The study area shown in Figure 1 is located at the confluence of the Nairobi and Thiririka rivers (1˚11'57.36"S - 37˚07'09.23"E). It shares a border between Ruiru sub-county in Kiambu County and Kasarani sub-county in Nairobi County. It covers a total area of approximately 17 km².

The climate is described as warm and temperate. It lies at an altitude of 1544 m above sea level and receives annual average precipitation of 752 mm.

According to the 2019 Census, Kasarani sub-county had a population of 780,656, and Ruiru sub-county had a population of 490,120 [30]. Figure 2 shows the decadal increase in population around our study area.

The main socio-economic activity in the area is farming, and over the past two decades, there has been a growth of peri-urban agriculture along the river channel. Therefore, we chose an area along the river channel with a continuous and a high concentration of peri-urban farms as our study area.

Figure 3 gives a graphical illustration of the methodology used in this study.

The health of vegetation can provide important ancillary information when modeling heavy metals’ spatial distribution in soil. Multi-temporal Sentinel 2 images of Nairobi County were acquired from the USGS Earth Explorer for a period ranging from January 2019 to December 2019. This study used a higher spatial resolution optical sensor, Sentinel 2 (10 m) to improve the prediction accuracy.

NDVI = NIR − R NIR + R (1)

HMSSI = CIred-edge PSRI (2)

PSRI = R 680 − R 500 R 750 (3)

CIred-edge = ( R 783 R 705 ) − 1 (4)

SAVI = ( B 8 − B 4 ) B 8 + B 4 + L × ( 1 + L ) (5)

WDVI = B 8 × B 4 (6)

where L = 1.

A study by [15] has shown that the health of vegetation can be an important indicator of heavy metal contamination in soil, and it could also improve the accuracy of a soil heavy metal prediction model. The indices used in this study were derived from Sentinel-2, and they include Normalized Difference Vegetation Index (NDVI), Soil Adjusted Vegetation Index (SAVI), Weighted Difference Vegetation Index (WDVI) [34] and the novel Heavy metal stress-sensitive index (HMSSI) by [35]. HMSSI was developed to improve the accuracy of detecting heavy metal stress in Chinese rice fields using multi-temporal sentinel-2 images.

In calculating HMSSI, two red-edge spectral indices, namely plant senescence reflectance Index (PSRI) and Red-edge chlorophyll Index (CIred-edge), were used. Low (CIred-edge) index values indicate low chlorophyll and high stress in vegetation, while an increase in PSRI indicates an increase in canopy stress [35].

This study created a prediction model for each element (Cd, Pb, and Zn) using the Random Forest package (version 4.6 - 14) in R version 3.6.1 [36]. Random forest operates by constructing multiple decision trees. Each tree is built from a random vector independently sampled from the input vector, and each decision tree casts a vote to find out the most popular class to assign the input vector [19].

The Random forest has some advantages over other classification and regression tree algorithms. In addition to eliminating bias, it reduces the variance in the predictions usually associated with tree-based approaches by growing the trees further, then averaging their predictions [37]. Another important advantage of Random Forest over other machine learning algorithms is when the training data is small; it has the ability to capture complex and non-linear relationships between predictors and the outcome [37]. It’s also important to note that with random forest, the accuracy of prediction increases with an increased number of predictor variables [38].

In this study, the various model outputs were validated using the “out of bag” (OOB) testing. The OOB samples are the observations not included in the model, and since they are not used to predict the model, they are used to test it.

To test prediction quality, 75% of the predictor variables were used for calibration, while the remaining 25% was used for validation. The datasets were chosen using a Latin hypercube sampling to ensure that both the validation and calibration datasets were appropriately represented.

After selecting the training and test sets, we fitted the random forest model using default parameters [36]. The number of trees (ntree) was set at 500. The model was then fine-tuned by changing the number of variables randomly sampled at each stage (mtry) to 13. Evaluation of the model was done using Root Mean Square Error (RMSE), Bias, and coefficient of determination (R²), which were calculated using the Out of Bag Error Estimation. In this, 25% of predictor variables were used to validate the trees.

RMSError = 1 − r 2 SDy (7)

where SDy is the standard deviation of y

Bias = E ( H ) − θ (8)

where H is the expected values of the estimator less the values θ being estimated

R 2 = MSS / TSS = ( TSS − RSS ) / TSS (9)

where MSS is the model sum of squares, and TSS is the total sum of squares associated with the outcome variable.

A total of 60 samples were collected from selected points within the study area and later analyzed for heavy metals in a lab. The metals’ different concentrations are shown in Figure 8, Figure 9, and Figure 10. Table 3 shows the safety thresholds for heavy metals recommended by WHO, FAO, and USEPA.

The results indicate that for Zinc heavy metal, 17 out of the 60 soil samples collected exceeded the WHO/FAO permissible limits. According to [41], Zinc concentrations in the study area can be presented by anthropogenic activities like waste combustion at Dandora dumpsite, Steel processing activities at Nairobi Industrial area, and stone quarrying.

Additionally, 12/60 Lead samples exceeded the WHO/FAO/USEPA permissible safety limits. Lead is mainly used in the manufacture of lead storage batteries. In this case, it’s highly likely that its presence results from leachates and run-offs from electronic waste components at the Dandora dumpsite. Lead poisoning occurs when there is direct ingestion of Lead contaminated soil. Vegetables produced in soils with less than 300 ppm of Pb contamination are considered safe for consumption. The risk increases with an increase in the concentration in soil.

High Cadmium levels were found. However, non-exceeded the WHO/FAO/USEPA permissible limits. Cadmium pollution is linked to industrial effluents and water treatment sludge. Agricultural inputs like pesticides and fertilizers also increase their total concentration in soils [42].

According to [41], the high Cadmium concentrations can be attributed to the fact that the Nairobi river passes through several environmental hotspots, like the Dandora dumpsite, Industrial area, Nairobi sewerage treatment plant, and high traffic networks like the busy Nairobi Eastern bypass.

The distinct variation in the heavy metals results from a combination of different anthropological activities like the application of agricultural inputs, discharge of effluents from Industries and a sewerage treatment plant, leachates, and run-offs from Dandora dumpsite into the river, and mining activities.

One of the benefits of RF and other classification and regression tree algorithms is that they do not require the input data to be normalized. Therefore, no box plots and histograms were required for this study.

The general statistics for (75%) Calibration and (25%) Validation are shown in Table 4 and Table 5, respectively.

Table 6 displays Pearson’s correlation between the three soil toxic metals. There was no significant correlation between any of the metals, implying that they possibly did not come from the same source [15] [42].

The validation results of the spatial modeling for soil heavy metals contamination are shown in Table 7. Generally, the calibration model performed well with regards to the R² and RMSE estimates.

Our validation results for both Lead and Zinc had a higher correlation coefficient than [15] R² (Zn = 0.51) and R² (Pb = 0.53). This improvement could be attributed to the use of finer spatial resolution (10 m) for environmental predictors and spectral images in comparison to [15] at 30 m and [16] at 1 km. Additionally, the use of a high number of evenly distributed sample points in a smaller study area (17 km²) also meant that the accuracy of prediction in our study was improved. On the other hand, the climatic difference between Kenya, Qatar [15], and Europe [16] could be a contributing factor to the difference in

Levels of significance *p < 0.05, **p < 0.01.

results. Nairobi has a warm and temperate climate; Qatar is a desert while Europe is generally temperate. The soil parent rock materials and anthropogenic activities are also different. For these reasons, the choice of variables for modeling was different for the different study areas.

The variable of importance is measured based on the out of bag samples. These are observations not included in the Random Forest model. Also, they are based on a mean square error accuracy measure. The value is averaged over all trees [36].

From the output, it’s evident that the model utilized all the variables for prediction but gave more emphasis to the most important ones.

For Lead (Figure 11), HMSSI and SAVI were dominant within the top ten important variables. HMSSI was the best performer while the land-use and land cover map also performed considerably well in the prediction.

For Zinc, 3 WDVI, 3 HMSSI, and 2 NDVI were selected among the top ten important predictors. At the same time, distance to environmental hotspots was in the 7^th position (Figure 12).

The top ten important variables for Cadmium’s prediction (Figure 13) included spectral indices (3 WDVI, 3 HMSSI, and 2 NDVI). The land-use and land-cover map also performed considerably well, occupying the 5^th position.

In the prediction, the random forest model included the vegetation spectral indices (NDVI, SAVI, WDVI, and HMSSI) within the top ten important variables for all the heavy metals. This indicates their importance in predicting the distribution of heavy metals, which is in line with previous studies [15] [16].

The distance to the environmental hotspots variable was high in the ranking of all the metals, implying that human activities highly influence their concentrations.

The land-use and land-cover map performed reasonably well in the predictions despite being a new additional variable absent in previous research [15] [16].

In order to improve the predictive capability of heavy metals in soil, spectral indices were calculated for all the Sentinel 2 images. Four spectral indices HMSSI, SAVI, WDVI, and NDVI were derived.

The four variables were present within the top ten important variables in the prediction of all the heavy metals. In the prediction of Zinc, NDVI was the dominant index, followed by SAVI and HMSSI. For Lead prediction, NDVI was the most dominant index within the top 10 important variables. Of the top 10 important variables for Cadmium prediction, NDVI and HMSSI contributed three indices, each within the top important variables, followed by SAVI and WDVI.

Three predicted maps are shown in Figure 14, Figure 15 and Figure 16. With a 300 m buffer along the rivers’ riparian, we can easily tell how the three different heavy metals are distributed within the peri-urban farms.

There is a high concentration of Cadmium on the easterly end of the river. This can be linked to the study area’s proximity to the Nairobi water treatment plant at Ruai. Its abundance in the water treatment plant is because, besides other sources of Cadmium, it can also occur as an impurity in detergents [41]. The water treatment plant serves a population of 4,397,073 residents, which dramatically increases the probability of high Cadmium concentrations within the wastewater. There is also a possibility that the treated wastewater being discharged into the river is still toxic.

Another possible source of Cadmium in the soil is the application of phosphate fertilizers and pesticides on the peri-urban farms. Additionally, the disposal of Industrial waste upstream, as the river passes through an industrial area, also increases the total concentration of Cadmium in soil.

Some farms have a high concentration of Lead in their soil. However, these soils are safe for agricultural production because they have not exceeded the WHO/FAO/USEPA permissible limits. Additionally, plants do not uptake Lead into their system unless the concentration levels rise above 300 ppm. Further, a study done by [41] indicates that Lead does not readily accumulate in the fruiting parts of a plant.

Below the 300 mg/kg permissible limit, Lead poisoning can only occur through direct ingestion of contaminated soil particles.

Lead is a significant component in lead storage batteries, cable coverings, and other electronic equipment. In this regard, the probable source of Lead in the water could be leachates and run-offs from the Dandora dumpsite.

Some farms had Zinc levels, which were above the WHO/FAO/USEPA recommended limit. Zinc occurs naturally in soils in concentrations between 10 to 100 mg/kg; it’s a highly toxic heavy metal at high concentrations for both plants and animals. Anthropogenic activities such as atmospheric deposition, waste combustion, mining, steel processing, and sewage sludge application continue to enrich the topsoils with Zinc. In this study, therefore, the most likely sources of Zinc are; The Dandora dumpsite where waste combustion takes place, the Nairobi Water and sewerage plant where treated wastewater is discharged into the river, and the Nairobi Industrial area where some industries carry out metal processing.