Caribbean Disaster Mitigation
Unit of Sustainable Development and Environment
Organisation of American States
II. Flow Simulation Modeling
III. Phase 1 - Spatial Structure
IV. Phase 2 - Variations of Flow Friction
V. Phase 3 - Dynamics of Rainfall and Funoff over Time
VI. Conclusions: Critical Factors and Options for Flood Management
The Caribbean Disaster Mitigation Project (CDMP), in collaboration with the Government of Belize, has contributed to the development of a flood-hazard model for the Belize River to support flood-hazard awareness and response. The CDMP is financed by The Office of Foreign Disaster Assistance of the United States Agency for International Development (OFDA-USAID) and is implemented by the Organization of American States.
The most severe floods on the Belize River can be traced to the Macal River, one of the two main tributaries of the system. (Figures 1 and 2) During wet periods, rain storms in the Maya Mountains sometimes cause sudden flood waves to descend the Macal River. These waves are so large and sudden that they flood the main channel of the Belize River and even flood upstream into other tributaries.
The report which follows describes how limited field data and a coarse digital elevation model have combined to highlight the factors making the Macal River prone to floods. The model is elaborated in three phases, and each of the three phases gives a different insight into the nature of the Macal watershed.
The model may be elaborated further to examine other hydrologic processes. As it is, the model reveals several important factors of the flooding problem in the system, and opens questions of public policy and flood management (Pages 29 and 30).
Belize, Central America, experiences sudden and dangerous floods along the river between San Ignacio and the capital, Belmopan. This is a farming district with moderate population density and several important transportation corridors. The floods come from rapid runoff in the Maya Mountains, to the south.
The National Meteorological and Hydrological Service of Belize has monitored this problem for many years. This report is a compilation of their observations combined with computer simulations as an aid to analysis.
The Belize River starts at the northwest of the Maya Mountains from the junction of two major streams. The Western Branch, or Mopan, comes from Guatemala, where it has flowed through more than fifty kilometers of rolling farmland on karst geology. The Mopan rises seasonally and contributes to floods downstream, but it has a slow response to rain storms. By contrast, the Eastern Branch, known as the Macal River, comes directly down from the mountains. The Macal often rises so suddenly that it causes backwaters where it joins with the Mopan. The accumulated waters of the two tributaries then become one flood wave which proceeds down the Belize River.
Downstream from the junction, the first thirty kilometers of the Belize River (straight-line approximation) are sinuous but constrained in a deep ravine. The banks are often 15 meters high with slopes of 35 degrees or more, so that flood waves stay concentrated. Low fields near the river are quickly flooded, but the most serious disruption comes from flood danger at bridges, fords, and ferries. The main artery of land transportation is the Western Highway (shown in red, Figure 2), along the south bank of the river. A large settlement north of the river (pale tan) is often cut off by high water at the river crossing.
Even when the Mopan is at high flow levels, flood waves from the Macal River are so extreme that they cause flow to reverse up the channel of the Mopan above the place where the two rivers join. (Figure 3, Arrow 1) After pooling in this area, the combined flood waters surge down the constricted channel of the Belize River to the northeast (Arrow 2), causing backwaters at other tributaries (Arrows 3 and 4).
The Flood wave from the Macal is the most powerful in this river system because the peak flows on the Macal come so suddenly. Timing is critical.
Data for understanding the floods on the Belize river come from two river gauge stations. One station is on the Mopan River at the town of Benque Viejo, and the other station is on the Macal River at Cristo Rey, just above San Ignacio. Records for stream flow at these two stations go back more than 16 years. (Figures 4 and 5)
Upon close examination, it appears that the flooding problem on the Macal River may be even worse than implied by the historical record shown on the previous page (Figure4). That long-term record was gathered by human observers paid to go to the riverside twice a day and make spot observations. There have also been records made by continuous-chart machines, but not as often and not for such a long period. When human and mechanical observations coincide, they do not always agree.
For instance, a mechanical chart recording shows that the flood crest of this storm in 1991 reached a flow of 1,869 m3/s. The human recorder missed one scheduled observation that night, so he missed the peak of the storm altogether.
Even if the spot observation had been made on schedule, it would probably have missed the true peak and under-reported it. If the observation had been 6 hours before the true peak, it would have reported 275 m3/s, off by 580%.
Considering this, it is fair to assume that extreme events are more common than the record shows. However, not enough of the peak flows have been observed to support statistical analysis, because the Macal River changes too rapidly. The careful interpreter must compare the middle and lower portions of the trace from one storm to another.
Because the peaks of the storms on the Macal River only show occasionally in the record, it is not possible to pick the biggest flood simply by picking the highest peak. Instead, it is necessary to look at the historical record for periods of high flow which were extended but distinct from periods before and after. The high flow must be extended because that implies that it was the result of especially high rainfall which took extra time to drain from the surface of the watershed. The high flow must also be be distinct from the generally high flows of the wet season. The wet season is such a regular event that settlement and land use in the district take it into account.
By these criteria, the worst flood on record was in November and December of 1996. The main wave lasted 28 days, and the residual flow tapered off for another 28 days after that. The flood would have been much worse, except that the antecedent moisture was unusually low for that time of year, the end of the rainy season.
This storm has the biggest profile overall, but it appears that the rising flood stalled briefly. There was a transient peak and a decline in flow before the waters rose to their peak for this storm. Because of this, peak flow was not a simultaneous concentration from the whole watershed. This may have been due to a pause in the rains, or it may be due to the nature of the Macal system.
Transient peaks are a recurring feature on the Macal River at Cristo Rey. Examining the storm of 1996 even more closely reveals two more peaks (Figure 8). Continuous chart recordings from confirm this pattern for other storms. Figure 9 shows a typical trace of gauge height from October 1991. (Note that the chart paper shows gauge height; peaks for flow rate are even steeper, because flow increases exponentially as water gets deeper.)
When the flow rate of a single storm is plotted over time, as a storm hydrograph, it is expected to be fairly smooth. (Figure 10) The fact that hydrographs for the Macal River look so different from the ideal raises questions about the nature of the system:
One possible explanation for the transient peaks on the Macal River is that the rainfall may be erratic as well. This is plausible, but difficult to substantiate with field data.
Rainfall gauges at Central Farm and Bull Run recorded the storm of November 1996 as it passed (Figures 11, 12 and 13). The flood wave at Cristo Rey derived from rains in the Maya Mountains. At that time of year, the weather is dominated by frontal storms which move slowly down from the north, and this storm fit the pattern. As the storm clouds reached the mountains they were lifted and cooled in a process called orographic lifting which accentuated the rainfall. Central Farm is at 90 meters elevation while Bull Run is at 600 meters. The higher altitude at Bull Run multiplied the rainfall by a factor of two or three.
Although the rain did vary over time, it was generally prolonged and area-wide. This is in contrast to the isolated thunderstorms in the earlier months of each year. It is not possible to be more specific, because the watershed south of the rain gauges is virtually uninhabited and impassible in the wet season. Even with recent improvements, there is no regular data collection south of Mountain Pine Ridge.
Simulation modeling combines field data and the laws of physics in a computer program which mimics a natural system.Simulation modeling allows combinations of factors to be tested in a controlled, systematic manner. The purpose of the simulation is not just to duplicate the effects observed in nature: given enough variables, simulation can produce any effect the modeler wishes. The key is to use a minimum of variables, to see how the system responds to slight changes, and to isolate the most important factors.
There are many simulation programs available for hydrology. The selection of the right one in this case must consider what the model is for, what it can do, and how to structure the data to show the essentials of the natural system.
On the previous pages, analysis of field observations has shown that:
To deal with floods on the Belize River, the focus should be on the Macal.
Flow on the Macal is erratic as well as extreme, and is poorly understood.
Analysis based on field data alone is stymied by inevitable gaps.
A deeper understanding of the Macal River is needed, in order to deal with the flooding problem which it causes. It is easy to speculate that land cover, soil, or human disturbance are to blame. Most likely, the problem is a combination of such factors.
The public-domain computer program CASC2D (Copyright 1994,1995,1996 by F.L.Ogden & B.Saghafian) has 43 input options which may be combined in many different ways to model different factors in the hydrologic cycle. CASC2D can model major processes separately, together, or ignore them altogether if they do not appear important.
It is also possible to choose between simple inputs and complex ones. A simple input might be to model rainfall as uniform in time, for a specific period, and uniform in space, over the entire watershed. If the simple rainfall does not produce realistic results, the model can be elaborated to have rainfall varying by time, by using a table of rain rates for specific times. If that is not enough, the model can be run again, using a time-series of maps that show rain varying in space and in time.
The ability to input maps ties CASC2D to data bases of weather maps. Weather maps can be combined with other maps, showing soil types, population patterns or any other spatial data. A computer database of maps, combined with the software to manipulate them, is called a "Geographic Information System" or "GIS."
CASC2D is released to the public free of charge. It runs in the GRASS Geographic Information System, which is also available free of charge. Figure 14 shows a simplified flow chart for CASC2D, with red for the options that proved important in this study. The entire package is available for download at http://www.baylor.edu/~grass/
The flexibility of CASC2D allows a phased approach: from simple to complex. The general parameters of the upper Macal watershed are easy to summarize. The area is almost uninhabited. It is forest, with scattered clearings and dirt roads from logging operations. Rainfall is heavy at times, due to orographic lifting as moist air travels over the high ground. There is a distinct wet season, where the ground is essentially saturated for months at a time.
The simplest approach to this system is to start with overland flow. Rainfall may be modeled as a simple input, uniform in time and space. The small upland stream channels may be ignored for the moment and treated as part of the generally forested landscape. The many unknowable details of leaf interception, surface puddles, underbrush, minor channels, ditch diversions and leaf litter may be approximated as friction.
One variable that can not be ignored is the shape of the land. Water flows down-hill, and the model must consider where the hills are and which way they lead. This can be done with a computer map of elevations. The computer map becomes the foundation for the rest of the model. Figures 15 and 16 contrast a visual map, as commonly understood, with a computer elevation map. It is important to understand that a computer map is both an image and a computational database at the same time.
The two images on this page both show the upper basin of the Macal River. They are different in appearance, purpose, and power.
Figure 15, like all the maps before it in this report, derives from the same satellite image as Figure 1. This set of maps derived from the satellite are suitable for visual interpretation and discussion, but they involve some trickery.
In fact, the original satellite image had hardly any green because the atmosphere had filtered it out. The green was replaced by the infrared, a colour invisible to the eye. This substitution is called false colour.
The illusion is furthered by hill-shading. The picture was taken in mid-morning, so the sunlight shining on the southeastern sides of the hills gives the impression of three dimensions.
Laid over the satellite image are blue lines for rivers and the red line for the Western Highway derived, in part, from scanned paper maps at the scale of 1:50,000. All of this was done to make the image informative for the human eye. Visual interpretation is powerful, but it is intuitive and imprecise.
By contrast, Figure 16 represents a map created for computers. This is called a "Digital Elevation Model" or "DEM." The map is structured as a grid of squares, and each square, or cell, corresponds to a location on the Earth with a finite distance from east to west and from north to south. The value assigned to the square is the characteristic elevation of that finite element of the Earths surface. Computers can make precise, reproducible calculations on this map.
A DEM is kept in computer binary code, so even Figure 15 is an interpretation intended for the human eye. Grey represents the highest elevation, which in this case happens to be Cooma Cairn at 953 meters.
Below that are red hilltops, yellow valleys, green and blue for the low lands. As an extra aid to the eye, the main channels of the river system are outlined in black.
The first task in simulation was to investigate the spatial structure revealed by the Digital Elevation Map. The digital elevation map (Figure 17) has a resolution of 30 seconds of arc (approximately 913 meters) per cell. It is derived from GTOPO30, a public database released by the United States Geological Service.
The elevation data needed to be smoothed to remove pits, and then the areas containing major stream channels (outlined in black) had to be individually edited to guarantee continuous drainage. Editing was kept to a minimum and cross-verified with data deriving from satellite imagery, raster scans and paper maps at scales of 1:250,000 and 1:50,000.
The stream channels were modeled as part of the landscape for overland flow. A separate algorithm to route channel flow turned out to be unnecessary. The GIS calculated the watershed (outlined in white) as approximately 1,493 square kilometers.
The entire Macal watershed entered into the calculations, but subsequent illustrations will window on locations along the main channel, as shown by the rectangle in dotted lines.
For the simplest simulations, rainfall was set as 20mm/hour, lasting for one hour at the beginning of the simulation. This will be referred to as the unit rain. Starting with the unit rain, the program calculated the water running off the surface with no consideration of local effects except slope and direction.
Results at Cristo Rey showed the hydrograph beginning with a gentle increase in flow, as would be expected from the small area of gentle slopes in the immediate area of Cristo Rey. This was followed by a distinct double peak as waters arrived from the mountains. (Figure 19) This double peak could only be a result of the configuration of the watershed, because the water input was a unit rain. Both peaks must have come from the mountains, because of the delay in their arrival.
The software allows for output at any point on the map, so it is possible to track these two flood peaks back upstream using simulations. The first place to check is the next junction of a major tributary.
The Rio On is a major tributary which drains an area on Mountain Pine Ridge. The Rio On joins the Macal just above a stretch of narrow channel at Vaca. The first peak on the hydrograph passes the cataracts at Vaca 12.5 hours after the start of the simulation and heads out of the mountains, reaching Cristo Rey about 15 kilometers and 15 hours later.
At first, it seems reasonable to ascribe this first flood wave to the single peak which passed Rio On an hour before and about three kilometers upstream of Vaca.
This simple explanation soon loses its simplicity. The third site site for Figure 20 is more than a kilometer of steam channel and 10 meters elevation above the junction with Rio On. It shows an early peak as well; a peak which is two hours before and two kilometers before Vaca.
Within the limits of this model, the early peak on the main channel above the junction is quite simultaneous or in phase with the wave coming down Rio On. It is also in phase for the first peak as it passes Vaca, and the first peak as it passes Cristo Rey, so it might be a serious contributor to floods on the lower river. Since the model is treating the channel as being a full cell wide, 913 meters, and since the site is well above the junction, backwater effects are not a plausible explanation.
Putting all the hydrographs together with the map of locations shows that the first flood wave becomes evident around Guacamayo and strengthens as it proceeds downstream. This strengthening is due to flows off Mountain Pine Ridge. The second flood wave is well-formed by the time it reaches Rubber Camp. It hardly changes over the next 35 km, but it trails behind because it has farther to go.
It is more than a coincidence that the flood peak from Rio On reaches the Macal in phase with the advance peak contributed by the other slopes of Mountain Pine Ridge.
Mountain Pine Ridge forms a sub-watershed distinct from the southern Maya Mountains. Mountain Pine Ridge is a granite formation, an oval intrusion which slopes to the northwest and which has eroded down the middle where the Macal river passes through it.
There are numerous small streams on Mountain Pine Ridge which the coarse elevation data can not show in detail. These streams have similar slopes and lengths, so that they come together like the ribs of a fan. The focussing effect of this configuration is clear, even though the streams themselves were not specified on the elevation model. The radial arrangement contributes to sudden surges of flow on the main stream.
The southern Maya Mountains have side streams which join dendritically - like the branches of a tree. The junctions are well-separated from each other and flow builds up incrementally.
The waters from these upper tributaries all pass through a break in the ridge between Rubber Camp and Guacamayo to join the lower section. About two-thirds (1000 Km2) of the total Macal watershed is in the upper section.
The simulation calculates overland flow by adapting the Manning equation, which was originally developed for flow in open channels:
|Where||Q||is the flow rate,|
|A||is the cross section of the flow,|
|R||is the hydraulic radius, area divided by wetted perimeter ,|
|S||is the energy gradient,|
|and||n||is a number called the Manning friction factor.|
The simulation treats each map cell as a wide, shallow channel. (Indeed, the cells are 913 meters wide and overland flow depth is usually less than a centimeter.) This simplifies the calculations, since and R vary only with flow depth, and S is equal to the slope of the land itself.
The first few model runs assumed that the entire watershed had the same resistance to flow. The Manning number n chosen to represent this was 0.075, which is quite high friction for a stream channel, but is moderate or low friction for overland flow through forest. This simple assumption accentuated the the spatial effects of the watershed map, but the travel times for flood waves where somewhat too slow.
The next stage in modeling was to experiment with friction factors. CASC2D can input an entire map, with each location having its own friction factor, so the experiments took the form of a series of friction maps and output hydrographs.
Values for n are tabulated in numerous reference books, but selection of the proper factor is not automatic. The different values are associated with short, qualitative descriptions and judgement is called for.
The following values served as a strating point (Gray, 1970):
|Mountain stream, no vegetation in channel, banks usually steep, trees and brush along banks submerged at high stages.||0.040||0.050||0.070|
|Flood plains, medium to dense brush, in summer||0.070||0.100||0.160|
By observation, the forest had many areas of dense undergrowth. A friction factor equal to 0.100 was high, but perhaps not too high.
The channels could drop to a Manning number of 0.050. That was also high, for a perennial stream.
Field observation and talks with Belizean hydrologists indicated that the stream channels and overland flow were even faster than the model had show so far. As a second refinement, narrow, first-order streams were kept at 0.050, but mid-slopes and main channels were given much lower Manning numbers. Specifically, there were some broad, gently sloping reaches in the mainstream, at such places as Guacamayo.
By keeping the same values for the streams, and reducing the friction over land down to 0.085, the model created hydrographs similar to the historic record. The flood waves from the upper tributaries, Rio On, and unmapped streams are now shown to overlap and add together as the river flows past Vaca and approaches the more level, settled areas around San Ignacio.
Note that the two peaks on Figure 26b are now 65 and 90 flow units, compared to 45 and 60 flow units on Figure 19. Peak flow is now faster, and higher as well. The two simulations were identical except for the friction factors. Both Figure 25 and 26 Compare well with the example of chart data shown in Figure 27.
This provides a partial explanation of the transient peaks observed in the historic record. The first flow wave here appears as a transient peak on the side of the main surge. Other transient peaks may be produced by sub-watersheds which the 913-meter DEM is too coarse to show.
This success justifies using the modified friction factors and moving on to experiment with other variables.
All the simulations so far had used an input rain of 20 millimeters per hour, for one hour. That standard rainfall had produced standardized hydrographs that could be compared from one place to another. The Digital Elevation Map and the map of friction factors passed their tests.
The next step was to see how the system responded dynamically. For instance, it is important to remember that flow speed varies with depth. By using the same rate of rainfall as the unit rain, but for a longer time, the model can show how some floods on the Macal River become so violent.
Figure 28 shows a flood wave from a single hour of rain at 20 mm/hr.
Figure 29, below, below, shows the system with all the same conditions as Figure 28, except that the rainfall lasted longer - two hours.
In both cases, as in all the tests so far, the rain was started at the beginning of the model run, and the simulation ran for four days.
The extra hour of rain added extra water to the system, the extra water added to the depth of flow, and the extra depth added to the speed of the flood wave, so that the peak flow in the second simulation arrived ten hours sooner and three times as high.
The system is quite sensitive to the volume and timing of rains. It is also sensitive to the sequence of rains in the days and weeks before an event, so that is is difficult in nature to isolate the effects of one storm the way the simulations have done.
To model a sequence of rains, and bring the simulations closer to the dynamic reality of a river, requires bringing together many elements at once:
Nevertheless, it was possible to proceed with a few reasonable assumptions.
Figure 32 matches the rainfall records at Bull Run, the flow records at Cristo Rey, and the simulation at Cristo Rey for November-December 1996.
Response time for interflow appears to be about one week: the rains around November 1 caused the slow increases in flow around November 8. Soils did not reach saturation until November 12. Surface runoff started at that time and reached Cristo Rey within three days. The rains slacked off around November 15 and increased suddenly on November 17. Soil remained near saturation during this gap, so that the second storm surge was higher than the first even though the rains were closely equivalent. Multiple peaks on the second surge may be due to variations in rainfall over time or space which were not documented.
The simulation only shows surface runoff. It did not include any initial channel flow and it was unable to simulate groundwater contributions to channel flow. That is all the more reason to interpret the flows before and after mid-November, the flows recorded as around 50 m3/s, as being interflow. Soil saturation appears to occur about the same time as interflow of 60 to 70 m3/s.
Several critical factors of the Macal River system appear in the analysis:
Factors 2, 3, 5 and 6, above, combine to make floods. The way it works is that a few days of rain cause interflow to start reaching the streams at about the same time (factor 5) that saturation is causing surface runoff to begin (factor 6). The configuration of Mountain Pine Ridge concentrates the first runoff into a steep wave (factor 2) and the second runoff comes so soon afterwards (factor 3) that it adds to the surge. All these factors are inherent in the watershed and difficult to alter.
Factors 1 and 4 mitigate the flood waves. The friction resistance of the dense ground cover (factor 4) retards surface flow and draws the flow waves out over a longer period. The land cover is sensitive to disruption, but not so sensitive as to preclude current land use if good practices are maintained. The present level of land use leaves most areas in natural cover for decades. Shifting timber-cutting operations occupy and abandon camp sites; disruption may be intense, but not widespread at any one time. Large-scale clear cuts or road building could sacrifice this safety factor. Erosion could remove soil and make recovery unlikely.
Good land management practices, including limiting the size of timber clear-cuts and respecting buffer zones around channels, will help protect this friction effect. The restrictions must apply in the mountains but the benefits would go to the areas far downstream, so voluntary or private-sector measures will not work without strong leadership. This is a problem for the public sector.
Factor 1 offers an opportunity for active measures. At present, the flow waves from the two sub-watersheds tend to overlap and add to one large surge (factor 3). An impoundment where the upper Macal River passes through the ridge above Guacamayo could retard the second wave. This is a simple concept, but it would require careful design, careful management, and adequate funding.
The design of an impoundment would have to provide adequate storage to delay high flow surges. Even after flooding, the channel would be long and narrow, so tha flood surges would attenuated but not eliminated. Pool level would rise suddenly and there would have to be empty capacity reserved for rare events. The design would also have to anticipate erosive changes because the basin would experience erosion and landslides from elevated water. The design would have to anticipate turbulence at the outlets due to storm surges and waves from landslides. The channel downstream would change as well. If the impoundment succeeded in attenuating the extreme flows, the channel would close in proportionally because the extreme floods would not keep it as open as it is now. These effects must be calculated in advance.
The management of an impoundment would have to keep empty storage capacity reserved for public safety. If the impoundment combined flood management with generation of electricity, the managers would be tempted to sacrifice flood capacity by storing extra water for electrical generation. This temptation would be highest toward the end of the rainy season, in November and December, but that is exactly the period when frontal storms and saturated soils present the greatest hazard.
Adequate funding would be a continuing concern. The greatest cost would be during construction, but it would be dangerous to neglect inspection and maintenance afterwards. Here again, a dual-use impoundment which combined flood management and hydroelectricity would have to follow careful priorities. There could be danger if the operation got into financial difficulties.
Timely information is critical to public safety because the Macal River has short response times. It appears that heavy rains on unsaturated soils become channel flow in about one week. Once the soils reach saturation, surface runoff surges rapidly and reaches settled areas in three days or less.
Despite the difficulties of working in the Maya Mountains, data gathering in that area should be maintained and improved if possible. This entire study depends on assumptions and generalizations about the Macal watershed, even though the rainfall and flow data are unknown except at the extreme northern edge of the watershed. In particular, rainfall needs to be better known. Modern improvements in automatic, stand-alone recording stations should be quite economical.
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