Accurate and high-resolution snowfall and fresh snow forecasts are important for a range of economic sectors as well as for the safety of people and infrastructure, especially in mountainous regions. In this article a new hybrid statistical postprocessing method is proposed, which combines standardized anomaly model output statistics (SAMOS) with ensemble copula coupling (ECC) and a novel re-weighting scheme to produce spatially and temporally high-resolution probabilistic snow forecasts. Ensemble forecasts and hindcasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) serve as input for the statistical postprocessing method, while measurements from two different networks provide the required observations.

This new approach is applied to a region with very complex topography in the eastern European Alps. The results demonstrate that the new hybrid method allows one not only to provide reliable high-resolution forecasts, but also to combine different data sources with different temporal resolutions to create hourly probabilistic and physically consistent predictions.

Large parts of our daily social and economic life strongly rely
on weather forecasts. In this article we focus on the governmental area of
Tyrol, Austria, which is located in the eastern Alps and consists of a large
number of narrow valleys surrounded by high mountains. The economic backbone
of Tyrol is tourism with more than 5.3 million visitors and more than
25 million overnight stays recorded during the winter season 2013/14

Weather forecasts are typically provided by numerical weather prediction
(NWP) models predicting the future atmospheric state on a global or regional
scale. Due to different influencing factors such as the model resolution,
necessary approximations and parameterizations but also imperfect initial
conditions and the chaotic behavior of the atmosphere, these forecasts are
never fully exact. Ensemble prediction systems (EPSs) address these issues by
running several independent forecasts for the same day using different and
slightly perturbed initial conditions and model formulations to provide
valuable additional information about the uncertainty of a specific weather
forecast. Due to the spatial discretization of the underlying NWP model the
EPS can only depict information on a grid-scale level and is not able to
provide reliable information on the point scale. Thus, EPS forecasts
typically show too little spread

A wide range of different ensemble postprocessing methods have been proposed,
including analog methods

Originally, distributional regression was only applied to specific locations,
but has also been extended for spatial and even spatio-temporal corrections
of the ensemble forecasts. Many of these extensions are based on anomalies

In terms of snow prediction several difficulties have to be considered. The
availability and quality of good and reliable snow observations are sparse,
even in the region of Tyrol. Measuring snow can be tricky due to possible
snow drift, melting processes, or liquid water input (rain) between two
observation times, which can yield large measurement errors

An alternative approach to predict fresh snow amounts is to make use of
precipitation and temperature forecasts rather than directly to predict snow.
The postprocessed temperature and precipitation forecasts can then be used as
a proxy to retrieve fresh snow amounts and snowfall forecasts. The
temperature forecasts are on the one hand required to determine whether
precipitation reaches the ground as rain or snow and on the other hand to
estimate the snow density. Snow density and its alteration are affected by
the prevalence of inversions, additional cooling effects due to melting and
evaporation of hydrometeors, and other local effects, and are thus an
extremely complex issue itself. For simplicity we will only regard the
problem of whether precipitation occurs as snow or rain and assume that
precipitation will fall as snow as soon as the 2 m dry air temperature falls
below

Major challenges of converting probabilistic precipitation and temperature forecasts into fresh snow predictions are the very different temporal resolutions of ensemble predictions, temperature observations, and precipitation observations. European Centre for Medium-Range Weather Forecast (ECMWF) hindcast and EPS forecasts, which we use in this study, have a temporal resolution of 6 and 1 h, respectively, temperature observations are usually available hourly, and precipitation or snow heights are often only measured once or a few times a day.

In this article we propose a new hybrid approach that combines standardized
anomaly model output statistics (SAMOS;

create full probabilistic spatial predictions,

provide probabilistic temperature and precipitation forecasts on an hourly temporal scale, and

create a physically consistent copula (pair of temperature and precipitation) which can be used to

create spatially and temporally high-resolution snowfall and fresh snow amount forecasts.

The structure of this article is as follows. Section

This section contains the three methodological blocks required to create
probabilistic snow forecasts. Distributional regression is explained in
Sect.

Statistical methods considering all parameters of a specific response
distribution can be summarized as “distributional regression models”. The
EMOS for temperature using a normal response distribution as originally
suggested by

Imagine a time series of 2 m temperature observations

The response

The coefficients

For the daily precipitation sums the model shown in
Eqs. (

While the model specifications in Eqs. (

Standardized anomalies of the observations (

The SAMOS procedure (Sect.

In order to retrieve probabilistic snowfall forecasts from the SAMOS
predictions, the marginal predictive distributions of temperature and
precipitation have to be combined such that correlations between them are
considered. This can be achieved by using ensemble copula coupling (ECC)
proposed by

There are different ways to draw a new sample from the postprocessed
distributions. It turned out (not shown) that the quantile mapping approach
with equidistant probabilities (ECC-Q;

The very same can be done for the daily precipitation sums using the inverse
distribution function of the power-transformed left-censored logistic
distribution:

Temperature and precipitation observation data are based on two different
observational networks with different temporal resolutions. The 2 m
temperature observations are available hourly, while precipitation sums are
only reported once a day (details in Sect.

As temperature shows a clear diurnal cycle, it is crucial to know at which
time of day precipitation is expected to be observed, as the timing can
highly affect the precipitation phase and thus the total fresh snow amount.
Therefore, the precipitation forecasts have to be temporally downscaled
before they can be combined with the temperature forecasts. For this purpose,
we extend ECC (Sect.

For stability reasons, the weights

Due to the ensemble copula (Sect.

Once ECC-Q and re-weighting are applied to the marginal distributions,
bi-variate time series of calibrated hourly precipitation sums and 2 m
temperatures are available for each of the

The threshold of 0.05

If one is interested in the snow height of fresh snow (

This section presents the data sets used for this study. These consist of two different EPS forecast data sets (ECMWF hindcast and operational EPS) and three different sources of observation data for model training and verification.

All predictions presented in this article are based on the ECMWF EPS. The
ECMWF EPS consists of 50 perturbed ensemble members and 1 control run
(

The presented application will focus on the winter season 2016/17 (1 December
2016 through 15 April 2017) and on predictions from

To train the SAMOS models we use ECMWF hindcasts, similar to the approach of

For the statistical postprocessing methods of 2 m temperature, all 6-hourly
intervals from

Two major different observation networks will be used in the following. As in

The second network consists of 89 automated weather stations operated by the national weather service (TAWES network; Zentralanstalt für Meteorologie und Geodynamik). Seventy-five out of these 89 stations provide at least 6 years of data. Observations are recorded every 10 min, of which all observations at every full hour are used for training and validation of the 2 m air temperature SAMOS models.

The TAWES network also provides automated precipitation measurements at a 10 min resolution. However, the length of historical records is much shorter compared to the time series provided by EHYD data set. Furthermore, the measurement errors of the automated rain gauges are expected to be larger than the errors from the daily manual records provided by the hydrographical service, especially during winter. Thus, we decided to not use the TAWES precipitation observations for model training and for the estimates of the spatio-temporal climatologies. Nevertheless, since observations from the hydrographical service are only available up to 2012 at this time (2018), we do use TAWES precipitation observations for validation. Therefore, daily precipitation sums are generated by taking the sum over all 10 min intervals between 06:10 and 06:00 UTC of the following day (yields 144 10 min values). Periods for which more than four 10 min values are missing are eliminated.

In addition to the temperature and precipitation observations from the
hydrographical service and the TAWES network, meteorological aerodrome
reports (METARs) from Innsbruck Airport are used in the verification section
as it is the only longer-term source of temporally high-resolution

Figure

Panel

This section presents the specifications of the models that will be compared
and tested in Sect.

All the models follow the approaches presented in Sect.

Table

All other models are spatio-temporal (in the case of 2 m temperature) and
spatial (in the case of daily precipitation sums) SAMOS models operating on
the standardized anomaly scale. Thus, the spatial and temporal
characteristics among all stations and for all lead times are already removed
from the data and do not have to be considered in the linear predictors for
location

The second and third pairs of models, named

Statistical model specification for 2 m temperature (left) and
24 h precipitation sums (right). For each model the linear predictors for

The first two subsections show the performance of the full predictive
distributions of the 2 m temperature (Sect.

Figure

The raw EPS performs poorly for the area of interest as the NWP model with
its current spatial resolution is not able to represent the local topography.
It performs even worse than the underlying climatology in terms of bias and
CRPS. All statistical postprocessing models perform significantly better and
are essentially bias-free. As expected, the station-wise statistical

Overall, all statistical models show promising values in terms of CRPS
(median 1.45–1.65

Scores for 2 m temperature forecasts based on the full predictive
distribution based on

Figure

The top row of Fig.

Scores for 24 h precipitation sums based on the full predictive
distribution for

Sections

To illustrate the effect of ECC-Q, Figs.

As ECC-Q uses quantiles based on equidistant probabilities, the quantiles
drawn from the full probabilistic distribution are ordered. Thus, the
forecasts of member 38 (

2 m temperature forecasts of member 38 for 10 March 2017
00:00 UTC. Top–down: raw EPS

As Fig.

Sections

Figure

To score the multivariate skill of the combined temperature and precipitation
forecasts, the bottom row of Fig.

(Stacked) ensemble rank histograms for hourly 2 m
temperature

To investigate the univariate predictive performance of hourly predictions
for different forecast horizons, Fig.

Continuous ranked probability skill scores (CRPSS) for 2 m
temperature

This section shows the verification for the main target variable. Due to the
limited availability of temporally high-resolution and reliable observations
this can only be done for one site, the regional airport in Innsbruck
(Fig.

For all three precipitation classes ECC-Q is able to outperform the raw EPS (less off-diagonal) and shows lower Brier scores and lower numbers for reliability while losing some resolution. ECC-Q is also beneficial over the mixed version using uncorrected precipitation sums. For snow the two methods using postprocessed temperature forecasts (mixed and ECC-Q) perform very similarly but show different biases. While the mixed model exhibits a wet bias (observed frequencies larger than forecasted probabilities), ECC-Q shows a dry bias. The results for snow should not be over-interpreted as snowfall is relatively rare at this station (7.5 % of all cases). The raw EPS again shows the well-known wet bias in all three classes.

Reliability diagrams for hourly predictions of precipitation
(snow

Next, Fig.

What can be seen is that the ECC-Q temperature predictions
(Fig.

Example prediction for 8 March 2017 (station 11315, Holzgau) for the
whole forecast horizon

As a last result, Figs.

While Fig.

Top–down: 1 h probability of precipitation (rain

Expected 1 h amount of liquid water content for 10 March 2017
00:00 UTC (

This article presents a new hybrid approach to combine standardized anomaly output statistics (SAMOS) with ensemble copula coupling (ECC) and a novel re-weighting scheme for probabilistic snow forecasts. The results demonstrate that the new approach provides a framework for accurate high-resolution spatio-temporal probabilistic forecasts for 2 m temperature, precipitation, and snowfall over complex terrain.

The use of ECMWF hindcasts for model training and ECMWF EPS for prediction
offers a computationally efficient way to get the required inputs for the
SAMOS method (see Appendix

The additional ensemble copula coupling (ECC-Q; Sect.

Nevertheless, the method is still able to strongly improve calibration and
reliability of the forecasts, especially for 2 m temperature, even though
the sharpness is rather low. The mean 80 % prediction interval width for
temperature is between 6.9 and 7.2

To improve the temperature forecasts, we include the temperature from the 850 hPa level as an additional covariate, which can be seen as a “free atmosphere” prediction over the area of interest. Furthermore, the 850 hPa temperature is a prognostic quantity which should be less strongly affected by possibly unrealistic surface processes (cooling/heating effects). In addition, surface pressure and 2 m dew point temperature are included to correct for weather-situation-dependent errors and very dry/wet conditions. The model shown in this article only includes the additional covariates as linear main effects and is more a proof of concept. We have also tested derived covariates such as 2 m potential temperature and nonlinear mixtures of 2 m temperature and 850 hPa temperatures to allow high-elevation stations to take the information from an elevated air mass (“free atmosphere”) rather than from the near surface. As none of these models showed large improvements, and for simplicity, we decided not to show the results of these more complex models in this article. However, the “extended heteroscedastic SAMOS model” demonstrates that the SAMOS model can easily be extended by including additional covariates which do not necessarily have to be linear. As shown, this allows one to further improve the predictive performance, even with this simple model. A more flexible SAMOS model might bring further improvements, e.g., by including a larger set of covariates, including interactions between the different covariates, or by using more flexible effects such as multi-dimensional effects which can be used to represent elevation-dependent effects and which will be worth investigating in more detail in the future.

As the results show (Fig.

One of the biggest advantages of the proposed hybrid approach is that forecasts can be produced on the same temporal scale as the current EPS even if the underlying data sets used for model training (hindcasts and observations) are available on coarser temporal scales or even different timescales for different variables. This allows one to combine the best information from (location-)independent sources to get the most reliable probabilistic predictions possible. For the present study, two observation networks have been combined, one providing long-term daily precipitation records, and one providing temporally highly resolved temperature measurements.

Overall the 2 m temperature and precipitation forecasts serve as a good proxy for probabilistic snowfall forecasts, which is the main target variable of this study. The results show very promising results in terms of calibration and reliability of both the expected amount of precipitation and fresh snow, but also the probability of observing snowfall at an hourly temporal resolution.

The main parts of this study are based on

Observations from the hydrographical service

For spatio-temporal ensemble postprocessing we followed the approach of

The spatio-temporal model for the 2 m temperature uses the geographical
location (longitude lon, latitude lat, and altitude alt), the “hour of the
day” (hour), and the “day of the year” (doy) as covariates and is
specified as follows:

As for Eq. (

Hindcasts are produced every Monday and Thursday (available Tuesday/Friday),
computed 2 weeks in advance. Taking hindcasts for

Schematic concept of the SAMOS postprocessing based on ECMWF hindcasts (black), ECMWF EPS forecasts (red), and observations (orange). Background climatologies (gray) are used to convert the data from the physical scale into standardized anomalies (blue) used to estimate the regression coefficients of the SAMOS postprocessing method. The SAMOS correction can be applied to the standardized anomalies of a new EPS forecast to obtain spatial or spatio-temporal probabilistic forecasts (full distribution). These results are used as input for the ECC approach.

Once the regression coefficients of the SAMOS model have been estimated,
future ensemble forecasts can be corrected by first computing standardized
anomalies using the same model climatology as for model training and
correcting the standardized anomalies of the ensemble forecast using the
estimated SAMOS models. As the outcomes (

Algorithm 1 presents pseudo-code for all steps. The same is shown in
Fig.

Figures

Stamps for

Stamps for

This study summarizes the ideas developed within our most recent research project by all the members, including RS, GJM, JWM, and AZ. The majority of the work for this study was performed by RS. The statistical models are, to a large extent, based on the two R packages bamlss and crch developed by JWM and AZ (and others). All the authors closely worked together discussing the results and findings and commented on this paper.

The authors declare that they have no conflict of interest.

This project was partially funded by the Austrian Science Fund (FWF), grant
TRP 290, and the Austrian Research Promotion Agency (FFG), grant no. 858537.
The data sets are provided by the Zentralanstalt für Meteorologie und
Geodynamik Vienna (ZAMG;