Weather-type-conditioned calibration of tropical rainfall measuring mission precipitation over the South Pacific convergence zone

RESEARCH ARTICLE Weather-type-conditioned calibration of Tropical Rainfall Measuring Mission precipitation over the South Pacific Convergence Zone Óscar Mirones 1 | Joaquín Bedia 1,2 | Juan A. Fern andez-Granja 3 | Sixto Herrera 1 | Sara O. Van Vloten 4 | Andrea Pozo 4 | Laura Cagigal 4 | Fernando J. Méndez 4 1 Departamento de Matem atica Aplicada y Ciencias de la Computaci on, Universidad de Cantabria, Santander, Spain 2 Grupo de Meteorología y Computaci on, Universidad de Cantabria, Unidad Asociada al CSIC, Santander, Spain 3 Santander Meteorology Group, Institute of Physics of Cantabria IFCA, CSIC-UC, Santander, Spain 4 Geomatics and Ocean Engineering Group, Departamento de Ciencias y Técnicas del Agua y del Medio Ambiente, Universidad de Cantabria, Santander, Spain Correspondence Óscar Mirones, Santander Meteorology Group, Department of Applied Mathematics and Computer Science, University of Cantabria, 39005 Santander, Spain. Email: [email protected] Funding information AFRICULTURES, Grant/Award Number: 774652; Beach4Cast, Grant/Award Number: PID2019-107053RB-I00; CORDyS, Grant/Award Number: PID2020-116595RB-I00; INDECIS, Grant/Award Number: 690462 Abstract The South Pacific region is an area affected by characteristic precipitation patterns undergoing extreme events such as tropical cyclones and droughts. First, a daily weather typing of precipitation is presented, based on principal component analysis and k-means clustering using precipitation and atmospheric circulation variables derived from sea-level pressure and wind reanalysis fields. As a result, five weather types (WTs) are presented, able to capture distinct precipitation spatiotemporal patterns, interpretable in terms of salient regional climate features. Second, we undertake the calibration of the TRMM precipitation product using a set of rain gauge stations as reference and scaling and empirical quantile mapping (eQM) as calibration techniques. Furthermore, we build upon the weather-type classification to compare the results with a WTconditioned calibration approach. Overall, our results underpin the need of adjusting the existing TRMM biases, mostly relevant for the upper tail of their distribution, and advocate the use of correction techniques able to deal with quantile-dependent biases—such as eQM—instead of a simple scaling, in order to obtain a more realistic representation of extreme precipitation events. The conditioning has shown only a marginal added value over the simple approach, although this minor improvement may prove relevant for applications focused on extreme event analysis. Furthermore, the weather types created can be applied to a wide variety of conditioned analyses in this region. KEYWORDS conditioned calibration, extreme precipitation, k-means clustering, principal component analysis, quantile mapping Received: 21 January 2022 Revised: 20 October 2022 Accepted: 25 October 2022 Published on: 6 November 2022 DOI: 10.1002/joc.7905 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2022 The Authors. International Journal of Climatology published by John Wiley & Sons Ltd on behalf of Royal Meteorological Society. Int J Climatol. 2023;43:1193–1210. wileyonlinelibrary.com/journal/joc 1193 1|INTRODUCTION Natural disasters related to extreme hydrological events result every year in economic, human and structural losses to the vulnerable populations of the South Pacific Islands (Johnson et al., 2021). Many of these hazardous events are related with erosion and flooding and have a compound origin, during which the adverse effects of waves and tides occur simultaneously with extreme precipitation (“compound events,”see, e.g., Anderson et al., 2019), most often associated with tropical cyclone occurrence. The South Pacific region in this study is located between the Equator and 30S and 160E and 150W (Figure 1). Here, the spatiotemporal characteristics of precipitation are driven by a number of processes operating at (a) (b) FIGURE 1 (a) Map of the South Pacific Ocean basin and (b) location of the study region, encompassing a rectangular domain between 0N and −30S and 160E and 150W. In (a), the arrows provide an approximated indication of the near-surface prevalent winds; the shading represents the bands of rainfall. The dashed ellipse locates the West Pacific Warm Pool (WPWP). Adapted from Australian Bureau of Meteorology and CSIRO (2011). In addition, the stars mark the locations of Suva (Fiji) and Apia (Samoa), used as reference for the calculation of the South Pacific Convergence Zone Index (SPI, Appendix A), whose SLP differences are envisaged as a quantitative synthetic descriptor of the SPCZ state (see, e.g., Salinger et al., 2014) [Colour figure can be viewed at wileyonlinelibrary.com] 1194 MIRONES ET AL. 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License multiple scales. For instance, the Intertropical Convergence Zone (ITCZ) and the South Pacific Convergence Zone (SPCZ) are prominent circulation patterns largely affecting precipitation in the area (Australian Bureau of Meteorology and CSIRO, 2011). These features form three extensive bands of large-scale wind convergence and associated rainfall (Figure 1a) leading in their confluence to the West Pacific Warm Pool (WPWP), partially overlapping in its northwestern part with the study area. The ITCZ is a band of precipitation located just in the north of the equatorial belt and is stronger between the months of June and August (Waliser and Gautier, 1993). In turn, the SPCZ is a band of high precipitation located between the Solomon Islands and the Cook Islands, strongest between December and February (Vincent, 1995) and exhibiting a significant temporal correlation with extreme precipitation events (Griffiths et al., 2003). The western part of the SPCZ lies within the WPWP, determined by oceanic surface temperatures above 28C (De Deckker, 2016), where precipitation is abundant and nearly constant throughout the year (Wyrtki, 1989). The Pacific Warm Pool provides an important source of moisture which serves as energy for the convective activity which drives the Walker circulation and a large part of the Hadley circulation (Wang, 2004). Similarly, the SPCZ position induces variability from interannual to multidecadal timescales (Salinger et al., 2001). In addition, the West Pacific monsoon (WPM) stands out because its arrival marks a change from very dry to very wet conditions in the far west region. Furthermore, a major source of interannual variability is induced by El Niño–Southern Oscillation (ENSO; Trenberth, 1976), often described in terms of a displacement of the SPCZ diagonal axis to the northeast/ southwest depending on positive(Niño)/negative(Niña) sea-surface temperature anomalies (Folland et al., 2002). As a result, the SPCZ position is considered as a reliable indicator of atmospheric circulation changes in the South Pacific (Vincent et al., 2011). A better understanding of precipitation patterns in this vulnerable region is of utmost importance in order to develop adequate hydrological modelling and planning, allowing for the implementation of prevention plans and the design of adequate protection measures and infrastructures. To this aim, it is essential to have a historical record of reliable precipitation observations and the development of an adequate multiscalar characterization of rainfall variability (see, e.g., Pike and Lintner, 2020). The precipitation data sources to this aim include not only the local precipitation series from the rain gauge networks operating in the region (see, e.g., Greene et al., 2008), but also the pseudo-observations derived from different reanalysis products (Harvey et al., 2019) and satellite measurement mission data (Huffman et al., 2016). In contrast to rain gauge data, reanalysis and satellite estimates provide spatially continuous and homogeneous time series for an extended time period, as required for instance for running hydrological model simulation experiments at the catchment scale (e.g., Viviroli et al., 2009; Usman et al., 2022). Nevertheless, in the case of reanalysis data precipitation is not directly assimilated and largely depends on the numerical model associated to the assimilation system (Arakawa and Kitoh, 2004), which may hamper its direct application (see, e.g., Bedia et al., 2012). In the same vein, satellite estimates offer a good alternative, but they can be affected by systematic biases, which can be problematic when applying the raw data in impact studies (see, e.g., Aghakouchak et al., 2009), particularly when it comes to extreme event analysis (Sekaranom and Masunaga, 2019). As a result, it is often required a calibration of the data prior to their usage in impact modelling studies (Almazroui, 2011). In this study, we focus on the Tropical Rainfall Measuring Mission (TRMM; Huffman et al., 2016), an observational dataset widely applied for hydrology studies in the Tropics. In the framework of climate change and climate model calibration, several recent studies emphasize the importance of putting calibration in the context of relevant atmospheric processes influencing the target variables (see, e.g., Maraun et al., 2017). Although the idea originally stems out from the potential pitfalls in climate model calibration, where the risk exists of artificially altering trends and the magnitude of the climate change signal, this approach may also help to deal with biased data in other applications (e.g., in seasonal forecasting; Manzanas and Gutiérrez, 2019). For instance, although biases are typically assumed to be time-independent, they may also vary in time, and this holds true also for remote sensing data of precipitation, for which large uncertainties exist regarding the estimation of precipitation amount from radar reflectivity measurements (Simpson et al., 1996; Sekaranom and Masunaga, 2019) or infrequent satellite overpasses (Aghakouchak et al., 2009). These biases are not constant but associated to particular meteorological situations, such as a systematic overestimation for wet periods (Almazroui, 2011). In particular, this work explores the potential of a reanalysis-based weather typing to improve the statistical adjustment of satellite series to adapt their statistical properties to those of in situ observations in the most reliable way possible. To this aim, prior to calibration we perform a weather typing of precipitation and other circulation variables using a clustering algorithm on reanalysis data. MIRONES ET AL.1195 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Therefore, our approach includes synoptic-scale information from circulation fields together with their weather response (i.e., precipitation). As a result, we expect the weather types to be relevant for the description of local precipitation characteristics (Cannon, 2012). Using this technique, we extract the most representative spatiotemporal patterns, resulting in a classification of a few distinct synoptic atmospheric situations describing the main precipitation features. We also put this classification in the context of the most prominent elements of the regional rainfall climatology, affected by the varying position of the SPCZ and its influence on tropical cyclone tracks. To our knowledge, this is the first study addressing a weather-type-conditioned calibration of the TRMM precipitation product. “Conditioning”is here based on applying separate statistical corrections for each of the generated weather types (which act as data “blocks”) and then merging them together into a single calibrated time series. The main hypothesis supporting this approach is that biases might be dependent on specific atmospheric conditions which can be partially captured by weather types, thus adapting the correction factors to specific synoptic conditions. Even though sample size is reduced through conditioning, calibration with subsamples may result in a clear benefit improving the reliability of the corrected series (Reiter et al., 2018). To this aim, the conditioned calibration approach is compared against an ordinary, nonconditioned calibration, considering a set of evaluation measures which take into account relevant distributional properties of the calibrated precipitation series, including extremes. We also assess the local adjustment undertaken through the analysis of their percentile adjustment functions (PAFs; Casanueva et al., 2018), considering two popular bias adjustment techniques widely used by the climate impact communities, namely scaling and eQM. Overall, our results underpin the need of adjusting the existing TRMM biases, mostly relevant for the upper tail of their distribution, and advocate the use of correction techniques able to deal with quantile-dependent biases (such as eQM) instead of a simple scaling, in order to obtain a more realistic representation of extreme precipitation events. The WTs generated offer a useful characterization of the spatiotemporal rainfall patterns building upon relevant synoptic-scale circulation fields, and proved useful for conditioned calibration. The improvements found with the conditioned calibration are marginal, and only relevant for weather types associated with extreme events, when tropical cyclone occurrence is concentrated. Furthermore, the weather typing may prove useful in other climate impact-relevant sectors beyond hydrological studies. 2|DATA AND METHODS 2.1 |Reanalysis data The weather types were constructed using the ERA5 reanalysis fields (Hersbach et al., 2020). ERA5 provides hourly data for a number of atmospheric, land and oceanic variables since 1979 onwards at a 0.25horizontal resolution grid for the entire globe. In particular, we retrieved the precipitation, mean sea-level pressure (SLP) and northward and eastward 10-m wind component fields for the period 1979–2019. The wind fields have been included for weather typing since it is more common to use wind as a circulation variable because of the inadequacy of the geostrophic approximation in the Tropics. We performed a daily mean aggregation (daily accumulated values for precipitation). Furthermore, we computed the SLP first-order time differences (SLP diff )asthe day-to-day difference of mean daily SLP at each grid cell. The SLP diff is a relevant circulation variable which approximates the atmospheric circulation patterns for the characterization of cyclonic situations (https://forecast.weather.gov/ glossary.php?word=deepening). The climatological maps of all input variables are included in Figure A1. 2.2 |Rain gauge data The reference observations used as predictand for calibration were taken from the Pacific Rainfall Database (PACRAIN; Greene et al., 2008). The PACRAIN Database consists of daily and monthly rainfall records from a comprehensive collection of rain gauge stations scattered across atolls and islands in the South Pacific region from different sources, such as the National Institute of Water and Atmospheric Research of New Zealand (NIWA; www.niwa.cri. nz), the US National Centers for Environmental Information (NCEI; https://www.ncei.noaa.gov/), the French Polynesian Meteorological Service (https://meteo.pf), the Schools of the Pacific Rainfall Climate Experiment (SPaRCE; https://sparce.ou.edu) and the Atlas of Pacific Rainfall (Taylor, 1973). We extracted a subset of available locations within the study area (Figure 1), and from them, we retained a final set of stations compliant with the criteria of adequate temporal coverage and low number of missing data, ensuring their fitness-for-purpose for a robust calibration of the TRMM dataset. The final set of rain gauge stations is described in Table 1. 2.3 |TRMM data In this study we focus on the calibration of the Tropical Rainfall Measuring Mission 3B42 Daily product (TRMM 1196 MIRONES ET AL. 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License TMPA Precipitation L3 1 day 0.25×0.25V7; Huffman et al., 2016,https://disc.gsfc.nasa.gov/datasets/TRMM_ 3B42_Daily_7/summary). This dataset provides daily accumulated precipitation with a temporal coverage from January 1, 1998 to January 1, 2020 with a daily resolution and a spatial coverage between 50.0N to 50.0S and 180.0E to 180.0W. The TRMM data were calibrated at each PACRAIN point, by extracting the nearest grid point to each rain gauge location (Table 1). 2.4 |Cyclone track data In order to gain a closer insight into the tropical cyclone (TC) conditional probabilities of occurrence associated to each weather type, we retrieved the full TC track record within the study area from the International Best Track Archive for Climate Stewardship (IBTrACS v4.0 database; Knapp et al., 2010), an open data transnational initiative to unify the TC data held by several climate agencies, storing a harmonized database of TCs from 1841 to present at a 0.1spatial resolution and temporal resolutions ranging from 3-hourly to daily. In this work, we consider the position coordinates of TC tracks within the region for the whole analysis period 1998–2019, allowing for the calculation of TC frequency and their spatial distribution for selected time periods and/or weather types. All TC track data have been aggregated to a daily time resolution prior to TC frequency analyses. 2.5 |Weather-typing method Principal component analysis (PCA) is extensively used in climate science (Preisendorfer and Mobley, 1988)to decompose space–time fields into a set of orthogonal spatial patterns (empirical orthogonal functions [EOFs]) and their associated uncorrelated time indices (principal components [PCs]). The geometrical constraints characterizing EOFs and PCs can be very useful in practice since the covariance matrix of any subset of retained PCs is always diagonal and can drastically reduce the dimensionality of the data, coming at the cost of potential shortcomings in their interpretability (Hannachi et al., 2007). In this work, a joint PCA of all five ERA5 daily-aggregated variables (precipitation, SLP, SLP diff 10 m uand vwind components, section 2.1) was applied, in order to eliminate the linear dependence among the variables to be clustered; this may not happen if PCA is performed separately for each variable, which may result in unwanted data redundancy. After inspecting the explained variance by each PC, we kept all PCs explaining up to 80%, resulting in a 45 PC matrix for cluster analysis (further details on PCA procedure are provided in Figure A2). For illustration of the PCA results, a summary of the five first EOFs/PCs is displayed in Figure 2. The k-means clustering method was then followed for obtaining representative patterns from the PCA analysis. This is a classical method for partitioning the feature space into a predefined number of clusters (k) based on an iterative search of group centroids aimed at the maximization of cluster distances while minimizing withincluster dispersion (see, e.g., Vrac and Yiou, 2010, for an application to regional precipitation regimes). A similar classification approach was followed in previous studies in the South Pacific region for the analysis of satellitederived precipitation (Pike and Lintner, 2020) or to investigate the structure and spatiotemporal variability of the SPCZ (Vincent et al., 2011; Matthews, 2012), for instance. In order to select a suitable value for k, different models have been analysed for kvalues ranging from 4 to 8 (see, e.g., Pike and Lintner, 2020). The final choice of k=5 was a compromise between representativity of each group (at least 2 years of data in each group) and a TABLE 1 Final set of rain gauge stations from the PACRAIN Database used in this study Station ID Station name Longitude Latitude Start End % missing data Altitude NZ75400 Kolopelu (Wallis and Futuna) 178.12W 14.32S Jan 1, 1998 Jan 1, 2012 9.74 36 NZ82400 Alofi (Niue) 169.93W 19.07S Jan 1, 1998* Sep 2, 2010 2.68 59 NZ84317 Rarotonga (Cook Islands) 159.80W 21.20S Sep 28, 1999 Jan 2, 2012 11.36 4 NZ99701 Raoul Island (New Zealand) 177.93W 29.23S Jan 1, 1998* Jan 1, 2012 0.72 49 SP00646 Port Vila (Vanuatu) 168.30E 17.72S Jan 26, 2000 Jun 1, 2013 18.13 24 US14000 Aoloau (American Samoa) 170.77W 14.30S Jan 1, 1998* Dec 31, 2019* 21.72 408 US14690 Nu'uuli (American Samoa) 170.70W 14.32S Jan 1, 1998* Dec 31, 2019* 0.037 3 Note: The columns show the PACRAIN ID, which indicates the source from which the data are derived (NZ is related with NIWA, US with NCEI and SP with SPaRCE, see section 2.2), station name (and location), longitude and latitude coordinates in degrees, time coverage of the time series (start and end dates, the asterisk indicates that the original PACRAIN database contains data before/after the indicated calibration start/end period, outside the TRMM period, thus discarded in this study), percentage of missing data within the start–end period and elevation (meters above sea-level). MIRONES ET AL.1197 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License minimization of the total within-cluster variance (expressed as the total sum of squared distances to the centroid of each group instance). Further groups did not provide relevant reductions of within-group variance and yielded less representative WTs (less than 600 days for the 21-year period 1998–2019). Further detail is provided in Figure A3. The robustness of the classification was assessed by partitioning the data in four temporal blocks (or folds, namely 1979–1988, 1989–1998, 1999–2008 and 2009– 2019) following a fourfold procedure. As a result, PCA was trained on each fold and the resulting EOF was projected onto the remaining folds. This procedure was repeated four times, one for each training fold, yielding consistent results in terms of WT climatologies and precipitation seasonality (Figure 3). This analysis served as an evidence of the robustness of the weather typing, whose results were largely independent of the 10-year training period chosen. All the results presented hereafter are referred to the period 1998–2019, whose PCA has been performed using the 2009–2019 (the most recent period), thus greatly alleviating the computational cost of performing PCA on the entire 40-year period, without affecting the final WT classification. Furthermore, this period is consistent with the TRMM database availability used for the conditioned calibration study (section 2.6). Principal component analysis and clustering have been undertaken using the functions available in the R package transformeR of the climate4R open source framework for climate data analysis (Iturbide et al., 2019; https://github.com/SantanderMetGroup/climate4R). 2.6 |Bias correction and WT-conditioned methodology Here, we analyse two contrasting calibration techniques, namely empirical quantile mapping (eQM) and scaling, next described. A simple scaling of the data is the most common approach for TRMM calibration (e.g., Almazroui, 2011), being here used as a benchmarking choice. Scaling is performed on the TRMM raw data using a correction factor given by the quotient between the mean of the predictand (PACRAIN rain gauge measurements, p rg ; Table 1) and the raw TRMM measurements p trmm for a training period. As a result, the calibrated TRMM series b ptrmm are computed as b ptrmm =ptrmm Prg Ptrmm :ð1Þ Our eQM implementation is the adaptation of Themeßl et al.( 2011), based on using empirical cumulative distribution functions (ECDFs), calibrated on climatological distributions and with the predictor and the 33.64 % 44.78 %39.3 %27.26 %18.45% EOFPC 0.004 0.003 0.002 0.001 0.000 0.001 0.002 0.003 0.004 5000 0 5000 10000 0 100 200 3000 2000 1000 0 1000 2000 0 100 200 2000 0 2000 4000 0 100 200 2000 0 2000 0 100 200 5 2 0 2 5 0 100 200 FIGURE 2 Upper row: first five EOFs and accumulated total explained variance (in %). Lower row: monthly aggregated first five principal components (PCs) [Colour figure can be viewed at wileyonlinelibrary.com] 1198 MIRONES ET AL. 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License predictand the same parameters. We denote b Xt,ias the corrected time series after applying quantile mapping on daily basis (t) and each grid cell (i). The resulting corrected b Xt,iis computed as b Xt,i=ECDFrg,cal−1 doy,iECDFtrmm,cal doy,iXt,i ðÞ  ,ð2Þ where X t,i is the uncorrected value for the corresponding day and grid cell, and ECDFtrmm,cal doy,iand ECDFrg,cal doy,iare the ECDFs for TRMM and PACRAIN, respectively, corresponding to the given calibration period (cal) and day of the year (doy). In the case of the weather-type-conditioned calibration, both techniques are applied separately for each WT, being the final calibrated series the result of joining each independent calibration into a single time series encompassing the entire calibration period. 2.7 |Evaluation of calibrated series 2.7.1 | Cross-validation scheme For a proper evaluation and intercomparison of different calibration methods (scaling and eQM) and choices (WTconditioned/nonconditioned), we apply a cross-validation scheme for model fitting, in order to avoid spurious results due to artificial skill. The cross-validation method allows to properly evaluate whether the calibration 024681012141618 WT 1 2 3 4 5 Jan Feb Mar Apr Ma y Jun Jul Au g Sept Oct Nov Dec 0 50 100 150 200 250 300 350 400 Days mm·day−1 (b) (a) WT1 WT2 WT3 WT4 WT5 15 10 5 Dot Size 125 50 75 100 10ºS 20ºS Days in cluster 1 : 2076 170ºW 180 170ºE 160ºE Days in cluster 2 : 1723 Days in cluster 3 : 1846 10ºS 20ºS Days in cluster 4 : 1570 10ºS 20ºS 170ºW 180 170ºE 160ºE Days in cluster 5 : 820 n o i t a tipic er P (mm·day −1 ) FIGURE 3 (a) Precipitation climatology (1998– 2019, mmday −1 ) conditioned to each weather type (WT). The number of days falling in each WT is also indicated. The precipitation distribution for each WT is displayed in the violin plot, where the median is represented by the dots. (b) Number of days for each WT and month. The wet annual periods (calculated as the months encompassing 80% of total annual precipitation for that WT) are delimited by lines. The dot size is proportional to the total number of days affected by TCs (1998– 2019) [Colour figure can be viewed at wileyonlinelibrary.com] MIRONES ET AL.1199 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License results are consistent outside the training period, in this case using a separate test period for prediction (Efron and Gong, 1983). Here, we consider a leave-one-year out validation setup, a variation of the classical k-fold crossvalidation in which each of the ktest folds is constructed with all data from a particular year, while the remaining years are used for training. The process is repeated ktimes (k=22 years of the 1998–2019 period), yielding 22 different independent predictions which are joined together into a complete calibrated series. The same procedure was used in the case of conditioned calibration, in this case considering, for each year, the daily records belonging to each different WT separately (section 2.6). 2.7.2 | Evaluation indices and measures The performance of the calibration, understood as the ability of the different calibration methods/approaches to bring the TRMM precipitation series to the PACRAIN observed reference in terms of their statistical properties, is measured as the relative bias between the raw and calibrated series, using to this aim a number of specific indices aimed at the characterization of mean and extreme properties of precipitation, consistent the validation framework proposed in the VALUE Framework for method intercomparison (Gutiérrez et al., 2019). These indices are summarized in Table 2. The calibration methods and the leave-one-year out scheme are implemented in the calibration and empirical statistical downscaling tools available in the R package downscaleR (Bedia et al., 2020) of the climate4R framework. The different evaluation indices displayed in Table 2have been computed with the standard definitions of the VALUE Framework (Maraun et al., 2015) implemented in the R package VALUE (https://github. com/SantanderMetGroup/VALUE). 2.7.3 | Percentile adjustment functions In order to gain an insight into the way the calibration is operating on the raw TRMM data series, we constructed the Percentile Adjustment Functions PAFs associated to each calibrated series. The PAF is envisaged as a diagnostic tool for eQM displaying the magnitude of the correction applied to each of the 99 percentiles of the training data (Casanueva et al., 2018). 3|RESULTS AND DISCUSSION 3.1 |Spatiotemporal characterization of precipitation by weather types The resulting weather-type (WT) classification depicts five different states of activity of the South Pacific Convergence Zone (SPCZ) and its interaction with the West Pacific Warm Pool (WPWP; section 1), leading to distinct precipitation patterns over the SPCZ band: low precipitation states (WT1 and WT2), an intermediate type (WT3) and high activity SPCZ types, characterized by the highest rainfall amount and tropical cyclone frequency (WT4 and WT5; Figure 3a). As a result, the WTs describe the characteristic SPCZ seasonal cycle (Figure 3b), related to the salient regional climate features, such as droughts and floods. Further details on SPCZ activity and tropical cyclone affection conditioned to each WT occurrence is given in Appendix (Figure A3). All WTs (particularly WT4 and WT5) exhibit the characteristic SPCZ band, extending from SE to NW of the study area. Therefore, there is a west–east-oriented part interacting with the WPWP, and a diagonally oriented part extending into the subtropics (Vincent, 1995), driven by the convergence between the northeasterly trade winds and the southeasterly circulation ahead of the Australian anticyclones (Trenberth, 1976). While the western zone is in contact with the WPWP, the eastern part is characterized by the interactions with the troughs of the mid-latitude circulation, leading to short-term variability of regional climate features (Kiladis et al., 1989; Vincent, 1995). During the austral winter, the WPWP displaces eastwards and the SPCZ retracts (as captured by WTs 1 and 2); in turn, during summer the SPCZ expands southeastwards and eastern WPWP retreats westwards (Linsley et al., 2008, reflected in WTs 4 and 5). As a result, austral summer is characterized by a more intense rainfall and tropical cyclone (TC) activity (captured by WTs 4 and 5; Figure 3), triggered by higher sea-surface temperatures (SST) and deep convection (Takahashi and Battisti, 2007). On the other hand, during the dry season the SPCZ weakens and the spatial pattern of precipitation is TABLE 2 Summary of the validation indices and measures used in this work Code Description Type SDII Mean wet-day (≥1 mm) precipitation Index R10 Relative frequency of days with precip ≥10 mm Index P98Wet 98th percentile of wet (≥1 mm) days Index R98p_TOT Quotient of total amount above 98th percentile of wet (≥1 mm) days and total precipitation Index Relative bias Measure Note: Their codes are consistent with the VALUE reference list (http://www. value-cost.eu/validationportal/app/\#!indices). 1200 MIRONES ET AL. 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License more homogeneous across the region, reaching the dry peak between June and August (Vincent, 1995), when precipitation is mostly restricted to the northwestern part, over the Solomon Islands, while Fiji, Tonga and Cook Islands experience dry conditions as they are located in the widening zone of the SPCZ (Figure 1), weak and sparse at this point (WTs 1–3; Figure 3). The characteristic “diagonal”shape of the SPCZ band is the result of the Pacific zonal SST gradient forcing and the accumulation of wave energy over the central South Pacific (Widlansky et al., 2011), as highlighted by the spatial pattern of WT5. This pattern gradually weakens in WT4 and WT3 and it is lost in WTs 1 and 2, corresponding to quiescent SPCZ conditions. In the same vein, TC activity goes in hand with the SPCZ state and concentrates mostly in WTs 4 and 5 (Figure A4). In order to gain a deeper insight into the temporal component of each WT, we characterize their annual cycles of precipitation. To this aim, we calculated the characteristic “wet”season of each WT, defined as the continuous monthly interval in which at least 80% of precipitation occurs, relative to the mean total precipitation for that particular WT (Figure 3b). The results underpin the adequate feature separation performed by the clustering algorithm also on the temporal aspect, able to consistently capture the precipitation seasonality. 3.2 |Bias correction results The intercomparison of precipitation datasets reveals an overall low bias of the TRMM product considering the complete series 1998–2019 (Figure 4a), exhibiting a few moderate negative biases (−0.5 or lower) in the representation of the R10 index for some of the sites (Kolopelu, Alofi, Raoul Island and Aoloau). Even though the biases EQM C EQM Scaling C Scaling TRMM ERA5 SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet Kolopelu Alofi Raoul Island Rarotonga Port Vila Aoloau Nu'uuli Relat iv e Bias EQM C EQM Scaling C Scaling TRMM ERA5 SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet SDII R10 P98Wet 1.0 0.5 0.0 0.5 1.0 Kolopelu Alofi Raoul Island Rarotonga Port Vila Aoloau Nu'uuli (a) Complete (b) WT5 R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT R98p_TOT FIGURE 4 Relative bias of (raw) precipitation products (ERA5, TRMM) and calibrated TRMM w.r.t. the reference PACRAIN rain gauge observations, for the seven locations indicated in Table 1. The calibration techniques are eQM, scaling, and their respective WT-conditioned counterparts (indicated with the suffix -C). The different validation indices (Table 2) are arranged in columns, and their relative bias indicated by the colorbar (reds for negative, blue for. In (a), the results are presented for the complete 1998–2019 period. The lower panel (b) shows the same information but extracting all data values belonging to WT5 only [Colour figure can be viewed at wileyonlinelibrary.com] MIRONES ET AL.1201 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License tracks emerge, unveiling how the SPCZ modulates the TC frequency and trajectory within each WT (Figure A4). This analysis also helps to better understand the “withincluster”variability, that could be captured through weather typing by defining a larger knumber (at the cost of obtaining less likely groups and thus lower calibration robustness). Considering the results for the WTs 4 and 5, highest precipitation and TC tracks are arranged in the midwesternpartofthework,inlinewiththecycloneprone area described by Deo et al.( 2021). The TC tracks tend to displace southwards starting from a generation point located in the area of highest precipitation. The bulk of TC activity concentrates within the area of strongest SPCZ influence, with a very few exceptions. Considering the medium SPI tertile, the arrangement of the traces becomes less evident, and TC frequency is relatively lower. An eastward broadening of the SPCZ causes a sparse distribution of the TC tracks within the region, whichiscommontoboth WTs. As a result, a SPI-conditioned probability of TC activity is found within the region within each 10ºS 20ºS WT1 SPI T1 ( 1000 ) 170ºW 180º 170ºE 160ºE WT1 SPI T2 ( 700 ) WT1 SPI T3 ( 376 ) WT2 SPI T1 ( 574 ) WT2 SPI T2 ( 656 ) 10ºS 20ºS WT2 SPI T3 ( 493 ) 10ºS 20ºS WT3 SPI T1 ( 624 ) WT3 SPI T2 ( 703 ) WT3 SPI T3 ( 519 ) WT4 SPI T1 ( 421 ) WT4 SPI T2 ( 443 ) 10ºS 20ºS WT4 SPI T3 ( 706 ) 10ºS 20ºS 170ºW 180º 170ºE 160ºE WT5 SPI T1 ( 70 ) WT5 SPI T2 ( 169 ) 170ºW 180º 170ºE 160ºE WT5 SPI T3 ( 581 ) 0 2 4 6 8 10 12 14 16 18 FIGURE A4 Precipitation climatology (1998–2019, mmday −1 ) conditioned to WT and South Pacific Convergence Zone Position Index (SPI) tertile (T1 upper tertile, T2 medium tertile, T3 lower tertile). The lines depict the TC tracks occurring in each case [Colour figure can be viewed at wileyonlinelibrary.com] 1208 MIRONES ET AL. 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License EQM C EQM Scaling C Scaling TRMM ERA5 SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT EQM C EQM Scaling C Scaling TRMM ERA5 SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT EQM C EQM Scaling C Scaling TRMM ERA5 SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT (a) WT1 (e) WT5 (d) WT4 (c) WT3 (b) WT2 EQM C EQM Scaling C Scaling TRMM ERA5 SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT EQM C EQM Scaling C Scaling TRMM ERA5 SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R98p_TOT SDII R10 P98Wet R95p_TOT SDII R10 P98Wet R98p_TOT Relative Bias Kolopelu Alofi Raoul Island Rarotonga Port Vila Aoloau Nu'uuli 1.0 0.5 0.0 0.5 1.0 FIGURE A5 Relative bias of (raw) precipitation products (ERA5, TRMM) and calibrated TRMM w.r.t. the reference PACRAIN rain gauge observations (Table 1). The calibration techniques are eQM, scaling, and their respective WT-conditioned counterparts (indicated with the suffix -C). The different validation indices (Table 2) are arranged in columns, and their relative bias indicated by the colorbar. In each panel (a–e), the results are shown after extracting all data values belonging to a particular WT (WT1–WT5) only [Colour figure can be viewed at wileyonlinelibrary.com] MIRONES ET AL.1209 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License WT. Considering the most cyclone-prone WTs 4 and 5, a high probability of TC occurrence over the midwestern part of the domain (New Caledonia, Vanuatu) can be expected in below-average SPI situations, while a much higher probability of TC affection can be expected in these WTs under above-average SPI events in the central part of the domain, mostly affecting the land areas of Fiji and Tonga. APPENDIX C: VALIDATION OF TRMM CALIBRATION FOR EACH WEATHER TYPE C In this section we show the calibration evaluation results, disaggregated by weather types. The WT5 results (panel e) are already shown in Figure 4b of the paper, but it is here repeated for completeness and ease of comparison. 1210 MIRONES ET AL. 10970088, 2023, 2, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.7905 by Csic Organización Central Om (Oficialia Mayor) (Urici), Wiley Online Library on [29/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License