**Khalil Ur Rahman 1, Songhao Shang 1,\*, Muhammad Shahid 1,2 and Yeqiang Wen <sup>1</sup>**


**\*** Correspondence: shangsh@tsinghua.edu.cn; Tel.: +86-10-6279-6674

Received: 16 July 2019; Accepted: 27 August 2019; Published: 29 August 2019

**Abstract:** Accurate estimation of precipitation from satellite precipitation products (PPs) over the complex topography and diverse climate of Pakistan with limited rain gauges (RGs) is an arduous task. In the current study, we assessed the performance of two PPs estimated from soil moisture (SM) using the SM2RAIN algorithm, SM2RAIN-CCI and SM2RAIN-ASCAT, on the daily scale across Pakistan during the periods 2000–2015 and 2007–2015, respectively. Several statistical metrics, i.e., Bias, unbiased root mean square error (ubRMSE), Theil's U, and the modified Kling–Gupta efficiency (KGE) score, and four categorical metrics, i.e., probability of detection (POD), false alarm ratio (FAR), critical success index (CSI), and Bias score, were used to evaluate these two PPs against 102 RGs observations across four distinct climate regions, i.e., glacial, humid, arid and hyper-arid regions. Total mean square error (MSE) is decomposed into systematic (MSEs) and random (MSEr) error components. Moreover, the Tropical Rainfall Measurement Mission Multi-Satellite Precipitation Analysis (TRMM TMPA 3B42v7) was used to assess the performance of SM2RAIN-based products at 0.25◦ scale during 2007–2015. Results shows that SM2RAIN-based product highly underestimated precipitation in north-east and hydraulically developed areas of the humid region. Maximum underestimation for SM2RAIN-CCI and SM2RIAN-ASCAT were 58.04% and 42.36%, respectively. Precipitation was also underestimated in mountainous areas of glacial and humid regions with maximum underestimations of 43.16% and 34.60% for SM2RAIN-CCI. Precipitation was overestimated along the coast of Arabian Sea in the hyper-arid region with maximum overestimations for SM2RAIN-CCI (SM2RAIN-ASCAT) of 59.59% (52.35%). Higher ubRMSE was observed in the vicinity of hydraulically developed areas. Theil's U depicted higher accuracy in the arid region with values of 0.23 (SM2RAIN-CCI) and 0.15 (SM2RAIN-ASCAT). Systematic error components have larger contribution than random error components. Overall, SM2RAIN-ASCAT dominates SM2RAIN-CCI across all climate regions, with average percentage improvements in bias (27.01% in humid, 5.94% in arid, and 6.05% in hyper-arid), ubRMSE (19.61% in humid, 20.16% in arid, and 25.56% in hyper-arid), Theil's U (9.80% in humid, 28.80% in arid, and 26.83% in hyper-arid), MSEs (24.55% in humid, 13.83% in arid, and 8.22% in hyper-arid), MSEr (19.41% in humid, 29.20% in arid, and 24.14% in hyper-arid) and KGE score (5.26% in humid, 28.12% in arid, and 24.72% in hyper-arid). Higher uncertainties were depicted in heavy and intense precipitation seasons, i.e., monsoon and pre-monsoon. Average values of statistical metrics during monsoon season for SM2RAIN-CCI (SM2RAIN-ASCAT) were 20.90% (17.82%), 10.52 mm/day (8.61 mm/day), 0.47 (0.43), and 0.47 (0.55) for bias, ubRMSE, Theil's U, and KGE score, respectively. TMPA outperformed SM2RAIN-based products across all climate regions. SM2RAIN-based datasets are recommended for agricultural water management, irrigation scheduling, flood simulation and early flood warning system (EFWS), drought monitoring, groundwater modeling, and rainwater harvesting, and vegetation and crop monitoring in plain areas of the arid region.

**Keywords:** precipitation estimation; soil moisture; SM2RAIN-CCI; SM2RAIN-ASCAT; multi-satellite precipitation analysis (TMPA); error decomposition; complex topography; diverse climate

#### **1. Introduction**

Precipitation is one of the most critical components of global energy and water cycles and ranked first by the Global Climate Observing System (GCOS) [1,2]. Reliable long-term temporal precipitation records at fine spatiotemporal (<20 km at daily and sub-daily scales) resolution is crucial for planning and managing water resources, drought assessment, flood forecasting, assessment of crop water requirements, hydrometeorology, and climate studies [3–7]. Precipitation also plays an important role in weather prediction, agricultural management, vector and water-borne diseases [8].

Precipitation is highly erratic spatiotemporally, which makes its estimation challenging both with ground observation (rain gauges and meteorological radars) and satellite precipitation products (PPs). The complex topography, varying climate, dense vegetation, and coastal regions attribute to further complexity in precipitation estimation [9,10]. Ground-based rain gauges (RGs) provide accurate local precipitation estimates [11], and are considered as the most reliable precipitation record source for hydrological modeling and monitoring purposes. However, their non-homogeneous coverage, limited spatial representativeness, and high maintenance cost restrain their global scale application [12].

Meteorological models, such as reanalysis products, are alternatively used to estimate precipitation, especially in regions with scarce RGs and reliable ground observations [13]. The uncertainties associated with these estimates in areas with scarce RGs can be substantial [14]. Therefore, in the past 30 years, different remote sensing techniques have been developed to improve the precipitation estimations and provide full regional and global spatial coverage [15]. The standard precipitation measurement methods are based on instantaneous precipitation measurements from space retrieved from microwave radiometers, radars, and infrared sensors [16]. These methods invert the atmospheric signals reflected or radiated by hydrometeors and known as the "top-down" approach [9].

PPs estimate precipitation from thermal infrared sensors onboard geosynchronous earth orbit (GEO), and microwave sensors (both passive and active) onboard low-earth orbit (LEO) satellites [10,17]. Some PPs combine infrared- and microwave-based estimates by utilizing high temporal resolution infrared platforms and shows high precision in precipitation estimation of microwave sensors [18]. Such PPs include the most recently developed PPs with high spatial (0.1◦) and temporal (30 minutes) resolution, i.e., Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG) of the Global Precipitation Measurement (GPM) mission [15], near-real-time and post real versions of the Tropical Rainfall Measurement Mission Multi-Satellite Precipitation Analysis (TRMM TMPA 3B42RT, 3B42V6/V7) [19], the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS) [20], Climate Prediction Center (CPC) Morphing (CMORPH) [21], Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) [22,23], Global Satellite Mapping of Precipitation (GSMaP) [24] and many more.

Soil Moisture (SM) TO RAIN (SM2RAIN) is an algorithm based on approaches provided by Crow et al. [25] and Pellarin et al. [26] and further developed by Brocca et al. [27], which can be used for direct precipitation estimation from in-situ and/or satellite-based SM observations. The method provides daily precipitation estimates on a global scale and has been successfully applied to satellite SM data [9,28,29]. SM2RAIN approach is appropriate for accumulated precipitation estimates and has been verified against in-situ SM data and single-sensor SM products [30,31] providing reliable results at the regional scale [32–34].

SM2RAIN is based on the "bottom-up" approach that estimates precipitation from various single-sensors surface soil moisture (SSM), as opposed to "top-down" approach of other PPs [27,30, 35,36]. The bottom-up approach differs from top-down approach in such a way that the bottom-up approach considers accumulated precipitation while the top-down approach is based on instantaneous

precipitation rate. The bottom-up approach has an edge over top-down when accumulated precipitation (e.g., daily precipitation) estimates are desirable as this approach requires a limited number of satellite sensors and measurements. On the other hand, the limitations of the bottom-up approach are its dependence on topography (low accuracy over complex topography) and land use (low accuracy over dense vegetation), unable to estimate precipitation in over-saturated soil, and applicable only to terrestrial rainfall [9].

The bottom-up approach has been extensively validated over extended-spectrum of spatial scales, including global [9,25,37], continental [35,38], and regional [32,39–42] scales. Different SM PPs are considered, such as SMOS (Soil Moisture Ocean Salinity Mission, [35]), ASCAT (Advanced SCATterometer, [43]), AMSR-E (Advanced Microwave Scanning Radiometer, [44]), and SMAP (Soil Moisture Active and Passive, [28,29]). Recently, a number of studies have employed precipitation estimates from satellites obtained through the bottom-up approach in hydrological and water resources applications [3,17,31,45]. These studies demonstrated the potential benefits and main limitations of the bottom-up approach in estimating precipitation from space. The accuracy of the bottom-up approach is strongly influenced by the accuracy and temporal resolution of satellite SM products [46].

The objectives of this study were two-fold, i.e., to assess the performance of SM2RAIN-CCI and SM2RAIN-ASCAT for the first time in Pakistan, a country with a complex topography and diverse climate, and to evaluate the performance of SM2RAIN-derived products against extensively evaluated PP in Pakistan (TRMM TMPA 3B42v7, hereinafter referred as TMPA). The analysis was performed in four climate regions of Pakistan, i.e., glacial, humid, arid and hyper-arid regions, during the period 2000-2015. This study is the first of its kind that evaluates the quality of SM2RAIN-based precipitation datasets across Pakistan. This study can be used as a reference for hydrological modeling, water resources management, and agricultural water management practices. Moreover, there are very limited studies on integrated performance evaluation of SM2RAIN-based precipitation datasets in regions with complex topography and diverse climate, especially in Pakistan.

Pakistan is a developing country that has very limited/scarce rain gauges (RGs), which are non-homogenously distributed. Even with a significant increase in the number of RGs over the last few decades, their density does not meet scientific and practical requirements. To overcome the current scenario, Pakistan needs the application of advanced remote sensing techniques for hydrological and meteorological applications, climate change studies, agricultural water management, and water resources management. This study evaluated the soil moisture-based precipitation datasets, which will be a useful alternative to conventional precipitation products for different hydrological and meteorological applications and will address the data scarcity problems in Pakistan.

The significance of the current study is: (1) This study demonstrates the worth/quality of SM2RAIN-based datasets by evaluation on spatial and temporal scales, (2) the spatial and temporal evaluation helps us to understand where, when and how these precipitation products might be used, (3) better performance of these products in the arid (and semi-arid regions), i.e., Punjab province of Pakistan considered as agricultural hub of the country, illustrates the potential application of SM2RAIN-based datasets for agriculture (vegetation and crop growth monitoring) and agricultural water management, and much more.
