Cave airflow patterns control calcite dissolution rates within a cave stream: Blowing Springs Cave, Arkansas, USA

Erosion rates within streams vary dramatically over time, as differences in discharge and sediment load enhance or inhibit erosion processes. Within cave streams, and other bedrock channels incising soluble rocks, changes in water chemistry are an important factor in determining how erosion rates will vary in both time and space. Prior studies within surface streams, springs, and caves suggest that variation in dissolved CO2 is the strongest control on variation in calcite dissolution rates. However, the controls on CO2 variation remain poorly quantified. Limited data suggest that ventilation of karst systems can substantially influence dissolved CO2 within karst conduits. However, the interactions among cave ventilation, air-water CO2 exchange, and dissolution dynamics have not been studied in detail. Here we analyze three years of time series measurements of dissolved and gaseous CO2, cave airflow velocity, and specific conductance from Blowing Springs Cave, Arkansas. We use these time series to estimate continuous calcite dissolution rates and quantify the correlations between those rates and potential physical and chemical drivers. We find that chimney effect airflow creates temperature-driven switches in airflow direction, and that the resulting seasonal changes in airflow regulate both gaseous and dissolved CO2 within the cave. As in previous studies, partial pressure of CO2 (pCO2) is the strongest chemical control of dissolution rate variability. However, we also show that cave airflow direction, rather than stream discharge, is the strongest physical driver of changes in dissolution rate, contrary to the typical situation in surface channel erosion where floods largely determine the timing and extent Preprint submitted to Journal of Hydrology May 22, 2020 of geomorphic work. At the study site, chemical erosion is typically active in the summer, during periods of cave downdraft (airflow from upper to lower entrances), and inactive in the winter, during updraft (airflow from lower to upper entrances). Storms provide only minor perturbations to this overall pattern. We also find that airflow direction modulates dissolution rate variation during storms, with higher storm variability during updraft than during downdraft. Finally, we compare our results with the limited set of other studies that have examined dissolution rate variation within cave streams and draw an initial hypothesis that evolution of cave ventilation patterns strongly impacts how dissolution rate dynamics evolve over the lifetime of karst conduits.


Introduction 1
The variation in geomorphic rates has an important influence on the 2 relationship between erosional processes and the landforms that they pro- airflow velocity and direction were measured using a Campbell Scientific where Q BS is discharge at Blowing Spring and Q LS is discharge at Little  therefore, it is likely that these rates are more accurate in natural settings. 178 The PWP equation also produces negative rates, which might suggest   is a strong correlation between specific conductance and stream discharge 225 (Q). The relationship between these parameters is explicitly displayed in 226 Figure 3 along with a 4th-order polynomial regression between log(Q) and 227 specific conductance given by where ρ in is the density of the air inside the cave, g is Earth's gravitational where D H is the hydraulic diameter of the flow path, f is the Darcy-Weisbach  The untraversable upper portions of the flow paths must also be substantially 286 smaller, because they are too small for a human to enter.

287
To make the link between airflow direction and the chimney effect mech-288 anism explicit in our further discussion, from this point on we will refer to 289 cave airflow direction as either "updraft" or "downdraft" ( Figure 5). Updraft 290 occurs during periods when the cave air is less dense than outside air (e.g.  The seasonal patterns in cave airflow and CO 2 in the air and water are well 299 aligned ( Figure 2). Additionally, there are strong relationships between CO 2 300 and cave airflow on short timescales ( Figure 6). During periods of diurnal 301 airflow reversals, CO 2 in the cave air also shows daily peaks and troughs.

302
When airflow direction switches from downdraft to updraft, cave air CO 2 303 drops suddenly to concentrations near atmospheric (∼ 500 ppm), as outside 304 air is quickly brought to the location of the sensor. When airflow switches 305 from updraft to downdraft, cave air CO 2 rises somewhat more slowly, likely 306 as a result of mixing of high and low CO 2 air within the cave atmosphere.

307
Dissolved CO 2 within the cave stream does not respond as rapidly to airflow 308 reversals as the cave air. However, the cave stream CO 2 does have a muted 309 response that has a lag of a few days ( Figure 6).   Cave air pCO 2 is high and therefore degassing of CO 2 from the cave stream is limited. Consequently, dissolved CO 2 and dissolution rates remain high along the main conduit. (b) During updraft (winter conditions), atmospheric air enters the cave through the large lower entrance and then flows upward through the high-CO 2 vadose zone. The cave air is disconnected from this high CO 2 zone and strong degassing of CO 2 occurs along the stream, reducing pCO 2 and dissolution rates. During winter storms, vertical flow of water can transport CO 2 through the vadose zone and effectively reconnect the cave stream to the CO 2 reservoir.   pCO 2 is also high and the water is undersaturated with respect to calcite.

331
Lower rates of dissolution occur during the winter months (frequently nega-332 tive PWP rates), when pCO 2 is low and the water is typically supersaturated.

333
The average of this seasonal signal is near calcite saturation (or zero disso-334 lution rate), but the stream spends slightly more time in the undersaturated 335 condition, when dissolution is active. In addition to the seasonal signal, there 336 is clear variability on daily to weekly timescales.

337
To study the chemical controls on dissolution rate variation, dissolution 338 rates averaged over daily timescales are plotted versus the two primary chem-339 ical drivers ( Figure 9): dissolved CO 2 and a proxy for dissolved load (SpC).

340
To quantify the correlations between the chemical drivers and dissolution 341 rate, we calculated Spearman's rank correlation coefficients. Both chemical 342 drivers correlate with dissolution rates (p-value<0.0001), but CO 2 is more  In addition to direct chemical drivers, dissolution rates vary as a function 348 of external physical controls that produce variations in those chemical drivers.

349
The two most important physical controls on chemical variation at the site are  To explore how dissolution rates vary during storms, we first examine rela-377 tionships between dissolved CO 2 and discharge, because CO 2 is the chemical  During the summer storm, downdraft conditions prevail, and, consequently, CO 2 concentrations in the air remain relatively high around 3000 ppm, 405 except for during two brief periods of airflow reversal that follow the storm.

406
Dissolved CO 2 is already high (4000 ppm) before the start of the event and 407 peaks around 5000 ppm during the event. Therefore, there is much less vari-408 ability of dissolved CO 2 during the summer storm than during the winter as is shown in Figure 14 for the storm events for which complete chemical 437 records exist. This suggests that cave airflow direction is an important con-438 trol on dissolution rate variation during storms, and that storm dissolution 439 rate variability is not primarily driven by dilultion. : Correlations between storm dissolution rate range and potential controls. Average airflow velocity during a storm event is highly correlated with the range in dissolution rates during the event. The range of discharge within the event is not significantly correlated with the range in dissolution rates. Data are shown for all identified storm events during the study period for which complete chemical records were available.  Covington and Vaughn, 2019), we find that the strongest chemical driver of 475 variation in dissolution rates is variation in dissolved CO 2 , which shows much 476 stronger correlation with dissolution rate at our site than does dissolved load 477 (Figure 9). In turn, dissolved CO 2 displays a strong seasonal pattern, ranging 478 from around 1000 ppm in the winter to around 5000 ppm in the summer.

479
This seasonal pattern is strongly correlated with seasonal changes in the cave 480 air CO 2 that are driven by the direction of cave airflow (Figures 2a-b and 7), it is also unclear how much ventilation might occur within the portion of the 536 aquifer that is upstream of the sump. Therefore, whereas there is a clear impact of cave ventilation on the annual CO 2 cycle, there may also be a sea-538 sonal signal driven by production. The magnitude of that production signal 539 is uncertain.

540
The mechanistic link between cave airflow direction and dissolved CO 2 541 in the stream is generated because the primary CO 2 source for the cave air   During winter storms, we hypothesize that storm water obtains CO 2 from 606 a reservoir of ground air and transports it quickly to the cave stream, produc-607 ing the CO 2 pulses that drive higher rates of variation in dissolution during 608 winter events. This produces variation in part because the winter airflow 609 regime has disconnected the cave stream from the CO 2 source (Figure 5b), 610 reduced the pCO 2 of the cave stream, and the pulse of high CO 2 has a large 611 effect. On the contrary, in the summer (downdraft) airflow regime the cave 612 air is already in contact with the ground air (Figure 5b), as the air is entering 613 the cave via the soil and vadose zone. Therefore, degassing is reduced and 614 the cave stream is maintained at high pCO 2 . Consequently, summer storms 615 produce much less variation in CO 2 within the cave stream and therefore less 616 variation in dissolution rate. This conceptual model is also supported by pre-  "well-aerated," and suggests that the cave stream is supersaturated because of ventilation and degassing of CO 2 . Therefore, it is plausible that episodic 686 storm-driven dissolution is a common pattern within highly ventilated karst 687 conduit systems, which typically have low concentrations of dissolved CO 2 .

787
Here we have categorized each study site into a single pattern/stage of 788 Figure 15, but most karst systems will contain a range of ventilation con-789 ditions within them. Therefore, the presented stages may also represent 790 spatial contrasts in dissolution rate dynamics within different portions of a 791 karst system that have different ventilation strengths. Processes such as CO 2 792 production, ventilation, and gas exchange are currently absent from numeri-793 cal models of speleogenesis. Developing and exploring mathematical models 794 for these processes would aid future understanding of the long-term inter-795 actions among ventilation, CO 2 dynamics, and calcite dissolution and how 796 they influence the rates and patterns of cave development.

Conclusions
We collected time series data from a stream cave in Arkansas to study the 799 temporal variation in calcite dissolution rates and the factors that drive them. that emerges as the primary driver of dissolution rate variability within the 809 cave stream. Dissolution rate is more strongly correlated with cave airflow 810 direction than it is with discharge, indicating that the standard framework 811 of geomorphic work partitioned by flood stage is inappropriate for this site. 812 We also find that the variations of dissolution rates during individual storm