AI-Hydro Interactive Module · Foundations

The Water Cycle in Motion

Every drop of rain that ever fell on your field started its journey here. Watch a water molecule trace the six fluxes that move it from ocean to cloud to stream — and learn why the whole thing is just a giant closed balance sheet.

Watch the film · Reveal the six fluxes · Drag the rain slider · Scrub the cycle · Pass the checkpoint

Your path through this module

🎬

Film

💧

Fluxes

⚖️

Balance

🔎

Scrub

✓

Check

📜

Sources

1 · Watch the cycle unfold

The animation below shows a parcel of water making one full lap of the hydrologic cycle — from the ocean surface through the atmosphere and back to the sea. Click Run to render it (requires Manim in the kernel environment; see the note if it's absent).

Tip If Manim is not installed in your kernel, skip to §4 where the interactive cycle diagram covers the same ground without any dependencies — just drag the scrubber.

Python · Manim Renders the water-cycle animation (~15 s at 480p)

from manim import *

class WaterCycle(Scene):
    def construct(self):
        self.camera.background_color = "#0a0a15"
        C, B, G, V = "#00FFFF", "#00A3FF", "#34d399", "#a78bfa"

        # ── Static scene ──────────────────────────────────────
        sea = Rectangle(width=14, height=2.2,
                        fill_color=B, fill_opacity=0.55, stroke_width=0)
        sea.move_to(DOWN * 3.2)

        land = Polygon(
            [-7, -2, 0], [7, -2, 0], [7, -4, 0], [-7, -4, 0],
            fill_color="#1a2b1a", fill_opacity=1, stroke_width=0
        )
        hill = Polygon(
            [-0.5, -2, 0], [1.5, -0.9, 0], [3.5, -2, 0],
            fill_color="#223322", fill_opacity=1, stroke_width=0
        )
        sun = Circle(radius=0.55,
                     fill_color="#FFD060", fill_opacity=0.9, stroke_width=0)
        sun.move_to(UP * 3.4 + RIGHT * 5.8)

        c1 = Ellipse(width=2.8, height=1.2,
                     fill_color=WHITE, fill_opacity=0.85, stroke_width=0)
        c2 = Ellipse(width=1.6, height=1.1,
                     fill_color=WHITE, fill_opacity=0.85, stroke_width=0)
        c3 = Ellipse(width=1.6, height=1.1,
                     fill_color=WHITE, fill_opacity=0.85, stroke_width=0)
        c2.shift(LEFT * 0.8 + UP * 0.4)
        c3.shift(RIGHT * 0.8 + UP * 0.4)
        cloud = VGroup(c1, c2, c3).move_to(UP * 1.8 + LEFT * 1.5)

        trunk = Rectangle(width=0.15, height=0.45,
                          fill_color="#6b4c2a", fill_opacity=1, stroke_width=0)
        trunk.move_to(RIGHT * 3.1 + DOWN * 1.45)
        foliage = Triangle(fill_color="#2d6a2d",
                           fill_opacity=0.9, stroke_width=0).scale(0.45)
        foliage.move_to(trunk.get_top() + UP * 0.3)
        tree = VGroup(trunk, foliage)

        self.add(sea, land, hill, sun, cloud, tree)

        # ── Phase 1: Evaporation ───────────────────────────────
        evap = VGroup(*[
            Arrow(sea.get_top() + RIGHT * x,
                  sea.get_top() + RIGHT * x + UP * 2.2,
                  color=B, stroke_width=2.5, buff=0.05,
                  max_tip_length_to_length_ratio=0.18)
            for x in [-2.5, -1.2, 0, 1.2, 2.5]
        ])
        e_lbl = Text("Evaporation", font_size=20, color=B)
        e_lbl.move_to(LEFT * 4.5 + DOWN * 0.8)

        self.play(LaggedStart(*[GrowArrow(a) for a in evap], lag_ratio=0.15),
                  run_time=1.4)
        self.play(FadeIn(e_lbl, shift=RIGHT * 0.3), run_time=0.5)
        self.wait(0.4)

        # ── Phase 2: Transpiration ─────────────────────────────
        tr = VGroup(*[
            Arrow(tree.get_top() + RIGHT * (i * 0.18 - 0.18),
                  tree.get_top() + RIGHT * (i * 0.18 - 0.18) + UP * 1.0,
                  color=G, stroke_width=2.2, buff=0.05,
                  max_tip_length_to_length_ratio=0.22)
            for i in range(3)
        ])
        t_lbl = Text("Transpiration", font_size=18, color=G)
        t_lbl.next_to(tree, RIGHT, buff=0.25).shift(UP * 0.5)

        self.play(LaggedStart(*[GrowArrow(a) for a in tr], lag_ratio=0.2),
                  run_time=0.9)
        self.play(FadeIn(t_lbl, shift=UP * 0.2), run_time=0.4)
        self.wait(0.4)

        # ── Phase 3: Condensation ──────────────────────────────
        cond_glow = cloud.copy().set_stroke(color=C, width=2.5)
        c_lbl = Text("Condensation", font_size=20, color="#ddddff")
        c_lbl.next_to(cloud, UP, buff=0.3)

        self.play(Create(cond_glow), FadeIn(c_lbl, shift=UP * 0.25),
                  run_time=0.9)
        self.wait(0.4)

        # ── Phase 4: Precipitation ─────────────────────────────
        rain = VGroup(*[
            Line(cloud.get_bottom() + RIGHT * (i * 0.55 - 1.1),
                 cloud.get_bottom() + RIGHT * (i * 0.55 - 1.1) + DOWN * 1.6,
                 color=B, stroke_width=2.8)
            for i in range(5)
        ])
        p_lbl = Text("Precipitation", font_size=20, color=B)
        p_lbl.next_to(cloud, LEFT, buff=0.35).shift(DOWN * 0.3)

        self.play(LaggedStart(*[Create(r) for r in rain], lag_ratio=0.1),
                  run_time=1.1)
        self.play(FadeIn(p_lbl, shift=LEFT * 0.2), run_time=0.4)
        self.wait(0.4)

        # ── Phase 5: Infiltration + Runoff ─────────────────────
        inf = VGroup(*[
            Arrow(hill.get_top() + RIGHT * (i * 0.3 - 0.3) + UP * 0.2,
                  hill.get_top() + RIGHT * (i * 0.3 - 0.3) + DOWN * 0.55,
                  color=V, stroke_width=2.2, buff=0.0,
                  max_tip_length_to_length_ratio=0.25)
            for i in range(3)
        ])
        i_lbl = Text("Infiltration", font_size=18, color=V)
        i_lbl.next_to(hill, LEFT, buff=0.25).shift(DOWN * 0.1)

        ro = Arrow(hill.get_right() + DOWN * 0.1,
                   sea.get_top() + RIGHT * 4.5,
                   color=C, stroke_width=3, buff=0.05)
        r_lbl = Text("Runoff", font_size=18, color=C)
        r_lbl.next_to(ro.get_center(), DOWN, buff=0.2)

        self.play(LaggedStart(*[GrowArrow(a) for a in inf], lag_ratio=0.15),
                  run_time=0.8)
        self.play(FadeIn(i_lbl, shift=LEFT * 0.2), run_time=0.35)
        self.play(GrowArrow(ro), FadeIn(r_lbl, shift=DOWN * 0.2), run_time=0.7)
        self.wait(0.4)

        # ── Phase 6: Close the loop ────────────────────────────
        loop = ArcBetweenPoints(
            sea.get_left() + UP * 0.7,
            evap[0].get_start(),
            angle=-TAU / 5, color=C, stroke_width=2.5
        )
        loop.add_tip(tip_length=0.2)
        title = Text("The Hydrologic Cycle", font_size=24, color=WHITE)
        title.move_to(DOWN * 0.6 + LEFT * 3.5)

        self.play(Create(loop), run_time=1.0)
        self.play(
            FadeIn(title, shift=UP * 0.2),
            *[lbl.animate.set_color(C)
              for lbl in [e_lbl, t_lbl, c_lbl, p_lbl, i_lbl, r_lbl]],
            run_time=1.3
        )
        self.wait(1.3)

2 · The six fluxes — one by one

The hydrologic cycle is simply six named arrows connecting four stores: the ocean, the atmosphere, the soil, and the snowpack. Scroll down to reveal each flux.

☀️💧

Evaporation

Liquid water at the ocean or lake surface gains enough energy from sunlight to escape as vapour — no plant needed.

Global mean: ~1 200 mm yr⁻¹ over ocean

🌿⬆️

Transpiration

Plants pump water from the soil through their roots and release it as vapour through tiny pores called stomata. Over forested land, T often exceeds direct E.

≈ 40 % of terrestrial ET

☁️❄️

Condensation

—

Rising moist air cools. When it reaches the dew point, vapour condenses onto tiny aerosols forming cloud droplets. No flux symbol — it's the process inside the cloud store.

≈ Dew point ↓ 1 °C per 100 m ascent

🌧️

Precipitation

Cloud droplets collide, coalesce and fall when large enough. Rain, snow, sleet, hail — all precipitation. It is the input flux in the land-surface water balance.

Global mean: ≈ 1 000 mm yr⁻¹ land

🪨⬇️

Infiltration

Rain that reaches the soil surface and soaks downward under gravity and capillary suction. Infiltrated water may become groundwater or be taken up by roots — it does not reach the stream immediately.

Rate: 1–300 mm hr⁻¹ depending on soil

🏔️➡️🌊

Runoff

Rain (or snowmelt) that does not infiltrate flows overland as surface runoff. Lateral groundwater that emerges at the stream bank becomes baseflow. Together they are the discharge, Q.

World rivers: ≈ 40 000 km³ yr⁻¹

The balance equation Over a long enough period for a closed catchment: P = ET + R + ΔS Precipitation equals evapotranspiration plus runoff plus the change in storage. This single equation underlies everything in the next six modules.

3 · The bathtub: mass balance in action

Imagine the catchment as a leaky bucket. Rain fills it from above; evaporation and runoff drain it. Drag the Precipitation slider to fill faster or slower — watch storage rise, overflow as runoff, or empty during a drought.

Precipitation (P) 3.0 mm day⁻¹

Evapotranspiration (ET) 2.0 mm day⁻¹

Fixed in this simple model — in reality ET varies with temperature, humidity, and vegetation.

          P
          3.0 mm/d
        
          ET
          2.0 mm/d
        
          R (overflow)
          0.0 mm/d
        
          ΔS / day
          +1.0

4 · Scrub the cycle — stop time on any flux

The controls below drive a cycle diagram frame-by-frame. Each stage illuminates one flux so you can linger exactly where you want. Works with or without Manim.

5 · Checkpoint

Three quick questions — get all three right to mark this module complete and unlock the next two.

1 · Which two processes return water vapour to the atmosphere?

Evaporation & Transpiration Precipitation & Runoff Infiltration & Condensation

Those move water downward, not into the atmosphere.

Infiltration goes underground; condensation forms clouds — neither is an upward flux to the air.

2 · Over many years, the water balance for a closed catchment is: P equals…

Runoff only (R) ET + R + ΔS ET only

Runoff only ignores ET and changes in soil/groundwater storage.

ET only ignores runoff and storage — valid only if R = 0 and ΔS = 0, which never holds in practice.

3 · Condensation happens because rising moist air…

Cools as it ascends and reaches its dew point Warms when it meets sunlight above the clouds Mixes with dry, cold ocean air at altitude

Sunlight warms surfaces, not air above the clouds. Condensation is driven by cooling, not heating.

While cold air plays a role in some weather, the primary mechanism is the adiabatic cooling of a rising parcel.

Sources & Further Reading

Dingman, S. L. (2015). Physical Hydrology, 3rd ed. Waveland Press. — The mass-balance equation and flux definitions follow Chapter 2.
USGS Water Science School. The Water Cycle — Plain-language flux descriptions and global magnitudes.
Trenberth, K. E., Smith, L., Qian, T., Dai, A., & Fasullo, J. (2007). Estimates of the Global Water Budget and Its Annual Cycle Using Observational and Model Data. Journal of Hydrometeorology, 8(4), 758–769. — Source for global mean evaporation and runoff magnitudes.

Author: Mohammad Galib · Purdue University
License: CC-BY-4.0 — free to reuse with attribution
Module ID: water-cycle-in-motion · v0.1.1
Course: Introduction to Hydrology · intro-hydro-2026
Data sources: No external data — all illustrations are synthetic / schematic
Animation: Manim Community v0.18+ (optional); falls back gracefully

Made with AI-Hydro CC-BY-4.0