Some issues in flood hydrology in the climate context Dennis P. Lettenmaier Department of Civil and Environmental Engineering University of Washington VAMOS VPM11 Miami March 27, 2008

Flood response is a function of: Basin geometry and orientation Precipitation intensity and other storm characteristics Channel characteristics (drainage density, cross-section, velocity, etc) Geology and soil characteristics Antecedent conditions (soil moisture, snow if present)

Role of basin shape and channel geometry on flood generation (from Baker et al, 1988)

Sensitivity of flood hydrographs to channel network characteristics and flood wave velocity RB = bifurcation ratio RA – area ratio RL = length ratio L1 = mean length first order streams normalized discharge Time (hours) From Rodriguez-Iturbe and Valdes, 1979

Three aspects of flood hydrology Extreme flood estimation (where failure would result in extreme property damage and/or loss of life) Flood frequency estimation (for planning purposes, e.g., delineation of 100-year flood plain) Flood forecasting (real-time)

1. Extreme flood estimation Typical application spillway design Standard approach (in U.S.) is PMP (probable maximum precipitation)/PMF (probable maximum flood) “PMP is the greatest amount of precipitation, for a given storm duration, that is theoretically possible for a particular area and geographic location.”  ”The PMF is the flood that may be expected from the most severe combination of critical meteorological and hydrologic conditions that are reasonably possible in a particular drainage area.” General approach is to maximize worst case conditions, sometimes hypothesized mechanism is one that has not, or only very rarely, has occurred (e.g., hurricanes in New England) Approach is in general deterministic; typically the PMF is not assigned a return period, for instance

Llyn Brian Dam spillway, Wales (visual courtesy Wikepedia)

Development of the PMP Development of the PMF  ”Scientists use both meteorological methods and historical records to determine the greatest amount of precipitation which is theoretically possible within a region. These rainfall data are subsequently maximized through "moisture maximization" and other numerical methods. Moisture maximization is a process in which the maximum possible atmospheric moisture for a region is applied to rainfall data from a historic storm. This process increases the rainfall depths, bringing them closer to their potential maximum. The PMP is determined for different storm periods, generally ranging from six to seventy two hours.” Development of the PMF “The Probable Maximum Flood is the flood which is a direct result of the Probable Maximum Precipitation. However, drainage areas with the same PMP may have different PMFs. For this reason, the PMF, not the PMP, must be used as a design criterion for a dam. “ From State of Ohio dam safety guidelines

2. Flood frequency estimation

Typical empirical flood frequency distribution with ~80 years of observations

Fitted flood frequency distribution, Potomac River at Pt of Rocks, MD Visual courtesy Tim Cohn, USGS

Problems with traditional frequency fitting methods

Problems with traditional fitting methods –mixed distributions

Flood frequency distributions can be dependent on climate conditions Visual courtesy Alan Hamlet, University of Washington

Are extreme floods increasing (hence frequency distributions shifting? American River, CA

Source: Updated from Lins and Slack, Geophys. Res. Lett., 26, p. 227 Trends in U.S. Streamflow, 1940-1999 435 Stations; p ≤ 0.05 Source: Updated from Lins and Slack, Geophys. Res. Lett., 26, p. 227 Visual courtesy Tim Cohn, USGS

Paradox: Given increases in precipitation and runoff, why are there so few significant trends in floods? Visual courtesy Tim Cohn, USGS

Explanation (?) (a)… [Lins and Cohn, 2002] A Statistical explanation with important physical implications [Lins and Cohn, 2002] Visual courtesy Tim Cohn, USGS

Explanation (?) (b)… [Lins and Cohn, 2002] From USGS regional regression equations [Lins and Cohn, 2002] Visual courtesy Tim Cohn, USGS

However, the jury is still out … e.g., We find that the frequency of great floods increased substantially during the twentieth century Milly et al Nature (2002) “Increasing risk of great floods in a changing climate”

3. Flood forecasting

Sources of flood predictability Precipitation predictability Hydrologic predictability Channel routing predictability

U.S. real-time stream gauge network

Illustration of data assimilation with a spatially distributed hydrology model Visual courtesy D-J Seo, NWS

U.S. flood frequency skill has not improved over last ~40 years (Welles et al, BAMS, 2007), why not? Hydrologic models have been essentially static Weather forecast data (QPF) not always used (this is changing) Degradation of in situ observation networks Weather forecasts have improved, but not necessarily QPF, which is the main hydrologic driver Lack of systematic approaches to updating forecast initial conditions (e.g., data assimilation) Lack of data documenting forecast performance