The hydrological cycle and hydrometeorology

The history of the evolution of hydrology as a multi-disciplinary subject, dealing with the occurrence, circulation and distribution of the waters of the Earth, has been presented by Biswas (1970). Man's need for water to sustain life and grow food crops was well appreciated throughout the world wherever early civilization developed. Detailed knowledge of the water management practices of the Sumarians and Egyptians in the Middle East, of the Chinese along the banks of the Hwang-Ho and of the Aztecs in South America continues to grow as archaeologists uncover and interpret the artefacts of such centres of cultural development. It was the Greek philosophers who were the first serious students of hydrology, and thereafter, scholars continued to advance the understanding of the separate phases of water in the natural environment. However, it was not until the seventeenth century that the work of the Frenchman, Perrault, provided convincing evidence of the form of the hydrological cycle which is currently accepted: measurements of rainfall and river flow in the catchment of the upper Seine published in 1694 (Dooge, 1959) proved that quantities of rainfall were sufficient to sustain river flow.

Hydrology as an academic subject became established within institutions of higher education in the 1940s. Valuable research contributions to the subject had been reported earlier but the expansion in the more widespread applications of hydrology resulted in at least five textbooks being published in that decade in the United States.

Over the last 50 years, advances in sensor technology coupled with the development of numerical models representing hydrological processes have led to a reappraisal of the content and definition of hydrology. Today's scientific hydrologists and engineering hydrologists now appreciate the need to combine accurate field measurement with appropriate numerical models. Equally, there is an awareness of the controlling influence of hydrometeorology on the water pathways that comprise the hydrological cycle at catchment and global scales.

1.1 The hydrological cycle and water pathways

The driving force of the natural circulation of water is derived from the radiant energy received from the Sun. The bulk of the Earth's water is stored on the surface in the oceans (Table 1.1) and hence it is logical to consider the hydrological cycle as beginning with the direct effect of the Sun's radiation on this largest reservoir. Heating of the sea surface causes evaporation, the transfer of water from the liquid to the gaseous

Table 1.1 One estimate of global water distribution

Store

Volume (1000 km3)

Per cent of

Per cent of

total water

fresh water

Oceans, seas and bays

1 338 000

96.5

_

Ice caps, glaciers and permanent snow

24064

1.74

68.7

Groundwater

23 400

1.7

-

Fresh

(10 530)

(0.76)

30.1

Saline

(12 870)

(0.94)

-

Soil moisture

16.5

0.001

0.05

Ground ice and permafrost

300

0.022

0.86

Lakes

176.4

0.013

-

Fresh

(91.0)

(0.007)

0.26

Saline

(85.4)

(0.006)

-

Atmosphere

12.9

0.001

0.04

Swamp water

11.47

0.0008

0.03

Rivers

2.12

0.0002

0.006

Biological water

1.12

0.0001

0.003

Source: Gleick, P. H. (1996) Water resources. In Encyclopedia of Climate and Weather, ed. by S. H. Schneider, Oxford University Press, New York, vol. 2, pp. 817-823.

Source: Gleick, P. H. (1996) Water resources. In Encyclopedia of Climate and Weather, ed. by S. H. Schneider, Oxford University Press, New York, vol. 2, pp. 817-823.

state, to form part of the atmosphere. It remains mainly unseen in atmospheric storage for an average of 10 days. Through a combination of circumstances, the water vapour changes back to the liquid state again through the process of condensation to form clouds and, with favourable atmospheric conditions, precipitation (rain, snow, etc.) is produced either to return directly to the ocean storage or to embark on a more devious route to the oceans via the land surface. Snow may accumulate in polar regions or on high mountains and consolidate into ice, in which state water may be stored naturally for very long periods. In more temperate lands, rainfall may be intercepted by vegetation from which some of the intercepted water may return at once to the air by wet-canopy evaporation. A significant proportion of the rainfall that reaches the land surface will return to the atmosphere by transpiration via plants, while the remainder travels over or beneath the land surface towards rivers by mechanisms described as runoff1 generation pathways.

1.2 Pathways generating river flow

In the later nineteenth and early twentieth century, it began to be recognised that different parts of a catchment area might produce different amounts of river flow. Again this was perhaps expressed first in France in the work of Imbeaux in a study of the Durance basin published in 1892. He tried to take account of the role of river flow generation at different distances from a catchment outlet in controlling the shape of the hydrograph, and of elevation in controlling the patterns of snowmelt during the melt season. The idea of delay in runoff reaching the catchment outlet can be represented in terms of a time-area histogram. It was later developed into the first storm event rainfall to river flow model to be widely used around the world that we now know as the unit hydrograph (see Section 12.5).

Use of the unit hydrograph for practical applications, however, requires that we try to estimate the proportion of storm rainfall that contributes to the storm hydrograph for a particular event (i.e. that river flow which appears soon after rainfall). It has long been known that not all the rainfall falling in an event contributes to the storm hydrograph. Some contributes to a much slower subsurface pathway or is lost back to the atmosphere by evapo-transpiration. Thus application of the unit hydrograph concepts required a rather arbitrary separation of the hydrograph into so-called stormflow and baseflow. This led to a rather easy assumption that the storm runoff in a river was made up of rainfall from the particular rain-event or snowmelt water.

In fact we now know that the situation is somewhat more complicated than that easy assumption because analyses of environmental tracers since the 1970s have shown that, in many environments, not all the storm hydrograph is made up of rainfall that fell in that storm (see Section 11.3). Some of the hydrograph comes from water that was already stored in the catchment prior to the rainfall event. That water is displaced from storage into the stream channels during the event as a result of rainfall infiltrating into the subsurface. This is really one of the most important conceptual advances in scientific hydrology since it has very important implications for understanding hillslope hydrology, water quality variations and ecological impacts of storm events.

The history of river flow generation concepts often starts with the ideas of Robert Elmer Horton, probably the most influential American hydrologist of the twentieth century. In a paper published in 1933 (and reproduced in Beven, 2006) Horton first expressed a concept of hillslope hydrology based on the idea that the storm hydrograph is made up of rainfall in excess of the infiltration capacity of the soil. This is the concept of infiltration excess (or Hortonian) overland flow. This idea leads to a nice simple interpretation of catchment response. If we know the volume of rainfall in an event, and we know the volume of stormflow (here meaning that river flow proportion above the hydrograph separation line; Fig. 12.5, Section 12.3) recorded at a river gauging site, then the difference must be what was infiltrated (on average) into the soil. This allows the infiltration capacity of the soil to be back-calculated (subject to some simple assumptions of how it might vary over time). This information can then be used in a simple runoff model to predict what might happen under different conditions. Combining this prediction of how much runoff will be generated by a given rainfall, and the unit hydrograph to predict the timing of the runoff is a technique that is still used to the present day (it still underlies some aspects of the UK Flood Estimation Handbook, for example, see Chapter 16).

The problem is, of course, that it is wrong. Some catchments in arid areas under high rainfall intensities, or the extreme case of impermeable surfaces in urban areas, might work like this, though even then it is unlikely that infiltration excess overland flow will occur everywhere, and overland flow generated on one part of a slope might later infiltrate further downslope. It is even unlikely that Horton saw this type of infiltration-excess overland flow in his own experimental catchment in New York State (Beven, 2004). However, as we have already noted, in very many catchments, much of the storm hydrograph is made up of displaced pre-event storage. Thus, other concepts of river flow generation are needed.

The first real reconsideration of the Hortonian concept was by Roger P. Betson in 1964. Betson worked for the Tennessee Valley Authority in the United States and realised that in the forested catchments of the Appalachians, there was no way that infiltration excess overland flow could occur everywhere, except perhaps in the most extreme rainfall events. He therefore suggested that overland flow would be generated on only part of the hillslopes and that since infiltration rates of soils tend to be lower when the soil is wetter (Section 5.1.1) and, as a result of downslope flows between events, soils will tend to be wetter in the lower parts of hillslopes, then the runoff generation would be most likely at the bottom of hillslopes close to the stream channels. He inferred from the analyses of storm runoff volumes that the proportion of the catchment generating overland flow could be quite small (as low as 2-4 per cent) in some catchments.

At about the same time, John Hewlett, working at the Coweeta catchments in North Carolina, suggested that the infiltration capacities of the soils in that area were so large that it was extremely unlikely that any runoff would be seen over the surface of the soil. Yet storm hydrographs were still recorded. He suggested that the storm runoff therefore must be generated by subsurface flows and by rainfall directly on to the stream channel and immediate riverside area. He also suggested that the water contributing to the river was not necessarily the rainfall, invoking a concept of so-called 'translatory flow' to explain the displacement of stored water by the infiltration of the rainwater. In fact, a previous Director of the Coweeta Laboratory, Charles Hursh, had expressed much the same idea in the 1930s, and had coined the term subsurface stormflow for this type of river flow generation mechanism. The concept of translatory flow had also already been mentioned in the 1930s but these concepts had been dominated by the Hortonian paradigm in the later engineering literature.

There are some circumstances, however, when overland flow can be generated on soils with high infiltration capacities. This is when the soil becomes saturated by a combination of downslope flow within a hillslope and rain falling on saturated areas. In fact, downslope flows can maintain the lower parts of hillslopes at, or close to, saturation for long periods of time in some circumstances, so that only small amounts of rainwater might be required before overland flow is generated. This will particularly be the case in relatively shallow soils overlying an impermeable base, and where there are convergent flow lines into the hillslope hollows. This was first demonstrated by the work of Tom Dunne in the Sleepers River catchments in Vermont in the late 1960s. He showed how saturated areas in the catchment could persist for long periods of time, how they varied seasonally, being most extensive at the end of the snowmelt season in Vermont, and how they were largely controlled by the patterns of downslope flow on the hillslopes. This type of overland flow became known as saturation overland flow that was generated on a variable contributing area in the catchment. In some cases the resulting overland flow will also have a component of return flow, which subsurface water forced back on to the surface through a seepage face; and one of the earliest studies of environmental tracers in storm runoff, by Mike Sklash and Bob Farvolden (1979), provided evidence to reinforce this concept. In an area of river flow generation in one of their study catchments, they showed that tracer concentrations were sometimes indicative of a rainfall source and at other times indicative of a subsurface, pre-event storage source.

Work elsewhere has revealed further complications. Darrell Weyman (1970) working in the East Twin catchment in the Mendips, UK, showed that saturated contributing areas could arise without the soil being completely saturated but where saturation built up above a soil horizon of lower permeability. He also showed that subsurface contributions to the stream channel could be hugely variable in space and might be associated with zones of higher soil permeability within a very heterogeneous soil. Bunting (1961) had earlier called such preferential pathways percolines and he treated them as a subsurface extension of the dendritic (tree-like) channel network. Recent modelling work has shown how, in heterogeneous soils, subsurface flow might be simulated as being channelled into channel network-like structures (e.g. Weiler and McDonnell, 2004), while tracer work has shown that, in some catchments, fast responding subsurface pipes produce storm runoff that may be made up predominantly of pre-event stored water rather than rainwater (Sklash et al., 1996).

It is perhaps worth finishing this brief summary of river flow generation pathways by saying that the different major concepts shown in Fig. 1.1 are not mutually exclusive. They might all occur in different events in the same catchment, or in the same event in different parts of a catchment, depending on the rainfall intensities; prior wetness of the catchment (antecedent conditions); topography of the hillslopes; type, structure and heterogeneity of the soil, regolith and rock; existence of percolines; channel

Fig. 1.1 River flow generation pathways for systems dominated by (a) infiltration-excess overland flow, (b) saturation overland flow, and (c) subsurface flow.

density; and other factors. An excellent review of where and when different types of runoff production might occur is given by Tom Dunne (1978) and Wilfred Brutseart (2005).

There is an underlying research question about how, over long periods of time, these different factors might be linked to the long-term development of the catchment soils, topography and vegetation cover, and how, in recent times, people might have affected the nature of the river flow generation processes through land management practices and urbanisation. Such questions are not yet fully resolved, and it is perhaps unlikely that they will ever be properly resolved given the complexities of short-term and long-term changes to which catchments have been subjected in different environments.

Fortunately, this is not a barrier to hydrological analysis and prediction. In many cases we are only interested in predicting river flow, and do not need to worry too much about the water pathways. This is one reason why unit hydrograph concepts have survived so long: if we can match river flow volumes and timings using these simple concepts, then we may be able to make some useful predictions even if the details of the pathways are incorrect. There are situations, however, particularly in understanding water quality variations, where it may be critical to appreciate the different surface and subsurface pathways. In such cases, an appreciation for the different mechanisms of river flow generation described above will be important. We will return to this in the discussion of predictive rainfall-runoff models in Chapter 12. First, we need to give an overview of how hydrometeorology regulates these river flow generation pathways and the pathways of evapo-transpiration (Chapter 10).

1.3 Hydrometeorological control of hydrological pathways

The science of meteorology has long been recognised as a separate discipline, though students of the subject usually come to it from a rigorous training in physics or mathematics. The study of hydrometeorology may be seen as a branch of hydrology linking the fundamental knowledge of the meteorologist with the needs of the hydrologist. In this text, hydrometeorology is taken to be the study of precipitation and evaporation, the two fundamental phases in the hydrological cycle, which involve processes in the atmosphere, and at the Earth's surface/atmosphere interface.

The hydrologist will usually be able to call upon the services of a professional meteorologist for weather forecasts and for special studies, e.g. the magnitude of extreme rainfalls. However, a general understanding of precipitation and evaporation is essential if the hydrologist is to appreciate the complexities of the atmosphere and the difficulties that the meteorologist often has in providing answers to questions of quantities and timing. A description of the properties of the atmosphere and of the main features of solar radiation will provide the bases for considering the physics of evaporation and the formation of precipitation.

1.3.1 The atmosphere

The atmosphere forms a distinctive protective layer about 100 km thick around the Earth. Although both air pressure and density decrease rapidly and continuously with

Fig. 1.2 Structure of the atmosphere. (Adapted from Strangeways, I. (2007) Precipitation: Theory, Measurement and Distribution, Cambridge University Press, Cambridge.)

increasing altitude, the temperature varies in an irregular but characteristic way. The layers of the atmosphere, 'spheres', are defined by this temperature profile. After a general decrease in temperature through the troposphere (Fig. 1.2), the rise in temperature from heights of 20-50 km is caused by a layer of ozone, which absorbs short-wave solar radiation, releasing some of the energy as heat.

To the hydrologist, the troposphere is the most important layer because it contains 75 per cent of the weight of the atmosphere and virtually all its moisture. The meteorologist, however, is becoming increasingly interested in the stratosphere and mesosphere, since it is in these outer regions that some of the disturbances affecting the troposphere and the Earth's surface have their origins.

The height of the tropopause, the boundary zone between the troposphere and the stratosphere, is at about 11 km, but this is an average figure, which ranges from about 8 km at the Poles to about 16 km at the Equator. Seasonal variations also are caused by changes in pressure and air temperature in the atmosphere. In general, when surface temperatures are high and there is a high sea-level pressure, then there is a tendency for the tropopause to be at a high level. On average, the temperature from ground level to the tropopause falls steadily with increasing altitude at the rate of 6.5° Ckm-1. This is known as the lapse rate. Some of the more hydrologically pertinent characteristics of the atmosphere as a whole are now defined in more precise terms.

1.3.1.1 Atmospheric pressure and density

The meteorologist's definition of atmospheric pressure is 'the weight of a column of air of unit area of cross-section from the level of measurement to the top of the atmosphere'. More specifically, pressure may be considered to be the downward force on a unit horizontal area resulting from the action of gravity (g) on the mass (m) of air vertically above.

At sea level, the average atmospheric pressure (p) is 100 kPa (1 bar or 100 000 N m-2). A pressure of 100 kPa is equivalent to 760 mm of mercury; the average reading on a standard mercury barometer. Measurements of atmospheric pressure are usually given in millibars (mb). It is common meteorological practice to refer to heights in the atmosphere by their average pressure in millibars, e.g. the top of the stratosphere (the stratopause) is at the 1 mb level. The air density (p) may be obtained from the expression p = p/RT, where R is the specific gas constant for dry air (0.29 kJ kg-1 K-1) and TK is the air temperature. At sea level, the average T = 288 K and thus p = 1.2 kg m- 3 (or 1.2 x 10-3 gcm-3) on average at sea level. Air density falls off rapidly with height. Unenclosed air, a compressible fluid, can expand freely, and as pressure and density decrease with height indefinitely, the limit of the atmosphere becomes indeterminate. Within the troposphere however, the lower pressure limit is about 100 mb. At sea level, pressure variations range from about 940 to 1050 mb; the average sea level pressure around the British Isles is 1013 mb. Pressure records form the basis of the meteorologist's synoptic charts with the patterns formed by the isobars (lines of equal pressure) defining areas of high and low pressure (anticyclones and depressions, respectively). Interpretation of the charts plotted from observations made at successive specified times enables the changes in weather systems to be identified and to be forecast ahead. In addition to the sea level measurements, upper air data are plotted and analysed for different levels in the atmosphere.

1.3.1.2 Chemical composition

Dry air has a very consistent chemical composition throughout the atmosphere up to the mesopause at 80 km. The proportions of the major constituents are as shown in Table 1.2. The last category contains small proportions of other inert gases and, of particular importance, the stratospheric layer of ozone which filters the Sun's radiation. Small quantities of hydrocarbons, ammonia and nitrates may also exist temporarily in the atmosphere. Man-made gaseous and particulate pollutants are found particularly in areas of heavy industry, and can have considerable effects on local

Table 1.2 Major constituents of air

Percentage (by mass)

Nitrogen 75.51

Oxygen 23.15

Argon 1.28

Carbon dioxide etc 0.06

weather conditions. Traces of radioactive isotopes from nuclear fission also contaminate the atmosphere. Although there is no evidence that isotopes have a significant effect on weather, their presence has been found useful in tracing the movement of water through the hydrological cycle.

1.3.1.3 Water vapour

The amount of water vapour in the atmosphere (Table 1.3) is directly related to the temperature and thus, although lighter than air, water vapour is restricted to the lower layers of the troposphere because temperature decreases with altitude. The distribution of water vapour also varies over the Earth's surface according to temperature, and is lowest at the Poles and highest in equatorial regions. The water vapour content or humidity of air is usually measured as a vapour pressure, and the units used are millibars (mb).

Several well-recognised physical properties concerned with water in the atmosphere are defined to assist understanding of the complex changes that occur in the meteorological phases of the hydrological cycle.

(a) Saturation. Air is said to be saturated when it contains the maximum amount of water vapour it can hold at its prevailing temperature. The relationship between saturation vapour pressure (e) and air temperature is shown in Fig. 1.3. At typical temperatures near the ground, e ranges from 5 to 50 mb. At any temperature T = T , saturation occurs at corresponding vapour pressure e = e .

Table 1.3 Average water vapour values for latitudes with temperate climates (volume %)

Height (km) Water vapour

CD 40

CD 40

Temperature (°C)

Fig. 1.3 Saturation pressure and air temperature, where ea — ed is the saturation deficit and Td is the dew point temperature.

Temperature (°C)

Fig. 1.3 Saturation pressure and air temperature, where ea — ed is the saturation deficit and Td is the dew point temperature.

Meteorologists acknowledge that saturated air may take up even more water vapour and become supersaturated if it is in contact with liquid water in a sufficiently finely divided state (e.g. very small water droplets in clouds). At sub-zero temperatures, there are two saturation vapour pressure curves, one with respect to water (ew) and one with respect to ice (e,; Fig. 1.3, inset). In the zone between the curves, the air is unsaturated with respect to water but supersaturated with respect to ice. This is a common condition in the atmosphere as will be seen later.

(b) Dew point is the temperature, Td, at which a mass of unsaturated air becomes saturated when cooled, with the pressure remaining constant. In Fig. 1.3, if the air at temperature Ta is cooled to Td, the corresponding saturation vapour pressure, ed, represents the amount of water vapour in the air.

(c) Saturation deficit is the difference between the saturation vapour pressure at air temperature, Ta, and the actual vapour pressure represented by the saturation vapour pressure at Td, the dew point. The saturation deficit, ea — ed, represents the further amount of water vapour that the air can hold at the temperature, Ta, before becoming saturated.

(d) Relative humidity is the relative measure of the amount of moisture in the air to the amount needed to saturate the air at the same temperature, i.e. ed/ea, represented as a percentage. Thus, if Ta = 30° C and Td = 20° C, relative humidity is ej 23 mb

(e) Absolute humidity (pw) is generally expressed as the mass of water vapour per unit volume of air at a given temperature and is equivalent to the water vapour density. Thus, if a volume V m3 of air contains mwv g of water vapour,

Mass of water vapour (g) mwv ^ w Volume of air (m3) V

(f) Specific humidity (SH) relates the mass of water vapour (mwv g) to the mass of moist air (in kg) in a given volume; this is the same as relating the absolute humidity (gm_3) to the density of the same volume of unsaturated air (p kgm_3):

(mwv + md)(kg) p where md is the mass (kg) of the dry air.

(g) Precipitable water is the total amount of water vapour in a column of air expressed as the depth of liquid water in millimetres over the base area of the column. Assessing this amount is a specialised task for the meteorologist. The precipitable water gives an estimate of maximum possible rainfall, though has the unreal assumption of total condensation and neglects the effect of advection.

In a column of unit cross-sectional area, a small thickness, dz, of moist air contains a mass of water given by:

Thus, in a column of air from heights z1 to z2, corresponding to pressures p1 and p2: the total mass of water mw is

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