It has been a vital issue to develop a method for continuous and quick estimation of the discharge rate of lava, to promote volcano research and disaster prevention planning. The discharge rate is one of the prime parameters that affects various aspects of eruptive activities. In effusive eruptions, the discharge rate is closely related to the length of lava flows (Walker 1973) and is also a critical input parameter that influences the results of lava-flow simulations (e.g., Ishihara et al. 1990; Miyamoto and Sasaki 1998). There are two ways to describe the discharge rate for effusive eruptions (Wadge 1981): the “eruption rate” is the average discharge rate throughout the activity period, and the “effusion rate” is the instantaneous discharge rate, which changes over the course of the activity. Notably, knowing the effusion rate is essential because it is closely related to the migration process of magma underground (Wadge 1981), as well as surface phenomena, including short-term events such as the growth pattern of lava domes (e.g., exogenous versus endogenous growth; Nakada et al. 1995), in addition to changes in the flow direction of lava or the formation of new effusing vents (Kaneko et al. 2019b).
Despite the importance of the effusion rate, its measurement is not straightforward. To obtain precise information on variations in the effusion rate, we need to make very complex topographic measurements over short intervals (e.g., Harris et al. 2007; Maeno et al. 2016; Nakada et al. 1999; Swanson et al. 1987). One method estimates the discharge rate based on a heat budget between heat supplied to the active flow unit by advection of lava and the heat loss from the flow surfaces (Coppola et al. 2013, 2019; Harris et al. 1997, 2007; Harris and Bologa 2009; Pieri and Bologa 1986; Wright et al. 2001). The problems with these methods are that various assumptions are required to estimate the discharge rate from low-resolution thermal infrared (TIR, e.g., 11 µm) or mid-wave infrared (MIR, e.g., 4.0 µm) satellite images, as discussed below, and the obtained discharge rate is a time-averaged value over a given period (time-averaged discharge rate) rather than an instantaneous value, that is, the effusion rate (Coppola et al. 2013, 2019; Harris et al. 2007; Harris and Bologa 2009; Wright et al. 2001). In the method proposed by Harris et al. (1997, 2007), Harris and Bologa (2009), and Wright et al. (2001), surface temperature of the active lava is regarded as uniform (Te effective radiation temperature). As Te is unknown, given a reasonable minimum–maximum temperature range (e.g., 100–500 °C), for several values of Te within this range, areas of active lava are calculated from the radiance values in the TIR images. Then, time-averaged discharge rates are calculated from the relationship between time-averaged discharge rates and the area of active lava (Pieri and Bologa 1986). In this method, however, the surface temperature (Te) of the active lava is assumed to be uniform, which is unrealistic for typical lava flows (Dragoni and Tallarico 2009). The assumption of a range of Te values also produces a wide range of volume fluxes (time-averaged discharge rates). Further, the empirical parameters relating to the rheological properties, the magma temperature, and the slope inclination need to be considered on a case-by-case basis (Harris et al. 2007; Harris and Bologa2009; Wright et al. 2001). These terms can be possible error factors. In contrast, Coppola et al. (2013, 2019) estimated the time-averaged discharge rate from the volcanic radiative power using MIR images by adopting the method for calculation of fire radiative energy used in the studies of wildfires (Wooster et al. 2003), coupled with an empirical parameter—radiant density. Calculation of the fire radiative energy is based on the fact that the ratio of total power emitted over all wavelengths to the power emitted at ~ 4.0 µm is almost constant in a temperature range of ~ 330–1230 °C. Unlike wildfires, however, a certain amount of the area of an active lava surface is considered to be below 330 °C, which can potentially cause some errors (Harris 2013).
We focused on the thermal anomaly in the 1.6-µm shortwave infrared (SWIR) images from the Himawari-8 satellite for the estimation. It is reported that in the effusive activity, thermal anomalies in the 1.6-µm satellite images show a temporal variation similar to that for the lava-effusion rate estimated by the topographic method—a positive correlation— in the 1991–1994 Unzen (Kaneko et al. 2002; Kaneko and Wooster 1999; Wooster and Kaneko 1998), the 2015 Raung (Kaneko et al. 2019a), and the 2017 Nishinoshima (Kaneko et al. 2019b) activities. If we can obtain a regression equation with sufficient accuracy between these two parameters, the effusion rate can be estimated by the satellite observation.
The method using a regression equation can simply calculate effusion rates without assuming particular temperatures or unconfirmed relationships. Especially, when similar activities continue in a volcano, once that activity’s regression equation is obtained, we can estimate effusion rate from the spectral radiance showing a thermal anomaly rather accurately, because differences in various factors, such as the magma temperature, the rheological properties, the content of crystals, the content and shape of bubbles (Llewellin and Manga 2005), or the emissivity (Rogic et al. 2019) are considered to be minimized.
As the 1.6-µm band is preferentially sensitive to high-temperature materials, such as incandescent lava (Wooster and Kaneko 1998; Wooster and Rothery 1997), the anomaly is thought to reflect the effusion of high-temperature lava near the vent, which is closely related to the instantaneous effusion rate (Kaneko et al. 2002, 2019a). By using the 1.6-µm band of Himawari-8, thus, we can obtain high-density temporal variations in the lava-effusion rate, including short-term events, by taking advantage of the high repetition rate of Himawari-8 observations. Such observational data cannot be obtained by other methods and are essential for understanding eruptive processes. The time-averaged discharge rate, determined by the method using TIR or MIR images, is not ideal for observing short-term phenomena (~ 1 h).
In this study, to estimate the effusion rate for low-viscosity lava, we developed a simple empirical method based on the relationship between the lava-effusion rate and the thermal anomaly in the 1.6-µm band measured by Himawari-8. We collected pairs of these parameters for the 2017 Nishinoshima activity and used them to obtain a regression equation. Then, this method was applied to the initial stage of the December 2019 Nishinoshima activity as a test case. The estimated effusion rate was verified by comparison with the value determined by the topographic method. Further, we used simulation software for lava flows to evaluate how the estimated effusion rate could improve the prediction of the location of hazardous areas.