“The highest form of human intelligence is the ability to observe without judging” Krishnamurti “The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift” Albert Einstein “The mind is everything, what you think you become” Buddha

U6115: Climate & Water Friday, July 11 2003 Precipitation Condensation, rainfall (spatial & temporal) Streams & Floods Nature and cause of floods Definitions The hydrograph Discharge vs. time Flood prediction Flood routing Flood frequency analysis

1) Precipitation Most of the precipitation falling on Continental USA originates from bordering oceans (up to 30-40% of precipitation over large land is derived from local evaporation)

1) Precipitation Spatial distribution dependent on: Latitude Elevation Distance from moisture source Position within continental land mass Prevailing winds Relation to mountain ranges Relative Tº of land and bordering oceans

1) Precipitation  precipitation Point measurements (depth): How do you measure precipitation? How do you extrapolate specific point measurements to an overall area? Non-recording vs. recording gages Weighing Tipping bucket Requires averaging of data over selected temporal/spatial scales  precipitation

 Event-based processes: uniformitarianism vs catastrophism 1) Precipitation However, record at any given point tends to be tremendously variable in time! Temporal record (hourly, daily) of precipitation  hyetograph  Precipitation is commonly organized into discrete storm events of varying intensity and duration!  Our ability to forecast temporal variation is limited to within a few hours (depending on the system), and is almost zero for a few days in advance!  Event-based processes: uniformitarianism vs catastrophism

1) Precipitation Temporal/Spatial variability!

1) Precipitation Temporal variability  Need for averages (graphical or numerical)

1) Precipitation Precipitation intensity  rate of precipitation over a specific time period (precipitation depth divided by time over which the depth was recorded)  Average precipitation intensity depends, by necessity, on the time period of the computation (longer time, lower intensity)  Relative measure of the likeliness of certain magnitudes of precipitation (probabilistic approach only appropriate under certain conditions).

1) Precipitation Precipitation intensity (Temporal characteristic of precipitation) hydrologists apply a technique called frequency analysis to describe the temporal characteristics of precipitation * we assume that precipitation data are samples of a random variable characterized by a probability density function *only mean annual precipitation appears to be normally (or Gaussian) distributed

1) Precipitation Precipitation intensity (Temporal characteristic of precipitation) precipitation can be described by a mean and a standard deviation *this information is useful to determine the exceedance probability (the probability that a certain annual precipitation value is exceeded in a given year) or the return period - the inverse of the exceedance probability). determination of exceedance probability using standard deviation, mean and the normal distribution:

What is the probability that precipitation will exceed 1m in Seattle? determination of exceedance probability using standard deviation, mean, the normal distribution, and the normalization of the data: What is the probability that precipitation will exceed 1m in Seattle? Mean = 941 mm Std Dev = 176 mm

What is the probability that precipitation will exceed 1m in Seattle? Mean = 941 mm Std Dev = 176 mm Z = 0.34 The cumulative distribution function (cdf) for a chosen value is the probability that a random process (x) will be less than or equal to the chosen value

1) Precipitation What is the probability that precipitation will exceed 1m in Seattle? Mean = 941 mm Std Dev = 176 mm Z = 0.34  37% chance of exceedance Treturn = 1/exceedance then Tr ~3yrs

What is the 100-year rain event in Seattle? 1) Precipitation What is the 100-year rain event in Seattle? cdf = 0.99 Z = 2.33 Mean = 896 mm Std Dev = 183 mm X = 1322 mm 1900-2002  Once!

Infiltration is influenced by type of soil and vegetation Fate of Precipitation Interception Infiltration Runoff Evaporation Infiltration is influenced by type of soil and vegetation

Nature and Cause of Floods Fate of Precipitation  runoff Rivers respond to precipitations Basic quantity to be dealt with is river discharge (as related to rain events)  rate of volume transport of water (L3/t) What is river discharge and how do you measure it? Both river discharge and depth (stage) change with time.

1) Nature and Cause of Floods A river discharge is (usually) not measured directly  inferred from stage (height) hydrograph Rating curves typically are nonlinear and often are approximated using power functions: Q = 76.5(stage)4.1 e.g. If stage peaks at 0.35m

Nature and Cause of Floods Rating curves typically are nonlinear and often are approximated using power functions: Q = 76.5(stage)4.1 e.g. If stage peaks at 0.35m (at t = 6 hours), then the corresponding peak discharge is Q = 76.5(0.35)4.1 = 1.0 m3.s-1 This way, a continuous measurement of river stage is used, in conjunction with established rating curve, to determine discharge as a function of time (almost all discharge hydrographs are determined this way)

Nature and Cause of Floods The nature of each hydrograph depends upon watershed and storm characteristics  strong relationship between hyetograph (precipitation) and hydrograph (stream runoff): -) The resulting peak in the hydrograph is called a flood regardless of whether the river actually leaves its banks and causes damage! -) Background discharge between floods is called baseflow and is supplied by inflow of groundwaters (Sta Cruz river in AZ)

Nature and Cause of Floods in rivers, floods and low flows are expressions of the temporal variability in rainfall or snowmelt interacting with river basin characteristics (basin form, hillslope properties, channel network properties) flooding may also be the result of sudden release of water from dams or lakes, ice jams floods cause the biggest natural hazard damage in the US, example: Mississippi flood, 1993; Honduras, Hurricane Mitch

(normalization is critical practice) Movement of flood wave Flood  may be thought as wave that propagates downstream. In an ideal channel (frictionless fluid) flood wave travels with no change However: Mechanical energy is lost (dissipated) due to friction (roughness of bed) Water also stored in pools, wetlands, and backwaters, and is subsequently released (delay) Thus magnitude of flood wave is reduced and its transfer is delayed as it travels downstream: Attenuation by friction and storage (normalization is critical practice)

Flood Routing flood routing: prediction of downstream hydrograph, if the upstream hydrograph is known How quickly a flood crest travels downstream How the height of the crest changes as it travels downstream flood routing in rivers and by reservoirs dV/dt = I-O Typically, in hydrology problems like these cannot be solved by differentials but must be solved numerically transforming the equation into one or more algebraic equations that can be solved more easily.

Vn+1 - Vn/Dt = In +In+1/2 - On+On+1/2 Flood Routing Prediction of downstream hydrographs requires An estimate of speed of wave crest An estimate of the volume added by inflow Influence of friction A complete understanding of hydrology & hydraulics of drainage basin The 2 most important variables: Depth velocity dV/dt = I-O Solving this equation requires 2 equations -) statement of conservation of mass -) conservation of momentum Need numerical method to transform DFQ into algebraic one: Vn+1 - Vn/Dt = In +In+1/2 - On+On+1/2

Flood Routing Reservoirs’ size and volume affect the routing very rapidly. When reservoirs increase in size (and volume)  store more water and rise in water (h) is smaller  increase in outflow is smaller (delay and reduction of O). A flood wave in rivers, on the other hand, must move through a long stretch of river before peak discharge is reduced as much as moderate-size reservoirs can accomplish in a relative short distance

Flood Frequency Analysis simplest approach: use worst event on record * past record key for the future? Statistical techniques use the following approach * highest discharges recorded in each year are listed * the floods are ranked according to magnitude, the largest flood is assigned a rank 1, the second largest rank 2, etc The flood statistics are estimated graphically by plotting the logarithm of discharge for each flood in the annual series against the fraction of floods greater than or equal to that flood; this fraction is given by r/(n+1), where r is the rank of the particular flood

Flood Frequency Analysis * The return period, the average span of time between any flood and one equaling or exceeding it, is calculated as Treturn = 1/(exceedance probability). * The 100 year flood can then be estimated from the graph * Normal distribution works often well with precipitation data and ln normal for discharge * Problems: not deterministic, based usually on non-adequate data, climate and terrestrial environment is variable