Learning Hub / Unit 3
Unit 3 of 6 · Round S-03 · target day 2026-11-25
Weather, climate and ENSO: probability is not a guarantee
A strong El Niño is under way in the tropical Pacific. Does that tell us tomorrow's high at Boston Logan? This unit separates three scales (weather, climate, ENSO), shows why "70% chance" is not a promise, and teaches the first honest way to improve a forecast: measure its average lean and correct for it.
热带太平洋正在发生一次强厄尔尼诺。它能告诉我们明天 Boston Logan 的最高温吗?本单元区分三个尺度(天气、气候、ENSO),说明「70% 的机会」为什么不是承诺,并教第一种诚实改进预测的方法:量出它平均偏向哪边,再修正。
60-minute lesson + 20-minute round touchReal data: Boston Logan, 47 daysRain-probability table is SYNTHETIC
Goals and exit evidence
- Sort statements into weather, climate and ENSO, and say why one Boston day cannot test El Niño.
- Write 20% as 0.2, score a probability with the Brier score, and explain why a 70% event that did not happen is not proof the forecast was wrong.
- Compute a forecast's bias (signed mean of forecast − observed) and apply a mean-bias (M3) or recent-bias (M4) correction using only past days.
Exit evidence: two sentences with sources (one observation, one prediction) from a CPC bulletin, and a probability explanation card.
- 把句子分为天气、气候、ENSO 三类,并说明为什么 Boston 的某一天不能检验厄尔尼诺。
- 把 20% 写成 0.2,用 Brier 分数给概率打分,说明「70% 的事没发生」不等于预测错了。
- 计算预报的偏差(预报 − 实测的带符号平均),只用过去的日子做平均偏差(M3)或近期偏差(M4)修正。
出口证据:从 CPC 公告中找出两句带来源的话(一条观察、一条预测),以及一张概率解释卡。
Story hook
A learner reads that NOAA's Climate Prediction Center has an El Niño Advisory in place and says: "So this winter in Boston will be warm, and my forecast for Wednesday should be warm too." Another learner opens the classroom data and notices that the public forecast for Boston has been missing in one direction more often than the other. Which of these two clues helps with Wednesday's high?
一位学生读到 NOAA 气候预测中心(CPC)正发布厄尔尼诺警报,便说:「所以今年 Boston 冬天会暖,我周三的预测也该偏暖。」另一位学生打开课堂数据,发现 Boston 的公开预报更常往同一个方向出错。这两条线索,哪一条对周三的最高温更有用?
Concepts
1 · Three scales
Weather: the temperature at one station on one day. Climate: the long-run statistical distribution of weather. ENSO: a large ocean-atmosphere state of the tropical Pacific that shifts the odds of some kinds of weather in some regions. Boston's winter link to ENSO is weak and not stable, so a short run of Boston scores is not a test of El Niño.
天气:某站某天的温度。气候:天气的长期统计分布。ENSO:热带太平洋大尺度的海气状态,会改变一些地区某类天气的概率。Boston 冬季与 ENSO 的关系弱且不稳定,所以 Boston 的短期成绩不是厄尔尼诺的检验。
2 · Probability and Brier
Define the event first (for example "at least 1.0 mm of rain in the window"). If it happens y = 1, else y = 0. Brier = (p − y)², averaged over events; smaller is better. 70% that does not happen costs 0.49 once. Only many forecasts can show whether 70% really behaves like 70%.
先定义事件(如「区间内累计降水至少 1.0 毫米」)。发生 y = 1,否则 y = 0。Brier = (p − y)²,多个事件取平均,越小越好。70% 没发生,这一次扣 0.49;只有很多次预测才能看出 70% 是否真像 70%。
3 · Bias and correction
Bias = average of (forecast − observed): positive means it runs warm. M3 adds the average past (observed − forecast) to today's forecast; M4 does the same with only the last 7 known pairs. Both may use only days complete before the cutoff (D−2 and earlier).
偏差 = (预报 − 实测) 的平均:正值表示偏暖。M3 把过去全部 (实测 − 预报) 的平均加到今天的预报上;M4 只用最近 7 对。两者都只能用截止前已完整的日子(D−2 及更早)。
About the current ENSO status. The status must come from NOAA CPC, not from this page. The latest source page copied for this course is the CPC ENSO Diagnostic Discussion issued 8 October 2026, which states "ENSO Alert System Status: El Niño Advisory"; the next discussion was scheduled for 12 November 2026. Before class, open the current page and record its date: cpc.ncep.noaa.gov ENSO Diagnostic Discussion. The same bulletin says impacts are more likely with a strong event, "though not certain".
关于当前 ENSO 状态。状态必须以 NOAA CPC 为准,而不是本页。本课程复制的最新来源页是 2026 年 10 月 8 日发布的 CPC ENSO 诊断讨论,写明「ENSO 警报系统状态:厄尔尼诺警报(El Niño Advisory)」;下一期计划于 2026 年 11 月 12 日发布。课前请打开当前页面并记下日期:CPC ENSO 诊断讨论。同一公告写明:强事件下出现相应影响的机会更大,「但不保证」。
Worked example with real Boston data: does the forecast lean?
Each bar is one day's (observed − forecast) in °F. Bars above zero: the day came out warmer than forecast. The page computes the average lean live. If most bars sit on one side, adding the average lean back (M3) might help, but only if the lean persists.
每根柱是一天的 (实测 − 预报),单位 °F。柱在零线上方:当天比预报暖。页面实时算出平均偏向。如果大多数柱在同一侧,把平均偏向加回去(M3)也许有用,但前提是这种偏向会持续。
…
Forecast: Open-Meteo previous-day archive, used as a stand-in for the M2 line. Observed: IEM ASOS daily max (preliminary, not the NWS CLI used for scoring).
预报:Open-Meteo 前一日存档,代替 M2 线。实测:IEM ASOS 日最高温(初步值,不是计分用的 NWS CLI)。
Activity A · Persistence vs climatology vs forecast vs correction
Choose where scoring starts (earlier days are only used as history). Every model walks forward and only sees days up to D−2. All rows are scored on their own valid days; compare n before comparing MAE. Predict the order before you press the button.
选择从哪一天开始计分(更早的日子只作历史)。每个模型逐日向前,只看得到 D−2 及以前。每行在各自的有效日上评分;比较 MAE 前先比较 n。按按钮之前先猜排序。
| Line | Rule | n | MAE °F | MAE °C | bias °F |
|---|
Activity B · Brier score calculator (SYNTHETIC)
Event: at least 1.0 mm of rain in the window. The rain amounts are a SYNTHETIC teaching table. Change the probabilities and watch the mean Brier score; compare it with a fixed 25% baseline.
事件:区间内累计降水至少 1.0 毫米。降水量是「合成」教学表。修改概率,观察平均 Brier 分数,并与固定 25% 基准比较。
| Day | Rain | y | Your probability % | (p − y)² |
|---|
Check for understanding
1. Classify: (a) "Tomorrow's Logan high may be 9 °C". (b) "A station's winter statistics for 1991–2020". (c) "The tropical Pacific ocean-atmosphere state". (d) "A downpour this week".分类:(a)「明天 Logan 最高温可能 9 °C」;(b)「某站 1991–2020 的冬季统计」;(c)「热带太平洋海气状态」;(d)「本周一次暴雨」。
Answer
(a) weather forecast, (b) climate statistics, (c) ENSO-type large-scale state, (d) weather observation.
(a)天气预测;(b)气候统计;(c)ENSO 类大尺度状态;(d)天气观察。
2. Using the default probabilities in Activity B (20%, 70%, 80%, 10%), find each Brier term and the mean. Is the 25% baseline better?用活动 B 默认概率(20%、70%、80%、10%)求每项 Brier 与平均。25% 基准是否更好?
Answer
0.04, 0.09, 0.64, 0.01: sum 0.78, mean 0.195. Baseline 25%: 0.0625, 0.5625, 0.0625, 0.0625, mean 0.1875. The baseline is slightly better on these four days. Deleting D3 to change the result is not allowed.
0.04、0.09、0.64、0.01,合计 0.78,平均 0.195。25% 基准:0.0625、0.5625、0.0625、0.0625,平均 0.1875。这四天基准略好。不能删掉 D3 来改变结论。
3. "It said 70% and it stayed dry, so the forecast was certainly wrong." Rewrite it.「说了 70% 却没下,所以预测必然错误。」请改写。
Answer
"One outcome went against the more likely side. A single result cannot show whether the 70% was well calibrated; that needs many pre-defined events scored the same way."
「一次结果与较高概率方向不同,但一次结果不足以判断 70% 是否校准;应按预定义事件长期检验。」
4. M3 uses all past bias pairs, M4 only the last 7. When would M4 do better, and why can neither use yesterday's observation?M3 用全部历史偏差,M4 只用最近 7 对。什么情况下 M4 更好?为什么两者都不能用昨天的实测?
Answer
M4 helps when the lean changes over time (for example as the season turns); M3 is steadier when the lean is constant and data are noisy. At the 18:00 EST cutoff yesterday (D−1) is not complete, so its high is unknown; using it would be a leak.
偏向随时间变化(如换季)时 M4 更好;偏向稳定而数据噪声大时 M3 更稳。18:00 EST 截止时,昨天(D−1)还没结束,最高温未知;用它就是泄漏。
5. Can you add a Brier score of 0.195 to an MAE of 0.71 °C to get one champion score?能把 0.195 的 Brier 与 0.71 °C 的 MAE 相加成一个总冠军分吗?
Answer
No. Different variables, units and loss scales. Show them separately.
不能。变量、单位、损失尺度都不同,应分开展示。
Classroom: 20-minute round touch
| 0–3 | Read the S-03 card (target 2026-11-25, cutoff 2026-11-24 18:00 EST = 23:00 UTC).读 S-03 题卡(目标日 2026-11-25,截止 2026-11-24 18:00 EST = 23:00 UTC)。 |
| 3–8 | Look at the public forecast and the lean you measured in Activity A. Decide: raw, or corrected?看公开预报和活动 A 量出的偏向,决定用原值还是修正值。 |
| 8–13 | Seal the forecast; write one sentence saying which clue you used (not ENSO alone).封存预测;写一句用了哪条线索(不能只写 ENSO)。 |
| 13–18 | After the reveal: your error vs lines M0, M2 and M5.揭晓后:你的误差与 M0、M2、M5 三条线对照。 |
| 18–20 | Read the CPC bulletin date aloud; find one observation and one prediction sentence in it.读出 CPC 公告日期;从中找一句观察、一句预测。 |
Full 60-minute lesson plan
| 0–10 | Three labels (weather, climate, ENSO): sort six sentences. Draw 10 boxes to show 20% and 70%.三张标签(天气、气候、ENSO)给六句话分类;画 10 个格子表示 20% 和 70%。 |
| 10–20 | Event definition: the 1.0 mm boundary, trace, and missing data (missing is not zero).事件定义:1.0 mm 边界、微量与缺测(缺测不是 0)。 |
| 20–32 | Brier for four days and the 25% baseline; accept that the baseline can win.算四天 Brier 与 25% 基准;接受基准可能更好。 |
| 32–45 | Real data: bias bars, then Activity A (M0, M1, M2, M3, M4).真实数据:偏差柱图,然后做活动 A(M0、气候替代、M2、M3、M4)。 |
| 45–53 | 0% and 100%: false confidence; why the CPC says impacts are not certain.0% 与 100%:虚假自信;为什么 CPC 说影响「不保证」。 |
| 53–60 | Exit card: event, p, y, one calculation, and what one result cannot show.出口卡:事件、p、y、一项计算、一次结果不能说明什么。 |
Age bands
10–12
Use 0%, 50%, 100% and the 10-box drawing; the teacher provides a squares table. Read the bias bars: more above or below?
用 0%、50%、100% 和十格图;教师提供平方表。读偏差柱:上方多还是下方多?
13–15
Full Brier table with the boundary cases; compute bias and the M3 correction for one day by hand.
完成含边界情况的 Brier 表;手算一天的偏差与 M3 修正。
16–17
If the true chance is q, expected Brier = (p − q)² + q(1 − q), lowest at p = q: honest probabilities are rewarded. Compare M3 and M4 as a bias-variance trade-off.
若真实概率为 q,期望 Brier = (p − q)² + q(1 − q),在 p = q 时最小:诚实报告概率会被奖励。把 M3 与 M4 当作偏差与方差的取舍来比较。
No-device alternative. Printed four-day table, ten-box paper and a squares hint card; no online weather or calculator purchase needed. For the bias step the teacher reads ten (observed − forecast) values aloud and learners tally above/below zero. Spoken explanations may be written down by the teacher and marked as transcribed.
无设备替代。打印的四日表、十格纸和平方提示卡即可,不需要在线天气或购买计算器。偏差步骤由教师朗读十个 (实测 − 预报) 值,学生统计零线上下各几个。口述解释可由教师代录并标代录。
Five numbers (after each round)
Math map for this unit
| RP-L2-PCTBASE | Percent base and which quantity is asked |
| SP-L2-COND | Conditional probability: what is given |
| NS-L2-NEGORDER | Ordering negatives on the number line |
| RP-L2-NOADD | Ratios are not directly addable or averageable |
| EE-L2-EVAL | Evaluate an expression with full operations |
Sources: SOURCES.json · CPC ENSO Diagnostic Discussion (8 Oct 2026 copy) · NOAA Climate.gov ENSO FAQ · lesson text merged from m681 lesson 3, spec 41 unit 3 and week 3 of the spec 48 merge plan.