Geographic segmentation, spatial dependencies, and evaluation of the relative position of rain-gauges based on gridded data of meanmonthly precipitation: application in Nigeria

The aim of the study is to present a combination of techniques for (a) the spatiotemporal analysis of mean monthly gridded precipitation datasets and (b) the evaluation of the relative position of the existing rain-gauge network. The mean monthly precipitation (P) patterns of Nigeria using ∼1 km grids for the period 1950–2000 were analyzed and the position of existing rain-gauges was evaluated. The analysis was performed through: (a) correlations of P versus elevation (H ), latitude (Lat) and longitude (Lon); (b) principal component analysis (PCA); (c) Iso-Cluster and maximum likelihood classification (MLC) analysis for terrain segmentation to regions with similar temporal variability of mean monthly P; (d) use of MLC to create reliability classes of grid locations based on the mean clusters’ characteristics; and (e) analysis to evaluate the relative position of 33 rain-gauges based on the clusters and their reliability classes. The correlations of mean monthly P versus H, Lat, Lon, and PCA highlighted the spatiotemporal effects of the Inter Tropical Discontinuity phenomenon. The cluster analysis revealed 47 clusters, of which 22 do not have a rain-gauge while eight clusters have more than one rain-gauge. Thus, more rain-gauges and a better distribution are required to describe the spatiotemporal variability of P in Nigeria. doi: 10.2166/nh.2016.095 ://iwaponline.com/hr/article-pdf/49/1/107/196493/nh0490107.pdf V. G. Aschonitis (corresponding author) G. Castaldelli Department of Life Sciences and Biotechnology, University of Ferrara, Ferrara 44121, Italy E-mail: schvls@unife.it G. O. Awe Department of Crop, Soil and Environmental Sciences, Faculty of Agricultural Sciences, Ekiti State University, Ado Ekiti PMB 5363, Nigeria T. P. Abegunrin Department of Agricultural Engineering, Faculty of Engineering, Ladoke Akintola University of Technology, Ogbomoso P.M.B 4000, Nigeria K. A. Demertzi D. M. Papamichail Department of Hydraulics, Soil Science and Agricultural Engineering, Aristotle University of Thessaloniki, University Campus, Thessaloniki 54124, Greece


INTRODUCTION
The development of gridded climatic data is usually performed either using climatic models (e.g., general circulation models) (Sheffield et  The climatic regionalization/segmentation of a territory based on the spatiotemporal variation of a gridded climatic parameter and its dependency on spatial features (e.g., elevation, latitude, longitude, etc.) can further be used to evaluate the representativeness of existing meteorological stations to describe the climatic variability of adjacent territories with no observed data. This information could be used as an additional tool for the evaluation of existing networks of meteorological stations, especially for rain-gauge stations, since precipitation is the most variable and one of the most important climatic parameters. The design of the spatial structure/distribution of rain-gauge networks is very complex and efforts regarding its evaluation have been performed using satellite images (Caselles & Figure S1(a)-S1(c), respectively.

Methods of imagery analysis
A combination of three statistical methods consisting of cor- iance. The standardization was performed with the following formula: where Ps i is the raster of standardized precipitation values for the month i, P i is the raster of real precipitation values for the month i, P i max is the maximum real value of precipitation in the P i raster, and P i min is the minimum real value of precipitation in the P i raster. The standardization of the rasters was performed in the Raster Calculator while the PCA analysis was performed using the 12 monthly standardized rasters of monthly precipitation and the following toolbox in Arc-Map (Spatial Analyst> Multivariate>PCs). The specific PCA analysis produces 12 PC rasters and a text file with their monthly factor loadings and the % of variance they explain.
Cluster analysis was used to segment Nigeria into a number of distinct territories (clusters) with similar intensity and temporal variability of mean monthly precipitation.
Cluster signatures were derived by the Iso Cluster algorithm (Ball & Hall ), which uses a modified iterative optimization procedure known as the migrating means technique.
The algorithm separates all cells into a predefined number of distinct unimodal groups (clusters) in the multidimensional space of the input bands. The algorithm iteratively computes the minimum Euclidean distance when assigning each candidate cell to a cluster. The process starts with arbitrary means assigned by the software for each cluster (the number of clusters is given by the user). Every cell is assigned to the closest of these means (all in the multidimensional attribute space). New means are iteratively recalculated for each cluster based on the attribute distances of the cells that belong to the cluster (200 iterations with sampling interval of 10 pixels were used in this study). The optimal number of clusters to specify is usually unknown.
For this reason, an initial trial is performed using a high number in order to allow the algorithm to give its maximum number of stable clusters, which is smaller than the specified showed that the slope, which describes the decrease of annual precipitation per latitude unit increase, is steeper in the low latitude areas. The mean latitudinal effect for the entire country was found equal to 212 mm of P reduction per 1 W of latitude increase. Splitting Nigeria into two regions between 4 W -9 W N and 9 W -14 W N the respective rates were found to be 468 and 130 mm of P reduction per 1 W of latitude increase. The graphs between mean annual P versus longitude Lon and elevation H are also given in Figure S2 (b) and S2(c), respectively, without providing fitting analysis due to weak correlation coefficients.
The 30   This shift is also responsible for the bimodal precipitation patterns in the southern regions during the wet season. It is indicative that the monthly variation of absolute correlation for P-Lat is maximized during the onset (April-May) and cessation (October) of rainfall reaching values |R| > 0.9. The negative correlation between monthly P and elevation H is probably related to the fact that the higher altitude areas are located in the drier northern regions.
In order to further explore the monthly correlations observed in Figure 2(b), PCA was performed and the corresponding eigenvalues and factor loadings are presented in Table S1 (available with the online version of this paper). The first two PCs (PC-1 and PC-2) account for 91.7% of the total variance in the mean monthly P and they are given in Figure 3. The PC-1 map (Figure 3(a)) explains 80.3% of the total variance in the mean monthly P and amplifies the difference between August and the rest of the period of September-July (Table S1 and Figure 3(c)). The factor loadings of PC-1 (Figure 3(c)) are relatively stable during the period of September-July while   Terrain segmentation based on the spatial and seasonal variation of mean monthly rainfall Cluster analysis revealed 47 clusters and their characteristics such as percent area coverage, mean elevation and mean monthly P values are given in Table 1 while their spatial distribution is given in Figure 4(a). The levels of % confidence of classification reliability for each classified pixel are also given in Figure 4(b).
The clusters were further grouped based on P modality. The clusters 1 up to 18 present unimodal while the clusters 19 up to 47 present bimodal monthly variation of P. The clusters belonging in the bimodal group present higher precipitation in comparison to the unimodal group (Table 1) justifying the bimodal response of the maximum monthly P variation for the whole country (Figure 2(a)). The spatial threshold between the unimodal and bimodal responses of P is given in Figure 5.
The % coverage of the unimodal and bimodal clusters was found equal to 69% and 31%, respectively (Table 1), justifying the dominance of the first group in the unimodal response of the mean monthly P variation for the whole country (Figure 2(a)). The general characteristics of the modality groups are the following: • The unimodal group is divided into two subgroups where the first (code 1.1) presents a unique P maximum extreme during August and the second one (code 1.2) during September (Table 1, Figure 5).
• The bimodal group is divided into three subgroups where: (a) for the first subgroup (code 2.1), the minimum extreme, which is responsible for the bimodal rainy season, appears during July while September is the most rainy month; (b) for the second subgroup (code 2.2), the minimum extreme, which is responsible for the bimodal rainy season, appears during August while September is the most rainy month; and (c) for the third subgroup Clusters with two rain-gauges. (code 2.3), the minimum extreme, which is responsible for the bimodal rainy season, appears during August while June or July is the most rainy month (Table 1, Figure 5).
• The clusters 6,9,10,11,14,16, and 42 present a distinct geographical dispersion in two different geographical regions (e.g., see black arrows for cluster 14 in • The mean monthly values of P for each cluster (Table 1) also provide the length of the rainy season and the total rainfall during the rainy season over the different areas of of clusters with more than one station, the reliability class can provide a good criterion for selecting the most representative one.
A coarser clustering, as is described by the zones of Figure 5, can also be used to analyze stations' distribution.
In this case, it was observed that the number of stations that are located in the modality subgroup zones with codes 1.1, 1.2, 2.1, 2.2, and 2.3 were 12, 3, 3, 12, and 3, respectively (Table 2). Their distribution is generally homogeneous in the three zones with codes 1.1, 2.1, and 2.2. In the case of 1.2 zone, the number of stations per unit area is the lowest and the stations are located close to the only one station ( Figure 5). In zone 2.3 are included the clusters 46 and 47 (Figure 4(a)) which are described by the highest annual precipitation (Table 1)  In the case of other climatic parameters (e.g., temperature, solar radiation, etc.), the proposed methodology is expected to be more robust. not as a complete method to substitute for other techniques since it is based on a coarse temporal resolution (mean monthly step), which is a limiting factor for capturing climatic peculiarities that may appear at smaller time steps.
The combination of the specific methods can be