Chapter 4 · The Hydrosphere

Problem 1

1. Two rivers flow into a dammed lake. The flow rate through the dam is measured to be 1,057,000 m³/day. The engineers want to know the flow rate of the rivers. Assuming no evaporation and assuming constant flow rates and δ¹⁸O values, compute the flow rates in each river if the δ¹⁸O values of input rivers A and B and the dam output are −4.5, −12.7, and −9.2‰, respectively. Which river is sampling waters from higher altitudes?
2. In summer, there is significant evaporation at the dam. Compute the amount of evaporation (and summer outflow rate) if the δ¹⁸O value of the output is now −4.9‰ and the fractionation between water and water vapor is 9‰. (Hint: for this part of the problem, assume that the input rates and δ values are identical to those of part (a), but that the outflow rate is now different from part (a).)

[Worksheet constructed.]

Problem 2

Many of the isotopic processes occurring during precipitation can be understood from a logical evaluation of fractionation, temperature, and amount. Sometimes a variable may appear to control the delta values of precipitation in a particular direction when, in fact, the opposite is observed. Consider the positive correlation between temperature and delta value, where lower temperatures are proportional to lower delta values. However, the fractionation between water and water vapor increases with decreasing temperature, so precipitation should have a higher δ value. Why, then, do T and δ have a positive correlation?

Problem 3

Table 4.1 gives the relative abundance and delta values for the different water reservoirs of the Earth. If all of the ice caps melt, what will the new δ¹⁸O and δD values of the ocean be?

[Worksheet constructed. The mass fractions and δ¹⁸O are the Table 4.1 values used in the printed answer; the δD of ice is reconstructed from the printed result, check vs print.]

Problem 4

1. Plot the δ¹⁸O values of a cloud mass and resulting precipitation as a function of F, given the following conditions. A total of 20% of water is lost to precipitation (F ranges from 1 to 0.8), T = 5 °C, δ¹⁸O_i(cloud) = −16‰. The fractionation between water and water vapor is given by the equation (Horita and Wesolowski, 1994)
   10³lnα_{water–water vapor} = a + b·10³/T + c·10⁶/T² + d·10⁸/T³signs per H&W 1994; check vs print

   a = −7.69,  b = 6.712,  c = −1.667,  d = 3.504
2. In fact, the temperature must decrease during extended periods of precipitation in order to maintain the condition of condensation. Using equations (4.18) and (4.19) in the text, and assuming a regular change of temperature between 10 and 0 °C, plot the δ¹⁸O value of the precipitation and calculate the average δ¹⁸O value of precipitation.

[Worksheet constructed, for part (a). Part (b) needs equations (4.18) and (4.19) from the text.]

The chapter's interactive Rayleigh distillation plot implements exactly this construction.

Problem 5

Craig defined SMOW in terms of NBS-1, a sample of Potomac River water, in the following way:

1. What is the δ¹⁸O value of NBS-1 relative to SMOW and relative to PDB?
2. What is the δD value of NBS-1 relative to SMOW?
3. Does NBS-1 fall on the global meteoric water line? Does NBS-1 fall on the local meteoric water line (use the meteoric water line for North Carolina in Fig. 4.4 as your proxy)?

[Worksheet constructed. The VSMOW→VPDB conversion constants are the chapter-2 values, not printed in this problem.]

Problem 6

Many sedimentological records indicate that far more windblown dust accumulates during glacial periods than at other times. Correlating this dust with humidity, would you expect the deuterium excess parameter d to be larger or smaller in glacial vs. interglacial periods? Think of two geological materials that would allow you to test your conclusions.