The frozen chart and the moving canal
A fleet operator plans a voyage against a chart of the world as it currently stands: draught restrictions, transit windows, weather routing advice, bunker prices at the ports of call. The plan is a statistical object whether anyone calls it one or not — it is an estimate of costs and risks built from a snapshot of conditions. The trouble is that the snapshot ages the moment it is taken, and maritime logistics is unusually punishing about how fast that ageing bites. A vessel three days into a passage to the Panama Canal can wake up to a transit-slot reduction announced that morning. The route that was optimal at departure is now wrong, and nothing in the original plan carries a signal saying so.
This is nonstationarity in its plainest form: the statistical properties of the process — mean transit time, variance in congestion, the correlation between weather and delay — do not hold steady across the voyage. A plan is an estimate; an estimate assumes the thing it estimates stays roughly put while the estimate is used. Canals, storms, bunker markets and port queues do not offer that courtesy.
What the fleet operator actually streams
Four feeds matter, and each drifts on its own clock. AIS tracks update every few seconds to several minutes depending on vessel class and give position, speed and heading — but coverage gaps near congested anchorages or in heavy weather mean the feed itself is intermittently missing, not merely noisy. Port congestion figures — berth occupancy, anchorage queue length — move on a scale of days, driven by labour disputes, customs backlogs or a single grounded vessel blocking a channel. Weather routing advisories move faster still, revised as forecast models re-run, sometimes hourly in a developing system. Bunker prices move daily against crude benchmarks and can gap overnight on a refinery outage or a sanctions announcement.
Canal authorities sit apart from all four. Their restrictions are step functions, not drifts: the Panama Canal Authority cut daily transit slots from 36 to 24 during the 2023 drought, then to 18, each cut announced with days rather than weeks of notice. A route locked in against the 36-slot regime does not degrade gracefully under an 18-slot regime. It becomes wrong at a specific hour on a specific day, and the size of the error is the whole difference between the two regimes, not a small increment.
Position one: model the transition law, not the world
The strongest response to all this is that nonstationarity is not a reason to keep watching everything — it is a modelling problem, and modelling problems have modelling solutions. Canal capacity, seasonal storm tracks, and bunker price seasonality are not random walks with no structure; they have known drivers. Drought risk at Gatun Lake correlates with El Niño indices published months ahead. Typhoon season in the South China Sea has a stable calendar even if individual storms are unpredictable. A state-space model with a properly specified transition law — capacity as a function of reservoir level, delay as a function of published queue statistics — absorbs the drift into the model rather than requiring the operator to re-observe the whole system continuously.
If you have correctly specified how the world changes, you do not need to keep watching it change. You need to watch the few variables that drive the change, and those variables are far cheaper to monitor than the full state.
This is a real position, not a straw one. A hierarchical model of canal throughput conditioned on reservoir level would have flagged the 2023 restriction risk months in advance, from public hydrological data, without a single AIS ping. The same argument extends to bunker prices: a model conditioned on crude futures and refinery margins captures most of the drift a spot-price feed would otherwise be needed to chase. Under this view, the operator's failure with the canal restriction was not a failure of intake frequency. It was a failure of model specification — nobody had encoded reservoir level as a leading indicator of transit capacity. Add the right covariate and a quarterly-updated model performs as well as one watching every stream every hour.
Position two: the filter still needs measurements
The reply is not that the modelling position is wrong. It is that even a correctly specified transition law is a filter, and a filter run without measurements diverges regardless of how good its dynamics are. A Kalman filter tracking canal capacity from reservoir level still needs the reservoir readings; a model of bunker price seasonality still needs to see this week's spot quote to know where in the cycle the market actually sits, because seasonality gives a shape, not a value. The transition law reduces how much has to be observed. It does not reduce that quantity to zero, and reservoir level itself is measured continuously by someone, somewhere, which means the "solved" version of the problem has simply relocated the continuous stream one level up rather than removed it.
There is a second bite. The transition law for canal capacity — the function mapping reservoir level to permitted daily transits — is itself an estimated object, fitted from a finite record of past drought responses. It changes when the canal authority changes its policy, as it did in 2023 when it tightened the relationship between water level and slot allocation beyond anything the historical record had shown. A model of the transition law is exposed to exactly the nonstationarity it was built to absorb, one level up, on a slower but not infinite clock.
Where the two positions actually collide
The disagreement narrows to a genuinely useful question: at what timescale does re-specifying the model become cheaper than watching the raw stream? For canal capacity, driven by reservoir hydrology with a lead time of months, the modelling position wins comfortably — a fleet operator who tracks Gatun Lake levels quarterly captures nearly everything achievable, and there is no case for pinging canal authority notices hourly. For bunker prices, which move within the day on refinery news with no comparable leading indicator published in advance, the modelling position has much less to work with; the transition law itself is close to a random walk, and there is no cheaper proxy than the price feed. For weather routing, the honest answer sits in between: forecast skill decays sharply past 72 hours, so a route locked in on departure-day weather is running on an estimate that the routing service itself will revise twice before arrival.
| feed | drift character | modelling absorbs it? |
|---|---|---|
| canal capacity | step change, months of hydrological lead time | largely, via reservoir covariate |
| bunker price | near-continuous, thin leading structure | poorly, needs live quote |
| weather routing | fast decay past 72h, partially forecastable | partially, still needs re-run |
| port congestion | days-scale, driven by discrete events | mixed, event-triggered not calendar-triggered |
The canal restriction failure that opened this page is instructive precisely because it sits at the boundary. The transition law existed — reservoir level was public, drought severity was forecast — but nobody had wired it into the routing decision as a covariate, so the operator was, in practice, running the frozen-corpus case: a plan fixed at departure with no live correction, on a variable that a modest continuous stream would have flagged weeks out. The failure was not proof that continuous streaming beats modelling in general. It was proof that this operator had neither.
The narrowing
Neither position is vindicated outright. The modelling reply is correct that a well-specified transition law shrinks the required observation rate, sometimes by orders of magnitude, and a fleet operator who tries to stream everything at maximum frequency is paying for resolution the process does not need — chasing bunker-price noise on an hourly basis buys little over a daily settle, and a hierarchical canal model beaten by three days of extra lead time is worth more than a live feed used badly. The continuous-intake reply is correct that no transition law, however good, removes the need for measurement, and that the law itself ages on a slower clock that someone still has to watch.
What the canal episode narrows is the claim from "continuous intake beats a frozen plan" to something smaller and more defensible: the intake rate has to match the drift rate of the specific variable, decided per stream, revisited when the drift rate itself changes — as canal policy did in 2023, moving reservoir level from a slow covariate to something closer to an operational trigger. That is a scheduling argument dressed as a categorical one. It still leaves nothing that can substitute for continuing to look.