Quantifying Diyala River basin rainfall-runoff models for normal and extreme weather events

The total water budget is a comprehensive evaluation of the water inflow to and outflow from the three interlinked systems (land, surface water, and groundwater) in a given water budget zone (Newsom et al. 2020). Precipitation, evaporation, transpiration, runoff, and water movement within the watershed, such as infiltration, recharge of groundwater, and reservoir storage, are all components in a water budget (Ontario Ministry of the Environment 2011; Rahi et al. 2019). It's a powerful tool for allocating river water for various demands. Uncertainty in accounting for water budget components, on the other hand, makes managing water resources challenging. There are basically two sources for this uncertainty: measurement errors and natural variability that occurs in components of the hydrologic cycle (Healy et al. 2007).

Both modeling and non-modeling techniques can be employed for generating a water budget. The most comprehensive method is the modeling technique, which involves utilizing numerical models to simulate processes in the land, surface water, and groundwater systems. Although it provides less precise results, the non-modeling approach employs assumptions, equations, and relevant available data to assist in comprehending the water budget (Al-Madhhachi et al. 2020; Lateef et al. 2020; Newsom et al. 2020). Various research utilizes different models to estimate water budget components and runoff. The WEAP-PGM model (Water Evaluation and Planning System – Plant Growth Model) was applied by Yaykiran et al. (2019) to the Sakarya River Basin in Turkey and gave an acceptable simulation of the stream flow. He et al. (2019) used the projections from 10 general circulation models to derive the Variable Infiltration Capacity (VIC) hydrological model for both mid-century and late-century to estimate changes in runoff in the major California watersheds. The results show that future runoff will be affected by climate change. Gao et al. (2018) used the SWAT (Soil and Water Assessment Tool) model to analyze the data. Findings produced by the HYPE (Hydrological Predictions for the Environment) model, used by Donnelly et al. 2016 to simulate runoff across Europe, reveal that it is efficient in simulating long-term means and seasonality, finding utility even for ungauged basins. Koneti et al. 2018 applied HEC-HMS (Hydrologic Engineering Center Hydrologic Modeling System) to analyze the impact of land use-land cover changes on the Godavari basin. Their results indicate an expansion in built-up lands and cropland associated with deforestation that led to reduce the evapotranspiration and increase runoff.

Rainfall-runoff models could be designed to simulate extreme events such as the Australian water balance model (AWBM), which was developed for low flow cases using daily time steps and flood studies for hourly water yields (Boughton 2004). Extreme events have a detrimental impact on the water service system's environmental conditions, including water supply, and cause serious damage to the ecosystem and population. As a result of global warming, such events are anticipated to be even more frequent throughout the world, posing a greater threat to water resources (World Health Organization Regional Office for Europe et al. 2011 (WHO-Europe)). Severe meteorological and hydrological phenomena are either rare within a particular location's statistical records or accumulate from ordinary data that is not extreme separately (Murray & Ebi 2012). Many studies in recent years have shown an increase in extreme events and anticipate an increase in the future. Using observed data from stations in the area, trends in Middle East climate extreme indices revealed significant increasing trends in temperature-related indices with non-significant and spatially incoherent precipitation-related indices (AlSarmi & Washington (2014)). Al-Faraj et al. (2014) employed the Medbasin-monthly rainfall-runoff model to simulate runoff in the upper part of the Diyalal river basin under several drought scenarios, including reduced precipitation (between 0 and 40%) and increased potential evapotranspiration rate (between 0% and +30%). Their findings show that climate change has a significant impact on the basin's water resources, which demands immediate strategies and measures to overcome them. ESCWA United Nations Economic and Social Commission for Western Asia et al. (2017) used two representative concentration pathways (RCPs) of 4.5 and 8.5 to explore future extremes in the region during the mid- and late-21st century. They also employed three hydrological models (HYPE, VIC, and HEC-HMS) based on the output of two scenarios (RCPs) 4.5 and 8.5 to anticipate runoff in the Tigris and Euphrates basins in the mid- and late-century as well as simulate the impacts of extreme events. In the basin's headwaters, the findings point to minor increases in winter runoff and reductions in summer runoff. The results of general circulation models were investigated by Waheed et al. (2019) to explore the impact of future precipitation and temperature scenarios on the hydraulic structures in the Diyala River basin. Their findings suggest that the basin's hydrologic system will face major vulnerabilities during the next 25 years. The HEC-HMS model used by Hamdan et al. (2021) to imitate the Al-Adhaim river basin's runoff discharge peaks. Naqi et al. (2021) conducted statistical research for the Diyala River basin to determine trends in extreme temperature and precipitation indices, finding that temperature trends were more significant than precipitation trends, implying an increase in maximum temperature over minimum temperature.

The Diyala River basin has been chosen due to its vulnerability to the extreme events, as it has suffered from the consequences of flood and dry events. In addition, Diyala River is one of the most important rivers in Iraq as it is the major source of irrigation and municipal water for Diyala city. This study aims to assess the water budget and predict runoff of the Diyala River basin, based on data availability (from 2000 to 2020) with no real cooperation between the two transboundary countries in terms of how data is exchanged and water allocated for this shared basin. In this study, stream flow modelling was conducted on two stream gauges (Derbendikhan dam and Hemmrin dam) using data from three meteorological stations (Khanakin, Sanandaj, and Sulymania) to achieve the main goals of this study, which were to:

• 1.

  Apply the water budget equation in the Diyala River basin for both the upper and the middle parts using a non-modelling approach of two rainfall-runoff models (the Tanh curve and the modified Tanh curve) to predict the stream flow.

• 2.

  Analyze the impact of extreme weather events on the runoff.

This study provides reasonable, practical, and accepted methodology to assist water managers and decision-makers in developing better watershed management plans and strategies.

The Diyala watershed's water management framework is separated into three areas. With an area of 17,900 km², the top section is mostly in Iran, and the rest is in Iraq, controlled by the Derbandikhan dam (Al-Faraj et al. 2014). With a transboundary area of 11,900 km², the middle part is located between the Derbandikhan and Hemrin dams. The lower part, which covers 2,800 km², is controlled by the Diyala weir. The Diyala Basin is divided into three climate zones, according to Al-Tamimi & Gamel (2016): it is semi-humid in the north, semi-dry in the middle, and dry in the south. The basin contains a dense network of dams and hydraulic works, with 12 dams in Iran's upper basin (five of them constructed between 1983 and 2010 and seven after 2010). The Diyala weir and two major dams (Derbandikhan and Hemrin) are located in Iraq's main river route. Within the Diyala Basin, irrigation projects consume the most water, followed by domestic use (Al-Faraj & Scholz 2015).

The average monthly discharge at Hemmrin dam inlet was 92.3 m³/month, the minimum discharge was 2.4 m³/month, and the maximum was 903.6 m³/month during the study period (2000–2020). For Derbendikhan dam, the mean, minimum, and maximum monthly discharge were 90.9, 2.2, and 766.2 m³/month, respectively.

Many software programs were used to achieve the objectives of this study, as mentioned below:

• 1.

  The Agricultural and Meteorological Software to perform goodness of fit test.

• 2.

  Geographical information system for Diyala River basin delineated, area calculation, and land cover map.

• 3.

  Microsoft Excel for equations, figures, least fit square error, percentile.

• 4.

  Sigma plot for t-test and ANOVA test.

Yihdego & Webb (2013) modified the Tanh water balance model and used it together with double mass curve analysis to distinguish the impact of land use change on stream flow from the climate variables (Equation (3)). This model is a useful tool for predicting runoff and estimating recharges for any given precipitation-evaporation system in a river basin, as follows:

• - Taking monthly evapotranspiration and subtracting it from rainfall [∈_i = RF_i–ET_i], and

• - Accumulating the resulting departure values []

In the studied area, evapotranspiration far exceeds the rainfall during the spring, summer, and autumn months of the year, when cumulative surplus rainfall is always negative (set to zero), and streams are either dry or have only base flow or flow from the transboundary country of Iran. Starting in December, there might be a cumulative excess of rainfall over evaporation; CSR values rise to a maximum, and the extra rainfall becomes runoff. CSR values decline after April, when an excess of evaporation over rainfall occurs, until they reach negative (zero) once more.

Base flow is a significant component of stream flow that is generated from groundwater and shallow subsurface storage and flows into the surface water (e.g., rivers, channels, streams, and lakes) over a certain period of time, as long as the water table remains above the surface water bottom (World Meteorological Organization [WMO] 2009). Assessing the base flow contribution to the stream flow is necessary to understand the hydrologic budgets of surface and ground water resources. During dry seasons, according to Smakhtin (2001), the base flow produces the whole runoff. According to Price (2011), basin variables such as aquifer characteristics, evapotranspiration, geomorphology, landscape changes, and soil types all influence base flow.

Al-Faraj & Scholz (2014) incorporate the flow duration curve method within digital filtering algorithms, as mentioned in Equation (4), to obtain the filter parameter with a high level of confidence by using daily flow data at the Derbandikhan hydrometric site for the upper part of the Diyala River basin and the Diyala Discharge Site for the combined upper and middle Diyala River basin. The results show that the filter parameter α with a value of 0.99732 produces a base flow index (BFI) that equates to the one derived from the flow duration curve analysis for both parts. This value of α is used in this study to extract the base flow for the upper and middle parts of the Diyala River basin using Equation (5).

The performance and the validation of the two rainfall–runoff models have been tested by comparing the predicted runoff, obtained by the models, with the observed runoff at the two dam's inlets (Hemmrin and Derbendikhan) using the goodness of fit indicators of the Agricultural and Meteorological Software available on: https://agrimetsoft.com/calculators/correlation%20coefficient. The results of the analysis should be considered valid, as data were filtered to eliminate odd values and obtain an accepted relationship between the predicted and observed runoff and to determine the range of rainfall and runoff amounts within which the model's results lie. In addition, the t-test (which was used to compare only two unrelated groups and indicate if there is a statistically difference between them at (p < 0.05)), and ANOVA test (which is used to compare the means of three or more unrelated groups to observe if any of them represent a statistically significantly difference) also have used to estimate the models credibility and show if there was a statistical difference between the observed and the predicted runoff or not.

The monthly data outcomes were the most inaccurate and cannot be accounted for due to their variability, followed by the modeled autumn results, which had the least amount of precipitation compared to the winter and spring seasons. The t-test for both of them indicated a statistically significant difference between observed and predicted data (P-value<0.001 and 0.012 for monthly and autumn data, respectively). The difference in the mean values of the two groups is greater than would be expected by chance. Figure 3 shows that the Tanh curve model can be run for Sulymania station (as an example) with monthly precipitation of less than 170 mm/month and monthly runoff of less than 50 mm/month. It also works for annual rainfall amounts between 350 and 950 mm/year and annual runoff of less than 300 mm/year.

At Khanakin and Sanandaj stations, the model can work for a monthly precipitation of less than 120 mm/month and a monthly discharge of less than 50 mm/month, and for annual precipitation amounts between 150 and 500 mm/year.

On the other hand, winter, spring, and annual data had accurate results. According to the t-test, there is not a statistically significant difference between observed and predicted runoff values for all of them (with p-values of 0.194, 0.588, and 0.458 for winter, spring, and annual data, respectively). The difference in the mean values of the two groups is not great enough to reject the possibility that the difference is due to random sampling variability. This indicates that the more rainfall amounts the better models’ performance. Sulymania station gave reasonable results, as it had a considerable amount of participation that contributed to the total runoff of the upper part of the Diyala River basin. In addition, it is near to the Derbendikhan hydrometric station, which is used to obtain discharge data for the upper part of the basin, as both of them are located within Sulymania city. Figure 4(a) is for winter (December, January, and February) results, which reveal that the Tanh curve model can run well for amount of rainfall less than 500 mm/season and runoff of less than 90 mm/season. The model fit well precipitation amounts less than 200 mm/season, and runoff less than (140, and 90) mm/season for Khanakin and Sanandaj respectively.

Results for Sanandaj and Khanakin were similar to those of Sulymania. There was a statistically significant difference between observed and predicted data for the monthly and autumn time scales, with the difference in the mean values of the two groups are greater than would be expected by chance. On the other hand, based on the t-test, the findings for winter, spring, and the annual period were accepted without a statistically significant difference between the observed and predicted runoff. This finding reveals that the Tanh curve model's performance depends mainly on rainfall amount not on the location of the meteorological station within the basin and how far it from the hydrological station. As both Sulymania and Sanadaj are within the Derbendikan dam's basin, with Sanadaj much farther away from the dam than Sulymania, as shown in Figure 1. However, both models demonstrated the same performance during the rainy periods. Table 3 shows the t-test results for all stations.

Both F and L variables were estimated based on the least-square method using the solver add-in application in Microsoft Excel to get the best fit values for the simulated runoff. It's important to mention that L values for all stations and all tested time scales were zero (except for annual data of Khanakin L = 97 mm/year). One reason for this is to compensate for the uncalculated discharge that comes from Iran by reducing the loss factor in this equation to increase the total predicted runoff. On the other hand, the F values, which represent water filtered into the ground, were changing from one station to another and from time to time, because infiltration rates depend on many different factors including: soil texture, soil-moisture content, land cover, soil temperature, etc.

Infiltration values at Khanakin station were the least among the three stations because it had the lowest amount of precipitation, while Sulymania with the highest amount of precipitation had the highest values of infiltration rate. For the same reason the wet extreme events had higher infiltration rates than the dry extreme events, as shown in Table 5. The goodness of fit indicators at the three stations using the Tanh curve model are shown in Table 6.

The base flow was calculated using two methods. The first is by using (Equations (6) and (7). The second, is by estimating its value using the least-square method to obtain the best fit value for the predicted runoff. The results of both methods were compared to the observed data using some statistical indicators to select the more accurate one. Modelled runoff with the constant G (which obtained by the best fit value using solver application) was more precise than with G values obtained from the filtered direct runoff equation for all indicators (except for R, where there was not any difference) for both normal and extreme data. This is consistent with Yihdego & Webb (2013) work, in which they estimate one constant value for G for each station using the least-squared method to compensate it in the modified Tanh model.

The monthly runoff values based on t-test did not show a statistically significant difference between observed and predicted data that were obtained from using the modified Tanh curve equation with p values equal to 1 (i.e. p>0.05). The goodness of fit indicators revealed strong relationship between the observed and the predicted monthly runoff.

Table 7 shows goodness of fit statistics at Sulymania and Sanandaj stations, indicating that the modified Tanh curve model works better for Sulymania station than Sanandaj station. One important reason for this is that Sulymania had a higher amount of precipitation than Sanandaj, indicating that higher amounts of precipitation at a station leads to more accurate predicted runoff.

The one-way ANOVA test for analysis of variance between observed and predicted monthly data showed that the Tanh curve model did have a statistically significant difference with the observed (p<0.001). The mean was 14.054 for the observed runoff and 5.6, and 5.37 for the predicted runoff at Sulymania and Sanandaj stations, respectively. However, the ANOVA test for analysis of variance between observed and predicted monthly runoff showed that the modified Tanh curve model did not have a statistically significant difference (p=1; mean of 14.054) for all the observed and the predicted runoff. This demonstrates that the modified Tanh model performed better than the original Tanh model, given that this model includes more of the water balance parameters than the Tanh curve model.

It is worth mentioning that the modified Tanh curve model can be applied only to the Sulymania and Sanandaj stations that had higher amount of precipitation and lower amount of AET than Khanakin station. This implies that it is only applicable to at least semi-humid climate regions with a significant amount of precipitation.

In this study, two models were used to predict discharge at two hydrometric stations within the Diyala River basin using observed precipitation and temperature data over the years (2000–2020). The first one was rainfall-runoff Tanh curve model, which represent an empirical model as it use only precipitation data as an input. The second was the modified water balance Tanh curve model, that consider as conceptual model as it includes many of water balance components. The later results applied only on Sulymania and Sanandaj stations because it can be applied on area with relatively high amount of precipitation (classified within the Simi-humid climate). The conceptual model results were more accurate than the empirical model according to the ANOVA test. This corresponds with Sitterson et al. (2017), who note that the conceptual models are more complicated but more accurate than the empirical models.

In this study AET from satellite data has used instead of the reference evapotranspiration (ET_°) which had used in the origin paper by Yihdego & Webb (2013). AET seemed to have a better performance than the ET_° when applying them to account for CSR in the modified Tanh curve model.

The Tanh curve model yielded better results at annual and seasonal time scales (except for autumn) than at the monthly scale, which approved the recommendation of Grayson et al. (1996). It would be best to use annual data or at least seasonal data to drive the values of the notional loss (L) and the notional infiltration (F), as both could satisfy the models’ need for approximately constant values of L and F, while monthly data could not meet this demand.

The impact of extreme events on runoff is also examined in this study. The wet extreme events determined by the percentile-based indices, precipitation and discharge with the 90th percentile corresponding to AET with a 10th percentile. On the other hand, the extreme dry events represented by precipitation and discharge with a 25th percentile correspond to AET with a 90th percentile. The wet events using a modified Tanh curve model gave considerable results, with non-significant differences between the observed and predicted runoff when using the t-test. Both wet and dry events had significant differences when using the Tanh curve model. ACSAD and ESCWA (2017), used the 90th percentile of the highest daily records for precipitation and temperature to represent wet and dry events, consequently, as well as variations in the frequency of extreme flows.

To obtain a comprehensive understanding on the impact of extreme events on the Diyala River runoff, a close examination on the monthly range of the rainfall and runoff amounts for normal, wet, and dry events within which the Tanh curve model run would be of great help. The normal events Figure 3(a) run within rainfall range (0–200) mm and runoff range (0–45) mm, the wet events (Figure 5) run within rainfall range (70–400) mm, and runoff range (5–120) mm, and the dry events (Figure 6) within rainfall range (0–70) mm, and runoff range (0–22) mm. The maximum edge of each range reveals that for wet events if the rainfall duplicate (from 200 to 400) mm, this would lead to an increase in runoff about three times more than the normal events runoff (from 45 to 120) mm. The maximum edge for dry events showed that if the rainfall decreases by about ⅓ (from 200 to 70) mm, this would cause runoff reduction by about ½ (from 45 to 22) mm. This underscores the fact that extreme weather and climate events have a great impact on water resources, thus compounding the impact of climate change itself. This finding is consistent with many other studies which explored the sensitivity of the Diyala River runoff to different dry and wet scenarios. For example, Al-Faraj et al. (2014) examined the impact of a severe drought scenario on the runoff in the upper part of the Diyala River basin. Their results showed that drought has a significant impact on the basin's water resources, which demands urgent measures to overcome it. Waheed et al. (2019) investigated the outcomes of precipitation and temperature from general circulation models to simulate the runoff in the Diyala River basin, revealing a significant risk in the Diyala River's hydrological system in the near future.

Our findings help in predicting the runoff when using empirical and conceptual models in the area of data scarcity to assist decision-makers in making proactive plans for better managing the watershed. This study is consistent with many other studies that use empirical and conceptual models to predict discharge and give valid results to quantify hydro-climate variables on a river basin scale (Al-Faraj & Scholz 2014; Ajaaj 2018; Rahi et al. 2019).

Water budget calculations play a crucial role in water allocation across different sectors. They serve to facilitate water conservation, reducing water management costs, and managing the available water resources during drought seasons. Therefore, water balance studies are critical, particularly for water-stressed areas. It's a fact that there is a huge lack of hydrometeorological data in general and in shared basins in particular in our region, which makes water balance estimation using the modeling technique difficult with a wide range of uncertainties. This work aims to investigate non-modeling approaches to account for the water budget components using as little data as possible to provide a general understanding of the Diyala River basin. Our study makes an important contribution to climate and water research, especially for extreme-related events. It helps decision-makers to improve management plans for the studied basin through a better understanding of the water balance across the basin based on real data and linking it to the incoming discharge at two dams in Iraq.

The authors used observed precipitation data from three meteorological stations and observed discharge data from two hydrometric stations across the Diyala River basin from 2000 to 2020 to examine the performance of empirical rainfall-runoff and conceptual water balance models at monthly, seasonal, and annual scales, utilizing the Tanh curve model and the modified Tanh curve model. Both extreme and normal events were tested during this study to analyze the predicted runoff versus the observed data. Both models work well for Sulymania and Sanandaj stations, with the performance of the modified Tanh model being more accurate according to the ANOVA test. However, the modified Tanh model did not work for Khanakin station (which has a semi-arid climate) as it required a considerable amount of precipitation. The Tanh curve model results yielded significant differences between the observed and predicted runoff during autumn and monthly time scales.

It should be noted that integrated water resources management demands data access, the validity of the information, and a better perception of present and future events. Moreover, the quantity of data in this study is a key constraint. More data over a longer time span and more stations within the Diyala watershed are required, primarily within Iran. Such data would lend the results of this study more credibility. The authors recommended using different empirical water balance models for both observed and simulated data in the future. This will enable us to obtain more precise results for both extreme and normal events in regions with data scarcity.

The authors of the present work express their deepest appreciation to Al-Mustansiriyah University (www.uomustansiriyah.edu.iq) and the Ministry of Water Resources for their support during the work.

The lead author, Noor M. Naqi, envisioned the research topic and collected and analyzed the data as part of her Ph.D. thesis. Abdul-Sahib T. Al-Madhhachi and Monim H. Al-Joboori supervised the research and supported the interpretation of the results and manuscript preparation.

This research received no external funding.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.