Prediction of Watershed Runoff

1. Prediction of Watershed Runoff Tom Dunne Winter 2008

2. Intent of Computer Modeling in the Course (Type A) Only very few of you are likely to become modelers or users of software developed by agencies, consulting firms, or academics. Most of this activity involves software developed or promoted by agencies to discharge their regulatory function and control/standardize/facilitate outside design work that they must evaluate. Most public-access agency software now being made user-friendly and marketed, including by private firms You will eventually become familiar with these and other computer models to a degree which is not possible in a course. The labs in this course will introduce you to examples of what is available and how careful, thorough, and insightful application is necessary. These things will run themselves, but not necessarily intelligently.

3. Intent of Computer Modeling in the Course (Type B) Most of you will not become modelers Not a management function Not high-status (just inaccessible!). Extent to which some modelers pull wool over managers eyes remains impressive. The servant of management Allows examination of the implications of various policy or design options Managers need some appreciation of what modeling involves, and what modelers think they are doing (both your own agency’s and a consulting firm’s) Managers need to understand the limits of modeling applicability --- what is the basic conceptual model underlying the construction of the model? Is it applicable to the situation under review? What is the expected reliability of predictions? What can be done to assure intelligent application, improved reliability, diligent application over the realistic range of conditions, and transparency? Managers and policy-makers should not frame a policy or management question the resolution of which requires predictions of an unattainable level of precision.

4. For these reasons, we are going to introduce you to various forms of hydrologic modeling for doing the most widely applied tasks in water resources management Remember that there is a large number of models for doing each task, and new ones are being generated continually --- though new conceptual models are very rare. So, don’t grab on to any model as the way of making calculations. If two models give radically different answers, work to reconcile or resolve the differences. There is a reason for it --- may lie in choice of parameter values, inappropriateness of one model for the conditions, etc. Differences in predictions often result from decisions made about how to set up and apply the models, and the different questions being asked or emphasized by competing interests.

5. Prediction of watershed storm runoff Volumes of storm runoff  Entire storm hydrographs Continuous simulation of streamflow (storm and dry-weather flow) Deterministic prediction of peak rates of runoff from small watersheds Probabilistic prediction of peak flows (from any size of watershed)

6. ---- There is a quasi-infinite number of methods of predicting watershed storm runoff---- Increasingly codified, computerized, and promoted with acronyms such as SWMM, SWAT, … other four-letter words are available---- But all based on one of a a few concepts… Soil moisture accounting (SMA) (Like water balance from ESM 203 applied to short time periods) Constant speed of runoff over a plane A “Curve Number” index of watershed responsiveness to rainfall Some are “lumped” models (basin is a single space) Some are “distributed” models (represent spatial variation of watershed characteristics and runoff itself)

7. Prediction of storm runoff volume (expressed as depth of runoff --- i.e. volume per unit area)Thompson, 1999, Hydrology for Water Management Baseflow is added to predicted storm flow, using the water balance method (see previous, or ESM 203)

8. Prediction of Volume of Flood Runoff Need some mechanism ( a runoff model) to convert a portion of the rain/melt into runoff to the channel system, and of representing the empirical observation that this proportion tends to increase through time during a storm or season as the watershed becomes wetter (stores more water) i.e. there is a feedback between the water stored in a watershed and the proportion of rain that is converted to runoff

9. Runoff models to choose Calculate the entire water balance including quickflow Precipitation-Runoff Modeling System (US Geological Survey) HEC-Hydrologic Modeling System (US Army Corps of Engineers) Soil Water Assessment Tool (US Dept of Agriculture) BASINS 3.0 (US Environmental Protection Agency) In lab we will concentrate on a use of HEC-HMS that emphasizes the quickflow component, and so is useful mainly for tributaries that have little or no baseflow The full models are combinations of the water-balance approach practiced in ESM 203 and several options for computing quickflow.

10. Representation of runoff in HEC-HMS, promoted by the US Army Corps of Engineers

11. HEC-HMS uses separate sub-models to compute each component of runoff Runoff volume (per storm or per day/month) Timing of direct runoff (quickflow) Baseflow (delayed flow) Speed and timing of channel and floodplain flow to a river basin outlet

12. There are options (models) for each step in runoffe.g. for computing runoff volume: Initial abstraction and constant ‘loss’ (infiltration, as expressed by the F–index in previous lecture) Green-Ampt infiltration model Soil Conservation Curve Number Individual rainstorms small basins or Hydrologic Response Units (HRUs) Soil Moisture Accounting (SMA) Water balance model Best for continuous modeling through many time steps in large basins or their HRUs or pixels Gridded SMA

13. There are options (models) for each step in runoffe.g. for computing runoff volume: Initial abstraction and constant ‘loss’ (infiltration, as expressed by the F–index in previous lecture) Green-Ampt infiltration model Soil Conservation Curve Number Individual rainstorms small basins or Hydrologic Response Units (HRUs) Soil Moisture Accounting (SMA) Water balance model Best for continuous modeling through many time steps in large basins or their HRUs or pixels Gridded SMA

14. There are options (models) for each step in runoff e.g. for computing runoff volume: Initial abstraction and constant ‘loss’ (infiltration) Green-Ampt infiltration model Soil Conservation Service Curve Number Individual rainstorms small basins or HRUs Soil Moisture Accounting (SMA) Water balance model Best for continuous modeling through many time steps in large basins or their HRUs or pixels Gridded SMA

15. ‘SCS’ method for prediction of storm runoff (QKFLO) volume (R, as a depth per unit area) Very widely used in prediction software Accounts for effects of soil, properties, land cover, and antecedent moisture Prediction of storm flow depends on total rainfall rather than intensity Based on a very simple conceptual model, as follows.

16. Prediction of storm runoff volume (‘SCS’ method)All quantities expressed in inches of water

17. It is assumed that a watershed has a maximum retention capacity, Smax (1)   where F8 is the total amount of water retained as t becomes very large (i.e. in a long, large storm.) It is the cumulative amount of infiltration   It is also assumed that during the storm (and particularly at the end of the storm) (2)

18. The idea is that “the more of the potential storage that has been exhausted (cumulative infiltration, F, converges on Smax), the more of the ‘excess rainfall’, or ‘potential runoff’, P-Ia, will be converted to storm runoff.” The scaling is assumed to be linear. One more relationship that is known by definition: (3) Combination of (2) and (3) leads to (4)

19. Another generalized approximation made on the basis of measuring storm runoff in small, agricultural watersheds under “normal conditions of antecedent wetness” is that (5) The few values actually tabulated in the ‘original’ report are 0.15-0.2 Smax. Thus (6)

20. Combination of these relations yields (7)

21. Soil Conservation Service Storm Runoff Relationship

22. The entire rainfall-runoff response for various soil-plant cover complexes is represented by a single index called (with exquisite creativity!) the Curve Number. A higher curve indicates a large runoff response from a watershed with a fairly uniform soil with a low infiltration capacity. A lower curve is the smaller response expected from a watershed with a permeable soil, with a relatively high spatial variability in infiltration capacity. SCS developed an index of “storm-runoff generation capacity”, (the Curve Number), which would vary from 0 to 100 (implying roughly the percent of ‘effective rainfall’ or ‘potential runoff’ that is converted to flood runoff).

23. This curve number was then related to back-calculated values of Smax (inches) from measured storm hydrographs and equation (2) above to yield a relationship of the form or or

24. CNs were then evaluated for many watersheds and related to: soil type (SCS soil types classified into Soil Hydrologic Groups on the basis of their measured or estimated infiltration behavior) vegetation cover and or land use practice  antecedent soil-moisture content A spatially weighted average CN is computed for a watershed.

25. Hydrologic Soil Groups are defined in SCS County Soil Survey reports

26. Classification of hydrologic properties of vegetation covers for estimating curve numbers(US Soil Conservation Service, 1972)

27. Runoff Curve Numbers for hydrologic soil-cover complexes under average antecedent moisture conditions

28. Curve Numbers for urban/suburban land covers (US Soil Conservation Service , 1975)

29. No consideration is given to rainstorm intensity or duration. Method can be applied successively to parts of a rainstorm, and volume of runoff could be calculated separately for each increment. [HEC-HMS does this in your lab exercise] the form of the rainfall mass curve that is imagined by the user makes a very large difference to the predicted volume of runoff and its peak rate. orographic influences on rainfall also have a critical effect on predicted runoff volumes. [See lab exercise] SCS Curve Number Method

30. No guidance given about the watershed size to which the method is applicable, except that the empirical relations were established for ‘small’ watersheds. Now that the method is computerized, it is relatively easy to separate a watershed into sub-watersheds, and to the runoff calculation for each one separately, and then combine the runoff hydrographs that result (see lab exercise) SCS Curve Number Method

31. Since rainfall is the largest term in any hydrologic calculation, it’s estimation is critical to runoff predictions No consideration is given to rainstorm intensity or duration. Method can be applied successively to parts of a rainstorm, and volume of runoff could be calculated separately for each increment. [HEC-HMS does this in your lab exercise] The form of the rainfall mass curve that is imagined by the user makes a very large difference to the predicted volume of runoff and its peak rate (about which more later). Orographic influences on rainfall also have a critical effect on predicted runoff volumes. [See lab exercise]

32. No guidance given about the watershed size to which the method is applicable, except that the empirical relations were established for ‘small’ watersheds. Now that the method is computerized, it is relatively easy to separate a watershed into sub-watersheds, and to the runoff calculation for each one separately, and then combine the runoff hydrographs that result (see lab exercise)

33.  Where tested against measured storm runoff volumes, method is notoriously inaccurate. BUT: 1. Method entrenched in runoff prediction practice and is acceptable to regulatory agencies and professional bodies. 2.   Attractively simple to use. 3.   Required data available in SCS county soil maps in paper and digital form. 4.   Method packaged in handbooks and computer programs 5.   Appears to give ‘reasonable’ results --- big storms yield a lot of runoff, fine-grained, wet soils, with thin vegetation covers yield more storm runoff in small watersheds than do sandy soils under forests, etc. 6.   No easily available competitor that does any better. The method is already hidden in various larger “computer models”, such as HEC-HMS). 7. The task for a watershed analyst or regulator is to decide how to interpret and use the results.

34. There are options (models) for each step in runoff  e.g. for computing runoff volume: Initial abstraction and constant ‘loss’ (infiltration) Green-Ampt infiltration model Soil Conservation Curve Number Individual rainstorms small basins or HRUs Soil Moisture Accounting (SMA) Water balance model Best for continuous modeling through many time steps in large basins or their HRUs or pixels Gridded SMA

35. Soil Moisture Accounting Method (SMA) in HEC-HMS

36. Prediction of Flood Runoff Problem is that many runoff processes act simultaneously in a large basin and we have no hope of specifying the conditions affecting all of them at all times in a large diverse basin. Instead we use a simplified statement of runoff from each HRU or cell in a tributary watershed, such as a short-time-step (1-30 day) water balance:

37. Prediction of runoff volume (R) generated during a time stepin a Hydrologic Response Unit

38. Timing of stormflow runoff The various procedures outlined above calculate the volume of storm runoff, which in general must be added to the base flow, calculated by the soil-water balance or recession-curve method [ESM 203]. We call this amount ‘what to route’. We call the topic of calculating the time distribution of runoff ‘how to route’. These are the two components of runoff hydrograph prediction

39. Options for routing flow down a channel network in HEC-HMS Lag --- constant flow velocity Puls storage reservoir method views each channel reach as a small reservoir Muskingum method Kinematic wave Many others

40. Verify predictions wherever possible by comparison with measured hydrographs

41. Calibration:Adjust values (parameters) in various components of the models until prediction fits observation ‘well enough’

42. How to route: three options for a conceptual model (1) Lag the water by a fixed time after it is generated. OK for small watersheds

43. How to route: three options for a conceptual model (2) View the watershed as an open book consisting of two planes and calculate the flow down these ‘representative hillslopes’, using Manning’s equation and an “equivalent roughness”. Manning’s roughness represents all the complications of the surface (including its spatial variability and flow paths) that will delay flow

44. How to route: three options for a conceptual model (3):The unit hydrograph The fixed geometry of a watershed --- topography (gradients, elevation, effect on rainfall distribution), distribution of soil properties, channel network structure --- is the dominant control on the timing of storm runoff. A unit depth of storm runoff generated in a fixed time interval will ‘always’ drain from the watershed at the same rate. This “unit hydrograph” can be estimated by superimposing and averaging storm runoff hydrographs, each of which has been reduced to a unit depth [If total is 3 inches, divide all ordinates by 3] The unit hydrograph is a characteristic of the watershed

46. Unit hydrograph averaged from four recorded hydrographs, normalized to one inch of runoff(27.4 sq mi. watershed, Coshocton Ohio)

47. The Synthetic Unit Hydrograph of a watershed We could (it used to be done) derive a unit hydrograph for each of a sample of watersheds in a region correlate the various features of these hydrographs (e.g. peak discharge, lag to peak, duration) with watershed geometrical characteristics (e.g. area, steepness,) Use the resulting regression equation to estimate parameters of a synthetic unit hydrograph for ungauged basins A few regional regressions of this type were derived, before ……

48. The Synthetic Unit Hydrograph of a watershed Taking an even more abstract view of storm runoff timing, hydrologists concluded that the geometrical characteristics of ‘most’ watersheds were sufficiently similar that a unit of storm runoff would drain from any landscape with approximately the same timing. Note, in their defense, these hydrologists were working in the rural US, and mostly in small watersheds This concept was enshrined in various approximations such as: “all” unit hydrographs approximate triangles:

49. The Soil Conservation Service Triangular Synthetic Unit Hydrograph

50. The Soil Conservation Service Triangular Synthetic Unit Hydrograph

51. The Soil Conservation Service Triangular Synthetic Unit Hydrograph

52. Tests of the SCS unit hydrograph method 1600 runoff plots in SW US: prediction of peak runoff greater than +/- 50% in 67% of cases. 139 watersheds in E. Australia “Marked lack of agreement” between CN values obtained by conventional means and those back-calculated from recorded flows of previously chosen frequencies

53. Emerging Forms of Flood Prediction and Forecasting Higher resolution spatially distributed modeling Greater use of topographic information in hydrologic predictions because of availability of Digital Elevation Models Greater use of computerized spatial databases of watershed characteristics (soil, land use, channel networks, etc.) Greater use of satellite records of rainfall, radiation, temperature, etc. for driving energy- and water-balance calculations.

54. Peak flows Can be predicted deterministically or estimated probabilistically (i.e. the risk of them can be imagined) 

55. The Rational Runoff Formula Unspoken conceptual model is Horton overland flow

56. Rational runoff model of a hydrograph

57. How to estimate tequilib (also called the time of concentration)? Various handbook empiricisms from the 1940s-50s, like the formula used by the National Resources Conservation Service (former Soil Conservation Service):

58. Derivation of runoff rate

59. Computation of rational runoff hydrograph (1) For rainstorms with duration, t > tequilib  Qpeak = C I A   Read Water in Environmental Planning pp 298-305 for an attempt to elucidate this equation. A= area I= rainfall intensity of the storm with duration =tequilib. Its duration, and therefore the estimation of tequilib strongly affect the chosen value of I because of the strong inverse relationship between rainfall intensity and duration and frequency. C = f(land surface condition). Represents the ‘loss rate’ of rainfall to infiltration.

60. Computation of rational runoff hydrograph For rainstorms with duration, t > tequilib  Qpeak = C I A   As if by magic …. If I is in inches/hr, A in acres (!), Q will be in cu. ft./s for a dimensionless C. This confirms our confidence that God gave this equation to our forefathers along with feet and inches.

61. Metric Rational Runoff Formula is For rainstorms with duration, t > tequilib  Qpeak = 0.278C I A   Where Qpeak is in cu. m/sec I is in mm/hr A is in sq km.

62. Rational equation predicts maximum discharge values for a given drainage area --- for conditions when the whole area is contributing runoff.Therefore, rational formula only used for small watersheds

63. Choice of rainstorm intensity is critical, but not arbitrary Suppose the watershed is rural, has an area of 400 acres, and has a tequilib of 30 min. And suppose we are interested in calculating the peak discharge in the 100-yr rainstorm (see later) Choose the intensity for a 30-minute storm with a recurrence interval of 100 yr. But then suppose you are asked what the 100 year peak discharge will be if the watershed is urbanized and its tequilib is reduced to 20 minutes. Choose the 20-min, 100 yr rainstorm intensity, which will be higher than c. A conservative approach to choosing the critical intensity for design is to calculate the peak discharge for a range of durations and choose the largest predicted value. (transparency)

64. Rational runoff coefficient, C, for land surfaces(Amer. Soc. Civil Engrs.)

65. In fact, C is not truly a constant, but varies with recurrence interval of storm. This is probably because infiltration capacity measured at a point varies spatially, and more intense, rarer storms bring a larger fraction of the watershed up to saturation. Most values are estimated for the 2- and 10-yr storms. For comparison, C10/C2 ˜ 1.33; C100/C10 ˜ 1.50   Variation of C with recurrence interval can be estimated by plotting measured values of rainfall intensity (over the duration of tequilib) and of flood peak against recurrence interval.Otherwise use values of C tabulated in handbooks and textbooks.

66. Prediction errors for the Rational Runoff Formula are very large Australian study 271 small basins:   63% gave errors of > ±50%; 42% >±100%.   Locally calibrated version behaved much better, but “requires a lot of data and work” (i.e. no one wants to analyze data any more!). C values did not vary with watershed characteristics as much as the tables of data in handbooks would have one believe. “Considerable judgment and experience are required in selecting satisfactory values of C for design” Check values against observed flows

67. Probabilistic prediction of peak discharges “What has happened and the frequency of events in a record are the best indicators of what can happen and its probability of happening in the future.” Requires a streamflow record of peaks at a station. The record is analyzed to estimate the probability of flood peaks of various sizes, as if they were independent of one another I.e. no persistent runs of wet and dry years) And then is extrapolated to larger, rarer floods. BUT most hydrologic records are short and non-stationary (i.e. conditions of climate and watershed condition change during the recording period). Magnitude of this problem varies, but needs to be checked in each case.

68. Flood-frequency Analysis and “Prediction” Analysis of empirical records of a flood at a place on a river network i.e. point-based, rather than spatial Concerned with events at a place, rather than processes distributed over a watershed Cannot be used for estimating the effects of environmental change on floods. Concept of “stationarity” is crucial. ……Mmm!

69. Basic Idea:Application of your PStat course Because of the hydroclimatology and watershed conditions upstream of a point, the probability distribution of floods to be expected at the point can be estimated from the frequency distribution of past floods recorded there The observed frequency distribution is a sample from which the parameters of a theoretical probability distribution fitting the observations can be estimated Once fitted to the observed record, the theoretical probability distribution can be used to estimate the probabilities of other hypothetical expected discharges, either through interpolation or extrapolation of the recorded range of flows.

70. Probabilistic prediction of peak discharges Data used are the annual-maximum flow series: the list of the largest flow of each year in a record of length n years. Annual-maximum instantaneous peak discharges and stages are available from the National Water Data Storage and Retrieval system (WATSTORE) at www.usgs.gov Arrange the flow values in descending order with rank m (largest rank = 1). mI is the rank of the ith flood peak in a set of n peaks

71. Probabilistic prediction of peak discharges T is the recurrence interval (yr). The long-term average interval between floods greater than Qi Plot calculated values of T against Qi to develop a flood-frequency curve. See examples in Water in Environmental Planning, pp. 307-308.

72. Modifications Other ‘plotting formulae’ are sometimes used instead of the Weibull formula: They are chosen (and argued about) by their proponents to avoid a variety of numerical biases that arise when the data series are extrapolated to estimate rare flows. An example is the Cunnane formula:

73. Probabilistic prediction based on 49 peak discharges In principle, we could plot the two datasets on any kind of graph But if we intend to extrapolate to the relation to larger recurrence intervals, we need some more guidance We use theoretical probability distributions for this

74. Fitting curves to flood-frequency data for extrapolation Several theoretical probability distributions fit the various observed frequency distributions of floods Each probability distribution can be represented by a straight-line fit to its cumulative form p{Q>Qi} plotted on the appropriate graphical scale (analogous to the normal distribution graph paper in your PStat course).

76. Probabilistic prediction of peak discharges Note that this procedure involves fitting a theoretical probability distribution to an observed sample drawn from an imaginary (but not well-understood) population The “true” theoretical probability distribution of flood discharges is not known, and we have no reason to believe it is simple or has only 1 or parameters. Plotting the data set on various types of graph paper with different scales, designed to represent various theoretical probability distributions as straight lines, yields graphs of different shapes, which when extrapolated beyond the limits of measurement predict a range of peak flood discharges.

77. Typical flood frequency curve(27.4 sq mi. watershed at Coshocton Ohio)

78. Flood frequency plots of same record on different probability papers

79. Probabilistic prediction of peak discharges Note that this procedure involves fitting a theoretical probability distribution to an observed sample drawn from an imaginary (but not well-understood) population There is no unique theoretical probability distribution of flood discharges, and we have no reason to believe it would be simple or have only 1 or 2 parameters. Plotting the data set on various types of graph paper with different scales, designed to represent various theoretical probability distributions as straight lines, yields graphs of different shapes, which when extrapolated beyond the limits of measurement predict a range of peak flood discharges.

81. Plethora of proposed theoretical probability distributions. How to choose? One common approach to choice of flood frequency plotting paper is to choose one on which the observed data plot as a straight line that can be extrapolated to estimate rare, large flood discharges. But …. A second is to choose one of the common ones, but this still leads to different predictions among analysts So, in 1967, with later refinements, US Interagency Advisory Committee on Water Data published “A Uniform Technique for Determining Flood Flow Frequencies”, Bulletin 17B, US Geological Survey.

82. Faced with the dilemma that several probability distributions might be chosen by different analysts and used for extrapolation of the size of rare floods So, in 1967 (updated in 1982), US federal agencies got together and decided that the theoretical probability distribution that most reliably fits observed annual-maximum flood frequencies is the Log Pearson Type III distribution. US Interagency Advisory Committee on Water Data published “A Uniform Technique for Determining Flood Flow Frequencies”, Bulletin 17B, US Geological Survey. In 1982, Easiest way to fit such a flood-frequency curve to observed data is to obtain a sheet of the appropriate cumulative probability graph paper and plot each observed Qi against its calculated Ti and then draw a line (or a curve) through the data points.

83. Cookbook procedure for curve fitting of log-Pearson Type III distribution to a flood series from one station: 1 (early steps should be recognizable from your PStat class) Obtain all annual-maximum flows for a station from (for example www.usgs.gov) Download to Excel and rank them Q1,…Qn. Convert each Qi to its logQi Use Excel to calculate Mean{log Qi }, STDEV {log Qi }, SKEW {log Qi }, and Ti Convert Ti back to probability of exceedence, pi

84. Cookbook procedure for curve fitting of log-Pearson Type III distribution to a flood series from one station: 2 (early steps should be recognizable from your PStat class) Calculate the average of SKEW {log Qi } for the station, ---- called Cs A single-station value of Cs can be inaccurate and biased, so it is corrected using data from other stations in its region, according to Cw = WCs + (1-W)Cm Cw is the weighted skew coefficient W is a weighting factor Cs is the coefficient of skewness computed using the sample data, Cm is a “generalized” regional skewness, which is determined from a published map of the US

86. Cookbook procedure for curve fitting of log-Pearson Type III distribution to a flood series from one station: 3  Var{Cm} obtained from mapped values for US in Tech Bull 17B Var{Cs} is obtained from A = -0.33+0.88¦Cs¦ if ¦Cs¦ =0.90 or A = -0.52+0.30 ¦Cs¦ if ¦Cs¦ >0.90 B =0.94 – 0.26¦ Cs¦ if ¦Cs¦ =1.50 or B = 0.55 ¦Cs¦ >1.50

87. Cookbook procedure for curve fitting of log-Pearson Type III distribution to a flood series from one station: 4  Then calculate the log {Q} for any Q value (such as your original Qi) from log Q = MEAN{log Qi} + K*STDEV{logQi} K is a frequency factor that depends on Cs and Ti (tabulated in Bull. 17B) Plot the values of Q against T Extrapolate by choosing larger values of T and calculating Q

88. Sample frequency factor table (Haan, 1977)

89. Published example

90. Published example

92. Bulletin 17Bhttp://acwi.gov/hydrology/Frequency/B17bFAQ.html Instructions for plotting formula Fits data with a Log Pearson Type III distribution Instructions for how to estimate the skew of the distribution that “should” fit your station, based on regional skew patterns How to deal with “outliers”

93. Bulletin 17B: Instructions for incorporating historical information Overcome the short length of most flood Written records Flood marks chiseled on structures Dated tree scars (from tree rings) Dates sediment deposits Indicate maximum flood in n years, or number of floods greater than some stage or discharge in a fixed interval

94. Outliers Where should the outlier be plotted? Does it really represent the discharge with a 70-yr recc. interval, or was it the “300-yr flood” that fortuitously occurred in the 49-yr long record?

95. Bulletin 17B: Instructions for incorporating historical information Overcome the short length of most flood Written records Flood marks chiseled on structures Dated tree scars (from tree rings) Dates sediment deposits Indicate maximum flood in n years, or number of floods greater than some stage or discharge in a fixed interval

96. Uncertainty in assessing flood risk Short records (Bulletin 17B suggests using ‘at least 10 years of record’!) There is no fundamentally representative theoretical probability distribution. Policy for using (say) Log Pearson Type III is based on the assessment that applying it to many flood records yields minimum standard errors of estimate. But reasons that are not understood physically. Persistence problem Climate change Watershed change --- e.g how to assess the influence of the non-steady expansion of logging through the Oregon Cascades? Some changes are reversible (e.g. canopy re-establishment) Others are not (e.g. many roads and ditches)

97. Uncertainty in assessing flood risk So, use the accepted methodology (remember that the acceptability of these and similar techniques is based on professional agreements), and THEN for important decisions focus on the evidence for extreme events, even if you can’t quantify their probability. Examine potential for ‘non-hydrologic’ floods, or conditions that would aggravate a hydrologic flood Landslide dam-break flood Trestle bridge that could block floating woody debris

98. Recurrence interval (return period) of the T-year flood Recurrence interval is the average interval between floods that are greater than a specified discharge E.g. if the probability of exceeding 20 m3/sec in any year at a station is 0.01, there should be on average 10 events larger than 20 m3/sec in 1000 years, if the conditions affecting floods at the site do not change. The average recurrence interval between floods is 100 years, so we refer to such a discharge as “the 100-year flood.”. The floods will not occur regularly every 100 years

99. The probability of exceedence of the 100-year flood remains the same in any year It is 0.01 the year after a flood of this size occurred Probability that a discharge of this size will not occur in any year is (1-p) Probability that such a discharge will not be exceeded in N years is [1 – p]N Probability that such a discharge would be exceeded in n years is Best way to refer to a T-year flood is by means of its odds ratio: --- it has a 1 in 100 chance of being exceeded in each year. Recurrence interval

100. Regional flood-frequency curves Multiple-regression formulae based on data from all the USGS gauging stations in a region. Typical formula:   where A = drainage area Ei are watershed characteristics, such as mean annual precipitation, average elevation, average slope, etc. Obtained from US Geological Survey publications entitled “ Regional flood-frequency analysis for (State)”. Average estimation errors for the Potomac R. basin: ± 20% for 2-yr flood; ± 25% for 10-yr flood; ± 40% for 50-yr flood.

101. Uncertainty in assessing flood risk Short records (Bulletin 17B suggests using ‘at least 10 years of record’!). There is no fundamentally representative theoretical probability distribution. Policy for using (say) Log Pearson Type III is based on the assessment that applying it to many flood records yields minimum standard errors of estimate. But reasons that are not understood physically. Best to try fitting more than one distribution and examining the uncertainty Methodological uncertainties (e.g. the outlier problem):

102. Uncertainty in assessing flood risk (contd.) Persistence problem Climate change Effects of dams --- confine analysis to post-dam period Watershed change --- e.g how to assess the influence of the non-steady expansion of logging through the Oregon Cascades? Some changes are reversible (e.g. canopy re-establishment) Others are not (e.g. many roads and ditches)