Isabelle Thériault Hydro-Québec 855 Sainte-Catherine Est Montréal (Québec) Canada, H2X 3P4

Transcription

1 Validation of the Mike-Ice model simulating river flows in presence of ice and forecast of changes to the ice regime of the Romaine river due to hydroelectric project Abstract Isabelle Thériault Hydro-Québec 855 Sainte-Catherine Est Montréal (Québec) Canada, H2X 3P4 Jean-Philippe Saucet Groupe-Conseil LaSalle 9620 Saint-Patrick Montréal (Québec) Canada, H8R 1R8 Wael Taha Groupe-Conseil LaSalle 9620 Saint-Patrick Montréal (Québec) Canada, H8R 1R8 As part of the Environmental Studies related to the new hydroelectric project La Romaine, Hydro-Québec had to forecast changes to the ice regime of the river reach affected by the project, with focus on the security of the ice cover for crossing snowmobiles. The Mike-Ice model was jointly developed as an add-in module of the Danish Hydraulic Institute s MIKE11 software for river ice modeling. It was used to reproduce the ice regime in present conditions and changes due to the water temperature and increase of winter flow. Since the study of Romaine River was among the first applications of MIKE-Ice, the model was validated on a similar river with available benchmarking data. This validation testcase reproduced a stretch of the Peribonka River, which is supplied throughout the winter season by water with temperatures above the freezing point. Satellite images were used to monitor, during winter, the evolution of ice covers on the river subjected to thermal erosion and flow rate variations, due to operation of hydroelectric generating stations.. The extent of the ice covers were clearly identified for about 20 to 30 instances in the course of a winter, which gives a timely representation that is far more detailed than most practically available methods, and allows the follow-up of rapid responses of the ice fields to hydro-meteorological variations. This data enabled us to validate the one-dimensional unsteady numerical model MIKE-ICE, which computes overall thermal balances and interactions between the flow and the different types of ice, static or drifting. A new formulation is proposed to model the openings of an ice cover subjected to thermal erosion.

2 1 Introduction The surface area of an ice cover downstream from a hydro-electric power project is likely to vary quickly within a few hours under the effects of thermal erosion caused by water flowing out of the reservoir at temperatures above 0 C, as well as under the effects of weather conditions and sometimes flow variability. It is important that such variations be controlled in view of the consequences for users accessing ice covers. Hydro-Québec, the LaSalle Consulting Group and the Danish Hydraulic Institute developed the Mike-Ice model jointly. The Mike-Ice model incorporates a large number of physical processes, which simulate ice formation and flow conditions in a stretch of river. Each of the physical processes has been validated individually, but until now there has been no validation of the model s capacity to reproduce this rapid change in ice covers in the presence of warm water. The Modis images (Nasa) are daily images that can be readily accessed, and, despite their moderate resolution and the frequent cloud covers, they can be used to track the changes in ice covers on average-size rivers. Limitations of these images (low resolution, cloud coverage) were compensated for, by their frequent availability on a daily basis. These images have made it possible to track the advance and retreat of ice covers on the Péribonka River, regulated for hydropower production and submitted to above zero water temperature all winter long. In a second case study, the model was used to forecast the extent and duration of the ice covers downstream of the projected Romaine-1 powerhouse on the Romaine River, with emphasis to environmental impacts and use by skidooers 2 Ice Model Description and Key Inputs The model simulates ice formation in a stretch of river throughout an entire winter season. At every time step and at every point on the river, it makes a full balance of thermal exchanges between the water, the atmosphere, and stationary or moving ice. The net balance between the gain and loss of heat brings about a change in water temperature, and then frazil ice grains are produced and drift in suspension. The model integrates the formulations describing every process responsible for the ice cover dynamics, which are the: Supercooling of the water and production of frazil ice downstream from the point where water temperature reaches 0 C; Rising of frazil ice grains and formation of ice pans on the surface; Upstream progression of the leading edge due to the juxtaposition of ice pans; Transportation of various types of ice under the stationary covers, deposition and formation of hanging dams; Border ice cover progression from the banks towards the centreline based on the cooling rate in contact with cold air, and flow velocity; Static ice cover thickness variations; Openings in the ice cover due to flow velocities in the presence of warm water (water temperatures higher than 0 C) and/or during warm trends (air temperature and solar radiation);

3 Increase in water levels due to thermal covers and hanging dams. A set of equations describes the water temperature variation and how the frazil ice grains can rise and agglomerate to form ice pans floating on the surface. The four unknowns of the problem are: surface concentration C, ice pan (average) thickness e, volumetric concentration of frazil σ and water temperature T; all four vary with time and position (from upstream to downstream). A first relation is provided by the heat balance: Φ atm ( 1 C) H = ρ c p dt dt Φ f [1] (a) (b) (c) (a): Surface flux per unit volume, Φ atm being the heat flux from open water to the atmosphere, H the average depth. This heat flux to the atmosphere is calculated by the model based on the weather conditions (air temperature, short- and long-wavelength solar radiation, wind speed, etc.). (b): (c): Variations in water temperature Heat flux between the frazil crystals and the water The surface temperature of suspended ice crystals is 0 C, whereas the water has a temperature T 0 C. Thus, there is a heat flux from the warm crystals to the cold water. This flux Ф f > 0 participates in the heat balance of the water mass (equation above) and is responsible for frazil generation. For an isolated crystal with a radius r, the heat flux can be shown to be: Ф r, T = - α k e r T N u for T 0 C [2] where α is a crystal shape factor, Nu is the Nusselt number of the ice crystal/water exchanges, and k e is the thermal conductivity of water at 0 C. The total flux Ф f for all of the crystals (in W/m 3 ) depends on the distribution n(r) of the radii in the crystal population : Φ f = r1 r 0 α k e r T N u n( r) dr [3] Considering an average Nusselt number, independent of crystal size, the heat flux can be related to the frazil ice volumetric concentration σ : k N e u Φ = σ T [4] f δ 2 with a characteristic crystal radius δ :

4 2 δ 1 r r0 r r = 1 α r 0 3 n( r) dr r n( r) dr [5] In the relatively simple model adopted here, a characteristic dimension δ = m is considered constant throughout the process of frazil formation. The corresponding Nusset number is Nu 5 for usual turbulent conditions in a river (see for instance Daly, 1984). The concentration σ increases due to the heat transfer Φ f and decreases because a fraction of the crystals rises and floats on the surface. It is assumed that the rate at which the crystals rise is proportional to the concentration of ice under the surface; the proportionality factor is designated as β. Thus: dσ f σ = Φ β dt ρ L H i [6] which can be written, by substituting (4) into (6), as: ρ L i dσ dt ke N u β = σ T ρi L σ [7] 2 δ H where L is the latent heat of fusion of the ice and ρ i its density. The parameter β (= m/s) measures how easily the suspended frazil rises and floats to form new ice pans. The rate at which crystals rise to the surface is β σ (m 3 /s/m 2 ), but it is only the fraction (1 C), which represents the open water area, that participates in the formation of new ice pans (with initial thickness e o and porosity p), since the fraction C of the surface is already covered with ice: dc dt β σ ( 1 C) = p e 0 [8] To resume, the three equations [1], [7], [8] permit the calculation of the three functions T(t), σ(t) and C(t) (water temperature, concentration of suspended frazil and concentration of surface frazil, respectively). The model s parameters are the radius characteristic of the frazil crystals δ, the rates at which the crystals rise β, as well as the initial thickness e o and the porosity p of the frazil ice pans. The three equations are solved simultaneously at each time step by a Runge-Kutta method. The ice mass M (kg/m 2 ) drifting on the surface increases since crystals are rising to the water surface (at the rate β σ (1 C)) as well as under existing pans (at the rate β σ C): dm = ρ i β σ [9] dt This permits the calculation of the surface ice mass M(t) once σ(t) and C(t) are known. The cross-section average thickness of the ice pans is then estimated using:

5 e M = ρi C ( 1 p) [10] The one-dimensional model was run for unsteady flow conditions, using a 60-second time step to maintain stability of the numerical scheme. The model used hydrometeorological data available on an hourly basis: Water flow rate and temperature at the upstream limit of the model and tributaries; Water level at the downstream limit of the model; Air temperature, measured at the Roberval meteorological station and related to the site location through the application of a model-integrated correction factor, which takes into account the altitude and latitude deviations. Other factors influencing the thermal balance, such as wind speed and cloud cover, may have been taken into account. But since no observation-based data was available in this case, mean regional values were adopted. The model also used a variable albedo of the ice field based on the average ice temperature over the four previous days, according to a formulation developed, in the course of another study, from field measurements using a radiometer. The extent of a static ice cover is controlled by several processes, which are the subject of this validation. The thickness varies based on heat exchanges with the atmosphere and with the underlying water when its temperature exceeds 0 C (thermal erosion). The leading edge may progress upstream due to juxtaposition of ice pans. The leading edge is defined as the transition between cross-sections completely closed by ice covers, and other partially open sections. Border ice can progress towards the river centre depending on the cooling rate Φ < 0 atm and local flow velocity. In a pseudo-2d representation, the local velocity V(y) in a crosssection from one bank to the other is varied with the local depth y: V ( y) = a V y H 2 3 [11] The average velocity V and the average depth H are established from the 1D computation. The constant a is computed by continuity, to match the discharge established from the 1D computation. The maximum local velocity which enables an ice cover to progress towards the river centre increases during cold spells and is calculated using a formulation close to that proposed by Matousek (1984): V max, prog. ( m / s) = max 0,30, Φ atm [12] 925 Conversely, border ice can retreat towards the shore due to thermal erosion where water temperature is above 0 C and local velocity is too high. The local flow velocity during the retreat towards the shore depends a priori on the water temperature and weather conditions, but no satisfactory formulation is available for this mechanism, which plays

6 an important role in the downstream retreat of the ice cover when the weather becomes milder or when flow rates and/or water temperatures begin to rise. A semi-empirical law has been adopted based on the following principles: The energy W (J/m 2 ) required to melt an ice cover with a thickness of e is measured by: W = ρ Le i [13] where ρ i is the ice density and L, the latent heat of fusion for ice. This energy is supplied by the net balance between the heat flux lost to the atmosphere (Φ atm ) and the heat flux transmitted by warm water (Φ water ); we can then write: i ( Φ Φ ) ρ L e = τ [14] water where τ is a time constant. atm The heat flux lost to the atmosphere is calculated by the model based on the weather conditions (air temperature, short- and long-wavelength solar radiation, wind speed, etc.). The heat flow transmitted by warm water to ice is computed using a relation of the type Dittus-Boelter: Φ = V A R 0.8 water 0. 2 H T [15] where V is the local flow velocity at the limit between open water and border ice, R H is the hydraulic radius, T is the water temperature and A is a constant. Using relationships [14] and [15], the limiting velocity V can be calculated as a function of ice thickness, water temperature and weather conditions. Border ice retreats towards the shore up to a position, such that the local velocity is equal to the limiting velocity. Constants τ and A can be used to adjust the model to confirm the observations and this has led to the adoption of τ = 3 days and A = Border ice progression and retreat determine the area of openings at free surface flow, which allow for the production of frazil ice grains where water temperature is 0 C. The grains then rise to the surface and form ice pans, which then drift further downstream. 3 The Péribonka river 3.1 Presentation and available observations and measurements The Péribonka River is regulated by the Chute-des-Passes power project and fed throughout the winter season by water with temperatures above the freezing point. The Passes Dangereuses reservoir is stratified, the water intake for the Chute-des-Passes power plant is very deep and draws water above 0 C throughout the winter season. The area being studied is the Péribonka River between the Chute-des-Passes power plant

7 tailrace (km ) and upstream of the Chute-du-Diable reservoir (km 87).( 1 ) The river drains a watershed with an area ranging from km² at the upstream limit of the model to km² at the downstream limit, and the mean annual flow rate ranges from 358 m 3 /s to 519 m³/s. At the end of winter, water from the Chute-des-Passes power plant represents over 90% of the total flow at the downstream limit of the modeled stretch. The geographical layout of the Péribonka River is shown in Figure 1. The climate is characterized by air temperature which may fluctuate from 0 C to some -30 C within few days. The average freezing index is C-days. Figure 1. Geographical Layout of the Péribonka River Early in winter the temperature of water flowing through the Chute-des-Passes power plant turbines is approximately 3 C; this temperature then gradually decreases to 0.7-0,9 C at the end of the month of March. The 100-km reach, between the upstream and downstream limits of the area under study, enables the water temperature to reach the freezing point and, as a result, causes the formation of ice. In addition to flow rate recordings, 104 transverse sections provided by bathymetric surveys and water level profiles, other data was made available in order to develop the model and validate the results, i.e.: 1 This stretch was divided in two by the priming of the Péribonka reservoir by Hydro- Québec in 2007, which impounded the reach upstream of km 151. The present study only concerns the situation which prevailed prior to the commissioning of this new power project.

8 Hourly water temperature measurements at different points on the river were used to validate the heat exchange calculations; Hourly water level measurements at different points on the river were used to validate the increase in water level due to the presence of ice covers; Photographic surveys were used to locate the position of the ice cover s leading edge on a few occasions during the winter season. 3.2 Results Leading edge advance and retreat Ice cover dynamics were simulated for two winter seasons, namely, winters and Since ice regime modelling is used chiefly to forecast snowmobile accessibility, we took a particular interest in defining the ice cover surface area and thickness. The modelling results highlighted the fact that, even though the water temperature at the upstream limit of the model remained practically unchanged from January to March, the ice cover surface area varies constantly in winter. It progresses upstream in cold weather and recedes downstream when warmer spells occur during winter, and this occurs regardless of flow variations. As a matter of fact, for the months of January to March 2002 the flow rate was practically constant around 550 m³/s, while the ice cover s leading edge moved constantly. For this reason, the two aerial photographic surveys carried out in December 2001 and February 2002 are not enough to verify if the ice cover actually evolved similarly to what was simulated by the Mike-Ice model. The images generated by the NASA Modis satellite were, therefore, used. The satellite takes a image of a given earth region every 24 hours Cloud covers frequently hide the Péribonka River, but 20 or 30 usable images are available each winter, which is much more than what the photographic surveys can provide. The image resolution is rather low, since one pixel equals 250 m for a river with a width ranging from 60 m to 1150 m, but we were still able to detect the position of the leading edge on a given date, this edge being defined by the upstream most location where the ice cover is continuous from one shore to the other. The images are used to find the ice cover formation dates, track the advance or retreat of the leading edge, and determine the date of the ice clearing. However, the resolution does not allow for detection of smaller openings, nor to determine whether the ice cover is accessible to snowmobiles. The photographic surveys, which took place on December 19, 2001, and February 27, 2002, were used to validate the interpretation of the ice cover s leading edge position determined from the satellite images. Figure 2 shows a sample of the satellite images, which were used to identify the leading edge position observed on March 20, 2005, and Photo 1 used to validate the leading edge position on February Several successive satellite images taken during the same winter were used to track the ice cover progression and observe how this cover reacted to the warm and cold episodes that follow one another in the course of a winter season. Figures 3 and 4 can, thus, be used to compare the leading edge position calculated for the two modeled winters with those which were detected using the Modis satellite images or photographic surveys.

9 March 20, 2005 Leading Edge at KP 125 Péribonka River kilometric points Figure 2. Péribonka River Kilometric Points and Ice Cover Leading Edge Position on March 20, 2005 Photo 1. Identification of the Ice Cover Leading Edge at KP 123 on February 27, 2002

10 Leading Edge Position (km) Dec 21 Dec 10 Jan 30 Jan 19 Feb 11 Mar 31 Mar 20 Apr Date Observations using satellite images Mike-Ice Model Photographic survey Figure 3. Leading Edge Position Observed and Calculated during the Winter Season Leading Edge Position (Km) Dec 21 Dec 10 Jan 30 Jan 19 Feb 11 Mar 31 Mar 20 Apr Date Observations using satellite images Mike-Ice Model Figure 4. Leading Edge Position Observed and Calculated during the Winter

11 3.2.2 Additional Validation Data Water level measurements also confirmed that the ice cover moves during winter according to air temperature variations. In times of low flow variations, as was the case from January to March 2002, an increase in the water level was observed during cold weather spells, when the ice cover progressed upstream, and a decrease in the levels during warmer spells until the levels match the ones obtained in free surface conditions. Figures 5 shows a comparison between the measured and calculated levels at KP during the winter seasons. The level that would prevail in free surface flow conditions is also presented and exemplifies the effect of ice on water elevation. Figures 5 and 6 show a comparison between the measured and calculated temperatures at KPs 152 and 154 during the simulated winter seasons. These locations are 1 and 3 kilometres upstream of the upstream most position reached by the ice cover s leading edge. 176,0 175,5 Water Level (m) 175,0 174,5 174,0 173,5 01 Dec 21 Dec 10 Jan 30 Jan 19 Feb 11 Mar 31 Mar 20 Apr Measured Level calculated in open water Level modeled with Mike-Ice Figure 5. Water Levels at KP during the Winter Season

12 Water Température ( C) Nov 21 Nov 11 Dec 31 Dec 20 Jan 09 Feb 01 Mar 21 Mar 10 Apr 30 Apr Measured Calculated Figure 6. Water Temperatures at KP 154 during the Winter Season 4 The Romaine river 4.1 Overview and problematic The Romaine River is a tributary of the St. Lawrence River on its north shore. The river drains a watershed with an area of km² at the downstream limit, and the mean annual flow is 327 m 3 /s. Four stations are projected between and 51.5 km for a total of MW and an expected average annual production of 8 TWh. One of the issues of the environmental impact study is the accessibility of the ice cover on a 50 km reach between the mouth and the first station, because it is on this reach that are concentrated human activities and especially the crossing by snowmobiles across many locations. 4.2 Validation The winter was atypical, with 531 C-days of freezing on March 14, compared to an average of C-days of freezing at this time and for the entire winter. The freeze-up was particularly late and the extent of the ice cover was reduced after late February. The numerical model proved to be robust enough to account for these unusual conditions as shown by comparisons between predicted and observed cover extent by areal surveys. The aerial surveys allow validating the computation of the border ice extent and partial openings, by the pseudo 2D approximation, which was impossible with satellite images. At km 35, for example, the river is closed from one bank to the other, on February 3 (Photo 2), and a partial opening is apparent on March 3 (Photo 3). The calculation reflects this trend, the figures 7 and 8 showing the plan view of the river and the right cover at km 35 on both dates.

13 Photo 2. Ice cover at KP 34, on February 3 Figure 7. Representation of the ice cover on February 3

14 Photo 3. Ice cover at KP 34, on March 3 Figure 8. Representation of the ice cover on March 3 Similarly, the model reflects the evolution of partial opening between these two dates at KP Results The model was operated to simulate 20 winters for natural conditions and after completion of the four projected power plants. For current conditions, the inputs are the sequence of air temperatures and flow rates measured during the winter. For future

15 conditions, input flows are simulated by another model that optimizes the operation of the watershed, and water temperatures at the outlet of reservoirs, simulated using a numerical model of thermal vertical 1D stratified reservoir. The results are analysed by extracting data on the accessibility to ice cover, defined as follows: Complete ice cover from one bank to another Minimum ice thickness of 20 cm This accessibility varies continuously from one place to another and from one moment to another. This accessibility is presented graphically in figures 9 and 10, which illustrate for each location and each time the frequency with which the river is accessible in natural conditions and in the future (Figure 10). For example, Figure 9 shows that at PK 26, the river is accessible on average from December 5, but this date may be, some winters, as early as November 29 or as late as December 27. In future condition, figure 10, the median date is December 18. Moreover, the model showed another characteristic behaviour of the ice cover in future conditions: it responds much faster to warm stretches. For example, after three days of above zero temperatures, a twenty-kilometer reach of the river, downstream the powerhouse becomes ice free or unsafe for crossing, whereas the ice cover can withstand such warm episodes in natural condition. This is characteristic of ice-cover subjected to thermal erosion. Based on these results, Hydro-Quebec decided to provide a permanent catwalk to allow safe crossing of the river. Figure 9. Accessibility matrix between KP 51 ant the mouth of the river, for natural conditions

16 Figure 10. Accessibility matrix between KP 51 ant the mouth of the river, for future conditions 5 Conclusion and Assessment of the Acquired Knowledge Despite their fairly modest resolutions, and the fact that they are often hazy due to cloud covers, the Modis images provide valuable and readily available data for studying the ice regime on an average-size river, such as the Péribonka River or on larger rivers in remote areas, because of their frequent availability in the course of one single winter. Even though on a day-by-day basis there are deviations between the observations provided by such images and the model results, the model was able to reproduce the seasonal variations of the ice cover s extent and the way it varied according to meteorological conditions. A simulation can thus be used to identify potentially unsafe areas on a river, as the cover may get thinner or disappear in warmer weather. A novel formulation has been proposed to describe the downstream retreat of the ice cover and its retreat towards the shore caused by thermal erosion. Simulating the ice regime in the presence of water with temperatures exceeding 0 C has thus shown that the extent of the ice sheet and its accessibility are highly sensitive to recent weather variations, as opposed to the natural conditions where occasional warmings have little impact on the ice. Conversely, the condition of the ice cover is not so much dependent on the cold weather cumulated since early winter, but it is largely dependent on the one cumulated since the last warming episode. The model also reproduces fairly well the increase in water level caused by the presence of an ice cover, even though at times there may be deviations between the calculations and the observations. As shown in figure 6, water temperatures are properly reproduced by the model, as well as their variability in a daily cycle. Once validated, based on the study performed on the Péribonka River, the Mike-Ice model was used to forecast the ice regime on another river, the Romaine River s

17 downstream reach, following the development of four power plants. The model has been used to identify the extent of the areas which are not recommended for snowmobiling, in order to specify the modifications to be made to ice clearing dates at locations which remain accessible, and provide gateways for maintaining accessibility. 6 References S. Daly, Frazil Ice Dynamics. CRREL Monograph 84-1 V. Matousek, Type of Ice Run and Conditions for their Formation. IAHR Ice Symposium Hambug. Modis Rapid Response System.