Rivers are dynamic, open systems. They take water from the global hydrological cycle, use it in their own local hydrological cycle and then return the water to the global cycle. The global hydrological cycle is a closed system. It (as far as you’re aware) doesn’t have any inputs or outputs, it remains constant¹.

When considering the hydrological cycle of a river, normally you look at the hydrological cycle of a river’s drainage basin. The drainage basin of a river is the area surrounding a river where precipitation flows into the river. It is sometimes called the catchment area because it is where the river “catches” its water. The boundary between two drainage basins is the watershed. Any precipitation that lands beyond the watershed lands in a different drainage basin and is part of a different river’s hydrological cycles.

Inputs & Outputs

A drainage basin is an open system meaning it has inputs and outputs. The most obvious input (at least here in Britain) is rain but snow, hail & dew all act as inputs too. These inputs (including rain) are grouped under the term precipitation, water that falls or condenses on the ground. Basins also have outputs that are, again, pretty obvious. Evaporation is a big one, where water turns into a gas and become part of the atmosphere. Transpiration is similar to evaporation but is the loss of water as a vapour from plant and tree leaves. The combined effect of evaporation and transpiration is called evapotranspiration. The final output, the one that a lot of people forget, is water flowing out of the basin. The technical name for this is river discharge.

Stores

A store is a way of storing water in a drainage basin. There’s a couple of different types of water storage. One is vegetation storage. Vegetation lives off of water right? Well, any vegetation in a drainage basin will take up precipitation and store it, simple. The vegetation storage is the total volume of water stored in the vegetation in a basin at one time.

Vegetation provides another type of storage too, intercepted storage. Vegetation doesn’t store all of the water it comes into contact with, some of it is intercepted by leaves where the water will remain until it evaporates or falls to the ground. Although vegetation is the most common interceptor of water, buildings and other structures will intercept water and act as stores too.

A lake or a pond is another type of storage as is their smaller cousin, a puddle. Yes puddles are small but they all add up to form surface storage. This can be a significant percentage of the total amount of water stored in a drainage basin. In addition to being stored on the surface, water is stored in the ground too. This is known as groundwater storage. This could be water that has been absorbed by the soil or it could be water that has percolated into rocks. You may have heard of a little something called the water table. The water table is a form of groundwater storage made up of lots of aquifers (permeable rocks) that have had their pores filled with water.

The final sort of storage is so obvious it isn’t obvious. Remember, we’re talking about stores in a drainage basin here, not the river itself, so any river channels that flow through the basin act as one giant store!

Flows

Flows are fairly simple, they’re just the different ways that water can move from point A to B in a drainage basin. One of the obvious types of flow is channel flow. The name gives it away, this is where water flows through a river channel at a speed dependent on the channel’s efficiency.

Another type of flow is overland flow. You may have heard of this as surface runoff. This is where water travels across the surface of the ground when it can’t infiltrate into it. You’ll get this sort of flow when the ground is baked (dried for extensive periods of time), saturated or frozen. You can also get overland flow when you have a lot of impermeable rocks that water can’t permeate through. Overland flow is fastest when the water is travelling down a steep sided hill and almost non-existent when the land is flat.

I used a term called infiltration in the previous paragraph. This is where water seeps into the soil through cracks and breaks in the surface. Once the water is in the soil, it can travel around in one of several different ways. One way is through throughflow where water moves downhill through the soil under the influence of gravity. The speed of throughflow is dependent on the type of soil and the presence of things like cracks and burrows which act as tunnels through which the water can flow. Instead of travelling through throughflow, the water can continue to seep into the soil and percolate down to the water table. At this point, it can travel above the water table through permeable rocks as interflow. Alternatively, it can travel beneath the water table as groundwater flow. If this groundwater feeds into a river, it’s called baseflow. The speed of interflow and groundwater flow is highly dependent on the permeability of the rocks the water’s travelling through. These processes are normally very slow but permeable rocks will make them faster². Vesicular³ rocks, such as pumice or vesicular basalt, allow water to percolate far more easily than rocks like granite, which aren’t vesicular.

There’s two more type of flow that we haven’t discussed, the first is stemflow. Like channel flow, the name’s a bit of a giveaway with this one. Stemflow is water that runs down the stems of plants or, alternatively, the trunks of trees. The second type of flow is throughfall (not to be confused with throughflow). This is where water drips off of leaves that have intercepted precipitation.

The Water Budget Equation(s)

Eep! Equations. Don’t worry, these equations (well, formulae if you want to get picky) are easy (they’re just addition), although there is a bit of Greek in them. The water budget equation(s) relate precipitation \(P\), evapotranspiration \(E\), run off \(Q\) & soil water storage \(S\). If you have a value for three of those variables, you can find the other one using simple addition. To find precipitation, for example:

\[ P = E + Q + \Delta S \]

That triangle is the Greek letter “delta”, it means change in, so that equation reads as “precipitation = evapotranspiration + run off + change in soil water storage”. You’ve already met precipitation, evapotranspiration and soil water storage but what’s run off? Run off is the volume of water passing the watershed; that is, flowing out of the drainage basin and into another one.

Typically, we use the water budget equations to calculate the amount of water stored in the soil rather than the precipitation in the drainage basin because it’s a lot easier to measure all the other variables than it is to measure the volume of water stored in the soil. From this point on, when I talk about the water budget, I’m referring to the amount of water stored in the soil with respect to precipitation, evapotranspiration & run off.

In the UK, or any place with a relatively temperate climate, the water budget changes in a predictable pattern throughout the year as the seasons (and hence the weather) change. In the winter months, there’s a large volume of precipitation but little evapotranspiration. This is primarily due to the colder, wetter climate and shorter daylight hours. When there’s more precipitation than there is evapotranspiration it’s called a ground water surplus. As the summer months approach, the climate becomes warmer & drier and the daylight hours increase⁴. This results in less precipitation and more evapotranspiration and we get ground water utilisation. All the water that was being stored in the soil in the wetter months is starting to be used up. By the middle of the summer, so much evapotranspiration has taken place and so little precipitation has fallen there isn’t much water left stored in the soil, this results in a ground water deficit. As the end of the summer approaches and the colder, wetter weather starts to appear again, precipitation once again begins to outnumber evapotranspiration and a ground water recharge takes place until we get a ground water surplus again. The cycle just keeps repeating itself over and over again.

You can graph the water budget if you want. If you plot evapotranspiration and precipitation on one axis and the month on another, you’ll get two curves. Here’s an example for a (fictional) drainage basin in the UK or some other temperate climate: