Basic interpretation of stream hydrographs

First, let's look at a place where copious examples of hydrographs are available from all across the United States, the US Geological Survey National Water Information System. Note that this video reviews the features of the older interface for continuous flow data (6:20 min).

Here is a brief video introducing similar features of the new NWIS interface for continuous flow data (2:39 min).

As with many sciences, understanding the basics of watershed hydrology begins with visualizing the patterns in a key dependent variable like stream flow as it changes over time, and thinking about what might be causing those patterns (this is hypothesizing in the language of science). Let's get some practice hypothesizing using stream hydrographs and talk about the motivations and potential misconceptions that may come from using arithmetic vs. logarithmic scales when interpreting patterns in flow (8:52 min).

Let's look at a few more watersheds with dramatically different hydrographs than our snowmelt drive hydrologic regime, and hypothesize about those patterns (8:43 min).

Using the relatively instantaneous flow measurements from a continuous gauge sometimes disguises the patterns we wish to interpret in trends over longer time scales. The first type of statistic applied to analysis of hydrographs is summary statistics over particular time periods of interest. Daily mean flow, monthly mean flow, and annual mean flow are examples of temporal summary statistics often applied to hydrographs. Here is a review of the formal method by which these statistics should be calculated, using our old friend from calculus, the integral (7:31 min).

Summary statistics calculated over daily, monthly, or yearly time periods are used for interpretation of different temporal scales of trends in hydrograph data. Let's review some examples of how they are used (5:05 min).

The summary statistics used for hydrographs are diverse and can be confusing, especially if the USGS standards for terminology are not observed. Clear description of the statistics being reported are a notorious problem in the hydrologic literature. For example the "daily mean flow" and the "mean daily flow" are very different things with very different interpretations. In fact, the "mean daily flow" is the average of multiple daily mean flows over a period of record. Here are some details on the appropriate terminology to use when differentiating the statistics discussed above from longer-term summary statistics calculated over multi-year periods of record (8:57 min).

Probabilistic approaches to hydrograph interpretation are often applied in risk assessments associated with water resource availability or flooding. These approaches are also useful in more academic efforts to summarize differences in storage dynamics or response to precipitation in comparisons across watersheds. Let's start with annual flow duration curves, which are based on the fraction of the year a given stream flow is exceeded across an annual hydrograph (7:36 min).

The same calculations can be applied to any hydrograph summary statistic over any period of record of interest, leading to a variety of useful interpretations. For example, applying these exceedance probabilities to annual maximum flow over a multi-year period of record is called a flood frequency analysis (5:06 min).

Flood frequency analyses are the origin of the very misleading statistic "100-year flood". Let's learn about interpretation of flood frequency curves and in particular learn how to avoid misinterpretation of the return interval statistic (7:14 min).

Risk analyses for flooding typically require compounding the annual flow exceedance probability across multiple years. A common flood risk analysis might ask a question something like, "What is the probability of a flood exceeding 1000 cubic meters per second occurring at least once in the next 20 years?" Answering questions like this requires careful consideration of the rules of operations with probabilities across many years, and may be trickier that it seems on the surface (9:58 min).

Students have asked me in the past whether this is more complicated than necessary. When applying union operations (i.e. "or" operations) to probabilities across multiple years, can't you just add them up? The answer to that question is only yes if the probabilities being added are for mutually exclusive events. The probabilities of a flood occurring each year are not mutually exclusive (i.e. the same flood under consideration can be exceeded 2 years in a row, or multiple times in a given period of record). The method above is actually a simple way to calculate a union of probabilities that are not mutually exclusive, because it turns out calculating that union directly requires a fairly involved algorithm. Here is a clarification with some more detail on the probabilistic conceptualization being applied (4:10 min).

Study guide

Click this link to download the MS Word file

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

Click this link to download the PDF file

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

Link to the portal web page for NWIS

Video about Yellowstone flooding from the Practical Engineering YouTube channel. Includes an excellent review of the frequently misinterpreted statistic "500 year flood" that was used rampantly in the reporting of this event. Also shows how any return interval beyond the length of the period of record may be a questionable extrapolation from where you have data. You need at least 500 years of data to estimate a 500 year flood without extrapolation, and you probably need way more than 500 years of data to feel like you can characterize a 500 year flood with any confidence.

Link to the web page and with tutorials and examples

Logarithmic scales are useful, but can distort interpretation of volumes of water by visualizing the area under the hydrograph. Be sure you are familiar with the nature of log scales.