## 1 Introduction
A variety of empirical models have been proposed, from linear functions [20], band ratios to log transformed regression models [21], and non-linear inverse models [22] with varying degrees of corrections applied (atmospheric, sun glint, seafloor). The evolution of empirical models has been largely linked to the chronology of satellite platforms: coarse spatial resolution using Landsat TM [13, 23, 24]; medium spatial resolution SPOT images in shallow waters [15, 25] or RapidEye in lakes [26]; and high spatial resolution with the use of commercial satellites such as WorldView [27, 28], QuickBird [29, 30] and IKONOS [31]. The first and most popular approach for deriving bathymetric estimates from remote sensing imagery was proposed by [PERSON] [20] in clear shallow waters using aerial photographs, identifying that the reflectance from the seabed is dependent on the bottom type and the water depth. Since then, a wide variety of empirical models have been proposed, although depth penetration is limited, water turbidity is an issue and the models require calibration, particularly in areas of variable bottom type. Although [32] have demonstrated an artificial neural network that is not influenced by bottom type or vegetation on the seabed. The Lyzenga method [20] is not restricted to imagery from a single satellite--imagery from Landsat TM [13, 21, 23, 24], QuickBird [29, 30], SPOT [15, 25] and WorldView-2 [27, 28] have all been employed. Nor is the source of the imagery limited to satellites--[PERSON] [33] have performed a comparison between mobile laser scanners and UAV imagery for bathymetric surveys of rivers. Due to the reduced viewing distance achievable with a UAV, this high resolution imagery can result in a ground sampling distance as low as 5 cm. Work presented by [PERSON] [30] has demonstrated that not only is the Lyzenga method [20] suitable for determining bathymetry but it is also suitable for classifying features on the sea bed such as sea grass. The methodology used in this research with respect to the remotely sensed imagery has its roots in that applied by [PERSON] and [PERSON] [21] which introduced an algorithm available in ENVI(tm) that uses a ratio of reflectance to retrieve depths from IKONOS imagery even in deep water (\(>\) 25 m) contrary to a standard linear transform algorithm. [PERSON] _et al._, [22] successfully automated the methodology of [PERSON] and [PERSON] [21], tested with IKONOS images, and implemented it as a module tool within the ArcGIS(tm) environment. For prediction model choice, we significantly extend that conducted in the related study of [PERSON] _et al._, [34], where the (spatial) geographically weighted regression (GWR) model [35] was shown to provide superior accuracy over a (non-spatial) multiple linear regression (MLR). For many spatial prediction studies, there exists a wide range of models to choose from (e.g., [36]), and as such, it is rarely sufficient to only compare two models. The skill is to choose a small but representative group of predictors, one of which can be taken as the best. In this respect, exploratory analyses with our study data indicated that the key relationship between the multibeam bathymetry and the reflectance data is not constant across the study area (_i.e._, the relationship is non-stationary), but also that significant spatial autocorrelation effects are present. Thus, GWR is still considered a good predictor choice, as it accounts for such spatially-varying relationships. However, as autocorrelation effects are also present, we aim to demonstrate a possible improvement to the study by [PERSON] _et al._, (2014) [34] above, by expanding the model comparison from two to five models. One predictor is a hybrid between GWR and kriging (GWRK) [37, 38] that captures both spatial effects.