For a typical catchment, the following precipitation and corresponding runoff data were observed;YearMean annual rainfall (mm) Mean annual runoff(mm)19901188374199112134201992161264319931443537199412034521995159071719961200428199715336821998157586319991480658200011784922001122347820021540883200311655512004127156520051440830A. Develop a simple linear rainfall-runoff model.1. Calculate the regression coefficients a and b using the established equations and express the rainfall-runoff relationship inlinear form.2. Verify your solution using excel spreadsheetB. Estimate goodness-of-fit criteria for the model developed in terms of:1. Coefficient of determination (r2)2. Coefficient of correlation (r)

Given: Year Mean annual rainfall Mean annual runoff 1990 1188 374 1991 1213 420 1992 1612…

For a typical catchment, the following precipitation and corresponding runoff data were observed; Mean annual rainfall (mm) Mean annual runoff (mm) 374 420 643 537 452 717 428 682 863 658 492 478 883 551 565 830 Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1188 1213 1612 1443 1203 1590 1200 1533 1575 1480 1178 1223 1540 1165 1271 1440 A. Develop a simple linear rainfall-runoff model. 1. Calculate the regression coefficients a and b using the established equations and express the rainfall-runoff relationship in linear form. 2. Verify your solution using excel spreadsheet B. Estimate goodness-of-fit criteria for the model developed in terms of: 1. Coefficient of determination (r²) 2. Coefficient of correlation (r)

For a typical catchment, the following precipitation and corresponding runoff data were observed; Mean annual rainfall (mm) Mean annual runoff (mm) 374 420 643 537 452 717 428 682 863 658 492 478 883 551 565 830 Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1188 1213 1612 1443 1203 1590 1200 1533 1575 1480 1178 1223 1540 1165 1271 1440 A. Develop a simple linear rainfall-runoff model. 1. Calculate the regression coefficients a and b using the established equations and express the rainfall-runoff relationship in linear form. 2. Verify your solution using excel spreadsheet B. Estimate goodness-of-fit criteria for the model developed in terms of: 1. Coefficient of determination (r²) 2. Coefficient of correlation (r)

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The following table represents a rainfall storm (start and end time is given in minutes): a) What is the duration of the storm (min, hr)? b) What is the total rainfall depth of this storm (mm, inch)? c) What is the average intensity of this storm? d) What is the maximum 30 min intensity? e) Expand the table to include: time interval, cumulative time, cumulative rainfall, and rainfall intensity (mm/hr). 5 columns have to be added to this table Time (AM) Rainfall during interval (mm) 6:50 7:00 7:10 5 7:15 7 7:35 20 7:45 8 8:00 8.
The rainfall intensity for each 20 min period are given below for a storm. The direct runoff from the basin is 2.5cm 20 MINUTES RAINFALL RAINFALL 1 2.5 2 5 a) What is the total storm rain? cm b) What is the Phi Ø index for the basin? 3 6.5 _cm/hr 4 3.5 5 1
The 60-year record shows that the annual maximum discharges for a river have a mean of 30,000 cfs, a standard deviation of 28,000 cfs, and a skewness coefficient of 3.15. If the annual maximum discharge can be described by the Extreme-value Type I distribution, what is the probability that the annual maximum discharge exceeds 100,000 cfs at least once in next 10 years? (Note: The sample size is 60. Conduct interpolation using exceedance probabilities or cumulative probabilities.)
Question 03 In a given year, a catchment with an area of 9536 km? received 1.3 m of precipitation. The average rate of flow measured in a river draining the catchment was 30 m³s1. a. How much total river runoff occurred in the year (in m³)? b. What is the runoff coefficient? c. How much water is lost due to the combined effects of evaporation, transpiration, and infiltration. (Express in m).
Problem 3 The table below contains the data for a one-hour unit hydrograph. Time Q (hr) (cfs/in) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0 145 246 359 979 432 246 134 65 32 0 (a) Determine the area of the watershed to which this unit hydrograph corresponds. Report your answer in acres. (b) Assume a very intense 3-hour storm occurs shortly after a rainy period, so the ground is very saturated. The runoff from the first one-hour interval of the storm totals 0.5 in., the runoff from the second one-hour interval is 2.5 in, and the runoff from the third one-hour interval totals 1.7 in. The baseflow during and after the storm is 80 cfs. Derive the storm hydrograph for this 3-hour storm. table that clearly indicates how you used the unit hydrograph, sample calculations Provide a with sufficient explanation, explanatory sketches, and a graph of the storm hydrograph. (c) Determine the peak discharge that will occur in the river if this 3-hour storm occurs.
How would you go about deriving a UH from a catchment for which data (catchment area, rainfall and discharge values) are available? Derive a hyetograph from the incident rainfall (losses do not need to be considered to derive a UH); Determine the UH using the formula "Ui = Qi/P" (for a single interval hyetograph) or using "deconvolution" (for a multiple interval hyetograph). Estimate direct runoff hydrograph by subtracting baseflow from observed stream flow data; Estimate the total runoff volume and the direct runoff depth over the catchment; Determine the UH ordinates using the formula "Unit hydrograph = Direct runoff hydrograph x 1/Direct runoff depth"; Estimate catchment losses and subtract these from the incident precipitation to obtain excess rainfall; the duration of the excess rainfall is used as the duration of the UH. Determine the precipitation volume for each time interval; Use UH superposition and proportionality principles to derive a direct unit hydrograph; Estimate…
A catchment is idealized as a 25 km × 25 km square. It has five rain gauges, one at each corner and one at the centre, as shown in the figure. G₂ G₁ O G5 GA G3 During a month the precipitation at these gauges is measured as G₁ = 300 mm. G₂ = 285 mm, G₂ = 272 mm, G₂ = 290 mm and G5 = 288 mm. The average precipitation (in mm up to one decimal place) over the catchment during this month by using the Thiessen polygon method is
Runoff is the portion of rainfall which flows through rivers or streams. Thereare several factors that affect the production of runoff such as precipitationcharacteristic, shape and size of the catchment, topography, meteorologicalcharacteristics and others. Choose one factor and discuss it in detail with helpof diagram how it affects runoff production.
Example 4. Following are the ordinates of a storm hydrograph of a river draining a catchment area of 423 km² due to a 6-h isolated storm. Derive the ordinates o f a 6-h unit hydrograph for the catchment Time from start of storm (h) -6 0 6 12 18 24 30 36 42 48 Discharge (m³/s) 10 10 30 87.5 115.5 102.5 85.0 71.0 59.0 47.5 Time from start of storm (h) 54 60 66 72 78 84 90 96 102 Discharge (m³/s) 39.0 31.5 26.0 21.5 17.5 15.0 12.5 12.0 12.0
Show full solution.According to rainfall data collected by a laboratory during storm events, the precipitation level in inches (X) varies jointly with runoff in cubic feet per second (Y). The joint probability mass function (PMF) of both variables are given by the following Table: Y 1 2 3 10 0.05 0.15 0 20 0.1 0.25 0.25 30 0 0.1 0.1 a. Determine and plot the marginal PMF of runoff.b. Determine the correlation coefficient between X and Y.
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Three cm of rain falls on a 20,000 hectares catchment area during a 24 hours period. If 70% of rainfall runs off, calculate the average rate of runoff in m3/s if runoff lasts for 72 hours. Show complete solution.