Question

During the heavy rain period in the river basin, a missing point occurred at observation point A, but at observation points B, C, and D in the vicinity

12.3, 14.8, and 11.9 cm of precipitation were observed, respectively. The annual mean/average precipitation for observation points A, B, C, and D were 1290, 1510, 1680, and 1375 mm, respectively, and the coordinates were (0,0), (6,4), (8,-6), and (-4,4), respectively.

Answer 1

We can calculate the missing precipitation at observation point A by utilizing the available data on the precipitation at observation points B, C, and D, as well as the annual mean precipitation for each point.

Let’s proceed with the calculation:

First, we need to determine the distance between observation point A and each of the other points (B, C, and D) using their coordinates. We can use the distance formula, which calculates the Euclidean distance between two points in a coordinate system:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

The distances are as follows:

• Distance between A and B: sqrt((6-0)^2 + (4-0)^2) = sqrt(36 + 16) = sqrt(52) ≈ 7.211
• Distance between A and C: sqrt((8-0)^2 + (-6-0)^2) = sqrt(64 + 36) = sqrt(100) = 10
• Distance between A and D: sqrt((-4-0)^2 + (4-0)^2) = sqrt(16 + 16) = sqrt(32) ≈ 5.657

Next, we can calculate the weights for each observation point based on the distances. The weights are determined by taking the inverse of the squared distances:

Weight = 1 / (Distance^2)

The weights are as follows:

• Weight for B: 1 / (7.211^2) ≈ 0.019
• Weight for C: 1 / (10^2) = 0.01
• Weight for D: 1 / (5.657^2) ≈ 0.035

Now, we can calculate the missing precipitation at point A by taking a weighted average of the precipitation at the nearby points. The formula is:

Missing Precipitation at A = (Weight of B * Precipitation at B) + (Weight of C * Precipitation at C) + (Weight of D * Precipitation at D)

Missing Precipitation at A = (0.019 * 1510) + (0.01 * 1680) + (0.035 * 1375)

Simplifying this expression will give us the missing precipitation at observation point A.