1 Introduction

An unperturbed patch of the Amazon forest appears homogeneous from the sky. In reality, the forest is a mosaic of landscapes with valleys, plateaus and slopes characterized by variable floristic compositions. At scales of the order of one kilometer, the characteristics of non-flooded tropical forest ecosystem, known as ‘Terra Firme’, presents spatial variability of vegetation, soil type [1], topography [2], water fluxes [3] and phreatic zone depths and gradients [4]. The variabilities are masked by dense forest cover. The heterogeneity of landscape affects the exchange of radiation, energy, water and carbon between land and atmosphere. The exchange processes are fundamental to the functioning of the ecosystem [5] and to the regulation of evapotranspiration (ET) and carbon balance [6, 7].

In the central region of the Amazon forest, the landscape usually comprises plateaus, slopes and valleys. The plateaus are covered with high forest and are bounded by slopes, which descend into low-gradient valley floors [8]. The water table in the valleys is near the surface, for most of the year, with pools, puddles and small streams in some places, known as ‘Igarapes’. It is estimated that, in the central Amazon, plateaus, valleys and slopes occupy 31%, 29% and 40%, respectively, of the total surface area [8].

The Amazon forest environments are dynamic. Ground water from plateaus and slopes flows continuously down the slopes keeping the water table in the valleys near the surface even in dry seasons [9, 10]. The floristic composition of species, such as leaf area and root depth, over the topographic gradients, play an important role in energy and water budgets. In valley areas, the species are adapted to conditions of episodic hypoxia as indicated by the presence of adventitious surface roots and poorly drained hydromorphic sandy soils [11]. Such episodes induce a decrease in stomatal conductance and photosynthetic rate, limiting plant growth [12, 13]. In plateau areas, the water table is about 30 m below the surface [3, 4]. The extraction of water by vegetation occurs up to eight meters below surface, especially in dry season, to maintain high photosynthetic rates [14]. In these areas, the soil is extremely clayey (‘Latosol’) with high porosity, low water availability, and high-saturated hydraulic conductivity [15]. While surface runoff is dominant in the valley, the physical properties of soils and plants affect the infiltration process in the plateau, impacting the amount of water available in the soil for extraction by plant roots.

The representation of complex landscape is not included in the current and past Earth System bio-geophysical models: BATS—Biosphere Atmosphere Transfer Scheme [16], SiB—Simple Biosphere [17], ISBA—Interactive Soil Biosphere Atmosphere model [18], CLASS—Canadian Land Surface Scheme [19], IBIS—Integrated Biosphere Simulator [20], CLM—Common Land Model [21], and JULE—Joint UK Land Environment Simulator [22]. These models consider tropical forest and its structure, as well as its functional characteristics, as being horizontally uniform, and thus a one-dimensional soil-vegetation column is sufficient for their description [23]. In order to characterize realistically the bio-geophysical processes, it is necessary that the models take into account the heterogeneities. For this purpose, it is important to better understand the differences between valley, slope and plateau in terms of water, energy and carbon budgets. The inability to account for these features may mask the real biosphere impact on climate functioning. A more accurate understanding of fine-scale spatial processes can lead to the development of more accurate parameterizations than those found so far.

Mathematical models with all the processes adequately included can play a crucial role in our ability to estimate the quantity of carbon that humanity can emit, in principle, to limit climate change and help the reduction of epistemic uncertainties in future climate scenarios and the changes in vegetation cover. This improves the comprehension of the impact of Amazon forest on global environmental change.

In spite of many modeling studies of the Amazon region, the mesoscale environments remain poorly explored. The present study aims to improve the understanding of the valley and plateau land surface fluxes. The objective of this work is to characterize and parameterize the landscape features (soil, vegetation and hydraulics) governed by relief attributes at local scale in a Land Surface Model, in order to simulate the differences in carbon, energy and hydrological fluxes between plateau and valley, at a central Amazon rainforest experimental site. In this paper, model results are compared with observational data. The following section describes details about the data and the methodology used in the work. Results and discussion are presented in Sect. 3. Section 4 draws some final considerations of the work.

2 Materials and methods

2.1 Study area description

The study area is an instrumented hydrological catchment of 6.37 km2 (54° 58′ W, 2° 51′ S) located in the Cuieiras Biological Reserve (CBR). The site location is 80 km northwest of Manaus within the pristine central Amazon tropical forest (Fig. 1). CBR presents a tropical rainforest climate (Af) according to Köppen classification [24]. Monthly average temperatures vary between 25 °C in July and 27 °C in November. Average relative humidity exceeds 80% any time of the year [25]. The annual rainfall varies from 1400 to 2800 mm with a climatological mean of approximately 2000 mm. The rainy season occurs between November and May and a relative dry season between June and October. This means that a rainy season is well defined, although temperature remains uniform and humidity remains high throughout the year. This seasonal variability is due to the South American monsoon variability and the annual migrations of the Intertropical Convergence Zone (ITCZ) and the equatorial trough.

Fig. 1
figure 1

Location of Cuieiras biological reserve, Manaus, Amazonas, Brazil. K34 and B34 points indicate the localization of the plateau and valley observation points, respectively

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The site is a highly incised headwater catchment consisting of plateau areas that vary in height between 90 and 110 m above sea level (asl). The slopes are steep and concave, leading to broad and flat valley bottoms at 40–60 m asl. This topography is typical of the Amazon rainforest [8]. The vegetation cover on the plateau and slope areas is composed of tall and dense non-flooding tropical forest, with canopy heights varying between 30 and 44 m. In the valley, the ground-cover vegetation is less dense, with canopy heights varying from 15 to 25 m [26]. Soil composition can be classified into three dominant types along the topographic gradient: clayey Oxisols on the plateaus (Yellow Latosols in the Brazilian system), transitioning to less clayey Ultisols on the slopes (Podzol in the Brazilian system) and sandy Spodosols in the valley areas [27]. In the valley, surface water table up to 100 m wide (swampy pools) is present yearlong. Detailed descriptions of the site can be found in other works [1, 2, 28,29,30]

2.2 Data sets

Meteorological and hydrological datasets used in this study are provided by the Large-Scale Biosphere–Atmosphere (LBA) Experiment in the Amazon. The local meteorological datasets come from two micrometeorological eddy flux towers located 600 m apart: one on the plateau (known as K34; 2° 36′ 32.67″ S, 60° 12′ 33.48″ W, 96 m asl), and the other on the valley bottom (known as B34; 2° 36′ 09.8″ S, 60° 12′ 44.5″ W, 42 m asl), with an elevation difference of 54 m (Fig. 2). The plateau tower provided the data for this study from January 2000 to December 2011, that includes air temperature (°C), precipitation (mm), downward shortwave and longwave radiation (W m−2), relative humidity, carbon dioxide CO2 (µ mol m−2 s−1), latent LE (W m−2) and sensible H (W m−2) heat fluxes, and wind speed (m s−1). The valley bottom tower provided data from January 2006 to December 2006. All measurements were conducted just above the tower top with temporal resolution of 60 min. Details about measured variables and descriptions about K34 and B34 tower instrumentation are found in other studies [28, 31]. Lastly, the climatological monthly average precipitation was obtained from National Institute of Meteorology (INMET), for the city of Manaus, between 1901 and 1999.

Fig. 2
figure 2

Topographical gradient at Cueiras site in central Amazon tropical rain forest (green line) and instrumentation. Blue triangle symbols show the height of the water table at the positions of boreholes for monitoring

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The hydrological data collected from the plateau and valley areas includes soil water content (m3 m−3), stream discharge (m3 s−1) and water table level depth (m). The plateau soil water content data was obtained by neutron probes from three sampling access tubes T1, T2 and T3, schematically shown in Fig. 2, installed 4.8 m depth, on weekly or biweekly basis from December 2001 to December 2006 [4]. It was also obtained by Time Domain Reflectometry (TDR) via six sensors at varying depths (0.8–8.0 m) installed along 15 m shaft walls, recording data on hourly basis between January 2003 and February 2006 [14]. The water table depth and stream discharge data in the valley area are available for the period July 2002—October 2006. The stream discharge was measured using the ultrasonic Doppler technique every 30 min and downloaded on a weekly basis [2]. The water table depth was measured weekly via seven piezometers (Polyvinyl Chloride tubes with 5 cm diameter and filters) placed over the valley area [3].

2.3 The INLAND model and development of an unconfined aquifer model

The INtegrated LAND surface Brazilian model (INLAND) was developed based on IBIS model [20, 32]. INLAND included all the main features of IBIS, using a modular and physically consistent framework to perform integrated simulations of water, energy, and carbon fluxes. Some improvements were embedded into INLAND modules (INLAND, v1.0) to simulate tropical processes [33, 34].

Land surface module of INLAND is based on the second-generation LSX model [35] with six soil layers of varying thicknesses and with an upper (trees) and a lower (shrubs and grasses) canopies. There are twelve plant functional types (PFTs), each with distinct carbon pools for leaves, stems and roots. The Amazon basin is represented by the tropical broadleaf evergreen tree PFT. INLAND model consists of three modules with their characteristic temporal scales: a land surface module (minutes to hours), a vegetation phenology module (days to weeks), and carbon balance and vegetation dynamics modules (yearlong). Here, we give a gist of the modules that are most relevant to this study.

Soil module simulates soil temperature, water content and ice content (when required) in each soil layer and solves the θ-based form of the Richard’s equation, where the soil moisture change in time and space is a function of soil water retention curve, soil hydraulic conductivity, upper and lower boundary conditions and plant water uptake. The plant root-water uptake, represented by a sink term in the macroscopic Richard’s equation, is a function of atmospheric demand, soil physical properties, root distribution, and soil moisture profile [32].

Drainage from the bottom soil layer is modeled assuming gravity drainage and neglects interactions with groundwater aquifers. The lower boundary condition for the drainage is set via an empirical coefficient ranging from 0 (no drainage) to 1 (100% free drainage). This methodology is applicable to plateau areas, where groundwater responses are more gradual due to longer water percolation time through a deep vadose zone. However, there is a clear limitation in the case of the valley areas, since baseflow is crucial to sustain discharge during the dry season. Moreover, there is a direct drainage dependence on the time-variation of the amount of water stored in the valley. Therefore, a lumped unconfined aquifer model [36, 37] was incorporated into INLAND, in order to represent the contrasting groundwater responses in both environments and, at the same time, keeping the model’s simplicity. The water table is interactively coupled to the soil column through the soil drainage fluxes (groundwater recharge), represented by the following water balance equation:

$$S_{y} \frac{dH}{{dt}} = I_{gw} - Q_{gw} ,$$
(1)

where Sy (dimensionless) is the specific yield of the unconfined aquifer; H (mm) is the water table level above the datum; Igw (mm day−1) is the groundwater recharge flux, which is the flux at the interface of unsaturated and saturated zones (i.e., the water table); and, Qgw (mm day−1) is the groundwater discharge to streams (i.e., groundwater runoff). Central Amazon rainforest valley sandy soils have Sy about 0.265 [38].

A regression analysis was performed to obtain a (nonlinear) relationship between the baseflow discharge and water table depth [36]. The regression data spanned over 5 years of baseflow discharge (Qgw) and water table level (Dgw) for the valley study site. A strong relationship was identified (coefficient of determination R2 = 0.85; Fig. 3). The baseflow flux was separated from the daily discharge using a digital recursive filter technique [39]. This method is widely used for the continuous partitioning of streamflow discharge between surface runoff and baseflow, since it is fast, efficient, reproducible and objective [36, 40,41,42,43].

Fig. 3
figure 3

Regression analysis between water table depth and baseflow data valley, from July 2002 to October 2006

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The groundwater model represented by (1) and fitting line shown in Fig. 3 were interactively coupled with the soil model in INLAND. The total height of the active unsaturated soil column can vary in response to water table depth fluctuations because the number of unsaturated layers is variable [36].

The INLAND model includes a non-linear root water extraction scheme to describe the impact of soil water stress [20]. The potential transpiration is first distributed over the entire rooted zone and, then, restricted to actual root water uptake by a soil water stress reduction function. A linear function was added to describe the soil water uptake reduction caused by root oxygen deficiency [44]. Under optimal moisture conditions, the maximum possible root water extraction rate, integrated over the rooting depth, is equal to the potential transpiration rate. Under non-optimal conditions (i.e. soil is either too dry or too wet), the root water extraction rate may be restricted, reducing transpiration. For saturated conditions, the reduction of root water uptake occurs between 0.83 and 1.0 degree of soil saturation, which leads to a reduction of 17–0% in the plant transpiration.

2.4 Simulations with INLAND Model for plateau and valley areas

Model simulations were run with the single-point offline version of the model (INLAND 1D) with the CO2 concentration in the atmosphere set to a constant value of 400 parts per million (ppm). The simulations were performed at plateau and valley areas to determine the land surface fluxes near the observed data locations. The model was forced with observed hourly meteorological data collected at K34 tower for 12 full years, from January 1st, 2000, to December 31th, 2011. The initial 60 min of the simulation, considered tune up, was discarded from the analysis.

Initially, we considered the model parameters calibrated for a plateau area for the same study site [45]. However, this calibration was performed without emphasis on soil water dynamics processes. Parameters for the valley area, such as Leaf Area Index (LAI), canopy height and optical reflectance were modified based on observed data and the structural characteristics of vegetation [4, 46,47,48,49,50]. In order to determine fitting parameters of the water retention curves and hydraulic conductivity functions of a soil column for both areas, we used observed data and data from literature for the study site. The Oxisol hydraulic properties of plateau areas were taken from previous studies [15, 51, 52], since PedoTransfer Functions (PTFs) derived using data from temperate region soils do not accurately represent the properties of tropical soils [53]. Although Oxisols have high clay content, they have low water availability and high-saturated conductivity. These characteristics differ from temperate clay soil characteristics. In the case of hydraulic properties for sandy soils located in the valley area, we used the soil parameters recommended by preceding researches [54, 55].

The six soil layer thicknesses in INLAND, top to bottom were set to 0.20, 0.30, 0.50, 1.0, 2.0 and 4.0 m, for the plateau area. In the valley, the total soil depth was set to 4 m, with layer thicknesses of 0.10, 0.20, 0.30, 0.40, 1.0 and 2.0 m. The parameters of the INLAND model were fitted via trial and error, comparing simulations with the observational data from both plateau and valley areas, including the latent heat flux (LE), sensible heat flux (H), net radiation (Rn), net ecosystem exchange of CO2 (NEE), soil moisture and water table level.

2.5 Balance equations and evaluation metrics

The simulated and observed energy and hydrological fluxes are based on the following balance equations:

$$R_{n} = H + LE + G$$
(2)
$$\Delta s/\Delta t = P - ET - R_{total}$$
(3)

where the net radiation Rn is the difference of shortwave solar radiation and the longwave terrestrial radiation, G is conduction of energy into the ground, and P is precipitation. LE is given by λ.ET, with λ as latent heat of vaporization and ET as evapotranspiration. All the terms in (2) have units of J m−2 s−1. However, G is neglected, since it is much smaller than the other three components. The left hand side of (3) is the rate of change of storage of water (s) in the soil. Total runoff (Rtotal) is the sum of the surface runoff (Rs) and subsurface drainage (D). We note that P, ET and Rtotal are always equal or greater than zero.

Statistical metric bias, coefficient of determination (R2), and the Root Mean Square Error (RMSE) are used to determine ‘goodness-of-fit’ and to check model performance [56].

3 Results and discussion

3.1 Water table dynamics and its simulation in the valley area

Since the water table at the plateau site remains deep, nearly 30 m, the model simulations with 6 m soil depth do not capture the water table depth (WTD) variability. Therefore, we discuss the WTD only at the valley site.

The lumped unconfined aquifer model coupled to the INLAND model was able to predict the observed weekly values of WTD satisfactorily. Figure 4a shows the simulated and observed variations over the study period (2002–2006) in the valley environment. The WTD is the response to the observed precipitation at the study site shown in Fig. 4b. It can be seen that almost all months in the study period received rainfall in excess of their respective climatological values (blue line), except in two conspicuous drought events, January—March 2003 and November—December 2004 (Fig. 4b). Significant wet periods were April—September 2003, January—May 2004, January—April 2005 and May—September 2006. Heuristically, we employed the following criteria: a drought episode is a period of two or more consecutive months in which the rainfall is less than 50% of the climatological value. A wet event is a period of two or more consecutive months in which the accumulated precipitation exceed the climatological value by 30%.

Fig. 4
figure 4

a Observed and simulated water table depth fluctuations in the valley area, from July 2002 to December 2006. b Observed precipitation during the same period (vertical bars) and climatological mean precipitation between 1901 and 1999 in the city of Manaus (dashed line)

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The observed peaks and depressions in water table level (black dots in Fig. 4a) are respectively almost simultaneous with maxima and minima rainfall, as in September 2002, April 2003, March 2004, April 2005 and March 2006, January 2003, October 2003, October 2004, August 2005 and October 2006 (with the exception of July 2006). This occurs because surface or near-surface water table variations respond almost immediately to the precipitation variations. The rainfall data in the graph are monthly-accumulated values, while WTD values are weekly, and therefore lags of less than a month between rainfall and WTD can not be delineated.

In the post dry season of 2003, the water table fell below 0.61 m depth in November, although the rainfalls in the preceding months (April through September 2003) were systematically higher than climatological values. The steep fall in water table level can not be explained by the small negative anomaly observed in October 2003 rainfall. The fall may be attributed to reduction of drainage flow from upstream portion of the Amazon Basin. The model also simulated satisfactorily higher values of WTD in November 2003. More strikingly, in the 10-month wet period November 2005 through August 2006 the water table remained very near to the surface (above 0.25 m) and the simulation correctly followed this long event. On the whole, the seasonality seen in the observed WTD is also seen in its simulated values. However, the curve of the simulated values is somewhat smoother than the observed data curve. That is, the model does not predict abrupt changes. Furthermore, the model could not capture the zero and near zero WTD events in March 2004 and April 2005. The WTD is overestimated by the model during the period September—November 2005. In spite of these minor deficiencies, the INLAND model adequately simulated the transitions between wet and dry conditions, showing reasonable agreement with observations. Statistical comparisons between the simulations and the observations are given in Table 1. The mean RMSE is 0.11 m with R2 = 0.65 in the wet seasons, while it is 0.12 m with R2 = 0.62 in the dry seasons. The observed and simulated mean WTDs for the whole period were, respectively, 0.21 and 0.22 m, during the rainy season (November–May), increasing to a depth of 0.26 and 0.31 m, respectively, in the dry season (June–October).

Table 1 Performance of INLAND model in representing the depth of the water table in the valley located in the study area during the period 2002–2006
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The INLAND simulations during 2002–2006 presented here were more representative than the CLM results reported by previous work [57]. Simulations with the Distributed Hydrology Soil Vegetation Model (DHSVM), at the same site, also produced higher standard deviation (RMSE = 0.25 m) during both wet and dry seasons (2002–2006), with an R2 of 0.60 and 0.72 for the wet and dry seasons, respectively [4].

3.2 Soil moisture variability in the plateau area

Soil moisture variations in the valley are not discussed because the soil in the valley remained always saturated at all considered depths.

The observed and simulated soil moisture variations at the plateau site in the six layers during the 6-year period 2001–2006 are shown in Fig. 5. First, we observe that the model simulations with default values for the hydrological and vegetation parameters (gray line) are far from the observed values at the site (black dots). Moreover, the simulated values with parameters adjusted to tropical forest conditions (red) show good agreement with both magnitude and seasonal variability in the observations, at all depths. Although the temporal frequency of observational data for the deepest layer was hourly, weekly averages are shown in the graph to match the observational data from the first five layers (obtained by neutron probe) from January 2003 to February 2006.

Fig. 5
figure 5

Observed and simulated soil moisture results for the six layers in the plateau. Observational data have a weekly or biweekly temporal frequency. Layers 1–5: from December 2001 to December 2006, obtained from neutron sonde. Layer 6: from January 2003 to February 2006, obtained from TDR. The grey line represents the soil moisture values considering default parameters of the model

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In the initial experimental setup, soil parameter values from the existing literature were utilized in the model run [15, 51, 52]. Further analyses demonstrated that three of the six soil parameters (Table S1, in supplementary material) were sensitive to a default setup: porosity (poros), Campbell’s parameter (bex) and hydraulic conductivity (hydraul) [14]. Tuning of these parameters was crucial for matching simulated soil moisture profiles with observations.

The simulated soil moisture content presents an annual cycle, with decreasing amplitude in the deeper layers. In the first four soil layers, the differences between dry and wet seasons were more pronounced compared to other layers. This behavior is related to a quick precipitation response in the topsoil layers and to their high macro porosity. At greater depths, the response to rain events is damped, particularly in the deepest two layers, which respond slowly to the seasonal precipitation variability.

In general, the model slightly underestimated the soil moisture content and presented an RMSE of 0.017 m3 m−3 with R2 of 0.54 for the first layer, and RMSE of 0.006 m3 m−3 with R2 of 0.71 for the sixth layer (Table 2). The RMSE decreased with depth because the temporal variability of moisture in deep soils is very small. The reason is due to high micro porosity and low permeability responsible for slow percolation at deeper layers [58]. Very small soil moisture variation in the last two layers on the seasonal scale indicates very little presence of roots and water availability for plants at these depths, as observed in previous work [59]. Therefore, these layers exhibit very little sensitivity to intra-seasonal, as well as seasonal variations in precipitation. The results indicate no significant water extraction from roots at these depths because there was sufficient water in the layers above 400 cm during most of the year [14]. For example, the sixth layer (depth of 4–8 m) had a nearly constant water content of 0.57 m3 m−3. The R2 increased from the surface up to 2 m depth and then decreased. The model is unable to deal properly with minuscule variations in soil moisture at deeper layers.

Table 2 The RMSE, bias and R2 calculated from weekly or biweekly soil moisture data
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A notable feature observed in the simulation results is the underestimation of soil moisture in the post dry season of 2005 (Sep–Dec) in the layers above 1 m. The observed data also indicated pronounced depletion of soil moisture during this period, perhaps due to more intense root uptake than normal. Differences in the water content at the end of the dry season of 2005 between the observational and simulated results could be due to differences in the actual versus assumed root distributions.

3.3 Water fluxes in the plateau and valley areas

3.3.1 Evapotranspiration

The identification and improvement of soil physical parameters for soil water dynamic simulation in a tropical forest had a positive impact on the modeling of surface fluxes, mainly on ET flux [14]. However, Amazon basin studies lack investigations of the soil physical parameters, mainly at deeper levels, and the climate models are forced to consider shallow and homogeneous soil. The inclusion of the most representative vegetation and soil parameter sets for plateau and valley forests (Table S1), along with the incorporation of the unconfined aquifer model into the INLAND model for the representation of water fluxes in valleys, allowed to simulate the differences in ET fluxes between the plateau and the valley satisfactorily (Fig. 6). First, we notice that the observed values in the rainy period, December through May, are equal in both locations. In the dry season, June through November, the plateau transpires more than the valley because the vegetation over the plateau is denser and the incoming solar radiation is larger. Its ET varies between 2.4 mm day−1 in December to 3.1 mm day−1 in July. Higher values of dry season transpiration are sustained by deep root water intake.

Fig. 6
figure 6

Mean monthly observed precipitation in the study area (P) and total evaporation (ET) simulated and observed in the plateau and valley areas, during 2006

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The annual mean simulated ET on the plateau is 3.7 mm day−1, higher than 3.2 mm day−1 in the valley. In both places, simulated values are close to their respective observed values (plateau = 3.0 mm day−1; valley = 2.9 mm day−1), which is in agreement with values reported in the literature, 3.8 mm day−1 on the plateau and 3.6 mm day−1 in the valley [9, 60]. The extraction of water from soil when water table is near surface is 0.5 to 1 mm day−1, while its value is approximately 3 mm day−1 when the water table is below 1 m depth. This is because surface water is used for evapotranspiration when available [9]. In general, the graphs show systematic overestimation in the simulations in all seasons. However, the seasonal variability is reproduced in the simulations. The ET overestimation over the plateau is larger by nearly 0.5 mm day−1. One interesting aspect is that the variability of monthly rainfall in a given season does not influence ET, as seen in Fig. 6. Then, vegetation density and solar radiation, instead of water availability, determine ET in the Amazon forest.

A possible explanation for the discrepancies in the results could be related to the lack of closure of the energy balance, a well-recognized problem of the eddy covariance method [61, 62] that was already reported by other studies in Amazonia [63,64,65,66]. The infrared gas analyzer (IRGA-LI-COR, model LI-7500) used to obtain LE is not reliable during rainy periods due to failure of the instruments caused by water drops standing over the sensors heads [67, 68]. Therefore, potential interference of rainfall can also be responsible for underestimation of LE in the study area, in both plateau and valley.

Mean ET over the year of 2006 corresponded to 55.7% of precipitation in the plateau and 45.4% in valley areas. Out of the total loss by ET, 76% were due to transpiration, at both sites. This percentage is higher than 53% found by previous work (same site) during the period from 2001 to 2004 [3] and the value of 56.9% obtained using the hydrological model DHSVM [4]. Higher ET percentage means that lesser part of precipitation is available for runoff and infiltration, according to (3). This indicates that the year 2006 was atypical.

The observed evaporation of the intercepted water (interception loss) represented 21.2% and 19.2% annually in the plateau and valley regions, respectively, while 2.5% and 3.8% were associated with direct evaporation from the soil in the plateau and valley, respectively. The direct evaporation is small because the surface atmospheric layer under the canopy is near saturation. Intercepted water simulated by INLAND during the wet season of 2002/2003 corresponded to 21.3% of ET in the plateau area, close to the observations of 21.4% [29]. The water interception by the valley canopy was slightly lower than over the plateau, while soil evaporation was about 52% higher than over the plateau. These results reflect lesser tree density [46], lower and a more open canopy [47, 48], lower LAI [4] and a tree composition with less species [49, 50], when compared to the plateau.

3.3.2 Surface runoff and deep drainage

The observations of surface runoff (Rs) and deep drainage (D) are for the whole CBR area and include contributions of plateau and valley areas, while the same flows simulated by INLAND are obtained for the valley and the plateau sites separately. The weighted mean of the valley and the plateau values are compared with the observations to assess model performance. The weights used are their respective fractional areas: 0.569 in plateau and 0.431 in valley [8].

Figures 7a and b show monthly means of the simulated surface runoffs and subsurface drainages, respectively, at the valley and plateau sites, along with the observed values for the whole CBR from 2002 to 2006. Runoff (Fig. 7a) and drainage (Fig. 7b) did not vary much during the relative dry period July through November. However, in the wet period they gradually increased from December to April, attaining observed peak values in the month of April when the region received the largest mean monthly rainfall of nearly 360 mm (equivalent to 12 mm day−1 on the average). The preceding month of March also received almost an equal amount of rainfall. It can also be seen immediately that the runoff is less than the drainage during both wet and dry periods.

Fig. 7
figure 7

a 5-Year mean surface runoff (Rs) simulated (blue) and observed (black) in plateau and valley from 2002 to 2006; b Same as in (a) except for groundwater drainage (D). Mean monthly observed precipitation in the study area (P) refers from 2002 to 2006

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For argument’s sake, here we make a heuristic analysis considering reasonable estimates of the components of hydrological balance Eq. (3) for the month of April. The mean runoff (Fig. 7a) and drainage (Fig. 7b) were in excess of roughly 2 mm day−1 and 4 mm day−1, respectively, resulting about 6.5 mm day−1. From Fig. 6, ET is estimated as 2.5 mm day−1. The difference (P–Rs–D–ET) of nearly 3 mm day−1 went into storage (accumulation in the soil and in the aquifer), which was used in the upcoming dry period, mostly for evapotranspiration.

Figure 7a and b also show that observed mean monthly D is higher than Rs in the period 2002 through 2006 (black lines), in all months. This characteristic is reproduced in the model simulations (blue lines). However, the simulated surface runoff and drainage values are higher than corresponding observed values in the rainy season and lower than observed values in the dry season, resulting in a higher amplitude of the seasonal variability by the model. Although the 0–8 m layer is sufficient to simulate ET and carbon assimilation [3, 14], a significant portion of the water transfer by free drainage from the unsaturated zone to the aquifer has not been taking into account. This reduces the efficiency of the model in representing the partitioning between vertical drainage and runoff.

Observed data runoff values are not available for each site separately. However, previous studies showed that over the plateau area, Rs is very low or even absent because the main mechanism of runoff generation is saturation overland flow [3, 69]. Simulated Rs in the plateau area presented an average of 3.9% of total precipitation, during 2002 to 2006, because the runoff is either very small or absent during the 6-months period July to December, which is in agreement with other studies in different regions of the Amazon Basin [70,71,72]. In the valley area, however, Rs simulated by INLAND represented a higher fraction of precipitation when compared to plateau, about 25.3%. Simulated deep drainage is dominant in plateau area and is related with precipitation. A well-defined seasonal cycle is depicted, with higher values during the wet season (Fig. 7b), when the water table in the plateau is located about 35 m deep [3, 4]. D values represent a large fraction of the total precipitation, corresponding to 41.3% and 27.2% in the plateau and the valley areas, respectively, similar to the values estimated previously for the same area [14].

Total simulated D flux (plateau + valley) was 3.7 mm day−1 and 0.9 mm day−1 during wet and dry seasons, respectively, while observations indicate 2.4 mm day−1 in the wet season and 1.5 mm day−1 in the dry season. In general, INLAND model overestimated D during the wet season (bias = 1.3 mm day−1) and underestimated in the dry season (bias = − 0.6 mm day−1). A likely explanation for these seasonal discrepancies are related to the fact that simulated D did not consider the slow travel time of the horizontal water transfer from the saturated zone of the plateau to the valley bottom, which is responsible for the seasonal time-scale basin response delay. It is estimated that the average transfer time is about 3 months, highlighting the reduction of D in dry season [3]. The RMSE was 1.7 mm day−1 and 0.8 mm day−1 in wet and dry seasons, respectively, suggesting a better model performance during wet season. There is an increase in the value of R2 from wet to dry season. The results showed an overestimation of the total runoff during wet season (bias = 0.4 mm day−1)—mainly in the first months of the year when the precipitation is higher, and underestimation in the dry season (bias = − 0.3 mm day−1). During the wet season, the RMSE was 0.6 mm day−1 and R2 was 0.60. In the dry season RMSE reduced to 0.3 mm day−1 and the correlation between the simulated and observed values, R2, decreased to 0.53.

Simulated discharge or total runoff (\({R}_{total}\)) averages during the period from 2002 to 2006 represented 45.2% and 52.5% of the total precipitation, for plateau and valley areas, respectively. The lower percentage of Rtotal in relation to precipitation in the plateau is due to the higher ET in this area when compared to the valley. The mean values of \({R}_{total}\) in relation to precipitation found in this study, in both areas, showed a close agreement with the values of 44.3% during the period from 2001 to 2004 [3], and of 49.3% obtained between 2000 and 2008 [14]. In addition, our results also corroborated the previously results obtained from 2002 to 2004 using the DHSVM model, which stated that the total runoff represented 47.5% of the total precipitation in the plateau [3].

The INLAND performance metrics for ET, Rs and D discussed above are summarized in Table 3.

Table 3 The INLAND model performance for the representation of total evaporation (ET) during 2006; surface runoff (Rs) and deep drainage (D) during 2002–2006, from hourly data
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3.4 Energy fluxes

Observations and simulations of the diurnal evolution of net radiation (Rn) in the wet and dry seasons are shown in Fig. 8a and b, respectively. We observe that net radiation in dry season (Fig. 8b) is positive from 07 to 17 Local Time (LT) and peaks around 11 LT to nearly 600 W m−2 at both valley and plateau sites. From 17 LT in the afternoon to 07 LT in the morning, the forest loses energy (Rn is negative), with a slow rate of 30 W m−2. The simulations (in red) properly follow the observations.

Fig. 8
figure 8

Mean hourly observed and modeled energy fluxes in the wet and dry seasons of 2006

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In the wet period, there is a dip around 50 W m−2 in the net radiation at 11 LT from about 500 W m−2 at 10 LT, in the valley site. This is probably due to cloud formation in the valley by the combined effect of downslope wind convergence and radiative heating. At 12 noon, the net radiation regains its intensity. However, there is no dip in Rn over the plateau exposed to solar radiation, meaning that the sky over the plateau remains mostly clear at this time of the day.

The simulations did not capture the late forenoon reduction in Rn in the valley. Although INLAND model takes into account the prescribed meteorological conditions, it is not capable to produce the convergent movements of surface air and the resulting cloud or fog formation. Moreover, the Rn simulated during daytime in the wet period (red lines in Fig. 8a), especially from 09 to 15 LT, was underestimated in comparison with observations at both valley and plateau site. Table 4 shows that the R2 of the Rn simulations was 0.99 at the plateau in both seasons with RMSE about 11.5 W m−2 and negative bias not greater than 4.3 W m−2. At the valley site, bias was positive and RMSE was of the order of 50 W m−2 in the wet season and 33 W m−2 in the dry season. The R2 was over 0.95 in both seasons.

Table 4 RMSE, bias and R2 calculated for the hourly energy fluxes
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The constant-value albedo simulated by INLAND in the valley was 10.5% in the wet season and 10.8% in the dry season. These values were about 4% higher than previous observational values [31, 73]. Furthermore, this difference could be due to the lower incoming longwave radiation, which is derived from meteorological data input in the model, in the plateau. Observed incoming longwave radiation is consistently higher on the valley than on the plateau [31]. The INLAND model simulated the albedo differences in both areas, showing higher values on the plateau, like 12% in the wet season and 12.3% in the dry season, in fair agreement with observed data (wet season = 11%; dry season = 12%) [31, 73]. In order to simulate such differences, reflectance of near infrared radiation from leaves represented by the parameter rhoeveg_NIR was adjusted to 0.31 and 0.26 for the plateau and valley, respectively (Table S1). The albedo difference between the two areas is due to the vegetation canopy structure [74]. In the plateau area, for example, the vegetation is denser, which favors a greater homogeneity of the vegetation, resulting in a greater reflectivity of the solar radiation. The seasonality of albedo also was correctly represented by INLAND, with higher values during the dry season. The forest canopy is darker during the rainy season due to greater radiation absorption by water, lowering the albedo [75].

The model was able to properly simulate the partitioning of available energy (Rn) with higher percentage used for LE (Fig. 8c, d) than for H (Fig. 8e, f), as verified in previous works [28, 63, 64]. Reasonable agreement between simulated and observed energy fluxes highlights an adequate model performance after the inclusion of improved vegetation and soil parameters (Table S1) and water table algorithm for the valley area. The LE annual averages corresponded to 84.9% of Rn, for the plateau, and 72.9% and for the valley, while H annual averages is 14.8% of Rn and 26.5%, respectively. These results are different from observed values, where LE is 60.4% of Rn for the plateau and is 50% of Rn for the valley. This shows that the LE flux is overestimated by the model. It can be noted in Fig. 6, which shows consistent overestimation of ET in all months compared to observations.

The simulated LE was higher for the plateau than for the valley, particularly in the dry season, agreeing with observed data. This difference is due to the higher simulated LAI on the plateau (6.1 m2 m−2) than in the valley (5.8 m2 m−2), which resulted in a higher evapotranspiration rate. Another possible reason is the excess water in the valley soils, which can produce oxygen-deficient roots and affect plant survival and functioning [76]. The overestimation of LE flux was higher on the plateau, where we found an RMSE of 63.8 W m−2 and R2 of 0.85 in the wet season and an RMSE of 66.8 W m−2 and R2 of 0.88 in the dry season (Table 4). The INLAND model was able to reproduce the seasonality of LE, showing higher values during the dry season for both areas (plateau = 124.6 W m−2; valley = 103.6 W m−2), when compared to the wet season (plateau = 97.2 W m−2; valley = 86.3 W m−2), which is in agreement with observed data.

In contrast, the simulated H fluxes (Fig. 8e, f) are higher for the valley area than over the plateau, in both wet (valley = 29.8 W m−2; plateau = 18.6 W m−2) and dry (valley = 39.8 W m−2; plateau = 19.5 W m−2) seasons, suggesting that more Rn was used to heat this environment. This behavior is in agreement with the observed H fluxes, mainly during the dry season (valley = 36.7 W m−2; plateau = 33.6 W m−2), indicating a good performance of INLAND. The diurnal cycle also reveals that the seasonality of the H flux was consistently reproduced by the model, presenting higher values during the dry season in both areas, again in agreement with observed data.

The higher values of H in the valley compared to the plateau also show a significant bias in the simulated values of H for the valley. The model overestimated the observed hourly totals by 11% and 2% during the dry (R2 = 0.78; RMSE = 34.9 W m−2) and wet (R2 = 0.66; RMSE = 34.3 W m−2) seasons, respectively. This overestimation in the H flux was related to one of the most relevant H simulation parameters, rhoeveg_NIR [77]. The vegetation-to-air sensible heat flux is a function of the leaf and stem temperatures. These two variables depend on solar radiation absorbed by the canopy and soil, and on the net absorbed fluxes of infrared radiation.

3.5 Net ecosystem exchange

Figure 9 shows the diurnal variations of the NEE fluxes simulated by the INLAND model and observations at the two sites, valley and plateau, for the wet season and the dry season of the year 2006. First, we note that the observations (black graphs) show larger negative diurnal peak values at the plateau site than at the valley site, which is attributed to higher density of vegetation. The peak in NEE over the plateau occurs at 11 LT in the wet season and 1 h earlier in the dry season. Another important observation is that NEE faces a reduction in flux between 11 and 12 LT in the wet season in the valley (Fig. 9a). This is caused by the dip in the net radiation (Fig. 8a), which is caused by reduced solar radiation due to clouding in the valley at those hours. Further exams over the observational data reveals that the nighttime positive values (respiration) continue up to 08 LT (early morning hours) in both seasons and remain negative (photosynthesis) up to 17 LT. The respiration rates during the night remain almost constant.

Fig. 9
figure 9

Observed and simulated diurnal variation of net ecosystem exchange (NEE) rates between the forest and the atmosphere. Negative values (daytime) represent uptake of CO2 from the atmosphere (photosynthetic activity is higher than respiration). Positive fluxes (nighttime) are associated with emissions of CO2 from the forest to the atmosphere (respiration activity only)

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In general, the simulated daytime and nighttime NEE flux patterns follow satisfactorily the observed patterns. However, there are significant differences. The simulated daytime negative peaks are less sharp in both seasons. The wet season noontime dip in NEE in the valley is not reproduced. Once again, this is because INLAND model does not produce changes in atmospheric flow dynamics and formation of clouds. The nighttime NEE fluxes are also smaller than their corresponding observed values.

However, INLAND properly captured the difference between the two areas due to fine-tuning of vegetation and soil parameters at the plateau and the valley sites (Fig. 9a, b). Adjustments in photosynthesis parameters (Table S1) were essential to reduce the bias between simulated and observed NEE values. The daytime negative peak of NEE is placed 1 h later than in the observation in the dry season by the model. These differences show that the INLAND model needs further fine tuning to fit the tropical forest characteristics and should be run in dynamic mode, i.e., in conjunction with the diurnal changes in atmospheric flow. The discrepancy in the nighttime respiration intensity seems to be due to constant values attributed which can be seen in the horizontality of the graphs of the simulated values.

During daytime (photosynthesis-dominated processes), the simulated NEE fluxes over the plateau were higher than in the valley, in both wet and dry seasons, agreeing with observed data. The average NEE flux simulated during daytime on the plateau was − 8.5 µmol m−2 s−1 and − 10.2 µmol m−2 s−1 in the wet and dry seasons, respectively (Table 5). In the valley, simulated NEE values were smaller by, approximately, 11.8% and 23.5% than the values over the plateau, for the wet and dry seasons, respectively. The higher NEE flux rate during daytime on the plateau suggests a stronger CO2 uptake rate due to increased photosynthetic activity from a higher biomass yield in this area [78]. In addition, it was found that the biomass variation between plateau and valley is mainly associated with nitrogen availability [79]. The plateau area soil and plant leaves have a greater amount of nitrogen than in the valley, indicating a larger nutrient availability for biomass growth in the plateau [1]. It was conducted a 3 year long litterfall experiment in an area of 10 km2 to the northwest of the present study site and measured a 3-year average yield of 8.3 tons C ha−1 of litter in the plateau, and 7.4 tons C ha−1 in the valley [69]. These results indicated that yield is greater over the plateau than in the valley. In addition, using sapflow data for the study site [80], it was showed that photosynthesis starts later and ends earlier in the valley area, presenting a direct relation with solar radiation fluxes [81]. Our results in Fig. 9 also show this characteristic.

Table 5 Average observed and simulated net ecosystem exchange (NEE) values for plateau and valley during the day (06:00–18:00 h), night (18:00–06:00 h) and daily totals. The daytime peak observed and simulated is also includes
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The simulated NEE fluxes during daytime indicate higher mean values of NEE in the dry season, probably due to higher solar radiation, mainly in the plateau area (about 20% higher compared to wet season), in agreement with literature [82]. In contrast, the observed NEE values were 3.3% and 10.2% higher during the wet season in the plateau and valley, respectively. The daytime NEE values observed by different authors are different. It was found a higher forest assimilation in the eastern Amazonian site during the dry season [83], opposing to earlier results with higher values in the wet season, related to the rainfall [75]. Although INLAND model does not represent adequately the 2006-year mean seasonality, there was a fair agreement between modeled and observed daily peaks, showing higher values during dry season, mainly in valley area. Lower values of respiration in the valley, in both seasons, may also be associated with a lower decomposition rate of organic matter in this area, due to reduced values of Carbon to Nitrogen ratio (C:N) because of the poor quality of the plant leaves [1]. This can be partially explained by the increased air humidity that favors intense organic matter decomposition by microorganisms [84]. In addition, during the wet season, a greater cloudiness and humidity is observed in the atmosphere, contributing to a lower loss of longwave radiation and less cooling on vegetation canopy. Thence, atmospheric turbulence increases favoring vertical transport and forest-borne CO2 mixing, both in the plateau and valley areas, during the wet season [31, 85]. Other studies have also found higher respiration values during the wet season [86, 87].

The underestimation of fluxes during dry season was also found by other study in the same area [82]. It is due to the overestimated NEE value obtained by the eddy covariance method, observed since the first tests performed using this methodology [88]. This method underestimates CO2 flux under stable atmospheric conditions during the night Miller et al. [86], when CO2 flow is characterized by autotrophic respiration and the decomposition of organic material from soil. CO2 drainage from high (plateau) to low (valley) areas also contributes to the forest CO2 flow underestimation at night, as at K34 tower site [89, 90].

The observed mid-day dip in NEE in the valley is not reproduced in the simulation. The dip can be attributed to systematic foggy conditions that reduce incoming solar radiation and therefore photosynthesis. This is one of the reasons for lower values of R2 found in the valley area, especially during the dry season (0.55), when compared to the wet season (0.63) (Table 6). The R2 values in the plateau (wet = 0.76; dry = 0.66) are higher than those found by other authors (wet = 0.54; dry = 0.41) in the same study area [45, 82]. On the other hand, the RMSE values of the two areas were similar. The mean values shown in Table 5 are comparable in magnitude to those reported in the literature, as 4.2 µmol m−2 s−1, in the plateau area [45]. The discrepancy between the observed and simulated NEE values is higher around the hours when the forest changes its physiological activity from respiration to photosynthesis and vice versa. This shows the need for further tuning of floristic, hydrological and soil parameters in the model.

Table 6 Performance of the INLAND model for the representation of the net ecosystem exchange (NEE) during 2006, from hourly data
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4 Summary and concluding remarks

This study shows the importance of incorporating the diversity of elements that compose the landscape in tropical forests such as vegetation characteristics, pedology and hydrological dynamics into terrestrial surface models. These elements are strongly associated with the local topographic heterogeneity (Fig. 2). The identification and quantification of these elements on a fine spatial scale were essential for the INLAND model, with a lump aquifer model included in it, to capture the main differences related to energy, water and carbon balances between two different environments along a topographic gradient in central Amazon region. The INLAND model with default parameters produced large errors in the simulations of the soil moisture (Fig. 5) and consequently in the hydrological cycle.

The simulated Latent heat flux (LE) was higher on the plateau than in the valley (Fig. 8c, d), in both seasons. The dry season LE is higher than the wet season LE both in the valley and on the plateau. In general, LE is several times greater than H, meaning that a substantial part of the net radiation Rn is expended for evapotranspiration (ET) (85% on the plateau and 76% in the valley) and a small part of energy is transferred by the forest directly to the atmosphere as sensible heat (H). In the dry season the proportion of H increases somewhat, at both valley and plateau sites. The present study, with floristic, topographic, hydrological and atmospheric parameters tuned to suit the tropical forest environment, simulated the fluxes and their seasonal and diurnal variabilities satisfactorily.

The inclusion of a lumped unconfined aquifer model proved essential to adequately simulate the water balance in the valley environment, highlighting that the valley presents water and soil dynamics distinct from the plateau. The model reasonably reproduced (R2 = 0.64 and 0.62) the temporal variability (seasonal as well as interannual) of the water table depth in the valley (Table 1). The simulations showed that the surface runoff (Rs) in the valley and on the plateau are approximately 25% and 3%, respectively, of the precipitation. The surface models are usually parameterized based on plateau data only [91]. Our results indicate that previous results might be overestimating ET by 8–16%.

In general, NEE flux (Fig. 9) is higher on the plateau during both wet and dry seasons. NEE in the valley is 26% and 9% less than over the plateau during the dry and wet seasons, respectively, showing heterogeneity in photosynthetic activity. In spite of some deficiencies in the simulations, the model results reproduced many important observed characteristics, with better representation than the results reported in earlier studies. Higher agreement (R2) between the simulations and the observation of NEE than in the experiments of earlier authors was an encouraging factor.

In this study we obtained an understanding of the differences between valley and plateau forests, both by examining the observational data and data simulated by INLAND model. One interesting example is the reduction (or dip) of net radiation (Rn, Fig. 8a) and net ecosystem exchange or CO2 emission fluxes (Fig. 9a) at the valley site around 11 LT and their re-intensification after an hour or two. This feature is not observed at the plateau site. However, this feature is not captured by the model. The mesoscale and small scale dynamics of the surface flow and the formation of clouds and/or fog in the valley at this time of the day in the wet season should make an interesting topic for research.

The results of this study clearly show spatial heterogeneity of hydrological, biophysical and energy exchange processes which should be taken into account in climate models used for simulating future scenarios. Furthermore, the results serve to validate the version of INLAND model in a typical tropical forest ecosystem. The next major challenge is to develop a land surface model integrated with a subgrid scale variability scheme that allows explicit consideration of the typical processes of each of the environments within the Amazon ecosystem (plateau, slope and valley). This grid refinement can contribute to reduction of uncertainties within the Earth System integrated models in future climatic scenarios. In addition, the modeling of forest ecosystems response and resilience to climate change can be improved by including the diversity of the landscape functionality.

Studies similar to this at contrasting landscapes such as forest and adjacent deforested areas, and inundated and nearby dry land areas, are capable of showing effects of heterogeneities in the Amazon Basin. These studies contribute to more accurate understanding of energy fluxes and carbon emission estimations in critical areas such as the Amazon rainforest, useful for mitigation strategies tackling the impacts of anthropogenic-induced climate change on the natural ecosystems.

The availability of an appropriate set of soil parameters at deeper layers validated with observed data is important for future model calibrations, especially for heterogeneous landscapes at finer scales.