Mapping water vapour variability over a mountainous tropical island using InSAR and an atmospheric model for geodetic observations

Highlights

• A case study over Montserrat mapping water vapour around mountainous terrain

• GPS water vapour and its effect on refractivity for InSAR are determined.

• Slantwise liquid water, water vapour and hydrostatic delay are explored using WRF.

• The ITCZ and trade wind asymmetry are used to discuss water vapour field variance.

• We describe a simple toolbox that helps identify good InSAR pairings based on climate.

Abstract

The three dimensional distribution of water vapour around mountainous terrain can be highly variable. This variability can in turn affect local meteorological processes and geodetic techniques to measure ground surface motion. We demonstrate this general problem with the specific issues of a small tropical island, Montserrat. Over a period of 17 days in December 2014 we made observations using InSAR and GPS techniques, together with concurrent atmospheric models using the WRF code. Comparative studies of water vapour distribution and its effect on refractivity were made at high spatial resolution (300 m) over short distances (~10 km). Our results show that model simulations of the observed differences in water vapour distribution using WRF is insufficiently accurate. We suggest that better use could be made of the knowledge and observations of local water vapour conditions at different scales, specifically the Inter Tropical Convergence Zone (ITCZ), the trade wind fields and the mountain flow (~30 m) perhaps using eddy simulation. The annual perturbations of the ITCZ show that the range of humidity is approximately the same expressed as the differential phase of InSAR imaging (~100 mm). Trade wind direction and speed are particularly important at high wind speeds driving vigorous asymmetrical convection over the island's mountains. We also show that the slant angles of radar can follow distinct separate paths through the water vapour field. Our study is novel in demonstrating how synoptic-scale features and climate can advise the modelling of mesoscale systems and sub-seasonal InSAR imaging on tropical islands.

Introduction

Variation in the refractivity of the Earth's atmosphere can change the path and travel time of radiation passing through it. Making use of this behaviour contributes to boundary-layer meteorology (Stull, 1988), geodetic techniques such as Global Navigation Satellite Systems GNNS (Hofmann-Wellenhof et al., 1995) and synthetic aperture radar interferometry (InSAR) (Hanssen, 2001). Changes in refractivity are characterized by air temperature and pressure, particularly the partial pressure of water vapour (Bevis et al., 1994). Water vapour content generally increases downwards through the atmosphere and is most variable within the atmospheric boundary layer (ABL), a few kilometres thick and is the dominant reservoir of water vapour (Bengtsson, 2010).

Here we are mainly concerned with the varying refractivity of the atmosphere as it affects data collected by the InSAR method in which two phase images of the scene of interest are acquired at different times, but from very similar orbital positions, yielding coherent images of differential phase “delay.” A common goal is to acquire the differential phase corresponding to land surface motion, having systematically removed or minimised the other “noise” effects (Hanssen, 2001). Of these effects, atmospheric water vapour variability has been the most difficult to remove. This is because of its rapid decorrelation over length scales of ~100s of km and time scales of ~10s of days that are typical of Low Earth Orbit (LEO) radars used for most InSAR missions. Ways to mitigate the atmospheric noise have included independent observations of water vapour (e.g. GNSS, Li et al., 2005); the use of statistical time series methods with long datasets (e.g. Bekaert et al., 2015a, Bekaert et al., 2015b; Li et al., 2019) and models that simulate the atmosphere at the time of radar imaging (e.g. Jolivet et al., 2011, Jolivet et al., 2014). The latter is the approach we use here, which is of considerable generality but difficult to apply in practice. For example, the initial conditions for the model are hard to generate, and convection is difficult to represent without using parameterizations. We do present other relevant data (e.g. GNSS and radiosonde), but do not attempt to combine them with atmospheric modelling to find an optimal joint solution. Montserrat is fortunate in having a dense network of GPS stations and a radiosonde site at a distance of ~100 km. We use these two sources to generate water vapour variability measurements to validate the numerical model-radar approach.

Conventionally for InSAR, the atmospheric contribution to the radar delay is considered to comprise four major components: Wet Delay (WD, due to water vapour), Liquid Water Delay (LWD), Hydrostatic Delay (HSD, due to atmospheric pressure) and Ionospheric Delay (due to electron density in the area of the atmosphere affected by solar radiation) (Hanssen, 2001). Recent studies (Feng et al., 2017; Fattahi et al., 2017) have shown that the ionospheric contribution can be significant for low frequency radars (e.g. L-band, 1.27 GHz) studying large length scales (several 100 km). For our scale of study, the magnitude of ionospheric phase delay at a much higher frequency (X-band, 9.65 GHz) and a much smaller length scale (~10 km), are of much lower magnitude, allowing us to ignore that component. Hydrostatic delay variation can be significant at times of large surface pressure change (Boehm et al., 2007), in areas of great topographic relief (~5 km, Elliott et al., 2008). We choose to ignore this effect in the case of Montserrat.

Differential InSAR, in which phase difference images are created from pairs of radar images separated in time, is sensitive to the changes in liquid water in clouds and particularly water vapour content along the radar path over this time period. Differential InSAR is an increasingly valuable tool for monitoring volcanoes (e.g. Lu and Dzurisin, 2014). Differential ground motions of a few mm can be detected and modelled in terms of pressurized magma storage and eruption processes (Pritchard et al., 2018; Ebmeier et al., 2018). However, many volcanoes have substantial edifices (>1 km high) such that the radar path to the base of the volcano has to pass through more water vapour than the equivalent path to the summit of the volcano. In this way the phase difference can be strongly modulated by topography. The resulting pattern of phase differences may be very similar to surface deformation generated by a pressure source centred within or below the edifice. This potential confusion of signals has been the subject of considerable study (e.g. Massonnet and Feigl, 1998; Wadge et al., 2002; Wadge et al., 2010). This is particularly relevant for volcanoes that have high relief and which generate complex patterns of airflow associated with that relief. In these cases it is not just the topography that modulates the water vapour field but the dynamic flow of air over and around it. Here we address these processes using repeated InSAR measurements and numerical models of the delay due to atmospheric water vapour content.

The physical and temporal scales of the radar results and the steep island terrain provides a set of constraints distinct from equivalent continental scale studies (~10⁵–10⁴ km²), that tend to rely on the analysis of large radar datasets (e.g. Bekaert et al., 2015a, Bekaert et al., 2015b; Alshawaf et al., 2015). This in turn gives us the opportunity to better understand small-scale (~10³–10² km²) processes involving the distribution of water vapour. Our investigation is set in the humid tropics. This has a distinctive climate driven by the Inter Tropical Convergence Zone (ITCZ) (Schneider et al., 2014), the Low-Level Jet (Munoz et al., 2008) and their interrelationship (Laderach and Raible, 2013) It is this combination of tropical climatology, diurnal boundary layer dynamics and localised, steep topography that is clearly important but little studied and forms the innovative basis of our study. Rather than relying on ever more difficult-to – constrain initial conditions to the simulation of local delay fields, we propose that bringing to bear climatological data and insights will enable improved models to be created. We demonstrate this approach qualitatively in Fig. 1.

The objectives of this study are to:

• Understand where and when tropical water vapour originates.

• Measure and simulate the water vapour field over a small mountainous tropical volcano using InSAR phase fields, equivalent atmospheric models and GNSS (and local field data) during a 17-day campaign.

• Show that the ambient state of the ITCZ, the trade winds and the radar viewing geometry can play important roles in the variability of water vapour.

These objectives provide the structural sub-headings used in the Discussion.