Water Dynamics over Longer Timescale

Read…

When we consider water dynamics over longer timescales, typically spanning a year or more, a notable fact emerges: the term representing water storage (g_w) tends to become relatively small. This might cause you to ask: why does this occur? As we've previously discussed, the significance of the g_w term can vary considerably from season to season, playing a crucial role in short-term water balance. However, over extended periods, regions generally do not undergo drastic shifts from being extremely wet to exceedingly dry. For instance, a location like State College, PA, doesn't transform from a tropical oasis to a barren desert within a single decade.

Given the relatively minor changes in storage over such timescales, we can reasonably assume that the g_w term essentially approaches zero (on long timescales). Additionally, we can assume that the dewfall (D) term is relatively small, since buckets and buckets (and buckets) of liquid water do not instantaneously leave the atmosphere on dewy mornings. Consequently, we simplify our equation to include just three terms:

$$\mathrm{\Delta } \mathrm{F} = \mathrm{P} - \mathrm{E}$$

While extremely simple, this has powerful implications. Firstly, if horizontal transport (ΔF) is absent (ΔF = 0), then precipitation (P) and evaporation (E) must perfectly balance at a particular location (P = E) to ensure water conservation. This concept aligns with our earlier discussions about energy budgets, as consistently higher precipitation than evaporation would imply a perpetual increase in surface moisture. This scenario is unsustainable in the long run. If we consider the planet as a whole (over which all ΔFs must cancel themselves out) P and E must be identically globally!

Moreover, the equation indicates that if we observe both precipitation and evaporation at a specific location and these two values are not equal, there must be some form of horizontal water movement into or out of that region to maintain this balance. As we discussed previously, when this water is on the surface, it's referred to as runoff. In the atmosphere, this corresponds to the movement of water northward or southward, eastward or westward due to atmospheric motion. Imagine a puffy cloud drifting overhead on a fair-weather day – this is a manifestation of ΔF in action within the atmosphere, transferring water from one place to another.

By observing P and E on the surface at different locations, we can form influential hypotheses regarding climate. First, let’s think about the global scale. The two figures below show what scientists call the “world water balance.” The first figure below illustrates what a cubic kilometer looks like in comparison to Manhattan, the Empire State Building, and the Burj Khalifa. In the second figure that follows it, the non-italic numbers represent the volume of water stored in different components of the cycle (in thousands of cubic kilometers -- a cube 1 km on each side), and the italicized ones show the volume transferred between these components annually (in a thousand cubic kilometers per year). For instance, the ocean is shown to have 1,335,040,000 cubic kilometers of water (remember we said, “more than a billion” in the first section!) Comparatively, the atmosphere contains a tiny fraction of the planet’s water at any given time (12,700 km³). For every single tiny drop of water in the atmosphere (say 0.05 mL) there is a corresponding 5 liters (more than two large soda bottles) of liquid water in the ocean!

However, let’s focus on the italicized terms representing the budget terms we’ve been discussing. Over the ocean, 413,000 km³ evaporate per year. We also observe that over the ocean, 373,000 km³ of water falls in the form of precipitation. So we have 40,000 km³ of extra water that is accounted for – that is, the amount evaporated into the atmosphere exceeds the amount that falls out of the atmosphere. We must have a non-zero transport term. In this simple framework, where the whole world is only ocean or land, this water must somehow be transported from above the oceans to above the land to balance things out, since we can’t just keep building up water in the atmosphere forever. This is known as “atmospheric transport” – and is associated with all sorts of motion, from small little clouds drifting eastward over San Francisco to giant hurricanes making landfall in Florida. This is shown as “ocean to land water vapor transport.”

Correspondingly, over land we see more precipitation 113,000 km³ versus evaporation 73,000 km³. This means that over land surfaces, we must have a surplus of water falling onto the surface. P minus E equals 40,000 km3! Therefore, we need water to be transported out of land regions (as surface runoff into oceans) to balance things out. That is the “surface and groundwater flow” arrow. All things put together, the Earth’s ocean acts as a source of water for the land surface, and this water is carried via atmospheric motions. After it precipitates on land, it is returned to the ocean via horizontal transport across (and below) the surface!

We can also take a slightly more granular look at this. Now, we could go down a rabbit hole and talk about the water balance for every county in the United States, but we have other things to discuss! So, let’s look at individual continents. Below is the continent-wide annual average evaporation (E), precipitation (P), and horizontal transport (ΔF) in mm/yy for the seven continents on Earth in average mm/year. A few things first stand out. First, South America has a lot of precipitation! If you have visited a place like Brazil, you know that it’s very tropical and associated with heavy rainfall rates. About 60% of precipitation evaporates back into the atmosphere, showing how important the land surface is to the global water cycle. Therefore, approximately 40% of a continent's precipitation is channeled back to the oceans through river systems (which roughly matches up with our figure above, which showed 40,000 km³ of runoff and 113,000 km³ of precipitation!)

A key metric of continental moisture is the runoff ratio, denoted by $\mathrm{\Delta } F / P$, which quantifies the proportion of precipitation that contributes to oceanic runoff rather than being reabsorbed into the atmosphere via evaporation. A higher ratio signifies that a greater portion of rainfall contributes to runoff, which is characteristic of wetter continents. Conversely, continents such as Africa and Australia, known for their arid climates, exhibit lower runoff ratios. So, the balance between these water budget terms is important for determining regional climate – we’ve shown this at the continental scale, but this certainly happens in much smaller regions, too! We don’t have the time to cover every single aspect of regional climate in this class, but in the next chapter, we’ll discuss how atmospheric circulation plays an important role in determining where this precipitation falls and why some areas are wetter than others even if it wouldn’t exactly make sense from looking at a map!