Citizen rain gauge improves hourly radar rainfall bias correction using a two-step Kalman filter

Low density of conventional rain gauge networks is often a limiting factor for radar rainfall bias correction. Citizen rain gauges offer a promising opportunity to collect rainfall data at higher spatial density. In this paper hourly radar rainfall bias adjustment was applied using two different rain gauge networks consisting of tipping buckets (measured by Thailand 10 Meteorological Department, TMD) and daily citizen rain gauges in a two-step Kalman Filter approach. Radar reflectivity data of Sattahip radar station and gauge rainfall data from the TMD and citizen rain gauges located in Tubma basin, Thailand were used in the analysis. Daily data from the citizen rain gauge network were downscaled to hourly resolution based on temporal distribution patterns obtained from radar rainfall time series and the TMD gauge network. The radar rainfall bias correction factor was sequentially updated based on TMD and citizen rain gauge data using a Kalman Filter. Results show that an 15 improvement of radar rainfall estimates was achieved by including the downscaled citizen observations compared to bias correction based on the conventional rain gauge network only. These outcomes emphasize the value of citizen rainfall observations for radar bias correction, in particular in regions where conventional rain gauge networks are sparse.


Introduction
Hydrometeorological hazards, like flash floods and landslides cause severe damage to economies, properties, and human lives worldwide.In this context, flood forecasting and warning systems are a valuable non-structural measure to mitigate damage.However, such systems require input of rainfall data at a high spatial and temporal resolution.In most regions of the world, automatic rain gauge networks are insufficient for this purpose.Weather radar, which can better capture the 25 variation of rainfall fields at fine spatial and temporal resolutions could be used as an alternative rainfall product for improving the accuracy of flash flood estimates and warning.(Collinge and Kirby, 1987;Sun et al., 2000;Uijlenhoet 2001;Bedient et al., 2003;Creutin and Borga, 2003;Mapiam et al., 2009aMapiam et al., , 2014;;Mapiam and Chautsuk, 2018;Corral et al., 2019).However, weather radar provides indirect measurement of backscattered electromagnetic waves called radar reflectivity data (Z).To

The Z-R calibration and radar rainfall aggregation
The Z-R conversion error is a crucial source of error in radar rainfall estimates.The Z-R relationship as shown in Eq.

𝑍 = 𝐴𝑅
(1) The Z-R calibration and verification are essential procedures to ascertain the parameters A and b in the relationship.
Firstly, the instantaneous 6-minute radar reflectivity was converted to rainfall intensity using the climatological relationship 100 Z=200R 1.6 proposed by Marshall and Palmer (1948).Secondly, the estimated 6-min initial instantaneous radar rainfall data were aggregated to 1-hour rainfall resolution using the accumulation algorithm proposed by Fabry et al. (1994).Thirdly, gauge rainfall was aggregated to 1-hour resolution.Fourthly, the optimal value of the A parameter was established by minimizing the mean absolute error (MAE) between the gauge and radar rainfall estimates, while the b exponent was considered to be fixed as 1.5 in our study.This is because radar rainfall estimates are relatively insensitive to b with typical values between 1.2 and 105 1.8 (Battan 1973;Ulbrich 1983).The value of 1.5 was generally suitable to represent the b parameter in the Z-R relation (Doelling et al., 1998;Steiner and Smith, 2000;Hagen and Yuter;2003;Germann et al., 2006;Chantraket et al., 2016).The mean absolute error is illustrated in Eq. ( 2).
where Gi,t is the gauge rainfall (mm/h) at gauge i for hour t, Ri,t is the radar rainfall accumulation (mm/h) at the pixel corresponding to the i th rain gauge for hour t, NG,t is the total number of radar-rain gauge pairs available at time t, N is the total number of radar-rain gauge pairs available, and T is the total period used in the calculation.The calibrated climatological Z-R relationship was validated against a second, independent dataset.Results found that a locally calibrated Z-R relationship that 115 was used in this study is Z=251R 1.5 .

Rainfall Data Collection
Data from the network of 297 continuous tipping-bucket gauge stations located within the Sattahip radar radius were 120 collected (Fig. 1).These 15-min rain gauges are owned and operated by the Thai Meteorological Department (TMD).All continuous rain gauges used in this study have tipping-bucket sizes of 0.5 mm.The data quality screening was first carried out using double mass curves method of two adjacent rain gauges.To avoid no-rainfall events and systematically underrecord https://doi.org/10.5194/hess-2021-262Preprint.Discussion started: 11 May 2021 c Author(s) 2021.CC BY 4.0 License.
rainfall accumulation of the tipping-bucket gauge for the analysis, hourly data greater than the tipping-bucket resolution of 0.5 mm were selected in the next step.A rain gauge with more than 80% of the dataset below the threshold was excluded from the 125 analysis.We found that rainfall data obtained from 134 rain gauges corresponding to the collected reflectivity datasets were used for the Z-R calibration and validation processes.For the bias adjustment computation, the selection of rain gauge networks with rainfall behavior similar to the study area is necessary.We selected 14 rain gauges of TMD in the region surrounding Tubma basin (Rayong and Chonburi provinces) based on spatial decorrelation analysis in the process.
Out of the total network, only one of the TMD rain gauge is located in the 197 km 2 Tubma basin.To increase the 130 density of the rain gauge network in the basin, low-cost citizen rain gauges were implemented in this study to better capture spatial heterogeneity of rainfall in the basin.Sixteen citizen rain gauges were installed (Fig. 1) with local residents taking daily measurements.This increased the density of rain gauges to 1 gauge/15 km 2 for the Tubma basin.All citizen rain gauge data were screened for errors and inconsistencies using double mass curves.If a citizen rain gauges reported >100mm/day rainfall (maximum capacity of the citizen rain gauge) this data was excluded from the analysis.If days with no-rainfall data were found 135 from all citizen rain gauges, the bias correction of that day was discarded from the assessment.By considering the data selection criteria, rainfall data recorded during August-October 2019 with rainy day more than 80% of the whole period for the bias adjustment process was then used for further evaluation.

Methods
The methodology for radar rainfall bias correction using tipping bucket and citizen gauges consists of the following steps.First, daily citizen rain gauge data were downscaled to hourly time scale to be used as input for bias correction.The 145 downscaling methods used in this paper are discussed in section 3.1.Next, an hourly radar bias correction model was developed combining rain gauge as well as downscaled citizen rain gauge data using a Kalman filter approach, as presented in section 3.2.

Downscaling daily to hourly rainfall
To downscale the daily citizen rain gauge data to hourly time-scale, information on the temporal storm distribution 150 pattern is needed.Methodologies to obtain the temporal rainfall distribution patterns are outlined in Table 1.The RMP downscaling pattern was applied to all citizen rain gauges.
The mean distribution pattern of radar rainfall.

GMP
Hourly gauge rainfall patterns of all 14 gauges in the region surrounding Tubma basin were averaged to construct the mean hourly distribution pattern of regional rain gauge rainfall.
The GMP was applied to all citizen rain gauges.
The mean distribution pattern of rain gauge rainfall.Mean field bias adjustment (MFB) is a common technique used for bias correction in radar rainfall relative to ground stations.It can be computed as the ratio of mean hourly radar rainfall estimate and rain gauge measurement (Anagnostou and Krajewski, 1999;Yoo and Yoon, 2010;Hanchoowong et al., 2013;Shi et al., 2018).However, direct application of MFB as a 160 multiplicative does not account for uncertainty of the bias associated with each radar-gauge measurement.Alternatively, a Kalman Filter (KF) has been adopted to estimate the spatially uniform mean field bias in real-time in several studies, including Ahnert et al. (1986), Smith and Krajewski (1991), Anagnostou et al. (1998), andSeo et al. (1999), Chumchean et al. (2006), Kim and Yoo, (2014), Shi et al. (2018).Kalman Filter has the benefit of accounting for noise in the observations by weighing the contribution of measurements by their respective variances (Kalman, 1960).Here we take advantage of the KF scheme by 165 combining two data sources with different uncertainty characteristics, hourly rain gauge data from TMD and hourly downscaled citizen rain gauge data.Any day that citizen rain gauge data are not available, the ordinary Kalman Filter scheme will be applied using only the TMD datasets as the observed mean field bias.Since the mean field bias (G/R ratio) is assumed to follow a log-normal distribution.However, the radar bias is modelled as random variables from a normal distribution in the KF process.Before application of the KF scheme, mean field radar rainfall bias at time t is thus log-transformed to follow 170 normal distribution as follows (Smith and Krajewski, 1991;Anagostou et al., 1998), where  is logarithmic mean field bias at hour t: The logarithmic mean field radar rainfall bias is frequently modelled as an Autoregressive order one (AR1) process having a stationary variance (Smith and Krajewski, 1991).The radar bias at time t can be modelled as a relationship between the bias at previous time ( ) and the process noise ( ) by the following equations.This first step of KF consists of estimating the logarithmic mean field bias and its associated error variance at the 205 current time step to obtain an a priori estimate of β (symbolized by  ).The  is estimated as shown in Eq. ( 7).

2) Measurement update step (Correction)
This step involves correcting the a priori estimate  using the observed data at the current time step.This corrected estimate is then referred to as the a posteriori estimate (symbolized by  ).The measurement update process starts with calculating the Kalman Gain (Kt) and is estimated as: 220 where  is the observation error variance at time t.Thereafter, the  and the a posteriori estimate error variance of  ( ) can be computed as follows.225 where  is observed logarithmic mean field bias at hour t.If there is no observation data available at any time t, this measurement process update will be skipped and the a priori estimate be calculated as below.

240
The state estimator for mean field bias at time t (Bt) are finally obtained by converting the estimated log bias,  into Bt using the following equation (Smith and Krajewski, 1991).Investigating the benefit of bias adjustment incorporating data from the citizen gauge network is the main goal of this study.The procedure starts with assessing the bias adjustment based on the ordinary KF approach using hourly rain gauge rainfall measured by the TMD gauges.At the end of each day, if daily observation data collected by the citizen rain gauges was available, these data were downscaled to hourly time-scale.Then, a second update was done using the same equations as 250 listed above (Eqs.9-11), but using the posterior values ( ,  ) from the first update as predictions ( ,  ) for the second update.
The procedure of the CKF consists of 4 steps, visualized in Figure 3. 1) Since the citizen rain gauge data were received at the last hour of day i, at an hour before obtaining the citizen rain gauge data, the ordinary KF and observed hourly data of TMD were used to predict and correct the hourly 255 bias adjustment factor of the day i.
2) If the citizen rain gauge data was available at the end of the day i, the citizen rain gauge data were downscaled to hourly time-scale, as explained in section 3.1.
3) The downscaled hourly citizen rain gauge data were used to back-calculate the hourly citizen rain gauges data for day i and to conduct a second measurement update in the KF process for all hourly time-steps of day i.260 4) Bias adjustment factors were applied every hourly time step to obtain the final product of hourly radar rainfall estimation of day i.The bias factor for the last hour of the day i was used afterward as the initial value for calculating the Ordinary KF of day i+1.

Parameter estimation
Parameter values were obtained by finding the optimal fit to the probability distribution by maximizing the marginal likelihood function (Bock et al., 1981;Harvey, 1990;Proietti et al., 2013;Pulido et al., 2018).As mentioned earlier, we have two sources of observed log mean field bias at hour t, from TMD ( ) and citizen rain gauge ( ).In case only TMD data was 270 available in the KF analysis, the expression for the marginal likelihood of the observed log mean field bias (p(D)) was computed according to Eq. ( 15), where D is the data vector that contains all observed values.The equation was later replaced with continuous variables sampled from the Gaussian distribution as shown in Eq. ( 16).
where  is the true hidden state of log mean field bias at hour t, and  is total hourly timesteps in the calculation.For the situation of combining TMD and citizen rain gauge datasets in the measurement updating, Eq. ( 17) and Eq. ( 18) were 280 applied for parameter estimation.Where  , and  , are the variance of the observation noise at hour t from rain gauges network of the TMD and citizen rain gauge, respectively.We assumed that the variance of the observation error ( ) could be represented by the variance of spatial average observed logarithmic mean field bias across all rain gauge location at time t as shown in Eq. ( 19).
Where ( ) is the variance of observed logarithmic mean field bias at time t, and  is number of observable rain gauges at 290 hour t.Therefore  , and  , were individually estimated for each dataset.

𝜎 = (19)
To obtain the optimal values of the two parameters  and  of the Kalman Filter that maximize the marginal 295 likelihood, the Nelder-Mead Simplex was used, which is an algorithm for searching a local optimum of a function (Lagarias et al., 1998;Luersen et al., 2004;Gao et al., 2012).

Verification of the proposed bias correction approaches
To investigate which bias adjustment technique among the MFB, KF, and CKF gives the most suitable radar rainfall estimates for the Tubma basin, the adjusted radar rainfall estimates were validated against measured rainfall data.There was 300 only one automatic TMD rain gauge available in the basin, which was insufficient for validation purposes.Consequently, for testing the performance of hourly rainfall bias correction, data from 13 TMD stations located within a 100 km radius from the center of the Tubma basin were used, together with 1 TMD station in the basin.Furthermore, daily time scale validation was conducted, using the daily rainfall data from 16 citizen rain gauges located in the Tubma basin.Leave-one-out cross-validation (LOOCV) algorithm was implemented to avoid bias occurring from selecting the validation rain gauges.The calibration rain 305 gauges were randomly selected to calculate the bias adjustment factor using the 3 different techniques, and 1 rain gauge was left out for validation.This was repeated for all combinations and then the error of radar rainfall estimates after correcting with the estimated bias factor at each radar pixel corresponding to the held-out gauge was computed for all trials.In this study, Root Mean Square Error (RMSE) and Mean Bias Error (MBE) were applied as statistical measures to evaluate the effectiveness of the different bias correction methods at each validation rain gauge.The RMSE and MBE at rain gauge i are shown in Eq. ( 20) 310 and Eq. ( 21), respectively.The number of possible combinations is equal to the total number of validated gauges (NG).Data for the period August-October 2019 were used in the evaluation.Four scenarios combining the 3 bias adjustment techniques were evaluated, summarized in Table 2.  KF-TMD: Thirteen TMD gauges from the total of 14 gauges were randomly separated for calculating the bias adjustment factors using MFB and KF and the remaining 1 TMD gauge was left out for validation.Aggregated hourly rainfall 325 between the adjusted radar and gauge rainfall data were compared to obtain the RMSE and MBE.

KF-TMD-D:
To identify which approach between MFB and KF is more accurate on daily rainfall simulation, fourteen TMD and 16 citizen rain gauges were used for the analysis.All TMD gauges were used for assessing MFB and KF, and estimated bias factors were applied for daily time-scale.Assessment of RMSE and MBE of daily rainfall was examined at all 16 citizen rain stations as the validation gauges.330 CKF-D: To evaluate the added value of using citizen rain gauges in the basin for bias correction, 15 citizen rain gauges (leave 1 citizen rain gauge out for validation) were used in addition to the TMD gauges following the CKF procedure explained in 3.2.2.Estimation of daily RMSE and MBE was carried out at the held-out citizen rain gauge.
CKF-H*: To test whether the CKF with the most suitable storm pattern could benefit radar rainfall estimates in the area further away from the Tubma basin, 14 TMD gauges were used to generate 4 cases of hourly rainfall distribution patterns 335 as described in Table 1 for downscaling the selected 16 daily citizen rain gauge data into an hourly time scale.The synthesized hourly citizen rain gauge data were later used to recompute the update procedure of the Kalman filter.Thirteen TMD gauges (leave 1 TMD out) were used to produce MFB and KF, and all 16 citizen rain gauges were merged for CKF computation.Five scenarios were investigated for radar bias correction using the Kalman Filter, based on TMD and citizen rain 345 gauge observations, including four scenarios comparing different hourly downscaling approaches for the citizen rain gauge data (Table 1).Parameter estimates of the Kalman Filters are shown in Table 3.These results indicate that the r1 parameter, the lag-one correlation coefficient of the logarithmic mean field bias, ranges from 0.15 to 0.53, depending on the hourly downscaling approach.While  representing the stationary variance of the logarithmic mean field bias remains relatively invariant (ranging from 0.24-0.28)over the same time-series period of simulation.350 Table 3: The parameters of the Kalman Filter estimated from different datasets of observation gauge rainfall.KF-TMD is using only TMD hourly rain gauge observations, CKF is using TMD and citizen rain gauge observations, where RP, RMP, GMP and GTubma represent different strategies for hourly downscaling of the citizen rain gauge observations (

Bias adjustment factor comparison
To test the performance of the bias adjustment techniques among KF-TMD, CKF-RP, CKF-RMP, CKF-GMP, and CKF-GTubma, all approaches were used to assess the mean field bias for each hour using the data period August -October 2019.The 370 results were compared to the MFB calculated using the 14 TMD rain gauges (MFB-TMD) in the Tubma basin and 100 km radius surroundings.Results summarized in figure 5 show that: -The daily observed bias is somewhat higher and shows larger variability for the citizen gauges compared to TMD gauges.The hourly observed bias based on downscaled citizen gauge data are in the same range as hourly bias based on TMD gauges, with somewhat higher median values and spread (25-75 %-ile range) for the RP and GTubma downscaling scenarios.375 -Hourly observation error variance is smallest for the CKF-RP downscaling approach and somewhat larger for the other CKF approaches compared to observation error variance for the TMD gauges.-Estimated hourly bias values based on KF-TMD show a slightly higher mean and smaller variability range compared to observations.The bias produced by the KF-TMD is close to the MFB-TMD if the observation error variance is small.In case that no measured data is available for the bias update, the computed bias factor ( ) progressively converged to 1.3, to 380 meet the climatological logarithmic mean field bias.
-Estimated bias values based on the CKF approaches are able to reproduce bias variability as observed by TMD gauges, with median values deviating by 0.2 to 0.4 and value range slightly larger for CKF-RP and smaller for CKF-RMP.
-CKF gives different bias values according to the storm distribution pattern and the availability of the daily citizen rain gauge data used in combination with the KF.In case that no citizen rain gauge data is available for updating, the bias 385 generated by the CKF for every combination is close to the ordinary KF with small differences depending on their respective  and  parameters.performing somewhat better than MFB-TMD especially in terms of RMSE.This confirms the ability of the KF approach that considers the error variance of observed hourly data as the weight for correcting the predicted mean bias instead of using only the calculated mean field bias (Smith and Krajewski, 1991;Chumchean et al., 2006).The two approaches show similar performance at the daily scale and improve RMSE by 20-30% and MBE by 50-60% (for median and upper 75%-ile, respectively) The added value of a KF-based approach is limited for this case, since 14 TMD rain gauges in the region were be used to compute observation variance which cannot represent the mean field bias behaviour in 415 the Tubma basin.RP bias adjustment significantly improves radar rainfall estimates at hourly time scale, compared to bias adjustment approaches based on TMD gauges only in the 0-40 km range closest to Tubma basin.While there is a modest improvement in mean RMSE, the upper 75%-ile RMSE is reduced from about 6 mm/h to 3.5 mm/h.Mean MBE is changed from 0.1 to -0.15 mm/h.For the 40-90 km range, CKF-RP performs similarly to MFB-TMB and KF-TMB.It is noted that the upper 75%-ile RMSE of the shorter range is remarkably high while using only TMD gauges for the bias adjustment.These errors occurred in 3 hours at 440 different 3-gauge locations when heavy rainfall data were only measured at the validated gauge location while there was relatively uniform light rainfall at all available surrounding TMD gauges used for the bias adjustment calculation.
Consequently, the calculated bias factors from the available gauges cannot represent the heavy rainfall at the tested location leading to the significant RMSE. Figure 8 appears that the considerable RMSE occurs from three hours for three days comprising 15 September 2019, 12:00; 21 September 2019, 15:00; and 22 September 2019, 14:00 associated with the validated 445 gauge 4780001, 4780005, and 4780003, respectively.However, these RMSE can considerably reduce if the CKF-RP was implemented only in the shorter range.

Conclusion
In this study we introduced a modified Kalman Filter approach in radar bias correction in the Tubma basin, eastern Thailand, that integrates daily data from a dense citizen rain gauge network with hourly data from a much sparser network of approaches.The question we aimed to answer is to what extent the downscaled citizen rainfall observations improve the 485 accuracy of hourly radar rainfall estimates.Results showed that citizen rain gauges significantly improve the performance of radar rainfall bias adjustment, up to a range of about 40 km from the centre of the Tubma basin (197 km 2 ) where the citizen rain gauge network is located.While a modest improvement in mean RMSE was obtained, the upper 75%-ile RMSE was reduced from 6 mm/h to 3.5 mm/h.The mean bias error was changed from 0.1 to -0.15 mm/h across the validation period (August-October, 2019).In the Tubma basin, beyond the 40 km range, no significant improvement by inclusion of the citizen 490 gauges was found.The rainfall distribution pattern is key for downscaling the daily measured citizen rain gauge observations into hourly temporal resolution.We found that in the Tubma basin downscaling based on the rainfall patterns derived from hourly radar rainfall at overlying radar pixels corresponding to the citizen gauge location was the most suitable technique, resulting in the smallest variation of observation error variances of the mean field bias.In the case of a sparse rain gauge network, the mean field bias and the Kalman filter approach both show improvement, and the degree of improvement was 495 similar between the two approaches.In other words, in a sparse gauge network, the added value of error information represented in the Kalman filter is limited.
Filter for mean field bias adjustment (KF)

Figure 2 :
Figure 2: On the left (a), a factor graph representation of the radar bias model: white circles depict random variables (bias at each time step), grey circles are rainfall observations (yt for TMD rainfall and zt for citizen rain gauge rainfall), and black squares are relations between variables (conditional normal distributions in this case).The right figure (b) depicts uncertainty propagation along the edges of the factor graph, from previous bias to current bias (Kalman prediction step) and from the observations to current bias (Kalman update step).200 /doi.org/10.5194/hess-2021-262Preprint.Discussion started: 11 May 2021 c Author(s) 2021.CC BY 4.0 License. = (1 −  ) (13) The Kalman Filter calculations based on the prediction and correction update steps can be visualized in the form of a graphical depiction showing the flow of the calculations over the edges of the factor graph in Fig. 2 (b).
https://doi.org/10.5194/hess-2021-262Preprint.Discussion started: 11 May 2021 c Author(s) 2021.CC BY 4.0 License.All bias adjustment techniques evaluated the effectiveness at the held-out gauge for all possible combinations of the LOOCV 340 procedure.4. Results and discussion 4.1 Simulation of bias adjustment factor 4.1.1Parameter estimation for the KF and CKF

Figure 4 :
Figure 4: Variation of fraction of 24-hour rainfall for each rainfall distribution scenario.

Figure 5 :
Figure 5: Comparison of (a) daily observed mean field bias based on TMD rain gauges in the region and the citizen rain gauges in the Tubma basin, (b) hourly observed mean field bias based on TMD rain gauge observations and downscaled citizen rain 390 gauge observationss, (c) hourly observation error variances and (d) hourly estimated mean field bias obtained based on MFB and the five different KF approaches.Bias calculations cover 16 citizen gauges in the Tubma basin and 14 TMD gauges within 100 km radius from the Tubma basin.Hourly scale calculations for the citizen gauges (CKF) are based on 4 different sub-daily interpolation scenarios (RP, RMP, GMP and GTubma, Table3).

Figure 6 :
Figure 6: Variation in RMSE and MBE across the cross-validation scenarios for the various evaluation cases: (a) case 1, hourly 405 bias updating based on MFB and KF using TMD gauges (b) case 2, daily bias updating based on MFB and KF using only TMD gauges and (c) case 3, daily bias updating using MFB, KF (TMD gauges) and CKF (TMD and citizen gauges).Validation covers 16 gauges in the Tubma basin for daily scale and 14 gauges within 100 km radius from the Tubma basin for hourly scale.
Figure 6 (c) shows cross-validation results at daily scale for the Tubma basin, comparing bias correction approaches using TMD only and TMD combined with citizen gauges.Following the CKF steps, citizen rain gauge data are downscaled to hourly time scale using four different approaches, resulting in variation in hourly observed bias and error variances as shown 420 in Fig. 5 (b) and (c), respectively.Cross-validation results after accumulation to daily scale show that CKF-RP outperforms the other approaches (CKF-RMP, CKF-GTubma, MFB-TMD, KF-TMD, and CKF-GMP) in terms of both RMSE and MBE.The performance of CKF techniques for radar rainfall simulation in the Tubma basin relates to the reliability of the downscaled hourly observations.This is reflected in the variation of the estimated observation error variances for CKF-RP as shown in Fig. 5 (b) and (c).The better performance of CKF-RP is explained by the smallest range in observation error variance, indicative 425 of better consistency observation bias.Comparison with No-bias, CKF-RP can improve RMSE by 32-25 % and MBE by 90-80 % for median and upper 75%-ile, respectively.While CKF-GMP exhibits the worst performance compared with the other CKF approaches with the improvement of RMSE by 13-16 % and MBE by 57-56 %, respectively.This apparently decrease in efficiency of the CKF can confirm by the highest median value of the estimated observation error variances of CKF-GMP (see Fig. 5(c)) with 33% higher than that of CKF-RP.430 Figure 9 (b).Conversely, in the 40-90 km range, bias correction at gauge locations consistently leads to over-or 455 underestimation of rainfall.This can be explained by gauge at larger distance being affected by different rainfall generation patterns, associated with their location closer to the coast or mountains (see Fig. 7 (a)).The influence of the southwest monsoon strongly affects all gauges located in the coastal region on the windward side of a mountain, while rain gauge locations on the leeward side have less rainfall amount.Figure 9 (c) shows that TMD gauges located on the leeward side (e.g., 4590009 and 4590011) obviously appear steady light rainfall accumulation, whereas the gauges on the windward side (e.g., 4590002 and 460 4590003) show the mass curves with a sharper gradient.

Figure 7 :
Figure 7: Comparison of the RMSE and MBE for different range interval from the centroid of the Tubma (a) Rain gauge locations at each range interval (b) the comparisons for the range 0-40 km (c) the comparisons for the range 40-90 km.For 465 CKF, only results for the CKF-RP approach are shown, based on its better performance at daily time-scale (shown in Figure 6c).

Figure 8 :Figure 9 :
Figure 8: Hourly rainfall hyetographs obtained from TMD rain gauge network available for each hour compared with the validated rain gauge occurring in 3 different days (a) storm event during 15 September 2019 based on using 4780001 as the validated gauge, (b) storm event during 21 September 2019 based on using 4780005 as the validated gauge, and (c) storm event during 22 September 2019 based on using 4780003 as the validated gauge.

Table 1 :
The four methods used in this study to downscale daily citizen rainfall amounts to hourly rainfall data.

Table 2 :
Simulation cases for evaluating the effectiveness of bias correction techniques.320 *CKF-H includes 4 scenarios for 4 different hourly downscaling patterns for the citizen rain gauges, according to Table1.

Table 1 )
Four hourly rainfall distribution patterns were obtained as outlined in Table1.