Response of closed basin lakes to interannual climate variability

Abstract

Lakes are key indicators of a region’s hydrological cycle, directly reflecting the basin-wide balance between precipitation and evaporation. Lake-level records are therefore valuable repositories of climate history. However, the interpretation of such records is not necessarily straightforward. Lakes act as integrators of the year-to-year fluctuations in precipitation and evaporation that occur even in a constant climate. Therefore lake levels can exhibit natural, unforced fluctuations that persist on timescales of decades or more. This behavior is important to account for when distinguishing between true climate change and interannual variability as the cause of past lake-level fluctuations. We demonstrate the operation of this general principle for the particular case-study of the Great Salt Lake, which has long historical lake-level and climatological records. We employ both full water-balance and linear models. Both models capture the timing and size of the lake’s historical variations. We then model the lake’s response to much longer synthetic time series of precipitation and evaporation calibrated to the observations, and compare the magnitude and frequency of the modeled response to the Great Salt Lake’s historical record. We find that interannual climate variability alone can explain much of the decadal-to-centennial variations in the lake-level record. Further, analytic solutions to the linear model capture much of the full model’s behavior, but fail to predict the most extreme lake-level variations. We then apply the models to other lake geometries, and evaluate how the timing and amplitude of a lake-level response differs with climatic and geometric setting. A lake’s response to a true climatic shift can only be understood in the context of these expected persistent lake-level variations. On the basis of these results, we speculate that lake response to interannual climate variability may play an important part in explaining much of Holocene lake-level fluctuations.

Appendix: Standard deviations in lake level

Discretizing Eq. (8) in to time increments, $\varDelta t$, and setting $P' = 0$, gives

$$\begin{aligned} h'_t= h'_{t-\varDelta t}\left( 1-\frac{\varDelta t}{\tau }\right) E'_t. \end{aligned}$$

(20)

We set $E'_t = \sigma _E \nu _t$, where $\nu _t$ is a normally distributed, stochastic white noise process. The variance of $h'_t$ is the expected value of $h'^2_t$, and is given by

$$\begin{aligned} \langle h'^2_t \rangle = \left( 1-\frac{\varDelta t}{\tau }\right) ^2\langle h'^2_{t-1} \rangle + 2 \left( 1-\frac{\varDelta t}{\tau } \right) \sigma _E \varDelta t \langle h'_{t-1} \nu _{t} \rangle + \sigma _E^2 \varDelta t^2 \langle \nu _{t}^2 \rangle . \end{aligned}$$

(21)

The following relationships hold: $\langle \nu _{t} h'_{t}\rangle =0$, $\langle h'^2_{t} \rangle =\langle h'^2_{t-1}\rangle$, and $\langle \nu _{t}^2 \rangle =1$. Upon substitution, and taking the limit of $\varDelta t<<\tau$ we obtain:

$$\begin{aligned} \langle h'^2_{t} \rangle = \frac{\sigma _E^2 \varDelta t^2}{{2\varDelta t}/{\tau }}, \end{aligned}$$

(22)

Therefore,

$$\begin{aligned} \sigma _{hE}= \sigma _E \left( \frac{\varDelta t \tau }{2}\right) . \end{aligned}$$

(23)

Similarly for lake-level variability due to $P'(t)$ alone:

$$\begin{aligned} \sigma _{hP}= \left[ 1-\gamma +\frac{\gamma A_B}{\bar{A_L}}\right] \sigma _{P} \left( \frac{\varDelta t \tau }{2}\right) . \end{aligned}$$

(24)

Provided that $P'$ and $E'$ are not correlated the variances can be combined as:

$$\begin{aligned} \sigma _{h}= \sqrt{\sigma _{hE}^2+\sigma _{hP}^2} \end{aligned}$$

(25)