Abstract
Rainfall data for the Netherlands have been used in this study to investigate aspects of heterogeneity of rainfall, in particular local differences in rainfall levels, time trends in rainfall, and local differences in rainfall trend. The possible effect of urbanization and industrialization on the distribution of rainfall has also been studied. Consideration has been given to whether local differences in rainfall justify a partition of the Netherlands into regions. Finally, the degree of areal reduction which is possible in hydrological design because of variation of rainfall in time and space has been investigated.A statistical analysis of these aspects is useful because they frequently appear in the hydrological literature. The statistical analysis presented in this thesis uses hydrological concepts, such as the statistical areal reduction factor, and attention is focused on moderately low return period events. Only rainfall levels and trends in rainfall have been investigated and not more complicated aspects, such as, trends in the variance of rainfall. Further, rainfall variations in time and space have been analysed separately.Estimates of the levels of the rainfall characteristics used in the investigation of homogeneity in time and space are given in Section 2.2. These are annual frequencies of exceedance during the summer or the winter period of a certain threshold value and the total annual rainfall (Tables 2.1 and 2.2). The expected daily rainfall has also been estimated for return periods in excess of half a year (Table 2.4, Figure 2.2). Time trends in rainfall averaged over the Netherlands have been estimated. For the period 19511979, the time trend is negative for the summer period; and for the period 19061979, the time trend is positive for the winter period (Table 2.5). Time trends in rainfall series were found to be related to the occurrence of circulation types (Figure 2.4).In Section 2.4 local differences in these rainfall characteristics have been investigated using the kriging method that gives the
best linear unbiased predictor. As may be expected, there are local differences, both in rainfall level (Figure 2.7), and in time trends in the rainfall series which were reduced by the annual mean (Figure 2.9). Many of the rainfall series investigated exhibit inhomogeneities (Table 2.7). Two possible causes of these inhomogeneities, changes in the frequency of occurrence of circulation types and anthropogenic activities, such as urbanization and industrialization, are discussed in Section 2.6.A possible partition of the Netherlands into regions is investigated by using rainfall data for the period 19511979. Earlier studies on the geographical distribution of certain rainfall characteristics in the Netherlands are presented in Section 2.5.1. The model to test the statistical significance of the partitions used in this study is presented in Section 2.5.2.One of the proposed partitions, an a posteriori partition based on mean annual rainfall (Figure 2.11D), is in agreement with the resulting spatial patterns of the levels of the rainfall characteristics considered (Table 2.10). Also, the level of hourly rainfall was found to be related to mean annual rainfall (Figure 2.18A), but, with a simple urban runoff model with a timestep of one hour, no differences were found between the number and quantity of overflow for 12 rainfall stations, classified according to this partition (Section 2.5.3).These partitions into regions are not satisfactory for rainfall trends, except for an a posteriori partition based on time trends for the period 19511979 (Figure 2.12). But both the geographical distribution of trends and the degree of trend in some longterm rainfall records are not in agreement with this partition. Apparently, the changes in rainfall pattern are recent. Because the partition is based on trends in reduced rainfall series (reduced by the annual mean), the changes are also local. Thus on the basis of data used in this study, it was not possible to devise a satisfactory partition of the Netherlands for rainfall trends. With regard to rainfall level it is suffice to assume that the design rainfall at a given location is proportionate to the mean summer or winter rainfall; therefore, a partition of the Netherlands into regions is not necessary. This has already been suggested in Buishand and Velds (1980).The influence of urbanization and industrialization on precipitation (urban effects) has been investigated by using the method of Lowry (1977), which allows for changes in frequency of occurrence of circulation types. In Section 2.6, this method is discussed and the findings of other studies on the occurrence, causes, and magnitude of urban effects are presented. In Section 2.6.1, the occurrence of urban effects is discussed, for instance, on the basis of changes in mean daily rainfall for 32 rainfall stations between the industrialized and urbanized period (19561979) and the nonindustrialized period (19321955), with a stratification of days according to season and circulation type (according to Hess, 1977), see Figure 2.22. Although the results were sometimes inconclusive and not always in. accordance with the hypothesis of an urban effect, there are indications of urban effects for the zonal circulation type and for three of the meridional circulation types (Tables 2.16 and 2.17; Figure 2.22). Moderate rainfalls were also found to be affected (Table 2.17, where a threshold value for daily rainfall of 15 mm has been considered), and urban effects in the summer period increase with rainfall depth.In Chapter 3 consideration is given to the degree of areal reduction which is possible in hydrological design because. of variations of rainfall in time and space. Use has been made of the IRF0 kriging theory, and semivariograms were estimated by the multirealization approach. The applicability of the IRF0 theory to predict the mean areal rainfall is discussed in section 3.2.1. Contrary to what had been expected, in a substantial number of cases the estimated order of the intrinsic random function differs from zero (Tabel 3.1). Further research is needed on the structure identification, both on the statistical aspects (estimation of the order k of the intrinsic random function and of the coefficients of the generalized covariance model) and on the physical aspects (semivariogram or generalized covariance model to be expected under certain assumptions regarding rainfall). The variation in semivariogram estimates for individual rainfall events was found to be large (Figure 3.3). In Section 3.2.2, the kriging predictor of areal rainfall is compared with the more commonly used arithmetic mean and Thiessen predictor. All three predictors yield similar results (Table 3.5), but the kriging predictor is more efficient (Table 3.4).Methods to estimate the statistical areal reduction factor (ARF) are presented in Section 3.3.1. With the methods proposed in USWB (19571960), NERC (1975), Bell (1976), and RodríguezIturbe and Mejía (1974) and Buishand (1977c), the areal reduction factor for daily rainfall (ARF _{24} ) has been estimated for three areas each of about 1000 km ^{2}in the Netherlands, for the summer period, the winter period, and the complete year. In Section 3.3.3, the variance of ARF _{24} is estimated. All four estimators of ARF _{24} were found to produce similar results (Tabel 3.12), and the three areas considered do not clearly differ with respect to ARF _{24} . These estimates of ARF _{24} are somewhat lower than those of USWB (19571960) for the United States and those of NERC (1975) for the United Kingdom (Figure 3.22), and they are in reasonable agreement with earlier estimates of ARF _{24} for the Netherlands (Table 3.14). For small areas, ARF _{24} is underestimated by the method which uses the marginal distribution of point rainfall and the fitted correlationdistance function. This is also evidenced by the higher ARF _{24} values in Kraijenhoff (1963). ARF _{24} depends heavily on season and return period (Table 3.7). Averaged over the three areas, the maximum areal rainfall occurs in the winter period in 33% of the years considered.In Section 3.4 ARF for hourly rainfall (ARF _{1} ) is estimated. As a function of areal size and return period, ARF _{1} has been estimated for the summer and the winter period (Figure 3.28) and for the complete year (Figure 3.21). These ARF _{1} estimates are somewhat lower than those of USWB (19571960) and NERC (1975) (Table 3.18), probably because few hourly rainfall data were available for this study. Especially the correlationdistance function for hourly rainfalls could not be estimated very satisfactorily.The stormcentred areal reduction factor (SRF) is discussed in Section 3.5. Models for SRF based on a literature survey of minimumrainfall curves are presented in Table 3.19. For equal areal size, SRF values from network data are generally lower than ARF values (Figure 3.29). The smaller the areal size and the shorter the period for which rainfall totals are considered, the closer SRF and ARF values.In this study, rainfall variations in time and space have been analysed separately. Because of this simplification of the problem, the results presented in Chapter 3 may be of less relevance to practical design issues related to areal rainfall. Areal reduction is partly caused by spatial differences in rainfall patterns in time. This aspect of areal reduction is not taken into account, when time aggregates of rainfall over a measurement interval are considered, and rainfall depths over consecutive intervals are assumed to be independent. For this reason, the degree of areal reduction applicable to regional transport systems of sewerage water cannot be determined by using the statistical areal reduction factor.When rainfall variations in time and space are analysed as being interdependent, the need for knowledge and understanding of meteorology increases because the rainfall events described have first to be classified. Further, instead of the univariate statistical methods as used almost exclusively in this study, multivariate methods are required. However, at present, data from a dense network of rainfall recorders, necessary for such an investigation, are not available for the Netherlands.Further research on the causes of homogeneities in rainfall series is necessary. Although this study of homogeneity has been restricted to rainfall records of good and even quality, many rainfall series are statistically inhomogeneous, and local differences in trend often seem inexplicable. To explain this, meteorological knowledge and knowledge of the station history of rainfall series used is essential.
best linear unbiased predictor. As may be expected, there are local differences, both in rainfall level (Figure 2.7), and in time trends in the rainfall series which were reduced by the annual mean (Figure 2.9). Many of the rainfall series investigated exhibit inhomogeneities (Table 2.7). Two possible causes of these inhomogeneities, changes in the frequency of occurrence of circulation types and anthropogenic activities, such as urbanization and industrialization, are discussed in Section 2.6.A possible partition of the Netherlands into regions is investigated by using rainfall data for the period 19511979. Earlier studies on the geographical distribution of certain rainfall characteristics in the Netherlands are presented in Section 2.5.1. The model to test the statistical significance of the partitions used in this study is presented in Section 2.5.2.One of the proposed partitions, an a posteriori partition based on mean annual rainfall (Figure 2.11D), is in agreement with the resulting spatial patterns of the levels of the rainfall characteristics considered (Table 2.10). Also, the level of hourly rainfall was found to be related to mean annual rainfall (Figure 2.18A), but, with a simple urban runoff model with a timestep of one hour, no differences were found between the number and quantity of overflow for 12 rainfall stations, classified according to this partition (Section 2.5.3).These partitions into regions are not satisfactory for rainfall trends, except for an a posteriori partition based on time trends for the period 19511979 (Figure 2.12). But both the geographical distribution of trends and the degree of trend in some longterm rainfall records are not in agreement with this partition. Apparently, the changes in rainfall pattern are recent. Because the partition is based on trends in reduced rainfall series (reduced by the annual mean), the changes are also local. Thus on the basis of data used in this study, it was not possible to devise a satisfactory partition of the Netherlands for rainfall trends. With regard to rainfall level it is suffice to assume that the design rainfall at a given location is proportionate to the mean summer or winter rainfall; therefore, a partition of the Netherlands into regions is not necessary. This has already been suggested in Buishand and Velds (1980).The influence of urbanization and industrialization on precipitation (urban effects) has been investigated by using the method of Lowry (1977), which allows for changes in frequency of occurrence of circulation types. In Section 2.6, this method is discussed and the findings of other studies on the occurrence, causes, and magnitude of urban effects are presented. In Section 2.6.1, the occurrence of urban effects is discussed, for instance, on the basis of changes in mean daily rainfall for 32 rainfall stations between the industrialized and urbanized period (19561979) and the nonindustrialized period (19321955), with a stratification of days according to season and circulation type (according to Hess, 1977), see Figure 2.22. Although the results were sometimes inconclusive and not always in. accordance with the hypothesis of an urban effect, there are indications of urban effects for the zonal circulation type and for three of the meridional circulation types (Tables 2.16 and 2.17; Figure 2.22). Moderate rainfalls were also found to be affected (Table 2.17, where a threshold value for daily rainfall of 15 mm has been considered), and urban effects in the summer period increase with rainfall depth.In Chapter 3 consideration is given to the degree of areal reduction which is possible in hydrological design because. of variations of rainfall in time and space. Use has been made of the IRF0 kriging theory, and semivariograms were estimated by the multirealization approach. The applicability of the IRF0 theory to predict the mean areal rainfall is discussed in section 3.2.1. Contrary to what had been expected, in a substantial number of cases the estimated order of the intrinsic random function differs from zero (Tabel 3.1). Further research is needed on the structure identification, both on the statistical aspects (estimation of the order k of the intrinsic random function and of the coefficients of the generalized covariance model) and on the physical aspects (semivariogram or generalized covariance model to be expected under certain assumptions regarding rainfall). The variation in semivariogram estimates for individual rainfall events was found to be large (Figure 3.3). In Section 3.2.2, the kriging predictor of areal rainfall is compared with the more commonly used arithmetic mean and Thiessen predictor. All three predictors yield similar results (Table 3.5), but the kriging predictor is more efficient (Table 3.4).Methods to estimate the statistical areal reduction factor (ARF) are presented in Section 3.3.1. With the methods proposed in USWB (19571960), NERC (1975), Bell (1976), and RodríguezIturbe and Mejía (1974) and Buishand (1977c), the areal reduction factor for daily rainfall (ARF _{24} ) has been estimated for three areas each of about 1000 km ^{2}in the Netherlands, for the summer period, the winter period, and the complete year. In Section 3.3.3, the variance of ARF _{24} is estimated. All four estimators of ARF _{24} were found to produce similar results (Tabel 3.12), and the three areas considered do not clearly differ with respect to ARF _{24} . These estimates of ARF _{24} are somewhat lower than those of USWB (19571960) for the United States and those of NERC (1975) for the United Kingdom (Figure 3.22), and they are in reasonable agreement with earlier estimates of ARF _{24} for the Netherlands (Table 3.14). For small areas, ARF _{24} is underestimated by the method which uses the marginal distribution of point rainfall and the fitted correlationdistance function. This is also evidenced by the higher ARF _{24} values in Kraijenhoff (1963). ARF _{24} depends heavily on season and return period (Table 3.7). Averaged over the three areas, the maximum areal rainfall occurs in the winter period in 33% of the years considered.In Section 3.4 ARF for hourly rainfall (ARF _{1} ) is estimated. As a function of areal size and return period, ARF _{1} has been estimated for the summer and the winter period (Figure 3.28) and for the complete year (Figure 3.21). These ARF _{1} estimates are somewhat lower than those of USWB (19571960) and NERC (1975) (Table 3.18), probably because few hourly rainfall data were available for this study. Especially the correlationdistance function for hourly rainfalls could not be estimated very satisfactorily.The stormcentred areal reduction factor (SRF) is discussed in Section 3.5. Models for SRF based on a literature survey of minimumrainfall curves are presented in Table 3.19. For equal areal size, SRF values from network data are generally lower than ARF values (Figure 3.29). The smaller the areal size and the shorter the period for which rainfall totals are considered, the closer SRF and ARF values.In this study, rainfall variations in time and space have been analysed separately. Because of this simplification of the problem, the results presented in Chapter 3 may be of less relevance to practical design issues related to areal rainfall. Areal reduction is partly caused by spatial differences in rainfall patterns in time. This aspect of areal reduction is not taken into account, when time aggregates of rainfall over a measurement interval are considered, and rainfall depths over consecutive intervals are assumed to be independent. For this reason, the degree of areal reduction applicable to regional transport systems of sewerage water cannot be determined by using the statistical areal reduction factor.When rainfall variations in time and space are analysed as being interdependent, the need for knowledge and understanding of meteorology increases because the rainfall events described have first to be classified. Further, instead of the univariate statistical methods as used almost exclusively in this study, multivariate methods are required. However, at present, data from a dense network of rainfall recorders, necessary for such an investigation, are not available for the Netherlands.Further research on the causes of homogeneities in rainfall series is necessary. Although this study of homogeneity has been restricted to rainfall records of good and even quality, many rainfall series are statistically inhomogeneous, and local differences in trend often seem inexplicable. To explain this, meteorological knowledge and knowledge of the station history of rainfall series used is essential.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution  
Supervisors/Advisors 

Award date  12 Dec 1984 
Place of Publication  Wageningen 
Publisher  
Publication status  Published  1984 
Keywords
 precipitation
 duration
 hydrology
 meteorological observations
 weather data