Final answer:
To estimate the annual-maximum streamflow with a return period of 50 years, we can use the general extreme-value (GEV) distribution. This distribution is defined by three parameters: location, scale, and shape. By converting the given skewness value to the shape parameter, we can then utilize the GEV distribution formula to estimate the streamflow. Eventually, plugging in the values for the parameters and the desired return period, we can solve for the estimated annual-maximum streamflow.
Step-by-step explanation:
To estimate the annual-maximum streamflow with a return period of 50 years, we can use the general extreme-value (GEV) distribution. The GEV distribution is defined by three parameters: location (μ), scale (σ), and shape (ξ). We can use these parameters, along with the return period, to estimate the streamflow.
- First, we need to convert the skewness value to the shape parameter (ξ). Skewness is related to the shape parameter as follows: skewness = (2/√6) * ξ. In this case, we have a skewness of 1.86, so ξ = (√6/2) * 1.86 = 2.668.
- Next, we can use the formula for the return period (T) of the GEV distribution: T = (1 - 1/k)^(-1) where k is the exceedance probability (1/T). In this case, we want a return period of 50 years, so k = 1/50 = 0.02.
- Finally, we can use the cumulative distribution function (CDF) of the GEV distribution to find the streamflow associated with the desired exceedance probability. The CDF is given by: F(x) = exp[-(1 + ξ * (x - μ)/σ)^(-1/ξ)]
- Plugging in the values for μ, σ, ξ, and k, we can solve for x, the streamflow associated with the desired exceedance probability, by rearranging the equation: x = μ + [σ * ((-log(k))^(-ξ) - 1)/ξ].
Now we can substitute the values for μ, σ, ξ, and k into the equation and calculate the streamflow. The estimated annual-maximum streamflow with a return period of 50 years is the value of x calculated using the equation.