Correction of TRMM 3B42V7 Based on Linear Regression Models over China

,


Introduction
Precipitation plays a vital role in global energy and water cycle exchanges, connecting the hydrosphere, atmosphere, lithosphere, and biosphere [ ]. e reliable spatial-temporal measurement of regional and global precipitation is critical for the hydrological modelling (particularly in distributed hydrological model), water resource management, and the prevention of natural disasters [ , ].However, the reliable and accurate estimation of precipitation remains a challenge due to the high spatial-temporal variability of climate and underlying heterogeneity [ , ].
Despite the insu cient spatial resolution of conventional precipitation gauges, gauge precipitation is still the most accurate source of direct precipitation measurement and continues to be the critical role in documenting the precipitation characteristics over regional and global land attributed to the long-term recording period [ -].Several datasets of precipitation products have been constructed over regional a n dg l o b a ld o m a i n sb a s e do nt h eg a u g ep r e c i p i t a t i o n :C R U TS .monthly grid precipitation dataset during coversalllandareasofearthwithspatialresolution .∘ [ ]; Global Precipitation Climatology Center (GPCC) datasets with spatial resolution of .∘ use the station database (SYNOP, CLIMAT) available via the Global Telecommunication System (GTS) of the World Meteorological Organization (WMO) from to [ ]; CPC uni ed gaugebased analysis of global daily precipitation has been constructed on a .∘ resolution over the entire global land a n di sr e l e a s e da t .∘ resolution over the global domain from to the present (https://climatedataguide.ucar.edu/climate-data/cpc-uni ed-gauge-based-analysis-global-dailyprecipitation); and other regional gauge based precipitation datasets [ -].Accordingly, the gauge based precipitation datasets were widely applied into the climate diagnostics and hydrological researches [ , -].Nevertheless, the utilization of gauge precipitation products is limited in the area with nongauge/sparse gauge networks such as ocean, Advances in Meteorology desert, and mountainous area, especially in developing countries [ , , ], due to the low spatial resolution and inaccuracy.
In order to better understand the spatial distribution of precipitation, some high resolution precipitation products based on the remote sensing data (infrared, passive microwave radiometers, and precipitation radar) and gauge p r e c i p i t a t i o nh a v eb e e np r o d u c e di nr e c e n ty e a r s :G l o b a l Precipitation Climatology Project (GPCP) product provides monthly precipitation products on .∘ grid from to the present [ ] and daily precipitation estimation on ∘ grid over the entire globe from October to the present [ ]; Precipitation Estimation from Remotely Sensed Information using Arti cial Neural Networks (PERSIANN) is a satellitebased precipitation retrieval algorithm that provides near real-time precipitation information, and the precipitation dataset covers TRMM version (TRMM V ) released in May contains two kinds: the real-time gridded precipitation product ( B RTV ) with a near-global ( ∘ N-∘ S) coverage and a gauge-adjusted, post-real-time research product ( B V ) with coverage from ∘ N-∘ S. Both B RTV and B V have a high spatial ( .∘ )andtemporal( hour)resolution.Numerous researches have pointed out that the TRMM V improves upon TRMM V in di erent countries including continental United States and China, notably the research product B V [ , ].
Although TRMM B V (TRMM precipitation) has been veri ed more realistically than other RSPPs, the utilization of TRMM precipitation is still limited by its regional inaccuracy and low resolution.Moreover, the real-time and high-density gauge precipitation is not available, and the open access gauge precipitation is always limited with lowdensity, particularly in developing countries such as China.As a result, high resolution precipitation remains a challenge to the scienti c community and public in China [ , , ].Nevertheless, several researches have shown that there is a good relation between TRMM precipitation and gauge prec i p i t a t i o n[ , , ] ,y e tr a r ee o r th a sb e e nf o c u s e do n the quantitative relation between TRMM precipitation and gauge precipitation.erefore, the objective of this paper is to construct linear regression models (LRMs) in order to correct and downscale TRMM precipitation based on the historical long-term and high-density gauge precipitation, and then the real-time and high resolution precipitation can be obtained from the timely TRMM precipitation through LRMs with the parameters estimated by the historical precipitation.To this regard, the suitable temporal scale was identi ed to correct the TRMM precipitation based on the relation between TRMM precipitation and gauge precipitation; then the TRMM precipitation was corrected and validated by the LRMs at di erent time scales.e paper is organized as follows: Section describes the study area and data preparation.Section provides a brief introduction of statistical indices and LRMs.Section presents the results and discussions, and the conclusions are given in Section .

Study Area and Data
2.1.Study Area.China is located in East Asia along the Paci c Ocean, and the spatial-temporal distribution of precipitation in China is mainly a ected by the East Asian monsoon.Besides, the terrain is complex and altitude is increasing from negative (eastern plains) to higher than m (Tibetan plateau) (Figures (a)  TRMM B version product from to ,hourly temporal and 0.25 ∘ × 0.25 ∘ spatial scales, was originated from the National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploratory Agency (JAXA) and had been accumulated into daily/monthly/ annual scales over China.It is necessary to note that there are about out of stations used into GPCC datasets, which were utilized to validate the TRMM dataset.us, the TRMM dataset is not independent of gauge precipitation data [ , ].
To compare the TRMM precipitation and gauge precipitation at station and grid scales, the daily TRMM precipitation at stations was obtained from grids covering the corresponding stations and was accumulated into monthly and annual TRMM precipitation.en TRMM precipitation   at stations was evaluated based on the gauge precipitation at station scale.Moreover, in order to evaluate the detailed spatial distribution of TRMM precipitation over China domain at grid scale, the TRMM precipitation was r e s a m p l e di n t og r i d sa t k mr e s o l u t i o n ,w h i c hi st h em o s t common resolution for TRMM precipitation downscaling [ -].Correspondingly, the monthly gauge precipitation was interpolated into grids with km resolution as the reference precipitation by the Inverse Distance Weighting (IDW) with a variable search radius of nearest gauge stations.

Advances in Meteorology
e IDW is a certain interpolation method and has been con rmed to be a suitable interpolation for precipitation in China, especially with the a dense gauge network [ , ].

Statistical Indices.
In order to identify the suitable time scale to construct the LRM between TRMM precipitation and gauge precipitation, the Pearson Correlation Coecient (PCC) was employed to analyse the relation between gauge precipitation and TRMM precipitation at di erent time scales.Furthermore, Root Mean Square Error (RMSE) Advances in Meteorology and Bias were applied to validate the TRMM precipitation, expressed as follows: where TRMM and Gauge are annual or monthly TRMM precipitation and gauge precipitation and TRMM and Gauge are the average values of TRMM and Gauge ,respectively .

Linear Regression Model.
e LRM was applied to quantify the statistic relation between TRMM precipitation and gauge precipitation at grid and regional scales.e o set parameter and scale parameter can be estimated by the ordinary least squares methods (OLS) as ( ) and ( ), and 2 and test statistic are used to identify whether the LRM ts into the relation between TRMM precipitation and gauge precipitation and formulated as ( ) and ( ).
where TRMM and Gauge are TRMM precipitation and gauge precipitation in month/year ,respectively, TRMM and TRMM are average monthly/annual precipitation from January to December , ̂ , ̂ are the estimation of o set and scale parameter, separately, is the random error, and is the length of series ( = 192 at monthly scale; =1 6at annual scale).
According to the previous researches, there is a good relation between gauge precipitation and TRMM precipitation at monthly and annual scales [ , , ].Consequently, the LRMs were constructed based on monthly and annual relation between gauge precipitation and TRMM precipitation, separately.For the monthly LRM, monthly corrected TRMM precipitation can be calculated from monthly gauge precipitation based on the monthly LRM, and annual corrected TRMM precipitation was accumulated by the monthly corrected TRMM precipitation.For the annual LRM, annual corrected TRMM precipitation was obtained from annual gaugeprecipitationbasedonannualLRM,andmonthlycorrected TRMM precipitation was computed by the following: and TRMM are the corresponding original TRMM precipitation.

Results and Discussions
: Distribution of PCCs between grid gauge precipitation and TRMM precipitation at monthly and annual scales over China.
grid gauge precipitation and TRMM precipitation at km resolution are gured out in Figure .It can be seen that there are more than .% of total grids with signi cant PCC at the level of = 0.01 (PCC =0.01,n=192 = .
)atmonthlyscale and only about three quarters of total grids with signi cant P C Ca tt h el e v e lo f = 0.01 (PCC =0.01,n=16 = . )a t annual scale.Additionally, the grids with low PCCs value are mostlylocatedinNorthwestChinaandTibetanplateauwith sparse gauge networks.

. 2 .L i n e a rR e g r e s s i o nM o d e lR e s u l t s .
e LRMs are constructed to correct and downscale the original TRMM precipitation at monthly and annual scales, separately.

Validation at Grid Scale.
Based on the monthly and annual grid gauge precipitation over China obtained from the spatial interpolation of gauges precipitation in , three TRMM precipitation datasets were validated on the km resolution grid-by-grid over China.e spatial distributions of annual grid gauge precipitation and original/corrected TRMMprecipitationin areshowninFigure .Itdemonstrates that spatial distribution of grid gauge precipitation and three TRMM precipitation datasets are consistent, and two corrected TRMM precipitation datasets improve the accuracy with statistics more approximated to that of grid gauge precipitation.Besides, the annual precipitation in the three regions was validated by grid-by-grid statistic (Table ); the results indicate that two corrected TRMM precipitation datasets improve the accuracy of annual precipitation with decreased RMSE, Bias, and increased 2 , yet there is no   N o r t h w e s tC h i n a .ep o s s i b l er e a s o ni st h a ts t a t i o ng a u g e precipitation is in good agreement with the corresponding TRMM precipitation in Mideastern China with high PCC, andthegridgaugeprecipitationobtainedfromhigh-density g a u g en e t w o r k si sa c c u r a t ea n dc o n s i s t e n tw i t hT R M M precipitation over Mideastern China.erefore, the statistics such as RMSE and 2 have a slight improvement attributed to the increase of samples from a statistic standpoint (number o fg r i d si sd r a m a t i c a l l yl a r g e rt h a nn u m b e ro fs t a t i o n si n Mideastern China).It also indicates that the grid gauge precipitation obtained by IDW interpolation is accurate and reliable in Mideastern China.In contrast, station gauge precipitation does not correlate well with the corresponding TRMM precipitation due to the complicated terrain and climate characteristics in Northwest China and Tibetan plateau.e reason is that the low-density and unevenly distributed gauge networks produce an inaccurate grid gauge precipitation, which contributes to the poor relation between grid gauge precipitation and TRMM precipitation there and result in a larger error of corrected TRMM precipitation.In addition, the interpolated precipitation from gauges precipitation is inevitably di erent from that from gauge precipitation and also brings error in the validation of corrected TRMM precipitation.Compared with the validation results at station scale, it can be inferred that there is almost no in uence of interpolated precipitation on the corrected TRMM precipitation in Mideastern China, yet the error of interpolated precipitation in Tibetan plateau slightly increases the error of corrected TRMM precipitation.Accordingly, the error of interpolated precipitation obviously reinforces the error of corrected TRMM precipitation in Northwest China due to the apparent deviation between gauge precipitation and original TRMM precipitation at station scale.

Advances in Meteorology
Subsequently, the average monthly grid gauge precipitation and original/corrected TRMM precipitation in the three r e g i o n si n a r es h o w ni nF i g u r e ,a n dt h es t a t i s t i c so f monthly areal original/corrected TRMM precipitation versus gauge precipitation in the three regions are listed in Table .It should be noted that the statistics in Table were calculated by the monthly areal original/corrected precipitation in the three regions and are di erent from the aforementioned statistics obtained at station or grid scale in the three regions.
erefore, the RMSE and 2 areincomparabletothoseinFigure .e result indicates that original TRMM precipitation is in good agreement with the gauge precipitation in Mideastern China, and it overestimated the precipitation in Tibetan Prec (mm) 0 100 200 400 600 800 1000 1200 1600 2000 3300 Prec (mm) 0 100 200 400 600 800 1000 1200 1600 2000 3300 Plateau and Northwest China during ooding season (Jul-Sep) and dry month (Jan-Mar), separately.Moreover, two corrected TRMM precipitation datasets have improved the accuracy of TRMM precipitation signi cantly with approximated mean areal precipitation in the three regions, yet the improvement in Northwest China is insigni cant.e reason is that the relation between gauge precipitation and TRMM precipitation is uncertain attributed to the low-density gauge networks and scarce precipitation there, which results in uncertainty in two LRMs.

Conclusions and Remarks
TRMM B V is an important remotely sensed precipitation products for precipitation estimation with high temporal-spatial resolution.In this study, monthly and  annual LRMs had been constructed to correct and downscale the TRMM precipitation based on the gauge precipitation at stations over China from to .en, the gauge precipitation at out of station in was used to validate the corrected TRMM precipitation at station and grid scales.
According to the results of LRMs, monthly LRM is more suitable for the correction of TRMM precipitation over China from a statistical standpoint, since there is less than .% of China mainland with insigni cant statistic in monthly LRM and about % of China mainland with insigni cant statistic in annual LRM at .signi cant level.Most of grids with insigni cant statistic concentrate in Northwest China and Tibetan plateau.Additionally, the o set parameter and scale parameter are more random and uncertain attributed to the shorter length of input series in annual LRM ( =1 6 ) than that in monthly LRM ( = 192), especially in Northwest China and Tibetan plateau.
Validations of original/corrected TRMM precipitation indicate that two LRMs have obviously improved the accuracy of TRMM precipitation with acceptable error, and monthly LRM performs slightly better than annual LRM in Mideastern China.Although the performance of corrected TRMM precipitation from LRMs has been increased in Northwest China and Tibetan plateau, the error of corrected TRMM precipitation is still signi cant due to the larger deviation between gauge precipitation and TRMM precipitation, which reinforces the error of interpolated precipitation, especially in Northwest China.
Consequently, it can be concluded that LRMs are essential accesses to obtain real-time and high spatial-temporal precipitation from open access TRMM precipitation in Mideastern China, which will be meaningful for the hydrological modelling and water resource management in the regions without (open access) gauge stations.Furthermore, it reveals that the performance of corrected TRMM precipitation signi cantly depended on the relation between original TRMM precipitation and gauge precipitation.e reasons are that ( ) the potential hypothesis in LRM is that there is good linear relation between dependent variable and independent variable.us the poor relation between gauge precipitation and TRMM precipitation will lead to signi cant error of corrected TRMM precipitation.( ) e poor relation between gauge precipitation and TRMM precipitation at station scale will be ampli ed by the spatial interpolation and has a profound in uence on the accuracy of corrected TRMM precipitation, especially in the regions with sparse gauge networks.

China
of China and geographic distribution of the precipitation gauges (a), distribution of average monthly precipitation (b), and a typical topographic pro le across China (c).
gauge precipitation and TRMM precipitation in stations.
Gauge are the monthly and annual corrected TRMM precipitation of th month ( = 1,2,...,12)a n d th year( = 1998, 1999, ...,2013)f r o ma n n u a lL R Ma n d TRMM , 4.1.Correlations between Gauge Precipitation and TRMM Precipitation.Relation between gauge precipitation and TRMM precipitation is complicated not only in spatial distribution b u ta l s oi nt e m p o r a ls c a l e s .H e n c e ,as u i t a b l et i m es c a l ei s important for the correction of TRMM precipitation.e cumulative distribution function (CDF) of PCCs between gauge precipitation and TRMM precipitation at stations at di erent time scales during -is shown in Figure .I tc a nb es e e nt h a tt h eP C C sa tm o n t h l ya n da n n u a ls c a l e s are signi cantly larger than the PCC at daily scale.It implies that TRMM precipitation at monthly and annual scales, especially at monthly scale, is in good agreement with gauge precipitation, which agrees with the previous researches[ ,  ].Furthermore, the monthly and annual PCCs between Figure shows the results of monthly LRM; the o set parameter ranging from − to over China mostly concentrates in the range between − and (Figure (a)).Meanwhile, the scale parameter is ranging from . to . in Eastern China and is unevenly distributed in Northwest China and Tibetan plateau (Figure (b)).
Figure (c)  sheds light on 2 of the LRM, and it illustrates that 2 is signi cantly larger than .over China, except for Northwest China and Tibetan plateau.e statistic of the LRM is distributed inFigure (d); it can be seen that there was about .× 5 km 2 accounting for .% of China mainland with statistic under .(the threshold at the .signi cant level when = 192), which indicates that monthly LRM is suitable for the correction of TRMM precipitation over China.e results of annual LRM are displayed in Figure .It illustrates that the range of o set parameter is obviously larger and more unevenly distributed than that in monthly LRM over China (Figure (a)).e distribution of scale parameter , 2 , test value are consistent with that in monthly LRM (Figures (b)-(d)), yet the value of 2 and statistic exhibit an apparent decrease.e reason is that the length of input series in annual model ( =1 6 )isobviously less that in monthly LRM ( = 192), which has a profound in uence on the parameter estimation and model test from a statistical standpoint.As a result, parameters and are more uncertain and unevenly distributed, and the value of 2 and statistic are signi cantly decreased.Based on the signi cance test result (Figure (d)), there is about .× 6 km 2 , accounting for about % of China mainland, with the statistic under .(the threshold at .signi cant level when =1 6 ) mainly located in Northwest China and Tibetan plateau.Compared with statistic result in monthly LRM, it can be inferred that monthly LRM is more suitable for the correction of TRMM precipitation over China from a statistical standpoint.4.3.Validation of Linear Regression Models 4.3.1.Validation at Station Scale.e gauge precipitation at stations in was used to validate original TRMM precipitation (TRMM prec ), TRMM precipitation corrected by monthly LRM (TRMM prec ), and TRMM precipitation corrected by annual LRM (TRMM prec ).e scatterplots of annual gauge precipitation versus original/corrected TRMM precipitation in the three regions at station scale are 80 ∘E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘ E 80 ∘ E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘ 80 ∘ E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘ 80 ∘ E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘regression model result over China: (a) o set parameter , (b) scale parameter ,(c) 2 ,and(d) statistic.in Figure .It can be seen that two LRMs have obviously improved the precipitation accuracy compared to the original TRMM precipitation with increased 2 and decreased RMSE and Bias, and monthly LRM performs slightly better than annual LRM with smaller RMSE in Mideastern China.Figure displays the scatterplots of monthly gauge precipitation versus original/corrected TRMM precipitation in the three regions at station scale.In comparison of the relations between gauge precipitation and original TRMM precipitation in the three regions, the original TRMM precipitation in Northwest China deviates more from the gauge precipitation at station scale than that in Mideastern China and Tibetan plateau.As a result, although 2 from two corrected TRMM precipitation datasets has a remarkable increase compared with that from original TRMM precipitation, it is still low in Northwest China.80 ∘ E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘ E 80 ∘ E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘ E 80 ∘ E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘ E 80 ∘ E 90 ∘ E 100 ∘ E 110 ∘ E 120 ∘ E 130 ∘ E 140 ∘ E regression model results over China: (a) o set parameter , (b) scale parameter ,(c) 2 ,and(d) statistic.
annual gauge precipitation versus original/corrected TRMM precipitation in the three regions at station scale.T: Validation of annual TRMM precipitation in the three regions in at grid scale.
monthly gauge precipitation versus original/corrected TRMM precipitation in the three regions at station scale.
spatial distribution of annual gauge precipitation (a), original TRMM precipitation (b), and corrected TRMM precipitation obtained from monthly (c) and annual (d) LRMs in over China mainland.
gauge precipitation and original/corrected TRMM precipitation in the three regions in .
∘ Sto ∘ Ngloballyata .∘ resolution and is available from March to the present [ , ]; CMORPH (CPC Morphing technique) produces global precipitation analyses covering ∘ Sto ∘ N globally at a very high spatial ( . ∘ ) and temporal ( minute) resolution from to the present; TRMM Multisatellite Precipitation Analysis generates a series of the most widely used precipitation products with a near-global coverage and adequate spatialtemporal resolution from to the present [ , ].
Validation of monthly original/corrected TRMM precipitation in the three regions in at regional scale.