Satellite irradiance forecasting: one cell, a patch or the whole field

A satellite sees the irradiance of a whole region every hour. It is tempting to give a forecaster the whole map. Holding the forecaster fixed and changing only what it reads shows how much of that map actually helps.

Cyril Voyant (Mines Paris – PSL, Centre O.I.E.), with Andreas Kazantzidis (University of Patras) and Jan Kleissl (University of California San Diego) · manuscript in preparation, open code and data extract

In brief

The finding

On this record, the hourly history of the cell itself carries most of what an hour-by-hour forecast of the next day can use. Reading the rest of the map adds parameters faster than it removes error: none of the seven compression methods tested and neither of the two deep networks reading the whole field reaches the per-cell model.

The question

Satellite irradiance comes as maps. Deep networks such as U-Nets and LSTMs read whole fields; compression methods shrink the field before a model reads it. Both add inputs and parameters. How much of that spatial information lowers the error of a forecast for each of the next 24 hours, and at what cost in stored parameters?

The theory, in plain words

One forecaster, several inputs. The forecaster is an extreme learning machine (ELM): a hidden layer of neurons drawn at random and never trained, and output weights fitted in one linear least-squares solve. Training takes seconds and the number of stored parameters is easy to count. The same forecaster reads either its own cell, a 3 × 3 patch, the whole field of 722 cells, or the field compressed by one of seven methods (Radon transform, DCT, wavelets, PCA, random projection, subsampling, autoencoder).

Fair references. Persistence repeats the last hour, the 24-hour persistence repeats the same hour of the previous day, and BLEND mixes the two. A model is worth its parameters only if it beats them.

Fair scoring. Errors are pooled over all cells, all lead times from 1 to 24 hours and all test hours where the Sun is more than 5° above the horizon. The nRMSE is divided by the mean scored observation of the test year, 407.9 W/m².

The example in figures

Pooled error against parameters stored by each model (log scale): the per-cell ELM is the lowest point; reading the whole field moves models to the right without moving them down
Pooled error against parameters stored by each model (log scale): the per-cell ELM is the lowest point; reading the whole field moves models to the right without moving them down

The data are HelioClim-3 irradiance (Heliosat-2 method, Meteosat images, SoDa service) on 1,148 points over Corsica, hourly, with 2005 for training and 2006 for testing.

What it brings, and its limits

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