Theoretical and Applied Climatology

, Volume 129, Issue 3–4, pp 711–727 | Cite as

Evaluation of TMPA 3B42 Precipitation Estimates during the Passage of Tropical Cyclones over New Caledonia

Original Paper

Abstract

This study evaluates the Tropical Rainfall Measuring Mission (TRMM) Multi-Satellite Precipitation Analysis (TMPA) 3B42 version 7 (V7) estimates of tropical cyclone (TC) rainfall over New Caledonia using the island rain gauge observations as the ground-truth reference. Several statistical measures and techniques are utilised to characterise the difference and similarity between TMPA and the gauge observations. The results show that TMPA has skill in representing the observed rainfall during the passage of TCs. TMPA overestimates light rainfall events and underestimates moderate to higher rainfall events. The skill deteriorates with increasing elevation, as underestimation by TMPA is greater at higher altitudes. The ability of TMPA also varies with TC intensity and distance from the TC centre, whereby it is more skilful for less intense TCs (category 1-2) and near the TC centre than in the outer rainbands. The ability of TMPA varies from case to case but a better performance is shown for TCs with a higher average rainfall. Finally, case studies of TC Vania (2011), TC Innis (2009), and TC Erica (2003) show that TMPA has the ability to represent the spatial distribution of the observed rainfall, but it tends to underestimate the higher rainfall events.

1 Introduction

Heavy rainfall associated with tropical cyclones (TCs) has been related to disastrous natural hazards such as flooding, landslide and related health and socio-economic problems (Dare 2013 and the references therein). As an example, severe tropical cyclone Erica (2003), struck New Caledonia and caused estimated damage of US$15.0 million, two deaths and injured hundreds (Regional Specialised Meteorological Centre Fiji 2003; Australian Government Bureau of Meteorology 2003). It also increased the chance of spreading dengue fever which was already endemic on the island (United Nations Office for the Coordination of Humanitarian Affairs 2003). Extreme rainfall over parts of the island was around 200 mm day-1. These consequences place a heavy socio-economic burden on the Pacific island countries (Terry et al. 2008).

Accurate measurement of precipitation during the passage of TCs is highly important as it has applications that would significantly aid in disaster mitigation and risk analysis. Such applications include better precipitation forecasting through improved model initialization and numerical weather model evaluation (Ebert et al. 2007; Yu et al. 2009). Accurate estimates of TC rainfall are also of interest to marine biologists in relation to the health of coral reefs which have a narrow tolerance limit to deviations in sea salinity (Jury et al. 2010). Yet having an adequate network of surface-based systems to accurately measure precipitation is difficult over oceanic, remote and developing countries (Ebert et al. 2007; Huffman et al. 2007; Scheel et al. 2011), for example the island countries in the south west Pacific region. This gap could be filled by satellite-based precipitation estimates providing coverage at fine spatial and temporal resolution.

To increase the quality of satellite-based precipitation estimates, scientists have progressively moved towards using a combination of remote sensing instruments onboard various satellites. These include the Tropical Rainfall Measuring Mission (TRMM) Multi-Satellite Precipitation Analysis (TMPA) (Huffman et al. 2007; Huffman and Bolvin 2014), the Climate Prediction Centre morphing method (CMORPH) (Joyce et al. 2004), the Naval Research Laboratory-Blended satellite Technique (NRL) (Turk and Miller 2005; Turk and Mehta 2007), the Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) (Sorooshian et al. 2000) and the recent Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (GPM) (IMERG) (Huffman et al. 2014; Huffman et al. 2015).

These precipitation datasets, however, have a shortcoming in that they are indirect estimates of precipitation where some physical quantity is measured (e.g. cloud top temperature for infrared based measurement and emission/scattering of microwave signals by hydrometeors for microwave based measurements) using satellite remote sensing techniques and is then correlated with precipitation (Janowiak et al. 2001; Wilheit 2003; Huffman et al. 2007). Thus, the satellite-based estimate needs to be validated using surface-based “ground truth” rain gauge data or (alternatively) calibrated radar data to evaluate its accuracy and limitations before it could be confidently used (Ebert et al. 2007; Yu et al. 2009; Chen et al. 2013b, c). Under a program of the International Precipitation Working Group (IPWG) and the more comprehensive study called the Pilot Evaluation of High Resolution Precipitation Products (PEHRPP) (Arkin et al. 2006), work has been conducted to validate nearly all operational satellite precipitation products (Ebert et al. 2007).

Several studies have evaluated the TMPA 3B42 estimates (hereafter referred to as TMPA) related to heavy precipitation associated with TCs over various regions such as over mainland China (Yu et al. 2009), Taiwan (Chang et al. 2013; Chen et al. 2013a), USA (Habib et al. 2009), India (Prakash et al. 2012) and the Australian region (Chen et al. 2013b). Chen et al. (2013c) also evaluated TMPA over the ocean (at atoll sites – assumed to be similar to open ocean conditions) as well as for “coastal and inland sites” in the Pacific basin. These studies, in general, show that TMPA has skill in revealing the overall band structures within the TCs, but it tends to underestimate the moderate and heavy rainfall events while overestimating the very light rainfall amounts. These studies further show that the skill of TMPA varies under different conditions such as latitude (Yu et al. 2009; Chen et al. 2013b), TC intensity, distance from TC centre (Chen et al. 2013b) and terrain (Chang et al. 2013; Chen et al. 2013b, c). TMPA performs quite well at lower latitudes, for intense TCs and near the TC centre. Chen et al. (2013c) explicitly show that a difference exists in the skill of TMPA over the ocean and over the land, where it tends to overestimate heavy rain frequency on atoll sites and underestimate heavy rain frequency on coastal and island sites. Moreover, this study shows that TMPA’s skill at coastal and island sites decreases with increasing elevation, suggesting that TMPA has difficulty in representing orographically-enhanced rainfall during TC landfall, as also reported by Chang et al. (2013).

While the above studies have advanced our knowledge about the skill of TMPA over the aforementioned regions, a similar study has not yet been undertaken to quantitatively evaluate the TMPA estimates of TC rainfall over New Caledonia. Such an evaluation is needed before TMPA can be confidently used for TC-related studies in this location. New Caledonia (Figure 1) is situated in the south west Pacific region, has mountainous islands and atolls and frequently experiences TCs (Dowdy et al. 2012). New Caledonia has a rain gauge network that is spread almost over the entire island (Figure 2), with several gauges also located over high terrain. Estimates of predicted TC rainfall over New Caledonia are highly dependent on the use of satellite-based estimates over the open ocean for approaching storms, but these estimates do not capture the effect of orographic enhancement. Thus evaluation of satellite-based estimates of rainfall over New Caledonia is needed. Ideally, satellite-based rainfall estimates could be effectively used during the passage of TCs and post TC events such as for numerical weather prediction model verification.
Fig. 1

Location of New Caledonia (enclosed in the dashed red rectangular box) in the southwest Pacific basin

Fig. 2

Rain gauge locations on the main island, Grande Terre, New Caledonia. The blue crosses are stations with elevation less than 300 m, and the red circles are stations with elevation greater than 300 m

The objectives of the study are as follows: (i) to evaluate the skill of TMPA for different altitudes, TC intensity, distance from TC centre and position of TCs with respect to the island and (ii) to examine the skill of TMPA during the passage of individual TCs. The paper is organised as follows. Section 2 introduces the data and methodology, section 3 presents the results of the composite TC data for the different conditions (i.e. altitude, TC intensity, distance from TC centre and position of TCs) followed by case studies. Section 4 contains a discussion and summary.

2 Data and methodology

2.1 TMPA

This study utilises the research version of the TMPA product. While the TRMM satellite was retired in October 2014, it has left behind a wealth of data for much of the globe over the period 1998 – 2014.

The TMPA product is a 3 hourly, 0.25° × 0.25° latitude-longitude resolution gridded product generated using the following datasets: the TRMM combined instrument (TCI) dataset comprising the TRMM Microwave Imager (TMI) and the TRMM precipitation radar (PR, 2B31) used as the source of calibration, the microwave (MW) data, the window-channel infrared (IR) data and gridded monthly rain gauge data (Huffman et al. 2007).

The precipitation-related MW data are collected from Low Earth Orbit (LEO) satellites which include the Advanced Microwave Scanning Radiometer-E (AMRS-E) on the Aqua satellite, the TRMM Microwave Imager (TMI), Special Sensor Microwave Imager (SSMI) and Special Sensor Microwave Imager/Sounder (SSMIS) on the US Defence Meteorological Satellite Program (DMSP), the Advanced Microwave Sounding Unit-B (AMSU-B) on US National Oceanic and Atmospheric Administration (NOAA) satellite series and the Microwave Humidity Sounders (MHS) on later NOAA-series satellites and the European Operational Meteorological (MetOp) satellite. The AMRS-E, TMI and SSM/I fields of view (FOVs) are then converted to precipitation estimates using the Goddard Profiling Algorithm (GPROF) (Kummerow et al. 2001). The GPROF precipitation estimation technique differs over the ocean and over the land (Wilheit 1986). The ocean surface has a lower emissivity and appears “cold” to the MW radiometer in relation to a “warm” emission signature of hydrometeors above. Thus differentiating the two is possible using the emission signature. The land surface, on the other hand, has a larger and variable emissivity, thus making the emission mode measurement challenging. Hence, over land the scattering mode is utilised. MW emission is dominated by liquid hydrometeors which have a direct physical relationship with surface rainfall, while MW scattering is dominated by frozen hydrometeors which have a less direct physical relationship with surface rainfall. Hence, estimation over the land is less accurate than that over the ocean. With the presence of liquid hydrometeors, which have a strong emission signature, the errors in the estimation over the land become more significant.

For the AMSU-B and MHS, the Zhao and Weng (2002) and Weng et al. (2003) algorithms are used. While the algorithms can differentiate between precipitating and non-precipitating ice bearing clouds, they have difficulty with clouds that lack the ice phase. The conical scanners (TMI, AMRS-E, SSM/I) have similar limitations over land, so AMSU-B and MHS estimates are roughly comparable.

The window-channel infrared (IR) data used in the TMPA are the merged Climate Prediction Centre (CPC-NOAA) half-hourly 4 km × 4 km latitude–longitude resolution IR data collected by the international constellation of geosynchronous earth orbit (GEO) satellites (Janowiak et al. 2001; Huffman et al. 2007). The rain gauge data utilised by TMPA are the GPCP monthly rain gauge analysis, developed by the Global Precipitation Climatological Centre (GPCC) (Rudolf 1993).

The TMPA estimates are produced in four stages. First, the MW estimates from individual sensors are calibrated using the TCI and then combined. Second, the IR estimates are created with MW calibration. Third, the MW and IR data are combined such that the MW estimates are taken “as is” with the IR estimates used to fill the gaps. Finally, the monthly rain gauge analysis is applied to minimise the bias, and this step has been shown to improve the accuracy of the estimation (Huffman et al. 2007).

The latest version (version 7 or V7) of TMPA, released in 2012, incorporates several changes from its predecessor (version 6) such as a new IR data set, uniformly reprocessed input data using current algorithms and additional output fields (Huffman and Bolvin 2014). A detailed description of the TMPA product is given by Huffman et al. (2007).

2.2 New Caledonia rain gauge data

The New Caledonia island rain gauge daily data are used to verify the TMPA estimates. As shown in Figure 2, which is a plot of the location of the rain gauges on Grande Terre, the main island of New Caledonia used in this study, the island has gauge stations that are spread almost over the entire island, with several of them also located at higher elevation. The climate division of Meteo-France, New Caledonia, collects and performs quality control on the data. Data that have been verified by the division are used for this study.

Rain gauge data are known to have systematic and random errors with possible sources from wind, wetting, splashing, evaporation and calibration (Habib et al. 2008). The wind-related error, which increases with increasing wind magnitude, is the principle source of the systematic error (Nešpor and Sevruk 1999; Habib et al. 2008; Wang et al. 2008). Under TC conditions, the wind-induced error would be quite significant and this has to be taken into consideration in our arguments and discussions, given that we do not have the requisite data to correct the gauge measurements. Nonetheless, gauge data are still considered to be the most accurate and direct measurement of rainfall and the optimal choice for evaluation of satellite precipitation estimates (Ebert et al. 2007; Chen et al. 2013b, c).

2.3 Methodology

TMPA estimates can be verified directly against the gauge data (grid to point) or against gridded analysis of the gauge data. High resolution gridded observation data, however, are not available for New Caledonia. Studies (e.g. Ensor and Robeson 2008) have also shown that interpolating to a grid tends to increase the frequency of light precipitation events while decreasing the incidence of heavy events. As this study is focusing on heavy rainfall during the passage of TCs, actual values of heavy precipitation are essential. Therefore, a ‘grid to point’ method has been employed here. The TMPA data are verified directly against the rain gauge observation by interpolating the TMPA data to the gauge stations using inverse distance weighting (IDW) (Shepard 1968).

As the focus of this study is on the heavy precipitation associated with TCs, TCs that made landfall and those having centres less than 200 km from any one station at any point in time during their passage are considered for this study. A total of 13 TCs, for the period 1998 – 2012, match these criteria. The dates and positions of TC centres are obtained from the International Best Track Archive for Climate Stewardship data (IBTrACS) (Knapp et al. 2010) portal. The data have a temporal resolution of 6 hours.

Rainfall at a gauge station is considered to be TC related, and the particular day for the station considered being a “TC day” if a TC centre, at any point in time during the daily accumulation period, is within 500 km from the gauge station. The 500 km criterion for TC related rainfall is consistent with other studies such as Lonfat et al. (2004), Lau et al. (2008), Jiang and Zipser (2010), Nogueira and Keim (2010) and Chen et al. (2013b, c). For the various declared “TC days”, the TMPA 3 hourly data, for the gauge accumulation period, are summed up to match the accumulation times of the daily gauge rainfall data.

Several statistical measures are used to validate TMPA. For rainfall pattern matching, the correlation coefficient (r), the relative bias, the root mean square error (RMSE) and relative RMSE are utilised (Wilks 2011). To evaluate the skill of the TMPA estimates, four common categorical statistics used in validation studies, namely the probability of detection (POD), the false alarm ratio (FAR), the frequency Bias (FBI) and the equitable threat score (ETS), are calculated using a contingency table (Table 1). These categorical statistics are based on different rain thresholds that define the transition between a rain and no-rain event. The rainfall thresholds used in this study are shown in Table 2 and the formulae of the various statistics are given in Appendix A. Each statistic provides partial information about the error, hence combinations of statistical measures are typically employed for an overall evaluation (Ebert 2007; Wilks 2011).
Table 1

Contingency table

 

Gauge rain ≥ threshold

Gauge rain < threshold

TMPA ≥ threshold

Hit

False alarm

TMPA < threshold

Miss

Correct negatives

Table 2

Rainfall categories and thresholds. Column 1 is used for analysing the RMSE, column 2 for the relative bias and column 3 for the categorical statistics

Rainfall categories (mm day−1)

Rainfall categories (mm day−1)

Rainfall threshold (mm day−1)

5–15

5–15

5

15–30

15–30

15

30–45

30–45

30

45–75

45–75

45

75–100

75–100

75

100–150

>100

100

>150

  
The skill of TMPA is evaluated for different altitudes, TC intensity, distance from TC centre and position of TCs with respect to the island. The categories of TC intensity used here are those used in the south west Pacific region by the Fiji Bureau of Meteorology and the Australian Government Bureau of Meteorology (BOM) (Table 3). Note this classification scheme differs from the Saffir-Simpson scale (Simpson 1974).
Table 3

TC categories and their corresponding central pressure as used by Australian BOM

Category

Central pressure (hPa)

1

>985

2

985–970

3

970–955

4

955–930

5

<930

The confidence intervals on some of the validation statistics are evaluated at a 95 % level using the bootstrapping technique (Efron and Tibshirani 1993) which involves re-sampling of the data. Some 15,000 random re-samples, with replacement, are constructed on which the bootstrapping is applied. The 50th percentile (median) is presented as the validation statistic and the 2.5th and 97.5th percentile as the 95 % confidence interval.

3 Results

To examine the overall quality of the TMPA estimates over the 15 year period, a 2D histogram of TMPA against gauge data (Figure 3) is presented first. A moderate positive linear association between the two is evident with a considerable number of outliers. While numerous TMPA samples occur above the 1:1 reference line at all observed gauge rainfall categories, more are below the reference line; for higher rain rates (greater than 100 mm day-1) almost all are below the reference line. For data with a threshold of zero, cases of missed detections (Gauge > 0, TMPA = 0) and false alarms (Gauge = 0, TMPA > 0) are evident. While missed detections do not occur for observed rain events greater than 40 mm day-1, numerous false alarms exist for moderate to high TMPA estimates, with some occurring for estimates greater than 100 mm day-1.
Fig. 3

2D histogram of TMPA against rain gauge data together with the line of perfect agreement for the period 1998–2012. The colour bar shows the number of observations in each bin

To compare TMPA with the gauge data, the continuous verification statistics of mean rain rate, bias, RMSE, relative RMSE and r were computed next and are given in Table 4. TMPA has a lower mean rain rate than the gauge which shows, on average, an underestimation by TMPA. Correspondingly, the bias is -0.0836 (-8.36%) which shows underestimation by TMPA. This underestimation could be higher since there may be wind induced under-catch associated with rain gauges as the quality controlled data does not include this correction. TMPA has a moderate linear association with the gauge data (r = 0.68). However, the RMSE value of 34.33 (relative RMSE of 1.15 or 115%), which measures the average magnitude of the error, shows a large deviation in the TMPA estimates. A plot of RMSE and the relative RMSE against seven categories of rainfall (rainfall categories are listed in column 1 of Table 2) is shown in Figure 4a. The RMSE increases with increasing rainfall, giving magnitudes of 20 – 55 mm day-1 for rainfall less that 150 mm day-1 and 112 mm day-1 for events greater than 150 mm day-1. The relative RMSE (the RMSE divided by the mean gauge), on the other hand, decreases with increase in rainfall. For rain rates less than 45 mm day-1 it is greater than 1 (or 100 %) and as high as 2.2 (220 %) for the 5 – 15 mm day-1 category, which shows large deviations in the estimates with respect to the average rainfall. For rainfall greater than 45 mm day-1 the relative RMSE ranges from 0.75 – 0.5 (75 – 50 %). Although this is large with respect to the average rainfall, it is still lower than that at lower rain rates.
Table 4

Pattern matching statistics for comparison of TMPA estimates with rain gauge observations. The entries in the bracket are the 95 % confidence interval

Mean gauge rainfall (mm day−1)

30.0 (28.34, 31.80)

Mean TMPA rainfall (mm day−1)

27.50 (26.04, 29.04)

Relative bias

−0.0836 (−0.1232, −0.0408)

RMSE (mm day−1)

34.33 (32.27, 37.25)

Relative RMSE

1.15 (1.08, 1.24)

Correlation coefficient

0.68 (0.65, 0.70)

Fig. 4

aRMSE and relative RMSE between the TMPA estimates and the gauge observations as a function of rainfall (mm day−1). The error bars indicate a 95 % confidence interval. b Percentage rainfall at each of the rainfall categories

To assess the relative importance of the RMSE statistic, a plot of percentage rainfall in each of the rainfall categories is shown in Figure 4b. The percentage ranges from 6 – 19 %, with 19 % of the total rainfall occuring for rare rainfall events (greater than 150 mm day-1). This shows that the rare events (heavy rainfall) are important for the total rainfall.

3.1 Skill with respect to elevation

The ability of TMPA under different conditions such as elevation, TC intensity, distance from the TC centre and position of TC centre with respect to the island is also investigated. A combination of validation statistics is used.

To assess the ability of TMPA for different elevations, the relative bias and the four commonly used categorical statistics (POD, FBI, FAR and ETS) have been computed. Samples were grouped according to elevation less than 300 m and greater than 300 m. This threshold is established based on studies (e.g. Sinclair (1994), Roe (2005) and Smith et al. (2009)) that show clear orographic enhancement at 300 m. It is also consistent with Chen et al. (2013b) who report a difference in the skill of TMPA above and below this elevation threshold. Figure 5a shows the relative bias of TMPA estimates against the gauge data for different elevations for six categories of rainfall (the rainfall categories are listed in column 2 of Table 2). Under all terrain conditions (that is without partitioning for different elevations), the bias is positive for rain rates below 45 mm day-1 and negative for rain rates above 45 mm day-1. This shows that TMPA overestimates the observed light rainfall but it tends to underestimate moderate to heavy rainfall events, in agreement with other validation studies (e.g. Yu et al. 2009; Chen et al. 2013b,c).
Fig. 5

a Relative bias as a function of gauge rainfall (yellow squares with solid line) on the island sites. The sites are further separated into two subgroups according to elevation: elevation less than 300 m (red circles with solid line) and elevation greater than 300 m (green diamonds with dashed line). The error bars indicate the 95 % confidence interval. b Percentage rainfall at each of the rainfall categories for the three groups computed with respect to the total rainfall of the respective group

Considering the partitioning for different elevations, for lower elevation (less than 300 m) TMPA overestimates light rainfall (less than 45 mm day-1) and underestimates moderate to heavy rainfall (greater than 45 mm day-1). On the other hand, for higher elevation (greater than 300 m) there is an underestimation by TMPA at all rain thresholds which worsens with increasing threshold. The underestimation of moderate to heavy rainfall (greater than 45 mm day-1) at higher elevation is also slightly larger than that for lower elevation. A possible reason for this could be the inability of TMPA to detect short-lived extreme rainfall events due to the orographic enhancement usually observed at higher elevations, as pointed by Chang et al. (2013) and Chen et al.(2013b, c).

To assess the relative importance of these statistics, a plot of percentage rainfall in each of the rainfall categories is shown in Figure 5b. The percentage rainfall of each group is computed with respect to the total rainfall in each group. The percentage contribution increases with increase in rainfall category. The rare rainfall events (greater than 100 mm day-1), however, have a relatively higher contribution (greater than 35 %) to the total rainfall at all elevations and it is more pronounced at higher elevation (50 %). These results show that the heavy rainfall events are important for the total rainfall, especially at higher elevations.

Figure 6 (a–d) shows the categorical statistics for all terrain conditions (i.e. without elevation stratification) and the less than 300 m and greater than 300 m elevation groups as a function of six rain thresholds (the rainfall thresholds are listed in column 3 of Table 2). Considering all terrain conditions, the POD (Figure 6a) decreases with increasing rain threshold but it remains above 0.5. Under different elevations, the POD is consistently higher for lower elevation (less than 300 m) than for higher elevation (greater than 300 m) which shows that the ability of TMPA decreases with increasing elevation.
Fig. 6

ad Categorical statistics: aPOD, bFAR, cFBI and dETS over the island (yellow squares with solid line). The sites are further separated into two subgroups according to elevation: elevation less than 300 m (red circles with solid line) and elevation greater than 300 m (green diamonds with dashed line). The error bars indicate the 95 % confidence interval. e Percentage rainfall above each of the rainfall thresholds for the three elevation groups computed with respect to the total rainfall of the respective group

The FAR (Figure 6b) over the island (without elevation stratification) increases with increase in rainfall but its response differs when stratified with respect to high and low elevations. While the FAR for lower elevations (less than 300 m) is similar to that of the “without elevation stratification” group, the FAR for higher elevations (greater than 300 m) is consistently lower than the lower elevation group at all rainfall thresholds. The response at the higher elevation data to changing thresholds is also different: the FAR increases from 5 – 30 mm day-1 and then there is a sharp decrease for thresholds greater than 30 mm day-1. This signifies that for the estimates made at a higher elevation, relatively fewer events (in comparison with lower elevation) are false alarms and this becomes more pronounced at moderate to higher rainfall thresholds (greater than 30 mm day-1).

The FBI score (which measures relative frequencies; Figure 6c) for all terrain conditions is less than 1 for lower rain thresholds (less than 15 mm day-1) and approximately 1 for moderate to heavy rainfall. This shows that the TMPA estimates correspond well with the observed frequency of moderate to heavy rainfall. At lower elevation, TMPA underestimates the frequency of light rainfall (less than 15 mm day-1) and it slightly overestimates (FBI ∼ 1.15) moderate to heavy rainfall (greater than 30 mm day-1). On the other hand, at higher elevations, TMPA significantly underestimates the frequency of the observed rainfall events, which shows the inability of TMPA to capture the observed rainfall at higher altitudes, in agreement with our earlier findings.

The ETS, which is a measure of relative accuracy with respect to random chance (Figure 6d), can be used to evaluate the skill under different conditions. For all elevations, the ETS is approximately equal to 0.37 for rain thresholds between 15 and 75 mm day-1 whereas for thresholds greater than 75 mm day-1 (i.e. at rainfall rates typical of TCs), it is slightly lower (∼ 0.3). Considering elevation, the ETS of the greater than 300 m group is less than that of the less than 300 m group for rainfall thresholds less than 75 mm day-1 but for rainfall thresholds 75 mm day-1 and above the ETS is approximately the same for the two groups. This shows that the relative accuracy of TMPA at small to moderate rainfall rates (less than 75 mm day-1) at higher elevation is less than that at lower elevation but at higher rainfall rates (greater than 75 mm day-1) the relative accuracy of the two groups are almost the same. The latter could be attributed to a significantly lower FAR at higher elevation arising from a lower FBI. Overall, the ETS over the island ranges from 0.2 to 0.4 and is approximately 0.3 and above during moderate to heavy rainfall events. This is somewhat higher than that reported by some studies (e.g. Yu et al. 2009 and Chen et al. 2013c). For example, the study by Chen et al. (2013c) over the islands and atolls reports ETS to be zero during higher rainfall events over land with high elevation. Similarly Yu et al. (2009) reports ETS to be zero during higher rainfall events over mainland China. The ETS shown here is comparable with that over Australia (Chen et al. 2013b), however.

To show the relative importance of the computed statistics, Figure 6e shows the percentage rainfall above each of the rainfall thresholds for the different elevations (the percentage rainfall below each threshold is simply 100 % minus the “percentage above”). The percentage rainfall decreases with an increase in the rainfall threshold but it is consistently higher for the greater than 300 m group at most of the rainfall thresholds. The percentage contribution by higher rainfall events (greater than 100 mm day-1) to the total rainfall occurring in the elevation groupings is larger (50 %) for the greater than 300 m group. As discussed before, these results show that the higher rainfall events are more important for the total rainfall at higher elevations than at lower elevations.

The above set of results (Figure 5 and 6), in general, shows that when all rain intensity categories are considered, the performance of TMPA deteriorates with increasing elevation with a general behaviour of underestimation of observed rainfall events. To further investigate this, we examined the mean gauge rain, the mean TMPA rain and the relative bias at each station (Figure 7). Results show greatest rain gauge averages over higher altitudes (Figure 7a), likely due to orographic enhancement. Comparatively, mean TMPA rainfall is commonly less than the mean gauge rainfall with pronounced underestimation at higher elevations (Figure 7b). This is clearly shown by the relative bias (Figure 7c) which is generally lower and negative at higher elevation stations in comparison with lower elevations. These results further confirm that the ability of TMPA deteriorates with increasing elevation.
Fig. 7

Average TC rainfall of gauge observations (a), TMPA estimates (b) and the relative bias (c) at station sites which have at least ten samples

3.2 Skill with respect to TC intensity, distance from TC centre and position of TC centre with respect to the island

To evaluate TMPA under different TC intensity (category), the samples are grouped according to category 1 – 2 (cat12) and category 3 – 5 (cat35). The four categorical statistics (POD, FAR, FBI, and ETS) are computed and are shown in Figure 8 (a–d). The POD (Figure 8a) for each category group is similar especially at moderate to higher rain rates. On the other hand, the FAR (Figure 8b) is higher for higher category TCs (cat35) than for lower category TCs (cat12). Similarly, the FBI (Figure 8c) is higher for cat35 than cat12. The FBI for cat35 is always above 1 for all rain thresholds and it increases with increasing rain threshold, while for cat12 it is always below 1. This shows that TMPA overestimates the frequency of observed rain events in higher category TCs and that the overestimation increases with increase in rainfall magnitude, while it generally underestimates the frequency of rain events in lower category TCs. The ETS (Figure 8d) is relatively higher for the cat12 group in comparison with cat35, which could be attributed to lower false alarms for the lower category TCs, hence a better skill of TMPA during the passage of less intense TCs. This is in contrast to the results of Chen et al. (2013b) which showed better ETS for higher category TCs over mainland Australia. Further information regarding the skill as a function of TC intensity is provided in section 4.
Fig. 8

ad Categorical statistics: aPOD, bFAR, cFBI and dETS for category 1–2 (cat12, yellow squares) and category 3–5 (cat 35, red circles) TCs. The error bars indicate the 95 % confidence interval. e Percentage rainfall above each of the rainfall thresholds for the two intensity groups computed with respect to the total rainfall of the respective group

Figure 8e shows the percentage rainfall above each of the rainfall thresholds for the different intensity groups. The percentage rainfall for the cat12 group is consistently higher than the cat35 group at almost all of the rainfall thresholds (except for the first). This higher percentage rainfall for the cat12 group is related to the higher contribution from the higher rainfall events (45 % contribution from the greater than 100 mm day-1 rainfall events compared to 23 % from the same threshold for the cat35 group) which shows that the higher rainfall events are more important for the total rainfall during the passage of less intense TCs.

While heavy rainfall also occurs in the TC outer rainbands, the most intense rainfall typically occurs close to the centre of the storm. Accordingly, we examined the performance of TMPA with respect to distance from the TC centre where samples are grouped according to distance less than 200 km and greater than 200 km from the TC centre and the four categorical skill scores (POD, FAR, FBI and ETS) are calculated. Figure 9 (a-d) shows the results for the two groups. The POD (Figure 9a) for TC centres near the island (less than 200 km) is higher than that for distant TCs (greater than 200 km). This shows that TMPA has a better performance closer to the TC centre. The FAR (Figure 9b) is higher for larger distance whereas there is a marginal difference in the FBI (Figure 9c). The ETS (Figure 9d) is higher closer to the TC centre which shows that TMPA has better skill when TCs are closer to the island. This is in agreement with findings of Chen et al. (2013b) which showed that TMPA performs better in locations closer to the TC centre.
Fig. 9

ad Categorical statistics: aPOD, bFAR, cFBI and dETS for TCs with centres less than 200 km (yellow squares) and greater than 200 km (red circles). The error bars indicate the 95 % confidence interval. e Percentage rainfall above each of the rainfall thresholds for the two distance groups computed with respect to the total rainfall of the respective group

Figure 9e shows the percentage rainfall above each of the rainfall thresholds for the two distance groups. The percentage rainfall of the less than 200 km group is consistently higher than the greater than 200 km group at most of the rainfall thresholds (except for the first threshold) which could be attributed to the higher contribution from the higher rainfall events for the less than 200 km group (47 % contribution from the greater than 100 mm day-1 rainfall events compared to 26 % from the same threshold for the greater than 200 km group). This shows that the higher rainfall events are more important for the total rainfall for stations closer to the TC centre.

TCs approach the Grande Terre Island from both the eastern and western side. Therefore, the performance of TMPA is also examined with regards to the position of the TCs with respect to the island (East or West). TC days are grouped as east TC (days when TCs had centres on the eastern side of the island) and west TC (days when TCs had centres on the western side of the island) and the various categorical statistics (POD, FAR, FBI and ETS) are calculated and shown in Figure 10 (a-d). The POD (FAR) of the western TCs is higher (lower) than the eastern TCs at all rain thresholds. This shows that TMPA has a better performance when the TCs are on the western side of Grande Terre at least for the sample of TCs analysed here. The FBI of the eastern TCs is higher (greater than 1) than the western TCs for rain thresholds between 15 and 75 mm day-1. A higher ETS is observed for western TCs which shows that TMPA has better skill when TCs are on the western side of the island. To explain the above results, the average distance of TC centres from the gauge stations is calculated for the respective TC days (Figure 11). TC days 1 to 5 refer to the consecutive days when the average distance of a TC is less than 500 km from the gauges i.e. 1 is the first day, 2 is the second day and so on. Results show that, on average, the western TCs are much closer to the island than the eastern TCs, which could be the reason for the better performance of TMPA for western TCs in our sample. This further confirms that TMPA performs better closer to the TC centres. Another possible explanation is that slopes on the western side of Grande Terre are not as steep as on the eastern side, thus orographic enhancement is less and so TMPA performs better, although further analysis would be required to confirm this.
Fig. 10

ad Categorical statistics: aPOD, bFAR, cFBI and dETS for east (yellow squares) and west (red circles) TCs. The error bars indicate the 95 % confidence interval. e Percentage rainfall above each of the rainfall thresholds for the two position groups computed with respect to the total rainfall of the respective group

Fig. 11

Average distance of TC centres from gauge stations for TC days 1, 2, 3, 4 and 5 for east (yellow squares) and west (red circles) TCs. The TC days are days (24 h) counted from the time a TC first enters within the 500-km zone from any gauge station

Figure 10e shows the percentage rainfall above each of the rainfall thresholds for the east and west groups. The percentage rainfall of the western TCs is consistently higher than the eastern TCs at majority of the rainfall thresholds (except for the first threshold) which could be attributed to the higher contribution from the higher rainfall events (45 % contribution from the greater than 100 mm day-1 rainfall events compared to 27 % from the same threshold for the eastern TCs). This shows that the higher rainfall events are more important for the total rainfall for western TCs.

3.3 Case studies

Figure 12a shows the gauge average, TMPA average and the relative bias of TCs that have at least ten samples and whose spatial correlation coefficient (r) between the gauge and TMPA is significant at the 95 % confidence level (12 such cases). The position of the TCs in this plot is based on the ascending order of average gauge rainfall. A varying association between the gauge rainfall and TMPA is evident. Excellent association (low relative bias) between the TMPA averages and the gauge averages are evident near the higher tail of the rainfall distribution (TCs 6 – 11 except 7) whereas cases of significant underestimation and overestimation (high relative bias) are more usual near the lower tail of the rainfall distribution (TCs 1 – 5). The spatial correlation between the gauge rainfall and TMPA (Figure 12b) varies among the TCs and ranges from 0.3 to 0.8. A majority (nine) of the TCs have r greater than 0.5, of which six (50 %) are greater than 0.7, while three are less than 0.5. The higher r is prominent with TCs comprising higher average rainfall. TCs 1 – 6 (except 3) are cases with a lower average rainfall and have r less than 0.6, whereas TCs 7 – 12, cases with a higher average, have r greater than 0.6. This shows a better representation of the pattern of observed rainfall for TCs with higher average rainfall.
Fig. 12

a Mean gauge rainfall, the corresponding mean TMPA estimates and the relative bias of the 12 TCs that have at least ten observations and whose spatial correlation coefficient (r) between the TMPA estimates and gauge observations are statistically significant at 95 % confidence level. The TCs are arranged in the order of ascending average gauge rainfall. The TCs used as case studies to demonstrate the ability of TMPA are shown in the brackets (name and year). The error bars indicate the 95 % confidence interval. bRMSE, relative RMSE and the spatial correlation coefficient (r) of the 12 TCs shown in a

The RMSE and the relative RMSE between the gauge and TMPA estimates of the 12 TC cases are shown in Figure 12b. The RMSE (relative RMSE) increases (decreases) with increasing average rainfall. This shows that the absolute error in the estimation at higher rainfall is large, but it is relatively lower (in comparison with lower rainfall) when normalised with respect to the corresponding average rainfall.

TC 7 (Vania, 2011), TC 9 (Innis, 2009) and TC 11 (Erica, 2003) are used to present the performance of TMPA for some individual TC cases. These TCs are chosen on the basis of varying bias, where the first has a high negative bias and the latter two have a low bias (Figure 12a). In addition, these are land-falling cases, hence they present the skill of TMPA when TCs hit land. TC tracks are shown in Figure 13. TC Vania made landfall on the south eastern coast of Grande Terre on January 14 at 2300 New Caledonia Time (NCT) (1200 UTC) as a category 1 (980hPa) TC with wind speeds of 83.3 km hr-1. TC Innis made landfall on the north eastern side on February 17, 2009 at 1100 hrs NCT (0000 UTC) as a category 1 (997 hPa) TC with wind speed of 56 km hr-1 (IBTrACs archive). In contrast, Erica was a high-intensity TC that reached category 5 on 13 March at 0700 NCT (12 March 1800 UTC) peaking with wind speeds of 240 km hr-1 on 13 March at 1700 NCT (0600 UTC). On the same day, Erica closely paralleled the southwest coast of Grande Terre, before making landfall on the south western coast on March 14 at 1100 NCT (0000 UTC) as a category 4 TC with wind speeds around 185 km hr-1. After passing the island, Erica underwent extra-tropical transition, weakening as it moved southwards (Australian Government Bureau of Meteorology 2003).
Fig. 13

Twenty-four-hour accumulated gauge and TMPA estimate rainfall of TC Vania (a and b, respectively), Innis (c and d, respectively) and Erica (e and f, respectively) on the landfall day (landfall date and time of each TC are respectively shown in the TMPA estimate panel). The black dashed line shows the track of the TCs

Figure 13 shows the 24 hour accumulated gauge and TMPA-estimated rainfall of the above three TCs for the landfall day. TMPA (Figure 13b, d, f) in general shows a spatial distribution that almost resembles the observed rainfall (Figure 13a, c, e), with regions receiving high gauge rainfall also captured to some extent. There is, however, a disparity between the observed and the estimated extreme values, with general underestimation shown for the TMPA data. Table 5 lists four extreme observed gauge rainfall events and their corresponding TMPA estimates for each TC. The maximum observed (estimated) rainfalls are 450.7 (127.4), 326.9 (76.2) and 200.0 (164.57) mm day-1 respectively for TC Vania, Innis and Erica. These results show that though TMPA is able to represent the regions of heavy rainfall events, the magnitude is mostly underestimated. This underestimation could be higher due to the wind-induced error in the gauge measurements that have not been corrected here.
Table 5

The four extreme gauge rainfalls with their corresponding TMPA rain estimates for TC Vania (2011), Innis (2009) and Erica (2003). The rainfalls are in mm day−1

TC Vania

TC Innis

TC Erica

Gauge

TMPA

Gauge

TMPA

Gauge

TMPA

450

127

327

76

200

165

426

134

275

171

192

123

385

134

244

111

179

117

383

141

215

72

172

118

Figure 14 shows a plot of the four categorical statistics of the three TCs for all the TC days. TC Vania shows a lower POD (especially for rain thresholds less than 75 mm day-1), a lower FAR (for rainfall greater than 15 mm day-1) and a lower FBI (consistently less than 1 at all rain thresholds) than the other two TCs. The ETS (or relative accuracy) of TC Vania, on the other hand, is higher than TC Erica (Innis) at all rain thresholds (greater than 45 mm day-1). The FBI values i.e. less than 1, ∼ 1, and values partially above and below 1 is consistent with the high negative bias of TC Vania and negligible bias of TC Erica and Innis respectively (Figure 12a). These results, together with Figure 12 and 13, show that the skill of TMPA varies from case to case.
Fig. 14

Categorical statistics: aPOD, bFAR, cFBI and dETS of landfalling TCs shown in Fig. 13 (i.e. Vania (2011), Innis (2009) and Erica (2003)). The error bars indicate a 95 % confidence interval

4 Discussion and Summary

This study has evaluated the ability of the TMPA 3B42 research product (version 7) to represent the 24 hour accumulated gauge rainfall associated with TCs affecting New Caledonia with the aim of providing insight into the accuracy and limitations of the TMPA 3B42 data. Combinations of statistics are used to demonstrate the disparity and similarity between the TMPA and gauge rainfall.

Overall, the study shows that TMPA has moderate skill (relative accuracy or ETS around 0.3 – 0.4 for moderate to high rainfall events) in estimating rainfall associated with TCs over the island. TMPA generally overestimates light rainfall events and underestimates heavy rainfall events, in agreement with other validation studies, for example Yu et al. (2009), Chang et al. (2013) and Chen et al. (2013b,c). TMPA has a spatial correlation (r) of 0.68 with the observations with large deviations (RMSE=34.33 mm day-1). This correlation is slightly higher than that reported by Chen et al. (2013c) over coastal and island sites (r=0.55). It is comparable with that obtained over mainland China (r=0.66) (Yu et al. 2009), however, it is lower than that over Australia (r =0.86) (Chen et al. 2013b). While the ETS (relative accuracy) over the island is comparable with that over Australia, it is higher than that over China and the coastal and island sites. The difference in the skill over different regions could be attributed, to some extent, to the varying skill of satellites with latitude: Ebert et al. (2007) report that satellite estimates have better skill over lower latitudes during summer. China encompasses higher latitudes than New Caledonia which could explain the difference. Over the Australian region, the TC days are heavily concentrated over lower latitude regions (Chen et al. 2013b), which could be a reason for a comparatively higher r than that obtained over New Caledonia.

The skill of TMPA also varies under different conditions such as elevation, distance from TC centre, TC intensity and TC location (east or west) with respect to the island. Under different terrain conditions, results show that the skill of TMPA decreases with increasing elevation, which could be due to TMPA’s inability to capture short-lived orographic enhanced rainfall. A possible factor for this could be the resolution of TMPA (3 hourly and 0.25° × 0.25°) which is not high enough to resolve the rapidly evolving small scale orographic enhancements over the small scale mountainous terrain of the island, as also suggested by studies in other locations (e.g. Chang et al. 2013; Chen et al. 2013b,c).

Considering distance from the TC centre, TMPA is in better agreement with the observations near the TC centre, consistent with the findings of Chen et al. (2013b). This could be attributed to the more organised convection and greater concentration of liquid and frozen hydrometeors in the vicinity of the eye-wall (usually the region of the extreme rainfall) than in the outer rainbands, leading to a relatively stronger scattering of MW signal which is then better correlated with surface rainfall.

With respect to TC intensity, results show that TMPA has better skill (relatively higher ETS) for less intense TCs. This could largely be due to the low number of false alarms (FAR) during the passage of these TCs which in turn is related to the low FBI (underestimation of the frequency of the observed rainfall). The reason for a low FBI could be that lower category TCs have much weaker organised convection and cloud cover (usually less hydrometeors) which correlates with weak MW scattering that could lead to an underestimation of the frequency of the observed rainfall. A low FBI thus leads to fewer false alarms. This better skill of TMPA for less intense TCs, however, is in contrast to the findings of Chen et al. (2013b) who reports better skill for higher category TCs over Australia. To ascertain the exact reason for the difference with that over Australia requires additional statistical information such as POD, FAR and FBI for the same region, which are not available. A further investigation is needed that is outside the scope of this paper.

Considering the TC centre location with respect to the island, TMPA exhibits higher skill for western than eastern TCs. A distance analysis shows that the former are relatively closer to the island than the latter. This therefore is likely an indication of better performance of TMPA closer to the TC centre, as shown previously.

The skill of TMPA, however, varies from case to case. TCs with higher (lower) average rainfall are mostly associated with low (high) relative bias, high (low) spatial correlation, high (low) RMSE and low (high) relative RMSE. TCs with high average rainfall could have more organised convection and greater concentration of hydrometeors aloft than TCs with low average rainfall. As discussed previously, this will lead to a relatively stronger scattering of MW signal which may then be better correlated with surface rainfall.

TC Vania (2011), Innis (2009) and Erica (2003), which are land-falling TCs with the former having a high negative bias and the latter two having a negligible bias, are chosen as case studies to demonstrate the ability of TMPA. While TMPA is able to show the spatial distribution of the observed rainfall pattern, it significantly underestimates the heavy rainfall events. In relation to Innis and Erica, TC Vania (i) has a lower POD (for rain rates less than 75 mm day-1) and FBI, which could be related to the high negative bias, and (ii) a higher ETS (especially for rain rates greater than 45 mm day-1) likely due to the less false alarms.

In summary, this study shows that TMPA is able to represent (with moderate skill) the observed TC rainfall over the island of Grande Terre. As an application for future TC related studies, the TMPA estimates could be blended with rain gauge data, which would take advantage of the strengths and mitigate the shortcomings of each data set, by producing blended gridded precipitation estimates for New Caledonia. Methods for such blending have been presented by several studies, for example Mitra et al. (2009), Vila et al. (2009), Li and Shao (2010) and Renzullo et al. (2011). Radar rainfall estimates could also be actively used in such blending but a prior thorough accuracy and error analysis of this data set would be required. In the near future, the GPM based precipitation product (Hou et al. 2014; Huffman et al. 2015), which is the successor of the TRMM based product, could also be incorporated. Such a blended data set is expected to provide a better precipitation estimate for New Caledonia.

5 Appendix

For comparison between TMPA estimates and the gauge observations, the statistics of correlation coefficient (r), relative bias and relative root mean square error (RMSE) are used (Wilks 2011). In addition, four categorical statistics commonly used in validation studies, that is the probability of detection (POD), the false alarm ratio (FAR), the frequency Bias (FBI) and the equitable threat score (ETS) (Wilks 2011), are calculated using a contingency table (Table 1).

The correlation coefficient (r) measures the linear association between the observation and the estimates. It does not take bias into account, therefore is used with other statistics.
$$ r=\frac{{\displaystyle \sum \left(E-\overline{E}\right)\left(O-\overline{O}\right)}}{\sqrt{{\displaystyle \sum {\left(E-\overline{E}\right)}^2}}\sqrt{{{\displaystyle \sum \left(O-\overline{O}\right)}}^2}} $$
(1)
The relative mean error (relative bias) measures the difference between the average observed and estimated values.
$$ \mathrm{Relative}\ \mathrm{bias}=\frac{\overline{E}-\overline{O}}{\overline{O}} $$
(2)
The root mean square error (RMSE) measures the average magnitude of error weighted according to the square of the error.
$$ RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum_{i=1}^n{\left({E}_i-{O}_i\right)}^2}} $$
(3)
$$ \mathrm{and}\ \mathrm{the}\ \mathrm{relative}\ \mathrm{RMSE}=\frac{RMSE}{\overline{O}} $$
(4)

where E = TMPA estimate; O = gauge observation and n = number of samples

The POD is the ratio of correct estimates to the number of observed “yes” events and ranges from 0 to 1 with 1 being the perfect score. It is sensitive to hits and the climatological frequency of the event, however ignores false alarms. Thus it is usually used together with the FAR.
$$ POD=\frac{hits}{hits+ misses} $$
(5)
The FAR is the fraction of false alarms to the number of estimated “yes” events and ranges from 0 to 1 with 0 being the perfect score. It is sensitive to false alarms and the climatological frequency of the event but ignores misses. It must be used together with the POD.
$$ FAR=\frac{false\; alarms}{hits+ false\; alarms} $$
(6)
The FBI is the ratio of number (frequency) of estimated “yes” events to the number of observed “yes” events and ranges from 0 to ∞ with 1 being the perfect score. An FBI less than 1 indicates underestimation and greater than 1 indicates overestimation.
$$ FBI=\frac{hits+ false\; alarms}{hits+ misses} $$
(7)
The ETS is a measure of relatively accuracy with respect to hits due to random chance. The score ranges from -1/3 to 1 with 0 being no skill and 1 a perfect score.
$$ ETS=\frac{hits- hit{s}_{random}}{hits+ misses+ false\; alarms- hit{s}_{random}} $$
(8)
$$ \mathrm{where}\ hit{s}_{random}=\frac{\left( hits+ misses\right)\left( hits+ false\; alarms\right)}{hits+ misses+ false\; alarms+ correct\; negatives} $$
(9)

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Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  • Anil Deo
    • 1
  • Kevin J. E. Walsh
    • 1
  • Alexandre Peltier
    • 2
  1. 1.School of Earth SciencesThe University of MelbourneMelbourneAustralia
  2. 2.Meteo-FranceNoumea CedexFrance

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