IJERD – International Journal of Environmental and Rural Development (2020) 11-2

Research article
erdApplicability of Tank Model in Mid-Sized Catchments inEastern Uganda
EMMANUEL OKIRIA
Graduate School of Agriculture, Tokyo University of Agriculture, Tokyo, Japan

HIROMU OKAZAWA*
Faculty of Regional Environment Science, Tokyo University of Agriculture, Tokyo, Japan
Email : h1okazaw@nodai.ac.jp

YURI YAMAZAKI
Faculty of Regional Environment Science, Tokyo University of Agriculture, Tokyo, JapanYUKIMITSU KOBAYASHI
Graduate School of Agriculture, Tokyo University of Agriculture, Tokyo, JapanSHINJI SUZUKI
Faculty of Regional Environment Science, Tokyo University of Agriculture, Tokyo, Japan
Received 27 January 2020

Accepted 29 October 2020(*Corresponding Author)

Abstract Long-term stream discharge data is indispensable in irrigation and drainage design.
However, in Uganda, this data is poor and insufficient, limiting irrigation system design.
Conversely, the rainfall monitoring network is denser than the river flow monitoring network.
Therefore, we attempt to build a model that calculates river discharge from input of rainfall.
In this study, the lumped parameter Tank Model was applied. The model was applied to the
Namatala River catchment (155 km2) in Eastern Uganda. The study sought to ascertain theapplicability of a lumped parameter model to a mid-sized catchment. Specifically, theobjectives were: 1) To calibrate the numerical values of Tank Model parameters, 2) To verify
the Tank Model parameters. This Tank Model required daily rainfall, evapotranspiration andriver discharge data during calibration. Data for years 2015 and 2016 was used for calibrationand validation respectively. During calibration, Monte Carlo simulation was used to find thenumerical values of 16 Tank Model parameters. The best performing calibration parameterset had Nash-Sutcliffe (NS) efficiencies of 0.608 and 0.257 in calibration and validation
respectively. However, among the 2015 calibration parameter sets, the one with a calibration
NS of 0.502 performed best in validation (NS = 0.526). Equifinality was observed during
parameter calibration. By using Tank Model, simulated discharge was divided into its surface
runoff, interflow and base flow components. Tank Model was adaptable to Namatala River
catchment.
Keywords Equifinality, lumped model, Monte Carlo simulation, parameter, Tank Model

INTRODUCTION
To buttress the vulnerable agricultural systems in Uganda, the government plans to promote
irrigation (MWE, 2013). Irrigation and drainage planning requires long-term observed hydrometeorological data. However, Uganda has a scarcity of this data. Numerous Ugandan rivers areungauged, and worse, only about 33% of installed water level gauging stations are operational (MWE,2013). Comparatively, the state of rainfall monitoring is better than that of the hydrologicalmonitoring. Further, Kobayashi et al. (2018) explored the accuracy of satellite rainfall observations
and found their detection accuracy to be acceptable. Satellite observed rainfall data is therefore apromising source of rainfall data.

Ⓒ ISERD

31

I
7
d
e
n
t
4
.
7
2
w
o
r
d
s

IJERD – International Journal of Environmental and Rural Development (2020) 11-2

Since rainfall data is more readily available, it is attempted to build a hydrological model tocalculate river discharge from inputs of rainfall. Tank Model (Sugawara, 1995) and TOPMODEL(Beven and Kirkby, 1979), are some of the successful hydrological models. Okiria et al. (2019)
applied the semi-distributed TOPMODEL to the Atari River catchment in Eastern Uganda. In thisstudy, an attempt will be made to represent the hydrological response of the Namatala River
catchment (NRc) using Tank Model. Whereas TOPMODEL is semi-distributed, and has fewer
parameters, it is comparatively complex, and separates the predicted hydrograph into only two
components, i.e., surface runoff and subsurface flow. On the other hand, Tank Model is simpler andseparates the predicted hydrograph into four components, i.e., surface runoff, inter flow, sub-baseflow and base flow. A weakness of Tank Model is that it is a lumped parameter model, with many
unknown parameters (16 parameters for a 4-tank Tank Model). Because it is lumped, it cannot
represent the heterogeneity in catchment characteristics. And due to the many unknown parameters,a more pronounced equifinality is expected. This equifinality might be caused by the interdependence
among parameters reported in Beven (1997).
Whereas Tank Model has been successful in the continuously wet soils in humid sub-tropicalclimates (Suryoputro et al., 2017; Xiong et al., 2009), its behaviour in tropical climates, with soils
that undergo both wet and dry periods, is not widely documented. Onyutha (2016) applied Tank
Model to the Blue Nile Basin in Ethiopia. In East Africa, Tank Model was applied to a catchment in
Rwanda (JICA, 2014). To date, the authors have not found published evidence of the application of
Tank Model in Uganda. Therefore, the novelty of this study is to pioneer the development of Tank
Model for a catchment in Eastern Uganda.
Before hydrological models are applied to ungauged catchments, they require calibration andvalidation. Model calibration involves the determination of unknown parameters and their predictive
performance. On the other hand, validation involves testing the predictive performance of thecalibrated parameters in a period other than that of calibration. Being one of the well gauged
catchments in Uganda, the NRc was chosen for the calibration of Tank Model.
The lumped parameter model assumption of a catchment scale homogeneous hydrologicalresponse is likely to fail for medium to large catchments. Therefore, the purpose of the study is toascertain the applicability of a lumped parameter model (Tank Model) to mid-sized catchments inEastern Uganda. The specific objectives are: 1) Calibration of Tank Model parameters; and 2)
Validation of the model parameters. In so doing, we strive to build a Tank Model that successfully
predicts daily stream discharge from inputs of daily rainfall and evapotranspiration.
METHODOLOGY

Study Area
The study area is the Namatala River catchment (NRc), a headwater catchment of Mt. Elgon in
Eastern Uganda, with a drainage area of 155 km2 at the stream gauging station. Its topography iscomprised of mountainous areas from where the Namatala River originates and flows to the relatively
flat plains. From ASTER GDEM, the difference in height between the lowest and the highest point
is 1,262 m. Of the 155 km2, 73% is agriculture, 24% is forest, 2% is built up areas and 1% is rangeland.
Under the Project on Irrigation Scheme Development in Central and Eastern Uganda (PISD)(JICA, 2017), hydro-meteorological monitoring equipment were set up in the NRc, viz., a mid-stream
rain-gauge to detect catchment rainfall, a downstream meteorological station to measureevapotranspiration parameters and a water level logger at a control section of the Namatala River.
Tank Model Concept
One version of Tank Model comprises of four tanks laid out vertically in series, so named tanks 1, 2,
3 and 4. Rainfall is added to the topmost tank while evapotranspiration is subtracted from it. If tank
1 is empty, evapotranspiration is deducted from tank 2. If both tanks 1 and 2 are empty, thenevapotranspiration is subtracted from tank 3 and so on. The storage tanks have side outlets, fromⒸ ISERD

32

IJERD – International Journal of Environmental and Rural Development (2020) 11-2

which runoff flows. Side outlets of tanks 1,2,3 and 4 release surface runoff, interflow, sub-base flow
and base flow respectively. Tanks 1,2 and 3 have bottom outlets as well, through which infiltration
to a lower tank occurs. Tank Model is calibrated to determine the value of 16 unknown parameters,
namely; A1 (coefficient of top side out let of tank 1), A2 (coefficient of lower side outlet of tank 1),
B1 (coefficient of side outlet of tank 2), C1 (coefficient of side outlet of tank 3), D1 (coefficient ofside outlet of tank 4), A0 (coefficient of bottom outlet of tank 1), B0 (coefficient of bottom outlet oftank 2), C0 (coefficient of bottom outlet of tank 3), AH1 (height of top side outlet of tank 1), AH2(height of lower side outlet of tank 1), BH (height of side outlet of tank 2), CH (height of side outletof tank 3), SA0 (initial height of water in tank 1), SB0 (initial height of water in tank 2), SC0 (initialheight of water in tank 3) and SD0 (initial height of water in tank 4), as in Fig. 2. The simulated riverdischarge is the sum of runoff from all the side outlets. Details of Tank Model are in Sugawara (1995).

ARc

SRc
NRc
Fig. 1 Location of Namatala River catchment(NRc) relative to Atari River catchment(ARc) and Sironko River catchment (SRc)

Fig. 2 Schematic of Tank Model

Computational Procedure of Tank Model
Evaluation of tank 1:
𝑆𝐴𝑡 = 𝑆𝑍𝐴𝑡 + 𝑅𝑡 − 𝐸𝑇0𝑡

(1)
SAt is water depth in the tank during calculation (mm), SZAt is water depth in the tank at the start andend of each time step calculation (mm), R is observed rainfall (mm/day), ET0t is potential
evapotranspiration (mm/day), and the subscript t is the time step of calculation (day).
𝐴 × (𝑆𝑍𝐴 − 𝐴𝐻𝑥 )𝑄𝐴𝑥𝑡 = { 𝑥0 𝑓𝑜𝑟 𝑆𝑍𝐴 < 𝐴𝐻𝑥(2)

QAxt is runoff from side outlet (mm/day), Ax is discharge co-efficient of side outlet, AHx is height ofside outlet (mm), and subscript x is side outlet under consideration (1 or 2).
𝑄𝐴0𝑡 = 𝐴0 × 𝑆𝐴𝑡(3)
QA0t is infiltration from tank 1 to tank 2 (mm/day), A0 is discharge co-efficient of tank 1 bottom
outlet.
𝑆𝑍𝐴𝑡 = 𝑆𝐴𝑡 − 𝑄𝐴1𝑡 − 𝑄𝐴2𝑡 − 𝑄𝐴0𝑡

Ⓒ ISERD

33(4)

IJERD – International Journal of Environmental and Rural Development (2020) 11-2

Evaluation of tank 2:
𝑆𝑍𝐵0 + 𝑄𝐴0𝑡 − 𝐸𝑇0𝑡 for day 1, and an empty tank 1
𝑆𝐵0 = {𝑆𝑍𝐵0 + 𝑄𝐴0𝑡 for day 1 and non − empty tank 1(5)

SB0 is water depth in the tank during calculation (mm), SZB0 is water depth in the tank at the startand end of each time step calculation (mm).
𝑆𝐵𝑡 = {𝑆𝑍𝐵𝑡 + 𝑄𝐴0𝑡 − 𝐸𝑇0𝑡 after day 1, and an empty tank 1
𝑆𝑍𝐵𝑡 + 𝑄𝐴0𝑡 after day 1 and non − empty tank 1(6)

SBt is water depth in tank during calculation (mm), SZBt is water depth in the tank at the start andend of calculation (mm).
𝐵 × (𝑆𝐵𝑡 − 𝐵𝐻)
𝑄𝐵1𝑡 = { 10 for 𝑆𝐵𝑡 < 𝐵𝐻

(7)

QB1t is runoff from tank 2 side outlet (mm/day), B1 is discharge co-efficient of tank 2 side outlet,
BH is height of tank 2 side outlet (mm).
𝑄𝐵0𝑡 = 𝐵0 × 𝑆𝐵𝑡(8)
QB0t is infiltration (mm/day) from tank 2 to tank 3, B0 is discharge coefficient of tank 2 bottom
outlet.
𝑆𝑍𝐵𝑡 = 𝑆𝐵𝑡 − 𝑄𝐵1𝑡 − 𝑄𝐵0𝑡

(9)The calculations for tanks 3 and 4 follow the same logic as the calculations for tank 2. Also, these
conditions must be met: 𝐴0 > 𝐵0 > 𝐶0 and 0 > 𝐶 > 1 where C is discharge coefficient.
Evaluation of Parameter Predictive PowerNash and Sutcliffe efficiency (NS), (Nash and Sutcliffe, 1970) and Root Mean Square
Error (RMSE) are the indices for evaluating model efficiency as in Okiria et al. (2019).
Novel Concept for Managing Competing Parameter Sets
Calibration of model parameters is an uncertain process with uncertainty increasing with increasing
number of unknown parameters. The Generalised Likelihood Uncertainty Estimation (GLUE)
framework was developed to eliminate competing parameter sets (Beven, 1997). To augment thisconcept, the authors suggested another method to manage uncertainty, i.e.: 1) Use the competingparameter sets to simulate the hydrograph for a period outside the calibration period (verification ofcompeting parameter sets). The parameters that perform poorly in validation are then rejected; 2)Plot hydrograph components predicted using non-rejected parameter sets and choose the most likelyhydrograph based on the depiction of the shape of the base flow component, which is supposed to be
fairly constant. The authors attempted to use 1) and 2) in combination, to eliminate competingparameter sets.
Data Requirement
The input data for Tank Model is rainfall (R), river discharge (Q) and evapotranspiration (ET0).
Table 1 Tank Model input data
Purpose

PeriodR (mm)ET0 (mm)

Q (mm)

Calibration

2015-Feb-27 to Oct-22 (238 days)

1,376

866

517

Validation

2016-Apr-27 to Dec-31(249 days)

1,004

921

467

Ⓒ ISERD

34

IJERD – International Journal of Environmental and Rural Development (2020) 11-2

RESULTS AND DISCUSSION
Like findings by Beven (1997), competing parameter sets were observed, making it impossible toidentify with certainty the optimum parameter set for Tank Model.
Table 2 shows two parameter sets from the calibration in 2015 as well as their calibration andvalidation performances. During calibration, the best performing parameter set had an NS value of0.608. However, during validation, its predictive power reduced to an NS of 0.257. On the other hand,the parameter set with the calibration NS of 0.502 had the best performance during validation, witha validation NS of 0.526. The difference between calibration and validation NS values could be
evidence that parameter sets are dependent on rainfall characteristics as reported in Okiria et al.
(2019). It can also be attributed to the obscurity in setting the initial condition during validation.
Figure 3 shows the best performing Tank Model parameters. Based on the new method to manage
uncertainty, the parameter set with calibration and validation NS of 0.608 and 0.257 respectively ispreferred since it has a very good calibration NS and a sufficient validation NS, and it also yields a
reasonable base flow curve – the classification of NS as good or sufficient is in Foglia et al. (2009).
Fig. 4 shows the observed and simulated hydrographs for 2015 during calibration while Fig.6
shows the observed and simulated hydrographs for 2016 during validation of 2015 parameters. In
2015, the trend of the simulated hydrograph was quite similar to that of the observed hydrograph.
However, in 2016, the trends between observed and simulated hydrographs were less similar. The
dissimilarity in 2016 could be attributed to input data error or in an ability of the model to accurately
represent the rainfall-runoff response of 2016. In both years, majority of the peak discharges were
underestimated. This could be attributed to under estimation of catchment rainfall and or the overestimation of evapotranspiration.
In Fig. 5 the components of the simulated hydrograph for 2015 during calibration are shown
while Fig.7 shows the components of the simulated hydrograph for 2016 during validation by 2015
calibration parameters. The simulated discharge was separated into its surface runoff, inter flow, subsurface flow and base flow components. Surface runoff was dominant during the rainy period whilebase flow was the dominant component in the dry period. In addition, base flow was generally stable
and showed delayed response to rainfall.

Fig. 3 Best performing parameters for Namatala River
catchment (NRc) calibrated in 2015

Ⓒ ISERD

35

B1

B0

.040

0.011

0.004

0.005

Fig. 5 Hydrograph components for 2015 during calibration

A0

1.108

A2

1.387

RMSEv

st parameter set from calibration in 2015 and their validation performance in 2016

Fig. 7 2016 Hydrograph components during validation by 2015

IJERD – International Journal of Environmental and Rural Development (2020) 11-2

C0

D1

SAinitial

SBinitial

SCinitial

SDinitial

AH1

AH2

BH

CH

NSc

RMSEc

NSv

0.026

0.001

0.013

31

690

759

78

98

89

664

952

0.608

1.141

0.257

C1

0.008 0.010 0.002 0.006 0.069 0.004 0.005
124
100
528
51
63
7
55
502 0.502
1.285
0.526
Note: NSc and RMSEc are NS and RMSE values respectively during calibration, and NS v and RMSEv are NS and RMSE values respectively during validation

0.257
1.141
0.608
952

NSv
NSc
CH

RMSEc

.008 0.010 0.002 0.006 0.069 0.004 0.005
124
100
528
51
63
7
55
502 0.502
1.285
0.526
e: NSc and RMSEc are NS and RMSE values respectively during calibration, and NS v and RMSEv are NS and RMSE values respectively during validation

Fig. 5 Hydrograph components for 2015 during calib

IJERD – International Journal of Environmental and Rural Development (2020) 11-2



664
89
98

BH
AH2
AH1

Table 2 Best parameter set from calibration in 2015 and their validation performance in 2016

IJERD – International Journal of Environmental and Rural Development (2020) 11-2

served and simulated hydrograph for best parameter of 2015

A2

0.041

0.040

0.011

B1

B0

C1

C0

0.004

0.005

0.026

0.001

D1

SAinitial

SBinitial

SCinitial

0.013

31

690

759

SDinitial

AH1

AH2

BH

CH

NSc

RM

78

98

89

664

952

0.608

1

Ⓒ ISERD

0.040
0.041

0.028

A2

Note: Qobs is observed discharge, Qsim is simulated discharge

36

36

36

Fig. 5 Hydrograph components forFig. 7 2016 Hydrograph components duⒸ ISERD

0.011

A0

Fig. 6 2016 Observed and simulated hydrograph using 2015 parametersNote: Qobs is observed discharge, Qsim is simulated discharge

0.001
0.026
0.005
0.004

36

Fig. 6 2016 Observed and simulated hydrograph using 2015 parameters

31
0.013

690

SAinitial
D1
B0
B1

C1

C0

Fig. 4 Observed and simulated hydrograph for best parameter of 2015

A1

RD

SBinitial

ote: Qobs is observed discharge, Qsim is simulated discharge

Fig. 4 Observed and simulated hydrograph for best parameter of 2015

759

0.008 0.010 0.002 0.006 0.069 0.004 0.005
124
100
528
51
63
7
55
502 0.502
1valuesrespectively
during calibration,
NS v Hydrographand RMSEv are NS
and RMSE values
respectively
duringbv
c and RMSE
c are NS and RMSE
Fig. 7and2016
components
duringvalidation
016 ObservedNote:and NS
simulatedhydrograph
using
2015
parameters
SCinitial

0.028

A0

78

A1

SDinitial

Table 2 Best parameter set from calibration in 2015 and their validation performance in 2016

IJERD – International Journal of Environmental and Rural Development (2020) 11-2

CONCLUSION
Tank Model was successfully applied to the Namatala River catchment to simulate its rainfall-runoff
process. However, due to equifinality, the model should be applied with caution. In addition, more
research needs to be done to better understand the shortcomings of the model. Acquisition of finer
spatial resolution input data is recommended. Studies on other catchments in Eastern Uganda could
be useful in confirming the applicability of lumped parameter models.
ACKNOWLEDGEMENTS
The study was done during graduate studies at Tokyo University of Agriculture, Tokyo, Japan,
courtesy of scholarship from Japan International Co-operation Agency (JICA), Japan. It goes without
thanking NTC-International Co., Ltd for the opportunity to advance my career.
REFERENCES
Beven, K. 1997. TOPMODEL: A critique. Hydrol. Process, 11, 1069-1085.
Beven, K.J. and Kirkby, M.J. 1979. A physically based, variable contributing area model of basin hydrology.
Hydrological Sciences Bulletin, 24 (1), 43-69.
Foglia, L., Hill, M.C., Mehl, S.W. and Burlando, P. 2009. Sensitivity analysis, calibration, and testing of a
distributed hydrological model using error-based weighting and one objective function. Water Resources
Research, 45 (6).
Japan International Cooperation Agency (JICA). 2014. The preparatory survey report on land-husbandry,water-harvesting and hillside-irrigation project in the Republic of Rwanda.
Japan International Cooperation Agency (JICA). 2017. The project on irrigation scheme development in central
and Eastern Uganda, Final Report, 1, Main Report.
Kobayashi, Y., Watanabe, F., Suzuki, S., Okiria, E. and Kanyike, T. 2018. Verification of availability of
GSMaP rainfall data based on the comparison of observed rainfall data in Africa. Journal of Arid Land
Studies, 28 (S), 85-88.
Ministry of Water and Environment (MWE). 2013. Uganda national water resources assessment, Kampala:
Directorate of water resources management. Ministry of Water and Environment, Uganda.
Nash, J.E. and Sutcliffe, J.V. 1970. River flow forecasting through conceptual models part I, A discussion ofprinciples. Journal of Hydrology, 10 (3), 282-290.
Okiria, E., Okazawa, H., Kobayashi, Y., Yamazaki. Y. and Suzuki, S. 2019. Identifying the minimum numberof observed rainfall events required for optimal TOPMODEL parameters in mid-sized equatorial
catchments. International Journal of Environmental and Rural Development, 10 (2), 113-119.
Onyutha, C. 2016. Influence of hydrological model selection on simulation of moderate and extreme flow
events, A case study of the Blue Nile Basin. Advances in Meteorology, 2016.
Sugawara, M. 1995. Tank model. In Singh, V.P. (Ed.) Computer models of watershed hydrology, U.S.A, Water
Resources Publications, 165-214.
Suryoputro, N., Suhardjono, Soetopo, W. and Suhartanto, E. 2017. Calibration of infiltration parameters onhydrological tank model using runoff coefficient of rational method. AIP Conference Proceedings, 1887
(September).
Xiong, J., Ohnish, Y., Takahashi, K. and Koyama, T. 2009. Parameter determination of multi-tank model withdynamically dimensioned search. Proc Symp Rock Mech Jpn, 38, 19-24.

Ⓒ ISERD

37