Continuous and long rainfall series are a necessity in rural and urban hydrology for analysis and design purposes. Local historical point rainfall series often cover several decades, which makes it possible to estimate rainfall means at different timescales, and to assess return periods of extreme events. Due to climate change, however, these series are most likely not representative of future rainfall. There is therefore a demand for climate-projected long rainfall series, which can represent a specific region and rainfall pattern as well as fulfil requirements of long rainfall series which includes climate changes projected to a specific future period.
This paper presents a framework for resampling of historical point rainfall series in order to generate synthetic rainfall series, which has the same statistical properties as an original series. Using a number of key target predictions for the future climate, such as winter and summer precipitation, and representation of extreme events, the resampled historical series are projected to represent rainfall properties in a future climate. Climate-projected rainfall series are simulated by brute force randomization of model parameters, which leads to a large number of projected series. In order to evaluate and select the rainfall series with matching statistical properties as the key target projections, an extensive evaluation procedure is developed.
In design of new and analysis of existing storm water drainage systems valid rainfall statistics are crucial. With climate changes anticipated to impact precipitation patterns, the historical rainfall statistics upon which the traditional design is based, is no longer valid for future design. There is therefore a need for climate projection of the rainfall statistics in order for these to represent the future loads on storm water drainage systems.
Traditionally many simple urban drainage systems are designed with intensity–duration–frequency (IDF) relationships, or types of design storms (e.g. Unit Hydrograph: Sherman, 1932; Chicago Design Storm, CDS: Keifer and Chu, 1957; SCS: NRCS, 1986) which represent statistics for rain with specific return periods. Climate projection of these types of design methods can be relatively simple, e.g. by multiplying the design rain by a bias climate factor (e.g. Semadeni-Davies et al., 2008; Olsson et al., 2009; Willems et al., 2012a; Willems, 2013b; Shahabul Alam and Elshorbagy, 2015), assuming that extreme rainfall events for a specific return period will be increased linearly with a given factor as a function of time. The most recognized approach for estimating climate factors is the downscaling of global circulation models (GCMs) and/or regional climate models (RCMs) (e.g. Wilby and Wigley, 1997; Fowler et al., 2007).
In general, statistical downscaling determines a statistical relationship between a large- and a local-scale climate variable based on historical records. The relationship can be used in a GCM/RCM to obtain local variables for a specific domain in a given time frame of climate projection (e.g. Wilby et al., 2002; Nguyen et al., 2007; Willems and Vrac, 2011; Willems et al., 2012b; Arnbjerg-Nielsen, 2012; Sunyer et al., 2015). The statistical downscaling approach requires long historical records of observations in order to establish the necessary statistical relationships. Based on various types of statistical downscaling assumptions and methods, climate factors for urban drainage design purposes (e.g for multiplication on IDF relationships) can be derived by statistically comparing contemporary climate conditions with projected future rainfall with regards to specific return periods, and aggregation levels (durations) or rainfall (e.g. Mailhot et al., 2007; Larsen et al., 2009; Madsen et al., 2009; Nguyen et al., 2009, 2010; Willems and Vrac, 2011; Olsson et al., 2012; Willems, 2013b).
Whereas a large proportion of the recent research described above has been conducted on estimating climate factors for design purposes, there is also a significant need, not only to describe future extremes (e.g. in the form of IDF relationships) but also to be able to project climate changes to continuous rainfall time series. Basically, simple design methods assume agreement between the return period of the rain intensity (for a given duration), and on the other hand the return period of the critical load in the drainage system (water level, flow, basin storage, etc.). Multiplication of climate factors to design storms, e.g. IDF relationships, is sufficient for many applications of urban drainage design; however, for more complex drainage systems with non-linear rainfall runoff response the simple design methods falls short. That is, for complex systems the return periods of the rainfall duration and intensity are not in agreement with the return periods of the corresponding drainage system state. Therefore, historical rainfall series (or climate-projected rainfall series) are required for complex systems in order to estimate maximum water levels in manholes, flooding, to estimate the return periods, and other loads on the drainage system such as outlet to recipient, inlet to wastewater treatment plants, combined sewer overflow, outlet flow, and pollutants loads in the future climate (e.g. Schaarup-Jensen et al., 2009; Thorndahl, 2009; Thorndahl et al., 2015).
According to Willems et al., (2012a, b) there are generally two methods that produce continuous climate-projected time series either by (1) stochastic rainfall generators which generate locally representative synthetic rainfall conditioned on climate variables in present and future climate or (2) statistical approaches to downscaling such as change factor, resampling or weather typing methods, in which future local rainfall is sought in historical rainfall records under equivalent historical climate conditions as projected in the future, or modified to represent future climate conditions.
In the literature, the most acknowledged methods for stochastically generating synthetic rainfall series are based on Poisson cluster processes and rectangular pulse models such as Bartlett–Lewis (Koutsoyiannis and Onof, 2001; Onof and Wheater, 1994, 1993; Segond et al., 2007; Onof and Arnbjerg-Nielsen, 2009; Paschalis et al., 2014; Kossieris et al., 2016) or Neyman–Scott (e.g. Entekhabi et al., 1989; Cowpertwait, 1991, 2010; Cowpertwait et al., 2002; Fowler et al., 2005; Burton et al., 2008; Paschalis et al., 2014; Sørup et al., 2016). Calibration of the generators is typically performed by comparing generated series to observed series and adjusting relevant parameters prior to climate projection. Methods for estimating point rainfall (e.g. Cowpertwait et al., 1996; Marani and Zanetti, 2007; Onof and Arnbjerg-Nielsen, 2009) and spatially distributed rainfall or multi-site generators with spatial dependency (e.g. Kilsby et al., 2007; Burton et al., 2008; Sørup et al., 2016) have been applied. These methods have been shown to provide valid results for hourly or daily time steps but also have significant shortcomings in terms of modelling rainfall at a finer temporal resolution. For urban hydrological applications with fast rainfall response, a temporal resolution of input data down to 1–10 min is required (e.g. Schilling, 1991; Willems, 2000; Thorndahl et al., 2008, 2016, 2017). Because we are interested in maintaining the fine temporal resolution of observed rainfall series, generation of synthetic rainfall series using Poisson clusters is rejected here as an applicable method.
Change factor, resampling or weather typing methods (Willems et al., 2012a, b)
of statistical downscaling outcomes of RCMs/GCMs can provide data in the required
temporal resolution, since directly based upon historical records.
Arnbjerg-Nielsen (2012) applied historical rain series
originating from another geographical region, which had a climate analogue
to the projected climate in order to obtain continuous representative
rainfall series for future climate conditions.
Zorita and Von Storch (1999),
Olsson et al. (2009),
Willems and
Vrac (2011), and Ntegeka et al. (2014) used historical records of rain and modified these records to
represent climate-representative continuous climate-projected rain series.
Ntegeka et al. (2014) alternated
the number of dry and wet days and used
The calculated Danish climate changes in annual and seasonal precipitation as well as extremes. The values are expressed as a multiplicative climate factor describing the difference between the reference period 1961–1990 and 2071–2100. The A1B scenario is presented in Olesen et al. (2014) and represents 14 regional climate model runs from the ENSEMBLES project. The climate factors from the two RCP scenarios are previously unpublished, but derived from the Euro-CORDEX-11 database (Jacob et al., 2014) and processed statistically for this paper. Standard deviation is listed in parentheses. The indices marked with bold are the ones used in this paper.
The approach presented in this paper is different from the methods presented
above, although it can be considered as a variation of
The procedure is divided into two major parts: (1) resampling of a historical point rainfall time series (“Method development”: Sect. 3.1; “Results and evaluation”: Sect. 4.1); and (2) climate projection of resampled time series (“Method development”: Sect. 3.2; “Results and evaluation”: Sect. 4.2).
The essential concept of the method is to stochastically generate a large number of either resampled historical series or climate-projected series, and to evaluate the statistical properties of the generated series against a number of key target variables. Rather than optimizing for the best parameter fit, the basic concept is to sample parameters from broad uniform distribution functions for each parameter and to either accept or reject each stochastically simulated series using a specified criterion. Repeating this procedure for a large number of realizations of rainfall series, it is possible to select a number of rainfall series which has a satisfying statistical representativeness in comparison with historical series or climate projection targets. The evaluation procedure is inspired by the generalized likelihood uncertainty estimation (GLUE) method (Beven and Binley, 1992; Thorndahl et al., 2008) and is presented in detail in Sect. 3.3.
The method assumptions and subjectivity are discussed in Sect. 5 and in Sect. 6 conclusions on this approach to climate projection of single-point historical rainfall series are provided.
Measured time series of the Sulsted rain gauge. The temporal resolution of rainfall data is 1 min.
The development of the model is based on rain gauge data from Denmark and projection of Danish climate conditions, but could easily be extended to other regions/countries of interest.
Specific statistical properties for the future precipitation in Denmark are
necessary in order to climate project the resampled rainfall series. In
Olesen et al. (2014) the Danish Meteorological
Institute has collected and processed data from the ENSEMBLES project
(
Recommended climate factors for design of drainage systems in Denmark according to WPC (2008, 2014) and Gregersen et al. (2014b). The climate factors are valid for a duration of 1 h but also recommended for other durations up to 3 h. The indices marked with bold are the ones used in this paper. The standard deviations are not provided directly in the references, but estimated from tables and figures.
The Water Pollution Committee of the Society of Danish Engineers has published reports (guidelines nos. 29 and 30) with recommendations for design of drainage systems considering climate change (WPC, 2008, 2014, background report: Gregersen et al., 2014b). Based also on the climate simulations of the ENSEMBLES project, the climate factors for drainage system design in Denmark are recommended (Table 2). Design rainfall, e.g. IDF relationships, with a specified return period is recommended to be multiplied by these climate factors. The values are derived for rainfall intensities over 1 h but also recommended for other durations (up to 3 h). In this paper these values are used to certify a correct representation of extreme events.
The rainfall series which are applied in this study has its origin in the rain gauge network of the Water Pollution Committee (WPC) of the Society of Danish Engineers. At present, the network consists of 145 tipping bucket rain gauges (DMI, 2014). The rain gauge no. 5047 located in Sulsted, North Jutland (lat 57.17, long 9.96), is applied since this is a station with a long recording time and few errors compared to other gauge records. The gauge has been in operation over a period of 34 years from 1979 to 2014, but due to minor interruptions in the dataset, the effective length of the series is 32 full years. The interruptions do not affect the statistical calculations as these are excluded from the data before the calculations are performed. The time series of 1 min. values for the Sulsted rain gauge is shown in Fig. 1.
In the WPC rain gauge network the temporal resolution of data is 1 min. The
start time of an event is determined at the minute of the first tip of 0.2 mm. All events therefore have initial values equivalent to a multiple of
0.2 mm min
Using Danish rainfall data on a daily scale Gregersen et al. (2014a) have been able to identify multidecadal climate oscillations (Ntegeka and Willems, 2008; Willems, 2013a) as well as climate-related changes in precipitation patterns over the past 140 years. Nevertheless, since this paper is based on evidently shorter rainfall series, it is assumed that no significant trends or climate changes in this period are present. The historical records from the Sulsted series are therefore assumed to be stationary in terms of climate properties.
The procedure of the method is presented in two sections: the
The objective is to create synthetic rainfall series resampled stochastically from a historical series such that the synthetic and the historical series have the same statistical properties. The first step is to divide the historical rainfall series into smaller parts in order to describe variability of intensities, event duration, and time between events over the year. We chose to divide the series into four seasons (winter: DJF; spring: MAM; summer: JJA; autumn: SON), although a finer division (e.g. monthly) could have been implemented. Because the target projections (Table 1) are implemented in seasons, this is the one used. The summer precipitation in the synthetic rainfall series is thus generated based on statistics calculated for every summer period's precipitation in the historical rainfall series and correspondingly for the other seasons.
The stochastic generation (resampling) is based on the following:
Statistics of the inter-event time (also referred to as Sampling of rainfall events including original event durations and
intensities randomly from the pool of historical rain events for each
season.
The concept is outlined in Fig. 2.
The inter-event times(
Molini et al. (2001) applied a Weibull distribution to describe the inter-event time of rainfall events. The Weibull distribution, along with exponential, gamma, and generalized Pareto distributions was also investigated for this paper, but was however outperformed by the mixed exponential distribution, especially in fitting both ends of the distribution.
As opposed to other rainfall generators which use a fixed timescale (e.g. Furrer and Katz, 2008), the time is sampled discontinuously in this case.
The sampling of the events is an automated process with random selection of events from the pool of historical rainfall events for each season. When sampling a specific event, the intensity sequence and consequently also the duration is maintained. Synthetic resampled time series are, therefore produced by random alternating sampling of the inter-event times and historical events from a specific season. It is possible to sample the same event more than once. The procedure is repeated until the length of the generated series corresponds to the length of the historical series or any other specified length shorter than the total length of the original series. The number and the chronology of events are therefore different from season to season and from year to year.
A vital assumption here is that events from the historical series can be sampled independently. Depending on the meteorological conditions at the time of a specific event there might potentially be some correlation to prior and posterior events due to short inter-event times. Extreme event statistics and development of IDF relationships from partial duration series in Denmark is also produced assuming independent events (Mikkelsen et al., 1998; Madsen et al., 2009), so in order to preserve this methodology, no inter-correlation between events has been implemented in the presented approach.
Diagram of the construction of the synthetic (resampled) rainfall series.
The climate-projected rainfall series is generated in three steps:
The inter-event time for each season is sampled using the same procedure as described in the
previous section; however, the parameters of the mixed exponential distribution for each season are
implemented as stochastic variables and thus sampled randomly from a uniform
distribution with fixed upper and lower boundaries. This allows for
different distributions of inter-event times than the ones used in the resampling of
historical series. In the climate-projected series, it is thus possible to
accommodate for climate changes in seasonal precipitation and the
distribution between small and large events, by changing the number of
events per season. As an example the method is able to accommodate a
moderate increase of total summer precipitation, and at the same time a
considerable increase in frequency and intensity of extreme events, with
generally a lower number of total events in summer as a result. Rainfall events are sampled from the pool of historical events for each
season in the same way as described in Sect. 3.1. The duration of each
event is not alternated under impact of climate change, since there is
presently no evidence that single events will become shorter or longer in
the future. This is obviously a crucial assumption, but nonetheless the best
current estimate, which also has been applied by, for example,
Olsson et al. (2009). The
sampling of events is therefore done without alternating the events from the
pool, other than multiplying by different change factors as presented below. The climate projection of the generated time series is inspired by the
delta change method. However unlike Olsson, the change factors are implemented as random variables.
The change factor for a given rainfall intensity, where For each season change factors are multiplied by intensities on the minute
scale. The change factor as a function of intensity, where For each projected rainfall series there is a different value of
The total number of random variables for generating climate-projected
stochastic rain series in the current setup with four yearly seasons is 20
(
The governing assumption behind the resampling procedure is that the
resampled rainfall series should have the equivalent statistical
characteristics as the historical series on a number of key target
variables. The climate-projected resampled series should therefore also have
the equivalent statistical characteristics by means of a number of key
target climate projections (as the ones presented in Tables 1–2). It is not
a necessity that the same target variables are used to evaluate resampled
historical rainfall series and the climate-projected series, but we
chose to do so in this paper in order to keep the evaluation procedures
the same regardless of generating series which should statistically
represent historical series or climate-projected series. The key target
variables are described in detail below:
Annual precipitation (ap). This target variable is included as it is a measure of the total
“mass” balance. Since the individual years of the resampled and historical
series are not directly comparable year by year, the mean of all years is
applied as target variable. Seasonal precipitation (sp). The mean seasonal precipitation is applied as a target variable in order to
ensure same distribution between seasons in the resampled series. The four
target parameters are labelled spwi, spsp, spsu, spau corresponding to winter, spring,
summer, and autumn precipitation respectively. Number of events above 10 mm per day (n10mm). This target variable provides a measure of the representation of extreme
events. Number of events above 20 mm per day (n20mm); same procedure as for no. 3. Maximum daily precipitation (mdp, as a mean of the maximum day for all years). This target variable also certifies the representation of extreme events. IDF relationships. The IDF relationships are traditionally applied in
design of urban drainage systems and are therefore relevant to include as a
target variable. In accordance with Table 2, it is chosen to use the mean
rain intensity over a duration of 60 min for return periods of 2 and 10
years respectively as a target value. The two values are labelled d60T2 and
d60T10 respectively.
The performance of each individual target variable is estimated using a
simple ratio measure between the target value and the corresponding modelled
value:
In order for a simulated rainfall series to be accepted
For the climate-projected series, it is possible to estimate individual
values of the performance using the standard deviations of the climate
factors (cf) given in Tables 1 and 2:
The fitted rate and weight parameters for the mixed exponential distribution specified for each season.
The combined performance measure
The individual weights are presented in Sect. 4.2 and Table 6. One could argue that each season should be given the same weight; however, because summer precipitation tends to be more important in terms of extreme events in Denmark this is given a higher weight. Moreover, because winter precipitation might be associated with larger measurement errors due to poor measurement of solid precipitation, this is given a smaller weight.
The synthetic resampled series are generated with the same total length as the original historical series – in this case 32 years.
The inter-event times for each season are sampled from the mixed exponential distribution as
detailed in Sect. 3.1. The estimated parameters are presented in Table 3.
By comparing the parameters, it is evident that there is a significant
difference for each season. Therefore, it is important that the inter-event times are sampled
individually for each season to ensure a representative number of events in
the resampled rainfall series compared to the historical rainfall series.
Figure 3 exemplifies empirical cumulative distribution functions for summer
inter-events times for the historical series and for the fitted mixed exponential distribution
of summer inter-event times. Furthermore, the empirical distribution from the resampled series
with the best combined performance measure is presented
There is a stringent dependency between inter-event times and number of events in the rainfall series. In order to generate a valid and representational resampled rain series, the number of events series should correspond somewhat to the number of events in the historical rainfall series. Table 4 therefore includes the mean and standard deviation of the number of events per year even though the number of events is not used as a target variable for estimating the individual performances.
Example of cumulative distribution functions for summer inter-event times.
The resampling of the observed rainfall series is performed generating 5000
different resampled rainfall series and assessing the performance of each
generated series using the method described in Sect. 3.3. Out of the 5000
realizations of simulated series, 275 (5.5 %) are accepted using the
criterion of a minimum individual performance measure (
Generally there is a good agreement between the historical series and the accepted series on the target parameters with the highest weights, i.e. the seasonal precipitation. This is actually the case for the majority of the 5000 realizations; however, the performance measures becomes rather low if the extreme events are not represented correctly in the resampled series and they are in that case rejected. The variability between the resampled series is only due to the randomness assembling events and inter-event times from the historical series because the mixed exponential parameters for each season are fixed corresponding to the fits (Table 3). The rejection of resampled series is therefore often due to either sampling of too few or too many “extreme” events within a season.
In many situations, only the one resampled series with the highest
performance measure is of interest. Table 4, therefore, lists target values
of the historical series and the resampled series with the highest
performance measure (best fit). Besides the best combined performance
measure of
To verify the representativeness of extreme rainfall, Fig. 5 (left) presents IDF relationships (from 10 to 360 min durations) for the historical and “best” resampled series for return periods of 2 and 10 years respectively. Grey areas represent the variability in all the accepted realizations. Generally, there is an acceptable agreement between the curves which verifies the resampling method. There is, however, a minor divergence for short durations of the 10-year return period. In general, the longer the return period the larger the divergence between the curves to be expected as a result of the random sampling of historical events in the generated series. Figure 6 shows the time series of the “best fit” resampled time series.
Target variables (mean and standard deviation) and performance measures for the historical series and the one resampled series with the highest performance measure.
Target variables and their values for comparing historical series and resampled series (in blue shades) and climate-projected historical series and climate-projected and resampled series (in red shades). For the climate-projected target (deep red) the uncertainty bounds (black lines) represent 2 times the standard deviation of Tables 1 and 2. For the resampled series the uncertainty bounds represent the total range of the accepted realizations.
IDF curves for historical and resampled rainfall series
Time series example of resampled rainfall series. The temporal resolution of rainfall data is 1 min.
The overall assessment of the previous evaluation indicates that the rainfall resampler can represent the historical rainfall series well based on the selected performance parameters. Due to the stochasticity of the sampling of inter-event times and rainfall events, there is obviously some variability from year to year and from series to series, but because none of the target variables are significantly biased, the overall performance of the resampler is accepted. As it is possible to produce resampled rainfall series with the same statistics as the corresponding original historical series, the resampling algorithm will be applied to generate climate-projected rainfall series in the following section.
Ranges of accepted parameter values for the mixed exponential distribution applied to sampling inter-event times and for the linear function applied to sample change factors for each season.
Climate factors of target variables and minimum acceptance criteria
of the individual performance parameters
Figure 4 and Table 6 provides results for the climate-projected rainfall series. The target variables (climate-projected historical) are estimated using Eq. (5) and are thus the mean values of the historical series of Table 4 multiplied by the climate factors specified in Table 6. In addition Fig. 4 provides an uncertainty estimate on the target values obtained from the standard deviations of Tables 1 and 2.
Because the climate projection of rainfall series involves randomization of
not only the event assembling but also randomization of
Table 5 presents the range of mixed exponential distribution parameters as well as ranges of change factor parameters for the accepted climate-projected realizations for each season. Comparing with Table 3 (in which the parameter assessment is based on fitting the historical data) it is clear that the parameter values obtained by random sampling have a broader range, indicating that an accepted realization with a high performance value can be obtained from a broad range of parameter values. Scatter plotting the performance values as a function of parameter values (not shown) shows flat tops indicating that an equal performance can be obtained from low and high values within the range (uniform distribution). This means that there is a dependency between inter-event time parameters and chance factor parameters.
As seen in Table 5, the change factor is allowed to be both smaller and larger than 1. This allows for both decrease and increase in precipitation amounts in each seasons. The climate-projected precipitation can thus be obtained from an insignificant change in seasonal precipitation, but a rather large increase in extreme precipitation.
Generally there is an acceptable agreement of climate-projected target
variables (
In Fig. 5 (right) the IDF curves for the climate-projected series are shown. There is a slight underestimation of extremes for the 10-year return period, but an overestimation of the 2-year return periods on low durations. Since the total length of the series is 32 years, return periods larger than 10 years are not presented well, since they the associated with large uncertainties (see e.g. Thorndahl, 2009). The uncertainty bands (grey areas) however cover the climate-projected intensities. Figure 7 shows the time series of the “best fit” resampled time series.
Time series example of climate-projected rainfall series. The temporal resolution of rainfall data is 1 min.
The overall performance of the climate projection of resampled rainfall series is considered to be acceptable within the range of uncertainties related to the climate projections. The introduction of 20 random variables and the random assembling of rain events obviously require many realizations in order to produce accepted rainfall series which have a satisfactory degree of agreement on all target parameters.
The developed procedure obviously involves a large degree of subjectivity in the choice of processes and parameters to include. This section will discuss and argue for some of these choices.
The target variables have been chosen to represent both annual and seasonal precipitation as well as more extreme values. The choice of the 10 specific target variables is closely connected to the fact that this is what is currently available for Danish future climate conditions. However, when other, maybe more detailed, target variables becomes available, it would be possible to redo the generation of climate-projected rainfall series with other target variables. It was initially decided only to present values from the RCP4.5 climate scenario; however, the implementation of the method could just as well have been implemented with another RCP or SRES scenario. Another possibility could be to implement other durations and return periods than for 60 min durations for 2 and 10 years respectively in order to emphasize specific extremes further.
It is of utmost importance that the chosen target variables are representative of the future precipitation patterns and that they are comprehensive in the way that they cover both annual/seasonal variations and single events and the statistics related to these. In this paper, we chose only to include yearly mean values of target parameters (except for the target variables related to return periods), but it could also be relevant to apply the year-to-year variability as a target in itself in order to certify the correct representativeness of the resampled series in comparison with the original historical series.
The weights applied in estimating the overall performance of resampled series are chosen in order to emphasize the accumulated precipitation values but, on the other hand, not neglect the extremes. Other weights could have been applied. One could imagine that the weights were chosen according to the purpose of use of the resampled and climate-projected series. If, for example, the series were to be used as an input to an urban drainage model simulating overflow from combined sewer systems to a recipient, it would probably be most important to have a good representation of the precipitation (event) totals. On the other hand if the purpose was simulating surcharge or flooding of a drainage system, the representation of extremes would be more important.
In the present approach a linear function and the probability of a given rainfall intensity for a given season is applied to derive the change factor as a function of intensity. The choice of parameters allows change factors to be both smaller and larger than 1. This might entail that the lowest fraction of intensities is allowed to be smaller in a future climate while the highest fraction of intensities will increase. Other continuous functions, rather than the applied linear function, might be an objective of future studies.
The proposed method applies two major assumptions which are relevant to discuss here. The first assumption is that events are sampled independently for each season. With inter-event times down to 1 h, this might constitute a problem in hydrological applications where the response time of the system in question is larger than 1 h. Hence, coupled events might impact the hydrological system response. The second assumption is that the duration of events does not change under changed climate signals. It has presently not been possible to find evidence for this contention in the scientific literature on climate change. Both of the assumptions are subject to further investigations.
This paper presented a procedure to generate both statistically representative resampled rainfall series from original historical rainfall series as well as climate-projected rainfall series, which includes the advantages in local historical rainfall series as well as projections on changes in rain patterns in the future climate.
The simulated rainfall series can represent the climate-projected target variables and it is shown possible to produce rainfall series which project not only accumulated seasonal precipitation but also extremes in correspondence with the climate projection of the RCP4.5 scenario. The procedure is generic, so if other climate scenarios and potentially other target variables for further precipitation patterns are available, the method will be able to adapt to these as well.
The procedure for generating resampled and climate-projected rainfall series fulfils a need for having local representative rainfall series which are valid both for the present and future climate. The series can be applied directly as inputs to urban drainage models in order to analyse the loads on a drainage system, e.g. combined sewer overflow, surcharge, storage filling, and flooding in the present and future climate.
The rainfall data used are a product of the Water Pollution Committee
of the Society of Danish Engineers and are made freely available for research purposes
by the Danish Meteorological Institute at
The authors declare that they have no conflict of interest.
The authors would like to acknowledge Cathrine Fox Maule at the Danish Meteorological Institute for providing RCM data from EURO-CORDEX database. Edited by: Nadia Ursino Reviewed by: Patrick Willems and Lars Bengtsson