Water and energy budgets of Earth systems

The most common method to delineate watersheds assumes that the general direction of water movement on or near the earth surface can be predicted by the direction of steepest topographic slope (i.e., the slope of the land surface). While that assumption is not always fully valid, it does allow approximate delineation of the land surface area draining to a given stream location with only elevation data. This topic is also a good opportunity to introduce the concept of the flow nets defined by the mesh of equipotential and flow lines, since topographic watershed delineation is basically just visualizing the flow net predicted by elevation head across the land surface. Let's review the basic conceptual models underlying watershed delineation (11:47 min).

Armed with some fundamental hydrologic principles and the ability to visualize the surface-derived flow net, let's work through an example of watershed delineation (13:09 min).

Hydrologists are quite fond of normalizing flows to area to allow comparisons of fluxes or yields that are independent of the size of the areas being studied. In the case of whole watersheds, runoff normalized to the area of the watershed is typically called the areal yield or specific discharge. Normalizing discharge to area provides a perspective on hydrograph comparisons that removes the variation in the data due to the size of the watershed. Therefore, yield is a fundamental watershed property that is useful for comparisons or interpretations of watershed function that are independent of watershed size (6:48 min).

A topographically delineated watershed defines a control volume of the Earth's surface for which we commonly want to understand the nature of the water budget. A water budget is defined by understanding all the potential inputs and outputs to the control volume, such that a conservation of mass equation an be used to define fundamental watershed behavior in partitioning the inputs into various outputs. So far, our perspective on the water budget has been based on simplifying assumptions. Let's review the details of deriving the conservation of mass equations necessary for characterizing the full water budget for a control volume on Earth's surface (8:54 min).

You might see water budgets expressed as total volumes over particular periods in time (e.g., annual water budgets) or as rates of flow over various periods of time. Let's review these different perspectives and think about how the change in storage term in a water balance ultimately influences the patterns we expect to see in hydrographs (8:28 min).

Fundamental understanding of a watershed's annual water balance typically provides critical context for any other hydrological investigation. Perspectives on annual water balances are simplified if the difference in stored water between the beginning and end of the summarized 12 months can be assumed to be zero. A common practice is therefore to define the start and end of the water year during the time of the calendar year when the volume of water stored in the watershed is generally at it's lowest. Let's explore why this tends to be at about the same time of year even in very different climates of the northern hemisphere (14:53 min).

When annual water budgets can be reasonably simplified to input from precipitation and outputs to evapotranspiration and runoff, ratios of various terms in the water balance become useful fundamental summaries of watershed partitioning behavior. The annual runoff ratio is a commonly applied summary of how a watershed partitions annual precipitation into either runoff or evapotranspiration (15:12 min).

Questions about why a given watershed might partition more precipitation to runoff or evapotranspiration inherently lead to the need to understand a whole string of internal partitionings driven by individual hydrologic processes. Characterization of these individual hydrologic processes quickly illustrates why an understanding of watershed's water budget is inseparable from an understanding of its radiant and thermal energy budget (4:53 min).

Water is critical to the movement of thermal energy in earth systems and thermal energy is critical to the movement of water in earth systems. The fundamentals of this feedback hinge on the fundamental thermal properties of water, which takes us back to properties of the water molecule (17:41 min).

The distribution of water on Earth is ultimately determined by energy and the unique property that it naturally occurs in all three phases of gas, liquid, and solid on Earth's surface (3:13 min).

While Earth is a relatively closed system to ordinary matter, it is most definitely not a closed system to energy. The radiant energy emitted by the very hot surface of the Sun dominates energy inputs to Earth's atmosphere, and is known as shortwave radiation due to its higher energy, higher frequencies, and shorter wavelengths (i.e. ultraviolet, visible, and near infrared spectra). Understanding the fate of incident shortwave solar radiation is the foundation of characterizing Earth's energy budget (7:08 min).

Matter at temperatures closer to those found on the surface of the earth (much cooler than the Sun) also emits radiant energy, but the lower temperatures result in emission of lower energy, lower frequency, and longer wavelength radiation (thermal infrared spectrum). The absorption and reemission of longwave radiation is the primary mechanism of the greenhouse effect in Earth's atmosphere and is critical to understanding the amount of thermal energy effectively stored in thermal feedbacks between the Earth's surface and its atmosphere (5:39 min).

With a grasp on the dynamics of radiant energy, we can round out Earth's energy budget by understanding sensible, advective, and latent heat exchanges (6:01 min).

A basic understanding of the heat and radiant energy exchanges driving Earth's energy budget provide the foundation to understanding the more detailed hydrologic processes that ultimately determine how watersheds partition inputs into output.

Study guide

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Study guides are designed to summarize the vocabulary, concepts, and mathematics learned in this module.

Readings from Dingman (3rd ed)

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A list of associated readings from Physical Hydrology by S. Lawrence Dingman (3rd edition)

Slides used in videos

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An extensive analysis of runoff ratio from watersheds across Utah

Link to download Mohammed and Tarboton 2008 report to the state government of Utah

Another description of Earth's energy budget