At subdaily resolution, rain intensity exhibits a strong variability in space and time, which is favorably modeled using stochastic approaches. This strong variability is further enhanced because of the diversity of processes that produce rain (e.g., frontal storms, mesoscale convective systems and local convection), which results in a multiplicity of space–time patterns embedded into rain fields and in turn leads to the nonstationarity of rain statistics. To account for this nonstationarity in the context of stochastic weather generators and therefore preserve the relationships between rainfall properties and climatic drivers, we propose to resort to rain type simulation.

In this paper, we develop a new approach based on multiple-point statistics to simulate rain type time series conditional to meteorological covariates. The rain type simulation method is tested by a cross-validation procedure using a 17-year-long rain type time series defined over central Germany. Evaluation results indicate that the proposed approach successfully captures the relationships between rain types and meteorological covariates. This leads to a proper simulation of rain type occurrence, persistence and transitions. After validation, the proposed approach is applied to generate rain type time series conditional to meteorological covariates simulated by a regional climate model under an RCP8.5 (Representative Concentration Pathway) emission scenario. Results indicate that, by the end of the century, the distribution of rain types could be modified over the area of interest, with an increased frequency of convective- and frontal-like rains at the expense of more stratiform events.

Stochastic weather generators are statistical models designed to simulate realistic random sequences of atmospheric variables (e.g., temperature, rain and wind). Their main target is to reproduce both the internal variability of each variable of interest and the relationships between these variables

Such changes in rainfall characteristics make rain statistics time-varying. In terms of stochastic modeling, this implies that the stochastic process used to model rainfall is nonstationary through time; i.e., the parameters of the stochastic model change over time. The most common way to deal with the nonstationarity of rain statistics is to define a priori (i.e., prior to model calibration) the time periods during which stationarity is assumed. Afterwards, a piecewise-stationary modeling is applied; i.e., model parameters are kept constant within a single stationary period but are allowed to vary between stationary periods. The temporal scale at which nonstationarity occurs is defined by the modeler according to prior knowledge and assumptions about the rain process at hand and ranges from seasons

In this context, the main goal of this paper is to propose a new approach to leverage the use of rain types for encoding nonstationarity in the framework of stochastic weather generators. However, the finality differs from that of classical weather generators

Overview of stochastic rain type generation (core of this study) and its application to simulate high-resolution synthetic rain fields whose statistical properties depend on meteorological conditions.

The remainder of the paper is structured as follows. First, Sect.

Before proposing a stochastic model able to mimic the rain type occurrence process (Sect.

We focus hereafter on a 100 km

Radar dataset used for rain typing.

Main features of a rain type time series (2001–2017) observed over central Germany.

In a nutshell, the classification method proposed by

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.

Figure

Statistics of meteorological covariates for each rain type. The meteorological data were extracted from the ERA5 reanalysis dataset.

The strong seasonality and interannual variability of rain type occurrence emerging from Fig.

Figure

Daily resolution stochastic weather generators do not distinguish between rain types and typically resort to Markov chain models to simulate rain occurrence

One alternative to account for such complexity is to consider high-order properties through a nonparametric approach based on the resampling of historical datasets

Schematic view of the MPS algorithm used for the nonparametric resampling of historical rain type time series.

Since MPS is a nonparametric approach, it does not require model calibration strictly speaking. Instead, it requires a training dataset to resample, which should include both the variable of interest (here a rain type time series) and optional covariates (here meteorological covariates). To produce reliable results and, in particular, meaningful uncertainty estimates, MPS requires large training datasets

Model performance is assessed by a cross-validation procedure, using the dataset introduced in Sect.

The 50 simulations are compared to the reference rain type time series in Fig.

Results of the cross-validation experiment.

Focusing next on the simulation of rain types, Fig.

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.

Monthly rain type occurrence stratified according to climate forcing:

Figure

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.

For illustration purposes, the stochastic rain type model developed in Sect.

For each 20-year period, 50 realizations are simulated conditional to bias-corrected RCM-derived meteorological covariates. To evaluate the projected changes in rain type distribution, Fig.

Changes in rain occurrence frequency (left panel) and rain type distribution conditional to the presence of rain (other panels) simulated using the stochastic rain type model developed in Sect.

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.

Hence, two main applications can be considered for stochastic rain type simulation. The first one, briefly illustrated in Sect.

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.

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.

All data and codes used in this study are open source and freely available in the following repositories:

radar data at

rain type data at

rain typing software at

stochastic rain type models at

MPS simulation software at

The supplement related to this article is available online at:

LB, MV and GM designed the study. LB performed the numerical experiments. LB wrote the paper with input and corrections from MV and GM.

The authors declare that they have no conflict of interests.

The authors are grateful to the editor and to the three reviewers for their comments and suggestions.

This paper was edited by Nadav Peleg and reviewed by András Bárdossy, Hjalte Jomo Danielsen Sørup, and one anonymous referee.