted previously, a noticeable limitation of SCAMP
Trends in observed predictors and predictands, as a result of global
warming, could be an additional issue. For instance, the mean elevation of
geopotential fields is often expected to increase with mean temperature.
Such trends may be detrimental for the simulations because the analogues
identification process would be carried out in a non-homogenous dataset. In
the present work for instance, trends in the second-analogy-level predictors
(VV600,
All in all, SCAMP
Precipitation and temperature data were downloaded from IDAWEB (
JC and DR developed the different models considered here. DR carried out the simulations and produced the analyses and the figures presented in this study. All authors contributed to the analysis framework and to the editing of the paper.
The authors declare that they have no conflict of interest.
We thank the editor and two anonymous reviewers for their constructive comments, which helped us to improve the manuscript.
This research has been supported by the Federal Office for the Environment (FOEN) of Switzerland; the Swiss Federal Nuclear Safety Inspectorate (ENSI); the Federal Office for Civil Protection (FOCP); and the Federal Office of Meteorology and Climatology, MeteoSwiss, through the project “Hazard information for extreme flood events on the rivers Aare and Rhine” (EXAR) (
This paper was edited by Carlo De Michele and reviewed by two anonymous referees.