Hydrologic cycle, budget, and models

Dr. Huidae Cho
Department of Civil Engineering...New Mexico State University

1   Hydrologic cycle

  • Sun-driven
  • Very complex
  • A closed system
  • Has many open-ended subsystems, which causes many problems of water supply and allocation

2   Six major components in the hydrologic cycle

See Figure 1.1.

  • $P$: Precipitation
  • $I$: Infiltration
  • $E$: Evaporation
  • $T$: Transpiration
  • $R$: Surface runoff
  • $G$: Groundwater flow

hydrologic-cycle.png

3   Distribution of precipitation input

See Figure 1.2.

4   Hydrologic budget equations

4.1   Surface-flow components

\begin{equation} P+R_1-R_2+R_g-E_s-T_s-I = \Delta S_s \label{eq:S_s} \end{equation}

4.2   Groundwater-flow components

\begin{equation} I+G_1-G_2-R_g-E_g-T_g = \Delta S_g \label{eq:S_g} \end{equation}

4.3   Combined

\begin{equation} P-(R_2-R_1)-(E_s+E_g)-(T_s+T_g)-(G_2-G_1) = \Delta (S_s+S_g) \label{eq:S} \end{equation} or \begin{equation} P-R-E-T-G = \Delta S \label{eq:S2} \end{equation}

For large river basins (thousands mi2 or km2), the groundwater influx and outflux can be assumed to be equal ($G=0$).

Over a long period of time (5+ years), seasonal excesses and deficits in storage tend to balance out in large watersheds ($\Delta S=0$).

For large watersheds over a long period of time, Eq. (\ref{eq:S2}) reduces to \begin{equation} P-R-ET=0 \end{equation}

5   Hydrologic models

All models are wrong, but some are useful Box (1976)

Hydrologic models

  • Physically-based models
  • Data-driven models

6   Modeling uncertainty

  • Our lack of understanding of the true system
  • Approximation of the system
  • Abstract parameters
  • Measurement errors
  • Commensurability issues
  • Naturally random phenomena

7   Example 1.1

The drainage area of the James River at Scottsville, Virginia, is 11,839 km2. If the mean annual runoff is determined to be 144.4 m3/s and the average annual rainfall is 1.08 m, estimate the ET losses for the area. How does this compare with the lake evaporation of 1 m/yr measured at Richmond, Virginia?

8   Problem 1.2

Assume you are dealing with a vertical-walled reservoir having a surface area of 500,000 m2 and that an inflow of 1.0 m3/s occurs. How many hours will it take to raise the reservoir level by 30 cm?

9   Problem 1.4

The annual evaporation from a lake is found to be 125 cm. If the lake’s surface area is 12 km2, what is the daily evaporation rate in centimeters and inches?

10   Homework: Hydrologic budget

  • Problem 1.7
  • Problem 1.8

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