1. Introduction
Extreme precipitation events have been shown to have significant impacts on the environment and society (Alfieri et al. 2015; Kundzewicz et al. 2013; Feyen et al. 2012). Ample studies have demonstrated that increases in extreme precipitation events are expected as the climate warms (Aalbers et al. 2017; Attema et al. 2014; Lenderink and Attema 2015). The relationship between precipitation and temperature might be affected by different factors such as temperature (Westra et al. 2014), duration, and type of the precipitation events (Molnar et al. 2015; Panthou et al. 2014), as well as seasonality and location of the precipitation occurrences (Berg et al. 2009; Wasko and Sharma 2014). Higher air temperatures increase the water vapor holding capacity of the atmosphere (6%–7% °C−1). This increase is known as the Clausius–Clapeyron (C-C) relationship and is used in many studies as a physical basis for assessing the variations in extreme precipitation with the dewpoint and air temperatures (Allen and Ingram 2002; Lenderink et al. 2011; Min et al. 2011; Westra et al. 2014). The scaling rate of precipitation to near-surface air temperature decreases with higher frequencies, while it increases with the duration of precipitation events (Wasko et al. 2015). Lenderink and van Meijgaard (2008) described the hourly extreme precipitation in the Netherlands (i.e., the De Bilt station is taken as a representative station) and found that the increase rate of extreme precipitation exceeds the C-C rate. Enhancements in the dependency of extreme precipitation on the C-C rate appear because of increases in latent heat driven by moisture convergence or convective precipitation (Berg et al. 2013; Haerter and Berg 2009; Lenderink and van Meijgaard 2010). Furthermore, Ali and Mishra (2017) explored the positive relationships between precipitation extremes with dewpoint and atmospheric air temperatures and used them as covariates for developing nonstationary (NS) models for understanding the extreme precipitation changes under the nonstationary climate condition.
Consequently, evidence on the dependence of the extreme precipitation time series on other factors violates the stationarity assumption to derive the existing precipitation intensity–duration–frequency (IDF) curves. In recent years, updating IDF curves was considered to confront precipitation extreme events in nonstationary environments (e.g., Agilan and Umamahesh 2018; Cheng et al. 2014; Cheng and AghaKouchak 2014; Mondal and Mujumdar 2015; Salas et al. 2018; Yilmaz and Perera 2014). For example, in the direction of developing nonstationary precipitation IDF curves, Cheng and AghaKouchak (2014) introduced time-varying nonstationary IDF curves and found the stationary assumption may lead to underestimation of extreme precipitation, and Agilan and Umamahesh (2018) revealed the significance of selecting covariates to develop the nonstationary models and IDF curves.
The incidence of extreme precipitation is increasing in the Netherlands, and several studies have identified increases in mean annual precipitation and trends in extreme indices because of climate change and internal variability across the Netherlands (Aalbers et al. 2017; Buishand et al. 2013; Rahimpour Golroudbary et al. 2017). Fairly rapid urbanization has also occurred during the last several decades in the Netherlands, based on the expansion of urban areas (Daniels et al. 2015b; Hazeu et al. 2011) and the increase in population growth rates (e.g., 1.05% in 2015; Department of Economic and Social Affairs 2015). Because of the lack of long-term observations (i.e., precipitation, dewpoint, and air temperatures) for Dutch cities, efforts to investigate extreme precipitation in urban areas in the Netherlands have been limited. Daniels et al. (2015a) simulated the effects of the urban-land-use type on precipitation for a 4-day period in May 1999 over the Netherlands and reported that no clear local response could be identified. In another study, Daniels et al. (2016) investigated the impacts of land-use changes during 19 summer days from 2000 to 2010. They found that the influence of the urban-land-use type on precipitation is not negligible, and it caused an increase in precipitation by 7%–8% regarding temperature perturbation in this decade for the Netherlands. Moreover, a similar result was found by Rahimpour Golroudbary et al. (2018) for hourly extreme precipitation at local urban stations when compared to nearby rural stations. These studies emphasize that variations in extreme precipitation may also occur because of urbanization and human activities that impact regional and local climates.
Despite the need of knowledge on precipitation discrepancy between urban and nonurban areas, efforts to investigate the extreme precipitation variations and its relationship with surface air temperature at 1.5 m above ground, dewpoint temperature, and atmospheric air temperature at 850 hPa during the long-term period in the Netherlands have been limited due to the lack of ground-based meteorological observations. We provide the scaling relationships between precipitation and these temperatures to develop the nonstationary changes of extreme precipitation events (Barbero et al. 2018; Lenderink et al. 2011; Lenderink and van Meijgaard 2009; Mishra et al. 2012). Moreover, the nonstationary model is developed with another covariate [North Atlantic Oscillation (NAO) index] to demonstrate the influence of annual precipitation cycle on extreme precipitation events (Sienz et al. 2010; Wakelin et al. 2003). The NAO index is used to represent a large-scale mode of climate variability, and it describes the variability in the North Atlantic Ocean from 80°W to 30°E and between 35° and 65°N as the normalized monthly sea level pressure (SLP) difference between stations in the Azores and Iceland (Hurrell 1995).
Given the above discussion, this study presents a physically based statistical analysis that assesses changes in extreme precipitation over the urban and nonurban areas in the Netherlands. The study is structured as follows. Section 2 describes the datasets and statistical methods used to assess the observed parameters and evaluate the nonstationary models. Section 3 highlights the results of scaling and analyzing extreme precipitation and the differences in precipitation extremes between urban and nonurban areas. Section 4 presents more details underlying the results obtained in this study and suggests possible mechanisms, and section 5 gives the conclusions of this study.
2. Data and methods
a. Precipitation gauges
Precipitation data in the Netherlands are available from the national weather institute (KNMI). The network of manual rain gauges includes 325 stations (http://www.knmi.nl/nederland-nu/klimatologie/monv/reeksen). This study considers the daily validated datasets (which contain less than 1% missing data) corresponding to 231 rain gauges for the 30-yr period extending from 1985 to 2014. The rain gauge data are used mainly for scaling precipitation, developing a nonstationary model, and identifying the daily maximum values for each month.
b. Precipitation radar
The 5-min radar-recorded precipitation on a 2.4-km grid is used when the high-frequency observational records at the rain gauges are unavailable. The radar data are used only for obtaining IDF curves for the selected representative month. The validated (bias corrected) radar records covering 17 years (1998–2014) from the two radar stations in the Netherlands (De Bilt and Den Helder) are used. The data are available and can be obtained from the KNMI website (https://data.knmi.nl/datasets/rad_nl21_rac_mfbs_5min/2.0?q=Precipitation&bbox=53.7,7.4,50.6,3.2).
c. Surface air temperature and dewpoint temperature
d. Atmospheric air temperature
The ERA and ECMWF datasets (i.e., the ERA-Interim data for 1985–2014), which have a resolution of 0.125 × 0.125, are used to provide estimates of the daily atmospheric air temperatures at 850 hPa (Ta; see more details on http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=pl; Dee et al. 2011). To avoid the effects of other factors, such as spatial differences in ground cover, on the differences in air temperature, data describing the daily atmospheric air temperature at 850 hPa (approximately 1.5 km) produced by ECMWF are used as a covariate for understanding the impacts of this quantity on precipitation. These atmospheric air temperature data (i.e., Ta) from ERA-Interim are provided at T255 resolution with 60 levels up to 0.1 hPa, which is adequately above the boundary layer of the atmosphere in comparison with the surface air temperature.
e. Circulation conditions
To obtain atmospheric circulation conditions, the method developed by Jenkinson and Collison (1977) is used to classify weather types. The Jenkinson–Collison type (JCT) classification scheme reproduces the subjective Lamb weather types. In this method, the circulation type is classified based on the variability in pressure around a region that contains 16 grid points. A domain that is larger than the study area (47°–58°N, 3°–13°E) is used to implement the classification scheme for mean sea level pressure from daily ERA Interim data (http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc). The cost733class software package (Philipp et al. 2016) is used to create weather types corresponding to the eight prevailing wind directions, plus one unclassified type. Types 1–8 represent the wind directions (W, NW, N, NE, E, SE, S, and SW, where W = 1, etc.), and 9 represents the unclassified weather type (light flow; for more information on this method, see Philipp et al. 2014).
f. Urban land cover
The Coordination of Information on the Environment (CORINE) land-cover dataset, which corresponds to the year 2012 and has 44 land-cover classes on a resolution of 100 m × 100 m (European Environment Agency 2017), is used to define urban and nonurban stations, consistent with previous studies in the Netherlands (e.g., Chrysanthou et al. 2014; Daniels et al. 2014; Rahimpour Golroudbary et al. 2017). The urban extent in this study consists of six categories: (i) discontinuous urban fabric; (ii) industrial or commercial units and public facilities; (iii) road and rail networks and the associated land; (iv) port areas and airports; (v) mineral extraction sites, dump sites, and construction sites; and (vi) green urban areas and sport and leisure facilities. The other types of land-cover classes are defined as the nonurban extent.
g. Scaling analysis
The regression slope is also estimated using the binning method by Lenderink and van Meijgaard (2008). In this method,
the observed daily events (precipitation ≥ 1 mm) for each station from 1985 to 2014 are paired with their corresponding predictor variable (i.e., Tmean, Tmax, Td, or Ta);
the pairs are sorted in ascending order according to their corresponding temperatures;
the ranked pairs are split into 20 bins at 1°C intervals such that approximately the same number of events are placed in each bin;
the linear regressions are performed by forming a dataset for each bin based on the median of their temperatures and the logarithm of the 95th percentile of precipitation; and
the change in the regression slope
h. Extreme value analysis
Here, 
3. Results
a. Scaling of extreme precipitation
The relationship between precipitation and air temperatures is investigated directly using data collected at rain gauges in the Netherlands. The rain gauge–based daily precipitation for a recent 30-yr period extending from 1985 to 2014 is investigated using the corresponding mean and maximum surface air temperature, dewpoint temperature, and atmospheric temperature Ta at 850 hPa, which are brought to the point scale of the rain gauges. The regression slopes are estimated using QR between the 95th percentile of precipitation (≥1 mm) and the predictors (Tmean, Tmax, Td, and Ta). The binning method is performed by dividing the precipitation values into 20 temperature bins that range from 0° to 20°C and have widths of 1°C. The percentage change in the P95th precipitation quantile in each temperature bin is then estimated for each station. The trend line of the fitted linear regression reveals the relationship between precipitation and temperature as a scaling rate 
Regression slopes 
Citation: Journal of Applied Meteorology and Climatology 58, 4; 10.1175/JAMC-D-18-0180.1
Figures 2a and 2b show the regression slopes between P95th and the mean and maximum daily temperature for each station. The regression slopes for the mean temperature are relatively similar to those for the maximum temperature at most of the stations. Increases in atmospheric temperature can induce more intense precipitation (Bengtsson 2010; Wentz et al. 2007). Similar to the surface air temperature, the regression slope using Ta indicates a positive change for all of the stations (Fig. 2c). The relationship between precipitation and Ta may provide more robust scaling rates rather than using Tmean and/or Tmax, which may be influenced by diurnal variations in surface temperature in response to precipitation (Ali and Mishra 2017). Ali et al. (2018) show a positive precipitation response to temperature for the most global stations using the binning technique (BT) or QR. They found a higher positive scaling with dewpoint temperature (median 6.1% K−1) than that with surface air temperature (median 5.2% K−1). The relationship between the P95th of precipitation and the dewpoint temperature, which represents a measure of absolute humidity, is considered instead of the surface air temperature (Fig. 2d). Dewpoint temperature was used instead of surface temperature to take into account the physical linkage between the water vapor available in the atmosphere and temperature (e.g., C-C equation). The relationship between dewpoint temperature and precipitation was observed in greater consistency with the C-C relationship (Barbero et al. 2018; Wasko et al. 2018). The regression slopes for P95th–Td indicate greater changes than P95th–Tmean at most of the stations. This result reveals that changes in relative humidity become important, as does the dewpoint temperature. In fact, the increase in the dewpoint temperature is somewhat more robust than that in temperature (Attema et al. 2014). Lenderink et al. (2011) found more reliable spatial variations in the changes in the dewpoint temperature compared to those in the surface air temperature over Europe. As precipitation forms in clouds, Td and Ta may be the predictor variables that are most appropriately used to estimate the temperature sensitivity of the P95th when compared using Tmean and Tmax.
Estimated regression slopes 
Citation: Journal of Applied Meteorology and Climatology 58, 4; 10.1175/JAMC-D-18-0180.1
b. Nonstationary conditions
To depict the distribution of extreme precipitation in the Netherlands, the monthly maximum of the maximum daily precipitation at the De Bilt station over a 30-yr period is shown by a box-and-whisker plot (Fig. 3a). Strikingly, some data points fall above the whiskers, which extend to 1.5 times the interquartile range. Moreover, these data points reflect positively skewed distributions, whereas the lower whiskers are limited to the boxes.
(a) Box-and-whisker plot of the maximum daily precipitation and the extended interquartile range (i.e., the whiskers extend to 1.5 times the interquartile range) for the De Bilt station during 1985–2014. The outlying data points are indicated by black dots. The median of the daily maximum precipitation is displayed by the black solid line shaded in the 95% confidence interval. The dashed and dot–dashed lines show the 0.25 and 0.75 quantiles. (b) The GEV model is fitted to determine the influences of the NAO index on annual maximum daily precipitation in De Bilt from 1985 to 2014. The dashed black, dotted blue, solid red, solid green, and solid blue lines depict the annual maxima, the NAO index, and the 2-, 10-, and 30-yr return level, respectively. This diagnostic plot shows that the 2-yr return level approximates the median of the GEV distribution.
Citation: Journal of Applied Meteorology and Climatology 58, 4; 10.1175/JAMC-D-18-0180.1
The maximum average occurs between July and October, which have larger boxes than the other months. Thus, it might be unrealistic to conclude that the extreme precipitation variation is stationary in the Netherlands. The seasonal variability and nonstationary nature of extreme precipitation are consistent with previous studies that have examined the Netherlands (Buishand et al. 2013; Rahimpour Golroudbary et al. 2017, 2016a). The seasonal precipitation changes are made obvious by the occurrence of larger boxes in the box-and-whisker plots for the summer and autumn, whereas smaller boxes are seen for winter and spring. Figure 3b demonstrates the fluctuations in the return levels associated with the assessment of impacts using the covariates for the nonstationary estimates (based on the annual block maxima approach) for the De Bilt station. This figure shows that the return levels vary for different return periods with the variations in the NAO index. With respect to study area and based on previous studies (e.g., Attema et al. 2014; Buishand et al. 2013; Rahimpour Golroudbary et al. 2016b), the NAO index is identified as a potential covariate to develop nonstationary models. Since daily precipitation extreme relationships with Ta and Td were explored using stronger-than-surface air temperature, we used the combination (Ta and Td) as covariates for developing nonstationary models. The covariates were also used separately to estimate nonstationary conditions. For example, change in 1-day 10-yr precipitation maxima was estimated under stationary and nonstationary conditions using the combination of Ta and Td, only Ta, and only Td as the covariates. Percentage changes in precipitation maxima that were found using the combination of Ta and Td are larger as compared to estimations considering Ta and Td separately. Furthermore, the small correlation coefficient (i.e., less than 0.5) at most stations might demonstrate the necessity of using both covariates together for the sake of better estimations.
The seasonal evolution is resolved by considering subannual (monthly) blocks, which are sufficiently long to obtain an appropriate convergence of the probability distribution functions (PDFs) of the maximum daily precipitation using the GEV model (Rahimpour Golroudbary et al. 2016b). The suitability of 1-month blocks (i.e., no significant improvement is achieved through the use of 2-month blocks) has been verified in our previous study (Rahimpour Golroudbary et al. 2016b) for rain gauge stations within the Netherlands during a similar period, where 1-month blocks were used to estimate GEV distributions. In this respect, the parameters of the GEV distribution are fitted for all of the precipitation maxima from each month separately (i.e., from January, February, and so on). The monthly nonstationary GEV models for the precipitation maxima are estimated using three covariates (i.e., Td, Ta, and the NAO index) in combination with the location and scale parameters at each station. They are combined as linear covariates for the location and scale parameters in Eqs. (8) and (9), respectively. The significance of the nonstationary models is tested using the LRT to assess the goodness of fit at each station. Table 1 shows the percentage of the number of stations that has implications to ensure that the considered nonstationary models are well founded against the stationary models. This demonstrates the improvement in the nonstationary models in determining their best fit for parameters’ distribution and shows the influence of the covariates at most of the stations for the individual months. Physically, the influence of other external factors such as geographical locations, unstable atmospheric conditions, and the sea surface temperature (SST; Attema et al. 2014; Lenderink et al. 2009) can impact the goodness of fit for nonstationary models for the stations throughout the individual months. For instance, Van Oldenborgh et al. (2009) found a significant increase in monthly SLP for the winter season over the Mediterranean and decrease over Scandinavia during the last 50 years. The changes in SLP pattern caused more humid air from the North Sea to be moved over the Netherlands. Moreover, the annual cycle of precipitation illustrates a discrepancy between the west coast and inland areas, which is mainly driven by circulation changes and increases in the SST, particularly during the summer half year (van Haren et al. 2013).
Percentage of stations (%) present the goodness of fit for the S and NS models. The goodness of fit was assessed using the LRT.
Assessing the influence of the covariates using the nonstationary GEV models results in less uncertain estimates (i.e., with smaller confidence intervals) at most of the stations, in that they fall within the confidence intervals of those obtained using the stationary GEV models. The nonstationary GEV model at each station (as determined by considering the effects of the covariates on the location and scale parameters) is used to estimate the return levels for each month at each station. Figure 4 shows the median of the estimated return levels given different return periods and months over all of the stations in the Netherlands. This figure shows clearly that most of the occurrences of precipitation with higher values happen between July and September, and high return levels of extreme precipitation prevail in August. The average precipitation return levels during the given return periods obtained using the nonstationary models are larger than those obtained using the stationary models. These differences show that the stationary models underestimate the return levels, especially in the summer months.
Monthly return level for the maximum daily precipitation (median of all rain gauge stations) vs the return period from the stationary models (dotted lines) and the nonstationary models (solid lines) in the Netherlands from 1985 to 2014.
Citation: Journal of Applied Meteorology and Climatology 58, 4; 10.1175/JAMC-D-18-0180.1
c. Classification of station types
Considering the circulation conditions, the study makes use of the JCT scheme with nine types to classify the weather and circulation type on each day. The frequencies of daily precipitation (0800–0800 UTC) occurrences are investigated according to the weather types for 231 rain gauges throughout the Netherlands from 1985 to 2014. Figure 5a shows that the median of the precipitation events is slightly larger for the southerly and westerly weather types than those events for the easterly and northerly weather types. Although the average precipitation is fairly similar among the different weather types, the amount and number of extreme precipitation events (i.e., the upper outliers on the box-and-whisker plots) show the impacts of circulation conditions on the occurrence of extreme precipitation. Therefore, a reliable assessment of the impacts of urban areas on extreme precipitation might be obtained by considering the land-cover type upwind of each station for each wind direction.
(a) Variations in precipitation ≥ 1 mm among the nine weather types during 1985–2014. (b) Locations of rain gauge stations (blue closed circles) and areas of urban land cover (gray shading) in the Netherlands (European Environment Agency 2017). The eighth of a circle with a radius of 20 km for the southwesterly geostrophic wind direction (W8) is for the De Bilt station.
Citation: Journal of Applied Meteorology and Climatology 58, 4; 10.1175/JAMC-D-18-0180.1
To reach this goal, we consider the possible effects of the weather types on precipitation events by defining the urban and nonurban stations separately for each wind direction. We have taken all possibilities for wind changes. For land use, since we used only one land-use map (CORINE) for the whole period, we did not analyze the seasonal changes of the land use in this study. Therefore, a rain gauge can change from being an urban or nonurban station depending on the direction of the wind, and the urban and nonurban classification was held constant for the individual wind directions. The land-cover types within 8 octants (eighths of a circle, given the 8 prevailing wind directions) surrounding each station are extracted from the CORINE dataset (Fig. 5b). These octants extend to a distance of 20 km from each station. Depending on the wind direction, the manual rain gauges are classified as urban stations for the corresponding octant when the six aforementioned land-cover categories cover more than 25% of the entire area of the octant; otherwise, they are classified as rural stations. Setting a threshold for defining urban land cover upwind of each station presents an almost similar number of urban and nonurban stations for each wind direction. Although this approach cannot select an area totally occupied with urban land use, it is helpful to distinguish areas where the overall feature includes the higher percentage of urban land cover. Therefore, the stations are classified in terms of the percentage of urban land use in the eight upwind directions and one in the whole buffer around the stations for the unclassified weather type (i.e., light flow). Throughout the study, the discrepancy between the urban and nonurban areas is evaluated by taking the difference between the average of all of the urban stations and the average of all of the nonurban stations for each wind direction.
d. Nonstationary return levels in urban and nonurban areas
The urban impacts on extreme precipitation are investigated using the rain gauges and the gridded datasets and by evaluating the return levels of extreme precipitation using the nonstationary models. The variations in the different return levels (i.e., 2, 5, 10, and 30 year) from January to December for the urban and nonurban stations are investigated using the nonstationary models and 30 years of historical data. Figure 6 shows that the return levels of extreme precipitation for the urban stations vary similarly to those of the nonurban stations: small values occur in winter, and large values occur in summer. The 2-yr return level of daily extreme precipitation varies between 10.7 and 20.6 mm for the urban stations and between 10.9 and 19.9 mm for the nonurban stations.
The 2-, 5-, 10-, and 30-yr return levels derived using nonstationary models median over urban (red lines) and nonurban (blue lines) rain gauge stations in the Netherlands from January to December. (a)–(i) The stations classified as W1–W9 because of the land-use types upwind of the stations.
Citation: Journal of Applied Meteorology and Climatology 58, 4; 10.1175/JAMC-D-18-0180.1
Likewise, similar differences between the ranges of the urban and nonurban return levels are estimated for the 5-, 10-, and 30-yr return levels (i.e., 15.5–30.4, 18.2–31.1, and 21.5–54.1 mm for the urban stations and 15.5–29.0, 18.4–36.3, and 22.6–51.1 mm for the nonurban stations, respectively). The differences in return levels between the urban and nonurban stations increase for larger return periods. The return levels for the urban stations are 5%–7% (i.e., the ratio between the difference in the return levels of the urban and nonurban stations at each return period and the return levels for the nonurban areas) greater than those of the nonurban stations in August throughout the urban type classified as W9. The return levels of extreme precipitation are larger for the urban stations than those for the nonurban stations over all of the months except those between April and June. Land-cover changes in the form of urbanization are modifications of surface covers in a roughly geometrical configuration (urban form) and a composite of urban settlements, buildings, and impervious materials. Urbanization leads to greater heat capacities and surface energy modifications in urban areas than in natural surrounding areas (Oke 1982). Changes in urban surface energy (e.g., the enhancement of heat capacity and release of stored heat to the atmosphere) influence temperature, wind flow, and turbulent mixing. The phenomenon by which temperatures are higher in urban areas than in surrounding rural or vegetated areas is known as the urban heat island (UHI) effect, which is particularly predominant in clear, calm weather conditions. Similar to sea breezes, urban circulation can be generated during calm-wind and fair-weather conditions, during which the surrounding nonurban blows toward the warm urban region. This circulation causes air to rise and can create clouds and precipitation (i.e., the warm and moist air rises in the atmosphere, colliding with the overlying cooler layer of air) over or downwind of the urban area. The discrepancies seen between the urban and nonurban areas during the second half of the year may be partly caused by the increases in temperature and convection caused by the UHI effect on winter precipitation (Trusilova et al. 2009, 2008).
e. Nonstationary IDF in urban and nonurban areas
To extract additional detail on the discrepancies in extreme precipitation between the urban and nonurban areas, precipitation intensities, rather than quantities, are investigated at short time intervals. The precipitation extremes in the Netherlands in August over short time intervals ranging from 5 min to 24 h are investigated using 17 years (1998–2014) of precipitation radar data. The 5-min radar data are extracted for 231 locations (i.e., the locations of the rain gauges) in the Netherlands. Furthermore, the 5-min precipitation values are aggregated for 15, 30, 60, 120, 360, 720, 980, and 1440 min at the location of each station. The intensity is obtained by dividing the precipitation amount by the duration of the period.
Against the current IDF curves, the nonstationary results assume that extreme precipitation is expected to alter regarding climate change, which may affect the reliability of infrastructure systems (Agilan and Umamahesh 2017; Cheng et al. 2014). Precipitation in the Netherlands could be influenced by the external forces from large natural variability and seasonal variations (Attema and Lenderink 2014; Rahimpour Golroudbary et al. 2016x). Therefore, the monthly IDFs regarding nonstationary climate may represent a better distribution than the annual IDFs ignoring the influences of large-scale variabilities. In this study, the nonstationary precipitation IDF curves for August are developed by using the identified covariates. Similar to the nonstationary models applied to the daily rain gauge data, Td and Ta are used as covariates of the precipitation intensities and applied to the extremes of the precipitation intensities. The NAO index is excluded from the covariates for estimating extreme precipitation intensity in August because of its negligible impact in the summer months (Haylock and Goodess 2004). Figure 7 shows the intensities at different durations and repetition times (i.e., 2-, 5-, and 10-yr return levels) averaged over the urban and nonurban stations separately. This figure shows that on average the return levels for precipitation intensities over the urban areas are larger than those over the nonurban areas over all of the classified stations (particularly for the urban type classified as W9). Although there is some variation in the maximum daily precipitation in the urban and nonurban areas, the urban areas show the highest values; in particular, the differences are clearly larger for longer return periods over all of the classified urban stations. The power (polynomial) regression lines exhibit similar behavior in the urban and nonurban precipitation-intensity return levels, whereas they are larger in the urban areas than in the nonurban areas. The effects of urban areas on extreme precipitation are clearer for shorter durations, where the urban and nonurban areas display larger differences between the precipitation return levels.
Precipitation-intensity return levels for 2-, 5-, and 10-yr return periods for nine stations classified as urban and nonurban for August within the Netherlands. The estimates are obtained using the nonstationary assumption at each station and averaged over the urban and nonurban stations. The regression lines for the urban (red) and nonurban (blue) stations are indicated by power-law trend lines. (a)–(i) The stations classified as W1–W9 because of the land-use types upwind of the stations.
Citation: Journal of Applied Meteorology and Climatology 58, 4; 10.1175/JAMC-D-18-0180.1
4. Discussion
The scaling relationship between precipitation and temperatures is used to simplify the nature of precipitation changes and understand the changes in intensity that may occur in a warming climate (Lenderink et al. 2011; Lenderink and Attema 2015). This work is carried out using QR and the binning method for each individual station. Unlike the binning method, QR estimates trends directly (i.e., it is unbiased with the sample size), and no discretization of the data is required (Wasko and Sharma 2014). Results obtained using the daily precipitation and temperatures (Tmean, Tmax, Td, and Ta) show similar trends in precipitation with the temperatures by both binning and QR methods. However, the regression slopes 
The influence of atmospheric circulation conditions is studied using the JCT classification scheme for all days between 1985 and 2014. The basic statistics of precipitation are investigated separately for each weather type on each day, and the results demonstrate the dependency of variations in the frequency and intensity of precipitation on the weather types. Whereas the mean of daily precipitation is higher for the W and SW weather types, the maximum daily precipitation is associated with the light-flow weather type. Although westerly winds are dominant in the Netherlands, it is unclear which weather type and circulation pattern favors extreme precipitation. Regardless of the lack of available long-term meteorological observations in urban areas in the Netherlands that can be used to assess urban microclimates and their effects on climatic variables (i.e., precipitation), this study considers rain gauge stations as either urban or nonurban stations for the different wind directions, depending on the types of areas located upwind of the stations (see section 2). This practice helps to produce a comparable discrepancy between the urban and nonurban areas in each classified urban type and tends to produce results that are generally applicable within the country.
The seasonal variations in precipitation are relatively uniform in summer and winter (Attema and Lenderink 2014; Buishand et al. 2013; Rahimpour Golroudbary 2018), while there is a coastal gradient in spring and autumn because of the proximity of the North Sea and the influence of the NAO index (Attema et al. 2014). Moreover, extreme convective precipitation is more likely to occur in the summer months, and extreme stratiform precipitation is expected to occur in other seasons (Daniels et al. 2016; Overeem et al. 2009). Therefore, monthly data are valuable for characterizing the dominant extreme precipitation. Trends in the monthly maximum precipitation that are significant at the 5% level have been found by previous studies, indicating that precipitation displays nonstationary variations (Buishand et al. 2013; Rahimpour Golroudbary et al. 2017, 2016b).
The GEV parameters for extreme precipitation are estimated for each station at every month. The nonstationary GEV model is developed based on the dewpoint and atmospheric air temperatures (i.e., Td and Ta) and a large-scale mode of climate variability (i.e., the NAO index) to demonstrate the distribution of monthly extreme precipitation and the return levels. The estimates obtained using nonstationary models fall within the confidence intervals of those obtained using stationary models at most of the stations in the Netherlands. The nonstationary increase in extreme precipitation identified in this study is in accordance with previous studies that have identified a statistically significant increasing trend in extreme precipitation in the Netherlands (Buishand et al. 2013; Overeem et al. 2008; Rahimpour Golroudbary et al. 2017).
The nonstationary models tend to produce more conservative estimates of the return levels of extreme precipitation. The results show that the downwind impacts of urban areas on the return levels of extreme precipitation over the country are relatively small in late spring (i.e., between April and June) and larger at other times. The exception in late spring may be caused by the suppression of shower activity (over the almost 50-km distance to the coast where most of the urban areas in the Netherlands are located) due to low sea surface temperatures. Daniels et al. (2015a) reported that the precipitation over the coastal areas in the Netherlands in spring is almost 25% less than that over inland areas because of triggering mechanisms (air traveling over the land and planetary boundary layer growth affect cloud formation).
However, urbanization alters the surface roughness and enhances the turbulence over urban areas (Han et al. 2014). The deeper boundary layers and temperature increases that occur in urban areas change the atmospheric water balance and enhance the water-holding capacity of air (Chen and Hossain 2016). The largest discrepancy between the urban and nonurban return levels is found under light-flow conditions (i.e., the urban type classified as W9). Extreme precipitation events are further found to be most strongly affected by urban land use in the summer months, especially August, and under the urban type classified as W9, among others. It is also found that the UHI is higher in August than in other months in the Netherlands (Rahimpour Golroudbary et al. 2018; Wolters and Brandsma 2012). The higher extreme precipitation in August is in accordance with the findings of previous Dutch studies on precipitation frequency during days where convection plays a relatively important role, and maxima occur during the evening and near sunset (Overeem 2009).
Intense precipitation may be caused by increases in the strength of convection due to intensive UHI (Chen et al. 2015; Rahimpour Golroudbary et al. 2018; Yang et al. 2017). The temperature discrepancy between urban and nonurban areas enhances instability and convective activity over urban and areas downwind from urbanized areas (Lin et al. 2011). Increased moisture and upward convergent movement are triggered by UHI circulation patterns (Yang et al. 2017). Thus, the higher temperatures in urban areas that are caused by the UHI circulation and sufficient water vapor could cause more precipitation in urban areas. In this respect, August is examined using high-spatial-resolution radar data to highlight the maximum precipitation return levels for different time durations for the urban and nonurban areas. The precipitation-intensity return levels indicate similar occurrences for the urban and nonurban stations, with more intensive events for the urban stations.
The better fits obtained using nonstationary models at most of the stations reveal that the IDF curves derived using the stationarity assumption underestimate extreme precipitation. If an IDF curve based on stationary estimates is used for designing urban infrastructure, neglecting other factors and the impacts of urbanization, the probability of infrastructure failure is high because of the more extreme precipitation events that are identified by the nonstationary models. In this respect, to obtain accurate IDF curves, the estimation methods should be updated by considering the influence of additional climate variability on extreme precipitation events.
The IDF curves, considering nonstationary conditions, at each station are necessary for designing infrastructure and projecting future precipitation return levels. It is important to note that such estimates are difficult to produce, and subject to uncertainties, because of the limited numbers of long time series of precipitation observations in urban areas. The differences between the urban and nonurban IDF curves require more consideration of nonstationary models in projecting future extreme precipitation, which requires careful choices of covariates. Understanding the physical causes that underlie extreme precipitation (i.e., circulation and temperatures changes) and the impacts of urbanization on climate may assist in the development of nonstationary models that can be used to produce improved assessments of the risks related to climate change.
However, the selection of covariates is important in finding the precipitation return levels. The results show that ignoring the effects of urbanization can lead to uncertain estimates of the intensity, duration, and frequency of extreme precipitation events, especially for short-duration precipitation. Although this study does not evaluate the uncertainties of the covariates, it shows that extreme precipitation associated with temperature differences between the urban and nonurban areas tends to give less uncertain estimates of return levels in the future.
For obtaining more reliable results on precipitation discrepancy between urban and nonurban areas, efforts are needed to examine the impact of bias corrections on observed precipitation variations. The ignored undetected errors in this study (i.e., wind speed–induced errors and seasonal variations) could impact the obtained precipitation discrepancy between urban and nonurban areas. The catch efficiency of precipitation, for example, might be larger in urban areas than that in nonurban areas, where urban stations surrounded by obstacles are exposed to less wind than nonurban stations in open areas. Therefore, the results could be influenced by bias-corrected precipitation data regarding temperature, wind speed, drop size, and snow percentage (Ding et al. 2007; Sun et al. 2013). Further, it is acknowledged that the investigated rain gauge and gridded radar datasets may not truly reveal the full microclimate over urban areas (i.e., other factors influence urban meteorology). A larger number of meteorological stations located in Dutch cities would be needed to fully characterize these microclimates, and these additional stations are currently unavailable. Note that the estimated precipitation return levels and IDF curves require longer-term observations in each region, the trends in the covariates such as the NAO index may not persist in the coming years, and use of climate-model simulations might enable extrapolation into the future. Therefore, care should be taken in extrapolating features seen in historical data into the future, especially for longer return periods, during which different physical causes (i.e., natural or anthropogenic forces) may influence the precipitation.
When scaling precipitation on temperatures for local scales, the influences of different mechanisms such as the regional and seasonal precipitation variations should be considered (Schroeer and Kirchengast 2017). Precipitation dependency on local temperature can be found in regions such as the Netherlands with enough moisture availability (Lenderink and van Meijgaard 2008; Westra et al. 2014). It is important to note that local temperature and global mean temperature usually scales linearly. However, connecting scaling relationships for local temperature and precipitation could be a controversial issue (IPCC 2013) where different factors are involved [e.g., thermodynamic effects (Barbero et al. 2017) and dynamic factors (Drobinski et al. 2018)]. Furthermore, changes in the temporal resolution of extreme precipitation and the covariates may cause changes in the scaling rate and the estimated return levels. Subdaily and hourly long-term data could provide more valuable information for obtaining robust assessments of the sensitivity of the scaling relationship between extreme precipitation and desirable predictor variables, such as the dewpoint temperature. For instance, Barbero et al. (2017) reported that the response of precipitation to temperature at an hourly resolution is better than that at a daily resolution. Furthermore, other factors, such as the types and sizes of cloud condensation nuclei (Drobinski et al. 2016) and the geographical characteristics of stations (Mishra et al. 2012; Wasko et al. 2016) can also affect extreme precipitation.
5. Conclusions
Knowledge of the impacts of climate warming and urbanization on the observed trends in extreme precipitation can lead to improved estimates for the return levels of extreme precipitation. This study considers the factors that likely influence extreme precipitation and extends existing statistical approaches by scaling extreme precipitation and examining nonstationary models that consider covariates (i.e., the dewpoint and air temperatures). The investigation of the appropriate covariates is done through applying QR and the binning method to precipitation and temperature datasets covering the Netherlands. Since the scaling of precipitation with increasing temperature is positive, the results suggest that the dewpoint and atmospheric temperatures are appropriate covariates for extreme precipitation. A linear combination of the dewpoint and the atmospheric temperature at the 850-hPa level, as well as the NAO index, which represents a large-scale influence mode, are applied to estimate the monthly precipitation return levels for different return periods. The study shows that presuming a nonstationary climate could lead to improved estimates of precipitation return levels where the stationary models underestimate the precipitation return levels.
The study makes use of the JCT with nine types to classify weather and circulation types. The dependence of precipitation on circulation conditions leads to the classification of stations as urban and nonurban areas based on their upwind land-use types for each wind direction to investigate the response of extreme precipitation to alternative land-cover types. The maximum daily precipitation for each month is compared between the stations in the regions downwind of urban areas (i.e., urban stations) and the other stations (i.e., nonurban stations). The results reveal that the frequency and intensity of extreme precipitation are higher in urban areas than in nonurban areas. August has the highest return level and frequency for maximum daily precipitation throughout the year. The urban type classified as W9 (light-flow conditions) demonstrates the magnitude of the differences between the urban and nonurban precipitation return levels. This study concludes that, apart from large-scale climate changes, increases in extreme precipitation can be induced by urbanization. Because of land use and urban climate change, the use of nonstationary models is advised to produce improved estimates of precipitation return levels and to project the frequency and intensity of precipitation in the future.
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