Dear Amit,

I suggest you start by consulting a course, or a book, or web-based resources to understand the nature of the R2 and RMSE statistics, and how they relate to each other. For instance, Google lists 122,000 web pages in response to a search for

"r2 versus rmse"

and the following page appears to be a good starting point:

http://people.duke.edu/~rnau/compare.htm

To answer more specifically your question, there is no particular reason why you obtained those values, other than these are the results of the calculation, assuming the latter was done correctly. In other words, no specific "meaning" is associated with a given value. These are two different indicators of the variability in the dataset you have assembled.

Please note also that an R2 value of 0.51 means that only about half of the variance in your relation is "explainable" by NDVI. Whether that's good enough or not depends on the purpose of this fitting exercise. In social sciences, an R2 of 0.5 is good, because humans are highly unpredictable, but as a characterization of a biogeophysical relation, I would not rate it "good". You need to sharpen your analysis and establish a benchmark or a statistical goal, and then evaluate that performance against your objective before deciding that it is good or not.

Good luck. Michel.

Dear Amit,

I suggest you start by consulting a course, or a book, or web-based resources to understand the nature of the R2 and RMSE statistics, and how they relate to each other. For instance, Google lists 122,000 web pages in response to a search for

"r2 versus rmse"

and the following page appears to be a good starting point:

http://people.duke.edu/~rnau/compare.htm

To answer more specifically your question, there is no particular reason why you obtained those values, other than these are the results of the calculation, assuming the latter was done correctly. In other words, no specific "meaning" is associated with a given value. These are two different indicators of the variability in the dataset you have assembled.

Please note also that an R2 value of 0.51 means that only about half of the variance in your relation is "explainable" by NDVI. Whether that's good enough or not depends on the purpose of this fitting exercise. In social sciences, an R2 of 0.5 is good, because humans are highly unpredictable, but as a characterization of a biogeophysical relation, I would not rate it "good". You need to sharpen your analysis and establish a benchmark or a statistical goal, and then evaluate that performance against your objective before deciding that it is good or not.

Good luck. Michel.

NDVI and SOC are related and an R square value suggests that their correlation can explain about 51% of the total variability in the model used.

Bottomline is that NDVI measures a vegetative cover and as cover increases so does the organic matter production as a function of photosynthesis of the plant canopy.

As a plant coverage decreases so will the net photosynthesis ergo the net result with be in less vegetated areas the SOC is less. When rainfall or irrigation is increased to increase the net photosynthesis there is greater potential for conversion of that material into stabilized SOC.

When there is are higher R square value there is higher ability to relate the variables in terms of predictive response if you have low R square your relationship is either not very strong or inappropriate models were applied for the correlation of the variables.

Keep things simple but look critically if your using the right statistics for your situation.

A good relationship between NDVI and SOC in small basins might not be a surprise. NDVI is linearly related to the fraction of photosynthetically active radiation (fPAR) absorbed radiation by vegetation, which is a major factor determining gross primary production. As Paul pointed out, vegetation photosynthesis is closely related to the formation of SOC. 

However, the NDVI and SOC relationship might become messier as the spatial extent expands. For small basins, the spatial variability of radiation and temperature is generally small, which contributes to the good relationship of NDVI and SOC. The increased spatial variability of radiation and temperature, along with other factors such as precipitation and soil drainage conditions, would dampen the NDVI-SOC relationship as these factors affect NDVI and SOC in different complex ways.  

The following paper is a good reference on the relationship between NDVI and productivity. A good text book on the carbon cycle would help understand the processes involved in the formation of SOC.

Yuan, W., Liu, S., Zhou, G., Zhou, G., Tieszen, L.L., Baldocchi, D., Bernhofer, C., Gholz, H., Goldstein, A.H., Goulden, M.L. and Hollinger, D.Y., 2007. Deriving a light use efficiency model from eddy covariance flux data for predicting daily gross primary production across biomes. Agricultural and Forest Meteorology, 143(3), pp.189-207.

I agree with all earlier three excellent explanations given by Michel , Paul and Shuguang . R2  for any  relation  between different variables  ( NDVI and SOC in your case) explains the coefficient of determination ( whose significance will depend upon the number of observations in how much  area  , in a special domain including the size of the grid,  accommodating each observational point )  , check the significance level at various levels like  5%, 1% , .. and see how statistically significant is your regression model.

Myriads of thanks to all the researchers/scientist for his valuable suggestions.

Regards

Amit Kumar

AHEC, IITR 

The above answers are valuable. I wish to add a bit more on the relationship between NDVI and SOC. As pointed above, NDVI is an index for productivity or aboveground biomass. As we know, SOC is the net OC stored in soil, which is the balance between inputs (primarily litterfall) and outputs (i.e., decomposition). In general, high biomass (i.e., high NDVI value) would lead to high SOC so one may find a linear regression between the two variables. However, decomposition is regulated by many factors, e.g., soil and climatic conditions. Therefore, the relationship between NDVI and SOC may not be so good over space when there are considerable variations in environmental variables.

Yes  Xiujun  I agree with you . Such relations need to be worked upon over space and time . And , a lot is depend upon the size and number of  samplings .