Flood Hydrology: The Role of Watershed Lands
Floods for small streams are often estimated using 'rational formula' assumptions . . . a 100-yr flood is found by finding a time-of-concentration, a 100-yr rainfall intensity for the time of concentration, and a runoff coefficient. Hydrologists often point out that rainfall frequency and runoff frequency in observed storms are often so dissimilar that this commonly used design assumption is whimsical. Nonetheless, the rainfall frequency = runoff frequency assumption is used even though designers of flood control facilities have not been shown to be more whimsical than the population at large.
What does happen in rare floods? Rare floods, including "100-yr" floods are often caused by the combination of infrequent high watershed moisture conditions and heavy but not extraordinary precipitation intensities. The high watershed soil moisture conditions are due to higher than normal seasonal precipitation, or are due to a series of storms prior to the storm that causes the rare flood. High watershed soil moistures may develop over a period of several months.
The effects of high watershed soil moisture conditions are dramatic. Photo 1 shows channels on
Stanford Universityland on the San Francisco Peninsulain . There was no flow in these channels for five consecutive years in the 1980's, and the gullies in Photo 1 during these dry years seemed to be ancient artifacts. Wetter winters starting in 1992 changed this pattern. Photos 2 to 4 were taken in mid-January, 1998. California
Winter season precipitation this year (1997-98) is well above normal. Photo 2 shows sheet flow on a hillside, and Photo 3 shows rills in a normally dry pasture. Gully formation, shown in Photo 4, is now active.
The land and channels in Photos 1 to 4 are in the San Francisquito Creek watershed. On Tuesday, February 3rd, 1998 a moderately heavy rainfall in the watershed caused the creek to flood for the first time since 1956. The wet watershed lands prior to this storm were very unusual, so the conditional or short-term flood frequency for the watershed was high by the end of January. The February 2nd/3rd storm was large by was not extraordinary.
Hydrologists and engineers in the 1930's and 40's were fully aware of the role of watershed lands during floods. Writing in 1944, W. W. Horner states;
"It is necessary to recognize that 'outstanding flood periods' are the result not only of great storms, but of the coincidence of great storms, and sometimes lessor storms, with the occurrence of either low infiltration capacity or small usable (soil moisture) storage condition.
Studies restricted to 'major flood periods' disregard the potential flood producing storms that have not produced major floods. Only by studying the mechanics of runoff at all flood levels . . . . can the hydrologist begin to isolate the controlling factors and their quantitative ranges."
. . . The Role of Land During Flood Periods by W. W. Horner, M. ASCE, Trans. Am. Society of Civil Engineers, Paper No. 2231, Vol. 109, 1944
Discussion of this paper by L. K. Sherman, who first suggested the "unit-hydrograph" in 1932, and by Hoyt and Langbein, Waldo Smith and others supported Horner's conclusions about the importance of the land, and advanced some alternate methods for handling hydrologic processes on the land. Horner's work shows that considerable activity was underway in the 1930's and 40's in data collection and in analysis to better understand hydrologic processes.
Understanding processes continues to be important. What is the relationship between rainfall frequency and runoff frequency during floods?
The data in Figure 1 are from a paper by Laura Marino and A. Allen Bradley, Jr. . . . Precipitation Frequency - Runoff Frequency Relationship in Hydrologic Design, paper presented at the 1986 AGU Fall Annual Meeting - San Francisco. The data are for Arroyo Del Hambre near
(15.1 sq. mi, mean annual rainfall 22 inches). The precipitation data were collected over 41 years, 1945 to 1986. Martinez, California
In Arroyo Del Hambre runoff that equals or exceeds 0.25 inches per hour has a 10-yr return period. Runoff that equals or exceeds 0.38 inches per hour has a 25-year return period.
Rainfall intensity-frequency data for a one hour duration for Arroyo Del Hambre are;
2 yrs, 0.50 in/hr
25 yrs, 0.89 in/hr
5 yrs, 0.63 in/hr
50 yrs, 0.96 in/hr
10 yrs, 0.75 in/hr
100 yrs, 1.03 in/hr
The highest Arroyo Del Hambre runoff, of 0.61 in/hr, was caused by a rainfall of 0.8 in/hr. A 0.61 in/hr runoff has a return period of approximately 150 yrs. A 0.8 in/hr rainfall has a return period of approximately 15 yrs. The highest rainfall of 1.3 in/hr, with a return period of 200 yrs. produced no significant runoff. Six other rainfalls with return periods between five and ten years produced zero or no significant runoff.
Eight rainfall events within the 41-year period studied produced runoff of 0.25 in/hr or greater, or 10 yr. return period streamflows. The return periods of the rainfalls that caused these events were 15 yrs, 4 yrs, 3 yrs, 2 yrs, 2 yrs, < 2 Yrs, < 2 yrs, and < 2 yrs. At all runoff return periods, the return period of the rainfall that causes peak runoff is typically much more frequent.
W. W. Horner's paper contains data similar to the Arroyo Del Hambre data.
One hour rainfalls are relevant for Arroyo Del Hambre since the watershed is relatively small and steep. Would highly variable amounts of runoff from rainfall be found if entire storms were considered rather than one-hour rainfalls? What if only very large storms were considered?
Figure 2 shows the runoff hydrographs from a storm in Lichau Creek, Ca (8.23 sq. mi.) when initial conditions in the watershed are at historic high and historic low soil moistures for the date of the storm, January 3rd and 4th. Precipitation in this storm was 7.5 inches in the Lichau watershed in 24-hrs, from 3pm January 3rd to 2pm January 4th, 1982. The 100-yr 24-hour rainfall in the watershed is 6.2 inches.
The intent of these notes is not simply to point out once more that rainfall and runoff frequency are different. The rainfall frequency = runoff frequency assumption negates the complexity and richness of actual hydrologic processes. Work to relate runoff and rainfall frequency, like the method that Marino and Bradley proposed, may not be developed. Experience reviewing hydrologic design 'failures', sometimes in legal cases, indicates that designers take risks when they over-simplify hydrologic processes. Flood control storages based on a 'design event' that fail in a series of lessor storms are a good example.
"Will a stream flood?", or "What is the current risk of a flood?"
The types of information typically available are;
1) short term flood forecasts for the next several days, based on current and forecast precipitation
2) long term mean flood risk, for example flood maps showing 100-yr or 1% flood plain.
Conditional flood frequency, the risk of a flood within the next week or several weeks, provides additional information for flood plain residents and flood control specialists. Conditional flood frequency is often quite different than the long term mean flood risk, and is a quantitative measure of the role of the land during floods.
Flood frequency, including the 100-yr or 1% flood in a watershed, is time variable. Flood frequency variability in time is due to the seasonal progression in climate and watershed conditions, and is due to differences in watershed soil moistures at any time during a season.
Figure 3 shows the conditional flood frequency for
for the month of January when the watershed soil moistures on January 1st are at historic maximum and historic minimum levels. Lichau Creek, CA
The conditional or near term flood frequency on January 1st, 1998 in Lichau Creek would have approached the historic maximum. High streamflows on February 2nd, 3rd and 4th, 1998, in Lichau Creek contributed to downstream flooding in the
valley. Petaluma River
Floods often seem to surprise flood plain residents and public safety officials despite the wide availability of flood maps and flood watch and warning broadcasts. This may be inevitable where a flood occurs only once in a generation. Nonetheless, appreciation of flood risk variability within different years is useful. The statement that a 100-yr flood in a stream has a 1% chance of occuring in any year is true only when the "year" is an undefined future year.
What is the chance that the long term mean 100-yr flood will happen within the next month? For Lichau Creek in Figure 3 this answer ranges from about 3% to a very low level - perhaps 0.1% or less.