Augmenting the spatial resolution of climate-change temperature projections for city planners and local decision makers

Before the 2010, studies in climate change (CC) projections embracing scales below 3° were difficult to find. This has changed dramatically over the past ten years, with literature addressing high resolution grids for climate studies, allowing a better understanding and forecasting of CC at finer scales. However, downscaling methods remain poorly explored in urban planning. Research shows that the main difficulties relate to mismatches between data needs and data availability, terminology, constraints of information technology and maps that inform spatial planning decision-making processes. Based on dynamic downscaled maps for RCP 4.5 and RCP 8.5 at 10 km resolution published by Ecuador’s Ministry of Environment and Water (MAAE), we develop a method for augmenting the resolution scale at 30 m. We use digital elevation models and Landsat 4/5/7/8 satellite imagery for land surface temperature (LST) and present a series of steps and equations before applying Stefan Bolzman’s law. We present the necessary equations between the filling-in of LST outliers, and their projection onto air temperature at 2 m height, taking surface emissivity estimates based on (Alves et al 2017 J. Hyperspectral Remote Sens. 7 91–100). We extrapolate the resulting air temperature in time with Fourier’s series, and for the purpose of coherence among scales, we upscale air temperature maps at 30 m to those at 10 km resolution. The resulting CC projection maps are validated with the temporal series of air temperature (max, min, mean) from the meteorological station in the Ecuadorian city of Portoviejo (Student’s t-test) for the period between 1981 and 2005, with Portoviejo city facing temperature increases of up to 2 °C under RCP 4.5 scenario in the period 2011–2040 vs 1981–2005. The final CC maps have an augmented resolution of 30 m, are compatible with those of MAAE, and offer a low-cost procedure for informing land-use and urban planners, as well as local development decision makers, of temperature anomalies due to climate change.


Introduction
With the forecast of 6.3 billion persons living in urban areas by 2050, it is expected that problems associated with the use of natural resources and the negative externalities of anthropogenic activity will become increasingly relevant. From the point of view of climate studies, this context highlights the need for downscaling methods and procedures in order to accurately assess and depict scenarios for climate change (CC) at urban/local scales of 12.5-50 km and below [1]. However, downscaling methods remain poorly explored in urban planning because urban planners and climatologists do not usually work together to tackle the effects of CC at small scales. The main difficulties relate to mismatches between data needs and data availability, terminology (which is not unified), constraints of information technology [1] and maps that inform spatial planning decisionmaking processes.
The advancement of computational resources and the combination of diversified strategies of dynamical and statistical downscaling (DDS and SDS) have boosted the field of CC studies, particularly since the beginning of the 2010s. At the same time, the development of the Global Climate Models, under the scope of the IPPC standards, combined with the creation of regional models, applied to several objectives (such as assessing the effects of temperature and precipitation variability on land use) has encouraged the emergence of specific models applied to increasingly higher resolution scales.
In Latin America, and especially Ecuador, several institutional frameworks have been developed which seek to incorporate CC criteria into public management at various sectors and scales.
In the case of Ecuador, the National Climate Change Strategy recognizes the importance of including the different sectors and administrative units, from the central government down to the municipalities or 'Decentralized Autonomous Governments' (GADs). As a result of the UN-Habitat III Conference in 2016, the bilateral cooperation agreement between the governments of Germany and Ecuador, and within the frameworks of its program 'Intermediate Sustainable Cities' (CIS), the Ministry of Urban Development and Housing in Ecuador and its counterpart, the German Technical Cooperation (GIZ), have collaborated with other ministries such as the Ministry of Environment and Water (MAAE). Their aim is to improve the enabling conditions for sustainable urban development, within the framework of the New Urban Agenda (NUA), the Sustainable Development Goals and the Paris Agreement. Initiatives for incorporating CC into the local development narrative have so far been addressed mostly in CIS's city-partners (Ambato, Cuenca, Lago Agrio, Latacunga, Loja and Portoviejo). However, land-use planning at several administrative scales, particularly when considering the Paris Agreement and the NUA, still require low-cost methods and procedures that accurately assess and depict scenarios for CC at urban/local scales. Additionally, if CC projections are to be incorporated into the spatial planning processes and be used by the spatial planning departments at municipal level, municipal departments and technicians require spatial representations of CC and of the relationships between the land-use planning elements.
Before 2010, studies embracing scales below 3 • of latitude were difficult to find. This has dramatically changed over the past ten years, with literature addressing high resolution grids for climate studies, allowing a better understanding and forecasting of CC at finer scales. Nevertheless, further advances in this field are constrained by procedures related to big data, data mining, stochastic processes, and the problem of reliability. Despite these challenges, the models developed so far have paved the way for new combinations of approaches and techniques associated with specific problems of urban and rural settlements. In the urban areas, especially, where more than 60% of the global population lives, CC will pose increasing and escalating challenges that will affect safety, health and mobility aspects of the human routine. For this reason, CC studies at local scales are becoming pivotal, with a focus on land-use and land-change planning. In this context, SDS and DDS (SDS and DDS) methods, based on robust sets of data, and the evolution of analytical resources with satellite imagery, may help planners and managers to better deal with CC at small scales.
For the purpose of narrowing our focus to the CC and land-use planning nexus, we first carried out a review of the literature examining which downscaling methods/models/tools are available, and how these have been used for spatial and land-use planning purposes. Our search strategy involved academic data bases (Science Direct, Emerald, Google Scholar and Taylor & Francis) and included the expressions 'downscale method' AND 'climate change' AND 'land use' AND 'planning' . Our selection of articles excluded those that were duplicated or incomplete, research posters, studies larger than six degrees of latitude, and those which had not undergone a peer review process. Based on these results (N:468 papers) we screened and reviewed 33 articles that addressed scales (a) from 99 km to 5 km; and (b) below 5 km (see table 1).
In addition to the literature review, we considered the advances made in Ecuador, in terms of its climate projections under the different emission scenarios. As part of its Third National Communication on Climate Change to the United Nations Framework Convention on Climate Change, MAAE produced a series of maps reflecting the climate projections for Ecuador under emission scenarios 2.6, 4.5, 6.0 and 8.5.
As part of its downscaling methods, MAAE considered approximately 15 global climate models, and selected finally four models (IPSL-CM5A-MR, MIROC-ESM, GISS-E2-R and CSIRO-Mk3-6-0), that best describe the atmospheric dynamics of the country. MAAE developed and published two types of scale reduction: (a) statistical (assembling the models of IPSL-CM5A-MR, MIROC-ESM, GISS-E2-R and CSIRO-Mk3-6-0); and (b) dynamic. Its statistical scale reductions were obtained for precipitation parameters, maximum, average and minimum temperatures for the Representative Concentration Pathway (RCP) 2.6, 4.5, 6.0, 8.5 scenarios in the historical  and future (2011-2100) periods. In addition to the selection of global climate models, dynamic scale reductions used the regional model called Weather Research and Forecasting (WRF) version 3.61 [35]. As a result, MAAE generated a series of climate projection maps at a resolution of 10 km (10 × 10 km) on a daily and monthly scale, for the parameters: (a) precipitation, (2) temperature, (3) relative humidity, (4) wind, and (5) radiation for the  While MAAE maps represent a great advance for regional planning, finer scale maps for cities, as well as improvements in knowledge and communication on climate projections for municipal and land-use decision processes, are still needed. Using the city of Portoviejo and its river watercatchment, we aim to develop a method for augmenting the resolution scale of dynamic CC projections and maps by MAAE, from a resolution of 10 km (10 × 10 km) to 30 m (30 × 30 m) using digital elevation models and Landsat 4/5/7/8 satellite imagery.
Structured in four sections, our paper first describes (in section 2) the data used for reducing the resolution scale of dynamic scale reduction projections by MAAE, detailing each of the steps for detecting satellite images' outliers as well as the procedure for approximating surface to air temperature and extrapolation methods of air temperature time series in time ranges from 1981 to 2040. The methods of adjusting the resulting satellite images with the dynamic scale reduction projections by MAAE are validated using local meteorological stations in Portoviejo. Section 3 presents the resulting maps at a resolution of 30 m and section 4 discusses the method

Data
This work is focused on the city of Portoviejo and its watershed. This is framed by the referential geographical coordinates of: 1 • 03 ′ 16 ′′ S and 80 • 27 ′ 16 ′′ W. Table 2 [37].
In order to augment the pixel resolution of MAAE's projections, satellite images were obtained from the Climate Engine Platform (http:// climateengine.org/) filtering those from Landsat 4/5/7/8 Top of Atmosphere [38]. Landsat's available images included the time range of 1997-2019, with a pixel resolution of 30 m. Finally, altitude was calculated with the digital elevation model STRM [39,40].

Outlier detection in satellite images
The outlier detection consisted of identifying the physical limits of the annual and monthly air temperatures [41][42][43]. In this work, the admissible range for air temperature was defined by the climatological behaviour of the meteorological station in Portoviejo, where the mean, maximum and minimum values are showed in table 3. It is important to note that, according to the definition of the World Meteorological Organization, 'air temperature' is registered at a height of 2 m above the surface [44].
In satellite images, values detected as 'no data' were considered as outliers, others were detected by the minimum and maximum values estimated from temporal series of air temperature recorded at the Portoviejo station within the period 1981-2010. The range of possible temperatures considered in this work was calculated between 18 • C and 38 • C.
Land Surface Temperature (LST) obtained by satellite images reported a considerable number of outliers (see figure 1) for the year 1997, with decreasing numbers up to 2015.
In order to overcome the missing data from outliers in previous years, we developed an automatized algorithm that recognized LST outliers of all satellite images by using equation (1): where, i and j are the pixel values of each row and column of minimum, maximum and mean LST, respectively. The pixel resolution of Landsat images was 30 m, which according to the study's extension frame shown in table 2, totalled 8696 490 pixel values.
Considering that satellite imagery is prone to a number of error data due, for example, to the presence of clouds, outliers were completed (filled-in) with the neighbourhood method as described by Chen et al [45] and as depicted in figure 2.
The corresponding neighbourhood analysis equation for filling-in, exemplified in figure 2, is specified in equation (2): where, H is the outlier data in [1,NR], (NR − 1) /2 is the approximated integer number to count the values of temperature registered by the satellite image, as a neighbourhood analysis to calculate each cell of the given raster image. The outlier is filled-in with  equation (2), however, the outlier data H may be equal to the NR value. The algorithm is iterative and ends when the number of outliers reaches zero (see figure 3).  Figure 2 shows how outlier data are detected and filled-in with equation (2), being i,j T s2 the outcome raster by this process. This procedure is applied to every single LST satellite image as obtained from Landsat 4/5/7/8 in the yearly range 1997-2019.

Air temperature approximation at 2 m height from surface level
Air temperature was approximated from the LST and based on Stefan Boltzmann's law, which essentially defines the Earth as a thermal emitter. With this assumption, the maximum irradiance emitted as superficial temperature was set and defined by equation (3) [46,47]: where, R S is the emitted radiation by the surface or LST T S , ε 0 is the emissivity coefficient of the surface and σ is Stefan Boltzmann's constant. Alves et al [47], estimate the surface emissivity as described under equation (4): where, LAI is the leaf area index based on data from Landsat satellite images, as it was suggested by Alves et al [47]. The air temperature system is modelled as a surface that emits radiation according to Stefan Boltzmann's law and is expressed as shown by equation (5): where, R a is the emitted radiation by the air, ε a is the air emissivity and T a is the air temperature. In this work, R a is approximated by the Beer Lambert law (R a = R s exp (δ)), where δ is the optical depth estimated by the atmosphere transmittance according to ln (1/τ SW ) [48]. The emissivity coefficient of air is expressed in equation (6): In equation (6), τ SW is the atmosphere transmittance for clear sky. Resulting values work only with satellite images that have no LST outliers and have been filledin as described in figure 2. In the work of Waters et al [46], transmittance is approximated by the mathematical relation expressed in equation (7): where, (H + 2) corresponds to the digital elevation model STRM (DEM) at 2 m from the land surface, with a pixel resolution of 30 m. Air temperature is thus estimated and followed by applying equations (5) and (6), where the input data are the raster of LST, the vegetation index and the digital elevation model.

Extrapolation of air temperature time series in the years 1981-2040
There are several ways to extrapolate time series according to statistical behaviour; however, the most common is based on trends and is a linear interpolation with least squares [49,50]. Other, nonlinear methods are more complex (see Mudelsee [49]) where the use of regression analysis under quadratic, polynomial, sinusoidal, and power, among other equations, challenges the ability to recognize such trends. This type of model allows to predict values in the near future or fill-in outliers in datasets. However, an important limitation of this type of analysis is extrapolating the time series to the far future, where mathematical functions may diverge, and uncertainty becomes an increasing concern.
For the purpose of this research, extrapolation of air temperature in time was estimated with the use of Fourier's series. Equation (8) was used for the calculation and analysis of Fourier series' as follows: where, T is the period, i are the amornics, x is the temporal series to be analysed, a i and b i are the Fourier coefficients. A higher number of i implies a better fit of the Fourier series over the air temperature temporal series [51,52]. In the present work, a i and b i coefficients are approximated with least squares and the period is equivalent to the range of years analysed and available from Landsat images. In this context, equation (8) was reformulated as shown in equation (9): In equation (9), y j are the values of air temperature, x j are the range of years (1981-2040) considered in the analysis, a (2i−1) y a (2i) are the coefficients to be determined with least squares. The functions related to Fourier's series in equation (9) are expressed in equation (10): Following from equation (10), the least squares method, determining the interpolation coefficients was solved by the resolution of the matrix shown in equation (11): Equation (11) can be solved if j ⩾ 2i, assuring that N equations with N unknowns can be solved following the well-known procedure of Gauss Jordan.

Pixels adjusted between satellite images projected in time vs climate change projections of MAAE
Adjusting pixels consisted of comparing air temperature maps (30 m) obtained from Landsat and those from MAAE (10 km) (RCP 4.5 and RCP 8.5 [53,54]). Figure 4 shows the 10 km pixel resolution of air temperature for January 2000 as published by MAAE. Adjusting the pixels from Landsat air temperature images with those projected for RCP 4.5 and 8.5 entailed rescaling the 30 m pixel resolution found on every pixel with those pixels' resolution of 10 km, following the expression of equation (12): In equation (12),X is the air temperature value of maps with pixel resolution of 10 km, a ij are the pixels with resolution of 30 m found inX, b ij are the pixels rescaled,ā is the mean of the a ij values, N and M are the maximum number of rows and columns for i and j, respectively.

Validation of the high-resolution model of climate projection
The validation of the resulting map with the high-resolution model for CC projections at a 30 m resolution consisted of comparing the temporal series of air temperatures obtained with the data registered by the meteorological station in Portoviejo [37]. Figure 5 shows the flux diagram for the validation process.
In figure 5, k T a and k T a ′ are the air temperature values obtained from the meteorological station in Portoviejo and the final map obtained from the high-resolution model, respectively. The interval specified in figure 5 covers 95% of the temporal series of each pixel within a normal distribution. This procedure guaranteed that the high-resolution model satisfies the Student's t-test with data from the meteorological station in the period 1981-2005 for mean air temperature.

Results
Following the procedure described in figure 3, resulting LST maps between 1997 and 2019 are shown in figure 6.
LST maps in figure 6, ranging from 1997 to 2015, show that at least for 1997, outliers reduced the quality and image resolution of this map. This behaviour can also be observed when using maximum and minimum LSTs. In the case of 2010 onwards, the number of outliers falls considerably, thus increasing the reliability of the resulting maps.
As for air temperature, this is estimated from LST according to equations (5) and (6) resulting in maps as shown in figure 7. Figure 7 shows the mean air temperature approximated with Stefan Boltzmann's law, extrapolated in time as a function of Fourier's series and following

Discussion and conclusions
Having defined the spatial boundaries at watershed scale, our model complements those perspectives in addressing the ecological environment, water quality, and ecological flows [34] as well as territorial dynamics. The final CC maps have an augmented resolution, showing coherence with those of MAAE, and offering a low-cost method for demonstrating temperature anomalies due to CC to land-use and urban planners, as well as local development decision makers. This information can be used for both mitigation and adaptation measures implemented by municipal  [13,19,29,30,32,56] on validating dynamic scenarios, were observed. In terms of our results, the model offers further research possibilities, for example in adding variables that consider urban sprawl, mobility patterns, urban densities, etc, which would increase accuracy. Nonetheless, when considering the technical limitations of hardware and software capabilities for most municipalities, as described by Ramyar et al [15], as well as the urgency of localizing CC at the urban scale, the resulting maps can go down to at least 1:1000 in scale (see, e.g. figure 8). As a scientifically sound means of communication, these maps contribute to incorporating CC data into planning  [57] Difficulties of replicating data Gulacha and Mulungu [58] Difficulties of collecting a large number of variables Gu et al [7]; Su et al [20] Data interpolation undermines the model quality Didovets et al [5] Uncertainty regarding model selection and results Khalyani et al [9]; Su et al [21]; Aich et al [3] RPC 4.5 scenario hinders insights into future temperatures Rana and Moradjkani (2015); Bastin et al [27] Difficulties of predicting future scenarios Yan et al [34] Topography is a challenge to the use of Regional Concentration Models (RCMs) Prömmel et al [14]; Sanjay et al [17] RCM outputs present bias Worku et al [59] WRF and statistical downscaling methods need improvements Jahangir and Moghim [8]; Tang et al [22] Uncertainties regarding model downscaling procedures Varikoden et al [23] Difficulties of combining downscaling models Mathis et al [11]; Akhter et al [4] Limitations of hardware and software capabilities make full-scale modelling for a city difficult Ramyar et al [15] Scale heterogeneity hinders the quality of the study McCarthy et al [12]; Reshmidevi et al [33] Scientific findings are difficult for society to understand Kjellström et al [10] Combination of models enables consistency of the procedures and methods Hu and Ayyub [55]; Hasan et al [28]; Seiler et al [18] as well as into development narratives at municipal scale. Based on existing CC projections at national/regional scale, the method and maps developed here are based on open access satellite imagery which can easily be made available to land-use planning decision makers at a resolution of 30 × 30 m, consistent with the dynamic downscaling maps for RCP 4.5 and 8.5 by MAAE at different scales (see, e.g. figure 9). Beyond their possible impact on policy making and CC mitigation and adaption measures at the local scale, such maps can also be employed on new land-use configurations, including nature-based

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.

Acknowledgments
We thank all our colleagues at IIGE, particularly those who provided insights and expertise assisting this research. We thank Mgs. Sebastián Espinoza for his backstopping assistance and institutional liaison with MAAE. We are grateful to MAAE and particularly Carlos Espinosa, Jorge Nuñez, Pablo Caza and Nicolás Zambrano for providing feedback and supporting all necessary spaces for discussion and exchange in developing this method. Special thanks are due to Mr. Pablo Caza who recognized the relevance and cross-cutting aspect of CC beyond institutional boundaries. We would also like to show our gratitude to the anonymous reviewers for their insights and comments on earlier versions of this manuscript, and to the CIS/ GIZ team for their technical support and the numerous workshops held in Portoviejo. Finally, we thank the GAD of Portoviejo for its receptiveness in its spatial planning processes as well as for its positive feedback loops. Special thanks to the Sustainable Intermediate Cities Programme implemented by the Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH on behalf of the Ministry of Economic Cooperation and Development (BMZ) of the German Federal Government.