SPATIAL AND TEMPORAL VARIATION OF RAINFALL AND RUNOFF IN HONG KONG

Transcription

1 409 SPATIAL AND TEMPORAL VARIATION OF RAINFALL AND RUNOFF IN HONG KONG A.W.Jayawardena Department of Civil & Structural Engineering University of Hong Kong, Hong Kong M. R. Peart Department of Geography & Geology University of Hong Kong, Hong Kong ABSTRACT Hong Kong lies in the tropics and experiences hot humid summers which contrast markedly with the cool dry winters. The incised topography is developed upon predominantly volcanic and intrusive igneous rocks. Considerable spatial variation of the hydrological variables can be seen in Hong Kong despite its small size. Maps of mean annual rainfall reveal spatial variation due to topography as well as due bo seasonal effects. A range of statistical Indices are also presented to quantify and illustrate the spatial variation of rainfall and runoff. Temporal variations of rainfall and runoff are illustrated with a time series analysis of the two sets of monthly data. INTRODUCTION The territory of Hong Kong consists of the Hong Kong and Lantau islands, the Kowloon peninsula, the New Territories and several small islands. It is situated between the latitudes 22 10'N and 22 35'N and the longitudes 'E and 'E. It has a total land area of approximately 1060 km, and has no major rivers or lakes which can act as long term storage for water. Its topography is developed upon predominantly volcanic and intrusive igneous rocks. Lowland in Hong Kong is restricted, being less than 20% of the land area. The only area of extensive lowland in the territory is found in the western part of the New Territories. Hong Kong lies in the tropics but experiences seasonal climatic changes unusual for the tropics. The seasons are controlled by cooling and heating of the land masses while the day-to-day weather is influenced by both tropical and temperate latitude synoptic disturbances. The summer monsoon blows from South or South-west, bringing in warm humid air, while the winter monsoon blows from North or North-east causing cool dry air to prevail. On a day-to-day basis the weather maps contain tropical cyclones centered over the Pacific region during summer and anti-cyclones centered over Siberia or China in winter. The atmosphere in summer is conditionally unstable most of the time and much of the rain falls in the form of showers or thunderstorms due to local convection. Nearly a quarter of the rainfall in Hong Kong is associated with tropical cyclones. In winter, the lower layers of the atmosphere are generally stable bringing in fine weather. Despite the small size, Hong Kong's hydrological parameters have a high degree of variability both in space and in time. In this study, an attempt is made to identify and describe quantitatively the spatial and temporal variation of the two main hydrological parameters rainfall and runoff.

2 410 SPATIAL VARIATION Hong Kong has one of the densest network of rain gauges in the world - over 120 stations for a land area of approximately 1060 km. The first rainfall recordings were taken in 1884 at the Royal Observatory. The majority of the other rain gauges have been installed after the war. The area drained by streams in natural basins and catchwaters for which runoff data is available cover just over 10Ô km or about 10 percent of the land area. In comparison to rainfall data the spatial coverage of Hong Kong for runoff is rather restricted. Moreover, malfunctioning of equipment for some gauging stations has resulted in the loss of some data such that some runoff records are incomplete. There is also a temporal restriction upon the length of data available in that some gauging stations were established comparatively recently in the middle to late 1970's. Nevertheless, the available data does permit comment as to the spatial variability of runoff. Rainfall The spatial variation of Hong Kong rainfall is predominantly due to its complex topography. Of the total land area of Hong Kong, approximately 22% is below 50m, 24% between m, 29% between m with the highest peak at 947m, all measured above mean sea level. Generally, the high rainfalls occur at high altitudes. Fig.1, reproduced from Kwan and Lee (1984), and based on 30 year mean rainfalls for the period , illustrates the spatial variation of annual rainfall. It also indicates that the lowlands in the western and northern parts of the New Territories form a rain shadow in the lee of the highlands to their southeast (Fig.1). Spatial variation can also be seen as being due to seasonal effects. Considerable spatial variation can be seen in Fig.2 for the months July and January which are characteristic of the two predominant seasons, summer and winter. For example, in July, a pronounced rainfall maxima occurs to the north of Tolo Harbour which Is not developed in January. The influence of relief upon rainfall can be discerned for both months. It is possible to provide a simple measure of the spatial variation of rainfall by using the ratio of the highest to lowest recorded at any two gauges in the network. A value of unity for the ratio indicates no spatial variability. On Hong Kong and Lantau islands and the New Territories, some 22 gauges have complete records for the period giving a reasonable spatial coverage. The ratios of the highest mean monthly rainfall to the lowest rainfall for these 22 gauges for the 30 year period of for the months January to December are 1.98, 2.00, 1.59, 1.68, 1.69, 1.90, 1.71, 1.66, 1.65, 1.69, 1.95 and 1.97 respectively. These ratios indicate that the rainfall exhibits most variation during the winter period. With respect to these gauges, which exclude those on the very small offshore islands, the location of minimum rainfall differs seasonally. For the winter three months, the minimum rainfall occurs in the Hong Kong Island whereas in summer it is in the lowland of the

3 411 western New Territories. If the offshore island stations with complete records are included then the location of minimum rainfall would always be at the Waglan light house station on a small offshore island to the southeast of Hong Kong Island. In terms of maximum rainfall there is no clear geographic trend to the location. Another measure of the spatial variation of rainfall is given in Table 1 where the monthly means and standard deviations of 23 rain gauges for the water years 1979/80 and 1982/83 are compiled. The gauges are fairly evenly distributed across the territory with approximately one gauge representing a grid of 6 km x 6 km (Fig.3). Therefore any bias in using only 23 gauges towards a particular region will be minimised. The year 1982/83 is a wet year with a total rainfall of mm whereas the year 1979/80 is an average year with 2591 mm, both as measured by the Royal Observatory rain gauge. The variability is significant as shown by the coefficient of variation. Excluding the months December in 1982/83, and October-January in 1979/80, the coefficients of variation range from to in'the wet year and to in the dry year. The months December in 1982/83 and October-January in 1979/80 have been extremely dry and the variability during these months is even greater. Runoff Runoff data have been obtained for 7 drainage basins (Fig. 3 ) for the water year 1981/82. Table 2 presents the results of a number of hydrological indices which have been used to characterise runoff production in the study basins. With respect to yield per unit area Table 2 indicates a considerable variation in runoff between basins and hence spatially. The maximum yield of 3134x10 m recorded for Yuen Long Flood Channel 'B* station is much higher in comparison to the other basins. The explanation for this higher yield may lie in the discharge of sewage effluent into the channel. Further evidence of spatial variation in runoff production as represented by these basins can be seen if consideration is given to the relative importance of the wet season (April-September) in comparison to the dry season (October-March). This can be expressed as a simple ratio, which may be regarded as a seasonality index of runoff production, and the results are presented in Table 2. It can be seen that five out of the seven basins have ratios of between 2.4 and 2.7. Of the remaining two basins that of Shek Pi Tau has a runoff seasonality index of 4.7. This suggests that in this basin, runoff production is seasonally rather more extreme in comparison to the other basins. The fourth column of Table 2 gives the maximum daily runoff expressed as a percentage of total annual runoff. The catchments exhibit a range of values for the contribution made by maximum daily flow to the total annual runoff. For example, in the Shek Pi Tau basin the maximum daily flow accounts for just under 10 '/. of annual discharge. In contrast, in the Yuen Long Channel 'B' catchment the maximum daily runoff constitutes only 2.6% of the years flow. Also presented in Table 2 is the date on which maximum daily flow was recorded in each basin. It is seen that the day of maximum runoff for all basins is within the wet season. However,

4 412 the day on which maximum runoff is recorded varies between the basins. Considerable spatial variability is evident in this index of runoff production. The spatial variation in the timing of maximum runoff may reflect the spatial differences in precipitation input. This could be accounted for by the development of local convectional cells. Alternatively it may reflect spatial variation in catchment conditions governing the response to a precipitation input. TEMPORAL VARIATION All hydrological variables can be considered as functions of time. In the short term, the temporal variation is influenced by the day-to-day weather systems. In the medium term, the variations are influenced by seasonal climatic conditions. In the long term, the variations are often not clearly defined and it is difficult to attribute such variations to a single causative factor. In this study, emphasis Is placed upon the medium and long term temporal variations when the hydrological variable is considered as a time series of monthly data. In the short term, there is a marked diurnal variation with summer heavy rainfalls occurring in the mornings. Using data for the period recorded at the Royal Observatory it is reported (Peterson, 1980) that rainfall maxima occurred at 7 p.m. in April and 3 p.m. in November. December and January exhibit rainfall maxima around 4 a.m. The summer months experience double maxima with peaks at 5-6 a.m. and a later peak at 9 a.m. The diurnal variation of rainfall can be explained by a number of theories. However, as Peterson (1980) states, none of them can account for all the observed diurnal rainfall maxima. The rainfall records of Hong Kong have varying lengths. The longest is that at the Royal Observatory rain gauge station in which the records extend from 1884 to 1941, and again from 1948 onwards. Records are unavailable for the war time period 1941 to In Hong Kong there are over 14 stream flow gauging stations (Hong Kong Government Water Supply Department) with varying periods of records. For this study, monthly discharges at the Shek PI Tau lowland stream gauging station (Fig.3) which drains a catchment area of 2792 hectares was chosen. The procedure adopted for the analysis of the rainfall and runoff time series consists of determining the basic statistical parameters of the series, carrying out tests to determine the presence or otherwise of trends and periodicities, describing such trends and periodicities in quantitative terms so that they may be removed, examining the stochastic component of the series which Is obtained by subtracting any trends and periodicities from the original series, fitting appropriate stochastic models to the stochastic component and obtaining the residues (errors) which cannot be represented in any deterministic form. The residues are then represented by some probability distribution functions. The different tests and methods of analysis are well documented (e.g. Box and Jenkins, 1976) and the procedure followed in this study Is taken directly from the author's work on similar studies (Jayawardena, 1986; Jayawardena and Lai, in press). The period of record used for rainfall data is from 1946 to 1984 whereas that

5 413 for runoff is from 1965 to Basic Properties Table 3 summarises the basic statistical properties of the two series. A high degree of dispersion about the mean value can be seen from the standard deviations which exceed the mean. For the rainfall series this is due to the seasonal variation of rainfall in Hong Kong which is highly uneven. It is reported that approximately 84% of the average annual rainfall takes place in the wet season (Apr il-september), about 3% in the winter months (December-February), and about 18%, which is more than twice the monthly average, in the month of August alone (Jayawardena, 1987). For runoff, the dry weather flow which exists during the winter months is significantly low compared to the flood flows resulting from typhoons during the wet season. The distributions are also skewed and there are more low values than high values. The runoff series is more skewed than the rainfall series. Stationarity and trend A test for stationarity of the data series was carried out by dividing the series into a number of sub-series of approximately equal lengths and examining whether the means of the sub-series are significantly different from that of the -original series. Both series passed the stationarity test, but the runoff series was found to have a slight negative trend. It was removed by a linear approximation. Periodicity All meteorological variables exhibit some cyclic behaviour. These can be detected by the autocorrelation function of the series, and the period of the periodicity, which is annual in this case, can be seen from the spectral density function. The periodicity is then represented by a Fourier series which may be expanded up to a maximum of six harmonics (maximum number of harmonics = half the period of the periodicity) in the form P/2 m = (i +? {A,cos(2n:iT/p) + B sin(2ttix/p)} (1) where m T is the harmonically fitted mean for each period T; fx is the population mean; p is the period; Ai and B± are the Fourier coefficients obtained by least squares estimation. Very often it is not necessary to expand the series up to the limit because, a fewer number of harmonics is sufficient to explain the variance to a reasonable degree of accuracy. In the case of the rainfall series, it was found that the first harmonic explains about 90.7% of the variance and that the first, third, fourth and second (in order of significance) harmonics together explain over 99% of the variance. For runoff data the first harmonic explains about 91.0% of the variance

6 414 whereas the first, second, fifth and sixth (in order of significance) harmonics together explain over 99% of the variance. A summary of the parameters is given in Table 4. Stochastic component Stochastic component refers to the remainder of the series when the deterministic components such as trend and periodicity as represented by their respective mathematical forms are subtracted from the original series. It usually contains a linearly correlated part and an uncorrelated random part. The linearly correlated part is represented by an Auto Regressive Moving Average (ARMA) type of models whereas the uncorrelated residue series was represented by some probability density functions. An ARMA(p.q) model takes the form p q z, = Ça.z.. + i). -? e.ri.. (2) t T p,l t-l t 1 q, l t-i where z t is the stochastic component; a p> j are the auto regressive parameters; 6q,i are the moving average parameters; T) t are the residuals. After fitting all possible ARMA models ranging from ARMA(l.O) to ARMA(2,2),it was found that ARMA(0,2) and ARMA(l.O) were the most parsimonious for the rainfall and runoff series respectively as determined by the Akaike Information Criterion, AIC (Akaike,1974). The parameters of the chosen model are given in Table 4. For the uncorrelated residuals, three probability distributions, Normal, Gamma and Log-normal were fitted and the Gamma and Log-normal distributions were found to give the best fit for the residues of rainfall and runoff series respectively on the basis of the Chi squared (% ) value for the goodness of fit. REFERENCES Akaike, H. (1974) A new look at the statistical model identification, IEEE Transactions on automatic control, AS-19, vol 6, Box, G.P. and Jenkins, G.M. (1976) Time series analysis - Forecasting and control, Holden day, California. Hong Kong Government Water Supplies Department (Annual) Hong Kong Rainfall and runoff. Jayawardena,A.W. (1986) Time series analysis: A practical introduction and its application to environmental data analysis, Report submitted to UNESCO Jayawardena, A.M. (1987) Water supply and resources development in Hong Kong, Proc. Symposium on Rivers and Water Resources in East Asia, Tokyo, Japan Jayawardena, A.W. and Lai, F.Z. (in press) Time series analysis of water quality data in Pearl River, China, Journal of Environmental Engineering, ASCE (accepted) Kwan, W. K. & Lee, B.Y. (1984) 30-year mean rainfall in Hong Kong , Royal Observatory, Hong Kong, Technical Note No.70 Peterson, P. (1980) A note on the diurnal variation of meteorological elements, Royal Observatory, Hong Kong, Climatological Note No.6

7 / /80 Month X er C V X <r C V Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Table 1. Monthly means (x), standard deviations (c) and coefficients of variation (C ) for 23 selected rain gauges for the water years 1982/83 and 1979/80 ( x and <r are in mm ) Basin Yield/km 2 ( 1000m 3 ) ratio of wet max.to dry max. Maximum daily runoff as a '/. of annual flow date of maximum runoff Shek Pi tau Tai Lam Chung Tai Lam Chung Yuen Long flood channel 'B' Sie Lek Yuen Sham Wat Kam Tin 'A' *B* Sept. 4 July 27 July 27 July 7 July 29 Sept. 6 Sept. 29 Table 2. Spatial variation of some parameters of runoff production Data series Period Number of records Mean Standard deviation Skewness coefficient Kurtosis Rainfall Runoff Table 3. Statistical parameters of the data time series (Units of rainfall are in mm; Units of runoff are in 1000 cubic meters)

8 416 Data Rainfall Runoff Harmonic analysis Model parameters i A. B Vl 6 0, A B i A. B. l l a l.l a l,2 " Table 4. Parameters of harmonic and stochastic analysis (A. B. are Fourier coefficients; 6 0.,6-? are moving average coefficients; a. «,'a. 'are auto regressive coefficients; A! B are skewness and scale parameters of the Gamma distribution; (i and <r are the mean and standard deviation of the Log-normal distribution)

9 417 / ' <S> 1 ^ if7 1 *i,400 Jp L. / j / ^ / - \?\S\ Y ' 0 \ C >> *^^ -" ** \6 ffmmmm 3L^ / 5^ -^ ^2400-jK^~"NoS Ci km 1 1! 1 J n isohyets in mm Elevation in metres Fig.l Annual rainfall distribution (By courtsey of the Royal Observatory, Hong Kong) ^ e D Runoff gauging stations Raingauge Fig. 3. Distribution of gauging stations used in the study

10 418 ^. p<f ^ \P <\? SfwL & ~2S 9 fi km I i i I i %i a ; Isohyets in mm Elevation in mstres 750 Î50 0 Fig.2a. Mean monthly rainfall distribution in January (after Kwan & Lee, 1984) Fig.2b. Mean monthly rainfall distribution in July (after Kwan & Lee, 1984)