We focus hereafter on a 100 km × 100 km squared area centered in the city of Jena in the federal state of Thuringia, Germany (Fig. a). This area has been chosen because its flat topography, and its location far from coastlines or major topographic barriers ensures spatially homogeneous rain fields, allowing for focusing on the temporal component of rainfall nonstationarity. Over this area, data used for rain typing consist of radar images extracted from the RADOLAN (RAdar-OnLine-ANeichung) dataset , which are provided in an open-access way by the German meteorological agency (Deutscher Wetterdienst – DWD). It consists of raw (i.e., not adjusted on rain gauges) radar image composites over all of Germany from 1 January 2001 to present. The RADOLAN radar image resolution is 1 km × 1 km in space and 5 min in time. In practice, however, we resampled radar images at a 10 min resolution and restricted our study to the period 1 January 2001–31 December 2017. The RADOLAN dataset is used as baseline information for rain typing, following a space–time classification approach . Using raw radar images can lead to biases in estimated rain intensities, but the impact of such biases on the classification are deemed negligible, since the adopted approach focuses on rainfall space–time behavior rather than rainfall intensity. A problematic source of errors would be the change of radar biases along time, which could alter the interannual frequency of rain types. To alleviate this problem, uniformly reprocessed radar images are used as the basis for the classification, which ensures a consistent data cube throughout the period of interest. In practice, no adverse trend is noted in the observed rain type distribution (Fig. ).

In a nutshell, the classification method proposed by and used hereafter for rain typing consists of the following. First, rainy time steps are defined as periods with more than 10 % radar pixels measuring rain. The other time steps are classified as dry and are not considered for rain typing. For classification, 10 statistical metrics are computed for each rainy radar image in order to assess the space–time intensity behavior of the rain field observed in the image. Among these metrics, three relate to the statistical distribution of rain intensity observed in the radar image; three characterize the spatial arrangement of rain patterns within the image; and four evaluate the temporal evolution of the rain field due to rain advection and diffusion between consecutive periods. Then, the 10 metrics are used as a basis for classification using a Gaussian mixture model (GMM). All details about the 10 metrics and the clustering approach with a GMM can be found in . The resulting clusters correspond to rain fields with similar space–time behaviors. The number of rain types is selected as a compromise between the goodness of fit to rain field statistics and model parsimony. In the present case, the parsimony is favored in order to allow for a physical interpretation of the resulting rain types. As a result, six rain types are identified in the example dataset (Fig. b). Among them, rain types 1 and 4 correspond to rather stratiform and spread rain events; rain type 3 corresponds to frontal rainstorms; and rain types 5 and 6 can be associated with rather convective rains. Rain type 2 cannot be associated to a specific rain behavior but rather gathers rain fields that are not classified otherwise and often correspond to partial rain coverage.

Using only radar images with more than 10 % wet pixels to define rain types ensures a reliable classification but at the cost of a dry bias (in the present dataset, 32 % of the images have a rain fraction between 0 % and 10 % and encompass 19 % of the rain total; cf. Fig. ). To deal with images with less than 10 % wet pixels, proposed classifying images with a small rain fraction (i.e., 0 % < rain fraction < 10 %) in a second step by assigning them the type of the closest classified image (i.e., nearest neighbor interpolation in time). This postprocessing scheme is not directly transferable to the context of simulation because no information about images with low rain coverage is available in simulation outputs. Two options can be considered to alleviate this problem. First, the rain type model defined in Sect.  can be calibrated on the final classification (i.e., including images with low rain coverage), which results in simulations that preserve the actual rain proportion. However, using a classification that includes the onset and the end of rainstorms leads to less clear relationships between climate covariates and rain type occurrence, which may degrade simulation results. Hence the second option, which we follow in this paper, which consists of (1) calibrating and running the rain type model for rain types defined only from radar images with more than 10 % rain coverage and then (2) readjusting the dry–wet balance by postprocessing. The dry bias is corrected assuming the ratio R=NsNl between the number Ns of images with low rain coverage and the number Nl of images with large rain coverage as a constant in observations and simulations. Subsequently, the number of epochs for which rain is simulated is increased by propagating the closest rain type to the R×Nl dry epochs located at the beginning and at the end of rainstorms. Section S1 in the Supplement shows that such postprocessing performs well to mitigate the dry bias originating from the use of a 10 % rain coverage threshold to define a wet image. However, since the present study focuses on climate–rain-type relationships, which are better defined when considering only the first step of the classification, the aforementioned postprocessing is not applied in the remainder of this paper. Hence, one should keep in mind that in the following the dry type also includes epochs with a low rain coverage (under 10 %) and that postprocessing is required if the end-use application involves the stochastic simulation of actual rain fields.

Figure  investigates the occurrence of rain types through time and highlights some features. Figure a displays the frequency of each rain type at the seasonal scale. It appears from Fig. a that the frequency of occurrence of individual rain types is strongly variable across the year. For example, stratiform rain types 1 and 4 occur mostly in winter, while convective rain types 5 and 6 are most common in summer. In addition, one can notice a strong interannual variability in rain occurrence, with summers 2003 and 2011 having a low occurrence of rain, while rain occurrence is particularly high during winters 2006 and 2011. Figure b displays the cumulative distribution function (CDF) of the duration of each rain type. Here rain type duration is defined as the duration (i.e., length along the time axis) of a segment of constant rain type. Each curve in Fig. b therefore corresponds to the probability that a rain event of a given type does not exceed the duration given in abscissa. This figure shows that all rain types are persistent in time with durations ranging from a few minutes to more than 3 h and that some types (e.g., rain types 4 and 5) are more persistent than others (e.g., rain types 2 and 3). Finally, Fig. c displays the empirical transition matrix between rain types and focuses on inter-type transitions (i.e., transitions to the same type are ignored and denoted by red crosses). This figure shows that the patterns of transition between rain types are complex and that the transitions involving type 0 (i.e., no rain) are largely dominant.

The strong seasonality and interannual variability of rain type occurrence emerging from Fig. a can be explained to a large extent by regional meteorological conditions. Hereafter, we investigate the links between rain type occurrence and a set of five meteorological covariates that are deemed to influence rainfall behavior , namely sea level pressure, temperature at 2 m, relative humidity, and the direction and intensity of synoptic wind at 850 hPa. The actual values of the meteorological covariates used in this study are extracted from the ERA5 reanalyzes and averaged over the whole area of interest before further use. Only parameters provided at daily resolution are used hereafter in order to be compatible with the temporal resolution of RCM projections used for the illustration of our framework (see Sect. ). To match the resolution of rain type data, the above daily resolution meteorological covariates are disaggregated to a 10 min resolution. To this end, the mean daily pressure, humidity, wind direction and wind intensity are assumed to occur at 00:00 LT (local time) and are then interpolated at a 10 min resolution using a polynomial interpolation. For temperature, the daily minimum is assumed to occur at 05:00 LT, and the daily maximum is assumed to occur at 15:00 LT; the diurnal cycle is captured by spline interpolation. This disaggregation framework leads to 10 min resolution meteorological covariates in good agreement with actual 10 min resolution observations carried out by a weather station located close to the center of the area of interest, and rain type simulations conditioned to these two sets of covariates (in situ observations and disaggregated reanalysis data) give very similar results (Sect. S2; Fig. S3).

Figure  displays the relationships between meteorological covariates and rain type occurrence and confirms the strong influence of temperature and wind speed on rain types. Indeed, stratiform rain types 1 and 4 occur at lower temperatures than convective types 5 and 6 and co-occur with stronger winds. The frontal rain type 3 is characterized by strong westerlies but occurs for a broad range of temperatures. In contrast to temperature and wind speed, the standalone knowledge of pressure, relative humidity or wind direction does not allow for discriminating between all rain types. However, when considered jointly (Sect. S2; Fig. S4), all meteorological covariates bring information about rain type occurrence. In particular, pressure and humidity are key drivers for rain occurrence (no matter the type) and are therefore useful to predict dry and wet spells. Furthermore, wind direction informs the occurrence of rain type 3 and helps to discriminate between rain types 5 and 6.

Model performance is assessed by a cross-validation procedure, using the dataset introduced in Sect. . In practice, we adopt a procedure of leaving 1 year out. For a given simulation year, the rain type model is first trained using data from the 2001–2017 period, excluding the year to simulate. Next, 50 realizations of rain type time series are generated for the year of interest by MPS simulation and conditioned to observations of the meteorological covariates derived from the ERA5 reanalysis as described in Sect. . Finally, the same procedure is iterated for each year of the test period (i.e., 2001–2017), and 50 realizations of 17-year-long rain type time series are obtained by concatenating in time the 17 yearly simulations.

The 50 simulations are compared to the reference rain type time series in Fig. . Focusing first on the ability of the model to simulate dry and wet conditions (i.e., without distinction between rain types), the first panel of Fig. a compares the observed and simulated frequencies of dry occurrence for each season of the validation period 2001–2017. The results show that our model properly simulates the overall proportion of rain (ratio of simulated to observed rain frequency is 0.93). In addition, the chronology of dry–wet occurrence at the seasonal scale is reasonably simulated (correlation between observed and simulated dry type occurrence is 0.6).

Focusing next on the simulation of rain types, Fig.  (lines 2–7) assesses the ability of the model to reproduce the typical features of rain type occurrence highlighted in Sect. , namely seasonality, persistence and transition. Figure a assesses rain type seasonality and shows that for strongly seasonal rain types (types 1, 5 and 6) the annual cycle of rain type occurrence is properly simulated. It is also worth noting that the interannual variability of the annual cycle is reasonably well simulated, as well as the interannual variability of weakly seasonal rain types (types 3 and 4). This shows that the proposed approach not only reproduces the annual cycle of rain type occurrence driven by monthly scale variations of the covariates but also captures the impact of short-term fluctuations of meteorological conditions that trigger rainstorms of types 3 and 4. However, when scrutinizing the minima and maxima in Fig. a, one can notice that peaks in observations are smoothed out in simulations, which traduces the difficulty of the model to simulate extreme cases. This is a known drawback of MPS simulations , and it constitutes the main limitation of the present approach for the simulation of future climates in which unusual climatic conditions are deemed to become more frequent. Regarding rain type persistence, Fig. b shows that this feature is in general very well reproduced, except for the long-lasting types 4 and 5, for which persistence is slightly underestimated. Finally Fig. c assesses inter-type transitions. One can notice that the transition patterns are almost perfectly reproduced, except for the transition from dry (and to a lesser extent from type 5) to rain type 6 that is underestimated (overestimated, respectively).

Overall, the proposed stochastic rain type model properly reproduces the main features of observed rain type time series. This good performance is linked to the ability of MPS to accurately reproduce high-order statistics of rain type time series.

To ensure that the proposed rain type model is able to capture the impact of climatic signals on rain type occurrence, the results of the cross-validation procedure are stratified according to annual climatic signatures. To this end, Fig.  compares simulated and observed rain type occurrences at the monthly scale for four sub-datasets: the 5 coldest years of the 2001–2017 period (Fig. a), the 5 warmest years (Fig. b), the 5 driest years (Fig. c) and finally the 5 wettest years (Fig. d). Observations (red curves in Fig. ) show that years with different climatic signatures indeed develop distinct dry / wet ratios and rain type distributions. Simulation results (blue curves in Fig. ) show that the proposed model properly reproduces these climatically driven differences in rain type distribution.

Figure  therefore allows for a detailed investigation of the impact of climatic signals on local rain type distribution over central Germany. Comparing first cold and warm years (Fig. a and b), one can notice that warm years tend to be drier, in particular in late winter and spring. This is mostly caused by a deficit of type 1 precipitation during warm years, which corresponds to less snow (type 1 occurs mostly at low temperatures; cf. Fig. ). Drier springs during warm years are also caused by a deficit of type 5 (slightly convective), which probably corresponds for this time of the year to rain and sleet showers. Finally, one can notice an increased occurrence of type 6 (strongly convective) during warm years, which is captured by the model despite a slight underestimation of this type for both cold and warm years. Comparing dry and wet years (Fig. c and d), one can notice that all months contribute to the rain imbalance but that the rain deficit is more pronounced in spring and autumn. In terms of rain type distribution, this is mostly caused by a deficit of rain types 1 and 4 (stratiform) as well as 5 (slightly convective) during dry years. It is also worth noting that rain type 3 (frontal) tends to be slightly more common during rainy years, but in contrast to other types, its increased occurrence is spread along the whole year.

Overall, the proposed approach properly captures the impact of climatic signals on rain type occurrence. This property is essential to preserve the relationships between rain types and climatological drivers and paves the way to RCM precipitation downscaling.

By introducing a step of rain type simulation in the framework of stochastic rainfall generators, we suggest that for high-temporal-resolution applications, the simulation of rain can be split in two steps (Fig. ). In a first instance, rain types are simulated conditional to meteorological covariates to account for the diversity of rainstorms at the regional scale. This first step is the main focus of the present paper. For subsequent applications, we assume that the rain intensity can be simulated conditional to rain types. This is the classical aim of space–time-distributed stochastic rainfall generators, which are becoming more and more common to address the needs of high-resolution hydrometeorological impact studies .

Hence, two main applications can be considered for stochastic rain type simulation. The first one, briefly illustrated in Sect. , consists of assessing the evolution of the statistical signature of rainfall in a changing climate simulated by RCMs. It is worth noting that if one wants to carefully evaluate the change in rain type occurrence that may emerge in the future, one should rely on a large ensemble of emission scenario, general circulation model and regional climate model combinations to properly capture the uncertainty on meteorological covariates. In addition, one should keep in mind that the present approach only accounts for changes in the distribution of existing rain types and therefore ignores the possible emergence of new rain types in response to climate conditions that have never been observed over the area of interest. Such new rain types could potentially be modeled by reparametrizing the stochastic rainfall model used to simulate local rain fields , by using rain analogs from areas that today experience the climate that is simulated in the future over the area of interest or by running a convection-permitting climate model for the newly emerging climate conditions. The development of a framework to model emerging rain types is however left for future research.

The second application is the simulation of rain intensity at high space–time resolution while preserving consistency with climatological drivers such as temperature, pressure, humidity and wind. As mentioned in the Introduction, simulating rain intensity would require setting up and calibrating a high-resolution stochastic rainfall model for each rain type over the area of interest and was therefore not considered in the present study except in Fig. b for illustration purposes. However, two advantages are expected to emerge from adding a rain type simulation step into stochastic rainfall modeling: first, a relatively low number of rain types can be specified, which implies that the model of rain intensity has to be calibrated a limited number of times. This ensures that enough observations are available to calibrate the rain intensity model for each rain type and therefore prevents model overfitting. The second advantage is the added flexibility to simulate rainstorm dynamics, which allows for generating intra-storm variations of the space–time rainfall statistics.

In this paper, a nonparametric approach based on the resampling of historical records using multiple-point statistics has been proposed and thoroughly tested for the simulation of rain type time series conditional to meteorological covariates. Evaluation results based on a 17-year-long rain type dataset in a mid-latitude climate (central Germany) show that MPS simulations are able to reproduce both the internal variability of rain type time series, as well as relationships with meteorological covariates. After validation, stochastic rain type simulation is applied to the downscaling of RCM projections over the 21st century. Rain type simulations conditioned to meteorological covariates simulated by a regional climate model under an RCP8.5 emission scenario indicate a possible change in rain type distribution by the end of the century, with an increased frequency of heavy rains driven by convection or active fronts, and a decline of low-intensity stratiform precipitations.

The ability of stochastic simulations to generate realistic rain type time series when conditioned to meteorological covariates advocates for including stochastic rain type simulation into rainfall generators in order to (1) reproduce the internal variability or rain type occurrence, in particular interannual variability, seasonality, persistence and inter-type transitions, and (2) preserve the relationships between rain statistics and meteorological covariates, in the present case temperature, pressure, humidity and wind. The above features make stochastic rain type simulation a convenient tool to account for the nonstationarity of rain statistics driven by meteorological conditions. This opens the door to the subdaily stochastic downscaling of climate projections and to improved stochastic rainfall simulations.