Selecting best mapping strategies for storm runoff modeling in a mountainous semi-arid area

The problem

Modeling is necessary to detect areas susceptible to runoff and erosion; however, the accurate spatial representation of these processes is limited by the model used and the inputs it requires. Physical models that work on a cell-by-cell basis can generate an accurate representation of soil losses and runoff in a catchment, but the accuracy of their predictions is determined by the accuracy of the data fed into the system. The soil and hydraulic properties required for a physical modelare usually input into the model using mapping units that are considered representative and that are limited by the available datasets existing for the catchment being studied. The most common mapping units employed are related to soil properties, suchas those from a soil classification map. If such a map is not detailed enough or does not exist, a different mapping unit or a different method to represent the property is required. Once a selection is made the researcher, in most of cases, sticks to it through the modeling process without considering the effects of using a different method to map the properties. Nevertheless, the selection of the mapping units and mapping methods may influence the output, particularly for properties with a strong variation within a short distance. On the other hand, it could be the case that regardless of the input given to the model the results, both spatially and at the outlet, are the same. As the models are usually calibrated at a single outlet there is uncertainty of their performance generating spatially the runoff and erosion through the catchment, which could be completely wrong. The question, then, is does whether the mapping units used for the inputs make any difference to the resulting output.

Inputs and outputs for runoff and erosion modeling

In semi-arid environments, heavy rainfall events may generate runoff and erosion by two mechanisms: Hortonian overland flow, where high rainfall intensities exceed the infiltration rate of the soil; and saturation overland flow, where the amount of rainfall exceeds the storage capacity of the soil. In sloping areas with shallow soils, sustainable land management both in terms of on-site soil loss and off-site effects of flash floods needs to address both. Changes in infiltration rate and capacity as a result of tillage or terracing will influence the hydraulic behavior of a catchment. Hence, for accurate predictions of runoff and erosion, physically based models require reliable values of other soil properties such as saturatedhydraulic conductivity, porosity, soil depth and cohesion. The two main outputs of physically based models that have to be correctly predicted are the runoff wave for the off-site effects downstream, and the spatial patterns of runoff and erosion (Jetten et al., 2003).

Approaches for measurement and spatial representation of model inputs

To know where to act in the landscape with conservation measures or to investigate the effectiveness of existing ones, accurate spatial representation of runoff and erosion is needed. However data availability and adequate spatial representation of input soil parameters are important constraints for realistic model outputs. Hydraulic soil properties such as K_s have large variations within the same soil (Kumar et al., 1994; Russo and Bresler, 1981), in what has been described as a nested hierarchy with low and high levels: low levels are usually at field measurement scales and present small spatial and temporal changes in the soil properties, and medium and high levels are usually represented by mapping unitsthat correspond to areas where the variability of the soil properties increases (McBratney, 1998; Sobieraj et al., 2004; Zeleke and Si, 2005). Medium and high levels imply a large number of field measurements per mapping unit to capture thisvariability (Jabro, 1992; Moustafa, 2000) or the selection of an adequate map unit size. For parameters with a low spatial variation such as porosity, the measurement procedures are relatively standard, while a property such as K_s can be measured in the field or laboratory using diverse equipment and methodologies which yield different results (Lee et al., 1985; Paige and Hillel, 1993; Mohanty et al., 1994; Mallants et al., 1997a). At the same time, a parameter such as soil depth can only be mapped with difficulty and relies on sufficiently deep augering, exposure of soil profiles along road cuts, or techniques such as ground penetrating radar or electric resistivity survey (Kuriakose et al., 2009; Sucre et al., 2011; Shafique et al., 2011).

If a soil property is not measured, but basic soil material properties such as texture, organic matter and bulk density are known, it can be predicted by means of pedotransfer functions (PTFs), which are stochastic models that relate properties of soil constituents and indicators of structure to soil hydraulic properties (Bouma, 1989; Bouma and van Lanen, 1987). Diverse methods for PTFs are available, some combined with interpolation techniques, to obtain soil properties such as K_s (e.g. Aimrun and Amin, 2009; Espino et al., 1996; Tietje and Hennings, 1996; Zeleke and Si, 2005; Ferrer Julià et al., 2004).

To assign a meaningful value of the property to mapping units, a common procedure is to statistically compare measured values within units and search for significant differences. Meaningful units, that result in significantly different hydrological units, can be derived from all type of maps that influence hydrology. Often this is a soil map, but also other maps that are linked to texture or structure can be a basis, such as land use (because land management influences soil structure and organic matter) or geology (parent material) or combinations. Once appropriate mapping units have been selected, meaningful values (e.g. average or median) are usually assigned to each unit. When a soil property has strong spatial variations within the unit, the use of an average value will hide these variations, converting the distributed model into a lumped model (Beven, 1989), and if a unit remains without a value it has to be assigned based on its similitude to other units, or be estimated based, for instance, on soil morphology properties such as stratification or texture (e.g. Wang et al., 1985).

Geostatistics is an alternative to single values per unit. Here the objective is to interpolate spatially the soil property for the area of interest, using, for instance. ordinary kriging. This has been widely employed for K_s (Bosch and West, 1998; Mallants et al., 1997b; Moustafa, 2000). Interpolation techniques such as ordinary kriging cope with lack of sampling; however, there may be sharp boundaries in the landscape, due mostly to changes in geomorphology, soil structure, land use/cover and soil genesis, that may be hard to capture with this technique.

With meaningful values of a property to mapping units, it is assumed that the variation of the soil property within a mapping unit is significantly less than between units, while with the geostatistics approach it is assumed that the soil property has a spatial correlation that can be described by modeling its variance. Geostatistical methods such as kriging with an external drift (KED) allow one to incorporate the spatial trend in soil properties within the unit that they belong to. With KED an external variable with a linear relationship with the variable to be predicted is used to help in the interpolation, assuming that the external variable represents the spatial trend of the variable to be interpolated and that their residuals can be kriged (Goovaerts, 1997; Hengl, 2003). This approach is increasingly used, for instance, for soil depth (Bourennane et al., 1996; Bourennane and King, 2003; Kuriakose et al., 2009; Francés and Lubczynski, 2011).

These different approaches will result in model dataset inputs with very different spatial patterns, and therefore likely generate different model results. However, there is often not a good reason to select one over the other. Because in runoff simulations complex catchments are usually calibrated with the discharge hydrograph at the outlet only, there is often insufficient information to select a single calibration strategy (e.g. Takken et al., 1999; Jetten et al., 2003). The results in the outlet may be similar regardless of the type of input employed, following the principle of equifinality (Beven and Freer, 2001), which states that ‘given sufficient interactions among the components of a system that, unless the detailed characteristics of these components can be specified independently, many representations may be equally acceptable’. In other words, different inputs could generate equally acceptable outputs. Nevertheless, calibration at the outlet only does not help in understanding the behavior of the runoff wave in the catchment. For decision making, an adequate representation of the spatial distribution of runoff and erosion is required, and the use of different inputs, even when calibrated at the output, may result in completely different spatial patterns: if only maps with a single value per unit are used it is difficult to expect outputs that are not lumped, but if that is not the case and the spatial output patterns are similar even using complex input maps, then the mapping unit used is irrelevant and perhaps the focus should be on a better characterization of other important data such as rainfall. In data-poor environments, such as less-developed countries, datasets are old, with small cartographic scales, and generic in nature, and therefore with lack of detail and poor representativeness of the conditions in the field (e.g. a soil classification map instead of soil physical properties maps). What is the best strategy for mapping inputs for hydrological modeling in these cases?

Objectives

In this paper, four different interpolation strategies to transfer physical soil properties to spatial input datasets for runoff modeling are explored. The modeling is done with two contrasting rainfall events in terms of intensity, using the OpenLISEM runoff and erosion model (Baartman et al., 2012; Jetten and De Roo, 2001). The hypothesis is that the higher the spatial complexity of the input dataset, the better the spatial processes of runoff and erosion will be simulated.

The objectives of this study are: (i) to explore the effect of four different input datasets with increasing spatial complexity on the simulated spatial patterns of runoff, erosion and resulting discharge; and (ii) to compare the calibration procedurefor each of these datasets and determine the best strategy for creating an input dataset in the context of Cape Verde problems.

Study area and data availability

The study area for this research is Santiago, a semi-arid island in the Cape Verde archipelago under Sahelian climate regime, subject to land degradation and erosion caused by poor agricultural practices and scarce but heavy rainfalls thatproduce flash floods. Cape Verde is an archipelago composed of eight main islands and 13 islets located around 500 km off the west coast of Africa (15.02^∘ N, 23.34^∘ W), in the North Atlantic Ocean (Figure 1). The climate of the country is arid to semi-arid. Rainfall depends strongly on relief and elevation, and varies from less than 100 mm annually at sea level to over 500 mm per year in the higher-altitude mountain ranges (Sanchez-Moreno et al., 2013). Rainfall is almost entirely concentrated in the months of August to October, when the Intertropical Convergence Zone (ITCZ) is active over the archipelago and the same latitudes in western Africa (Mannaerts and Gabriels, 2000). The largest island of Cape Verde is Santiago (991 km²). Rainfall in Santiago is highly variable and influenced by topography (Sanchez-Moreno et al., 2013). For Santiago Island, when available, spatial data are limited, outdated or not very detailed. Most of the information regarding soils and geology was prepared by the Portuguese, from the times when Cape Verde was a colony (pre 1975). Available data provided by Cape Verde institutions and used in this study comprise a general soil map (Faria, 1970), a geology map (Bebiano, 1932) and a soils capability map for agriculture (SCET-AGRI, 1982; referred by Bertrand, 1996). Rainfall data are limited to daily precipitation, with a network that is not evenly distributed and comprised mainly of semi-automatic gauges with records registered by visual inspection. The climate characteristics of Cape Verde, and particularly Santiago Island, makes it an interesting laboratory for research. In Santiago Island is located Ribeira Seca, the catchment object of this study, with an area of 71.5 km². Ribeira Seca is an area of important soil degradation through water erosion and has a significant role in livestock and rainfed agriculture. Land use in Ribeira Seca is predominantly agricultural, with beans and corn as principal crops, and a few forested areas on hilltops (Bertrand, 1996). The Cape Verde islands are of volcanic origin. In the Ribeira Seca catchment, the geology is characterized by basalts and basanites, heterogenic conglomerates of volcanic ashes and slags, and alluvions (Figure 2). The soil classification of Santiago Island was prepared by Faria (1970) based on the French classification of Aubert (1965) (Figure 2). The rugged relief and highly variable, scarce but intense rainfall events have caused lithosols, regosols and vertisols to be predominant ((Faria, 1970). Soils in Cape Verde are young, and with depths varying between 0.20 m in high slope areas up to 1.00 m in the valleys. The soil map of Santiago Island prepared by Faria (1970) has general units described in terms of the soil order and color, and without description of soil families, hence without information about texture per soil unit type. Given the scarce information from the soils map, geology, land use and land capability units were considered for mapping units. A land capability classification (LCC) is a grouping of soils based on their crops and pasture potential that does not deteriorate over time (Klingebiel and Montgomery, 1966). The LCC map for Santiago Island was produced by SCET AGRI in 1981, using the land capability classification from the United States Department of Agriculture (USDA) (Klingebiel and Montgomery, 1966), and including slope and climatic parameters (Bertrand, 1996). The land capability map of Santiago presents detailed units that are somehow related to the soil type and land use. This map was used to prepare a soil texture map of the catchment.

Runoff and erosion modeling inputs

Runoff modeling was done using the Limburg Soil Erosion Model OpenLISEM (Baartman et al., 2012; Jetten and De Roo, 2001) a physically based distributed model that uses as rainfall input a single storm event. OpenLISEM was developed for small to medium-size catchments and has been tested in catchments bigger than 250 km² (not documented). Technically, OpenLISEM can be used with catchments of any size. The main constraints for large areas is the spatial distribution of rainfall, which should not be considered homogeneous. OpenLISEM does not take into account groundwater and base flow, considering the existing rivers dry. For large catchments the cell size of the input parameters should be small, no bigger than 50–100 m, depending on the type of terrain, because slope and the kinematic wave are sensitive to the cell size. The 90 m resolution DEM image captured quite well the drainages that transport water during rainfall events in the Ribeira Seca catchment. A higher DEM resolution may allow for a more accurate model, and changes in the cell size employed for the model highly influence the final result (Jetten et al., 2003), but a high-resolution DEM will not improve the model outputs if the other input parameters are averaged over the study area. Details on the underlying physical principles of OpenLISEM can be found in Baartman et al. (2012) and Jetten and De Roo (2001).

Secondary data acquisition

A 90 m resolution digital elevation model (DEM) from the Shuttle Radar Topography Mission (SRTM) was obtained from the National Map Seamless Server from the US Geological Survey (USGS, 2010). Land use was retrieved from a supervised classification of an ALOS-AVNIR image of June 2009. Impermeable areas were retrieved from Bertrand (1996) and the land use map classification. Soil type and soil characteristics were obtained from Faria (1970) and Amorós-Hernandez (2008), and complemented with exploration and samples taken during field campaigns in this study (see below).

Rainfall data

Rainfall with a temporal resolution of 3 min was measured with a Parsivel OTT disdrometer (Löffler-Mang and Jürg, 2000) installed in August 2008 in the National Institute for Agricultural Research and Rural Development of Cape Verde(INIDA) (point 2 in Figure 1). Rainfall measured by the disdrometer was compared to the rain gauge in Station Saõ Jorge recording daily rainfall and located 200 m north from the disdrometer (Sanchez-Moreno et al., 2012). Two storms were used for the model: one on 21 August with a duration of 121 min (event 08212010), and one on 12 September of 2010 with a higher intensity and a duration of 130 min (event 09122010). Figure 3a presents the rainfall distribution for Santiago Island for the period 1997–2010, and for the Ribeira Seca catchment for 2010. Note the highly variable rainfall depth, fluctuating between 100 mm (1998) to more than 500 mm (2010). Figure 3a also shows the maximum daily precipitation values. Few single strong rainfall events can control the seasonal pattern (Sanchez-Moreno et al., 2013). Figure 3b shows how, for Santiago Island, there are dry periods between daily events. In the same way that seasonal rainfall can be controlled by a few events, daily rainfall is usually comprised of a single strong event that controls the precipitation pattern. This is sometimes accompanied by smaller showers with low intensity and short duration. Infiltration rate was calculated in OpenLISEM with a one-layer Green and Ampt model (De Roo et al., 1996).

Field data

The rough topography of the catchment limits accessibility. Hence the measurement of soil properties was done using random sampling for accessible areas, and purposive sampling along roads and based on land capability units for inaccessible areas. Three campaigns were conducted between September and October of 2008–2010, corresponding to the rainy season. Purposive sampling or judgment sampling is a type of nonrandom sampling where the units from the population for study are based on the opinion of an expert on the representativeness of the population parameters (Deming, 1947, 1950). In total 79 K_s points were retrieved in the study area, 75 within the Ribeira Seca catchment, and 52 points for additional soil properties suchas cohesion, random roughness and porosity (Table 1). The samples were taken during the dry periods between storms. Infiltration was measured in the field with a mini-disk infiltrometer (Decagon, 2011), and saturated hydraulic conductivity was calculated using the procedure of Zhang (1997), improved by Dohnal et al. (2010). During the first campaign 49 infiltration points were measured with the mini-disk infiltrometer; in the second campaign 21 additional infiltration points were measured and 23 core samples for laboratory were taken that were used to measure porosity as well. In the laboratory K_s was measured in the 23 samples using an Eijkelkamp laboratory permeameter. The results from three constant head measurements and five falling head measurements were employed for K_s. The other samples were damaged or resulted in values considered outliers.

Cohesion was measured in the field with a torvane tester. For each sampling point four measurements spaced between 0.50 and 1 m were taken randomly and averaged. Soil depth was measured with tape along roads, channels and slope cuts. In flat areas it was measured using the pocking pole method, with an iron bar driven into the soil (Kuriakose et al., 2009); however,this method was not preferred because it was difficult to detect the bedrock due to the high stoniness in the catchment and because weathered rock was easily pierced.

Surface roughness was measured in the field using the chain method (Saleh, 1993, 1997). The dimensionless roughness factor C_rr (Equation 1) was converted into random roughness (RRF) in millimeters (Allmaras et al., 1966; Currence and Lovely, 1970; Kamphorst et al., 2000), which is incorporated into OpenLISEM using the equation proposed by Gilley and Kottwitz (1995), for an initial condition without rainfall (Equation 2):

(1)

(2)

Where L₁ is the original length of the chain (1 m), L₂ is the horizontal length of the chain in a rough surface and

(3)

(4)

In Equations 3 and 4 rainfall is expressed in millimeters.

Erosivity was estimated using the kinetic energy flux–intensity equation KE_time − I from Sanchez-Moreno et al. (2012), developed using data from the Parsivel OTT disdrometer (Equation 5).

(5)

It is important to note that erosion, deposition and stream sediment contents were not measured in the catchment, and therefore these erosion parameters are entirely model estimates.

Model calibration

Calibration for each of the four input maps was done at observation point 3, which is the only point where reliable measured data were available (Figure 1). Points 1 and 2 are used to describe discharge differences after calibration. Calibration was done on the measured discharge at point 3 by changing initial moisture content, suction at the wetting front and Manning's n, using a multiplication factor to match both the discharge peak and volume. The initial moisture content priorto calibration was assumed to be 80% of porosity. The maps representing K_s resulting from the four interpolation strategies (see below) were not modified. Spatial patterns of erosion from the different model scenarios were compared visually to the areas with runoff and erosion generated in the catchment. Small isolated areas with evidence of rill erosion were found, but due to their size these did not contribute to the overall erosion.

Mapping strategies

Interpolation accuracy and validation

For the geostatistical computations and map generation, the R environment (Ihaka and Gentleman, 1996) and gstat package (Pebesma, 2004) were used. To assess the interpolation models’ accuracy, cross-validation using the leave-one-out method (LOOCV) was employed, where the prediction was done for every point using the remaining observations as training data (Goovaerts, 1997; Isaaks and Srivastava, 1990). The goodness of fit of the interpolation results was evaluated by the root mean square error (RMSE), the normalized root mean square error (NRMSE) and the mean error (ME). The quality of the interpolation was assessed by the mean squared deviation ratio (MSDE), which is the ratio between the squared errors and thekriging variance. A model was considered accurate when the MSDE was equal to 1.

Soil property values and variation within mapping units

Table 1 presents the summary and statistics of the soil properties measured. In Ribeira Seca soil properties have important variations between the maximum and minimum. In the study area relief varies strongly over short distances, hence variables such as soil depth, which is dependent on slope, vary accordingly. The main activity in Ribeira Seca is agriculture. Tillage combined with a high stoniness affects the structure of the soil and influences variables such as soil cohesion and hydraulic conductivity.

Figure 4 presents the box plots for K_s within land use units, within the soils map from Faria (1970) and within the soil texture map based on land capability units. The soil texture map, with small units, produces the largest differentiation of K_s values. The variation of K_s within land use is not so strong because in the study area land use is not directly influenced by the soil type; therefore similar K_s values can be found for different land uses (Figure 4a). The variation of K_s (and other soil properties) is not properly captured in the soil map from Faria, as it has large units where a wide range of values that are averaged can be found (e.g. units lithosols/regosols), and some medium-size units with few measured points (e.g. brown soils). In ASG1 the average of all values within a class is assigned to the map units of that class (e.g. all map units CL get a K_s value of 25 mm h^− 1). ASG2 considers only the map unit boundaries and assigns the measured value to the unit in which it occurs. If a unit remains without a value, it should be merged with other units based on similarities in their characteristics or proximity to other units.

From Figure 4a it follows that land use does not determine the K_s strongly; while there are differences in averages between the units, the ranges overlap in most cases. Average input maps hide the spatial variability of the soil properties; however, the size of the unit where the averaging takes effect is important in retaining at least partially the spatial variability: from the box plot in Figure 4c it can be seen that small units (with observation values), such as texture in this case,capture better the spatial variability of the soil variable than large units such as those from the soils map from Faria (1970) (Figure 4a). On the other hand, if there are not strong spatial variations of the parameter, small units will not contribute to improve the map. As the number of observations per mapping unit and the variation of the parameter observed within the unit will determine the average value, more observations in a unit with strong variations may capture better the property variability than few ones.

For KED the drift variables were selected based on the actual relationship between the variables, and on the linear correlation between the predictor and the drift variable: soil depth is influenced by the slope, and therefore this parameter was used as external drift, while porosity and cohesion are related to soil texture, soil roughness to land use (e.g. an agricultural area with tillage has a different roughness to a forest), and K_s to the percentage of clay and texture. In several cases the correlation was weak, which is reflected on the accuracy of the results.

Figure 5 presents the fitted and sample variograms for the different input maps considered for interpolation. The variograms were selected based on visual inspection of the data, trying to obtain low RMSE and an MSDR closer to 1. The sample variogram for K_s shows a poor spatial correlation, a result of the erratic nature of K_s: for the same soil unit K_s can have important differences caused by crusting, soil compaction, initial moisture content, variations in texture and in organic matter, which can occur within a few meters. Table 2 presents the results from OK, and Table 3 the results from KED, with the co-variable employed for the prediction.

The interpolation models for porosity and cohesion produced the highest NRMSE for both OK and KED; this can be attributed to variations caused by the stoniness of the soil and errors during sampling and measurement. For porosity using KED a model with an MSDR of 1.22 was selected in order to control the maximum values produced by the interpolation. Variogram models resulting in a MSDR closer to 1 produced unrealistic porosity values above 0.60 for small units located in the extreme of the catchment, where the observed values ranged between 0.55 and 0.57. OK is an exact predictor at the observation points, meaning that the predicted value is the same as the observed; however, the surface generated presents a smooth pattern that seems not representative of the real conditions in the field. Conversely, the R² resulting from KED was lower, as the prediction relies on the correlation with the parameter used as a drift, which in several cases was not strong. Soil depth with KED was interpolated using slope as external drift, resulting in few pixels with a negative value that were converted into 0 (Table 3). The slope was calculated from a 90 m resolution image; however, given the rough topography, within the pixel area the soil depth and local slope have abrupt changes that are not captured by the image, and that will also cause local differences in the soil depth prediction. The maximum and average values obtained by OK and KED were similar, with variations on the prediction patterns caused by the external drift geometry and the variogram model employed for the predictions.

The first two strategies (ASG1 and ASG2) are based on calculating an average value per unit. Such an approach requires ‘design-based’ sampling which should be based on random sampling and is not compatible with purposive sampling. Geostatistics is model based and is appropriate in cases where the sampling schema is affected by accessibility, although there may be concerns about bias.

Figure 6 presents the input maps resulting from the four methodologies described above (‘Mapping strategies’). As expected, the four mapping methods resulted in variations in the maximum and minimum values of the soil properties, with the most noticeable differences occurring for soil depth and K_s due to their strong spatial variability even within short distances. The KED maps clearly follow the spatial trend of the map used as external drift, e.g. soil depth follows the slope pattern, while random roughness follows land use.

Soil property maps

Figure 7 shows the frequency distributions of K_s values for the four types of input maps. While K_s values for KED and OK follow a normal distribution, K_s for ASG1 and ASG2 show a concentration of values around 20 mm h^− 1 and between 2 and 10 mm h^− 1, respectively, evident also in Figure 6. This will influence the runoff behavior: large areas with low K_s imply poor water infiltration into the soil, and potentially more runoff. ASG1 and ASG2 inputs will cause the area to function much more like a threshold system: large areas will produce runoff or not. Figure 6 shows that porosity and soil depth also present important variations depending on the mapping strategy: while in OK and KED the minimum porosity is below 1%, in ASG2 the minimum porosity is 47%, closer to the maximum value measured. Soil depth also shows extreme variations between maps: in ASG2 the maximum soil depth is 390 mm, resulting from averaging the lowest and highest values within the same unit, while the maximum measured value was 1000 mm, which was closer to the values estimated with OK and KED.

Model calibration against discharge

Figure 8 shows the relationship between rainfall intensity (mm h^− 1), cumulative rainfall depth (mm) and measured discharge (m³ s^− 1 for events 08212010 and 09122010. Runoff starts with a cumulative rainfall depth of 26 mm for event 08212010 and of 24 mm for event 09122010, with a maximum cumulative precipitation of 50 mm and 65 mm respectively. Figure 8 indicates that there is a threshold of about 25 mm where additional rainfall becomes runoff. From this threshold it isevident that short-duration but strong storms can produce runoff immediately, but also that long-duration showers with few amounts of rainfall may need a longer time to generate runoff.

Figure 9 presents the runoff results for the four types of input maps under events 08212010 and 09122010, at the three observation points. Table 4 presents the multiplication factors applied to the input parameters to reach the measured volume and peak discharge. In the case of initial moisture content, the multiplication factor represents the fraction of the porosity used for calibration, while for Manning's n and suction at the wetting front the multiplication factors represent the value for which the initial input parameter was multiplied.

For both events the calibration values were almost the same (only a small difference in n-OK and psi-KED). In all cases the initial moisture content had to be varied to generate the right amount of infiltration, and Manning's n was alsodecreased to generate faster overland flow (and representing changes in the soil due to seasonality of the crops and previous rainfalls). Both ASG1 and ASG2 needed a very low initial moisture content to have sufficient storage, to avoid excessive saturation excess overland flow. While the soils can be very dry for part of the year, the low multiplication factor is seen as unrealistic because the events occur in the wet season months of August and September. In the case of OK and KED, Manning's n had to be decreased more strongly to simulate the correct peak flow. At point 2 (Figure 9b), the input maps produce similar runoff with the exception of ASG2, which gives a lower peak discharge. At point 1 (Figure 9c), the four input mapsgenerate different peak discharges, the only similarity being for the OK and KED inputs. These results indicate that OK and KED are equivalent methods to reach peak discharges; however, for event 08212010, OK requires a slightly smoother surface (lowManning's n) compared to KED, but since both the peak and volume do not coincide perfectly with the measured ones, these differences are irrelevant.

The general conclusion is that all datasets can be calibrated on the measured discharge, which shows in fact the equifinality aspect of this exercise. In general terms the scenarios ASG1 and ASG2 are more difficult to calibrate, because of the threshold nature of the maps as shown by the frequency distribution. Moreover, ASG1 and ASG2 do not represent correctly the real behavior of certain parameters (e.g. soil depth varies with slope rather than with land capability). Runoff is switched on or off for large areas with minor changes in the input. This suggests that at least scenarios OK and KED give a more realistic response. A second effect of the available dataset is that calibration at the observation point in the top half of the area does not say a lot about the runoff wave leaving the catchment, as the spatial patterns above point 3 have a strong influence on the discharge before it leaves the catchment. An option to capture the variation of runoff along the catchment is to add measuring points inside the catchment, but unless they conform a dense network they will tell little about the spatial distribution of the runoff wave, which is key for decision making. In this sense, calibration at the discharge point is not enough and the selection of the best modeling scenario also requires verification of the spatial distribution of the outputs against the actual runoff and erosion in the field.

Spatial variation of runoff and erosion

Figure 10 shows the runoff maps obtained by the four types of input for (a) event 08212010 and (b) event 09122010. For the same mapping strategy, the runoff patterns are similar for both events, with differences in the areas where runoff starts depending on the input map complexity and the runoff mechanism generated by the inputs. While for OK and KED most of the runoff starts at the northwest of the catchment, in ASG1 runoff initiates at two isolated areas in the north and south of the catchment, and for ASG2 runoff starts in the east and in the south.

Figure 11 shows soil storage capacity maps for the initial uncalibrated condition (a), where moisture is assumed to be 0.80% of porosity, and for the calibrated parameters (b), where Manning's n, suction at the wetting front and the initial moisture varied, as shown in Table 4. As soil depth and porosity have strong variations between mapping strategies, the storage capacity of the soil varies accordingly. Because ASG2 produced the lowest soil depths, the storage capacity is compensated by high porosity estimates (Figure 6). The patterns of runoff in Figure 10 clearly coincide with the areas of low soil storage capacity of Figure 11, while the coincidence with low values of K_s, given its high spatial variability, is less evident, except for extreme low values. Rough topography results in shallow soils coinciding with steep slopes and therefore a higher storage capacity is expected in the valleys.

Figure 12 presents the frequency distribution of storage capacity for the four mapping strategies, along with the rainfall events, as vertical lines, for the uncalibrated (a) and calibrated conditions (b). The only calibrated parameter that is relevant for storage capacity is moisture, and its variation altered to a great extent the former, particularly for ASG1 and ASG2. For the uncalibrated condition, where the moisture content is assumed to be 80% of porosity, both rainfall events exceed the storage capacity of the whole catchment, with the exception of KED, where for 10% of the catchment the storage capacity is not reached. For the calibrated condition, where the moisture content is reduced and storage capacity is therefore increased, the behavior varies depending on the type of input map: while for ASG2 about 10% percentage of the catchment exceeds the storage capacity for both events, for ASG2 the storage capacity was increased for the whole area and is not reached, and for OK and KED rainfall exceeds the storage capacity for about half of the catchment. As ASG1 has isolated large units, a reduction of the storage capacity in a single big unit can control the runoff generated for the whole catchment. In the case of ASG2, where similar units can appear as independent small areas, a decrease in storage capacity produces runoff areas appearing as patches with runoff dissimilar to the one in adjacent mapping units (Figure 10). These dissimilar patterns in runoff between adjacent units causes connectivity problems that are reflected in areas without water flow in between areas with clear runoff, as shown for ASG2 (Figure 10).

The variation in storage capacity according to mapping units suggests that OK and KED datasets, with less abrupt changes, show a better behavior regarding runoff distribution. In the frequency distribution of K_s (Figure 7) it can be noticed that while the maximum hydraulic conductivity is about 18 mm h^− 1 for ASG1, and between 40 and 50 mm h^− 1 for the other different datasets, the maximum rainfall intensities for both events are 145 and 168 mm h^− 1 (Figure 9), withintensities above 50 mm h^− 1 appearing early in event 08212010. In the Ribeira Seca catchment, the infiltration capacity of the soil is easily reached for most of the area at an early stage, even for rainfall events of low intensity as event 08212010. Antecedent moisture from previous events contributes to produce Hortonian overland flow, as it reduces the infiltration capacity by saturation, but as the soil storage capacity is quickly reached, saturation overland flow starts to appear and the storage capacity takes precedence over K_s in runoff generation. The runoff patterns seem to confirm this hypothesis, with runoff appearing in areas that coincide with low storage capacity (Figure 10). For the low-intensity event, more sources appear, particularly in high elevations with shallow soils dominated by Hortonian flow. Water that has reached the infiltration capacity of the soil moves towards the valleys where soils are deeper and therefore with more storage capacity, until saturated.

The four mapping strategies show the difficulty of proper characterization of the parameters controlling runoff, moreover, if the purpose is to describe its spatial distribution rather than just obtaining discharge volumes. For shallow soils with antecedent moisture, soil storage capacity seems a good indicator of areas where runoff is prone to appear.

Figure 13 presents the erosion in the catchment under the two rainfall events. Table 5 summarizes the detachment, deposition and remaining suspended sediments estimated by the eight models using the calibration values and rainfall events in Table 4. The erosion patterns show a similar distribution compared to the runoff patterns, indicating that the catchment is transport limited: the transport capacity determines the soil loss, not the sediment production. Important is that in spite of similarcalibrated runoff amounts the soil loss from the catchment is very different between ASG2 versus ASG1, OK and KED, while the detachment is similar. More sediment is deposited with the ASG2 dataset. Apparently a larger number of map units or a high spatial complexity causes a very different combination of detachment sources and deposition sinks.

Overall, the results from the four strategies seem to agree with the observed soil losses in the field: catchment observation indicates that the zones more affected by runoff and erosion under low-intensity rainfalls are located upstream of the catchment, while in the case of extreme events in all sub-catchments runoff and erosion are generated. The input datasets also model correctly the Ribeira Seca riverbed as the main sink, especially upstream, where all the sediments generated in the surrounding slopes arrive. However, there is no quantitative information to determine which scenario gives a correct soil loss amount: while AGS2 seems low, the datasets OK and KED seem very high, with an average of 39 and 42 tons ha^− 1 for a single event.

It is clear that, from the predictive point of view, additional spatial information is required to verify the presence of runoff and erosion in the field compared to the model estimates, particularly to determine areas where conservation and protection measures are required.

Rainfall distribution over the catchment is also relevant for modeling, with its importance increasing with the size of the catchment. From the data acquisition point of view, while lack of rainfall data can be compensated using indirect estimates, for instance from satellite imagery (such as MeteoSat, TRMM, among others; e.g. Sanchez-Moreno et al., ) or with statistical procedures to derive rainfall series from available data. Lack of soil property measurements requires more sophisticated techniques if direct measurement is not employed. From the modeling output point of view, for small to medium-size catchments, rainfall needs to be extremely variable to create important differences in runoff, whereas soil properties such as K_sat or soil depth are more likely to have strong variations, influencing the runoff and erosion generated.

As rainfall on Santiago Island is not continuous during the season, meaning that there are dry periods between showers, the soil can recover its storage and infiltration capacity before the next event, keeping in most cases a minimal amount of antecedent moisture. For year 2010 there were clear exceptions around 9 September and 22 October, where the deep rainfall (generated by strong events) were preceded by smaller events, which implies a reduction on storage and infiltration capacity that shouldbe considered when modeling these events, and that may be reflected in higher amounts of runoff and erosion.

The main load of sediments in the Ribeira Seca catchment are discharged into the ocean. Loss of soil is recognized as a problem in Cape Verde, and conservation measures in the form of terraces have been implemented over the country but without knowing with certainty their effectiveness. This study provides results based on real data and at a relatively high resolution, on areas susceptible to erosion for Santiago Island. Taking this research as a departing point, it will be possible to assess whether the existing conservation measures are being located in the places where more soil losses are occurring, and whether additional measures need to be placed. This research also provides strategies to generate inputs for better simulations of hydrological processes in poor data environments.