Barium in sediments
The concentration of Ba in Kupa River measured in 2003 y. may be fitted by an exponential law:
Ba = Ba0 exp (-b x). (2)
In the exponential function Ba0 = 1060 (ppm) is the concentration value at the entrance of Kupica to the river Kupa, and x is the distance from the entrance. The best fit is obtained for b = 0.0167 ± 0.0014 (with RMSE = 83 on 12 df). Let us also note that the law behind the exponential function is: d(Ba)/dx = - b Ba with the initial condition equal to Ba0.
In order to explain how did the Ba concentration arrive to the distribution shown in Figure 7 during 70 y since the barite mine in Homer started operating and Ba rich particles from the mine waste penetrated the vulnerable karstic underground and through it reached the Kupica River source, a sediment transport model is considered.
The transport model for the concentration of Ba (C) in Kupa is given by:
∂Ba/∂t = + D ∂2Ba/∂x2 - v ∂Ba/∂x (3)
with the boundary condition Ba∣x=0 = Ba0 and the initial condition Ba∣t=0 = 0, for every x > 0.
The first term in (3) accounts for diffusion of particles while the second term accounts for advection downstream from the entrance of Kupica into Kupa. Since we have no data from which to determine the diffusion coefficient and furthermore, since the turbulent diffusion coefficient is from10−7 to 10−5 cm2/s (Wörman 1998), this term may be safely neglected in considered longitudinal transport.
What remains is the advection of sediment downstream. There are at least two processes of importance for movement of sediment downstream. The first is that during higher precipitation, the horizontal velocity of water increases, increasing vertical turbulent water movement and entrainment of sediment into the water column. This increases advection of sediment downstream. The second process is deposition of sediment at places further downstream where the slope and velocity of water are smaller.
The advection model is discretized with a step ∆x = 1 (km) and run for 70 y with a ∆t = 1 (y) given the fact that once in a year we have an exceptionally high river flow due to the snow melt, and a constant boundary concentration Ba0 = 1060 (ppm) at the entrance of Kupica into Kupa where x = 0. The initial condition is set to Ba = 0 for all x > 0. Since no velocity of sediment was available, we used the discrete law which states:
Ba(j,i) = Ba(j,i-1) + c Ba(j-1, i) – d Ba(j,i-1); j = 1, …, 300, i=1,…,70 ; (4)
and adjusted c = 0.75 and d = 0.76 for the best fit to data measured in 2003 y.
The resulting simulation is shown in Figure 8.
From Figure 8 it is seen that the initial concentration at t = 0 is located only at the entrance of Kupica into Kupa. Through the 70 years it has gradually moved downstream. Finally, it appears as an exponential distribution of Ba in sediments reaching over 200 km downstream Kupa River.
It is important to point out that an attempt to use a = b failed to fit the data from 2003 y for any value of a since it produced too steep a slope of Ba concentration. This strengthens the discovery that indeed at any distance downstream from the entrance of Kupica into Kupa, 75% of the sediment containing Ba is added per km per year from upstream and 76 % of the sediment found at the location is transported downstream.
Verification using the data of 2018 y.
Using the same transport parameters a and b, the model was run until 2018 y. The comparison until 130 km downstream the entrance of Kupica into Kupa reveals a good agreement to the data (Figure 9).
For the explanation of the “bump” in the distribution occurring from 2003 to 2018 y downstream from 130 km shown in Figure 9, one has to invoke at most two new factors to the model. The first is that downstream beyond 130 km, the elevation slope is significantly smaller so the deposition potential is greater. The second factor is that in this time interval, one or more violent precipitation events may have happened which caused entrainment of heavier sediment into the water column at the stretch of the river prior to 130 km (where the water velocity is greater) and deposition downstream beyond 130 km where the river water flows practically along a flat plain causing significantly slower movement of water and hence greater deposition potential of sediment from the water column.
In the model only the first factor has been simulated as a gradual slightly greater deposition then loss past 130 km during 15 y, i.e. from 2003 to 2018 y.
The Figure 9 shows the result of two pieces of simulation. The last exponential function (the envelope) until 130 km represents the result that the distribution would have had if the same simulation, which is shown on Figure 8, is continued to 2018 y i.e. 15 year longer.
The concentration “bump” is obtained by simulation of the part beyond 130 km with c = 0.75 and b = 0.74. Another words, with the same import from upstream as in the period until 2003 y but with only slightly greater deposition, or equivalently, with smaller release of sediment downstream from 2003 until 2018 y.
However, as stated above, the same shape of the distribution beyond 130 km downstream the source may be explained by one or more violent precipitation events which have moved sediment from the upper part of Kupa over the sudden change of elevation slope into the flat land. Indeed, the examination of historical data on violent precipitation events in the last 100 y. reveals the highest flood during 2015 y and the second highest flood during 2014 y. The floods in 2014 and 2015 alone could have moved the sediment downstream in agreement with the data in Figure 4.
Finally, high concentration of Ba in sediments measured in Kupa 200 m upstream from the entrance of Kupica (station 52) during 2003 and 2018 may be explained by diffusion of sediments upstream. As for the explanation of the two somewhat higher values above the background level of Ba closer to the source of Kupa, the likely mechanism may be that during an event of intensive precipitation in the Kupa watershed, Ba is transported into Kupa through the porous karstic bedrock from the mine deposit uphill. The same mechanism was found to be responsible for occurrence of Pb in the beach sediments which were transported through porous karstic rock from uphill lead processing workshop into the Punat Bay of the Adriatic Sea (Legović et al. 1990).
From measurement and modelling results it may be predicted what will happen to Ba concentration in Kupa during the next 20 y.
First, the Ba source will not cease any time soon. It may decrease further but it will not completely vanish in the near future. Given the fact that barite mine was closed in 1990, we see Ba concentration upstream of Kupica entrance into Kupa is still increasing in 2018, 38 years later. This means that Ba entrance into Kupa through a porous karstic rock is still higher than erosion downstream. Likewise, Ba concentration downstream Kupica entrance into Kupa is still increasing testifying again that entrance is higher than erosion downstream. However, there is a sign that this process started decreasing as Ba concentration in sediment at the location 51 (Kupica River just before its inflow into Kupa River) was in the year 2018 about 4 times lower than in 2003 (see Table 3). Also, at the first downstream location from the Kupica confluence (50) Ba concentration in sediment was almost 30% lower in the year 2018 than it was in 2003 (see Table 3). This is obviously a sign that parts of karstic underground leading towards Kupica River source are gradually being washed out. If this process persists, in the future we might expect further decreasing of Ba concentrations in the upper course of the Kupa River, while in the lower course this will not happen so soon. Finally, a peak of Ba concentration downstream from 130 km has a potential to increase further and in part be transported further downstream. Hence, by the end of next 20 y we do not expect that Ba concentration will decrease in the lower part of the Kupa River, especially downstream of Ozalj powerplant. To the contrary, we expect an increase throughout Kupa, except on part of its upper flow just downstream of Kupica River inflow.