**1. Introduction**

Precipitation is an important variable in weather and climate research and many other applications. Precipitation data are needed as input for hydrological models, for flood and drought monitoring or for water management in agriculture or power generation. However, estimating precipitation accurately is difficult because of its high spatial and temporal variability. This is especially true for sub-Saharan Africa, where most of the rainfall is produced during the monsoon season by convective rainstorms, which are very localized [1,2].

Rain-gauges are the most direct way to measure precipitation. However, the gauge networks in Africa are not dense enough to derive high resolution precipitation estimates. Indeed, the rain-gauge distribution is sparse in many African regions and their number has been decreasing in recent decades [3]. During the same period, many efforts have been made to derive precipitation estimates from satellite data. Satellites do not measure precipitation directly but have the advantage of covering large areas. This is especially interesting for Africa where gauge networks are sparse and there are also almost no radar observations available.

There is an increasing number of satellite-based rainfall products, providing rainfall estimates at different spatial and temporal resolutions. Most rainfall products use additional sources of data, such as gauge estimates, for bias correction. Bias correction methods focus on correcting the intensity. However, the intensity is not the only possible error in precipitation. Rainfall events are coherent moving systems and, in the case of convective rainstorms, they are also very localized. This can lead to errors in the estimation of the position and shape of the rain events beside the errors in their intensity. For some applications, such as hydrological modeling [4,5], flash flood warnings [6] or data assimilation in a numerical weather model [7,8], detecting the correct location of the rain events can be as important as their intensity.

The position errors in weather forecast models, including precipitation, have been taken into account in the field of forecast verification. Several spatial verification approaches have been developed [9,10]. They can be divided into four categories: neighborhood, scale-decomposition (e.g., References [11–13]), object- (or feature-)based (e.g., References [14–16]) and field deformation. In this study, we focus on a method belonging to the latter category. We now give an overview of field deformation method used for weather-related variables. Field deformation methods are based on a spatial mapping or displacement that makes a field (e.g., forecast) more similar to a target field or observation. The deformation is determined by minimizing a cost function. The Feature Calibration and Alignment technique (FCA [17–19]) is one of these methods. FCA has also been used for correcting position errors in cloud or water vapor related fields in the framework of data assimilation. For instance, References [18,20] corrected position error in a numerical weather model background fields using integrated water vapor measurements from satellite. In Reference [21], the FCA is used as a prepossessing step of an ensemble-based variational assimilation scheme for (satellite) brightness temperature. Reference [22] tested this method with several types of observations—integrated water vapor, lower level pressure, brightness temperature and simulated radar reflection. Other feature alignment techniques have been developed and used in data assimilation schemes, such as Reference [23] (for simulated radar observation), References [24,25] (for some idealized cases). The FCA technique has been applied directly to rainfall data in Reference [19]. They corrected rainfall estimates derived from SSM/I data with ground-based radar estimates. They illustrated the performance of their approach for different types of rainfall events, such as Hurricane Andrew, a squall line in Oklahoma and coastal rainfall in Australia.

Some field deformation methods for spatial verification originate from image processing, such as the optical flow techniques developed in Reference [26,27] or in Reference [28] and evaluated in References [29,30]. Image warping has also been used in data assimilation frameworks. Reference [31] assimilated integrated water vapor from satellite to improve a numerical weather model forecast. However, this method requires the manual selection of pairs of points to perform the image warping. Reference [32] combined image morphing with an ensemble Kalman filter for a wild fire model. They use an automatic registration technique that only requires two fields to derive the displacement field, without any manual specification needed. Using the same morphing and registration method, a morphing fast Fourier transform (FFT) EnKF for radar precipitation is described in Reference [33]. However, this morphing FFT EnKF is not implemented and applied to rainfall data.

This present study investigates the use of the morphing approach for the position correction of rainfall estimates, using the approach proposed by References [32,33]. While the goal of Reference [33] was to derive a method to assimilate radar precipitation into a numerical weather model, we aim to correct the position error of satellite-based precipitation estimates using gauge measurements. We apply the morphing approach to real precipitation data, namely the (non-gauge adjusted) IMERG-Late estimates and the new Trans-African Hydro-Meteorological Observatory (TAHMO) gauge network.

The morphing and automatic registration methods, including the case of irregularly spaced observations, are described in Section 2. The morphing approach is applied to two cases. The first case uses synthetic rainfall events represented by ellipses (Section 3.1). The second case is a real rainfall event occurring in southern Ghana during the monsoon season (Section 3.2). Both the convergence of the automatic registration and the performance of the warping are examined in Section 4. The results of the two cases are compared and discussed in Section 5, before the conclusion in Section 6.
