Coupling WRF and NRCS-CN Models for Flood Forecasting in Paraíba do Meio River Basin in Alagoas, Brazil

Coupling the WRF and NRCS-CN models was assessed as a tool for a flood forecast system. The models were applied to the Paraíba do Meio River basin, located in Alagoas, Brazil. FNL (Final Analysis GFS) data provided by the Global Forecast System model were used as initial conditions for WRF. Precipitations and observed discharges were collected in data collection platforms. Nine microphysics configurations were used to optimize WRF forecast. For hydrological, the automatic calibrations, available in HMS was used to get the optimum CN model parameters. Optimized precipitations Model performance was assessed with the indicators: bias, root-mean-square error, Pearson’s linear correlation coefficient, Nash-Sutcliffe coefficient, Heidke skill score, hit rate and false alarm rate. WRF ´ s predictive ability for the optimum configuration was satisfactory. The NRCS-CN yielded good results. The predictive ability of the hydrological model was ranked between satisfactory and acceptable. In a flood forecasting step, the coupled model yielded Nash-Sutcliffe of 0.749 and 0.572 for Atalaia and Viçosa basins. Overall, the method showed potential for the development of a flood alert system.


Introduction
Many studies have been done coupling meteorological to hydrologic models for improving decisions on water resources management and planning. Thom et al. (2017) used gridded rainfall products in SWAT model, to estimate discharges in Srepok River Catchment in Vietnam. Givati et al. (2012) coupled the WRF model to the Hydrological Model of Karst Environment (HYMKE) for predicting streamflow operationally for the high Jordan River Basin. Shrestha et al. (2014) used data from downscaling from of the HadCM3 global circulation model as input for the hydrological model in HEC-HMS to study the impacts of climate change in Kulekhani Hydropower Project in Nepal. Alves et al. (2012) coupled a regional atmospheric spectral model (RSM) to SMAP hydrological model for defining reservoir release rules in semiarid region of Brazil.
The coupling of forecasting precipitation models with hydrological models with a short-term horizon is fundamental for developing flood alert systems in urban and rural areas. The prediction of floods and the issuance of warnings to populations can save human and animal lives and reduce damage. Many studies have focused on the improvement of coupled models and their assessments (Chen et al., 2011;Linares-Rodriguez et al., 2015;Yang et al., 2015;Shahid et al., 2017;Ratna et al., 2017).
The coupling of climate and hydrological models can be unidirectional (off-line) or bidirectional (online). In unidirectional coupling, meteorological data predicted using an atmospheric model and rainfall and evapotranspiration are used as input data in a hydrological model. This coupling offers improved flexibility and operational autonomy. In bidirectional coupling, there is an exchange of data between meteorological and atmospheric models, resulting in an integrated model called a hydrometeorological model. The incompatibilities of time and spatial scales are considered the major problems in bidirectional coupling. Nevertheless, bidirectional coupling has great potential for flood forecasting (Yu et al., 1999). This method was applied by Meller et al. (2014) for flood forecasting in the Paraopeba River basin, located in the state of Minas Gerais, using the Model for Large Basins of the Hydraulics Research Institute -MGB-IPH) and rainfall forecasts developed at the University of São Paulo. The results showed promise for identifying and predicting floods. Calvetti and Pereira Filho (2014) applied the WRF model coupled to TopModel, in hourly time step, for streamflow prediction in Iguaçu river basin in southern Brazil. The authors found better results using more complex microphysics schemes.
In this paper, the coupling of the WRF atmospheric model with the NRCS-CN hydrological model using the software HMS (NRCS: Natural Resources Conservation Service; CN: Curve Number; HMS: Hydrological Model Systems) was analyzed for developing a flood forecasting and alert system for the Paraíba do Meio River. To improve our knowledge of atmospheric models, nine microphysics and convection configurations were assessed for the WRF model. In addition to the coupling of the atmospheric and hydrological models, this study is innovative in that it yielded an optimal microphysics and convection configuration for the WRF coupled with optimal NRCS parameters in the coast of Northeastern Brazil. Unidirectional coupling was adopted due to its potential for providing flowrate forecasts and its easy model coupling.

Study Area
The hydrographic basin of the Paraíba do Meio River (HBPM) is located between latitudes 8°44' and 9°44' south and longitudes 36°48' and 35°52' west. It measures 3,148.5 km2, of which 1,964.66 km2 is in the state of Alagoas and 1,183.8 km 2 in the state of Pernambuco (Fig. 1).
The HBPM is underlain by two geological domains. Crystalline soils prevail in the upstream portion, and sedimentary soils prevail in the downstream portion. The elevation of the basin ranges from 1,024 m at the riverhead to 1.0 m at the river's mouth. The relief ranges from rugged to undulatory in the upper valley, in the region of the Borborema Plateau. The lower valley is characterized by smooth relief in the region of the coastal tablelands and in the fluvial-lagoonal plains.
The head of the Paraíba do Meio River is located in the city of Bom Conselho, state of Pernambuco, at an elevation of 800 m. The river empties into the Mundaú-Manguaba estuarine lagoon complex in the city of Pilar, on the coast of the state of Alagoas. The river generally flows southeast, is 172 km long, and has a perennial fluvial regime.
The HBPM is located in the eastern part of northeastern Brazil. In this region, 60% of the rainfall occurs during the four months of April to July. The mean annual rainfall ranges from 1,300 mm at the coast to 700 mm at the riverhead (Rao et al., 1993;Vitorino et al., 1997).
The following synoptic systems act in the region: cold fronts and their remnants (Kousky, 1979), waves from the east (Yamazaki and Rao, 1977), VCANs (Gan and Kousky, 1986), CCMs (Alves, 2001) and wavelike disturbances of the trade winds. The number of rainy days ranges from 70 to 120 (Silva et al., 2012).

Data
Two series of rainfall and flowrate data, collected at data collection platforms (DCPs) ( Table 1), were used. The rainfall series spanned a 120-hour period from July 27 to 31, 2011, and the series used in the validation phase spanned 192 h from June 1 to 8, 2013. The flowrate series used in the calibration and validation of the hydrological model contained 120 records (July 1 to 5, 2013) and 192 records (July 9 to 16, 2013), respectively. For the hydrological modelling, the rainfall and flowrate data were stored in the data storage system (DSS) of the Hydrologic Engineering Center (HEC). The spatial distribution in the basin was obtained using the Thiessen polygon.
As initial boundary conditions for the WRF, data in a 1.0°x 1.0°grid were operationally prepared every six hours (12 a.m., 6 a.m., 12 p.m. and 6 p.m. Universal Coordinated Time (UTC). The data were provided by the National Center for Environmental Prediction (NCEP) of the Final Operational Global Analysis (FNL). The FNL data were generated using the same model used by the NCEP in the Global Forecast System (GFS) (Almeida and Marton 2014).

WRF atmospheric model
The WRF is a cutting-edge numerical atmospheric model developed by several research centers and government agencies in the United States, including the National Center for Atmospheric Research (NCAR), Mesoscale and Microscale Meteorology Division of the National Oceanic and Atmospheric Administration (NOAA), the National Center for Environmental Prediction (NCEP), and the To find the best configuration for the simulation, the nine microphysics and convection parametric schemes listed in Table 2 were evaluated. The results simulated with the WRF in domains D2 and D3 in two sub-basins, Atalaia (sub-basin SB12) and Viçosa (sub-basin SB9), and their upstream contribution areas were evaluated. No significant differences were observed between the results in domains D2 and D3; therefore, to reduce the computational effort, domain D2 was selected.
With the combinations of the microphysics and convection schemes, a matrix with nine elements was created ( Table 3). The schemes referring to the surface boundary layer, soil surface layer, planetary boundary layer and atmospheric radiation were specified.
The WRF model was executed using the configuration listed in Table 4. The simulation spanned the 120 h from July 27, 2011, at 00Z, to July 31, 2011, at 00Z.

NRCS-CN hydrological model
Estimation surface runoff from rainfall data is of major importance in hydrological engineering and watershed management. Among the various methods available, the NRCS-CN methodology is widely accepted and popular (Verma et al., 2017). For the hydrological modelling using NRCS-CN, HEC-HMS software was used. The HMS allows the simulation of many hydrological processes in a hydrographic basin. The loss function was used to estimate the fraction of rainfall that converts to direct surface runoff. The transformation function used data from a hyetograph and made it possible to obtain the hydrograph at a control point in the basin. The HMS provided an automatic calibration tool to estimate the parameters of the hydrological model. The HMS is widely used in association with other HEC software to study floods in urban centers, flood frequency and flood losses (Singh and Woolhiser, 2002). In addition, the HMS is a multi-model program that allows the user to develop the most appropriate model for the analyzed system For the loss function, the curve number (CN; NRCS, 1986) was applied. The method uses the CN coefficient, which depends on the use and type of soil. The exceeding rainfall was estimated using Eq. (1): where Pe is the effective rainfall of the event (mm), P is the total rainfall of the event (mm), Ia corresponds to the initial losses (mm), and S is the potential maximum retention of rainfall (mm). The value of Ia was estimated using Eq. (2): Combining Eqs.
The CN ranges from 0 to 100 and varies as a function of the soil group and use, the occupation and the initial moisture condition. The CN values were tabulated by the NRCS (NRCS). The estimated CN can be refined by performing the automatic calibration available in the HMS model, which provides 14 objective functions for the calibration.
For converting the exceeding rainfall to a flowrate, the NRCS unit hydrograph method was used (Soil Conservation Service, 1972). It is one of the most widely used models in practice, due to its simplicity and ease of application (Milde et al., 2002).

Analysis of model performance
The performance of the model was assessed in the WRF configuration phase, in the WRF/HMS coupling and in flood forecasting. In the configuration and coupling phases, the following metrics were used: the bias (Eq. (5)), the root-mean-square error (RMSE; Eq. (6)) and the correlation coefficient r (Eq. (7)). These three equations are as follows: where M i is the i-th value obtained from the modeling (rainfall or flowrate), O i is the value observed at the surface (rainfall or flowrate), and N is the number of data analyzed.

RMSE =
ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where M i is the i-th value estimated by the model, O i is the value observed at the surface, and N is the number of data analyzed.
where r is the linear correlation coefficient between O i and M i ; and S M i and S O i are the standard deviations of M i and O i , respectively. For the evaluation of the predictive ability, the Nash-Sutcliffe (NS) coefficient, the Heidke skill score (HSS), the hit rate (H) and the false alarm rate (FAR) were used.
The NS values for the WRF model and for the coupled models were calculated using Eq. (8): where O i is the observed value, P i is the simulated value, and O is the mean observed value; all variables may be for the rainfall or flowrate. For rainfall, the HSS, estimated using Eq. (9), was applied by assuming two conditions: rainfall and no rainfall.

HSS
where x indicates that the model predicted rainfall and that rainfall occurred, y indicates that the model predicted rainfall but that rainfall did not occur, z indicates that the model did not predict rainfall but that rainfall occurred, and w indicates that the model did not predict rainfall and that rainfall did not occur. The value of H (dimensionless) was estimated using Eq. (10): where n indicates the number of observations (x and w were defined earlier). The value of FAR was estimated using Eq. (11): (y and x were defined earlier). For the flood discharges, for alert purposes, the HSS was applied to three conditions: low flowrate or a normal condition, average flowrate or a watch condition, and a high flowrate or a warning condition. The HSS was calculated using Eq. (12): where n(F i ,O j ) is the number of forecasts in category i that corresponded to observations in category j, N(F i ) is the number of forecasts in category I, N(O j ) is the number of observations in category j, and N is the total number of forecasts. Table 5 presents the categories used to determine the HSS.
The HSS values can range from -1 to 1, where the value of 1 indicates a perfect forecast; zero indicates no predictive ability or a forecast equivalent to a reference forecast, i.e., a fortuitous coincidence; and -1 indicates performance inferior to a random forecast. Table 6 presents the results of the nine combinations corresponding to Atalaia station. At this station, a negative bias prevails in the predictions by the WRF model, given that eight of the nine combinations yielded negative values. Combination MPK-KF yielded the lowest bias (-0.01 mm/h). The second-lowest biases were those produced by combinations MPT-KF (-0.07 mm/h) and MPL-KF (0.07 mm/h). Combination MPT+KF produced the lowest RMSE (1.55 mm/h) and the highest r (0.68 mm/h). The correlation obtained in the analysis (0.68 mm/h) was acceptable and was rated as strong based on the classification of Callegari-Jacques (2003). Thus, combination MPT-KF performed best among the nine combinations: it performed best based on two indicators and second best based on the third indicator.

Calibration of the parametric configuration
At Viçosa station, the WRF model captured the rainfall events well, although it underestimated the rainfall intensities there much more than it did at Atalaia station. The area scale factor used for the mean rainfall could be responsible for the lower quality of this forecast. The Viçosa area is much smaller than the Atalaia area. Table 7 shows that all the biases are negative, and the lowest value was -0.42 mm/h. H values exceeding 50% were obtained, except with combination MPT-KF, which yielded values of 44.54% and 42.86% for the Atalaia and Viçosa stations, respectively. The analysis revealed that the best H was produced by combination MPL-G3D: approximately 80%.
For FAR values, the worst result was produced by combination MPT-KF, which yielded values of 55.46% and 53.21% for Atalaia and Viçosa stations, respectively. The best result was produced by combination MPK-BMJ, which yielded FARs of 21.43% and 13.95% for Atalaia and Viçosa stations, respectively.
Eight of the nine combinations yielded positive HSSs, indicating performance better than a random forecast. The highest HSS values, 0.5817 for Atalaia station and 0.5319 for Viçosa station, corresponded to combination MPL-G3D. The worst result was obtained with combination MPT-KF, which yielded values of 0 (zero) and -0.0836, indicating that this combination is inadequate for rainfall forecasting in this region.
Based on these results, combination MPT-KF performed poorly. In contrast, the adjustments represented by combinations MPT-G3D and MPL-G3D provided the best rainfall simulations in the Paraíba do Meio River basin. Combination MPL-G3D was selected for use in the WRF model, given that it provided the best overall results.

Validation -application of the selected configuration
For the validation of the WRF model, simulations spanning a 192-h time period were performed, i.e., 72 h longer than that of the configuration (calibration). Table 8 presents the results of the statistical analysis.
The RMSE obtained from the validation was within acceptable limits despite the high value corresponding to Atalaia station. HSS values of 0.37 and 0.61 were obtained for Viçosa and Atalaia stations, respectively (Table 8).

Hydrological modelling
The NRCS-CN hydrological model was calibrated using, as input, a time series of rainfalls with 120 records from the period of July 1 to 5, 2013. The basin was subdivided into 14 sub-basins (Fig. 2). Two flowrate stations were used in the calibration: the DCP of the city of Viçosa, located in sub-basin SB9, and the DCP of Atalaia (subbasin SB12).

Calibration of the hydrological model
For the calibration, manual and automatic searches for the best NRCS-CN parameters were performed. The manual method consisted of varying the parameters until an optimal response was produced based on the judgment of the analyst. Due to its simplicity, this method is widely applied. During each trial, the adjustment of the maximum flowrates, the shape of the calculated hydrograph, the adjustment of the flood peaks and the calculated volume were analyzed. The CNs and response times (RTs) were thus calibrated.
The automatic calibration consisted of using the search tool available in the HEC-HMS. The parameters of the NRCS-CN hydrological model were adjusted to minimize the percent error peak objective function available in the HMS.
The results of the calibration are presented in Table 9. The adjustment provided simulated flowrates very close to the observed values. Based on the calibration, the predictive ability of the model was rated as adequate and good according to the classification developed by Motovilov et al. (1999). The mean NS coefficient of 0.822 between two points of analysis was obtained; a higher value was obtained for sub-basin SB12 (0.836). The relation between the simulated and observed series indicated a very strong correlation, with a mean coefficient of 0.921 and a median amplitude between the simulated and observed values of 0.57, according to the RMSE. The model tended to underestimate the observed flowrate in the calibration phase; however, the flood peaks were satisfactorily simulated.
The hydrographs in Fig. 3 allow for a comparison between the observed and simulated series. Good fits of the flood peaks can be observed.
In addition, in the calibration phase, one of the most important aspects of a simulation of the flowrate for an alert system is the prediction of the hydrographs and the sizes of the peaks. Therefore, an adjustment that yielded better results in terms of these two properties was sought. Meenu et al. (2013) calibrated the HEC-HMS in an evaluation of the impacts of climate changes in the hydrographic basin of the Tunga-Bhadra River in India. The results were statistically compatible with those obtained in this study. The consistency tests yielded satisfactory predictive ability, with an NS coefficient of 0.48 and r equal to 0.85. According to Oleyiblo and Li (2010), despite the simple structure of the HEC-HMS, when calibrated, the

Validation of the hydrological model
The validation consisted of a model simulation using the parameters following their adjustment during another series of observed flowrates and rainfall amounts. The selected period spanned 192 hours from July 9 to 16, 2013. The results are presented in Table 10.
The calibrations for sub-basins SB12 and SB9 yielded NS coefficients of 0.809 and 0.591, respectively. Both values are satisfactory, particularly the value for SB12. The r values were 0.945 and 0.908 for SB12 and SB09, respectively, indicating good correlations.
The flowrate peaks were simulated well by the model (Fig. 4). Although the peak in sub-basin SB9 (Fig. 4a) was below the observed value, the predictive ability of the model is considered satisfactory (NS = 0.591), based on the classification of Motovilov et al. (1999).
The model underestimated the flowrates, based on the bias. However, low discrepancy between the two series was observed, based on the RMSE. Thus, the validation demonstrates the acceptable calibration of the model. The timing and intensity of the flood peaks were identified satisfactorily.
Given the results of the validation, coupling of the WRF atmospheric model and the NRCS-CN hydrological model was performed to evaluate the technique as a tool for forecasting hydrologic events in the Paraíba do Meio River basin.

Unidirectional coupling of the hydrological model with the WRF
Following the calibration and validation, the model was used to simulate the flowrate of the Paraíba do Meio River, using the rainfall simulated by the WRF atmospheric model as forcing in the NRCS-CN hydrological model. The grid points generated by the WEF model were selected in the BRPM limits for use as hypothetical pluviometers. The goal of this coupling of the WRF with the NRCS-CN model was to predict the flowrate in the extremely short term. The period of the coupling spanned from July 1 to 5, 2013.
The criteria were used to evaluate the efficacy of the coupling. The results of the evaluation are presented in Table 11. The technique proved to be suitable based on the statistical results. The implication is that the coupling is adequate to satisfactory, based on the NS coefficient. The  HSS, consistent with the Nash coefficient, indicates that the coupled system performed satisfactorily in sub-basin SB12. The system also yielded PA values of 84% and 61% in the flowrate simulations in sub-basins SB12 and SB9, respectively. The correlations are 0.76 and 0.75 for sub-basins SB9 and SB12, respectively, indicating a low combined variation between the two series, which, consequently, led to a strong correlation. Cabral et al. (2016) obtained an r of 0.48 for the coupling of the RAMS atmospheric model with the SMA hydrological model of the HEC-HMS when applied to the hydrographic basin of the Alto Jaguaribe River, in the state of Ceará.
In this study, the coupling yielded slight underestimation in sub-basin SB9. The relation between the observed series and the series simulated with the simulated rainfall is considered satisfactory, based on the low RMSE value. In sub-basin SB12, the coupling over-estimated the observed flowrates, based on much higher values of the bias and RMSE (Table 11). However, this sub-basin is large, and the bias of 13.15 m3/s is not large in comparison to the flood flowrates, which exceed 100 m 3 /s. Fig. 5 presents hydrographs of the observed and simulated flowrates. Although the predictions imperfectly simulated the peaks in the hydrographs, the technique was able to capture the flowrate variations in the basin during the period of analysis.
Based on the results, the method exhibits certain limitations, but it has demonstrated its potential as a flood forecasting tool starting with meteorological forecasts. However, further development is still necessary with regard to the configuration of the atmospheric model, given that the meteorological forecasts control the performance of the coupling.
According to Habets et al. (2004), despite all breakthroughs in atmospheric modelling, rainfall is still one of Figura 4 -Observed and simulated flowrates (observed rainfall) in the validation of the HMS, with the contribution of the rainfall throughout the basin and with analysis at the DCPs of sub-basins SB9 (a) and SB12 (b). The rainfall event spanned from July 9 to 16, 2013. the most difficult variables to predict in that it displays large temporal and spatial variations. Nevertheless, despite the WRF model's great dependency on simulated rainfall values, the coupled model shows promise for the creation of a flood alert system.

Conclusions
This study of the configuration of the WRF atmospheric model indicates that the best parametric combination among the microphysics and convection schemes for extremely short-term rainfall forecasting in the Paraíba do Meio River basin are the schemes proposed by Purdue Lin (microphysics) associated with Grell 3D (convection). The model shows satisfactory predictive ability, based on our evaluation of statistical indicators.
The unidirectional coupling (WRF -NRCS-CN) proved to be suitable for extremely short-term flowrate forecasting and for decision-making regarding flood alerts. The coupling yielded correlation coefficients exceeding 0.75. The predictive ability of the coupled system was good, based on NS coefficients of 0.749 and 0.572 for subbasins SB12 and SB9, respectively.
The HSS values corresponding to three flowrate categories (Q≤50, 50< Q≤100 and Q>100 m 3 /s) were 0.73 for Atalaia station and 0.25 for Viçosa station. The most severe flooding hazard is in Atalaia, where the upstream discharge area is large (2517.73 km 2 ).
In summary, the unidirectional coupling of the WRF, using the optimized configuration, with the NRCS-CN, using the optimized hydrological parameters, could serve well in developing flood alert systems.
Figura 5 -Observed and simulated flowrates (simulated rainfall) from the coupling of the HMS (hydrological) and WRF (atmospheric) models, with contribution of rainfall throughout the basin and with analysis at the DCPs of sub-basins SB9 (a) and SB12 (b). The rainfall event spanned from July 1 to 5, 2013.