Spring and Neap Tides
Spring tides are the largest tides, at new and full moon when Sun and Moon line up; neap tides are the smallest, at the quarter moons.
Definition
Spring tides are unusually large tides, with very high highs and very low lows, and they occur at new moon and full moon, when the Sun and Moon line up and pull together; neap tides are unusually small tides that occur at the two quarter moons, when the Sun and Moon pull at right angles to each other. At syzygy, new or full moon, the tidal bulges raised by the Sun and the Moon add together for the greatest range, while at quadrature, first or third quarter, the Sun's bulge partly cancels the Moon's for the smallest range, and each type recurs about every two weeks. The two tidal forces are vector fields that superpose: at syzygy their axes coincide and the equilibrium amplitude scales with $M_{\text{Moon}}/d_{\text{Moon}}^3 + M_{\text{Sun}}/d_{\text{Sun}}^3$, while at quadrature it scales with the difference between them, and because the solar-to-lunar tidal ratio is about $0.46$, spring and neap ranges come out near $1.46$ and $0.54$ times the lunar range alone. The very largest spring tides, called perigean spring tides or king tides, happen when syzygy coincides with the Moon at perigee, and on real coastlines the spring-neap cycle typically lags the Moon's phases by a day or two.
Example
At full moon a beach may show a much wider stretch of uncovered sand at low tide than usual, while a week later at the quarter moon the tide barely seems to move at all. If the Moon alone would raise a $1.0\ \text{m}$ range and the Sun alone a $0.45\ \text{m}$ range, a spring tide comes out to roughly $1.45\ \text{m}$ and a neap tide to roughly $0.55\ \text{m}$, since the Sun's pull is a little under half the Moon's. Working the ratio directly: $(M_{\text{Sun}}/M_{\text{Moon}}) \times (d_{\text{Moon}}/d_{\text{Sun}})^3 = (2.7 \times 10^7) \times (384{,}400 / 1.496 \times 10^8)^3 \approx 2.7 \times 10^7 \times 1.7 \times 10^{-8} \approx 0.46$.
Key Insight
Spring tides have nothing to do with the spring season; the name means the tide "springs up," and the cycle repeats twice every month all year round, at both full moon and new moon alike, because it makes no difference whether the Moon sits on the same side of Earth as the Sun or the opposite side, since the two sets of bulges line up either way. Coastal flooding forecasts hinge on this cycle: a storm surge that arrives during a perigean spring tide can flood far more than the same surge at neap, so emergency planners along the Carolina coast watch the Moon's phase and distance as closely as they watch the weather.