Madison River Below Hebgen Lake Near Grayling, MT
Custom dates & interval
What is this?
The green line shows discharge — how much water is passing the gage right now, measured in cubic feet per second (CFS). For context: 10 CFS is a small creek, 100 CFS is a healthy mid-size river reach, 1,000 CFS is major flood-stage on many rivers. The blue line (when available) is gage height — the physical water depth at the gage. Scroll or pinch to zoom; drag to pan. Click any point to see the exact reading.Each point is the reported instantaneous discharge \(q_t\). To convert to gallons per minute: $$1\ \mathrm{CFS} = 448.831\ \mathrm{gal/min}$$
What is this?
All readings from the past 24 hours are sorted from highest to lowest and plotted on a log scale. The x-axis shows "how often is flow this high or higher?" — far left means unusually high today, far right means unusually low. The red dot shows where the current reading sits. If you see 125 CFS at the 30% mark, flow has been at 125 CFS or above 30% of the time in this window.Sort the \(n\) unflagged readings from highest to lowest, \(q_1 \ge q_2 \ge \dots \ge q_n\). The exceedance percentage of the reading ranked \(i\) is $$P_i = \frac{i}{n} \times 100\%$$ — the share of the window during which flow was at \(q_i\) or above. The red dot places the latest reading at the fraction of readings greater than or equal to it.
What is this?
The x-axis shows CFS ranges (bins) and the y-axis shows how many readings fell into each bin over the last 24 hours. A tall bar on the left means flow stayed low; a tall bar on the right means flow stayed high; a spread-out histogram means flow varied a lot. Red stacked bars are flagged (data quality issue) readings.The window's readings are split into 10 equal-width bins between the minimum and maximum observed flow: $$h = \frac{q_{\max} - q_{\min}}{10}$$ Bin \(k\) covers \([\,q_{\min} + kh,\ q_{\min} + (k+1)h\,)\); the last bin also includes its upper edge so \(q_{\max}\) is counted.
What is this?
Discharge (green) and gage height (blue, when available) over the selected date range. The dashed line is a rolling average — it smooths out short-term spikes to reveal the underlying trend. Scroll or pinch to zoom; drag to pan. Click any point for the full reading.The dashed line is a trailing simple moving average. With a rolling window of \(d\) days at a chart interval of \(\Delta t\) minutes, the window spans \(w = \max(1,\ \mathrm{round}(d \cdot 1440 / \Delta t))\) readings, and each plotted value is $$\mathrm{SMA}_t = \frac{1}{n_t} \sum_{k=t-w+1}^{t} q_k$$ where \(n_t \le w\) because missing readings are skipped rather than treated as zero.
What is this?
Daily average flow for each year, plotted on the same axis (MM-DD). Use this to directly compare whether this year's flow for a given calendar date was higher or lower than the same date in prior years. Every year with data for this gage is overlaid; the current year is drawn heaviest.Each point is one day's mean of the unflagged readings, $$\bar{q}_D = \frac{1}{|D|} \sum_{t \in D} q_t$$ plotted at the same month-day position for every year so the same calendar date lines up vertically across years.
What is this?
Same year-over-year comparison as above, but showing gage height (ft) instead of flow (CFS). Useful when stage is a better proxy for local conditions than discharge — for example, when the rating curve is uncertain or when monitoring fish passage depth. Only shown when gage height data is available for this station.Each point is one day's mean stage over the unflagged readings, \(\bar{h}_D = \frac{1}{|D|} \sum_{t \in D} h_t\), with this year's date matched against the same month-day one year earlier.
What is this?
Each day's min and max flow are shown as the shaded band; the center line is the daily mean. A wide band means flow fluctuated a lot that day (e.g., 40–120 CFS). A narrow band means flow was steady (e.g., 58–63 CFS). Useful for spotting irrigation diversion patterns or storm pulses.For each calendar day \(D\), only unflagged readings count. The band spans \(\min_{t \in D} q_t\) to \(\max_{t \in D} q_t\) and the center line is the daily mean $$\bar{q}_D = \frac{1}{|D|} \sum_{t \in D} q_t$$ where \(|D|\) is the number of readings that day.
What is this?
All readings in the selected period are sorted from highest to lowest and plotted on a log scale. The x-axis shows how often flow is at that level or higher — far left is the highest flows, far right the lowest. The red dot shows where the most recent reading sits in the distribution.Sort the \(n\) unflagged readings from highest to lowest, \(q_1 \ge q_2 \ge \dots \ge q_n\). The exceedance percentage of the reading ranked \(i\) is $$P_i = \frac{i}{n} \times 100\%$$ — the share of the period during which flow was at \(q_i\) or above.
What is this?
Each dot is a reading flagged as anomalous. Red = statistical z-score outlier (more than N standard deviations from the local mean). Orange = sudden spike (flow changed by more than X% from the prior reading). Gray = sensor-flagged (data quality sentinel). The x-axis spans the full selected date range — days with no anomalies are shown but have no dots. Use the thresholds above to tune sensitivity.Z-score: each reading is compared against the mean \(\mu_t\) and sample standard deviation \(s_t\) of the unflagged readings in the trailing 30 days (the reading itself excluded): $$z_t = \frac{q_t - \mu_t}{s_t}$$ and flagged when \(|z_t|\) meets the Z threshold above (default 3).
Sudden change: consecutive readings are compared as $$\Delta_t = \frac{q_t - q_{t-1}}{\max(q_{t-1},\ 1)}$$ and flagged when \(|\Delta_t|\) meets the % change threshold above (default 0.5 = 50%). The floor of 1 CFS in the denominator keeps near-zero baseflow from producing huge, meaningless ratios.
| Type | Timestamp | Flow (CFS) | Detail |
|---|
Get alerted when Madison River Below Hebgen Lake Near Grayling, MT moves
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Is Madison River Below Hebgen Lake Near Grayling, MT running high or low this year?
This tab answers that. It charts every year of data we hold for this gage — today's flow against the historical range for the date, each year overlaid on one seasonal axis, and year-by-year totals — so wet years, dry years, and "about normal" are obvious at a glance.
Browsing without an account covers the last 7 days. Year-over-year comparisons come with a free account.
| Timestamp | Flow (CFS) | Flagged | Quality Codeⓘ |
|---|---|---|---|
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