Project Knotenlinie

A forecast, not a prediction

Knotenlinie is a research model. It works out how many earthquakes above a given magnitude to expect in each cell of a map, for each day and for longer horizons. We run it on past earthquake catalogues; it issues no live forecasts. It does not say that an earthquake will strike at a given place and time; no method has been shown to do that reliably.

This is research, not an official forecast. Do not use it for safety decisions. A low probability does not mean that a place is safe, and a high one is not a warning. Official hazard information comes from national agencies: AFAD and the Kandilli Observatory in Turkey, INGV in Italy and the USGS in the United States. Gradiva is not affiliated with any of them, or with CSEP.

The name is Hegel’s: the nodal line of measure relations, a line of steady change in quantity with nodes where the change becomes one of kind. It names the question we put to the data, not something we claim to have found.

How we work

We started wide. The work began in late September 2026 with the Earth as one system, from the Moon and the Sun down to the outer core. We listed thirteen physical channels that could add stress to faults, among them the solid Earth tide, the ocean tide, the pole tide, changes in the length of day, air pressure, rain, groundwater, ice and sea level, plate loading, the stress one earthquake passes to the next and the slow relaxation of the crust after a large one.

Then we measured them. Six came first: the solid Earth tide, the ocean tide, the pole tide, changes in the length of day, continental water, and ice with sea level. We scored two base models with all six channels on and with each one left out in turn, on the earthquakes of 2011–2015: 16 models, five and a half million rows. No channel added more than about 0.0001 nats per earthquake. That does not prove the effects are zero. In the region and magnitude range we tested they were far too small to help a forecast; published work reports tidal effects on the size of large earthquakes that a test like ours could not see. Simple versions of plate loading, from published fault slip rates, and of the stress passed between earthquakes were later tested on their own and dropped as well (below). Physical models of plate loading are still being built and will have to clear the same bar. Air pressure, rain and the rest are on hold: they come back only with a way to show how they would move the score.

That changed the rule. Since 4 October 2026 a layer has to earn its place. It is added on its own, scored against the same baseline as everything else and kept only if its gain clears a bar fixed in advance: larger than the smallest effect the data can show, and significant (one-sided p < 0.05, with a check against time-shifted data). No layer is dropped on a guess that its effect is small; it is measured first.

And it narrowed the goal. First match the best published models, like for like; then try to beat them. What we keep today is, in outline, an ETAS-type model for days ahead and a smoothed-seismicity map with a fault layer for years ahead.

How we test it

• On earthquakes the model has not seen, where we can. The rows in the table below were fitted on data up to 2010 (2005 for the ten-year California row) and scored on later years. Models for the blind window will be fitted on data up to the end of 2015. In Italy, the Aegean and Turkey, 2016–2020 is a blind window that we open once, after the rules are fixed. California and New Zealand are our development regions, so their rows run to 2020 and are not blind. Everything from 2021 on is sealed everywhere until a final model is frozen.
• Against published models, like for like. A daily model is compared with a daily model and a five-year model with a five-year model, on the same grid, at the same magnitudes, on the same earthquakes. Where a published forecast file exists we use it as it was frozen: the CSEP-Italy forecasts, and the Helmstetter, Kagan and Jackson forecast, the most informative in California’s RELM experiment. Where it does not, we rebuild the model from its published method, as with ETAS-LM, the daily ETAS model of CSEP-Italy and part of Italy’s operational forecasting system, or convert it to the same grid and horizon, as with SEIFA, the seismicity-and-fault rate model of the European hazard model ESHM13, in the Aegean. In California and New Zealand the daily rows compare with a standard ETAS that we built ourselves.
• One score. Information gain per earthquake: on average over the earthquakes that happened, how much more probability our model gave them than the baseline did, in natural-log units, with a correction for the total number each model expected. It is a geometric average: +0.1 means about 10% more, +0.35 about 40% more. We use the paired tests and consistency tests of CSEP, the international collaboration that tests earthquake forecasts.
• Tests that allow for clustering. Earthquakes come in clusters. A test that treats them as independent rejects good forecasts too often and makes the error bars on a comparison between two models too narrow. So besides the standard tests we use a negative binomial count test, standard errors that allow for dependence between days and a rank test when there are few earthquakes. Our scoring code gives the same numbers as pyCSEP, the collaboration’s open-source toolkit, on the cases we compared, and it was checked by a separate AI reviewer that did not write it.
• The rule comes first. What counts as beating a baseline will be written down, registered and published here, with its date, before the blind window opens. The result will be published either way.
• Every result says what kind of evidence it is. Prospective: the forecast was deposited before the earthquakes happened. Pseudo-prospective: the model was frozen before a past test window, and nothing in it was chosen by looking at that window. Development: the parameters were fitted on earlier data, but we chose what to keep while looking at the test years. Retrospective: everything else.

Where we stand, October 2026

Each value is the information gain per earthquake with one standard error. “Ahead” means the paired test is significant at the 5% level; otherwise there is no clear difference. With this few earthquakes only large differences can show: in the Italian daily row a gain of 0.1 would need about 425 earthquakes to show reliably, and seven earthquakes cannot separate anything under about 0.3.

All six rows are development scores: we tried several versions over these years and kept the best, so they are not yet a clean test. The forecast files behind them are not public yet (see below). Details that change how to read them:

• HAZFX is the strongest of the three CSEP-Italy models we compared against. It is a ten-year forecast and the Helmstetter, Kagan and Jackson forecast a five-year one; we scaled both to the length of our test period. Our fault database is a 2013–2015 version, so the long-term rows are not entirely free of later knowledge.
• The five- and ten-year rows count mainshocks only, because these models are not built to forecast aftershocks. Counting all earthquakes would give −0.02 ± 0.26 in Italy and +0.43 ± 0.08 in the Aegean. In the ten-year California row the sign flips, to −0.16, with another way of separating mainshocks from aftershocks.
• In California and New Zealand both our model and the standard ETAS expected far fewer earthquakes than happened, between about half and two thirds, so those gains are relative.
• The Italian and Aegean rows were read again with the clustering-aware tests, and the daily California row with the standard errors that allow for dependence; none of their verdicts changed. In the same re-reading our five-year Italian result against TripleS, a weaker CSEP-Italy model, fell from significant to not significant. The New Zealand and ten-year California rows have not been re-read yet.
• Of the models behind the table, only the Italian daily rows have had a separate review so far.

In short: against the published models no row shows a clear difference. Against a standard ETAS of our own we are ahead in California and not in New Zealand.

What did not work

Each of these was added to our model, measured against the same baseline and dropped because its gain, if any, did not clear the bar. Several showed a small positive gain that was not enough.

• Coulomb stress transfer with rate-and-state friction.
• Renewal models, which use the time since the last large earthquake on a fault.
• Fault slip-rate budgets, and a strain-rate map as a background layer (a coarse version of the map, tested in Italy and the Aegean).
• A finite-source kernel that spreads aftershocks along the rupture.
• A correction for the earthquakes that go undetected right after a large one.
• A STEP-type short-term component and a gradient-boosted machine-learning model.
• Combinations of models whose weights we chose on 2006–2010 data.

A plain equal-weight mix of our ETAS and ETAS-LM did slightly better than ETAS-LM alone (+0.07 ± 0.07, not significant); we are carrying it forward to the blind window.

A survey of the literature in October 2026, read mostly from abstracts, points largely the same way. Several of these have shown gains in pseudo-prospective tests, on one earthquake sequence or in one region, but we found no prospective test in which they beat an established baseline. Two exceptions are worth naming. STEP is itself a published daily model, and it was among the most informative in the CSEP California tests from 2007 to 2012. And a global model that merges smoothed seismicity with strain rates has early prospective support. As layers in our own model, neither raised the score.

What has been shown to work

In prospective tests, three kinds of model have done best:

• Days ahead: ETAS and related models of earthquakes triggering earthquakes, such as STEP.
• Years ahead: smoothed maps of where small earthquakes have happened, in California and New Zealand. In Italy the best five-year models also used the historical catalogue and the fault database.
• Months to a few years ahead: EEPAS, in which every earthquake raises the chance of larger ones in the months and years after it. Its prospective record comes from New Zealand; a global version looks promising in pseudo-prospective tests.

In our development scores we cannot tell ourselves apart from the first kind, or from the smoothed maps in California and the Aegean. We do not have the third yet.

What you can check, and what stays ours

Today you can check the method, the baselines and the rules. The forecast files behind the table are not public yet; they will be published with the blind-window results. Until then, treat the table as our claim. From the blind window on, we work like this:

• One register. Before the window opens we announce a single Zenodo record that lists every model we freeze for it. We score and publish all of them, not only the best, and a model that is not in the register does not count.
• Dated in advance. For each frozen model the register holds a fingerprint, a SHA-256 hash, of its forecast files. Zenodo gives each version of the record a DOI. Because some fields of a Zenodo record, its date among them, can be edited later, we also record the fingerprints with an independent timestamp service.
• Opened afterwards. Once the window has been scored we publish the forecast files themselves. Anyone can score them again with pyCSEP and check them against the fingerprints.
• Ours. The code, the model’s settings and how we prepare the data. If a reviewer needs to see an internal record, we show it to them privately.

To score a forecast you need only its numbers. Whether those numbers were made without sight of the test years, only a forecast deposited before the earthquakes can show, which is why only those count as prospective.

Next

1. Find a prospective anchor: score our model against the daily forecasts that the CSEP California models made prospectively from August 2007 to August 2018, at magnitude 3.95 and above. The archive is public on Zenodo.
2. Add the medium term: EEPAS combined with our ETAS, three months and one year ahead.
3. Close the Italian five-year gap with the historical catalogue and the fault database.
4. Freeze the test rule, open the register and publish both here, then open the 2016–2020 window once.

What we will not publish

• Earthquake predictions, meaning a date, a place and a size.
• A probability for a single city or a single large earthquake. A test on moderate earthquakes cannot show how well a model judges a rare large one in one place.

Earthquake catalogues are credited to their providers, among them INGV in Italy, the Southern California Seismic Network, GeoNet in New Zealand and the Global CMT project. Questions and corrections: write to the address at the foot of this page.