HYDROLOGICAL CYCLE

There has always been tension between theorists and practitioners of science and engineering. Practitioners are driven by observations and by trial-and-error attempts to make something work. Theorists attempt to develop unifying models to explain natural phenomena. History provides examples of stunning accomplishments for engineered water diversion on a mass scale and heroic efforts to make clean drinking water supplies widely available. It also provides examples where practitioners wasted their time because they ignored important principles, or where theorists neglected key observations and promoted absurd explanations of the world around them. The history of understanding the hydrological cycle provides stunning examples of both successes and failures.

A Brief History

Solar energy is now recognized as the fundamental driver of the hydrologic cycle. Water evaporated from the ocean is transported by air currents into continental interiors, where it can precipitate. Most of this precipitation evaporates and returns to the atmosphere, where it mixes with remnant vapor derived from the ocean, and then moves on. The remaining precipitation recharges rivers and groundwater systems, and driven by gravity, ultimately returns to the ocean. Although this elementary picture is fully accepted today, authoritarian dogma, devoid of an observational basis, impeded recognition of this process for centuries.

Recognition of Earth’s hydrological cycle was based on an ancient and fundamental observation, famously codified in Ecclesiastes 1:7: “All the rivers flow into the sea but the sea is not full; unto the place from where the rivers come, there they return again.” Nevertheless, the details of this cycle were debated for centuries, and many peculiar theories were advanced to explain it. A synopsis follows.

Written records and physical evidence for hydrologic observation from the earliest civilizations reflect the need for practical outcomes to ensure available water for agriculture and navigation. This is well illustrated by the extensive canal systems developed by the Sumerians in Mesopotamia, and by Sanskrit illustrations for construction methods. In China, India, and Egypt meticulous meteorological and water elevation records were gathered to determine the best time to plant. Water development and management was soundly based on observations in these early civilizations, even though these cultures were deeply religious and ritualistic.

Greek civilization differed somewhat due to aspiring philosophers who sought fundamental explanations for the natural world. The earliest philosophers were influenced by mythology, and much of their work on the natural sciences was subsequently integrated into the prolific writings of Aristotle. Unfortunately, Aristotle promoted many erroneous ideas that influenced western thought for more than a thousand years, even though they had no observational basis. Not until the Age of Enlightenment with its observational and mathematical triumphs were more correct explanations of the hydrological cycle to emerge. Some examples of this historical development are useful.

Early Greek philosophers dating back to 7th century BC attempted to explain the origin of water. Thales of Miletos postulated that Earth floated on water, likely drawing on earlier Babylonian and Egyptian beliefs. Anaximander of Miletos argued that water evaporated and transformed into land masses over time. Both philosophers adhered to the belief that all things are derived from a single primary element of nature, congruent to Greek teachings at the time. In contrast Xenophanes of Colophon (6th to 5th century BC) taught that water and wind were derived from the sea and produced clouds, rain, springs and rivers. He argued that fossils observed in rock outcrops on high mountains are remains of animals that once lived beneath the sea. In a step backwards Plato (5th to 4th century BC), and his protégé Aristotle absurdly argued that the pressure of the ocean forces seawater to flow uphill through subterranean rocks, which filter out the salt, to recharge mountain rivers by their upward flow from below. Both argued that water was a primary element that was ultimately derived from an underground reservoir called Tartarus; new water was created inside Earth’s mountains from condensation of air that seeps out to produce rivers and springs. They recognized that rainfall contributes to these surface flows, but thought that their perennial versus ephemeral nature depends on the size of the particular mountain postulated as their source. Roman philosophers such as Seneca and Lucretius perpetuated the Aristotelian belief that seawater is pushed into and filtered through rocks to make fresh streams and springs. Following the decline of the Roman Empire and the rise of the Catholic Church, many ancient Greek writings survived in church abbeys. Early scholars in these abbeys periodically wrote secular pieces that included sections on water, but their contents were largely derived from Greek teachings.

Leonardo Da Vinci (1452 – 1519 AD) has been credited with accurately describing the hydrologic cycle, but even he was so strongly influenced by Aristotelian teachings that his notions for the sources of spring and river waters were quite inaccurate. Nevertheless, his stunning contributions to art, science and technology include his accurate description of mass conservation principles. The first realistic description of the hydrologic cycle was written by an obscure individual named Bernard Palissy (1510 – 1590 AD). He was an artisan of stain glass, but turned to surveying to make a living. He wrote the exceptional treatise “Discours Admirables” that argued that springs, rivers, and groundwater are derived from infiltrated, gravity-driven rain, and countered Aristotle’s postulate that subterranean air condensed into water. He also argued that artesian wells are driven by groundwater positioned further uphill. Unfortunately, Palissy’s work was mostly overlooked by his contemporaries and in later works. Aristotelian explanations of the hydrologic cycle survived even in writings by Kepler, Descartes, and Castelli, who became famous for their seminal contributions to planetary motion, mathematics, and continuity theory.

It was not until the mid-17th century that observational efforts were made in Europe to determine whether rainfall was sufficient to generate river and spring flows. Pierre Perrault (1628 – 1703 AD) first showed by mass balance that rainfall amounts were sufficient to explain river flow. However, he did not believe that rain also recharged groundwater because he had no direct observation. Edmé Mariotte (1620 – 1684 AD) diligently pursued similar mass balance reasoning in his “Treatise on the Motion of Water” in which he demonstrated the quantitative concordance of his rainfall and discharge measurements. Edmund Halley (1656 – 1742 AD) experimentally proved that evaporating seawater condensed into fresh rainwater, thereby completing the analysis of all essential components of the hydrologic cycle. The rise of secular thought and scientific methods of investigation ensured the acceptance of these observationally-based conclusions.

Hydrologic postulates not based on observation have a high probability of being incorrect. This is clearly the case for Aristotle’s ideas about hydrology, but he was very influential in his time and a prolific writer. The records of him and his followers dominated what survived the collapse of the Roman Empire, so they profoundly influenced the educated class of Europe until the Age of Enlightenment. Ultimately, genuine intellectual skepticism and simple observational facts put these Aristotelian notions to rest.

Today’s Observational Basis for the Hydrological Cycle

Recognizing that almost all flowing water on the continents originates as rain and snow melt derived from evaporated sea water, we can readily offer a simple mass balance relationship to describe the annual hydrological cycle

where P is the annual precipitation sum, R is the total runoff, ET is evapotranspiration, and ΔS is a much smaller term representing the change in storage, which here represents the difference between the replenishment and discharge of groundwater and soil water. Each of these water balance components are introduced and briefly described below, to be discussed in detail in subsequent, dedicated chapters.

Precipitation

Even a casual observer knows that Earth’s air temperatures undergo dramatic changes each day and over the course of a year. Daytime is almost always warmer than night, with an obvious connection to sunlight. Sunlight hours are short during winter when typical days and nights are cold, and long during summer when temperatures are warm. Cloudy days tend to be cooler than sunny ones. With a little more attention an observer may also note that the wind sometimes starts to blow as the sun sets, or that dew or frost often cover outdoor surfaces at dawn. He might also notice that evaporation is rapid on hot sunny days, particularly if the wind is strong. All these observations provide evidence of the dynamic character of Earth’s atmosphere. Although our atmosphere has been studied for centuries and is in many respects well understood, rather than inundate the reader with all the explanations at once, details will be deferred to the precipitation chapter.

Early Greeks knew that the Earth is nearly spherical, but this idea did not become popular in western culture until Christopher Columbus’ famous journey and Ferdinand Magellan’s circumnavigation of the globe. The spherical shape requires that sunlight is most intense per square meter along Earth’s equator, and least intense at high latitudes, so that average air temperatures are higher near the equator than at high latitudes. This is shown by the mean annual daily temperatures for various continental locations located near the ocean (Figure 1).

Figure 1. Mean annual air temperatures for a number of near-coastal, low elevation locations shows how equatorial regions are warmer on average than polar areas. This phenomenon is driven by the incident angle of sunlight, because every place on earth receives an annual average of 12 hours of direct sunlight per day.

Clearly, temperatures at equatorial and polar regions are dramatically different, demonstrating how the incident angle of sunlight affects air temperature. These temperature differences generate variations in density, water and energy content that provide the driving force for atmospheric circulation and global wind patterns.

Atmospheric temperature also decreases with increasing altitude. This decrease is known as the lapse rate, and in mid-latitude regions it is typically around 6.5°C for every kilometer of elevation gain. This effect would be insignificant if it weren’t for another key factor that drives the hydrological cycle. This factor can be observed simply by boiling some water. At room temperature water is a liquid that is stable along with a small amount of atmospheric vapor, but upon heating to its boiling point, the water converts entirely to water vapor. The vapor always rises because the air above the water surface is hot. Figure 2 illustrates how the density of water vapor (measured as partial pressure) above liquid water changes with increasing temperature; also shown is the variation of air density with temperature. Note that as temperature increases, the density of the air decreases, and it can hold more water vapor. Sufficiently warm air is buoyant, but can hold a high amount of water vapor. Since low density substances tend to rise above higher density ones (for example a mixture of oil and water), warm moist air commonly rises in the atmosphere. However, the rising air column will cool during ascent, forcing the condensation of entrained water vapor, forming clouds and sometimes precipitation. Note this view is actually too simplistic because rising air columns simultaneously expand and cool, requiring comparison to a curve known as an adiabat (see Precipitation). Nevertheless, because 70% of Earth is covered by water and equatorial regions are warm, warm moist air masses are continually being generated and give rise to the global water cycle.

Figure 2. Isobaric (1 atm) vapor pressure of water inversely correlates to air density. As a result rising warm air with high water content is the primary drive of global precipitation patterns.

Early world adventurers and map makers recognized long before satellite technology that the Earth has many distinctive climatic zones. Nearly one-third of the globe is occupied by land masses, with Africa, South America, and southeast Asia spanning the equatorial regions, North America, Europe, and Asia, the northern hemisphere, and Australia and Antarctica the southern hemisphere (Fig. 3). The equatorial landmasses are naturally covered by dense tropical vegetation due to consistent high levels of precipitation and year-around warm temperatures. In contrast, roughly at thirty degrees north and south latitudes, annual precipitation is dramatically lower than along the equator, as illustrated by the African Sahara and other desert areas of the Asian and Australian interiors, the American southwest, and the southwestern parts of Africa and South America. These climatic differences are due to the complex atmospheric circulation patterns and these are discussed in detail in the precipitation chapter.

Figure 3. World physiographic map shows the different climatic regions on Earth with tropical areas surrounding the equator, dry regions predominantly in the 30° north and south latitudes, and frozen regions on our poles.

Surface Runoff

Almost all of us have watched a local stream gently flow during dry weather, and have seen how hard it can flow during precipitation events. We also know that streams flow downhill, from a higher area defined by local topography. These higher regions from which a particular stream or river flows is called its drainage basin, catchment area, or watershed, all of which are interchangeable terms for the source area that provides the water. This area is encompassed by a topographic rim that funnels all surface water toward a “main stem” river or stream. As the river flows downstream, it typically combines with flows from adjacent drainage areas, forming a larger river whose drainage area progressively increases. An example of a watershed is illustrated in Figure 4.

Figure 4. The coastal watershed of the Carmel River above Carmel, CA is highlighted in the left Google Earth image (looking southeast) and illustrates how tributaries lead into a main stem channel as pictured on the right for the river near the coast (photo CA DWR).

Braided Streams

No two rivers are exactly the same, but river geometry tends to conform to one of several basic patterns related to formational processes in the natural landscape. Rivers that are “immature”, being relatively young in geologic time, occur at higher elevations where runoff draining from steep slopes causes active erosion. Below these steep canyons, particularly if there is a sharp decrease in the topographic gradient, the watercourse will experience large variations in volumetric flow and sediment load, and will commonly modify its course by dividing into multiple channels. This type of river is known as a braided stream (Fig. 5a). The multiple channels weave in and amongst themselves forming numerous sand bars and islands. However, during high flow periods, all individual channels and islands will be inundated and a larger, somewhat straight and single watercourse temporarily forms. During these high flows the stream energy is high enough to carry coarse-grained material ranging from sand size to large boulders.

Figure 5. a) Braided stream observed from a Landsat satellite above South Island, New Zealand. Note the grey and brown areas along the stream course showing river banks during high stage flows. b) Mississippi River below Memphis, TN illustrates meandering flow alongside older meander remnants that form lakes known as oxbows.

Meandering Rivers

In contrast, “mature” rivers that have developed on low slopes or evolved over a long geologic period tend to have a sinuous geometry, and are called meandering streams (Fig. 5b). Meandering rivers tend to have large flows generated in huge catchment areas. These large rivers are familiar to us as they represent the dominant drainage pattern of large, flat continental terrains. Many cities throughout the world are located on the banks of meandering rivers. Because coarse-grained sediments have dropped out further upstream, the sediment load is finer grained than for braided rivers, usually sand, silt and clay. An important feature of meandering rivers is the formation of natural levees. A levee is a low elevation ridge along the river bank that was deposited during high flows. As the water level rises, the water will crest over its natural channel and spread out over the landscape, which causes the velocity and hence the energy of the water to decrease. This causes coarse material being carried by the water to rapidly settle out along the bank. Over time these deposits form the natural levee. Of course, as the muddy floodwater continues to spread away from the bank it now mostly carries silt and clay, which slowly settle out over the landscape. This region of settling is known as the flood basin or floodplain.

One of the most egregious examples of human defiance of nature is the attempt to control large meandering rivers and usurp their shape. For over a century many channels have been straightened, dirt has been added to levees to increase their height, flow-control structures have been placed in channels, and floodplains have been drained and developed as residential and commercial property. The most dramatic of these cases is the Mississippi River, where in order to maintain river trade using barges, the Army Corps of Engineers has built more than 30 locks and dams, increased the height of hundreds of miles of levees, and constructed thousands of in-channel structures whose aggregate length far exceeds the length of the river. These developments have divorced the river from its natural flood plains, and encouraged the conversion of productive agricultural bottomlands into commercial real estate. Although mostly successful in taming river flow from year-to-year, numerous unpredictable events have caused extensive flooding of these developed floodplains. Government insured bailouts of this precarious real estate have perpetuated a cycle of great losses followed by redevelopment.

Estuaries

Estuaries are large natural water bodies found in the transition zone between freshwater rivers and seawater. Topographic gradients are low, and the low water velocities are driven by the amount of riverine discharge and by tides. Estuarine waters are always under tidal influence which drives mixing of fresh and saline water. This transition zone co-mingles terrestrial and oceanic nutrients that make estuaries some of Earth’s most ecologically productive areas (Fig. 6).

Figure 6. Aerial view of Elkhorn Slough tidal marsh and estuary on the central California coast supports over 700 species of plants and animals. Part of the estuary is a State marine conservation area and an additional 8000 acres is preserved under a private/public agreement. Nevertheless, development pressure continues in the area as seen by the adjacent gas-fired power plant and cultivated agricultural land.

Estuaries have various morphologies controlled by the geologic nature of the continental coast. Along many passive geologic margins such as Chesapeake Bay, estuaries are drowned river valleys created by rising sea levels since the last ice age. Another common type along passive margins is located behind barrier islands, where lagoonal environments exist between the continent and open sea.

As another example, fjords are flooded, formally glaciated valleys that are common along the Scandinavian coast. These transition to deep water faster than riverine estuaries. Lastly, structurally controlled estuaries can form where active faults or uplifts translate geologic strata along the coast in ways that limit the connection of rivers to the open ocean. San Francisco Bay and the Sacramento-San Joaquin Delta is an example of this type.

Estuaries are important zones of sediment and soil carbon accumulation. This accumulation gives rise to island formation that results in complex, sinuous channel flows and a co-dependent terrestrial and aquatic ecosystem. Furthermore, so much sediment accumulates over geologic timeframes that it drives slow sagging of the continental margin, with elevation being maintained by a balance between land subsidence and sediment replenishment.

Figure 7. Before and after effects of hurricane Katrina in August 2005 shows areas under water in the Mississippi River delta. Catastrophic events such as these are aggravated by longstanding channel straightening for navigation and loss of regular flood sediment loads in adjacent flood plains that have caused land subsidence.

Unfortunately, human encroachment of coastal estuaries has disrupted this balance (Fig. 7). Agricultural development of nutrient-rich soils, accompanied by intentional water drainage and levee construction, has effectively cut off the delivery of sediments needed to offset erosion and subsidence. Furthermore, tilling of the organic-rich, once water-saturated soils has caused rapid oxidation of carbon to CO2. Together these processes have destabilized surface elevation, so that many developed areas in and around estuaries now lie below sea level and require higher levees (Fig. 8). Of course, urban encroachment has aggravated the problem making flood control even more imperative, while further destroying natural habitat and decreasing water quality. This is often directly observed by turbidity increases, which reduce sunlight penetration in the photic zone and decrease the primary productivity of the aquatic ecosystem. Examples from the Sacramento San Joaquin Delta in California shows how river levels are higher than adjacent land which is now up to twenty feet below sea level in many areas due to agricultural development.

Figure 8. Example where levees have deprived cultivated bottomland of sediment replenishment, and dewatering has caused the loss of soil organic matter by oxidation. In this case these processes have progressed to the point where river water levels are normally higher than the adjacent flood plains (red arrows), requiring permanent pumping and levee maintenance.

Evaporation/Evapotranspiration

Evaporation and sublimation are processes where water molecules are removed as vaporous emanations from exposed surfaces of liquid water or ice, respectively. Transpiration is the dynamic loss of moisture from plant leaves as part of their metabolic process, and evapotranspiration is used to describe the complex combination of all such processes that return molecular water to the atmosphere. Evaporation from Earth’s immense ocean, which covers more than two-thirds of the surface, accounts for most atmospheric water vapor. Although no direct observation of evapotranspiration can easily be made, thermal images from satellite platforms can record surface temperature variations that correlate to vegetation patterns (Fig. 9). Here active evapotranspiration of photosynthesizing plants causes evaporative cooling of the leaf surfaces, which can be imaged in the infrared as cool vegetated regions and warmer, non-vegetated areas. This approach has been used to map cultivated crops and define regions of poor productivity. Of course in areas fully covered by vegetation, such as tropical areas, the temperatures are more uniform. As might be expected, tropical regions have the highest rate of vapor respiration while deserts have the least. Evaporation and evapotranspiration are discussed in further detail in a subsequent, dedicated chapter.

Figure 9. Thermal satellite image on the right correlates with the visible light image on the left, where bluer regions are cooler and represent areas of active evapotranspiration associated with dense vegetation.

Groundwater Circulation

Most readers have dug a hole in the ground and noticed that the deeper down you go, the moister the soil. The more ambitious of you may have dug so deep that water begins to pool. The level where water pools is called the water table, and represents the point where the soil pore spaces are fully saturated with water; the hole is ostensibly a water well. Hand dug wells were made by humans long before recorded history, dating at least as far back as the early Neolithic, nearly 10,000 years ago. Of course, modern well construction has advanced considerably over the years, but the underlying principles remain the same.

Regional records of water wells provide a means to map the water table (Fig. 10). In a natural setting, the water table is approximately parallel to the surface topography, but in areas of heavy water extraction, a water table map is a useful tool to define “cones of depression” that document zones of over-extraction. Water table levels vary over the course of the year, rising and falling due to rainfall delivery, groundwater flow, river levels and pumping.

Approximately 20% of all water used in the USA is derived from groundwater withdrawals, which totals about 100 billion gallons per day. Groundwater is most important in arid regions where perennial surface water is scarce, and less important in areas with high rainfall and large rivers, with treated surface water providing the main supplies for domestic and industrial use. In arid regions, chronic and sometimes acute over-extraction forces water tables to drop, causing wells to run dry or to become saline due to the upwelling of deeper, lower water quality groundwater.

Figure 10. Water table contours of groundwater in the southern Sacramento Valley, CA show in the west decreasing elevation that follows topography. In contrast, in the east the groundwater is effectively mined by over pumping, resulting in two large cones of depression that are recharged by adjacent river water.

The role of groundwater in the hydrologic cycle can be easily illustrating using a potted plant. Many of us have watered house plants and directly observed how the water seeps into the soil. Less than a minute later you may also see the water seeping out the bottom of the pot into an underlying tray that you hopefully remembered to have placed. The seepage into the potted soil is analogous to rain or snowmelt seepage into the soils of the natural environment. The soil wetting process creates a partially saturated condition that allows water to flow deeper by force of gravity. Plant roots will intercept some of this water in the process of evapotranspiration, whereas the remaining water will continue to flow downward. The water dripping out the bottom of your potted plant illustrates how seepage can eventually reach the water table, a process referred to as recharge.

Water below the water table has saturated the pores of the adjacent sediments. At this point the groundwater can move under the influence of gravity and the surrounding water pressure. A quantity known as hydraulic head, which combines the key effects of pressure and elevation, defines how water will flow in the subsurface, ultimately to discharge at a surface point having lower elevation. Such low elevation areas occur at various locations depending on the particular region. Most low points in natural environments are along river valleys, so groundwater commonly seeps into flowing surface waters. However, this can only happen if the groundwater head is higher than the level of the adjacent river. Of course in areas where groundwater is heavily pumped, the groundwater head may be low and surface water will tend to seep into the ground, and the river becomes a “losing stream”.

A desert oasis provides another familiar example of a low elevation point where groundwater seeps to the surface (Fig. 11). Here the water table intersects the topographic surface, and the groundwater emerges as a spring. Many springs eventually flow into larger surface streams, but in arid regions, the rate at which spring water emerges is commonly balanced by the rate of evapotranspiration, and only a pool remains.

Figure 11. Saharan desert oasis in Libya shows how the groundwater table can break the surface and discharge as spring water. In this case, all the spring water is lost as evaporation and evapotranspiration from surrounding vegetation.

Groundwater and hydraulic head are discussed in much greater detail in a following chapter. An entire research community arose during the past century that is dedicated to understanding these important topics, driven by historical and continuing problems of groundwater depletion and contaminant migration. However, much groundwater research, education and most textbooks have become negligently divorced from scientific observations, being far more focused on complex mathematical descriptions of unrealistic problems than on basic observations and practical problems. We seek to redress this gap.