Definitions for every measurement, label, and factor shown in this application.

Estimated Wave Height
The primary output of the model — the significant wave height (H_s) at the Merrimack River mouth and bar. Significant wave height is defined as the average height of the highest one-third of all waves, which corresponds closely to what an experienced mariner would estimate by eye. Displayed in feet or metres via the unit toggle. The value integrates all six contributing factors: wind, swell, bar shoaling, ebb steepening, river outflow, and standing wave interaction.

Range (±20% / ±30%)
Uncertainty band around the estimated wave height. The model carries ±20% uncertainty under normal conditions and ±30% when an easterly-ebb standing wave is active, reflecting the added complexity of wave–current interaction at the bar. The low and high ends of this range are shown on the wave forecast chart as dashed bounds.

CALM / CHOPPY / ROUGH / DANGEROUS
Condition badge derived from the estimated significant wave height at the river mouth: Calm — below 1 ft; Choppy — 1–2 ft; Rough — 2–4 ft; Dangerous — above 4 ft. These thresholds are specific to the Merrimack entrance bar, which concentrates and steepens waves more severely than the same height in open water.

Tide Level (ft MLLW)
Current water surface elevation at NOAA station 8440466 (Newburyport) referenced to Mean Lower Low Water — the standard datum for US coastal charts. A higher tide means more depth over the Merrimack bar, which reduces wave shoaling and breaking. A lower tide means shallower water, amplifying wave height and increasing the likelihood of breaking crests.

Rising / Falling (tide phase)
Whether the tide is currently coming in (flood / rising) or going out (ebb / falling). An ebbing tide creates a seaward current that opposes incoming waves, steepening them and increasing height. A rising tide allows waves to enter the mouth more freely. The arrow updates in real time from NOAA prediction data.

Tidal Range (24hr Hi/Lo)
The vertical distance in feet between the highest and lowest predicted tide levels within the current 24-hour period. The Merrimack typically experiences a semi-diurnal tidal range of 8–10 ft. A larger range produces stronger ebb currents, which cause greater wave steepening at the bar.

Wind Speed (kt)
10-metre wind speed in knots at the river mouth, sourced from the NOAA HRRR model via Open-Meteo. Wind is the primary driver of locally-generated waves. The compass bearing shown below the speed is the direction from which the wind is blowing. A gust value (e.g. "G18") appears when gusts exceed mean speed by more than 3 kt.

Onshore / Offshore Wind
Whether wind is blowing toward the shore (onshore, roughly NE–SE) or away from it (offshore). Onshore winds have a fetch of 10–12 km of open water and generate the largest local wind waves. Offshore winds are limited to the ~2.5 km channel fetch and produce much smaller waves.

Offshore Sea State
Wave energy arriving from the open Atlantic, measured at a model grid point ~5 nautical miles offshore of Newburyport. Swell is generated by distant storms and arrives as long, organised wave trains. The primary value shows swell height; the subtitle shows period (seconds) and compass bearing. Only a fraction penetrates the Merrimack inlet — the model uses a transmission coefficient (Kt ≈ 0.38 for onshore swell) to estimate how much energy enters the mouth.

River Level (ft · Newburyport)
Gage height in feet at USGS station 01100870 on the Merrimack at Newburyport, approximately 2 miles from the river mouth. This reading is influenced by both freshwater flow and tidal backwater. It provides situational context but is not used directly in the wave height calculation.

River Flow (cfs · Lowell)
Freshwater discharge in cubic feet per second (cfs) at USGS station 01100000 at Lowell, ~30 miles upstream. This is the primary active discharge gauge for the lower Merrimack watershed. Flow is converted to an estimated outflow velocity at the mouth and added to the tidal ebb current to compute total opposing flow. Higher discharge means stronger seaward current and steeper waves at the bar. Qualitative labels: very low <500 cfs · low 500–1,500 · moderate 1,500–4,000 · high 4,000–8,000 · very high 8,000–15,000 · flood >15,000 cfs.

Wave Period (seconds)
The dominant period of waves at the river mouth — the time in seconds between successive wave crests passing a fixed point. Longer periods mean waves are spaced further apart and are less likely to break; shorter periods mean waves arrive rapidly and are steeper. The displayed period accounts for Doppler shortening by the ebb current. The subtitle shows the full estimated range (minimum to maximum) across current conditions.

Steepness (gentle / moderate / steep / very steep / near-breaking)
Wave steepness is the ratio of wave height to wavelength (H/L). A steepness above ~0.08 in shallow water indicates waves are close to breaking. Gentle <0.025 · Moderate 0.025–0.05 · Steep 0.05–0.08 · Very steep 0.08–0.12 · Near-breaking >0.12. Breaking waves at the bar are the most dangerous condition for small craft.

Air Pressure (mb)
Atmospheric surface pressure in millibars at the river mouth from the NOAA HRRR model. Contextual labels: High pressure >1013 mb (generally fair, offshore winds) · Near normal 1000–1013 mb · Low pressure <1000 mb (often associated with approaching storms, onshore winds, and larger swell).

⚡ Easterly Wind + Ebb Standing Wave Alert
This alert appears when easterly winds from the ENE–ESE sector (70°–110°, peak hazard at ~80°) coincide with an outgoing tide. Incoming ocean waves meet the combined tidal ebb and river outflow head-on at the bar, producing near-standing waves — crests that stack up and can be far taller and more abrupt than offshore data suggests. This is the most hazardous condition at the Merrimack entrance and a leading cause of capsize accidents on the bar.

Tidal Ebb Current (kt)
Estimated seaward tidal current speed in knots at the river mouth during ebb, derived from tidal range using a sinusoidal ebb model. Typical values range from 0.5 to 2.5 kt depending on tidal range. Combines with river outflow to form the total opposing current.

River Outflow (kt)
Seaward velocity in knots contributed by freshwater discharge, converted from USGS cfs using the estimated cross-sectional area of the mouth (~800 m²). Under high river flow this can add 0.5–1 kt to the opposing current.

Total Opposing Flow (kt)
The sum of tidal ebb current and river outflow velocity in knots — the net seaward current that waves must propagate against. As this approaches the wave group speed (C_g), waves shorten, steepen, and can ultimately be blocked entirely (wave blocking). This is the most critical number for predicting bar conditions.

Standing Wave Boost
The additional wave height produced by the easterly-ebb standing wave mechanism, on top of the base wind and swell height. Classified as Weak, Moderate, Strong, or SEVERE based on the product of wind directional alignment (how directly from the east the wind blows) and outflow strength.

Wave Anatomy Diagram — Height Bracket
The vertical bracket to the left of Wave 1 shows how the total estimated wave height is built up from each factor. Each coloured segment is proportional to that factor's contribution in the current conditions. Reading bottom to top: each factor adds height on top of the previous one, until the total crest height is reached.

Wind wave (height factor)
Height generated by local wind blowing across the water surface, computed using the SPM SMB formula with inputs of wind speed, fetch length, and duration. With onshore winds and a 12 km fetch this is typically the largest single contributor to wave height at the mouth.

Tide / ebb (height factor)
Additional height caused by tidal ebb current steepening. Waves propagating against an opposing current become shorter and taller — the model applies a steepening factor of (C_g/(C_g–V_c))^1.2, where C_g is the shallow-water group velocity and V_c is the ebb current speed.

Bar shoaling (height factor)
Amplification of wave height as waves transition from deeper offshore water onto the shallow Merrimack bar (~1.5 m above MLLW at its shallowest). As depth decreases, wave energy concentrates, increasing height. The shoaling coefficient K_s = (d₀/d)^0.25 is applied to the base wave height.

Swell (height factor)
Offshore Atlantic swell energy that penetrates through the inlet. Transmission coefficient Kt ≈ 0.38 for onshore swell (most energy is reflected or dissipated by the narrow inlet geometry), 0.12 for other directions.

River flow (height factor)
Additional steepening caused by the freshwater outflow current. Treated analogously to tidal ebb for wave–current interaction, capped at a maximum velocity of 1.8 m/s to prevent unrealistic amplification.

Standing (height factor)
Extra height produced by the easterly-ebb standing wave resonance — only non-zero when easterly winds coincide with ebb. Added linearly (not by energy) because it represents a coherent resonant effect. Capped at the depth-limited breaking height (0.78 × bar depth).

Wave Anatomy Diagram — Period Bar
The double-headed amber arrow (λ) between the two wave crests represents one wavelength — the crest-to-crest distance. The coloured bar beneath shows how the dominant period is split among contributing factors. Positive contributors (Wind, Swell, Tide/bar) fill left to right; the hatched red Ebb Doppler overlay at the right end shows how much the ebb current has shortened the period.

λ (wavelength)
The horizontal distance between two successive wave crests. In shallow water: λ = T × √(g × d), where T is wave period, g is gravitational acceleration (9.81 m/s²), and d is water depth at the bar. Longer wavelength at the same height means lower steepness and less danger.

Wind (SMB) (period factor)
The contribution of locally-generated wind waves to the dominant period, estimated from the SMB formula: T_wind = 0.54 × (U/g) × (gF/U²)^0.28. Wind-generated waves at the Merrimack mouth typically have periods of 3–7 seconds. The energy-weighted share of wind versus swell determines how much of the dominant period is attributed to each.

Swell (period factor)
The contribution of offshore Atlantic swell to the dominant period. Offshore swell typically arrives at 8–14 s, shortened somewhat by the Doppler effect when the ebb current is active. When swell energy is dominant, this segment spans most of the period bar.

Tide / bar (period factor)
A small positive addition to wave period from the shallow bar. In shallow water, waves travel slower (group velocity C_g = √(g·d)), which has the effect of slightly lengthening the apparent period relative to deep-water conditions. Estimated at approximately 8% of the deep-water base period.

Ebb Doppler (period factor, hatched red)
The shortening of apparent wave period caused by the opposing ebb current. Waves propagating against a current appear to arrive more frequently: T_apparent = T_deep / (1 + V_c/C_g). The hatched red overlay shows how much period has been removed by this effect — the difference between the deep-water period (T_max) and the observed dominant period (T_dom).

MWL (Mean Water Level)
The horizontal reference line in the wave anatomy diagram, representing the average undisturbed water surface. Wave height is measured vertically from MWL to crest. In the model, MWL is set at the current predicted tide level at NOAA station 8440466.

MLLW (Mean Lower Low Water)
The tidal datum used by NOAA for US coastal charts — the average of the lower of the two daily low tides over a 19-year period. Tide levels, gage heights, and water depths in this application are all referenced to MLLW. Nautical chart depths are also referenced to MLLW, so these values are directly applicable to navigation planning.

Wave Height & Period Chart (±12 Hours)
Time-series chart centred on NOW showing estimated wave height at the Merrimack mouth. The solid coloured line is the central estimate (green <1 ft · orange 1–2 ft · red 2–4 ft · dark red >4 ft). Dashed bounds show the uncertainty range. The amber dashed overlay uses the right axis to show estimated dominant wave period in seconds. ⚡ markers indicate easterly-ebb standing wave conditions.

Wind Forecast Chart (±12 Hours)
Time-series of 10-metre wind speed in knots from the NOAA HRRR model. The solid line is mean speed; the shaded envelope shows gusts. Wind direction arrows are plotted at each hour pointing in the direction the wind is blowing toward.

Tide Chart (±12 Hours)
Time-series of NOAA predicted tide levels at Newburyport (station 8440466) in feet above MLLW. High and low water times and levels are annotated on the curve. The NOW marker shows current tide level and phase.

SMB Formula (Sverdrup-Munk-Bretschneider)
An empirical formula for estimating fetch-limited wave height and period from wind speed and fetch length. Developed in the 1940s–1950s and still widely used for coastal engineering estimates. The key inputs are wind speed (U), gravitational acceleration (g), and fetch length (F). Output: H_s = 0.283(U²/g) tanh(0.0125(gF/U²)^0.42).

Fetch
The unobstructed distance over which wind blows across open water in a consistent direction, generating waves. Longer fetch allows waves to grow larger and longer-period. At the Merrimack mouth: onshore (easterly) fetch ≈ 12 km to the open Gulf of Maine; offshore (westerly) fetch ≈ 2.5 km within the river channel.

Group Velocity (C_g)
The speed at which wave energy travels through the water — for shallow-water waves, C_g = √(g × d). This is the key velocity used in wave–current interaction calculations. When the ebb current speed approaches C_g, waves are slowed dramatically, steepen, and can be blocked entirely.

Breaking Wave Indicator (Wave Anatomy Diagram)
When breaking conditions are detected, the foreground wave in the anatomy diagram changes from a smooth swell shape into an asymmetric plunging breaker — leaning forward, with a curling white crest, foam dots on the steep face, and a red BREAKING badge. Breaking is assessed using three criteria: (1) wave steepness H/L exceeds 0.08; (2) estimated wave height reaches 85% or more of the depth-limited breaking cap (0.78 × bar depth); or (3) the raw calculated height was clamped by the depth limit, indicating the model ceiling was hit. Any one criterion triggers the breaking wave display. The background (Wave 2) remains a normal shape to preserve the wavelength bracket for period measurement.

Wave Blocking
A phenomenon where an opposing current is so strong that it exactly equals the group velocity of the incoming waves — the waves can make no forward progress and their energy stacks up, producing a sharp, steep breaking crest in place. The Merrimack bar approaches wave-blocking conditions during extreme ebb + storm wave events.

NOAA CO-OPS Station 8440466 (Newburyport, Merrimack River, MA) provides real-time tide predictions and current water level via the NOAA Tides & Currents API (api.tidesandcurrents.noaa.gov). Wind speed, direction, gusts and pressure now come from the Open-Meteo HRRR model (see below).

Open-Meteo Forecast API (NOAA HRRR) provides wind speed, wind direction, wind gusts, and surface pressure using NOAA's High-Resolution Rapid Refresh model (3 km, updates hourly). This is the best available short-range forecast model for coastal New England. No API key required (api.open-meteo.com/v1/forecast?models=best_match&wind_speed_unit=kn).

Open-Meteo Marine API provides offshore wave height, wave period, swell height/direction and wind wave height for the coastal point offshore of Newburyport (~42.82°N, 70.80°W) — no API key required.

Open-Meteo Forecast API provides 10m wind speed and direction for the river mouth location, cross-referenced with NOAA station data.

USGS National Water Prediction Service (NWPS) provides river data from two stations: USGS 01100870 (Merrimack at Newburyport, ~2 mi from mouth) for water level, and USGS 01100000 (Merrimack at Lowell, ~30 mi upstream) for freshwater discharge (cfs) — the primary active lower-Merrimack discharge gauge. Lowell discharge drives the river outflow component of the wave model.

Wave Height Model: The estimate uses a physics-informed empirical model with six components: (1) Wind waves via the SMB fetch-limited formula (10–12 km fetch for onshore winds, 2.5 km for offshore); (2) Swell penetration — offshore waves transmit through the inlet at Kt≈0.38 for onshore swell; (3) Bar shoaling — amplitude amplification Ks=(d0/d)^0.25 over the shifting bar at ~1.5m MLLW depth; (4) Ebb current steepening — opposing tidal current shortens wavelengths by (Cg/(Cg–Vc))^1.2; (5) River outflow — USGS discharge converted to mouth velocity adds persistent seaward flow.

⚡ Easterly Wind + Ebb Standing Wave Model: When winds blow from the ENE–ESE sector (70°–110°, peak hazard) during an outgoing tide, incoming ocean waves driven by the easterly wind meet the combined tidal ebb and river outflow head-on. This creates steep, near-standing waves at the bar — the most dangerous condition at the Merrimack entrance. The model computes a separate standing-wave amplification component: H_standing = H_incoming × ((Cg/(Cg–Vc))² − 1 + 0.6 × windStrength × outflowStrength). Both wind speed (via windStrength = Uwind/30 kts) and outflow velocity (tidal ebb + river discharge) are factored in. A directional alignment function (Gaussian peak at 90°/due East) tapers the effect toward the edges of the easterly sector. The standing wave component is added linearly (coherent resonance) to the energy-summed base height, then capped at the depth-limited breaking height (0.78 × bar depth).

Plain-English Guide to the Wave Model

Overview
The model assembles a final wave height from six separate physical processes, then applies the same logic to estimate wave period. Each factor reflects something real that happens at the Merrimack mouth and bar.

1. Local Wind Waves
The model takes the current wind speed and direction and asks: how much wave energy can this wind build up before reaching the river mouth? The key variable is fetch — the length of open water the wind blows across. When the wind blows from the northeast through southeast (the onshore direction), it has about 7.5 miles of open Atlantic water to work with. When it blows offshore, it only has about 1.5 miles of river channel. Using the classic Shore Protection Manual (SPM) formula, wind speed and fetch are combined to estimate the height the wind can generate. A 15-knot onshore wind produces roughly 1–1.5 ft; a 25-knot onshore wind produces 2–3 ft.

2. Offshore Sea State
Swell is wave energy generated by distant storms far out at sea that has organised itself into long, rolling wave trains. The model reads swell height and direction from a marine forecast point about 5 nautical miles offshore. Not all of it makes it in — the Merrimack inlet is narrow, and the bar and channel geometry blocks and scatters much of the energy. If the swell is coming from an onshore direction, about 38% of it penetrates to the river mouth. If it comes from an offshore direction, only about 12% gets in.

3. Bar Shoaling
As waves move from deeper offshore water onto the shallow Merrimack bar, they slow down, shorten, and get taller — this is shoaling. The bar is about 5 feet deep at low tide. The shallower the water, the more waves are amplified. The model calculates a shoaling coefficient based on bar depth: at low tide the bar is shallow and waves are amplified significantly; at high tide there is more water over the bar and the amplification is smaller. The formula is Ks = (10 ft / bar depth)^0.25, capped at a factor of 2.2×.

4. Ebb Current Steepening
When waves travel against an opposing current — like the outgoing tidal ebb — their wavelength compresses and their height increases. Think of cars bunching up when they hit a slow zone on a highway. The model calculates the tidal ebb current speed based on the tidal range (bigger tidal range = faster ebb), then applies a steepening factor: (wave group speed / (wave group speed − current speed))^1.2. The tidal range at Newburyport is typically 8–10 feet, which produces ebb currents of 1–2.5 knots at the mouth.

5. River Outflow Steepening
The freshwater discharge from the Merrimack watershed adds a persistent seaward current on top of the tidal ebb. Even at high tide when the tidal current reverses, the river keeps pushing water outward. The model converts the river flow in cubic feet per second to a velocity at the mouth using an estimated channel cross-section of about 800 square metres. Under normal flow (~1,500 cfs), this adds roughly 0.1–0.2 knots. During spring floods (>8,000 cfs), it can add nearly a knot.

6. Easterly Wind + Ebb Standing Wave
This is the most dangerous and most Merrimack-specific factor. When the wind blows from the ENE through ESE (between 70° and 110°, with peak effect at around 80°) while the tide is ebbing, ocean waves are driven directly into the mouth while the combined tidal and river current flows directly out. The two opposing wave trains interact to form near-standing waves — crests that pile up and become much taller and more abrupt than wind or swell height alone would suggest. The model scales this extra height by: how closely the wind direction aligns with due east; wind speed; and total outflow speed. It then computes a wave-blocking amplification: as the outflow approaches the wave's group speed, energy can no longer propagate outward and stacks up. This standing-wave component is added directly to the base height — not via energy addition — because it is a coherent resonance effect, not random-phase wave noise.

How the Six Factors Are Combined
Wind waves, swell, and river steepening are combined using energy addition — their heights are squared, summed, and square-rooted. This reflects the fact that they are independent, randomly-phased wave systems whose energies superpose rather than their heights. Shoaling and ebb steepening are multiplicative — they are physical transformations applied to all waves passing over the bar. The standing-wave component is additive. Finally, there is a hard depth-limited cap: waves cannot be taller than about 78% of the water depth before they must break. If the raw calculated height exceeds 0.78 × bar depth, it is clamped to that value and a breaking wave warning is triggered. The result carries an uncertainty band of ±20% under normal conditions and ±30% when the easterly-ebb standing wave is active.

How Wave Period Is Estimated
Wave period (the time between crests) is calculated separately and then Doppler-adjusted for the opposing current. The deep-water wind wave period comes from the same Shore Protection Manual formula used for height. The swell period is read directly from the offshore marine model and attenuated slightly (×0.85) to account for filtering by the inlet. When waves propagate against an opposing current, their apparent period shortens — the model divides the deep-water period by (1 + outflow speed / wave group speed). The dominant period displayed is an energy-weighted average of wind-wave and swell periods. During an easterly-ebb standing wave, the apparent period shortens further as energy stacks up, which is why the period range can span from under 2 seconds to over 8 seconds simultaneously. Wave steepness — the ratio of height to wavelength — is computed last and used to classify the wave state and determine whether breaking waves should be flagged.