water world

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Technical papers in hydrology 7

Scientific framework of world water balance

to the International

Unesco

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Technical papers in hydrology I

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In this series:

Perennial Ice and Snow Masses. A Guide for Compilation and Assemblage of Data for a World Inventory.

Seasonal S n o w Cover. A Guide for Measurement, Compilation and Assemblage of Data.

Variations of Existing Glaciers. A Guide to International Practices for their Measurement.

Antarctic Glaciology in the International Hydrologkal Decade.

Combined Heat, Ice and Water Balances at Selected Glacier Basins. A Guide for Compilation and Assemblage of Data for Glacier Mass Balance Measurements.

Textbooks o n Hydrology. Analyses and Synoptic Tables of Contents of Selected Textbooks.

Scientific Framework of World Water Balance.

Flood Studies. An International Guide for Collection and Processing of Data.

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A contribution to the

International Hydrological Decade

Scientific framework of world water balance

Unesco Paris 1971

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The selection and presentation of material and the opinions expressed in this publication are the responsibility of the authors concerned, and do not necessarily reflect the views of Unesco. Nor do the designations employed or the presentation of the material imply the expression of any opinion whatsoever on the part of Unesco concerning the legal status of any country or territory, or of its authorities, or concerning the frontiers of any country or territory.

Published in 1971 by the United Nations Educational, Scientific and Cultural Organization,

Place de Fontenoy, 75 Paris-7e Pnnted by ImprimerieReliure M a m e

@ Unesco 1971 Printed in France SC. 70/XXI.7/A

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Preface

The International Hydrological Decade (IHD) 1965-1974 was launched by the General Conference of Unesco at its thirteenth session to promote international co-operation in research and studies and the training of specialists and technicians in scientific hydrology. Its purpose is to enable all countries to make a fuller assessment of their water resources and a more rational use of them as man’s demands for water constantly increase in face of developments in population, industry and agriculture. In 1970 National Committees for the Decade had been formed in 105 of Unesco’s 125 Member States to carry cut iiationu! ~ctivities 2nd t~ contri- bute to regional and international activities within the programme of the Decade. The implemeiita- tion of the programme is supervised by a Co- ordinating Council, composed of twenty-one Member States selected by the General Confer- ence of Unesco, which studies proposals for developments of the programme, recommends projects of interest to all or a large number of countries, assists in the development of national and regional projects and co-ordinates international co-operation.

Promotion of collaboration in developing hydrological research techniques, diffusing hydrological data and planning hydrological installations is a major feature of the programme of the IHD which encompasses all aspects of hydrological studies and research. Hydrological investigations are encouraged at the national, regional and international level to strengthen and to improve the use of natural resources from a local and a global per- spective. The programme provides a means for countries well advanced in hydrological research to exchange scientific views and for developing countries to benefit from this exchange of information

in elaborating research projects and in implement- ing recent developments in the planning of Iiydro- logical installations.

As part of Unesco’s contribution to the achievement of the objectives of the IHD the General Conference authorized the Director-General to collect, exchange and disseminate information concerning research on scientific hydrology and to facilitate contacts between research workers in this field. To this end Unesco has initiated two collections of publications: ‘Studies and Reports in Hydrology’ and ‘Technical Papers in Hydrology’.

The collection ‘Technical Papers in Hydrology’

is intended to provide a means for the exchange of informatioil on hydrological techniques and for the co-ordination of research and data collection.

The acquisition, transmission and processing of data in a manner permitting the intercomparison of results is a prerequisite to efforts to co-ordinate scientific projects within the framework of the IHD.

The exchange of information on data collected throughout the world requires standard instruments, techniques, units of measure and termino- logy in order that data from all areas will be comparable. Much work has been done already towards international standardization, but much remains to be done even for simple measurements of basic factors such as precipitation, snow cover, soil moisture, streamflow, sediment transport and ground-water phenomena.

It is hoped that the guides on data collection and compilation in specific areas of hydrology to be published in this collection willprovide means whereby hydrologists may standardize their records of observations and thus facilitate the study of hydrology on a world-wide basis.

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Foreword

The aim of this publication is to define the world This technical paper was prepared by the Panel water balance, to specify the purposes of study, to on Scientific Framework of the IHD Working summarize the current state of knowledge, to review Group on the World Water Balance, under the available or proposed means for accomplishment chairmanship of R. L. Nace. Unesco gratefully of objectives, and to suggest how necessary work acknowledges this work.

and study may be carried out.

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1 General nature of the

Natural waters are unified and interrelated in their cyclic movement. The study of water balances on continental and planetary scales must therefore be a co-operative international undertaking. Such a study is prerequisite to rational management on similar scales.

Though the volume of global water is very large, serious environmental and water-supply problems in many parts of the world have been caused by wasteful exploitation of fresh water, reckless release of deleterious and even dangerous water-borne wastes into rivers, lakes and the ground, and care- less management and mismanagement of water- sheds, recharge areas and aquifers. Most of these problems, which relate to both the dry and densely populated areas of the world, could have been forestalled with proper foresight, based on understanding of the hydrological cycle.

Precisely because of these facts, the Co-ordinating Council for the IHD, during its first session in 1965, declared that: ‘The establishment of a

study

global water balance-that is, estimation of the gross distribution and movement of water in the total environment-is one of the major international projects, since it will involve the majority of the countries of the world and because it is related to practically all scientific activities of the International Hydrological Decade’ (Co-ordinating Council, 1965, p. 15).

Deeper understanding of the principles governing water movement and occurrence will provide the basis for more reliable future computation and forecast of water balances and balance components.

By successively closer approximations, it will be possible to estimate more accurately the water resources of individual continents and of individual States. As the margin narrows between water demand and water supplies on the land, it becomes increasingly important to predict what future supplies willbe at given times and places. At present this can be done only in general terms.

I I

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2 Definitions

The following paragraphs define several terms that are essential for the purposes of this discussion:

system, hydrological cycle, water balance and resi- dence time.

Systems

Following Dooge’s (1968) excellent discussion of the hydrological cycle as a system, w e may define a system as a structure or scheme that interrelates an input of matter, energy or information with a corresponding output or response.

The region with which w e are concerned is the earth, including its atmospheric envelope. Within this region, nearly all the energy that drives the hydrological cycle is derived from the sun. The system is, in effect, a giant heat engine and it oper- ates because there is a surplus of incoming radia- tion over back radiation. For practical hydrological purposes the input of solar energy and the output of back radiation into space may be taken as con- stants for the system as a whole (although there may be significant changes on time scales relevant to climatic epochs). Essentially no water enters or leaves the system. For these reasons, the global system m a y be treated as a closed system so far as the water itself is concerned. N o sub-division of the system is closed, however, and study of sub-divisions is handicapped by the usual difficulties with open systems. Both matter and energy enter and leave the open systems and it is seldom possible to mea- sure accurately all the inputs and outputs.

T h e hydrological cycle

The hydrological cycle is the occurrence and move- ment of all waters, together with their dissolved

and entrained constituents, above, on and below the earth’s surface. Nearly all water is continually in motion. Whether or not in motion, it obeys basic universal laws. Therefore it is understandable, even though achievement of understanding is as yet incomplete. The hydrological cycle is the central theme of the science of hydrology.

Considering the earth system as a whole, water in the world ocean is overwhelmingly the largest component of the system. The amount of water in the atmosphere at any instant of time is very small, but traffic of water through the atmosphere in the course of a season or a year is large. Water on or near the surface of land areas, therefore, may be regarded as an incidental effect of the interactions at the interface between the ocean of water below and the ocean of air above.

Water balance

The study of water balances is the application in hydrology of the principle of conservation of mass, often referred to as the continuity equation. This states that for any arbitrary volume and during any period of time, the difference between total input and output will be balanced by the change of water storage within the volume. In general, there- fore, use of a water-balance technique implies measurements of both storages and fluxes (rates of flow) of water, though by appropriate selection of the volume and period of time for which the balance will be applied, some measurements may be elimi- nated. For example, if the balance is computed for a year or over a number of years, the change in storage in any component of the hydrological cycle wili usually be smaller than errors in the measure- ment of inputs and outputs.

A c o m m o n use of the water-balance equation is 12

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Definitions

to infer one term from measurements of the others, as when evaporation from the earth’s surface is determined from measurements of changes in soil moisture. But if all relevant terms are measured their balance, or lack of it, can be used to check the accuracy of measurements and the understanding of principles. The world water-balance project is mainly concerned with the measurement of all relevant terms on the global scale. It is a central problem of hydrology, involving the entire hydrological cycle. Thus the world water balance cons- titutes a general framework for the study of water balances in various areas (river basins, continents, etc.) and for different periods of time.

The water balance equation can be usefully employed on its own in studies of the land components of the hydrological cycle. W h e n atmospheric water is to be considered, difficulties of measuring fluxes or phase changes of water vapour usually lead to the use of techniques for indirect measurement or estimation, based on the principle of conservation of energy. Consideration of water balances involving phase changes, therefore, nor- mally requires study of heat balances; that is, the measurement of all, or all but one, of the terms in the energy-balance equation.

The concept of a global water balance is most easily envisaged for the atmosphere, the oceans and the polar ice caps. For the land components of the hydrological cycle, not all space and time scales are equally meaningful. There is little physical significance, for example, in the volume of stored soil moisture for a continent, or of ground water storage in a small section of an aquifer, or of

stream flow out of a region of unco-ordinated drainage. Meaningful space and time scales for any component of the hydrological cycle may possibly be derived from consideration of the hydrological régime expressed in terms of the distribution of residence times.

Residence times

Residence time is conceptually simple but the phenomena to which it refers are complex. It is the length of time during which an increment of water remains in a given sector of the hydrological system.

Recharge water which enters an aquifer near a discharge area may reappear in a seep or spring within a few minutes. Recharge water that enters an areally extensive aquifer far from points of discharge may remain in the aquifer for years, decades or centuries. Analogous statements are applicable to water in other sectors of the hydrological system.

Obviously there is no such thing as one specific residence time for a given storage, and the spectrum of residence times will depend on the mechanism of flow through the storage medium. Regardless of this mechanism, the average (conventional) residence time can be computed as the ratio of the long-term average storage volume to the long-term average throughput (input or output). This average value is a useful characterization of the hydrological régime, and may determine which method of analysis is most appropriate to a particular situation.

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3 Development

of the water-balance concept

Study of the origin and interrelations of waters in the hydrological cycle has a long history. Besson (1569) and Palissy (1 580) both recognized the plu- vial origin of ground water, but they made no measurements. The first quantitative approach, based on the water-balance concept, was that of Perrault (1674), w h o showed that the annual volume of precipitation on the upper basin of the River Seine in France was at least seven times the volume of discharge of the river. I-Ie correctly established the concept of the allocation of preci- pitation as evaporation, transpiration, runoff and ground-water recharge. His conclusions were confirmed by Mariotte (1686), and also by Halley (1687), w h o showed that evaporation from the Mediterranean was greater than the volume of river flow into it.

The problem of water balances attracted much attention in Russia among outstanding scientists (Gmelin, 1774; Lomonosov, 1934; Rychkov, 1762, chap. 1 and 2; Tatischev, 1793, chap. I to III;

and others). These were concerned with the reasons for the endorheic drainage of the Caspian Sea basin and the water balance of the basin.

A significant contribution to the development of water-balance concepts was that of Dalton (1802) w h o inquired into the quantitative relations be- tween precipitation, evaporation and runoff and into the origin of springs. He was the first to attempt to determine the water balance of England and to develop a formula for calculation of evapo- ration from free-water surfaces.

Academician V. V. Petrov (1821) made impor- tant studies of evaporation from snow and ice during 1808 and 1809, and he determined the rela- tions between evaporation, ‘dryness of the air’, air pressure and wind speed.

In general, the nineteenth century witnessed the initiation in many countries of systematic observa-

tions of river stages. Late in the century, after the invention of reliable velocity meters, discharge measurements were systematized. This permitted more effective study of the relations among hydro- logical parameters of river basins, a problem which interested many eminent scientists and engineers (Heinz, 1898; Newell, 1894; Oppokov, 1906; Penck, 1896; Voeikov, 1884). Newell demonstrated a direct relation between runoff and precipitation and prepared maps showing isopleths for their mean values in the United States of America.

Albrecht Penck and E. V. Oppokov made some theoretical generalizations and were the first to develop a water-balance equation (Penck-Oppokov equation) for closed and open river basins* :

R = P - E f A G

where: R is runoff; P is precipitation; E is evapora- tion; and G is ground water.

Oldeskop (1911, p. 197) made further generali- zations and developed a formula for calculation of evaporation, depending on precipitation and maximum possible evaporation. The later develop- ment of formulas along these lines is well chro- nicled in many treatises.

One of the earliest known attempts to calculate world total river discharge to the sea was that of John Keill (1698). He estimated 26,308 mi3 yr-l (109,668 km3), or nearly four times the amount of modern estimates. Another early attempt was that of Buffon (1749), w h o calculated a value of 230,000 km3, or nearly eight times current estimates.

First to present a general scheme of the global hydrological cycle was Bruckner (1905). Assuming

1. In this context a closed basin is one in which the boundaries of the ground-water basin coincide in general with those of the surface-water catchment. In an open basin they do not coincide.

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Development of the water-balance concept

that the total amount of water on the earth is constant, he expressed the annual water balance as follows:

where the subscripts o and I refer to oceans and land areas respectively; D o is the annual amount of water vapour transported by the atmosphere from the oceans to the land; D 1 is the annual transport of vapour from land to sea; and R is the annual discharge of rivers to the oceans.

During the twentieth century large-scale water balances have attracted wide attention among scientists. Original studies based on the physical nature and mechanisms of the processes of evaporation, precipitation and runoff are those of Albrecht (1960), Budyko (1956), Keller (1962, p. 520), L'vovich (1945), Meinardus (1911, 1934), Wüst (1920, 19361, and Zubenik (1956). Nace (1969) prepared a summary water balance, based upon an extensive review of scientific literature.

For many years after the work of Bruckner (1905) it was generally believed that precipitation on the land was derived mainly from continental evaporation. This led to far-reaching conclusions about the effects of forest cover, of land-reclama- tion measures and of other practices on the water balances of large areas. An important result of twentieth-century studies has been the gradual elu- cidation of the actual contributions to continental precipitation of oceanic vapour transported advec- tively to the land and of continental evaporation.

ít is now known that the contribution of local evaporation to local precipitation is relatively small.

Despite great advance in knowledge during recent decades, wide differences occur in the calculations by sundry authors on average precipitation, evaporation and runoff. These calculations do not attain the degree of accuracy that could be achieved by use of the latest data and methods available and by collection of data from areas which, hydro- logically, are nearly blank spaces on maps.

O f all water discharged by rivers to the sea, perhaps no more than 60 per cent is accurately measured at the present time. The Amazon was not carefully measured until 1963. Its average annual discharge (175,000 m3 ^s-') is nearly 20 per cent of the estimated total of all rivers.

Opinions diverge considerably also about the amounts of water in rivers (channel storage), in lakes and swamps, in glaciers and ice caps, in the soil and vadose zones, and in aquifers.

Calculations of soil-moisture storage and ground water differ by orders of magnitude. Underground discharge to the sea is known only qualitatively and estimates of various authors differ by a factor of 100.

Lack of data, as noted above, prevents accurate estimation of the total amount of water that actually participates in the water cycle. Moreover, practically all classical studies were concerned with long-term average annual quantities. Under present conditions it is sometimes necessary to study water balances for given years or even shorter periods-so-called current accounting of water.

A very large amount of water is locked up as water of crystallization and of composition in minerals. Geological processes continually release some of this water and other processes incorporate water in minerals. This water is not cyclic in the usual hydrological sense and hence is not of direct concern in water-balance studies. However, this water has long-term importance and its study by geologists should be encouraged. Undoubtedly the processes are especially significant in areas of mineralized ground water.

The origin of fresh waters is well known: the natural evaporation and precipitation processes of the sea-atmosphere system. The origin of water itself, however, is a highly speculative topic. Accord- ing to some theories, water is being synthesized continually in the interior of the earth and finds its way to the surface. A synthesis rate averaging 3 km3 yr-I during 4,000 million years would account for all water now in existence. Owing to the wide- spread occurrence of oceans during Cambrian times, other theories hold that most, if not all, water originated during a relatively short period of geologic time and little or no new water is being generated now. This problem also is outside the main concern of the Working Group. Nevertheless it has both scientific and practical interest because of popular misconceptions about so-called juvenile water. The problem deserves study by scientists and scientific organizations.

Study of trends in mean ocean levels as indica- tors of non-equilibrium between oceanic and terres- trial waters has somewhat more direct interest

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Scientific framework of world water balance

than water of crystallization or composition, or than juvenile water. Commonly, changes in sea level during the past 8,000 years have been attribu- ted to waxing and waning of glaciers and ice caps.

Recent changes have been so small that this is not necessarily the only plausible explanation.

Expansion and contraction of oceanic waters by

warming and cooling is one possible cause. Geolo- gical warping of the sea floor is another possibility, alone or in combination with emergence or sub- sidence of land areas and submarine volcanism.

Other causes may be imagined. Study of this tapic by oceanographers and geophysicists should be encouraged.

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4 State of knowledge

about specific parameters

The parameters which are relevant to water balances are indicated in Table 1. Symbols shown are those The following discussion outlines the relative

TABLE 1. Parameters of the hydrological cycle1

that will be used subsequently in balance equations. Storage Fluxes

importance ofthese parameters.

Storage and residence times

It is important to know how much

Atmospheric water (W) Evaporation (E)

Oceans and seas (O) (from bare and vegetated Lakes and reservoirs (L) land; from oceans and River channels (V) other water bodies; from

Swamps (S) snow and ice)

Biological water (B) Horizontal vapour flux

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water partici- Moisture in soil and unsatu- Precipitation (P) pates in the hydrological cycle. For that purpose

it is necessary to know how much water is in a given sector of the cycle (storage) and how long it remains in that sector (residence time). The voíu- metric values in the following discussion are similar

rated zone (M) Groundwater(G?

Frozen water

Runoff (R)

Infiltration; deep percolation Recharge, underflow and dis- (ice caps; glaciers; pack

ice; ice shelves; perma- Rates of movement frost)

charge (Gd)

to those suggested by Nace (1969), and are listed

in Table 2. ^1.

Atmospheric water. Many calculations have been made of the amount of water in storage in the atmosphere and its residence time. Most calculations

TABLE 2. Recent estimates of storage volumes and average residence times of parameters of the world water balance

Other fluxes affect the hydrological cycle, such as ocean cur- rents and heat fluxes. Though these are not recognized in the discussion that follows, they would not be overlooked in water-balance studies. Heat fluxes, for example, affect eva- poration, but we dedi here only with evaporation, once it has been determined or estimated. Similarly for other factors.

Parameter Volume (km9 Equivalent depth’ Average residence time

Atmospheric water Oceans and seas

Fresh-water lakes and reservoirs River channels

Swamps Biological water Moisture in soil and the Ground water

unsaturated zone

Frozen water

13 O00 1370 x loE

125 O00 1 700 3 600 700 65 O00 4 x 108 to 60 x 30 x lo8

25 mm 2.5 k m 250 mm

3 mm 7 m m 1 mm 130 m m

loE 8-12Om 60m

8-10 days 4 O00 + years 2 weeks

Of the order of years 1 week

2 weeks to 1 year

From days to tens of thousands of Tens to thousands of years

years

1. Computed as though the storage were uniformly distributed over the entire surface of the earth.

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Scientific framework of world water balance

indicate average storage values of the order of 13,000 k m 3 and average residence time of 8 to 10 days. The values vary seasonally, and local values vary widely from time to time and from place to place. Further study will permit refinement of values, but precise determination is unlikely in the foreseeable future. While gross storage and residence time are peripheral to the immediate problem of the world water balance, the im- portance of atmospheric moisture fluxes requires continued observations and analyses as an essential part of the aerological approach to regional water- balance computations.

Oceans and seas. The storage volume of oceans and seas is of the order of 1,370

x

lo6 km3, and mean residence time of water in the world ocean undoubtedly exceeds 4,000 years. These facts are important because of the function of oceans for the storage and distribution of heat and energy.

However, no conceivable refinements of these values will, in themselves, materially affect studies of water balances. They are therefore peripheral and not of immediate concern.

Lakes and reservoirs. Large lakes and reservoirs, as defined by the Co-ordinating Council, are impor- tant, especially in relation to national and regional water balances. Fresh-water lakes of the world probably contain about 125,000 k m 3 of water.

Most of this water is in lakes whose individual capacities exceed 10 km3. Their storage function in water balances is considerable. The storage func- tion of the hundreds of thousands of smaller lakes is small except in local balances. A still greater storage is that of saline lakes, such as the Caspian Sea and the Aral Sea.

The inventory of large lakes of the world should be pursued vigorously in order to obtain an improved estimate of water storage on the continents.

Total storage in reservoirs changes from year to year as new ones are built. Values for the current total are not readily available internationally but should be easily obtainable by national groups.

Values for the United States of America, for example, are 60,000 k m a of surface area and 445 k m 3 of storage volume. A tabular summary would be easy to prepare for all reservoirs having a capacity exceeding, say, 5

x lo6

m3.

Once a reservoir is filled it functions as a lake.

Inventories and balance studies of reservoirs should be correlative with those of lakes.

River-channel storage. Total storage in river channels would be impossible to compute for all rivers of the world, and such a computation would have little apparent value. For water-management pur- poses channel storage is regularly computed for certain reaches of some rivers. That is, techniques are available. Calculations for a few major rivers should provide the basis for an order-of-magni- tude estimate for all rivers. O n e crude estimate (Nace, 1969) of total channel storage for all rivers is about 1,700 km3, equivalent to their mouth discharge during about two weeks.

The short residence times of river water and of atmospheric vapour point up the precarious nature of the land phase of the water cycle and the need to understand it better. They also lend emphasis to the importance of the base-flow component of river discharge.

Swamps. Swamps have received relatively little attention from hydrologists. They are areas where the water table is at or near the land surface and the open-water areas m a y be considered as out- crops of the water table. Water stored in the peat layer of peat bogs is estimated to be 1,800 km3, with a similar value for water stored in swamp lakes and streams, in swamps with a thin peat layer, and in the marshy areas of tundras. This volume is comparable to that of river-channel storage, but the residence time of this water (exclud- ing its upper layers) is much longer than the resid- ence time of water in river channels.

Swamps have vast interest to ecologists but in general they are peripheral to the problem of the world water balance. Study for other purposes is encouraged in connexion with land drainage, recla- mation, and ecological problems.

Biological water. Stored biological water, estimated to be equivalent to 1 m m over the earth’s surface, is so small as to be negligible in water balances of regional or larger scale. It does not seem to warrant much attention. The flux of water through plants is large among parameters of the land phase of the water cycle, but this flux is included as part of total evaporation from the land.

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State of knowledge about specific parameters

Water in the unsaturated zone. This zone is a crucial one in the water cycle and one for which storage is very difficult to estimate. For long-term average balances storage is generally treated as a constant which can be neglected. For shorter terms and for specific areas it is definitely variable, especially in the soil zone, and it cannot be ignored. In the vadose (below the soil) zone water content probably is an actual near-constant. The critical zone, therefore, is the soil, for which data are extremely scarce, owing to the difficulty of direct measurement.

Data for this zone are not essential to large-scale balances but should be pursued for local balance studies.

Ground water. Ground-water storage far exceeds that in all lakes and rivers, if we accept recent estimates ranging from 4

x

IO6 to 60

x

IO6 km3, according to the depth considered. In other words, virtually nothing is known about the total storage volume. Since this is a major component of the land phase of the hydrological cycle, information should be pursued vigorously. Only a very small part of this volume (perhaps about 6,000 km3) con- tributes directly to the flow of rivers. Nevertheless this contribution is vital to the sustained flow of streams. and it deserves increased attention.

Frozen water. One estimate of the water equivalent of glaciers and ice caps is 30 >i

lo6

km3-much more than the total of all fresh liquid water. The average residence time of water in these ice bodies is long: from tens of years in alpine glaciers to many thousands of years in ice caps. For both

~i>rlg-~erm iarge-seaie -water baialices, therefore, storage may be treated as a constant.

The International Commission of Snow and Ice, the Special Committee on Antarctic Research, the International Geophysical Programme and others are giving special attention to glaciers and ice caps. The Co-ordinating Council of the IHD has requested that glaciologists give more attention to the hydrology of snow and ice, and symposia on that subject have been scheduled.

Pack ice and shelf ice are considered to be peripheral to the water-balance problem. However, they have high albedos, affect heat balances, and hence affect large-scale water balances. There is no evidence that permafrost is significant in water balances.

Findings concerning frozen water are of general

interest in the world water balance, but for that project storage and residence times do not seem to require special attention beyond what they are already receiving from specialists. Seasonal snow cover is, of course, an important factor in local and regional balances.

Fluxes

Whereas storage and residence times are important for inventory purposes, long-term average inventories actually give no conception of water balances.

For that purpose, fluxes and changes in storage have paramount importance.

Evaporation. Evaporation is a controversial topic.

While many point measurements have been made and are made daily, no generally usable method is available for measuring evaporation directly from areas more than a few tens of square metres in area.

The fact is that data are very deficient for large areas of the globe, including the vast expanse of the world ocean. Estimated annual evaporation from the seas is of the order of 400,000 km3. This calculated value, however, is based on extensive extrapolations of sparse observational data.

The average depth of the world’s oceans is somewhat more than 3 k m but their widths are 1,000 to 3,000 times that amount. Because of this geometry the sea-atmosphere interface is the most important interface at the earth’s surface and it has a preponderant role in the hydrological cycle.

Because of its nature, this interface is the one for

WIIIUI UdLd are most sparse, especially in the south- ern hemisphere.

Hydrologists, as such, do not usually study oceanic evaporation. The Panel, therefore, under- scores the need for more attention to this problem by oceanographers, meteorologists and atmospheric physicists.

A n approximate value for evaporation from land areas is 70,000 k m 3 yearly. This value may be somewhat more accurate than that for the oceanic areas, but the percentage accuracy is not known.

The value is calculated, as no large-area direct measurements are possible. Calculations depend largely on observed or inferred radiation balances but, for vast areas of the world, direct observations of radiation balances are unavailable.

--.l-:..L a-&,.

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Scientific framework of world water balance

Evaporation is one of the most poorly known of hydrological parameters, and the world water- balance project requires a vigorous programme to obtain additional data for bare and vegetated land, for wetlands of all kinds, and for free-water surfaces of ponds, lakes and inland seas.

Horizontal vapour flux. Atmospheric horizontal vapour fluxes have received enlarged attention during recent years, but they need and deserve much more attention. Study of vapour-flux diver- gences is one aerological method for indirect deter- mination of precipitation and evaporation. Stations for the determination of vertically integrated fluxes, however, are far too few for hydrological purposes.

Atmospheric vapour fluxes are primarily a concern of the aerologist. Nevertheless the phe- nomenon has great interest and importance for w ater-balance studies.

Precipitation. Developed areas of the world have accumulated considerable stores of data on pre- cipitation. Coverage is not uniform, however, and data are scarce for high-altitude areas. More- over, data are scarce to non-existent for vast areas in the continents. Lack of data is a serious hin- drance to planning and development for these areas. Improvement of precipitation networks is a high-priority item in the world water-balance study.

Runof. Estimates of world-wide runoff to the sea are based heavily on extrapolation because a consid- erable percentage of runoff is not directly measured.

Even in developed areas, few rivers are measured at their mouths. O n e reason for this is methodolo- gical. Most so-called river-mouth measurements actually are made up-stream above the limit of tidal inñuence. The Potomac river of North Amer- ica, for example, is gauged about 140 k m above the mouth. The gauge on the Amazon at Obidos is about 680 k m above the mouth. About 14 per cent of the Amazon’s total flow is derived from the drainage area below the gauge.

M a n y other examples could be cited, but the point is evident that knowledge of river discharge is quite inadequate. This applies not only to dis- charge at the mouths but, in many countries, to discharge at points in the interiors of the continents.

Interior discharge is important not only for local water management and the study of local water balances, but for regional balances of basins that occupy more than one country.

Infiltration; deep percolation. Infiltration and deep percolation are largely unmeasured-again, for methodological reasons. Knowledge about them is important for local study but in large-scale balance studies during long periods they can be ignored.

Recharge, underflow and discharge of ground water.

The remarks about infiltration and deep percola- tion apply equally here, except that no balance equation properly accounts for ground-water dis- charge directly to the sea. The amount of such discharge must be very small, compared to stream- flow. However, in some local areas it is known to be relatively large.

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5 Methods of investigation

Measurement

Instruments and techniques for measurement of hydrological parameters range from reasonably satisfactory to wholly inadequate. For example, it might seem that rainfall would be simple to measure, but standard instruments are unreliable and biased under nearly all conditions.

Similar statements could be made for evaporimeters, in spite of great progress in the development of sensitive weighing evaporimeters.

W e shall not belabour the subject of the short- comings of classical types of instruments and techniques. Standardization is receiving the attention of several international groups and we wish only to emphasize its importance. Comparability of results is the important need.

W e stress also the importance of research and development or adaptation of new technology for hydrological purposes. The International Atomic Energy Agency has sponsored or catalysed a great deal of work on the application of nuclear techniques in hydrological studies. Much of this study bas concerned micro- and meso-scaie phenomena : tracers, moisture probes, snow measurements, and many others. O n the macro-scale the study of airborne nuclides and their precipitation has yielded important data on large-scale phenomena. This is an example of adaptation of technology and its continuation should be encouraged.

Some other adaptations are less advanced but hold considerable promise. Among these are remote-sensing instruments and techniques.

Remote sensing. Many remote-sensing techniques have been used with airborne instruments and their practicality has been demonstrated. Considerable work has been done also to evaluate their potential use in orbiting or sun-synchronous satellites. All

these methods depend on some segment of the electromagnetic spectrum (Parker and Wolff, 1965).

The familiar techniques of black-and-white and colour photography willnever be wholly displaced.

By photography, for example, a flood can be accurately mapped while it is in progress and at successive stages. O n the other hand, infra-red photography and scanning are superior to classical photography for many purposes. A photograph, for example, commonly does not define a shoreline sharply, especially where the adjacent sea or lake floor is shallow. The camera sees through the shallow water and photographs the bottom. Infra- red photography is superior because infra-red rays penetrate the water only slightly and they give sharp definition of the shoreline. The atmosphere is opaque to some wavelengths of infra-red, owing to absorption by water vapour. However, there are two so-called windows in the atmosphere for wavelengths of 3 to 5 and 8 to 14 microns.

These wavelengths are suitable for infra-red scanning, as distinguished from photography. The scanning equipment electronically converts the photograph.

Infra-red radiation has been used with great success also to map ocean currents, the movement and dispersion of heat and pollution loads in water, the occurrence of shoreline and submarine springs, snow and ice cover, areas wetted by storms, the occurrence and distribution of diseased vegetation, the distribution of certain kinds of soils and geological formations, and many other phenomena.

This mapping depends on temperature distribution in the area photographed. The infra-red sensor can detect temperature differences of as little as a small fraction of a degree.

There seem to be real prospects for the use of infra-red sensing as a means of determining radiatior, sefi& t= ax ; m o n o i L i # u g ” th-t C I I U C v e c e m h l e s I L . . u ~ L I I ” I ” 2

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Scientific framework of world water balance

rainfall patterns in sparsely settled areas, monitor- ing soil moisture in unvegetated areas (Rose and Thomas, 1968), and possibly as a basis for computing evaporation from bare areas and grassland.

Aeroplanes can carry sensors to heights up to about 17 km. For greater heights, satellites are necessary. For some purposes it may be desirable to replace aeroplanes with satellites. Routine repe- titive surveys with aeroplanes are expensive because each overflight costs the same amount. The initial cost of a satellite is high but, once it is operational, production of data ad infinitum costs very little.

Infra-red photography and imagery are more advanced than some other remote-sensing techniques, but the possibilities are not limited to that range of the electromagnetic spectrum. Radar scanning and imagery of topography and drainage patterns have yielded some striking results. Other sectors of the non-visible spectrum also are under study.

Analytical methodology

Classical analytical methods in hydrology relied heavily on long historical records. Recognizing the random nature of hydrological events, these events were evaluated in terms of statistical probability of recurrence. Long records were needed also to compute mean values.

Modern methods involving the use of stochastic or deterministic mathematical models make it possible to generate hypothetical long-term records on the basis of short-term real records, and to extrapolate to ungauged catchments. These methods should help to solve the data problem for areas where long-term records are scarce or lacking.

Wide use of these methods would be a great contribution to studies of water balances.

Water-balance computations. In general, the use of a water-balance technique implies measurements of all relevant storages and fluxes listed in Table 1, but it is usual to eliminate the need for some measurements by appropriate selection of the volume and the period of time for which the equation willbe applied. Taking all applications into account, the number of possible combinations of parameters and time scales is very large, and examples will be given here only of large-scale balances.

In the following equations, the symbols given with the list of parameters refer to an average value per unit area of the region considered. The symbol A denotes change in storage over the period considered, and the symbol

$

indicates integration around a boundary of length A enclosing an area A.

Atmosphere

(1) The residence time of atmospheric water is very short (of the order of a few days), so the last term becomes negligible for long periods. Thus, for periods of one month or more, the equation becomes

E - P = ? $ d A (2) This is the basis of the aerological method for determining the difference between evaporation and precipitation. The right-hand side of equation (2) can be substituted for (E- P) in any of the following equations relating to extended periods of time, and it can be used as a rough check on the accuracy of conventional measurements of precipitation and evaporation. As a working tool in water-balance computations, it has most promise for estimating (E-P) over the oceans; for these areas the prospects of radical improvements in conventional observations seem less promising than improvements in the network of coastal aerological measurement stations.

Oceans

where R a and Gdo are runoff and ground-water discharge into the oceans.

The last two terms on the left side of the equation are relatively small, and for periods of a year or more, AO may be neglected, in the absence of evidence of a general rise or fall of mean sea level.

Significantly large ground-water discharge to the oceans will be mainly from large ground-water reservoirs with comparatively long residence times (of the order of a few to hundreds of years). There- fore, it can be assumed that Gdo will be constant

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Methods of investigation

from year to year. The best prospects for determining G d o appear to lie in studies of temperature or chemical composition of water in outflow areas on the ocean floor.

Continents and large islands

For any period, changes in storage of biological water willbe negligible compared with the other terms, and AB may be omitted from the equation.

For periods of one year or more, changes in all storages above ground water will be small compared with the other terms. Therefore, for annual and long-term balances

If there is evidence that major ground-water storages are in long-term equilibrium with inputs and outputs, then AG may also be omitted from equation (5).

Large river basins

P = R

+

E f AL

+

A V

+

AS

+

AB

+

AA4

+

AG

+

^Gnet (6) where G,,, is the net discharge of ground water from the basin.

As before, AB may be neglected for all cases, and for periods of one year or more changes in river channel storage a h iiiaj: bc negkcted. The annual balance may then be expressed as

For the particular case where the boundaries of a ground-water aquifer coincide with the surface catchment (the ‘closed’ basin), and where all ground-water discharge appears as base flow, Gnet = O. In this situation, assuming no trend in piezometric levels, the equation for the long-term balance is

P 1 R i - E (7)

Lakes

where Rnet is the difference between surface inflow and outflow, and Gnet is the difference between subsurface outflow and inflow. It will not usually be possible to neglect AL over periods of one year or less, but the long-term balance will be

When a lake is ephemeral, the short-term situation is much more complex, because the area of water surface varies through a wide range. For that reason it is necessary to account for variations in soil moisture and vadose water near the edges of the lake.

Swamps. Similar equations can be used for swamps, although the details of the computations may be different.

Frozen water. Glaciologists have developed special methods for computing the mass balances of glaciers and ice caps. These methods are described in guidance material prepared by the International Commission of Snow and Ice of the International Association of Scientific Hydrology.

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6 Conclusion and recommendations

In the light of the foregoing discussion, the Panel reached the conclusion that the objectives of the World Water Balance Programme should be actively pursued along three main lines: (a) Synthesis of existing data; (b) Accumulation of new data;

(c) Development of new approaches.

Specific recommendations will be made under each of these headings. Further recommendations refer to the need for international co-operation in the World Water Balance Programme.

Synthesis of existing data

All available data should be used to obtain the best possible approximations of long-term (and annual, if possible) water balances for river basins, countries, large natural regions, and continents, in that order. T o this end, National Committees should be encouraged to: (a) develop water balances for their own territory, seeking technical assistance, if required, for this task; (b) co-operate with National Committees of neighbouring countries in the development of water balances for international river basins and natural regions.

The proposed project for preparation of world evaporation and precipitation maps should be activated. Consideration should be given also to the preparation of a world runoff map at the same scale.

The type of projection of base maps, isoplethic intervals, and other matters also should receive attention.

As an example of a co-operative study in a region where the quantity of existing data is relatively high, a co-ordinated water-balance estimate should be developed for Europe.

Existing aerological data for large regions should be synthesized into annual maps of P-E for com- parison with the results of classical techniques. This

work should be co-ordinated by the World Meteoro- logical Organization.

The inventory of large lakes of the world should be completed as soon as possible.

National Committees should be encouraged to prepare maps showing existing information on the extent and nature of ground-water resources, taking account of recommendations concerning hydrological maps.

Although many publications deal with methods of computation of water balances, preparation of a general methodological guide may help national studies and improve the comparability of results.

Accumulation of new data

Improvement in the areal coverage of many existing data networks should be undertaken as a high priority need.

In the expansion of data networks, emphasis should be given to the standards of accuracy and reliabi- lity of new instruments. Where direct measurements of a variable are impracticable, adequate calibration should be undertaken to ensure the comparability of results obtained in different countries.

In both these tasks the contribution of the WWW (World Weather Watch) should be recognized in relation to the atmospheric aspects of the hydrological cycle. Where appropriate, measurements of the land phases of the cycle could be related to the WWW network.

Adequate data networks may not be practicable in some areas, and advantage should be taken of remote-sensing techniques to fill the gaps in these areas.

Particular attention should be given to improvement of the state of knowledge on ground water, soil moisture and lakes.

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Conclusion and recommendations

The efforts of the World Meteorological Orga- nization and the International Oceanographic Commission to improve estimates of precipitation and evaporation over the oceans should be sup- ported.

Support should be given to studies of snow and ice, including the hydrology of glaciers.

Study should be encouraged of the geochemical cycling of water in minerals, of the origin of waters of the earth, and of the causes of recent and current oscillations of mean sea level.

models to the much larger scale meteorological models.

A continuing study should be made of developments of remote sensing relevant to the assessment of water balances and heat balances, giving particular attention to the integration of these techniques with data obtained from existing networks.

The study of heat balances should be actively pursued, particularly in relation to the estimation of evaporation from large areas of land.

International co-operation Development of new approaches

The importance to the World Water Balance Programme ofGARP(Globa1 Atmospheric Research Programme), in developing mathematical models of global atmospheric circulation, must be empha- sized. As the long-term aim of the World Water Balance Programme should be to develop a combined hydrological-meteorological model, an initial study should be undertaken of the problems in relating existing small-scale hydrological

National Committees should be encouraged to co-ordinate their efforts with the Nationai C o m - mittees of neighbouring countries. The World Water Balance Programme can be a model for improved scientific co-operation between nations.

As the world water balance involves all phases of the hydrological cycle, it requires study by all relevant disciplines. International agencies should co-operate in this programme with the aim of ensuring the maximum of interdisciplinary effort.

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