Learning Hub / Bonus B1
Bonus unit B1 · practice track · no round binding
Tides and the Moon
Air temperature is hard to forecast a day ahead. Sea level in Boston Harbor is, most of the time, predictable months ahead, because the main driver is the motion of the Moon and the Sun. This bonus unit uses real NOAA water levels to find that rhythm, and then looks at the part the astronomy cannot predict: the weather.
提前一天预报气温都很难。Boston 港的海平面却大多可以提前几个月预报,因为主要驱动力是月亮和太阳的运动。本附加单元用真实的 NOAA 水位找出这个节律,再看天文学预报不了的那一部分:天气。
45–60 minutesReal data: NOAA CO-OPS 8443970 Boston
Goals and exit evidence
- Read a water-level chart: datum (MLLW), unit (feet), local time.
- Measure the spacing between high tides from real data and connect it with the Moon's daily motion.
- Split observed water into prediction plus residual, and explain why the residual is where weather shows up.
Exit evidence: a measured high-tide spacing with its method, and one sentence about the largest residual in the window.
- 读懂水位图:基准面(MLLW)、单位(英尺)、当地时间。
- 从真实数据量出相邻高潮的间隔,并与月亮每天的运动联系起来。
- 把实测水位拆成预报 + 残差,解释为什么天气体现在残差里。
出口证据:一个带方法说明的高潮间隔测量值,以及关于窗口内最大残差的一句话。
Story hook
NOAA publishes tide predictions for Boston long before the day arrives. Sailors, harbour pilots and people who walk the beach rely on them. Yet on some days the water arrives higher than predicted. The classroom notes for this dataset mention a nor'easter in late September 2026. Can you find it in the numbers, without being told the date?
NOAA 很早就发布 Boston 的潮汐预报,船员、引航员和海边散步的人都依赖它。可有些日子海水比预报更高。这份数据的课堂说明提到 2026 年 9 月下旬有一次东北风暴(nor'easter)。不看日期,你能从数字里找到它吗?
Concepts
1 · Two bulges
The Moon's gravity pulls the ocean into two bulges, one facing the Moon and one on the far side. As Earth turns, a coast passes through both, so most places get two high tides a day.
月球引力把海洋拉成两个隆起:一个朝向月球,一个在背面。地球自转时,海岸依次经过两个隆起,所以多数地方一天有两次高潮。
2 · 12 hours 25 minutes
The Moon moves along its orbit while Earth turns, so it returns overhead about 50 minutes later each day (a lunar day of about 24 h 50 min). Two highs per lunar day gives about 12 h 25 min between highs. You will measure this.
地球自转的同时月球也在公转,所以月亮每天约晚 50 分钟回到头顶(一个太阴日约 24 小时 50 分)。一个太阴日两次高潮,相邻高潮约隔 12 小时 25 分。你将亲手量出来。
3 · Prediction plus weather
The Sun adds its own, smaller tide: when Sun and Moon line up (new and full moon) the range is larger (spring tides). Wind and low air pressure can push water above the astronomical prediction. Observed − predicted = residual; a large positive residual during a storm is called storm surge.
太阳也产生较小的潮汐:日月成一线(新月和满月)时潮差更大(大潮)。风和低气压能把海水推到天文预报之上。实测 − 预报 = 残差;风暴期间的大正残差称为风暴增水。
Worked example: one day of real water levels
Hourly water level at Boston (station 8443970), feet above Mean Lower Low Water, local time (EDT throughout this window). Highest predicted values of each half-day are found live; the time of each high is refined between hours by fitting a parabola through the three hours around the peak.
Boston(8443970 站)逐时水位,单位英尺,相对平均较低低潮面(MLLW),当地时间(本窗口内均为 EDT)。页面实时找出预报高潮;高潮时刻用峰值前后三个整点拟合抛物线,估到小时之间。
| High tide | Predicted time | Predicted ft | Observed ft | Residual ft |
|---|---|---|---|---|
| Loading data… | ||||
Activity A · Measure the rhythm
Pick a three-day window and look at the two curves. Then press the button: the page finds every predicted high tide in the 23-day file and reports the average spacing. Guess first: 12 h 00 min, 12 h 25 min or 24 h?
选一个三天窗口,看两条曲线。然后按按钮:页面找出 23 天文件中每一次预报高潮并报告平均间隔。先猜:12 小时 0 分、12 小时 25 分,还是 24 小时?
Activity B · Find the storm in the residual
Residual = observed − predicted, for every hour of the window. The page reports the mean absolute residual and the hour with the largest residual. Is the largest residual where you expected the nor'easter?
残差 = 实测 − 预报,覆盖窗口内每个小时。页面报告平均绝对残差和残差最大的时刻。最大残差是否出现在你预想的风暴时段?
Observed values up to 2026-09-30 19:00 are NOAA's verified hourly heights; later hours are top-of-hour preliminary 6-minute water levels. No data after 2026-10-07 is used. NOAA CO-OPS data is U.S. government public domain; use local official sources for any safety decision.
2026-09-30 19:00 之前的实测为 NOAA 已核验逐时水位;之后为 6 分钟初步水位的整点值。不使用 2026-10-07 之后的任何数据。NOAA CO-OPS 数据属美国政府公有领域;任何安全决定请以当地官方来源为准。
Check for understanding
1. If a high tide is at 03:10 today, roughly when is the next one, and when is the matching high tomorrow?如果今天 03:10 高潮,下一次大约几点?明天对应的高潮大约几点?
Answer
About 15:35 today and about 04:00 tomorrow: highs come roughly 50 minutes later each day.
今天约 15:35,明天约 04:00:高潮每天约推迟 50 分钟。
2. The water reads 0 ft. Is the harbour empty?水位读数 0 ft,港口没水了吗?
Answer
No. 0 ft means the level equals the datum, Mean Lower Low Water: the average of each day's lower low tide. Negative values are lower than that average. Always read the datum and unit.
不是。0 ft 表示水位等于基准面 MLLW,即每天较低低潮的平均值;负值表示比它更低。读图一定要看基准面和单位。
3. Why can tides be predicted months ahead but tomorrow's air temperature cannot?为什么潮汐能提前几个月预报,明天的气温却不能?
Answer
The main tidal forcing comes from regular orbits that are known far ahead. Air temperature depends on the chaotic atmosphere. Even tides have an unpredictable part, the weather residual.
潮汐的主要强迫来自规律的轨道运动,可以远期推算;气温取决于混沌的大气。潮汐也有预报不了的部分,即天气残差。
4. Convert a residual of 1.5 ft to centimetres.把 1.5 ft 残差换算成厘米。
Answer
1 ft = 30.48 cm, so 1.5 ft = 45.72 cm.
1 ft = 30.48 cm,所以 1.5 ft = 45.72 cm。
5. A big residual appeared during one storm. Does that prove every nor'easter brings that much surge?一次风暴出现了大残差。这能证明每次东北风暴都有这么大的增水吗?
Answer
No. One event in one 23-day window. Surge depends on wind direction, duration, pressure and timing with high tide.
不能。只是 23 天窗口中的一次事件。增水取决于风向、持续时间、气压以及与高潮的时间配合。
Classroom: 20-minute version
| 0–4 | Read the chart: datum, unit, local time. What does 0 ft mean?读图:基准面、单位、当地时间。0 ft 是什么意思? |
| 4–10 | Guess the spacing; run Activity A.猜间隔;做活动 A。 |
| 10–16 | Guess the storm days; run Activity B.猜风暴日;做活动 B。 |
| 16–20 | One sentence: what the Moon explains and what it does not.一句话:月亮能解释什么,不能解释什么。 |
Full 60-minute lesson plan
| 0–10 | Two-bulge model with a ball and a lamp; learners act out Earth turning.用球和台灯演示两个隆起;学生扮演地球自转。 |
| 10–25 | Worked example: find two highs on one day by hand; then Activity A.例题:手找一天的两次高潮;然后做活动 A。 |
| 25–40 | Activity B: residuals, mean absolute residual, the largest residual.活动 B:残差、平均绝对残差、最大残差。 |
| 40–52 | Check questions; link to forecast error in Unit 2 (residual is an error of the astronomical forecast).自测题;联系第 2 单元的预测误差(残差就是天文预报的误差)。 |
| 52–60 | Exit sentence and five numbers.出口句与五个数。 |
Age bands
10–12
Find two highs on one day by pointing at the chart; subtract the times in hours and minutes.
在图上指出一天的两次高潮;用时分相减。
13–15
Compute the average spacing and mean absolute residual; convert feet to centimetres.
计算平均间隔与平均绝对残差;英尺换算厘米。
16–17
Explain the parabola refinement; derive 24 h 50 min from Earth's spin and the Moon's ~27.3-day orbit.
解释抛物线细化;由地球自转与月球约 27.3 天的公转推出 24 小时 50 分。
No-device alternative. Print one day of hourly values; learners plot them on squared paper, mark the two highs and subtract the times. A ball and a lamp show the two bulges.
无设备替代。打印一天的逐时数值;学生在方格纸上描点,标出两次高潮并相减时间。用球和台灯演示两个隆起。
Five numbers
Math map for this unit
| F-L2-TRIG | Periodic motion |
| MD-L2-UNITSENSE | Units and quantity sense |
| NS-L2-NEGORDER | Ordering negatives |
| CC-L2-DIFF | How many more or fewer |
Sources: SOURCES.json · NOAA CO-OPS 8443970 · tide basics are standard textbook physics.