Understanding the Concept of Double Mass Curve Analysis

It's possible that larger regions could also be less well correlated, but in these specific examples, it seems that the smaller regions were identified as having less reliable data. It's important to look at the specific data and circumstances to determine which regions may have less reliable data. In summary, the double mass curve method is used to determine correlation between two data sets by plotting them against each other. If the resulting line is not straight, the less reliable data can be identified by looking at the correlation. In the examples given, the smaller regions of the graph were identified as having less reliable data and were extrapolated from the larger region.
  • #1
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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  • #2
Refer to here
 

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  • #3
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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  • #4
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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  • #5
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 ?
 
  • #6
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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  • #7
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 ??
 
  • #8
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 .
 
  • #9
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 ?
 
  • #10
I'm afraid I don't know the answer to that.
 

Related to Understanding the Concept of Double Mass Curve Analysis

1. What is Double Mass Curve Analysis and how does it work?

Double Mass Curve Analysis is a graphical technique used to identify trends and patterns in time series data. It involves plotting two cumulative variables against each other and analyzing the resulting curve. The method works by comparing the shapes of the two curves, looking for shifts or changes in slope which can indicate changes in the relationship between the two variables over time.

2. When is Double Mass Curve Analysis typically used?

This method is commonly used in hydrology and environmental sciences to analyze streamflow, precipitation, and other time series data. It is also used in economics, engineering, and other fields to study the relationship between two variables over time.

3. How is the Double Mass Curve constructed?

The Double Mass Curve is constructed by plotting two cumulative variables, typically on a scatter plot. The x-axis represents the independent variable and the y-axis represents the dependent variable. The data points are then connected to form a curve, and the curve is analyzed for any shifts or changes in slope.

4. What are the advantages of using Double Mass Curve Analysis?

One of the main advantages of this method is that it is simple and easy to understand, making it accessible to a wide range of users. It is also a visual tool, allowing for quick identification of trends and patterns in the data. Additionally, it can be useful for detecting data errors or anomalies, and can provide insights into the relationship between two variables that may not be apparent from other statistical methods.

5. Are there any limitations to using Double Mass Curve Analysis?

While this method can provide valuable insights, it does have some limitations. It is best used for linear relationships between two variables, and may not be suitable for highly complex or non-linear relationships. It also relies on accurate and consistent data, so any errors or missing data can affect the results. It is important to also consider other factors and context when interpreting the results of a Double Mass Curve Analysis.

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