Josh Berger and Jordan Wright

Journal of Undergraduate Research
Volume 8, Issue 3 - January / February 2007

Estimating Spatially Variable Monthly Precipitation Inputs to the Tiribí River basin, Costa Rica

ABSTRACT

Knowledge of available water resources is crucial, but often limited, in many developing countries. A simple, yet physically meaningful technique is used to maximize the benefit of the available precipitation records in the Tiribí Basin, which supplies much of the freshwater to the Costa Rican capital, San Jose. A gridded data base of mean monthly precipitation is developed within the basin at a resolution of about 1km2 employing the dependency of precipitation on elevation and a DEM of the same resolution. Precipitation data are available at 15 stations in and around the Tiribí between 1950 and 1989. Linear regression is used to establish the changing monthly relationship between elevation and precipitation. Percentage errors in estimation of mean monthly precipitation at the 6 calibration stations falling within the basin, range both seasonally and between stations. Statistical tests of the performance of the procedure applied to 4 validation stations not used in model calibration revealed unacceptable performance in only about 5% of the months. The efficacy of the methodology is illustrated by comparison to 3 other standard methods of estimating precipitation inputs to the basin. The approach has the potential for use in other mountainous areas of the developing world.

INTRODUCTION

In many developing nations even the most basic of information concerning the available water resources and the operation of the hydrologic cycle is poor or totally unavailable. Such knowledge is essential for the development of a host of functions such as agriculture, hydroelectric power, transportation infrastructure, the provision of adequate safe potable water, and waste water disposal. It is therefore important to develop methodologies that enable the optimal use of the limited available data by extrapolating them over space. Much of this work has been developed in temperate areas of relatively simple terrain (Huff and Shipp, 1969; Gandin et al., 1970; Hendrick et al., 1970; Hong et al., 2005). The most basic starting point for the study of available hydrologic resources in an area is the correct estimation of precipitation into drainage basins. This input is subsequently modified by hydrologic processes operating within drainage basins, yielding soil moisture, evapo-transpiration and runoff in rivers. Over 70% of Latin American countries generate more than half of their power from hydroelectricity, and this figure rises to over 80% in Costa Rica. Per capita, Costa Rica has one-fifth of the crop land of the United States and 25% of that land is irrigated, compared to 10% in the United States. Only 20% of the population of Costa Rica does not have access to good sanitation and drinking water, resulting in some of the lowest incidences of cholera and malaria in Latin America (Gleick, 1993).

This study investigates the spatial and temporal variability of monthly precipitation into the Tiribí river basin, which provides water and sanitation of the heavily populated metropolitan area around the capital city, San José. Although the results are specific to this area, the problems and methodologies developed in their solution are of relevance to many tropical montane locations in developing countries, in which wind directions change seasonally and elevation exerts strong, but seasonally changing, controls on precipitation. The paper proceeds by reviewing standard available methodologies, followed by a discussion of elements of the physical environment pertinent to the generation of rainfall, the availability of historic records and a consideration of the regime of mean monthly precipitation monthly. A simple model relating elevation to precipitation is calibrated in each month, the coefficients are examined from a physical perspective, and the model validated against previously unused historic data. Estimates of monthly input are then compared to those of the other established techniques.

METHODS

Estimates of rainfall inputs over large spatial units such as to basins have generally been made by one of 3 methods; arithmetic mean, Thiessen polygons, and isohyets (Gray, 1970).

Arithmetic Mean: Rainfall figures from only those stations within the basin are considered and an arithmetic mean is calculated and applied equally to the entire basin. The technique is simple and unambiguous but ignores the possibility of potential spatial clustering of stations in a particularly wet or dry area and excludes potentially valuable information from nearby.

Thiessen Polygons: The area (basin) under study is divided up into irregular polygons defined such that any point within a polygon lies closer to the recording station within the polygon than any other station. The area of each polygon that intersects with the basin is calculated and expressed as a proportion of the total basin area. This proportion is then used as a weighting by which the rainfall observed at the circumscribed station is multiplied. The weighted products are summed for all polygons that intersect the basin. In this way, an attempt is made to include a representative measure of the importance of each station and to include pertinent data from surrounding stations; however, the division of space, and hence the calculation of the weighting factors, is based solely upon the distribution of the rainfall stations rather than the process of rainfall.

Isohyets: In this case the areal units and their subsequent weightings are defined by the patterns of rainfall observed at the stations in and around the basin. These are extrapolated over space using algorithms of various complexity and isohyetal maps drafted. Proportions of the basin lying within isohyetal limits are used as the weighting factors to be multiplied by the mean rainfall believed to fall between the isohyets. Operator decisions about extrapolation techniques and isohyetal intervals may influence the results. Likewise, in mountainous areas the assumption of smooth, gradual changes in rainfall over space may not be appropriate.

In mountainous areas, elevation has been shown to exert a strong control on precipitation received (Barros and Lettenmaier, 1994). In this paper the numerical nature of that relationship in and around the Tiribí is investigated on a monthly basis using available historic data. The validity of the derived numerical representations is then tested by forecasting mean monthly precipitation at four test sites which possess some historic records, but which had not been previously employed in establishing the relationship. The various monthly relationships are then applied to a digital elevation model (DEM) of the basin and gridded precipitation calculated.

Figure 1. Topographic map of Costa Rica (upper) showing location of Tiribí basin and a topographic cross-section (lower) constructed along the solid line of the topographic map .

Figure 2. Map of mean annual precipitation (mm) in and around the Tiribí basin, showing the locations of stations used in model calibration (triangles, see Table 1) and validation (circles, see Table 2).

STUDY AREA AND DATA

The basin of the río Tiribí (Figure 1) occupies 302 km2 to the south and east of San José (about 10°N), draining the flanks of the Cordillera Central to the northeast, and the Cordillera Talamanca to the south, both of which rise locally to over 2500m, 1500m above the valley floor. It serves much of the water needs of over one million people in the metropolitan area located at the eastern extreme of the densely populated western central tectonic depression of Costa Rica.

Map No.	Station Name	Lat. °.’ N	Long. °.’ W	Elev. (m)	Years of Record	Percent of months missing
Table 1. Names, locations, and periods of monthly records available of the rainfall stations used in model calibration in and around the Tiribí basin.
1	Avance de Tres Ríos	9.59	83.58	1870	1939-1986	6.4
2	La Cangreja	9.48	83.58	1830	1962-1993	3.6
3	Commandancía Cartago	9.52	83.55	1440	1960-1993	2.2
4	Coronado	9.59	84.00	1382	1942-1973	6.3
5	Hacienda La Laguna Curridabat	9.54	84.02	1240	1955-1986	0.0
6	Desamparados	9.54	84.04	1162	1957-1986	1.9
7	El Alto de Ochomogo	9.54	83.57	1546	1950-1982	10.6
8	Hacienda Concepción Tres Ríos	9.55	84.00	1320	1954-1984	7.3
9	Las Nubes	9.59	83.58	1850	1971-1993	2.9
10	Paraíso de Cartago	9.50	83.52	1380	1953-1985	9.1
11	Rancho Redondo	9.57	83.57	1780	1951-1986	0.2
12	Sanatorio Duran	9.56	83.53	2337	1935-1990	2.7
13	San Ignacio de Acosta	9.48	84.10	1095	1950-1979	5.8
14	San José	9.56	84.05	1172	1866-1989	0.4
15	Santa Ana	9.56	84.11	909	1941-1986	0.4

Map No.	Station Name	Lat. °.’ N	Long. °.’ W	Elev. (m)	Years of Record	Percent of months missing
Table 2. Names, locations, and periods of monthly records available of the rainfall stations used in model validation in and around the Tiribi basin.
I	San Joaquin de Santa Ana	9.56	84.09	905	1955-1969	0.0
II	San Antonio de Escazu	9.54	84.08	1830	1962-1993	4.3
III	San Juan de Dios	9.53	83.05	1440	1960-1993	2.7
IV	IPIS de Guadalupe	9.58	84.02	1382	1942-1973	2.0

The lower lying Cerro de Carpintera (1500 m) to the east provides the local divide between waters draining westward to the Pacific and those draining eastward to the Caribbean.

This regional setting and the local topography have considerable influence upon the temporal and spatial distribution of monthly rainfalls. Elevation generally causes air masses to rise and cool—a process known as orographic lifting—producing clouds and precipitation on the windward side and clear dry conditions on the leeward side. Seasonally changing wind directions interact with the topography to produce very pronounced dry (November-April) and rainy seasons (May-October).

The historic records (1950–1989) of monthly precipitation at 15 meteorological stations (Table 1 and Figure 2 ) lying within or around the basin were provided by National Meteorological Institute of Costa Rica (Ministerio de Recursos Naturales, Energia y Minas, 1989). Within this period each station has at least 30 complete years of data. Mean monthly precipitation is estimated for each calendar month at each site. A digital elevation model (DEM) of topography within the area is available at a scale of 1 km2. A representative elevation (m) is calculated and placed in the center of each cell.

RAINFALL REGIME

The Tiribí basin lies in a volatile climatic zone where winds from both the Caribbean Sea and Pacific Ocean blow on an annual basis. During much of the year (November-April) the dominant global winds are the Northeast Trades or Alisios, which place the Tiribí on the leeward side or “rainshadow” of the Cordillera Central (Waylen et al., 1998). This dry season (Figure 4), known locally as the verano, can occasionally be interrupted by outbursts of cold air and the preceding cold fronts, or nortes, which originate over the cold North American continent. The cool, dense air general remains low in the atmosphere and is therefore constrained to the Pacific flank. Its effects may pick out lower lying areas, like the Cerro de Carpintera, to invade the Pacific slope locally (Schultz et al., 1998).

The global pattern of air flow is disrupted in the boreal summer (May-October) by the northward migration of a large area of low atmospheric pressure, the Intertropical Convergence Zone (ITCZ). The average northernmost latitude of the ITCZ in the eastern equatorial Pacific corresponds to that of the Tiribí (Hastenrath, 2002), bringing heavy convective rainfall and winds from the southwest off the Pacific. The rainy season is interrupted by a short, drier period, the veranillos or “little summer,” which is variable in length, but generally occurs at the end of July and beginning of August.

A simultaneous strengthening of the Caribbean trade winds has been observed (Magaña et al., 1999, Poveda et al., in press), particularly in an area to the east of the Costa Rica-Nicaragua border, known as the Caribbean, or San Andrés, Jet. The trades pass through the topographic gap along the international boundary, emerging over the Pacific and Gulf of Papagayo as off-shore winds. Warm surface waters are blown out to sea and cooler waters up-well to replace them, thereby reducing convective precipitation associated with the ITCZ. The resultant clearer skies permit greater solar radiation to reach the sea surface, which then slowly warms the surface waters again. The lag time between the commencement of the intensified trades and the subsequent warming corresponds to the period of the Veranillos.

In September activity of the ITCZ reaches its peak. Rainfalls generated during September and October are the highest of any time of the year. Cross-equatorial westerlies occurring during this period are greatly enhanced by the indirect effect of tropical cyclones over the Caribbean, which reverse the normal pressure gradient across the isthmus. Coincidentally, this post-Veranillos period is also the time of maximum tropical storm activity in the Atlantic Basin. Southward migration of the sun and cooling of sea surface temperatures at the end of the season cause the southward migration of the ITCZ.

RESULTS

Figure 3 plots mean annual precipitation at the stations in and around the Tiribí. Those stations nearby, but on the Caribbean side of the divide, display a very different relationship from those on the Pacific side. This figure shows the major role of elevation in determining precipitation and illustrating the potential pitfalls of methods that assume gradual changes in precipitation patterns between recording stations located in regions of variable topography. Removing the stations within the Caribbean watershed, on good physical and graphical evidence, shows a fairly strong linear relationship (r² = 0.647) between the two variables:

Annual Precipitation (mm) = 921.8 + 0.912 . Elevation (m)

The only station which is a notable outlier from this relationship is El Alto de Ochomogo, which lies exactly on the basin divide between the Caribbean and Pacific slopes and deviates in a manner indicative of that location (i.e., lower precipitation for a given elevation similar to the pattern observed at the Caribbean sites). There is little evidence of the non-linear relationship that has been observed at some tropical locations (Hastenrath, 1991).

Figure 3. (Upper) Hypsometric curve of the Tiribí basin, showing the percentage of the basin falling below given elevations and the situation of the precipitation recording stations. (Lower) Scatter plot of basin elevation and mean annual rainfall at the 15 recording stations, identifying those stations falling within the Pacific and Caribbean drainage and those within the Tiribí itself.

Of the four different methods proposed to estimate mean annual precipitation in the basin (Table 3), the Thiessen polygon and isohyetal methods yields almost identical values, while the arithmetic mean returns a value about 90 mm higher. By constrast, application of the regression relationship to the elevations in the DEM yields a value about 250 mm higher than the former two methods and 150 mm greater than the latter. Only the 6 stations that fall within the basin determine the arithmetic mean. The polygons and isohyets employ information from more stations, but in the case of station 12, Sanatorio Duran, this involves the artificial imposition of lower Caribbean rainfalls onto the most northeasterly portions of the basin, which are also the highest elevations within the basin on the flanks of Volcan Irazú. Figure 2 illustrates the marked contrast between precipitation experienced at such high elevations between the Caribbean and Pacific slopes. Use of the regression relationship excludes this Caribbean influence and allows for extrapolation beyond the altitude of the highest Pacific station, which constitutes about 20% of the basin.

Table 3. Mean annual basin precipitation estimated via the 4 different methods
Method	Estimated Mean Annual Precipitation (mm)
Arithmetic mean	2102.3
Thiessen Polygons	2017.1
Isohyets	2010.7
Topographic regression	2245.5

Application of this topographic method to the strongly seasonal patterns of mean monthly precipitation yields tremendous variability in the coefficients, but variability that is consistent with, and interpretable in terms of, the noted seasonal wind patterns and sources of atmospheric moisture (Figure 4). During the season when the Pacific drainage lies to the leeward of prevailing trade winds (January-April), intercept, slope, and correlation coefficient are all low, implying the lack of precipitation (intercepts). During the rainy season and months immediately following, the coefficients and power of elevation explain spatial variations in mean monthly precipitation rise. Even the slight reduction in the intensity of activity associated with the ITCZ and the weakening of the westerly winds during the veranillos is clear in the values of the coefficients for July and August. November and December, the period of the nortes, is conspicuous in a sudden drop of the value of the intercept. This implies that elevation still exerts a strong control on precipitation (high values of slope and r²), but that the absolute levels of monthly precipitation are low. This is consistent both with the precipitation generating process at this time of year and the overall precipitation regime. The very low measures of model explanatory power in the dry season are not of a major concern as very little rain falls, and, due to the atmospheric physics of the leeward position, this is to be expected physically.

Figure 4. Regression coefficients of mean monthly precipitation versus elevation (upper) and the monthly precipitation regime at San José (lower). In the lower box-and-whisker plot; dots represent the historic 5th and 95th percentiles; whiskers the 10th and 90th; limits of the boxes the 25th and 75th percentile, and the median is shown by the solid horizontal line. Mean monthly precipitation is shown by the dashed line.

Figure 5. Observed monthly precipitation totals at six of the calibration stations falling within the Tiribí basin (box-and-whisker plots), and the mean monthly precipitation estimated through the topographic regression method.

VALIDATION

Figure 5 shows measures of the observed monthly rainfall regime, their interannual variability at the 6 calibration stations, and estimates made using station elevation and the regression method, which fall well within the interquartile range, and very close to the median in most cases. The one exception where the model always overestimates mean monthly rainfalls is El Alto, which, as has been noted previously, sits on the locally low drainage divide.

Comparison of observed and expected means at the stations which had been used in model calibration is not a fair test of model performance. It is better to validate the model by applying it to record from stations not employed in the calibration. The previously unused records of 4 stations, in and around the basin and possessing between 15 and 20 years of record were employed for this purpose (Figure 6, Table 4). Unfortunately, 3 of the validation stations lie outside of the basin, but do lie sufficiently close to fall within the geographic realm of the stations used in calibration and provide a representative sample of rainfalls within the study area. Elevations of the calibration stations are input to the various monthly regression models and comparisons made between the estimated and observed data. Graphical comparisons can be interpreted in the same manner as before. Application of a one tailed t-test to the 48 months of validation revealed 2 statistically significant overestimates of monthly means, 1 underestimate at the 0.05 significance level, and an additional overestimate when the significance level is dropped to 0.10. It should be noted that none of the estimates was found to be significantly different at the only station within the basin itself, San Juan, which also has the longest period of record.

Figure 7 provides a comparison of estimated mean monthly precipitation input to the Tiribí basin using each of the 4 methods discussed. It is impossible to know how much rainfall actually falls in the basin and therefore to decide which is the “best” method. However, it is clear that the proposed methodology employing elevation yields the largest estimates, particularly in those months of the rainy season during which elevation has been shown to exert the greatest control. This probably reflects the extra significance assigned to the 20% of the basin, in the northeast, which lies above the elevation of the highest recording station. By contrast, the isohyetal and Thiessen polygon methods generally ascribe to this area a rainfall value influenced by, or associated with, the station Sanatorio Duran, in the drier, more leeward, Caribbean basin. It should be noted that such an attribution may not be misplaced at lower points on the drainage divide, as indicated by the characteristics exhibited by El Alto de Ochomogo.

Figure 6. Historic monthly precipitation characteristics (box-and-whisker plots) and the estimated mean monthly precipitation at the validation stations. Months marked by black ellipses indicate significant differences at the 0.05 level, the grey ellipse indicates differences at 0.10 level. Symbols for historic 5th and 95th percentile levels are absent when insufficient historic data exist for their estimation.

Validation Station	Jan (mm)	Feb (mm)	Mar (mm)	Apr (mm)	May (mm)	Jun (mm)	Jul (mm)	Aug (mm)	Sep (mm)	Oct (mm)	Nov (mm)	Dec (mm)
Table 4. Estimated (upper row) and observed (lower row) mean monthly precipitation at the four validation stations. Months with bold characters on a white background are significantly different at the 0.10 level, those on a grey background are different at the 0.05 level.
I	2.9	11.7	15.4	61.9	236.2	273.3	184.6	237.4	328.1	321.3	124.9	19.4
I	9.4	20.6	16.6	61.9	215.5	266.3	194.6	180.2	402.3	328.9	129.1	18.5
II	20.7	17.2	17.4	57.5	261.2	310.6	208.8	263.0	368.8	376.7	172.8	61.5
II	18.6	12.6	19.2	73.9	273.2	297.4	207.1	285.7	358.0	337.7	141.0	46.7
III	11.6	14.4	16.4	59.8	248.3	291.4	196.3	249.8	347.9	345.3	148.2	37.7
III	14.7	11.6	10.4	41.7	277.1	279.0	180.2	250.7	359.5	338.7	150.3	36.8
IV	18.7	16.6	17.2	58.0	258.3	306.5	206.1	260.1	364.2	365.2	167.4	52.8
IV	20.9	13.2	10.6	34.0	223.7	298.1	240.9	277.2	345.6	286.2	154.1	49.9

Figure 7. Mean monthly precipitation falling in the Tiribí basin estimated through the 4 proposed methods.

CONCLUSIONS

This study uses a reasonable and testable means of estimating precipitation input into a small but important tropical montane basin of complex topography. The methodology is simple, yet takes full advantage of the limited available precipitation data and the ready accessibility to DEMs to provide a means of estimating seasonal rainfall variability in the Tiribí basin of Costa Rica. The model displays results that are meaningful in terms of the physical processes of rainfall generation and the climatology of the region. Despite the model’s linear nature, it can be applied to the DEM and appropriate monthly regression coefficients to reproduce a complex and temporally shifting spatial pattern of precipitation. The method and coefficients could be used for planning purposes in estimating available precipitation into any sub-basin within the study area, for instance to evaluate the suitability of a location for the installation of new hydraulic infrastructure, like water extraction or micro hydroelectric power generating plants, or for determining potential impacts of planned land use chances within the designated area. The method itself is applicable for any region in the world in which topography is an important control on precipitation, although the specific coefficients would have to be recalibrated for the specific geographic location.

REFERENCES

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