Model of Tonle Sap
Tonle Sap is the largest lake in South-East Asia and is a wetland of international importance and is recognised by the Ramsar convention. Like most wetlands its area varies significantly through the year, from 2000 km2at its lowest to ten times that figure at its largest. The bed of lake is close to sea level and its maximum level is normally only 10 m above sea level. The channel from the lake to the Mekong can flow in either direction. When levels in the lake are higher than those in the Mekong water flows out of the lake toward the Mekong (generally from October to April) and for the rest of the year it flows in the opposite direction.
The following map shows three significant locations for level and/or flow measurement. Levels in the lake are recorded at Kampong Loung.
| |Figure 1 - Important measuring sites related to the model of Tonle Sap
Levels and flows in the Mekong are measured at Kampong Cham and in the channel connecting the lake to the Mekong at Prek Kdam.
| |Figure 2 - Level measurement on the Mekong at Kampong Cham
| |Figure 3 - Level measurement on Tonle Sap River at Prek Kdam The next chart shows the level at Kampong Cham and in Tonle Sap Lake. Two features are worth noting:
- there is approximate synchronicity in the timing of the two sets of levels but with peaks in the Mekong generally being a bit earlier than those in Tonle Sap
- the range of levels in the Mekong, about 15 m, is higher than in the Lake, about 7 m.
As the water levels are recorded relative to local data it is not possible to know from this graph the relative levels between the two measuring locations.
|Figure 4 - Water levels in Tonle Sap Lake and the Mekong at Kampong Cham|
The next chart shows the flow at Prek Dam in the Tonle Sap River. During the period of October to April water flows from the lake to the Mekong. During the rest of the year the flow is toward the lake from the Mekong.
| |Figure 5 - Flow in Tonle Sap River at Prek Kdam
The above data sets, levels in the lake and the Mekong and flow via the Tonle Sap channel give us many of the important elements for a model of Tonle Sap. However there are a number of other important factors. These are:
- Flow into the lake from surrounding rivers
- The relationship between depth, volume and area of the lake
- Precipitation on the lake
- Evaporation from the lake
There are four usable records of flow into the lake. There are shown on the following map and comprise he flows records at Battombong (Stung Sangker), Kampong Kdey (Stung Chikriang), Kampong Chen (Stung Staung) and Pursat (Stung Sen). There are other level records but they do not have an accurate rating curve linking levels and flows.
| |Figure 7 - Relationship between Level and Volume in Tonle Sap Lake
The curves on the chart were fitted using Excel. In the case of the flood area the relationship is:
Area = 30.061(Level)2+ 1094.1(Level) + 716.69
Where the surface area of the lake is in square kilometres and level is in metres.
The equivalent relationship for volume is:
Volume = 0.914(Level)1.883
...where the volume of the lake is in cubic kilometres.
The final elements for a model of the lake, rainfall and evaporation were based on average values taken from climate stations around the lake. For each daily time step the volume of rainfall and evaporation were based on the amount in millimetres multiplied by the area of the lake. The model also included a further loss mechanism. As Tonle Sap contracts in size during the October to April period water evaporates from the exposed soil which, given there is little rain in this period, becomes very dry. When, later, Tonle Sap again expands the water flows from the lake over land which has been dry for, in some cases, several months. This water then sinks into the voids in the soil. The model applied this loss cumulatively. If the area of Tonle Sap was expanding the loss was equivalent to the total evaporation during the period of expansion at that point in time. The maximum loss by this mechanism was 200 mm. Once the lake started contracting then the loss from this component was set to zero.
The basic formula for the lake model was:
Volume[t+1] = Volume [t] + Inflows – Outflows
The model operated on a daily time step and was developed as an Excel file.
The inflows were: flow from local rivers, flow via the Tonle Sap channel and rainfall on the lake. During calibration it was found the estimate of local inflows based on the above method (adjusted in proportion to the drainage area) overestimated the inflow by a factor of two. A preliminary analysis suggested two reasons for this. One is that the area used refers to the area of the Tonle Sap ecosystem which might be larger than the drainage area upstream of the level measuring point. The second is that the gauging stations receives water from the upland parts of the drainage basin and therefore exaggerates the average runoff. Since the contribution from the surrounding rivers is small compared to the contribution from the Mekong through the Tonle Sap channel this parameter is not of great importance to the overall accuracy of the model.
The flow via the Tonle Sap channel was based on the following equation:
Flow = a * (Mekong level – Tonle Sap level – b)c
If the flows were toward to the lake then this formula was used as above. If it was toward the Mekong then it adjusted by a further factor d.
The values of the four parameters a, b, c and d were obtained by using the ‘Solver’ add-in of Excel. ‘Solver’ adjusts each of the four parameters to see how they change the accuracy of the model. In this case the accuracy of the model is defined as the sum of the squares of the errors in the estimation of the levels in Tonle Sap Lake.
The outcome of Solver optimisation process is that the formula became:
Flow = 1126 * (Mekong level – Tonle Sap level – 3.98)1.32
The value of ‘d’, relating to the direction of flow, was 0.59. In reality this parameter is compensating for some hydraulic factors not included in this model. A full solution of the equations would take account of the inertia of the water in the Tonle Sap channel; in simple terms when the relative levels in the lake and the Mekong change they first have to stop the river flowing in one direction before they can increase its flow in the opposite direction.
The values of parameter ‘b’, 3.98 m, which allows for the difference in the datum at Kampong Cham and at Prek Kdam is compatible with Figure 4of water levels at the two sites above.
Another factor not included this model is the time delay between changes in relative water levels. To have included a hydraulic model would have required information on the channel shape and dimensions and a whole project on its own.
The next chart shows the simulated and observed flow of the Tonle Sap channel.
| |Figure 8 - Simulated and observed flow in Tonle Sap River
At first sight this does not look encouraging. In particular the peak inflows are not well represented.
However examination of the current meter gaugings carried out in 2008 to 2010 suggests a reason. The following chart is for the ‘out’ period only; that for flows in the other direction is very similar. It shows that for mid-range levels there is a reasonably consistent relationship between flows and levels but at low levels and high levels, when the flow direction is changing, the relationship is unclear. In the case of the following chart levels from 6 to 8 metres can be associated with either increasing flow, as in 2009, or falling flow, as in 2010. The flow associated at that level can also vary from 1,000 m3/s to almost 20,000 m3/s.
| |Figure 9 - Current meter gaugings in Tonle Sap River
This suggests that the calculation of actual flow values at Prek Kdam might not be consistent and that to simulate them might be as much a case of simulating peculiarities of the flow calculation as of representing the underlying flow patterns.
It should also be noted that the simulation of flows in the Tonle Sap channel is not an end in itself. The overall objective is to simulate water levels in Tonle Sap Lake. The following chart shows that very simulation.
| |Figure 10- Simulated and observed levels in Tonle Sap Lake
As can be seen the simulation is generally accurate. Many of the peaks of water level are slightly underestimated but otherwise it is good. The correlation between observed and simulated levels is 0.967.
It can therefore be concluded that the simulation of water levels in Tonle Sap Lake is sufficiently accurate for the model of lake levels to be used to study flooding around the lake.
In a separate part of the project flows of rivers within Cambodia and the whole of the Mekong were simulated using the HYSIM rainfall/runoff model (http://www.watres.com/software/HYSIM/). The hindcast values of all climate models reported on in the IPCC Technical Assessment Report of 2012 were analysed and the models rated on 4 factors: representation of observed monthly temperature, representation of observed monthly rainfall, representation of monthly temperature anomaly, representation of monthly precipitation anomaly. It was concluded that the MIROC model was most
appropriate for Cambodia.
Using the calibrated hydrological model and the climate projections, flows were projected for a 30 year period centred on 2045.
The following chart shows the observed (or more strictly, simulated using observed meteorological data) and projected levels.
Figure 11 - Observed and projected water levels in Tonle Sap Lake
The following table shows the change in the level of Tonle Sap Lake for different return periods.
The work described above was performed while the author was working for SweRoad under a contract providing support to the Ministry of Rural Development of Cambodia, financed by the Nordic Development Fund and supervised by the Asian Development Bank. Any views expressed or those of the author and do not necessarily represent those of the other parties.