The MRB is located in Southeast Brazil within the states of Minas Gerais (45% of the area) and Rio de Janeiro States (55%) with a drainage area of 8126 km² (Figure 1). The Muriaé river is the last main tributary of the Paraíbado Sul river flowing to the Atlantic Ocean.

In this study, hydrological simulations were performed for Carangola and Patrocíniodo Muriaé subbasins (hereafter referred to as CLA and PMU respectively). Carangola stage level gage is at the main tributary of the eponymous river with a drainage area of 742 km². The Patrocíniodo Muriaé stage level gage is

at the Muriaé river and has a catchment area of 2990 km².

The Digital Elevation Model (DEM) used was the product of the Shuttle Radar Topography Mission (SRTM) operated by the National Aeronautics and Space Administration (NASA). The images were available at 30-meter horizontal spatial resolution and 1-meter vertical resolution. In Table 1 the land use and soil type of CLA and PMU are presented. The MRB terrain (Figure 2) is characterized by rugged terrains with topographic features of 1500 m altitude in the northwest quadrant and flat plains in the southeast quadrant.

The region climate is classified as hot and humid with a dry winter, Köppen class Aw [37]. Temperatures are high throughout the year, with a rainy summer (December to March) and a dry winter (June to August) when monthly rainfall averages are less than 50 mm (Figure 3). The average annual rainfalls are 1400 mm (PMU) and 1200 mm (CLA), while the average flow values are 48 m³∙s⁻¹ (PMU) and 13 m³∙s⁻¹ (CLA).

The Climate Prediction Center Morphing Technique – CMORPH [27] is an SQPE with a high spatial-temporal resolution (~8 km and 30 min). The method is based on precipitation rates estimated from PMW sensors. The PMW images are obtained from three sensors, located at polar orbit satellites which yield images for a specific location with a 3-hour temporal resolution (Table 2).

The IR images on board of geostationary satellites (METEOSAT and GOES) are used to increase the spatial-temporal resolution of the final product through wind vectors from the Cloud System Advection Vector (CSAV) method [41]. The wind vectors advect the PMW rainfall rate fields in space and time. Consecutive PMW images are advected forward and backward in time. In morphing, two images from the same time step are composed to generate the final product.

*Classes defined by [36].

Overland, both temperature and emissivity are highly variable, which makes the microwave background signal unpredictable and makes it difficult to use images from emission-based frequencies for precipitation estimates [42]. Therefore, over continents, PMW-based precipitation estimates rely solely on the scattering of higher frequencies microwave from frozen hydrometeors.

An alternative to minimize precipitation errors is through the SOAS method [21]. An efficient interpolation technique [43] was initially developed to integrate radar precipitation estimates and rain gauge measurements. Recently, the methodology was also used to integrate SQPE [33].

The analyzed precipitation at a given grid point is obtained by adding precipitation estimates by remote sensing (radar or satellite) at the point and the sum of the product of the weights of the differences between rain gauges measurements and those estimated by remote sensing [17]. In this case, the error variance will be the sum of the squares of the differences between the measured values and the actual values. Therefore, the weights of the analyzed values will be dependent on the error variance of the precipitation estimates. The analysis is performed so that the error variance is less than the error variance of the measurements. The SOAS equation [21] is:

P a ( x i , y i ) = P r ( x i , y i ) + ∑ k = 1 K w i k [ P g ( x k , y k ) − P r ( x k , y k ) ] (1)

where P a ( x i , y i ) is the analyzed precipitation at a point i of the grid [mm]; P r ( x i , y i ) is the estimated precipitation by remote sensing at a point i of the grid [mm]; P g ( x k , y k ) is the measured precipitation by the rain gauge at point k [mm]; P r ( x k , y k ) is the estimated precipitation by remote sensing at point k [mm]; w i k is the weight that will be set a posteriori; k is the number of rain gauges; (x, y) are the coordinates in UTM [km].

One premise of the method is that both rain gauge measurements and precipitation estimates are not correlated or biased. Thus, it is possible to obtain the weights through:

∑ l = 1 K W l ( ρ k l + ε k 2 ) = ρ k i ;     for     1 ≤ k ≤ K , (2)

where ρ k l is the correlation between the rain gauges k and i errors; ρ k i is the correlation between point i of the grid and the rain gauge k errors; ε k 2 is the normalized observation error; W l is the weight that will be set a posteriori.

The analysis error can be normalized by applying previously elaborated algorithms [44] in the error covariance matrices. The expected analysis error variance (NEXERVA) ( ε a 2 ) can be expressed as:

ε a 2 = 1 − ∑ l = 1 K ρ k i W l (3)

NEXERVA is the ratio between the expected analyzed data error variance and the remote sensing estimates error variance. Thereby, it is possible to determine the spatial distribution of the errors in the analyzed field [21]. In general, NEXERVA is minimal at the rain gauge locations.

The matrix of the covariances of the estimated value errors used to normalize Equations (1) and (2) is the most crucial component of the SOAS [21]. This matrix has great importance in the accuracy of the analysis.

ρ k l = 〈 ( P R k − P a k ) × ( P R l − P a l ) 〉 〈 ( P R k − P a k ) 2 × ( P R l − P a l ) 2 〉 (4)

where ρ k l is the correlation between pixels k and l errors; P R k ( l ) are the precipitation estimates by remote sensing in pixel k(l); P a k ( l ) is the average long-term precipitation estimates by remote sensing in pixel k (l).

TOPMODEL is a rainfall-runoff model defined as deterministic, dynamic, physical-based parameters, and semi-distributed [12]. The model was developed for small humid basins of temperate climate [45]. The model is considered semi-distributed because only the parameter related to the topography, the topographic index, is spatially distributed. The topographic index (λ) can be expressed as λ = ln(α/tanβ), where α is the drainage area per unit of contour and tanβ is the terrain slope. High values of λ indicate points more likely to reach saturation and consequently more likely to generate runoff [45]. Points with equal weights of λ are treated as regions with similar hydrological responses.

Beven and Kirkby (1979) [12] and Beven et al. (1984) [45] described TOPMODEL as a physical-based conceptual model that represents surface and soil dynamics based on the relationship between discharge and storage established from flows in saturated zones due to slope. According to the authors, TOPMODEL combines the advantages of the simplicity of lumped models with the distributed effects of variable areas of contribution and flows through the drainage network. It is also possible to determine the parameter values from the knowledge of the physical characteristics of the hydrographic basin.

The transformation of precipitation into flow into a hydrological model can be divided into two stages: the soil water balance and the flow propagation through the basin [19]. In TOPMODEL, a series of three interconnected reservoirs represents the flow generation process and is the average response of the homogeneous capacity basin: the vegetation reservoir (S₁), the soil unsaturated zone reservoir (S₂), and the soil saturated zone reservoir (S₃) [17]. For each time step, the reservoirs S₁ and S₂ are filled with the levels S ′ 1 and S ′ 2 respectively. The saturation deficit (S) of each time step is the difference between the maximum reservoir level S₂ ( S 2 * ) and the instantaneous level ( S ′ 2 ).

This three reservoirs system generates four possible flows [19]: subsurface flow at the saturated zone (q_s), vertical subsurface flow at the unsaturated zone (q_v), surface runoff generated by infiltration excess (q_h) (Horton mechanism), and surface runoff generated by saturation excess (q_as) (Dunne mechanism) [46] [47].

In the next step, TOPMODEL propagates the surface runoff for the basin outlet hydrograph composition [48]. The main processes involved in the model are presented in Figure 4.

The model uses the premise that the simulation occurs after a dry period which implies the following initial conditions [19]:

· the unsaturated soil zone (S₂) is completely dry (i.e. S ′ 2 = 0 );

· the discharge in the basin outlet is generated exclusively by the subsurface flow, represented by the parameter qs0.

The TOPMODEL’s parameters are presented in Table 3.

For both subbasins, the same calibration methodology was used for all cases, the Shuffled Complex Evolution developed at the University of Arizona (SCE-UA) [49]. The methodology was developed to increase the probability that the best set of parameters found is a global minimum rather than a local minimum. The SCE-UA method was successfully used in the calibration of several hydrological models, such as NAM/MIKE 11 [50], Sacramento Soil Moisture Accounting (SAC-SMA) [51] [52], and TOPMODEL [53].

The probability of a global minimum was increased by the SCE-UA method. This method evolves multiple groups of parameter sets independently with the Competitive Complex Evolution (CCE) [49] [51]. After each round of the simulation, the parameter sets are rearranged to evolve with different partners. The simulation is repeated until the user-defined objective function of the best parameter set meets convergence criteria.

The SCE-UA calibration methodology was applied through the rtop library [54] of free software R (version 3.3.2). The objective function chosen was the Nash-Sutcliffe efficiency [55], which is given by:

NSE = 1 − ∑ i = 1 n ( Q s i − Q o i ) 2 ∑ i = 1 n ( Q o i − Q ¯ ) 2 , (5)

where NSE is the Nash-Sutcliffe efficiency; Q s i is the simulated discharge at time step i; Q o i is the observed discharge at time step i; Q ¯ is the mean observed discharge of the whole period; n is the number of time steps.

For the simulations, a period of 4 years was selected between 2009 and 2013. To meet TOPMODEL’s premise that simulations must start in a dry period (i.e. absence of surface runoff), the month of September was defined as the beginning of the hydrological year. The hydrological years of 2009/2010 and 2010/2011 were chosen for calibration, while the hydrological years of 2011/2012 and 2012/2013 were selected for validation.

Daily rain gauge precipitation accumulation measurements between 1000 UTC (Coordinated Universal Time) of consecutive days and respective CMORPH precipitations estimates were used in the integration process with SOAS. Both rain gauges and discharge data were obtained from the Brazilian Hydrometeorological Network, which is operated by the Brazilian Water Agency (ANA). The SOAS method is described in detail in Pereira Filho et al. (2018) [33]. Evapotranspiration data were obtained from the closest weather station (Itaperuna, OMN #83695), operated by the Brazilian National Institute of Meteorology (INMET) in which evapotranspiration is measured with a lysimeter.

Fifteen (15) rain gauges were selected (Figure 5(A)) for the SOAS method at the MRB. In the expected analysis error variance (NEXERVA) results (Figure 5(B)), it can be noted the influence of the rain gauges of the pluviometers, in which the greater the proximity to the observed data, the more significant the reduction of the error variance. The NEXERVA values for CLA (0.34) and PMU (0.38) subbasins show that the SOAS methodology reduced the CMORPH estimates uncertainties by approximately 65%.

The calibrated parameters of each simulation and the distribution of the topographic index of each subbasin are shown in Table 4 and Figure 6, respectively.

To comprehend the importance of each parameter, sensitivity tests were applied to all simulations (Figure 7 and Figure 8). The sensitivity analyses were

obtained through simulations in which only a given parameter has a variable value to determine its relevance in the calibration efficiency.

It can be noted that for all four simulations, three parameters presented the greatest sensitivity: qs0, m, and Srmax. The primary relevance of the parameter m coincides with previous studies [17] [45], which indicates the importance of the soil transmissivity variation with depth. The significance of the parameter qs0 suggests that the basin’s initial condition has great importance in the model’s performance. The high sensitivity of the parameter Srmax indicates the evapotranspiration importance. Higher values of Srmax for PMU are in agreement with the physical characteristics of its subbasin, which has greater forest coverage and less urban area (Table 1). The parameter vr (i.e. runoff speed) had higher values with SOAS, which indicates that in this system, precipitation tends

to be delayed with CMORPH, which makes greater speed necessary to compensate for the shorter time.

In PMU, simulations with CMORPH datasets (Figure 9) yielded similar performance for both calibration (NSE = 0.67) and validation (NSE = 0.66) (Table 5). Most peak flows were underestimated. Simulations with SOAS (Figure 10) presented higher performance for calibration (NSE = 0.60) in relation to validation (NSE = 0.39) (Table 5). Most peak flows were underestimated in the calibration and overestimated for validation for the hydrological year 2011/2012 and underestimated for 2012/2013.

In CLA, simulations with CMORPH (Figure 11) yielded a better result for the validation period (NSE = 0.61) over calibration (NSE = 0.54) (Table 5). In most cases, peak flows were underestimated. The fact that the validation efficiency was superior to that of calibration is an indication that the calibrated parameters satisfactorily represented the characteristics of the subbasin. In simulations with SOAS (Figure 12), the calibration period presented good efficiency (NSE = 0.85), with peak flows been well represented in the hydrological year 2010/2011 (Table 5). However, the simulations were not satisfactory for the validation period (NSE = −0.04). In the 2011/2012 hydrological year, the peak flows were overestimated approximately 100%, which explains the negative NSE value (i.e. the series mean would have been a better predictor).

For both subbasins, the highest NSE values were obtained with CMORPH data. However, in the analysis of high-level discharges (Table 6), simulations with SOAS resulted in a higher success rate (28% and 18% for PMU and CLA respectively) compared to CMORPH (18% and 13%).