Integrate an actual discharge archive without inventing an instantaneous peak

1. Define the process and evidence

A stream hydrograph records flow through time, but its interpretation depends on how each value was formed. An instantaneous measurement, daily mean and daily maximum are not interchangeable. A daily mean preserves the volume integral over its day when multiplied by that day’s duration; it cannot recover the exact timing or height of an unrecorded subdaily peak.

2. Connect mechanism and boundary

This lesson supplies actual USGS daily mean discharge for station 01646500, Potomac River near Washington at Little Falls Pump Station, for 1–8 January 2023. All eight retained values carry qualifier A, meaning approved for publication. Approval does not mean zero measurement uncertainty or immunity to later revision. The source RDB, uniform CSV and provenance are downloadable and distinguish original values from derived quantities.

The source unit is cubic feet per second. The international foot gives exactly 1 ft³=0.028316846592 m³. Integrate a selected daily mean by multiplying the converted rate by 86400 seconds; the selected January dates contain no daylight-saving transition. For multiple days, sum these volumes rather than treating an average rate as a volume.

The eight-day interval was selected as one complete consecutive packet, not filtered to show only high or low flows. It does not establish a flood return period, a long-term trend or a cause such as rainfall, snowmelt, reservoir operation or groundwater release. Those interpretations need longer or independent observations. Retain source version, units, approval flags and the exact analysis window before drawing conclusions.

3. Reconstruct the worked packet

The first two daily means are 9710 and 10000 ft³/s. Their mean is 9855 ft³/s; selected volume is (9710+10000)×0.028316846592×86400 m³. The larger daily mean is not necessarily the larger instantaneous peak.

Actual USGS archive: geo-usgs-daily-discharge@1

POTOMAC RIVER NEAR WASH, DC LITTLE FALLS PUMP STA, site 01646500. Parameter 00060, statistic 00003: daily mean discharge, originally in cubic feet per second.

All eight consecutive source values; A means approved, not uncertainty-free

Date	Discharge (ft³/s)	Qualifier
2023-01-01	9710	A
2023-01-02	10000	A
2023-01-03	11300	A
2023-01-04	11900	A
2023-01-05	11600	A
2023-01-06	11500	A
2023-01-07	10500	A
2023-01-08	9460	A

Uniform CSV · Archived original RDB · Provenance JSON · Original USGS query

All eight consecutive daily mean discharge records from 1–8 January 2023, no outcome-based omission. Original discharge values in cubic feet per second and A approval qualifiers retained; renamed column labels, no numeric changes. Exact conversion 1 ft³ = 0.028316846592 m³ is applied only in the model.

Daily means are not instantaneous peaks. A means approved for publication, not uncertainty-free. The source may later revise records; its retrieval header is dynamic, so a fresh source download need not share this archived byte hash. This January interval has eight standard 86400-second days; no daylight-saving transition.

USGS-produced data are U.S. public domain; credit U.S. Geological Survey, inspect third-party exceptions and imply no endorsement. USGS reuse and exception policy.

Retrieved 2026-10-30T22:47:05Z. Archived source SHA-256: 616971a7ccc9b7dbb7cd2072cabd1307651fe602d1df1ddd11750c50dfd5fbe1.

Retain the source audit before feedback

Save the source identifier, query dates, archive hash, parameter/statistic, units, approval flags and reuse terms. Verify raw rows against the RDB, then save your first volume calculation separately from the source observations. State why the daily maximum, event cause and long-term flood frequency are not identified by this packet. A reviewer must assign a genuinely unfamiliar source/window for independent transfer.

4. Predict and investigate

Predict first: Does a daily mean retain enough information to identify the day’s maximum instantaneous discharge?

Download the original RDB, CSV and provenance. Verify one original value and approval flag, reproduce the exact unit conversion, and calculate a one-day and two-day volume. Explain what remains unknown within each day and why approval is not a zero-uncertainty claim.

5. Test a changed case

Apply the evidence to a changed case

For 7–8 January, daily means are 10500 and 9460 ft³/s. What mean rate and volume formula follow?

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

The mean is 9980 ft³/s. Volume is 19960×0.028316846592×86400 m³. These are actual daily-mean-derived quantities, not instantaneous peaks or evidence of a unique upstream mechanism.

6. Retain a defensible process notebook

Preserve first predictions, complete source/units, geometry, flux and storage boundaries, calculations and competing interpretations. Only the explicitly labeled USGS discharge archive is actual measured-derived source data; all other numerical packets and diagrams are invented. Public practice does not certify independent reasoning, actual field competence or a safe environmental decision.

Mechanism or dataset reference, checked 30 October 2026. Original prose, calculations, diagrams and questions; source observations retain agency and provenance.