Liu et al. (2013), in their Comment on Hudson and Quade (2013), clearly state our conclusion that the pattern of lake expansions during the early Holocene on the Tibetan Plateau was the result of a plateau-wide increase in precipitation during an intensified summer monsoon. However, the magnitude of this increase, as recorded by the ratio of greatest paleolake area ratios to modern lake area ratios (lake area/total catchment area) for 130 plateau lake systems, was nearly twice as large in the western Tibetan Plateau compared with the east (Hudson and Quade, 2013; our figure 3). Liu et al. are correct to point out that precipitation is far from the only factor affecting the hydrologic budget of closed-basin lake systems, and suggest that we do not clearly account for three controls on hydrologic budget. These potential controls on are: (1) catchment area “supply coefficients” creating differing responses for individual lake systems; (2) input of stored glacial melt runoff into the lakes in addition to seasonal precipitation runoff; and (3) drainage diversion changing the net catchment areas of adjacent lake systems.

(1) The “supply coefficient,” defined by Liu et al. as the ratio of total catchment area to lake area of a closed-basin lake system, is the reciprocal of the “lake area ratio” used in our analysis (lake area/total catchment area). The authors correctly state that more arid catchments must have larger supply coefficients (smaller lake area ratios) to maintain hydrologic balance. This relationship is clearly supported by the correlations between modern basin-averaged precipitation and modern lake area ratios in our lakes data set (Hudson and Quade, 2013; our figure 3, inset). We chose to compare lake area ratios directly to precipitation, but the modern decrease in lake area ratios (increase in supply coefficients) from south to north cited by the authors in response to a south-north precipitation gradient is supported by our data set. Liu et al. state that lakes with high supply coefficients (low lake area ratios) would have undergone larger areal expansion than those with small supply coefficients (high lake area ratios). This would be the case if lake area ratio (supply coefficient) did not change with increased precipitation, but in lake basins where the total catchment area does not change, the lake area ratio must increase (and the supply coefficient must decrease) as excess precipitation fills the lake. Consider the simplified hydrologic budget for a closed-basin lake system (Equation 1) where P, ET, and E represent the unit area fluxes of precipitation, evapotranspiration, and evaporation, respectively, and Ab and Al represent the relative fractions of the total catchment area covered by land and lake, respectively. 
graphic

The left side of the equation represents net input into the hydrologic budget, while the right side represents output. Lake area ratio is expressed Al/Ab and supply coefficient is expressed Ab/Al. For an increase in precipitation with no change in ET and E, the hydrologic balance can only be maintained by an increase in lake area and a proportional decrease in land area. This increases lake area ratio and decreases supply coefficient. For example, a lake that undergoes a 5× expansion from a lake area ratio of 0.05 to 0.25 must have a reduction of supply coefficient from 20 to 4. So, the statement that lake systems with higher supply coefficients would have undergone greater expansion is incorrect, because supply coefficient must decrease with lake expansion to balance the hydrologic budget. Supply coefficient, as defined by Liu et al., is a result of the lake system reaching hydrologic balance, not a hydrologic parameter affecting the hydrologic balance.

(2) Liu et al. suggest that input from glacial melt may contribute to lake expansion without requiring asymmetric precipitation increase. This was clearly addressed by us. We considered modern glaciated and nonglaciated lake systems separately in our analysis explicitly to investigate and rule out this factor. Glacial melt runoff supplements the hydrologic budget of many lake systems on the Tibetan Plateau, and modern glaciated basins often have higher lake area ratios given the same modern precipitation when compared to nonglaciated basins (our figure 3, inset). In contrast to this difference, the magnitude of Holocene lake expansion shown by glaciated and nonglaciated basins is similar across the plateau (our figure 3). In fact, if either data set were removed, the same pattern is observed. Furthermore, glacier volume in each catchment is controlled by temperature (Rupper and Roe, 2008), elevation, aspect, and debris cover, all heterogeneous variables between lake basins (e.g., Scherler et al., 2011). It is extremely unlikely that the volume of melt water flux for each lake system, with peak elevations for individual systems ranging between 5124 m asl and 7057 m asl (Hudson and Quade, 2013; our Data Repository Table DR3), could augment each lakes’ hydrologic budget to the correct degree to result in the observed coherent pattern of lake expansions despite vastly differing elevation, aspect, and basin latitude.

3) Lastly, the authors suggest drainage diversions may have contributed to changes in hydrologic budget unrelated to climate. We agree that this is a potential concern for individual lake systems through time. However, individual geomorphically controlled drainage diversions, like glacier melt in individual systems, cannot explain the coherent east-west differences in lake expansion spanning the entire Tibetan Plateau without requiring widespread coeval drainage diversions carrying equal runoff from every lake system (with highly variable lake and catchment areas) in the western Tibetan Plateau to every basin to the east, giving the appearance of much greater lake expansions in the west relative to the east.

To conclude, despite the other possible factors affecting the hydrologic budget of closed-basin lakes suggested by Liu et al., an asymmetric precipitation increase during the early Holocene provides the most logical explanation for the coherent pattern of lake expansions observed by us for the interior of the Tibetan Plateau.

This research was funded by the Comer Science and Education Foundation.