Information on sediment concentration in rivers is important for design of
reservoirs and for environmental applications. Because of the scarcity of
continuous sediment data, methods have been developed to predict sediment
loads based on few
Only for a few rivers in the world and over a limited period, sediment concentrations have been measured at a daily or shorter frequency. In order to determine sediment loads in the absence of these measurements, models and rating curves have been used. Knowing the total sediment loads from rivers is essential for evaluating the siltation of reservoirs (Ali et al., 2014), assessment of soil erosion and nutrient loss (Walling, 1977). As a result knowledge of sediment concentration is important in most environmental applications because among other things it hampers fish reproduction and reduces the esthetic value of surface waters (Vijverberg et al., 2012).
In the Blue Nile Basin, where the construction of the Grand Ethiopian Renaissance Dam is and planning of other hydroelectric dams are under way, determining sediment loads is becoming more urgent. At the same time concern for the environment has been increasing and it has been noted that the fish production in Lake Tana is decreasing due to increasing sediment concentrations (Vijverberg et al., 2012). Thus, the ability to predict accurately the sediment concentrations and loads to the lakes and man-made reservoirs has become important in the Ethiopian highlands where these are not available.
Modeling sediment loss is fraught with difficulties that unlike runoff is not bounded by the amount of rainfall. So there is no upper bound for sediment load in the absence of data. The models most commonly used for predicting soil loss are the Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 1965) and its derivatives such as RUSLE (Revised Universal Soil Loss Equation) (Renard et al., 1991) and MUSLE (Modified Universal Soil Loss Equation) (Williams and Berndt, 1977) Hydrologic Engineering Center River Analysis System, (HEC-RAS; HEC, 1995), Water Erosion Prediction Technology (WEPP, Nearing et al., 1989), Agricultural Non-Point Source Pollution (AGNPS; Young et al., 1989), Erosion Productivity Calculator (EPIC; Jones et al., 1991), Soil and Water Assessment Tool (SWAT; Arnold et al., 1998) and Chemicals, Runoff and Erosion from Agricultural Environment Systems (CREAMS; Knisel, 1980). More sophisticated models used are the neural differential evolution (NDE), artificial adaptive neuro-fuzzy inference system (ANFIS), and artificial neural network (ANN) models (Masoumeh and Mehdi, 2012; Özgür, 2007). However, it is cumbersome to obtain the required data for these models especially in developing countries. The reason is that these models were originally developed for areas that have large amounts of data. For example, in the land use and land cover map, the leaf area index data that SWAT needs are not available. Similarly, the soil data in Ethiopia are very coarse and are missing basic information such as soil texture, hydraulic conductivity and other parameters that are difficult to measure in Ethiopia. Additional challenges using these models are the following: (i) the models have been developed in regions with a semi-arid temperate climate where the runoff mechanisms are governed by infiltration excess unlike the highland areas where saturation excess runoff is dominating (Steenhuis et al., 2009; Bayabil et al., 2010; Tilahun et al., 2013a, b, c) and (ii) almost all of the models need intensive data with many parameters that might be available centrally in developed countries but not in developing countries such as Ethiopia. Therefore, historically when concurrent concentration and discharge measurement were taken at irregular intervals, rating curves were often the preferred choice for predicting sediment loads (e.g., Walling, 1990) but also recently (e.g., Horowitz, 2010; Kokpinar et al., 2015; Choi and Lee, 2015; Kheirfam and Vafakhah, 2015). The abundance of papers on load rating curves in the refereed literature should not be surprising since the purpose of the measurements was to determine the amount of sediment that potentially could be deposited in rivers and reservoirs. In the literature, a limited number of articles developed sediment concentration rating curves. These few studies were carried out in Sweden (Fenn et al., 1985); Ontario, Canada (Irvine and Drake, 1987), British Columbia in Canada (Sichingabula, 1998), southern Australia (Sun et al., 2001) and for the Himalayan glacier in India (Arora et al., 2014). Thus, compared to the sediment load rating curves that are available throughout the world for many rivers, there are very few sediment concentration rating curves and none for a monsoon climate.
There is a connection between models and rating curves in sediment studies. Rating curves have been used to validate models. Previous simulations to predict sediment load in the Lake Tana basin such as Easton et al. (2010) and Setegn et al. (2009), used sediment load rating curves to generate the observed sediment load data for calibrating and validating the sediment load models. Developing better rating curves will result in better predictions generated from observed flows.
There are at least 20 different ways to convert the measured concentration
and discharge data to a rating curve (Phillips et al., 1999: Horowitz, 2010).
The most often used is a power function (Eq. 1) that relates sediment load (product
of discharge and concentration) to discharge (Miller, 1951;
Muller and Foerstner,
1968; Phillips et al., 1999; Masoumeh and Mehdi, 2012).
The concentration,
Various reasons are given for the decrease in concentration with the
progression of the rainy phase: Tilahun et al. (2013b) pose that with the
progression of the rainy phase of the monsoon the value of
Since the traditional method of determining rating curves for sediment loads assumes that the sediment concentrations are a unique function of the discharge, this method cannot be used in environmental applications for predicting sediment concentrations when the sediment concentration decreases throughout the season for a given amount of discharge. The objective of this paper is, therefore, to develop a realistic method in determining the decreasing sediment concentration with the progression of the monsoon using the limited data common in most of the tropics. The study is carried out in the Ethiopian highlands. Two groups of watershed sizes were selected to test how well the concentration rating curve performed. These consisted of four major rivers and their watersheds in the Lake Tana basin and three small well-monitored 100 ha watersheds in another part of the Blue Nile basin.
To include the observed decreasing sediment concentration with the
progression of the rainy season in predicting sediment concentrations,
Steenhuis et al. (2009) and Tilahun et al. (2013b, c) adapted the theory
originally developed by Hairsine and Rose (1992). This relationship as
depicted in Fig. 1 is based on the assumption that the sediment load in the
beginning of the rainy monsoon phase is at the transport limit when sediment
is available from the plowed land and then linearly decreases with cumulative
effective rainfall to a source-limited concentration. Source limiting
describes the condition when the rate of detachment from the soil determines
the sediment concentration. Transport limiting occurs when deposited
and detached sediment are in equilibrium and the stream carries its
maximum amount of sediment (Foster and Meyer, 1975). This is the case in the
Ethiopian highlands when fields are plowed in the beginning of the rainy
monsoon phase. Once the rill network is fully developed and stable, the
sediment concentration will become source limited (Tilahun et al., 2013b).
Finally, as the surface runoff ceases and only base and interflow feeds the
river, there will be small amounts of sediments that the water picks up from
the riverbed or stirred up by animals or humans. Therefore, the sediment
concentrations were calculated separately during the rainy monsoon phase and
during the dry phase. Since the start of the rainy phase varies from year to
year and from one location to another, we will use the cumulative effective
rainfall,
Relationship between sediment concentrations and cumulative effective rainfall.
Characteristics of the study watersheds in the Lake Tana Basin and the three 100 ha watersheds in the Ethiopian highlands.
MoWIE*: Ministry of Water Irrigation Electricity.
Location maps of the Lake Tana watersheds (Gilgel Abay, Gumara, Ribb and Megech) and 100 ha watershed 100 ha watersheds (Debre Mawi, Anjeni and Maybar) in or close to the Blue Nile Basin.
Based on these observations we redefine the “a
The value of the exponent
The load rating curve (Eqs. 1 and 2) and concentration rating curves (Eqs. 4 and 5) are evaluated for the rivers in the four major watersheds in the Lake Tana basin: Gilgel Abay, Gumara, Megech and Ribb. These are named, hereafter, as the “Lake Tana watersheds”. In addition, three small (approximately 100 ha) watersheds are selected for the assessment of scale effects in the concentration rating curve: Anjeni, Debre Mawi and Maybar. We will call these hereafter “100 ha watersheds”.
The 15 000 km
Irregularly measured discharge and sediment concentration data by Ministry of Water, Irrigation and Energy (MoWIE) for the major four rivers in Lake Tana basin were available from 1964 to 2008. The numbers of observations available for the Lake Tana watersheds used for this analysis period were 23, 53, 52, and 16 for the Gilgel Abay, Gumara, Ribb and Megech watersheds, respectively. The data of the 100 ha watersheds were collected for Anjeni and Maybar by ARARI (Amhara Region Agricultural Research Institute). The Debre Mawi data were collected partly by ARARI and us and are described in Tilahun et al. (2013a, b).
The calibrated sediment rating curve parameters and the specific dates where the sediment transport ends and the sediment limiting phase starts.
The sediment concentrations in the Lake Tana watershed have been increasing since the initial measurements were made in 1964 (Ayana et al., 2014). We selected the following periods for analysis: 1968–2008 for Gilgel Abay, Gumara and Rib. The Megech data were only available and the analysis was made for 1990–2007. The analysis for the Anjeni was made for 1996 and for Anjeni in 1994 when the watershed was stabilized from the soil and water conservation practices that were installed in the mid-1980s. For the Debre Mawi watershed the data in the years 2010 and 2011 were used before large-scale conservation practices were installed in 2012.
Climate data: rainfall and temperature data for the Lake Tana watersheds
(Table 1) were available from 1994 to 2008 by the National Metrological
Agency of Ethiopia (NMAE), Bahir Dar branch. The areal rainfall was
calculated by using Thiessen-polygon method for the available rainfall
stations for the Lake Tana watersheds as these watersheds have two or more
rainfall stations. The method was chosen because it
Potential evapotranspiration was estimated based on observed temperature data with the method developed by Enku and Melesse (2014).
Effective precipitation was calculated by subtracting the evaporation from rainfall each day. Cumulative effective precipitation was calculated during the rainy phase of the monsoon.
Rating curves were determined by either fitting the loads (i.e., the load rating curve) or the concentrations (concentration rating curve). Note that both the load and concentration rating curves can predict both the load and the concentration and thus the naming is based on the method of determining the rating curve.
The sediment load rating curve: the original MoWIE load rating curve was
obtained for the Lake Tana watersheds by linearly regressing the logarithm of
the sediment load vs. the logarithm of the discharge for the period from
1964 to 2008. The slope of the line is
Performance of sediment concentration predicted by MoWIE load rating curve and the concentration rating curve.
Performance measures of sediment load predicted by MoWIE load rating curve and the concentration rating curve.
NS
The concentration rating curve: rating curve was found by regressing the
observed sediment concentrations and the discharge with Eq. (4). Four fitting
parameters were required: three for the rainy phase, i.e., the amount of
rainfall
For the Lake Tana watersheds, precipitation and evaporation were only
available for 1992–2000. In order to establish a
We first tested for outliers and those either less than half or more than
twice the expected discharge or concentrations were removed from further
analysis. In none of the cases no more than 5 % of the data points were
discarded. The goodness of fit of the rating curves were determined with the
correlation coefficient (
The available sediment concentration data for the Lake Tana watersheds calculated from the sediment load of the Ministry of Water Irrigation and Electricity (MoWIE) are shown in Fig. 3. There were three periods when samples were taken for determining the rating curve. These were from 1964 to 1968, 1980 to 1996 and 2004 to 2008 (Fig. 3a and Tables S2–S5 in the Supplement). Gumara and the Ribb have the richest data set and the Gilgel Abay with only 23 data pairs is the poorest. Gumara and Ribb have also the greatest concentrations (Fig. 3). The concentration from the Megech is the smallest likely due to the Angereb man-made reservoir (which provides water supply for Gonder town) which was constructed in the early 1980s.
Observed sediment concentration and discharge for the four Lake
Tana watersheds: Gilgel Abay, Gumara, Megech and Ribb.
Predicted vs. observed sediment concentration using
concentration rating curve and MoWIE load rating curve for the Lake Tana
watersheds
When these concentrations are plotted as a function of the day of the year independent of the year (Fig. 3b), the familiar pattern appears with the concentrations usually small in the base flow period from early October to the start of the rainy phase when concentrations increase. The elevated concentrations start around 15 May in the Gilgel Abay watershed, which is earlier than the other watersheds because the rain starts earlier in this part of the watershed. The concentrations in the other watersheds start to increase in late June (Table 2) and beginning of July. The maximum concentration occurs in late June and early July (Fig. 3b) while the discharge is still relatively small (Fig. 3c) and decreases with progression of the rainy phase while discharge is elevated.
The relationship between the observed vs. predicted sediment concentration for the Lake Tana watersheds is presented in Fig. 4 and the fitting statistics in Table 3. Both the concentration and sediment rating curves are used for obtaining the predicted sediment concentrations. Note that the concentration sediment rating curve refers to Eqs. (4) and (5) and involves four fitting parameters. Best fit values are shown in Table 2. The concentrations with the load rating curve are obtained by fitting the loads first and then obtaining the concentrations by dividing the load by the discharge. Here we use the values obtained by MoWIE load rating curve in Table 1.
For the Lake Tana watersheds, the sediment concentrations are under predicted
by the MoWIE load rating curve and indicated poor prediction performance
(Table 3, Fig. 4). The concentration rating curve fits the concentrations
satisfactorily with Nash–Sutcliff values of 0.52 to 0.61 and
Predicted vs. observed sediment load using concentration rating
curve and MoWIE load rating curve for the Lake Tana watersheds
Using the same rating curve parameters as in the concentration predictions
above, the observed vs. predicted sediment loads for the Lake Tana watersheds
are shown in Fig. 5 and the goodness of fit in Table 4. The sediment loads
(Fig. 6) are predicted to be between satisfactory and good with both the MoWIE load and
concentration rating curves for Gilgel Abay, Ribb and Megech with
After testing the sediment concentration rating curves for the Lake Tana
watersheds, we investigated the applicability of the concentration rating
curve for small watersheds. The three watersheds selected had good quality
data. The concentration rating curve using Eqs. (3) and (4) gave a
reasonably good fit with the observed values (Fig. 6) with
Predicted and observed sediment concentration using concentration
rating curve for the 100 ha watersheds
We will first discuss the loads and concentration predictions in the Lake Tana basin with the two types of rating curves followed by a comparison of the sediment load and concentration prediction with the concentration rating curve for the 100 ha and Lake Tana watersheds.
Similar to the predictions of the loads, the concentration rating curve fitted the observed concentrations better than those predicted by the MoWIE load rating curve. In addition to the reasons given for the poor fit (i.e., number of fitting parameters and log–log fit), the inherent assumption of a constant sediment concentration for the MoWIE rating curve was clearly problematic for fitting observed concentrations. In the Ethiopian highlands concentrations are far from constant and usually follow a typical pattern where the concentrations are elevated during the beginning of the rainy season and decrease with the progression of the rainy season (Fig. 3b) while the discharge increases (Fig. 3c). Again similar to the loads, the Gilgel Abay fitted reasonably well because the concentrations were reasonably the same during the rainy phase (Fig. 3b, black squares).
For the Lake Tana watersheds, the concentration rating curve (Eq. 4) fitted the observed sediment load more accurately than the MoWIE load rating curve (Eq. 1) as shown in Fig. 5. The only exception was the sediment load predictions for the Gilgel Abay (Fig. 5a) that was slightly better predicted by the MoWIE load curve than the concentration rating curves. One could expect that the concentration rating curve would perform better because it has four fitting parameters compared to the MoWIE sediment rating curve with only two parameters. In addition, there were few measurements taken early in the rain phase when sediment concentrations could have been elevated (Fig. 3).
However this does not explain the unexpected poor fit with slopes of much less than 1 for the remaining three watersheds in the Lake Tana basin (indicating that the sediment loads for the large storms are severely under predicted). This poor fit for the three watersheds originates from using the log-transformed values for fitting the sediment load and discharge. To demonstrate that the MoWIE log rating curve fits the log transformed values well we re-plotted Fig. 5a in the Supplement (Fig. S1) with a log scale. The log-transformed values give more weight to the small values of parameters than the larger values. Thus, by using the log scale a good fit was obtained, while the same points in the non-transformed values fit poorly (Fig. 5a).
All fitting parameters for the concentration rating curve were remarkable
independent of the size of the watershed (Table 2). There was not a systemic
difference in parameter values for the seven watersheds. The amount of
effective rainfall (
In further discussion of the sediment transport parameters we will exclude
the Megech, since the gage station is located below the reservoir. Sediment
is deposited in the reservoir and the parameters are not representative of
the watershed that is subject to heavy gullying. For the remaining six
watersheds, the source factor
There was a 3-fold difference in transport coefficients (but
independent of watershed area as indicated in Table 2). It varies in the
Lake Tana basin between 1.6 g L
Finally the “
In the Ethiopian highlands sediment concentrations in the rivers decrease
with progression of the rainy phase of the monsoon. Using this observation
while developing the sediment rating curve significantly improves for
predicting the sediment concentration and load. The method developed by the
Ministry of Water Irrigation and Energy and used for predicting daily loads
throughout Ethiopia will likely remain the method of choice for most rivers
especially for larger basins where concentrations remain relatively constant.
Although more research has to be done, there is an indication that the
coefficients in the newly developed concentration rating curve can be related
to landscape characteristics. Therefore, these parameters might have a physical
meaning which would help to generate the parameters from the physical
Funding for this program is provided by the US Agency for International Development (USAID) through PEER Science program and Higher Education for Development (HED), International Science Foundation (ISF). The runoff and sediment data were made available by Ministry of Water and Energy. We would like to thank MoWIE for making the rating curve data available to us.Edited by: B. van Wesemael