Evaluation of Disaggregation Methods for Downscaling MODIS Land Surface Temperature to Landsat Spatial Resolution in Barrax Test Site

Thermal infrared (TIR) data are usually acquired at a coarser spatial resolution (CR) than visible and near infrared (VNIR). Several disaggregation methods have been recently developed to enhance the TIR spatial resolution using VNIR data. These approaches are based on the retrieval of a relation between TIR and VNIR data at CR, or training of a neural network, to be applied at the fine resolution afterward. In this work, different disaggregation methods are applied to the combination of two different sensors in the experimental test site of Barrax, Spain. The main objective is to test the feasibility of these techniques when applied to satellites provided with no TIR bands. Landsat and moderate imaging spectroradiometer (MODIS) images were used for this work. Land surface temperature (LST) fromMODIS images was disaggregated to the Landsat spatial resolution using Landsat VNIR data. Landsat LST was used for the validation and comparison of the different techniques. Best results were obtained by the method based on a linear regression between normalized difference vegetation index (NDVI) and LST. An average RMSE = ±1.9 K was observed between disaggregated and Landsat LST fromfour different dates in a study area of 120 km

Sharpening ECOSTRESS and VIIRS Land Surface Temperature Using Harmonized Landsat-Sentinel Surface Reflectances

Land surface temperature (LST) is a key diagnostic indicator of agricultural water use and crop stress. LST data retrieved from thermal infrared (TIR) band imagery, however, tend to have a coarser spatial resolution (e.g., 100 m for Landsat 8) than surface reflectance (SR) data collected from shortwave bands on the same instrument (e.g., 30 m for Landsat). Spatial sharpening of LST data using the higher resolution multi-band SR data provides an important path for improved agricultural monitoring at sub-field scales. A previously developed Data Mining Sharpener (DMS) approach has shown great potential in the sharpening of Landsat LST using Landsat SR data co-collected over various landscapes. This work evaluates DMS performance for sharpening ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) LST (~70 m native resolution) and Visible Infrared Imaging Radiometer Suite (VIIRS) LST (375 m) data using Harmonized Landsat and Sentinel-2 (HLS) SR data, providing the basis for generating 30-m LST data at a higher temporal frequency than afforded by Landsat alone. To account for the misalignment between ECOSTRESS/VIIRS and Landsat/HLS caused by errors in registration and orthorectification, we propose a modified version of the DMS approach that employs a relaxed box size for energy conservation (EC). Sharpening experiments were conducted over three study sites in California, and results were evaluated visually and quantitatively against LST data from unmanned aerial vehicles (UAV) flights and from Landsat 8. Over the three sites, the modified DMS technique showed improved sharpening accuracy over the standard DMS for both ECOSTRESS and VIIRS, suggesting the effectiveness of relaxing EC box in relieving misalignment-induced errors. To achieve reasonable accuracy while minimizing loss of spatial detail due to the EC box size increase, an optimal EC box size of 180–270 m was identified for ECOSTRESS and about 780 m for VIIRS data based on experiments from the three sites. Results from this work will facilitate the development of a prototype system that generates high spatiotemporal resolution LST products for improved agricultural water use monitoring by synthesizing multi-source remote sensing data

機械学習を用いた空間ダウンスケールの気温予測法及び都市ヒートアイランドへの応用に関する研究

This study introduced a temperature spatial downscaling method based on machine learning algorithm to downscale air temperature from 1 km to 250 m for high-resolution atmosphere urban heat island (UHI) analysis. The core of this downscaling method is to establish the regression model between urban structure and temperature, and then we used the unchanged characteristics of regression models at different scale to predict high-resolution temperature data with high-resolution resolution urban structure, thereby analyzed atmosphere urban heat island. Finally, we compared the similarity and differentiation between atmosphere UHI and surface UHI. The results indicated the following: (1) The machine learning method was proved to be suitable for the air temperature spatial downscaling predication; (2) The UHI characteristics of metropolitan areas in different climatic regions of Japan are different; (3) There are great differences in intensity and spatial distribution between atmosphere UHI and surface UHI is great.北九州市立大

Modelling actual evapotranspiration using a two source energy balance model with Sentinel imagery in herbaceous-free and herbaceous-cover Mediterranean olive orchards

To the European Space Agency for the imagery of the Sentinel Missions and its open access. Special thanks to Radoslaw Guzinski for share and make accessible (https://github.com/radosuav/pyDMS) the implemented software for the used sharpening process (likewise to Hector Nieto for the implemented TSEB-PT, https://github.com/hectornieto/pyTSEB).To the Group of Castillo de Canena for the use of their farm as an experimental site and their people for continuous cooperation. We also give special thanks to Andrew S. Kowalski for his advice and suggestions. We would like also to express our gratitude to the anonymous reviewers for their comments and suggestions that enhanced this work. This work was supported by the Spanish Ministry of Science and Innovation through project CGL2017-83538-C3-1-R (ELEMENTAL) and PID2020-117825GB-C21 (INTEGRATYON3) Including European Union ERDF funds [grant number PRE2018-085638]. Funding for open access charge: Universidad de Granada/CBUA.Precipitation deficit and more extreme drought and precipitation events are expected to increase in the Mediterranean region due to global warming. A great part of this region is covered by olive orchards, representing 97.5% of the world’s olive agricultural area. Thus, the adaptation of olive cultivation demands climate-smart management, such as the optimization of water use efficiency, since evapotranspiration is one of the most important components of the water balance. The novelty of this work is the combination of the remote sensing data fusion and the Two Source Energy Balance (TSEB) model (through Sentinel-2 and Sentinel-3 imagery) to estimate the actual daily evapotranspiration (ETd), at high spatial (20 m) and temporal (daily) resolution, in an olive orchard under two management regimes: herbaceous free (HF) and herbaceous-cover (HC); along a three years period, based on the hypothesis that TSEB is still able to track and estimate the evapotranspiration over more complex canopies. The study was carried out from 2016 to 2019 in an olive orchard in the South of Spain, where the flux estimates were validated and assessed by in situ eddy covariance (EC) measurements. The results show better agreement in HC for net radiation (Rn) and the soil heat flux (G), but similar for both surfaces regarding the sensible (H) and latent (λE) heat fluxes, as well as ETd. On both surfaces greater differences obtained at higher H, and the magnitude of overestimation of λE and ETd were influenced by the EC energy imbalance. By contrast, G was overestimated with HC probably influenced by herbs, and equally underestimated for HF surfaces. The obtained results are in agreement with similar studies in tree crop orchards, and show the consistency of the used methodology and its usefulness for some farming activities, even on the more heterogeneous surface.Spanish Government CGL2017-83538-C3-1-R PID2020-117825GB-C21European Commission PRE2018-085638Universidad de Granada/CBU

Feasibility of Using the Two-Source Energy Balance Model (TSEB) with Sentinel-2 and Sentinel-3 Images to Analyze the Spatio-Temporal Variability of Vine Water Status in a Vineyard

In viticulture, detailed spatial information about actual evapotranspiration (ETa) and vine water status within a vineyard may be of particular utility when applying site-specific, precision irrigation management. Over recent decades, extensive research has been carried out in the use of remote sensing energy balance models to estimate and monitor ETa at the field level. However, one of the major limitations remains the coarse spatial resolution in the thermal infrared (TIR) domain. In this context, the recent advent of the Sentinel missions of the European Space Agency (ESA) has greatly improved the possibility of monitoring crop parameters and estimating ETa at higher temporal and spatial resolutions. In order to bridge the gap between the coarse-resolution Sentinel-3 thermal and the fine-resolution Sentinel-2 shortwave data, sharpening techniques have been used to downscale the Sentinel-3 land surface temperature (LST) from 1 km to 20 m. However, the accurate estimates of high-resolution LST through sharpening techniques are still unclear, particularly when intended to be used for detecting crop water stress. The goal of this study was to assess the feasibility of the two-source energy balance model (TSEB) using sharpened LST images from Sentinel-2 and Sentinel-3 (TSEB-PTS2+3) to estimate the spatio-temporal variability of actual transpiration (T) and water stress in a vineyard. T and crop water stress index (CWSI) estimates were evaluated against a vine water consumption model and regressed with in situ stem water potential (Ψstem). Two different TSEB approaches, using very high-resolution airborne thermal imagery, were also included in the analysis as benchmarks for TSEB-PTS2+3. One of them uses aggregated TIR data at the vine+inter-row level (TSEB-PTairb), while the other is based on a contextual method that directly, although separately, retrieves soil and canopy temperatures (TSEB-2T). The results obtained demonstrated that when comparing airborne Trad and sharpened S2+3 LST, the latter tend to be underestimated. This complicates the use of TSEB-PTS2+3 to detect crop water stress. TSEB-2T appeared to outperform all the other methods. This was shown by a higher R2 and slightly lower RMSD when compared with modelled T. In addition, regressions between T and CWSI-2T with Ψstem also produced the highest R2.info:eu-repo/semantics/publishedVersio

Remote Sensing Monitoring of Land Surface Temperature (LST)

This book is a collection of recent developments, methodologies, calibration and validation techniques, and applications of thermal remote sensing data and derived products from UAV-based, aerial, and satellite remote sensing. A set of 15 papers written by a total of 70 authors was selected for this book. The published papers cover a wide range of topics, which can be classified in five groups: algorithms, calibration and validation techniques, improvements in long-term consistency in satellite LST, downscaling of LST, and LST applications and land surface emissivity research

Calibration of DART Radiative Transfer Model with Satellite Images for Simulating Albedo and Thermal Irradiance Images and 3D Radiative Budget of Urban Environment

Remote sensing is increasingly used for managing urban environment. In this context, the H2020 project URBANFLUXES aims to improve our knowledge on urban anthropogenic heat fluxes, with the specific study of three cities: London, Basel and Heraklion. Usually, one expects to derive directly 2 major urban parameters from remote sensing: the albedo and thermal irradiance. However, the determination of these two parameters is seriously hampered by complexity of urban architecture. For example, urban reflectance and brightness temperature are far from isotropic and are spatially heterogeneous. Hence, radiative transfer models that consider the complexity of urban architecture when simulating remote sensing signals are essential tools. Even for these sophisticated models, there is a major constraint for an operational use of remote sensing: the complex 3D distribution of optical properties and temperatures in urban environments. Here, the work is conducted with the DART (Discrete Anisotropic Radiative Transfer) model. It is a comprehensive physically based 3D radiative transfer model that simulates optical signals at the entrance of imaging spectro-radiometers and LiDAR scanners on board of satellites and airplanes, as well as the 3D radiative budget, of urban and natural landscapes for any experimental (atmosphere, topography,…) and instrumental (sensor altitude, spatial resolution, UV to thermal infrared,…) configuration. Paul Sabatier University distributes free licenses for research activities. This paper presents the calibration of DART model with high spatial resolution satellite images (Landsat 8, Sentinel 2, etc.) that are acquired in the visible (VIS) / near infrared (NIR) domain and in the thermal infrared (TIR) domain. Here, the work is conducted with an atmospherically corrected Landsat 8 image and Bale city, with its urban database. The calibration approach in the VIS/IR domain encompasses 5 steps for computing the 2D distribution (image) of urban albedo at satellite spatial resolution. (1) DART simulation of satellite image at very high spatial resolution (e.g., 50cm) per satellite spectral band. Atmosphere conditions are specific to the satellite image acquisition. (2) Spatial resampling of DART image at the coarser spatial resolution of the available satellite image, per spectral band. (3) Iterative derivation of the urban surfaces (roofs, walls, streets, vegetation,…) optical properties as derived from pixel-wise comparison of DART and satellite images, independently per spectral band. (4) Computation of the band albedo image of the city, per spectral band. (5) Computation of the image of the city albedo and VIS/NIR exitance, as an integral over all satellite spectral bands. In order to get a time series of albedo and VIS/NIR exitance, even in the absence of satellite images, ECMWF information about local irradiance and atmosphere conditions are used. A similar approach is used for calculating the city thermal exitance using satellite images acquired in the thermal infrared domain. Finally, DART simulations that are conducted with the optical properties derived from remote sensing images give also the 3D radiative budget of the city at any date including the date of the satellite image acquisition

Εκτίμηση της συμβολής της αστικής μορφολογίας και λειτουργίας στο αστικό θερμικό περιβάλλον με την ανάπτυξη προηγμένων τεχνικών δορυφορικής τηλεπισκόπησης

Στο πλαίσιο της παρούσας διδακτορικής διατριβής επιχειρήθηκε μία πολυδιάστατη μελέτη του θερμικού περιβάλλοντος του πολεοδομικού συγκροτήματος της Αθήνας. Η ερευνητική προσπάθεια είχε ως στόχο την εκτίμηση της επίδρασης της αστική μορφολογίας και λειτουργίας στο αστικό θερμικό περιβάλλον. Η μελέτη υλοποιήθηκε κατά κύριο λόγο με την ανάπτυξη τεχνικών δορυφορικής τηλεπισκόπησης και επικουρικά με την εφαρμογή Γεωγραφικών Συστημάτων Πληροφοριών και αριθμητικής προσομοίωσης. Τα υφιστάμενα δορυφορικά συστήματα δεν διαθέτουν την ταυτόχρονη υψηλή χωρική και χρονική διακριτική ικανότητα η οποία απαιτείται για τη λεπτομερειακή διερεύνηση των ενδοαστικών διαφοροποιήσεων. Για τον σκοπό αυτό, πραγματοποιήθηκε αρχικά βελτίωση των υφιστάμενων μεθοδολογιών της στατιστικής υποκλιμάκωσης, κατά την οποία το LST ενισχύεται χωρικά βάσει της σχέσης που εμφανίζει με επιφανειακές παραμέτρους. Η υποκλιμάκωση πραγματοποιήθηκε με τη χρήση πολλαπλών μεταβλητών πρόβλεψης, υψηλής χωρικής ανάλυσης τιμών του συντελεστή εκπομπής έπειτα από φασματική ταξινόμηση, και εξετάζοντας διαφορετικούς γραμμικούς και μη γραμμικούς αλγορίθμους παλινδρόμησης. Εφαρμόστηκε στις καταγραφές θερμικής ακτινοβολίας του αισθητήρα Moderate Resolution Imaging Spectroradiometer (MODIS) των δορυφόρων Aqua και Terra, για τη χωρική ενίσχυσή τους από το 1 km στα 100 m. Βρέθηκε ότι η προτεινόμενη μέθοδος υποκλιμάκωσης —με τη χρήση του αλγορίθμου παλινδρόμησης τύπου ridge— παρείχε αξιόπιστες, χωρικά ενισχυμένες τιμές LST με σφάλμα μικρότερο των 2 K (τετραγωνική ρίζα μέσου τετραγωνικού σφάλματος, Root Mean Square Error – RMSE) και με σταθερά καλύτερη ακρίβεια (∼0.5 K) συγκριτικά με τις μεθόδους αναφοράς. Στο επόμενο στάδιο της μελέτης πραγματοποιήθηκε, σε υψηλή χωρική διακριτική ικανότητα (100 m), ο προσδιορισμός των χαρακτηριστικών της αστικής μορφολογίας, της λειτουργίας και των ροών ενέργειας της Αθήνας, και επακόλουθα ο συνδυασμός τους σε έναν δείκτη θερμικής επιβάρυνσης. Χρησιμοποιώντας πλήθος γεωχωρικών δεδομένων, κατέστη δυνατή η πλήρης περιγραφή του κτηριακού περιβάλλοντος, συμπεριλαμβανομένου του λόγου του ύψους των κτηρίων προς το πλάτος των δρόμων —αναλογία διαστάσεων αστικής χαράδρας (H/W)— για κάθε οδό της πόλης. Επακόλουθα, αξιοποιώντας το υψηλής χωρικής και χρονικής ανάλυσης LST από το πρώτο τμήμα της εργασίας, πραγματοποιήθηκε ο προσδιορισμός της αισθητής (QH) και της λανθάνουσας ροής θερμότητας (QE). Χρησιμοποιήθηκαν επιπρόσθετα παρατηρήσεις από μετεωρολογικούς σταθμούς και εφαρμόστηκε η μέθοδος της «αεροδυναμικής αντίστασης». Για την αξιολόγηση της ακρίβειας της εκτίμησης των ροών χρησιμοποιήθηκαν μετρήσεις μικρομετεωρολογικού πύργου· βρέθηκε μέσο σφάλμα RMSE ∼45 W/m2 για το QH και ∼15 W/m2 για το QE. Από τις παραπάνω τυρβώδεις ροές ενέργειας υπολογίστηκε στη συνέχεια ο λόγος Bowen β = QH/QE. Η ανθρωπογενής ροή θερμότητας (QF) προσδιορίστηκε μέσω της ανάπτυξης αλγορίθμου που συνδυάζει τις «bottom-up» και «top-down» προσεγγίσεις και είναι προσαρμοσμένος στα διαθέσιμα ενεργειακά δεδομένα της Αθήνας. Εντοπίστηκαν υψηλές ανθρωπογενείς εκπομπές θερμότητας για το κέντρο της πόλης (QF > 100 W/m2). Οι παραπάνω μεταβλητές (H/W, β και QF) μαζί με την εκτιμώμενη «καθαρή» μεταβολή του ρυθμού αποθήκευσης θερμότητας (ΔQs) ενσωματώθηκαν κατόπιν στον προτεινόμενο δείκτη θερμικής έκθεσης (Urban Heat Exposure, UHeatEx), χρησιμοποιώντας τη μέθοδο της ανάλυσης σε κύριες συνιστώσες (Principal Component Analysis, PCA). Ο παραπάνω δείκτης αποτύπωσε τα σημεία του αστικού ιστού της Αθήνας με τη δυσμενέστερη θερμική ποιότητα και κατά συνέπεια μπορεί να καταστεί ιδιαίτερα πολύτιμος σε μελέτες αστικού σχεδιασμού. Επιπρόσθετα, ο UHeatEx κατάφερε να αναδείξει τα ιδιαίτερα χαρακτηριστικά ως προς τη μορφολογία και το ενεργειακό ισοζύγιο της πόλης, κάτι που σε σημαντικό βαθμό δεν μπορούσε να επιτευχθεί μέσω της ταξινόμησης των «Τοπικών Κλιματικών Ζωνών» (Local Climate Zones, LCZ). Στο τελευταίο μέρος το ενδιαφέρον μετατοπίστηκε στην αξιολόγηση της μέσης επίδρασης στο θερμικό περιβάλλον εκτενέστερων αστικών ενοτήτων τοπικής κλίμακας (1 km). Συγκεκριμένα, αρχικά διερευνήθηκε η επίδραση βασικών αστικών μορφολογικών παραμέτρων —το ποσοστό των αδιαπέρατων επιφανειών, το ποσοστό της επιφάνειας κάλυψης από κτήρια και το ύψος των κτηρίων— στην επιφανειακή θερμοκρασία όπως αυτή καταγράφεται από τον δορυφορικό αισθητήρα MODIS. Με σκοπό μια ευρύτερη γενίκευση των συμπερασμάτων ως προς την επίδραση της αστικής μορφολογίας στο LST, παράλληλα με την περίπτωση της Αθήνας εξετάστηκαν 24 επιπλέον ευρωπαϊκές πόλεις. Η στατιστική ανάλυση κατέδειξε ότι η πυκνή και υψηλή δόμηση έχει εν γένει ασθενή θετική ή ακόμα και αρνητική σύνδεση με το LST κατά τη διάρκεια της ημέρας, ενώ αντίθετα εμφανίζει ισχυρή θετική επίδραση τη νύχτα. Το παραπάνω ήταν ιδιαίτερα εμφανές για την Αθήνα, όπου και εξετάστηκαν επιπλέον μορφολογικές παράμετροι και πραγματοποιήθηκε ερμηνεία των αποτελεσμάτων με βάση τις τάξεις των LCZ. Στη συνέχεια, τα χαρακτηριστικά της αστικής μορφολογίας και λειτουργίας της Αθήνας ενσωματώθηκαν στο ατμοσφαιρικό μοντέλο WRF για τη διερεύνηση της προγνωστικής ικανότητάς του, όσον αφορά το αστικό θερμικό περιβάλλον. Τα αποτελέσματα της εφαρμογής του WRF (σε πλέγμα χωρικής ανάλυσης 1 km) σε συνδυασμό με ένα τροποποιημένο σχήμα αστικής παραμετροποίησης έδειξαν ότι το μοντέλο μπορεί να αναπαραγάγει τις κύριες διαφοροποιήσεις εντός του αστικού ιστού, αναφορικά με την επιφανειακή θερμοκρασία (RMSE ∼2.4 K) και τη θερμοκρασία αέρα κοντά στο έδαφος (RMSE ∼1.7 K).In this PhD thesis, a multifaceted study of the thermal environment of Athens was conducted. The motivation of the research work was to assess the influence of urban form and function on the urban thermal environment. The work was carried out primarily by applying and developing satellite remote sensing techniques, and to a lesser extent via Geographical Information Systems (GIS) methodologies and the implementation of numerical simulations. The current satellite systems do not have the synchronous spatial and temporal frequency which is needed in a detailed study of intra-urban variability. To this end, an improvement of the standard statistical downscaling methodologies was firstly developed, where LST is disaggregated based on its relationship with surface parameters. The downscaling was accomplished using multiple predictor variables, high resolution land cover-based emissivity values, and assessing various linear and non-linear regression algorithms. It was applied to sharpen the thermal observations of the Moderate Resolution Imaging Spectroradiometer (MODIS) from 1 km to 100 m. It was found that the suggested downscaling method —using the ridge regression downscaling algorithm— produced a robust, spatially sharpened LST, with an average Root Mean Square Error (RMSE) less than 2 K and a consistent better performance compared to the reference methods. At the next stage, the urban form, function, and energy fluxes were mapped at a high resolution (100 m) and subsequently combined in an urban heat exposure indicator. Utilizing a wide range of spatial data, a full description of the building environment was accomplished, as well as the derivation of the building height to road width ratio —urban canyon aspect ratio (H/W)— at street level. Next, using the downscaled satellite-derived LST from the first part of the study and meteorological observations, the sensible (QH) and latent heat flux (QE) were calculated, applying the “aerodynamic resistance” methodology. To assess the accuracy of the calculations, micrometeorological observations; an overall RMSE error of ∼45 Wm2 for QH and ∼15 Wm2 for QE was obtained. From the above turbulent fluxes, the Bowen ratio β = QH/QE was subsequently derived. To determine the anthropogenic heat flux (QF) a new algorithm was developed, combining the “bottom-up” and “top-down” methodologies, adapted to the available data for the study area. Particularly high anthropogenic heat emissions were found for the city center (QF > 100 W/m2). Subsequently, the above urban parameters (H/W, β και QF) together with the net heat storage (ΔQs) were integrated into the proposed Urban Heat Exposure (UHeatEx) indicator through Principal Component Analysis (PCA). The indicator outlined the diverging thermal quality of the different building blocks in Athens and thereby can be valuable to urban planning adaptation responses. Moreover, UHeatEx managed to highlight the city-specific features of the urban form and energy budget of the city, which to a great extent could not be captured by the classification of the Local Climate Zones (LCZ). At the final stage of the study, focus was shifted to the study of the integrated neighborhood-scale effect (1 km) on the urban thermal climate. Specifically, it was initially assessed how basic urban morphological parameters —the impervious fraction, the building fraction, and the building height— are interlinked to the surface temperature variations, as captured by a spaceborne sensor (MODIS). To promote the generalization of conclusions, in addition to Athens, 24 additional European cities were examined. The statistical analysis showed that the closely spaced and high-rise buildings have generally a weak positive or even a negative relation to LST in daytime and a strong positive effect at night. This finding was significantly pronounced for Athens, where further urban parameters were also evaluated and the results were linked to the LCZs classes. Next, urban form and function of Athens were incorporated in the WRF model to study its predicting ability of the thermal environment. Using WRF along with a modified urban parameterization scheme (at a 1 km grid), results indicated that the prevailing intra-urban spatial patterns can be reproduced in the simulations, regarding the surface temperature (RMSE ∼2.4 K) and the near-surface air temperature (RMSE ∼1.7 K)

A Combination of TsHARP and Thin Plate Spline Interpolation for Spatial Sharpening of Thermal Imagery

There have been many studies and much attention paid to spatial sharpening for thermal imagery. Among them, TsHARP, based on the good correlation between vegetation index and land surface temperature (LST), is regarded as a standard technique because of its operational simplicity and effectiveness. However, as LST is affected by other factors (e.g., soil moisture) in the areas with low vegetation cover, these areas cannot be well sharpened by TsHARP. Thin plate spline (TPS) is another popular downscaling technique for surface data. It has been shown to be accurate and robust for different datasets; however, it has not yet been attempted in thermal sharpening. This paper proposes to combine the TsHARP and TPS methods to enhance the advantages of each. The spatially explicit errors of these two methods were firstly estimated in theory, and then the results of TPS and TsHARP were combined with the estimation of their errors. The experiments performed across various landscapes and data showed that the proposed combined method performs more robustly and accurately than TsHARP