How flow generation controls stream hydrographs

Posted on April 9, 2020 by Anne Jefferson

The big picture

Now that you’ve learned all about the four different ways to generate streamflow, you might be asking yourself why they matter. Here’s why it matters: The streamflow generation mechanisms working in the landscape control how quickly the stream responds to precipitation – and how quickly the stream responds to precipitation controls how high the peak flow gets.

Fundamentally, it comes down to whether water moves to the stream over the land surface (as overland flow) or underground (as subsurface or groundwater flow). Even though a landscape might be covered with grass or trees, it’s still a lot easier for water to move downhill at the surface than to work its way through pores a few microns in size in soil and rock. Even when macropores are acting as super-highways of subsurface flow, they are still smaller, more tortuous, and less well connected than surface flow paths.

steep rocky slope on left, soil profile on right

Imagine you are water. Which way easier to move downward – flowing overland on the rough slope or squeezing through tiny pores in the soil?
Photos by Lhoon on Flickr and the Noble Research Institute.

If you have a very small headwater stream that is fed by a few hillslopes, and water gets down those hillslopes very quickly, it doesn’t matter whether the rain drops fall on the top of the slopes or the bottoms, all of the water will arrive in the stream at very similar times. And if all of the water arrives in the stream at once, you will get a very high peak flow. But if your water movement is slower, then rain falling on the upper parts of the hillslopes will reach the a long time after the water from the rain that fell on the lower parts of the hillslopes. With those staggered arrivals, you will get a lower peak flow.

(There are analogies that you can make with rush hour on city streets and freeways. Can you think of them?)

Putting it together, overland flow is faster than subsurface flow, and faster flow on/in the hillslopes leads to higher peak flows in the streams. (There’s a little wrinkle here in terms of the way we are talking about speeds, but we’ll get to that in a few paragraphs and this works for now.) Said another way, the shorter the lag time between precipitation and streamflow response, the higher the peak flow.

Now let’s add some nuance and think about the streamflow generation mechanisms one by one.

Infiltration excess overland flow

Infiltration excess (or Hortonian) overland flow is generated when it’s raining too hard for the soil to infiltrate into the subsurface. So the water always stays above ground. A little bit gets caught in the microtopography and ponds, but most of it runs off downslope. Water flowing at the surface will quickly collect from sheet flow into rills, which funnel water efficiently into streams. These rills will form in the steepest paths downhill and the flowing water will smooth out the land surface, decreasing friction and increasing the velocity of flow. [In urban areas, where impervious surfaces promote infiltration excess overland flow (which we call stormwater), gutters and storm sewers make super-smooth, super-speedy pathways for water to flow.] It take just minutes for overland flow to reach the stream. And when it stops raining, overland flow will finish draining to the stream quickly, usually completely stopping within hours. Infiltration excess overland flow is the proverbial hare in the foot race – fast as a flash for a little while, then stops moving.

Groundwater flow

In contrast, groundwater flow is ssssssllllooooooooowwww. Water infiltrates, percolates downward to the water table, and then moves down the hydraulic gradient as a function of hydraulic conductivity and hydraulic gradient (more-or-less slope of the water table) until it reaches the stream. Almost all of this movement happens through pore spaces that are a few microns to tens of microns in size. It can take months to years for groundwater to move from a hillslope into a stream.

That doesn’t mean that if it rains on April 10, that a groundwater-fed stream won’t start to rise in July. Instead, the new water molecules that recharge groundwater as a result of a storm help raise the water table and steepen the hydraulic gradient. That in turn causes water molecules that were already in the aquifer (old water) to flow a tiny bit faster toward the stream. So, if it rains April 10, a groundwater-fed stream may rise on April 11-13 (i.e., groundwater-fed streams respond on timescales of days). But that slow groundwater movement will also keep flow in the stream for weeks to months between storms. Groundwater flow is the proverbial hare – it just keeps plodding along. [Karst is an important exception to this generalization.]

An important aside: velocity vs. celerity

For water that moves through the subsurface, there is an important distinction between velocity (the variation of a water molecule’s position over time) and celerity (the speed at which a signal is propagated). Velocity controls the transit time (or age) of the water in the system and affects things like weathering and contaminant transport. Celerity controls the hydrograph shape – how quickly water rises and falls in the stream. The difference between velocity and celerity exists for overland flow as well, but since both timescales are so short, it’s less important for our purposes.

I like to think about water from the hose when I'm mentally separating velocity and celerity.

I like to think about water from the hose when I’m mentally separating velocity and celerity.

If you are struggling with the distinction between velocity and celerity, here’s the analogy I like to use: It’s a hot summer day, and you decide to get a drink from the hose. You turn the water on at the tap and water starts to come out the other end of the hose within a few seconds, so you bend down to take a drink. Ew!! The water is all hot and gross. But give it a minute or two and the water cools down and tastes much better. The quick response of water coming out of the hose as soon as you turn the tap on is a function of the celerity, but the change in temperature and taste is a function of velocity. Water coming from the tap pushes the old, hot water out the other end of the hose (celerity of the signal), but it takes a while for the fresh cold water from the tap to make it down the length of the hose (velocity of the molecules).

The illustration below may also help. It is from Hrachowitz et al., 2016 Transit times – the link between hydrology and water quality at the catchment scale, WIREs Water.

Follow what happens to the red dot over time vs. the release of water (i.e., cumulative streamflow) (Image from Hrachowitz et al., 2016, used under fair use)

Follow what happens to the red dot over time vs. the release of water (i.e., cumulative streamflow) (Image from Hrachowitz et al., 2016, used under fair use)

So if infiltration-excess overland flow is the fastest and groundwater flow is the slowest, where do subsurface stormflow and saturation overland flow fit in?

Subsurface stormflow

Subsurface stormflow exploits macropores and preferential flowpaths to move through the subsurface more quickly than most groundwater flow. It also doesn’t go as deep in its path from hillslope to stream. But it’s still in the subsurface, so the velocity of the water molecules is still quite slow and transit times are likely in the range of weeks to months. However, preferential flow paths help accelerate the celerity of response. New water moving rapidly downward in preferential flow paths helps generate saturation just above the lower conductivity layer, increasing hydraulic conductivity in the soil and increasing the hydraulic gradient. That causes old water to move out of the soil and into the stream, raising water levels in the stream within a few hours of the rainfall.

Saturation Overland Flow

Now let’s get to saturation overland flow, which is the trickiest to wrap our heads around because it’s really a combination of all of the above. Where saturation overland flow is occurring, water is moving on the land surface and everything I said about infiltration excess overland flow applies. It’s fast and efficient. And for the direct precipitation on saturated areas, that’s all that matters, and timescales of response are in minutes.

BUT! Some of the water that becomes saturation overland flow is “return flow”, i.e., it is subsurface stormflow that has returned to the surface because the water table has reached or exceeded the surface elevation. So then we have to think about the relevant time scales for subsurface stormflow and for transit times, that means return flow overland flow may be weeks to months old. For hydrograph response (celerity), it may be hours, not minutes. Add direct precipitation and return flow together, and you end up with a hydrograph response from saturation overland flow that is a bit slower than you get with pure infiltration-excess overland flow.

Remember also that it takes time to saturate different pieces of the landscape – that’s related to the variable source area concept – so in whatever period exists between the start of rainfall and developing saturation overland flow in a particular area – everything I wrote about subsurface stormflow is what applies.

Real Watersheds

This is true more generally. No watershed has a completely spatially uniform response to a rainstorm. There is always going to be some mix of flow generation mechanisms happening, because of variability in soils, topography, vegetation and human impacts even in small areas. This means that no one scenario above is going to apply for a whole watershed – even during a single storm – instead it will be a blended, splendid mess that you will try to interpret in the context of the watershed characteristics and flow generation mechanisms that are likely to be at work.

As you get to larger watersheds, these flow generation mechanisms still matter and are likely to be even more heterogeneous, but the shape and size of the channel network also starts to matter a lot. At some point (~50-100 km2), the channel network tends to become much more important than the hillslopes. We’ll pick up on that theme in the coming weeks.

Where does this leave us? What’s the TL;DR version?

  • There is a difference between velocity and celerity. Celerity is what matters when we are trying to connect flow generation mechanisms to hydrograph responses. But velocity matters for other things, like water quality.
  • Infiltration excess overland flow generates the fastest hydrograph response (smallest lag time) – and the highest peak flows.
  • Urbanization promotes infiltration excess overland flow, which is why urban streams are so notoriously flood prone.
  • Saturation overland flow also results in fast hydrograph responses and high peak flows, but not quite as extreme as infiltration excess overland flow.
  • Both overland flow mechanisms can give us peak flows that occur * Subsurface stormflow produces a hydrograph response within hours in small watersheds and it’s peak flows can be big, but not as big as those from overland flow.
  • Groundwater is slow but steady and mostly supports baseflow. Left on its own, it produces peak flows that are much, much smaller than any of the other flow generation mechanisms.
  • Real watersheds, even small ones, rarely have a single flow generation mechanism operating at all times. That means that real hydrograph responses are going to have a mixture of the characteristics described here and we can’t usually invert a hydrograph to tell us what flow generation mechanism produced it.

In graphical form:
Does this figure make sense based on what you've read? It's from David Knighton's Fluvial Forms and Processes book (used under fair use) Does this figure make sense based on what you’ve read? It’s from David Knighton’s Fluvial Forms and Processes book (used under fair use).

Categories: by Anne, hydrology

How does water that falls on land get to streams?

Posted on April 8, 2020 by Anne Jefferson

It’s a rainy day and you can see that the water level is rising in your local stream. That’s because of the rain falling on the stream channel and its tributaries, right? Wrong.

In most watersheds, <1% of the land area is covered by streams, lakes, and wetlands, and that means that more than 99% of rain lands on vegetation or land rather than on water.  So in order to explain why water levels in streams and rivers rise during storms or shortly thereafter, we have to get the water from land downhill to the stream network. We call the processes that do that work streamflow generation mechanisms or runoff generation mechanisms. 

There are four classic streamflow generation mechanisms and I’ve cobbled together videos on each of them. If you’ve ever wanted to know more about what is happening under your feet in wet weather, and you’ve got about an hour to spare, you can learn all about it by working your way through the videos below. 

If videos aren’t your thing, or you want to supplement what you watch with some informative web pages and even practice quizzes, check out this resource from the COMET program.

Start here to learn about streamflow generation
If you’ve only got time for one video, this one is the content-rich introduction that you are looking for:

Terminology note: In the video above and in other resources listed below, you may see the phrase “runoff generation” used. I prefer the term “streamflow generation” because I’m interested in all of the ways that water gets to streams (or other water bodies), not just ways that involve surface runoff or overland flow. I also use the term streamflow generation to talk about how we get baseflow (i.e., water in the stream between storms), which is not runoff. 

More about infiltration-excess (or Hortonian) overland flow

I’ve put together the video below to tell you more about what happens when it rains too hard for a soil to infiltrate all of the water.

Thanks to Todd Walter of Cornell University for the illustrations in the middle of the video. To play with those some more or learn about the history of our understanding of infiltration excess overland flow, you should visit his website.

More about subsurface stormflow
In humid, vegetated areas, we often have low enough rain intensity and high enough infiltration capacity for water to infiltrate rather than run off overland. But even though the water is in the soil, it can still cause an increase in streamflow. I made a video to explain how.

More about saturation overland flow (and the variable source area concept)
Even if rain intensity is low and infiltration capacity is high, if it rains long enough things get really wet. Sometimes water runs off overland because the ground is saturated. The wetter things become, more areas become saturated. I try to explain in the video below.d

Thanks again to Todd Walter at Cornell for the excellent illustrations. To learn more about saturation overland flow and the related concept of variable source area, you should visit at Todd Walter’s page on saturation overland flow and variable source area to review the animated sequences (and much more).

Taking it slow: More about groundwater and its connection to streams
OK, so water can get to streams during and shortly after rain storms. But where does water in streams come from when it’s not raining? Or when it hasn’t rained in a long time? The answer is groundwater, and this video does a great job of talking us through some really basic concepts, including connections between groundwater, streams, and lakes and the potential effects of pumping groundwater.

Just can’t get enough? Master class on streamflow generation

If you think that streamflow generation mechanisms are just about the coolest thing that you’ve ever heard of, then you can learn so much more about them from one of the world’s leading experts on hillslope hydrology: Jeff McDonnell in this 3 hour short course. When I was a graduate student I got to take a 10 week hillslope hydrology class with Dr. McDonnell and it changed the way I think about the world beneath my feet. Listening to 3 hr recorded presentation isn’t nearly as good, but you could still learn a lot if you want to do a deep dive. 

Still can’t get enough? You can watch videos from McDonnell’s 10 week course. But as you do that, you should consider graduate school in hydrology, because you have clearly got the bug. I bet you get excited by mud, snowmelt, floods, and good, heavy rain storms too.

Categories: by Anne, hydrology

Measuring infiltration capacity in the field

Posted on March 15, 2020 by Anne Jefferson

Infiltration is the act of water moving from the land surface into the soil. Usually, we think about infiltration occurring in response to rainfall, where water is applied over the whole land surface. In that case, infiltration is important because it’s one of the deciding factors in how much rainfall becomes available to plants and groundwater, versus running off over the land surface and potentially causing erosion and flooding.

Infiltration is also important for applications like irrigation – where furrows or drips might apply water to one part of the surface and not others, in order to more efficiently provide water to crops. And infiltration is extremely important for stormwater green infrastructure, like rain gardens and bioretention cells, because we are explicitly designing them to be able to infiltrate water from impervious surfaces like parking lots and roof tops. For green infrastructure, the engineered soil properties are carefully designed to promote just the right amount of infiltration, but the performance of the green infrastructure can also be affected by the infiltration capacity of the surrounding “native” soils and sub-soil.

Based on the above, there are a lot of reasons hydrologists want to be able to measure infiltration, but what exactly are we going to measure? First we need some definitions. Typically, we talk about infiltration as a rate: how fast is water entering the soil? But let’s say it’s raining 0.5 cm/hr, sort of a drizzle. A lot of soils can soak that water in, no problem, giving an infiltration rate that is equal to rainfall rate. So, just talking about infiltration rate might not be helpful. Instead, we talk about infiltration capacity, the maximum rate at which water can enter a soil. But here’s the funny thing, infiltration capacity changes over the course of a rain storm (or irrigation event), so you can’t just measure infiltration capacity at any random point of time and assume you’ve captured a value that applies at other times.

Graph of infiltration rate (y-axis) vs. time (x-axis), curve decreases over time towards asymptote marked as ksat = 0.52 cm/hr

Infiltration rate in an Oklahoma sandy loam decreases over time, in a typical exponential fashion. The asymptote is the saturated hydraulic conductivity. [Image by Oklahoma State U., clink image for source.]

Fortunately, after a long enough period of time, the infiltration capacity starts to asymptotically approach a constant value. We call this steady-state rate the equilibrium infiltration capacity, which conveniently (and logically) is approximately equal to the the saturated hydraulic conductivity. And it’s that steady state rate that we most often want to measure. But how do we do it?

Cutaway view of two gray rings at land surface and a bulb of water below the soil surface, with a darker blue plume indicates water from the inner ring

Schematic of infiltration below a double ring infiltrometer. [Image by SDEC. Click image to go to source.]

The most common way to measure equilibrium infiltration capacity is through a double ring infiltrometer. These devices consist of two concentric rings (30 cm and 45-60 cm in diameter) pounded slightly into the soil and filled with water. The water from the outer ring helps wet the soil and infiltrates both vertically and laterally into the dry soil. The infiltration rate is measured in the inner ring , where infiltration and percolation are happening only vertically, thanks to the water from the outer ring doing the lateral movement. Water levels are maintained at the same depths in both rings. We say that outer ring reduces the boundary effects for the measurement of vertical infiltration in the inner ring. You can do infiltration capacity measurements with a single ring infiltrometer, but it’s considered less accurate because of these boundary effects.

Tests can be conducted in two ways: falling head and constant head. In a falling head test, water is added to the rings and the water level declines over time as infiltration occurs. In high infiltration capacity soils, it may be necessary to add water several times before steady state is achieved. Falling head tests require less equipment than constant head tests, but the math is a bit more complicated. In constant head tests, a device called a Mariotte bottle is added to the infiltrometer. A Mariotte bottle releases water so that a constant level (or head) is maintained inside the rings. This simplifies the math considerably.

The video below shows a falling head double ring infiltrometer test. [It’s probably not necessary to watch the whole thing, once you have a sense of how things are going.]

The next video is a fantastically informative USDA instructional video for how to set up and use a constant head double ring infiltrometer. [I personally enjoy watching this one slightly sped up.]

Can’t get enough double ring infiltrometer action? You can check out this video with step-by-step instructions for set up, with some sweet elevator music in the background.

As you are probably starting to realize, it takes a fair amount of work and quite a bit of water to make a double ring infiltrometer measurement. What happens if you need to get into a remote site or have a limited amount of water? Another device, called a Guelph permeameter, can help you out here. The Guelph permeameter works on a similar principle as the infiltrometer, but water coming out of it sets up a wet bulb of a specific known shape, from which you can calculate equilibrium infiltration capacity. With a Guelph permeameter, you make measurements at two different specified heads (usually 5 and 10 cm), and in each case allow infiltration to occur until a steady rate is reached. Then you plug your steady rates and your chosen head values into an equation to get a number for saturated hydraulic conductivity.

Here are some Watershed Hydrology students using a Guelph permeameter along the banks of a Pennsylvania stream. Note how much faster the water infiltrates at the 10 cm head (second half of the video) than the 5 cm head (first half of video). [Question for Watershed students: Can you figure out why?]

Another cool thing about Guelph permeameter is that you can fairly easily get vertical profiles of hydraulic conductivity or get the measurement at single specified depth below the surface (this would be useful for green infrastructure design, for example). The video below gives pretty detailed instructions for how to set up and use a Guelph permeameter and includes a demonstration of the capability to got deep.

Categories: by Anne, hydrology, teaching

How easily water moves in soil depends on how big the soil pores are, how well they are connected, and how wet they are

Posted on March 12, 2020 by Anne Jefferson

Hydraulic conductivity is the term used to describe how easily a fluid moves through a porous medium. In the case of water infiltrating into soils, the fluid is the water and the porous medium is the soil. We often use K to represent hydraulic conductivity when we are writing equations.

When all of the soil pores are full of water, we call this saturated hydraulic conductivity, Ksat. Saturated hydraulic conductivity is a function of how big and how well connected the soil pores are. In general, soils with lots of smaller particles (silts, clays) have smaller and less well connected pores than soils with lots of larger particles (like sands). Therefore, sandy soils have higher K than silty and clay-rich soils (even if they have less total pore space).

Circles showing sand grains and big pores and clay soil and small pores

Illustration of the different characteristics of pores relative to grain sizes

The difference in K can be several orders of magnitude:

Diagram showing the range of hydraulic conductivity values for different types of rocks and sediments

Image from: Heath, R.C., 1983. Basic ground-water hydrology, U.S. Geological Survey Water-Supply Paper 2220, 86p. (Public domain)

Across the full range of rocks and sediments, we can measure K over a range of 12 orders of magnitude (an order of magnitude is a factor of 10). Across a typical range of soils, K might vary by 4-5 orders of magnitude. That means that water can flow 10,000 times more easily in some soils than others.[Isn’t that mind-blowing?]

But in all soils, water moves more easily when all of the pores are water filled (Ksat) than when some pores have air in them (Kunsat). Why is that? This video explains…

Curious about the figure in the upper left part of the screen at the beginning of the video? Here’s a video that explains the soil characteristic curves for wetting and draining:

Categories: by Anne, hydrology

How wet is the unsaturated zone?

Posted on March 12, 2020 by Anne Jefferson

In my Watershed Hydrology class, we’ve been talking about soil moisture and water potential in relation to evaporation and infiltration. An important concept is the idea of the unsaturated zone, where the pores (or open spaces) in the soil, sediment or rock are not completely filled with water most of the time. In class, I went over a diagram of the unsaturated zone and talked about the capillary fringe. I found the figure below to be quite useful in summarizing the different parts of the unsaturated zone and how wet those parts usually are. Take a look at the figure now, and then I’ll define the relevant terms below the image.

Diagram of unsaturated zone showing root zone, intermediate zone, capillary fringe, groundwater, etc. usual range of water content and pressure state are also shown.
Figure 6-15 from Dingman, Physical Hydrology, 2nd Ed. Posted under fair use.

On the left, there is the usual range of water content, where water content is noted with θ (theta). All the way down, water content is always equal to or less than porosity (φ, phi). In the rooting zone, where both infiltration and evapotranspiration occur, water content is usually someplace above θpwp, where pwp stands for the wilting point. Below the rooting zone, there isn’t much effect from evapotranspiration, so water content tends to stay at or above θfc, the field capacity, which is when drainage due to gravity stops. Below the water table, you find the saturated zone, where water content is equal to porosity (φ, phi), by definition. Just above the saturated zone is the weird world of the capillary fringe. Here too water content is approximately equal to porosity, because water is drawn up into this zone by capillary effects (just like a sponge gets wet higher than level of the water when it is placed in a pool of water).

On the right side of the diagram, you can see the water potential, in this case expressed as pressure. All the way down to the water table, potential is negative and in the form of matric potential (ψ, psi). Remember, matric potential is always negative, and represents the tension being exerted on the water in the pores. At the water table, matric potential is zero and pressure potential is zero. Below the water table, matric potential goes away and pressure potential is positive, caused by the weight of the overlying water. One last point is that the top of the capillary fringe is where the matric potential, ψ, is equal to the air entry tension (ψae). That’s the point at which a significant amount air starts to occur in the pores, when then starts to change how easily water moves through them.

Want it drawn out for you again? The video below is a great explanation of the unsaturated zone (sometimes called the vadose zone) and related concepts.

Categories: by Anne, hydrology, teaching