EARLIEST CONCEPTS: THE ATMOSPHERIC WATER CYCLE

For as long as humans have been on Earth, they must have been acutely aware of their dependency on different forms of water in their environment. Water was literally vital for their health and sustenance but it could also be destructive and even lethal in severe weather, floods, and the other hazards they faced in their daily lives. Already in the earliest writings there are indications that among natural peoples in their primal stage it was a common notion that water in nature moves continually between different states in some repetitive, if not cyclical, fashion. Whatever is left of these early writings is not always easy to interpret, mainly because the meanings of even the most elementary concepts have evolved in the meantime. Nor is it always easy to distinguish profane views and naturalistic descriptions from the more sacred narratives and religious interpretations. Nevertheless, a cursory scan of some better known early writings yields several instances of water related imagery even in widely different cultural settings, in which the evidence is fairly clear, and which provide some idea on the thinking of early humans.

As early as the eighth century BCE in Greece, the poet Hesiod presented a remarkable description. In a passage with advice to farmers to get dressed warmly and to finish the work in time (Hésiode, 1928; also Hesiod, 1978; vv. 547–553), he wrote the following.

DEFINITION AND SCOPE

Hydrology is literally the science of water. Etymologically, the word has its roots in ancient Greek, and is a composite, made up of ὕδωρ, water, and λόγος, word. Obviously, defined this way, the term is much too broad to be very useful, as it would have ramifications in all scientific disciplines.

Actually, the word hydrology has not always been well defined and even as recently as the 1960s it was not very clear exactly what hydrology was supposed to cover and encompass. Price and Heindl (1968), in a survey of many of the definitions that had appeared in the literature over the previous 100 years, were compelled to conclude that the question “What is Hydrology?” had not been resolved by their review. Still, they felt that, in general, there seemed to be a consensus that hydrology is a physical science, which is concerned mainly with the water cycle of land and near-shore areas; moreover, there had been a tendency to broaden the term rather than to narrow it, even to the point of including socio-economic aspects.

Over the past few decades, however, with the growing activity level and the increasing maturity of this field of endeavor, a more precise definition has emerged.

In terms of the water quantities transported on a global basis, evaporation is the second most important component of the hydrologic cycle, after precipitation. The general climatology of the hydrologic cycle reviewed in Chapter 1, indicates that over the landsurfaces of the Earth evaporation amounts on average to approximately 60% to 65% of the average precipitation. But this estimate provides only an idea of the order of magnitude to be expected; the actual evaporation rate at any given time and place is likely to be quite different from the climatological mean, and more thorough analysis is often called for.

EVAPORATION MECHANISMS

As a physical phenomenon, evaporation is the transition of water from the liquid phase to the vapor phase. This transition requires first, an energy supply to provide water molecules the necessary kinetic energy to escape from the liquid surface; and second, some mechanism to remove the escaped molecules from the immediate vicinity of the liquid surface thus preventing that they would return to condense (see Figure 4.1). These two requirements have traditionally given rise to two classes of methods to describe evaporation, namely

1. (i) mass transfer or aerodynamic formulations, which consist primarily of the description of the water vapor transport mechanisms in the near-surface air of the atmosphere, and

2. (ii) energy budget formulations, in which the main focus is on the energy supply aspects of the phenomenon.

Water in its different forms has always been a source of wonder, curiosity and practical concern for humans everywhere. The goal of this book is to present a coherent introduction to some of the concepts and relationships needed to describe the distribution and transport of water in the natural environment. Thus it is an attempt to provide a more thorough understanding, and to connect the major paradigms that bear upon the hydrologic cycle, that is the never-ending circulation of water over the continents of the Earth.

Continental water transport processes take place above, on and below the Earth's landsurfaces. Accordingly, in Part I, water is considered as it passes through the lower atmosphere; this part consists of a general description of atmospheric transport in Chapter 2, followed by the application of these concepts to precipitation and evaporation in Chapters 3 and 4, respectively. In Part II, water transport on the Earth's surface is dealt with; this part consists of a general description of the hydraulics of free surface flow in Chapter 5, which is then applied to overland runoff and streamflow routing in rivers in Chapters 6 and 7, respectively. Water below the surface is the subject of Part III; again, a general introduction to flow in porous materials in Chapter 8 is followed by applications to phenomena involving infiltration and capillary rise in Chapter 9, and groundwater drainage and baseflow in Chapter 10.

In this chapter different formulations are considered that are available to transform the lumped water input by rainfall or melt events directly into streamflow output from the catchment area. The basic philosophy of this type of approach is that the physical processes are assumed to take place at the scale of the catchment, without consideration for the detailed subscale processes or for the intricacies of the flow paths inside the watershed. In a sense, this is analogous with the view espoused in continuum mechanics or thermodynamics (albeit in their own respective scale ranges), where only the “macro” or “everyday” properties of the fluids are taken into account, without consideration of their properties at the molecular or nuclear scales. Because by far most applications of the lumped approach in the past have been based on the assumptions of linearity and stationarity, these will be treated first and in greatest detail.

STATIONARY LINEAR RESPONSE: THE UNIT HYDROGRAPH

Basic concept

Definition

The unit hydrograph, or unit graph, can be defined as the hydrograph of unit volume of storm runoff produced by a unit volume of uniform (in space and in time) intensity excess rainfall over a unit period Du, with the basic assumptions of linearity and time invariance. As defined here, the unit hydrograph is the response function of a linear system, which is treated in more general terms in the Appendix, and can be denoted by u(Du; t).

Owing to the irregular topography of the Earth's continents, surface runoff, that is the flow of water over land, takes place in many different ways. When for some reason, such as rainfall, snowmelt, the overtopping of small depressions, or the emergence of groundwater at a source, surface flow is initiated, it may at first proceed as a thin sheet flow; however, as a result of local irregularities, the flow soon gathers in small gullies and rills, which in turn join to form rivulets in the fashion of a tree-like network. Eventually these merge with others to become larger rivers, which finally end up in some lake or in the ocean. Thus the flow system consists of an intricate combination of many different types of flow regimes, in channels of different geometries and sizes. For purposes of analysis, to describe the basic hydraulic elements of landsurface runoff, it is convenient and useful to distinguish between two major types of free surface flow; these are first, sheet flow or overland flow, which is most likely to occur under conditions of heavy precipitation in source areas where runoff is being generated which feeds into streams; and second, the flow that occurs in larger permanent open channels. Both types of flow are usually unsteady and spatially varied. In this chapter a general description is given of free surface flow. The general principles are then applied to overland flow and to channel flow and streamflow routing in the next two chapters.

On account of the short residence time and great mobility of water vapor in air, the lower atmosphere is one of the critical pathways in the global hydrologic cycle; it transports water and energy around the globe without regard to continental boundaries and thus links the continents, the upper atmosphere, and the oceans. The transport and distribution of water vapor in the lower atmosphere, where it is most abundantly present, are among the main factors controlling precipitation and evaporation from the surface; these processes, in turn, determine soil and groundwater storage and the different runoff phenomena.

WATER VAPOR IN AIR

Global features

The global amount of water vapor contained in the air is roughly (see Table 1.3) equivalent with a layer of liquid water covering the earth, with a thickness of around 25 mm on average. The thickness of this layer, which is the total liquid equivalent of water vapor in the atmospheric column at a given location, is also called the precipitable water, Wp. However, this quantity of water vapor is not distributed uniformly and it can greatly vary over a wide range of scales in space and in time. For instance, the water vapor content of the atmosphere, just like the temperature, generally tends to decrease with increasing latitude. Available data (Randel et al., 1996) show that the precipitable water is more likely to be well below 5 mm near the Poles, and close to 50 mm near the Equator.

Also called flood routing and channel routing, this is one of the classical problems in applied hydrology. The word routing refers in general to the mathematical procedure of tracking or following water movement from one place to another; as such, the word also includes the description of the conversion of precipitation into various subsurface and surface runoff phenomena. However, streamflow routing refers specifically to the description of the behavior of a flood wave as it moves along in a well-defined open channel. In practical terms, the problem consists of the determination of the discharge hydrograph Q = Q(t) at a given point along a stream, from a known hydrograph further up- or downstream and from a knowledge of the physical characteristics of the channel. The wave may be the result of inflows into the channel following various events such as heavy rainfall, snowmelt, failure or overtopping of natural or artificial dams due to landslides or earthquakes, tidal interactions and releases from artificial reservoirs.

Over the years different methods have evolved. The more fundamental approaches are based on hydraulic theory of open channel flow and consist of ad-hoc solutions of some form of the complete shallow water equations by numerical techniques on digital computer. A detailed treatment of such techniques is beyond the scope of this book and good reviews of available methods to solve the complete Saint Venant equations have been presented by, among others, Liggett and Cunge (1975) and others in Mahmood and Yevjevich (1975), Cunge et al. (1980), and Montes (1998).

Because the entire hydrologic cycle is basically driven by it, precipitation has to be considered the main component. Indeed, it is a truism that wherever there is no precipitation, there is also not much of a hydrologic cycle. The detailed study of precipitation and of all its aspects is properly the domain of meteorology. In hydrology, precipitation is primarily of interest after it reaches the ground surface, and this is reflected in the organization of this chapter. However, to gain a better understanding of the occurrence and distribution of precipitation and its temporal and spatial scales, it is also useful to have a knowledge of at least some elementary aspects of its generation mechanisms and of its major types.

FORMATION OF PRECIPITATION

Mechanisms

Several processes take place jointly in the formation of precipitation. In brief, these are the production of supersaturation of the air, condensation of water vapor into ice crystals and droplets, the subsequent growth of these condensation products, and the supply of moist air to where the first three processes occur. These processes involve a number of different mechanisms, which are briefly reviewed in what follows.

Cooling of the air

As indicated in the previous chapter, the water-holding capacity of air decreases, as its temperature decreases. Thus, air can become supersaturated by being cooled down.

This chapter deals with the flow of water in the partly saturated zone of the near-surface soil, and with the transfer through the atmosphere–soil interface. At the local scale, as precipitated water reaches the ground surface, infiltration into the soil takes place. In between precipitation events, the atmosphere exerts its drying effect, and the water in the soil profile may move to the surface by vapor diffusion and by liquid capillary rise, where it evaporates.

As illustrated in Figure 8.23, a small decrease in water content below saturation can cause a significant decrease in conductivity, so that in most soils the difference in hydraulic conductivity above and below the water table can be large. At an interface between soils with different conductivities, the streamlines are known to exhibit a pronounced refraction; therefore, in many situations unsaturated flow above the water table can be assumed to be nearly vertical, whereas the saturated flow below the water table can be assumed to be more horizontal or parallel to underlying impervious layers. Accordingly, in this chapter, infiltration and related flow phenomena in the partly saturated zone of the soil are analyzed in a one-dimensional vertical framework. Similarly, in Chapter 10, it is shown how many saturated flow situations can be analyzed in the one-dimensional framework of hydraulic groundwater theory. Because the infiltration capacity constitutes an upper limit of maximal rate of entry into the soil, it is treated first in Sections 9.2 and 9.3; rain infiltration is treated in Section 9.4.