The Hydrological Regime in a Highly Acid Crater Lake: Lake Katanuma in Naruko Volcano, Japan

1. Introduction

In Japan, there exist 111 active volcanoes, which are defined by the Japan Meteorological Agency (JMA) as volcanoes erupted within ca. 10,000 yrs or at present accompanied by fumarolic activity [1]. Some of the volcanoes contain caldera lakes or crater lakes adjacent to the volcanic mountains or inside the mountains. In states of high volcanic activity, volcanic lakes could trigger limnic eruptions, lahars, phreatic eruptions, etc., as magma rises. In relation to disaster mitigation measures, much discussion about such volcanic lakes has been conducted, mainly from a geochemical viewpoint [2]. Under more quiescent volcanos, where the thermal and chemical monitoring for the lakes is often possible, it can be explored how hydrological, thermal and chemical conditions are built up in the lakes. The findings are useful for the precursor of a next eruption and the development of disaster mitigation measures. For example, thermal and chemical variations in a volcanic lake often provide an indicator of the conditions of underground heat sources connected to the lake [3,4]. Especially, in temperate to subtropical volcanic lakes, the geothermal heat flux at bottom can be estimated from a temporal change of thermal storage in the bottom layer under condition of the thermal stratification, since the downward heat transfer from lake surface is then suppressed by the strong pycnal stability [5,6].

Here, hydrological, thermal and chemical features of a highly acid crater lake under relatively high volcanic activity are clarified by in situ elaborate water quality surveys and the monitoring of meteorology and lake water’s temperature and electric conductivity. Thereby, geothermal effects on a groundwater flow connected to the lake are investigated.

2. Study Area

There are three volcanoes, Kurikoma, Naruko and Zao, in Miyagi Prefecture, Japan (Figure 1a). Naruko Volcano and Zao Volcano contain Crater Lake Katanuma and Crater Lake Okama [3,4], respectively. Lake Katanuma (38°44′0.8″ N, 140°43′28.1″ E: water surface elevation, 306 m asl (above sea level)) has the water surface area of 0.1239 km² (nearly oval shape at 460 m east-west and 320 m north-south) at the highest water level (Figure 1b). As shown by the water divide in Figure 1b, the lake has a catchment area of 0.4462 km², including the lake area. Naruko Volcano consists of an unclear caldera (ca. 7 km in diameter) and some central lava domes, surrounding the lake. Naruko Volcano erupted five times for the past 10 ka, which is presumed to have occurred at or around Lake Katanuma (URL: https://gbank.gsj.jp/volcano/cgi-bin/volcanic.cgi?id=029 (accessed on 7 May 2026)). The latest active eruption of the volcano occurred in 837 as a phreatic eruption. A geothermal area with high fumarolic activity is located on the northeastern slope, where some fumes are also observed (Figure 1b). The earth temperature in most of the geothermal area was ca. 21 °C higher than air temperature in 2017 and 2018 [7], and the fumarole temperature was 97.2 °C at maximum on 8 July 2026 (personal communication with A. Goto, Tohoku University). An artificial steam well is situated on the western shore to produce hot spring water of pH = 5–6, where stream water in the neighboring catchment is supplied using a siphon system. The Naruko Hot Spring area, ca. 1 km northwest of the lake, has many highly alkaline or highly acid hot spring sites. About two million people per year enjoy the hot spring.

A bathymetric map of the lake is shown in Figure 2, which was obtained as that at a relatively high water level at site L (Figure 1b), based on the echo sounding on 23 August 2023. The water level in Figure 2 corresponds to that just before the overflow at site O. Using the bathymetry, the lake volume and mean depth were obtained at 6.09 × 10⁵ m³ and 4.92 m, respectively. As a feature of the basin shape, a subaqueous sill exists at water depth of 8.6 m on a point ca. 100 m south-southwest of site MD1 (red square in Figure 2). Thereby, the lower basin is divided into the northwestern and southeastern parts, of which each has a maximum depth point at site MD1 (20.1 m depth) or site MD2 (12.6 m depth). Through a water pathway at site I, the lake constantly receives the mixed water (pH = 6.1–7.1) of the supplied stream water and the hot spring water produced at the steam well. Meanwhile, the increase of lake level by heavy rainfalls or snowmelt produces the overflow at site O, which produces a pool of less than 2500 m² in area on the northwestern shore.

The geology around the lake is shown in Figure 3. This is a seamless geologic map drawn on the 3D topographic map (URL: https://www.web-gis.jp/GM1000/GM_Red1/GM_Red1-012.html (accessed on 1 May 2026)). It is noted that the lacustrine sediment at less than 2.58 Ma is distributed around dacite and rhyolite of Pleistocene at less than 0.126 Ma which produced a central lava cone group. This indicates that a large caldera lake once existed and buried in mud and debris. Thereafter, an eruption of Naruko Volcano produced the lava cone group and Lake Katanuma. Consequently, the bed rock of the volcano is the lacustrine sand-gravel layer with high permeability, which is exposed at less than 340 m asl to the northwest from Mt. Kurumiga-take (Figure 1b) [8].

3. Methods

3.1. Field Observations

In order to explore geothermal and hydrothermal effects on Lake Katanuma, onboad observations and monitoring of water temperature and electric conductivity (EC) were carried out in 2023–2025. At site MD1 in Figure 2, the mooring system consisting of 11 temperature loggers (HOBO MX2201 and TidbiT v2, Onset Computer, Inc., USA; accuracies of ±0.5 °C and ±0.2 °C, respectively) and an EC logger (HOBO U24-001, Onset Computer, Inc., USA; accuracies of ±2 mS/m for EC and ±0.1 °C for temperature), which recoded water temperature and EC at 1 h interval (Figure 4a). The EC logger was set at 6 m, 7 m or 9 m above lake bottom, considering the sill’s depth (Figure 2). Similarly, nine temperature loggers were moored at site MD2 (Figure 4b).

The onboard observations were performed a few times in May–November of 2023–2025, when lake water and bottom sediment were sampled and vertical profiles of some water quality items (water temperature, electric conductivity at 25 °C (EC25), dissolved oxygen (DO) and bulk water density) were obtained at 0.1 m depth interval by using a self-recording profiler, called “RINKO-Profiler” (Advantech, Co., Ltd., Japan) (URL: https://www.jfe-advantech.co.jp/eng/products/ocean-rinko.html (accessed on 11 May 2026)). Time required for one profiling was then a few minutes. The bulk water density was obtained by using the water temperature and total dissolved solids (mg/L) from the EC25 values. The sampled water and the pore water in the sediment were chemically analyzed by using ion chromatography (type Dionex ICS-1600 (cation) and ICS-2100 (anion), Thermo Fisher Scientific Inc., Japan; URL https://www.thermofisher.com/jp/ja/home.html (accessed on 14 May 2026)). Concentrations of major ions (K⁺, Na⁺, Mg²⁺, Ca²⁺, Cl⁻, SO₄²⁻) were then measured. Meanwhile the bicarbonate ion (HCO₃⁻) concentration was obtained by using the 0.1 mol hydrochloric acid titration. During the onboad observations, it was seen that the lake water surface bubbles with volcanic gases such as H₂S and CO₂ up to ca. 100 m off the southern shore.

At site M in Figure 1b and Figure 2b, some meteorological factors (air temperature, relative humidity, air pressure, wind speed, wind direction, solar radiation, rainfall) were measured at 30 min or 1 h interval in 2023–2025. The height of the measurements was ca. 2 m above the lake water surface. These data were utilized to estimate the water budget of the lake, including water surface evaporation related to the latent heat flux. In order to determine whether the precipitation over the lake is rainfall or snowfall in winter, the air temperature at site M and the precipitation data of the Kawatabi weather station, 3.34 km east-northeast of the lake, were utilized. Daily precipitation at site M in December–March, in which some days with daily mean air temperature of less than 2 °C appear, was estimated by using a regression equation (y = 0.903x, where x and y are daily rainfalls (mm/d) at Kawatabi and site M, respectively) with the high correlation (R² = 0.970, p < 0.01) between Kawatabi and site M.

At site L, the pressure logger was set, and the lake level was obtained at 1 h interval from a difference between the air pressure plus water pressure at site L and the air pressure at site M. The lake level was then given as water depths of the logger fixed on a sandbag, and the continuity from record to record in the logger was maintained by sporadic leveling between lake level and a benchmark.

During the onboard observations, water temperature, pH and EC25 was measured at site I by a thermocouple thermometer and portable pH and EC meters (HORIBA Advanced Techno, Co., Ltd., Japan; URL: https://www.horiba.com/usa/water-quality/pocket-meters/ (accessed on 14 May 2026)). Simultaneously, the inflow through the water pathway at site I was measured by the one-point method. The outflow at site O occurred a few days as overflow from the rapid increase of lake level by heavy rainfalls (more than 50 mm/d) or snowmelt. Unfortunately, the outflow was not able to be measured because of the spontaneous occurrence of the overflow and the outflow’s large variation in a short time period.

3.2. Hydrological Budget Estimate for Lake Katanuma

In order to quantify a geothermal effect on groundwater flow in Lake Katanuma, the inflow and outflow of groundwater for the lake were evaluated by estimating hydrological and chemical budgets of the lake. Here, only the closed condition of the lake without any outflow at site O is considered. In the rainfall season, when the lake has an open water surface, the hydrological budget equation is then given in the following [3]:

V/t = (P − E)A₀ + R_in + G_in − G_out

(1)

where V is the water volume (m³), A₀ is the water surface area (m²), P is the rainfall (m/s) to the lake surface, E is the evaporation (m/s) at the lake surface, R_in is the river inflow (m³/s), and G_in and G_out are the groundwater inflow and outflow (m³/s), respectively, and t is the budget time period. The evaporation E was calculated as follows:

E = Q_E/(λρ_w)

(2)

Q_E = λρ_aC_Eu(q_s − q_a)

(3)

where Q_E is the evaporative latent heat flux (W/m²), ρ_w is the water density (kg/m³), λ is the latent heat for evaporation (J/kg), ρ_a is the air density (kg/m³), u is the wind speed (m/s), CE is dimensionless bulk transfer coefficients for latent heat flux (here, CE = 0.0014 was given as constant at 2 m above lake surface, assuming a neutral atmosphere at all times)., qa is the specific humidity of air, and qs is the saturated specific humidity at surface water temperature. Using the records at site M, the u, T_a and q_a values were also given as those at 2 m above the water surface.

Under condition of non-rainfall, Equation (1) yields:

G = G_in − G_out = V/t + EA₀ − R_in

(4)

Here, the net groundwater inflow G is provided by the calculation of water volume change and total evaporation EA₀ over the lake surface with surface water area A₀ changed following the lake level and the in situ measurement of river inflow R_in.

3.3. Chemical Budget Estimate for Lake Katanuma

The chemical budget equation for the closed lake is as follows:

Δ(C_LV)/Δt = C_RinR_in + C_FPA₀ + C_GinG_in − C_LG_out − S

(5)

where C_L is the ionic concentration (g/L) averaged over the lake volume, C_Rin, C_F, and C_Gin are the ionic concentrations (g/L) of an inflowing river, rainfall and inflowing groundwater, respectively, and S is the net depositional flux (kg/s) related to the chemical reaction of the ion. The volume-averaged ionic concentration, C_L, of the lake is given as that of groundwater outflow, since it is unknown at which depth the lake water leaks out as groundwater. The ionic concentration C_Gin of inflowing groundwater is here given by that of pore water within bottom sediment.

The magnitude of S is inferred by considering the lake water chemistry based on the ionic analysis. If a non-rainfall period is adopted as a budget period, the second term on the right side of Equation (5) is zero. Here, as an ion specifying the ionic concentration in Equation (5), an ion with a small influence of the chemical reaction was selected.

3.4. Evaluation of Groundwater Inflow and Outflow for Lake Katanuma

Under condition of non-precipitation, the simultaneous equations for Equation (5) and Equation (4) from the hydrological budget equation yield to:

G_out = (C_Gin G − D)/(C_L − C_Gin)

(6)

G_in = G_out + G

(7)

where D =Δ(C_LV)/Δt − C_RinR_in + S. The D values are given by incorporating the chemistry of the stream and lake waters into the hydrological terms.

3.5. Relation Between Groundwater Outflow and Lake Level

How groundwater outflow G_out is related to lake level is shown by applying the Darcy’s law. If G_out occurs as a confined groundwater flow, the Darcy’ law yields to the following equation:

G_out = KA_L(H₀ − H_L)/L

(8)

where K is the hydraulic conductivity (m/s) of sediment below lake bottom, L is the length of groundwater pathway, H₀ is the lake level, H_L is the water head at a spring site, and A_L is the outflowing area from the lake. Here, K, L and H_L are considered to be constant, when the spring site is at any time located at the same point. Thus, G_out holds the linear relationship with lake level H₀, if A_L is nearly constant. If H₀ is proportional to lake volume V, i.e., H₀ = gV (g, constant of proportionality),

G_out = aV − b

(9)

a º gKA_L/L, b º KA_LH_L/L

(10)

Here, both a and b are nearly constant. G_out is then given as a linear expression of lake volume V.

4. Results

4.1. Meteorology and Hydrological Response of Lake Katanuma

Time series of daily mean lake level and air temperature and diurnal precipitation for 18 April 2023–19 November 2025 are shown in Figure 5. The lake level varied with the amplitude of ca. 0.7 m at most. This amplitude is much smaller than ca. 1.5 m for Lake Kuttara [9] and ca. 6 m for Crater Lake Okama [10], of which both are of closed type without river outflow. The stream inflow at site I was very small at 0.006–0.017 m³/s from five measurements, and the evaporation at lake surface at 0.00099 m³/s on average during non-rainfall of April–September. Hence, the small amplitude of lake level variations suggests that the groundwater inflow G_in and the groundwater outflow G_out are in a near-equilibrium state quantitatively throughout the year. When the lake level is more than 2.40 m (horizontal dotted line in Figure 5), the overflow occurred at site O. However, regardless of whether there is the outflow at site O, the lake level increased by a mere 0.1–0.2 m in response to rainfalls of more than 40 mm/d. This suggests that a variation of groundwater inflow G_in is small, being independent of an increase in the infiltration of rainwater on the ground surface around the lake by heavy rainfalls. The variation of lake level is small also in January–February with relatively small precipitation and negative air temperature (Figure 5). This suggests that snowmelt by the geothermal heat around the lake is in progress even in mid-winter.

Meanwhile, as shown by Equation (8), the groundwater outflow from the lake should occur as confined groundwater flow, following the Darcy’s law, where the magnitude of outflow could exhibit a linear relationship with the lake level or lake volume.

4.2. Characteristics of Thermal and Chemical Structures of Lake Katanuma

Vertical profiles of water temperature, EC25, bulk water density and DO at site MD1, obtained by the onboad observations in 2024, are shown in Figure 6. On 22 May and 17 July, the water temperature, EC25 and water density greatly changed at three depths (or boundaries) as (a) thermocline, (b) halocline and (c) pycnocline, respectively. Thereby, the lake water is divided into the four layers of A to D. Here, the water depth of a certain boundary was defined as that with an inflection point or a maximum-change point on a vertical profile accompanied by a vertical change (per 1 m in depth) of more than 1 °C, 10 mS/m or 0.3 kg/m³. The EC25 profiles were similar in shape to the water density ones (Figure 6b,c). This indicates that the lake water stability is controlled by the EC25 rich in dissolved solids. The DO profiles then decreased greatly between A and B layers. This suggests that, during the pycnal stability, the water deoxygenated by volcanic gases from the lake bottom extends up to the boundary of A and B layers. Thus, the B to D layers were probably formed by the intrusion of groundwater through three different pathways under condition of a geothermal heat source weakened downward but dissolved solids more abundant downward. The boundaries between B and C layers are located at the water depth (8.6 m) of the subaqueous sill in Figure 2. Thus, the northwestern basin is likely to have a unique water quality at depths below the sill. The 18-September profiles indicates that the cooling at lake surface produced the mixing in the upper layer. Thereby, the boundaries between A and B layers were lost, and those between B and C layers were deepened. Meanwhile, the lowest D layer still continued, since the whole mixing was not yet established. On 22 October, the more cooing made all the boundaries disappear, and all the vertical distributions were then almost uniform, indicating that the mixing was complete and continuous in the whole lake.

Vertical profiles of water temperature, EC25, bulk water density and DO at site MD2 on the same days are shown in Figure 7. On 22 May, the relatively weak thermocline, halocline and pycnocline were located at two water depths of 2 m or less, and the lowest boundaries at 3.9–4.8 m depth were similar in depth to the upper boundaries of the B layer at site MD1. The DO distribution at site MD2 is also similar to that at site MD1 on 17 July. However, on 22 May and 18 September, the lower layer at more than 4 m depth is relatively rich in DO. This suggests that the supply of volcanic gases from lake bottom is relatively weak.

Being different from the distributions at site MD1, water temperature, EC25 and water density at site MD2 were vertically almost uniform at depths of more than 8 m (here, called “E layer”), where water temperature and EC25 were larger and smaller than at site MD1, respectively. The top of the subaqueous sill is at 8.6 m depth at the lake level of 2.40 m (Figure 2 and Figure 5). Hence, the E layer at depths of more than 8 m appears to exist separately from the C layer at site MD1. In the E layer, the groundwater heated by a geothermal heat source stronger than the C layer at site MD1 likely inflows. On 18 September and 22 October, the vertical distributions of water temperature and EC25 were similar between sites MD1 and MD2. This means that the vertical mixing due to the cooling at lake surface similarly occurred at less than 12 m in depth.

4.3. Temporal Variations of Thermal and Chemical Structures in Lake Katanuma

Using the 1-h data recorded in the mooring systems at sites MD1 and MD2, temporal variations of daily mean water temperature were obtained (Figure 8). In June–September of 2023 and 2024, the thermoclines in Figure 6 clearly exist, while, in early October—middle January of 2023 and 2024 and in late March—early April (2024) or early June (2025), the vertical mixing occurred in the whole layer. Hence, Lake Katanuma belongs to a dimictic lake accompanied by the whole mixing in spring and autumn, irrespective of the high acidity and high geothermal activity. The existence of the clear stratification and mixing indicates that the thermal structure of the lake is controlled by the net heat flux at lake surface rather than the geothermal heat input at lake bottom. In the two winters of December–March, the inverse stratification (less than 3 °C at lake surface and a little more than 4 °C at bottom) occurred, but this stratification was stronger and longer in December 2024–March 2025 than in December 2023–March 2024. This relatively strong stratification is due to the colder winter of December 2024–March 2025, as shown by the lower air temperature in Figure 5. Actually, air temperature averaged over 1 December 2024–31 March 2025 was 0.49 °C, which was lower than 1.64 °C averaged over 1 December 2023–31 March 2024.

Temporal variations of daily mean water temperature (WT) and EC25 obtained from the EC logger at 7 m (10 August 2023–17 September 2024), 9 m (19 September 2024–14 March 2025) and 6 m (17 May–19 November 2025) above lake bottom at site MD1 is shown in Figure 9. Data failure occurred for 15 March–16 May 2025. Irrespective of the three different heights above bottom, the water temperature and EC25 appear to be recorded in a continuous sequence. This is due to the relatively long existence of the C layer in the stratification season of May–September (Figure 6 and Figure 8). Every mid-September, highest water temperature and lowest EC25 occurred almost simultaneously. As shown by Figure 6, Figure 7 and Figure 8, in the stratification season, water temperature increased and EC25 decreased, while, in the mixing season of October–December and March–April or June, water temperature decreased and EC25 increased.

The largest water density at EC25 of 240–400 mS/m (equivalent to 1.23–1.94 PSU (Practical Salinity Unit)) and its water temperature are 1000.99–1001.56 kg/m³ and 3.55–3.71 °C under 1 atm, respectively [11]. In Figure 8, the inverse stratification seems to be established in the winters, irrespective of the bottom temperature at more than 4 °C. This is probably because EC25 slightly increases downward. For example, assuming that EC25 and water temperature are 380 mS/m and 1 °C at lake surface, 390 mS/m and 4 °C in the lower layer, and 400 mS/m and 4.5 °C at bottom, respectively, the water density is calculated at 1001.45, 1001.53 and 1001.55 kg/m³, respectively. This downward increase furnishes the pycnal stability in the whole layer.

Relatively large rainfall often occurred after the snowmelt season of March (Figure 5). For example, the total rainfall for 1 May–30 September 2024 occupied 67.5% of the annual precipitation in 2024. Then, the infiltrated rainwater touched with the underground geothermal heat source is thought to have intruded mainly into the lake as relatively hot but diluted groundwater. The geothermal heat source could be strongest at depths of 4–8 m (B layer) and be gradually weakened at depths of 8–16 m (C layer) and more than 16 m (D layer) (Figure 6). In the mixing season, the net heat flux at lake surface works for cooling and heating the lake in autumn and spring, respectively. In the winters of the inverse stratification, the inflow of groundwater with relatively high EC25 but low temperature seems to have prevailed (Figure 9). The EC25 value finally reached a peak around mid-January. This suggests that the inflowing groundwater reached to a state of equilibrium with lake water for EC25.

Sato [12] investigated thermal and chemical conditions of Lake Katanuma in the mixing, stratification and inverse stratification seasons of 1986–1994. During the stratification,, such a four-layer structure (or three-step structure) of water temperature and salinity as in Figure 6 was then not observed. The water temperature and salinity were vertically almost uniform at more than ca. 4 m in depth, although there existed the non-DO (H₂S rich) layer. Sato [12] also found out that, in the mixing season of March, the bottom temperature was relatively high (14.4 °C) at site MD1. However, as in Figure 8, the bottom temperature at site MD1was not high at 5–6 °C. Hence, the inflowing groundwater pathway and the spatial distribution of geothermal heat source below the lake bottom is judged to have changed after 1994. When and how these drastic changes occurred is not clear. Meanwhile, the Iwate-Miyagi Inland Earthquake of magnitude 7.2 occurred on 14 June 2008, which damaged the Naruko Hot Spring Area by seismic intensity of lower 6 (URL https://en.wikipedia.org/wiki/2008_Iwate%E2%80%93Miyagi_Nairiku_earthquake, accessed on 30 June 2026) (Figure 1b). The sedimentary structure of the lacustrine sand-gravel layer, which is the bedrock of Naruko Volcano (Figure 3), may then have changed.

5. Discussion

5.1. Heat Storage Change in Lake Katanuma

Vertical profiles of water temperature, EC25, bulk density and DO at sites MD1 and MD2 in the stratification season of 2025 are shown in Figure 10. At site MD1, the lake water is vertically divided into four layers, A–D, by three boundaries (Figure 6), while, at site MD2, lake water was nearly uniform in the layer deeper than the sill’s top (Figure 2 and Figure 7). As in Figure 6, the intrusion of groundwater with three different water quality is judged to have produced the B–D layers.

Here, by using the thermal difference between the two vertical profiles in each stratification season of 2024 and 2025, the heat storage change was calculated for each of the A–D layers and the E layer deeper than the sill’s top in the southeastern basin including site MD2. Then, the bathymetric map in Figure 2 was utilized to get the volume of each layer. It was then assumed that horizontal water temperature exhibits a same value at a certain depth (i.e., horizontal multilayer structure).

Calculated results are shown in Table 1. The heat flux was calculated by dividing the heat storage change by the area at the upper boundary of each layer. The heat flux for the whole layer of B–E was obtained by dividing the total heat storage change by the area of the boundary between the A and B layers. Of all the layers, the A layer shows the highest heat storage change, but the B layer exhibits the highest heat flux. The heat storage change in the D layer was a little negative in 2024, even though there was an increase in water temperature (Figure 6a). This is because the thermocline became deeper on 17 July.

As shown in Figure 6d and Figure 10d, only the A layer had enough DO. Hence, only the A layer is probably affected by the net heat flux at lake surface, while the lower layers including volcanic gases receive the inflow of groundwater heated geothermally. The B layer seems to receive the strongest geothermal heat because of the highest heat storage change and heat flux. In the northwestern basin (Figure 2), the deeper the layer, the weaker the geothermal heat became. The D layer little contributes to the thermal budget of the lake, although the chemical effect is very large (Figure 6b and Figure 10b). Meanwhile, the E layer in the southeastern basin appears to have an independent heat source below the bottom.

The calculated heat flux at 29.9 and 28.6 W/m² for the whole layer of B–E is comparable in magnitude to that at 29.0–35.8 W/m² in 1998–2002 by Shikano et al. [13] and 23.6 W/m² in 2022 by Goto and Chikita [14]. In Shikano et al. [13], the B–E layer structure was not observed, but the hypolimnion with vertical uniform temperature. Thus, the geothermal heat source below the bottom appears to exist stably, although the spatial distribution may have changed after 2002.

5.4. Chemistry and Its Relations to EC25 and pH

Stiff diagrams of lake surface water and pore water from the sediment, sampled at site MD1 on 28 July 2025 (Figure 10b), are shown in Figure 11. Chemical components of the waters are commonly dominated by sulfate ion, where the pore water exhibits higher acidity and EC25. This characteristic water chemistry is similar to that of the highly acid hot spring in the Naruko hot spring area, ca. 1 km northwest of Lake Katanuma (Figure 1), of which the formation mechanism is explained by Noguchi and Nakagawa [15] as follows:

“Hydrothermal water rising from deep underground (generally, a few kilometers underground) is hot, alkaline, and rich in chlorides, sulfides and other salts. However, upon reaching the surface, the high temperature causes the hydrogen sulfide, initially dissolved in sulfide form, to become free and vaporize. This vapor rises away from the hydrothermal water along with water vapor, where it is oxidized by the air to produce a large amount of sulfuric acid. This sulfuric acid then mixes with shallow groundwater, resulting in the formation of acidic springs.”

Thus, the relatively low temperature of such highly acid hot spring water as in Lake Katanuma is likely due to the mixing with shallow groundwater.

Relations between pH or EC25 and SO₄²⁻ concentration for lake water and pore water sampled on 28 July 2025 are shown in Figure 12. There exist clearly linear relationships for lake water and pore water. Thus, the in situ measurement of EC25 can provide us with both the SO₄²⁻ concentration and pH.

A 25. at site MD1 and volume-averaged EC25 is shown in Figure 13. The volume averaged EC25 was obtained by eight vertical EC25 profiles at each of sites MD1 and MD2 in 2023–2025 and the bathymetry in Figure 2, the EC logger and the volume-averaged SO₄²⁻ concentration, applying Figure 12b. Thus, selecting SO₄²⁻ as an ion specified in the chemical budget of the lake, the temporal change of total weight for SO₄²⁻ in Lake Katanuma (left side of Equation (5)) is numerically obtained from the records of the EC logger and lake level in Figure 5. It is because there is also a linear relationship between lake level and lake volume (Figure 14).

5.5. Estimate of Groundwater Inflow and Outflow for Lake Katanuma

By using Equations (6) and (7), groundwater inflow G_in and groundwater outflow G_out for Lake Katanuma were calculated on the base of daily mean data of lake level, surface water temperature and meteorology. First, considering the stability of lake level or lake volume, periods of non-precipitation for more than four days were chosen as the water budget periods. This is because the lake level varied greatly in quick response to the precipitation amount (Figure 5), which could induce a large error in calculated G_in and G_out values. For D = Δ(C_LV)/Δt − C_RinR_in + S in Equation (6), the stream inflow R_in and the stream’s SO₄²⁻ concentration C_Rin at site I ranged over 0.0019–0.017 m³/s and 2.6–9.4 mg/L, respectively, thus giving C_RinR_in = 0.015–0.089 g/s. Here, the depositional flux S with respect to SO₄² was assumed to be negligibly small, since deposits such as gypsum dihydrate (CaSO₄·2H₂O) form only a little in the lake because of the very small amount of Ca²⁺ (Figure 11). Meanwhile, the rate of change, Δ(C_LV)/Δt, in total SO₄²⁻ of the lake was calculated on the 10 g/s order. Thus, the mass flux C_RinR_in by stream inflow at site I is also neglected.

First, G_in and G_out in the mixing season were calculated, since the SO₄²⁻ concentration C_Gin for groundwater inflow G_in in Equation (6) is uniquely presumed. The budget periods, accompanied by non-rainfall of more than four days were 11–14 October 2023, 30 December 2023–2 January 2024 and 24–27 April 2025 (Figure 5 and Figure 8). Then, C_Gin was given at 4422 mg/L in the SO₄²⁻ concentration, corresponding to 395 mS/m (Figure 12a). This C_Gin value is based on the record of the EC logger at site MD1 (Figure 9), where the EC25 reached to the peak of 395 mS/m on 21 January 2024 after the mixing season and 10 January 2025 before the stratification season. The EC25 peak occurred probably because the SO₄²⁻ concentrations reached equilibrium between lake water and inflowing groundwater.

Applying this C_Gin value and the time series of Δ(C_LV)/Δt, C_L and G calculated from Figure 13 and Figure 14 and the water budget, G_out and G_in were calculated as in Table 2. Relations between lake level and the G_out values are shown in Figure 15. There exists a clear linear relationship between the two variables for the three budget periods. The negative G values at −0.017, −0.010 and −0.023 m³/s decrease lake level at 0.012 and 0.0072 and 0.016 m/day during non-precipitation, respectively. Referring to Figure 14, when a numerical value of 2.453 is added to lake level H₀ in Equation (8), the proportional constant g in Equation (10) is given at 7.932 × 10⁻⁶. Similarly, a and b are obtained at 2.415 × 10⁻⁶ and 1.202, respectively.

The G_out values in the stratification season should also hold the linear relationship with the correspondent lake levels or lake volumes. If the linearity given by G_out (m³/s) = 2.415 × 10⁻⁶ V − 1.202 in the mixing season is applied to relations between G_out and V in the stratification season, a unique unknown factor is the SO₄²⁻ concentration C_Gin of inflowing groundwater in each budget period.

The C_Gout values estimated by holding the linearity in the stratification season are shown in Table 3, and the relation between lake volume and G_out, including those in the mixing season, are shown in Figure 16a. Pore water from the sediment sampled on 28 July 2025 gave SO₄²⁻ concentrations of 2258 mg/L and 1226 mg/L at sites MD1 (19.1 m depth) and MD2 (12.5 m depth), respectively. Similarly, SO₄²⁻ concentrations of pore water at bottom depths of 0.8 m, 6.2 m and 16.2 m southwest of site MD1 were 1686 mg/L, 2527 mg/L and 2128 mg/L, respectively (Figure 2). Meanwhile, the SO₄²⁻ concentration for C_Gin was then estimated at 2241 mg/L (No. 13 in Table 3). Hence, compared with vertical profiles of 28 July 2025 (Figure 10), the groundwater inflow is considered to have occurred in the B–D layers, although G_in in each of the B–D layers is unknown. The G_out and G_in values in Figure 16a were given as Mean ± SD (standard deviation) at 0.258 ± 0.042 m³/s and 0.238 ± 0.041 m³/s, respectively, for the lake volume of 6.05 × 10⁵ ± 1.74 × 10⁴ m³. Hence, the small G (=G_in − G_out) or the small SD is considered to be one of hydrological characteristics of Lake Katanuma, which produces the high adjustability to lake level.

For comparison, a relation between G_out and lake volume for Okama Crater Lake in Zao Volcano is shown in Figure 16b [10]. There also exists the clearly linear relationship for Okama Lake. The G_out and G_in values were then obtained at 0.031 ± 0.014 m³/s and 0.018 ± 0.012 m³/s, respectively for the lake volume of 1.27 × 10⁶ ± 1.44 × 10⁵ m³. Thus, G_out and G_in in Lake Katanuma were 8.3 times and 13.6 times larger than in Okama, respectively, even though the lake volume is 48% of Okama’s volume. The much larger groundwater flow in Lake Katanuma is probably due to the high permeability (probably, the order of K = 0.1–1 m/s) of the lacustrine sand-gravel layer as bed rock. In contrast, the bedrock of Okama is pyroclastic rock with relatively low permeability (probably, the order of K= 10⁻⁴–10⁻³ m/s [16]). Thus, the bedrock geology could control the scale of a groundwater flow system in a volcanic lake.

6. Conclusions

Crater Lake Katanuma in Naruko Volcano, Japan, is dominantly rich in SO₄²⁻ with high acidity of pH = 1.8–2.2, and is characterized by the vertically three-step structure for water temperature, electric conductivity at 25 °C (EC25) and bulk water density in the stratification season of May–September. Then, in the whole lake, the larger the water temperature, the smaller the EC25. However, the step structure vanished in the mixing season of October–December and March–April, when water temperature, EC25 and bulk water density were vertically almost uniform. Meanwhile, the inverse stratification (water temperature decreases upward from ca. 4 °C at bottom) appeared in mid winters of January—February. Here, the thermal budgets in the stratification season were estimated by vertical temperature profiling and lake bathymetry. Also, in order to clarify the hydrological regime in the lake, the hydrological and chemical budgets of the lake were estimated by using the daily mean data of meteorology, lake level, water temperature and EC25 in 2023–2025. The conclusions are as follows:

(1)

The seasonal variation of the thermal structure in the lake basically follows the net heat flux at lake surface, but during the stratification, rainwater infiltration probably produced the lower three layers by the inflow of groundwater heated geothermally with volcanic gas. Then, the three layers is judged to have been produced by groundwater passing through three different pathways under condition of the geothermal heat source varied vertically. The heat source is probably centered at ca. 6 m below lake surface and diminishes downward with increasing SO₄²⁻ concentration of groundwater.

(2)

The water budget estimate in non-rainfall periods always gave the negative net groundwater inflow, meaning groundwater outflow larger than groundwater inflow. The negative net inflow offers the high adjustability to the lake level which could increase greatly in response to heavy rainfalls.

(3)

A coupling of the water budget estimate with the chemical budget estimate quantified the groundwater inflow G_in and groundwater outflow G_out in the mixing season, when the peaked SO₄²⁻ concentration in equilibrium between lake water and groundwater was given as the SO₄²⁻ concentration, C_Gin, of inflowing groundwater. The calculated G_out exhibited the linear relationship with lake level or lake volume as evidenced by the Darcy’s law.

(4)

Assuming the linearity between G_out and lake level or lake volume, G_in and G_out in Lake Katanuma were quantified also in the stratification season. Compared with the relations between G_out and lake volume for Crater Lake Okama in Zao Volcano, G_out and G_in in Lake Katanuma were 8.3 times and 13.6 times larger than in Okama, respectively, even though the lake volume is 48% of Okama’s volume. The much larger groundwater system in Lake Katanuma is probably due to the high permeability of the lacustrine sand-gravel layer as bed rock.

When and how the three groundwater pathways were built up is not yet clear, since such a step structure was not observed in 2002. The Iwate-Miyagi Inland Earthquake on 14 June 2008 may have changed the sedimentary structure of the bed rock. We need to investigate the current underground structure and groundwater distribution by a geophysical exploration, e.g., by the TEM (Transient Electromagnetic) method, which is suitable for the shallow (50–100 m) underground exploration (URL https://guidelinegeo.com/methods/transient-electromagnetics-tem/, accessed on 26 June 2026).