16-Civ-B4 Engineering Hydrology · December 2017

Question 1 of 7: Hydrologic Cycle Processes, Groundwater and Surface Runoff

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Question 1: Hydrologic Cycle Processes, Groundwater and Surface Runoff (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

1(i) — Three ways global warming influences hydrologic processes (7 marks)

The hydrologic cycle is a closed mass balance driven by an energy supply. Warming changes the energy supply, and every flux in the cycle responds. The schematic below identifies the main processes; the three influences discussed afterwards are keyed to it.

1. Precipitation becomes more intense and more episodic. The Clausius–Clapeyron relation fixes the saturation vapour pressure of air, and near surface temperatures it increases by roughly seven per cent for each degree Celsius of warming. A warmer atmosphere therefore holds more water and, when a storm organises, has more water available to precipitate.

Given. A regional warming of $\Delta T = 2.0\ ^\circ\text{C}$ and the Clausius–Clapeyron scaling of about 7 % per degree.

Find. The proportional change in the moisture the atmospheric column can hold.

Compounding the scaling over the two degrees gives

Annual totals do not rise by anything like that amount, because precipitation is limited by the surface energy budget rather than by moisture supply. What changes is the distribution: the heavy tail of the storm-depth distribution grows at close to the Clausius–Clapeyron rate while the number of rain days falls, so a design engineer sees larger short-duration depths on the intensity–duration–frequency curve and longer dry spells between events. Environment and Climate Change Canada’s IDF_CC tool exists precisely to re-issue Canadian IDF curves under this shift, and it is now normal practice to check a drainage design against the climate-adjusted curve as well as the historical one.

2. The snowmelt freshet arrives earlier and carries less water. Over most of Canada the largest annual flow is not a rainstorm response at all but the spring freshet. Warming raises the winter freezing level, so a larger share of winter precipitation falls as rain rather than snow, and it advances the date at which the pack begins to melt. The result on a snow-dominated basin is a freshet peak that arrives several weeks earlier, is somewhat lower, and is followed by a longer and drier late-summer recession. Reservoir operators in British Columbia and Alberta must then draw down for flood control earlier in the year while facing a longer period during which storage, not inflow, supplies the demand. On glacier-fed rivers the same warming first increases summer flow as the ice wastes, then decreases it permanently once the glacier reserve is depleted.

3. Evapotranspiration rises, and soils and reservoirs lose more water. Potential evapotranspiration increases with temperature, with the vapour-pressure deficit and with the length of the growing season. Where soil moisture remains available, actual evapotranspiration rises with it, drying the soil profile between storms; where it does not, the basin shifts from an energy-limited to a water-limited regime and the excess energy simply raises surface temperature. Either way the antecedent soil-moisture condition at the start of a storm becomes drier on average and more variable, which makes runoff response less predictable and widens the confidence band on any design flood estimate. Open-water evaporation from reservoirs and prairie sloughs also rises, so a given storage yields less firm supply.

These three effects do not act independently: less snow storage plus higher evapotranspiration plus more episodic rainfall together move a basin towards a flashier, more variable regime, which is exactly the combination that stresses both flood works and water-supply works.

1(ii) — Three water-management differences between confined and unconfined aquifers (7 marks)

Difference 1 — the source and vulnerability of recharge, and therefore of contamination. An unconfined aquifer is recharged vertically over its whole extent, so a spill, a leaking tank, a manure application or road salt anywhere on the capture zone can reach the well. A wellhead protection plan for an unconfined supply must therefore control land use across the entire time-of-travel capture zone, and the aquifer is properly classed as GUDI-vulnerable where the overburden is thin. A confined aquifer is sealed beneath a low-permeability aquitard and is recharged only where it outcrops, which may be tens of kilometres away. It is naturally protected from surface contamination, and the management burden shifts to protecting that remote recharge area and to maintaining the integrity of every borehole that penetrates the aquitard — an improperly abandoned well is the usual pathway by which a confined supply becomes contaminated.

Difference 2 — the volume of water released per metre of head decline. This is the sharpest practical contrast, and it is worth putting numbers on.

Given. The management comparison starts from a 10 km² well field pumped down by one metre, in each of two aquifers with the properties tabulated below.

Find. The natural through-flow available from the confined aquifer, and the volume each aquifer releases for one metre of head decline.

Approach. Apply Darcy’s law to the confined section to establish the sustainable through-flow, then compare $V = S A \Delta h$ for the two storage mechanisms.

1. Establish the transmissivity and the flow area. For a confined aquifer of uniform thickness, $$T = Kb = (40)(20) = 800\ \text{m}^2/\text{d}, \qquad A_{\text{sec}} = bw = (20)(800) = 16\,000\ \text{m}^2$$
2. Apply Darcy’s law to the section. With $Q = KA_{\text{sec}}(dh/dL)$, $$Q = (40)(16\,000)(0.004) = \boxed{2560\ \text{m}^3/\text{d}} = 0.0296\ \text{m}^3/\text{s}$$ That is the whole natural flux crossing the section; abstracting more than this must come out of storage or must capture discharge elsewhere.
3. Compare the water released by one metre of drawdown. Storage release is $V = S \, A \, \Delta h$, so $$V_{\text{conf}} = (4\times 10^{-4})(10\times 10^{6})(1) = 4000\ \text{m}^3, \qquad V_{\text{unconf}} = (0.20)(10\times 10^{6})(1) = 2.0\times 10^{6}\ \text{m}^3$$

The unconfined aquifer yields five hundred times as much water per metre of drawdown. The management consequence follows directly: in a confined aquifer, a modest abstraction produces a large and very widely spread drawdown, because the pressure signal propagates fast through an elastic medium without dewatering it. Interference between wells extends for kilometres, artesian pressure can be lost, and in thick compressible aquitards sustained depressurisation causes land subsidence that is not recoverable. In an unconfined aquifer the drawdown is local and modest, but it is achieved by physically dewatering the pore space, which reduces the saturated thickness, reduces the transmissivity as pumping proceeds, and can dry out the springs, wetlands and stream reaches that the water table supports.

Difference 3 — the monitoring and the water-quality treatment each demands. An unconfined supply must be monitored for surface-derived determinands (nitrate, chloride, pathogens, pesticides) and typically needs disinfection and often filtration; its response to drought is fast and visible in the water table, so an operating rule tied to water-table elevation is workable. A confined supply is usually microbiologically secure but is often geochemically difficult, because long residence times in a reducing environment mobilise iron, manganese, hydrogen sulphide, fluoride and, in parts of the Canadian Prairies and the Atlantic provinces, arsenic. Treatment is therefore chemical rather than microbiological. Monitoring is of potentiometric head rather than water table, and because the response is regional the licensing authority must manage the whole aquifer as one allocation unit rather than well by well.

1(iii) — Three reasons only a small percentage of precipitation becomes surface runoff (6 marks)

Reason 1 — infiltration removes most of the rainfall before it can run off. Rain arriving on a pervious surface enters the soil at a rate that begins high and decays towards the saturated conductivity as the profile wets up. For any storm whose intensity stays below that infiltration capacity, no Hortonian overland flow is generated at all. Only when the intensity exceeds the current capacity, or when the profile saturates from below, does water pond and move downslope.

Reason 2 — interception and depression storage absorb an initial abstraction. Canopy and litter intercept the first few millimetres and return most of it to the atmosphere by evaporation; surface depressions, furrows and puddles hold more until they fill. On a forested or agricultural basin this initial abstraction is commonly 3 to 8 mm, which alone consumes an entire ordinary rainfall.

Reason 3 — evapotranspiration returns most of the infiltrated water to the atmosphere. Over a Canadian basin, annual evapotranspiration typically consumes between forty and seventy per cent of annual precipitation, and on the southern Prairies it approaches all of it. Of the water that does infiltrate, only the fraction that percolates past the root zone becomes recharge and eventually baseflow; the remainder is transpired.

The three effects are sequential, so their combined effect is multiplicative rather than additive. A worked example makes the size of the result plain.

Given. A moderate storm on a well-vegetated basin with the Horton infiltration parameters listed: total rainfall $P = 45$ mm falling over $t = 6$ h; initial infiltration capacity $f_0 = 25$ mm/h; final capacity $f_c = 4$ mm/h; decay constant $k = 1.5$ h⁻¹; interception plus depression storage $I_a = 5$ mm.

Find. The depth of surface runoff and the resulting runoff coefficient.

Approach. Integrate the Horton curve over the storm to get the cumulative infiltration, subtract it and the initial abstraction from the rainfall, and express the remainder as a fraction of the rainfall.

1. Integrate the Horton infiltration curve. With $f(t) = f_c + (f_0 - f_c)e^{-kt}$, the cumulative depth over the storm is $$F = f_c t + \frac{f_0 - f_c}{k}\left(1 - e^{-kt}\right)$$ Substituting, $$F = (4)(6) + \frac{25 - 4}{1.5}\left(1 - e^{-(1.5)(6)}\right) = 24 + 14(1 - 0.000123) = 38.00\ \text{mm}$$
2. Close the storm water balance. The runoff is what the soil and the surface did not take: $$R = P - F - I_a = 45 - 38.00 - 5 = \boxed{2.00\ \text{mm}}$$
3. Express the result as a runoff coefficient. $$C = \frac{R}{P} = \frac{2.00}{45} = 0.044 \quad \text{i.e. } \boxed{4.4\%\ \text{of the rainfall}}$$

Four per cent is entirely typical of a pervious rural basin under an ordinary storm, and it explains why the runoff coefficient is so strongly non-linear: double the rainfall on the same soil and the infiltration term barely moves, so the runoff more than doubles. It also explains why urbanisation is so consequential — paving removes both the infiltration and the depression-storage terms, and the coefficient jumps from a few per cent to sixty or ninety.