Streamflow Time Series & Gauge Comparison Metrics

Mean flow is the arithmetic average of all discharge values within the selected time window.

• What it measures: The overall scale of flow moving through the gauge.
• Real-world relationship: Larger drainage areas, wetter climates, major tributaries, and groundwater-fed systems usually have higher mean flow.
• Hydrologic meaning: Useful for comparing the general size or water-yield of streams, but it can be strongly influenced by floods.
• Watch for: A few major storm events can pull the mean upward and make the river look “wetter” than normal day-to-day conditions.

Median flow, or P50, is the middle value of the streamflow record.

• What it measures: The central everyday flow condition.
• Real-world relationship: Often better than the mean for describing normal stream conditions because it is less distorted by isolated floods.
• Hydrologic meaning: A high median suggests sustained flow; a low median with a high mean suggests a flashy watershed dominated by occasional storm pulses.
• Watch for: In intermittent streams, the median may be very low or zero, which is important for drought and habitat interpretation.

Standard deviation measures how much streamflow values deviate from the mean.

• What it measures: Absolute variability in discharge.
• Real-world relationship: High values often indicate storm-driven peaks, seasonal flood pulses, dam operations, or highly variable runoff response.
• Hydrologic meaning: Helps identify whether a site behaves steadily or swings widely between low and high flow.
• Watch for: Standard deviation naturally increases with river size, so it should not be used alone to compare a small creek against a large river.

Minimum and maximum flow represent the lowest and highest recorded discharge values in the selected period.

• What it measures: The observed range of hydrologic conditions.
• Real-world relationship: Minimum flow relates to drought, baseflow, withdrawals, or intermittent stream behavior. Maximum flow relates to storms, floods, releases, or backwater events.
• Hydrologic meaning: The min/max range gives a fast read on how extreme the system became during the selected time window.
• Watch for: Extreme values may reflect sensor error, ice, debris, rating-curve issues, or temporary gauge problems.

P10 is the flow rate exceeded only about 10% of the time.

• What it measures: The upper-flow portion of the record without relying only on the single maximum value.
• Real-world relationship: High P10 values may reflect wet seasons, frequent storms, snowmelt, reservoir releases, or consistently large runoff contributions.
• Hydrologic meaning: Useful for identifying high-water conditions that are common enough to matter operationally but not necessarily extreme floods.
• Watch for: Compare P10 against median flow. A very large gap suggests a flashy or flood-prone response.

P90 is the flow rate that the stream stays at or above about 90% of the time.

• What it measures: The lower-flow portion of the record.
• Real-world relationship: Higher P90 values often suggest groundwater support, spring input, wetlands, or regulated minimum releases. Lower P90 values suggest drought vulnerability or weak baseflow.
• Hydrologic meaning: Important for ecological thresholds, water supply, drought screening, and identifying perennial versus intermittent behavior.
• Watch for: A low P90 combined with a high P10 usually points to a flashy stream with poor dry-weather support.

Coefficient of variation standardizes variability by dividing standard deviation by mean flow. CV = Standard Deviation ÷ Mean

• What it measures: Relative variability independent of river size.
• Real-world relationship: High CV often indicates flashy runoff, urbanization, arid-climate response, steep terrain, or limited storage. Low CV often indicates groundwater support, lake influence, wetlands, or reservoir smoothing.
• Hydrologic meaning: Good for comparing a small creek to a large river because it scales variability to the size of the flow.
• Watch for: CV can become unstable when mean flow is near zero.

Richards-Baker Flashiness Index compares the sum of timestep-to-timestep absolute flow changes against total flow.

• What it measures: How rapidly and frequently flow changes through time.
• Real-world relationship: High flashiness is commonly associated with impervious cover, storm drains, channelization, steep slopes, thin soils, arid watersheds, and low infiltration.
• Hydrologic meaning: Helps identify watersheds that rapidly convert rainfall into runoff.
• Watch for: Flashiness is timestep-sensitive. Five-minute data can produce different values than 15-minute or hourly data.

First-order autocorrelation measures how strongly flow at one timestep resembles flow at the previous timestep.

• What it measures: Persistence and smoothness in the hydrograph.
• Real-world relationship: High AC1 often occurs in large rivers, groundwater-fed streams, reservoir-regulated systems, and basins with strong storage. Low AC1 often occurs in flashy urban creeks, ephemeral channels, or noisy records.
• Hydrologic meaning: High values indicate slow, predictable transitions. Low values indicate sudden changes and limited hydrologic memory.
• Watch for: Very high values may also occur in artificially smoothed or regulated systems.

Maximum ramp rate identifies the steepest change in discharge over a fixed time window, such as one hour.

• What it measures: The most abrupt surge or drop in the record.
• Real-world relationship: High ramp rates may indicate flash flooding, intense rainfall, dam gate operations, urban runoff, or rapid tributary inflow.
• Hydrologic meaning: Important for flood warning, safety at low-water crossings, aquatic habitat stress, and rapid-stage-change risk.
• Watch for: Unrealistically high ramp rates may indicate gauge noise, telemetry errors, debris, or rating-curve problems.

Data density is the number of matched timestamp pairs available between two gauges.

• What it measures: Sample size for pairwise comparison.
• Real-world relationship: Low N may indicate one gauge was offline, the gauges operated during different periods, or one record has missing data.
• Hydrologic meaning: A strong correlation based on low N may not be reliable enough for decision-making.
• Watch for: Sparse overlap can make lag scans, bias, RMSE, and NSE unstable.

Nearest-match logic pairs observations from two gauges if their timestamps fall within a set window, such as ±10 minutes.

• What it measures: Whether two records can be compared at nearly the same time.
• Real-world relationship: Gauges often report at different intervals, especially when one reports every 5 minutes and another every 15 minutes.
• Hydrologic meaning: Good alignment is critical when evaluating flood waves, storm peaks, and rapid flow changes.
• Watch for: A wide matching window can blur fast-moving events and weaken real hydrologic timing signals.

Pearson r measures the linear relationship between two gauge records at matched timestamps.

• What it measures: Whether high and low values at one gauge linearly correspond to high and low values at another gauge.
• Real-world relationship: High same-time Pearson r suggests gauges respond together with little delay. Low same-time r may occur when gauges are separated by travel time, affected by tributaries, or controlled by different rainfall patterns.
• Hydrologic meaning: Useful for testing whether one gauge can serve as a real-time proxy for another.
• Watch for: Pearson r may underestimate connection when a downstream gauge responds later than the upstream gauge.

Spearman correlation measures whether two gauges generally rise and fall together after ranking their values.

• What it measures: Monotonic relationship, even if the relationship is not perfectly linear.
• Real-world relationship: Useful when two watersheds respond similarly but one has larger peaks, nonlinear routing, rating-curve differences, or outlier events.
• Hydrologic meaning: Helps determine whether the two gauges share the same general hydrologic pattern.
• Watch for: Spearman can show strong association even when actual flow volumes differ substantially.

RMSE measures the average size of the difference between paired gauge values, with larger errors weighted more heavily. RMSE = √mean((Y - X)²)

• What it measures: Magnitude of prediction error in discharge units.
• Real-world relationship: High RMSE may indicate different drainage areas, tributary inflow, diversions, reservoir operations, localized storms, or poor proxy performance.
• Hydrologic meaning: Tells you how wrong one gauge may be when used to estimate another gauge.
• Watch for: RMSE grows with river size, so compare it alongside normalized metrics and drainage area.

NSE compares prediction error against the natural variance of the observed gauge.

• What it measures: Whether one time series predicts another better than simply using the compared site’s average flow.
• Real-world relationship: High NSE suggests strong predictive connection. Low or negative NSE suggests the reference gauge is a poor estimator, possibly because of travel time, tributaries, diversions, regulation, or watershed differences.
• Hydrologic meaning: Strong for judging whether a reference site is operationally useful as a surrogate gauge.
• Watch for: NSE can be very sensitive to high flows and may penalize peak timing errors strongly.

Bias measures whether one gauge consistently reports more or less flow than another.

• What it measures: Directional difference in total or average flow volume.
• Real-world relationship: Downstream positive bias may indicate tributary inflow, groundwater gain, return flow, or larger drainage area. Downstream negative bias may indicate diversions, losing reaches, irrigation withdrawals, bank storage, or evapotranspiration.
• Hydrologic meaning: One of the most useful metrics for identifying possible gaining or losing reach behavior.
• Watch for: Always account for drainage area before interpreting bias as groundwater gain or loss.

Best lag is the time shift that produces the strongest correlation between two gauges.

• What it measures: The apparent delay between flow response at one gauge and flow response at another.
• Real-world relationship: Longer lags often occur in low-gradient channels, broad floodplains, wetland systems, reservoirs, or long river reaches. Short lags often occur in steep, confined, or highly connected drainage systems.
• Hydrologic meaning: Useful for estimating flood-wave travel time and routing behavior.
• Watch for: Best lag usually reflects wave movement, not necessarily the travel time of an individual parcel of water.

Correlation at best lag is the optimized relationship after shifting one gauge in time.

• What it measures: How strongly two gauges relate after accounting for physical delay.
• Real-world relationship: If correlation improves after lagging, the gauges may be strongly connected but separated by channel travel time.
• Hydrologic meaning: Helps distinguish “not connected” from “connected, but delayed.”
• Watch for: If lagged correlation is still weak, the sites may be influenced by different storms, tributaries, human controls, or poor data quality.

A double mass curve compares cumulative discharge from two gauges.

• What it measures: Whether the proportional relationship between two gauges stays stable over time.
• Real-world relationship: A slope break may indicate land-use change, diversion, groundwater pumping, new reservoir behavior, gauge relocation, or rating-curve revision.
• Hydrologic meaning: Helps detect when a watershed or gauge relationship changed.
• Watch for: A slope change can be physical or data-related, so check gauge history and metadata.

A flow duration curve ranks discharge from highest to lowest and plots flow against percent exceedance.

• What it measures: How often different flow levels occur.
• Real-world relationship: Steep curves suggest flashy runoff and limited storage. Flat curves suggest groundwater support, wetland storage, lake influence, or regulation.
• Hydrologic meaning: Excellent for comparing runoff efficiency, baseflow support, drought sensitivity, and flood-prone behavior.
• Watch for: Normalizing by drainage area helps compare watersheds of different sizes more fairly.

This analysis compares the timing of rainfall peaks against discharge peaks.

• What it measures: How quickly streamflow responds after rainfall.
• Real-world relationship: Short lag times suggest steep slopes, urbanization, compacted soils, shallow bedrock, low infiltration, or efficient drainage. Long lag times suggest storage, wetlands, low gradients, or groundwater influence.
• Hydrologic meaning: Useful for estimating watershed response speed and comparing time of concentration between basins.
• Watch for: Rain gauges may not represent rainfall over the full watershed, especially during localized storms.

Baseflow separation estimates the slower groundwater-supported portion of total streamflow.

• What it measures: The estimated fraction of streamflow supplied by baseflow.
• Real-world relationship: High BFI suggests groundwater contribution, aquifer storage, springs, wetlands, or sustained release from basin storage. Low BFI suggests stormflow dominance and limited groundwater support.
• Hydrologic meaning: Useful for identifying gaining reaches, drought resilience, and groundwater/surface-water connection.
• Watch for: Digital filters are estimates, not direct measurements. Results depend on filter choice and parameter settings.

Recession analysis evaluates how quickly streamflow declines after runoff events.

• What it measures: The rate at which stored water drains from the watershed.
• Real-world relationship: Slow recession suggests groundwater support, deep storage, permeable alluvium, wetlands, or bank storage. Fast recession suggests thin soils, steep slopes, low storage, or runoff-dominated behavior.
• Hydrologic meaning: Useful for comparing aquifer support and basin storage between gauges.
• Watch for: Recession analysis should avoid periods with active rainfall, reservoir releases, or obvious operational controls.

This tool compares pasted monitoring-well water-level data with stream baseflow behavior.

• What it measures: Whether groundwater-level changes appear to correspond with streamflow or baseflow changes.
• Real-world relationship: A coordinated rise in groundwater levels and baseflow may indicate recharge response or groundwater/surface-water connection.
• Hydrologic meaning: Useful for screening whether a nearby well and stream may be hydraulically related.
• Watch for: This is a proxy analysis. Specific yield, well depth, screen interval, aquifer type, and distance from the stream matter.

The Wilcoxon Signed-Rank Test evaluates whether paired upstream and downstream flows differ consistently.

• What it measures: Whether paired differences are systematically above or below zero.
• Real-world relationship: Consistent upstream-downstream differences may support interpretation of gaining reaches, losing reaches, diversions, tributary gains, or regulation effects.
• Hydrologic meaning: Helps separate meaningful reach behavior from random noise.
• Watch for: Statistical significance does not automatically prove physical causation. Use mass balance and site context.

MOVE.1 uses the relationship between gauges to estimate missing values or extend comparison periods.

• What it measures: A statistical relationship that can estimate one gauge from another.
• Real-world relationship: Useful when nearby gauges share hydrologic behavior but one has a shorter or incomplete record.
• Hydrologic meaning: Helps compare gauges across equivalent climatic periods instead of biased overlapping windows.
• Watch for: MOVE.1 works best when the gauges have a stable relationship. It should not be blindly applied across major watershed changes or regulation shifts.

• Likely metric pattern: High CV, high flashiness, high ramp rate, steep flow duration curve, short rain-to-flow lag, low BFI.
• Real-world meaning: Rainfall becomes streamflow quickly because infiltration and storage are limited.
• Common causes: Pavement, storm drains, steep slopes, thin soils, channelization, compacted ground, or sparse vegetation.

• Likely metric pattern: Higher P90, high BFI, high AC1, low CV, flatter flow duration curve, slow recession.
• Real-world meaning: Streamflow is buffered by aquifer discharge or basin storage.
• Common causes: Springs, alluvial aquifers, carbonate systems, wetlands, bank storage, or gaining stream conditions.

• Likely metric pattern: High AC1, lower flashiness during normal operations, abrupt ramp rates during releases, altered high-flow and low-flow thresholds.
• Real-world meaning: Flow behavior is partly controlled by operations rather than natural runoff alone.
• Common causes: Flood-control releases, hydropower peaking, minimum-flow requirements, or staged dam-gate operations.

• Likely metric pattern: Downstream flow lower than expected, negative downstream bias, declining low-flow support, weak mass balance after accounting for tributaries.
• Real-world meaning: Water may be leaving the channel between gauges.
• Common causes: Seepage to aquifer, irrigation diversion, bank storage, evapotranspiration, or transmission losses in dry channels.

• Likely metric pattern: Downstream flow greater than expected, positive downstream bias, stronger P90 downstream, higher baseflow, sustained recession.
• Real-world meaning: Water is being added to the channel between gauges.
• Common causes: Groundwater discharge, springs, tributary inflow, return flows, or larger contributing drainage area.

• Likely metric pattern: Impossible ramp rates, flatlined data, sudden unexplained shifts, poor correlation during stable conditions, inconsistent double mass curve breaks.
• Real-world meaning: The strange pattern may not be hydrology.
• Common causes: Sensor fouling, ice, debris, backwater, telemetry gaps, rating-curve changes, datum corrections, or equipment malfunction.