The Hydrological Cycle

"Counting Every Drop…"

 

Although water is a very common, if not ubiquitous, substance in the Universe, Earth is the only planet in the solar system that benefits from an extremely generous share of liquid water on its surface. About 70% of its surface is covered by liquid water. Because of a particular combination of temperature and pressure conditions on Earth's surface and within the atmosphere, water can exist here in three states: solid (ice), liquid, and gas (vapor). The total quantity and annual circulation of water on Earth represent by far the most abundant and largest movement of any chemical substance at the surface of our planet (Berner and Berner, 1996; Schlesinger, 1997). Water vapor in the atmosphere acts as our “heat blanket”. Without it, Earth would not experience the warm and cozy temperatures produced, in a large part, from the water-induced greenhouse effect. Furthermore, through evaporation and precipitation, water transfers much of the surplus heat energy received by the tropics to the “cooler”, heat-deficit, poles. Movements of water through the atmosphere determine the distribution of rainfall on Earth, and the annual availability of water on land is the single most important factor that determines plant growth. Where precipitation exceeds evapotranspiration on land (the combined process of water evaporation from wet soil surfaces and plant transpiration), there is runoff which is equivalent to water flow into rivers. Runoff carries the product of mechanical and chemical weathering of rocks to the sea, thus linking the world's heat energy budget to that of minerals and chemical compounds. In this lab, we will review some of these concepts and explore, in more depth, some dealing with freshwater availability and human use. (Picture on the left from “A Drop of Water”; Walter Wick – 1997 - Scholastic Trade)

Objectives:

In this exercise, the primary goals are to

  1. Understand the concepts of reservoirs and fluxes.
  2. Analyze and understand the temporal variations in the hydrological cycle at the regional scale.
  3. Comprehend quantitatively how these variations affect water management practices.

 

After this exercise, and in conjunction with lecture material, you should have a better sense of the various reservoirs and rates shaping the Global hydrological cycle. You should also be able to understand how resource availability (e.g. water) and specific management practices can affect the development of certain regions that undergo limitations or even shortages of these resources.

Introduction:

Water exists in such large quantities on the surface of the Earth that it is traditional to represent the "pools" (reservoirs) and transfers (fluxes) of water in units of cubic kilometers (km3). Each cubic kilometer contains 1012 or a thousand billion liters and weighs 1015 or a million billion grams. In total, there are 1459 106 km3 of it in its three phases (solid, liquid, and gas) on Earth's surface. Not surprisingly, the oceans are the dominant reservoir in the Global water cycle comprising over 96% of the total reservoir (see Figure 1 below). The remaining ~4% are either on the continents or in the atmosphere. The amount of water in the atmosphere, in the form of vapor, is tiny in comparison with the other reservoirs (approximately 0.001% of the total). However, as mentioned previously, it plays a very important role in the water and Global heat energy budget of the planet. Of the freshwater stored on continents, around one quarter is in the form of ice in polar ice caps and glaciers. Most of the rest of continental water is present either as subsurface groundwater or in lakes and rivers. Global estimates of groundwater reservoirs are poorly constrained and range from as low as 4.2 106 to as high as 15.3 106 km3 (Berner and Berner, 1996; Schlesinger, 1997). Because most groundwater is not directly accessible to human, except as a result of exploitation activities, only less than 1% of the Earth's total water can be drawn by human for their water supplies.

 

Software: Microsoft Office

Figure 1. Simplified view of the Global hydrological cycle. The numbers represent the quantities present in specific reservoirs (blue values in braces, in millions of cubic kilometers: 106 km3) or fluxes (black values in parentheses, in millions of cubic kilometers per year: 106 km3/yr). All data from Berner and Berner (1996) Global Environment: Water, Air, and Geochemical Cycles – Prentice Hall.

 

Water does not remain in any one reservoir, but is continually moving from one place to another. This is illustrated in Figure 1 with arrows indicating the direction of movement (the magnitude of the movement per unit time is indicated in parentheses in millions of cubic kilometers per year: 106 km3/yr). With the exception of chemical reactions, water is neither created nor destroyed on the surface of the Earth thus the overall quantity of water is close to constant over time. (Note: the transformation of water into organic matter during photosynthesis indeed transforms water: CO2 + H2O + Energy -> CH2O +O2. However, this process is insignificant in terms of reducing the total amount of water on Earth. First of all because the fraction of water present in the biosphere is close to insignificant in relation to the total Global reservoir (0.0001%). Secondly, because a large fraction of the photosynthesized organic matter is transformed back into water and CO2 under the reverse respiration reaction (CH2O +O2 -> CO2 + H2O + Energy) thus returning water to the atmosphere through plant transpiration). Hence, the conservation of mass allows us to build a Global water balance linking all reservoirs and fluxes. For any specific reservoir of study, the water balance will depend on the following conditions:

dM = I - O

Where dM is the change in the amount of mass (or volume) in storage (the Greek symbol D means change), I is the input(s) to the reservoir, and O is the output(s) from the reservoir. In some instances, the reservoir is limited in size and M cannot grow beyond a certain point (think of a tub, or a pool. If you put too much water into it, it will spill out). If inputs and outputs happen to be the same, then there is no change in the amount of water in the system of study, dM = 0, and the size of the reservoir remains constant over time. This condition is called dynamic equilibrium or steady state. As mentioned previously, we can consider that the overall water cycle on Earth is very close to being in steady state since the overall quantity of water doesn't change substantially over time (DM = 0). On the other hand, subreservoirs of the hydrological cycle (e.g. the atmosphere, the oceans, a lake) are not necessarily in steady state, particularly over long periods of time. And we will be working on this in the following lab.

Assumption of a constant volume of water in a given reservoir (water mass) enables the use of the concept of residence time. Residence time is defined as the volume (or mass) of water in a reservoir divided by the rate of addition (or loss) to (from) it. It can be thought of as the average time a water molecule spends in a given reservoir.

t = M/I (or M/O)

M = tS

Where t is the residence time of water in the selected reservoir, M is the total mass of water in that reservoir, and I is the input(s) to the reservoir. For example, evaporation removes about 434,000 km3 of water from the world's oceans every year whereas it removes only about 71,000 km3 of water from the continents directly from soil and water surfaces as well as from plant transpiration. Once in the atmosphere, water can either be transported to another location or recondense into liquid form and precipitate out. The total mass of water present in the atmosphere at any given time (15,500 km3; see Figure 1) divided by the total inputs (505,000 km3/yr) thus gives a residence time of water in the atmosphere of only ~11 days. This suggests that water remains in the atmosphere as water vapor for only very short time, before it falls back to the surface as snow or rain. In contrast, the total mass of water present in the oceans (1400 106 km3; see Figure 1) divided by the total outputs to the atmosphere (434,000 km3/yr) gives a residence time of water in the oceans of ~3200 years. The much longer average time of residence for every water molecule in this reservoir relative to the atmosphere reflects the very large volume of water in the oceans relative to that present in the atmosphere. Hence, we can use the amount of water in each reservoir and the fluxes into and out of these reservoirs to tell us something about the dynamics of the systems. Moreover, any change in volume in the reservoir indicates a departure from steady state and may lead to a new balance (we will explore this in the next lab).

 

Part I. Climate Change and the Hydrological Cycle

Climate is the average weather at any specific location (from regional to large-scale geographical areas). Climate is what you expect in terms of atmospheric conditions such as precipitation, temperature, sunshine, wind speed and direction, etc. Weather is what you actually get… That is, the day-to-day variations in these conditions. We will be exploring the world of climates and climate variation in our next lab. Here I only want to explore how the hydrological cycle could change and adapt in the likely possibility of climate change.

It is widely believed that Global change in the earth’s climate could result in warming conditions that would entrain many resulting conditions such as melting of polar ice caps, a more humid world (higher evaporation rates) and a more rapid hydrological cycle (enhanced movements of water through evaporation, precipitation and runoff). Most of the anticipated temperature change is confined to high latitudes. Moreover, due to the higher thermal "inertia" (resistance to temperature change) of oceans relative to that of continents, the oceans are expected to warm more slowly than land surfaces. This increased temperature on continental surfaces may lead to higher evapotranspiration rates leading in turn to less soil moisture and more arid conditions in certain continental areas. Because most precipitation is generated from the oceans (see Figure 1), land areas may thus experience severe drought conditions during the transient period of Global warming. Such changes in precipitation and evaporation will lead to large-scale adjustments in the distribution of vegetation and global net primary production.

If evapotranspiration from Earth’s land are were to diminish by 20% uniformly over the land area, as might result from the widespread removal of vegetation (desertification and deforestation), what changes would occur on the Global precipitation rates on land surfaces and in globally averaged runoff from the land to the sea? Let’s try to answer that, seemingly, complicated question in steps.

This is a box-model problem requiring a careful identification of boxes and fluxes between them. An immediate guess is that precipitation would decrease by 20%; but this would be incorrect (it would actually be too easy and you know by now I wouldn’t let out go that easy). The existence of runoff from the sea and evaporation transfers are linking the two boxes, the land and the sea, and implies that some evaporation from the sea actually falls as precipitation land. Because this portion of land precipitation will not be affected by the 20% decrease in evapotranspiration from land, then the overall effect of a reduced evapotranspiration will be less than 20%.

To solve the problem, we have to define the Global water budget in terms of evaporation/precipitation. The following water fluxes refer to Figure 2 below and can be defined as:

Pl = Rate of precipitation on land

Ps = Rate of precipitation on the sea

R = Rate of runoff from land into the oceans

Ell = Rate of evapotranspiration from the land that falls as precipitation on the land

Els = Rate of evapotranspiration from the land that falls as precipitation on the sea

Esl = Rate of evaporation from the sea that falls as precipitation on the land

Ess = Rate of evaporation from the sea that falls as precipitation on the sea

Figure 2. Evaporation/Precipitation fluxes in the Global hydrological cycle.

 

Our problem can thus be restated in terms of these definitions: How will R (runoff) and Pl (precipitation on land) change if Ell (evapotranspiration onto land) and Els (evapotranspiration onto the sea) both diminish by 20%?

We will be using a water balance approach and using this approach there are three water-conservation relations among the seven quantities we have defined. I will state these relations in words and you will need to write them, in turn, in algebraic form (use the symbols):

1)        The sum of the precipitation on the sea and rate of runoff is equivalent to the total rate of evaporation from the sea (equation 1).

2)        The rate of precipitation on land is equivalent to the sum of runoff and total evaporation from the land (equation 2).

3)        The sum of the runoff rate and evapotranspiration from the land onto the sea is equivalent to the rate of evapotranspiration from the sea onto the land (equation 3).

4)        Combine equations 2 and 3 to express the precipitation on land (Pl) as a function of the evapotranspiration from the land onto the land (Ell) and the evaporation rate from the sea onto the land (Esl).

5)        Combine equations 1 and 3 to express the precipitation on the sea (Ps) as a function of the evapotranspiration from the land onto the sea (Els) and the evaporation rate from the sea onto the sea (Ess).

OK. To do the rest you need to know that approximately 75% of evapotranspiration from the land falls back as precipitation on the land, the other 25% precipitates onto the sea (Ell = 3 Els). (Note: to make it clearer to do the rest I suggest you list all equations you’ve come up with onto a sheet of paper and number them). Using all these equations and the values for fluxes in Figure 1, answer the following questions.

1)        What is the evapotranspiration rate from the land that falls back as precipitation on the land (Ell)?

2)        What is the evapotranspiration rate from the land that falls back as precipitation on the sea (Els)?

3)        What is the evaporation rate from the sea that falls back as precipitation on the land (Esl)?

4)        What is the evaporation rate from the sea that falls back as precipitation on the sea (Ess)?

Knowing that the new evapotranspiration rate from the land that falls back as precipitation on the land is 80% of the original one (NEll = 0.8 Ell) and that the new evapotranspiration rate from the land that falls back as precipitation on the sea is also 80% of the original one (NEls = 0.8 Els),

5)        What is the new runoff rate (NR)?

6)        What is the precipitation rate on land (NPl)?

7)        By how much will the Global precipitation rate change?

Part II. Local Temporal Variations in Hydrological Cycle – Use and Supplies

"Water, water, everywhere, nor any drop to drink"

Samuel Taylor Coleridge "The Rime of the Ancient Mariner"

As you can guess from Figure 1, "the drop to drink" on Earth is about one hundredth of one percent of the world water. Indeed, the proportion of freshwater on our planet is larger than that, slightly more than 4% of the total amount, but the largest part is locked in continental ice caps and mountain glaciers (about 3% of the total) as well as deep down in the ground (about 1% of the total). Seawater is there, in plenty, but as an untouchable precious substance, seawater is either too corrosive or plain toxic to land-based animals and plants, including humans and their industrial activities. But really, looking at it honestly, even a hundredth of a percent is an astounding number: land masses receive a surplus of approximately 36,000 km3 as precipitation each year, and another 130,000 km3 of water reside at any one time in surface land water reservoirs formed by rivers and lakes (see Figure 1 above). Those are not small numbers. But although that seems like there is a lot to go around (indeed, it is thought that it could in principle sustain a world population of about twice the size projected for the end of the 21st Century), water is in fact becoming a scarce commodity. The total amount of water withdrawn globally from rivers, underground aquifers and other sources has increased nine fold since the onset of the 20th Century and by 1996 it was estimated that humans use was withdrawing over half of all available runoff. Over the past 100 years, humankind has designed networks of canals, dams and reservoirs so extensive that the resulting distribution of freshwater from one place to another and from one season to the next actually accounts for a small but measurable change in the wobble of the Earth as it spins! Today, human-made reservoirs inundate 120 million acres (~506,000 km2) of land and hold more than 1,500 cubic miles (~6,250 km3 or 6.25 1015 liters), which represent as much water as that present in Lake Michigan and Lake Ontario combined, and about 17% of the annual freshwater river runoff from land to the oceans. In the United States alone, the more than 7,000 dams are capable of capturing and storing half of the annual river flow of the entire country.

Water structures, like dams, generate a high benefit for societies that depend on them. Thanks to improved sewer systems, water-related diseases such as cholera and typhoid, once endemic throughout the world, have largely been conquered in the more industrial nations. Vast cities, incapable of surviving on their local resources, have bloomed in the desert or water-deprived areas with water brought from hundreds and even thousands of miles away (think of Las Vegas, the US city experiencing the most growth at the turn of the 21st century). Nearly one fifth of all electricity generated worldwide is produced by turbines spun by the power of falling water. Finally, food production has kept pace with soaring populations mainly because of the expansion of artificial irrigation systems that make possible the growth of 40% of the world's food. Actually, irrigation used in agriculture today accounts for two thirds of water use worldwide and as much as 90% in many developing countries. Hence, concerns over impending water shortages are not so much about thirst as about hunger: irrigation is the key to our ability to feed the future world.

The history of human civilization has soared with how we've managed to control our environment. How we've learned to manipulate water has played a big role in this development. Since the first irrigation systems were built in Mesopotamia by Sumerians, six thousand years ago, we have never relaxed our grip on water. As Philip Ball states so appropriately in the title of his recent book, water is the "Life's Matrix". Not only biological life at large, but modern human life as well. We are who we are, thanks to water. We are where we are, thanks to the ways we've controlled and used it.

Yet, all these developments, these positive signs of human progress, these "water works", carry very high environmental costs that are not always too apparent but integral part of our health, political and economic future. This past March 22nd, the UN Secretary-General, Mr. Kofi Annan, illustrated the need to recognize the significance of water to human societies during the observation of the first World Water Day. His message is summarized in its first few lines: "Access to safe water is a fundamental human need and, therefore, a basic human right. Contaminated water jeopardizes both the physical and social health of all people. It is an affront to human dignity". Mr. Kofi Annan's address came as a result of a series of high profile reports and publications on worldwide water availability and quality (UN: http://www.un.org/events/water/; Gleick, 2000). One of these reports states that, despite our progress, more than one billion people lack access to clean drinking water (that's about one in every six people), and some two and a half billion do not have adequate sanitation service (that's about two out of every five people on Earth). And when water is made available, through infrastructures, problems sprout on other levels: millions of people have been displaced due to land inundation (the latest example is the mammoth development in the Chinese Yangtzee River); worldwide dams prevent the migration of aquatic species to their spawning grounds (More than 20% of all fresh-water fish species are now threatened or endangered, whereas in the US alone, the population of Pacific and Atlantic salmons have fallen to less than 1% of historical levels due to dams and reservoirs blocking their way to reproduction sites); because of extensive tapping of their waters, several of the world's great rivers no longer reach the sea for at least part of the year (the Aral Sea in Central Asia has undergone irreversible destruction as the product of diversion to irrigate cotton agriculture; the diversion of waters from the Colorado River in the Western US for industrial, agricultural and municipal needs of California and Arizona, has left the receiving Gulf of California in Mexico with just a trickle of water); certain irrigation practices degrade soil quality and reduce agriculture productivity; and groundwater aquifers are being pumped down faster than they are naturally replenished (as much as 8% of worldwide food crop production grows on farms that use groundwater at a faster rate than the aquifers replenishment). And all this is without counting contamination by heavy metals and pesticides, and salinization (the toxic buildup of salts and other impurities due to removal of freshwater) of surface and ground waters due to human activities. And disputes over shared water resources have led to political tensions that sometimes have resulted in violent conflicts (a comprehensive chronology of water related conflicts can be found at www.worldwater.org/conflictIntro.htm).

So water demands management. Water is available, freshwater that is. But not equally for all. Rainfall is not evenly distributed throughout the world (Figure 3) and in many regions of the World, the supplies of water are dangerously sporadic and scanty.

Figure 3. Worldwide annual precipitation in centimeters (cm) or inches (in). Figure fromGeosystems: An Introduction to Physical geography (3rd Ed. 1997) – Robert Christopherson – Prentice Hall).

People's access to water depends on both natural availability but also on other factors such political and economic conditions, changing climate patterns, and available technology. Estimated annual water availability per person in 2025 (see Figure 4 below) reveals that at least 40% of the then World's 7.2 billion people may face serious water-related problems. Severe shortages could even also strike particular regions of water-rich countries, such as the US and China.

Figure 4. Estimated annual water availability per person in 2025. Figure from Making every drop count – Peter Gleick - Scientific American. Feb. 2001, p. 40-45.

However, the picture is not so stern. Although the total amount of water withdrawn globally from rivers, underground aquifers, and other sources has increased nine fold since 1900, water use per person has only doubled in that time, however, and it has even declined slightly in the last two decades. Using the table below let's examine if such a trend has occurred in the US by answering the following questions.

Table 1. This table shows estimated freshwater withdrawals used for public supply (in billions of gallons per day: 109 g/d or bgd), total freshwater withdrawals (surface and ground waters combined; in 109 g/d or bgd), and population (in millions: 106) in the United States from 1950 to 2000 (USGS "Water Use in the United States", Apr. 2004).

Year

Public Supply

withdrawals

(bgd)

Freshwater withdrawals

(bgd)

Population

(106)

1950

14

174

151

1955

17

227

164

1960

21

240

179

1965

24

270

194

1970

27

318

206

1975

29

342

216

1980

34

373

230

1985

36.5

338.2

242

1990

38.5

338.4

252

1995

40.2

340.4

267

2000

43.3

345.3

285

8)        Using these data, calculate the public supply utilization in gallon per capita (per person) per day (gpcd) and enter your values in the first column of the Excel spreadsheet that you will find by clicking on the following link: Water in the US.

9)        Now imagine that you are a water manager and the year is 1985. You have calculated the trends in water utilization for the past 35 years and seen a very steady and constant increase in consumption per capita every year. Using the per capita consumption you calculated above, use the rate of change over time for the period 1950-1985 to calculate the projected utilization you anticipate to see from 1985 to 2000. Note: a) do that by increments of five years from 1985 to 2000, and b) use the same values you've previously calculated for 1950 to 1985. Enter your values in the Excel spreadsheet.

10)     Print the graph with your name on it (make sure you submit this and every other graphs from this lab to you TA for grading).

11)     Do you see a difference between your projections and the actual values? Please explain the reason(s) behind the presence or absence of differences you observe. You can find your answer(s) directly in your lecture notes but you may also want to search the web. (For this question, you can find information in some of the web sites found at: http://www.worldwater.org/links.htm#nongov).

12)     Compare the per capita utilization of public supply water vs. total freshwater withdrawals. Discuss your results (rate of change for similar periods, proportion of one to the other). What does this tell you about total water consumption in the U.S.

Two definitions of lack of water are given in water management worlds: Water-stressed and water-scarce. Water-stressed regions can only provide between 260,000 and 420,000 gallons per person per year. Water-scarce regions have less than 260,000 gallons per person per year. If you know that the US could provide approximately 1,650,000 gallons per person for the whole year of 1990,

13)     What is the percentage of that total availability that was actually withdrawn in 1990 (from the values you calculated in question 12)?

14)     What is the percentage of that total availability that was projected to be withdrawn back in 1975 (from the values you calculated in question 9)?

Although your answer will tell you the overall US is "water-rich" and shouldn't be classified amongst the water-stressed regions of the world, some local hydrological cycles do create shortage conditions in specific regions (e.g. the South West; see Figure 4 above).

Much of the information presented in this lab has been synthesized from many readings. Let me acknowledge here the sources and point to them in the case you desire to obtain more information on the subject of water in the world.

Ball P. (1999) Life's Matrix: A Biography of Water – Farrar, Straus and Giroux. New York, USA.

Berner E.K. and R.A. Berner (1996) Global Environment: Water, Air, and Geochemical Cycles. Prentice Hall. New Jersey, USA.

Gleick P. (2000) The Changing Water Paradigm: A Look at Twenty-First Century Water Resources Development –Water International. Vol. 25, Number 1. p. 127-138.

Gleick P. (2001) Making every drop count - Scientific American. Feb. p. 40-45.

Schlesinger W.H. (1997) Biogeochemistry: An Analysis of Global Change (2nd Ed). Academic press. London, UK.

Thompson S.E. (1999) Water Use, Management, and Planning in the United States – Academic Press. San Diego, USA.