"In instances where there exists a low correlation between TRMM (Tropical Rainfall Measuring Mission) data and precipitation predicted by the model through linear regression analysis, is there a method available to enhance this correlation coefficient?"
It depends on why the correlation is low. If this is due to random measurement error (unreliability in the measurements) you could try to enhance the measurement precision / reduce error. Measurement error adds random noise (error variance) to the scores, leading to an underestimation ("attenuation") of the correlation coefficient.
If you knew the reliabilities of the measurements, you could apply a correction for attenuation based on classical test theory. See my Youtube video:
https://youtu.be/jJ-qLImQYZs
Also, especially in smaller samples, outliers or extreme scores can have an impact on the estimated correlation.
In other instances, the correlation may just be low and that's simply the result.
In addition to the first answer, correlation depends on data RANGE and also it assumes that relationship is best-fit linear i.e. it is shape dependent. RANK correlation, on the other hand, is NOT shape dependent and you should get higher value (fit quadratic, cubic... polynomial model to check if shape is non-linear...
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