Usability of Standard Monitored Rainfall-Runoff Data in Panama, …572949/FULLTEXT01.pdf · 2012....

Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 242

Usability of Standard Monitored Rainfall-Runoff Data in Panama,

Juan Diaz River Basin

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

José Eduardo Reynolds Puga


Uppsala universitet, Institutionen för geovetenskaperExamensarbete D, 15 hp i HydrologiISSN 1650-6553 Nr 242Tryckt hos Institutionen för geovetenskaper, Geotryckeriet, Uppsala universitet, Uppsala, 2012.

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.

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.

Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 242

Usability of Standard Monitored Rainfall-Runoff Data in Panama,

Juan Diaz River Basin


Copyright © José Eduardo Reynolds Puga och Institutinen för geovetenskaper, Luft‐, vatten –och

landskapslära, Uppsala Universitet.

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.

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.

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 cuenca del 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. WASMOD 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

1

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


April−Dec 1991.…………………………………………………………………………………………………………….36


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

2


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.


B corresponds to the period between May−Dec 1990. ………..……………………………………...43

Figure 19. Observed versus Calculated Daily Runoff / WASMOD ‐ Juan Diaz.


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


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

3

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

4

5

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

6

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. STU

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8

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.

9

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.

10

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

The WA

For this

catchme

only 4 p

2.2.1.2

The WA

potentia

observe

precipit

2.2.1.3

The sch

catchme

the eva

storage

evapotr

routing

1. WASMO

ASMOD syst

s study, sin

ent, the mo

parameters

2. INPUT D

ASMOD sys

al evapotra

ed daily (or

tation and p

3. WASMO

heme of the

ents, all the

potranspira

, smt, as

ranspiration

routine wa

Fig

OD

tem has 3 t

nce the Ju

odel will sim

were used.

DATA

stem accep

anspiration,

r monthly)

potential ev

OD MODE

e model for

e precipitat

ation losses

active ra

n, et, to the

s added to

gure 2. WAS

M

to 7 param

uan Diaz Ri

mulate the

ts different

temperatu

discharge f

vapotranspir

EL STRUCT

r a snow fre

ion, pt, is ra

s, et. The re

ainfall. Lat

fast flow co

the fast flow

MOD Model

Modified from

11

meters, depe

iver basin

streamflow

t combinat

ure and rel

for calibrat

ration were

TURE

ee catchme

ainfall, rt. O

emainder of

ter, the s

omponent,

w compone

l Structure fo

m Frevert an

ending on t

is characte

ws generate

ions of dai

ative humid

tion. For th

e used as in

ent is show

ne part of t

f rainfall co

soil moistu

ft, and to t

ent to distri

or a Snow Fr

nd Singh (200

the climate

erized by b

d only from

ly (or mon

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put data for

wn in Figure

this rainfall

ontributes t

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he slow flow

bute it in ti

ree Catchme

02).

e of the stu

being a sn

m rainfall; th

nthly) preci

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daily (and m

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e 2. For this

contribute

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ge contrib

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ow free

herefore

pitation,

ong with

monthly)

l.

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moisture

utes to

ent, st. A

12

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

13

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. For this 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.

In this s

an ener

m

where

a4: is th

lim

the

study, the s

rgy limited s

min

he paramet

ited system

e greater the

Figu

system is an

system is de

1

ter that de

m, a4 is cons

e actual eva

ure 3. Budyco

n energy lim

efined by eq

, ,

termines th

strained by

apotranspir

14

o Diagram (S

mited syste

quation (2):

………………

he actual e

0 <= a4 <=

ration losses

Sivapalan, 20

em. The equ

:

…………………

evapotransp

1. The sma

s will be.

001).

uation that

…….............

piration los

ller the valu

WASMOD

..................

sses. For an

ue of param

uses for

.......(2)

n energy

meter a4,

15

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.

16

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)

17

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.

18

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 (m.a.s.l.)

Period of Available 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.

19

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 (m.a.s.l.)

Period of Available 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 sta on 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 sta on 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. H

Nowada

location

from w

upstrea

The elev

102 km

the Juan

ETESA a

missing

87% of t

Every da

each da

Figure 4

h

w

HYDROLO

ays, there is

n of this sta

here the Ju

m from wh

vation posi2 (area high

n Diaz River

also provide

data from

the daily da

aily record

ay.

4. Flood Pro

hydrological

with informa

OGICAL DA

s only one a

tion is 9° 0

uan Diaz Ri

ere the floo

tion of the

hlighted in o

r basin.

ed daily reco

1985 till 19

ata from 19

correspond

one Areas d

l station and

ation from d

ATA

active hydro

3´ 00" N an

iver begins

od prone ar

hydrologica

orange in F

ords of this

987, also in

85 till 2005

ds to the ave

ue to the Ju

d the light bl

documents o

20

ological sta

nd 79° 26´ 0

in Cerro A

reas begin (

al station is

Figure 5), a

s station fro

1994, 1995

were availa

erage hourl

uan Diaz Ri

lue areas re

of ETESA (199

tion within

00" W, appr

Azul and it

Figure 4).

s 8 m above

nd for this

om 1985 till

5 and from

able.

ly discharge

ver. The re

present the

99) and SINA

the Juan D

roximately 1

is situated

e sea level.

study, this

2005. Thes

2000 till 20

e from 00:00

d dot repre

flood prone

APROC (2005

Diaz River ba

17 km dow

at less tha

This statio

area is ref

se daily reco

005. For th

0 till 24:00

esents the J

e areas. Map

5).

asin. The

nstream

an 1 km

n covers

ferred as

ords had

is study,

hours of

uan Diaz

p created

Figure 5

a

Figure 6

D

As it ca

records

station

1980

. Location of

and outside

6. Summary

Diaz River ba

an be seen

available w

that had th

19

P ‐ Cerro P ‐ Hato PP ‐ UtiveP ‐ Altos d

f meteorolog

the Juan Dia

of the avail

asin on a yea

in Figure

were Cerro

e same yea

985

AzulPintado

de Pacora

gical and hy

az River basi

lable data fr

arly time sca

6, the met

Azul and T

ars of availa

1990

21

drological st

in.

rom the diff

ale.

teorological

ocumen re

ble records

1995

tations with

ferent statio

l stations w

spectively.

s as the Juan

2000

P ‐ Las CumP, Pan EvaP ‐ Loma BQ ‐ Juan D

available re

ons within a

with the sh

The latter w

n Diaz statio

20

mbresp, Temp, HumBonitaiaz

ecords locate

and outside

hortest and

was the on

on.

005

m ‐ Tocumen

ed within

the Juan

longest

ly active

2010

22

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

Cerro Azul

*1

Las Cumbres

*1

Hato Pintado

*1

Tocumen*2

Utive*1

Loma Bonita

*1

Altos de

Pacora*1

Juan Diaz

*1

Cerro Azul*1 ‐ 17.30 21.41 11.53 9.30 18.33 11.23 13.14

Las Cumbres*1

17.30 ‐ 9.83 17.26 24.89 33.67 28.44 13.20

Hato Pintado*1

21.41 9.83 ‐ 15.52 26.30 33.60 33.82 10.72

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 Bonita*1

18.33 33.67 33.60 18.05 9.20 ‐ 14.98 23.01

Altos de Pacora*1

11.23 28.44 33.82 23.82 10.53 14.98 ‐ 23.32

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.

23

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.

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

0

1

2

3

4

5

6

7

8

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

Number of Floods Registered

Time in Years

24

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.

25

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 lowest one was chosen. The days, in which there was not a clear pattern in

which value to choose, were flagged.

26

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

*1: For eve

in each

4. Percentage

record and

ry station with m

h row represent t

e difference

d the annual

missing precipitat

he 3 stations use

e between th

precipitatio

ion data (these a

d for each case t

27

he annual p

on of the thre

are shown in the

to estimate the m

precipitation

ee closest st

second column f

missing precipitati

of the stati

tations with

for every year), t

ion data.

ion with the

available da

the values highlig

e missing

ata *1

ghted in bold

3.1.3. D

After fil

consiste

average

individu

precipit

Change

instrum

A straig

station

double

for ever

conditio

then the

Figure 8

a

DOUBLE M

lling the m

ency of the

e precipitat

ual station b

tation of on

s can be

ment, metho

ght line was

against the

mass plot o

ry station, i

ons. If a stra

e changes i

. Double ma

and the othe

MASS ANA

issing preci

e rainfall da

ion of certa

because the

ne station i

understood

od of observ

s obtained

e annual a

of the Tocum

t can be sa

aight line w

n slope sho

ass plot betw

er 6 stations

ALYSIS

pitation rec

ata. This m

ain number

eir errors co

is sensitive

d as a cha

vation.

when plott

ccumulated

men station

id that the

was not obta

uld have be

ween precipit

s with availab

28

cords, doub

method is b

r of station

ompensate

to the cha

ange in th

ting the ann

d average

n shown in F

records of

ained in the

een adjuste

tation recor

ble records.

ble mass an

based on th

ns is not se

each other

anges that

e location

nual accum

precipitatio

Figure 8). Si

each statio

e double ma

d.

ds of the To

nalysis was

he fact tha

nsitive to t

r; meanwhi

occur to th

of the in

mulated prec

on of the o

ince the pre

on were obt

ass plot of a

cumen mete

used to ch

at the accu

the changes

le the accu

his (Cedeño

nstrument,

cipitation f

other statio

evious was

tained by t

any of the s

eorological s

heck the

mulated

s of one

mulated

o, 1997).

type of

or every

ons (e.g.

the case

he same

stations,

station

29

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

o

a

To obta

register

located

seen in

precipit

the curv

. Elevation r

on top; 3D v

are in meter

ain the elev

red on all t

was plotte

n Figure 10

tation and e

ve with the

ranges of the

view is show

rs. Map Sour

vation facto

he stations

ed (the prev

0, a curve

elevation. F

data.

e Juan Diaz R

wn below). D

rce: USGS (20

or a graph

(from 198

vious data

was then f

For this plot

30

River basin a

Dimensions

011).

showing t

5 till 2000)

of each sta

fitted to th

t, Las Cumb

at the discha

in the color

he long te

versus the

ation are sh

he data to

bres station

arge station

bar and in t

rm accumu

e elevation

hown in Tab

find a rel

n was omitt

(plant view

the axes "x"

ulated prec

in which th

ble 5). As it

ationship b

ted for bett

is shown

" and "y"

ipitation

hese are

t can be

between

ter fit of

TABLE

met

Name

Hato

Tocum

Cerro

Las C

Utive

Loma

Altos

Figure

met

From Fi

long ter

basin. T

at the a

precipit

5. The lon

teorological

e of Station

Pintado

men

o Azul

umbres

e

a Bonita

s de Pacora

10. The lo

teorological

gure 10 (or

rm precipit

The elevatio

average ele

tation at the

ng term ac

stations wit

Acc

ong term a

stations wit

r by using th

tation was

on factor res

evation of

e Tocumen

ccumulated

th available

cumulated P1985−2000

31

28

47

35

40

42

57

accumulated

th available

he equation

calculated

sults from t

the upper

station. For

31

precipitatio

records and

Precipitation0 (mm)

1,955

8,435

7,738

5,253

0,798

2,307

7,146

d precipitat

records vers

n derived fro

at the ave

the division

part of the

r this study,

on register

the elevatio

ion register

sus the eleva

om the fitte

rage elevat

n of the long

e basin and

, the elevat

red (from

on in which t

Eleva(m above

6

2

8

red (from

ation in whic

ed curve), a

tion of the

g term estim

d the long

ion factor w

1985 till 2

these are loc

vation e sea level)

45

14

660

200

80

100

850

1985 till 2

ch these are

an estimatio

upper par

mated prec

term accu

was 1.54.

2000) at

cated.

2000) at

located.

on of the

rt of the

ipitation

mulated

32

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 long gaps 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.

33

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.

34

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.

35

Figure 11. O

bserved M

onthly Discharge

‐Juan

Diaz (dark blue line) an

d M

onthly Precipitation‐Tocumen (red bars) 1985−2005.

Figure 1

(red

figu

men

Frequen

runoff v

purple d

Figure 1

(red

max

eve

12. Observed

d bars) Aug−

ure were fix

ntion.

ntly occurri

value 11.16

dashed circ

13. Observed

d bars) April

ximum prec

en though th

d Daily Disc

−Dec 2005. T

xed to 100

ing values w

6 mm was

le in Figure

d Daily Disc

−Dec 1991. T

cipitation an

ere were hig

charge‐Juan

The maximu

mm, even

were found

repeated c

13).

charge‐Juan

The purple d

nd observed

gher values t

36

Diaz (dark

um precipita

though the

d and flagg

consecutive

Diaz (dark

dashed circle

discharge v

than the pre

blue line) a

a on and ob

ere were hi

ged on the

ely from 01

blue line) a

e represents

values in thi

evious menti

nd Daily Pre

bserved disc

igher values

daily scale

1−Oct−91

nd Daily Pre

s a frequent

s figure wer

ion.

ecipitation‐T

charge value

s than the

e. For exam

ll 23−Dec−

ecipitation‐T

occurring va

re fixed to

Tocumen

es in this

previous

mple, the

−91 (see

Tocumen

alue. The

100 mm,

Zero va

consecu

zero val

Figure 1

(red

max

eve

Quality

compar

During t

records

versa w

found in

irregula

difficult

are goo

inspecti

alues were

utive zero v

lues were v

14. Observed

d bars) Jun−

ximum prec

en though th

control o

ring the dail

the rainfall

compared

were found a

n which the

ar cases we

ties in the s

od or not,

ion.

also found

alues from

ery unlikely

d Daily Disc

−Dec 1986.

cipitation an

ere were hig

f the obse

ly runoff res

‐runoff com

to rainfall

as it can be

e discharge

re flagged

imulations.

it will be

d and remo

27−Jul−86

y because m

charge‐Juan

The orange

nd observed

gher values t

erved disch

sponses to t

mparison so

events an

seen in Fig

was decrea

but not rem

This decisi

subjective

37

oved from

ll 12−Aug−

most of them

Diaz (dark

e circle rep

discharge v

than the pre

harge data

the daily ra

ome inconsi

d no discha

gures 15 and

asing even

moved from

ion was tak

e to discre

the series.

−86 (see ora

m occurred

blue line) a

presents a lo

values in thi

evious menti

a was follo

infall pulses

istencies su

arge respon

d 16. In add

thought the

m the data,

ken because

dit the rec

For examp

ange circle i

during the

nd Daily Pre

ong series o

s figure wer

ion.

owed by a

s.

uch as low o

nses to rain

dition to the

ere was a r

even thou

e it is not kn

cords by a

ple, there w

in Figure 14

rainy seaso

ecipitation‐T

of zero val

re fixed to

a visual ins

observed d

nfall pulses

e latter, cas

rainfall puls

gh they ma

nown if the

applying jus

were 17

4). These

on.

Tocumen

ues. The

100 mm,

spection

ischarge

s or vice

ses were

e. These

ay cause

e records

st visual

Figure 1

(red

A co

May

pre

the

A

B

C

15. Observed

d bars). The

orresponds

y−Dec 1998

cipitation an

re were high

d Daily Disch

green circle

to the perio

8. C corres

nd observed

her values th

harge‐Juan

s represent

od between

ponds to t

d discharge v

han the prev

38

Diaz (dark b

inconsistenc

May−Dec 1

the period

values in thi

vious mentio

blue lines) a

cies found in

1995. B corr

between M

s figure wer

on.

and Daily Pre

n the rainfal

esponds to

May−Dec 19

e fixed to 10

ecipitation‐T

l‐runoff com

the period

999. The m

00 mm, eve

Tocumen

mparison.

between

maximum

n though

Figure 1

(red

run

wer

After th

coefficie

precipit

evapotr

0.66, ca

for the

by doin

year, all

Even th

modelin

hydrolo

TABLE 6

YEAR

1985

1986

1987

1988

1989

1990

16. Observed

d bars) May

off compari

re fixed to 10

he previou

ent results

tation (Q/P

ranspiration

alculated as

21 years of

g the sum

l the years o

hough stran

ng from 19

ogically repr

. Long term

RunoffCoefficie

0.52

0.69

0.78

0.64

0.73

0.70

d Daily Disc

y−Dec 2003.

ison. The ma

00 mm, even

s cases we

from the d

P). This coe

n losses. As

s the sum o

f available r

of all the d

obtained a

nge rainfall

985 till 200

resented by

runoff coeff

f ent

YEAR

1991

1992

1993

1994

1995

1996

charge‐Juan

The green

aximum pre

n though the

ere flagged

division bet

efficient is

is shown in

f all the day

records. Wh

ays in whic

runoff coeff

and runoff

05 to deter

y records of

ficient.

Runo

Coeffic

0.8

0.6

0.7

0.6

0.5

0.6

39

Diaz (dark

circles repr

ecipitation a

ere were hig

d, the runo

tween long‐

expected

n Table 6, t

ys in which

hen calculat

ch there wa

fficient belo

f behaviors

rmine how

the availab

off cient

YEA

87 199

63 199

2 199

62 200

4 200

64 200

blue line) a

esent incon

nd observed

gher values t

off coefficie

‐term obse

to be belo

the runoff c

there was

ting the run

as an obser

ow to 1, exc

s were foun

well the J

ble instrume

AR Run

Coeffi

97 0.5

98 0.5

99 0.5

00 0.6

01 0.4

02 0.6

nd Daily Pre

sistencies fo

d discharge

than the prev

ent was ch

rved discha

ow 1 due

coefficient f

an observe

noff coeffic

ved dischar

ept for the

nd, these d

Juan Diaz R

entation.

off cient

YEA

51 200

58 200

59 200

68 ALLTHEDAT

47

68

ecipitation‐T

ound in the

values in th

vious menti

hecked. The

arge and lo

to the lon

for all the d

ed discharg

ient for eve

rge record

year 2005.

data were u

River basin

AR Ru

Coeff

03 0

04 0

05 1

L E ATA

0.

Tocumen

e rainfall‐

his figure

on.

e runoff

ong term

ng term

data was

e record

ery year,

for each

used for

can be

noff ficient

.51

.47

.41

.66

3.6. FL

The ava

shown

known t

3.6.1.

First, th

observe

register

Accordi

precipit

register

values (

precipit

unlikely

Figure 1

dot

reco

high

LOOD DAT

ailable histo

in Section

to what ext

QUALITY

he observed

ed discharg

red, there w

ng to the f

tation regis

red (see gre

(below 20

tation value

y as well.

17. Observed

s). Green cir

orded. Purp

h precipitati

TES REGIST

orical flood

2.3.3. From

tend these r

CONTROL

d discharge

ge data are

was no obse

flood dates,

stered, as w

een circle

mm) were

es registere

d discharge

rcle represen

le square re

on recorded

TERED

records of

m 1985 till

records are

L OF THE F

e and rainfa

daily aver

rved discha

, there wer

well as in

in Figure 1

found regi

ed above 4

and rainfall

nts flood eve

epresents flo

d.

40

the Juan D

2005 there

correct.

FLOOD RE

all recorde

rages and n

arge record

re flood eve

days when

17), which i

stered duri

45 mm (see

recorded d

ents register

ood events r

iaz Townsh

e are 31 fl

ECORDS

d on the fl

not daily m

ed, perhaps

ents in day

n there wa

is unlikely.

ing the floo

e purple sq

during flood

red with low

registered w

ip are not c

oods regist

lood dates

maxima. In

s due to its

ys when the

as a low o

Also low o

od dates in

quare in Fi

dates from

w precipitatio

with low disc

complete, a

tered, but

were plott

four of th

magnitude

ere was litt

observed d

observed d

n which the

igure 17), w

1985 till 20

on and low d

charge recor

as it was

it is not

ted. The

e floods

.

tle or no

ischarge

ischarge

ere were

which is

005 (blue

discharge

rded and

41

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):

∑

∑

where

: are t

: is the

: are t

For eve

left afte

were 36

Table 7

daily an

b1 was t

the bes

tried wi

model r

upper p

*1: For an e

In an at

were es

runoff.

∑

∑……

the observa

e mean of t

the predicte

ery WASMO

er the warm

65 days and

shows the

nd monthly

tried for 0,

st results w

ith 1 and 2,

results were

part of the b

TABL

energy limited sys

tempt to im

stimated ag

…………………

ations of the

he depende

ed values of

OD simulatio

m up period

d 36 months

best mode

simulations

0.5, 1 and

ere obtaine

and the be

e obtained

basin is a fo

E 7. Best mo

stem, a4 is const

mprove the

gain, using t

………………..

e dependen

ent variable

f the depen

on, both ob

d. The warm

s respective

el paramete

s.

2. Since th

ed when b1

est results w

when a6 wa

rest area (s

odel paramet

rained by 0 <= a4

model qua

the average

42

..................

nt variable

e

dent variab

bjective fun

m up perio

ely.

er set obtai

he Juan Dia

1 was fixed

were obtain

as closed to

ee Section

ter set obtai

4 <= 1.

lity in the d

es of 3, 5, 10

..................

ble

nctions wer

ds for the d

ined from t

z River bas

to 0 or 0.5

ned when b2

o zero, this

2.2.1.6).

ined from m

daily simulat

0 and 30 da

..................

re calculate

daily and m

the manual

in is located

5 (see Secti

2 was fixed

could be re

manual calibr

tions, both

ays of obser

..................

ed with all t

monthly sim

l calibration

d in an arid

ion 2.2.1.5)

to 1. Also,

easonable s

ration.

objective f

rved and ca

.......(15)

the data

mulations

n for the

d region,

. b2 was

the best

since the

unctions

alculated

5. RESU

5.1. W

No goo

monthly

On the

observe

discharg

runoff r

above 5

every y

most of

season

in the fi

18.

Figure 18

/

A

B

A

B

ULTS

WASMOD S

od represen

y resolution

daily scale,

ed daily dis

ge records f

ranged in t

50 mm repr

ear, at som

f the years

was April. W

irst 5 years

8. Observed

/ WASMOD

A correspon

B correspon

SIMULATIO

ntation of t

n. In both th

, all the ob

charge reco

from 1985 t

he same pe

resented le

me point du

s, when ref

When refer

of simulatio

d (red line) ve

‐ Juan Diaz.

ds to the pe

ds to the pe

ONS

the observ

here were u

served pea

ords below

till 2005 ran

eriod from

ss than 0.3

uring the d

ferring to re

ring to resid

ons, especia

ersus Calcula

riod betwee

riod betwee

43

ved dischar

underestima

aks above 3

w 32 mm w

nged from

0 to 49 m

5% of the a

ry season t

esiduals, th

duals, the b

ally in the m

ated (dark b

en May−Dec

en May−Dec

ge records

ation and ov

32 mm were

were undere

almost 0 to

m. The obs

available re

the calculat

he month b

best simulat

month of De

blue line) Dai

1989.

1990.

was found

verestimati

e underesti

estimated. T

o 214 mm. T

served daily

cords of th

ted daily ru

best simula

tions of the

ecember, as

ily Runoff

d in the d

on of peaks

imated. 50%

The observ

The calculat

y discharge

he rainy sea

unoff was z

ted during

e rainy seas

s is shown i

aily and

s.

% of the

ved daily

ted daily

records

son. For

zero. For

the dry

on were

in Figure

After th

the beg

In gene

From 19

was mo

after 19

the obs

most of

As is sh

produce

simulati

all the o

of its irr

Figure 19

/

A

B

A

B

he first five y

ginning or at

ral, for mos

986 till 199

ostly under

995, the ob

served daily

f the years t

hown in Fi

ed a poor

ions from A

observed di

regular beh

9. Observed

/ WASMOD

A correspon

B correspon

years of sim

t the middle

st of the yea

95, during t

estimated

bserved dai

y runoff wa

the observe

igures 18 a

fit since th

August−200

ischarge da

avior (see S

d (red line) ve

‐ Juan Diaz.

ds to the pe

ds to the pe

mulation, th

e of it.

ars the dry

he first mo

until July. D

ly runoff w

as mostly u

ed runoff wa

and 19, th

he biggest

5 ll Decem

ta registere

Section 3.5.1

ersus Calcula

riod betwee

riod betwee

44

e best fits o

season was

onths of the

During the

was overest

underestima

as overestim

e general

peaks wer

mber−2005

ed during th

1).

ated (dark b

en May−Dec

en May−Dec

of the rainy

s underestim

e rainy seas

previous m

timated. Fro

ated. Durin

mated.

perception

re not well

shown in F

hat period w

blue line) Dai

1999.

2005.

season occ

mated from

son, the ob

months, for

om Septem

g Decembe

is that th

simulated

Figure 19.B

were under

ily Runoff

curred rando

m February

bserved dail

most of th

mber till No

er and Janu

he daily sim

. As expec

were poor

restimated

omly at

till April.

ly runoff

he years

vember,

uary, for

mulation

ted, the

. Almost

because

45

Figure 20. O

bserved (red line) versus Calculated (dark blue line) Monthly Runoff / W

ASM

OD ‐ Juan

Diaz (1988−2005).

46

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 Data

Calibration Data

Time Scale

Objective Function

1 dayaverage

3−day average

5−day average

10−day average

30−day average

Tocumen (pt, ept)

Juan_Diaz (Observed Discharge)

Daily

Nash‐Sutcliffe

0.296 0.402 0.442 0.486 0.551

R2 0.302 0.410 0.451 0.498 0.564

Monthly

Nash‐Sutcliffe

0.554 ‐ ‐ ‐ ‐

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. LIN

Many

evapotr

variable

observe

overest

The set

consiste

Since so

the pred

rainfall

On the

observe

linear m

discharg

rainy se

best mo

of it (e.

months

Novemb

observa

NEAR MU

combinatio

ranspiration

e, the total

ed daily an

imations of

of indepen

ed of precip

ome of the

dictions too

pulses.

Figure 21

daily scale,

ed discharge

multiple reg

ge records

eason. Whe

onth simula

.g. Figures

s of the rai

ber, most

ations were

ULTIPLE RE

ons of i

n, humidity

runoff. No

nd monthly

f the peaks.

ndent varia

pitation, po

independen

ok a cardiog

1. Observed

Linea

, all the ob

e records be

gression, ran

above 37 m

en referring

ted during

22.A and 2

ny season

of the o

half overes

EGRESSION

ndependen

y and tem

one of thes

y runoff. I

bles that ga

tential evap

nt variables

gram behav

(red line) ve

ar Multiple R

served pea

elow 24 mm

nged from

mm repres

g to residua

the rainy se

22.B). For m

(until Augu

observation

stimated an

47

N

nt variable

mperature,

se combinat

In both ca

ave the bes

potranspira

s used in th

vior as show

ersus Estimat

Regression ‐

aks above 2

m were ove

0 to 37 mm

ented less

als, there w

eason, this w

most of the

ust) were o

s were u

nd half unde

es, such

were used

tions gave

ases there

st fit using

ation, temp

is approach

wn in Figure

ted (dark blu

Juan Diaz (1

24 mm were

restimated

m from 198

than 1% o

was not a cl

was random

e years, all

overestimat

nderestima

erestimated

as precip

d to predi

a good rep

were und

the linear m

erature and

h did not dir

21, even w

ue line) Daily

1999).

e underesti

. The estima

5 to 2005.

f the availa

ear pattern

mly at the m

the dry se

ed. Then fr

ted. Durin

d.

pitation, p

ict the de

presentatio

derestimatio

multiple re

d relative h

rectly affec

when there

y Runoff /

imated. 65%

ated daily r

The observ

able record

n of which

middle or at

eason and

rom Septem

ng Decemb

potential

pendent

n of the

ons and

gression

umidity.

t runoff,

were no

% of the

unoff by

ved daily

ds of the

was the

the end

the first

mber till

ber, the

Figure 2

Similar t

Decemb

behavio

As is sh

linear m

peaks o

B

A

C

2. Observed

/ Linear M

A correspo

B correspo

C correspo

to the WAS

ber−2005 (s

or of the ob

hown in Fig

multiple reg

of the observ

d (red line) ve

ultiple Regre

onds to the p

onds to the p

nds to the p

SMOD simul

shown in F

servations d

ures 21 an

gression is t

ved dischar

ersus Estima

ession ‐ Juan

period betwe

period betwe

period betwe

lation, the m

Figure 22.C)

during that

d 22, the g

that it was

rge in the w

48

ated (dark bl

n Diaz

een May−De

een May−De

een May−De

multiple reg

) did not g

period.

general per

poor since

whole series

lue line) Dai

ec 1986.

ec 1995.

ec 2005.

gression est

ive good re

ception of

e it could n

.

ly Runoff

timation fro

esults beca

the estima

ot well rep

om August−

ause of the

ated daily ru

present the

−2005 ll

strange

unoff by

e highest

49

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 Data

Calibration Data

Time Scale

Objective Function

1 dayaverage

3−day average

5−day average

10−day average

30−day average

Tocumen (pt, ept, Temp, Rel. Hum.)

Juan_Diaz (Observed Discharge)

Daily

Nash‐Sutcliffe

0.228 0.307 0.327 0.341 0.353

R2 0.228 0.314 0.340 0.365 0.379

Monthly

Nash‐Sutcliffe

0.526 ‐ ‐ ‐ ‐

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 es mated

runoff, did not give the same results or even approximately to the one using monthly data.

50

ib

d(

dli

)i

d(d

kbl

li)

hl

ff/

ilil

ii

()

Figure 23. O

bserved (red line) versus Estimated (dark blue line) Monthly Runoff / Linear M

ultiple Regression ‐ Juan

Diaz (1985−2005).

51

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.

Input Data Calibration

Data Time Scale

Objective Function

Sm: 3 days

acc.

Sm: 5 days

acc.

Sm: 10 days

acc.

Sm: 30 days

acc.

Tocumen ("Soil Moisture", pt, ept, Temp, Rel. Hum.)

Juan Diaz (Observed Discharge)

Daily

Nash Sutcliffe

0.247 0.252 0.262 0.275

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 the 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.

Figurre 24. ObservRegressioA correspB correspC corresp

ved (red lineon ‐ Soil Moiponds to theponds to theponds to the

e) versus Estisture Proxy e period betw period betwperiod betw

52

imated (dar(total rainfaween May−Dween May−Dween May−D

k blue line) Dall of the 30 Dec 1986. Dec 1989. Dec 1998.

Daily Runoffprevious day

f / Linear Muys) ‐ Juan Di

ultiple az.

5.3. LO

To esta

against

shown i

Every ye

on the

most of

were th

availabl

2005).

The obj

result o

than th

around

expecte

the obs

regressi

ONG TERM

blish a lon

rainfall dat

in Figure 25

early datum

days in wh

f the years

he ones whi

e data, on

jective func

obtained wi

ose obtaine

the regre

ed values in

served yea

ion curve, s

Fig

M RAINFAL

g term rain

a was plott

5, the 95% c

m shown in

ich there w

have missi

ich had mo

ly 3 did no

ction used

ith this fun

ed in the d

ession curv

the regress

arly values

ome observ

gure 25. Obse

The bla

The red

LL‐RUNOF

nfall‐runoff

ed in the ye

confidence l

Figure 25

was an obse

ng discharg

re than 70%

ot satisfy th

in this sec

ction with

daily and m

e. The sta

sion curve w

fell within

vations mis

erved Yearly

ack curve rep

d curves rep

53

FF RELATIO

f relationsh

early scale a

limits on th

represents

erved daily

ge data, the

% of their d

he previous

ction was th

the yearly

onthly reso

andard dev

was 213 mm

n the range

sed the reg

y Runoff vers

presents the

resent 95%

ONSHIP

ip, a graph

and a curve

e regressio

the accum

discharge r

e years take

daily dischar

s condition

he coefficie

available d

olution, but

viation betw

m. It has to

e of the 9

gression cur

sus Yearly R

e regression

confidence l

h showing o

e was fitted

n curve wer

ulated daily

registered fo

en into acc

rge data. Fr

(these we

ent of dete

ata was 0.7

t still the d

ween the

be noticed

95% confide

ve by 350 m

ainfall Data

curve.

imits of the

observed d

to the prev

re also calcu

y rainfall re

for each yea

ount for th

rom the 21

re 2001, 2

ermination,

70, which i

ata were s

observed

that even w

ence limits

mm or more

(blue dots).

regression c

ischarge

vious. As

ulated.

egistered

ar. Since

his graph

years of

004 and

R2. The

s higher

cattered

and the

when all

s of the

e.

curve.

54

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.

55

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 in the 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.

56

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.

57

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.

58

REFERENCES

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de 2006. Panamá.

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.

Cedeño, D. (1997): Apuntes de Hidrología. Universidad Tecnológica de Panamá. Facultad de

Ingeniería Civil, Departamento de Hidráulica, Sanitaria y Ciencias Ambientales.

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medición hidrológica. Empresa de Transmisión Eléctrica, S.A. Departamento de

Hidrometeorología, Sección de Hidrología.

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interpolation of rainfall. The University of Michigan. Department Civil and Environmental

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LUE/.mean/.temp/>

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59

McKay, A. (2004): Las inundaciones del 17 de septiembre de 2004 en el este del Distrito de

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60

Xu, C.‐Y. (2010a): Introduction to Hydrologic Models. Uppsala University, Department of

Earth Sciences, Air, Water and Landscape Sciences Program.

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Sciences, Air, Water and Landscape Sciences Program.

61

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

catchment).

Hydrological Process Equation

Actual Evapotranspiration (for an energy limited systems)

min 1 , ,

where is available water

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 Equation

max , 0

ANNEX

(UNESC

B. Annua

CO, 2008). R

al Potentia

Reprinted w

al Evapotra

with permiss

62

anspiration

sion from ET

n Map cre

TESA.

eated by EETESA, 19771−2002

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