Uncertainty in Estimated Trends Using Gridded Rainfall Data: A Case Study of Bangladesh

This study assessed the uncertainty in the spatial pattern of rainfall trends in six widely used monthly gridded rainfall datasets for 1979–2010. Bangladesh is considered as the case study area where changes in rainfall are the highest concern due to global warming-induced climate change. The evaluation was based on the ability of the gridded data to estimate the spatial patterns of the magnitude and significance of annual and seasonal rainfall trends estimated using Mann–Kendall (MK) and modified MK (mMK) tests at 34 gauges. A set of statistical indices including Kling–Gupta efficiency, modified index of agreement (md), skill score (SS), and Jaccard similarity index (JSI) were used. The results showed a large variation in the spatial patterns of rainfall trends obtained using different gridded datasets. Global Precipitation Climatology Centre (GPCC) data was found to be the most suitable rainfall data for the assessment of annual and seasonal rainfall trends in Bangladesh which showed a JSI, md, and SS of 22%, 0.61, and 0.73, respectively, when compared with the observed annual trend. Assessment of long-term trend in rainfall (1901–2017) using mMK test revealed no change in annual rainfall and changes in seasonal rainfall only at a few grid points in Bangladesh over the last century.


Introduction
Trend analysis provides important information required for planning adaptation and mitigation to climate changes [1].Therefore, a large volume of literature is available on trend analysis of various climatic variables using different methods [2,3].One of the major impediments to the analysis of climatic trends is the availability of long-term quality climate data.Reliable analysis of climatic trends requires high-quality data for at least 30 years [4], which is often difficult to obtain for many regions of the world.Gridded climate data are suggested for such study in regions where long-term high-quality climate data are not available.With the pace of development, the reliability of gridded climate data in replicating actual properties of regional climate has been improved, and therefore such data has been widely used for climatic trend analysis across the world.
Though reliability in trends obtained using gridded data has been reported in many studies [3,[5][6][7][8], uncertainty in results is still a major issue.Gridded climate data can be broadly classified as gauge-based, remote-sensing based, reanalysis, or a hybrid of those methods [9].The uncertainty in

Climate of Bangladesh
Bangladesh, located in the deltas of large powerful rivers, has an extremely flat topography, except for some uplifted lands and hills in the northeast and the southeast (Figure 1).According to the Köppen classification, Bangladesh has monsoon (Am), tropical savanna (Aw), and humid subtropical climates (Cwa).The country has four seasons, namely hot summer pre-monsoon (MAM), rainy monsoon (JJAS), autumn post-monsoon (ON), and dry winter (DJF).The rainfall of Bangladesh varies spatially, from 1500 mm in the northwest to about 4400 mm in the northeast [11] (Figure 2).Monsoon rainfall accounts for the majority of the total annual rainfall of Bangladesh [11,28,29].
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Climate of Bangladesh
Bangladesh, located in the deltas of large powerful rivers, has an extremely flat topography, except for some uplifted lands and hills in the northeast and the southeast (Figure 1).According to the Köppen classification, Bangladesh has monsoon (Am), tropical savanna (Aw), and humid subtropical climates (Cwa).The country has four seasons, namely hot summer pre-monsoon (MAM), rainy monsoon (JJAS), autumn post-monsoon (ON), and dry winter (DJF).The rainfall of Bangladesh varies spatially, from 1500 mm in the northwest to about 4400 mm in the northeast [11] (Figure 2).Monsoon rainfall accounts for the majority of the total annual rainfall of Bangladesh [11,28,29].

Observed Data
Daily observed rainfall data of 34 stations distributed over Bangladesh (Figure 1) for 1979-2010 were collected from the Bangladesh Meteorological Department.Long-term rainfall records are available for many locations in Bangladesh.However, data before 1979 contain a large number of missing records, while missing data after 1979 is very uncommon.Complete daily rainfall data after 1979 was available at 10 stations.Missing data at other stations was less than 1%.The missing data was mostly random.Continuous missing data for two to three months a year were found at four stations.Data for the whole year was discarded when it was found that data was missing continuously for a month.Randomly missing data were filled up using an artificial neural network (ANN) model developed by Shahid [30].The ANN model was used to estimate the missing value at the station of interest from the rainfall of six neighbouring stations.
The complete daily rainfall data generated for the period 1979-2010 (after filling the missing data) was used in this study.The double mass curve method [31] was used to detect the non-homogeneity in the annual rainfall time-series where an almost straight line without any breakpoints was observed at all

Observed Data
Daily observed rainfall data of 34 stations distributed over Bangladesh (Figure 1) for 1979-2010 were collected from the Bangladesh Meteorological Department.Long-term rainfall records are available for many locations in Bangladesh.However, data before 1979 contain a large number of missing records, while missing data after 1979 is very uncommon.Complete daily rainfall data after 1979 was available at 10 stations.Missing data at other stations was less than 1%.The missing data was mostly random.Continuous missing data for two to three months a year were found at four stations.Data for the whole year was discarded when it was found that data was missing continuously for a month.Randomly missing data were filled up using an artificial neural network (ANN) model developed by Shahid [30].The ANN model was used to estimate the missing value at the station of interest from the rainfall of six neighbouring stations.
The complete daily rainfall data generated for the period 1979-2010 (after filling the missing data) was used in this study.The double mass curve method [31] was used to detect the non-homogeneity in the annual rainfall time-series where an almost straight line without any breakpoints was observed Water 2019, 11, 349 6 of 23 at all the stations.Besides, a Student's t-test [32] was used, which revealed that the variations between different sub-samples of rainfall data were statistically insignificant at a 95% level of confidence.

Gridded Datasets
Six gridded rainfall datasets were used in this study: (1) 2 presents a summary of datasets used.An elaborate review of the datasets is presented in the following sections.The spatial distributions of average annual rainfall obtained using each dataset are given in Figure 2.Although APHRODITE and PGF are available at a resolution of 0.25 • × 0.25 • , these were aggregated to 0.5 • × 0.5 • resolution for uniform presentation and comparison.

Evaluation of Gridded Datasets
The performance of six gridded rainfall datasets was evaluated based on their ability to replicate: (a) the monthly observed rainfall at 34 stations; and (b) the spatial pattern in the magnitude and significance of annual and seasonal rainfall trends in Bangladesh.Prior to evaluation, APHRODITE, CPC, and PGF daily rainfall were converted into monthly rainfall.A flowchart showing an overview of the methodology used in this study is presented in Figure 3.There are two general ways to compare gridded data with station observation: (i) areal average precipitation for each grid box is computed from available station data and then a grid-to-grid comparison is conducted; (ii) gridded data is interpolated to station location and then compared with observed data [1,10,33].Both the methods were used in this study for the comparison of the performance of gridded data.For the assessment of the gridded rainfall using the second approach, the monthly rainfall series of the four nearest grid points surrounding a station were interpolated at the station location using the inverse distance weighting method [10].These interpolated series were compared with the observed gauge series.Four established statistical indices were adopted to evaluate the performance of gridded data in simulating the monthly observed rainfall: these are the Root-Mean-Square Error (RMSE), Kling-Gupta Efficiency (KGE) index, modified index of agreement (md), and Skill Score (SS).These statistical indices are widely used in the evaluation of gridded data [7,10,34].RMSE represents the standard deviation of error in simulation.Developed by Gupta et al. [35], KGE (Equation ( 1)) is an integrated index that represents the correlation and bias, and similarity in variability between observed and gridded data.The md calculates the additive and proportional differences between the mean and variance of observed and gridded data [36], as in Equation (2).The SS (Equation (3)) measures the overlap between the observed and simulated probability distribution functions [37].The optimal value of RMSE is zero.Therefore, values of KGE, md, and SS near to 1 indicate a better match between observed and gridded data.
where r is person's correlation; µ and σ represent mean and standard deviation, respectively, of simulated (sim) and observed (obs) data; n referrers to the number of grid points; x obs,i is the observed time-series of station i; x sim,i is the interpolated time-series from the gridded data at station i; x obs is the mean of x obs ; j is an arbitrary positive power; and f sim and f obs are the probability distribution of gridded and observed data, respectively.
represents the standard deviation of error in simulation.Developed by Gupta et al. [35], KGE (Equation ( 1)) is an integrated index that represents the correlation and bias, and similarity in variability between observed and gridded data.The md calculates the additive and proportional differences between the mean and variance of observed and gridded data [36], as in Equation ( 2).The SS (Equation ( 3)) measures the overlap between the observed and simulated probability distribution functions [37].The optimal value of RMSE is zero.Therefore, values of KGE, md, and SS near to 1 indicate a better match between observed and gridded data.
where  is person's correlation;  and  represent mean and standard deviation, respectively, of simulated (sim) and observed (obs) data; n referrers to the number of grid points;  , is the observed time-series of station i;  , is the interpolated time-series from the gridded data at station i;  is the mean of  ; j is an arbitrary positive power; and  and  are the probability distribution of gridded and observed data, respectively.

Trend Analysis
Sen's slope [38] was used to calculate the magnitude of change in observed and gridded monthly rainfall data, while MK [39,40] and mMK [41,42] tests were used to assess the significance in change.The non-parametric MK method is widely used for trend tests since it needs only the assumption of data independence as serial autocorrelation in data can increase the chance of significance in trend [18,43].However, recent studies have shown that the significant trends over time were also sensitive to the

Trend Analysis
Sen's slope [38] was used to calculate the magnitude of change in observed and gridded monthly rainfall data, while MK [39,40] and mMK [41,42] tests were used to assess the significance in change.The non-parametric MK method is widely used for trend tests since it needs only the assumption of data independence as serial autocorrelation in data can increase the chance of significance in trend [18,43].However, recent studies have shown that the significant trends over time were also sensitive to the assumptions of whether the underlying data have short-term or long-term autocorrelation.Koutsoyiannis and Montanari [44] stated that MK trend test statistic is heavily affected by long-term autocorrelation due to multi-decadal variability of climate.Thus, the MK test overestimates the significance of trend due to long-term fluctuation in time series caused by natural variability in climate.Hamed [42] proposed an mMK trend test that takes scaling of the data into account to discriminate Water 2019, 11, 349 8 of 23 the multi-scale variability from unidirectional trends.Several recent studies in different regions have concluded that significant trends in hydro-climatic data obtained using the MK test resulted from ignoring the natural variability of climate [3,6,20,45,46].Therefore, the mMK test was used in this study to confirm the trend detected using the MK test.In the mMK test, the significant trend found in time series was first removed.The equivalent normal variants of the rank of the de-trended series were then obtained to derive the Hurst coefficient and its significance.If the Hurst coefficient was found to be significant, the significance of the mMK trend was estimated using a function proposed by Hamed [42].The full description of the Sen's slope, MK, and mMK methodologies can be found in [3,[39][40][41].

Assessment of Spatial Similarity
Four indices were used to assess the spatial similarity between the rainfall change maps prepared using observed data and different gridded data: (a) Jaccard similarity index (JSI); (b) md; (c) SS; and (d) the percentage of bias (Pbias).The md and SS are described in Section 4.1.Those four indices were used to compare the Sen's slope obtained at each 0.5 • grid point against the interpolated Sen's slope estimated using observed data at a resolution of 0.5 • .
The Jaccard similarity index (JSI) [47,48] is a statistical measurement of the similarity between two sets of data using the concept of intersection over union.It can be mathematically calculated as: where J(X, Y) is the JSI between X and Y datasets based on a similarity threshold value.
The JSI computes the number of data shared between two sets and represents it as a percentage of the total number of data in both sets.Thus, it can have a value between 0 and 100%, where a higher percentage represents more similarity between the datasets.Yin and Yasuda [49] compared the JSI with 19 other well-known similarity assessment indices and found JSI was the best for providing stable and discriminable results.
Pbias measures the difference between the Sen's slopes obtained using gridded data and interpolated observed data as below: Pbias = x sim,i − x obs,i x obs,i × 100 (5)

Assessment of Accuracy in Trends
The results of the MK and mMK tests were used to estimate the positive or negative trend at each grid point.As this result is categorical, the Probability of Detection (POD) index was used to assess the reliability of gridded datasets in detecting the spatial pattern of trends.POD (Equation ( 6)) measures how many significant trend signs obtained using observed data were correctly estimated by gridded data.For example, if the sign of an observed trend is found to be the same as the sign of the trend in the corresponding grid point, the POD counts it as a correct detection.The sign means either positive, negative, or no trend.This means that if no significant trend at an observed location is also detected at the corresponding grid point, the POD counts it as a correct detection.The optimal value of POD is 1.The POD was calculated for both the MK and mMK tests at all the gauge locations.

POD =
Count of observed trend signs which were detected by gridded data Total number of stations (6) Water 2019, 11, 349 9 of 23

Evaluation of Gridded Datasets
Two methods as mentioned in methodology section were used to assess the performance of six gridded rainfall data for the period 1979-2010 using four statistical indices.Figure 4 presents box plots of the statistical metrics results obtained using the grid-to-grid comparison method, while Figure 5 presents the results obtained using the point-to-point comparison method.Consistency in results was obtained using both the methods.Both the methods revealed the superiority of GPCC in replicating the observed monthly rainfall of Bangladesh.Although both the GPCC and APHRODITE showed the lowest RMSE median (121 mm), the range of RMSE for GPCC was lower than that obtained for APHRODITE.The KGE median scores for GPCC were found to be much nearer to the optimal value compared to other datasets.This indicates that the correlation of GPCC with observed data is higher, bias is lower, and variability is smaller.The md for GPCC was found to be higher than others in term of median and 3rd quantiles.APHRODITE ranked as the second best in terms of md, while CPC ranked as the worst.GPCC data was also found to generate Probability Distribution Functions (PDFs) that overlapped the observed rainfall PDFs at different grid points.Therefore, the mean SS of GPCC was higher (0.95 and 0.91 for grid-to-grid and point-to-point comparison methods, respectively) than that obtained for other gridded datasets.
Water 2018, 10, x FOR PEER REVIEW 9 of 23

Evaluation of Gridded Datasets
Two methods as mentioned in methodology section were used to assess the performance of six gridded rainfall data for the period 1979-2010 using four statistical indices.Figure 4 presents box plots of the statistical metrics results obtained using the grid-to-grid comparison method, while Figure 5 presents the results obtained using the point-to-point comparison method.Consistency in results was obtained using both the methods.Both the methods revealed the superiority of GPCC in replicating the observed monthly rainfall of Bangladesh.Although both the GPCC and APHRODITE showed the lowest RMSE median (121 mm), the range of RMSE for GPCC was lower than that obtained for APHRODITE.The KGE median scores for GPCC were found to be much nearer to the optimal value compared to other datasets.This indicates that the correlation of GPCC with observed data is higher, bias is lower, and variability is smaller.The md for GPCC was found to be higher than others in term of median and 3rd quantiles.APHRODITE ranked as the second best in terms of md, while CPC ranked as the worst.GPCC data was also found to generate Probability Distribution Functions (PDFs) that overlapped the observed rainfall PDFs at different grid points.Therefore, the mean SS of GPCC was higher (0.95 and 0.91 for grid-to-grid and point-to-point comparison methods, respectively) than that obtained for other gridded datasets.

Comparison of Trends
The characteristics of rainfall data were analyzed before trend analysis to reveal the presence of autocorrelations and multi-decadal variability in time series.The autocorrelation function (AFC) was used in this study to find a significant correlation for various time lags, while the presence of decadal and multidecadal variability in the time series of climate indices were assessed through wavelet decomposition of time series data [50].The AFC plot of annual rainfall data at two locations is shown in Figure 6.The vertical lines in the plot that exceed the blue confidence band (horizontal lines) indicate significant correlation.The figure clearly shows positive autocorrelation up to 7-lag years in the time series.
Different levels of decompositions reveal the presence of different cycles in the time series.The obtained results for annual rainfall at two stations are shown in Figure 7.The fourth-level decomposition of data revealed the presence of a cycle of nearly 20 years in both stations.The x-axis of the graph shows the number of years and the y-axis shows the decomposed precipitation anomaly.Similar results were obtained at other stations.The results indicate the presence of short-and long-term autocorrelations in the annual rainfall of Bangladesh.The presence of such multi-decadal variations in annual rainfall time series can significantly affect the trend in rainfall if it is not taken into consideration during trend analysis.Therefore, the mMK test along with the MK test was also used in the present study.

Comparison of Trends
The characteristics of rainfall data were analyzed before trend analysis to reveal the presence of autocorrelations and multi-decadal variability in time series.The autocorrelation function (AFC) was used in this study to find a significant correlation for various time lags, while the presence of decadal and multi-decadal variability in the time series of climate indices were assessed through wavelet decomposition of time series data [50].The AFC plot of annual rainfall data at two locations is shown in Figure 6   Changes in annual and seasonal rainfall in Bangladesh were assessed using six gridded and observed rainfall data for the period 1979-2010.The monthly rainfall data were converted to annual and seasonal total rainfall to assess the trends.The obtained results were used to prepare maps to show the spatial pattern of the change (Sen's slope) in the annual and seasonal rainfall at 0.5° × 0.5° grid.For the comparison of slopes in observed and gridded data, observed data were gridded to the resolution of gridded data (0.5° × 0.5°) and the areal average rainfall for each grid box was computed.The grid-to-grid comparison of slopes was conducted by comparing the Sen's slope estimated for the areal average of observed rainfall at each grid box with the Sen's slope estimated for gridded data.
The spatial distribution of the changes in annual rainfall in Bangladesh obtained using different gridded data and observed data is shown in Figure 8.The colour gradients of the maps in Figure 8 represent the Sen's slopes and the signs (positive or negative) represent the significance of trends at a 95% level of confidence at the grid/station location.The black signs represent significance in trend estimated by MK test while the white signs represent the significance of trend estimated by MK and mMK.Table 3 represents the percentage of areal coverage where different gridded data products showed a significant change in rainfall at a 95% level of confidence.Different levels of decompositions reveal the presence of different cycles in the time series.The obtained results for annual rainfall at two stations are shown in Figure 7.The fourth-level decomposition of data revealed the presence of a cycle of nearly 20 years in both stations.The x-axis of the graph shows the number of years and the y-axis shows the decomposed precipitation anomaly.Similar results were obtained at other stations.The results indicate the presence of short-and long-term autocorrelations in the annual rainfall of Bangladesh.The presence of such multi-decadal variations in annual rainfall time series can significantly affect the trend in rainfall if it is not taken into consideration during trend analysis.Therefore, the mMK test along with the MK test was also used in the present study.Changes in annual and seasonal rainfall in Bangladesh were assessed using six gridded and observed rainfall data for the period 1979-2010.The monthly rainfall data were converted to annual and seasonal total rainfall to assess the trends.The obtained results were used to prepare maps to show the spatial pattern of the change (Sen's slope) in the annual and seasonal rainfall at 0.5° × 0.5° grid.For the comparison of slopes in observed and gridded data, observed data were gridded to the resolution of gridded data (0.5° × 0.5°) and the areal average rainfall for each grid box was computed.The grid-to-grid comparison of slopes was conducted by comparing the Sen's slope estimated for the areal average of observed rainfall at each grid box with the Sen's slope estimated for gridded data.

Decomposed Precipitation Anomaly
The spatial distribution of the changes in annual rainfall in Bangladesh obtained using different gridded data and observed data is shown in Figure 8.The colour gradients of the maps in Figure 8

Decomposed Precipitation Anomaly
Bogra Khulna Changes in annual and seasonal rainfall in Bangladesh were assessed using six gridded and observed rainfall data for the period 1979-2010.The monthly rainfall data were converted to annual and seasonal total rainfall to assess the trends.The obtained results were used to prepare maps to show the spatial pattern of the change (Sen's slope) in the annual and seasonal rainfall at 0.5 • × 0.5 • grid.For the comparison of slopes in observed and gridded data, observed data were gridded to the resolution of gridded data (0.5 • × 0.5 • ) and the areal average rainfall for each grid box was computed.
The grid-to-grid comparison of slopes was conducted by comparing the Sen's slope estimated for the areal average of observed rainfall at each grid box with the Sen's slope estimated for gridded data.
The spatial distribution of the changes in annual rainfall in Bangladesh obtained using different gridded data and observed data is shown in Figure 8.The colour gradients of the maps in Figure 8 represent the Sen's slopes and the signs (positive or negative) represent the significance of trends at a 95% level of confidence at the grid/station location.The black signs represent significance in trend estimated by MK test while the white signs represent the significance of trend estimated by MK and mMK.Table 3 represents the percentage of areal coverage where different gridded data products showed a significant change in rainfall at a 95% level of confidence.
The spatial distribution of Sen's slope in annual rainfall (Figure 8) showed negative values (0 to −183 mm/decade) in most parts of Bangladesh.A significant decrease in annual rainfall was observed at two stations (Chandpur and Faridpur) by both MK and mMK tests and a significant increase at two stations (Teknaf and Khepupara) by only MK test at a 95% level of confidence.None of the gridded rainfall data showed exactly the same spatial distribution of Sen's slope obtained using observed data.However, GPCC showed a significant positive trend in annual rainfall in the southwest corner of the country (216 mm/decade) and negative trends in the south-central region (−183 mm/decade) where positive and negative trends were detected using observed data.The CPC showed a significant increase in annual rainfall in most of the country, while CRU and PGF showed no change at any grid point over Bangladesh.The spatial distribution of Sen's slope in annual rainfall (Figure 8) showed negative values (0 to −183 mm/decade) in most parts of Bangladesh.A significant decrease in annual rainfall was observed at two stations (Chandpur and Faridpur) by both MK and mMK tests and a significant increase at two stations (Teknaf and Khepupara) by only MK test at a 95% level of confidence.None of the gridded rainfall data showed exactly the same spatial distribution of Sen's slope obtained using observed data.However, GPCC showed a significant positive trend in annual rainfall in the southwest corner of the country (216 mm/decade) and negative trends in the south-central region (−183 mm/decade) where positive and negative trends were detected using observed data.The CPC showed a significant increase in annual rainfall in most of the country, while CRU and PGF showed no change at any grid point over Bangladesh.
The spatial distributions of the trends in pre-monsoon rainfall are shown in Figure 9. Overall, the Sen's slope estimated negative changes (−31 to −121 mm/decade) in pre-monsoon rainfall in the centre region and positive changes (93 mm/decade) in the southeast of Bangladesh.Trend analysis results showed that the Sen's slopes estimated using observed data were significant only at a few grid points in the central and south-central regions (negative) and mountainous southeast corner (positive).A very similar result was obtained using GPCC, which showed negative trends in pre-monsoon rainfall in the central region and positive trends in the southeast corner.However, GPCC showed negative trends at more grid points in the central region compared to that obtained using observed data.On the contrary, CRU showed a negative trend for both MK and mMK tests in the southeast corner.CPC showed no change in the central region, however showed increases in pre-monsoon rainfall in the northeast and southeast.The spatial distributions of trends in monsoon rainfall are presented in Figure 10.The Sen's slope estimated for monsoon rainfall using observational data showed negative slopes (0 to −81 mm/decade) in most parts of Bangladesh, except at a few locations in the southeast, northeast, and northwest.Trend analysis results obtained using MK and mMK tests revealed that the slopes were not significant at any of the stations.Among the six gridded data, only GPCC showed no significant trend in monsoon rainfall at any grid point, while the others showed increasing/decreasing trends in different parts.CPC showed an increase in rainfall in most parts of the country, APHRODITE showed a significant increase in the southeast, CRU showed a decrease in the northeast, PGF showed a decrease in the north, and UDel showed a decrease at three grid points in the central region.The results revealed highly contradictory results in the trends of monsoon rainfall, which shares a major portion of annual total rainfall in the country.The spatial distributions of trends in monsoon rainfall are presented in Figure 10.The Sen's slope estimated for monsoon rainfall using observational data showed negative slopes (0 to −81 mm/decade) in most parts of Bangladesh, except at a few locations in the southeast, northeast, and northwest.Trend analysis results obtained using MK and mMK tests revealed that the slopes were not significant at any of the stations.Among the six gridded data, only GPCC showed no significant trend in monsoon rainfall at any grid point, while the others showed increasing/decreasing trends in different parts.CPC showed an increase in rainfall in most parts of the country, APHRODITE showed a significant increase in the southeast, CRU showed a decrease in the northeast, PGF showed a decrease in the north, and UDel showed a decrease at three grid points in the central region.The results revealed highly contradictory results in the trends of monsoon rainfall, which shares a major portion of annual total rainfall in the country.The spatial distributions of the Sen's slopes estimated for post-monsoon rainfall are presented in Figure 11.The spatial distribution of slopes obtained using GPCC and APHRODITE was found to be consistent with that obtained using observed data.A significant increasing trend in post-monsoon rainfall was found only at two stations located in the southern coastal region using the mMK test.Only GPCC was found to replicate the spatial distribution of the observed trend in post-monsoon rainfall.GPCC also showed a significant increasing trend at two grid points near to those observed stations but only one using the mMK test and another using the MK test.A large variation in trends was found for other data products.The CPC showed an increase in post-monsoon rainfall over the whole country except in the southeast.The increase was found to be significant for most of the grid points by the MK test and in the central and southern areas for the mMK test.APHRODITE also showed a significant increase in the southern coastal region and the north of Bangladesh.CRU showed no significant change at any grid point, while UDel showed a decrease at a few grid points in the central and southern regions, where APHRODITE and PGF showed an increase.The results clearly indicate large variability in the spatial pattern of post-monsoon rainfall trends obtained using different gridded data products.The spatial distributions of the Sen's slopes estimated for post-monsoon rainfall are presented in Figure 11.The spatial distribution of slopes obtained using GPCC and APHRODITE was found to be consistent with that obtained using observed data.A significant increasing trend in post-monsoon rainfall was found only at two stations located in the southern coastal region using the mMK test.Only GPCC was found to replicate the spatial distribution of the observed trend in post-monsoon rainfall.GPCC also showed a significant increasing trend at two grid points near to those observed stations but only one using the mMK test and another using the MK test.A large variation in trends was found for other data products.The CPC showed an increase in post-monsoon rainfall over the whole country except in the southeast.The increase was found to be significant for most of the grid points by the MK test and in the central and southern areas for the mMK test.APHRODITE also showed a significant increase in the southern coastal region and the north of Bangladesh.CRU showed no significant change at any grid point, while UDel showed a decrease at a few grid points in the central and southern regions, where APHRODITE and PGF showed an increase.The results clearly indicate large variability in the spatial pattern of post-monsoon rainfall trends obtained using different gridded data products.Compared to other seasons, better consistency in rainfall changes among the gridded data was observed for winter (Figure 12).Nevertheless, a large variation was noticed in the patterns of significant trends.CRU showed a significant decrease in winter rainfall mostly in the southwest, UDel in the southcentral region, and PGF in the north, while APHRODITE showed almost no changes and CPC showed an increase in the whole central and southern regions.Station data showed a decrease in winter rainfall only at two stations, one located in the north and the other in the southwest, which was found to match better with APHRODITE and GPCC.GPCC showed an increase in winter rainfall at two grid points, one in the north and the other in the southwest, while APHRODITE showed a decrease in rainfall at two grid points in the southwest.Compared to other seasons, better consistency in rainfall changes among the gridded data was observed for winter (Figure 12).Nevertheless, a large variation was noticed in the patterns of significant trends.CRU showed a significant decrease in winter rainfall mostly in the southwest, UDel in the south-central region, and PGF in the north, while APHRODITE showed almost no changes and CPC showed an increase in the whole central and southern regions.Station data showed a decrease in winter rainfall only at two stations, one located in the north and the other in the southwest, which was found to match better with APHRODITE and GPCC.GPCC showed an increase in winter rainfall at two grid points, one in the north and the other in the southwest, while APHRODITE showed a decrease in rainfall at two grid points in the southwest.The JSI was calculated for Sen's slope maps prepared for each gridded data against the observed data at 0.5° resolution (Figures 6 to 10).The results (Table 4) showed more similarly of the GPCC map with the observed map for annual and all seasonal rainfall except pre-monsoon.The JSI was found to be 22%, 21%, 80%, and 22% for annual, monsoon, post-monsoon, and winter rainfall for GPCC.APHRODITE was found to be more similar for pre-monsoon rainfall.However, it was found to score zero for annual rainfall.The JSI was calculated for Sen's slope maps prepared for each gridded data against the observed data at 0.5 • resolution (Figures 6-10).The results (Table 4) showed more similarly of the GPCC map with the observed map for annual and all seasonal rainfall except pre-monsoon.The JSI was found to be 22%, 21%, 80%, and 22% for annual, monsoon, post-monsoon, and winter rainfall for GPCC.APHRODITE was found to be more similar for pre-monsoon rainfall.However, it was found to score zero for annual rainfall.Several studies have revealed GPCC to be the most suitable rainfall dataset in neighbouring countries of Bangladesh [54,55].For instance, Prakash et al. [54] compared the performance of four gauge-based land-only rainfall products with the Indian Meteorological Department gridded rainfall dataset and reported that APHRODITE and GPCC rainfall showed the highest scores in term of different skill indices compared to other rainfall products.Additionally, Kishore et al. [55] investigated the features of Indian rainfall using reanalysis and gauge datasets and found that GPCC has a high degree of similar characteristics.
The GPCC data was used for the assessment of long-term trends (1901-2017) in annual and seasonal rainfall in Bangladesh using the MK and mMK tests.The spatial patterns of trends using both tests are presented in Figure 13.The trend in annual rainfall showed an increase at a point in the north and decrease at two points in the south, while the mMK test showed no change in annual rainfall at any locations in Bangladesh.This result indicates that the annual rainfall trend estimated at the three grid points in Bangladesh by the MK test may be due to its insensitivity to natural variability of climate.Using similar analysis, it was observed that the pre-monsoon rainfall in Bangladesh is increasing at two grid points in the north and at three grid points in the southwest mountainous region.Monsoon rainfall was found to decrease significantly at two grid points in the central-west region.The winter rainfall was found to increase in the southeast, while the pre-monsoon rainfall was not found to change at any locations by the mMK test.
Water 2018, 10, x FOR PEER REVIEW 20 of 23 land-only rainfall products with the Indian Meteorological Department gridded rainfall dataset and reported that APHRODITE and GPCC rainfall showed the highest scores in term of different skill indices compared to other rainfall products.Additionally, Kishore et al. [55] investigated the features of Indian rainfall using reanalysis and gauge datasets and found that GPCC has a high degree of similar characteristics.
The GPCC data was used for the assessment of long-term trends (1901-2017) in annual and seasonal rainfall in Bangladesh using the MK and mMK tests.The spatial patterns of trends using both tests are presented in Figure 13.The trend in annual rainfall showed an increase at a point in the north and decrease at two points in the south, while the mMK test showed no change in annual rainfall at any locations in Bangladesh.This result indicates that the annual rainfall trend estimated at the three grid points in Bangladesh by the MK test may be due to its insensitivity to natural variability of climate.Using similar analysis, it was observed that the pre-monsoon rainfall in Bangladesh is increasing at two grid points in the north and at three grid points in the southwest mountainous region.Monsoon rainfall was found to decrease significantly at two grid points in the central-west region.The winter rainfall was found to increase in the southeast, while the pre-monsoon rainfall was not found to change at any locations by the mMK test.

Conclusion
The spatial pattern in rainfall trends in Bangladesh was assessed using six gridded rainfall data, namely APHRODITE, CPC, CRU, GPCC, PGF, and UDel, in order to understand the uncertainty in results.The results revealed a large variation in the spatial pattern of the trends in annual and seasonal rainfall.Determining the spatial pattern in rainfall trends is vital for climate change impact assessment and adaptation planning.The use of gridded climate data without proper validations can be misleading regarding the understanding of climate change impacts.The ability of gridded data to replicate the mean and variability of rainfall is not sufficient to use it for any hydro-climatic studies.The gridded data should be validated according to their ability to replicate the phenomena for which they are to be used.

Conclusions
The spatial pattern in rainfall trends in Bangladesh was assessed using six gridded rainfall data, namely APHRODITE, CPC, CRU, GPCC, PGF, and UDel, in order to understand the uncertainty in results.The results revealed a large variation in the spatial pattern of the trends in annual and seasonal rainfall.Determining the spatial pattern in rainfall trends is vital for climate change impact assessment and adaptation planning.The use of gridded climate data without proper validations can be misleading regarding the understanding of climate change impacts.The ability of gridded data to replicate the mean and variability of rainfall is not sufficient to use it for any hydro-climatic studies.The gridded data should be validated according to their ability to replicate the phenomena for which they are to be used.
The results of the present study revealed a better performance of GPCC over other gridded rainfall data used in this study in estimating monthly observations and in the assessment of rainfall trends in Bangladesh.However, large differences were still observed in annual and seasonal trend distributions between the GPCC and observed rainfall maps.The long-term trend analysis of rainfall using GPCC revealed no change in annual and post-monsoon rainfall, increase in pre-monsoon rainfall at a few grids in the north and southeast regions, decrease in monsoon rainfall in the central-west region, and increase in winter rainfall in the southeast region.It is expected that the findings of this study will help to understand the uncertainty in the spatial pattern of the trends estimated using gridded climate data.The results of long-term rainfall trend analysis can be helpful for understanding the impacts of climate change and necessary mitigation planning for Bangladesh.

Figure 1 .
Figure 1.Geographical map of Bangladesh showing ground elevation obtained using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) and rainfall gauge locations.

Figure 1 . 23 Figure 2 .
Figure 1.Geographical map of Bangladesh showing ground elevation obtained using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) and rainfall gauge locations.

Figure 2 .
Figure 2. Spatial distribution of average annual rainfall in Bangladesh during 1979-2010 obtained using different gridded and interpolated observed (Obs) rainfall data at a resolution of 0.5 • × 0.5 • .

Figure 3 .
Figure 3. Flowchart of the methodology used in this study.

Figure 3 .
Figure 3. Flowchart of the methodology used in this study.

Figure 4 .
Figure 4. Box plots of the four indices-(a) Root-Mean-Square Error (RMSE), (b) Kling-Gupta Efficiency (KGE), (c) modified index of agreement (md), and (d) Skill Score (SS)-used to evaluate the performance of monthly gridded rainfall data against observed rainfall data recorded at 34 locations distributed over Bangladesh during 1979-2010 using the grid-to-grid comparison method.

Figure 4 . 23 Figure 5 .
Figure 4. Box plots of the four indices-(a) Root-Mean-Square Error (RMSE), (b) Kling-Gupta Efficiency (KGE), (c) modified index of agreement (md), and (d) Skill Score (SS)-used to evaluate the performance of monthly gridded rainfall data against observed rainfall data recorded at 34 locations distributed over Bangladesh during 1979-2010 using the grid-to-grid comparison method.

Figure 5 .
Figure 5. Box plots of the four indices-(a) RMSE, (b) KGE, (c) md, and (d) SS-used to evaluate the performance of monthly gridded rainfall data against observed rainfall data recorded at 34 locations distributed over Bangladesh during 1979-2010 using point-to-point comparison method.
. The vertical lines in the plot that exceed the blue confidence band (horizontal lines) indicate significant correlation.The figure clearly shows positive autocorrelation up to 7-lag years in the time series.

Figure 6 .
Figure 6.Plots of the autocorrelation function of the annual rainfall of Bangladesh for the period 1979-2010 at: (a) Bogra, in the north; and (b) Khulna, in the south.

Figure 7 .
Figure7.The fourth-level decomposition of the annual rainfall data for Bogra (black) and Khulna (red), which revealed the presence of multi-decadal variability with a cycle of nearly 20 years.

Figure 6 .
Figure 6.Plots of the autocorrelation function of the annual rainfall of Bangladesh for the period 1979-2010 at: (a) Bogra, in the north; and (b) Khulna, in the south.

Water 2018 , 23 Figure 6 .
Figure 6.Plots of the autocorrelation function of the annual rainfall of Bangladesh for the period 1979-2010 at: (a) Bogra, in the north; and (b) Khulna, in the south.

Figure 7 .
Figure 7.The fourth-level decomposition of the annual rainfall data for Bogra (black) and Khulna (red), which revealed the presence of multi-decadal variability with a cycle of nearly 20 years.

Figure 7 .
Figure 7.The fourth-level decomposition of the annual rainfall data for Bogra (black) and Khulna (red), which revealed the presence of multi-decadal variability with a cycle of nearly 20 years.

Figure 13 .
Figure 13.Spatial distribution of long-term trends (1901-2017) in annual and seasonal rainfall in Bangladesh obtained using Global Precipitation Climatology Centre (GPCC) data.

Figure 13 .
Figure 13.Spatial distribution of long-term trends (1901-2017) in annual and seasonal rainfall in Bangladesh obtained using Global Precipitation Climatology Centre (GPCC) data.

Table 1 .
Summary of recent studies on rainfall trend in Bangladesh.

Table 2 .
Summary of the gridded rainfall datasets evaluated in the present study.

Table 3 .
Percentage of the area where gridded data showed significant positive (+ve) or negative (−ve) change in annual and seasonal rainfall using the Mann-Kendall (MK) and modified MK (mMK) tests during 1979-2010.

Table 4 .
The Jaccard similarity coefficient calculated for annual and seasonal rainfall changes estimated for the period 1979-2010.The highest values for different seasons are presented using bold font.

Table 4 .
The Jaccard similarity coefficient calculated for annual and seasonal rainfall changes estimated for the period 1979-2010.The highest values for different seasons are presented using bold font.