V3 · Sonnet

Waterfalls the day after a downpour

The rain has stopped.

The chart is drawn by a script, which is not running here. The values for the example scenario (40 mm over 6 h) are given in the table beside or below, and the model’s assumptions are described in the section “How the model calculates”.

Rainfall: 40 mm over 6 h (average 6.7 mm/h)

Model: two flow curves after a single rainfall Flow as a multiple of baseflow over 72 hours from the start of the rainfall. The dashed curve is dry ground (variant A), the solid blue one is saturated ground (variant B), both on the same scale. Both peaks fall after the rain has ended. This is a teaching model, not a measurement. 2× 3× 4× 5× 1× = baseflow MODEL · not a measurement
0 h24 h48 h72 h
  • A · dry ground (model) 1.28×
  • B · saturated ground (model) 2.21×
Model, not a measurement. Horizontal axis: hours from the start of the rainfall. Vertical axis: notional flow as a multiple of the baseflow state (1× = before the rain), one scale for both curves and for every rainfall. Both curves are calculated for the same rainfall; the only difference between them is the state of the ground.
  • end of rainfall · 6 h
  • reading · 30 h from the start

The stream is still responding.

When does the rain stop?

The total rainfall stays the same; only the time over which it falls changes.

6 h
How much fell?
40 mm
When to take the reading?

The 40 mm of rain ended after 6 h, yet the model still calculates a rise: the peak of A comes 4.0 h after the rain ends, the peak of B 5.7 h after. 24 h after the rain ends, A is at 1.28× baseflow (36% of the peak excess), B at 2.21× (58%). Indicative values for the default scenario; the script recalculates them on the fly.

Teaching model, no measurements. Unit: multiple of baseflow.
IndicatorA · dryB · saturated
Reading: 24 h after the rain ends1.28×2.21×
Peak height1.79×3.07×
Rise continues after the rain ends for a further4.0 h5.7 h
Reading as a share of the peak excess36%58%

The peak of B comes 1.7 h later than the peak of A.

The same threshold, two readings

The drawing below shows the same schematic rock threshold at the reading time taken from the chart. The thickness of the water layer is notionally proportional to the excess flow. It illustrates a principle; it is not a profile of Olchowaty or of any other threshold, nor an assessment of how the water really looks. Without the script, the drawing shows the default state: 40 mm in 6 h, reading 24 h after the rain ends.

Diagram of the threshold, variant A, dry ground A rock threshold with three steps and a thin layer of water, whose thickness corresponds to the model flow for dry ground at the chosen reading time.
A · dry ground. 1.28× baseflow
Diagram of the threshold, variant B, saturated ground The same rock threshold with a thicker layer of water, whose thickness corresponds to the model flow for saturated ground at the chosen reading time.
B · saturated ground. 2.21× baseflow

Dashed line in the drawing: notional water level at baseflow (1×). Both illustrations have the same geometry and the same scale.

How the model calculates and where it ends

Assumptions

Each hour of rain triggers its own delayed response of the stream, and the model adds these responses together. The shape of the response comes from version V2: it builds up with a time constant of 4 h and decays with a time constant of 16 h (A, dry ground) or 27 h (B, saturated ground). The notional runoff coefficient is 0.38 for A and 0.82 for B. Baseflow is 1.

Q(t) = 1 + (P/10) · c · [G(t) − G(t−D)] / D, where P is the total rainfall in mm, D its duration in hours, c the runoff coefficient and G the integral of the response shape. As D tends to zero, the formula returns to V2, in which all the rain fell at time 0.

The peak always falls after the rain has ended. This is a property of the way the model is built (the response starts from zero), not the result of a measurement in the stream. With a total of 0 mm there is no wave, so the peak, the delay and the share of the excess are undefined, not equal to zero.

Why saturated ground responds for longer

Saturated ground takes up less additional water, so a larger part of the rainfall can reach the streams, and subsurface recharge persists after the rain has ended. Slope, bedrock and the distribution of rainfall across the catchment also matter. [3]

Limits

  • The project contains no field measurements or station data. The curves follow from the assumed parameters, not from calibration.
  • This is not a forecast for Olchowaty, Dołżyczka or Dynysów, and it does not indicate when they are worth visiting.
  • The rainfall is uniform across the whole catchment and has constant intensity. The model leaves out snow, ice, blockages and in-channel storage.
  • Range: rainfall of 1–24 h, 0–80 mm, axis up to 72 h. Outside this range the model is not drawn.

In the field: after a downpour, check the notices from the land manager and from GOPR (the mountain rescue service). Do not enter the channel, do not cross a swollen stream and do not go near the edge of a threshold. The noise or clarity of the water is no sign of safety.

What changed relative to V2

  • The field notebook with browser storage and the custom markers on the axis were removed, because they drew attention away from the phenomenon. The page saves nothing.
  • The separate rainfall totals for A and B were removed. With the same rain in both variants, the ground alone explains the difference.
  • The time slider was replaced by a reading taken relative to the end of the rainfall, and the fixed “+1.8 h” peak delay is now calculated from the model.
  • The A/B diagram switch was replaced by two thresholds side by side. The photograph was not embedded, so that the page works offline.

Three thresholds, one caution

The descriptions were taken over from V2 together with the links. In this version they were not checked against the sources again.

  • Olchowaty · Duszatyn

    A natural monument. A publication of the landscape parks describes a slide waterfall on a massive block of sandstone, 3.7 m high, with erosion grooves and smaller steps below. [2]

  • Dołżyczka · near Komańcza

    The forest district lists the Dołżyczka cascade as a natural monument. A waterfall need not be a vertical drop; rock thresholds and cascades count as well. [1]

  • Dynysów · Mików

    A forestry overview points to two waterfalls on the small Dynysów stream. We give neither a height nor directions. [1]

Sources to check

  1. Nadleśnictwo Komańcza: Wodospady okolic Komańczy [Komańcza Forest District: Waterfalls around Komańcza] (2021). Link carried over from V2, not opened in this session.
  2. Zespół Karpackich Parków Krajobrazowych: Pomniki przyrody nieożywionej [Carpathian Landscape Parks Complex: Inanimate natural monuments], description of Olchowaty, pp. 34–35. Link carried over from V2, not opened in this session.
  3. USGS: Surface Water in Hawaii, general processes of runoff and subsurface recharge. Link carried over from V2, not opened. A source from outside the region, used only for the principle; to be replaced with a study of Carpathian flysch.
  4. Context photograph of the Olchowaty stream from V2: Henryk Bielamowicz, 23 October 2010, Wikimedia Commons, licence CC BY-SA 4.0 according to V2. Link only, the image is not embedded; the licence was not checked in this session.

The hydrological model on this page is the V3 author’s own teaching simplification and does not follow directly from any of the sources above.