Lecture ERS 482/682 (Fall 2002) Precipitation ERS 482/682 Small Watershed Hydrology

Lecture ERS 482/682 (Fall 2002) Watershed definitions watershed –ridge or stretch of high land dividing the areas drained by different rivers or river systems (e.g., Continental Divide) –the area drained by a river or river system waterbody –geographically defined portion of navigable waters, waters of the contiguous zone, and ocean waters under the lakes, wetlands, coastal waters, and ocean waters (NRC 2001) watershed management (per Lee MacDonald, CSU) –the art and science of managing the land and water resources of a drainage basin for the production and protection of water supplies, water resources, and water- dependent resources

Lecture ERS 482/682 (Fall 2002) Precipitation Water that falls to the earth (and reaches it) –Rain –Snow –Ice pellets (sleet) –Hail –Drizzle

Lecture ERS 482/682 (Fall 2002) Process of precipitation Global circulation Formation of precipitation –uplift –temperature

Lecture ERS 482/682 (Fall 2002) Global circulation Distribution of solar radiation intensity Figure 3-4: Dingman (2002)

Lecture ERS 482/682 (Fall 2002) Global circulation Earth’s rotation Figure 4.1: Manning (1987)

Lecture ERS 482/682 (Fall 2002) Formation of precipitation Water vapor importation Cooling of air to dewpoint temperature Condensation Growth of droplets or crystals See Appendix D for more detail

Lecture ERS 482/682 (Fall 2002) Air cooling Cyclonic uplift Figures 4.2 and 4.3: Manning (1987)

Lecture ERS 482/682 (Fall 2002) Air cooling Thunderstorm uplift Figure 4.4: Manning (1987) Figure 4-7: Dingman (2002)

Lecture ERS 482/682 (Fall 2002) Air cooling Orographic uplift Figure 4.5: Manning (1987)

Lecture ERS 482/682 (Fall 2002) Condensation Figure 2.1: Hornberger et al. (1998)

Lecture ERS 482/682 (Fall 2002) Condensation Assumption: Pressure is constant Figure 2.1: Hornberger et al. (1998)

Lecture ERS 482/682 (Fall 2002) Formation of droplets Figure D-7: Dingman (2002) Condensation requires condensation nuclei

Lecture ERS 482/682 (Fall 2002) Measuring precipitation Units –Depth (L) –Intensity (L T -1 ) Figure 2-2; Dunne and Leopold (1978)

Lecture ERS 482/682 (Fall 2002) Precipitation characteristics Typical precipitation intensities <1”/hr General rule: longer storm duration  lower average intensity

Lecture ERS 482/682 (Fall 2002) Figure 4-51 (a): Dingman (2002)

Lecture ERS 482/682 (Fall 2002) Figure 4-51(c): Dingman (2002)

Lecture ERS 482/682 (Fall 2002) Precipitation characteristics Typical precipitation intensities <1”/hr General rule: longer storm duration  lower average intensity Larger area  lower average intensity

Lecture ERS 482/682 (Fall 2002) Rainfall amounts between 5:30 and 11:00 MDT on 7/28/97 for Fort Collins, CO ( ~1 mi

Lecture ERS 482/682 (Fall 2002) Precipitation characteristics Typical precipitation intensities <1”/hr General rule: longer storm duration  lower average intensity Larger area  lower average intensity –Cannot extrapolate directly from point to area; must correct for area! Extremely variable in time and space!!!Extremely variable in time and space!!! -more precipitation  less relative variability

Lecture ERS 482/682 (Fall 2002) Precipitation-gage networks World Meteorological Association recommendations: Table 4-6 (Dingman text) Need ~ 1 gage every km 2 (250 acres) to get error under ~10%

Lecture ERS 482/682 (Fall 2002) Figure 4-31 Dingman text

Lecture ERS 482/682 (Fall 2002) Precision Precision improves with: –Increasing density of gage network –Extending period of measurement –Increase in time and cost! How close can we get to the true value?

Lecture ERS 482/682 (Fall 2002) Probable maximum precipitation (PMP) –“theoretically the greatest depth of precipitation for a given duration that is physically possible over a given size of storm area at a particular geographical location at a certain time of year” –Available in HMRs (Fig V&L (1996)) Extremes – Hershfield (1961) 24-hr PMP Mean of 24-hr annual maximums over period of record 15 Std dev of the 24-hr maximums

Lecture ERS 482/682 (Fall 2002) Extremes Probable maximum precipitation (PMP) –General guidelines: Critical storm size  basin size Critical duration  time of concentration –Significance: Used to determine the probable maximum flood (PMF) PMF is used to –Design dam spillways –Locate essential public utilities

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) –Determine point rainfall depth for storm of particular Return period (e.g., 25-year, 100-year, etc.) Duration (e.g., 1-hr, 2-hr, 6-hr, 24-hr, etc.)

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the data Plot frequency distribution (histogram) Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probability Plot on normal probability paper Estimate recurrence intervals or depths Transform data yesno

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Discrete vs. continuous data Discrete data can only take on discrete values within a range Continuous data can take on any value within a range

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Normal distribution 2-parameter distribution: –Mean (  ) –Standard deviation (  ) estimated by estimated by s  data are symmetric

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Plot cumulative probability Calculate cumulative probability for the sorted (i.e., ranked) data points with plotting position formula: – - Weibull: m = rank n = number of observations

Lecture ERS 482/682 (Fall 2002) log scale

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Lognormal distribution Plotting the log of the data resembles a normal distribution Mean (  LX ) is estimated by Standard deviation (  LX ) is estimated by taking the std. dev. of the ln x i data:

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno log, ln,

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) Collect/calculate data (e.g., annual maximum) Rank the dataPlot frequency distribution (histogram)Plot probability distribution (divide by N observations) Evaluate normality Calculate cumulative probabilityPlot on normal probability paperEstimate recurrence intervals or depthsTransform data yesno

Lecture ERS 482/682 (Fall 2002) Calculate mean (AVERAGE), standard deviation (STDEV) and use NORMINV function in Excel non-exceedence probability = 1 – EP Note: If you have transformed your data, you should use the mean and std dev of the transformed data and UNTRANSFORM the result!!!

Lecture ERS 482/682 (Fall 2002) Extremes Depth-Duration-Frequency analysis (DDF) –Determine point rainfall depth for storm of particular Return period (e.g., 25-year, 100-year, etc.) Duration (e.g., 1-hr, 2-hr, 6-hr, 24-hr, etc.) –Adjust point estimate to areal estimate Equation 4-29 or Figure 4-52 or Figures and of Viessman and Lewis (1996)