We prove the
K
(
π
,
1
)
conjecture for affine Artin groups: the complexified complement of an affine reflection arrangement is a classifying space. This is a long-standing problem, due to Arnol’d, ...Pham, and Thom. Our proof is based on recent advancements in the theory of dual Coxeter and Artin groups, as well as on several new results and constructions. In particular: we show that all affine noncrossing partition posets are EL-shellable; we use these posets to construct finite classifying spaces for dual affine Artin groups; we introduce new CW models for the orbit configuration spaces associated with arbitrary Coxeter groups; we construct finite classifying spaces for the braided crystallographic groups introduced by McCammond and Sulway.
Irrigated agriculture is the primary driver of freshwater use and is continuously expanding. Precise knowledge of irrigation amounts is critical for optimizing water management, especially in ...semi-arid regions where water is a limited resource. This study proposed to adapt the PrISM (Precipitation inferred from Soil Moisture) methodology to detect and estimate irrigation events from soil moisture remotely sensed data. PrISM was originally conceived to correct precipitation products, assimilating Soil Moisture (SM) observations into an antecedent precipitation index (API) formula, using a particle filter scheme. This novel application of PrISM uses initial precipitation and SM observations to detect instances of water excess in the soil (not caused by precipitation) and estimates the amount of irrigation, along with its uncertainty. This newly proposed approach does not require extensive calibration and is adaptable to different spatial and temporal scales. The objective of this study was to analyze the performance of PrISM for irrigation amount estimation and compare it with current state-of-the-art approaches. To develop and test this methodology, a synthetic study was conducted using SM observations with various noise levels to simulate uncertainties and different spatial and temporal resolutions. The results indicated that a high temporal resolution (less than 3 days) is crucial to avoid underestimating irrigation amounts due to missing events. However, including a constraint on the frequency of irrigation events, deduced from the system of irrigation used at the field level, could overcome the limitation of low temporal resolution and significantly reduce underestimation of irrigation amounts. Subsequently, the developed methodology was applied to actual satellite SM products at different spatial scales (1 km and 100 m) over the same area. Validation was performed using in situ data at the district level of Algerri-Balaguer in Catalunya, Spain, where in situ irrigation amounts were available for various years. The validation resulted in a total Pearson’s correlation coefficient (r) of 0.80 and a total root mean square error (rmse) of 7.19 mm∕week for the years from 2017 to 2021. Additional validation was conducted at the field level in the Segarra-Garrigues irrigation district using in situ data from a field where SM profiles and irrigation amounts were continuously monitored. This validation yielded a total bi-weekly r of 0.81 and a total rmse of −9.34 mm∕14-days for the years from 2017 to 2021. Overall, the results suggested that PrISM can effectively estimate irrigation from SM remote sensing data, and the methodology has the potential to be applied on a large scale without requiring extensive calibration or site-specific knowledge.
This paper introduces a modified version of the DisPATCh (Disaggregation based on Physical And Theoretical scale Change) algorithm to disaggregate an SMAP surface soil moisture (SSM) product at a 20 ...m spatial resolution, through the use of sharpened Sentinel-3 land surface temperature (LST) data. Using sharpened LST as a high resolution proxy of SSM is a novel approach that needs to be validated and can be employed in a variety of applications that currently lack in a product with a similar high spatio-temporal resolution. The proposed high resolution SSM product was validated against available in situ data for two different fields, and it was also compared with two coarser DisPATCh products produced, disaggregating SMAP through the use of an LST at 1 km from Sentinel-3 and MODIS. From the correlation between in situ data and disaggregated SSM products, a general improvement was found in terms of Pearson’s correlation coefficient (R) for the proposed high resolution product with respect to the two products at 1 km. For the first field analyzed, R was equal to 0.47 when considering the 20 m product, an improvement compared to the 0.28 and 0.39 for the 1 km products. The improvement was especially noticeable during the summer season, in which it was only possible to successfully capture field-specific irrigation practices at the 20 m resolution. For the second field, R was 0.31 for the 20 m product, also an improvement compared to the 0.21 and 0.23 for the 1 km product. Additionally, the new product was able to depict SSM spatial variability at a sub-field scale and a validation analysis is also proposed at this scale. The main advantage of the proposed product is its very high spatio-temporal resolution, which opens up new opportunities to apply remotely sensed SSM data in disciplines that require fine spatial scales, such as agriculture and water management.
Efficient water management strategies are of utmost importance in drought-prone regions, given the fundamental role irrigation plays in avoiding yield losses and food shortages. Traditional ...methodologies for estimating irrigation amounts face limitations in terms of overall precision and operational scalability. This study proposes to estimate irrigation amounts from soil moisture (SM) data by adapting the PrISM (Precipitation Inferred from Soil Moisture) methodology. The PrISM assimilates SM into a simple Antecedent Precipitation Index (API) model using a particle filter approach, which allows the creation and estimation of irrigation events. The methodology is applied in a semi-arid region in the Ebro basin, located in the north-east of Spain (Catalonia), from 2016 to 2023. Multi-year drought, which started in 2020, particularly affected the region starting from the spring of 2023, which led to significant reductions in irrigation district water allocations in some of the areas of the region. This study demonstrates that the PrISM approach can correctly identify areas where water restrictions were adopted in 2023, and monitor the water usage with good performances and reliable results. When compared with in situ data for 8 consecutive years, PrISM showed a significant person’s correlation between 0.58 and 0.76 and a cumulative weekly root mean squared error (rmse) between 7 and 11 mm. Additionally, PrISM was applied to three irrigation districts with different levels of modernization, due to the different predominant irrigation systems: flood, sprinkler, and drip. This analysis underlined the strengths and limitations of PrISM depending on the irrigation techniques monitored. PrISM has good performances in areas irrigated by sprinkler and flood systems, while difficulties are present over drip irrigated areas, where the very localized and limited irrigation amounts could not be detected from SM observations.
Maps of irrigation systems are of critical value for a better understanding of the human impact on the water cycle, while they also present a very useful tool at the administrative level to monitor ...changes and optimize irrigation practices. This study proposes a novel approach for classifying different irrigation systems at field level by using remotely sensed data at sub-field scale as inputs of different supervised Machine Learning (ML) models for time-series classification. The ML models were trained using ground-truth data from more than 300 fields collected during a field campaign in 2020 across an intensely cultivated region in Catalunya, Spain. Two hydrological variables retrieved from satellite data, actual evapotranspiration (<inline-formula><tex-math notation="LaTeX">ET_{a}</tex-math></inline-formula>) and soil moisture (<inline-formula><tex-math notation="LaTeX">SM</tex-math></inline-formula>), showed the best results when used for classification, especially when combined together, retrieving a final accuracy of <inline-formula><tex-math notation="LaTeX">90.1 \pm 2.7\%</tex-math></inline-formula>. All the three ML models employed for the classification showed that they were able to distinguish different irrigation systems, regardless of the different crops present in each field. For all the different tests, the best performances were reached by ResNET, the only Deep Neural Network model among the three tested. The resulting method enables the creation of maps of irrigation systems at field level and for large areas, delivering detailed information on the status and evolution of irrigation practices.
This study aims to analyze the potential of different drought indices for identifying drought periods and predicting cereal yield in two semi-arid regions, Lleida in Catalonia and Kairouan in ...Tunisia, which have similar Mediterranean climates but different agricultural practices. Four drought indices, namely the Soil Moisture Anomaly Index (SMAI), the Vegetation Anomaly Index (VAI), the Evapotranspiration Anomaly Index (EAI), and the Inverse Temperature Anomaly Index (ITAI), were calculated from remote sensing data. Drought periods were identified from 2010/2011 to 2021/2022 based on the aforementioned indices. A correlation study between drought indices and wheat and barley yields was performed in order to select the most informative index and month for yield prediction. In the rainfed cereal area of Lleida, the strongest correlation was found between the EAI and VAI with barley yield (0.91 and 0.83, respectively) at the time of cereal maturity in June. For wheat, the strongest correlation was found between the EAI and VAI (0.75 and 0.72, respectively) at the time of cereal maturity in July. However, the VAI, EAI, and SMAI showed the best performance as an earlier indicator in March with a correlation with barley yield of 0.72, 0.67, and 0.64, respectively; the lowest standard deviation was for the SMAI. For wheat yield, the best earlier indicator was the SMAI in March, showing the highest correlation (0.6) and the lowest standard deviation. For the irrigated cereal zone of Kairouan, the strongest correlation (0.9) and the lowest standard deviation are found between the EAI and cereal yield in April. In terms of advanced prediction, the VAI shows a high correlation in March (0.79) while the SMAI shows a slightly lower correlation in February (0.67) and a lower standard deviation. The results highlight the importance of the EAI and SMAI as key indicators for the estimation and early estimation (respectively) of cereal yield.
This study developed a multi-year classification model for winter cereal in a semi-arid region, the Kairouan area (Tunisia). A random forest classification model was constructed using Sentinel 2 (S2) ...vegetation indices for a reference agricultural season, 2020/2021. This model was then applied using S2 and Landsat (7 and 8) data for previous seasons from 2011 to 2022 and validated using field observation data. The reference classification model achieved an overall accuracy (OA) of 89.3%. Using S2 data resulted in higher overall classification accuracy. Cereal classification exhibited excellent precision ranging from 85.8% to 95.1% when utilizing S2 data, while lower accuracy (41% to 91.8%) was obtained when using only Landsat data. A slight confusion between cereals and cereals growing with olive trees was observed. A second objective was to map cereals as early as possible in the agricultural season. An early cereal classification model demonstrated accurate results in February (four months before harvest), with a precision of 95.2% and an OA of 87.7%. When applied to the entire period, February cereal classification exhibited a precision ranging from 85.1% to 94.2% when utilizing S2 data, while lower accuracy (42.6% to 95.4%) was observed in general with Landsat data. This methodology could be adopted in other cereal regions with similar climates to produce very useful information for the planner, leading to a reduction in fieldwork.
A generalization of Dowling lattices was recently introduced by Bibby and Gadish, in a work on orbit configuration spaces. The authors left open the question as to whether these posets are shellable. ...In this paper we prove EL-shellability and use it to determine the homotopy type. Our result generalizes shellability of Dowling lattices and of posets of layers of abelian arrangements defined by root systems. We also show that subposets corresponding to invariant subarrangements are not shellable in general.
Let V be a vector space endowed with a non-degenerate quadratic form Q. If the base field F is different from F2, it is known that every isometry can be written as a product of reflections. In this ...article, we detail the structure of the poset of all minimal length reflection factorizations of an isometry. If F is an ordered field, we also study factorizations into positive reflections, i.e., reflections defined by vectors of positive norm. We characterize such factorizations, under the hypothesis that the squares of F are dense in the positive elements (this includes Archimedean and Euclidean fields). In particular, we show that an isometry is a product of positive reflections if and only if its spinor norm is positive. As a final application, we explicitly describe the poset of all factorizations of isometries of the hyperbolic space.
A theorem proved by Dobrinskaya
9
shows that there is a strong connection between the K(π,1) conjecture for Artin groups and the classifying spaces of Artin monoids. More recently Ozornova obtained ...a different proof of Dobrinskaya's theorem based on the application of discrete Morse theory to the standard CW model of the classifying space of an Artin monoid. In Ozornova's work, there are hints at some deeper connections between the above-mentioned CW model and the Salvetti complex, a CW complex which arises in the combinatorial study of Artin groups. In this work we show that such connections actually exist, and as a consequence, we derive yet another proof of Dobrinskaya's theorem.
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