PRECIPITATION-BASIC PRINCIPLES OF NETWORK DESIGN

A. F. RAINBIRD (*)

SUMMARY

The wide range of areal and time variability of precipitation and of terrain over the world, the diversity of problems in which precipitation data are applied and variations from one region to another in the importance of each problem or in the accuracy of basic data required for its solution make it impracticable to derive a universally satis­factory procedure for the design of precipitation gauge networks.

Accuracy of data required and the relative importance of each significant problem or project involving use of precipitation data should be surveyed to determine themost significant areas (their locations and size) and time intervals for which precipitation should be measured in a particular region.

A basic network of long term base stations should be established immediately in all areas, even if this is sparse initially. Networks of secondary stations operated for a few years only should be used to improve the geographic sampling of precipitation depth. At least one representative catchment (500 sq.mi. or less) with a relatively dense gauge network should be established in each principal climatic and or physiographic region.

In general the optimum density of gauges and length of record can be determined only after adequate sampling of the areal and temporal variability of precipitation within a region.

1. INTRODUCTION

Systematic measurements of rainfall appear to have been made in some areas thousands of years ago. Around 300 B.C. rules such as the following were available for predicting the "even" distribution of rainfall through the rainy season in India:

"A forecast of such rainfall can be made by observing the position, motion and pregnancy of Jupiter, the rise and set motion of Venus and the natural or unnatural aspect of the sun." This rule implies that systematic records of rainfall had already been kept in India for some time (Kurtyka, 1953).

Rain gauges were in use in Korea as early as 1442, and a self-recording tipping-bucket gauge was invented by Sir Christopher Wren in 1662.

Despite these early beginnings, relatively few places have reliable systematic records of precipitation exceeding 100 years in length, and efforts to establish and maintain networks of gauges for the organised study of the depths and variability (spatial and temporal) of precipitation over areas larger than the immediate sur­roundings of an individual precipitation gauge appear to have a quite short history in many parts of the world.

Inaccessibility, sparseness of population and economic factors have retarded the establishment of precipitation measurement networks in many areas. These factors cannot be overcome entirely, but emphasis is being given in the programme of the U.N.'s International Hydrological Decade to the establishment of basic networks and the expansion of existing networks to provide fundamental data on hydrological systems varying in size from small watersheds to the world as a whole. (UNESCO 1964).

In these circumstances, many agencies will wish to know what minimum and optimum densities of precipitation gauge networks they should aim at establishing within the geographical areas for which they are responsible. Simple or universally valid answers cannot be given to these questions, as the density of precipitation

(*) Bureau of Meteorology, Melbourne, Australia.

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measurement stations required within a specific area and the periods for which these stations need be operated are governed by a number of factors including: the size of area and lengths of time interval over which precipitation must be measured, type of rain to be measured, the purposes which the data are intended to serve, and the accuracy with which areal or temporal distribution of precipitation must be known to adequately satisfy each such purpose.

Special purpose networks are frequently established for specific projects, such as watershed management research or the evaluation of weather modification experi­ments; but these networks often have only limited existences which are determined by the needs of the various projects for which they are established.

Of more general interest are the precipitation measurement networks which must provide basic data for the solution of a diversity of problems, some of which may not yet be apparent.

Practical considerations of site accessibility, geographical distribution of popu­lation and availability of finance influence the actual distribution and density of gauges in a general purpose network. However these factors are peculiar to each specific area or region, and this paper discusses only some of those principles which are relevant to the design of a precipitation measurement network in any area.

2. FACTORS INFLUENCING THE OCCURRENCE AND VARIABILITY OF PRECIPITATION

The precipitation process is complex, but notable advances have been made in the last two decades in knowledge of the physics of clouds and precipitation (Wexler 1954, Mason 1957, Gibbs 1958, Squires 1962).

The intensity of precipitation is a function of: the vertical velocity of the air; the vertical extent of up-motion; the amount of water vapour in the ascending air; and, particularly in the case of convective cloud systems, the humidity of the "environmental" air.

The main source of moisture for precipitation is water vapour evaporated from the oceans and from large lakes. In many areas the isohyetal pattern of mean annual precipitation shows a fairly regular decrease of precipitation depth with increase in distance from the nearest coastline; that is, from a source of atmospheric moisture supply. However, that proximity to a moisture source is not the only significant factor which determines the depth of precipitation experienced at a particular location is obvious from the increase in precipitation depth observed on the windward slopes of mountain barriers, even when these are situated at appreciable distances from a coastline.

The variation of precipitation in space and time is largely determined by spatial and temporal variations of the vertical motion of air needed to produce cooling of the air and condensation of its contained water vapour in amounts sufficient to produce significant depths of precipitation.

Vertical motion of air is produced by processes within the atmosphere and by interactions between the atmosphere and the underlying surface of the earth. Both types of process operate on small and large scales.

Those vertical air motions due principally to atmospheric processes occur in typical patterns which Gibbs (1964) has classified as convective, banded and general.

Convective vertical motion occurs in cells with a diameter of about one to five miles and a vertical extent from a few thousand to more than 50,000 ft. The cells generally have a life cycle of about one hour (Byers and Braham, 1949) and the amount of rainfall they yield is closely related to their vertical extent and the amount of water vapour in the air.

Isohyetal patterns of precipitation from convective cells are characterised by steep gradients o f precipitation depth over short horizontal distances. Gradients

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exceeding 0.5 inch per mile occur commonly and values in excess of 0.8 inch per mile have been observed with a network of 50 gauges in an area of 400 sq.mi. (Stout 1960). Rainfall gradients are less steep as the outer limits of the isohyetal "cell", which for intense thunderstorm rainfall often covers an elliptical area about three miles wide and nine miles long, are approached. Hence a greater range of rainfall occurs over any given size and shape of area near the "cel l" centre than along its edges.

Dense gauge networks are needed to measure with a high degree of accuracy either total water yield or the spatial variability of precipitation amount from con-vective systems.

However, spatial variability of precipitation depth tends to decrease with increasing mean areal storm precipitation amount (Huff & Neill 1957°), with the result that, for a given gauge density, the mean percentage error in areal depth estim­ates would be smaller for heavy than for light shower type precipitation.

Studies using dense gauging networks have shown that over relatively featureless terrain the spatial development and movement of convective cells is essentially random (Linsley and Kohler 1951, Brunt 1960, Osborn & Reynolds 1963). Integration of the rainfall due to all individual cells experienced over an area in a period of a month or longer would be expected to lead to a smoothing of isohyetal patterns and decrease of rainfall gradients with horizontal distance. Studies have confirmed that this smoothing of areal variability of rainfall from convective systems does occur when periods of a month or more are considered. (Linsley & Kohler 1951, Huff & Neill 1957 & 1957a).

When the ground surface has marked orographic relief, there is a tendency for convective cells to develop over hills and mountain peaks rather than over vallevs. However radar studies of convective cloud development over a mountainous area near Tucson, Arizona (Ackerman 1960) revealed that the location of the major con­vective activity varied considerably from day to day, indicating spatial randomness of the convective process over mountainous as well as flat terrain.

Rainfall in the tropics occurs mainly in the form of showers and the convective cell mechanism predominates in the warm season rainfall of many other regions.

Banded vertical motion, in which the up-motion usually occurs over a band from a few miles to about 50 miles in width and several hundreds of miles in length, is usually associated with a front or other zone of convergence or is the result of oro­graphic uplifting of an air stream. A banded system may have a life cycle varying from a few hours to more than five days in length.

Spatial variability of rainfall resulting from a banded system depends to a large extent on the stability of the lifted air. If the air is convectively unstable, convective cells may develop with much the same characteristics and associated rainfall patterns as in the purely convective case. When the atmosphere is convectively stable there is often little horizontal variation in storm precipitation depth within the band, although marked short period variations in precipitation intensity can occur over small distances. In a study for South Australia where frontal uplifting is a major contributory cause of rainfall, Cornish et al. (1961) found that the axis of maximal correlation between rainfall observing stations was parallel to the axis of the frontal systems, illustrating the tendency for relatively uniform rainfall depths to occur within banded systems.

General vertical motion is associated with large scale synoptic features such as depressions and upper cold lows. The classical extratropical cyclone model postulates the relatively gentle uplifting of air masses over frontal surfaces and a rather uniform areal distribution of precipitation. This concept has been widely accepted, but air­craft, satellite and radar observations are now providing a better knowledge of the distribution of cloud and precipitation within large scale storm systems.

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Elliott & Hoving (1964) in studies of U.S. Pacific Coast storms noted three com­ponents of the storm precipitation which they described as:

"storm mean convergence motion" precipitation which is the result of large scale air-mass lifting,

"orographic" precipitation due to lifting of the air stream by topographic features, "convection band" precipitation which is superimposed upon the others and is associated with convective overturning plus the convergence field of moving con­vection bands within the storm system.

These authors postulated that organized convection bands occur commonly within extratropical storms. The isohyetal patterns of large scale storm systems should then frequently display features of the spatial variability of precipitation depth which are associated with convective vertical motion systems. Isohyetal "cells", with horizontal gradients of rainfall depth similar to those experienced with convec­tive systems, are sometimes observed when large scale storm systems occur over dense networks of precipitation gauges. However isohyetal patterns for the complete duration of such storms frequently lack any significant cellular features, possibly because of spatial randomness of the cells in successive convection bands within the storm system. Areal skewness of precipitation depth could often be more pro­nounced if much shorter time intervals than the complete storm duration were con­sidered, as the influence on the isohyetal pattern of individual convective cells within the storm system could then be quite significant.

Many of the earth-atmosphere interactions which produce significant vertical air motions are fixed in space, and any precipitation which results from them falls within rather closely defined geographical limits. Examples are the lifting of an air stream by a mountain barrier or through an abrupt change in the frictional "drag" of the underlying surface on the low level air flow, such as may occur at coastlines and at the boundaries of forested areas. Even in the absence of precipitation obser­vations, it is possible to determine qualitatively the geographical location of many zones wherein spatially fixed earth-atmosphere interactions could be expected to cause significant areal variability in storm precipitation depths.

However quantitative estimation of the magnitude of this variability is much more difficult. For example, wind direction and speed, as well as air mass stability and moisture content, influence the magnitude of the orographic component of precipitation which results from the lifting of an air stream over a mountain barrier. Although the spatial variability due to orography has been evaluated successfully in some studies of seasonal or annual precipitation depths in mountainous terrain (Spreen 1947), large errors could occur if the results of such analyses were used to estimate the areal variability of precipitation depth in individual storms.

In some mountainous regions the direction of air inflow and air mass charac­teristics for many storms affecting the area are not markedly different from one storm to another, resulting in a reasonably constant ratio of storm precipitation depth experienced over the elevated terrain to that over low lying sectors. Charac­teristically, greater precipitation depths are observed at the higher elevations, and these may be 2 to 3 times more than depths observed at lower elevations.

Several investigations of precipitation over mountainous terrain have shown that in some synoptic situations, notably those associated with "cold lows" at higher levels of the atmosphere, the distribution of storm precipitation is relatively independ­ent of terrain (Mink 1960, Walker 1960, Williams and Peck 1962). A relationship between precipitation and other parameters designed to take account of terrain effects (e.g. Spreen 1947), could lead to large errors if used to estimate precipitation depths at ungauged points for this type of storm.

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3. INFLUENCE OF DATA USE ON NETWORK DESIGN

Precipitation depth or intensity data find application in the solution of many problems in synoptic meteorology, climatology, hydrology, agriculture and other scientific or technological fields. The degree of accuracy desired in these data for the solution of individual problems, and the relative importance of each problem, influence the density of gauges required in a precipitation measurement network and the period for which individual gauges should be maintained.

Some studies, such as the investigation of secular trends in depth of precipitation (e.g. O'Mahony 1961), can be based on observations of precipitation depth at a "point" (the catch area of a precipitation gauge). The minimum and optimum periods of years for which the "point" observations should be maintained to answer problems with acceptable accuracy are the aspects of network design of principal interest in such cases.

The error to be expected in a mean annual value derived from t years of record is approximately proportional to l/t (Benham 1956, Lee 1956). Thus the error in an annual mean value will be about 30 per cent less if based on a 20 year record than on a 10-year record. The minimum number of years for which precipitation obser­vations should be maintained to achieve a stable estimate of the mean annual value is a function of the between-years variability of precipitation and varies between climatic zones (Section 4).

The solution of many problems requires information on the frequencies of events (e.g. frequency of occurrence of rainfalls exceeding 3.0 ins in 24 hours) or on the magnitude of extreme events, and it is then often difficult to determine the length of record required to evaluate these factors with a stated degree of accuracy (Lee 1956). Thus the unending collection of observations from selected stations is undoubtedly justified.

Many studies require the estimation of the mean areal dep th of precipitation, for a variety of durations, over areas which are either fixed (e.g. a river basin) or variable (e.g. area receiving precipitation from a particular atmospheric disturbance) in space. Design of a precipitation network then involves consideration of the mini­mum and optimum areal densities of gauges, in addition to the period of years for which each gauge should be operated. These two factors cannot be evaluated independ­ently. For example, in a study of precipitation over the Upper Colorado River, Marlatt and Riehl (1963) found that annual precipitation depths observed at individual stations were not normally distributed, but annual precipitation depths for the river basin (100,000 sq.mi.) estimated from records at thirteen stations did approach a Gaussian distribution closely. The number of years of record required to adequately define the frequency distribution of basin annual precipitation is thus related in this case to the number of stations used to estimate basin precipitation depths.

The areal density of gauges required to determine mean areal precipitation depths with a specified mean error of estimate has been determined through two types of studies—one based on statistical theory of sampling error, a n d the other on the comparison of areal depth estimates from networks of varying density with those from a very dense network of gauges (Kohler 1958).

The standard error of the mean of n independent samples is proport ional to \j\'n, but "point" observations of precipitation within the size of a rea involved in many hydrological and agricultural studies etc. are frequently not independent. Empirical studies using dense gauge networks suggest that the error of the areal mean derived from observations at n gauges is inversely proportional to n to the 0.6 or 0.7 power. (Kohler 1958, Linsley 1958).

Specific gauge network densities which will prove adequate o r the most suitable in all situations cannot be stated. The size of area and length of time interval for which precipitation depth estimates are needed, and the desired accuracy of such

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estimates, vary from one data application to another. The relative importance of indi­vidual data applications may also vary from one region to another. In addition not all future data requirements can be anticipated and a network density which is adequate for all current major requirements may subsequently prove inadequate for the solu­tion of a major but unforeseen problem.

Prior to initial planning or any subsequent revision of the precipitation measure­ment network in a particular region, a comprehensive survey should be made of the current and potential data needs that the network will be required to satisfy This survey, to be fully effective, will generally involve a collaborative study between all major agencies concerned with the analysis and application of precipitation data within the region. Kohler (1958) has summarised a number of the major design and operational problems which may need to be considered.

The aim should be to formulate the data requirements for each specific problem in terms such as the following:

(i) the locations of "points" or areas, and the sizes of these areas, for which precipitation depth data are required;

(ii) the duration(s) (e.g. 15-minutes, hour, day, month) for which measurements or areal estimates of precipitation depth are required at locations in (i);

(iii) the magnitude of mean and extreme errors in estimates of areal precipitation depths acceptable for each data application;

(iv) desired minimum length of records at locations in (i);

(v) relative economic and/or social importance of each data application.

Establishment o f special purpose, high density networks may be warranted for the more important projects, but most requirements for data must be met from a multi-purpose gauge network. Design of this network should aim at a density and distribution of gauges which will provide precipitation data with an error frequency distribution acceptable for as many as possible of the various data applications.

Systematic errors in areal rainfall estimates often may be relatively unimportant when rainfall data a r e correlated with other parameters, as the errors may be absorbed in empirical constants. However the same errors could be of greater significance if the data are to be used in a water balance study. The importance of obtaining basic data suitable for water balance studies has been emphasised in preliminary plans for the International Hydrological Decade (UNESCO 1964), and Kohler (1963) has summarised a number of the applications for analyses of this type that have been suggested by various writers. The method of data analysis to be used in solution of each design or operational problem should therefore be considered when assessing the accuracy desired in the data.

4. LENGTH OF OPERATION OF GAUGES

The period of precipitation record needed to answer a problem within an appro­priate safety factor depends upon the nature of the problem and on the time variations in precipitation in t he region of interest.

If, for example, the frequency distribution of mean annual precipitation depth at a point or over an area becomes essentially stable after a certain period, the addition of further years of observation will not add significantly to accuracy (Lee 1956, O'Mahony 1964). T h e length of record needed to achieve a stable frequency distri­bution varies between seasons and regions. For example, analysis of a 75 year record for the Sutlej catchment (India) showed that deviations of 35 year means from the 75 year means were within ± 1 0 per cent for the May—October season, and within ±15 per cent for t h e November—April season (Panchang and Ganguli 1956).

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On the basis of limited studies, Landsberg and Jacobs (1951) proposed the following tentative estimates of the number of years needed to obtain stable frequency distri­butions of precipitation amount:

Islands Shore Plains Mountains Extra-tropical regions 25 30 40 50 Tropical regions 30 40 40 50

These figures emphasise that some records should be commenced immediately for at least a few benchmark stations in every major climatic zone, even though the current requirements for da ta may be only minor or less pressing than those for other areas.

The incidence of precipitation in arid areas is notably erratic, and McDonald (1960) has suggested that temporal variability of precipitation is more important than spatial variability in such regions. In a study of data for selected long-record stations in southwestern Arizona, McDonald (1957) found that even a 50 year mean could be non-representative of the long term mean. The 95% confidence half-widths of season precipitation means were found to be about 10% of the mean, even for stations with 80 years of record; and these confidence half widths rose to 20% of the mean for records as short as 20 years.

These findings underline the necessity for special efforts to establish benchmark stations in arid areas, even if only a low areal density of gauges is possible.

Although there is justification for continuing observations at selected stations indefinitely, unlimited operation of all stations may not yield the most efficient return from funds employed in operating a network. Correlation between rainfall depths observed at neighbouring stations results in some measure of duplication of infor­mation between the stations which becomes increasingly uneconomical with increase in length of record at the stations and in the degree of correlation between them.

Langbein (1954) proposed the establishment of a fixed network of base stations to sample the temporal variability of streamflow and a group of secondary stations to be operated for relatively shor t periods in a series of locations to provide geographic sampling. The same principle can be applied in design and operation of a precipitation network. Langbein developed formulae for estimating the optimum number of base stations, but Kohler (1958) has pointed out that it is often extremely difficult to make realistic estimates of some of the factors involved in applying these formulae.

The need to retain all gauges of an existing network should be reviewed from time to time. It may often be possible to discontinue some stations for which future data could be estimated with sufficient accuracy through correlation with records at one or more neighbouring stations which will be continued. The level of import­ance of the potential uses to which the data may be applied, and the accuracy required in the observed or estimated data for an observation station will determine whether or not observations at the station could be discontinued.

Periodical reviews of a station network should be made, even when the mean areal density of gauges in a region is below the desired level. The relocation of some gauges may be possible if a high degree of inter-station correlation exists between particular groups of stations in the network.

5. AREAL DENSITY OF GAUGES

In general the spatial variability of precipitation is greater in arid and mountainous regions and over small areas, t han in humid and flat regions and over large areas. This indicates that denser networks will be required to obtain a desired degree of accuracy in estimating areal precipitation depth for the former group of conditions. However there are no fundamental meteorological laws by which one can determine the gauge density needed in a particular region in order to measure the spacial variability of

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precipitation depth with a specified degree of accuracy. The required station density depends on the areal variability of precipitation which, in turn, can be determined only after adequate sampling has been carried out in the region of interest.

Some investigators (Panchang and Ganguli 1956) have based estimates of the net­work density needed to measure areal rainfall depth with a specified standard error on the assumption tha t the distribution of rainfall in space is 'normal' (Court 1961). However their approach cannot be applied in the absence of data on the spatial variability of storm precipitation in the region.

Direct, reliable measurement of precipitation over areas larger than a few square feet is not yet possible, but various studies with very dense networks of gauges have given mean areal depth estimates which, for practical purposes, are probably very close to the " t rue" precipitation over the areas covered by the gauge networks. Com­parisons between precipitation depths estimated from the complete networks and from less dense networks selected from them provide quantitative guidance to the density of gauges needed to estimate areal precipitation depth with a specified mean error of estimate (Light 1947, Linsley and Kohler 1951, Huff and Neil 1957, McGuiness 1963).

In general the sites for studies of this type have been so chosen to minimize oro­graphic effects, and the studies have concentrated on measurement of convective shower type rains with their high spatial variability over short distances. Results of these studies can probably be transposed with sufficient accuracy to other relatively featureless areas and could be used to determine the gauge density needed to estimate areal precipitation from convective systems with a desired level of accuracy. McGuiness (1963) has suggested that some adjustments may be needed for possible differences from one geographic region to another in the rainfall gradient associated with convective systems, but the need for modifications of this kind requires further investigation.

The gauge densities suggested by these studies as necessary to estimate areal precipitation with a specified accuracy would be greater than those actually needed for storm precipitation resulting from widespread cyclonic and frontal systems which have a greater spatial homogeneity of precipitation amount than convective type sys­tems. However the relative gauge densities needed to obtain with a desired degree of accuracy, estimates of mean precipitation depth from convective and general (or banded) precipitation systems have not been evaluated in any of the studies found in the literature.

Few studies with very dense gauge networks have been reported for areas where orographic influence are marked. It is usually difficult and expensive to establish and maintain high density networks in such locations, and in addition the results of these studies would have very limited application outside the specific area covered by each network. In one study for a mountainous watershed, a clear relationship was found on the average between mean storm precipitation depth and the spatial variability of precipitation amount (Wilm, Nelson and Story 1939). More gauges were needed to get a small standard error for small storms than for large storms. This finding, which is confirmed by other studies (Marlatt and Riehl 1963), led to the suggestion (Wilm et al.) that to avoid an impracticably large number of gauges, requirements for accuracy of areal precipitation depth estimation should be modified in inverse relation to the size and importance of storms.

Gauging density versus error of areal depth estimation criteria based on analysis of data from dense networks cannot be transposed with confidence to or between the many areas in which the effects of earth-atmosphere interactions on the depth and distribution of precipitation cannot be neglected. The optimum density of gauges in such areas is fixed b y the maximum distance between stations which is possible while maintaining an adequate degree of correlation. Two examples of inter-station corre­lation studies have been given by Stenhouse and Cornish (1958) and Cornish and others (1961). The correlation between stations will depend upon the type of precipitation

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(convective, banded or general) and the time interval (storm, m o n t h , year) considered The major purposes that the data are intended to serve will d ic ta te what degree of inter-station correlation and density of stations are required.

Although the diversity of terrain over the world and the diversity of problems to which precipitation data are applied make it impossible to formulate network densities which will meet all situations, the World Meteorological Organization (1965) has formulated minimum densities of gauging networks which are desirable in various climatic zones and types of terrain.

Solution of some problems requires information on the temporal as well as the areal distribution of storm precipitation, or precipitation intensity—duration—frequency data for particular locations o r areas. These data are obtained f rom automatic record­ing precipitation gauges, the number of which in a data collection network is frequently determined mainly by economic factors. However the WMO (1965) has suggested that at least 10 per cent of precipitation gauges be equipped wi th recorders in warm climates, where convective type precipitation predominates, a n d 5 per cent in cold climates where general or banded precipitation systems with their smaller spatial variability of precipitation depth are experienced more frequently.

Techniques have been developed for extending rainfall intensity data from a limited network of recorders to estimate similar data at locations for which only 24 hour precipitation totals are available (U.S. Weather Bureau 1961, R e i c h 1963). Although observed data are to be preferred to estimates, it does appear pract icable to estimate rainfall intensity data for some location with a reasonable accuracy provided that there are records of 24 hour precipitation totals for the site.

Whilst it is generally impracticable to establish high density networks of rain gauges and recorders over large areas, especially in mountainous terrain, it has been suggested that one or more representative catchments, 500 sq .mi . or less in areas. should be established in each of the principal climatic and/or physiographic areas of a region (Linsley 1958, Osborn and Reynolds 1963, WMO 1965). Density of the gauge network in these representative catchments should be substantially higher than that in the general regions surrounding the catchments. The aim of t he se small, relatively well instrumented catchments is to obtain data on the spatial a n d temporal variability of precipitation over small areas and short time intervals which c a n be applied generally within the broader surrounding regions.

6. LOCATION AND DISTRIBUTION OF GAUGES

Observations at each precipitation gauge site are assumed t o represent temporal variability and mean depth of precipitation over a surrounding a r e a which is very large in relation to the gauge catch area. The gauge must therefore be s i t ed to be as represent­ative as possible of conditions over its surroundings (WMO 1965).

The likelihood that some marked change in exposure may o c c u r with time should be considered in selecting the site for any gauge which is to be maintained as a long-terra base station.

Gauges sited in cities and large towns are likely to be subjected to complex exposure changes as the urban areas grow and change with time, and for th i s reason it would seem that precipitation records from rural areas or small towns should be more stable with time than those from large cities. This expectation was not confirmed however in a study of U.S. records (McDonald and Green 1960), when city records a s a whole were found to have no greater degree of internal inhomogeneity than records for small towns and rural areas. It would be of interest to learn whether this experience has been repeated in other regions, as proper maintenance and inspection of gauges could often be more easily achieved in larger population centres than in rural areas.

Several investigations suggest that precipitation depths tend t o be higher over large towns, cities and forests than over their immediate surroundings (Landsberg 1956,

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Bergeron 1960, Stout 1960) and observations taken at gauges located in cities etc. may be unrepresentative of the depths experienced outside their limits. Similarly, obser­vations made on isolated hills or near coastlines would be unrepresentative in many situations of depths experienced over surrounding areas due to the influence of local­ised earth-atmosphere interactions on storm predipitation depths.

Investigations based on high density gauge networks (Light 1947, Linsley and Kohler 1951, Huff and Neill 1957") have shown that , for rainfall which is essentially random in space (convective type precipitation in areas where orographic effects are unimportant): a centrally located gauge gives, on the average, the best measure of area! precipitation ; errors in estimates of areal precipitation are less for a uniformly spaced than for a randomly spaced network.

In a study of rainfall in South Australia, Stenhouse and Cornish (1958) found that inter-station correlation was greatest along an axis parallel to the cold fronts moving over the area and least along an axis normal to these fronts. This indicates that, for the measurement of areal depths from banded precipitation systems, gauge spacing could be greater along the axis o f maximal correlation than along the axis of minimal corre­lation. However the permissible gauge spacing, when some specified degree of inter-station correlation is desired, can only be determined by analysis of precipitation data for the area of interest.

Recording precipitation gauges should be distributed uniformly in space, except in areas where orographic or other spatially-fixed influences are likely to cause signif­icant differences over short distances in the frequency, intensity or duration of precip­itation. For example, precipitation may often commence earlier and continue longer over elevated land t h a n over lower lying areas to windward or leeward. The network of recording gauges should be arranged to sample as adequately as possible any likely significant horizontal gradients in the frequency, intensity or duration of precipitation within a region.

Measurement of precipitation in mountainous regions is difficult because of the high spatial variability of precipitation and the practical difficulties associated with establishment and operation of dense gauging networks in these areas. Elevation is usually the major topographic influence on precipitation depth and is also usually the easiest to define. Marlat t and Riehl(1963) found that elevation was slightly more impor­tant than distance between observing stations in accounting for variability between average annual precipitation at individual stations in the Upper Colorado River Basin. Slope of the ground surface and orientation of slopes would be expected to influence the orographic component of precipitation depth in mountainous country and Spreen (1947) has demonstrated the importance of these parameters in graphical correlation studies.

Wilm, Nelson a n d Story (1939) developed a method for determining the distribution of gauges in a mountainous small watershed based on "facets of slope"— small sub-areas described by a single value of slope and orientation. The principles of this method can be applied to design of gauge networks in larger mountainous regions. Each eleva­tion zone and major " facet of slope" should be sampled in proportion to the percentage of total area that it represents. Generalized contours of land elevation would assist in outlining the nature and extent of the principal ground slopes and orientation of slopes in the region.

7. CONCLUSIONS

It is impracticable to derive a universally satisfactory procedure for the design of precipitation gauge networks. The density of gauges required in any region depends upon the size of a r ea and length of time interval over which precipitation must be measured, the type of precipitation (convective, banded, general) and the purposes to be served by the da ta . A comprehensive survey of these factors should be made for each

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region, and in particular the relative importance of various data uses and the accuracy of measurement required in each type of data application should be assessed. This survey should be most effective if made jointly by all of the principal agencies concerned with the analysis and application of precipitation data.

Results of studies made wi th high density gauge networks provide guidance on the gauge density needed to measure convective (shower) type precipitation over feature­less terrain with a desired level of accuracy.

In general, however, the areal and temporal variability of precipitation, which determine the optimum density of observing stations and record length, can be deter­mined only after adequate sampling. Because of the quite long periods of record (30-50 years) required to obta in a stable frequency distribution of precipitation amount, a network of long term base stations should be established immediately, even if only a sparse network is possible at present. The WMO has formulated desirable minimum densities of networks for several major climatic and physiographic types of region.

Ideally gauge sites should b e free of potential long term exposure changes and should be representative of the broader regions surrounding them. Special attention should be given to the location of gauges in regions of marked orographic relief. Although the network may be sparse, it should aim to sample various elevation zones, and the orien­tation and gradient of land slopes in proportion to their areas.

Network of secondary stations, operated for a limited number of years only, should be used to improve the sampling of spatial variability of precipitation. These stations should be operated for a sufficient period to establish reliable correlations with the long term base or principal stations. Unless dictated by the priorities of specific projects, secondary station networks should be established initially in areas where significant spatial variability of precipitation depth can be anticipated due to earthatmosphere interactions, or in areas where the correlation between principal stations is lowest.

Efforts should be made to establish in each principal climatic and/or physiographic region at least one representative catchment (area 500 sq.mi. or less) with a network density exceeding the WMO recommended minimum for the region by a factor of at least three to five times.

REFERENCES

(x) ACKERMAN, B., 1960 : Orographic-Convective Precipitation as Revealed by Radar. In: Physics of Precipitation, Amer. Geophys. Un., Geophys. Monograph 5.

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