**3. Methodology**

The gauging station 1 ka31 (Little Ruaha at Mawande) was used for SWAT2009 model calibration for the period 1971–1979. Daily stream flow data from this station were checked for quality, and this involved the identification of errors from suspicious extreme values. **Figure 3** illustrates the percentage of available data points, missing data points, and removed data points. Six percent (6%) of the data was deleted from the time series, and 2% of the data was missing. Therefore only 92% of the record was used for the calibration method. Both manual and automatic calibration approaches were used for this study. The pre-calibration parameter sensitivity analysis was performed to identify parameters that are expected to have a strong influence on the model simulation results.

**Figure 3.** Summary of the screened daily stream flow data used in this study.

In this study, the Sequential uncertainty fitting (SUFI-2) approach was combined with SWAT to quantify parameter uncertainty of the stream flow simulations for the Little Ruaha River (5195 km2 ). The SWAT2009 model was setup for the whole GRR basin but the analysis presented here is based on one major tributary only. The hydrological response units (HRU) were characterized using the dominant land use, soil, and slope to keep the complexity of the analysis to a practical limit for the uncertainty propagation. Daily stream flow data from this station were checked for quality, and this involved the identification of errors from unexplained extreme value.

#### **3.1. Sensitivity analysis**

area varying from 1 to 2 ha per household. Large-scale farming is limited a few numbers of individuals and companies (often parastatals). Maize is the dominant crop in most of the smallholder farming systems. Maize is grown in mixtures most often beans but intercropping with sunflower and cowpeas are also common. Peas are very important crop and are often grown at the beginning of the dry season and are most often grown on broad ridges. Sorghum and millet are also grown, but the production is very minor compared to maize even in the drier areas where, the more drought resistant sorghum would be more appropriate than maize which is much more water demanding. In the area potatoes are an important crop where transport facilities are good they are often grown as a cash crop. The area under cultivation varies considerably within the zone approximately 25–75% with the highest land use pressure in the area around Iringa, where there has been severe overutilization of the land resources which has led to severe erosion.

The gauging station 1 ka31 (Little Ruaha at Mawande) was used for SWAT2009 model calibration for the period 1971–1979. Daily stream flow data from this station were checked for quality, and this involved the identification of errors from suspicious extreme values. **Figure 3** illustrates the percentage of available data points, missing data points, and removed data points. Six percent (6%) of the data was deleted from the time series, and 2% of the data was missing. Therefore only 92% of the record was used for the calibration method. Both manual and automatic calibration approaches were used for this study. The pre-calibration parameter sensitivity analysis was performed to identify parameters that are expected to have a strong

**3. Methodology**

influence on the model simulation results.

54 Achievements and Challenges of Integrated River Basin Management

**Figure 3.** Summary of the screened daily stream flow data used in this study.

Sensitivity analysis allows for the identification of model parameters that exert a strong influence on the model output, thus largely controlling the behavior of the simulation process. In this study, a sensitivity analysis was carried out using the Latin Hypercube One-factor At a Time (LH-OAT) algorithm [8, 14]. The Sensitivity analysis minimizes the number of parameters to be used in the calibration step. The Latin Hypercube simulation is based on a Monte Carlo approach with stratified sampling. The results of the sensitivity analysis are parameters arranged in ranks, where the parameter with a maximum effect obtains rank 1, and parameter with a minimum effect obtains the rank which corresponds to the number of all analyzed parameters. The parameter that has a global rank 1 is categorized as "very important," rank 2–7 as "important," rank 8–27 "slightly important" and rank 28 as "not important" [14].

The sensitivity analysis in this study was done using (i) automatic global sensitivity analysis in SUFI-2, (ii) manual analysis of the sensitive parameters based on the output of the global sensitivity analysis. The global sensitivity analysis in SUFI-2 is not able to analyze all the parameters in SWAT; it analyses the sensitivity of the pre-defined 27 parameters (**Table 1**). In this approach, parameter sensitivity is determined using the multiple regression equations, which regresses the Latin Hypercube generated parameters against objective function values. The *t*-stat and p-value are statistical measures used to evaluate sensitivity in SWAT-CUP. A *t*-stat is used to identify the relative significance of each parameter by providing a measure of sensitivity (larger absolute values are more sensitive). p-Values determined the significance of the sensitivity where a value close to zero has more significance. Both manual and automatic calibration followed the sensitivity analysis. The manual calibration was performed based on the understanding of the sub-basin characteristics. The results of the global sensitivity analysis indicated the sensitive parameters and helped to guide the initial parameter ranges. The calibration procedure involved the following steps:



response units. **Table 2** shows the initial parameter ranges of the sensitive 20 parameters,

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The identifiability of parameters was examined visually using scatter plots of model parameter values versus CE. **Figure 4** shows scatter plots with the values of each parameter defined versus their corresponding Nash-Sutcliffe efficiency (CE), where the parameter values were obtained from Latin Hypercube sampling of the initial range defined using 2000 simulations. Scatter plots of the parameter values versus objective function were used to examine the identifiability of individual parameters. Based on the scatter plots the identifiable parameters are expected to show a distinct maximum, and lack of a distinct maximum indicates the difficulty in getting the optimal values that give a good model performance, therefore, the parameter becomes poorly identifiable. It is evident that none of the parameters are identifiable.

**Parameter Lower limit Upper limit Change option** v\_\_ALPHA\_BF.gw 0.00 1.00 Replacement r\_\_CN2.mgt −50 50 Relative v\_\_SURLAG.bsn 0.00 24.00 Replacement v\_\_REVAPMN.gw 0.11 0.80 Replacement r\_\_SOL\_K (2).sol 0.39 4.28 Relative a\_\_GWQMN.gw 1983 2889 Absolute r\_\_SLSUBBSN.hru 0.13 0.33 Relative v\_\_BLAI{120}.CROP.DAT 3.63 6.95 Replacement v\_\_CANMX.hru 2.87 8.51 Replacement v\_\_CH\_N2.rte 0 0.3 Replacement r\_\_HRU\_SLP.hru 0 10 Relative a\_\_GW\_REVAP.gw 0.02 0.12 Absolute r\_\_BIOMIX.mgt 0.11 0.69 Relative v\_\_EPCO.hru 0 0.4 Replacement r\_\_SOL\_AWC (2).sol 0 0.9 Relative v\_\_RCHRG\_DP.gw 0 1 Replacement v\_\_ESCO.hru 0 1 Replacement a\_\_GW\_DELAY.gw 0 129 Absolute v\_\_CH\_K2.rte 24.27 94.18 Replacement r\_\_SOL\_K (1).sol 0.66 5.55 Relative

**Table 2.** Defined upper and lower limits of initial parameter ranges, the extension of the files in which they are located,

where the most sensitive parameters are presented in row 2–10.

**3.3. Parameter distributions**

and the option used for carrying out changes.

**Table 1.** Parameter sensitivity ranking and category of the most sensitive parameters.

#### **3.2. Assigning initial parameter ranges**

The results of the sensitivity analysis indicated the sensitive parameters and helped in guiding the setup of the initial parameter ranges. It was important to consider the physical meaning of each parameter and its effects on the sub-basin behavior. Therefore, the initial parameter sets were guided by the understanding of the physical basin characteristics and the default upper and lower limits established in SWAT. In SWAT default parameters can be modified for the whole sub-basin (lumped), or in a distributed way for individual sub-basins or hydrological response units. **Table 2** shows the initial parameter ranges of the sensitive 20 parameters, where the most sensitive parameters are presented in row 2–10.

#### **3.3. Parameter distributions**

**3.2. Assigning initial parameter ranges**

The results of the sensitivity analysis indicated the sensitive parameters and helped in guiding the setup of the initial parameter ranges. It was important to consider the physical meaning of each parameter and its effects on the sub-basin behavior. Therefore, the initial parameter sets were guided by the understanding of the physical basin characteristics and the default upper and lower limits established in SWAT. In SWAT default parameters can be modified for the whole sub-basin (lumped), or in a distributed way for individual sub-basins or hydrological

**Parameter Description** *t***-Stat** *p***-Stat Rank Process**

SURLAG Surface runoff lag time (days) −1.54 0.12 3 Runoff

SLSUBBSN Average slope length (mm−1) 1.17 0.19 7 Topography

HRU\_SLP Average slope steepness of the HRU −0.56 0.57 11 Topography GW\_REVAP Groundwater "revap" coefficient −0.46 0.63 12 Groundwater

RCHRG\_DP Deep aquifer percolation fraction −0.21 0.83 16 Groundwater

BLAI Leaf area index for crop 1.05 0.29 8 Crop CANMX Maximum canopy storage (mm) 0.60 0.54 9 Runoff

BIOMIX Biological mixing efficiency −0.39 0.69 13 Soil

−34.23 0.00 1 Ground water

−1.51 0.13 4 Groundwater

−1.28 0.19 6 Groundwater

0.58 0.55 10 Channel

0.24 0.80 14 Evaporation

−0.10 0.91 17 Evapotranspiration

0.09 0.92 18 Groundwater

0.07 0.94 19 Channel

0.21 0.82 15 Soil

−12.90 0.00 2 Runoff

−1.39 0.16 5 Soil

ALPHA\_BF Base flow alpha factor for recession constant (days)

moisture condition II

56 Achievements and Challenges of Integrated River Basin Management

shallow aquifer for revap (mm)

shallow aquifer for flow (mm)

CN2 SCS runoff curve number for

REVAPMN Threshold water depth in the

GWQMN Threshold water depth in the

SOL\_K(2) Saturated hydraulic conductivity soil layer 2 (mm h−1)

CH\_N2 Manning's "n" value for the main channel

EPCO Plant evaporation compensation factor

SOL\_AWC Available soil water capacity (mm

ESCO Soil evaporation compensation factor

GW\_DELAY Movement of water from shallow

CH\_K2 Channel effective hydraulic

aquifer to the root zone

conductivity (mm h−1)

**Table 1.** Parameter sensitivity ranking and category of the most sensitive parameters.

O/mm soil)

H2

The identifiability of parameters was examined visually using scatter plots of model parameter values versus CE. **Figure 4** shows scatter plots with the values of each parameter defined versus their corresponding Nash-Sutcliffe efficiency (CE), where the parameter values were obtained from Latin Hypercube sampling of the initial range defined using 2000 simulations. Scatter plots of the parameter values versus objective function were used to examine the identifiability of individual parameters. Based on the scatter plots the identifiable parameters are expected to show a distinct maximum, and lack of a distinct maximum indicates the difficulty in getting the optimal values that give a good model performance, therefore, the parameter becomes poorly identifiable. It is evident that none of the parameters are identifiable.


**Table 2.** Defined upper and lower limits of initial parameter ranges, the extension of the files in which they are located, and the option used for carrying out changes.

**3.4. Final calibrated parameter ranges**

**Table 3.** Final parameter ranges calibrated using SUFI-2.

Latin Hypercube sampling was used to sample parameters within the initial ranges using 2000 ensembles and a uniform distribution. The CE was used to get optimum parameter values and to separate behavioral from non-behavioral parameter sets, where a cutoff limit of CE = 0.45 was used. **Table 3** shows the parameter range and optimal value for the best simulation. ALFA\_BF is the most sensitive parameter followed by CN. **ALPHA\_BF** parameter is a direct index of ground water flow response to changes in recharge. The ALPHA\_BF value between 0.1 and 0.3 reflects an area with the slow response to changes in flow, a value of 0.9–1 reflects an area with a rapid response to changes in flow. For the Little Ruaha sub-basin, a value of 0.25 was obtained. The CN is the parameter that determines the amount of runoff to be generated from a sub-basin, so it was expected to be sensitive for the Little Ruaha sub-basin with an optimal value of −1.69. **SURLAG** was the third most sensitive parameter and is the fraction of runoff that reaches a sub-basin outlet on any given day. SURLAG was sensitive for this sub-basin because of the low time of concentration, and an optimum value of 3.5 days was obtained. **REVAPMN** presents the threshold depth of water in the shallow aquifer for return flow to the root zone to occur. This parameter is most important in areas where the water table is high or areas with deep-rooted crops. An optimum

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**Parameter name Lower limit Upper limit Optimal SUFI-2**

v\_\_ALPHA\_BF.gw 0.00 1.00 0.25 r\_\_CN2.mgt −50 50 −1.69 v\_\_SURLAG.bsn 0.00 24.00 3.5 v\_\_REVAPMN.gw 0.11 0.80 0.57 r\_\_SOL\_K (2).sol 0.39 4.28 1.36 a\_\_GWQMN.gw 1983 2887.18 2071.38 r\_\_SLSUBBSN.hru 0.13 0.33 0.32 v\_\_BLAI{120}.CROP.DAT 3.63 6.95 4.82 v\_\_CANMX.hru 2.87 8.51 5.95 v\_\_CH\_N2.rte 0 0.3 0.06 r\_\_HRU\_SLP.hru 0 10 0.75 a\_\_GW\_REVAP.gw 0.02 0.12 0.10 r\_\_BIOMIX.mgt 0.11 0.69 0.40 v\_\_EPCO.hru 0 0.4 0.004 r\_\_SOL\_AWC (2).sol 0 0.9 1.10 v\_\_RCHRG\_DP.gw 0 1 1.94 v\_\_ESCO.hru 0 1 0.02 a\_\_GW\_DELAY.gw 0 129 −31.05 v\_\_CH\_K2.rte 24.27 94.18 59.94 r\_\_SOL\_K (1).sol 0.66 5.55 0.66

**Figure 4.** Scatter plots of the calibrated parameters of Little Ruaha River basin (Gauging station 1 ka31) versus Nash-Sutcliffe efficiency, obtained from Latin Hypercube sampling of the large initial range using 2000 simulations.

However, it should be noted that in-identifiability of a parameter does not indicate that the model was not sensitive to these parameters. The sensitivity analysis results identify the most sensitive parameters to be considered for calibration but do not consider the interactions between parameters, therefore having the most sensitive parameters does not mean that the parameter will be identifiable. Estimation of an-identifiable parameters is difficult because there may be many combinations of these parameters that would result in similar model performance (equifinality). Many factors might have led to the non-identifiability of parameters in this study. The interactions between parameters may have contributed to the equifinality which might be associated with the simplified representation of the sub-basin (dominant HRU). Interactions between soil parameters (soil depth and available water capacity) and ground water parameters (Groundwater delay) is expected in SWAT. It is hard to explain these interactions since SWAT considers two soil layers (root zone and unsaturated zone) and ground water (conceptual shallow and deep aquifer stores) and there is not enough information regarding sub-surface water processes to will enable a better explanation of the parameter interactions.

#### **3.4. Final calibrated parameter ranges**

Latin Hypercube sampling was used to sample parameters within the initial ranges using 2000 ensembles and a uniform distribution. The CE was used to get optimum parameter values and to separate behavioral from non-behavioral parameter sets, where a cutoff limit of CE = 0.45 was used. **Table 3** shows the parameter range and optimal value for the best simulation. ALFA\_BF is the most sensitive parameter followed by CN. **ALPHA\_BF** parameter is a direct index of ground water flow response to changes in recharge. The ALPHA\_BF value between 0.1 and 0.3 reflects an area with the slow response to changes in flow, a value of 0.9–1 reflects an area with a rapid response to changes in flow. For the Little Ruaha sub-basin, a value of 0.25 was obtained. The CN is the parameter that determines the amount of runoff to be generated from a sub-basin, so it was expected to be sensitive for the Little Ruaha sub-basin with an optimal value of −1.69. **SURLAG** was the third most sensitive parameter and is the fraction of runoff that reaches a sub-basin outlet on any given day. SURLAG was sensitive for this sub-basin because of the low time of concentration, and an optimum value of 3.5 days was obtained. **REVAPMN** presents the threshold depth of water in the shallow aquifer for return flow to the root zone to occur. This parameter is most important in areas where the water table is high or areas with deep-rooted crops. An optimum


**Table 3.** Final parameter ranges calibrated using SUFI-2.

However, it should be noted that in-identifiability of a parameter does not indicate that the model was not sensitive to these parameters. The sensitivity analysis results identify the most sensitive parameters to be considered for calibration but do not consider the interactions between parameters, therefore having the most sensitive parameters does not mean that the parameter will be identifiable. Estimation of an-identifiable parameters is difficult because there may be many combinations of these parameters that would result in similar model performance (equifinality). Many factors might have led to the non-identifiability of parameters in this study. The interactions between parameters may have contributed to the equifinality which might be associated with the simplified representation of the sub-basin (dominant HRU). Interactions between soil parameters (soil depth and available water capacity) and ground water parameters (Groundwater delay) is expected in SWAT. It is hard to explain these interactions since SWAT considers two soil layers (root zone and unsaturated zone) and ground water (conceptual shallow and deep aquifer stores) and there is not enough information regarding sub-surface water processes to will enable a better explanation of the

**Figure 4.** Scatter plots of the calibrated parameters of Little Ruaha River basin (Gauging station 1 ka31) versus Nash-Sutcliffe efficiency, obtained from Latin Hypercube sampling of the large initial range using 2000 simulations.

58 Achievements and Challenges of Integrated River Basin Management

parameter interactions.

1.91 and 0.36, respectively. These results confirm quite large uncertainty of the simulated discharge due to the large equifinality in parameters and reliability of input data (precipitation and daily evaporation data). **Table 4** shows a summary of model performance for the calibrations and a comparison between all parameter sets (full range) and behavioral parameter sets.

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In presenting results, the following performance measures were used;

• The percentage of observations covered by the 95PPU (P-factor)

)

**Table 4.** Summary of performance statistics for the best simulation.

**Figure 6.** Calibration at 1 ka31-Mawande (95PPU for full range simulations).

• Nash-Sutcliffe efficiency (CE) • Coefficient of correlation (R<sup>2</sup>

• The relative distance between the observed data and the 95PPU (R-factor)

**Station Simulations P-factor R-factor CE R2** 1ka31 Full range 0.58 1.91 54% 62%

Behavioral 0.21 0.36 54% 62%

**Figure 5.** Spatial variations in leaf area index within the Little Ruaha basin.

value of 0.57 was obtained. SOL\_K (2) is the saturated soil hydraulic conductivity (mm h−1). In this study, a SOL\_K value of 1.66 mm h−1 was used. This parameter relates to water flow rate to the hydraulic gradient and is a measure of the rate of water movement through the soil.

The **GWQMN** is the threshold water level in the shallow aquifer for return flow to occur (mm). The ground water flow to the main channel is allowed only when the depth of water in the shallow aquifer is equal to or greater than the threshold depth of water in the shallow aquifer required for the return flow to occur. An optimum value of 2071.38 (mm) was obtained. The obtained value for the mean slope steepness of the basin (**SLSUBBSN**) is 0.32, indicating that the sub-basin is influenced by low to moderate slopes and has implications for the runoff generation process. The optimum value for the maximum potential **LAI** is 4.82. The value corresponds to the MODIS data which indicates LAI for the Little Ruaha catchment ranges from low to moderate values (**Figure 5**). **CANMIX** represents the maximum canopy area, and an optimum value of 5.95 mm was obtained. This value corresponds to the leaf area index indicated in (**Figure 5**). The Manning roughness coefficient "n" for channel flow (**CH\_N (2)**) is the parameter that influences channel roughness, an optimum value of 0.06 was obtained.
