Drylands cover 30 % of the Earth's land surface and 50 % of Africa (Franz et al., 2010). Projections of the IPCC (Intergovernmental Panel on Climate Change, 2007) indicate that the extent of these regions will likely increase in the coming decades. Dryland expansion would have a considerable additional impact on water resources, which should be taken into account by water management plans (Franz et al., 2010).

In water-controlled ecosystems, the vegetation assumes a critical role influencing all components of the hydrological cycle (Rodriguez-Iturbe et al., 2001; Manfreda and Caylor, 2013). For instance, actual evapotranspiration (aET) may account for more than 90 % of the annual precipitation in water-controlled areas (Zhang et al., 2016; Jasechko et al., 2013). Montaldo et al. (2005) affirmed that the use of constant LAI (leaf area index) values, commonly used in hydrological applications, produces large errors in land surface flux predictions. Given the strong control exerted on aET by the vegetation, reliable estimates of spatio-temporal variations of vegetation patterns are vital to obtain trustworthy predictions of available water resources (Andersen, 2008). In this sense, ecohydrological modeling becomes essential in order to include the vegetation dynamics as an additional state variable (Rodriguez-Iturbe et al., 2001).

Evidence of aET being a prevalent driver of hydrological records of streamflow and water table depth, i.e., available water resources, has been observed in many studies (Bond et al., 2002; Nyholm et al., 2003; Gribovszki et al., 2008; Conradt et al., 2013). Recently, Tsang et al. (2014) showed that adding a better evapotranspiration scheme in a widely used runoff model improves streamflow predictions. Conradt et al. (2013), who compared three different strategies for deriving sub-basin aET, affirmed that incorporating spatial variation of aET in a semi-distributed model increases its robustness. Conversely, Stisen et al. (2011) and others stressed that those improvements are not necessarily seen in the outlet hydrograph. However, it could also be interpreted in the inverse sense; good performances in terms of the outlet hydrograph do not necessarily mean more reliable estimates of aET.

The streamflow record is traditionally the only observation used for the calibration of hydrological models, but several studies demonstrated the limited capabilities of such an approach when models are validated at interior points of a river basin. Discharge represents an integrated catchment response, and hence provides only limited insight on the lumped behavior of a catchment (Stisen et al., 2011; Koch et al., 2016a; Michaud and Sorooshian, 1994; Reed et al., 2004; Smith et al., 2013). In that sense, Conradt et al. (2013) provided several examples for large simulation errors within the model domain and they mentioned, among others, the outcomes given by Feyen et al. (2008), Merz et al. (2009) and Smith et al. (2012). Moreover, Wi et al. (2015) also pointed out that caution is needed when using an outlet calibration approach for streamflow predictions under future climate conditions. This leads to the idea of using spatial state variables, and the new era of distributed (temporal and spatial) models emerges in order to balance the conceptual distributed nature of this kind of model (Stisen et al., 2011).

Traditional observation, which generally consists of point data with little spatial support, is effectively strengthened by remote sensing data, which offer the capacity to provide detailed spatial coverage and pattern information (Franssen et al., 2008; McCabe et al., 2008; Stisen et al., 2011). Additionally, satellite data have the great advantage of also being available in data-scarce areas. In this sense, the application of remotely sensed data represents an excellent source that provides information with a fairly good spatial and temporal resolution (Yang et al., 2012). In modeling, remote sensing data have been utilized in three different ways: (1) as forcing data (Xiao et al., 2004; Yuan et al., 2010; Samaniego et al., 2011; Stisen et al., 2011), (2) as a priori information of particular parameters (Winsemnius et al., 2008; Stisen et al., 2011) and (3) for model calibration and validation (see next section for an in-depth discussion of this point).

Satellite imagery provides not only temporal information but also valuable information on spatial patterns, which can facilitate a spatial-pattern-orientated model evaluation. As highlighted by Koch et al. (2015), spatial model evaluation is an active field of research not only in hydrology but also in other disciplines such as atmospheric sciences (Brown et al., 2011; Gilleland et al., 2010). However, up to now, there exists no formal guideline on how to assess the goodness of fit of the simulated spatial patterns and little information can be found about how to effectively utilize spatio-temporal data. Some authors, such as Conradt et al. (2013), Graf et al. (2014) and Koch et al. (2015, 2016b), focused on developing and testing metrics to be employed when spatio-temporal data are involved. For example, Koch et al. (2015) compared kappa statistics, fuzzy theory and empirical orthogonal function (EOF) analysis in an attempt towards a true spatial model evaluation of distributed models. But, besides these efforts, there are only a limited number of spatial validation studies that fully embrace the availability of satellite remote sensing data by means of true spatial performance metrics (Koch et al., 2016b). EOF analysis is a versatile methodology to investigate the spatio-temporal patterns of fluxes and states in the soil–vegetation–atmosphere continuum (Fang et al., 2015). As mentioned previously, Koch et al. (2015) carried out a validation of a distributed model using satellite-based land surface temperature data by means of an EOF analysis. With other statistical purposes, the EOF analysis was used by Graf et al. (2014), Kim and Barros (2002) and Liu (2003). A fine-scale study was carried out by Drewry and Albertson (2006) who used EOF analysis to associate spatial pattern in the errors of a canopy-atmosphere model with errors in the parameters. However, to our knowledge, EOF analysis has not been applied in model calibration yet.

In summary, the main objectives of this research are the following: (1) to incorporate spatio-temporal data into the calibration process by applying the EOF methodology as an objective function and (2) to exploit satellite data as a proxy of reliable estimates of vegetation dynamics for both the calibration and validation of an ecohydrological model. To address these key challenges, a distributed parsimonious ecohydrological model was applied in a water-controlled basin located in Kenya.

The applicability of remote sensing to calibrate and/or validate a model by exploiting information on spatial patterns still remains a challenging task. In order to better understand this issue in more detail, a bibliographic survey of the ISI Web of Knowledge science citation index was undertaken using the following word combinations in the topic search: (1) satellite calibration, (2) satellite implementation, (3) satellite ecohydrological modeling and (4) remote sensing ecohydrology. From the total number of publications obtained by this search, only those that incorporated satellite data to specifically model calibration were selected.

On the plot scale, Quevedo and Francés (2008) and Pasquato et al. (2015) calibrated and validated a parsimonious ecohydrological model using satellite information. More recently, Ruiz-Pérez et al. (2016) discussed the applicability of satellite data during the calibration process comparing the results obtained by a parsimonious model calibrated using only satellite data against the results obtained by a complex model calibrated using field measurements on the pixel scale. Similarly, Quevedo and Francés (2008) and Pasquato et al. (2015) used time series of NDVI to validate a parsimonious ecohydrological model named HORAS. On the catchment scale, Immerzeel and Droogers (2008) used satellite-based evapotranspiration in combination with observed streamflow to calibrate the semi-distributed SWAT model. Zhang et al. (2009) concluded that multi-objective calibration of the SIMHYD model against streamflow and satellite-based aET produced better daily and monthly runoff compared to calibration with streamflow alone. More recently, Rientjes et al. (2013) calibrated a semi-distributed hydrological model using streamflow data and satellite-based aET. Regarding other satellite products, GRACE data, which can be used to detect variations in terrestrial moisture storage (e.g., Lettenmaier and Famiglietti, 2006), have been used to calibrate both global and regional-scale surface hydrology models, in combination with stream discharge data (e.g., Lo et al., 2010). Zhang et al. (2011) calibrated the AWRA-L model with streamflow, NOAA-AVHRR LAI and TRMM-MI (Tropical Rainfall Measuring Mission's, TRMM, Microwave Imager, TMI) soil moisture using a multi-objective calibration framework. Only few studies carried out the calibration exclusively against remote sensing data. For instance, Gutmann et al. (2010) calibrated landscape hydraulic properties in the Noah land surface model using only MODIS surface temperatures from 14 different sites and using observed flux data for model verification. Also, Velpuri et al. (2012) modeled Lake Turkana water levels using only satellite information. All the above-mentioned studies shared the same conclusion: including remote sensing data into the model calibration and/or validation improves the overall performance.

In general, from the total of reviewed publications, calibration using only satellite data was performed in the 47 % of cases, while a combination of satellite data and field measurements (especially streamflow at the outlet) was used in the remaining contributions. Similar results were obtained regarding the validation: 35.3 % of publications only adopted field measurements (especially historical streamflow), employing satellite data exclusively for the model calibration; 47 % used a combination of field measurements and satellite data; 11.8 % only used satellite data; and one publication without any specification. However, more interesting is how the different calibrations were carried out. In most of the cited examples, a sort of multi-objective calibration was used adopting only some points or pixels to calibrate the entire catchment. In other cases, lumped or semi-distributed models were implemented instead of fully distributed ones, considering aggregated values of the satellite data. In other words, the spatial heterogeneity of the basin is neglected and the full potential of satellite imagery, namely the information on spatial patterns, is not fully exploited. Therefore, a method able to make use of the potential of the spatio-temporal information contained in remote sensed data is highly desirable and a calibration scheme which relies solely on remote sensing data will be greatly beneficial in modeling of data-scarce catchments (Kunnath-Poovakka et al., 2016).

The upper Ewaso Ngiro basin is located in the Laikipia region of Kenya (Fig. 1). The basin is part of the Laikipia plateau, which lies between Mount Kenya (south east) and the Aberdare mountains (south west). The basin has a drainage area of 15 200 km2, with the largest river being the Ewaso Ngiro. This region is characterized by distinct rainy and dry seasons. The first rainy season occurs from March to May, while the second rainy season occurs from October to December. Both air temperature and precipitation patterns are heavily influenced by elevation. A full description of the precipitation patterns in the region can be found in Franz (2007).

Soil texture ranges from sandy clay to clay soils (according to the 1980 UNESCO soil map). Although the most characteristic landscape is savanna, higher elevations are dominated by forests and a large piece of land has been converted to cropland (Franz, 2007). The remaining surfaces of the study region are classified as grassland, shrubland and wooded grassland (savanna ecosystems).

As meteorological data, we used the weather stations of the natural resource monitoring, modeling and management project (NRM3) of Nanyuki, Kenya (illustrated in Fig. 1). Daily precipitation and temperature from 1959 to 2003 were validated by Franz et al. (2010). Considering the available hydrological information, we selected a sub-basin with an area of about 4600 km2 for the present study (Fig. 1). The selected catchment is equipped with a streamflow gauge at the outlet (operational from 1980 to 2002). The reference evapotranspiration (ET0) was calculated using the Penman–Monteith equation with the simplifications proposed by Allen et al. (2006). This approach is extremely useful to describe the spatial distribution of solar radiation and to derive the ET0 maps during any day of the year (Manfreda et al., 2013).

Regarding the satellite data, we adopted the Normalized Difference Vegetation Index (NDVI) included in the MOD13Q1 and MYD13Q1 products provided by NASA (NASA Land Processes Distributed Active Archive Center, LP DAAC). This satellite product is available from 2000 to present. The MOD13Q1 and MYD13Q1 data are provided every 16 days at 250 m of spatial resolution. The used NDVI products (MOD13Q1 and MYD13Q1) are in level 3, which means that they are not raw satellite data. NDVI indices are retrieved from daily, atmosphere-corrected, bidirectional surface reflectance.

Finally, based on previous experiences (Ruiz-Pérez et al., 2016; Pasquato et al., 2015) and in similar climatic conditions, we declined to use other products such as LAI or ET derived from MODIS because these kinds of products are produced by models. And, for example, Ruiz-Pérez et al. (2016) found large discrepancies between the LAI provided by satellite and the LAI measured in field. At this point, we had no information to determine the accuracy of these particular models and the spatial information used to implement them. In contrast, NDVI values are calculated by direct differences of spectrum bands, i.e., no models are involved and we therefore decided to use this latter product instead of satellite LAI and/or ET.

The proposed model, called TETIS-VEG, is based on a distributed hydrological model called TETIS (Francés et al., 2007) coupled with a dynamic vegetation model. Both models have simplicity of model structure in common. The used equations are as simple as possible in order to reduce the number of parameters (Table 1). The sub-models are inter-connected. The transpiration calculated in the hydrological sub-model depends on the LAI simulated by the dynamic vegetation model. At the same time, the simulated LAI depends on the water stress, which is calculated using the hydrological sub-model. The hydrological sub-model can be used on different timescales (from a few minutes up to daily time steps), while the vegetation dynamic sub-model has to be applied on a daily scale. Hence, the TETIS-VEG model must be used on a daily scale. Both sub-models can be used on a broad range of spatial scales. In this research, the resolution of the implemented model was 90 m × 90 m.

One of the main objectives of this research was to explore the potential of satellite remotely sensed data for model calibration. The TETIS-VEG model was calibrated purely against MODIS NDVI according to the following three steps: (1) a manual calibration in order to obtain a first approximation of model parameters, (2) an automatic calibration based on the combined use of EOFs and a genetic algorithm in order to refine model parameterization and (3) a model validation carried out with both remote sensed data and traditional data (such as streamflow measurements). Since the meteorological data (precipitation and temperature) were available from 1960 to 2003 and the MODIS NDVI was available from 2000 to present, we decided to use the year 2003 as the calibration period and the period from 2000 to 2002 for validation. In order to avoid the effect of the initial conditions, we used one year as warming-up period (the year 2002 and 1999 for model calibration and validation, respectively).

For these purposes, we adopted the NDVI as a descriptor of the state of the vegetation assuming that LAI and NDVI are intimately related. Studies on various vegetation types, e.g., agroecosystems (Cohen et al., 2003), grasslands (Friedl et al., 1994), shrublands (Law and Waring, 1994), conifer forests (Chen and Cihlar, 1996) and broadleaf forests (Frassnacht et al., 1997) have led to the general conclusion that the spectral vegetation indices such as NDVI have considerable sensitivities to LAI. The relationship between LAI and NDVI can be considered linear for low values, while it becomes nonlinear for the higher values of NDVI due to the greenness saturation (e.g., Turner et al., 1999). In this case study, the maximum LAI values are around 2.0–2.5, according to Franz (2007), and are lower than the greenness saturation threshold. Therefore, the relationship between the observed NDVI and the simulated LAI is expected to be linear.

From the a priori manual calibration step to the model validation step, it was possible to identify a behavioral pattern which would also be observed during the following automatic calibration and validation steps: EOF1 explains more than 60 % of the spatial variance, EOF2 around 10 % and EOF3 around 5 %, while the remaining EOFs could be considered negligible. The fact that EOF1 and EOF3 of the observed NDVI were related to the land cover and soil type maps, respectively, was consistent with our expectations that NDVI is a suitable proxy of vegetation dynamics.

After the automatic calibration, the model matched the observed loadings of EOF1 and its accuracy was slightly poorer for EOF2 and EOF3. Thus EOF1 captured the predominant pattern that was found in both the observed NDVI and the simulated LAI data. On one hand, the temporal variation of EOF1 loadings seemed to be related to the two typical growing seasons in the catchment: the first one during March–May and the second one during October–December (Franz et al., 2010; Fig. 3). On the other hand, the loadings of EOF2 and EOF3 were not strongly connected with any feature. The loadings of the remaining EOFs were scattered, which implies that mainly measurement and model noise were covered by these EOFs.

The weakness of the proposed calibration methodology is that, although the associated weights to the loading deviation in Eq. (6) are needed, they are also misleading some spatial information. New ways to weigh the loading deviations must emerge in future research as proposed by Koch et al. (2015). In fact, due to the portion of variance explained by EOF1, this first main pattern controlled the calibration process. In future applications, the proposed error index may be improved by focusing or excluding specific EOFs. A popular method for deciding which EOF to keep and which to discard is to use “selection rules”. Basically, there are three classes of selection rules depending on whether they focus on the amount of variance explained by each EOF, the loadings or the EOF maps (Preisendorfer, 1988). Another option could be to rotate the EOFs as proposed by Bonaccorso et al. (2003). As each rotated EOF will not explain the same variance of the unrotated one, this approach would be an option to use different combinations of EOFs, which explain different amounts of variance in order to reduce the influence of EOF1.

The automatic calibration process worked satisfactorily as shown by the additional metrics: temporal Pearson correlation coefficient, spatial Pearson correlation coefficient in the main land covers and the comparison between the gradient maps. In terms of spatial Pearson correlation coefficient, the weakest values were obtained in the higher portion of the basin near Mount Kenya and the Aberdare mountains, while the remaining cells within the study area showed a good agreement between observed NDVI and simulated LAI. This same behavior was also observed when calibrating manually. Two reasons could explain such results. First, the observed NDVI in some cells of those areas had a really bad quality as testified by the unrealistic oscillations of the NDVI from 0.8 to 0.1 (even zero) in just one week. These unrealistic oscillations could be produced by the presence of clouds over the area near to the mountains. The second reason is related to the conceptual limitation of the proposed model. The TETIS-VEG was designed to be used only in water-controlled areas. Franz (2007) analyzed the correlation between the fractional woody cover and the mean annual precipitation within the catchment and they were strongly correlated. However, two different slopes were observed. The transition point, which indicates when water availability had a smaller influence on the fractional woody cover, occurred approximately around 800 mm year-1. Physically, the transition point is believed to be a good approximation of the transition from a water-controlled ecosystem to a nutrient-controlled ecosystem. This approach allowed us to define the higher areas within the study catchment (where Mount Kenya and the Aberdare mountains are included) as nitrogen limited ecosystems instead of water-controlled.

With the exemption of these two areas, a strong correlation between NDVI and LAI existed, i.e., the model captured the temporal dynamic of LAI. However, this did not necessarily mean that the magnitude of LAI was reasonable. This last point was proven by calculating the good performance in terms of spatial Pearson correlation and the comparison between the gradient maps. No differences and good agreements were observed along the main land covers: trees, shrubs and grasses.

Finally, there were four parameters in the automated calibration which changed substantially (in relative terms) in comparison to the values obtained during the manual calibration: the correction factor of the maximum static storage, the correction factor of the reference evapotranspiration, the factor related to the distribution of roots between the first and second static storage layers and the maximum LAI sustainable by the system (Table 1). These parameters directly affect the transpiration process and the amount of available water to be consumed by the plants. In any case, all obtained values were consistent with the reviewed literature (embedded in Table 1). All of them are completely included in the searching boundary used during the automatic calibration.

The validation process confirmed (1) the model was able to capture completely EOF1 while the model performance worsened in EOF2 and EOF3, (2) the simulated LAI and the observed NDVI were temporally correlated in most of the catchment and (3) the spatial distribution of LAI was consistent as shown by the comparison between the gradient maps and the value of the spatial Pearson correlation coefficient at any time.

An additional interesting outcome provided by the validation was the comparison between simulated and observed hydrograph data at the outlet. The simulated stream flow was promising, but not completely convincing. This limitation is obvious since the model parameters were calibrated on NDVI data, i.e., the model was calibrated on vegetation dynamics. Therefore, a direct comparison between hydrographs should not be too exigent when no information about the parameters involved in the river flow routing or aquifer discharge was included in the calibration.

We strengthened our discharge analysis by using the concept of FDCs. By graphical comparison (Fig. 8), it could be observed that the model is able to reproduce the shape of the observed FDC, while some discrepancies were found in terms of magnitude. However, its performance improved considerably year by year. Since the FDC shape is an important indicator of the relevant hydrological processes occurring on the basin scale, this result pointed out the capability of the proposed model calibration methodology to reproduce the main hydrological behavior of the study basin.

The main two objectives of this research were (1) to explore if it is possible to calibrate and validate an ecohydrological model using only satellite information and (2) to incorporate spatio-temporal data about a model state variable into the automatic calibration process. In order to tackle these challenges, a parsimonious distributed ecohydrological model was calibrated by exclusively using NDVI data provided by MODIS. A methodology based on EOF analysis was proposed to carry out manual and automatic calibration of the model. Finally, the results were validated using satellite data referring to different periods and the observed discharge at the basin outlet, which was not used for calibration.

In general, the proposed model was able to properly reproduce the vegetation dynamics and the observed stream flow. The results highlight the usefulness of satellite data. It was possible to implement the hydrological and the vegetation components of the TETIS-VEG daily model using only NDVI data and also to validate the model with satisfactory results. Such outcomes are promising because they demonstrate that satellite data could be exploited in order to predict river discharge in ungauged basins. More specifically, we expect this result given the key role played by vegetation in water-controlled areas such as the upper Ewaso Ngiro river basin in Kenya, where having an appropriate description of vegetation and transpiration is critical for a correct description of the water balance on the local and basin scale.

The proposed automatic calibration was completely designed to incorporate spatio-temporal data in order to take maximum advantage of the available satellite data. After calibrating, the simulated vegetation patterns display good agreement with measured NDVI in most of the basin except for some portions at higher altitudes. This non-satisfactory result may be due to the bad quality of the NDVI data and/or the limitation of the vegetation sub-model (that was specifically designed for semiarid regions).

Model limitations along with poor data quality and resolution negatively affected the overall model performance, but the proposed procedure allowed us to exploit the amount of information available addressing the critical issue of identifying a procedure for the calibration of a distributed model. This allowed us to obtain a correct description of vegetation dynamics in space and time also providing, as a marginal benefit, a fairly good streamflow prediction. In this context, it was mandatory to adopt a daily time step in order to have a coherence with satellite NDVI data and also removing the need for a runoff propagation module in our model.

Finally, we should consider that the potential of the present study is due to the large availability of remote sensing information (not only satellite) concerning spatial state variables and more information will be available in the future. Many efforts are being made to improve the quality and quantity of remote sensing data (drones, better devices, etc.). Additionally, the scientific community must also be ready to exploit the enormous amount of information contained in this data (temporal, spatial and spatio-temporal). Therefore, we should identify the best way to use all of this new available information, not only for data assimilation but also for model calibration and validation.