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A monitoring system does not test a satellite time series once. It looks again whenever another valid observation arrives. That repeated opportunity can shorten detection delay, but it also creates more chances for noise to cross an alert boundary. The alert rule must be designed as a sequence, not as a stack of unrelated one-date tests.
Open the chapter contents · Remote Sensing root · Gold Standard of Education · How X Works
Chapter contents
Choose the route closest to the question, or read from Chapter 1 for the complete argument. The chapters remain open on the page; these grouped routes are an index.
Route 1 · Define the monitoring sequence
Route 2 · Work a cumulative alert
Route 3 · Budget delay and false alerts
Route 4 · Check evidence and limits
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE MONITORING SEQUENCE
1. Monitoring is a sequence of decisions
Let y(t) be a quality-screened observation and m(t) the expected value under a stable-history model. A sequential detector examines residuals y(t) − m(t) as new valid dates arrive. It can stop and alert, continue monitoring, or declare that the baseline itself needs repair.
This differs from fitting one breakpoint after collecting a fixed series. The earlier guide on change-point detection and false event alarms explains event fitting. Here, the decision time is part of the outcome.
CHAPTER 2 OF 12 · DEFINE THE MONITORING SEQUENCE
2. Event, observation, processing and alert times
A disturbance may occur between satellite visits. The next scene may be cloudy. Processing may arrive later, and the detector may require several consistent observations. Record event time from reference evidence, first usable observation, product availability and alert issue time separately.
An alert delay is therefore not one mechanism. Observation lag, data lag and algorithm lag can dominate in different places. Shortening a detector threshold cannot remove cloud gaps.
| Time | Question |
|---|---|
| event | when did the world change? |
| first valid observation | when could the sensor first see it? |
| product ready | when was evidence usable? |
| alert | when did the rule stop? |
CHAPTER 3 OF 12 · WORK A CUMULATIVE ALERT
3. Work a one-sided cumulative alert
Use an original teaching CUSUM for negative residuals. Standardized residuals over six valid dates are 0.2, −0.4, −1.3, −1.1, −0.9 and −0.2. Define S(t) = max{0, S(t−1) + (−r(t) − 0.3)} with S(0)=0, and alert when S exceeds 2.0.
The scores are 0, 0.1, 1.1, 1.9, 2.5 and 2.4. The first crossing occurs on date 5. A single −1.3 residual does not alert; several negative departures accumulate evidence. The reference allowance 0.3 and threshold 2.0 are constructed for illustration, not calibrated operating values.
| Valid date | Residual r | CUSUM S | Decision |
|---|---|---|---|
| 1 | 0.2 | 0.0 | continue |
| 2 | −0.4 | 0.1 | continue |
| 3 | −1.3 | 1.1 | continue |
| 4 | −1.1 | 1.9 | continue |
| 5 | −0.9 | 2.5 | alert |
| 6 | −0.2 | 2.4 | already stopped |
CHAPTER 4 OF 12 · WORK A CUMULATIVE ALERT
4. A repeated-look error is not a one-date error
If a one-date test has false-positive probability α and independent tests are repeated n times, the chance of at least one false positive is 1 − (1 − α)^n. Real residuals are often autocorrelated, so independence is usually wrong; the formula is a warning, not a calibration shortcut.
A sequential false-alert budget is commonly expressed through run length, probability of alert within a monitoring horizon, or false alerts per area-time. Choose the unit that matches operations. Pixel-date, site-year and issued incident are not interchangeable denominators.
CHAPTER 5 OF 12 · WORK A CUMULATIVE ALERT
5. Changed context: clouds stretch calendar delay
Keep the same residual sequence and stopping rule, but insert two cloudy acquisitions between valid dates 3 and 4. The detector still needs five valid looks, yet the calendar alert arrives two revisit opportunities later.
The algorithmic evidence requirement is unchanged; observation lag grew. This transfer check prevents a cloudy region from being judged as though its detector processed the same information more slowly. Report valid-look delay and calendar delay together.
CHAPTER 6 OF 12 · BUDGET DELAY AND FALSE ALERTS
6. Thresholds trade delay against false alerts
Lowering the CUSUM threshold would alert earlier in the worked sequence, but stable noise would also cross sooner. Increasing the reference allowance can ignore small persistent shifts. Requiring confirmation from another band or sensor may reduce false alerts while adding availability delay.
Calibrate the whole stopping rule on stable histories and known events held apart from development. A threshold selected on the evaluation region underestimates operational error.
CHAPTER 7 OF 12 · BUDGET DELAY AND FALSE ALERTS
7. Baseline quality controls every later look
BFAST Monitor separates a stable history from a monitoring period and predicts expected trend-seasonal behaviour. If the history includes an unmodelled disturbance, sensor transition or land-cover shift, repeated monitoring can accumulate model error rather than new evidence.
Audit residual seasonality, missingness and variance before deployment. Resetting a baseline after an alert is a model decision: an unverified false alert should not automatically rewrite “normal.”
CHAPTER 8 OF 12 · BUDGET DELAY AND FALSE ALERTS
8. Spatial multiplicity needs an incident rule
Monitoring millions of pixels multiplies opportunities again. Adjacent alerted pixels may represent one disturbance, correlated atmospheric contamination or registration error. Define how pixel signals become an incident: connectivity, minimum area, persistence and cross-sensor checks.
Measure false incidents as well as false pixels. Operational reviewers act on incidents, while map validation may still require area-adjusted pixel or polygon estimates.
CHAPTER 9 OF 12 · CHECK EVIDENCE AND LIMITS
9. Limits and misconceptions
A fast alert is not necessarily an accurate event date. The detector may stop after several looks but estimate a breakpoint earlier. Keep estimated event time and issue time separate.
No repeated-look correction repairs biased inputs. Cloud masks, co-registration, seasonal sampling and sensor harmonization remain upstream conditions. Sequential methods also do not guarantee independent residuals.
The CUSUM example demonstrates accounting. It is not a recommended threshold for vegetation, hazards or any named location.
CHAPTER 10 OF 12 · CHECK EVIDENCE AND LIMITS
10. A practical evidence check
Replay each historical sequence as if observations arrived one at a time. Prevent the algorithm from seeing future scenes. Store every valid-look score, threshold, data-quality flag and alert version.
Evaluate stable site-years and independently dated events. Report false alerts per area-time, detection probability by lag, calendar and valid-look delay, and the share of alerts changed by later quality control. Stratify clouds, seasons, sensors and event magnitude.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Questions readers should ask
Why not test every date at five per cent?
Because repeated opportunities change the probability of at least one false alert. Calibrate the sequence and its stopping rule as a whole.
Is the alert date the event date?
No. It is when accumulated available evidence crossed a rule. The event may precede the first usable observation.
Does confirmation always improve a detector?
It may reduce false alerts but can increase delay and miss short events. Measure both sides on the intended monitoring population.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Continue through verified routes
Begin with the Remote Sensing root, Gold Standard of Education and How X Works. Pair Rare Change and False Alarms with Revisit Gaps, Cloud Cover and Missed Events and the immediate change-point guide.
Read Verbesselt, Zeileis and Herold’s primary BFAST Monitor paper and the US Forest Service record for Timeliness in Forest Change Monitoring. They support stable-history monitoring and delay decomposition; the CUSUM arithmetic is an original teaching example.
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