It is possible to do a correlation. Be sure to check if there is a time lag between the two gauges (that would equal the time the water needs to travel from gauge A to gauge B).

You can subsequently use the regression equation to fill in for example missing data from one station.

Just make sure that you check the value of the regression model with standard statistical tests.

It goes without saying that if the correlation of the two gauges is poor, you can not use this method.

Dear Loannis thank you for your input. Regarding Nima question, my concern is to determine stage height of up stream by using the data of downstream. Up stream data is available only for Nine month but downstream data that is stage height is more then 20 years. So i just want to determine past data form these data...and i want to know how to estimate error form this estimation.

Our research group developed a simple method for relating stage and discharge for two gauging stations. The method is easy to apply and works very good. You just need the knowledge of the geometry of the river section at the two stations.

You can find here on Research Gate the last publication on that model:

https://www.researchgate.net/publication/230719343_Enhancement_and_comprehensive_evaluation_of_the_Rating_Curve_Model_for_different_river_sites?ev=prf_pub

Article Enhancement and comprehensive evaluation of the Rating Curve...

Thank you Luca for providing paper.

check out the Center of Ecology and Hydrology in the UK they collected data from all national agencies and process it to create one database the have developed many different interpolation methodologies. So there experience may be useful the have many publication which most are free the also have some pre-written code for this job that can be downloaded.

http://www.ceh.ac.uk/index.html

Thank you Carig.

In case of river stations, the accuracy of correlation between two river gauge stations depends on the uniformity of conditions especially, the discharge regime of two study rivers.

Please note that:

1- All ranges of low flow, medium flow and high flow data should be used to extract the correlation.

2- Similar catchment is not reason enough to uniformity of conditions and similarity of discharge regime in two rivers. they can be different because of many topographical or geological reasons.

What is the difference in catchment area draining to each gauge? The closer these are, the easier it will be to estimate the stage height at one gauge based on measurements at the other. As noted above, you will need to correct for the time for a peak to travel from the upstream to downstream gauge. I used this method for estimating the river level in Queanbeyan based on the level in Googong dam during the 2012 flood.

A more sophisticated method would be to use the flow rates rather than the levels. The advantage of this is that you can use conservation of mass (though you would have to add the additional flow added between the gauges). The disadvantage is that you need the rating curves for both gauges, and this then introduces more uncertainty. An alternative method would be to use a model that does not include the mass balance. Check out recent papers by Keith Beven and Peter Young on modelling flood heights in the UK.

One has to watch out for changes in vegetation cover, land use and instream water abstractions between the two stations in the past 20 years that can affect the runoff at either station, and could constitute some uncertainity in hindcasting the upstream stage data estimates 20 years back from the downstream estimates. One can see at least visually if there has been a lot of deforestation for instance, from tools like http://world.time.com/timelapse/

This can then potentially help refine the extrapolated values at the upstream station.

You might want to study the methodologies proposed by other researchers and institutions (search on Google Scholar; Scopus; ISI Web of Science etc.) and then suitably adapt them to the catchment soils, rainfall dynamics, hydrological processes and runoff modelling techniques and resolution relevant to your application.

For example, the papers by Luca, Silvia and Angelica referred to above look very interesting and promising.

A different approach has been advanced by the UK Centre for Ecology & Hydrology (CEH), in Wallingford, Oxfordshire. This was a method to estimate QMED (the 2-year flood event) at ungauged locations on most UK rivers. They called this the ‘Flood Estimation Handbook’ approach and the software and the associated 5-volume publication was first published by the Institute of Hydrology in 1999 (ISBN 0 948540 94 X), but has been updated since c. 2005.

The Flood Estimation Handbook approach includes the hydrological soil behaviour variables SPRHOST, which is the standard percentage runoff for each soil type, estimated at a 1km grid resolution, and also BFIHOST, which is designed to index baseflow contributions for different soils.

As part of a study of spatial variations in river flood power, our Hydro group worked to combine the CEH Flood Estimation Handbook approach with Digital Elevation Model based-values for stream slope, to calculate downstream changes in flood risk at c.60m intervals along whole river mainstems. I called this the CAFES (Combined Automated Flood, Elevation and Stream power) system, and we are using this system to test our CAtchment-scale Stream Power (CASSP) model.

We enjoyed collaborating in this research with David G. Morris, Helen N. Davies and Elizabeth J. Stewart of the CEH Flood Estimation Handbook team at the Centre for Ecology & Hydrology. Our first results were published in a 2009 paper in Earth Surface Processes and Landforms (DOI: 10.1002/esp.1723). I have attached a copy of this paper so you have some of the references to hand.

I hope this helps. Good luck!

In real world, it is almost impossible to derive useful correlation between two gauge locations.

On second though, it might be possible if you have three pieces of information. The first is a correlation of flows: q1/q2 = (a1/a2)^n; this can be derived if you have flow measurements at both sites. The second and third are the rating curves: q1 = f1(y1) and q2 = f2(y2); this is generally available at gauge stations. One can combine these three equations to get a relation between two gauge heights: in the form of y2 = f3(y1).