Figure 1. Mean annual rainfall in the Netherlands for the period 1971-2000.

Rainfall frequency analysis in the Netherlands has often been based on rainfall measurements at the KNMI observatory in De Bilt, in the middle of the country. The latest update was presented in 2004 (1,2). For this update hourly data for the period 1906-2003 were used. Apart from the hourly record of De Bilt, ten daily rainfall series from different locations were analysed. It was concluded that for the time being relative regional differences in mean annual rainfall could be used to account for regional differences in the quantiles of the distributions of extreme rainfall for durations of 24 h or longer. Further research using more rainfall data was recommended.

Frequent flooding in coastal areas has led to discussions whether extreme rainfall might occur more often along the coast than is assumed in present-day hydrologic design practices. For extreme daily rainfall within the Delfland Water Authority area, situated to the west of Rotterdam, it was found that the adjustment of the quantiles of the extremes for De Bilt needs to be larger than what the ratio of the mean annual rainfall amounts of both places suggests (3). In an other study seven hourly rainfall records were compared by calculating the extreme water levels for six different water systems (4). The 5-year events obtained from the Rotterdam record turned out to be considerably higher than those from the De Bilt record. Relatively high water levels were also found for Valkenburg, near the west coast to the north of The Hague, but these were less high than for Rotterdam.

A detailed study on regional differences in extreme rainfall climatology in the Netherlands has been completed recently (5). For this study the daily rainfall records from 141 rainfall stations for the 55-year period 1951-2005 were analysed. The stations were evenly distributed over the country. The selected records did not reveal serious artificial breaks regarding daily rainfall events of 10 mm or more. The analysis of extreme values and the application of the results are discussed below.

The analysis of extreme values
For each of the 55-year records the annual maximum rainfall amounts were abstracted for durations D of 1, 2, 4, 8 and 9 days. These durations are the same as those considered in the latest rainfall frequency analysis for De Bilt (1,2). As in that previous work, the Generalized Extreme Value (GEV) distribution was used to describe the distribution of the annual maximum amounts for each duration. The quantile x(T) that is exceeded on average once in T years (the ‘T-year event’) for a given duration D can then be represented as:





For k=0, the GEV distribution reduces to the Gumbel distribution, for which





The GEV distribution has three parameters: a location parameter μ, a dispersion coefficient γ, and a shape parameter k. Note that x(T) = μ if T = 1/(1–1/e) =1.58 years, i.e., the location parameter corresponds to the value that is on average exceeded in 100/1.58 = 63% of the years. The dispersion coefficient γ is a measure of the year-to-year variability of the rainfall extremes (comparable to the coefficient of variation). The shape parameter k is important if one is interested in very rare events (T >= 100 years). For k<0 the GEV distribution has a heavier upper tail than the Gumbel distribution, implying that very rare events occur more frequently. The converse holds if k>0.

The three GEV parameters determine the magnitude of regional differences in extreme rainfall climatology. Regional variation in the shape parameter is discussed first, followed by the regional differences in the dispersion coefficient and the location parameter.

The shape parameter

Koutsoyiannis (6) analysed the 1-day annual maxima in long rainfall records from the USA, UK and Mediterranean and came to the remarkable conclusion that the shape parameter is the same in these geographical regions. Research in Belgium and the Netherlands has also not revealed any systematic differences between the values of the shape parameter for the two countries (7,8). Based on this research, the following relationship between k and the duration D (expressed in days) has been derived in the latest rainfall frequency analysis for De Bilt1):

k = - 0.090 + 0.0170 D

Note that k is negative for D >= 5 days (heavy tailed distribution) and positive for D <= 6 days. This relationship was needed because it is not possible to obtain a reliable estimate of k from a single rainfall record. In line with that work, the same values of k were employed in the research described here.
Figure 2. Dispersion coefficient (left) and location parameter (right) of 4-day annual maximum rainfall versus mean annual rainfall. The horizontal line in the left panel depicts the average dispersion coefficient. The straight line in the right panel represents a proportional relationship between the location parameter and mean annual rainfall.
Figure 2. Dispersion coefficient (left) and location parameter (right) of 4-day annual maximum rainfall versus mean annual rainfall. The horizontal line in the left panel depicts the average dispersion coefficient. The straight line in the right panel represents a proportional relationship between the location parameter and mean annual rainfall.

The dispersion coefficient
In Figure 2 (left panel) the estimated dispersion coefficients of the 4-day rainfall extremes for the 141 selected rainfall stations are plotted versus the mean annual rainfall. There seems to be no relationship between the two quantities. This was confirmed by a generalized least-squares regression. Generalized rather than ordinary least squares is necessary here because of the correlation between the estimated dispersion coefficients at neighbouring stations resulting from the spatial dependence of rainfall. This correlation decreases with increasing distance between stations (Figure 3). It further turned out that the difference between the dispersion coefficients for coastal and inland stations is statistically not significant. Similar results were obtained for the 1-day and 9-day rainfall extremes, so that we may assume that the dispersion coefficient is constant across the Netherlands for a given duration.
Figure 3. Correlation between the estimated dispersion coefficients as a function of the distance between stations for the 4-day rainfall extremes. The estimates for the individual station pairs are printed in yellow. These estimates are based on a bootstrap technique. The red line represents a fitted curve that was used in the generalized least squares regressions.
Figure 3. Correlation between the estimated dispersion coefficients as a function of the distance between stations for the 4-day rainfall extremes. The estimates for the individual station pairs are printed in yellow. These estimates are based on a bootstrap technique. The red line represents a fitted curve that was used in the generalized least squares regressions.

From the assumption of a constant k and γ, it follows that x(T)/μ is also constant over the Netherlands for a given duration, or in other words the distribution of the extremes is everywhere the same after scaling with the location parameter. This corresponds with the index-flood assumption in hydrology. The ratio of the T-year events at two locations A and B is then equal to the ratio of their location parameters:






for any T. This alone does not justify a scaling based on mean annual rainfall yet. It is also necessary that the location parameter is proportional to mean annual rainfall.

The location parameter
The right panel of Figure 2 shows that for the 4-day rainfall extremes the location parameter μ increases with mean annual rainfall. This relationship is statistically significant. However, it also turned out that a proportional relationship between the location parameter and mean annual rainfall performs poorly. From Figure 2 it can be seen that the estimated location parameter deviates up to 6 mm (more than 10%) from the value obtained from such a relationship. Therefore, the linkage with mean annual rainfall was abandoned. Instead, another simple rainfall attribute was chosen that summarises the values of the location parameter for the five considered durations:






with μD the value of the location parameter for duration D, μD the average of the μD’s for the 141 selected rainfall stations, and wD a weight (wD = 1/4 for D = 1, 2 and 4 days and wD = 1/8 for D = 8 and 9 days). This relative location parameter gives a better picture of the regional differences in the location parameter than mean annual rainfall (deviations from the estimated location parameter for the individual durations are reduced by a factor 2 to 3).

Adjusting for regional differences in extreme rainfall climatology
The parameter μrel varies from 0.90 to 1.18 on the 141 selected rainfall stations. The country average of μrel equals 1, which also happens to be the value for De Bilt. The rainfall frequency distributions for this station can therefore be regarded as average rainfall frequency distributions for the Netherlands. Consultation with representatives of regional water authorities has led to the recommendation to adjust the quantiles of extreme rainfall in areas where μrel deviates more than 5% from the value for De Bilt. These areas are indicated in Figure 4. The multiplying factors in this figure are equal to the average values of ?rel for the respective areas. From the figure it is clear that the extreme rainfall climatology of De Bilt applies to the larger part of the country. However, adjustments of +8% and +14% are advised for a region along the west coast. The higher adjustment in this region applies to the Rotterdam area. This adjustment is larger than an adjustment based on mean annual rainfall. A 14% adjustment is also recommended for the outermost south-east of the Netherlands. Areas with a negative adjustment are mainly found in the eastern part of the country.

The multiplying factors apply to extreme rainfall for durations of 1 to 9 days. Relatively large values of the location parameter are also found in a region along the west coast for the 24-h rainfall extremes in the radar data set, which is discussed in the highlight by Overeem et al. in this Triennial Report, but this region does not show up for the 60-min rainfall extremes. Distinct areas with relatively low values of the location parameters are also not found for the 60-min extremes. The use of the multiplying factors from Figure 4 is therefore discouraged for durations shorter than 1 day.
Figure 4. Multiplying factors for converting the quantiles of extreme rainfall for De Bilt to other locations in the Netherlands.
Figure 4. Multiplying factors for converting the quantiles of extreme rainfall for De Bilt to other locations in the Netherlands.

Conclusion
Regional differences in the extreme rainfall climatology in the Netherlands were explored using daily rainfall data from 141 rainfall stations. A number of areas were identified where the distributions of extreme rainfall for durations of 1 to 9 days significantly deviated from that in De Bilt. It appeared that a simple scaling of the quantiles of these distributions with the ratio of mean annual rainfall is insufficient to describe the regional differences accurately. Instead, another rainfall attribute (relative location parameter) is suggested to account for regional differences in the quantiles of the distributions of extreme rainfall.

Acknowledgements
The research was part of the project “From Rainfall to Damage”, which was coordinated by HKV Consultants, and partially funded by the Dutch knowledge impulse programme “Living with Water”, the Foundation of Applied Water Research (STOWA), the Province of South-Holland, and the Verbond voor Verzekeraars.

References

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