On modeling the paleohydrologic response of closed‐basin lakes to fluctuations in climate: Methods, applications, and implications

Abstract

Climate reconstructions using tree rings and lake sediments have contributed significantly to the understanding of Holocene climates. Approaches focused specifically on reconstructing the temporal water-level response of lakes, however, are much less developed. This paper describes a statistical correlation approach based on time series with Palmer Drought Severity Index (PDSI) values derived from instrumental records or tree rings as a basis for reconstructing stage hydrographs for closed-basin lakes. We use a distributed lag correlation model to calculate a variable, x t that represents the water level of a lake at any time t as a result of integrated climatic forcing from preceding years. The method was validated using both synthetic and measured lake-stage data and the study found that a lake's ''memory'' of climate fades as time passes, following an exponential-decay function at rates determined by the correlation time lag. Calculated trends in x t for Moon Lake, Rice Lake, and Lake Mina from A.D. 1401 to 1860 compared well with the established chronologies (salinity, moisture, and Mg/Ca ratios) reconstructed from sediments. This method provides an independent approach for developing high-resolution information on lake behaviors in preinstrumental times and has been able to identify problems of climate signal deterioration in sediment-based climate reconstructions in lakes with a long time lag.

Essentials of Endorheic Basins and Lakes: A Review in the Context of Current and Future Water Resource Management and Mitigation Activities in Central Asia

“…Due to the sensitivity of lakes, especially closed systems, to climate change, there has been ongoing research on lakes as sentinels or indicators of climate change [9,[61][62][63][64]. Paleoarchives concealed in lake sediments have been used for decades to assess the state of past climates worldwide [65] and in Eurasia [66][67][68][69].…”

Quantifying the Response Time of a Lake–Groundwater Interacting System to Climatic Perturbation

“…As discussed in the introduction, the concept of a response time or time constant is well developed in relation to the theory of groundwater flow and lakes (e.g., Liu and Schwartz [14]). In practice, the time required for hydraulic heads in a flow system to readjust to a perturbation can be determined from a set of measurements, for example, from water-level measurements in a piezometer [1] or in a lake [12].…”

“…In either approach, the response time is defined on the basis of a characteristic associated with the mathematical function that fits the time series. Hvorslev [1], as well as others, e.g., [14,23], found that an exponential function works well. Equation (1) is of that form [23], ( ) ( )…”

“…Langbein [12] used a simple, water-balance approach with a geometric function to weight inflow contributions backwards in time. The time lag parameter defined by Langbein, based on a geometric function, is different than time lag defined assuming an exponential decay in time used for example by others [1,14]. In practice, however, similar results are obtained from either function.…”

“…Liu and Schwartz [14] developed a statistical modeling approach that utilizes historical Palmer Drought Severity Index values (PDSI) [15], derived from instrumental records and tree ring archives, as a basis for reconstructing the water-level responses of closed-basin water bodies. The distributed lag correlation model makes it possible to calculate a parameter that represents the water level of a lake at any time t in terms of the integrated history of climatic forcings from preceding years.…”