SURFACE WATER
A watershed, catchment, or basin is the upstream area that provides the surface runoff that flows past a given point along a stream. Because surface water flows downhill, the reference point has a lower elevation than any other point in the basin. While any location along the stream can be chosen for reference, one would normally select a confluence, reservoir, gauging station, or other site of interest.
The boundaries of the watershed, called “divides”, are defined by topography. Most famous in the United States is the Continental Divide, a continuous line along the crest of the Rocky Mountains. Precipitation that falls to the west of this line ultimately flows into the Pacific Ocean, and that which falls to the east ultimately flows into the Atlantic.
Geomorphology
Natural Systems
A large fraction of Earth’s land surface has been sculpted by surface water, so a rich nomenclature and many evolutionary concepts have been devised. Attention here will be confined to key features that can be observed along typical streams (Fig. 1). The stream channel is the depressed area, bounded by steep banks, that contains the stream under normal conditions. Typical channels are single, somewhat sinuous slots, but if sediment loads are high, an anastomosing network of multiple channels can be present, together constituting a braided stream. The channels of meandering streams exhibit pronounced sinuosity in plan, and these normally occur in lower reaches with very flat topography.
Figure 1. Aerial view of base flow for Cache Creek in southwestern Sacramento Valley, CA showing broad distribution of gravel and sand deposits laid down by periodic high runoff flooding.
Under high flow conditions, the flow of water can exceed the capacity of the channel. The excess water flows over the banks to occupy the surrounding, flat area called the floodplain. Such flows are properly termed floods, though that name is commonly applied to water levels that exceed an arbitrary “flood stage” defined by impacts to roads, property or structures. Under natural conditions, floods are intermittent but not rare, and water will occupy at least part of the floodplain every few years, or several times a year, depending on the site.
The distal part of the floodplain commonly terminates in a steep bluff. Uplands exist at greater distance. In steep terranes, however, “V-shaped” stream channels are common, and floodplains are small or absent. In glaciated areas, “U-shaped” valleys may occur.
Man-made Structures
Diverse works are constructed along streams. Common types, their purposes and unintended problems are discussed below.
Dams and Reservoirs
Large dams and reservoirs are constructed for water supply, flood control, and hydropower, and sometimes as an aid to river navigation (Fig. 2). Additional purposes, especially for smaller dams, are for livestock watering or to create fishing and recreation areas. These obvious benefits are offset by a host of negative consequences. Bottomlands, wetlands and riparian forests are irretrievably lost, along with valuable farms, wildlife habitat, and the capacity of natural systems to cleanse water and store floodwater. Benthic fauna are destroyed, and fisheries permanently damaged. Many reservoirs will ultimately fill up with silt, which will eliminate all benefits while creating a permanent problem.
Figure 2. June 30, 2011. Aerial view of Grand Coulee Dam releasing large flows of over 5,000 m3/s on June 30, 2011. The huge turbines in this facility can generate 6480 megawatts of hydropower. Credit USBR http://www.usbr.gov/pn/grandcoulee/news/gallery/index.html
Locks and Dams
Locks and dams are primarily constructed to benefit river navigation, but are sometimes claimed to provide water supply and recreational benefits (Fig. 3). As is true for dams and reservoirs, bottomlands and wetlands are permanently flooded, and increased water depths can destroy the benthos. Fish migration is impeded, as is the movement of small vessels that have no need of such structures. Some structures appear to worsen flooding.
Figure 3. Lock and Dam #26 on the Mississippi River above St. Louis is about 500m wide. This structure increases the river depth upstream by about 4 m to benefit large towboats, one of which (upper left) has just moved out of the lock and is moving downstream.
Levees
Levees are long earthen works constructed parallel to rivers, whose intended purpose is to protect property from recurrent flooding (Fig. 4). This overused strategy destroys wetlands and eliminates the natural floodwater storage capacity, while displacing excess floodwater to downstream properties. As a result, competing interests construct higher and higher levees over time, and water levels progressively increase in the constricted rivers. Eventual levee failures release high energy water that destroys structures, scours deep channels, and deposits thick layers of coarse sand on farmland.
Figure 4. Earthen levee along the lower Missouri River, near the Labade Power Plant. The small levee is successfully holding back the moderate flood of May 22, 2010, but was overtopped during the 1993 flood.
Wing Dikes
Wing dikes, wing dams or groins are rock structures typically constructed perpendicular to river channels (Fig. 5). Their intent is to force the river into a narrow, deep, predictable channel that facilitates the passage of large vessels. Channelization of rivers by these and related structures destroys a complex natural habitat that once included sandbars, islands, and other features. Small vessels and humans are threatened by turbulent flows around these structures. Case studies show that wing dikes worsen flooding because they narrow the channel and impede water flow.
Figure 5. Prominent wing dikes along the lower Missouri River north of St. Louis, looking northwest, during the low flow conditions of July 31, 2002.
Revetments
Revetments, retaining walls, riprap, and associated works are concrete structures or rock piles along banks that protect property and prevent erosion. Though commonly necessary, they destroy habitat and are an eyesore.
Figure 6. Retaining wall along a small stream in St. Louis County is pictured on the right; such unsightly structures channelize streams and cause environmental damage. On the left is the same site before construction.
Measurements
Stage
The level of water in a stream channel or lake is called the stage. Stage is typically reported relative to an arbitrary, local datum, so a simple additive adjustment is normally needed to convert the reading to elevation relative to sea level. Stage is the most simple measurement of water conditions that can be made, and it is of special importance during both flood and low-water conditions. Direct measurement of stage can be made with a staff gauge, which is basically a long ruler attached to a post, bridge pier, or other convenient structure (Fig. 7). Of course, the staff gauge may be inclined if the divisions are scaled to account for the tilt angle.
Figure 7. Staff gauge along the Sacramento River, north of the City of Sacramento CA, staggered to permit convenient reading at different river levels.
Long term records of stage are available for thousands of sites. In many cases, these are daily readings of a staff gauge. However, continuous records of stage may be acquired by several devices, a common type being a float in a stilling well (Fig. 8). Fixed pressure sensors can likewise record variations in stage, as can acoustic devices that measure the time interval between vertically-directed sound beeps and the return echo from the water surface.
Figure 8. Stilling wells damp out effects of turbulence, waves and wind, facilitating readings of water levels (photo credit NOAA/NWS).
Discharge
The rate of flow of water in a stream channel is called the discharge, and is normally reported in m3/s, or in the United States, in cubic feet per second (ft3/s, abbrev. cfs). Discharge is a dynamic quantity that cannot be simply measured, but it is important to reservoir operations, water balance studies, and theoretical calculations. Several methods have been devised to quantify discharge, but reported values can have large uncertainties.
Volumetric Method
In an ideal case, as for relatively low flows that issue from a pipe, discharge can be measured by determining the time required to fill a vessel of given volume. This method was first proposed for spring discharge nearly 2000 years ago by the Greek Philosopher Hero of Alexandria.
Velocity-Area Method
Discharge is the product of the average velocity of the water and the cross-sectional area of the stream. In practice, flowing streams are divided into several width segments. The width and depth of each segment is measured, and the average velocity of water is determined, by using a flow meter to make measurements of velocity at multiple depths. For small streams, a wading rod is used to measure velocity, which is a device with a calibrated propeller (Fig. 9). For larger streams, measurements can be made by lowering a device from a bridge or boat, and more recently, acoustical methods have been developed to measure water velocity in streams.
Figure 9. Your Government in Action! Left hand image shows USGS using a wading rod and tape to calibrate stream discharge with the velocity-area method (http://water.usgs.gov/edu/streamflow2.html). Right hand image shows dedicated personnel measuring discharge by same method (http://water.usgs.gov/edu/photos-measure.html#drop)
In a small stream, the average velocity of a segment is approximated by a single velocity measurement made 60% of the way down, or by averaging two measurements made at 20% and 80% of the way down. The total flow of the stream is made by summing up the results for all the segments: Q = Σ(viwidi), where Q is discharge and vi, wi, and di are the average velocity, width and depth of each segment, respectively.
Rating Curves
For most sites, both stage and discharge vary with time. By combining readings of a staff gauge with discharge determinations made by one of the above methods, and repeating under a wide range of flow conditions, a rating curve can be customized for a site. Basically, a rating curve is a functional relationship that shows how Q depends on S. A simple quadratic polynomial,
Q = a + bS +cS2, Eq 1
where a, b and c are fitted constants, provides a good approximation for data from many sites. Because of channel irregularities, however, a table or graph will normally be more accurate (Fig. 10). Rating curves may change over time, due to channel scour, growth or disappearance of sand bars, temporary or permanent obstructions, etc.
Figure 10. Current rating curve (red) for the Mississippi River at St. Louis, compared to hourly data reported at that location in 2014 (blue points). The indicated quadratic equation provides a good approximation to the rating curve.
Wiers
Discharge can be measured with a weir, which is a barrier in the flow channel that has a slot of simple shape. Most common is a 90o “V-notch” weir (Fig. 11). Weirs can be calibrated by volumetric/time methods, discussed above, so a rating curve can be devised. A widely used approximation for the discharge of a V-notch weir is:
Q = aH2.5 Eq 2
where a is a constant and H is the water depth above the nadir of the V-notch. Chow (1964) provides equations for flow trough pipes or through weirs with slots of various shapes. HEC (1972) provides useful nomograms for flow through culverts of different dimensions and types.
Figure 11. V-notch weir provides a fixed geometry for streamflow and a convenient and consistent means to measure discharge.
Empirical Equations
If measurements are not available, discharge can be estimated using empirical equations. The Chezy equation provides the average velocity (U, m/s) of the water:
where c is the Chezy constant and S is the dimensionless channel slope (m/m). The hydraulic radius (R, m) is defined as the cross sectional area of the water divided by the wetter perimeter, i.e., the ordinary perimeter minus the water surface.
A more widely used formulation is the Manning equation:
where n is the roughness coefficient, available in tables. Note that the asserted dependence of U on R is different than given by the Chezy equation. There is no evident theoretical basis for either proportionality, which both differ from that for laminar flow (see below). To determine discharge, the velocity returned by either the Chezy or Manning equations must be multiplied by the cross-sectional area of the flowing water in the channel.
Theoretical Equations
No simple theory gives an adequate explanation for flow in natural stream channels, and even when boundary conditions are highly simplified, turbulent flow is difficult to model. However, slow, laminar flow of a Newtonian fluid can be treated for several geometries. For such fluids, stress is proportional to the velocity gradient.
For laminar flow in a filled circular pipe or radius a, the velocity U depends on radial distance r:
U = c(a2 - r2) Eq 5
where c is proportional to the pressure gradient in the pipe divided by the viscosity. For flow in a filled slot,
U = c’(a2 - y2) Eq 6
where a is one-half of the total height of the slot, and position y is measured from the slot center. These equations give a parabolic profile, such that velocity is maximum at the center and zero along the walls (Fig. 12).
Figure 12. Open channel and pipe flow can be described mathematically by parabolic velocity profiles.
Though highly idealized, these equations provide useful insights into natural streams, which may be approximated as a half-filled slot or pipe. Velocity will be highest at the stream surface, in the center of a straight channel. Moreover, divers can observe tiny insects and crustaceans easily walking along the bottoms of clear channels, but they are rapidly swept away if displaced upward into the flowing water.
Floods
Floods are any intermittent occurrences of high water levels, but attention here is focused on events along streams. While interesting in their own right, floods have great importance when people or property are at risk. Damage is caused not just by high water levels. Many floodwaters have high kinetic energy, so they can sweep away houses, cars, and anything else in their path. They can deposit or erode massive amounts of sediment, destroying structures or fields. Floods also create diverse health risks. Most floodwaters are filthy, bearing high concentrations of pollutants and bacteria, so they can pollute water supplies and contaminate homes, while fostering multitudes of disease-carrying insects.
Dynamics of Floods
Floods are dynamic phenomena, so time is a key variable. The principal diagram used to study temporal variations is called a hydrograph, and there are two types. A stage hydrograph is a plot of water levels vs. time, while a discharge hydrograph is a plot of flow vs. time.
On unmanaged streams, flood hydrographs display several common characteristics. The beginning of a flood event features a sharp rising limb, where both stage and discharge increase rapidly (Fig. 13). The early part of this rise is normally concave up, but an inflection point is passed, and the curve becomes concave down as the flood peak is approached. The flood peak then occurs, an event that postdates rainfall delivery by an interval called the lag time. This mathematical maximum is followed by an extended period of flood recession, with the hydrographs being concave down at first, but it quickly reaches a second inflection point and thereafter becomes concave up. Contrary to common opinion, flood recession is not exponential, a claim refuted by lengthy, concave-up recession intervals on hydrographs from thousands of sites when plotted as log Q vs. time.
Figure 13. Pictured on the left is the spring of 1997 Red River flood topping the Sorlie Bridge in Grand Forks, ND. A hydrograph of the flood on the right shows the steep, concave-upwards rising and falling limbs. The hydrograph departs from theoretical are cartoon depictions commonly used in hydrology because of the duration of the flood event (weeks) and the arrival of multiple runoff pulses, due likely to rapid snow melt. (Photo and data from USGS).
Causes of Floods
Floods on flowing streams are mostly caused by heavy rainfall in the upstream watershed. However, the rate of rainfall delivery can be more important than the total amount of precipitation. Thus, an intense cloudburst that delivers 3 cm of rain in an hour can produce a much higher flood peak than a storm that steadily delivers 10 cm of rain over 3 days. In addition, flood peaks are commonly magnified by human activities, and humans are entirely responsible for economical flood damages.
Annual floods occur along many rivers, especially in temperate regions. A common cause is heavy spring precipitation coincident with the normal warm-up that melts accumulated snow. The spring rise is followed by a lengthy recession that continues into late fall. Of course, superimposed on this annual pattern are shorter, sharper events caused by individual storms.
Regional floods result from protracted periods of heavy rainfall in large watersheds, or from rapid snowmelt events. Rain on snow events can produce flooding due to rapid runoff from the frozen surface. Ice blockages of channels can also cause flooding in cold regions. Along large rivers, water levels commonly increase by less than 25 cm/day, though levels may rise for weeks or months.
Flash floods mostly occur in small watersheds, which can rapidly respond to intense rainfall events. Water levels can increase 5m or more in a few hours, endangering humans, particularly at night. Many fatalities are caused when attempts are made to drive across flooded roads, because a car will float in only a few feet of water. When that happens, all control is lost, and occupied vehicles can be quickly swept into fast water, where they will rapidly sink.
Floods are caused by many other phenomena, depending on the location. Storm surges, hurricanes, and tsunamis can cause enormous problems in low-lying coastal areas, particularly when peak conditions coincide with high tides. Dam and levee breaks produce catastrophic results. In small basins, undersized culverts, or culverts or bridges clogged with woody debris, can cause serious flooding in the proximal upstream area.
Basic Proportionalities
The relationship between streamflow and rainfall is a complex function of several variables, but, basin size is most important. In a given region, the long-term mean annual discharge of streams is directly proportional to basin size (Fig. 14). This observation is easy to understand, because for a given annual rainfall depth, the total volume of water delivered to any basin depends on its size, so a 1:1 proportionality results. A group of watersheds from another region that receives a different amount of annual rainfall would likewise exhibit a unit slope, but its y-intercept would be different, so the lines would be parallel but not coincident. Scatter about any regional line is caused by several factors (Problem 4).
Figure 14. Log-Log graph showing the relationship between the mean (Qmean), medial annual peak (Q2), and record flows (Qpk; all in cfs) vs. basin area A (sq mi) for all USGS gauging stations in the states of Illinois and Indiana. Mean flows representing the long-term average, strongly correlate with basin area, exhibiting a 1:1 slope because stream runoff arises from the precipitation delivered to the particular watershed. Flood flows involve short term meteorological conditions, which can strongly affect small basin in a disproportionate way, so the slopes of the trend lines are lower. In small basins, flood flows can be 1000x or more larger than mean flows, so flash floods are very dangerous. See Winston and Criss (2016).
More interesting results are seen when all-time record flood peaks are plotted against basin size. For a given area, a linear trend also appears on a log-log plot, but the slope is much lower than unity, indicating a power-law relationship. Moreover, both the slopes and y-intercepts are different for different regions. The low slopes of these trend lines have a very important ramification. Record flows in small basins may be several thousand times greater than mean flows, while record flows on large rivers are less than tenfold greater than average flows. Because floods in small basins can develop in only an hour or less, these dangerous flows are difficult to predict.
Peak flow magnitudes also appear to correlate with other variables, including channel slopes and the percentage of impervious cover. Empirical relationships suggesting proportionality of peak flows to the product of basin area, slope and impervious cover, each raised to an irregular fitted power, are sometimes proposed. Such relationships are preposterous from the viewpoint of dimensional analysis, but their advocates argue that they provide useful estimates of possible flow magnitudes in basins where no measurements are available.
Flood Risk
The return intervals for small floods are easy to predict, but those for large floods are not. It is far easier to document the glaring failures of various proposals than it is to develop a viable predictive algorithm.
One useful approach, at least for flows of relatively short return intervals, is to use the historical record from gauging stations. Problems immediately appear. At some sites, annual peak discharge seems to be normally distributed, so a relatively straight trend appears on a standard probability plot. At other sites, linear trends appear when log Q is plotted in this manner, and the discharge data are said to be log normal. Elsewhere, peak stages seem to be normally distributed. Still other statistical models have been proposed. Trends on probability plots can accurately predict the magnitudes of “2-year” and “10-year” floods, but when the trends are extrapolated to define the magnitudes of “100-year” or “500-year” floods, problems abound. For one thing, the lengths of most historical records are far too short to accurately define infrequent events, so misleading terms such as “100-year” floods should not even be used. Another problem is that flood magnitudes at many sites are increasing with time, so the probably of occurrence of an event of given magnitude is higher now than a century ago. This effect is caused by humans, who profoundly modify stream channels and entire watersheds in ways that aggravate flooding, as well as by climate change.
On the other hand, it is easy to define the how many floods of a stated return interval are expected in a period of given length. For example, a flood at or exceeding a “5-year” flood magnitude has a 20% probability of occurring in any given year. We define the quantity x as being the reciprocal of the return interval, so in this case, x =0.2. The complementary probability that no such flood would occur is 80%, so define y=0.8. Similarly, for a “50-year” flood, x=0.02 so y=0.98. Note that x plus y always equals one. The likelihoods of all possible outcomes for flooding during any n-year period are easily calculated by expanding the term (x+y)n, to give:
1 = xn + nx(n-1)y + 0.5n(n-1)x(n-2)y2 +…… Eq 7
The first term (xn) on the right gives the probability that no “ x-1 - year” floods will occur in the n-year interval, while 1-xn gives the probability that one or more such floods will happen. The second term on the right gives the chance that one and only one such flood will occur in the stated interval, so 1 – xn - n x(n-1)y gives the probability that two or more such floods will occur during the n-year period. Such math is trivial. Unfortunately, it is difficult to define what flows or stages correspond to actual floods of infrequent return intervals, such as “100-year” floods.
Geomorphology provides the best indicator of long-term flood risk. Floodplains are easily recognized, both in the field and on topographic maps, and they are places that have been repeatedly occupied by natural floodwaters in recent times. Such conditions will persist, even though human beings commonly pretend that their structures insure they will not. Real flood victims include those stuck with the bill for human folly.
Anthropogenic Changes
Large Basins
Many activities of man aggravate flooding. Dams and levees, many constructed to prevent flooding, encourage development in floodplain areas, and result in colossal damages when failures occur. These structures also eliminate wetlands or isolate rivers from their floodplains, greatly reducing the floodwater storage capacity of the natural system. Channelization reduces river width and impedes flow, causing flood levels to rise over time.
Significant changes to watershed cover can also increase flooding. Deforestation can produce such effects, because evapotranspiration is higher in natural forests than in prairies than in croplands. Deep infiltration of the remaining water decreases in the same order, thus, surface runoff should increase during this progression. It is difficult to document such changes with real data because they typically have occurred over decades or centuries. During that long interval, most rivers have become impounded or channelized, while many levees, etc., have been constructed. Besides, long-term gauging records are few, and even when they are available, it is difficult to evaluate the accuracy of old discharge calculations.
Small Basins In small, urban and suburban watersheds, the percentage of impervious cover can be large. Commonly asserted consequences are accelerated surface runoff, shortened lag times, low infiltration and increased runoff volume, together causing high peak flows followed by nearly dry channels. Several of these assertions are difficult to prove, because few small basins have been gauged for more than two decades, and because rating curves are poorly calibrated during the sharp flood peaks that convey a large fraction of annual runoff at such sites. Moreover, developed areas have detention basins that modify flow delivery, as well as sewers that can move runoff either into or out of a basin. So what can be learned? Plenty, if a basic observational approach is used. Interviews with long-term residents document repeated, episodes of extremely high water in areas downstream of impervious developments. Dry channels between storms can be observed, and compared to perennial flows in forested watersheds nearby. Channel morphology also offers abundant evidence for increased, sharp flooding in developed areas. Channels become widened and deeply incised, isolating the stream from its natural floodplain. Pipes and roots become exposed, and trees sag into the widened channel. Sediments become very coarse as all fines are all swept away, and large gravel antidunes may be present. All these features attest to rapid delivery of most of the basin’s water during intense, repeated flash floods. Climate Change Climate change, both natural and human induced, has the potential to grossly modify precipitation patterns. Annual precipitation amounts as well as the seasonal and short term delivery patterns can all change, with different consequences. Predictions are difficult. Available forecasts suggest that drought will intensify in some areas, while flooding will intensify in others. It is difficult to quantify such changes with available streamflow records, which are too short, too uncertain, and affected by changes to channels and watershed cover. One hallmark of human activities, however, is to increase the chaos of natural systems. A key concern is that storms will intensify, so that intense rainfall events may become more frequent. The number of hurricanes may increase, affecting low-lying coastal areas already threatened by rising sea level due to glacial melting. Such changes will also increase flash flooding in developed areas, where most of the world’s people reside. Water Quality Surface waters carry much higher quantities of suspended materials, salts, chemicals, contaminants, and organic matter than meteoric precipitation. These materials all have negative impacts on water quality. Suspended Materials The amount of suspended material in ordinary surface water varies widely, even at a single site. This material affects the turbidity of the water, a quantity that is normally reported in NTU (nephelometric turbidity units). Electronic optical devices are normally used to measure turbidity. However, a simple device called a secchi disk can be lowered into lake or ocean water until the pattern on it disappears, that depth providing a proportional measure of turbidity. Different types of suspended material can be present. In lakes and ocean water, turbidity is commonly caused by organisms such as algae, diatoms, or plankton. Cold, unpolluted, low-nutrient water can be very clear, particularly for deep bodies far from shore. On the other hand, most turbidity in flowing streams is due to suspended sediment, although organisms can also be present. Stream turbidity tends to vary dramatically with discharge. Fast, turbulent water can mobilize and carry great quantities of sediment, with the turbulence keeping small particles suspended. Turbidity is normally highest on the rising limb of the hydrograph, when surface runoff contributions are great and the rising water levels encounter and mobilize surface debris. Turbidity rapidly attenuates as flooding develops, as the water slows down and particles settle out. However, small clays particles, particularly montmorillonite, can remain suspended indefinitely if they become electrically charged and repel each other. However, such clays settle out quickly as rivers enter the ocean, and ions become attached to the clays, eliminating their mutual repulsion. Long-term changes to turbidity have occurred on many large rivers. Deforestation and prairie destruction, commonly accompanied by increases in plowed cropland, have increased soil erosion rates, so more material has been delivered to streams. However, stream turbidity in many areas, for example along the lower Missouri River, has actually decreased because sediment is now trapped in upstream reservoirs. Turbidity is the single most important indicator of water quality as it relates to human health. Several toxic metals including lead and mercury are mostly associated with the suspended load. Even more importantly, bacteria and viruses are particles, so they move along with suspended sediment particles or are attached to them. Thus, bacteria counts correlate strongly with turbidity. For this reason, the earliest attempts to purify water for human consumption utilized filtration or settling basins to clarify water. Salts Normal surface waters carry far higher quantities of dissolved ions than ordinary meteoric precipitation, common concentrations being 100 to 500 ppm for total dissolved solids. Higher values are common in semiarid areas and in areas where agricultural runoff is large. Concentrations also tend to increase downstream, but the opposite may hold if the upstream part of a watershed has a drier climate than that downstream, as is the case for the Missouri River. The electrical conductivity of water can be rapidly and accurately measured in the field with hand-held instruments, and the values are roughly proportional to total concentration for a given water type. Natural waters are classified according to their dominant cations and anions. Most commonly, the dominant cations in surface waters are Ca++, Mg++ or Na+, while the dominant anions are bicarbonate (HCO3-), SO4=, or Cl-. Thus, CaMg bicarbonate waters are most common, but many other types occur, such as sodium chloride waters, sodium sulfate waters, etc. Ionic concentrations at a given site normally vary with discharge. Concentrations under high flow conditions may be greater than 5x lower than those during low flows, when groundwater contributions are most important. Even under the highest flows, however, concentrations do not approach zero, but asymptotically approach some finite level. This is because groundwater contributions can still be important, and because ions are rapidly transferred from surface materials and suspended sediments into flowing water, so the dilute rain acquires ions almost as soon as it falls. Fertilizers/Pesticides In many developed countries, huge quantities of agrichemicals are applied to fields. In large parts of the United States, application rates of nitrate exceed 100kg/ha/y, a quantity much larger than plants can absorb. Phosphates and sulfate may also be applied in large quantities, along with various herbicides, pesticides, etc. Many of these chemicals are directly added to water which is then distributed in into furrows to irrigate fields, a practice called flood irrigation. It is no surprise that huge amounts of these chemicals ultimately end up in flowing streams that drain watersheds with agricultural activity. Consequences vary. Many of these chemicals are poisonous to plants or animals, and they can accumulate up the food chain. Others are plant nutrients that foster growth, which can be a huge problem where growth is not wanted. Many receiving waters are affected by thick algal or plankton blooms, and when these die and sink, their decomposition robs the water of all oxygen. Such eutrophic conditions affect many water bodies, and are harming the fisheries in a large part of the Gulf of Mexico. Problems 1. A famous “triple divide” is Triple Divide Peak, Montana; another is near Hibbing, Minnesota. Do these triple divides represent lines, or single points? To what water bodies will surface runoff flow that falls near Triple Divide Peak? 2. Many widely used equations in hydrology have hidden units. What are the units of the Chezy constant c in equation 3 and the Manning roughness coefficient in eq. 4? 3. Explain why the turbidity of Lake Superior is much lower than that of Lake Erie. 4. Suggest reasons for the scatter about the unit-sloped line in Fig. 14, a plot of mean annual discharge vs. basin area.