Spatial Distribution Of Surface Temperature Research Articles

The Effect of Land Cover Change on Urban Heat Island Phenomenon Based on Remote Sensing in Probolinggo City

Probolinggo City is located in East Java Province, Indonesia. Based on BPS data for the City of Probolinggo in 2023, it shows an increase in population growth rate of 1.7% annually. The development of the number and increase in the activity of the population of Probolinggo City certainly affects the increase in the number of built-up areas to meet human needs. An increase in the number of built-up land has led to changes in the environment and urban land use, characterized by declining air quality and global warming due to the increasing phenomenon of Urban Heat Island (UHI). This research was conducted to determine the spatial distribution of surface temperature and the Urban Heat Island (UHI) phenomenon and the effect of land cover on the UHI phenomenon. The research was conducted using UHI analysis using the Landsat 8 OLI remote sensing approach to obtain surface temperature values and high-resolution aerial photographs through data extraction. Based on the data processing results carried out over five years in 2013, 2017, and 2022, it is known that high and very high temperatures dominate the surface temperature of Probolinggo City. In addition, there is an effect of land cover on surface temperature based on the results of a simple linear regression analysis.

Geographic analysis of the distribution of surface temperature, vegetation cover and its relationship with socioeconomic indicators – Cuiabá/MT

In Brazil and around the world, the problems resulting from urban planning, changes in land cover and the increase in urban infrastructure influence temperature change. The aim of this research is to understand the difference in temperature over the last 36 years (1985-2021) in the city of Cuiabá/MT, and its relationship with vegetation and socioeconomic and racial-ethnic factors. Annual images (36 images) from the Landsat 5 and 8 satellites between 1985 and 2021 were used, and Google Earth Engine was used to obtain this data for the urban area of the city of Cuiabá. Mapping of the spatial distribution of surface temperature, vegetation and changes in land use and cover was carried out using data from the MapBiomas project and socio-economic data from the Instituto Brasileiro de Geografia e Estatística (IBGE, Brazilian Institute of Geography and Statistics in English) 2010 census. The results indicated that over the last 36 years Cuiabá's surface temperature has increased by an average of 13°C, as part of the result of the growth of urban infrastructure and loss of vegetation cover, specifically in the peripheral areas. There is an inequality between the high-income population living in neighborhoods with milder temperatures and the low-income population living in neighborhoods with higher temperatures. In the temperature and skin color data, the white population generally lives in neighborhoods with milder temperatures, unlike the black population, which mostly suffers from high temperatures.

Effects of different irrigation methods on regional climate in North China Plain: A modeling study

Agricultural irrigation is important in boosting crop yields in especially water-stressed regions, but little is known about the distinct climatic effects induced by different irrigation methods, particularly in the North China Plain (NCP) where irrigation is applied extensively. Here we examine the climatic effects of flood (FI), sprinkler (SI) and drip irrigation (DI) over NCP during the growing season using dynamic irrigation schemes implemented into a coupled land-atmosphere model. The model generally captures the spatial distribution of surface temperature, relative humidity and precipitation. The changes in regional average surface temperature induced by FI, SI and DI are –0.43, –0.53 and –0.19 °C, respectively. The relatively larger cooling effect for SI than that for FI is associated with enhanced cloud formation. By shifting the surface energy balance, FI and SI cause a wet, cool, cloudy and shallow planetary boundary layer, while DI exhibits the smallest effect and indeed inhibits cloud formation. The increases in convective available potential energy and precipitable water induced by FI and SI enhance convective precipitation over NCP by 0.8–1.2 mm d–1. In contrast, the reduced precipitation due to surface cooling within DI leads to a warmer and drier surface from June to August, which likely increases upper-level geopotential heights and in turn suppresses precipitation in a series of climate feedbacks. The distinct hydrometeorological interactions and feedbacks arising from different irrigation methods are likely related to different irrigation rates, frequencies and approaches of water application. While DI is recognized as the most water-saving method, it also generates the least surface cooling among the three methods and is thus less effective in safeguarding grain yields against rising temperatures. Our study emphasizes the need for more sustainable and adaptive irrigation methods to ensure food security, water conservation and climate stability in the face of climate change.

Monitoring PV Output Power in Tropical Climates Under Surface Temperature Distribution Area

The performance parameters of a solar panel are influenced by many factors, including the type of panel, area, solar radiation, ambient temperature, and weather. This study aims to analyse the effect of solar radiation and temperature on the performance of monocrystalline solar panels. This research was located in Palu, one of the cities with high temperatures in tropical Indonesia. The study used 50 Wp PV, which was placed in the eastern Palu area based on the spatial distribution of surface temperature with the highest temperature distribution. Data sampling is 25 times per day from 11:00 am – 03:00 pm. The result is that increased surface temperature of the solar panel impacts the decrease in the output power of the PV. The environmental temperature of 32.87 °C in the East Palu area causes a decrease of PV power by 2.3%.

Effect of silica fume content in concrete blocks on laser-induced explosive spalling behavior

This experimental study investigated the effect of silica fume mixed in concrete blocks on laser-induced explosion behavior. We used a 5.3 kW fiber laser as a thermal source to induce explosive spalling on a concrete surface blended with and without silica fume. An analytical approach based on the difference in the removal rate and thermal behavior was used to determine the effect of silica fume on laser-induced explosive spalling. A scanner was employed to calculate the laser-scabbled volume of the concrete surface to derive the removal rate. The removal rate of the concrete mixed with silica fume was higher than that of without silica fume. Thermal images acquired during scabbling were used to qualitatively analyze the thermal response of laser-induced explosive spalling on the concrete surface. At the early stage of laser heating, an uneven spatial distribution of surface temperature appeared on the concrete blended with silica fume because of frequent explosive spalling within a small area. By contrast, the spalling frequency was relatively lower in laser-heated concrete without silica fume. Furthermore, we observed that a larger area was removed via a single explosive spalling event owing to its high porosity.

Projections of future temperature-related cardiovascular mortality under climate change, urbanization and population aging in Beijing, China.

Climate change is causing the surface temperature to rise and the extreme weather events to increase in frequency and intensity, which will pose potential threats to the survival and health of residents. Beijing is facing multiple challenges such as coping with climate change, urbanization, and population aging, which puts huge decision-making pressure on decision maker. However, few studies that systematically consider the health effects of climate change, urbanization, and population aging for China. Based on the distributed lag nonlinear model (DLNM) and 13 global climate models in the Coupled Model Intercomparison Project Phase 6 (CMIP6), this study obtained the temporal and spatial distribution of surface temperature through statistical downscaling methods, and comprehensively explored the independent and comprehensive effects of urbanization and population aging on the projection of future temperature-related cardiovascular disease (CVD) mortality in the context of climate and population change. The results showed that only improving urbanization can reduce future temperature-related CVD mortality by 1.7-18.3%, and only intensified aging can increase future temperature-related CVD mortality by 48.8-325.9%. Taking into account the improving urbanization and intensified aging, future temperature-related CVD mortality would increase by 44.1-256.6%, and the increase was slightly lower than that of only intensified aging. Therefore, the intensified aging was the biggest disadvantage in tackling climate change, which would obviously magnify the mortality risks of temperature-related CVD in the future. Although the advancement of urbanization would alleviate the adverse effects of the intensified aging population, the mitigation effects would be limited. Even so, Urbanization should be continued to reduce health risks for residents. These findings would contribute to formulate policies related to mitigate climate change and reduce baseline mortality rate (especially the elderly) in international mega-city - Beijing. In addition, relevant departments should improve the medical health care level and optimize the allocation of social resources to better cope with and adapt to climate change.

Assessing the effect of volcano-tectonic activity on the spatial distribution of surface temperature in the Main Ethiopian Rift, using integrated approach of remote sensing data

ABSTRACT Heat energy continuously flows from the interior of the earth’s layers to the surface, usually associated with rifting and faulting the earth’s crust. So, the spatial distribution of heat energy in the earth’s crust differs laterally and vertically depending on several factors, such as radioactive isotopes in the area’s rock, volcano-tectonic, and hydrological nature. The study was conducted in the Northern segment of the Main Ethiopian Rift. Geological and volcanic structures have been considered to determine the effect of volcano-tectonic activity on the spatial variability of surface temperature. The surface kinetic temperature was retrieved from Landsat 8 imagery using the Emissivity Modulation method, resulting in minimum and maximum values of 21 and 45.9°C. The higher surface temperature anomalies (>45°C) has been found in the region of densely concentrated geological and volcanic structures. Based on this present study’s analysis, the effect of volcano-tectonic activity has been observed on the spatial distribution of surface temperature over the study area. Most of these areas have been found in Dofan to Fantale volcanic fields. Moreover, it is observed along the Main Ethiopian rift axis in which recent volcano-tectonic activity was found.

Seasonal analysis on land surface temperature (LST) and normalized difference vegetation index (NDVI) variations in the Iguatu semi-arid hinterland, ceará

The following paper analyzes the seasonal behavior of surface temperature and vegetation conditions from Landsat 8 satellite images in Iguatu, located in South-central Ceará, Brazil. The guiding method was the Urban Climate System (UCS) along with works with specific literature. Concerning the LSTs during the wet season, the urban area recorded 30.8°C, whereas the countryside verified milder thermal conditions than in downtown, especially in the southwestern region (19.2°C to 23.1°C). The NDVI values in April (wet season) for the urban area and part of the suburbs showed (0.00) because of civil constructions and little vegetation present in the area, except for the surroundings of the Bastiana and Cocobó lagoons – ranging between (0.59 and 0.79), which represents a green area. In August (dry season), there was an expressive spatial distribution of surface temperature around 32 °C. The NDVI was (-0.01) in the densely occupied area and (0.67) in the urban lagoons during the same period. The land use and its plant cover reflect significantly in the distribution and intensity of surface temperatures, as verified in the research.

Measurement Uncertainty of Surface Temperature Distributions for Laser Powder Bed Fusion Processes.

This paper describes advances in measuring the characteristic spatial distribution of surface temperature and emissivity during laser-metal interaction under conditions relevant for laser powder bed fusion (LPBF) additive manufacturing processes. Detailed descriptions of the measurement process, results, and approaches to determining uncertainties are provided. Measurement uncertainties have complex dependencies on multiple process parameters, so the methodology is demonstrated on one set of process parameters and one material. Well-established literature values for high-purity nickel solidification temperature and emissivity at the solidification temperature were used to evaluate the predicted uncertainty of the measurements. The standard temperature measurement uncertainty is found to be approximately 0.9% of the absolute temperature (16 AC), and the standard relative emissivity measurement uncertainty is found to be approximately 8% at the solidification point of high-purity nickel, both of which are satisfactory. This paper also outlines several potential sources of test uncertainties, which may require additional experimental evaluation. The largest of these are the metal vapor and ejecta that are produced as process by-products, which can potentially affect the imaging quality, reflectometry results, and thermal signature of the process, while also affecting the process of laser power delivery. Furthermore, the current paper focuses strictly on the uncertainties of the emissivity and temperature measurement approach and therefore does not detail a variety of uncertainties associated with experimental controls that must be evaluated for future generation of reference data.

Assessing the thermal regime of poorly monitored reservoirs with a combined satellite and three-dimensional modeling approach

ABSTRACT The thermal regime of lakes and reservoirs is a major driver of their functioning, yet water temperature measurements are scarce and time-series are frequently interrupted by missing data in many lakes and reservoirs. Our aim was to assess whether satellite imagery combined with 3-dimensional (3D) modeling can overcome this limitation. We assessed the performance of a 3D model (Delft3D-Flow) and compared simulated temperature to satellite data on Karaoun Reservoir in a semiarid region of Lebanon. Surface water temperatures were retrieved from Landsat 8, atmospherically corrected using a single channel algorithm and adjusted with in situ measurements as a proxy of bulk temperatures. With limited calibration, the model reproduced water level fluctuations, water temperature, stratification, and mixing, with low discrepancies from measurements. Satellite temperatures agreed well with observations and simulations. Satellite temperature distribution across the reservoir exhibited low spatial heterogeneity. The 3D model partly reproduced this spatial distribution of surface temperature and generally was able to simulate the thermal regime of the reservoir with limited datasets for initial conditions and for hydrological and meteorological forcing, and with limited calibration. For validating 3D hydrodynamic models, satellite temperatures constitute a valuable source of data complementary to point measurements. Coupling satellite imagery and modeling can improve operational surveys of poorly monitored lakes and reservoirs and enhance knowledge of their thermal functioning.

Assessing of Land Surface Temperature at the Seulawah Agam Volcano Area using the Landsat Series Imagery

Seulawah Agam, a stratovolcano located in the Aceh province, Indonesia, has not erupted for a long decade after the last eruption in 1839. Thermal infrared remote sensing has been used to determine the land surface temperature (LST) of the volcano area. However, the application of remotely sensed thermal imagery in identifying the LST of the Seulawah Agam volcano, as a precursor of geothermal energy and eruption hazard, has not been completely monitored. The volcano locates relatively close to residential areas, which is a challenging approach to apply thermal bands in determining geothermal identities. In this research, we assess the LST and vegetation index for the detection of the thermal activity of the mountain. These characteristics were retrieved from Landsat 7 ETM+ and Landsat 8 TIRS/OLI imageries, acquired on 23 April 2004 and 16 March 2015 over the Seulawah Agam area, respectively. The normalized difference vegetation index (NDVI) threshold method for emissivity retrieval and split-window algorithm for land surface temperature (LST) were utilized. The results show that the vegetation index changes moderately over the geothermal area, especially at the residential area and western side of the volcano which is in line with a fault structure of the Seulimeum segment. We calculated the LST from the thermal bands of Landsat images 2004 and 2015 with approximate results are 28 – 35 °C. The spatial distribution of surface temperatures at the mountain derived from the classified image 2015 varies considerably compared with the classified image 2004. The surface temperature and vegetation index changes indicate a thermal activity at the Seulawah Agam volcano. It can be concluded that the Landsat 7 ETM+ and Landsat 8 TIRS/OLI imageries are potentially used to study the thermal status of the Seulawah Agam geothermal area.

Critical Heat Flux of Confined Round Single Jet and Jet Array Impingement Boiling

This study involves experimental investigation of key parameters influencing CHF for confined round single jets and jet arrays impinging normally onto square heated surfaces. The experiments are performed using R-134a, a fluid widely used for thermal management of electronic and power devices, especially in aerospace applications. A comprehensive R-134a CHF database is acquired that considers the effects of various geometrical parameters and operating conditions. Close examination of the data trends reveals several strategies to augment CHF, such as increasing jet velocity and/or total mass flow rate and employing larger jet diameters for a fixed velocity or smaller diameters for a fixed flow rate. Higher CHF is also achieved by increasing saturation pressure for a fixed inlet fluid temperature (i.e., higher saturation pressures combined with higher inlet subcooling). Fluid exit qualities point to two different CHF mechanisms: subcooled CHF at high flow rates and saturated CHF at low flow rates. Underlying mechanisms are also propounded for two types of CHF transients: a sudden sharp temperature escalation at lower flow rates and a mild gradual increase at higher flow rates. Close inspection of the heating surface following CHF tests shows localized burnout patterns which provide significant insight into both the flow characteristics within the confinement region and the spatial distribution of surface temperature resulting from jet interactions. Statistical inference techniques are used in conjunction with the new understanding of fluid flow and heat transfer physics to formulate a new correlation form for CHF. The resulting correlation, which is based on a consolidated database of the present R-134a and previous FC-72 data, shows good prediction accuracy, evidenced by a mean absolute error of 16.66% for both fluids and over broad ranges of geometrical parameters and operating conditions.

Spatial Distribution of Surface Temperature and Land Cover: A Study Concerning Sardinia, Italy

Land surface temperature (LST) is a key climate variable that has been studied mainly at the urban scale and in the context of urban heat islands. By analyzing the connection between LST and land cover, this study shows the potential of LST to analyze the relation between urbanization and heating phenomena at the regional level. Land cover data, drawn from Copernicus, and LST, retrieved from Landsat 8 satellite images, are analyzed through a methodology that couples GIS and regression analysis. By looking at the Italian island of Sardinia as a case study, this research shows that urbanization and the spatial dynamics of heating phenomena are closely connected, and that intensively farmed areas behave quite similarly to urban areas, whereas forests are the most effective land covers in mitigating LST, followed by areas covered with Mediterranean shrubs. This leads to key policy recommendations that decision-makers could implement to mitigate LST at the regional scale and that can, in principle, be exported to regions with similar climate and land covers. The significance of this study can be summed up in its novel approach to analyzing the relationship between LST and land covers that uses freely available spatial data and, therefore, can easily be replicated in other regional contexts to derive appropriate policy recommendations.

Análise da temperatura de superfície de vilas e aglomerados de Belo Horizonte através de série temporal de imagens de sensoriamento remoto

In view of the low coverage by official meteorological stations to assess urban climatic phenomena, remote sensing stands out as an interesting resource, which can be used for the detection of heat cores. Thus, the research aimed to study the temporal and spatial distribution of surface temperature in the city of Belo Horizonte, identifying the possible relationship of heat cores with the location of villages and settlements, which occupy 5% of the territory. Images from the Landsat-8 satellite were used between the years 2013 and 2020, from which the surface temperature was calculated for a set of 29 different dates. The results indicated that not necessarily the villages and settlements appear as significant thermal cores, having been more associated with warehouses and structures with extensive metallic coating, which were up to 8.7°C warmer, on average, than the surrounding surfaces. The survey, however, was not enough to answer whether, from the point of view of air temperature, the spaces investigated show different behavior when compared to neighborhoods with an orderly pattern of streets and buildings.

Perubahan Tutupan Lahan dan Pengaruhnya Terhadap Pola Persebaran Suhu di Kota Gorontalo

Gorontalo City is one of the regions in Gorontalo Province. Urban development and population growth, causing pressure on land use patterns. Changes in land use are carried out to meet the community's needs for infrastructure. At present, development in Gorontalo City is still ongoing. The increase in temperature is expected to continue and can trigger heat island. This is very important to be studied for the Gorontalo City development planning that is more environmentally friendly. This study aims to analyze the heat island phenomenon through the relationship of the spatial distribution of surface temperature with various types of land cover and vegetation characteristics. The object of this research is the Gorontalo City area on Landsat path-row 121- 65 satellite imagery media. The research material is the wavelength of visible light, near-infrared and moderate infrared and thermal wavelengths on satellite imagery of Landsat TM and OLI TIRS. The results showed an increase in temperature in Gorontalo City since 1990, 2003, and 2017. The correlation between surface temperature and land cover is negative. The value of the correlation coefficient (r) in 1990 was -0.41. The correlation coefficient (r) in 2003 was -0.448. The correlation coefficient (r) in 2017 is -0.402. Changes in surface temperature in Gorontalo City are influenced by changes in the land cover which is marked by the similarity of patterns of changes in surface temperature distribution with patterns of land cover changes.

Linkage of meteorological parameters and anomalous radio propagation profile over Nigeria

The vertical distribution of refractivity gradient is important in determining anomalous propagation condition. Thirty five years of meteorological parameters, obtained from Era-Interim archive of European Centre for Medium-Range Weather Forecasts has been used to analyze and investigated surface meteorological data linked with refractivity gradient aloft altitude across Nigeria. Spatial distribution of surface temperature, relative humidity and refractivity gradient at 0.1 km, 0.5 km, 1.0 km and 1.5 km over Nigeria were plotted. Vertical distribution of temperature, relative humidity, refractivity and refractivity gradient were obtained for some locations across Nigeria. Similarly, spatial distribution of coefficient of determination between surface temperature, relative humidity and refractivity gradient at four different height were estimated. Linear regression were developed to investigate the relationship between surface data and refractivity gradient at different altitude. The result revealed existence of sub refractive, super refractive, and ducting across the country at 0.1 km and 0.5 km however occurrence of ducting and sub refractive disappeared at 1.0 km and 1.5 km. Likewise, the existence of temperature inversion was noticed between surface and 100 m across all the locations except in Lagos. Values of refractivity across the observed locations converged around 0.5 km. Through result of correlation coefficient and statistical parameters, significant linked have been established between surface data and refractivity gradient at different height.

DERIVATION OF LAND SURFACE TEMPERATURE (LST) FROM LANDSAT 7 & 8 IMAGERIES AND ITS RELATIONSHIP WITH TWO VEGETATION INDICES (NDVI AND GNDVI)

Land surface temperature (LST) fluctuation is a global problem that is responsible for regional and global climate change. Abnormal LST causes drought, depletion of ozone layers, skin and lung diseases and also affect crops production. Spatial distribution of surface temperature has become an issue especially to less developed countries with little or absent of temperature stations to report daily or monthly temperature of the area. This study utilized remote sensing approach to estimate land surface temperature, NDVI and GNDVI of Port Harcourt, Rivers State, Nigeria. The study was conducted using Landsat imageries of two epochs (1990 and 2017) which was downloaded using path 188 and row 57. The images were converted from DN to TOA radiance using algorithm specified in the Landsat user’s guide. The highest estimated LST in 1990 and 2017 map was 28.77°C and 29.37°C. Also, in 1990 the highest LST was recorded in Diobu and part of Old Port Harcourt Township while in 2017 maximum temperature extended from Diobu to Trans-amadi. The increase LST was due to urbanization and industrialization in the city. The study observed mean difference between estimated LST of 1990 and 2017 and that observed by NIMET as 1.24°C and 2.91°C respectively. There was positive correlation coefficient of 0.09 and 0.4 between LST against NDVI in 1990 and in 2017 and between LST against GNDVI of 0.19 and 0.30 was also observed in both years. This study justified that remote sensing and GIS can be used to derive LST which can be used for environmental studies and research purposes. For further study, LST should be estimated in all the state and their values validate with in-situ observations.

Characterization of thermal environment over heterogeneous surface of National Capital Region (NCR), India using LANDSAT-8 sensor for regional planning studies

Land surface temperature (LST) is an essential indicator of the Earth's surface energy budget. It is essential for urban micro-climate change studies and acts as a controlling variable in climatic models. The present study, LST retrieves with the improved mono-window algorithm from the Landsat-8 Thermal Infrared Sensor Band 10. The proportion of vegetation cover coupled with Normalized Difference Vegetation Index (NDVI) used for the estimation of emissivity. The derived emissivity and surface temperature over different ground features have compared with field observation as well as those in the literature and found in an accepted range (error of around 1–2%). Herein, results show that the spatial distribution of surface temperature was significantly affected by landscape characteristics. The built-up and commercial/industrial areas display higher surface temperature in comparison with surrounding other vegetated lands. Whereas, the cooling effect towards the surrounding urban built-up area are found increasing in the vegetated area, and inside the green zones. A strong correlation is observed between the LST with NDVI over different land cover and land use (LCLU) classes. The Geoinformation technique provides a practical-based theoretical model of the land characterization of an urban thermal environment which assists in regional planning and decision-making process.

Evaluation of Urbanization Dynamics and its Impacts on Surface Heat Islands: A Case Study of Beijing, China

As the capital of China, Beijing has experienced a continued and rapid urbanization process in the past few decades. One of the key environmental impacts of rapid urbanization is the effect of urban heat island (UHI). The objective of this study was to estimate the urbanization indexes of Beijing from 1992 to 2013 based on the stable nighttime light (NTL) data derived from the Defense Meteorological Satellite Program’s Operational Line Scanner System (DMSP/OLS), which has became a widely used remote sensing database after decades of development. The annual average value nighttime light Digital Number (NTL-DN), and the total lit number and urban area proportion within Beijing’s boundary were calculated and compared with social-economic statistics parameters to estimate the correlation between them. Four Landsat thematic mapper (TM) images acquired in 1995 and 2009 were applied to estimate the normalized difference vegetation index (NDVI) and normalized land surface temperature (LSTnor), and spatial correlation analysis was then carried out to investigate the relationship between the urbanization level and NDVI and LSTnor. Our results showed a strong negative linear relationship between the NTL-DN value and NDVI; however, in contrast, a strong positive linear relationship between existed between the NTL-DN value and LSTnor. By conducting a spatial comparison analysis of 1995 and 2009, the vegetation coverage change and surface temperature difference were calculated and compared with the NTL-DN difference. Our result revealed that the regions of fast urbanization resulted in a decrease of NDVI and increase of LSTnor. In addition, choropleth maps showing the spatial pattern of urban heat island zones were produced based on different temperatures, and the analysis result indicated that the spatial distribution of surface temperature was closely related with the NTL-DN and NDVI. These findings are helpful for understanding the urbanization process as well as urban ecology, which both have significant implications for urban planning and minimize the potential environmental impacts of urbanization in Beijing.

Temperature distribution and heat radiation of patterned surfaces at short wavelengths.

We analyze the equilibrium spatial distribution of surface temperatures of patterned surfaces. The surface is exposed to a constant external heat flux and has a fixed internal temperature that is coupled to the outside heat fluxes by finite heat conductivity across the surface. It is assumed that the temperatures are sufficiently high so that the thermal wavelength (a few microns at room temperature) is short compared to all geometric length scales of the surface patterns. Hence the radiosity method can be employed. A recursive multiple scattering method is developed that enables rapid convergence to equilibrium temperatures. While the temperature distributions show distinct dependence on the detailed surface shapes (cuboids and cylinder are studied), we demonstrate robust universal relations between the mean and the standard deviation of the temperature distributions and quantities that characterize overall geometric features of the surface shape.