Evaluation of Satellite Precipitation Estimates over Australia
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remote sensing Article Evaluation of Satellite Precipitation Estimates over Australia Zhi-Weng Chua 1 , Yuriy Kuleshov 1,2, * and Andrew Watkins 1 1 Long-Range Forecasts, Bureau of Meteorology, Docklands 3008, Australia; zhi-weng.chua@bom.gov.au (Z.-W.C.); andrew.watkins@bom.gov.au (A.W.) 2 SPACE Research Centre, School of Science, Royal Melbourne Institute of Technology (RMIT) University, Melbourne 3000, Australia * Correspondence: yuriy.kuleshov@bom.gov.au or yuriy.kuleshov@rmit.edu.au; Tel.: +61-3-9669-4896 Received: 16 January 2020; Accepted: 14 February 2020; Published: 19 February 2020 Abstract: This study evaluates the U.S. National Oceanographic and Atmospheric Administration’s (NOAA) Climate Prediction Center morphing technique (CMORPH) and the Japan Aerospace Exploration Agency’s (JAXA) Global Satellite Mapping of Precipitation (GSMaP) satellite precipitation estimates over Australia across an 18 year period from 2001 to 2018. The evaluation was performed on a monthly time scale and used both point and gridded rain gauge data as the reference dataset. Overall statistics demonstrated that satellite precipitation estimates did exhibit skill over Australia and that gauge-blending yielded a notable increase in performance. Dependencies of performance on geography, season, and rainfall intensity were also investigated. The skill of satellite precipitation detection was reduced in areas of elevated topography and where cold frontal rainfall was the main precipitation source. Areas where rain gauge coverage was sparse also exhibited reduced skill. In terms of seasons, the performance was relatively similar across the year, with austral summer (DJF) exhibiting slightly better performance. The skill of the satellite precipitation estimates was highly dependent on rainfall intensity. The highest skill was obtained for moderate rainfall amounts (2–4 mm/day). There was an overestimation of low-end rainfall amounts and an underestimation in both the frequency and amount for high-end rainfall. Overall, CMORPH and GSMaP datasets were evaluated as useful sources of satellite precipitation estimates over Australia. Keywords: satellite precipitation estimates; Australia; rain gauge precipitation measurements; satellite precipitation validation 1. Introduction Precipitation is an essential climate variable and is one of the most important climate variables affecting human activities [1]. Variations in the intensity, duration, and frequency of precipitation directly impact water availability for many millions of people and industries. Measuring rainfall over broad areas enables efficient water management and disaster response and recovery. The conventional method of using rain gauges to estimate spatial patterns of rainfall provides a direct measurement of surface rainfall but spatial density can be an issue across many parts of the world, including over the oceans, where the installation of an adequate rain gauge network is economically or physically unfeasible [2]. This greatly affects the ability to accurately assess rainfall across a region as it is a variable that exhibits a high degree of spatial variation and a point-based measurement may not provide an ideal representation of an area. Rain gauge estimates are subject to instrumental errors with many relying on manual sampling methods. Clock synchronization and mechanical faults are examples of potential issues [3]. Furthermore, they are also affected by localised effects including wind (precipitation can be prevented from entering the gauge), evaporation (some Remote Sens. 2020, 12, 678; doi:10.3390/rs12040678 www.mdpi.com/journal/remotesensing
Remote Sens. 2020, 12, 678 2 of 17 of the precipitation is evaporated before it can be recorded), wetting (some of the precipitation can be left behind in the gauge) and splashing effects (precipitation can incorrectly splash in and out of the gauge) [4,5]. For example, Groisman and Legates (1994) found biases due to wind-induced effects could be quite significant, especially around mountainous areas where the bias was as large as 40% [6]. Alternative physical-based precipitation datasets include those derived from ground-based radars and satellites. Radar estimates are derived from the detected reflectivity of hydrometeors but suffer from problems such as topography blockage, beam ducting, range-related and bright band effects [7,8]. Van De Beek et al. (2016) found that for a 3-day rainfall event in the Netherlands, the radar underestimated rainfall amount by over 50%, though after correction the difference was only 5-8% [9]. Correction to rain gauges is critical but this means radars are likely to perform poorly in areas that lack gauge coverage, hindering their ability to replace gauges. As a ground-based source, they are also affected by the same physical and economical limitations that are applicable to installation of rain gauge networks. The use of meteorological satellites to monitor rainfall was introduced in the 1970s, providing a means to estimate rainfall across most of the globe. The first methods inferred precipitation intensity based on visible or infrared (IR) data by linking cloud-top temperature or reflectivity to rain rates through empirical relationships. Later methods used passive microwave (PMW) sensors that detect the radiation from hydrometeors and link this to rainfall rates, thereby providing a more direct interpretation of precipitation. However, the coverage of PMW satellites is much less than that of their IR counterparts. Consequently, techniques have been developed to combine the increased accuracy of PMW estimates with the coverage provided by IR satellites. One method which can be referred to as the cloud-motion advection method involves using IR images to derive cloud-motion vectors and then using these vectors to advect PMW-based precipitation estimates to cover areas lacking in PMW coverage. The Climate Prediction Center morphing technique (CMORPH) developed by the National Oceanic and Atmospheric Administration (NOAA) was the first product of this kind and was followed by the Japan Aerospace Exploration Agency’s (JAXA) Global Satellite Mapping of Precipitation (GSMaP) dataset [10,11]. CMORPH and GSMaP have undergone multiple advancements since their inception. The key improvements have been the introduction of the Kalman filter to modify the shape and intensity of the advected rainfall and the implementation of bias-correction using gauge data [10,12,13]. Many past verification studies have been performed with modern-day satellite technology, showing that, at least on a monthly basis, the technology can possess good potential [14]. However, few studies have been performed over Australia, with even fewer, if any, using the latest CMORPH and GSMaP datasets. Continental studies in the past have indicated that performance varies greatly with rainfall type, amount, and season, with performance tending to be better for heavier rainfall regimes including those during summer and in the tropics [15,16]. Ebert et al. (2007) evaluated the performance of multiple satellite datasets, including CMORPH, over Australia for a two-year period and found the estimates were relatively unbiased over summer but the accuracy greatly deteriorated in winter [15]. Pipunic et al. (2015) examined Tropical Rainfall Measuring Mission (TRMM) 3B42RT satellite data over mainland Australia across a nine-year period and found a similar conclusion with detection of light rainfall (
Remote Sens. 2020, 12, 678 3 of 17 April 2014 to March 2016 and showed that GSMaP overestimated light precipitation (32 mm/day) [20]. Hit bias rather than false or missed event bias was noted as the major error with false event bias also being more significant than missed event bias. The introduction of a bias-correction scheme is largely able to correct a positive bias by scaling down the magnitudes, but the inability to correct missed events means there has been much less success in correcting the negative bias [13]. Previous studies have also indicated that a significant degradation of performance occurred over orography, with satellites underestimating rainfall over higher elevations [18,21]. The bias can be worse during winter where the poor detection of snowfall, as well as rainfall, over cold surfaces leads to both missed events and an underestimation of intensity [22]. Derin et al. (2016) performed an evaluation over the western Black Sea region of Turkey, an area featuring complex topography in the form of a mountain range, from 2007 to 2011, and found that CMORPH exhibited a bias of −54% for the windward side of the region during the warm season, increasing to −82% during the cold season [21]. Kubota et al. (2009) found that the greatest biases in GSMaP were over coastal areas with frequent orographic rainfall and that estimates were generally better over the ocean than over the land [23]. Coastal regions are likely to present difficulties as the retrieval algorithm struggles to account for both ocean and land surfaces in a single grid point. This study aims to contribute to the validation of satellite rainfall data. It differs from earlier studies by evaluating satellite precipitation estimates over a relatively long period of record (18 years) with a focus on Australia, which has a relatively dense rain gauge network over a large area when compared to other world regions [15]. The use of a percentile-based verification statistic is an innovative feature of this study, while the use of both gridded and point gauge data as a reference adds additional insight compared to using just one. The CMORPH and GSMaP datasets were chosen due to their provision as part of the World Meteorological Organization (WMO) Space-based Weather and Climate Extremes Monitoring Demonstration Project (SEMDP) [24]. This project aims to introduce operational satellite rainfall monitoring products based on these two datasets, to East Asia and Western Pacific countries, of which many lack adequate rainfall monitoring capabilities due to the absence of an extensive and accurate rain gauge network. The verification of these datasets is thus an important step for the creation of these products. Moreover, the cloud-motion advection method used to blend PMW and IR data ranks amongst the best in terms of performance across various satellite methods used to estimate precipitation [25]. The variance of the errors in the satellite precipitation estimates with location, season, and rainfall intensity was investigated. The paper is organised as follows. Section 2 describes the study area, datasets, and methods used in the study. Section 3 presents the results while Section 4 discuss the findings. Section 5 summarises the major findings and provides directions for future work. 2. Materials and Methods 2.1. Study Area Australia has a land area of around 8.6 million km2 , making it the sixth-largest country in the world by land size. Its large geographical size means that it experiences a variety of climates, including temperate zones to the south east and south west, tropical zones to the north, and deserts or semi-arid areas across much of the interior [26]. The main orographic feature occurs in the form of the Great Dividing Range (GDR), a mountain range along the eastern side of the country that extends more than 3500 km from the north-eastern tip of Queensland, towards and along the coast of New South Wales, and into the eastern and central parts of Victoria. The width of the GDR ranges from about 160 to 300 km with a maximum elevation of 2228 m, though the typical elevation range for the highlands is from 300 to 1600 m [27]. In Figure 1, the domain of analysis is shown, with the stations used in the study also marked.
Remote Sens. 2020, 12, 678 4 of 17 Remote Sens. 2020, 12, x FOR PEER REVIEW 4 of 18 (a) (b) Figure Figure1.1.Domain Domainofofanalysis. analysis.(a)(a) Stations are Stations aremarked markedasasblue bluedots; dots;(b) (b)scale scaleofoftopography. topography. 2.2.Datasets 2.2. Datasets AsAspart partofofthetheWMO WMOSEMDP,SEMDP,access accesstotoGSMaP GSMaPand andCMORPH CMORPHdata datawere wereprovided providedby byJAXA JAXAand and NOAA,respectively. NOAA, respectively.Both Bothdatasets datasetsofofsatellite satelliteprecipitation precipitationestimates estimatesemploy employthe thecloud-advection cloud-advection techniqueintroduced technique introduced in Section in Section 1. The1.GSMaP The GSMaPversion used version wasused GSMaP was GSMaP Gauge-adjusted Gauge-adjusted Near-Real- Near-Real-Time (GNRT) Version 6. To allow for a faster data Time (GNRT) Version 6. To allow for a faster data latency, gauge adjustment over land latency, gauge adjustment over landwas was performedagainst performed againstthethegauge-calibrated gauge-calibratedversion version(GSMaP (GSMaPgauge) gauge)from fromthethepast pastperiod, period,which, which,itself, itself, is calibrated by matching daily satellite rainfall estimates to a global is calibrated by matching daily satellite rainfall estimates to a global gauge analysis, CPC Unified gauge analysis, CPC Unified Gauge-BasedAnalysis Gauge-Based AnalysisofofGlobal GlobalDaily DailyPrecipitation Precipitation(CPC (CPCUnified) Unified)[28].[28].Further Furtherdetails detailscancanbebefound found ininthe theGSMaP GSMaPtechnical technicaldocumentation documentation[28]. [28]. Two versions of CMORPH Two versions of CMORPH were used. These were used. These werewere the bias-corrected the bias-corrected CMORPH CMORPH(CMORPH (CMORPH CRT) CRT) and theand the gauge-blended gauge-blended CMORPH CMORPH (CMORPH(CMORPH BLD)BLD) datasets. datasets. BiasBias correction correction overover land land waswasalso also performedusing performed usingthetheCPC CPCUnified Unifiedanalysis analysisbut butusing usinga adifferent differentalgorithm algorithmthat thatinvolves involvesmatching matchingtoto probabilitydistribution probability distributionfunction function(PDF) (PDF)tables tablesfromfromthe thepast past30 30days. days.The Thegauge-blended gauge-blendedversion versionuses uses thebias-corrected the bias-correctedversionversionas as aa first first guess guess and then incorporates incorporates the the gauge gaugedatadatabased basedon onthethedensity densityof the observations; further details can be found of the observations; further details can be found in [10,13]. in [10,13]. Consequently,this Consequently, thisstudy studyused usedtwo twogauge-corrected gauge-correctedsets sets(GSMaP (GSMaPand andCMORPH CMORPHCRT) CRT)and andone one thathad that hadbeen beenfurther furtherprocessed processedby bycombining combiningCMORPH CMORPHCRT CRTwithwithgauge gaugedatadata(CMORPH (CMORPHBLD). BLD). The reference datasets used were both based on the Bureau The reference datasets used were both based on the Bureau of Meteorology (BoM) rain gauges of Meteorology (BoM) rain gauges withthe with theAustralian AustralianWater WaterAvailability AvailabilityProject Project(AWAP)(AWAP)analysis analysisbeingbeingused usedasasthe thereference referencedataset dataset forthe for thegridded griddedcomparison comparisonand andthe thevalues valuesfrom fromthe thestations stationsthemselves themselvesbeing beingused usedfor forthe thepoint point comparison. The AWAP rainfall analysis is generated by decomposing comparison. The AWAP rainfall analysis is generated by decomposing the field into a climatology the field into a climatology componentand component andan ananomaly anomalycomponent componentbased basedon onthe theratio ratioofofthe theobserved observedrainfall rainfallvalue valuetotothethe climatology[29]. climatology [29].The The Barnes Barnes successive-correction successive-correction technique techniqueisisapplied appliedtoto thetheanomaly anomaly component component and added and addedto the to monthly the monthly climatological climatological averages, whichwhich averages, were were derived using using derived a three-dimensional a three-dimensional smooth splice approach smooth [29]. The splice approach climatological [29]. averagesaverages The climatological were generated from 30 years were generated from of 30 monthly years of totals monthly[29]. For the point comparison, only ‘Series 0’ stations were chosen as these stations totals [29]. For the point comparison, only ‘Series 0’ stations were chosen as these stations are Bureau- are Bureau-maintained and conform maintained andto International conform to Civil Aviation Civil International Organization Aviation(ICAO) standards. Organization The minimum (ICAO) standards. number The of stations minimum used across number the period of stations was 4764. used across As discussed the period was 4764. earlier, even though As discussed earlier,rain evengauge though network rain measurements gauge can be taken ascan network measurements ‘truth’, they as be taken still‘truth’, contain errors, they still which containwill artificially errors, which inflate the errors will artificially attributed inflate to satellite the errors measurements. attributed to satellite measurements. Detailson Details onthe thespatial spatialandandtemporal temporalresolutions resolutionsofofthe thegridded griddeddatasets datasetsalongalongwith withtheir theirdomains domains are shown in are shown in Table 1.Table 1.
Remote Sens. 2020, 12, 678 5 of 17 Table 1. Details about dataset used. Dataset Resolution (◦ ) Start of Temporal Domain Latitude Range (◦ ) Longitude Range (◦ ) CMORPH BLD 0.25 Jan 1998 (−45, 40) (50, 200) CMORPH CRT 0.25 Jan 1998 (−45, 40) (50, 200) GSMaP 0.25 Apr 2000 (−45, 40) (50, 200) AWAP 0.05 Jan 1900 (−44.525, −9.975) (111.975, 156.275) The longest common period across the datasets using full years was chosen for the analysis (i.e., January 2001 to December 2018). A spatial domain of latitude from −44.625◦ N to −10.125◦ N and longitude from 112.125◦ E to 156.125◦ E was chosen as this domain centers on Australia. Ocean data were masked. 2.3. Method The satellite datasets were compared against the gauge-based datasets. Both a gridded comparison and point comparison were performed. When performing the comparisons, all the datasets were linearly interpolated to the same spatial resolution. An interpolation to the coarsest resolution was chosen (i.e., 0.25◦ ). Values at each grid box from these interpolated grids could then be compared against each other for the gridded comparison. For the point comparison, values corresponding to the location of a station were linearly interpolated from each grid. These values could then be compared to the actual station value. Inclusion of the AWAP dataset was done to provide an additional reference. A complication arose from the fact that the gauge-based data values were 24 h accumulated values to 0900 local standard time (LST), while the satellite data values were values to 00 UTC. As this study is focused on monthly comparisons, the longer period greatly reduces the impact of this timing inconsistency. An elementary remedy would be to have shifted the gauge and AWAP values one day ahead of their satellite counterparts, reducing the inconsistency to two hours or less. Doing this adjustment resulted in improvements of less than 2% and so the unadjusted datasets were used for simplicity. Both continuous and percentile-based statistics were calculated. The continuous statistics calculated were the mean bias (MB), root-mean-square error (RMSE), mean average error (MAE), and the Pearson correlation coefficient (R). The MB is the average difference between the estimated and observed values, which gives an indicator of the overall bias. The MAE measures the average magnitude of the error. To remove the effect of higher rainfall averages leading to larger errors, the MAE was also normalised through division by the average rainfall producing the normalised mean average error. The RMSE also measures the average error magnitude but is weighted towards larger errors. R is commonly known as the linear correlation coefficient as it measures the linear association between the estimated and observed datasets. In addition to continuous verification statistics, a percentile-based verification can also be performed to measure how well the datasets reproduce the occurrence of low- and high-end values. This is a novel verification metric that the authors have deemed useful to assess because, even if the satellites performs poorly in terms of absolute values, they may still produce accurate values relative to their own climatology, meaning there is the potential to produce percentile-based products. Such products have already been produced (e.g., both NOAA and JAXA have generated satellite-derived versions of the Standardized Precipitation Index, as well as rainfall values expressed as high-end percentiles). The quintile for an observed month at a location could be derived by ranking that value against the same month but for different years across the verification period. The ranking can then be converted to a percentile through linear interpolation. If a bottom or top quintile was observed, the value from the satellite dataset was then investigated. If it was also registered in the same quintile, this was recorded as a success; otherwise, it was recorded as a failure. The number of successes was then converted to a hit rate. This hit rate was only calculated for the gridded comparison as the varying number of stations across the verification period made a point-based comparison more difficult. The
Remote Sens. 2020, 12, x FOR PEER REVIEW 6 of 18 Remote Sens. 2020, 12, 678 6 of 17 The equations for the metrics are summarised in Table 2 with Ei representing the estimated value at a of use point or grid quintiles box i, Ogreater provided i being the observed value, differentiation and Nvalues of extreme being than the number of samples terciles or quartiles,(across the while the whole length record domainwas andconsidered period) fortoo theshort continuous metrics. for the use of deciles. The equations for the metrics are summarised in Table 2 with Ei representing the estimated value at a point or grid box i, Oi being the Table 2. Summary observed value,ofand metrics used.the number of samples (across the N being whole domain and period) for the continuous Equation Metric metrics. Range Perfect Value Unit 1 Mean bias (MB) of Table 2. Summary metrics used. [0, ∞) 0 mm/day Metric Equation 1 Range Perfect Value Unit Mean average error (MAE) | | [0, ∞) 0 mm/day N Mean bias (MB) 1 P (Ei − Oi ) (−∞, ∞) 0 mm/day N 1 i=1 ∑ | | Normalised mean average error N [0, ∞) 0 1 P 1i| [0, ∞) Mean average error (MAE) N |Ei − O ∑ 0 mm/day i=1 1 PN Normalised mean average error i=1 Ei −Oi [0, ∞) 0 1 N 1 PN i = 1 Ei Root-mean-square error (RMSE) N [0, ∞) 0 mm/day s N Root-mean-square error (RMSE) 1 ( E i − Oi ) 2 [0, ∞) 0 mm/day P i∑ N =1 Pearson correlation coefficient (R) [0, 1] 1 ∑i=1 [(Ei −E)(O i −O)] ∑ PN Pearson correlation coefficient (R) [−1, 1] 1 q q PN 2 PN 2 i=1 ( i E −E ) i=1 (Oi −O) 3. Results 3. Results The results of the gridded continuous comparison against AWAP data are presented in Figure 2. The Thelinear correlation results of thecontinuous of the gridded satellite rainfall estimates comparison ranges against AWAPfromdata0.77are to presented 0.88, whileinthe MAE Figure 2. ranges from 0.61 to 0.43 mm/day. The trend amongst all the metrics is the same with performance The linear correlation of the satellite rainfall estimates ranges from 0.77 to 0.88, while the MAE ranges being0.61 from thetobest 0.43for CMORPH mm/day. BLD, amongst The trend then CMORPH CRT, and all the metrics lastly is the sameGSMaP. CMORPH being with performance CRT and the GSMaP best display similar for CMORPH BLD, performances, then CMORPHwhile therelastly CRT, and is a clear GSMaP. increase CMORPH in performance for CMORPH CRT and GSMaP display BLD. performances, while there is a clear increase in performance for CMORPH BLD. similar Figure 2. Gridded continuous comparison of satellite datasets against Australian Water Availability Figure 2. Gridded continuous comparison of satellite datasets against Australian Water Availability Project (AWAP) from January 2001 to December 2018. Mean bias (MB), root-mean-square error (RMSE), Project (AWAP) from January 2001 to December 2018. Mean bias (MB), root-mean-square error mean average error (MAE), Pearson correlation coefficient (R) and normalised mean average error (RMSE), mean average error (MAE), Pearson’s correlation coefficient (R) and normalised mean (Norm. MAE) are displayed. average error (Norm. MAE) are displayed. The gridded percentile-based comparison against AWAP data is shown in Figure 3. The satellite The gridded percentile-based comparison against AWAP data is shown in Figure 3. The satellite datasets obtain around a 70%–80% hit rate for the bottom quintile whilst scoring around 10% less for datasets obtain around a 70%–80% hit rate for the bottom quintile whilst scoring around 10% less for
Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 18 Remote Sens. 2020, 12, 678 7 of 17 the top Remote quintile. Sens. 2020, 12,This suggests x FOR the rainfall PEER REVIEW values produced by the satellites are relatively accurate 7 of in 18 terms of climatological occurrence, with better performance exhibited for low-end extremes. There the top quintile. appears This suggests to be potential the rainfall in generating values produced percentile-based by the products satellites from satellitearedata. relatively accurate in climatological occurrence, with terms of climatological with better better performance performance exhibited exhibited forfor low-end low-end extremes. extremes. There appears to be potential potential in in generating generating percentile-based percentile-based products products from fromsatellite satellitedata. data. Figure 3. Gridded percentile-based comparison of satellite datasets against AWAP from January 2001 to December 2018. Bottom- and top-quintile hit rates are displayed. Figure Figure 3. Gridded percentile-based 3. Gridded percentile-based comparison comparison ofof satellite satellite datasets datasets against against AWAP AWAP from from January January 2001 2001 to December 2018. Bottom- and top-quintile hit rates are displayed. to December Figure 2018. Bottom- 4 displays and top-quintile the continuous hit rates statistics are point using displayed. gauge data as truth. The comparison against point4 gauge Figure displaysdata supports the the gridded continuous comparison statistics with using point the CMORPH gauge BLD error data as truth. being about The comparison Figure 50% larger 4 than displays the datathe AWAP continuous error and statistics CMORPH using point CRT and with gauge GSMaP data as truth. The comparison against point gauge supports the gridded comparison the being CMORPH aboutBLD 150% larger. error The being MB about against is point negative forgauge all data the supports satellite the gridded datasets, comparison indicating a slightwith the CMORPH tendency for BLD error being underestimation of about overall 50% larger than the AWAP error and CMORPH CRT and GSMaP being about 150% larger. The MB is 50% larger than the AWAP error and CMORPH CRT and GSMaP being about 150% larger. The MB rainfall. negative for all the satellite datasets, indicating a slight tendency for underestimation of overall rainfall. is negative for all the satellite datasets, indicating a slight tendency for underestimation of overall rainfall. Figure 4. Comparison Figure 4. Comparisonofofsatellite satellitedatasets datasetsagainst point against gauge point datadata gauge fromfrom January 2001 2001 January to December 2018. to December 2018. The ranking Figure of performance 4. Comparison between of satellite theagainst datasets satellite datasets point gaugeremains theJanuary data from same for both 2001 tothe continuous December and the Thepercentile-based 2018. statistics. between ranking of performance The benefittheofsatellite blending in gauge datasets data isthe remains again displayed, same for bothwith the CMORPH continuousBLD andshowing significant improvement the percentile-based statistics. over The the unblended benefit datasetsinand of blending skill comparable gauge data is again to AWAP. As the The ranking displayed, trend with CMORPH between of performance MB, BLD showing MAE, betweenRMSE, and R the satellite significant is the same, future datasets over improvement remains references the same for the unblended to continuous both and datasets the statistics continuous will refer and to the just MAE, normalised percentile-based MAE statistics. and The R for brevity. benefit skill comparable to AWAP. As the trend between MB, MAE, RMSE, and R is the same, future of blending in gauge data is again The values displayed, references with to and CMORPH continuous residualsBLD of showing statisticsthe willdatasets toagainst significant refer just MAE, point gauge data improvement normalised over are MAEtheshown in Figure unblended and R for 5. There datasets brevity. and appears skill The tovalues be a tendency comparable to AWAP. towards As an the overestimation trend between for MB,low rainfall MAE, months RMSE, and and and residuals of the datasets against point gauge data are shown in Figure 5. There R an is underestimation the same, future for high to references appears rainfall to months.statistics becontinuous a tendency AWAP an towards and, will to a to refer lesser overestimation extent, just MAE, CMORPH normalised for low BLD and MAE rainfall months were able andRan to capture the forunderestimation brevity. high-end for high rainfall Therainfall months values months. and residuals more AWAP accurately, ofand, the datasets with to a lesser observation against extent,point CMORPH of months gauge BLD where data were are shownmore than able toincapture Figure40 the mm/day 5. There high- was recorded, appears to be being a distinctly tendency better. towards an All datasets overestimation appear forto struggle low with rainfall end rainfall months more accurately, with observation of months where more than 40 mm/day was very months high-end and an rainfall months underestimation (>60 for mm/day). high recorded, being These rainfall months. distinctlygauge AWAP totals better. Allsitdatasets and, toalong a lesserthe lower extent, appear boundary, toCMORPH which BLD struggle with indicates were very that able to capture high-end the the rainfall datasets high- months observed end (>60 rainfalllittle mm/day). rainfall months Thesemore while gauge the gauges accurately, totals sitwith observed along a significant observation the lower of amount. months where boundary, The fact which more that even thanthat indicates AWAP 40 mm/day does was the datasets not depict recorded, these being totals distinctly well suggests better. All that datasetsgridded appear datasets to systematically struggle with observed little rainfall while the gauges observed a significant amount. The fact that even AWAP very struggle high-end with these rainfall very months high-end (>60 not values. does mm/day).depictTheseA likely these gaugereason totals is suggests totals well that the gridded sit along datasets thegridded that lower smoothsystematically boundary, datasets down point which values indicates that struggleas the part of these their datasets with objective observed very high-endanalysis process little values. rainfall andthe Awhile likely so it is expected gauges reason thethat observed is that ahigh-end gridded totals significant datasets will beThe amount. smooth underrepresented down fact thatvalues point even AWAP bypart as the grids. does The not impact depict from these this totals effect well would suggests be worse that if there gridded were nearby datasets gauges systematically of their objective analysis process and so it is expected that high-end totals will be underrepresented with low struggle totals. with these very by thehigh-end values. grids. The A from impact likelythis reason is would effect that thebegridded worse ifdatasets smooth there were down nearby pointwith gauges values lowas part totals. of their objective analysis process and so it is expected that high-end totals will be underrepresented by the grids. The impact from this effect would be worse if there were nearby gauges with low totals.
Remote Sens. 2020, 12, 678 8 of 17 Remote Remote Sens. Sens.2020, 2020,12, 12,xxFOR FORPEER PEERREVIEW REVIEW 8 of 188 of 18 Figure 5. Scatterplot comparisons of satellite datasets against point gauge data from January 2001 to Figure5.5. Scatterplot Figure December 2018. Scatterplot comparisons comparisons of of satellite satellite datasets datasets against against point point gauge gauge data data from fromJanuary January2001 2001to to December 2018. December 2018. 3.1. Variation with Geography 3.1. Variation with Geography 3.1. Variation A griddedwith Geography was performed over the Australian domain with the geographical comparison A gridded representations comparison the MB andwas performed shown in over the Australian domain withCMORPH the geographical A griddedofcomparison MAE was performed Figure over the6. The CMORPH Australian CRT and domain BLD with the geographical representations datasets were of the MB chosen to and MAE allow an shown in Figure investigation into 6. The the CMORPH effects of CRT gauge and CMORPH correction. BLD datasets Generally, the BLD representations of the MB and MAE shown in Figure 6. The CMORPH CRT and CMORPH were chosen to allow satellite-derived dataan investigation overestimate into the rainfall, effects except of western over gauge correction. Tasmania Generally, where therethe is asatellite-derived significant datasets were chosen to allow an investigation into the effects of gauge correction. Generally, the data overestimate rainfall, except over western Tasmania where there is a significant underestimation. underestimation. satellite-derived data overestimate rainfall, except over western Tasmania where there is a significant underestimation. Figure 6. Cont.
Remote Sens. 2020, 12, 678 9 of 17 Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 18 Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 18 Figure Figure 6. Mean Mean 6. 6. bias, bias, meanmean average average error, error, and normalised and normalised mean meanmean average average error error for for bias-corrected bias-corrected Climate Figure Mean bias, mean average error, and normalised average error for bias-corrected Climate Prediction Prediction Center Center morphing morphing technique technique (CMORPH (CMORPH CRT) and CRT) and gauge-blended gauge-blended CMORPH CMORPH (CMORPH Climate Prediction Center morphing technique (CMORPH CRT) and gauge-blended CMORPH (CMORPH BLD) BLD) datasetsBLD) datasets fromdatasets from Januaryfrom January 2001January 2001 to December to December 2018 using AWAP as truth. (CMORPH 2001 to2018 using AWAP December as truth. 2018 using AWAP as truth. The The effects of normalisationare effects are indicated alongalong the the northern coast coastofofAustralia Australiaand andin western The effectsofofnormalisation normalisation areindicated indicated along the northerncoast northern of Australia and ininwestern western Tasmania Tasmania where where thethe unnormalised unnormalised errors errors were were previously previously the the greatest greatest but but improve improve to about to about average average Tasmania where the unnormalised errors were previously the greatest but improve to about average after after thethe adjustment, adjustment, atat leastfor least forthe theCMORPH CMORPHBLD BLD dataset. dataset. after the adjustment, at least for the CMORPH BLD dataset. The The effect of gaugecorrection effect correction is especially evident evident around western westernTasmania, Tasmania,as well asas around The effectofofgauge gauge correctionisisespecially aroundwestern especially evident around Tasmania, asaswell well around as around western parts of Western Australia, the southern Australian coastline, the northern coastline of New western parts of Western Australia, the southern Australian coastline, the northern western parts of Western Australia, the southern Australian coastline, the northern coastline of New coastline of New South Wales, the Australian Alps, and the southwestern coast of Western Australia. In these areas, South SouthWales, Wales,thethe Australian AustralianAlps, Alps,andand thethe southwestern southwestern coast of Western coast of WesternAustralia. In these Australia. areas, In these there areas, there are significant improvements in the normalised errors from the uncorrected dataset to the arethere significant improvements are significant in the normalised improvements errors from in the normalised thefrom errors uncorrected dataset to the uncorrected the corrected dataset to the corrected one, indicating that there is a problem with satellite rainfall detection that cannot be one, indicating corrected one,that there is athat indicating problem there with satellite rainfall is a problem detection with satellite that cannot rainfall be accounted detection that cannotfor beby accounted for by higher rainfall averages. Possible reasons will be discussed in the next section. accounted higher foraverages. rainfall by higherPossible rainfall averages.will Possible reasons will be next discussed in the next section. A point-based comparison reasons using rain gaugesbe discussed in the categorised section. by states supported the gridded Apoint-based point-basedcomparison comparison using using rain rain gauges gauges categorised by states supported the thegridded comparison with the results shown in Figure 7. The unnormalised MAEsupported A categorised by states values suggest gridded that comparison comparison with withisthe the results results shown shown in Figure 7. The unnormalised MAE values suggest that performance decreased in theintropical Figure 7.regions The unnormalised MAE values and in Tasmania, suggest but after that performance normalisation, the performance is decreased in is the decreased tropical in regionsthe tropical and in regions Tasmania, and but in after Tasmania, but normalisation, after the normalisation, performance is the much performance is much higher even across the states. The performance is slightly worse in Queensland performance moreandeven South is much across Australia, higher the states. evenperformance The while gauge across the states. correction The to performance is slightly appears worse have the in is slightly effect worse Queensland greatest inand in Queensland South Tasmania. Australia, and South Australia, while gauge correction appears while gauge correction appears to have the greatest effect in Tasmania. to have the greatest effect in Tasmania. Figure 7. Point-based comparison categorised by states from January 2001 to December 2018 using Figure Figure Point-based 7. 7.gauges station Point-based comparison comparison categorised as truth. categorised by states states from from January January2001 2001totoDecember December2018 2018using using station gauges as truth. station gauges as truth.
Remote Sens. 2020, 12, x FOR PEER REVIEW 10 of 18 Remote Sens. 2020, 12, 678 10 of 17 3.2. Variation with Seasons A seasonal Remote 2020,analysis Sens. with 12, wasREVIEW x FOR PEER completed by categorising the data into four seasons with December, 10 of 18 3.2. Variation Seasons January, and February (DJF); March, April, and May (MAM); June, July, and August (JJA); and A seasonal 3.2. Variation September, analysis with October, andwas Seasons completed November (SON)byrepresenting categorisingaustral the data into four summer, seasons autumn, with December, winter, and spring January, and respectively. February (DJF); March, April, and May (MAM); June, July, and August (JJA); A seasonal analysis was completed by categorising the data into four seasons with December, and September, October, and and A gridded January, November February (SON) comparison (DJF);representing showing the austral March, April, summer, normalised and May MAE (MAM); autumn, June, winter, from the and July,CMORPH and spring August BLDrespectively. (JJA);dataset and is A gridded displayed in comparison Figure 8. Theshowing greatest the normalised seasonal MAE variation offrom the the CMORPH error is BLD observed September, October, and November (SON) representing austral summer, autumn, winter, and spring dataset towards is displayed the interior in Figure 8. The andrespectively. greatest seasonal variation of the error is observed towards the around the northern coastline with winter possessing the worst performance and summer havinginterior and around the thenorthern coastline best.A gridded with winter comparison possessing showing the worst performance the normalised MAE from the and summer BLD CMORPH having the best. dataset is displayed in Figure 8. The greatest seasonal variation of the error is observed towards the interior and around the northern coastline with winter possessing the worst performance and summer having the best. Figure8.8. Gridded Figure Gridded comparison comparison categorised categorised by by seasons seasons from from January January 2001 2001totoDecember December2018 2018using using Figure 8. Gridded comparison categorised by seasons from January 2001 to December 2018 using AWAP AWAP as truth. as truth. Normalised Normalised mean mean average average error from CMORPH BLD is displayed. AWAP as truth. Normalised mean averageerror errorfrom from CMORPH CMORPH BLD BLDisisdisplayed. displayed. Ananalysis An analysis using point gauge data datawas also performed with thethe results shown in Figure 9. The An analysis usingpoint pointgauge gauge data wasalso was also performed performed withwiththe resultsresults shownshown in Figurein 9.Figure The 9. MAE The MAE is the MAE isis thesmallest the smallest in SON smallestininSON and SONand largest andlargest in DJF largestininDJF DJF where where where the thethe error error error is approximately is approximately is approximately 50% 50% greater. greater. greater. Normalisation Normalisation of the errors results in the smallest relative error occurring in DJF Normalisation of the errors results in the smallest relative error occurring in DJF and the largest in in of the errors results in the smallest relative error occurring in DJF and and the the largest largest in MAM MAM MAM and andand JJA, JJA,JJA,supporting supporting supporting the gridded thethegridded comparison. griddedcomparison. The linear Thelinear comparison. The correlation linearcorrelation correlation coefficients coefficients coefficients across across across the the the seasons seasons also seasons also suggest also suggest suggest that that that DJF DJFDJF has hashas the thethe best best best performance across performanceacross performance across the the the seasons. seasons. seasons. The TheThe performance performance performance increase increase increase is is more more prominent isprominent more prominent inin in the the thenon-gauge non-gauge non-gauge blended blended blended datasets, datasets, datasets, where where where the the the improvement improvement improvement atisleast is at is at least least 10%. 10%. 10%. Figure 9. Cont.
Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 18 Remote Sens. 2020, 12, 678 11 of 17 Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 18 Figure 9. Point-based comparison categorised by seasons from January 2001 to December 2018 using Figure 9. Point-based Figure 9. Point-basedcomparison comparisoncategorised categorised by by seasons seasons fromJanuary from January2001 2001 to December 2018 using station gauges as truth. Mean average error (MAE), normalised MAE, and to December R are 2018 displayed. using station gauges station as truth. gauges Mean as truth. average Mean averageerror error(MAE), (MAE), normalised MAE,and normalised MAE, andR R are are displayed. displayed. Overall, the Overall, the performance performanceappears appearstotobe berelatively relativelysimilar similar across the seasons withthethe exception Overall, the performance appears to be relatively similaracross across the the seasons with seasons with the exception exception of of DJF, DJF, of which which shows showsshows DJF, which a somewhat a somewhat superior superior a somewhat performance performance superior performance to to the the rest. rest. to the rest. 3.3. Variations with 3.3. Variations Rainfall with Intensity Rainfall Intensity TheThe The effects effects ofofthe effects the intensity of intensity the ofof intensity ofthe the rainfall rainfall the onon rainfall thethe on accuracy accuracy accuracy ofthe of of the the data data datawerewere werealso also analysed. analysed. also analysed. The The Thedata were categorised into these bins: 0–0.2, 0.2–1, 1–2, 2–3, 3–4, 4–6, 6–9, and >9 mm/day. These rainfall data were data categorised were categorised into these into thesebins: bins:0–0.2, 0–0.2, 0.2–1, 0.2–1, 1–2, 1–2, 2–3, 2–3, 3–4, 3–4, 4–6, 4–6, 6–9, 6–9, and and >9 >9 mm/day. mm/day. TheseThese rangesrainfall rainfall were ranges ranges were chosen were to chosen chosen ensure to ensure tothere ensure were there there were a reasonable were a reasonable reasonable amount amount amount of values ofofvalues in eachin values each in bin binthe each with with bin the the with values of 0.2 values values and of 1 mmof 0.2 0.2 and and being1 mm1 mm beingspecifically being specifically specifically chosen chosen as chosen they as they as they correspond correspond correspond totothe to the rainy-day rainy-day the rainy-day thresholdthreshold forand threshold for BoM for aBoM BoM andand commonly a commonly a commonly used inused value used valueinincontingency value contingency contingency statistics statistics statistics studies, studies, studies,respectively respectively respectively [15]. [15]. Continuous Continuous [15]. Continuous statistics for statistics statistics for these bins were calculated along with a comparison of occurrence frequencies and and these binsfor were these bins were calculated alongcalculated along with with a comparison a comparison of occurrence of occurrence frequencies frequencies and cumulative volumes. cumulative volumes. These are shown in Figure 10. cumulative These volumes. are shown These10. in Figure are shown in Figure 10. Figure 10. Point-based comparison categorised by rainfall intensities from January 2001 to December 2018 using station gauges as truth. Occurrence frequencies, cumulative volumes, mean average error (MAE), and normalised MAE are displayed.
Remote Sens. 2020, 12, x FOR PEER REVIEW 12 of 18 Remote Sens. 2020, 12, 678 Figure 10. Point-based comparison categorised by rainfall intensities from January 2001 to December 12 of 17 2018 using station gauges as truth. Occurrence frequencies, cumulative volumes, mean average error (MAE), and normalised MAE are displayed. The datasets appear to capture the correct frequency best for rainfall amounts between 3 and 6 mm/day. For higher The datasets amounts, appear the the to capture satellite-derived correct frequency data underestimate best the frequency, for rainfall amounts between while 3 and 6for lower amounts, mm/day. the frequency For higher amounts, is the underestimated satellite-derived for data veryunderestimate low values (
Remote Sens. 2020, 12, x FOR PEER REVIEW 13 of 18 Figure 11. Gridded comparison of satellite datasets and AWAP against ERA5 reanalysis from January 2001 to December 2018. Mean bias (MB), root-mean-squared error (RMSE), mean average error Remote Sens. 2020, 12, 678 13 of 17 (MAE), R and normalised MAE are displayed. Figure Figure 12. Gridded comparison 12. Gridded comparison ofof satellite satellite datasets datasets and and AWAP AWAP against against ERA5 ERA5 reanalysis reanalysis from from January January 2001 2001 to to December December 2018. Quintile comparison 2018. Quintile comparison is is displayed. displayed. The The results results of of the the error error analysis analysis of of the the gridded gridded comparison comparison are are supported supported by by the the point-based point-based comparison comparison where both satellite datasets and AWAP were compared to station gauges with where both satellite datasets and AWAP were compared to station gauges with the errors the errors in AWAP being smaller but still within the same order of magnitude in AWAP being smaller but still within the same order of magnitude as those from the satellite as those from the satellite dataset. This highlights dataset. the caution This highlights theneeded cautionin understanding needed that the gridded in understanding comparison that the gridded results are comparison unlikely results are to be a proper depiction of the true error of the satellite unlikely to be a proper depiction of the true error of the satellite datasets. datasets. There There areare certain certain regions regions where where the the performance performance of of satellite satellite rainfall rainfall detection detection is is decreased. decreased. Past Past studies studies have have indicated indicated that that the the detection detection of of cold cold frontal-based frontal-based rainfall rainfall is is poor poor [15,17]. [15,17]. TheThe absence absence of of ice ice crystals crystals inin the relatively low the relatively low precipitating precipitating cloudsclouds typically typically associated associated with with frontal frontal rainfall rainfall hinders hinders the the ability ability ofof satellites satellites to to detect detect rainfall rainfall via via scattering scattering [15]. This is [15]. This is aa likely likely factor factor behind behind the the large large errors errors over Tasmania, Western Australia, South Australia, and central Australia, over Tasmania, Western Australia, South Australia, and central Australia, areas where the prevalent areas where the prevalent rainfall rainfall generation generation mechanism mechanism is is cold cold frontal frontal systems. Errors are systems. Errors are pronounced pronounced over over thethe western western halfhalf of of Tasmania Tasmania and and the the southwestern southwestern coast coast of of Western Western Australia, Australia, areas areas of of relatively relatively high high rainfall rainfall duedue to to increased increased exposure exposure to to westerly westerly flowflow and and associated associated coldcold fronts. fronts. Performance Performance is is also also known known to to be be decreased decreased over over topography topography [18,21]. [18,21]. Decreased Decreased performance performance is is observed observed along along the the eastern eastern coastline coastline near near the the Great Great Dividing Dividing Range. Range. The The errors errors are are greatest greatest alongalong thethe northern northern NSWNSW coastline coastline and and thethe Australian Australian Alps Alps where where thethe Great Great Dividing Dividing RangeRange is is atat its its highest highest elevations, leading to a strong orographic influence elevations, leading to a strong orographic influence on rainfall. on rainfall. A high-qualityrain A high-quality raingauge gauge network network is extremely is extremely valuable valuable for improving for improving the accuracy the accuracy of of satellite- satellite-derived rainfall estimates as satellite estimates rely on gauges to derived rainfall estimates as satellite estimates rely on gauges to calibrate or correct their raw values.calibrate or correct their raw values. The significantly The significantly greatergreater number number of gauges of gauges towards towards thethe coastline coastline wheremost where most of of Australia’s Australia’s population population resides allows for a much greater improvement from gauge correction in contrast to resides allows for a much greater improvement from gauge correction in contrast to the the interior of the continent. Consequently, areas towards the coastlines interior of the continent. Consequently, areas towards the coastlines that experience problematic that experience problematic regimes regimes such such as cold-frontal rainfall as cold-frontal rainfall and and orographically orographically influenced influenced rainfall rainfall greatly greatly benefit benefit fromfrom gauge gauge correction, correction, resulting in a performance similar to unproblematic regimes. However, the lack of resulting in a performance similar to unproblematic regimes. However, the lack of rain rain gauges gauges towards the interior means there are still large normalised errors in this region, even in the towards the interior means there are still large normalised errors in this region, even in the gauge-corrected gauge-corrected dataset.dataset. ThisThis is is compounded compounded by by the the tendency tendency of of rainfall rainfall toto be be lighter lighter towards towards the the interior interior compared comparedtotothe thecoast coast as as light rainfall light has has rainfall beenbeen shown to beto shown a problematic be a problematicregimeregimeas well as[17,18]. well Low mean rainfall is another factor that would contribute to a large normalised MAE. Some [17,18]. areasLow of large mean normalised rainfall is MAE another around factorthe interior that wouldofcontribute the continent to a can large benormalised seen to generallyMAE. Some align with areasareas of low of large mean rainfall normalised MAEvalues,aroundasthe seen in Figure interior 13, continent of the which depicts can betheseen seasonal mean rainfall to generally align across Australia. This is especially true during the austral winter ‘dry’ season with areas of low mean rainfall values, as seen in Figure 13, which depicts the seasonal mean rainfall for central Australia and northwards towards the Northern Territory coast. across Australia. This is especially true during the austral winter ‘dry’ season for central Australia and northwards towards the Northern Territory coast.
Remote Sens. 2020, 12, 678 14 of 17 Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 18 Figure Figure13. 13.Mean MeanCMORPH CMORPHBLD BLDrainfall rainfallby byseason seasonfrom fromJanuary January2001 2001totoDecember December2018. 2018. The Theimportance importanceofofgauge gaugecorrection correctionisisreduced reducedfor for unproblematic unproblematic regimes. regimes. ForForexample, example,the the normalised normalised errors for forthethecorrected corrected andand uncorrected uncorrected datasets datasets around around the northern the northern coastlinecoastline of of Australia Australia are relatively similar, highlighting how the raw satellite algorithms exhibit decent are relatively similar, highlighting how the raw satellite algorithms exhibit decent performance in these performance areas, leading intothese gauge areas, leadingbeing correction to gauge correction less crucial. being less crucial. Tropical-based rainfallTropical-based has been notedrainfall to be onehasof been noted to be one ofregimes the better-performing the better-performing regimes for satellite rainfall for satellite detection [15]. rainfall detection [15]. Satellite-derived Satellite-derivedprecipitation precipitationestimates estimates for for austral austral winter demonstrate the the worst worst performance, performance,a aresult resultthat thatagrees agreeswith with pastpast studies studies [15]. [15]. TheThe difficulty difficulty of detecting of detecting cold-frontal cold-frontal rainfall, rainfall, which which is is more more frequentfrequent during during winter,winter, is mostislikely mosta keylikely a key factor. The factor. The introduction introduction of snowchallenge of snow is another is another for challenge for satellite satellite detection detection of of precipitation andprecipitation and is likely is likely a contributing a contributing factor factor to the to the poor performance poor observed performance in western Tasmaniaobserved and inthe western Tasmania Australian Alps. By and the Australian contrast, the greater Alps. By contrast, prevalence the greater of convective-based prevalence of convective-based rainfall in summer is a reason for rainfall in summer this season is a reason performing the best for[15,17]. this season performing the best [15,17].An overestimation (underestimation) of low (high) rainfall rates was observed and is consistent withAn pastoverestimation literature [19,20]. (underestimation) of low (high) rainfall rates was observed and is consistent with past It is literature natural to[19,20]. expect that CMORPH BLD (a gauge-blended dataset) should have at least equal It is natural performance to to expect(athat AWAP CMORPHanalysis) gauge-based BLD (a gauge-blended as it relies on dataset) shouldwhere using gauges have at theleast dataequal exist performance whilst depending to AWAP more(a gauge-based heavily analysis) on satellites where asthere it relies on using is little gaugesdata. to no gauge where the datathe However, exist key whilst depending assumption here is more that heavily satelliteon satellites depiction ofwhere rainfallthere is littleto is superior tointerpolation no gauge data. However, methods the key in areas with assumption here This little to no data. is that satellite is not depiction necessarily true,of as,rainfall is superior even though to interpolation satellites methods are sourcing their in areasa data through with littlesensor, physical to no data. This is still this process not necessarily relies heavily true, as, even though on calibration to rainsatellites are sourcing gauge data. theirwhere For locations data through a physical there is little sensor,data, to no gauge thiscalibration process still and,relies heavily onperformance subsequently, calibration will to rain gauge data. be severely For hindered. locations Furthermore, whereAWAP there usedis little to no gauge a minimum data, of number calibration and, subsequently, stations exceeding 3000 whileperformance will be the satellite datasets severely hindered. are calibrated Furthermore, to the CPC Unified AWAP gaugeused a minimum analysis, which has number of stations a minimum exceeding number 3000 while of stations across the satelliteatdatasets Australia least anare calibrated order to the CPC of magnitude less Unified than that gauge of AWAPanalysis, which [29,30]. Thehas a minimum ingestion number of less data is oflikely stations across Australia to contribute at least an observed. to the discrepancies order of magnitude less than that of AWAP [29,30]. The ingestion of less data is likely to contribute to the discrepancies observed.
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