You can get some info from here about rainfall elasticity in Australia.

https://www.researchgate.net/publication/248952874_Estimation_of_rainfall_elasticity_of_streamflow_in_Australia

There should be similar results for other places - my guess is your interest is in the tropics ...

But you really should try to get some evaporation proxy. See here for methods to get a low input estimate of streamflow change

https://www.researchgate.net/publication/223837460_Estimating_the_Sensitivity_of_Mean_Annual_Runoff_to_Climate_Change_Using_Selected_Hydrological_Models

Article Estimation of rainfall elasticity of streamflow in Australia

Article Estimating the Sensitivity of Mean Annual Runoff to Climate ...

I think that rainfall is the most important. Other climate variables can pull from nearest stations. Suggestion from Dr Roger Neville Jones should be considered. Finally you can do it. You have to choose right model. Some hydrological models don't need temperature, i.e, regression model. You should be reliable data then

Hi,

Although it is about climate variability rather than climate change specifically, the paper below shows that in the extratropics in winter, it is possible to use rainfall information alone or even a large scale rainfall proxy like the North Atlantic Oscillation to make successful stream flow predictions. 

I suspect for the tropics or for summer then temperature is also important but you could first try to predict recent observed seasonal stream flows in your region of interest to see if rainfall is sufficient to do that and then apply the same prediction method to the climate change signal.

For more info' see http://iopscience.iop.org/1748-9326/10/6/064006/article

Hope that is of interest,

Adam

Where you have several decades of stream or river flows, like we have here in the USA, you can pick out climate variations very easily when they occur on a daily basis, when you look at the daily discharge averaged over a long period of time, like my local creek that you can see at http://waterdata.usgs.gov/ca/nwis/dvstat/?site_no=11164500&por_11164500_1=2208259,00060,1

You see that like clockwork, we get out first big rain after the normal summer drought on October 13 and 14, then it is dry until another smaller rain on October 26, then dry again until November 6-8, and then the rainfall season starts Nov. 12 with heavy rain each year like clockwork on Nov. 18-20 etc.

If you use the daily flow numbers as the constants, then use the actual flows and you could write a program to detect how far one way or the other from the constants your local climate changes are diverting.

When you have a four year drought, if you use only rainfall, one meter of rain on the environment that has been dried out by long term droughts does not equal one meter of rain under normal rainfall conditions.  So using the daily averaged stream flows, actually works as a filter for the rainfall numbers, when that rainfall goes through the watershed and produce more accurate results on the environment to produce the stream flow numbers.  

In certain large river basins less affected by human activities, you can do that because the correlations of the runoff with the area-averaged rainfall are generally very good. An example is the Yangtze River, with the correlations of the runoff near the mouth with the area-averaged rainfall of the basin reaching as high as 0.92 during 1960-2000, indicating that the variations in discharges are dominantly due to the rainfall. Please refer to Ren et al. (2003), and other publications.

It is very difficult to calibrate a model without PE.

But you still can arbitrarily fix a PE value, or even calibrate the PE value.

You Better Generate The Other Weather Parameters Using WGen and other methods even Instead Of Using Rainfall Only. or You can take the other parameters from the nearby stations. Unless seek for regression models which use rainfall only