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This manuscript provides a methodology for the reconstruction of a rainfall field when there are scarce rain-gauge stations available. This situation typically arises when measurements are taken from meteorological stations across time, and the information for the complete field is required as an input for larger scale models. The proposed method is based on a wavelet reconstruction technique that requires no distributional assumptions, but relies on the relation between rainfall and normalized difference vegetation index to account for the unobserved spatial variability of the field. The methodology is applied over a region of the southern Peruvian Andes where data gathered from meteorological stations provide enough statistical significance. A comparison with respect to an alternative source of spatial variability and common practices is provided.

Data acquisition for parameterization is one of the most important limitations for the use of potato crop growth models. Non-destructive techniques such as remote sensing for gathering required data could circumvent this limitation. Our goal was to analyze the effects of incorporating ground-based spectral canopy reflectance data into two light interception models with different complexity. A dynamic- hourly scale- canopy photosynthesis model (DCPM), based on a non-rectangular hyperbola applied to sunlit and shaded leaf layers and considering carbon losses by respiration, was implemented (complex model). Parameters included the light extinction coefficient, the proportion of light transmitted by leaves, the fraction of incident diffuse photosynthetically active radiation and leaf area index. On the other hand, a simple crop growth model (CGM) based on daily scale of light interception, light use efficiency (LUE) and harvest index was parameterized using either canopy cover (CGMCC) or the weighted difference vegetation index (CGMWDVI). A spectroradiometer, a chlorophyll meter and a multispectral camera were used to derive the required parameters. CGMWDVI improved yield prediction compared to CGMCC. Both CGMWDVI and DCPM showed high degree of accuracy in the yield prediction. Since large LUE variations were detected depending on the diffuse component of radiation, the improvement of simple CGM using remotely sensed data is contingent on an appropriate LUE estimation. Our study suggests that the incorporation of remotely sensed data in models with different temporal resolution and level of complexity improves yield prediction in potato.

Remotely sensed data are often used as proxies for indirect precipitation measures over data-scarce and complex-terrain areas such as the Peruvian Andes. Although this information might be appropriate for some research requirements, the extent at which local sites could be related to such information is very limited because of the resolution of the available satellite data. Downscaling techniques are used to bridge the gap between what climate modelers (global and regional) are able to provide and what decision-makers require (local). Precipitation downscaling improves the poor local representation of satellite data and helps end-users acquire more accurate estimates of water availability. Thus, a multifractal downscaling technique complemented by a heterogeneity filter was applied to TRMM (Tropical Rainfall Measuring Mission) 3B42 gridded data (spatial resolution ~ 28 km) from the Peruvian Andean high plateau or \\textit{Altiplano} to generate downscaled rainfall fields that are relevant at an agricultural scale (spatial resolution ~ 1 km).

Potato bacterial wilt, caused by the bacterium Ralstonia solanacearum race 3 biovar 2 (R3bv2), affects potato production in several regions in the world. The disease becomes visually detectable when extensive damage to the crop has already occurred. Two greenhouse experiments were conducted to test the capability of a remote sensing diagnostic method supported by multispectral and multifractal analyses of the light reflectance signal, to detect physiological and morphological changes in plants caused by the infection. The analysis was carried out using the Wavelet Transform Modulus Maxima (WTMM) combined with the Multifractal (MF) analysis to assess the variability of high-resolution temporal and spatial signals and the conservative properties of the processes across temporal and spatial scales. The multispectral signal, enhanced by multifractal analysis, detected both symptomatic and latently infected plants, matching the results of ELISA laboratory assessment in 100 and 82%, respectively. Although the multispectral method provided no earlier detection than the visual assessment on symptomatic plants, the former was able to detect asymptomatic latent infection, showing a great potential as a monitoring tool for the control of bacterial wilt in potato crops. Applied to precision agriculture, this capability of the remote sensing diagnostic methodology would provide a more efficient control of the disease through an early and full spatial assessment of the health status of the crop and the prevention of spreading the disease.

Quantifying rainfall at spatial and temporal scales in regions where meteorological stations are scarce is important for agriculture, natural resource management and land-atmosphere interactions science. We describe a new approach to reconstruct daily rainfall from rain gauge data and the normalized difference vegetation index (NDVI) based on the fact that both signals are periodic and proportional. The procedure combines the Fourier Transform (FT) and the Wavelet Transform (WT). FT was used to estimate the lag time between rainfall and the vegetation response. Subsequently, third level decompositions of both signals with WT were used for the reconstruction process, determined by the entropy difference between levels and R^2. The low-frequency NDVI data signal, to which the high frequency signal (noise) extracted from the rainfall data was added, was the base for the reconstruction. The reconstructed and the measured rainfall showed similar entropy levels and better determination coefficients (>0.81) than the estimates with conventional statistical relations reported in the literature where this level of precision is only found for comparisons at the seasonal levels. Cross-validation resulted in @?10% entropy differences, compared to more than 45% obtained for the standard method when the NDVI was used to estimate the rainfall in the same pixel where the weather station was located. This methodology based on high resolution NDVI fields and data from a limited number of meteorological stations improves spatial reconstruction of rainfall.

Understanding spatial patterns is a critical and under‐explored aspect of remote sensing. This paper describes how multifractal theory can be applied to characterize these heterogeneous patterns in remotely sensed data as well as to determine the operational scale. An example based on the characterization of ulexite distribution on the world's largest salt flat (10 000 km2), located in Bolivia, using a binarized Landsat Thematic Mapper (TM) 4/7 ratio image, is used to describe the step‐by‐step procedure. Distribution was well characterized by the multifractal parameters and expressed through the f–α, τ–q and D–q relationships. Moments from q = −2 to 5 showed a linear trend in scales from approximately 0.007 to 10 000 km2. This implies that the attribute analysed could be measured at different scales, within defined boundaries, and up‐ and down‐scaled using the multifractal parameters. In addition, the asymmetry shown by the f–α spectrum indicates the presence of clusters with high probability of finding u...