Spatial extrapolation of statistically downscaled weather data over the Northwest Himalayas at major glacier sites

Highlights

• The MPS technique can spatially extrapolate weather data over the Himalayas.

• Training data of smaller domains are used to simulate data for larger domains.

• Large-sized training domains simulate well in comparison to small-sized domains.

• The extrapolated data is also estimated for selected point locations of glaciers.

• MPS shows good accuracy in extrapolating data both in domains and at glacier sites.

Abstract

Generating fine-resolution weather data over the Himalayan region is difficult due to complicated topography and harsh weather. In this study, we set up a Multiple-Point Statistics (MPS) based statistical model to spatially extrapolate fine-resolution rainfall and temperature data in five spatial domains and at ten-point locations of glaciers over the northwest Himalayas. The training domain consists of thirteen years (2001–2013) of daily rainfall and temperature data at 30 and 10-km spatial resolution which generates multiple realizations of fine-resolution information for the year 2014 in the larger domain. Small range of RMSE (2.46–6.68 mm) and MAE (1.12–4.15 mm) for rainfall suggests that MPS performs well in spatial domains. Furthermore, at the glacier sites, we observe that the training data of smaller training domains are insufficient while data of larger domains perform well. Overall, MPS shows encouraging results in extrapolating fine-resolution weather information over the complex region of northwest Himalayas.

Introduction

The Himalayan region is home to hundreds of glaciers which serve as the origin of major Asian rivers such as the Indus, Ganges and Brahmaputra, thus, influencing various economic activities (Singhal and Jha, 2021a). The glaciers are significantly influenced by the rainfall from the south-west monsoon season since the peak melting of these glaciers coincides with the monsoon season (Thayyen et al., 2005). Moreover, the presence of complex topography and atmospheric circulation patterns leads to the unique distribution of rainfall and temperature over the Himalayas (Bookhagen and Burbank, 2010). Even small variations in rainfall and temperature influence the glacio-hydrology of the glaciers (Immerzeel et al., 2010). Previous studies suggest that the changing weather over the Himalayas has caused a majority of these glaciers to retreat (Mukhopadhyay and Khan, 2014; Wood et al., 2020). In the Himalayan catchments, limited availability of fine-resolution is a major obstacle. The complex topography and harsh climate lead to an insufficient network of rain gauges in the region. In setting up a Weather Research and Forecasting (WRF) model, the topographical complexity poses a major challenge. In the case of existing WRF data in a smaller domain, a novel cost-effective alternative could be to spatially extrapolate the information to a larger domain having similar characteristics.

Spatial extrapolation is a method to estimate data in a larger region by extending the pattern of known information of a related smaller region. The concept of spatial extrapolation has been investigated in multiple areas of research such as soil mapping (Stockmann et al., 2015), air pollution concentration (Ma et al., 2019), wind speed (Xu et al., 2018), local weather information (Lo et al., 2011; Bracho-Mujica et al., 2019), temperature (Strauss et al., 2013) etc. However, to the best of our knowledge, limited studies have focused on the extrapolation of rainfall data. For this purpose, we set up a statistical downscaling model which can extend the coverage of fine-resolution rainfall data to a larger domain. To this end, the model uses the coarse and fine-resolution data of a smaller domain (as training data) and extrapolates the downscaled information to a larger domain. The concept behind such extrapolation is that if detailed information about a (known) domain is available, it may be possible to extrapolate the information to a relatively larger (unknown) domain. In the context of rainfall, the application of such extrapolation technique may be significant for the generation of fine-resolution data in a feasible manner, especially over-complicated regions such as the Himalayas where the availability of data is generally limited. In the case of modelling spatially correlated variables, geostatistics is a natural tool to apply.

Multiple-Point Statistics (MPS) is a widely known geostatistical technique which has the potential to offer an approach for spatial extrapolation. Conceptually, MPS is a stochastic simulation technique which reproduces the patterns from a 2D or a 3D training image (TI) and fills a simulation grid (SG) when the patterns of SG match with those of TI. In the past decade, it has found several applications in various areas of research, such as in geophysics (Comunian et al., 2013), remote sensing (Mariethoz et al., 2012; Yin et al., 2016; Rasera et al., 2020), climate sciences (Jha et al., 2013a), hydrological sciences (Jha et al., 2015; Benoit et al., 2020), river morphology (Jha et al., 2013b) etc. Several studies have applied MPS for spatial downscaling of weather data. For instance, Jha et al. (2015) used twenty years of precipitation and temperature data to successfully downscale them from 50 km to 10 km spatial resolution in Southeastern Australia. Recently, Singhal and Jha (2021b) successfully applied MPS to downscale rainfall and temperature data from 30 km to 10 km spatial resolution over the highly complex northwest Himalayas using 12 years of training data. The authors also examined the efficacy of the model to generate fine-resolution data in ten administrative districts of the region and at various point locations of extreme precipitation and avalanches. More details about MPS can be found in Guardiano and Srivastava (1993) and Mariethoz et al. (2010). The concept of MPS has been successfully applied in downscaling of a wide range of variables; however, limited studies have examined the efficacy of MPS for spatial extrapolation of data. For instance, Malone et al. (2016) applied MPS to extrapolate fine resolution soil information (at recipient site) on the basis of information collected from a nearby donor site having similar characteristics. Similarly, Oriani et al. (2020) extended the coverage of fine-resolution multispectral satellite images to a region where similar fine-resolution data was found using the concept of MPS. However, to the best of our knowledge, no study has utilized the concept of MPS for spatial extrapolation of rainfall data by overcoming its high spatiotemporal variability.

Various algorithms have been developed using the concept of MPS; however, in this study, we select the Direct Sampling (DS) algorithm developed by Mariethoz et al. (2010). The potential of DS algorithm has been examined in various research fields for the simulation of spatial data (Oriani et al., 2016; Dembélé et al., 2019; Zuo et al., 2019, 2020; Bai and Mariethoz, 2021; Hosseini et al., 2021). The advantage of using DS is that it is able to handle both univariate and multivariate simulations of categorical and continuous variables (Straubhaar and Renard, 2021). Moreover, it does not require the storage of any database of spatial patterns prior to the simulations since it extracts the samples directly from the TI (van der Grijp et al., 2021). The TIs represent conceptual models that contain the spatial features of the variable to be estimated. The idea here is to utilize a TI with the spatial information from a smaller domain in order to learn the spatial features of a larger domain without actually training the model for the larger region.

In this study, we set up a statistical model based on our previous work presented in Singhal and Jha (2021b) over the northwest Himalayas. The present study is an extension of the previous work and offers a broader understanding regarding the cost-effective generation of fine-resolution weather information over the region. In Singhal and Jha (2021b), the location and size of training and simulation domain were the same. Hence, the model was used primarily for downscaling the coarse resolution weather data. In this work, however, we train the model by providing training data only in a smaller domain (training domain) and extend the downscaled fine-resolution data of rainfall and temperature to a larger domain (simulation domain). In other words, the training domain contains both coarse and fine-resolution data while the simulation domain contains only the coarse-resolution information which is downscaled to obtain the corresponding fine-resolution information in the larger domain. The extrapolation approach allows researchers to study glaciers located in the simulation domain (where WRF is not set up) by borrowing information from the training domain (where the WRF is actually set up). Here, each grid in the training domain acts as the donor site while the point locations of glaciers in the simulation domain act as the recipient sites. To this end, we choose five spatial domains in this study, with each succeeding domain larger than the previous one. The DS algorithm, if recognizes similar spatial patterns, uses the coarse resolution information of the larger domain to generate fine-resolution data by sampling the TI. Multiple realizations of data are generated for each larger domain which is subsequently verified with the available reference dataset. It is important to note here that the algorithm does not require fine-resolution information of variables for the larger domain to simulate the data. The specific objectives of this study are: (a) to set up a statistical model over the northwest Himalayas which utilizes coarse and fine-resolution information of rainfall and temperature in smaller domains in a common time period and estimates the fine-resolution information in larger domains in another time period; (b) to determine the appropriate size of the simulation domain to which the extrapolation of data is possible; (c) to determine the smallest size of the training domain which can provide sufficient information for the extrapolation of data; (d) to examine the performance of the model in generating extrapolated fine-resolution weather information at ten selected glacier sites.

The rest of the paper is organized as follows. Section 2 describes the study area and dataset. The methodology and experimental runs are explained in Section 3. In Section 4, results from the experimental runs are presented, followed by the discussion of the results in Section 5. Section 6 deals with conclusions regarding the efficacy of the DS simulations in extrapolating the downscaled fine-resolution weather information.