I am a research hydrologist with a special interest in hydroclimatology, watershed hydrology, mountain hydrology, hydrologic engineering and arid zones.
EDUCATION
PhD in Hydrology, Université Paul Sabatier, Toulouse - France
RESEARCH, TEACHING, or OTHER INTERESTS
Water Science and Technology, Earth-Surface Processes, Environmental Engineering, Earth and Planetary Sciences
35
Scopus Publications
1123
Scholar Citations
18
Scholar h-index
19
Scholar i10-index
Scopus Publications
Estimation of Flood Thresholds for Hydrological Warning Purposes Using Sentinel-1 SAR Imagery-Based Modeling in the Tumbes River Basin (PERU) Juan Carlos Breña Aliaga, James Vidal, Oscar Felipe, Luc Bourrel, Pedro Rau, et al. Remote Sensing, 2026 Flood monitoring in dry tropical basins, such as the Tumbes River (Peru), faces critical challenges due to persistent cloud cover that restricts the operability of optical sensors during extreme events, coupled with the operational gap between satellite products and conventional hydrological monitoring. To overcome these limitations, this research developed a comprehensive methodological framework in Google Earth Engine that unifies automated image thresholding and Sentinel-1 SAR time series analysis for flood detection and the estimation of early warning thresholds. The Bmax Otsu and Edge Otsu algorithms were evaluated, previously calibrated using high-resolution imagery (PlanetScope) as reference data, topographically constrained by the HAND (Height Above the Nearest Drainage) model, and validated against established change detection algorithms. The analysis of seven hydrological events between 2017 and 2024 confirmed the statistical superiority of Bmax Otsu; although both methods achieved high overall accuracy (Bmax 95.8% versus Edge 95.7%), Bmax Otsu outperformed Edge Otsu in spatial consistency (Kappa 66.1% vs. 63.7%; IoU 45.6% vs. 45.0%). Based on this, a time series analysis was applied to discriminate permanent water bodies and isolate flood dynamics. Subsequently, the functional discharge–impact response was evaluated by linking the instantaneous flood extent captured by the SAR overpasses to their corresponding peak discharges. Validated against official INDECI damage reports, it was determined that significant impacts begin at an activation threshold of 743.49 m3/s (151 flooded ha, 157 affected inhabitants) and scale linearly up to extreme peak events of 1629.02 m3/s, compromising 1234 agricultural ha and 749 inhabitants. This methodology provides a validated, low-cost tool to translate SAR observations into critical thresholds for early warning systems in data-scarce regions.
Hydrological Partitioning and Subsurface Water Storage in Puna Andean Grasslands Revealed by a Paired Catchment Approach Juan Diego Bardales‐Zegarra, Pedro Rau, Katy Medina Marcos, Edwin Loarte Cadenas, Junior Gil Ríos, et al. Hydrological Processes, 2026 Mountain headwaters in the tropical Andes are vital for regional water security, yet the extensive Puna grassland biome remains largely understudied. To help address this gap, we employed a paired‐catchment design in two Peruvian Puna catchments and used high‐resolution hydrometric data, over the period [2012–2014] at hourly time‐step, to investigate controls on hydrological partitioning and subsurface storage. Our findings provide a field‐based perspective on the classic ‘sponge versus pipe’ paradox by showing that peat‐forming wetlands (bofedales) perform a dual hydrological role. Their saturated surfaces act as efficient ‘pipes’ that enhance event runoff, while their porous subsurface provides event‐scale buffering that dampens hydrograph recessions, defining them as seasonal buffers rather than long‐term dry‐season stores. Streamflow recession analysis further supports a dual‐reservoir conceptualization, in which infiltrated water is partitioned between a shallow system connected to local streamflow and a deeper system linked to regional groundwater recharge. The catchment with greater apparent percolation capacity produced lower annual water yield, consistent with a ‘leaky’ catchment interpretation involving inter‐catchment groundwater flow that bypasses the topographic outlet. Our comparison also suggests that the naturally flashier response of this catchment may be further accentuated by more intensive grazing, although this land‐use signal should be interpreted as secondary to hydrogeomorphic controls. Overall, the results indicate that hydrological functioning is organized hierarchically: subsurface and surficial hydrogeomorphic setting controls the distribution of bofedales and flow paths, while land use modulates the resulting response. This perspective reframes Puna headwater catchments as three‐dimensional systems characterized by a trade‐off between local streamflow resilience and regional aquifer recharge, underscoring the need to preserve bofedal connectivity and mitigate soil‐degrading land uses.
Assessing Shrub and Grassland Degradation Portfolios as Benchmarks for Potential Water Quantity Benefits: Application of the RIOS and SWAT Model to Rimac Basin, Peru Alfredo Salinas-Castro, Alberto Santillán-Fernández, Pedro Rau, Luc Bourrel Land, 2026 The Rimac River Basin supplies drinking water to more than ten million people in Lima, Peru, yet its hydrological regulation capacity is increasingly constrained by land degradation, with over 35% of the basin lacking vegetation cover. Nature-based solutions implemented through conservation and restoration of natural ecosystem offer a potential complement to grey infrastructure, although their basin-scale hydrological benefits remain scantily quantified. This study proposes an inverse assessment framework that uses future degraded states as hydrological benchmarks to quantify redistributed water as a proxy for the volumetric benefits that conservation or restoration could potentially provide. Degraded Andean shrubland and grasslands were identified and prioritized using the RIOS investment assessment tool, resulting in three degradation portfolios (2826; 6566; and 10,720 ha) for the 2011–2016 period. Their hydrological responses were then simulated using the SWAT model, with a focus on dry-season dynamics. The model achieved a Kling Gupta Efficiency of 46.9% and a seasonally targeted Nash–Sutcliffe efficiency of 70% during the dry season, ensuring that despite the basin anthropization, the low flow dynamics key for water security are reliably represented. Water availability indicators and flow-duration curve metrics were applied to evaluate changes in hydrological regulation. Results show that all portfolios increased dry-season streamflow relative to baseline conditions, with the largest portfolio producing a 2.39% increase, equivalent to approximately 4 hm3 during the critical June–August period. These findings indicate that degradation alters flow redistribution within the basin water cycle and suggest that conservation or restoration may reverse these effects. The intermediate and large portfolios provided the most informative benchmarks, supporting spatially explicit decision making for basin-scale water regulation.
Understanding the Impacts of Climate Change and Landcover/Land Use Transformations on Highlands Hydrological Ecosystem Services in the Piuray–Ccorimarca Watershed (Andean Cordillera of Peru) Cristian Montesinos, Danny Saavedra, Luc Bourrel, Pedro Rau, Renny Daniel Diaz, et al. Climate, 2026 Watersheds provide fundamental hydrological ecosystem services for human well-being and the environment, such as water provisioning, hydrological cycle regulation, and erosion control; however, these services face increasing anthropogenic and climatic pressures. This study assessed individual and combined impacts on the hydrological functionality of the Piuray–Ccorimarca watershed (Cusco, Peru) using a calibrated Soil and Water Assessment Tool (SWAT) model, analyzing water yield, soil water storage, and sediment transport across 20 scenarios. An ensemble of 10 Coupled Model Intercomparison Project Phase 6 (CMIP6) models with bias correction was implemented, integrated with land transformation projections contemplating urban expansion associated with airport development and forest recovery through Payment for Ecosystem Services mechanisms. The results reveal climate change as the dominant driver, generating water yield increases and soil water content improvements primarily due to evapotranspiration decoupling that increases the runoff coefficient. In contrast, land use change produces substantially smaller hydrological effects but critically intensifies sediment yield. Spatial vulnerability analysis identified eight persistently critical sub-basins (20.5% of area) where soil water content emerged as the dominant limiting factor. These findings establish a clear management hierarchy prioritizing climate adaptation over land use interventions, with differentiated strategies required for critical zones demanding structural interventions versus non-critical areas amenable to flexible conservation approaches.
Validating daily precipitation products estimated by remote sensing with rainfall stations in the Vilcanota basin, Peru Eber Risco, Waldo Lavado, Pedro Rau, Thomas Condom, and Tecnologia Y Ciencias Del Agua, 2025 La precipitación representa uno de los elementos más importantes dentro del ciclo del agua para la representación de la oferta hídrica en cuencas hidrográficas. Debido a una inadecuada distribución de estaciones, seguridad, relieve, accesibilidad, etcétera, existe escasez de estos datos en cuencas andinas del Perú. Esto representa uno de los principales inconvenientes que afrontan los investigadores en ciencias de la tierra y ciencia del clima para la representación de manera espacial y temporal de la precipitación. En los últimos años, el avance de las tecnologías permite la estimación de las variables hidrológicas a partir de técnicas de sensoramiento remoto. Estos datos deben ser evaluados con observaciones meteorológicas. En esta investigación se evaluaron 11 productos de precipitación estimada por sensoramiento remoto (PPEDsr) que estiman la precipitación. La evaluación de los PPEDsr se realizó para el periodo 1981-2018 a paso de tiempo: diario, de diez días y mensual. Se utilizaron los estadísticos descriptivos: error medio (ME), correlación de Pearson (R), raíz del error medio cuadrático (RMSE), error absoluto medio (MAE) y BIAS relativo (BIAS). Además, de los estadísticos categóricos: probabilidad de detección (POD), tasa de falsas alarmas (FAR), índice de éxito crítico (CSI). Los productos MSWEP, CHIRPS, TRMM-3B42 y PERSIANN-CDR resultaron ser más eficientes para representar la variabilidad espacial de las precipitaciones diarias y acumuladas en la cuenca del Vilcanota. Los datos de sensoramiento remoto mostraron ser útiles para representar la variabilidad espacio-temporal de la precipitación la cuenca Vilcanota, los resultados sugieren que los datos de sensoramiento remoto podrían ser utilizados para simular el balance hidrológico en cuencas hidrográficas de montaña andinas con escasa información in-situ.
Empirical rainfall thresholds for mudflow events in an arid basin of the Peruvian coast Andres Goyburo, Leonardo Gutierrez, Pedro Rau, Waldo Lavado-Casimiro Frontiers in Water, 2025 Mudflows, a highly destructive natural phenomenon, frequently occurs in arid regions due to the activation of basins by extreme climate events. In Peru, the Pacific coastal basin and steep regions is particularly vulnerable to these events, which have caused significant damage and loss of life in recent years. This study aims to establish hourly rainfall thresholds for the initiation of mudflows events in Punta Hermosa, a region prone to these hazards. Acknowledging the shortcomings due to lack of observed precipitation data, this study utilizes gridded rainfall data to simulate mudflows events at an hourly scale. This methodology enables a more thorough investigation of rainfall patterns and their relationship with the occurrence of mudflows. Results indicates that the total rainfall during an event significantly influences the initiation of mudflows, with thresholds exceeding 10 mm consistently triggering these events. Furthermore, rainfall events lasting at least 5 h with an intensity of 1.13 mm/h or greater pose a substantial risk. The study emphasizes the significance of rainfall intensity, demonstrating that intensities surpassing 1.25 mm/h consistently result in mudflows. These findings offer valuable insights for developing reliable early warning systems and implementing effective mitigation strategies to safeguard vulnerable communities and infrastructure in Punta Hermosa and the applicability of this methodology for any other location in the Peruvian coast.
Dynamics and patterns of land cover change in the Piura River Basin (Peruvian Pacific slope and coast) in the last two decades Fiorela Castillón, Pedro Rau, Luc Bourrel, Frédéric Frappart Frontiers in Remote Sensing, 2025 Land use and land cover (LULC) changes in the Piura River Basin, Peru, were analyzed from 2001 to 2022 using global MODIS and ESA-CCI datasets harmonized into six major land cover classes (Forest, Non-Forest Vegetation, Cropland, Bare Soil, Water and Urban) for comparative analysis. Pearson correlation analyses with hydroclimatic variables, including precipitation (PP), maximum (Tx) and minimum (Tn) temperatures, and El Niño Southern Oscillation (ENSO) indices (Eastern Pacific, Central Pacific, and Coastal El Niño), complemented the intensity analysis to explore environmental drivers. The analyses focused on the lower-middle and upper basin regions during wet (December-May) and dry (June-November) seasons. MODIS detected more dynamic LULC transitions, with 32.8% of pixels showing changes, compared to 6.8% detected by the ESA-CCI product. These differences reflect the distinct sensitivities of MODIS and ESA-CCI products to short-term fluctuations and long-term variations, respectively. Specifically, MODIS identified higher annual change intensities and more frequent transitions, especially in the upper basin, whereas ESA-CCI provided a more conservative view of land cover trends. Both datasets consistently indicated a decline in cropland areas and an increase in bare soil, suggesting agricultural degradation and potential desertification processes. Correlation analyses revealed significant relationships between vegetation dynamics and climatic variables, notably ENSO events, precipitation, and temperature extremes, highlighting how hydroclimatic factors drive vegetation variability. The upper basin experienced notable urban expansion and deforestation dynamics linked to temperature fluctuations and intensified El Niño events, particularly after 2011. These findings underscore the critical influence of climatic extremes and human activities on vegetation dynamics, emphasizing the need for integrated, adaptive management strategies to mitigate desertification in lowlands and enhance forest conservation in highlands.
Scientific evidence of the hydrological impacts of nature-based solutions at the catchment scale Morgane Lalonde, Fabian Drenkhan, Pedro Rau, Jan R. Baiker, Wouter Buytaert Wiley Interdisciplinary Reviews Water, 2024 The introduction of nature‐based solutions (NbS) in catchments has the potential to increase the cost‐effectiveness, flexibility, and reliability of water management practices aimed at improving water security. However, the scientific‐evidence base of the hydrological impacts of NbS is still weak, and there is therefore a risk that catchment interventions might not lead to the desired hydrological outcomes. This is especially important when assessing NbS‐based catchment interventions before their implementation, as this requires robust simulation tools capable of effectively managing the uncertainties associated with future forecasts. This study aims to review the hydrological impacts of different NbS intervention types for water management. First, we present an NbS typology and the corresponding dominant hydrological impacts. We then use this typology to review the strength of the current evidence of the effect of NbS interventions on the hydrological response at the catchment‐scale. Our results demonstrate that the effectiveness of each NbS type hinges on specific conditions such as location, design, and environmental factors. For instance, micro‐reservoirs notably enhance surface storage and evaporation, while infiltration trenches reduce runoff but can increase soil erosion. Our global analysis highlights the need for an improved understanding of NbS catchment impacts and careful planning of NbS interventions as a key for successful long‐term implementation of NbS. These include participatory approaches with stakeholder involvement in NbS co‐design, knowledge co‐production, and novel data collection to support locally relevant adaptation strategies, and to increase water security on the long term.This article is categorized under: Science of Water > Hydrological Processes Engineering Water > Planning Water Water and Life > Conservation, Management, and Awareness
Estimation of Flood Thresholds for Hydrological Warning Purposes Using Sentinel-1 SAR Imagery-Based Modeling in the Tumbes River Basin (PERU) JC Breña Aliaga, J Vidal, O Felipe, L Bourrel, P Rau, W Lavado-Casimiro Remote Sensing 18 (10), 1493 , 2026 2026
Hydrological Partitioning and Subsurface Water Storage in Puna Andean Grasslands Revealed by a Paired Catchment Approach JD Bardales‐Zegarra, P Rau, KM Marcos, EL Cadenas, JG Ríos, ... Hydrological Processes 40 (5), e70566 , 2026 2026
Assessing Shrub and Grassland Degradation Portfolios as Benchmarks for Potential Water Quantity Benefits: Application of the RIOS and SWAT Model to Rimac Basin, Peru A Salinas-Castro, A Santillán-Fernández, P Rau, L Bourrel Land 15 (4), 638 , 2026 2026 Citations: 1
Socio-hydrological dynamics under drought-flood extremes in a Peruvian Amazonian community A Matano, M Mazzoleni, MH Barendrecht, HD Mendoza, A van Loon, ... EGU26 , 2026 2026
Understanding the Impacts of Climate Change and Landcover/Land Use Transformations on Highlands Hydrological Ecosystem Services in the Piuray–Ccorimarca Watershed (Andean … C Montesinos, D Saavedra, L Bourrel, P Rau, RD Diaz, ... Climate 14 (2), 49 , 2026 2026
Monitoring with remote sensing and low-cost sensors: Surface water variability and ecohydrological dynamics of Yuracmayo reservoir K Visitación, Y Estrada, M Cordova, AC Pires, MP Bonnet, V Sollier, ... IGARSS 2025-2025 IEEE International Geoscience and Remote Sensing Symposium … , 2025 2025 Citations: 1
A Paired-Catchment Approach for Characterizing Hydrological Functioning in Data-Limited Headwaters of the Peruvian Andean Puna JD Bardales, P Rau, KM Marcos, EL Cadenas, JG Ríos, T Condom, ... Authorea 2025 (0612) , 2025 2025 Citations: 1
Dynamics and patterns of land cover change in the Piura River Basin (Peruvian Pacific slope and coast) in the last two decades F Castillón, P Rau, L Bourrel, F Frappart Frontiers in Remote Sensing 6, 1529044 , 2025 2025 Citations: 6
Validating daily precipitation products estimated by remote sensing with rainfall stations in the Vilcanota basin, Peru E Risco, W Lavado, P Rau, T Condom TECNOLOGIA Y CIENCIAS DEL AGUA 16 (3) , 2025 2025
Tecnología y ciencias del agua E Risco, W Lavado, P Rau, T Condom Tecnología y ciencias del agua 16 (3), 176-229 , 2025 2025 Citations: 1
Empirical rainfall thresholds for mudflow events in an arid basin of the Peruvian coast A Goyburo Peña, L Gutierrez, P Rau, W Lavado-Casimiro Frontiers in Water 7, 1637115 , 2025 2025
El Niño y su influencia sobre la distribución de las precipitaciones en el Ecuador M Ilbay-Yupa, W Lavado-Casimiro, P Rau, R Zubieta, F Castillón Instituto Geofísico del Perú , 2025 2025
Scientific evidence of the hydrological impacts of nature‐based solutions at the catchment scale M Lalonde, F Drenkhan, P Rau, JR Baiker, W Buytaert Wiley Interdisciplinary Reviews: Water 11 (5), e1744 , 2024 2024 Citations: 38
Long-term monitoring of the titicaca lake water storage variations: From nadir altimetry to swot F Frappart, C Normandin, L Bourrel, K Visitacion, P Rau, W Lavado, ... IGARSS 2024-2024 IEEE International Geoscience and Remote Sensing Symposium … , 2024 2024 Citations: 2
Development of a spatial projection map of glacial retreat based on vulnerability maps in the Central Cordillera, Peru A Arias, N Núñez, P Rau, P Venail Journal of Water and Climate Change 15 (6), 2863-2884 , 2024 2024 Citations: 2
Watershed scale soil moisture estimation model using machine learning and remote sensing in a data-scarce context H Loayza, P Rau, N Montoya, C Baca García, M Bueno Scientia Agropecuaria , 2024 2024 Citations: 4
Evaluación de la respuesta hidrológica al cambio de la cobertura terrestre en una cuenca amazónica peruana impactada por la deforestación mediante el modelo SWAT KP Paiva Lopez, C Montesinos, W Lavado-Casimiro, L Bourrel, F Frappart MDPI , 2024 2024
Identifying runoff generation areas for flood control in an ephemeral basin. P Zuloeta, P Rau, A Goyburo 2024
R en el río: Procesando datos de geociencias en el terreno P Rau Conferencia Latinoamericana sobre Uso de R en Investigación+ Desarrollo , 2024 2024 Citations: 1
Evaluation of the impact of urban expansion and hyper concentrated flow generation in a dry creek A Escobar, N Castro, P Rau 22nd LACCEI International Multi-Conference for Engineering, Education and … , 2024 2024
MOST CITED SCHOLAR PUBLICATIONS
Correction of TRMM 3B43 monthly precipitation data over the mountainous areas of Peru during the period 1998–2007 T Condom, P Rau, JC Espinoza Hydrological Processes 25 (12), 1924-1933 , 2011 2011 Citations: 192
Regionalization of rainfall over the Peruvian Pacific slope and coast P Rau, L Bourrel, D Labat, P Melo, B Dewitte, F Frappart, W Lavado, ... International Journal of Climatology 37 (1), 143-158 , 2017 2017 Citations: 161
Updating regionalization of precipitation in Ecuador M Ilbay-Yupa, W Lavado-Casimiro, P Rau, R Zubieta, F Castillon Theoretical and Applied Climatology , 2021 2021 Citations: 81
Rainfall along the coast of Peru during strong El Niño events J Sanabria, L Bourrel, B Dewitte, F Frappart, P Rau, O Solis, D Labat International Journal of Climatology , 2017 2017 Citations: 78
Low‐frequency modulation and trend of the relationship between ENSO and precipitation along the northern to centre Peruvian Pacific coast L Bourrel, P Rau, B Dewitte, D Labat, W Lavado, A Coutaud, A Vera, ... Hydrological processes 29 (6), 1252-1266 , 2015 2015 Citations: 64
PISCO_HyM_GR2M: A model of monthly water balance in Peru (1981–2020) H Llauca, W Lavado-Casimiro, C Montesinos, W Santini, P Rau Water 13 (8), 1048 , 2021 2021 Citations: 55
Assessing near real-time satellite precipitation products for flood simulations at sub-daily scales in a sparsely gauged watershed in Peruvian andes H Llauca, W Lavado-Casimiro, K León, J Jimenez, K Traverso, P Rau Remote Sensing 13 (4), 826 , 2021 2021 Citations: 55
Assessing multi‐decadal runoff (1970–2010) using regional hydrological modelling under data and water scarcity conditions in Peruvian Pacific catchments P Rau, L Bourrel, D Labat, D Ruelland, F Frappart, W Lavado, B Dewitte, ... Hydrological Processes , 2019 2019 Citations: 55
Comparison of three daily rainfall-runoff hydrological models using four evapotranspiration models in four small forested watersheds with different land cover in South-Central … N Flores, R Rodríguez, S Yépez, V Osores, P Rau, D Rivera, F Balocchi Water 13 (22), 3191 , 2021 2021 Citations: 50
Scientific evidence of the hydrological impacts of nature‐based solutions at the catchment scale M Lalonde, F Drenkhan, P Rau, JR Baiker, W Buytaert Wiley Interdisciplinary Reviews: Water 11 (5), e1744 , 2024 2024 Citations: 38
Hydroclimatic change disparity of Peruvian Pacific drainage catchments P Rau, L Bourrel, D Labat, F Frappart, D Ruelland, W Lavado, B Dewitte, ... Theoretical and applied climatology 134 (1), 139-153 , 2018 2018 Citations: 38
Assessment of present and future water security under anthropogenic and climate changes using WEAP model in the Vilcanota-Urubamba catchment, Cusco, Perú A Goyburo, P Rau, W Lavado-Casimiro, W Buytaert, J Cuadros-Adriazola, ... Water 15 (7), 1439 , 2023 2023 Citations: 35
High-resolution grids of daily air temperature for Peru-the new PISCOt v1. 2 dataset A Huerta, C Aybar, N Imfeld, K Correa, O Felipe-Obando, P Rau, ... Scientific data 10 (1), 847 , 2023 2023 Citations: 30
Can artificial neural networks estimate potential evapotranspiration in Peruvian highlands? W Laqui, R Zubieta, P Rau, A Mejía, W Lavado, E Ingol Modeling Earth Systems and Environment 5 (4), 1911-1924 , 2019 2019 Citations: 25
Validation of TRMM daily precipitation data for extreme events analysis. The case of Piura watershed in Peru J Cabrera, RT Yupanqui, P Rau Procedia Engineering 154, 154-157 , 2016 2016 Citations: 25
Hydrological response assessment of land cover change in a Peruvian Amazonian Basin impacted by deforestation using the SWAT model K Paiva, P Rau, C Montesinos, W Lavado-Casimiro, L Bourrel, F Frappart Remote Sensing 15 (24), 5774 , 2023 2023 Citations: 22
La distribución de las lluvias en la vertiente del Pacífico peruano y su relación con El Niño P Rau, L Bourrel, B Dewitte, D Labat Instituto Geofísico del Perú , 2017 2017 Citations: 19
Análisis espacio temporal de la precipitación en las zonas de montaña de Perú (1998-2007) P Rau, T Condom Revista Peruana Geo-Atmosferica 2 (1), 16-29 , 2010 2010 Citations: 19
Temporal variability and annual budget of inorganic dissolved matter in Andean Pacific Rivers located along a climate gradient from northern Ecuador to southern Peru JS Moquet, JL Guyot, S Morera, A Crave, P Rau, P Vauchel, C Lagane, ... Comptes Rendus Geoscience 350 (1-2), 76-87 , 2018 2018 Citations: 14
Assessment of bottom-up satellite precipitation products on river streamflow estimations in the Peruvian Pacific drainage J Qquenta, P Rau, L Bourrel, F Frappart, W Lavado-Casimiro Remote Sensing 16 (1), 11 , 2024 2024 Citations: 7