\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}

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5 Hydrologic models

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

Hydrologic models

Physically-based models
Data-driven models

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6 Modeling uncertainty

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

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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?

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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?

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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?

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10 Homework: Hydrologic budget

Problem 1.7
Problem 1.8

Show your full work.

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