To calculate 75% of dependable rainfall from a probability distribution of annual rainfall, you'll need to follow these steps:
Organize the Data: Start by organizing the annual rainfall data in ascending order, along with their corresponding probabilities of occurrence. This will give you a clear picture of the distribution.
Calculate Cumulative Probabilities: Calculate the cumulative probabilities by adding up the probabilities of occurrence as you go down the list. This will give you a running total of the likelihood of rainfall being less than or equal to a certain value.
Identify the Value: Find the value in the cumulative probability column that is closest to, but not exceeding, 0.75 (75%). This value will correspond to the dependable rainfall level.
Understand the Probability Distribution Table: The probability distribution table should provide different levels of annual rainfall along with their corresponding probabilities.
Identify the 75th Percentile: The 75th percentile represents the value below which 75% of the data falls. In the context of rainfall, it's the level of rainfall that is exceeded in 75% of the years.
Interpolate if Necessary: If the exact value corresponding to the 75th percentile is not listed in the table, you might need to interpolate to get an approximate value.
Calculate 75% of Dependable Rainfall: Once you have identified the value corresponding to the 75th percentile, you can calculate 75% of dependable rainfall by simply multiplying that value by 0.75.
Let's say you have a probability distribution table of annual rainfall levels and their probabilities:
Rainfall Level (mm) Probability
500 0.10
600 0.20
700 0.30
800 0.25
900 0.10
Identify the 75th percentile: In this example, the 75th percentile falls between the 700 mm and 800 mm rainfall levels.
Interpolate: If you interpolate and estimate that the 75th percentile is around 750 mm (midway between 700 mm and 800 mm), you can proceed to the next step.
Calculate 75% of Dependable Rainfall: 75% of dependable rainfall = 0.75* 750 mm = 562.5 mm
So, in this example, 75% of dependable rainfall is approximately 562.5 mm.
Remember that the actual process may vary based on the specifics of the probability distribution table and whether interpolation is required. Always ensure that your calculations are accurate and appropriate for the context of the data you are working with.
1. Arrange the rainfall data (annual, monthly, decadal, or weekly) in descending order
2. Use one of the methods of computing probability, for instance, Weibull’s method:
P = m/n+1 X 100
Where P is the probability of occurrence, m is the rank of the rainfall value (after arranging the data in descending order) and n is the total number of observations
3. Plot the P values (x-axis) against rainfall values (y-axis) on the log-normal scale
4. Fit a trend line and use it to determine the rainfall values that correspond to 75% OR
5. Use the trend equation to compute the rainfall values by substituting 75 as the x value