Rainfall-Riverflow Trends of Enyong Creek in Akwa Ibom State, Nigeria

: Rainfall-riverflow is crucial for effective hydrology and water resource management. Hence, the objective of this study was to evaluate the rainfall-riverflow trends of Enyong Creek in Akwa Ibom State, Nigeria, utilizing daily hydro-meteorological data of daily rainfall, river discharge, and temperature data collected from the period 2018 to 2023 and modeling the data by Vector Autoregressive (VAR) models. The results show that the VAR model successfully captured the dynamic relationships among water discharge (WD), rainfall (RF), and average temperature (AVE.TEMP). Equations revealed the influence of past values on the current state of each variable. Correlation matrix and graphical representations confirmed model adequacy. Validation results demonstrated the model's accuracy, with model R-squared value of 0.8781 indicating a strong correlation. The performance measurement of evaluation for the developed model showed a Mean Average Error (MAE), Root Mean Square error (RMSE), and Mean Absolute Percentage Error (MAPE) values of 5.5066, 6.7831, and 7.4203 respectively, revealing a satisfactory accuracy and precision. Information derived from this study offers valuable insights for government officials, policymakers, and planners in accurate flood forecasting, emergency management, land use

Stochastic modeling of rainfall-riverflow plays a pivotal role in hydrology and the management of water resources.The stochastic rainfall-river flow modeling involves the use of probabilistic and statistical methods to simulate the variability and uncertainty of rainfall and river flow patterns (Ahaneku and Otache, 2014).This methodology utilizes probabilistic and statistical approaches to model the variability and uncertainty inherent in rainfall-riverflow patterns.The significance of stochastic rainfall-riverflow modeling is underscored by its contributions to various aspects, including comprehending hydrological processes, managing floods and droughts, optimizing reservoir operations and water allocation, designing infrastructure, adapting to climate change, conducting risk assessments, facilitating hydropower generation, ensuring environmental protection, addressing datascarce regions, and supporting research and education.Flood forecasting system integrating meteorology, hydrology, technology, and communication, is instrumental in issuing early warnings to mitigate the impacts of flooding.This field continuously advances alongside developments in science and technology, aiming to enhance the protection of people and property against the consequences of this natural disaster, flood (WMO, 2023).Floods, recognized as one of the most recurring and devastating natural hazards, profoundly affect human lives and result in substantial economic losses globally (Khan et al., 2011).It is acknowledged that the risks associated with flooding will persist in the future, exacerbated by climate change leading to increased intensity and AUGUSTINE, C. U; AHANEKU, I. E; AWU, J. I. frequency of floods in various regions worldwide (Jonkman and Dawson, 2012).Flood occurrences are primarily driven by the rapid accumulation and release of runoff waters, triggered by intense rainfall.The swift rise to peak discharge and subsequent rapid decline characterize these events.The prevalence of flooding is a significant concern in hydrological and natural hazards science, ranking high among natural disasters in terms of both global population impact and individual fatalities (Borga et al., 2014).The potential for flood-related casualties and damages is further increasing in numerous regions due to ongoing social and economic development, exerting pressure on landuse, particularly through urbanization.The frequency and severity of flood vulnerability are anticipated to escalate due to the impacts of global climate change, characterized by intense weather events such as heavy rainfall and river discharge conditions (Dihn et al., 2014).Addressing the current trajectory and potential future scenarios of flood risks necessitates accurate spatial and temporal information on potential hazards and risks associated with floods.As reported by Chang and Guo (2006), heavy convective rainfall often results in flooding in urban areas.The conversion of agricultural land, depletion of natural vegetation, and population growth in flood-prone areas exacerbate this risk, disrupting natural infiltration processes.The consequences of flooding vary across regions, with Nigeria experiencing its share of flood events resulting in significant losses of lives and property.In Nigeria, the various factors contributing to flooding, including the accumulation of refuse leading to blockages in natural waterways, high-intensity rainfall on gentle slopes, dam failures, and rapid unplanned settlement affecting drainage systems.While complete eradication of floods may be impractical, minimizing their impact is feasible through a holistic understanding of contributing factors.Implementing an early warning system becomes crucial for effective risk assessment in spatial planning, facilitating resource allocation for emergency response teams and infrastructure protection.Forecasting plays a fundamental role in flood management, guiding decisions related to closing flood gates, activating protective measures, and enabling communities to prepare for potential flooding through evacuations and resource provisioning.The components of flood forecasting systems encompass data collection, involving monitoring weather conditions, river levels, snowpack, and soil moisture.Mathematical and computational models predict how changes in these variables impact river discharge and water levels.Warning systems, automated to issue alerts to emergency management agencies and the public, and effective communication of forecasts are critical elements in minimizing flood-related risks and protecting human life, property, and natural ecosystems.
However, Flood forecasting encompasses various types of floods, such as riverine floods, flash floods, coastal floods, and urban floods, each requiring tailored forecasting methods based on the specific flood type and geographical location (Parker and Wilby, 2005).Technological advancements over the years have significantly enhanced the precision and timeliness of flood forecasting, utilizing tools like weather radar, satellite imagery, remote sensing, and computer modeling to deliver more accurate predictions.As a multidisciplinary field integrating meteorology, hydrology, technology, and communication, flood forecasting aims to provide early warnings and mitigate the impacts of flooding (Merz et al., 2020).It continually evolves with scientific and technological progress to enhance protection against this natural disaster.However, it is not without challenges, facing uncertainties in weather forecasts, the intricate nature of hydrological processes, the influence of urbanization on local drainage systems, and the necessity for effective communication to ensure public responsiveness.Public education and community involvement are integral aspects, contributing significantly to the effectiveness of the forecasting system when communities are well-informed about risks and have clear guidance on responding to warnings.Historical advancements in meteorology and hydrology from the late 19th to the early 20th century, including the utilization of precipitation data, laid the foundation for more comprehensive flood forecasting (Kidd and Huffman, 2011).The mid-20th century witnessed the introduction of numerical weather models, enhancing precipitation forecasting and understanding its potential impact on flooding.Concurrently, hydrological models, simulating water movement in river basins, emerged to improve forecasting accuracy.The 21st century has brought challenges from climate change, resulting in more frequent and intense rainfall events and altered flood patterns.In response, forecasting models and techniques are being updated to accommodate changing climate conditions (Alfieri and Pappenberger, 2019).Recent advancements in big data analytics and machine learning enable more sophisticated flood forecasting models capable of processing and analyzing vast amounts of data in realtime, thereby improving accuracy and lead time in flood predictions.Therefore, this objective of this study was to evaluate the rainfall-riverflow trends of Enyong Creek in Akwa Ibom State, Nigeria, utilizing hydro-meteorological data of daily rainfall, river discharge, and temperature data collected from the period 2018 to 2023 and modeling the data by Vector Autoregressive (VAR) model.

MATERIALS AND METHODS
Study Area: The study area is situated between latitudes 5°11′ to 5°28′ N and longitudes 7°51′E, covering a geographic expanse of 55.63 km2 (Figure 1).Geologically, the region displays a diverse range of formations, ranging from the Asu River Formations within the Abakiliki Anticlinorium to recent alluvium in the southern part.The Asu River Group predominantly underlies the northern section of the study area, featuring intense fracturing evident in outcrops like those in Uburu.The Albian-aged Asu River Group comprises three formations, characterized by bluish-grey to olive-brown shales, sandy shales, fine-grained micaceous and calcareous sandstones, along with some limestones.The landscape is marked by structurally controlled ridges, denudational hills such as the 150m high Obotme conical hill, steep-sided valleys, and geographical features like saddles and cols at Obot Ito Ikpo.Extensive wetlands and alluvial plains contribute to soil covers consisting of silty clay, sandy areas, and heavily weathered loamy and alluvial deposits.The region experiences a tropical climate, with temperatures ranging from 26 to 32º C. Temperature fluctuations are relatively uniform, except during the dry months when temperature increases are more pronounced than during the extended wet period (March to October).The proximity to the main Cross River Channel results in high humidity levels (84%).The average annual rainfall in the basin measures 2200mm, with a significant contribution from southwest tropical maritime air-masses.This rainfall equation models (Equation 4.4) the current rainfall (RFt) as a function of several factors.It includes an intercept term of 15.357379, the auto-regressive terms RFt-1, RFt-3, and RFt-4, the lagged effects of average temperature (ATt-1 and ATt-2).The equation suggests that current rainfall is influenced by its past values and average temperature in previous time steps.Positive coefficients on the RF terms indicate a positive auto-regressive effect, while negative coefficients on the AT terms imply a dampening effect on rainfall.This equation essentially describes the dynamic relationship between rainfall and these variables.
= 6.767784 − 0.017099  −1 + 0.463519  −1 + 0.093533  −1 + 0.095567  −3 − 0.156961  −4 3 This equation models the current Average temperature (ATt) as a function of various factors.It includes an intercept term (6.767784), auto-regressive effects (ATt-1, ATt-2, ATt-3, and ATt-4), and a lagged effect of rainfall (RFt-1).The equation implies that the current Average temperature is influenced by its past values and the previous value of rainfall.The coefficients on these terms indicate how much impact these variables have on the current Average temperature.
The significance of these equations lies in their ability to capture the dynamics and interactions among water discharge, rainfall, and Average temperature.By estimating the coefficients, you can quantify the relationships and predict how changes in these variables at different time   The descriptive graph from Figure 3 to 5 shows that the validation model graph performed very well as it was observed that the predicted line followed in a consistence pattern to the actual data.Though there were little or non-significant deviation from the actual but, generally, made a good model.From Figure 3, the model validation graph for the water discharge shows that the model only over predicted the actual dataset from the 20 th to the 28 th of August 2023 while the rainfall validation model as shown in Figure 4, underpredicted only on the 15 th and the 28 th of August 2023, as well as, the Average Temperature validation graph as shown in Figure 5.The Figure 6 shows that the model made a good prediction with R-squared value of 0.9873.This value of Rsquared gotten from the forecasted model indicate a very strong correlation with the actual dataset.The performance evaluation measurement results for the developed VAR model is given in Tables 6 to 8 The performance evaluation for the water discharge as shown in Table 6

Fig 2 :Fig 2 :
Fig 2: The structural Block Diagram of Vector Autoregressive Model Development (Source: Helmut Luetkepohl, 2007)RESULTS AND DISCUSSIONThe VAR model was modeled evaluated and compared on a number of different factors.The numerical and graphical assessment of their performance in terms of accuracy, reliability, and lead time for flood forecasting were determined.The descriptive graph representation of data visualizing to know whether the parameters (Water Discharge (WD), Rainfall (RF), and Average Temperature (AVE.TEMP)) data is stationary or non-stationary is shown in Figure2The data graph visualization for the Water Discharge(WD) is represented as blue color, rainfall Humidity(RH) is represented as orange color and Average Temperature (AVG_TEMP) is represented as green color.
descript modeled graph for the three parameters used for the developed VAR model are shown in Figures 3 to 5

Fig 3 :Fig 4 :Fig 5 :
Fig 3: The descript graph of the actual Vs. the predicted graph of the developed

Table 1 :
The Statistical Summary of Regression Results

Table 2 :
The Statistical Summary Results for Water Discharge (WD) equation meaning that if the water was discharged in a particular level in the previous time step, it is likely to continue in that level.

Table 4 :
The Statistical Summary Results for equation AVGTEMP It's a popular choice when giving more weight to larger errors.The implications of an RMSE of 6.7831 means that, on average, the model's predictions for water discharge differ from the actual values by approximately 6.7831 units, with a stronger emphasis on larger errors.

Table 6 :
The performance evaluation measurement results for the developed Water

Table 7 :
The performance evaluation measurement results for the developed Rainfall

Table 8 :
The performance evaluation measurement results for the developed Average Also, the Mean Absolute Percentage Error (MAPE) measures the average percentage difference between the actual values and the predicted values, making it a relative error metric.The significance of MAPE is useful for understanding the model's accuracy in terms of percentage errors.It's especially informative when to assess the model's performance relative to the scale of the data.From Table6, the implications of a MAPE of 7.4203% means that, on average, the model's predictions for water discharge differ from the actual values by approximately 7.4203% in terms of relative error.However, the Rsquared, also known as the coefficient of determination, measures the proportion of the variance in the dependent variable (water discharge in this case) that is explained by the independent variables (the VAR model predictions) provides insights into how well the model fits the data.An R 2 value of 0.8781 which is close to +1 suggests that the model explains a substantial portion of the variance in the data.It indicates that approximately 87.81% of the variability in water discharge can be accounted for by the VAR model, which suggests that the model is providing a good fit to the data.Generally, these validation metrics help assess the accuracy, precision, and goodness of fit of your VAR model for water discharge.A low MAE, RMSE, and MAPE indicate good prediction accuracy, while a high R-squared suggests that the model is a good fit for the data.These metrics collectively provide a comprehensive evaluation of the model's performance and can help determine its utility in making forecasts or predictions.The study employed Vector Autoregressive models (VAR) for rainfall-riverflow modeling of Enyong Creek, Akwa Ibom State, Nigeria.The model effectively captured the dynamic relationships between water discharge, rainfall, and average temperature, Conclusion: