Río Paraná · onda de crecida · tramo Corrientes – Rosario
The rain over Brazil and the Argentine northeast is in the river. It is at Corrientes now. Rosario has barely moved. This is the arithmetic of the gap between those two facts.
Figures are this analysis, not an official forecast. INA publishes to 27 October only; everything past that date is extrapolation and carries the wider band.
Two things arrived at the same time. Abundant rain on the unregulated upper Paraná above Itaipú pushed inflow at Guaíra to 22,000 m³/s, and the dam is now spilling to hold reservoir level, with outflow at 20,100 m³/s. Separately the Iguazú peaked on 14 October at 16,200 m³/s at Andresito. Those two met at Yacyretá, whose outflow of 38,700 m³/s is far above normal for October and is still climbing.
That combined volume is what is now moving down the Paraná. Corrientes is rising 0.4 to 0.5 m a day. Itatí, Barranqueras, Ituzaingó, Libertad, Eldorado and Santa Ana have already passed alerta or evacuación. Below Goya the river has hardly moved. That is travel time, not an absence of water.
Rosario starts low, at 3.35 m against a 5.00 m alert. That starting level matters as much as the size of the wave: the same crest upstream produces a much lower crest at Rosario when the lower river begins from a low base, which is the main reason the answer lands below the alert line rather than above it.
Plate 1
Daily levels since 1 September, with INA's numeric forecast for 20 and 27 October shown as the central value and its published range. All three gauges are in metres on their own hydrometric zero, so the lines share one axis but their alert thresholds differ.
Plate 2
Observed to 16 October, then INA's published track to 27 October, then this analysis to 10 December. The band is INA's own range where one exists and the historical spread of analogue events beyond it, floored by the regression residual. Crossing dates are marked where the central line passes each threshold.
| Level | Meaning | Earliest | Central | Latest |
|---|
Plate 3
Each dot is one Corrientes peak above 6.00 m and the Rosario crest that followed it, from 126 years of daily records, 76 waves in all. The line is the fitted relationship evaluated at today's Rosario base of 3.35 m. The orange marker is where this wave lands on it. Hover any dot for its dates and lag.
The Corrientes gauge record starts in 1901 and Rosario's in 1900, with both reading on 99% of the 46,309 days since. That holds 76 waves big enough to put Corrientes above 6.00 m. Whether they all behave alike decides how much the projection above can be trusted, so it is worth testing rather than assuming.
They do not all behave alike, and the thing that varies is the one you would expect to be fixed.
Plate 4
Rosario's rise above its own starting level, with every wave aligned on the day Corrientes peaked. Orange is the four largest Corrientes peaks in the record. Blue is three waves that began from a Rosario base within 0.15 m of today's 3.35 m. Measuring rise rather than level, and aligning on the upstream peak, is what makes waves from different decades comparable at all.
Plate 5
Every one of the 76 waves, plotted as the height of the Corrientes peak against the days it then took Rosario to crest. The seven events from plate 4 are picked out in colour. The downward slope is the point: a bigger wave moves through the reach faster, because it is travelling down a channel the preceding water has already filled.
Divide Rosario's rise by the Corrientes rise that caused it and the answer is close to 0.36 almost every time: 0.37 for the four record waves, 0.36 for the three that started low. Sorted by starting level the bands give 0.36, 0.35 and 0.41. Sorted by peak size, 0.29 to 0.46 with no trend. This is the one number in the whole analysis that behaves like a physical constant, and it is what makes a 1923 wave useful for 2026.
Counting the days Rosario sits within 0.25 m of its crest gives 18 days for the record waves and 20 for the base-matched ones. The crest is a plateau two to three weeks long in every case. The steep part of the climb is also consistent, between +0.27 and +0.67 m in the fastest five-day stretch.
The four record waves crested Rosario a median of 16 days after Corrientes. The three that started from today's low base took 26. Across all 76 the correlation between peak height and lag is −0.34, and the eight waves above 7.5 m averaged 20 days against 28 for everything below 7.0 m. Quoting a single travel time for this reach is wrong; it ranges from 3 to 45 days in the record.
1983 holds the record at Corrientes, 9.02 m on 18 July, and the March wave catalogued here reached 8.39 m. It lifted Rosario just 0.36 m, to 6.17 m, because Rosario was already at 5.81 m. February 1990 peaked half a metre lower and lifted Rosario 1.66 m, because it started at 3.47 m. The same upstream wave writes a different number at Rosario depending on how full the lower river already is, which is why this year's answer lands near 4.8 m rather than near 6.
One correction worth making: 1902 was not a flood year on this river. Its highest Corrientes reading was 5.10 m, below the threshold used here. The great early-century event is 1905, at 8.57 m, and it is the third largest in 126 years.
It is natural to picture the flood as a bulge of water sliding down a pipe of roughly constant width, arriving at Rosario in the shape it had at Corrientes, only later. The channel really is fairly uniform, so the picture is reasonable. The record says it is wrong, and the way it is wrong is the single most useful fact about this river.
Corrientes sits about 792 river kilometres above Rosario. The fitted travel time is 24 days, which works out at 33 km a day, or 0.38 m/s. Water in this reach moves at roughly 1 m/s, and a kinematic wave travels at about 1.5 times the water velocity, so translation alone would deliver the wave in six days. It takes four times longer. Nor does the shape survive the journey: the crest arrives 4.2 times broader than it left, and the fastest five-day rise falls from 0.82 m at Corrientes to 0.18 m at Rosario.
Something is taking the water in and giving it back slowly. Between Corrientes and Santa Fe the Paraná runs in a floodplain tens of kilometres wide against a main channel of one or two. Water leaves the channel sideways, sits in the valle aluvial, and drains back over weeks. That is storage, not translation, and it is why the answer at Rosario depends so little on the peak upstream and so much on how full the lower river already is.
Plate 6
Fit a single linear reservoir to the whole daily record and the reach gives up three numbers: a three-day dead time, a storage constant of 21.2 days, and a steady gain of 0.92. This is the resulting kernel, the share of any change at Corrientes that reaches Rosario on each following day. It explains 90 % of Rosario's daily level from Corrientes alone, with a residual of 0.42 m.
Plate 7
The same Corrientes hydrograph, put through two different ideas of what the reach does, against what the river is actually doing. All three lines are metres of rise above Rosario's level on 1 September, so they share one axis. Corrientes is observed to 16 October, follows INA's published forecast to 27 October and then recedes on the constant implied by INA's own numbers.
Treated as a travelling wave, the +4.79 m rise at Corrientes would land at Rosario almost intact, putting it at 7.51 m on 26 October. That is a metre and a quarter above the 1992 record of 6.27 m, and it is simply not going to happen. The storage filter puts the same input at 4.94 m on 6 November. This page's peak-to-peak regression, which knows nothing about reservoirs or kernels, says 4.76 m on 15 November. Two methods built on entirely different reasoning land 0.18 m apart, and the intuitive one misses by two and three quarter metres.
The filter also explains where the attenuation figure comes from. A reach with a 21.2-day storage constant cannot fill before a short pulse has gone past: an 11-day crest, which is Corrientes' median, comes out at 0.92 × (1 − e−11/21.2) = 0.37 of its height. The measured attenuation over 76 waves is 0.36. The constant that looked like an empirical regularity is a consequence of the storage, and that is also why it holds steady while travel time does not: changing the size of a wave barely moves the storage constant, but it does change how fast the wave can push through an already full channel.
Fitting a Fourier series to the hydrograph itself is the wrong tool, and the record says so plainly. Annual harmonics explain 14.5 % of Rosario's daily variance, and going from one harmonic to six moves that to 15.3 %. Take the seasonal cycle out and the periodogram of what is left has no power worth the name at any event timescale: 0.0003 of the variance at 90 days, 0.0000 at 60, 30, 14 and 7. Nothing periodic is left to expand. A flood is one transient pulse, a truncated sine series of a pulse rings at the flanks and goes negative in the trough, and a periodic basis extrapolates periodically, which is the worst possible prior for a forecast.
The frequency domain pays off on the reach rather than on the event. The annual harmonic peaks on 11 March at Corrientes and 17 April at Rosario, and its amplitude falls from 0.791 m to 0.713 m. That is a 37-day phase lag and a gain of 0.90 at one cycle a year, measured without touching a single flood. At event frequencies the gain is 0.36. The reach is a low-pass filter: it passes the slow regime nearly whole and flattens anything quick. Plate 6 is that same statement written in the time domain.
None of this changes the published figure. The filter is the better description of the whole hydrograph but the worse predictor of the crest, missing it by 0.32 m on average with a 0.25 m low bias against 0.19 m for the peak-to-peak regression, because it has one input, no local tributaries and no term for the starting state. And working in a transformed space does not help: refitting in log stage gives R² 0.884 and in a discharge-like h1.6 gives 0.897, against 0.900 for plain stage. Over a range of two to seven metres this reach is close enough to linear in stage that the transforms cost more than they return.
For every Corrientes peak above 6.00 m since 1901, find the matching Rosario crest within −5 to +50 days. That yields 76 waves. Regress the crest on the Corrientes peak and on Rosario's own level five days before it. The base term is not optional: drop it and the fit overstates Rosario by about 0.4 m at today's low starting level.
With C_peak 7.31 m and R_base 3.35 m this gives 4.76 ± 0.33 m, dated 26 days past 20 October, which is 15 November. The regression alone would say ± 0.25 m; the wider figure adds the forecast error on the Corrientes peak and the disagreement between the three methods. The section below sets out the budget term by term.
Over 13,389 day-pairs the two gauges track each other almost deterministically, with Rosario three days behind. This converts INA's Santa Fe forecast into an independent Rosario track and fixes what Santa Fe has to reach for Rosario to hit its alert.
INA's Santa Fe central value is 5.16 m on 27 October and still rising, which maps to Rosario near 4.82 m on 30 October and climbing past it.
Seven waves since 1901 began from a Rosario base under 3.75 m with a Corrientes peak above 6.60 m, which is this wave's situation. Their median Rosario trajectory supplies the curve past INA's horizon, and they crested a median of 27 days after the Corrientes peak. Their median rise was 0.96 m.
A third check, independent of both: Rosario's rise has run at about 0.36 of the Corrientes rise for 126 years, and a 3.36 m rise at Corrientes implies 1.21 m here, so 4.56 m. The fit says 4.76, the nearest analogues say 4.33. The page takes 4.76 m and carries that spread as the band. An earlier version of this page fitted on 1990-2026 only and published 5.16 m; that sample happened to hold mostly waves starting from a far higher base, which inflated it.
Every figure on this page is a central value plus or minus a spread, and the spread is calculated rather than assumed. Five terms go into it. They are independent of one another, so they combine as the square root of the sum of squares rather than by addition, which is why the total comes to 0.33 m and not the 0.62 m you would get by stacking them end to end.
An earlier version of this page quoted ± 0.24 m. That was the first term only, the scatter of past waves about the fitted line. It left out two real sources of error that the regression cannot see: the Corrientes peak is itself a forecast with its own published range, and the three independent estimators disagree by about a fifth of a metre.
| Source | What it covers | σ |
|---|
| Confidence | Reading | Lower | Central | Upper |
|---|
| Level | Meaning | Chance |
|---|
Two checks on the figure. Refitting the model 76 times, each time leaving one wave out and predicting it back, gives errors with a standard deviation of 0.25 m, no bias, and a central 90 % running from −0.28 to +0.47 m. That is narrower than the 0.33 m quoted here, as it should be: the backtest feeds the model an observed Corrientes peak, not a forecast one, and it cannot charge for the disagreement between methods. On the sixteen waves of this one's size the backtest error has a standard deviation of 0.23 m and a bias of −0.01 m, so the fit is not systematically wrong on big waves.
The date carries its own spread. Travel time fitted against peak size gives 25 days from the Corrientes peak with a residual standard deviation of 8 days, so the crest date is 15 November ± 8 days, and the sixteen comparable waves ran anywhere from 3 to 37 days. This is the weakest part of the forecast, and plate 5 shows why: the level attenuates like a physical constant, the timing does not.
One figure not in the budget: a second wave. Everything here assumes the one wave now in transit and no fresh rain above Itaipú. That is a condition, not an error term, and no standard deviation covers it.
| Station | Level | Δ 24 h | Alerta | Evacuación | State |
|---|
New rain on the unregulated upper Paraná. The current estimate assumes the one wave now in transit and no second one behind it. INA's seven-day outlook has only light rain over the upper basin, with moderate cores over the Paranaíba, which is regulated. A fresh abundant event above Itaipú in the next fortnight pushes both the crest and its date up.
Travel time stretches with volume. INA says so explicitly for this wave. Every date here is more likely to slip later than earlier, which is why the band's lower edge never reaches 5.00 m and its upper edge only just gets there, on 9 November.
The press date of 28 October does not survive arithmetic. Several outlets quote the alert being crossed around 28 October. INA's own numeric forecast has Rosario at 4.39 m on 27 October, and no plausible rate covers 0.6 m in a day at that gauge. Early to mid November is the defensible reading.
INA reissues on Tuesdays and Fridays. The anchor used here is the Tuesday 13 October run, at 7 and 14 days. The Friday run, at 4 and 11 days, had not posted when this was compiled. Re-running the scripts against a newer run will move these dates.
Prefectura Naval, altura de los ríos FICH-UNL, cuenca del Paraná INA, reporte diario 15 Oct INA, pronósticos numéricos INA a5, series observadas
Observed series are INA a5 series 19 (Corrientes), 30 (Santa Fe) and
34 (Rosario), variable 2, daily records from 1901 for Corrientes and 1900 for Rosario. Numeric forecasts are the
*_prono.csv files, which carry a lower, central and upper value for each
horizon. Every figure on this page is reproducible from those two endpoints alone.