Understanding the Concept of Double Mass Curve Analysis

[tzx9633]

Homework Statement

In this first photo , we can see that the adjusted is found by extending the longer portion of straight line . The line is extended to the upper part of the graph.( We can see that there's a break in the line , the longer portion of the line is extended , and taken as adjusted slope) . And the shorter part of the line is taken as the original slope .
So , the lower part is the adjusted slope .

But , in the 2nd example , we can see that the adjusted slope is found by extending the loner portion of line too . But , in this , the line is extended to the below part . And the shorter portion of line is taken as original slope...

P/ s : Photo 707 and 708 are for case 1 , the others are for case 2 .

Homework Equations

The Attempt at a Solution

So , based on understanding , can I conclude that for double mass curve . there's always a break in the line . So , for the shorter part , it's always taken as the oriiginal slope . For the longer part , it's extended to get the adjusted slope . Is my concept wrong ?

 

[tzx9633]

Refer to here

 

[CWatters]

Hydrology isn't really my subject but...

I've read the explanation in 707 and it looks like they are assuming that the part of the curve that has more data points is the most accurate. They then extrapolate to "correct" that part of the line for which they have less data. So..

In the first example (708) most of the data is at the lower end so they extrapolate upwards.

In the second example (711) most of the data is at the upper end so the extrapolate downwards.

 

[CWatters]

can I conclude that for double mass curve . there's always a break in the line .

No.

707 says that a change in slope implies part of the data is "inaccurate or non homogeneous". If you have a data set that is accurate and homogeneous you will just have a straight line with no change in slope. For example suppose in the second case you only had data from 1930 to 1942.

 

[tzx9633]

Hydrology isn't really my subject but...

I've read the explanation in 707 and it looks like they are assuming that the part of the curve that has more data points is the most accurate. They then extrapolate to "correct" that part of the line for which they have less data. So..

In the first example (708) most of the data is at the lower end so they extrapolate upwards.
View attachment 212168
In the second example (711) most of the data is at the upper end so the extrapolate downwards.
View attachment 212169

so , the conclusion is we extrapolate the site which has less data ?

 

[CWatters]

I'm struggling to explain it in words..

If you have two data sets and you want to know if they are correlated you plot one on X and one on Y. If you get a straight line the data is correlated.

For example if you want to prove Y = X² you can plot a curve of X² against Y and you should get a straight line. In this case with a slope of 1:1.

If the data isn't correlated you won't get straight line.

If the line isn't straight then you need to decide which part of it is unreliable by looking at the correlation. In the two examples you posted they have concluded that smaller regions of the graph are less well correlated. So they have extrapolated the data from the larger region to the smaller for station X.

 

[tzx9633]

hey have concluded that smaller regions of the graph are less well correlated. So they have extrapolated the data from the larger region to the smaller for station X.

this theory applies to all type of questions in hydrology when we are asked to use double mass curve method ??

 

[tzx9633]

I'm struggling to explain it in words..

If you have two data sets and you want to know if they are correlated you plot one on X and one on Y. If you get a straight line the data is correlated.

For example if you want to prove Y = X² you can plot a curve of X² against Y and you should get a straight line. In this case with a slope of 1:1.

If the data isn't correlated you won't get straight line.

If the line isn't straight then you need to decide which part of it is unreliable by looking at the correlation. In the two examples you posted they have concluded that smaller regions of the graph are less well correlated. So they have extrapolated the data from the larger region to the smaller for station X.

Thanks , i really appreciate your effort to explain ... Can you help me in the following thread ?
https://www.physicsforums.com/threads/missing-precipitation-data-hydrology.927607/

This is a hydrology problem .

 

[tzx9633]

they have concluded that smaller regions of the graph are less well correlated.

why is it so ? Cant be the larger region of the graph are less well correlated ?

 

[CWatters]

I'm afraid I don't know the answer to that.