Questions & explanations
1. Explain the concept of 'over-year storage' and how it relates to yield analysis.
Over-year storage means the reservoir is large enough to carry water from one year to the next. This is needed when the dry season lasts more than one year, such as in a multi-year drought. In yield analysis, if the reservoir only has within-year storage, it can only even out seasonal variation, not inter-annual droughts. When the storage is large enough for over-year regulation, the firm yield becomes closer to the average annual inflow, because the reservoir can store surplus in wet years. The analysis then uses many years of data, often 30 to 50 years, to capture long dry spells. Without over-year storage, the yield is limited by the driest single year. Many major water supply reservoirs are designed with over-year storage to provide a reliable supply during prolonged droughts.
2. How does a reservoir's storage capacity affect its yield?
Generally, larger storage allows a reservoir to hold more water from wet years to use in dry years, so the yield can be higher. But the relationship is not linear; doubling the storage does not double the yield because the extra storage may fill only during very wet years. The yield also depends on the inflow pattern and evaporation losses. For a given inflow, there is a limit to how much water can be reliably supplied, called the safe yield, which increases with storage up to a point. Beyond a certain storage, adding more storage gives very little extra yield because most floods are already captured. This is called the storage-yield curve, which helps engineers find the most cost-effective reservoir size. So storage and yield are directly related, but with diminishing returns.
3. Compare the Green-Ampt model and the Horton model for infiltration.
Green-Ampt is a physically based model that assumes a sharp wetting front moving into the soil. It uses soil properties like saturated hydraulic conductivity and capillary suction. Horton's model is an empirical equation where infiltration starts high and decays exponentially to a constant rate. Green-Ampt requires soil texture data; Horton needs calibration from field measurements. Green-Ampt can be used for different rainfall intensities, while Horton is simpler but less flexible. Both models assume uniform soil and constant initial moisture, which is a simplification. In practice, Green-Ampt often gives more accurate results for sandy soils, while Horton works better for clay soils. The choice depends on data available and the desired precision.
4. Compare McCarthy's original Muskingum method with the Muskingum-Cunge method.
McCarthy's Muskingum method uses two parameters (K and X) that are calibrated from observed inflow and outflow data. It is empirical and does not use channel geometry. The Muskingum-Cunge method, developed later, derives K and X from physical channel properties like length, slope, and roughness using the Cunge formula. This makes it more physically based and applicable to ungauged reaches. Muskingum-Cunge also simulates wave attenuation more accurately because it accounts for diffusion. However, it requires detailed channel cross-section data. Both methods assume a linear storage relationship, but Muskingum-Cunge is superior for channels where calibration data are lacking. In practice, Muskingum-Cunge is now more common in modern hydrologic models.
5. Compare the water balance of a natural lake and a man-made reservoir. What is the main difference?
Both follow the same basic equation: inflows minus outflows equals change in storage. The main difference is that a reservoir's outflows are often controlled by humans through gates and valves. Natural lakes have a fixed outlet at the natural spillway elevation. In a reservoir, managers can release water to meet demands downstream or to reduce flood risk. Also, reservoirs are often built in locations with high inflows, but they may have larger evaporation losses due to a large surface area. Natural lakes typically have more stable water levels because they are in equilibrium with the landscape. Both are affected by climate, but reservoirs can be operated more flexibly. However, both require a careful water balance to maintain their functions.
6. How do you compute the firm yield of a reservoir?
Engineers use a computer model or manual mass curve analysis. The mass curve plots cumulative inflow over time. They start with a trial yield, like 10 million cubic meters per year. They simulate the reservoir's storage, subtracting yield and net evaporation from inflows each month. If the storage never drops below zero, the yield is possible. They repeat with higher yields until they find the highest yield that keeps the reservoir from emptying during the worst recorded drought. That yield is the firm yield. It is usually lower than the average inflow because water is needed during dry periods. The firm yield depends on the reservoir size, the inflow pattern, and the acceptable risk of failure. This method ensures a reliable water supply.
7. Explain how the diffusion wave approximation accounts for backwater effects.
The diffusion wave equation includes a term for the water surface slope (the gradient of the water depth plus the bed slope). This means the flow not only depends on the bed slope but also on the difference in water depth between upstream and downstream. If there is a downstream obstruction, the water depth rises upstream, reducing the water surface slope and thus slowing the flow. The diffusion wave can model this effect, unlike kinematic wave. For example, if a bridge partly blocks a channel, the diffusion wave can simulate the backwater profile. It does so by solving the mass and momentum equations with the pressure term. However, because it neglects acceleration, the backwater effect is only approximated for slowly changing conditions.
8. Give an example applying the Philip infiltration model to a storm event.
Philip's model uses a two-term equation: infiltration rate = sorptivity*time^(-0.5) + hydraulic conductivity. Sorptivity describes how fast the soil draws water in by capillary force. For a sandy loam soil with sorptivity 1.0 cm/min^0.5 and conductivity 0.1 cm/min, we can predict infiltration during a storm. If rainfall intensity is 0.5 cm/min, at the start infiltration exceeds rain, so all water infiltrates. After some minutes, infiltration rate drops below rainfall, and ponding begins. The model then computes cumulative infiltration over time. For example, after 10 minutes, cumulative infiltration is about 5 cm. This helps determine when runoff starts and how much runoff occurs. Philip's model works well for short, intense storms.
9. Explain why the water balance of a lake can change between wet and dry seasons.
In the wet season, inflows from rain and rivers are high, often much more than evaporation. So the lake receives more water than it loses, and its volume increases. In the dry season, rain is scarce and inflows drop. At the same time, evaporation may stay high or even increase due to hotter temperatures. Now outflows can exceed inflows, and the lake volume decreases. Some lakes may have no outlet, so they only lose water by evaporation, causing them to shrink dramatically. The water balance equation is a snapshot over time, so seasonal changes reflect the difference in inputs and outputs. These seasonal cycles are important for ecosystems and human water use. Engineers use long-term averages to plan for both wet and dry periods.
10. Explain how confidence intervals are used in probabilistic flood assessment.
A confidence interval gives a range where the true flood level likely falls, with a certain probability like 90%. For example, we might say with 90% confidence that the 100-year flood level is between 4.5 and 5.5 meters. This is based on the spread of model results. To build such intervals, we repeat the flood calculation many times with different possible inputs. The middle portion of the simulated flood levels forms the confidence interval. Wider intervals mean more uncertainty; narrower means less. These intervals are very useful for engineers. For instance, a levee might be designed to withstand the upper end of the interval, not just the middle estimate. Confidence intervals make the uncertainty visible to decision-makers.
11. What is the difference between USLE and RUSLE?
RUSLE stands for Revised Universal Soil Loss Equation. It updates and improves the original USLE by using better data and more flexible input values. For example, RUSLE has a more accurate rainfall erosivity factor, especially for areas with snowfall. It also allows the cover-management factor (C) to vary month by month instead of being a fixed annual value. RUSLE includes a new factor, the soil erodibility factor (K) for different seasons. The basic equation form is the same: A = RKLSCP. RUSLE is more reliable for complex situations like cropland with rotations. Both models estimate sheet and rill erosion, not gully or stream bank erosion. RUSLE is now more commonly used by professionals in the US and many other countries.
12. How does the Muskingum-Cunge method improve upon the original Muskingum method?
Muskingum-Cunge replaces empirical calibration with physically based equations to compute K and X using channel characteristics. K is related to the travel time through the reach, which is calculated from the wave celerity and reach length. X is derived from a cell Reynolds number (related to roughness and slope) to control diffusion. This makes the method more accurate and applicable to rivers without historical data. It also better represents wave attenuation because the diffusion coefficient is explicitly linked to channel properties. Additionally, Muskingum-Cunge can handle variations in flow and channel shape more flexibly. It has become the standard for flood routing in many hydrologic models like HEC-HMS and SWMM.