Stage and Time rating shifts  concept investigation
USGS calculation of flow
The calculation of flow is primarily based on the common approach of passing the time series record though a 'flow rating', the applicable rating table may change over the period of record a family of rating tables.The trigger for changing rating tables can be due to many things, primarily a physical change on site has caused a change in the level/flow relationship.
In the period between rating changes there is often a need to 'tweak' the rating relationship by small amounts. There may be one or many tweaks of the relationship applied in the course of the ratings application period. There is a need to interpolate the tweaking between tweak definition points.
Tweaking is equivalent to the release of a new rating table with very minor change and a phased change between the rating tables.
A tweak definition may result from a single gauging observation that deviates from the existing rating more than the allowed amount.
In practice the tweaking is implemented by adjusting the incoming stage record rather that adjusting the rating. The process is to adjust the observed river level (called shifting) to the effective river level.
Thus a rating shift is not a shift on the rating, it is a shift on the gage data before being passed through the rating.
The diagram below illustrates how a rating table is connected to a family of shift tables, the rating may have zero or many shift tables.
Flow calculation process
Step 
Action 
1. Raw gage height 

Datum and quality correction 
2. Computed gage height 

Determine gage height adjustment (stage shift) to be applied to the computed gage height 
3. Effective stage  shifted gage height 

Look up flow rating 
4. Computed flow 
 Need input on best practice USGS shift terminology
The diagram below shows how the effective stage is calulated using the raw gage reading and the stage shift tables.
WMO shift documentation excerpts
Taken from : WMO Manual on stream gauging  Volume II Computation of discharge  Rating shifts
Shift adjustments varied by time only
"The simplest way to vary shift adjustments between discharge measurements is by time interpolation. Timevaried shifts are usually used for periods when stage does not change very much, and the shifting control is affected by a gradual change due to scour or fill. For example, such a condition might be caused by gradual accumulation of falling leaves on a section control."
shift adjustments varied by stage only
"The use of a stagevariedshift adjustment is equivalent to drawing a new numbered rating curve and may be preferable for temporary rating changes. The shiftvariation diagrams shown in Figure II.6.3 are typical stageonly diagrams, as escribed in a previous section. They are applied over a period of time by manually or automatically determining the shift for each stage value for which discharge is computed during the specified time period."
WMO documentation of applying stage and time shifts
"The interpolation procedure is described in the following stepbystep example:
(a) Two shift curves, numbered 001 and 002 for example, are defined graphically for use at dates and times, t_{1 } and t_{2}, respectively;
(b) An interpolated shift, S_{n}, is required for unit value, G_{n}, at an intermediate date and time, t_{n};
(c) The electronic processing system computes the shifts, S_{1} and S_{2}, corresponding to the unit
value, G_{n}, from each of the shift curves, 001 and 002, respectively;
(d) The electronic processing system performs an unweighted, linear time interpolation of shifts
S_{1} at time t_{1}, and S_{2} at time t_{2}, to obtain the shift, S_{n}, at time t_{n};
(e) The same interpolation procedure is used to estimate shifts for all other unit values resulting between times, t_{1} and t_{2}."
Consideration of WMO doco
After reading thoght the WMO doco, I am confident that the method described above is a compund of both the stage and time shift methods. Either method could be implmented in its own right or both methods implmented together thought a single mechanisim.I propose that the method coumented be implmented in the model.
WaterML2.P2 implications
There are there are several option on implementing the shift paradigm. The options change the location of the computation complexity of determining the shift applied. The complexity could be located at the data providers end or the data receivers end. The rules for determining the 'shift' amount are complex, there is a risk that if the calculation of the shift is passed onto the client, then the rules will not be well understood or correctly applied.
The numbers in the below optins refer to the data steps in the table Flow calculation process
Option 1: Provide calculated shift
Supply a WML2 time series of 3 and the rating tables.
Option 2: Receiver calculated shift
Supply a WML2 time series of 2 and the rating tables and shifts to enable calculation of 3
Option 3: Provide shifted tables
Supply rating tables with stage shifts applied, the user time interpolates between the tables. This is a pragmatic, low complexity approach suggest by Stu. It is acknowldged that the final number will not be teh same as usign the documented approach by may be adequate. Further investigation is required.
Useful references
WMO
A useful reference is the WMO manual of stream gauging 1044 Vol II section 6.11.1
http://www.wmo.int/pages/prog/hwrp/publications/stream_gauging/1044_Vol_II_en.pdf
A
excerpt of the rating shift component of the document is attached to this
page.
USGS
U.S. Geological Survey, Techniques of WaterResources Investigations, Book 3, Chapter A13
http://pubs.usgs.gov/twri/twri3a13/
http://wwwrcamnl.wr.usgs.gov/sws/SWTraining/RatingsWeb/Shift_by_stage.proc.pdf
http://wwwrcamnl.wr.usgs.gov/sws/SWTraining/RatingsWeb/Index.html
http://wwwrcamnl.wr.usgs.gov/sws/SWTraining/RatingsWeb/RatingShifts/ShiftsDevelopment.swf
Section 1 Abstract, Introduction, Field data requirements, Datum and gageheight corrections, List of discharge measurements, Discharge ratings TWIKI copy
Section 2 Manual computation of gageheight record, Computation of discharge record TWIKI copy
Section 3 Computation of discharge record (cont'd) Station analysis, Progress documentation, Quality assurance, References cited, Glossary TWIKI copy

PaulSheahan  20 Jun 2013