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Floods have caused significant human and economic losses in the Cazones River Basin, located on the Gulf of Mexico. Despite this knowledge, steps towards the design and implementation of an early warning system for the Cazones are still a pending task. In this study we contributed by establishing a hydrological scheme for forecasting mean daily discharges in the Cazones Basin. For these purposes, we calibrated, validated and compared the HyMod model (HM) which is physics-based, and an autoregressive-based model coupled with the Discrete Kalman Filter (ARX-DKF). The ability of both models to accurately predict discharges proved satisfactory results during the validation period with RMSE
_{HYMOD} = 2.77 [mm/day]; and RMSE
_{ARX-DKF} = [2.38 mm/day]. Further analysis based on a Streamflow Assimilation Ratio (SAR) revealed that both models underestimate the discharges in a similar proportion. This evaluation also showed that, under the most common conditions, the simpler stochastic model (ARX-DKF) performs better; however, under extreme hydrological conditions the deterministic HM model reveals a better performance. These results are discussed under the context of future applications and additional requirements needed to implement an early warning hydrologic system for the Cazones Basin.

The interaction between global warming and natural variability affects the magnitude and frequency of extreme hydrological events, i.e. droughts and floods [

In Mexico, communities around river basins within humid-subtropical climates could especially benefit from accurate hydrological modeling. These humid-subtropical climates result from the interaction between several ocean-atmosphere teleconnections, i.e., the El Niño Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO), the Arctic Oscillation (AO), the North Atlantic Oscillation (NAO), and the Atlantic Multidecadal Oscillation (NAO). These ocean-atmosphere interactions generate flooding and landslides that can result in important socio-economic losses, particularly in the floodplains of the basins.

To mitigate the impacts associated to these extreme events, during 2002 the Mexican government established an Early Warning System for Tropical Cyclones (EWSTC), which is the main tool used to monitor the intensity, trajectory and distance of the cyclones. The information generated by EWSTC is then used by federal and state agencies who take supportive measures. Despite this centralized system has demonstrated to be effective for early warning of meteorological disasters, the role of local agencies is still pending in terms of expanding the “hydrological knowledge” about it e.g. calibration and validation of hydrologic models that deal with specific physical characteristics of the basins or those sustained in new algorithms of data assimilation.

In order to advance towards the development of an early warning hydrological system for the Cazones Basin, in this study we have established a first approximation for forecasting mean daily discharges in the basin. For these purposes, we calibrated, validated, and compared two lumped hydrological models The first model is HyMod (HM), a physics-based model that accounts for all components of the water balance [

The Cazones River Basin is located between the coordinates 20˚18' and 21˚15'N and 97˚17' and 98˚32'W, in the Hydrological Region N˚27 North, called Veracruz Tuxpan-Nautla [^{3}/s, but for a single day this value can reach a maximum of about 1250 m^{3}/s [^{2} distributed in three states of Mexico (^{2}. Grasslands and agricultural fields represent more than 70% of the total land area of the basin (

Much of Mexico has a monsoon climate, with a rainy season during the summer months (JJA) and a relatively dry winter season (DJF) [

The Cazones Basin drains over its west-facing slopes. The drainage enters the lowlands around the town of Poza Rica in the state of Veracruz, an important petroleum production area. Extreme meteorological events affecting the area cause high runoff over the saturated soils of the basin, resulting in significant damage [

Daily streamflow forecasting in the Cazones Basin was conducted using two lumped models (one physics-based and one systems-based). In the definition of HM model we considered the formal steps of model building as stated by [

The input forcing data used in this study include daily, spatially aggregated rainfall amounts (2008-2011) obtained from a total of nine raingauges, mean daily flows obtained from Poza Rica stream gauge (

Code | Station/Location | Type | North Latitude | West Longitude | State |
---|---|---|---|---|---|

13034 | Tenango de Doria | Rain gauge | 20˚20'22" | 98˚13'30" | Hidalgo |

13099 | Metepec | Rain gauge | 20˚14'14" | 98˚19'18" | Hidalgo |

13130 | Santa Ma. Asunción | Rain gauge | 20˚90'16" | 98˚16'29" | Hidalgo |

21118 | Huauchinango | Rain gauge | 20˚11'37" | 98˚30'35" | Puebla |

21127 | Xicotepec | Rain gauge | 20˚20'18" | 97˚50'41" | Puebla |

21142 | Venustiano Carranza | Rain gauge | 20˚30'34" | 97˚40'60" | Puebla |

21147 | Apapantilla | Rain gauge | 20˚14'14" | 98˚19'18" | Puebla |

30125 | Papantla | Rain gauge | 20˚26'44" | 97˚19'30" | Veracruz |

30132 | Poza Rica | Rain gauge | 20˚32'30" | 97˚28'20" | Veracruz |

27002 | Poza Rica | Stream gauge | 20˚32'48" | 97˚28'30" | Veracruz |

potential evapotranspiration (PET) calculated using Hargreaves Method [

The physical or mathematical principles governing the entire behavior of the hydrologic system were summarized for each model through the use of simple conceptual Directed Graphs (DG), which are an explicit representation of the major processes occurring within the hydrological system, their structural organization, and their results [

On the other hand, physical conditions are not considered in the formulation of the ARX-DKF model, which is intended to find the best mathematical or causal relation(s) between the input and the output of the hydrological system [

This stage consisted of developing a group of hypotheses regarding the mathematical forms of the process equations that are believed to describe the physical processes linking the subsystem components (see i.e. [

Model | Reservoir/ Component | Water Balance or State Equations | Constitutive Relations | State Variables | Model Fluxes | Model Parameters | |
---|---|---|---|---|---|---|---|

HyMod | Soil Moisture (S_{m}) | S_{m} is the soil moisture in the upper soil layer [mm]. S_{q}_{1} is the total water content in tank 1 [mm]. S_{q}_{2} is the total water content in tank 2 [mm]. S_{q}_{3} is the total water content in tank 3 [mm]. S_{s} is the total water content in the lower soil layer [mm]. S_{m} = 0; at t = 0 is the initial basin storage [mm]. S_{q} = 0; at t = 0 is the initial storage of quick-flow tanks [mm]. S_{s} = 0; at t = 0 is the initial storage of slow = flow tanks [mm]. | P is the Precipitation [mm∙d^{−1}]. Pe is the effective Precipitation [mm∙d^{−1}]. ET is the Evapo-transpiration from the soil [mm∙d^{−1}]. PET is the Potential Evapotranspiration [mm∙d^{−1}]. Q_{qi} is the quick surface runoff in S_{qi} [mm∙d^{−1}]. Q_{S} is the slow groundwater runoff in S_{s} [mm∙d^{−1}]. | ^{−1}]. Ks is the conductivity of the slow-routing tanks [0.001-0.95 day^{−1}] Nq is the number of quick flow linear tanks [ | |||

Quick Routing Reservoir 1 (S_{q}_{1}) | |||||||

Quick Routing Reservoir 2 (S_{q}_{2}) | |||||||

Quick Routing Reservoir 3 (S_{q}_{3}) | |||||||

Slow Routing Reservoir (S_{S}) | |||||||

ARX | Autoregressive Component | ^{3}∙s^{−1}]. ^{3}∙s^{−1}]. | α is a parameter calculated from the autoregressive component applied to streamflow. β is a parameter calculated from the autoregressive component applied to rainfall. na is the lag number for streamflow. nb is the lag number for rainfall. | ||||

DKF | Discrete Kalman Filter Component | | A and B are matrices containing α and β parameters from the series of streamflow and rainfall data in the ARX model. H is a transformed matrix that contains the states of the measurements. Q and R are matrices containing the covariance for the noise in the process and the measurements. | ||||

The computational implementation of both models was coded using a Matlab^{TM} routine, which was packaged in a toolbox^{1} format to facilitate usage. From the historical records of mean daily streamflows, the year 2008 was selected to calibrate the initial parameters of both models, because it contained the largest number of flood events (see _{Mod}) and observed (Q_{Obs})

streamflows for each day i under analysis

predictive capacity of each model; however, it can also be used to apply bias correction schemes in a similar way of that performed over Global or Regional Climate Models (GCMs or RCMs); that is, by calculating an av-

eraged version of SAR (averaged Bias Correction Factor) over all n days under analysis:

For the HM model the selection of the final set of parameters from the 2008 calibration was used to define the physical processes associated with hydrological responses in the Cazones Basin. For instance, the MSE_{HM} obtained fell as low as 8.79 mm, and all the parameters converged after completing the optimization scheme (

Test | Equation | Description |
---|---|---|

(1) Mean Squared Error (MSE) | n is the total number of days. | |

(2) Root Mean Squared Error (RMSE) | ||

(3) Nash-Sutcliffe Efficiency (NSE) |

the land use in the basin which is dominated by grasslands and agricultural fields (>70%) must play a significant role in modulating the hydraulic properties and consequently the infiltration capacity of soils. For instance, some studies have found that grasslands have lower (higher) infiltration (runoff) rates than forests [

For the ARX-DKF model the best set of parameters α and β calculated during the calibration period and then used to predict daily streamflows was identified when we combined the streamflow of the previous day (Q_{t-1}) and the rainfall that occurred in the prior two days (P_{t-2}). This means that the largest autocorrelation of the observed streamflows is achieved at lag t − 1 (days), and the largest cross-correlation between rainfall and observed streamflows is achieved at lag t − 2 (days). Similar findings have been reported by [

During the validation period, the performance of the chosen parameters was tested, revealing that both models are able to satisfactorily reproduce the mean daily discharges in the Basin. In fact, the forecasting performance of both models was improved during the validation period as evaluated through error measures. The MSE_{HM} was about 35% larger than MSE_{ARX-DKF} and these results were also consistent when looking at RMSE and NSE measures (

A significant relationship between SAR_{HM} and SAR_{ARX-DKF} (r = 0.68) revealed interesting additional details about the performance of the models (in a validation period of 982 days). For instance, the joint distribution of SAR revealed four different regions (

Model | MSE [mm] | RMSE [mm] | NSE [-] |
---|---|---|---|

HM | 7.66 | 2.77 | 0.75 |

ARX-DKF | 5.68 | 2.38 | 0.81 |

Judging from the hydrographs of both models (^{3}/s (~67.2 mm/day) on July 17^{th }(

The use of predictions from the centralized EWSTC allows for the generation of pre-alert scenarios with larger lead time; however, this scheme does not contain information about the states of the hydrological system i.e. it cannot be used to determine possible damages of hydraulic infrastructure. This is the most important pending task of local agencies as a way to expand the hydrological knowledge of EWSTC. This knowledge will have to develop new early warning hydrological systems dedicated to represent hydrological response based on the intrinsic characteristics of the Basins or dependent on new algorithms of data assimilation. In this study we contributed to establish a hydrological scheme for forecasting mean daily discharges in the Cazones Basin. For in- stance, based on classical validation schemes and the application of SAR, we determined that under normal con-

ditions ARX-DKF model performs slightly better than HM; however, this latter model performs better under extreme conditions. These hydrological statements and the information generated from both models can be used to warn the emergency coordinators in a different way than that currently offered by EWSTC, and thus are of great value to pre-manage a probable hydraulic emergency. An additional and important component of this validation process will be based on the coordination between public agencies, decision-makers, and stakeholders, and how these members make use of these tools and the information generated by the models to define appropriate policies towards the development of early warning hydrological systems at catchment scale i.e. temporal resolution of interest, selection of models, and ranges of applicability.

This study evaluated two lumped hydrological models to contribute in advancing towards the development of an early warning hydrologic system in the Cazones River Basin. HM and ARX-DKF were calibrated, validated, and compared to determine the best modeling system for forecasting mean daily discharges in the basin. The results from error measures and SAR revealed that the performance of the autoregressive-based ARX-DKF model (less underestimation) was slightly better than the performance of the physics-based HM model (greater underestimation). Despite these differences, under extreme hydrological conditions HM performs slightly better than ARX-DKF. The implementation of SAR proposed for this study showed to be a practical alternative to evaluate and compare the performance of hydrological models, and it seems to be promising for applying bias correction schemes over raw predictions obtained from hydrological models. The application of these methods is aimed to improve the predictions and reduce the uncertainty of hydrological models of course future studies will have to deal with the validation RCMs for the basin i.e. precipitation estimates provided by real-time satellite-based products as CMORPH, PERSSIANN or TMPA, combined with different lumped and spatially distributed hydrological models i.e. SACRAMENTO, HYMOD, HBV, TOMODEL, among others. The success or failure of these tools and the use of the information they provide will continue being a challenge since hydrologists have to also deal with climate models outputs coming with an additional source of uncertainty; therefore, the level of coordination attained between national agencies, decision-makers and stakeholders, in developing policies aimed to adequately implement new early warning systems including maybe not all but several scenarios of uncertainty, will play a central role for improving water governance schemes at catchment scale.

The authors of this study greatly appreciate to Consejo Nacional de Ciencia y Tecnología (CONACyt); and the NASA-USAID SERVIR Program (Award 11-SERVIR11-58) for their support in the realization of this study.

Fernando González-Leiva,Rodrigo Valdés-Pineda,Juan B. Valdés,Laura A. Ibáñez-Castillo, (2016) Assessing the Performance of Two Hydrologic Models for Forecasting Daily Streamflows in the Cazones River Basin (Mexico). Open Journal of Modern Hydrology,06,168-181. doi: 10.4236/ojmh.2016.63014