Understanding the Concept of Double Mass Curve Analysis

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Discussion Overview

The discussion revolves around the concept of double mass curve analysis in hydrology, focusing on the interpretation of slopes in graphical representations of data. Participants explore how to identify adjusted and original slopes based on data distribution and correlation, as well as the implications of breaks in the line.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes the process of determining adjusted and original slopes in double mass curves, noting that the shorter part of the line is taken as the original slope and the longer part is extended for the adjusted slope.
  • Another participant suggests that the assumption in the examples is that the part of the curve with more data points is considered more accurate, leading to extrapolation to correct less populated areas.
  • A participant challenges the idea that there is always a break in the line, stating that a straight line indicates an accurate and homogeneous data set without changes in slope.
  • There is a discussion about the correlation of data sets, where one participant explains that a straight line indicates correlation, while a non-straight line suggests the need to identify unreliable data regions.
  • Another participant questions whether the larger region of the graph could also be less well correlated, indicating uncertainty in the reasoning presented.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of breaks in the line and the reliability of data regions. There is no consensus on whether the larger or smaller regions of the graph are less correlated, indicating ongoing debate and uncertainty in the discussion.

Contextual Notes

Participants reference specific examples (photos 707, 708, and 711) to illustrate their points, but the discussion does not resolve the mathematical or conceptual nuances involved in 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 ?
 
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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.
708.PNG

In the second example (711) most of the data is at the upper end so the extrapolate downwards.
711.PNG
 
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tzx9633 said:
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.
 
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CWatters said:
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 ?
 
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.
 
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CWatters said:
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 ??
 
CWatters said:
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 .
 
CWatters said:
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 ?
 
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I'm afraid I don't know the answer to that.
 

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