1. Introduction
Heavy precipitation associated with tropical cyclones (TCs) can pose great risk to society through landslides and flooding (Villarini et al. 2014; Dominguez et al. 2021; Hemmati et al. 2022), as exemplified by several recent cases including Hurricane Harvey (2017) in Texas, Tropical Cyclone Idai (2019) in Mozambique, and the remnants of Hurricane Ida (2021) in New York (e.g., Risser and Wehner 2017; Emerton et al. 2020; LeComte 2022; Hemmati et al. 2022). Emergency preparedness and disaster management of impacts from extreme tropical cyclone precipitation (TCP) requires weather and climate services to provide information to decision makers several days or even weeks in advance (Beatty et al. 2019; Nkiaka et al. 2019; Hemmati et al. 2022). Examples of necessary TC forecast information include landfall probability, rain swath, and rain rates (Leroux et al. 2018; Emerton et al. 2020).
TCP is important not only because of their societal impact associated with flooding (Dominguez et al. 2021), but also because TCs contribute significantly to the total annual precipitation (P) in several tropical and subtropical regions (Skok et al. 2013; Prat and Nelson 2016; Khouakhi et al. 2017). For example, in Baja California, the Philippines, and northwestern Australia, TCs contribute 35%–50% of the total annual rainfall, measured by the ratio TCP/P (Breña-Naranjo et al. 2015; Khouakhi et al. 2017; Franco-Díaz et al. 2019). This means variability in TCP is a large part of total P variability in TC-active regions (Dominguez and Magaña 2018). Accurate and skillful forecast information of TCP on time scales beyond a few days could be used to inform water management and streamflow services (White et al. 2017; Robertson et al. 2020).
Subseasonal forecast systems have been developed in the past decade to fill the gap between the ranges covered by traditional numerical weather prediction (1–7 days) and seasonal forecasts (3–6 months) (White et al. 2017; Meehl et al. 2021; Stan et al. 2022; Domeisen et al. 2022). For example, the World Climate Research Program’s Subseasonal to Seasonal (S2S) Prediction Project and database was created and is maintained with the purpose of understanding and improving forecast skill at 2–4-week lead times (Vitart and Robertson 2018; Robertson et al. 2020). Several studies have shown that S2S forecasts have the potential to provide decision-makers with valuable information about TCs (e.g., Lee et al. 2018) but a good understanding of the skill and fidelity of models is needed to use forecasts in a meaningful way (Camargo et al. 2019), e.g., to avoid frequent false alarms.
(Re)forecasts from dynamical and statistical–dynamical models have been evaluated for their representation and prediction skill of several aspects of TC activity. For instance, the skill of S2S forecasts has been assessed for TC occurrence or frequency (TCF) (Camp et al. 2018; Vitart and Robertson 2018; Gregory et al. 2020; Befort et al. 2022), accumulated cyclone energy (ACE; Lee et al. 2020; Camargo et al. 2021; Switanek et al. 2023; Hansen et al. 2022), genesis (Lee et al. 2018; Gregory et al. 2019; Li et al. 2022), the characteristics of tracks (Camargo et al. 2021), the circulation patterns associated with TC landfalls (Xiang et al. 2022), and landfall statistics (Camp et al. 2015; Johnson et al. 2022). However, TCP has not been assessed in the S2S models.
Several recent studies evaluated TCP in general circulation models (GCMs) used for weather and seasonal forecasts as well as climate projections. At weather prediction time scales, Peatman et al. (2019) showed that a global weather prediction system, the Met Office model, underestimates TCP in the tropical western North Pacific due to too short TC lifetimes and too weak TCP over land when compared to observations. At the seasonal time scale, Zhang et al. (2019) found that models from the Geophysical Fluid Dynamics Laboratory have limited skill in reproducing the interannual variability of TCP and that the spatial distribution of TCP is determined by the distribution of TCF.
Moreover, process-based assessments of the global distribution of TCP and storm-scale (≈500 km) precipitation structure have recently been carried out in relatively high-resolution (25–50 km) models (Kim et al. 2018; Moon et al. 2020b), including simulations from phase 6 of the Coupled Model Intercomparison Project (CMIP6) activity, the High-Resolution Intercomparison Project (HighResMIP; Roberts et al. 2020; Vannière et al. 2020; Huang et al. 2021; W. Zhang et al. 2021; Moon et al. 2022). The key findings from these assessments are that in GCMs: peak precipitation rates tend to be overestimated (Kim et al. 2018; Moon et al. 2022), the mean TC precipitation rates are strongly linked with the storm intensity (Kim et al. 2018; Moon et al. 2020b), TCP rates over open ocean are better represented than over land, and higher horizontal resolution generally improves the representation of TCP (Moon et al. 2020b; W. Zhang et al. 2021).
Similar assessments of the climatological representation of TCP are required for assessing the subseasonal prediction skill of TCP in the S2S models, and this is the goal of this study. Specifically, we assess the global distribution of TCP, which is then related to the simulation of the azimuthal structure of precipitation, TC activity, and other sources of model biases that affect the simulation of TCP.
The remainder of this study is structured as follows: section 2 describes the observational and S2S datasets as well as the methodology used to evaluate the models. Then, section 3 shows how S2S models represent the global distribution of TCP and its contribution to the total annual rainfall. Next, section 4 investigates the origins of TCP biases and examines the storm-scale precipitation structure, the relationship between TC intensity and TCP, and the TCP seasonality. A summary and a discussion of the main findings are given in section 5.
2. Data and methods
a. Observational datasets
Observed TC tracks and derived statistics are obtained from the International Best Track Archive for Climate Stewardship (IBTrACS; Knapp et al. 2018) version 4 (v04r00) for the period 1998 to 2020. Following previous studies (see e.g., Tu et al. 2021), we only use records at 0000, 0300, 0600, 0900, 1200, 1500, 1800, and 2100 UTC. We have removed tropical disturbances, tropical waves, and extratropical cases (using both IBTrACS labels and all cases poleward of 40°N/S) and all storms with a lifetime maximum intensity (LMI) lower than 34 kt (1 kt ≈ 0.51 m s−1).
The observed precipitation estimates are taken from three satellite precipitation products: the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) (3B42 v7.0; Huffman et al. 2007), which include observations from the Global Precipitation Measurement (GPM) mission from 2014 to 2019, the Climate Prediction Center (CPC) morphing technique (CMORPH; Xie et al. 2017; NOAA CDR Program 2022) and the Global Precipitation Climatology Project (GPCP) v1.3 (Huffman et al. 2001; Adler et al. 2016). The data were obtained from the Frequent Rainfall Observations on Grids (FROGS) dataset repository (Roca et al. 2019), on a common 1° × 1° grid as daily mean averages. The original resolution of these datasets are 0.25° for TRMM and CMORPH and 1° for GPCP which may affect the precipitation amount estimates. The coverage period of the data spans 1998–2020 for GPCP and CMORPH and 1998–2019 for TRMM, as TMPA products were discontinued in December 2019 (Huffman 2016).
CMORPH and TRMM are available on a higher-resolution grid and higher frequency from other sources. However, we use the relatively coarse and low-frequency versions of these datasets available from FROGS to roughly match the horizontal resolution and daily frequency of the S2S data. Results from these three different datasets inform the observational uncertainty, but we mostly focus on the results from CMORPH, because the results are similar regardless of the products used.
In addition to precipitation, we use estimates for total column water (TCW). TC rainfall area and azimuthally averaged precipitation rates are strongly related to the available moisture in TCs both in observations and model simulations (Jiang et al. 2008; Guzman and Jiang 2021; Moon et al. 2022). Here we analyze TCW to evaluate whether the total precipitable water available explains model differences or biases in TCP. The observed TCW was taken from the Hamburg Ocean Atmosphere Parameters and Fluxes Satellite Data (HOAPS; Andersson et al. 2017), available on a 0.5° × 0.5° resolution, obtained from Copernicus Climate Change Service (2022).
b. The S2S dataset
The S2S database is constantly updated, as different modeling centers upgrade their model versions at their discretion (Stan et al. 2022). In this study, we use the most recent model versions with at least one year of complete reforecasts. The S2S reforecast dataset is available on a common 1.5° × 1.5° horizontal grid. A summary of the S2S models is provided in Table 1, including their names, abbreviations used in this study, as well as their main characteristics. The fields used in this study are daily accumulations of precipitation and daily mean TCW. Note that TCW is not available for all S2S models.
Summary of the S2S models and data used in this study, including their full names, abbreviations, native resolution (horizontal resolution and the number of vertical levels), the coverage period used in this study, the ensemble size, reforecast frequency, and the LMI threshold. Models were classified into low (LR), medium (MR), and high (HR) resolutions.
The TCs in the S2S models were tracked at the common grid using the methodology described in Vitart and Stockdale (2001). The algorithm has two steps. First, for each time step the algorithm finds low pressure systems with a warm core for each time step. The criteria for this selection are local minima of mean sea level pressure (SLP) with a maximum vorticity larger than a threshold (>3.5 × 10−5 s−1) and the distance between the maximum thickness between 200–1000 hPa and minimum SLP must not exceed 2°. The second step is to connect all the time steps of the detected low pressure systems into a coherent trajectory. Our analysis only considers storms that lasted at least two days. Further details of the S2S database and of the tracking methodology can be found in previous studies (Vitart 2017; Lee et al. 2018, 2020; Meehl et al. 2021; Wang et al. 2021).
Previous studies have shown that TC tracks diagnosed in global models can be sensitive to the tracking algorithm, particularly for low-resolution models (Horn et al. 2014; Zarzycki and Ullrich 2017). The uncertainty associated with the tracking algorithm has been discussed in previous studies using these tracks from the S2S dataset (Vitart and Robertson 2018; Lee et al. 2018, 2020), which highlighted how the algorithm has been specifically adjusted for the S2S models. The low resolution of the models has been taken into account by the tracker and the common grid in the models reduces the potential impact of tracking artifacts on our results (Vitart and Robertson 2018; Lee et al. 2018). Using the same tracking algorithm as previous studies from the S2S project allows the diagnosis of TCP by this study to be related to previous work regarding genesis and occurrence (Lee et al. 2018, 2020).
c. Methods
TCs from the S2S models were selected using a similar LMI threshold methodology to our treatment of the observed TCs from IBTrACS (section 2a). Only storms that reached an LMI that is comparable to the tropical storm threshold used for the observations in IBTrACS are used in this study. The LMI threshold for each model is found through quantile matching the observed and simulated intensity distributions (Camargo and Barnston 2009; Lee et al. 2018, 2020), i.e., for each model we find the LMI value that corresponds to 34 kt in observations: 18th percentile value in the LMI cumulative density function (Lee et al. 2018, their Fig. 1), see Table 1.
The IBTrACS data were interpolated to daily frequency, to match the frequency of the S2S track database (Vitart and Robertson 2018). The first track point in observations and forecasts is defined as genesis. The storm-scale precipitation structure in models and observations was analyzed using one of the NOAA’s Model Diagnostics Task Force (MDTF) packages (Kim et al. 2018; Moon et al. 2020b, 2022).
TCP is defined as the daily accumulated precipitation occurring within a radius of 500 km from the storm center, as in previous studies (Breña-Naranjo et al. 2015; Khouakhi et al. 2017; Niu et al. 2022). We also compute the average TCP rate (TCPR) as the precipitation rate area-averaged over the circle with a 500-km radius from the storm center. The analysis of the storm-scale precipitation structure and TCPR considers only TCs located in the tropics between 35°S and 35°N. The observed and simulated TCs were stratified for different storm intensities following Moon et al. (2022) in order to analyze the azimuthally averaged precipitation structure and the mean TCPR.
Model climatologies of TC activity, TCP, etc., were calculated at weekly resolution at lead times of 1–7 days (week 1), 8–14 days (week 2), etc. However, we only show results for week-2 forecasts, except where otherwise indicated and for JMA. Due to the low reforecast frequency (every 10 days) of this model, climatologies for JMA are shown for week-2 and week-3 forecasts.
The climatologies of the global distribution of TC activity and TCP are quantitatively compared to observations using two evaluation metrics: the normalized root-mean-square error (NRMSE) and the pattern correlation coefficient (PCC). The PCC is oriented such that larger values indicate a better spatial correlation between model forecasts and observations. NRMSE is a unitless quantity computed by normalizing the RMSE by the observed mean such that lower values indicate a smaller error of the model mean compared to the observed mean. These metrics have been used in previous model assessments of TCP (e.g., W. Zhang et al. 2021) and for comparisons of precipitation in general (Chen et al. 2020; Ngoma et al. 2021). Note the high agreement among the three observational datasets for the various quantities diagnosed in the following section (Table S1 in the online supplemental material).
3. Climatology of TCP
The main goal of this study is to characterize the global distribution of TCP in S2S models and understand the sources of model biases that affect how S2S models represent the temporal and spatial distribution of TCP. First, the representation of TCP and its contribution to the total annual rainfall is characterized and discussed for observations and the S2S models.
a. Global distribution of TCP
Figure 1 shows the spatial distribution of annual TCP accumulations in CMORPH and the S2S models, as well as the definitions of the TC basins. In observations, the TCP highest values occur in the western North Pacific (WNP) and eastern North Pacific (ENP) regions, reaching up to 600 mm yr−1. High values of TCP are also observed across large areas of the south Indian Ocean (SIN), the North Atlantic (ATL), and the South Pacific (SPC) basins, although the peak values are not as large as in the WNP and ENP. These results broadly agree with previous observational studies (Khouakhi et al. 2017; W. Zhang et al. 2021).
Tropical cyclone precipitation (TCP) annual accumulation (mm day−1) climatology for S2S models week-2 forecasts and observations (CMORPH, shown in the top-left panel). The pattern correlation coefficient (PCC) and the normalized root-mean-square error (NRMSE) between each model and CMORPH are shown at the bottom of each panel. The boundaries of the TC basins are shown in the HMCR model panel.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
S2S models have a good representation of the spatial distribution of TCP (Fig. 1) with an average PCC of ≈0.7 across models. However, some biases are noteworthy (see also Table S1). Forecasts from ECCC, KMA, and UKMO significantly overestimate TCP in most basins, particularly over the SIN and the SPC basins. Several (55%) models overestimate TCP in the ENP and underestimate TCP in the ATL.
Only ECCC, CNRM, KMA, and UKMO reasonably simulate the spatial pattern and magnitude of TCP in the ATL. The relatively good representation of the ATL TCP pattern in these models accounts for the relatively higher-than-average PCC. Overall, JMA and HMCR greatly underestimate TCP in most basins. In contrast, ECMWF forecasts show the highest PCC and lowest NRMSE of TCP, indicative of the best representation of the spatial distribution and magnitude of TCP among these models.
b. Total precipitation (P) and TCP/P
The analysis of total P is also relevant to our assessment of TCP. First, total P biases may be evidence that some models are generally too wet or too dry in the tropics, regardless of their TC climatology characteristics. Second, TCP biases may contribute to a significant fraction of the total P biases in regions with TCs.
Figure 2 shows that S2S models share some common biases in total P. For instance, relative to CMORPH, S2S models show wet biases in the Pacific intertropical convergence zone (ITCZ), the South Pacific convergence zone (SPCZ), and the equatorial Indian Ocean, as well as an Atlantic ITCZ southward shift bias, which agrees with previous studies (de Andrade et al. 2019). Based on the PCC and NRMSE metrics (see also Table S1), ECMWF shows the best agreement of P with CMORPH, whereas HMCR has the worst scores due to this model’s distinct dry bias.
Annual accumulated precipitation climatology in CMORPH and the S2S models for forecast week 2. The PCC and NRMSE for each model are shown in the models’ panels.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
Biases, computed as differences between forecast and CMORPH climatologies, of TCP and total P (Figs. S4 and S5), show that TCP biases are not negligible compared to total P biases. In fact, for some models, TCP biases in some regions account for more than half of total P biases, such as in the SPC, SIN, and ENP basins for ECCC, KMA, and UKMO forecasts. The biases in total P and TCP in the UKMO and KMA forecasts are very similar in the SIN and ENP basins. This similar bias can be explained by the fact that both forecast systems are run with the atmospheric component of the Met Office Unified Model (UM), and the UM has known wet biases in the equatorial Indian Ocean and east Pacific ITCZ, as described in previous studies (Williams et al. 2018; Walters et al. 2019; Jin et al. 2019; Taguela et al. 2022).
In addition to the evaluation of TCP and total P individually, assessments of TCP frequently also characterize the contribution of TCP to total P (see e.g., Skok et al. 2013; Khouakhi et al. 2017; Zhang et al. 2019; Vannière et al. 2020), through the ratio TCP/P. TCP may have biases due to the biases in the model mean state. For example, an overall wet bias in a region would lead to a positive TCP bias. Therefore, normalizing TCP by P can be considered as an effort to reduce the effect of overall wet or dry biases on TCP biases.
Figure 3 shows the climatology of TCP/P. In the observations, TCP/P reaches more than 35% in regions such as the SIN, western Australia, and the WNP and TCP/P maximizes near the Baja California peninsula, which agrees with previous studies (Skok et al. 2013; Breña-Naranjo et al. 2015; W. Zhang et al. 2021). The TCP/P biases in Fig. 3 are mostly positive (blue), except for the ATL basin, which means that in most basins TCs in these forecasts contribute a larger fraction to the annual total rainfall than observed TCs. CNRM and ECMWF are the most realistic models, both lowest NRMSE and highest PCC, to capture the contribution of TCs to total annual rainfall (see also Fig. S6 and Table S1). One exception is the excess TCP/P found in ECMWF forecasts off the western coast of Africa, which is due to a spurious cluster of Atlantic tracks, reported in Camargo et al. (2021). In CNRM, the most apparent bias is an overestimation of TCP/P in the equatorial Indian and western Pacific Oceans.
TCP/P S2S model biases (difference between model and observations) for week-2 forecasts compared to CMORPH. Note that the left color bar indicates the CMORPH (top-left panel), and the right color bar indicates all other panels that show differences between model and observations.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
Negative biases of TCP/P are found in several models over the Caribbean Sea, the Gulf of Mexico, and the Baja California peninsula. The observed large fraction of TCP/P (40%–50%) in the Baja California peninsula (Breña-Naranjo et al. 2015) is not captured by S2S models. The opposite case is seen for western Australia and Madagascar, where TCs also have a relevant contribution (Khouakhi et al. 2017), and S2S models significantly overestimate TCP/P. In these regions where the observed TC contribution is large, the biases in TCP/P may have important consequences for overall precipitation and streamflow forecasts.
TCP/P has a large seasonal variability (Villarini and Denniston 2016; Franco-Díaz et al. 2019) due to the seasonal characteristics of TC activity (Lee et al. 2018; Peatman et al. 2019; Befort et al. 2022). Figure 4 shows the seasonal cycle of TCP/P in models and observations for each basin. The observational datasets TRMM and CMORPH agree well with each other, whereas GPCP slightly underestimates the ratio TCP/P compared to the TRMM and CMORPH in all basins, likely due to the low original resolution of GPCP being unable to capture the highest TCP rates.
Monthly mean TCP/P averaged basinwide for observations and week-2 forecasts. The regions used for these averages are illustrated in the HMCR panel of Fig. 1. For each model, the correlation coefficient obtained by comparing the seasonal cycle of TCP/P to the mean of the three observational datasets, averaged for all basins, is shown in brackets.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
The S2S models capture the seasonality of TCP/P reasonably well. However, noticeable biases in the magnitude and seasonality of TCP/P are apparent and differ from model to model. In the ATL, most S2S models correctly simulate the seasonal cycle of TCP/P characterized by a sharp peak in TCP/P in September. However, ECCC and CNR-ISAC overestimate TCP/P at the beginning of the TC season, whereas CNR-ISAC and ECCC overestimate TCP/P at the end of the observed TC season. Moreover, CNR-ISAC forecasts simulate peak TCP/P in the month of October while all other models correctly simulate the maximum TCP/P occurring in September.
In the ENP, several models overestimate the magnitude of TCP/P, most prominently the NCEP forecasts. In turn, ECCC and CNR-ISAC misrepresent the seasonality of TCP since they significantly overestimate TCP/P in the early and late TC season in the ENP. Most models overestimate TCP/P near Australia and the SPC basin (Fig. 4), especially during the peak TC season where the simulated TCP/P is more than double compared to the observations. Moreover, ECCC and CMA simulate a nonzero (≥5%) contribution of TCs to total annual rainfall in the off-season (June–October).
The wet TCP bias in the SIN, as previously noted in Figs. 1 and 3, is also evident in Fig. 4. All models, except the JMA and HMCR forecasts that show a significant underestimation of TCP in all basins, significantly overestimate TCP/P in all months. The magnitude of the wet bias reaches a maximum value during the peak TC season (January–March). Another common feature in Fig. 4 is that CNR-ISAC and ECCC generally overestimate TCP/P across all basins and misrepresent the seasonality of TCP/P for several regions (SIN, ENP and NIN) by simulating TCP/P greater than 0.05 during seasons where TCs are typically not observed. Based on the mean correlation coefficient, ECMWF and UKMO are the best models at simulating the magnitude and seasonality of TCP/P, according to the correlation coefficients, despite notable biases in individual basins.
c. Multimodel mean biases
The skill of a multimodel mean ensemble (MME) has been shown to be generally higher than individual model skill for different precipitation skill scores in S2S and seasonal forecasts (Vitart et al. 1997; Palmer 2000; Bombardi et al. 2017; Vigaud et al. 2017; Gregory et al. 2020; L. Zhang et al. 2021). For this reason, the MME of TCP, P, and TCP/P were constructed to evaluate biases across the S2S model cohort. The HMCR model is not included in the MME because of its poor representation of P, TCP, and TCP/P, as shown in the previous sections.
The MME biases (Fig. 5) follow closely the main results from the analysis of individual models, i.e., the overall pattern of TCP and P biases indicate wet biases at equatorial regions and dry biases of TCP/P in the Atlantic and the northwestern coast of Mexico. Based on Fig. 5, the magnitude of the biases in TCP is roughly 50% of the total P biases in the SPC, the ENP and the SIN basins. The positive TCP/P biases in the MME also imply a relevant role for TCs in the S2S total P climatology. These results imply that TC-related biases may have important consequences for the prediction skill of the S2S models of mean or extreme total P in these regions.
Biases of P, TCP, and TCP/P for the multimodel mean ensemble (MME) for forecast weeks 1–4. Biases are computed relative to CMORPH, and hatching denotes differences where the MME mean is higher or lower than the observed interannual variability.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
The TCP climatology varies only slightly with lead time, as the overall patterns and signs of the biases remain unchanged from week 1 to week 4. The total precipitation biases grow slightly with lead time in the SPC and WNP basins whereas the TCP biases only appear to grow slightly in the SPC at week 4. TCP/P biases show no appreciable changes with lead time.
4. Sources of model TCP biases: TC activity and storm-scale TCP
The previous section shows biases in various aspects of the representation of TCP in the S2S models. These TCP biases may arise from different biases associated with the simulation of TCs including TC occurrence, the magnitude and structure of storm-scale TCP, and the average TCPR (Peatman et al. 2019; Zhang et al. 2019; Vannière et al. 2020; L. Zhang et al. 2021). This section first diagnoses relevant biases in TC activity. Then, the storm-scale structure and average precipitation per TC is analyzed. Finally, a decomposition of TCP biases illustrates how these two types of bias contribute to the TCP biases.
a. TC activity
TCP is tightly connected to TC frequency (TCF), defined as the frequency of TC occurrence, because TCF is a function of genesis frequency and location, and storm lifetime duration. These factors ultimately determine how often a region or grid point will have TCP (see e.g., Peatman et al. 2019; W. Zhang et al. 2021). The observed climatology of TCF for 1998–2020 (Fig. 6) is characterized by high activity in the WNP and ENP basins. Most S2S models overestimate TCF in the Indian Ocean (NIN and SIN), the SPC, and the Maritime Continent but they underestimate TCF in the East China Sea and the ATL basin. These biases are frequently found in 1° resolution global models (Roberts et al. 2020; Camargo et al. 2020). Globally, JMA and HMCR have too few TCs whereas CMA, CNR-ISAC, KMA, UKMO, and ECCC simulate more than double the observed global number of TCs (see also Table S2). Overall, these biases seem to agree with the results of Fig. 1 such that regions with higher TCF are also regions with too much TCP and vice versa.
(top left) Climatological annual mean count or TCF binned in a 3° × 3° grid for observations. The other panels show S2S model biases in TCF for week-2 forecasts. The dots denote differences that are larger than the observed interannual standard deviation. The annual average global number of TCs (NTCs) for each dataset is shown in brackets at the top of each panel and for each hemisphere.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
The genesis biases (Fig. S2) and track length biases (Table S3 and Fig. S3) can partially explain the track density biases. For example, a low bias in both genesis track density can be found in the Gulf of Mexico for almost all models. In the near equatorial SIN, SPC, WNP, and ENP regions of positive TCF biases are generally collocated with regions with positive genesis biases. In contrast, in the CMA, ECCC, and KMA models, the positive genesis bias is only found in the near-equatorial regions but TCF biases are positive extend to the subtropics and cover most of the basins. In turn, most models simulate TC lifetimes that are shorter (median of 5 days) than observations (median of 6 days, see Table S3).
In particular, TCs in BoM, CNRM, ECCC, and UKMO have a median lifetime 2 days shorter than observations. This bias may offset some of the positive biases in the number of tropical cyclones (NTCs) in Fig. 6. JMA forecasts show negative TCF biases due to the extremely low NTCs simulated and despite the relatively longer TC lifetimes simulated by JMA forecasts (Table S3). The genesis biases are consistent with the results of Lee et al. (2018), in which previous versions of some S2S model reforecasts (ECMWF, KMA, and CMA) were used, indicative of small changes in genesis climatology with the most recent model updates.
b. Storm-scale precipitation structure
The storm-scale precipitation structure is analyzed in this section via storm-relative azimuthal averages composited over TCs over different intensity bins, following previous studies (Vannière et al. 2020; W. Zhang et al. 2021; Moon et al. 2022). Figure 7 shows the azimuthally averaged structure of TCP in all TCs, as well as stratified for three intensity bins: ≤34, 35–45, and >55 kt. The fraction of cases in each bin is shown on the top-right corner of each panel.
Azimuthally averaged precipitation as a function of the distance from the storm center for different intensity ranges. (a) All storms, (b) <34 kt, (c) 35–45 kt, and (d) >55 kt. Only TCs over the ocean are considered. In (b)–(d), the inset panel shows the relative frequency of cases in each storm intensity interval for each dataset.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
These barplots are evidence that TCs in the S2S forecasts are, on average, too weak compared to observations (see also Fig. S1 and Lee et al. 2018). Note, for example, that most S2S model storms belong to the intensity range shown in Fig. 7b. All models struggle to simulate TCs that reach the highest observed intensities, which may affect many aspects of their representation of TCP, as will be discussed below. This low intensity bias is not surprising for these models, given the horizontal resolution of the archived S2S data (1.5°). In fact, as discussed in previous studies (Davis 2018; Moon et al. 2020a), there is an upper bound on the ability of models of relatively coarse grid spacing to represent TC intensity, as is the case for S2S models.
GPCP precipitation rates in the inner region are lower compared to the estimates from TRMM and CMORPH. The average precipitation at radii larger than 300 km in the three observational datasets is very similar, approximately coinciding with the 1.5° grid spacing. The observed and the simulated radial structure of precipitation show two distinct features: smooth radial gradients of precipitation and lack of a relatively drier eye feature. These characteristics are commonly found in observational datasets and models at resolutions of 1°–1.5° whereas relatively higher-resolution (0.25°–0.5°) models do show features like a dry eye (Vannière et al. 2020; Moon et al. 2020b, 2022).
Considering all storms (Fig. 7a), the peak rainfall near the storm center (r < 100 km) is higher in observations (TRMM and CMORPH) than in the forecasts. At larger radii (r > 300 km) most models simulate similar or even higher precipitation rates. In other words, the observed radial structure is sharper than the forecasts which have smoother radial gradients of precipitation. The two models with the coarser original grids (see Table 1), BoM and HMCR, have the smoothest radial gradients, with TCP being greater than 10 mm day−1 even at radii as large as 750 km in all panels. Since the overestimation of precipitation rates extends from 300 to 500 km in some models (ECCC, CNRM, BoM), TCP values averaged in a circle around the storm center of 500 km for these models may be similar to observations. In other words, the dry bias near the storm center would cancel the wet bias at larger radii. This possibility is examined in the next section.
Peak rainfall rates and the sharpness of the radial profile of precipitation increase with storm intensity (Figs. 7b–d). The simulated rain rates near the storm center is larger than observations for most models at intensities higher than 35 kt. In particular, in the 35–45-kt case (Fig. 7b), almost all models overestimate precipitation rates at all radii. For the strongest simulated TCs (Figs. 7c,d) there is a great overestimation of TCP relative to observed TCs of similar intensities.
The relationship of TCP with intensity is better seen in Fig. 8 which shows that average TCP in a 500-km radius generally increases with intensity. However, the increase with intensity is greater in the S2S models than in observations, particularly for BoM, CNRM, and ECCC forecasts. Therefore, Fig. 7 suggests that the underestimation of the peak precipitation rates near the storm center in all TCs (Fig. 7a) is due to too many weak storms simulated by S2S models.
Average TCPR binned by deciles of the intensity distribution, i.e., 10 bins, for observations and each model independently. For the observational datasets, the length of the error bar represents one standard deviation.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
In addition to the azimuthally averaged precipitation structure, we analyze storm-centered composite averages of TCP and TCW in each model for cases with an intensity (I) of tropical storm category (34 ≤ I ≤ 63 kt). TCW is also shown, where available, because TCP has been shown to be modulated by the environmental total available water vapor (Liu et al. 2019; Guzman and Jiang 2021) and has been used in previous TCP model assessments (Kim et al. 2018) as a process-oriented diagnostic.
Observational and model evidence suggest that total TCP as well as azimuthally averaged precipitation rates are related to the TCW (Jiang et al. 2008; Guzman and Jiang 2021; Moon et al. 2022) A reasonable hypothesis based on this evidence is that models with higher (mean or maximum) precipitation rates would also be the models with higher (mean or maximum) TCW. This possibility for the case of the S2S models is examined in Fig. 9, which shows that most models (except BoM and ECMWF) overestimate precipitation near the storm center at the TS intensity range. However, model differences in peak precipitation rates appear unrelated to peak TCW (see also Fig. S7).
Composites of precipitation (shading; mm day−1) and total column water (TCW; white contours; kg m−2) for TCs of tropical storm intensity. The observational product for the TCW is the HOAPS dataset. Composites of TCs over the ocean. Note that the four models in the bottom row do not output TCW.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
The differences in TCP appear to be more related to resolution since HR models have higher peak precipitation rates and sharper gradients of precipitation with distance to the storm center. For example, the resolution of JMA and CMA models is relatively higher and they have similar peak precipitation rates but TCW is much higher in CMA. BoM, the lowest original resolution model, has the highest values of TCW but the lowest average precipitation rates. However, ECMWF has the highest resolution, and its forecasts do not have the largest TCPR near the storm center. Therefore, neither TCW nor resolution explain intermodel differences or biases in TCP. Further investigation is needed to understand if, and how, TCP in individual cases is modulated by TCW and how the relationship is associated with each model’s representation of moisture–precipitation coupling (e.g., Rushley et al. 2018).
In short, most S2S models underestimate the average peak TCP rates near the storm center compared to observations because S2S models simulate too many weak TCs (<34 kt). In some models, this dry bias is offset by positive biases in TCP rates at relatively larger radii (r > 250 km). However, for TCs with intensities higher than 34 kt, all S2S models overestimate the TCP rates, both near the storm center and at larger radii, in agreement with previous studies (e.g., Moon et al. 2022).
c. P per TC biases
Next, this section analyses average TCP per TC using the average precipitation rate within 500 km from the storm center (TCPR) and the spatial distribution of the mean precipitation per TC. The magnitude of TCPR has been shown to differ over land and over ocean (W. Zhang et al. 2021), with land TCPR being less influenced by storm intensity and more by storm size, intensity changes and previous storm intensity history (Touma et al. 2019; Niu et al. 2022).
Figure 10 illustrates the probability density of the distribution of TCPR in models and observational datasets for land and ocean separately. TCPR is higher over ocean than over land across models and observational datasets (with the exception of CNR-ISAC), in agreement with previous studies (W. Zhang et al. 2021). The land versus ocean difference in TCPR is reversed for CNR-ISAC with higher precipitation rates over land, which is consistent with the positive TCP bias over regions such as Australia in this model.
Rain cloud plot of the distribution of area-averaged precipitation found within 500 km of the storm center (TCPR). Violin plot, boxplots, and the scatter of raw data illustrate the probability density, median, and interquartile range of (a) ocean and (b) land-only TCPR, respectively. Outliers in the boxplot are shown as black markers. The order (from left to right) of the datasets/models is from the lowest to highest values of mean TCPR.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
Approximately 65% of the S2S models underestimate TCPR compared to CMORPH and TRMM, whereas NCEP, BoM, and CNRM overestimate TCPR. These biases in average TCPR can be attributed to the radial structure of TCP (Fig. 7a) and competing biases in TCP as a function of radius. Models, such as UKMO and ECMWF, in which the underestimation of peak TCP rates dominates near the storm center have lower TCPR than observed. In contrast, in BoM, CNRM, and NCEP, the overestimation of TCP dominates at larger radii (r > 300 km) leading to an overall positive bias of TCPR. In addition, the very large values of TCPR in the CNR-ISAC (over land), CNRM, and NCEP forecasts could potentially explain their large positive biases in TCP and TCP/P (Figs. 1 and 3).
In observations, TCP also has significant spatial variability, i.e., regional averages of TCP show differences that are unrelated to storm intensity differences (Lavender and McBride 2021), which has been linked to different environmental conditions of each basin (Lin et al. 2015; Tu et al. 2021; Guzman and Jiang 2021). For this reason, the spatial distribution of the average TCP per TC in S2S models is evaluated by computing the ratio of the mean annual accumulated TCP to the mean annual frequency of TCP occurring at each grid point (Peatman et al. 2019; L. Zhang et al. 2021). Following Vannière et al. (2020), the frequency of TCP occurrence is defined as the annual sum of days in which a grid point is found within 500 km of a TC, which we refer to as TCF500. The calculation of TCF500 is similar to the standard TCF except that all grid points within 5° are counted, not just the closest one.
Therefore, the global distribution of the mean ratio TCP/TCF500 in Fig. 11 illustrates the mean precipitation for a given grid point for each time a TC was within 500 km. Note that grid points were considered only if the climatological TCF500 is higher than 0.25 (NTC yr−1). The observed distribution of TCP/TCF500 shows that regions such as Baja California and the subtropical Atlantic are characterized by the lowest TCP/TCF500 rates (10 mm per TC) whereas the highest rates are found in the WNP and the SPC basins (40–50 mm per TC). The observed spatial distribution of this quantity agrees qualitatively with the results of Lavender and McBride (2021). The interbasin differences of TCP in the S2S models are characterized by larger values of TCP/TCF500 in the near-equatorial Indian and western Pacific Oceans and lowest values in the subtropical ENP and ATL basins, which broadly agrees with observations.
Climatology of the ratio of TCP/TCF (mm per TC). Both TCP and TCF are calculated for occurrences in a 500-km radius and only grid points with a TCF500 higher than 0.25 NTC yr−1 are plotted. The NRMSE and PCC are only computed for matching valid grid points.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
Forecasts from CNRM, NCEP, and BoM overestimate (NRMSE > 0.5) the TCP/TCF500, whereas ECCC, ECMWF, and UKMO reasonably simulate both the spatial distribution and magnitude of this quantity (NRMSE < 0.4 and PCC > 0.5). CNR-ISAC clearly overestimates TCP/TCF500 over land such as Australia and Central America, which explain the positive biases of TCP (Fig. 10). The best scores (PCC and NRMSE) for TCP/TCF500 are found for ECMWF and UKMO forecasts, which means that these models have the potential to have the lowest biases in TCP if they had a perfect representation of TCF. The forecasts from CNRM, BoM, and NCEP show a clear latitudinal dependency in TCP/TCF500, which is higher near the equator compared to subtropical latitudes, a feature that is not seen in observations.
The zonal-mean values of TCP/TCF500 (Fig. 12) for models and observations exhibit a meridional structure, which is characterized by a maximum TCP/TCF500 at about 10°N/S of the equator and slightly lower values at both equatorial and subtropical latitudes. The lower values of TCP/TCF500 at equatorial latitudes in observations and several S2S models are likely due to the average larger distances to typical storm centers leading to a lower value of TCP for each TC, as TCs typically do not occur very close to the equator. In the latitude band of 10°S–10°N all models tend to overestimate TCP/TCF500.
Zonal mean of the TCP/TCF500, as in Fig. 11.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
The forecasts from BoM, CNRM, and NCEP show the opposite meridional structure to observations, i.e., the largest rates of TCP/TCF500 in these models are found at equatorial regions. The difference of the average TCP/TCF500 at equatorial latitudes compared to the subtropics can be more than 30 mm NTC−1 which corresponds to about 100% difference. The fact that these models are also the wettest models (Fig. 10) may be related to this overestimation of the average TCP per TC count near the equator, which is investigated in the following section.
d. Bias decomposition
The first term on the right-hand side of Eq. (1) represents what the TCP bias would be if the TCP/TCF500 field was perfectly represented by the models. The second term measures what the TCP bias would be if the model had a perfect spatial distribution of TCF. Figure S8 illustrates this decomposition for CNRM, which has notable biases in both TC occurrence and storm-scale precipitation structure.
The results of the decomposition for all models (Fig. 13) shows that, for most models, the TC frequency bias dominate the contribution to the TCP biases. The TCP/TCF500 contribution is generally smaller and contributes significantly only in a few basins for a few models. In CNRM, for example, the positive TCP/TCF500 contribution in the SIN and equatorial WNP basins is comparable to the contribution from frequency biases. Other cases where the TCP/TCF500 biases are comparable to the frequency bias are the wet biases in the ENP and the equatorial Indian Ocean diagnosed in the NCEP, CNR-ISAC, UKMO, and KMA forecasts. In these cases, the TCP/TCF500 contributes a significant fraction of the total TCP biases.
Decomposition of annual-mean TCP biases (mm yr−1) in S2S models due to biases in (left) TC frequency and biases in (center) mean precipitation per TC and (right) the total estimate.
Citation: Weather and Forecasting 38, 9; 10.1175/WAF-D-23-0029.1
Nevertheless, for the models with the largest positive TCP biases, e.g., CMA, KMA, UKMO, and ECCC, the biggest contribution to TCP biases is from TCF biases. In most models, the negative TCP biases in the WNP and the Baja California peninsula are explained by low frequency biases, especially in the JMA forecasts. In short, the results from this decomposition show that, albeit a few exceptions, the frequency biases are responsible for the TCP biases across models and basins.
5. Discussion and conclusions
This study analyzed the representation of TCP in subseasonal forecasts from the S2S project. The global distribution of TCP diagnosed in the S2S models showed that most models overestimate TCP in the ENP and WNP but underestimate TCP in the ATL basin. Our findings showed that TCP biases contribute a significant fraction of total precipitation biases in these forecasts.
The fraction of TCP/P at equatorial latitudes is often overestimated indicating that the role of TCs for the water resources of regions such as the Maritime Continent and western Australia is overestimated by the S2S models. In contrast, in regions such as the Baja California peninsula, where TCP is a major contributor to total rainfall (Breña-Naranjo et al. 2015; Franco-Díaz et al. 2019), several S2S models underestimate TCP/P. The analysis of biases in the MME shows that total P, TCP, and TCP/P biases are mostly positive, with the exception of the ATL basin, and vary little with forecast lead time.
The accurate representation of global TCP is challenging for GCMs because TCP is a function of many factors such as storm intensity (Lavender and McBride 2021; Moon et al. 2022), size (Lavender and McBride 2021), TCF spatial and temporal distribution (W. Zhang et al. 2021), and the storm-scale structure of precipitation (Moon et al. 2022).
For this reason, the analysis of model biases was separated into TC activity and storm-scale precipitation. The biases in TCF in the S2S models are characterized by low Atlantic TC activity and high TCF in the SPC and SIN. These TCF biases are typically found in GCMs of similar resolutions (Camargo 2013; Shaevitz et al. 2014; Roberts et al. 2020; Camargo et al. 2020), and are consistent with previous studies of S2S and seasonal forecast models (Lee et al. 2018; Camp et al. 2018).
S2S models underestimate average peak TCP rates near the storm center because they simulate too many weak storms and few strong TCs. In addition, for strong storms, all models overestimate TCP. However, some models overestimate TCP rates at larger radii (300–500 km) from the storm center. This result means that there are offsetting biases in the azimuthally averaged structure of TCP. The regridding from native model grids to the common S2S grid likely affects our assessment of TCP given the known impact of horizontal resolution on storm structure (Kim et al. 2018; Roberts et al. 2020). In this case, regridding could have effects such as smoothing the radial gradient of precipitation.
The fraction of TCP/TCF500 was used to evaluate how S2S models simulate the spatial variability of the mean precipitation per TC. Most S2S models simulate more precipitation for each pass of a TC in the tropics. In particular, forecasts from BoM, CNRM, and NCEP show a bias in TCP/TCF500 being too large at the equatorial latitudes compared to the observed peak of TCP/TCF500 at 12°S. This means that, to some extent, the origin of the positive biases in TCPR in the wettest models of the S2S cohort is an overestimation of the average TCP per TC (Fig. 11) in the tropics.
The main results of this study were summarized by quantifying the contribution of biases in frequency and with TCP/TCF500 to the total TCP biases. Most of the negative TCP biases, typically found in the ATL, WNP, and the Baja California peninsula are due to low TCF biases. The TCF biases are the main contributor to the wet TCP biases found in the SIN, SPC and southern WNP in 75% of the S2S models. The TCP/TCF500 contribution is generally smaller than the frequency contribution.
The ECWMF forecasts simulate the more realistic climatologies of the diagnostics evaluated by this study, according to our evaluation metrics (PCC and NRMSE). Other models represent some quantities with fidelity but show notable biases in other aspects. For example, the UKMO simulates TCP/TCF500 well but significantly overestimates TC activity in the Southern Hemisphere. In short, S2S models show notable biases in both TCF and the azimuthally averaged structure of TCP. The bias in the storm structure may be relevant for the climatology and forecast skill of extreme precipitation. These results indicate that, to reduce TCP biases, both TC activity and the storm-scale precipitation structure require model improvement.
The biases diagnosed in this study may have relevant implications for mean and extreme precipitation, and streamflow forecast skill. Given that in several active TC regions, such as the western coast of Australia, there is a significant TCP/P fraction and TCP biases that account for almost 50% of total precipitation biases in the MME, previous analyses of forecast skill of mean and extreme precipitation (Vigaud et al. 2017; L. Zhang et al. 2021) may have been affected by these biases in TCP. Further investigation into the role of TCs and TCP for precipitation forecast skill is needed to confirm this hypothesis.
Acknowledgments.
The authors acknowledge support from NASA MAP program (80NSSC21K1525, 80NSSC21K1495) for this work. DK was also supported by NOAA MAPP program (NA21OAR4310343), NOAA CVP program (NA22OAR4310608), and KMA R&D program (KMI2022-01313).
Data availability statement.
The S2S data are publicly available at https://apps.ecmwf.int/datasets/data/. S2S data and S2S TC tracks are available to the research community at http://s2sprediction.net. The gridded precipitation datasets are available from the FROGS database at ftp://ftp.climserv.ipsl.polytechnique.fr/FROGs/. The IBTrACS dataset is publicly available (Knapp et al. 2018) at https://www.ncei.noaa.gov/products/international-best-track-archive.
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