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An argument can be made that water is the single most important molecule on our planet. First and foremost, it is crucial for sustaining life – you and I literally can’t live without it! It’s also a critical part of our planet’s climate system. The role of water is evident in extreme weather events like seasonal floods and droughts, and it is vital for the health of natural ecosystems and human societies. It serves as a connecting medium among the primary components of the climate system. And it’s incredibly unique in that it’s one of only a handful of substances that exist in solid, liquid, and gaseous states within the Earth’s atmosphere (and on its surface) at any one time.

While you have certainly talked about the states of water somewhere before, let’s make sure we are all on the same page. It's important to understand that water can exist in three primary phases: solid, liquid, and gas. These phases refer to the physical state that water takes under different temperature and pressure conditions. Let's explore the three phases below.

Water, with its distinctive characteristics, is abundant on Earth. It's interesting to note that over two-thirds of our planet's surface is enveloped by water, predominantly over the oceans. In fact, oceans hold approximately 97% of Earth's water, amounting to an astonishing volume – over a billion cubic kilometers. The rest, a mere three percent, is distributed among the polar ice caps, various lakes, rivers, streams, and as groundwater, which is water contained within soil, sand, or rock crevices.

You’ll notice that I only mentioned water on the surface – notoriously absent was any discussion of the atmosphere. In fact, only a very tiny amount of water (by volume) exists in the atmosphere (about 0.03 percent), and nearly all of it exists as water vapor. Still, the small fraction that exists as water vapor in the atmosphere is enough to fuel all the extreme weather we observe on Earth, including tornadoes, hurricanes, and blizzards. What little water vapor exists in the atmosphere at any given moment doesn't last for long because water is regularly changing phases, and being exchanged between the surface and the atmosphere. Remember, water vapor is a variable gas, meaning that its concentration changes in time and space, from near zero to four percent of atmospheric gases (by volume). The possible paths that water can take as it changes phases and gets transported between the surface and the atmosphere make up the hydrologic cycle (or "water cycle"), a simplified version of which is shown in the graphic below.

A simplified hydrologic cycle diagram. Water enters the atmosphere primarily through evaporation and transpiration, and is returned to the surface through precipitation.

Credit: The Water Cycle. Global Precipitation Measurment (NASA) (Public Domain).

Before we analyze the hydrologic cycle's components, we need to formally define some important processes. Water exists in these three states, and an individual water molecule frequently bounces between them -- in other words, it exists in different phases during its lifetime as a water molecule. The process of moving between these phases is known as a "phase change." For example, think about what happens when you take an ice cube out of the freezer and leave it on the counter. Over time, the ice melts into liquid water—that’s a phase change from solid to liquid. These transitions are not only fundamental to understanding how water behaves in different environments but also essential for grasping its role in the climate system. They affect things from weather patterns to life on Earth, influencing a wide range of natural processes.

I will assume you are already familiar with melting (where a solid changes to a liquid) and freezing (where a liquid changes to a solid). But the other transformations of interest are:

• Evaporation: The process by which liquid water changes to water vapor, as bonds between neighboring liquid water molecules break, and molecules escape to the air as water vapor. Watch vapor rise off asphalt after a mid-summer thunderstorm, and you are witnessing evaporation.
• Condensation: The process by which water vapor changes to liquid (the reverse of evaporation). Ever grab an ice-cold beverage out of the fridge and notice that water droplets grow on the outside of the bottle? That is water vapor from the air condensing on the bottle’s cold surface!
• Sublimation: the process by which ice changes directly to water vapor without becoming liquid first. This can be observed if you leave an ice cube tray in the freezer too long—eventually, there’s nothing left!
• Deposition: the process by which water vapor is deposited directly as ice. If you’ve ever seen cool (no pun intended!) frost patterns on a window first thing in the morning, you’ve observed deposition.

Water evaporating off a field after a summer rainstorm

Credit: n.a. “Evaporation.” National Geographic. October 19, 2023.

Water that has deposited (i.e., gone from vapor directly to solid) on a window, forming something known as "fern frost" where the deposition patterns look like little ferns!

Credit: Schnobby, CC BY-SA 3.0, via Wikimedia Commons

Remember, these are all “phase changes” where water in one phase is transformed into another through either the release or uptake of energy (more on that later). There is one more term we need to define, which isn’t technically a phase change, but is important for understanding how water on Earth’s surface can get moved into the atmosphere.

• Transpiration: The process by which plants release water vapor into the air (plants transport water from their roots to the leaves, where they "sweat," and the water evaporates into the air).

Movement of Water Through the Earth-atmosphere Cycle

Now that we understand these concepts, we can explore the movement of water through the Earth-atmosphere system. Water in its liquid form, found in lakes, streams, rivers, and oceans, evaporates into the atmosphere. This is supplemented by transpiration from plants and the evaporation of groundwater from soil, among other sources. As air ascends, some of the water vapor forms cloud droplets. When clouds become sufficiently dense, water returns to Earth as precipitation. Some of this water replenishes groundwater, while the rest flows into lakes, streams, rivers, and eventually back to the oceans, where it can evaporate again, continuing the cycle.

Evaporation is the primary way water vapor enters the atmosphere, with transpiration and sublimation contributing to a lesser extent. In the hydrologic cycle, the largest movements of water occur through evaporation and precipitation. The water quantity near the Earth's surface remains fairly stable over short time spans (like a year), indicating that global precipitation is approximately equal to global evaporation. We'll cover this in more detail in a little while.

Interestingly, once water vapor enters the atmosphere, it doesn't linger there for long. On average, it takes about 11 days for a water molecule to evaporate (or enter via transpiration or sublimation), condense into a cloud, and return to Earth as precipitation. However, water stays much longer in its liquid or solid state on Earth. A water molecule in the ocean typically remains for about 2,800 years before evaporating, and one in a glacier might stay frozen for tens of thousands of years.

This explains why a relatively small amount of water in the Earth-atmosphere system exists as water vapor: it spends a brief period in the atmosphere before returning to the Earth. Most of the water is found in oceans or ice sheets, as water molecules reside there for extended periods before evaporating. Despite this, the small fraction of water that cycles through the atmosphere as water vapor and then as precipitation significantly influences the weather. Therefore, understanding the phase changes of water, especially evaporation and condensation, is crucial in the hydrologic cycle. Let's delve deeper into these phase changes in the following sections.

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Since evaporation and condensation are such important phase changes for water day-to-day in the climate system, they deserve more of our attention. We defined them in the previous section, but now, let’s look closer at how these processes work.

Evaporation is when liquid water molecules break their bonds with neighboring molecules and transform into water vapor. You might recognize it as a natural cooling mechanism from sweating on a hot summer day as your body's way of regulating temperature. But what exactly causes this cooling effect?

Firstly, it's essential to understand that water molecules with the highest kinetic energy, those with the fastest vibrations, are the most likely to break their bonds with neighboring molecules and transition into vapor. Remember, the kinetic energy of a group of molecules is directly related to the material’s temperature. Kinetic energy refers to the speed at which molecules, or their constituents in a vibration, move. The faster they move, the higher the temperature. This removal of high energy water molecules during evaporation reduces the average kinetic energy of the remaining liquid water because the most energetic molecules have gone off and transformed into vapor. Since the most energetic molecules are gone, we are left with molecules not moving quite as fast. This reduction in kinetic energy leads to a decrease in the remaining water's temperature.

Secondly, the process of breaking bonds between liquid water molecules requires energy. Where does this energy come from? The surrounding air! Simply put, as water evaporates, it extracts kinetic energy from its surroundings, including the air. So it’s a bit of a double whammy -- both the fact that high-energy molecules leave less energetic (somewhat cooler) water behind and that evaporation “steals” energy from the air -- that overall gives us cooling during evaporative processes.

As water evaporates from your skin, it feels cooler, right? That's because the fastest-moving water molecules (the ones with the most energy) are 'jumping' off into the air, taking energy with them. Meanwhile, the water molecules left on your skin are slower-moving and less energetic, corresponding to a lower temperature. Or think about mist rising off a swimming pool on a warm day. That mist is water evaporating into the air and then condensing into small droplets, carrying energy away from the pool and cooling the surface in the process.

Overall, water’s phase changes involve either absorbing kinetic energy from or releasing kinetic energy to the surrounding environment, as demonstrated in the “energy staircase” diagram for ice, water, and water vapor below. While this diagram encompasses all possible phase changes of water, our primary focus will be on two of particular interest: evaporation and condensation.

Starting with liquid water, a select group of highly energetic water molecules can gradually break their bonds with neighboring molecules and transition to the vapor phase over time. To accomplish this transition, a specific amount of energy is necessary – 600 calories from every gram to move from the “liquid” stair to the “vapor” stair. This energy input is required to break all the bonds and facilitate the rapid transformation of all the water into the gaseous state of water vapor, representing the highest energy step. This process, in turn, leads to a cooling effect on the surrounding air.

The energy levels associated with ice, water, and water vapor can be considered a set of steps. Changing from one phase (solid, liquid, or gas) to another requires either an addition of energy (stepping up) or a release of energy (stepping down).

Credit: David Babb© Penn State University is licensed under CC BY-NC-SA 4.0

So, if evaporation is a cooling process, what about its reverse -- condensation (the process by which water vapor changes to liquid)? When water vapor condenses back into water, there's a step-down in energy levels, so if you think condensation is a warming process… well, you're correct! Indeed, the energy used to evaporate water in the first place is never lost (a consequence of the conservation of energy), so as water vapor condenses into liquid water and bonds form between molecules, energy is released (600 calories per gram -- identical to the amount required for evaporation) to keep the energy books balanced. The release of this energy, called “latent heat of condensation,” warms up the surrounding air. In a way, you can think of condensation like a campfire. As the wood burns, it releases heat, warming up the surrounding air. Similarly, when water vapor condenses into a liquid, the energy that was used to evaporate it is now released back into the environment, warming it up.

So, any time a phase change (such as evaporation) causes water to go “up the energy staircase,” energy is required to break bonds between molecules (just as climbing requires effort), which cools the surrounding air. Any time a phase change (such as condensation) causes water to go “down the energy staircase,” energy is released -- after all, it is much easier to go downstairs! This warms up the surrounding air.

The warming that occurs with condensation is not easily noticeable to humans, but I bet you've noticed the impacts of evaporational cooling. When you step out of the shower, you sometimes feel a chill as the water evaporates off your skin, even in a warm room. Now you know that the cooling sensation directly results from evaporation pulling energy away from your body.

It's intriguing to realize that evaporation and condensation continually unfold in your surroundings, if their effects remain imperceptible at the macroscopic level. These dynamic processes operate on the molecular scale. Observable phase changes become apparent when there is a “net” condensation event, signifying that the rate of condensation surpasses that of evaporation, resulting in the formation of liquid water droplets. Conversely, when “net” evaporation occurs (assuming an initial presence of liquid water), it implies that the evaporation rate exceeds the condensation rate. A notable instance of net evaporation can be witnessed during the descent of raindrops. In this scenario, small raindrops diminish or completely vanish as the rate of evaporation outpaces that of condensation.

One last thing I want you to take home -- phase changes of water are critical for energy. Water can store energy and give off energy through these transitions. If water vapor moves around (for example, moist air from the Gulf of Mexico traversing up to New England it eventually rains out), it acts as a powerful transporter of energy! Water's ability to transport energy through phase changes is essential not only for weather but also for large-scale climate patterns. For example, as water evaporates over the warm oceans, it transforms kinetic energy into potential energy between the water vapor molecules that is carried up into the atmosphere. Winds can then move this water vapor and the potential energy associated with it across continents. When the water vapor eventually condenses to form liquid drops and precipitation,  the potential energy between water molecules is transformed to kinetic energy and the environment warms up. We'll talk more about this soon!

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In the preceding section, I made what perhaps can be considered a somewhat surprising assertion: evaporation and condensation are ongoing processes that happen constantly in your surroundings! However, these processes often go unnoticed because they occur at the molecular level, making their results imperceptible to the naked eye. Observable phase changes occur under specific conditions when there is either a “net” condensation or a “net” evaporation, provided there is an initial presence of liquid water. 

Net Condensation and Net Evaporation

“Net” condensation refers to a situation where the rate of condensation surpasses that of evaporation, resulting in the formation of liquid water droplets. Remember our cold drink bottle from a warm day? Conversely, when starting with liquid water, “net” evaporation occurs when the evaporation rate exceeds the condensation rate – water rising off a wet roadway after our summer thunderstorm leaves and is replaced by sunny skies. This leads to the shrinking or complete disappearance of liquid water droplets and the drying up of puddles on the ground. 

The concepts of “net” evaporation and “net” condensation hold significant importance for climate scientists, particularly in their implications for cloud and precipitation formation, as well as the evaporation of precipitation, which contributes to evaporational cooling and the movement of water in the climate system. To better understand these processes, let’s explore what controls the evaporation rate (how many water molecules become vapor) and the condensation rate (how many vapor molecules turn back into liquid).

To begin, it's essential to understand that the bonds holding water molecules together in the liquid phase are relatively weak in the grand scheme of things – that is why water can so easily change shape, whether in a glass or poured out onto a counter. Consequently, occasional natural vibrations of water molecules can break these bonds, resulting in evaporation. As you may already know, temperature directly influences molecular vibrations: the higher the temperature, the greater  amount of energy contained within vibrating molecules. Consequently, liquid water molecules are more likely to break free from their neighboring molecules and transition into water vapor at higher temperatures. Therefore, water temperature plays a pivotal role in regulating the rate of evaporation. Lower water temperatures lead to diminished evaporation rates, whereas higher water temperatures result in increased evaporation rates. Cool water = slow evaporation, warm water = fast evaporation!

Condensation Rates

Now, let's turn our attention to the factors affecting the condensation rate. Let's conduct a simple experiment to explore what determines condensation rate. Begin with a sealed, empty container containing dry air (in other words, no water vapor molecules). Now, let's pour some liquid water into the container and observe the ensuing processes. Over time, water molecules break their molecular bonds with neighboring water molecules and evaporate into the airspace above the water, gradually increasing the concentration of water vapor molecules in that space. As time progresses and more water molecules enter the vapor phase above the water surface, some water vapor molecules will randomly come into contact with the interface between the liquid water and the air above, causing them to condense back into a liquid state.

An experiment that begins with a container free of water molecules (left). In the second step of the experiment, water is added to the container, and the water begins to evaporate. At the same time, water molecules in the gas phase are free to condense back into the liquid. At first, the evaporation rate far exceeds the condensation rate.

Credit: David Babb© Penn State University is licensed under CC BY-NC-SA 4.0

Initially, the condensation rate is low because only a few water vapor molecules are present, and the probability that any of them will come in contact with the interface between air and water is low. In fact, the evaporation rate far exceeds the condensation rate early on (net evaporation occurs). But, as time goes on and net evaporation continues, the air above the water contains an increasing number of water vapor molecules. As the number of water vapor molecules increases, the chance of a water vapor molecule contacting the interface between air and water and condensing back into liquid also increases, which translates to an increase in the condensation rate.

So, as the number of water vapor molecules increases in the air above the water, the condensation rate increases, too. The condensation rate will continue to increase until it matches the evaporation rate. This is a state called equilibrium, meaning the condensation rate equals the evaporation rate. At equilibrium, the temperature of the remaining water is lower than that at the start of the experiment. That's because That's because kinetic energy was consumed in moving water molecules from the liquid to gas phase during evaporation, thereby lowering the average kinetic energy (in other words, the temperature) of the water left behind. Moreover, the temperature of the remaining water equals the temperature of the “air” above the water. This means that the energy exchange between the water and the air has balanced out. This state of equilibrium, where the condensation rate equals the evaporation rate, is depicted on the left below.

In the second phase of the experiment, a container at equilibrium (left) is heated. When water temperature increases (right), the evaporation rate also increases. In turn, the amount of water vapor in the “airspace” above the water increases. Eventually, the condensation rate increases and balances the increased evaporation rate, reaching a new equilibrium.

Credit: David Babb© Penn State University is licensed under CC BY-NC-SA 4.0

What happens if we take our container in equilibrium and increase the temperature (depicted on the right above)? The increase in water temperature causes the evaporation rate to increase, and, for a time, net evaporation occurs. But, with increased evaporation, more water molecules exist in the air above the water, increasing the condensation rate! The condensation rate again increases until it equals the evaporation rate, and a new equilibrium is achieved (with greater evaporation rates and condensation rates than the original equilibrium, shown above on the right).

$$\mathrm{RH} = \frac{\text{ condensation rate }}{\text{ evaporation rate }}\times 100 \mathrm{\%}$$

Relative humidity (RH) is equal to the condensation rate divided by the evaporation rate, multiplied by 100 percent.

How do evaporation rates and condensation rates relate to climate?

Well, they're the basis for a variable that perhaps you are familiar with -- relative humidity. Although you may have heard the term “relative humidity” before, you may not know what it's really telling you. For starters, relative humidity is the rate of condensation divided by the rate of evaporation, multiplied by 100 percent (shown on the right). Relative humidity usually ranges from just a few percent (when the evaporation rate is much larger than the condensation rate) to 100 percent, which occurs at equilibrium. Note: 100 percent is not the absolute upper limit of relative humidity because, in reality, the condensation rate sometimes exceeds the evaporation rate slightly (that's how water droplets grow). But that's just a fun fact for you.

What does relative humidity tell us? It tells us how close the condensation rate is to the evaporation rate. As relative humidity nears 100 percent, the condensation rate nears the evaporation rate. Low relative humidity values mean that the evaporation rate greatly exceeds the condensation rate. But, because relative humidity depends on the evaporation rate, which depends on temperature, relative humidity doesn't tell us how much water vapor is present in the air. For example, the relative humidity is 100 percent in both stages of our experiment above in which the condensation rate equals the evaporation rate (equilibrium), but more water vapor molecules are present in the state of equilibrium after we've increased the temperature. By itself, relative humidity is also not a good indicator of how muggy or humid the air feels to most humans. You can have 95% relative humidity in Alaska and 95% relative humidity in Hawaii and feel much (MUCH) different!

In practice, we can't calculate relative humidity using the equation above because we can't easily determine the evaporation and condensation rates at any given time. However, we can relate evaporation and condensation rates to weather variables we can measure easily. Since we know that the condensation rate is controlled by the amount of water vapor present, and we use dew points to assess the amount of water vapor present, it stands to reason that condensation rates are connected to dew points. Indeed, higher dew points yield higher condensation rates. Meanwhile, temperature controls evaporation rates (higher temperatures yield higher evaporation rates), so relative humidity depends on dew point (which reflects the amount of water vapor present) and temperature. I should point out, however, that we can't just substitute dew point and temperature into the equation for relative humidity above and do a simple calculation. The mathematical connections between condensation rates and dew point, as well as evaporation rates and temperature, are too complex for that and are beyond the scope of this course. Still, understanding the basic connections between temperature and evaporation rates, and dew point and condensation rates leads us to the following important lesson learned:

Important Applications

This lesson has many important applications in understanding broader climate processes. For example, evaporational cooling plays a crucial role in regulating surface and atmospheric temperatures, particularly in regions with high evaporation rates, such as coastal areas and deserts. When there's a large difference between temperature and dew point, the rate of evaporation greatly exceeds the rate of condensation, resulting in significant cooling. Over time, this cooling affects local climate patterns, influencing everything from vegetation types to the intensity of heat waves and drought conditions.

These concepts are also vital for understanding long-term cloud formation patterns and the role of clouds in the climate system (net condensation). Later in the course, we’ll examine how changes in global evaporation and condensation rates, driven by increasing temperatures, influence cloud coverage and precipitation patterns over decades. You may have heard the misconception that “clouds form because cold air can't hold as much water vapor as warm air,” but in reality, it all comes down to the balance between evaporation and condensation rates, which are impacted by the warming climate.

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So far, we have primarily focused on the interplay between evaporation rates, condensation rates, and the concept of net condensation and net evaporation. However, let's shift our attention to essential moisture variables - specifically, dew point and relative humidity.

Dew Point

To begin, let’s define the “dew point temperature” – you have probably encountered this term when watching a local weather forecast on TV. It represents the approximate temperature at which the water vapor in the air must cool (at constant pressure) to condense into liquid water droplets. Remember, the phase transition between liquid water and water vapor (and vice versa) is associated with a certain amount of energy and energy is tied to temperature. So, cooling a parcel of air that contains water vapor will eventually induce a phase transition of the water to liquid. This relationship is governed by something known as the Clausius-Clapeyron relationship, which tells us that as the temperature increases, the maximum amount of water vapor the air can contain at equilibrium at a given temperature also increases. Therefore, the dew point temperature serves as an absolute measure of the amount of water vapor present. In simple terms, a higher dew point indicates a greater concentration of water vapor molecules in the air, whereas a lower dew point signifies fewer water vapor molecules.

The Clausius-Clapeyron Relationship

The Clausius-Clapeyron relationship underlines the crucial role of temperature in controlling moisture in the atmosphere. It is one of the single most important principles in climate science! As temperatures rise, the air can hold more gaseous water vapor (see my sidebar below). Consequently, when dew points are higher, the air can support a more significant quantity of water vapor. This elevates the likelihood of water vapor molecules condensing onto surfaces, resulting in higher condensation rates. Conversely, lower dew points indicate lower saturation-specific humidity levels, which translate to lower condensation rates. See the graphs below. The x-axis contains temperature, and the y-axis is a value called “equilibrium vapor pressure” – for our purposes, we can consider this the maximum amount of vapor a parcel of air can hold at that temperature before it must condense (or deposit in the case of ice). As we move from left to right on the bottom axis, we increase the temperature. We also see that as air gets warmer, the amount of water vapor it can hold prior to saturation increases.

The equilibrium vapor pressure above a liquid water surface, as calculated by the Clausius–Clapeyron Equation. ***The y-axis label is incorrect; it should say “equilibrium vapor pressure (hPa)”.*** The line for liquid water can be extended below 273 K, the freezing point, because water can remain liquid at those low temperatures and become a “super cooled” liquid.

William Brune

Relative Humidity

While the dew point tells us something about the mass of water in the air, it doesn’t necessarily tell us how close we are to reaching the maximum amount of water vapor that air can hold. That is where relative humidity comes in. Although not an absolute measure of water vapor concentration, relative humidity is an exceptionally valuable variable when studying the atmosphere. As you have previously learned, it serves as a comparison between condensation rates and evaporation rates, expressed as a percentage. Relative humidity depends on both dew point and temperature, with the gap between these two variables influencing the outcome. A larger difference results in lower relative humidity, while a smaller difference yields higher relative humidity. When the condensation rate equals the evaporation rate at equilibrium (when the dew point equals the temperature), relative humidity reaches 100 percent.

So, the blue curve in our above graph shows “how much water vapor is held in a parcel of air when the relative humidity is 100 percent.” It also shows how much water vapor is in the atmosphere when the dew point temperature and temperature match – the further right you get on the curve, the further up the y-axis (water vapor) you go. You may have heard someone say at some point “warmer air can carry more moisture,” this is what they were referring to. Note, that’s a bit simplistic, the correct framing is “warmer air can hold more water vapor given the same relative humidity” but now you can tell them it’s thanks to this thing you learned about at Penn State called the Clausius-Clapeyron relationship!

As you see, dew points, temperature, and relative humidity are intimately connected atmospheric variables. Relative humidity depends on both the dew point and temperature. As the temperature nears the dew point, the evaporation, and condensation rates become increasingly similar, and relative humidity increases. On the other hand, if the difference between temperature and dew point grows, relative humidity decreases.

We’ll see that this relationship is very important in the climate system for determining where and how hard it rains and how our weather- particularly extreme precipitation- may change as our climate warms. We’ll talk more about this in the next chapter, but I want to leave you with one last piece of information that ties this together. All other things being equal, a warmer atmosphere can hold more water vapor. We also know that it is warmer near the equator than it is at the poles. So, if this is true, we should be able to look at a graph of water vapor as a function of latitude and see that it is highest where it is warmest. Do we see that?

NCEP Reanalysis climatological mean precipitable water (y-axis) was a function of latitude (x-axis).

Colin Zarzycki @ Penn State is licensed under CC-BY-NC-4.0

Above is a zonally averaged graph (we talked about these earlier!) showing a variable called total precipitable water. Precipitable water is the amount of water vapor (remember, vapor = the gaseous form) above you if you were standing on a 1 square meter patch of Earth. We call it “precipitable water” because the idea is it’s the amount of vapor that could be converted to precipitation if we cool the atmosphere sufficiently to “wring” all the water out of it. It is indeed highest at the equator – warm areas have more water vapor in the atmosphere than cool areas. We’ll find that this will be important in the next chapter.

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Water is an important determinant of the local climate. We know Nevada can have temperatures similar to Florida's, but the characteristics of the plants that grow in both regions are wildly different! Why do we have rainforests in South America but a relatively arid climate in Australia?

Previously, we delved into the concept of budgets when examining the energy dynamics of our planet. Budgets serve as valuable tools because they help us comprehend that certain variables, like energy, cannot be created or destroyed within a closed system. Instead, they shed light on how these elements are redistributed within the system—in our case, within the intricate framework of our climate system.

Water Budget: Key Components

To gain insights into how local climates are sustained, we can employ a local surface water budget for water. Imagine delineating a square area on a patch of ground in a park. We can assess the water budget of that square using four key components. Each component of the water budget represents a different way water can enter or leave our defined patch.

• Precipitation (P) – This includes any form of water (liquid or solid) that descends from the atmosphere onto our defined patch.
• Dewfall (or frost) (D) – This encompasses water vapor that condenses or is deposited directly onto our patch.
• Evaporation + transpiration (evapotranspiration) (E) – This refers to water leaving our patch, either through evaporation into the atmosphere or through release by plants.
• Horizontal “movement,” a.k.a. runoff ($\mathrm{\Delta }\mathrm{F}$) – This represents the lateral flow of water across the surface, exiting our square patch. A positive value indicates water moving away from our patch.

We can construct our water budget by simply adding these terms together:

Water Budget = $P+D-E-\mathrm{\Delta }F$

Water Budget Equation: Breakdown

Let's break down this equation. To increase the amount of water within our patch, we need to introduce more water into it. The primary sources in this equation for adding water are precipitation (P) and dewfall (D), which bring water from the atmosphere. On the contrary, we must account for water leaving our patch, represented by the negative terms. This includes both water returning to the atmosphere through evaporation and transpiration (E), as well as horizontal movement ($\mathrm{\Delta }\mathrm{F}$). Remember that when $\mathrm{\Delta }\mathrm{F}$ is positive, it indicates water is flowing away from our area, so subtracting a positive value results in less water remaining in our square.

Now that we understand the equation, let’s explore one crucial element: runoff, the horizontal movement of water across the surface. We’ve all seen runoff before—it’s the flow of water across surfaces, like rain streaming down a street during a heavy storm. Runoff occurs when the ground becomes saturated, frozen, or unable to absorb additional water (not unlike an asphalt road). Positive runoff typically signifies water flowing away from a particular location. For instance, if you stand at the top of a hill during a heavy rain, you are measuring positive runoff. Conversely, if you find yourself in a valley and water accumulates around you, you are experiencing negative runoff.

Water Budget's 5th Term: Storage

Now, it's important to recognize that the cumulative effect of all four of these terms doesn't instantaneously reach zero. In other words, at any given moment, the positive terms don't necessarily have to offset the negative terms precisely. For instance, we've all observed situations where there is more evaporation than precipitation during a hot, humid, sunny afternoon or significantly more runoff than dewfall during a heavy rainfall event. To account for these variations, we introduce a fifth and final term known as the “storage” term:

$$gw=P+D-E-\mathrm{\Delta }F$$

Think of the storage term as a mechanism for managing any surplus water from precipitation or dewfall and facilitating the release of water for processes like evaporation, transpiration, or runoff. If more precipitation occurs, it accumulates on our patch, much like your Venmo balance increases when you receive more money than you spend. The surface primarily stores water through three key mechanisms: soil moisture (reflecting the ground's level of saturation), groundwater storage (representing the water held beneath the surface we stand on), and snowpack (referring to water that remains locked into the surface as a solid and cannot flow like liquid water).

Schematic showing the five terms in the surface water budget with arrows representing precipitation, evaporation, groundwater, and runoff.

Credit: Colin Zarzycki © Penn State University is licensed under CC BY-NC-SA 4.0

Seasonal Cycle of Water Storage: Snowpack

I want to focus a bit more on this storage term. While it may seem quasi-insignificant, it can be significant for our lives. Water storage on both seasonal and shorter time scales is a critical component of freshwater availability. It acts as a buffer for local climates, particularly in regions that receive large amounts of snow in the winter, such as the northeastern United States or the Mountain West.

During periods of heavy snowfall or rainfall, not all the water runs off immediately. Instead, it gets absorbed into the ground, snowpack, or underground aquifers. This stored water is gradually released during drier months, helping stabilize local climate conditions by ensuring a continuous water supply. This stability is essential for ecosystems, agriculture, and human consumption, especially when precipitation is irregular.

For example, snowpack is a vital water source in many areas, supplementing rivers and streams during dry seasons. It acts as a natural reservoir, accumulating water (in the g_w term) during the winter months (via the P term) and gradually releasing it as snowmelt during the spring and summer (via the $\mathrm{\Delta }\mathrm{F}$ term).

In other words, as snow accumulates in the winter, it stores water that would otherwise be unavailable for immediate use. When temperatures rise in the spring and summer, this snowpack melts, providing a steady and reliable source of freshwater downstream. This slow release of water is invaluable for agricultural activities, ensuring a consistent water supply for crop irrigation exactly when it's needed most.

Agriculture heavily relies on this seasonal cycle of water storage provided by snowpack. In regions with pronounced snowmelt-driven water sources, such as the western United States, much of Europe, and parts of Asia, the timing and volume of snowmelt directly impact crop growth and yields. Farmers can efficiently manage their water resources, optimizing the use of available freshwater during the growing season.

This seasonally stored water also replenishes groundwater reserves, ensuring that agricultural activities have access to a sustainable and consistent supply of freshwater year after year. Thus, the seasonal storage and release of water from snowpack contribute significantly to the resilience and productivity of agricultural systems worldwide.

As we’ll discuss in this class, changes in this aspect of the water cycle can be very problematic for areas that rely on this annual water cycle!

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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!

• Water exists in three main phases—solid, liquid, and gas—and moves between them via phase changes like evaporation, condensation, sublimation, and deposition. These changes are crucial to the hydrologic cycle and climate system.
• Two important phase changes: evaporation cools by absorbing heat; condensation warms by releasing heat.
• Evaporation and condensation are continuous processes that shape climate by dictating water movement between the surface and the atmosphere, influencing everything from local weather to global climate patterns.
• Relative humidity, a ratio of condensation to evaporation rates, is an important indicator of atmospheric moisture content and is pivotal for understanding weather conditions, cloud formation, and overall climate dynamics.
• The Clausius-Clapeyron relationship explains how air's capacity to hold water vapor increases with temperature. As air warms, the amount of vapor contained within a parcel of air increases.
• Five terms—precipitation, evaporation, dewfall, runoff, and storage—explain the surface water budget.
• Over long periods of time, precipitation and evaporation are generally balanced at a location—if they are not, transport either of liquid water across the land surface or water vapor and water-containing particles through the atmosphere must be occurring.
• Generally, the ocean serves as a moisture source for land areas.
• The runoff ratio is a special quantity that can tell you how “wet” a continent is.

Hopefully, now you've learned that water is much more than just something you drink! It exists in three states—solid, liquid, and gas—and moves between these states through phase changes like evaporation, condensation, sublimation, and deposition. This constant “dance” not only shapes our daily weather but also deeply influences the global climate system. Whether it's the snow capping mountains, rivers flowing to the ocean, or water vapor forming clouds, each phase and transition has a significant role in the hydrologic cycle!