High spatio-temporal resolution observations of crater lake temperatures at Kawah Ijen volcano, East Java, Indonesia

Abstract

The crater lake of Kawah Ijen volcano, East Java, Indonesia, has displayed large and rapid changes in temperature at point locations during periods of unrest, but measurement techniques employed to date have not resolved how the lake’s thermal regime has evolved over both space and time. We applied a novel approach for map** and monitoring variations in crater lake apparent surface (“skin”) temperatures at high spatial (∼32 cm) and temporal (every 2 min) resolution at Kawah Ijen on 18 September 2014. We used a ground-based FLIR T650sc camera with digital and thermal infrared (TIR) sensors from the crater rim to collect (1) a set of visible imagery around the crater during the daytime and (2) a time series of co-located visible and TIR imagery at one location from pre-dawn to daytime. We processed daytime visible imagery with the Structure-from-Motion photogrammetric method to create a digital elevation model onto which the time series of TIR imagery was orthorectified and georeferenced. Lake apparent skin temperatures typically ranged from ∼21 to 33 °C. At two locations, apparent skin temperatures were ∼4 and 7 °C less than in situ lake temperature measurements at 1.5 and 5-m depth, respectively. These differences, as well as the large spatio-temporal variations observed in skin temperatures, were likely largely associated with atmospheric effects such as the evaporative cooling of the lake surface and infrared absorption by water vapor and SO₂. Calculations based on orthorectified TIR imagery thus yielded underestimates of volcanic heat fluxes into the lake, whereas volcanic heat fluxes estimated based on in situ temperature measurements (68 to 111 MW) were likely more representative of Kawah Ijen in a quiescent state. The ground-based imaging technique should provide a valuable tool to continuously monitor crater lake temperatures and contribute insight into the spatio-temporal evolution of these temperatures associated with volcanic activity.

Appendix 1

Equations for heat flux terms

Short-wave radiant heat flux from the sun (q _sun , MW) was calculated according to

$$ {q}_{sun}=185+5.9\phi -0.22{\phi}^2+0.00167{\phi}^3A{10}^{-6} $$

(2)

following Linacre (1992) and Pasternack and Varekamp (1997), where Φ is latitude (8.06°) and A is lake area (395,000 m²). Long-wave radiant heat flux from the atmosphere (q _atm , MW) was calculated according to

$$ {q}_{atm}=\left(208+6{T}_a\right)\left(1+0.0034{C}^2\right)A{10}^{-6} $$

(3)

following Linacre (1992) and Pasternack and Varekamp (1997), where T _a is atmospheric temperature (°C), estimated as

$$ {T}_a=\left(27-0.008{\phi}^2\right)-0.006\kern0.28em elev $$

(4)

where elev is lake elevation (2154 m). T _a was similar to measured value on 18 September 2014 (14 °C). In Eq. 3, C is average cloud cover (octos), calculated as

$$ C=5.1946-0.23227\phi +6.7727\kern0.28em {10}^{-3}{\phi}^2-4.9495\kern0.28em {10}^{-5}{\phi}^3 $$

(5)

The short-wave radiant heat flux from the lake surface (q _rad , MW) was calculated according to the Stefan-Boltzmann law:

$$ {q}_{rad}=\varepsilon\;\sigma {T}_w^4\;A\;{10}^{-6} $$

(6)

where ε is the emissivity of the lake surface (0.98), σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴), and T _w is the skin temperature of the lake (K). For the case where a uniform T _w value (33 °C = 306 K) was assumed, A was set to 395,000 m². For the case where T _w was allowed to vary across the lake surface based on apparent skin temperatures in an orthorectified TIR image (4:08 a.m. on 18 September 2014), we (1) assumed that the apparent skin temperature distribution in this image that covered ∼40 % of the total lake area was representative of the entire area, (2) divided the total lake area by the number of apparent skin temperature observations in the orthorectified TIR image and set A equal to this value (0.1 m²), (3) calculated q _rad corresponding to each observed apparent skin temperature value and A = 0.1 m², and (4) summed these values to estimate the total q _rad value for the lake.

The evaporative heat flux from the lake surface (q _evap , MW) was calculated as a function of wind speed (u, m s⁻¹) based on Ryan et al. (1974):

$$ {q}_{evap}=\left[2.7{\left({T}_{wv}-{T}_{av}\right)}^{1/3}+3.2\kern0.28em u\right]\left({e}_w-{e}_a\right)A\kern0.28em {10}^{-6} $$

(7)

where e _w and e _a (mbar) are the saturated water and atmospheric vapor pressures at T _w and T _a , respectively. For an absolute temperature T, e is

$$ e=9.667\cdot {10}^{-6}{T}^4-1.091\cdot {10}^{-2}{T}^3+4.648\cdot {T}^2-8.856\cdot {10}^2T+6.360 $$

(8)

(Haar et al. 1984). T _wv (K) and T _av (K) are the virtual air temperatures derived from T _w and T _a , respectively. For an absolute temperature T and vapor pressure e, the virtual temperature T _v is

$$ {T}_v=T/\left(1-0.378e/{P}_a\right) $$

(9)

where P _a is the atmospheric pressure (785 mbar). For the case where a uniform T _w value (33 °C = 306 K) was assumed, A was set to 395,000 m² in Eq. 7. For the case where T _w was allowed to vary across the lake surface based on apparent skin temperatures in an orthorectified TIR image (4:08 a.m. on 18 September 2014), we calculated q _evap corresponding to each observed apparent skin temperature value and A = 0.1 m² as described above for q _rad and summed these values to estimate the total q _evap value for the lake.

For comparison, we calculated q _evap as a function of u following Hurst et al. (2012), who combined a forced convection term from Sartori (2000) with a free convection term from Ryan et al. (1974) using the Adams et al. (1990) method of the square root of the sum of squares:

$$ {q}_{evap}={\left[{\left[2.7{\left({T}_{wv}-{T}_{av}\right)}^{1/3}\right]}^2+{\left[L\left(0.00407{u}^{0.8}{X}^{-0.2}-0.01107{X}^{-1}\right)/{P}_a\right]}^2\right]}^{1/2}\left({e}_w-{e}_a\right)A\kern0.28em {10}^{-6} $$

(10)

Here, L is the latent heat of vaporization of water (2257 × 10³ J kg⁻¹) and X is the distance the wind travels across the lake (fetch = 900 m). For the case where a uniform T _w value (33 °C = 306 K) was assumed, A was set to 395,000 m² in Eq. 10. For the case where T _w was allowed to vary based on an orthorectified TIR image, we calculated q _evap corresponding to each observed apparent skin temperature value and A = 0.1 m² as described above for q _rad and summed these values to estimate the total q _evap value for the lake.

The conductive heat flux from the lake surface (q _cond , MW) was calculated according to

$$ {q}_{cond}=0.61\left[\left({T}_w-{T}_a\right)/\left({e}_w-{e}_a\right)\right]{q}_{evap} $$

(11)

(Brown et al. 1991). q _cond was determined as a function of q _evap calculated from Eqs. 9 and 10 as described above. The flux term associated with heating of meteoric water input to the lake up to the lake’s temperature (q _rain , MW) was calculated based on

$$ {q}_{rain}=f{A}_cI\left({T}_w-{T}_r\right){C}_{pw}\;{10}^{-6} $$

(12)

(Pasternack and Varekamp 1997), where f is a conversion factor (0.64 mol dm⁻³ s⁻¹), A _c is the catchment area (1.3 × 10⁶ m²), I is the average precipitation rate for Kawah Ijen for the month of September (1.7 × 10⁻³ m day⁻¹), T _r is the rain water temperature (283 K), and C _pw is the average heat capacity of water (75.42 J mol⁻¹ K⁻¹; Robie et al. 1979).