Mass Curve Analysis for Rainfall Intensity

The question asks us to estimate the maximum intensity of rainfall for a 20-minute duration from a given mass curve of rainfall data. A mass curve of rainfall shows the accumulated rainfall depth over time. To find the intensity for a specific duration, we need to calculate the change in cumulative rainfall over that duration and then divide by the duration.

Understanding Rainfall Intensity

Rainfall intensity is defined as the rate at which rainfall occurs, typically expressed in units of depth per unit time (e.g., millimeters per hour, mm/h). In the context of a mass curve of rainfall, the intensity for a given period can be determined by finding the difference in cumulative rainfall between the start and end of that period, and then dividing by the duration of the period.

For this problem, we are specifically interested in the maximum intensity of rainfall over any 20-minute duration within the 100-minute storm. This means we need to examine each possible 20-minute interval within the provided data.

Step-by-Step Calculation of Rainfall Intensity

We are provided with the following cumulative rainfall data:

To find the rainfall intensity for each 20-minute duration, we will calculate the rainfall for each consecutive 20-minute interval and then convert it to mm/h.

• Interval 1: From 0 minutes to 20 minutes
  • Rainfall depth = Cumulative rainfall at 20 min - Cumulative rainfall at 0 min
  • Rainfall depth = \(5 \text{ mm} - 0 \text{ mm} = 5 \text{ mm}\)
  • Duration = \(20 \text{ minutes}\)
  • Intensity = \(\frac{5 \text{ mm}}{20 \text{ min}} = 0.25 \text{ mm/min}\)
  • To convert to mm/h: \(0.25 \text{ mm/min} \times 60 \text{ min/h} = 15 \text{ mm/h}\)
• Interval 2: From 20 minutes to 40 minutes
  • Rainfall depth = Cumulative rainfall at 40 min - Cumulative rainfall at 20 min
  • Rainfall depth = \(12 \text{ mm} - 5 \text{ mm} = 7 \text{ mm}\)
  • Duration = \(20 \text{ minutes}\)
  • Intensity = \(\frac{7 \text{ mm}}{20 \text{ min}} = 0.35 \text{ mm/min}\)
  • To convert to mm/h: \(0.35 \text{ mm/min} \times 60 \text{ min/h} = 21 \text{ mm/h}\)
• Interval 3: From 40 minutes to 60 minutes
  • Rainfall depth = Cumulative rainfall at 60 min - Cumulative rainfall at 40 min
  • Rainfall depth = \(26 \text{ mm} - 12 \text{ mm} = 14 \text{ mm}\)
  • Duration = \(20 \text{ minutes}\)
  • Intensity = \(\frac{14 \text{ mm}}{20 \text{ min}} = 0.70 \text{ mm/min}\)
  • To convert to mm/h: \(0.70 \text{ mm/min} \times 60 \text{ min/h} = 42 \text{ mm/h}\)
• Interval 4: From 60 minutes to 80 minutes
  • Rainfall depth = Cumulative rainfall at 80 min - Cumulative rainfall at 60 min
  • Rainfall depth = \(32 \text{ mm} - 26 \text{ mm} = 6 \text{ mm}\)
  • Duration = \(20 \text{ minutes}\)
  • Intensity = \(\frac{6 \text{ mm}}{20 \text{ min}} = 0.30 \text{ mm/min}\)
  • To convert to mm/h: \(0.30 \text{ mm/min} \times 60 \text{ min/h} = 18 \text{ mm/h}\)
• Interval 5: From 80 minutes to 100 minutes
  • Rainfall depth = Cumulative rainfall at 100 min - Cumulative rainfall at 80 min
  • Rainfall depth = \(35 \text{ mm} - 32 \text{ mm} = 3 \text{ mm}\)
  • Duration = \(20 \text{ minutes}\)
  • Intensity = \(\frac{3 \text{ mm}}{20 \text{ min}} = 0.15 \text{ mm/min}\)
  • To convert to mm/h: \(0.15 \text{ mm/min} \times 60 \text{ min/h} = 9 \text{ mm/h}\)

Maximum Rainfall Intensity Determination

After calculating the rainfall intensity for each 20-minute duration, we list them to find the maximum:

• Interval 0-20 min: \(15 \text{ mm/h}\)
• Interval 20-40 min: \(21 \text{ mm/h}\)
• Interval 40-60 min: \(42 \text{ mm/h}\)
• Interval 60-80 min: \(18 \text{ mm/h}\)
• Interval 80-100 min: \(9 \text{ mm/h}\)

Comparing these values, the maximum intensity of rainfall for a 20-minute duration is \(42 \text{ mm/h}\). This occurs during the interval from 40 minutes to 60 minutes.

Therefore, the estimated maximum intensity of rainfall for a 20-minute duration of the storm is \(42 \text{ mm/h}\).