Editing Hydrograph (section)

==Lag-1 hydrograph==

A Lag-1 hydrograph is a graph of discharge which can be accomplished without a time axis (Koehler 2022).<ref>Koehler, R. 2022. ''In preparation'', The Lag-1 Hydrograph – An Alternate Way to Plot Streamflow Time-Series Data. American Institute of Hydrology Bulletin, Winter 2022.</ref> This technique allows data properties such as Q, dQ/dt, and d<sup>2</sup>Q/dt<sup>2</sup>, and trends of increasing, decreasing or no change flow to be readily seen and understood on a single graph. Flow pulse reference lines can easily be added and interpreted. The methodology is based on the time-series serial correlation lag-1 graph and uses the normally unwanted (but still valuable) autocorrelation present within the streamflow data. 

The x-axis represents the discharge for a date, Q<sub>t</sub>, while the y-axis represents the discharge for the next day, Q<sub>t+1</sub>.
Data preparation and plotting methods are identical to an autocorrelation lag 1 plot, where 1 indicates a 1-day or daily time step. The table below shows how the time-series discharge are shifted. It is critical that the temporal sequence is maintained for the data. Thinking of the x values as “flow for today” and the y values as “flow for tomorrow” helps visualize the order of the data.
[[File:Lag-1 hydrograph.jpg|thumb|Lag-1 hydrograph example (day number associated with Q<sub>t</sub>).]]

{| class="wikitable"
|+ Data shift example (USGS site Colorado River at Lees Ferry, AZ, discharge in cubic feet per second (cfs)
|-
! Date !! Q<sub>t</sub> (x) !! Q<sub>t+1</sub> (y)
|-
| 11-Sep-1927|| 43,200 || 43,300
|-
| 12-Sep-1927|| 43,300 || 88,100
|-
| 13-Sep-1927|| 88,100 || 103,000
|-
| 14-Sep-1927|| 103,000 || 110,000
|-
| 15-Sep-1927|| 110,000 || 78,900
|-
| 16-Sep-1927|| 78,900 || 55,900
|-
| 17-Sep-1927|| 55,900 || 45,300
|-
| 18-Sep-1927||| 45,300 || 33,300
|}