Usability of Standard Monitored Rainfall-Runoff Data in Panama, ISSN 1650-6553 Nr 242 Juan Diaz River Basin

Examensarbete vid Institutionen för geovetenskaper Usability of Standard Monitored Rainfall-Runoff Data in Panama, ISSN 1650-6553 Nr 242 Juan Diaz River Basin

José Eduardo Reynolds Puga Usability of Standard Monitored Water resources demand and natural disasters related to hydro meteorological events have increased the interest in hydrological studies in Panama. Runoff estimations are Rainfall-Runoff Data in Panama, important for effective water resources management in any catchment, but the limited quantity and quality of the available hydrological and meteorological data in Juan Diaz River Basin Panama make it hard for researchers to come to conclusive statements that can help in good planning. This issue has to be addressed, but meanwhile, the challenge is to try to understand the hydrological processes occurring in any catchment with the available data.

The relationship between rainfall and runoff in the Juan Diaz River basin is not well understood and its fast response due to high rainfall intensities in the area is a concern in the community and authorities. The meteorological and hydrological data in the Juan Diaz River basin are also limited. The main objective of this thesis was José Eduardo Reynolds Puga to establish how well the Juan Diaz River basin can be hydrologically represented by records of the available instrumentation. This was performed with a hydrological, WASMOD, and a statistical model, linear multiple regression. Both models simulated daily and monthly runoff for a period of 21 years. For the long term water balance, a graph showing discharge against rainfall data was plotted in the yearly scale to establish a relationship between the two variables.

Precipitation records from an active meteorological station, which was the closest to the basin from the ones with available records, were used in this study to estimate the areal mean precipitation of the basin, since nowadays there are no active meteorological stations within the basin.

It was not possible to represent the Juan Diaz River basin well with the two models in the daily and monthly resolution. Uncertainties in the precipitation input and in the discharge output data were considered to be the reasons for the poor simulations. That said, it can be stated that the available instrumentation at this point is not sufficient for modeling. In the long term water balance, the instrumentation can be used for water estimations, but care has to be taken if this approach is used since the limited quantity of data in this scale were scattered around the predictions.

Efforts have to be made to encourage decision makers to increase the available instrumentation in the Juan Diaz River basin, in order to make accurate simulations or forecasting that will better support water resources management.

Uppsala universitet, Institutionen för geovetenskaper Examensarbete D, 15 hp i Hydrologi ISSN 1650-6553 Nr 242 Tryckt hos Institutionen för geovetenskaper, Geotryckeriet, Uppsala universitet, Uppsala, 2012. Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 242

Usability of Standard Monitored Rainfall-Runoff Data in Panama, Juan Diaz River Basin

José Eduardo Reynolds Puga

Tryckt hos Institutionen för geovetenskaper, Geotryckeriet, Uppsala universitet, Uppsala, 2012

ABSTRACT

USABILITY OF STANDARD MONITORED RAINFALL‐RUNOFF DATA IN PANAMA, JUAN DIAZ RIVER BASIN.

Reynolds, J., Department of Earth Science, Uppsala University, Villavägen 16, SE−752 36, Uppsala, Sweden.

Water resources demand and natural disasters related to hydro meteorological events have increased the interest in hydrological studies in Panama. Runoff estimations are important for effective water resources management in any catchment, but the limited quantity and quality of the available hydrological and meteorological data in Panama make it hard for researchers to come to conclusive statements that can help in good planning. This issue has to be addressed, but meanwhile, the challenge is to try to understand the hydrological processes occurring in any catchment with the available data.

The relationship between rainfall and runoff in the Juan Diaz River basin is not well understood and its fast response due to high rainfall intensities in the area is a concern in the community and authorities. The meteorological and hydrological data in the Juan Diaz River basin are also limited. The main objective of this thesis was to establish how well the Juan Diaz River basin can be hydrologically represented by records of the available instrumentation. This was performed with a hydrological, WASMOD, and a statistical model, linear multiple regression. Both models simulated daily and monthly runoff for a period of 21 years. For the long term water balance, a graph showing discharge against rainfall data was plotted in the yearly scale to establish a relationship between the two variables.

Keywords: Juan Diaz, WASMOD, Linear Multiple Regression, Available Instrumentation

RESUMEN

USABILIDAD DE REGISTROS TÍPICOS DE LLUVIA‐ESCORRENTÍA MONITOREADOS EN PANAMÁ, CUENCA DEL RÍO JUAN DÍAZ

Reynolds, J., Departamento de Ciencias de las Tierra, Universidad de Uppsala, Villavägen 16, SE−752 36, Uppsala, Suecia.

La demanda de recursos hídricos y la ocurrencia de desastres naturales relacionados con eventos hidro‐meteorologicos han incrementado el interés de estudios hidrológicos en Panamá. Estimaciones de escorrentía son importantes para el manejo efectivo de los recursos hídricos en cualquier cuenca, pero la calidad y cantidad limitada de registros hidrológicos y meteorológicos en Panamá hacen difícil a los investigadores llegar a conclusiones contundentes que puedan ayudar a una buena planificación. Este problema debe ser abordado, pero entretanto, el reto es tratar de entender los procesos hidrológicos que ocurren en las cuencas con los registros disponibles.

La relación lluvia‐escorrentía en la lcuenca de Río Juan Díaz no se entiende completamente y su rápida respuesta debido a las lluvias de alta intensidad en el área es una preocupación en la comunidad y en las autoridades. Los registros meteorológicos e hidrológicos en la cuenca del Río Juan Díaz son limitados. El objetivo principal de esta tesis fue establecer que tan bien se podía representar hidrológicamente la cuenca del Río Juan Díaz con los registros disponibles de la instrumentación existente hoy en día en la misma. Esto se realizo con un modelo hidrológico, WASMOD, y con un modelo estadístico, regresión lineal múltiple. Ambos modelos simularon escorrentía diaria y mensual por un período de 21 años. Para el balance hídrico a largo plazo, se graficaron en la escala anual los datos de caudal contra los datos de precipitación para establecer una relación entre ambas variables.

Registros de precipitación de una estación meteorológica activa, la cual era la más próxima a la cuenca de las estaciones con registros disponibles, fueron utilizados en este estudio para estimar la precipitación promedio areal de la cuenca, dado que hoy en día no hay ninguna estación meteorológica activa dentro de la misma. En la escala diaria y mensual, no fue posible representar bien la cuenca del Río Juan Díaz con los dos métodos seleccionados. Incertidumbres en los datos de entrada y salida fueron consideradas las razones de las pobres simulaciones. Dicho lo anterior, se puede concluir que la instrumentación existente en la cuenca hoy en día no es suficiente para su modelación hidrológica. En el balance hídrico a largo plazo, la instrumentación existente podría usarse pero cuidado debe tenerse si esta aproximación es utilizada ya que la cantidad limitada de datos en esta escala estaba dispersa alrededor de las predicciones.

Esfuerzos tienen que hacerse para alentar a los tomadores de decisiones en Panamá para aumentar la instrumentación existente en la cuenca del Río Juan Díaz, para así poder hacer la misma posible para predicciones que servirán para una mejor planificación de sus recursos.

Palabras Claves: Juan Díaz, WASMOD, Regresión Lineal Múltiple, Instrumentación Existente. REFERAT

ANVÄNDBARHET AV TILLGÄNGLIGA ÖVERVAKNINGSDATA FÖR NEDERBÖRD OCH VATTENFÖRING I JUAN DIAZ‐FLODENS AVRINNINGSOMRÅDE, PANAMA

Reynolds, J., Institutionen för geovetenskaper, Uppsala Universitet, Villavägen 16, 752 36 Uppsala

Behovet av vattenresurser och den höga frekvensen av hydrometeorologiska naturkatastrofer har ökat intresset för hydrologiska studier i Panama. Vattenföringsuppskattningar är viktiga för en effektiv vattenförvaltning i varje avrinningsområde men den begränsande mängden och kvalitén på hydrologiska och meteorologiska data i Panama gör det svårt för forskare att dra meningsfulla slutsatser som underlag för en god vattenförvaltning. Detta problem måste adresseras och under tiden är forskningens utmaning att klarlägga så mycket som möjligt av ett avrinningsområdes hydrologiska egenskaper utifrån tillgängliga data.

Förhållandet mellan nederbörd och avrinning i Juan Diaz‐flodens avrinningsområde är otillräckligt känt och det snabba svaret på intensiv nederbörd i området är ett samhällsproblem. Meteorologiska och hydrologiska data är begränsade i Juan Diaz‐flodens avrinningsområde. Huvudsyftet med detta examensarbete var att fastställa hur väl den hydrologiska regimen i Juan Diaz‐flodens avrinningsområde kunde förstås med tillgängliga data från befintliga mätstationer. Studien genomfördes med hjälp av en hydrologisk modell, WASMOD, och en statistisk modell, linjär multipel regression. Båda modellerna simulerade dagliga och månatliga vattenföringar för en 21‐årsperiod. Avrinningsområdets långsiktiga vattenbalans beräknades med ett diagram där flerårsmedelvärden av vattenföring ritades upp mot flerårsmedelvärden av nederbörd.

Det fanns inga aktiva väderstationer inom avrinningsområdet och nederbördsmätningar från den aktiva väderstation med tillgängliga data som låg närmast användes för att skatta nederbördens arealmedelvärde.

Det gick inte att representera Juan Diaz‐flodens dagliga eller månatliga vattenföringsdynamik på ett tillfredställande sätt med de två modellerna. Osäkerheten hos nederbördsindata och vattenföringsdata för kalibrering ansågs vara orsak till de dåliga simuleringarna. De nuvarande hydrologiska och meteorologiska mätstationerna räcker inte för att modellera denna dynamik. Nuvarande mätdata kan användas för att fastställa avrinningsområdets vattenbalans över flera år men även denna är osäker med stor spridning av värdena.

Det behövs insatser för att övertala beslutsfattare att utöka befintliga mätprogram för Juan Diaz‐ flodens avrinningsområde om vattenförvaltningen inom området skall kunna grundas på tillförlitliga hydrologiska beräkningar.

Nyckelord: Juan Diaz‐floden, WASMOD, linjär multipel regression, befintliga mätstationer

CONTENTS

LIST OF FIGURES...... 1

LIST OF TABLES...... 3

1. INTRODUCTION...... 5

2. STUDY AREA AND METHODS...... 7

2.1. Study Area...... 7

2.1.1. Generalities...... 7

2.2. Literature Review and Methodology...... 9

2.2.1. Description of the Hydrological Model...... 10

2.2.1.1. WASMOD...... 11

2.2.1.2. Input Data...... 11

2.2.1.3. WASMOD Model Structure...... 11

2.2.1.4. Evapotranspiration Losses...... 12

2.2.1.5. Slow Flow Component...... 15

2.2.1.6. Fast Flow Component...... 15

2.2.1.7. Routing Routine of Fast Flow Component...... 16

2.2.1.8. Calculated Runoff and Water Balance...... 16

2.2.2. Linear Multiple Regression Analysis...... 17

2.3. Available Data...... 18

2.3.1. Meteorological Data...... 18

2.3.2. Hydrological Data...... 20

2.3.3. Historical Flood Records...... 23

3. DATA PREPARATION...... 24

3.1. Precipitation...... 24

3.1.1. Quality Control of the Precipitation Data...... 24

3.1.2. Estimation of Missing Precipitation Data...... 26

3.1.3. Double Mass Analysis...... 28

3.1.4. Precipitation as Input Data...... 29

3.2. Potential Evapotranspiration...... 32

3.2.1. Estimation of Missing Pan Evaporation Data...... 32

3.2.2. Quality Control of Potential Evapotranspiration Data...... 32

3.3. Temperature...... 33

3.3.1. Estimation of Missing Temperature Data...... 33

3.4. Relative Humidity...... 33

3.4.1. Estimation of Missing Relative Humidity Data...... 33

3.5. Observed Discharge...... 34

3.5.1. Quality Control of Observed Discharge Data...... 34

3.6. Flood Dates Registered...... 40

3.6.1. Quality Control of the Flood Records...... 40

4. MODEL QUALITY...... 41

4.1. ODWASM Calibration and Quality of the Simulations...... 41

5. RESULTS...... 43

5.1. WASMOD Simulations...... 43

5.2. Linear Multiple Regression...... 47

5.3. Long Term Rainfall‐Runoff Relationship...... 53

6. DISCUSSION...... 54

7. CONCLUSIONS...... 56

ACKNOWLEDGEMENTS...... 57

REFERENCES...... 58

ANNEX A. List of Equations used in this thesis for the WASMOD system (snow free catchment) ...... 61

ANNEX B. Annual Potential Evapotranspiration Map created by ETESA, 1971−2002...... 62

LIST OF FIGURES

Figure 1. Location of the Juan Diaz River Basin (Map Source: ETESA, 1999)…….………………...…7

Figure 2. WASMOD Model Structure for a Snow Free Catchment. Modified from Frevert and Singh (2002)………..……………….………..………………………………….11

Figure 3. Budyco Diagram (Sivapalan, 2001)…………………………………………………………………..……14

Figure 4. Flood Prone Areas due to the Juan Diaz River. Map created with information from documents of ETESA (1999) and SINAPROC (2005)……………………..……20

Figure 5. Location of meteorological and hydrological stations with available records located within and outside the Juan Diaz River basin..…………..……………...... 21

Figure 6. Summary of the available data from the different stations within and outside the Juan Diaz River basin on a yearly time scale……..….………………………..……21

Figure 7. Number of Floods Registered per Year in the Juan Diaz Township….……………..…….23

Figure 8. Double mass plot between precipitation records of the Tocumen meteorological station and the other 6 stations with available records.……….……………..28

Figure 9. Elevation ranges of the Juan Diaz River basin at the discharge station. Map Source: USGS (2011)……………………..…………………………………………………...... …………...30

Figure 10. The long term accumulated precipitation registered (from 1985 till 2000) at meteorological stations with available records versus the elevation in which these are located.……………………………………………..31

Figure 11. Observed Monthly Discharge ‐Juan Diaz and Monthly Precipitation‐Tocumen 1985−2005………………..…………………..……………………….…35

Figure 12. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen Aug−Dec 2005.…………………………………….…………………………………………………………………….…36

Figure 13. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen April−Dec 1991.…………………………………………………………………………………………………………….36

Figure 14. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen Jun−Dec 1986.…………………………………..……………………………..……………………………………….…37

Figure 15. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen. A corresponds to the period between May−Dec 1995. B corresponds to the period between May−Dec 1998. C corresponds to the period between May−Dec 1999….……………………..…………………….…38

Figure 16. Observed Daily Discharge‐Juan Diaz and Daily Precipitation‐Tocumen May−Dec 2003.………………………………………………………………………………………………………….…39

Figure 17. Observed discharge and rainfall recorded during flood dates from 1985 till 2005………..……………………………………………………………………….………………………….…40

Figure 18. Observed versus Calculated Daily Runoff / WASMOD ‐ Juan Diaz. A corresponds to the period between May−Dec 1989. B corresponds to the period between May−Dec 1990. ………..……………………………………...43

Figure 19. Observed versus Calculated Daily Runoff / WASMOD ‐ Juan Diaz. A corresponds to the period between May−Dec 1999. B corresponds to the period between May−Dec 2005……………………………………………….…44

Figure 20. Observed versus Calculated Monthly Runoff / WASMOD ‐ Juan Diaz (1988−2005)…………………………………………………………………………………………………………………45

Figure 21. Observed versus Estimated Daily Runoff / Linear Multiple Regression ‐ Juan Diaz (1999)…………………………..……….……………………...47

Figure 22. Observed versus Estimated Daily Runoff / Linear Multiple Regression ‐ Juan Diaz A corresponds to the period between May−Dec 1986. B corresponds to the period between May−Dec 1995. C corresponds to the period between May−Dec 2005…………………………..……………………..48

Figure 23. Observed versus Estimated Monthly Runoff / Linear Multiple Regression ‐ Juan Diaz (1985−2005)……………………………………………….……………………………………………...50

Figure 24. Observed versus Estimated Daily Runoff / Linear Multiple Regression ‐ Soil Moisture Proxy (total rainfall of the 30 previous days) ‐ Juan Diaz. A corresponds to the period between May−Dec 1986. B corresponds to the period between May−Dec 1989. C corresponds to the period between May−Dec 1998…………………….……………………………52

Figure 25. Observed Yearly Runoff versus Yearly Rainfall Data…………………..………………….……53

LIST OF TABLES

Table 1. Summary of the available daily precipitation records of the meteorological stations located once within the Juan Diaz River basin…….………………….18

Table 2. Summary of the available daily precipitation records of the meteorological stations located in the neighboring basins of the Juan Diaz River basin…………………………………………………………………………………………………….19

Table 3. Distance in kilometers between meteorological and hydrological‐stations…………………………………………………………………………………………………….22

Table 4. Percentage difference between the annual precipitation of the station with the missing record and the annual precipitation of the three closest stations with available data………………………………………………..…………………..27

Table 5. The long term accumulated precipitation registered (from 1985 till 2000) at meteorological stations with available records and the elevation in which these are located…..…………………………………………………………..31

Table 6. Long term runoff coefficient………………….……………………………………………………………...39

Table 7. Best model parameter set obtained from manual calibration……………………..…………42

Table 8. Values of objective functions applied to the calculated runoff by WASMOD from 1985−2005…………………………………..………………………………………….……..46

Table 9. Values of objective functions applied to the estimated runoff by linear multiple regression from 1985 to 2005……..…………………………………………………..49

Table 10. Values of objective functions applied to the estimated runoff by linear multiple regression when an approximation of soil moisture was added as independent variable. Estimation performed on a daily scale from 1985−2005……………………………………………………………………………………………….…51

1. INTRODUCTION

Accurate runoff estimation is one of the biggest challenges (if not the biggest) in hydrological modeling. This information is essential for effective water resources management, e.g., for urban planning, flood risk assessment, water supply, irrigation, long term water balance.

According to the World Meteorological Organization (Arcia, 2006), the country of Panama is one of the nations with small water scarcity problems (second in Central America). It has 52 watersheds and close to 500 rivers (350 flowing to the Pacific coast and 150 flowing to the Caribbean coast). The mean annual volume of water generated by the precipitation events in the whole country is around 224 thousand million cubic meters (ANAM, 2004), but less than 10% is used.

Many sectors in the country, such as hydropower, inter‐oceanic navigation, agriculture and human consumption, are dependent on water resources, but its misuse and lack of protection threaten its availability. According to The National Authority of Environment (ANAM, 2004), Panama has a surface area capable for irrigation of close to 1,870 km2, but due to the uneven spatial and temporal distribution of rainfall, surface runoff for irrigation is only used on 717 km2. This means, that there is a water deficit on almost 62% of the areas capable for irrigation. According to the National Census of 2010 (INEC, 2010), Panama has close to 3.5 million habitants. In 2006, around 11 % of the population of the country lacked drinking water supplies, and only a group of between 27% and 35% got drinking water continuously (Arcia, 2006).

All this is happening in a country that is growing fast, that projects the drinking water demand to double in the next 30 years (ANAM, 2004) and that projects the expansion of the Panama Canal by 2014, which will demand more water in order to permit the traffic of more ships through it.

To complicate matters even more, Panama has one of the highest rainfall intensities in the world (Hoyos, 2011), making it vulnerable to flood events. Panama District, where Panama City (the main city) is located, has close to 450,000 habitants (INEC, 2010) and is experiencing an accelerated expansion. In the whole country, Panama District is considered to be the zone with the highest flood risk (McKay, 2004).

The township with the biggest surface area and with the most habitants living within Panama District is Juan Diaz (36 km2 and close to 100 thousand habitants, according to the National Census of 2010). The flood events that occur in the Juan Diaz Township and in some neighboring townships are mainly caused by an accelerated urbanization growth and planning that is not taking the flood risk into consideration. Next to the principal river of this area, in the lower part of the basin, landfills have been carried out to establish housing projects. This has decreased the hydraulic capacity of the river, increasing the risk for flooding. Previous studies have been made in the Juan Diaz River, mostly focused on 5 hydraulic aspects and frequency analysis of its records. According to some studies, the riverbed can handle runoffs that occur on average every 2.33 to 5 years (CALTEC, 2010; ETESA, 1999).

All of the above have increased the interest in hydrological studies, but the limited quantity (and quality) of the available hydrological and meteorological data makes it hard for researchers to come to conclusive statements that can support good planning.

Back in 1999, ETESA (a Panamanian energy company), in coordination with SINAPROC (National System of Civil Protection), put in practice a system for real time forecasting of floods in the Juan Diaz River basin, in which its meteorological and hydrological network was increased, but due to the regular occurrence of the events and because the system was not solving the problem, stakeholders and participants lost their interest, and presently the records obtained from those stations (nowadays inactive) are not available (or were lost). Despite the system is no longer in practice, a learning feedback should be made of this project in order to apply (or not) the lessons learned from it in any new flood forecasting system that will be implemented in the country.

The issue of limited quantity of data has to be addressed, but meanwhile the challenge is to try to understand the hydrological processes occurring in any catchment with the available data.

The relationship between rainfall and runoff in the Juan Diaz River basin is not well understood, and its fast response due to high rainfall intensities in the area is a concern in the community and authorities, but little efforts have been made to solve this flood problem and to solve the actual and upcoming water supply problem. By understanding the hydrological processes occurring in this basin, plans can be developed for better flood risk management or for better use of this water resource. The main objective of this thesis was to establish how well the Juan Diaz River basin can be hydrologically represented by records of the available instrumentation.

From the main objective, this study had the following specific objectives:

1. To find a relationship between rainfall and runoff from the available data of the basin in the daily and monthly resolution and in the long term. 2. To determine if the available instrumentation is sufficient for modeling.

2. STUDY AREA AND METHODS

2.1. STUDY AREA

2.1.1. Generalities

The Juan Diaz River basin is located south‐east of Panama City (Figure 1). This basin covers a surface area of 120 km2 and drains to the Pacific Ocean. Its main rivver has a length of approximately 24 km. The basin has a rough topography and its elevation ranges from 0 m to 691 m above sea level according to a Diggital Elevation Model with a spatial resolution of 90 m x 90 m that was obtained from the USGS HydroSHEDS data base (USGS, 2011). The Juan Diaz River basin has abrupt changes in elevation from its highest point until it reaches 100 m above sea level, and its longitudinal profile shows slopes in the order of 110% (ETESA, 1999). These characteristics create a lack of storage capacity in the upper part of the basin, which drains runoff faster to the lower part of the basin, with small concentration times generating high instantaneous discharges. In a study made by ETESA (1999), an aveerage speed of the river flow of 1.5 m/s was assumed and with that in mind, the concentration time of the river flow from its highest point till the urban area and till the coast was given as 3.61 and 4.90 hrs, resppectively.

Figure 1. Location of the Juan Diaz River Basin (Map Source: ETESSA, 1999).

Climatologically speaking, Panama has two precipitation regimes, the Pacific regime and the Atlantic regime. These two are mainly caused by the yearly migration of the Intertropical Convergence Zone (ITCZ), by the semi‐permanent anti‐cyclone from the North Atlantic, by Panama's proximity to both the Atlantic and Pacific Oceans, and by the topography of the area, which results in a high spatial variation of the rainfall. These two precipitation regimes are limited by the continental divide. At the same time, two well defined climate seasons are distinguished in Panama: the dry season that begins in January (when the ITCZ is south of Panama) and finishes in April, and the wet season that starts in May (when the ITCZ is moving north of Panama) and finishes in December. When the ITCZ is established, there is a secondary dry season where the rain decreases between July and August. By the end of August, beginning of September, the ITCZ starts moving south generating the rains with the highest intensities of the rainy season. Normally, September and October are the rainiest months (ATIES, 1996; ETESA, 1999).

The Juan Diaz River basin is found in the Pacific regime, where the weather that prevails is arid, and that is characterized by abundant rainfall events normally occurring between the evening and early night time hours. In the Pacific regime, between 85% and 93% of the annual rainfall happens during the wet season (UNESCO, 2008).

The average temperature of the basin is around 27 OC. The minimum and maximum temperatures of the basin are around 24 OC and 32 OC respectively. The average relative humidity of the basin is around 79% (information based on records from 1985 to 2005 belonging to the Tocumen meteorological station. Records provided by ETESA).

Generally, the rainfalls of the basin are convective and orographic. According to ETESA (1999), the annual mean precipitation of the upper part of the basin (above 300 m above sea level) and the lower part of the basin are 3,200 mm/annual and 2,000 mm/annual, respectively. The Cerro Azul meteorological station, once an active station within the Juan Diaz River basin located at an elevation of 660 m above sea level, registered a mean annual precipitation of 4,256 mm from 1976 till 1985 (McKay, 2004), with high records in 1979 (5,065 mm), 1980 (6,861 mm) and 1981 (8,423 mm).

The geology of the basin is variable. The oldest rocks of the basin are of sedimentary origin and are composed of marine sandstone, alluvium, limestone, lavas and shale (ATIES, 1996).

The rocks of the central upper part of the basin are composed of limestone, basalt, lavas, tuffs and agglomerates, while the rocks on the bottom part of the basin are composed of an unconsolidated material and alluviums. In the northwestern and western part of the basin, the "Panama Formation" can be found, which is composed by strata of agglomerates and by andesitic tuffs, inter spread with alluvial conglomerates. The high permeability of the "Panama Formation" makes a high volume of precipitation to drain into the groundwater storage (ATIES, 1996). Meanwhile in the northern and northeastern part of the basin, substrate igneous of lavas and tuffs of basalt and andesite, spaced by bodies of diorites and dacites can be found.

2.2. LITERATURE REVIEW AND METHODOLOGY

Different disciplines, such as hydrology and civil engineering, are interested in the amount of runoff generated in a basin due to a given pattern of precipitation (Cedeño, 1997).

Many studies have been made with the purpose of developing a relation between precipitation, evaporation and runoff, but the variability of many other factors that affect these processes, such as precedent rainfall, soil moisture, infiltration, make it hard to understand the runoff responses to each rainfall event (Cedeño, 1997; Hoyos, 2011).

To establish how well the Juan Diaz River basin can be hydrologically represented by the available data, one hydrological model and a statistical method were applied. Both methods were performed in daily and monthly time steps in an attempt to find a relationship between rainfall and runoff in both resolutions from the available data of the basin. For the long term water balance, a graph showing discharge against rainfall data was also plotted in the yearly scale to establish a relationship between the two variables.

2.2.1. DESCRIPTION OF THE HYDROLOGICAL MODEL

A hydrological model is a simplified version of the processes that take place in a catchment. Unfortunately, most of these hydrological processes are complex and if we plan to understand some of the aspects occurring in a catchment, it is necessary to simplify the description of some of them (Xu, 2010a).

If most of these hydrological processes occurring in a catchment are well understood, the effects or impacts caused by changes can be determined. Another and one of the most important objectives in hydrological modeling is to forecast floods and runoff volumes to asses future spatial and temporal distribution of water resources in a catchment.

There are many hydrological models available, but the choice of the best model depends on the problem, objectives and available data (Haan, 1982).

A conceptual model applies physical laws but in a simplified form (Xu, 2010a). This type of model is mostly used for understanding rainfall‐runoff processes (Hoyos, 2011), and it is also well known for modeling with limited information (Morales, 2010).

In terms of spatial variability of the inputs, outputs, or parameters, lumped models treat the catchment as a homogenous whole. Lumped models use average values of the catchment characteristics that affect the runoff volume. These models are mostly used for flood forecasting, water resources assessment, dam‐reservoir design and operation (Xu, 2010a).

For this study, the Water And Snow balance MODeling system (WASMOD) was chosen. WASMOD is a conceptual lumped model used for streamflow simulations from both snowmelting and rainfall. This model was chosen because it has been used for water balance investigations, as well as for river flow forecasting in countries with widely diverging climates and soil characteristics. Another reason this model was chosen, was because of the flexibility of its equations and its input requirements.

2.2.1.1. WASMOD

The WASMOD system has 3 to 7 parameters, depending on the climatee of the study area. For this study, since the Juan Diaz River basin is characterized by being a snow free catchment, the model will simulate the streamflows generated only from rainfall; therefore only 4 parameters were used.

2.2.1.2. INPUT DATA

The WASMOD system accepts different combinations of daily (or monthly) precipitation, potential evapotranspiration, temperature and relative humidity as input data, along with observed daily (or monthly) discharge ffor calibration. For this study, daily (and monthly) precipitation and potential evapotranspirration were used as input data for the model.

2.2.1.3. WASMOD MODEL STRUCTURE

The scheme of the model for a snow freee catchment is shown in Figuree 2. For this type of catchments, all the precipitation, pt, is rainfall, rt. One part of this rainfall contributes first to the evapotranspiration losses, et. The remainder of rainfall contributes to the soil moisture storage, smt, as active rainfall. Later, the soil moisture storage contributes to evapotranspiration, et, to the fast flow component, ft, and to the slow flow component, st. A routing routine was added to the fast flow component to distribute it in time.

Figure 2. WASMOD Model Structure for a Snow Free Catchment. Modified from Frevert and Singh (2002).

2.2.1.4. EVAPOTRANSPIRATION LOSSES

The actual evapotranspiration losses, et, "describes all the processes by which liquid water at or near the land surface becomes atmospheric water vapor under natural conditions" (Xu, 2010a). The evaporation loss is one of the water‐balance least understood components because of its complex processes and difficulty to measure (Jones, 1997).

The actual evapotranspiration reaches its maximum value when the water supply to plants and soil surface is unlimited. This unlimited water supply is called potential evapotranspiration, ept. This last one is approximately equivalent to the evaporation that will occur from a big surface of water, such as a lake (Cedeño, 1997).

The WASMOD system considers two factors to calculate the actual evapotranspiration losses, et : daily (or monthly) potential evapotranspiration, ept, and the available water, wt, during a day (or a month) t. The actual evapotranspiration is a function of the two factors just mentioned (Frevert and Singh, 2002).

The available water during a day (or month) t is defined by equation (1).

………………………………………………………………...... (1) where wt: available water during a day (or month) t, pt: total rainfall during a day (or month) t, smt‐1: available storage from the previous day (or month) t. It is an approximation of the wetness of the soil. For every time step, this has to be greater than or equal to 0.

The relationship between actual evapotranspiration, et, potential evapotranspiration, ept, and the available water, wt, during a day (or month) t can be better understood by the following statements:

 et increases with ept and wt

 et = 0 when wt = 0 or ept = 0

 et <= ept, and et <= wt

 et = ept when wt = ∞

In this study, potential evapotranspiration was unavailable. In principle, it can be estimated from net radiation, wind, temperature and humidity, or by a measurement that relates the previous variables, such as pan evaporation.

In practice it is very common to estimate lake evaporation by measuring pan evaporation. Pan evaporation consists of measuring the daily difference of the water level from an iron pan, which is positioned around 0.20 m above the ground surface on a small plinth. This pan evaporation measured is higher than the evaporation that occurs from a lake surface. This is 12 caused by radiation and heat changes effects. Pan evaporation has to be adjusted with a correction factor (Cedeño, 1997). This correction factor is not constant in time, and its variation depends on the type of pan, climate and location of the measurement (Jones, 1997). Normally this factor varies from 0.5 and 1.0 (Xu, 2010a), but specific correction factors may have to be found by calibration for any given situation.

The pan used in the country of Panama is the US NWS Class A pan. It consists of a cylinder with a diameter of 1.22 m, and a height of 0.25 m. sFor thi type of pan, the correction factor is between 0.60 and 0.80 (Jones, 1997).

After choosing the correction factor, some long term water balance considerations have to be checked. The long term sum of potential evapotranspiration, Ep, plus the long term sum of the observed discharge, Q, should be larger or much larger than the long term sum of precipitation, P (Xu, 2010a). This is because the long term sum of actual evapotranspiration, E, plus the long term sum of the observed discharge, Q, should be equal to the long term sum of precipitation, P (Sivapalan, 2001); and the long term sum of actual evapotranspiration, E, should be smaller than the long term sum of potential evapotranspiration, Ep (Xu, 2010a). The above can be resumed by the following statements:

 Ep + Q >> P  E + Q = P

 E < Ep

To calculate actual evapotranspiration, the WASMOD system uses two equations. One for energy limited systems and the other for water limited systems. Water limited systems refer to those where the actual evapotranspiration is controlled by the available rainfall in it; it doesn't matter how high the potential evapotranspiration is (Sivapalan, 2001). These systems are characterized by low annual precipitation, by infiltration events that barely wet the vegetation root zone and by transpiration processes limited by the water availability in the soil (Guswa, 2005). Water limited systems are found in arid climates. Energy limited systems are the opposite of water limited systems. In other words, if water is plentiful, then the system is energy limited. Energy limited systems are found in humid climates.

One way to determine if the system is water limited or energy limited is by the Budyko diagram (Figure 3), which represents the ratio of the long term evapotranspiration losses divided by the long term precipitation (E/P) as a function of the long term potential evapotranspiration divided by the long term precipitation (Ep/P). "E/P is a measure of annual water balance", meanwhile "Ep/P is a measure of the climate" (Sivapalan, 2001). Ep/P values above 1 represents water limited systems, while Ep/P values below 1 represents energy limited systems.

Figure 3. Budyco Diagram (Sivapalan, 2001).

In this study, the system is an energy limited system. The equation that WASMOD uses for an energy limited system is defined by equation (2):

, min 1 ,……………………………………...... (2) where a4: is the parameter that determines the actual evapotranspiration lossses. For an energy

limited system, a4 is constrained by 0 <= a4 <= 1. The smaller the value of parameter a4, the greater the actual evapotranspirration losses will be.

2.2.1.5. SLOW FLOW COMPONENT

The slow flow component depends on the available storage in the catchment during the day (or month) t in study. The slow flow component is defined by equation (3):

…………………………………………………………………...... (3) where a5: is a positive parameter, which controls the fraction of the runoff that represents the base

flow. A high value of a5 produces a greater fraction of base flow. The latter is expected to be the case in forest areas and in areas with sandy soil (Frevert and Singh, 2002). b1: is a positive parameter related to the slow flow component. Since this parameter is highly

correlated to a5, it takes standard values (e.g., 0, 0.5, 1 or 2). For arid regions, b1 is fixed to 0.5 or 1.

2.2.1.6. FAST FLOW COMPONENT

The fast flow component depends on the active rainfall, nt, on the soil moisture storage, smt, and on the physical characteristics of the catchment that are reflected in the parameters.

The active rainfall is defined by equation (4):

, 1 ……………………………………………………………...... (4) where rt: is rainfall

The fast flow is defined by equation (5):

………………………………………………………………...... (5) where a6: is a positive parameter, which controls the fraction of the runoff that represents the fast flow. The higher the degree of urbanization, the average basin slope and the drainage

density, then higher the parameter a6 should be. Lower values of this parameter are expected in forest areas (Frevert and Singh, 2002). b2: is a positive parameter related to the fast flow component. Since this parameter is highly

correlated to a6, this one is fixed to 1 or 2.

2.2.1.7. ROUTING ROUTINE OF THE FAST FLOW COMPONENT

A routing routine parameter was introduced to the fast flow component to distribute it in time. This parameter gives a sense of the response time of any basin (Morales, 2010). The routing routine applied in this study is explained by equations (6 to 8) (Westerberg, 2010):

………………………………………………………………………...... (6)

………………………………………………………………………………...... (7)

………………………………………………………………………...... (8) where sct: is the routing storage for the day (or month) t rft: is the routed fast flow component for the day (or month) t

Rf: is a positive parameter, which controls the fraction of the routing storage that represents the direct runoff of a day (or month) t. Rf is constrained by 0 <= Rf <= 1.

2.2.1.8. CALCULATED RUNOFF AND WATER BALANCE

The calculated daily (or monthly) runoff is defined by equation (9):

……………………………………………………………………………...... (9) where dt: calculated runoff for a day (or month) t.

The soil moisture storage at the end of the day (or month) t is updated by the water balance equation (10), which is:

max , 0………………………………………………...... (10)

2.2.2. LINEAR MULTIPLE REGRESSION ANALYSIS

The statistical method used to find a relationship between rainfall and runoff was the linear multiple regression. The general objective of the linear multiple regression is to learn about the relationship between several independent variables and a dependent variable (Xu, 2010b). This method is utilized to predict one variable with the knowledge of others. The linear multiple regression estimates a linear equation of the form:

∗ ∗ ….. ∗ …………………………………………...... (11) where

Y: dependent variable

X1, X2,..Xp: independent variables

A, b1, b2…bp: regression coefficients

The regression coefficients represent the contribution of each independent variable to predict the dependent variable.

The dependent variable was the total (or calculated) runoff, and the independent variables were precipitation, potential evapotranspiration, relative humidity and temperature for a day (or month) t. In this method, the whole data series was used to predict the dependent variable.

Additional linear multiple regressions were performed to study the runoff responses to accumulated rainfall events. In this approach, an approximation of soil moisture was added to the independent variables set to predict the observed discharge records. This approximation of soil moisture for each day t was assumed to be the accumulated value of previous rainfall events (for example: the total rainfall of the previous 3, 5, 10 or 30 days). The whole data series was used in this approach to predict the dependent variable.

2.3. AVAILABLE DATA

2.3.1. METEOROLOGICAL DATA

Back in the beginning of the 70s, until the late 90s, the Juan Diaz River basin used to have two active meteorological stations within it: "Cerro Azul" and "Las Cumbres". Nowadays, there are no active meteorological stations within the basin.

From these two stations, ETESA provided daily precipitation records. A summary of those rainfall records is shown in Table 1.

TABLE 1. Summary of the available daily precipitation records of the meteorological stations located once within the Juan Diaz River basin.

Station Latitude Longitude Elevation Period of Available (m.a.s.l.) Data (years) Cerro Azul 9° 10´ 00" N 79° 25´ 00" W 660 1993−1998 *1 Las Cumbres 9° 05´ 00" N 79° 32´ 00" W 200 1985−1997 *2

ETESA also provided daily precipitation records of other meteorological stations located in neighboring basins: "Hato Pintado*3", "Tocumen*4", "Utive*5", "Loma Bonita*5" and "Altos de Pacora*5", all of which are active stations except the Utive station. A summary of the rainfall records obtained from these five (5) stations is shown in Table 2. All the stations mentioned in this section are (or were) rain gauge stations, where only one daily measurement of the amount of rainfall is (or was) taken on each station at 7:00 a.m.

*1: With missing data in 1995, 1997 and 1998 (92% of the daily data from 1993−1998 were available).

*2: With missing data in 1995 and 1997 (99% of the daily data from 1985−1997 were available).

*3: Belongs to a hydrographical basin located between the Caimito and Juan Diaz Rivers.

*4: Belongs to a hydrographical basin located between the Juan Diaz and Pacora Rivers.

*5: Belongs to the hydrographical basin of the Pacora River.

TABLE 2. Summary of the available daily precipitation records of the meteorological stations located in the neighboring basins of the Juan Diaz River basin.

Station Latitude Longitude Elevation Period of Available (m.a.s.l.) Data (years) Hato Pintado 9° 00´ 00" N 79° 31´ 00" W 45 1987−2003 *1 Tocumen 9° 03´ 56" N 79° 23´ 31" W 14 1985−2005 *2 Utive 9° 09´ 00" N 79° 20´ 00" W 80 1985−1999 *3 Loma Bonita 9° 10´ 00" N 79° 15´ 00" W 100 1985−2003 *4 Altos de Pacora 9° 14´ 44" N 79° 20´ 59" W 850 1985−2002 *5

The Tocumen station is the only active station that measures several types of meteorological parameters. Besides the precipitation records, records of three other parameters were obtained from the Tocumen station for this study: pan evaporation, relative humidity and temperature. The available daily records of these three parameters were from 1985 till 2005.

For every year, at least one daily pan evaporation datum was missing. 93% of the daily pan evaporation data from 1985−2005 of the Tocumen staon were available.

The daily relative humidity records were complete in the years 1985, 1987, 1994 and 1999. For the rest of the years, at least one daily relative humidity record was missing. 97% of the daily relative humidity data from 1985−2005 of the Tocumen staon were available.

In 11 out of the 21 years of available daily temperature data, there was at least one missing datum. 98% of the daily temperature data from 1985−2005 of the Tocumen station were available.

*1: With missing data in 1987 (97% of the daily data from 1987−2003 were available).

*2: Also available in hourly scale from 1986 until 2005.

*3: With missing data in 1989 and 1994 (99% of the daily data from 1985−1999 were available).

*4: With missing data in 1992, 1994, 1997, 2002 and 2003 (96% of the daily data from 1985−2003 were available).

*5: With missing data in 1986, 1987, 1992, 1996, 1997, 1998, 1999, 2001 and 2002 (94% of the daily data from 1985−2002 were available).

2.3.2. HHYDROLOGICAL DATA

Nowadays, there is only one active hydrological station within the Juan Diaz River basin. The location of this station is 9° 03´ 00" N and 79° 26´ 00" W, approximately 117 km downstream from where the Juan Diaz River begins in Cerro Azul and it is situated at less than 1 km upstream from where the flood prone areas begin (Figure 4).

The elevation position of the hydrological station is 8 m above sea level. This station covers 102 km2 (area highlighted in orange in Figure 5), and for this study, this area is referred as the Juan Diaz River basin.

ETESA also provided daily records of thiss station from 1985 till 2005. These daily records had missing data from 1985 till 1987, also in 1994, 1995 and from 2000 till 20005. For this study, 87% of the daily data from 1985 till 2005 were available.

Every daily record corresponds to the average hourly discharge from 00:00 till 24:00 hours of each day.

Figure 4. Flood Prone Areas due to the Juuan Diaz River. The red dot represents the Juan Diaz hydrological station and the light blue areas represent the flood prone areas. Map created with information from documents of ETESA (1999) and SINAPROC (2005).

Figure 5. Location of meteorological and hydrological stations with available records located within and outside the Juan Diaz River basin.

1980 1985 1990 1995 2000 2005 2010 P ‐ Cerro Azul P ‐ Las Cumbres P ‐ Hato Pintado P, Pan Evap, Temp, Hum ‐ Tocumen P ‐ Utive P ‐ Loma Bonita P ‐ Altos de Pacora Q ‐ Juan Diaz

Figure 6. Summary of the available data from the different stations within and outside the Juan Diaz River basin on a yearly time scale.

As it can be seen in Figure 6, the meteorological stations with the shortest and longest records available were Cerro Azul and Tocumen respectively. The latter was the only active station that had the same years of available records as the Juan Diaz station.

TABLE 3. Distance in kilometers between meteorological and hydrological‐stations

Cerro Las Hato Tocumen Utive Loma Altos Juan Azul Cumbres Pintado *2 *1 Bonita de Diaz *1 *1 *1 *1 Pacora *1 *1 Cerro Azul*1 ‐ 17.30 21.41 11.53 9.30 18.33 11.23 13.14 Las 17.30 ‐ 9.83 17.26 24.89 33.67 28.44 13.20 Cumbres*1 Hato 21.41 9.83 ‐ 15.52 26.30 33.60 33.82 10.72 Pintado*1 Tocumen*2 11.53 17.26 15.52 ‐ 11.19 18.05 23.82 4.91 Utive*1 9.30 24.89 26.30 11.19 ‐ 9.20 10.53 15.54 Loma 18.33 33.67 33.60 18.05 9.20 ‐ 14.98 23.01 Bonita*1 Altos de 11.23 28.44 33.82 23.82 10.53 14.98 ‐ 23.32 Pacora*1 Juan Diaz*3 13.14 13.20 10.72 4.91 15.54 23.01 23.32 ‐

From Table 3, it can be seen that the closest meteorological station to the Juan Diaz hydrological station is the Tocumen station (4.91 km).

*1: Rain gauge station.

*2: Meteorological station, which measures several types of meteorological parameters.

*3: Discharge station.

2.3.3. HISTORICAL FLOOD RECORDS

The historical flood records of the Juan Diaz Township were obtained from the SINAPROC data‐base. As a complement of the SINAPROC records, additional flood days were added according to other documents of ETESA and other articles (McKay, 2004), where the last had flood dates that are not registered in the first one.

The historical flood records are from 1978 till 2009. In that period, there were 56 flood events recorded in the Juan Diaz Township. From those 56 events, 6 were recorded from 1978 till 1990, 27 were recorded from 1993 till 2000, and 23 were recorded from 2004 till 2009. At first sight of Figure 7, it can be stated that the flood records are incomplete because there are few events before 1990 (this could be attributed to the fact that SINAPROC started to work as an entity at the beginnings of the 80s), additional to the last, there are no flood events in 1991, 1992, 1994, 1999 and from 2001 till 2003. For this thesis, the flood records of interest were from 1985 till 2005.

6 Registered 5 Floods 4 of

3 Number

0 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Time in Years

Figure 7. Number of Floods Registered per Year in the Juan Diaz Township

3. DATA PREPARATION

Uncertainties in any model prediction result from errors in input data, errors in output data (data for model calibration), errors in parameters, and errors in model structure (Xu, 2010a; Refsgaard and Storm, 1996).

One way to reduce errors in the input and output data is by performing quality control to the available data.

3.1. PRECIPITATION

Precipitation is the largest quantity in the hydrological cycle (Xu, 2010a). Previous studies have shown that errors in precipitation data are more (if not the most) important than errors in other input variables (Westerberg, 2009).

3.1.1. QUALITY CONTROL OF THE PRECIPITATION DATA

Quality control of the precipitation data started with a visual data inspection along with some considerations for each case.

All the daily precipitation records were plotted to identify extreme rainfall events (daily values greater than 100 mm), as well as the monthly precipitation records were plotted to identify seasonality.

For extreme rainfall events recorded in each station, some considerations were taken in order to consider if those events actually happened. First, the average precipitation of the 3 closest stations to the one who recorded the extreme rainfall on that day was calculated. If the average precipitation of that day from these three stations was below 20 mm, the extreme rainfall event was removed. This was the consideration with the highest weight to remove extreme rainfall events.

Another consideration taken to check extreme rainfall events was to check if there was any precipitation registered (on the same station) in previous days to this extreme event, as well as the day of the week in which this event occurred (e.g., Monday, Tuesday, ...Sunday). This was done to check if the extreme rainfall event registered on that day was not an accumulation of rainfall events that occurred in previous days (e.g., it could be the case that the observer was absent to register the precipitation records for various days, and when the observer came back to register the rainfall records, the observer could have registered for one day the accumulated precipitation of the previous days when he or she was absent). For this study, all the cases when the extreme rainfall event had no precipitation on the previous days, the average precipitation of the three closest stations to the one who recorded the extreme rainfall event was above 20 mm, therefore no extreme rainfall event was removed due to this consideration.

Frequency of recurrence for every month was also checked. Values were flagged if there were more than 10 values (or integer numbers) repeated within a month, which is highly unlikely.

Sequence dry days longer than eight (8) were checked if they happened during the rainy season.

Quality control was more extensive for the Tocumen meteorological station since hourly records were also available. For effects of comparison, for every day a daily precipitation value was calculated by doing the sum of the hourly precipitation records from 00:00 till 24:00.

When the accumulated hourly precipitation record (AHPR) was different to the observed daily precipitation record (ODPR) of any given day, some considerations were taken to choose one or the other.

Rounding errors were found in some days when comparing the AHPR to the ODPR (e.g., on one case the ODPR was 10.8 mm and the AHPR was 1.8 mm). This type of errors may be cause by incorrectly readings of the glasses. In these cases, the AHPR were chosen.

There were days where the ODPR was lower than the AHPR, but not by a significance amount (e.g., on one case the ODPR was 3.7 mm and the AHPR was 4.3 mm). This could be explained by imprecise measurements due to water spillage, wetting, evaporation or imperfections on the equipment. In these cases, the AHPR were also chosen.

There were sequences of days in which the ODPR and the AHPR did not match, but when comparing the accumulated precipitation of both during those days, both sums were the same (or very close). This could be the case that the observer was absent to register the daily records for some days and he (or she) distributed what he read on the day he came back in the days he was absent. In these cases, the AHPR were also chosen.

There were days where the ODPR was too high compared to the AHPR, or vice versa (e.g., on one case the ODPR was 48.2 mm and the AHPR was 0.00 mm). In these cases, a comparison with the records of the other meteorological stations was performed on those days (similar to the one done to check if the extreme rainfall events happened). If the precipitation records of the other meteorological stations in that given day were considerably high (above 20 mm in average), then the highest value between the ODPR and the AHPR was chosen; if not, then the elowest on was chosen. The days, in which there was not a clear pattern in which value to choose, were flagged.

3.1.2. ESTIMATION OF MISSING PRECIPITATION DATA

In addition to the errors mentioned above, missing data in the precipitation records also had to be dealt with (see Tables 1 and 2); because of the absence of observer or due to technical problems of the equipment.

To estimate missing and removed precipitation data (during the quality control), the Arithmetic Mean Method with a correction factor was used. This method consists of the simple arithmetic mean of the daily precipitation records of the three closest stations (with available records) to the one where the record is missing, plus a correction factor. This correction factor was used when the annual precipitation of at least one of these three stations differed more than 10% from the annual precipitation of the station with the missing record (Cedeño, 1997). As it can be seen in Table 4, the previous was the case for all the years. The Arithmetic Mean Method with a correction factor used in this study is defined by equation (12).

...... (12) where

P: estimated daily precipitation of the station with the missing record.

Pa, Pb, Pc: daily precipitation of the three closest stations to the one where the daily precipitation record is missing.

N: Annual accumulated precipitation of the station with the missing record(s). When more than the half of the records in a year was missing, the value of N was estimated. First, an annual average was estimated with the annual records of this station that had no missing data. The percentage of contribution by every month to calculate this annual average was estimated as well. The value of N used in a given month to estimate its missing daily record(s), for a year that had more than half of its records missing, was assumed to be the annual average (estimated previously) minus the percentage contributed by this month (when their records were complete).

Na, Nb, Nc: Annual accumulated precipitation of the three closest stations to the one where the record is missing. For every case, the three stations chosen had no missing data in that year.

As it can be seen in Figure 6, because of the small numbers of stations with available records after the year 2000 (4 stations in 2001 and 2002, 3 in 2003, 2 in 2004 and 1 in 2005), it was decided to only fill the missing records for every station from 1985 till 2000.

TABLE 4. Percentage difference between the annual precipitation of the statiion with the missing record and the annual precipitation of the three closest stations with available data *1

*1: For every station with missing precipitation data (these are shown in the second column for every year), tthe values highlighted in bold in each row represent the 3 stations used for each case to estimate the missing precipitatiion data.

3.1.3. DDOUBLE MASS ANALYSIS

After filling the missing precipitation reccords, double mass analysis was used to check the consistency of the rainfall data. This method is based on the fact thaat the accumulated average precipitation of certain number of stations is not sensitive to the changes of one individual station because their errors compensate each other; meanwhile the accumulated precipitation of one station is sensitive to the changes that occur to this (Cedeño, 1997). Changes can be understood as a change in the location of the innstrument, type of instrument, method of observation.

A straight line was obtained when plotting the annual accumulated preccipitation for every station against the annual accumulated average precipitation of the other stations (e.g. double mass plot of the Tocumen station shown in Figure 8). Since the previous was the case for every station, it can be said that the records of each station were obtained by the same conditions. If a straight line was not obtained in the double mass plot of aany of the stations, then the changes in slope should have been adjusted.

Figure 8. Double mass plot between precipittation records of the Tocumen meteorological station and the other 6 stations with availabble records.

3.1.4. PRECIPITATION AS INPUT DATA

The precipitation input data for the models have to be introduced as an areal mean precipitation. Errors in areal mean precipitation are due to the high spatial and temporal variability of precipitation (Xu, 2010a). This spatial variability can be explained in part due to the orographic effect of the topographic characteristics of any catchment, since at higher elevations rainfall intensity tends to be higher than at lower elevations (Hoyos, 2011; Goovaerts, 1999).

In small catchments, one rain gage may produce sufficient information for long term water balance forecasting (Hoyos, 2011; Xu, 2010a). A very dense network of rain gauges is necessary for an accurate estimation of the spatial and temporal distribution of rainfall in a catchment, as well as for accurate runoff estimations (Goovaerts, 1999). Records from a network of rain gauges are useful for estimating flood peaks or for determining the spatial variability of runoff production from individual events (Xu, 2010a).

For this study, only one station was used for estimating the areal mean precipitation of the Juan Diaz River basin. The Tocumen meteorological station was chosen because it is an active station, being the closest to the basin, and because its available records matched with the observed discharge records of the hydrological station (from 1985 till 2005). Since this station is located at an elevation of 14 m above sea level and at higher elevations rainfall intensities are expected to be higher, the precipitation records of the Tocumen station had to be adjusted with an elevation factor to get an estimation of the long term rainfall at the average elevation of the basin at the discharge station.

The average elevation of the Juan Diaz River basin upstream the discharge station is 171 meters above sea level. This elevation was calculated with equation (13) (Monsalve Sáenz, 1999).

∑ ∗ ...... (13) ∑ where n: corresponds to the total numbers of cells that integrates the basin in the Digital Elevation Model. Every cell dimension of the Digital Elevation Model available was 90 m x 90 m.

"Area i": corresponds to the area of each cell that integrates the basin, for this case every cell had an area of 0.0081 km2.

As it can be seen in Figure 9, the Juan Diaz River basin has two large contributories, one that comes from the north and one that comes from the west.

Figure 9. Elevation ranges of the Juan Diaz River basin at the discharge station (plant view is shown on top; 3D view is shown below). Dimensions in the color bar and in the axes "x" and "y" are in meters. Map Source: USGS (20011).

To obtain the elevation factor a graph showing the long term accumulated precipitation registered on all the stations (from 1985 till 2000) versus the elevation in which these are located was plotted (the previous data of each station are shown in Tabble 5). As it can be seen in Figure 10, a curve was then fitted to the data to find a relationship between precipitation and elevation. For this plot, Las Cumbres station was omitted for better fit of the curve with the data.

TABLE 5. The long term accumulated precipitation registered (from 1985 till 2000) at meteorological stations with available records and the elevation in which these are located.

Name of Station Accumulated Precipitation Elevvaation 1985−2000 (mm) (m above sea level) Hato Pintado 31,955 45 Tocummen 28,435 14 Cerro Azul 47,738 6660 Las Cumbres 35,253 2200 Utive 40,798 80 Loma Bonita 42,307 100 Altos de Pacora 57,146 8850

Figure 10. The long term accumulated precipitation registered (from 1985 till 2000) at meteorological stations with available records versus the elevation in which these are located.

From Figure 10 (or by using the equation derived from the fitted curve), an estimation of the long term precipitation was calculated at the average elevation of the upper part of the basin. The elevation factor results from the division of the long term estimated precipitation at the average elevation of the upper part of the basin and the long term accumulated precipitation at the Tocumen station. For this study, the elevation factor was 1.54.

3.2. POTENTIAL EVAPOTRANSPIRATION

The pan evaporation records of the Tocumen meteorological station were used as the potential evapotranspiration data with a correction factor. But first, the missing data in the pan evaporation records had to be filled.

3.2.1. ESTIMATION OF MISSING PAN EVAPORATION DATA

The pan evaporation records of the Tocumen station had at least one missing daily datum in every year of the series. Most of the missing gaps (91% of the missing data) were 1 to 4 days long. There were only 3 gaps longer than 5 days. One was a 6−day gap (from 22−Dec−89 to 27−Dec−89), another was a 15−day gap (from 28−Sep−02 to 12−Oct−02), and the last one was a 28−day gap (from 21−Sep−93 to 18−Oct−93).

For all these gaps, the pan evaporation missing records were estimated by doing linear interpolation between the value before and after each gap. After all the missing data were filled, the average pan evaporation was calculated for the months where the longest missing gaps were filled, and then compared to the long term monthly average pan evaporation in which those longs gap happened. For example, the 28−day gap occurred between September and October, after filling that gap, then the average pan evaporation of those two months in particular (with estimated values) were compared with the long term average pan evaporation of September and October. The monthly average pan evaporation of the two longest gaps was similar to the long term monthly average pan evaporation in which these gaps occurred.

3.2.2. QUALITY CONTROL OF POTENTIAL EVAPOTRANSPIRATION DATA

The correction factor used for this study was set to 1 in order to satisfy the long term water balance condition (EP + Q >> P).

As a comparison, the annual average of the estimated potential evapotranspiration was compared to the annual average potential evapotranspiration map of Panama created by ETESA (UNESCO, 2008). See the previous map in ANNEX B.

The annual average of the estimated potential evapotranspiration in this study was 1,589 mm (from 1985 to 2005) and the annual average from the potential evapotranspiration map was 1,388 mm (from 1971 to 2002). Although these two differed approximately 15%, the correction factor was considered to be good enough for modeling since the long term water balance condition was satisfied with the value chosen.

3.3. TEMPERATURE

The temperature records of the Tocumen meteorological station were used as a reference of the temperature of the Juan Diaz River basin. No modification was made to the available temperature records. These records also had missing data which had to be filled.

3.3.1. ESTIMATION OF MISSING TEMPERATURE DATA

There were 4 gaps of missing data longer than 6 days: a 61−day gap (from 01−May−94 to 30−June−94), a 59−day gap (from 01−Jan−94 to 28−Feb−94), a 14−day gap (from 29−Sep−02 to 12−Oct−02), and an 8−day gap (from 23−Nov−03 to 30−Nov−03). These 4 gaps represented 80% of the missing data.

All the missing data from 1994 till 1999, including the two longest gaps were filled using the atmospheric data‐base of the International Research Institute for Climate and Society (IRI, 2011). The following two longer gaps (the one with 14− and the one with 8−day gap) were filled using the Wunderground data‐base (Wunderground, 2011). Both data‐bases have Tocumen as a reference.

For all the other gaps, the missing temperature records were estimated by doing linear interpolation between the value before and after each gap.

3.4. RELATIVE HUMIDITY

The relative humidity records of the Tocumen meteorological station were used as a reference of the relative humidity of the Juan Diaz River basin. No modification was made to the available relative humidity records. These records also had missing data which had to be filled.

3.4.1. ESTIMATION OF MISSING RELATIVE HUMIDITY DATA

There were 5 gaps of missing data longer than 5 days: a 30−day gap (from 01−April−88 to 30−April−88), two 27−day gaps (from 05−Jan−92 to 31−Jan−92, and from 01−Mar−93 to 27−Mar−93), a 14−day gap (from 29−Sep−02 to 12−Oct−02), and an 8−day gap (from 23−Nov−03 to 30−Nov−03). These 5 gaps represented 54% of the missing data.

For the three longest gaps in the relative humidity records (the one of 30 and the two of 27 days), there were no data‐base found to fill their missing values. All the missing data from 1996 till 2005 were filled using the Wunderground data‐base, including the following two longer gaps (the one of 14 and the one of 8 days).

Besides the three longest gaps, which could not be filled, most of the missing data before 1996 were 1− to 3−day gaps. These last were estimated by doing linear interpolation between the value before and after each gap.

3.5. OBSERVED DISCHARGE

There is high uncertainty in every observed discharge record, since these are based on water level measurements taken in river cross sections that change in time due to erosion and sedimentation processes (Westerberg, 2008).

The available observed discharge records also had missing data, but for this study those values were not filled. Since it is not known how uncertain the available data is, applying methods such as linear interpolation will make the records more uncertain. Even though the missing data was not filled, some quality control was made of the available discharge records.

The original unit of the observed daily discharge records was volume per time (m3/s). This was transformed to runoff (mm) by using the area of the Juan Diaz River basin upstream of the discharge station (102 km2).

3.5.1. QUALITY CONTROL OF OBSERVED DISCHARGE DATA

Quality control of the discharge records in this study started with a visual data inspection.

Observed monthly discharge records were plotted to identify seasonality (Figure 11). From this plot, the observed monthly discharge records from August−2005 ll December−2005 were flagged and checked on the daily time scale because these discharge records were high compared to previous years. As it can be seen in Figure 12, the daily data from August−2005 till December−2005 besides being high values, no pattern could be found. This uncommon behavior during this period was expected to cause difficulties in the simulations.

The precipitation values shown in Figures 11 to 17 and in Figure 25 correspond to the adjusted precipitation values obtained in Section 3.1.4. The observed discharge values shown in Figures 11 to 25 correspond to the transformed runoff records in Section 3.5.

2005. − 1985 bars)

(red

‐ Tocumen Precipitation Monthly and

line)

blue

(dark

Diaz

Juan ‐ Discharge

Monthly Observed

11. Figure

Figure 12. Observed Daily Discharge‐Juan Diaz (dark blue line) and Daily Preecipitation‐Tocumen (red bars) Aug−Dec 2005. The maximum precipitaon and observed discharge values in this figure were fixed to 100 mm, even though there were higher values than the previous mention.

Frequently occurring values were found and flagged on the daily scalee. For example, the runoff value 11.16 mm was repeated cconsecutively from 01−Oct−91 ll 23−Dec−91 (see purple dashed circle in Figure 13).

Figure 13. Observed Daily Discharge‐Juan Diaz (dark blue line) and Daily Preecipitation‐Tocumen (red bars) April−Dec 1991. The purple dashed circle represents a frequent occurring value. The maximum precipitation and observed discharge values in this figure werre fixed to 100 mm, even though there were higher values than the previous mention.

Zero values were also found and removed from the series. For example, there were 17 consecutive zero values from 27−Jul−86 ll 12−Aug−86 (see orange circle iin Figure 14). These zero values were very unlikely because most of them occurred during the rainy season.

Figure 14. Observed Daily Discharge‐Juan Diaz (dark blue line) and Daily Preecipitation‐Tocumen (red bars) Jun−Dec 1986. The orange circle represents a long series oof zero values. The maximum precipitation and observed discharge values in this figure werre fixed to 100 mm, even though there were higher values than the previous mention.

Quality control of the observed discharge data was followed by a visual inspection comparing the daily runoff responses to the daily rainfall pulses.

During the rainfall‐runoff comparison some inconsistencies such as low observed discharge records compared to rainfall events and no discharge responses to rainnfall pulses or vice versa were found as it can be seen in Figures 15 and 16. In addition to the latter, cases were found in which the discharge was decreasing even thought there was a rainfall pulse. These irregular cases were flagged but not removed from the data, even though they may cause difficulties in the simulations. This decisiion was taken because it is not known if the records are good or not, it will be subjective to discredit the records by applying just visual inspection.

Figure 15. Observed Daily Discharge‐Juan Diaz (dark blue lines) and Daily Preecipitation‐Tocumen (red bars). The green circles represent inconsistencies found in the rainfall‐runoff comparison. A coorresponds to the period between May−Dec 1995. B corresponds to the period between May−Dec 1998. C corresponds to the period between May−Dec 1999. The maximum precipitation and observed discharge values in this figure were fixed to 100 mm, even though there were higher values than the previous mention.

Figure 16. Observed Daily Discharge‐Juan Diaz (dark blue line) and Daily Preecipitation‐Tocumen (red bars) May−Dec 2003. The green circles represent inconsistencies found in the rainfall‐ runoff comparison. The maximum precipitation and observed discharge values in this figure were fixed to 100 mm, even though there were higher values than the prevvious mention.

After the previous cases were flagged, the runoff coefficient was checked. The runoff coefficient results from the division between long‐term observed discharge and long term precipitation (Q/P). This coefficient is expected to be below 1 due to the long term evapotranspiration losses. As is shown in Table 6, the runoff coefficient for all the data was 0.66, calculated as the sum of all the days in which there was an observed discharge record for the 21 years of available records. When calculating the runoff coefficient for every year, by doing the sum of all the days in which there was an observed discharge record for each year, all the years obtained a runoff coefffficient below to 1, except for the year 2005.

Even though strange rainfall and runoff behaviors were found, these data were used for modeling from 1985 till 2005 to determine how well the Juan Diaz River basin can be hydrologically represented by records of the available instrumentation.

TABLE 6. Long term runoff coefficient.

Runoff Runoff Runoff Runoff YEAR YEAR YEAR YEAR Coefficient Coefficient Coefficient Coefficient 1985 0.52 1991 0.887 1997 0.51 2003 0.51 1986 0.69 1992 0.663 1998 0.58 2004 0.47 1987 0.78 1993 0.72 1999 0.59 2005 1.41 1988 0.64 1994 0.662 2000 0.68 ALL 1989 0.73 1995 0.54 2001 0.47 THE 0.66 1990 0.70 1996 0.664 2002 0.68 DAATTA

3.6. FLOOD DATES REGISTERED

The available historical flood records of the Juan Diaz Township are not complete, as it was shown in Section 2.3.3. From 1985 till 2005 there are 31 floods registered, but it is not known to what extend these records are correct.

3.6.1. QUALITY CONTROL OF THE FFLOOD RECORDS

First, the observed discharge and rainfaall recorded on the flood dates were plotted. The observed discharge data are daily averages and not daily maxima. In four of the floods registered, there was no observed discharge recorded, perhaps due to its magnitude.

According to the flood dates, there were flood events in days when there was little or no precipitation registered, as well as in days when there was a low observed discharge registered (see green circle in Figure 17), which is unlikely. Also low observed discharge values (below 20 mm) were found registered during the flood dates inn which there were precipitation values registered above 45 mm (see purple square in Fiigure 17), which is unlikely as well.

Figure 17. Observed discharge and rainfall recorded during flood dates from 1985 till 2005 (blue dots). Green circle represents flood events registered with low precipitation and low discharge recorded. Purple square represents flood events registered with low discharge recorded and high precipitation recorded.

4. MODEL QUALITY

Two performance measures (the Nash‐Sutcliffe model efficiency coefficient and the coefficient of determination) were used to assess the quality of the hydrological and statistical simulations.

4.1. WASMOD CALIBRATION AND QUALITY OF THE SIMULATIONS

To assess the quality of any hydrological model, first its parameters have to be calibrated. Calibration consists of the search for the "best" parameter set, which is the set that gives the best fit between the observed and calculated runoff (Xu, 2010a).

The WASMOD calibration was performed manually and subjectively by changing the parameter sets until most of the peak flows in the observed hydrograph were matched. How much we can trust from a simulation depends on how well it reproduces the observations. The calibration period, as well as the simulation period, was from 1985 till 2005.

Two objective functions were used to determine the quality of the simulations. One of the objective functions was the Nash‐Sutcliffe model efficiency coefficient. This coefficient is "one of the most widely used performance measures in hydrology" (Westerberg, 2010). The Nash‐Sutcliffe coefficient is defined by equation (14):

∑ 1 …………………………………………………………………...... (14) ∑ where

R2: Nash‐Sutcliffe coefficient qt: observed discharge for a day (or month) t. dt: calculated runoff for a day (or month) t.

: mean observed discharge

The Nash‐Sutcliffe coefficient compares the residual variance (described by the numerator) to the initial variance (described by the denominator). This coefficient can range from ‐∞ to 1. An efficiency of 1 indicates a perfect fit between the observed and the calculated runoff. An efficiency of 0 indicates that the calculated runoff is as accurate as the mean observed discharge. Efficiency values below 0 indicate that the mean observed discharge is a better predictor than the calculated runoff (Nash and Sutcliffe, 1970).

The other objective function used to determine the quality of the simulations was the coefficient of determination, R2. This coefficient ranges from 0 to 1. When this is expressed as a percentage, it represents the ratio that can be predicted by the regression line (Xu, 2010b). The coefficient of determination, R2, is defined by equation (15):

∑ ……………………………………...... (15) ∑ where

: are the observations of the dependent variable : is the mean of the dependent variable

: are the predicted values of the dependent variable For every WASMOD simulation, both objective functions were calculateed with all the data left after the warm up period. The warm up periods for the daily and monthly simulations were 365 days and 36 months respectively.

Table 7 shows the best model parameter set obtained from the manuall calibration for the daily and monthly simulations. b1 was ttried for 0, 0.5, 1 and 2. Since the Juan Diaz River basin is located in an arid region, the best results were obtained when b1 was fixed to 0 or 0.5 (see Sectiion 2.2.1.5). b2 was tried with 1 and 2, and the best results were obtained when b2 was fixed to 1. Also, the best model results were obtained when a6 was closed to zero, this could be reasonable since the upper part of the basin is a forest area (see Section 2.2.1.6).

TABLE 7. Best model parametter set obtained from manual calibration.

*1: For an energy limited system, a4 is constrained by 0 <= a4 <= 1.

In an attempt to improve the model quality in the daily simulations, both objective functions were estimated again, using the averages of 3, 5, 10 and 30 days of observed and calculated runoff.

5. RESULTS

5.1. WASMOD SIMULATIONS

No good representation of the observed discharge records was found in the daily and monthly resolution. In both there were underestimation and overestimation of peaks.

On the daily scale, all the observed peaaks above 32 mm were underestiimated. 50% of the observed daily discharge records below 32 mm were underestimated. The observed daily discharge records from 1985 till 2005 ranged from almost 0 to 214 mm. The calculated daily runoff ranged in the same period from 0 to 49 mm. The observed daily discharge records above 50 mm represented less than 0.35% of the available records of thhe rainy season. For every year, at some point during the dry season the calculated daily runoff was zero. For most of the years, when referring to residuals, the month best simulated during the dry season was April. When referring to residduals, the best simulations of the rainy season were in the first 5 years of simulations, especially in the month of December, as is shown in Figure 18.

Figure 188. Observed (red line) versus Calculated (dark blue line) Daily Runoff / WASMOD ‐ Juan Diaz. A corresponds to the period between May−Dec 1989. B corresponds to the period between May−Dec 1990. 43

After the first five years of simulation, the best fits of the rainy season occcurred randomly at the begginning or at the middle of it.

In general, for most of the years the dry season was underestimated from February till April. From 1986 till 1995, during the first months of the rainy season, the obbserved daily runoff was mostly underestimated until July. During the previous months, for most of the years after 1995, the observed daily runoff was overestimated. From September till November, the observed daily runoff was mostly underestimated. During December and January, for most of the years the observed runoff was overestimated.

As is shown in Figures 18 and 19, the general perception is that the daily simulation produced a poor fit since the biggest peaks were not well simulated. As expected, the simulatiions from August−2005 ll December−2005 shown in Figure 19.B were poor. Almost all the observed discharge data registered during that period were underestimated because of its irregular behavior (see Section 3.5.11).

Figure 199. Observed (red line) versus Calculated (dark blue line) Daily Runoff / WASMOD ‐ Juan Diaz. A corresponds to the period between May−Dec 1999. B corresponds to the period between May−Dec 2005. 44

2005). − (1988

Diaz

‐ Juan WASMOD

Runoff Monthly

line)

blue

(dark

Calculated

versus

line)

(red Observed

20. Figure

On the monthly scale, there were also overestimations and underestimations. The observed monthly discharge records from 1985 till 2005 ranged from 15 mm to 764 mm. In these records, 5 months were above 500 mm, all underestimated. Of those 5, 4 were found in 2005 (from August till November). The calculated monthly runoff by WASMOD ranged from 0 to 499 mm in the same period. Most of the calculated monthly runoff data above 400 mm were overestimations, except one. During the dry and rainy season, the months best simulated for most of the years, when referring to residuals, were April and December, respectively. As it can be seen in Figure 20, WASMOD had difficulties to simulate most of the peak values in every rainy season, less in 1988, 1989, 1992 and 1996.

TABLE 8. Values of objective functions applied to the calculated runoff by WASMOD from 1985−2005.

Input Calibration Time Objective 1 day 3−day 5−day 10−day 30−day Data Data Scale Function average average average average average Nash‐ 0.296 0.402 0.442 0.486 0.551 Daily Sutcliffe Juan_Diaz 2 Tocumen R 0.302 0.410 0.451 0.498 0.564 (Observed (p , ep ) Nash‐ t t Discharge) 0.554 ‐ ‐ ‐ ‐ Monthly Sutcliffe R2 0.560 ‐ ‐ ‐ ‐

The values of the objective functions in Table 8 indicate that the WASMOD simulations poorly represented the Juan Diaz River basin with the records of the available instrumentation. Both objective functions were low on the daily scale. On the monthly scale, the basin was better represented, but still poor. These results confirm what was shown graphically; no perfect fit was achieved.

Both objective functions estimated for the 3, 5, 10 and 30 days averages of the observed and calculated runoff (referring to the ones shown in Table 8) are the best results obtained for every case, but each case was not estimated by averaging the "best" single daily simulation (referring to the one calculated with the parameters shown in Table 7). In other words, more single daily simulations were performed with different parameter sets; from these single daily simulations, many series of n−days average were obtained, and for each series the objective functions were calculated. From all the single daily simulations, the best objective functions for every case were not obtained by averaging the "best" single daily simulation.

When comparing the values of the objective functions resulting from the 30−day averages of the observed and calculated runoff to the ones obtained in the monthly simulation, similar results were obtained.

5.2. LINEAR MULTIPLE REGRESSION

Many combinations of independent variables, such as precipitation, potential evapotranspiration, humidity and temperature, were used to prediict the dependent variable, the total runoff. None of thesse combinations gave a good representation of the observed daily and monthly runoff. In both cases there were underestimations and overestimations of the peaks.

The set of independent variables that gaave the best fit using the linear mmultiple regression consisted of precipitation, potential evappotranspiration, temperature and relative humidity. Since some of the independent variables used in this approach did not dirrectly affect runoff, the predictions took a cardiogram behavior as shown in Figure 21, even when there were no rainfall pulses.

Figure 21. Observed (red line) veersus Estimated (dark blue line) Daily Runoff / Linear Multiple Regression ‐ Juan Diaz (1999).

On the daily scale, all the observed peaaks above 24 mm were underestiimated. 65% of the observed discharge records below 24 mm were overestimated. The estimated daily runoff by linear multiple regression, ranged from 0 to 37 mm from 1985 to 2005. The observed daily discharge records above 37 mm represented less than 1% of the available records of the rainy season. When referring to residuals, there was not a clear pattern of which was the best month simulated during the rainy season, this was randomly at the middle or at the end of it (e..g. Figures 22.A and 22.B). For most of the years, all the dry season and the first months of the rainy season (until August) were overestimated. Then frrom September till November, most of the observations were underestimated. During December, the observations were half overestimated and half underestimated.

Figure 22. Observed (red line) versus Estimated (dark blue line) Daily Runoff / Linear Multiple Regression ‐ Juan Diaz A corresponds to the period between May−Dec 1986. B corresponds to the period between May−Dec 1995. C corresponds to the period between May−Dec 2005.

Similar to the WASMOD simulation, the multiple regression estimation from August−2005 ll December−2005 (shown in Figure 22.C) did not give good results becaause of the strange behavior of the observations during that period.

As is shown in Figures 21 and 22, the general perception of the estimaated daily runoff by linear multiple regression is that it was poor since it could not well represent the highest peaks of the observed discharge in the whole series.

On the monthly scale, there were also overestimations and underestimations. Similar to the WASMOD simulation, from the 5 months above 500 mm in the observed discharge series, all were underestimated. The estimated monthly runoff using linear multiple regression ranged from 0 to 397 mm from 1985 to 2005. All estimated monthly runoff data above 330 mm were overestimations of the observed discharge. As it can be seen in Figure 23, the best fits, when referring to residuals, occurred at the end of the rainy season and at the beginning of the dry season. Still, during the dry and rainy season from year to year; there was not a single month, in which it could be said that it was the best estimated; the month best estimated in both seasons varied randomly. For every rainy season, almost every peak value was poorly estimated, less in 1992 and 1997.

TABLE 9. Values of objective functions applied to the estimated runoff by linear multiple regression from 1985 to 2005.

Input Calibration Time Objective 1 day 3−day 5−day 10−day 30−day Data Data Scale Function average average average average average Nash‐ 0.228 0.307 0.327 0.341 0.353 Sutcliffe Daily Tocumen 2 Juan_Diaz R 0.228 0.314 0.340 0.365 0.379 (p , t (Observed ept, Temp, Nash‐ Discharge) 0.526 ‐ ‐ ‐ ‐ Rel. Hum.) Sutcliffe Monthly R2 0.519 ‐ ‐ ‐ ‐

The results of the objective functions in Table 9, indicate that the linear multiple regression estimations also poorly represented the Juan Diaz River basin with the records of the available instrumentation. The estimated runoff by linear multiple regression did not fit the observations well. The values of the objective functions obtained in the linear multiple regression estimations were lower than those obtained in the WASMOD simulations.

The monthly estimation was better than the daily estimation, but its representation of the upper part of the basin was still not good. Using 30−day averages of observed and esmated runoff, did not give the same results or even approximately to the one using monthly data.

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To study the runoff responses to accumulated rainfall events, a new independent variable, namely rainfall that occurred 3, 5, 10 and 30 days before the day t, was included to take soil moisture into consideration. A resume of the values of the objective functions obtained in every case is shown in Table 10.

TABLE 10. Values of objective functions applied to the estimated runoff by linear multiple regression when an approximation of soil moisture was added as independent variable. Estimation performed on a daily scale from 1985−2005.

Sm: Sm: Sm: Sm: Calibration Time Objective Input Data 3 days 5 days 10 days 30 days Data Scale Function acc. acc. acc. acc. Nash Tocumen 0.247 0.252 0.262 0.275 Juan Diaz Sutcliffe ("Soil Moisture", (Observed Daily p , ep , Temp, t t Discharge) Rel. Hum.) R2 0.247 0.251 0.261 0.275

When adding as independent variable an approximation of soil moisture, the quality of the daily estimations barely increased from when this was not used (compare daily values of the objective functions obtained for 1 day average runoff in Table 9 to those shown in Table 10). The quality of the estimations increased when more days were summed in the approximation of soil moisture, but the results of the objective functions indicated that the estimation was poor.

In this approach, the best estimations were obtained when the total rainfall from the 30 previous days was used as soil moisture proxy. For this case, all the observed daily peaks above 24 mm were underestimated. 61% of the observed daily discharge records below 24 mm were overestimated. The estimated daily runoff using this approach ranged from 0 to 34 mm from 1985 to 2005. The observed daily discharge records above 34 mm represented less than 2% of the available records of the rainy season. When referring to residuals, there was not a clear pattern of which month was the best estimated during the rainy season, this was randomly at the middle or at the end of it (e.g. Figure 24).

In general, for most of eth years the dry season was underestimated during February and March. Then, during April and the first months of the rainy season (until August), the estimated runoff seemed to exceed the observations. From September till November, most of the observed runoff data were underestimated. During December and January, most of the estimated runoff exceeded the observations.

The general perception of this approach was that the estimations were poor, since it was not able to predict the high peaks.

Figure 24. Observed (red line) versus Estiimated (dark blue line) Daily Runofff / Linear Multiple Regression ‐ Soil Moisture Proxy (total rainfall of the 30 previous days) ‐ Juan Diaz. A corresponds to the period between May−Dec 1986. B corresponds to the period between May−Dec 1989. C corresponds to the period between May−Dec 1998.

5.3. LONG TERM RAINFALL‐RUNOFF RELATIONSHIP

To establish a long term rainfall‐runofff relationship, a graph showing observed discharge against rainfall data was plotted in the yearly scale and a curve was fitted to the previous. As shown in Figure 25, the 95% confidence limits on the regression curve were also calculated.

Every yearly datum shown in Figure 25 represents the accumulated daily rainfall registered on the days in which there was an observed daily discharge registered foor each year. Since most of the years have missing discharge data, the years taken into account for this graph were the ones which had more than 70% of their daily discharge data. From the 21 years of available data, only 3 did not satisfy the previous condition (these were 2001, 2004 and 2005).

The objective function used in this secction was the coefficient of determination, R2. The result obtained with this function with the yearly available data was 0.70, which is higher than those obtained in the daily and monthly resolution, but still the data were scattered around the regression curve. The staandard deviation between the observed and the expected values in the regression curve was 213 mm. It has to be noticed that even when all the observed yearly values fell within the range of the 95% confideence limits of the regression curve, some observations missed the regression curve by 350 mm or more.

Figure 25. Observed Yearly Runoff versus Yearly Rainfall Data (blue dots). The black curve represents the regression curve. The red curves represent 95% confidence limits of the regression curve.

6. DISCUSSION

The main objective of this thesis was to establish how well the Juan Diaz River basin could be hydrologically represented by records of the available instrumentation, using a hydrological model and a statistical method. In both approaches, the same input data were used, however more variables were considered in the statistical method.

Precipitation is the largest quantity and perhaps the most important in the hydrological cycle. Between 5 and 10 stations for every 250 km2 is recommended to capture the rainfall variability in a catchment (Cedeño, 1997). This is not the case in the Juan Diaz River basin. Precipitation data in the basin are scarce. Nowadays, there are no active meteorological stations within the basin. Precipitation records from some active and inactive meteorological stations located in the proximity of the Juan Diaz River basin were available.

Several methods, such as Thiessen polygon and the isohyetal method can be used for estimating the areal mean precipitation of any catchment. The Thiessen polygon was not used in this study because it would have given biased estimations since the studied site is close to the sea and mountains. The isohyetal method was not used either because it requires an extensive gage network to draw accurate isohyets (Goovaerts, 1999; Cedeño, 1997). Precipitation records from an active meteorological station, which was the closest to the basin from the ones with available records, were used in this study to estimate the areal mean precipitation of the basin. Accurate estimation of the spatial and temporal distribution of rainfall in a mountainous catchment with only one station is a difficult task. The lack of precipitation data to accurately calculate the areal mean precipitation of the basin makes the application of any hydrological model unreliable.

In addition, many inconsistencies were found in the precipitation input data and the observed discharge data. Inconsistencies such as no runoff responses with rainfall pulses or vice versa, frequently occurring values or low observed discharge records compared to the rainfall events, made it difficult to establish an acceptable relationship between rainfall and runoff both in the daily and monthly resolution and in the long term.

For this thesis the calibration of the hydrological model was performed manually, based on visual comparison of plots and by using two objective functions to measure the quality of the simulations. The calibration and simulation of the hydrological model was complicated because of the inconsistencies found. Unknown uncertainties in the precipitation input data and on the observed discharge data for calibration make any hydrological representation questionable.

For comparison, these two objective functions were also calculated in the statistical method. According to the objective functions, WASMOD simulated the observed discharge better. Even though some peaks were well simulated, most of them were underestimated by the two methods. The values of the objective functions indicated that the estimations by both methods were poor.

When an approximation of soil moisture, based on an accumulated value of previous rainfall events, was added as an additional independent variable, the quality of the daily simulation barely increased. The quality of the estimations increased when more days were summed in the approximation of soil moisture, but the values of the objective functions indicated that the simulations with this approach also performed poorly.

Additional linear multiple regressions using only the data of the flood dates were planned to be performed, but at the end this approach was disregarded because of the inconsistencies found in the flood dates registered.

The simulations of any model are not reliable when it is not known how large the error in the input and output data is. It can be stated that the Juan Diaz River basin cannot be represented accurately in the daily and monthly resolution with the available instrumentation within (and close to) it at this point. In the long term, the available instrumentation gave a better relationship between the rainfall and discharge data but care has to be taken if this approach is used since the limited quantity of data in this scale were scattered around the regression curve and some of the values varied more than one and a half times the standard deviation.

Resources have to be put in the Juan Diaz River basin to address the issue of limited data quantity. By increasing the precipitation network data in any catchment, modeling uncertainties will be reduced and reliable simulations can be obtained for better planning of the available water resources. A network of at least five rain gauges would be reasonable to have within the Juan Diaz River basin in order to cope with the spatial and temporal variability of precipitation. One should be placed at the west of the basin, close to previous location of the inactive Las Cumbres station. Three more should be placed at the north east to account for the rainfall pattern in the higher elevations of the basin. The last one should be placed at the central part of the basin to account for the rainfall pattern ine th lower parts of it.

To reduce uncertainty in the observed discharge records, two more hydrological stations could be desirable within the basin. Both could be placed at the central part of the basin, just upstream from where the two largest contributories from the north and west connect (one for each contributory).

For rainfall and observed discharge compatibility, both should be measured at the same time and with the same time spans (30 to 60 min) in order to make effective modeling possible.

McKay (2004) points out the necessity of creating a national network for hydro‐ meteorological monitoring and to adopt a plan for integral management of the hydrographic basins in Panama, but that is an objective that has not been achieved yet. Hopefully the results obtained in this thesis will encourage decision makers to increase the available instrumentation in the Juan Diaz River basin and others.

7. CONCLUSIONS

 Accurate estimation of the spatial and temporal distribution of rainfall in a mountainous catchment like the Juan Diaz River basin with only one station is not feasible.  Inconsistencies in the input and output data were found. These inconsistencies made it difficult to establish an acceptable relationship between rainfall and runoff in the daily and monthly scale. In the long term a better relationship was found than in the two previous scales, but care has to be taken if this approach is used since the limited quantity of data in this scale were scattered around the predictions.  Unknown uncertainties in the precipitation input data and in the observed discharge data for calibration make any hydrological representation questionable.  Neither the hydrological model, WASMOD, nor the statistical method, linear multiple regression, could well represent the Juan Diaz River basin with the records of the available instrumentation.  The meteorological station chosen for this study could not well represent the Juan Diaz River basin.  The available instrumentation of the basin is not sufficient for modeling or forecasting at this point. This emphasizes the importance of having an adequate and active precipitation network within the basin of study in order to capture its rainfall variability and to make it possible for simulation or forecasting that will support better water resources management.  Inconsistencies in the flood dates registered were found. Flood records must be improved in order to find a relationship between floods and hydro‐meteorological events.

ACKNOWLEDGEMENTS

I would like to thank Sven Halldin, Lars‐Christer Lundin and Chong‐Yu Xu, my supervisors, for their guidance, advice and patience during this study project. I wouldn't have made this far in this project without their support. Thanks also to Jose Luis Guerrero for his help and tips with the WASMOD programming.

I would like to also thank the Swedish International Development Cooperation Agency (Sida) for giving me the opportunity to study in Sweden and being part of the project "Research Capacity Building in Nature‐Induced Disaster Mitigation in Central America 2008−2010".

Many thanks to ISP for taking care of me and my wife during our time in Sweden.

Thanks also to Juan Antonio Gomez of the Panama University (Universidad de Panama) for linking me with Sida and for his guidance to earn this fellowship.

Thanks to the Department of Hydro‐Meteorology of ETESA (Gerencia de Hidrometeorología de ETESA), who provided me the data used in this project and also for giving me permission to reprint some figures of past documents prepared by them (Figure 1 and figure shown in ANNEX B in this study).

Thanks also to Murugesu Sivapalan for letting me reprint a figure from one of his lecture notes (Figure 3 in this project).

Special thanks to Nilsa, my wife, who has always believed in me and has never stopped encouraging me to aspire for better things.

Thanks to my mom for her unconditional support and for all the sacrifices she made to make me the person I am now. To my sister, that even with the distance has always been there for me.

Finally, but not least, thanks to my friends in Panama and to the new ones I met in Sweden for always being there and for their support during my studies in Sweden.

REFERENCES

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ATIES (1996): Caracterización de las Aguas del Río Juan Díaz e Inventario de sus Afluentes Contaminantes. Asociación de Técnicos en Ingeniería Sanitaria.

CALTEC (2010): Diagnostico y medidas de protección para las cuencas de los ríos Juan Díaz, Tocumen y Cabra, Ciudad de Panamá.

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ANNEX A. List of Equations used in this thesis for the WASMOD system (snow free catchment).

Hydrological Process Equation

Actual min 1 ,, Evapotranspiration (for an energy where is available water limited systems)

Slow Flow Component

Fast Flow Component , where 1 is active rainfall

Routing Routine of the Fast Flow Component where is the routing storage

Total Runoff

Water Balance max , 0 Equation

ANNEX B. Annual Potential Evapotranspiration Map created by ETESA, 1971−2002 (UNESCO, 2008). Reprinted with permission from ETESA.

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