Was the extreme rainfall that caused the August 2022 flood in Pakistan predictable?

Pakistan suffered from severe floods in the past, but in August 2022, the country experienced exceptional extreme rainfall events that caused widespread and catastrophic flooding. The 2022 flood affected all aspects of socio-economic lives including agriculture, infrastructure, and mortality of humans and livestock. The two-day accumulated extreme rainfall on 17–18 August was anomalous and contributed the most to the flood in the southern provinces of Pakistan. The damage caused by extreme rainfall and the subsequent flooding has raised questions regarding the predictability of extreme rainfall by the existing weather forecasting models. Here, we use ensemble forecasts from four numerical weather prediction models under THORPEX Interactive Grand Global Ensemble datasets to examine the predictability of extreme rainfall at a six-day lead. The extreme precipitation during 17–18 August 2022 was predictable a week before the event that contributed the most to the flooding. All the forecast models provided an early warning at a six-day lead time. UK Meteorological Office and European Centre for Medium-Range Weather Forecasts models produced comparable results to observations at all the lead times. Our findings highlight that an integrated framework of extended quantitative precipitation forecasts and hydrological modeling can help reduce the country’s flood vulnerability and risk associated with it.


Introduction
Floods in Pakistan have been a recurring natural disaster with devastating consequences, affecting both the human population and the country's infrastructure (Shah et al 2020, Khan et al 2021).Pakistan has experienced 23 major floods between 1947 and 2015, resulting in a loss of approximately 38 billion USD (Aslam 2018, AFR 2021).As over 60% of the land area of Pakistan is vulnerable to flood, the country has suffered severe economic losses (Ahmad et al 2011, Manzoor et al 2013).Pakistan ranks 18th (out of 191) on the Global Risk Index.However, according to the climate risk index, Pakistan is the seventh-most vulnerable country in the world to climate change (Shah et al 2022).Furthermore, due to high glacier melt and increased summer monsoonal rainfall, the frequency and magnitude of floods in Pakistan are projected to rise under the warming climate (Dankers et al 2013, Hirabayashi et al 2013, Alfieri et al 2017, Aslam 2018, WMO 2022).
In August 2022, Pakistan experienced an exceptional flood caused by the multi-day anomalously high rainfall (Nanditha et al 2023).Pakistan received about twice (180%) of the long-term mean rainfall in July 2022 (Qamer et al 2023) that saturated the soil before the extreme precipitation event in August.Subsequently, in August 2022, the rainfall departure from its climatology exceeded 500% (PMD 2022a), which triggered flash floods in Pakistan.The flood was also ranked among the most severe floods worldwide in the recent years (Hoshyar Pakistan 2022).During the 2022 flood, almost one-third of the land surface of Pakistan was reported underwater, which damaged approximately 3.6 million acres of cropland (Bhutta et al 2022).The 75% of the flood-affected districts were endangered by mosquito and water-borne illnesses (Sarkar 2022).There were 639 children among 1717 reported fatalities, while nearly 2.1 million people were left homeless or living in temporary shelters due to the 2022 flood in Pakistan (NDMA 2022).
Pakistan has witnessed a rise in flood risk due to the increased frequency, intensity and duration of floods in recent decades (Ali et al 2022, Waseem andRana 2023).The risk is further compounded due to the large number of people exposed to flooding in the Indus basin, which ranks second globally in terms of flood-exposed population (Tellman et al 2021).The population exposure due to floods has significantly increased between 2002 and 2015 due to urbanization and more settlements in flood-prone areas (Ceola et al 2014, Liu et al 2020, Tellman et al 2021).After the major flood of 1995, the flood incidents in 2010 and 2022 show growing evidence of the increasing flood risk.The devastating floods in 2010 and 2022 made notable occurrences, and both disasters dramatically altered how the community understood and responded to risk.In 1995, the flood resulted in the loss of 600 lives and displacement of 600 000 individuals (Nanditha et al 2023).Moving forward to 2010, the flood covered an extensive area of 160 000 km 2 , claiming 1985 lives and displaced approximately 20 356 550 people.However, the flood of 2022 surpassed the previous two events, with an even larger affected area of 265 365 km 2 , tragically resulting in 1739 fatalities, and leaving an overwhelming 33 million people displaced (Nanditha et al 2023).These figures indicate a worsening trend of flood impacts, highlighting the increasing severity and consequences of the devastating floods on the people and infrastructure of Pakistan.
Pakistan's existing flood forecasting system relies on empirical regression (Adams 2019) and needs an ensemble hydrological forecasting system to incorporate the uncertainties in the forecast and early warning system (Nanditha andMishra 2021, Vegad andMishra 2022).Several countries have employed ensemble forecasting for early flood warnings (Troin et al 2021).Ensemble flood prediction based on weather forecasts and data assimilation can assist the decision-makers in providing an actionable early warning (Wu et al 2020).Even with suitable structural safeguards, the development of early warning and prediction systems can help limit projected damage and manage floods (Aziz and Tanaka 2011).Pakistan needs a robust framework for establishing an ensemble forecast-based comprehensive flood forecast and warning system.The flood prediction skill of these systems primarily depends on the skill of rainfall forecast (Schwanenberg et al 2015, Emerton et al 2016).This emphasizes the importance of having precise rainfall forecasts well in advance.
The development and enhancement of numerical weather prediction (NWP) models have increased considerably during the last decade (Charba et al 2003, Zhao et al 2011, Liu et al 2022).The THORPEX Interactive Grand Global Ensemble (TIGGE) datasets have been widely used for precipitation forecasts, which was established through The Observing System Research and Predictability Experiment (THORPEX) project.Several studies have assessed the effectiveness of TIGGE forecasts for meteorological and hydrological applications (Zhao et al 2011, Tao et al 2014, Louvet et al 2016, Liu et al 2019, Saedi et al 2020, Shu et al 2021).For instance, Zhao et al (2011) compared forecasts from different models including the European Centre for Medium-Range Weather Forecasts (ECMWF), the National Center for Environmental Prediction (NCEP), and the China Meteorological Administration (CMA).They found that ECMWF exhibited better performance than the other models; however, the forecast skills of all models decreased significantly after five days of lead time.Many previous studies highlighted the favorable performance of the UK Meteorological Office (UKMO) and ECMWF models compared to other models (Saedi et al 2020).Bhomia et al (2017) reported that forecasts from UKMO, NCEP, and ECMWF demonstrated satisfactory performance for rainfall predictions and tropical cyclones in India.Mukhopadhyay et al (2021) utilized various NWP models, including the NCEP-based operational Global Ensemble Forecast System (GEFS), to predict the Kerala floods in 2018 and 2019.In this study, we evaluated the predictability of the Pakistan 2022 flood by analyzing the performance of selected NWP models.Specifically, we focused on the models from the TIGGE dataset, which included ECMWF, GEFS, UKMO, and KMA.These models were chosen based on their established reputation and track record of performance in previous research studies (Saedi et al 2020, Endris et al 2021, Mishra and Malik 2023).Additionally, we included GEFS as an Indian model to gain valuable insights that could have relevance and applicability to the neighboring country Pakistan.
The relief organizations and authorities have performed several assessments on the 2022 Pakistan flood (UNICEF 2022, PMD 2022a).However, the climate and meteorological conditions that caused the flooding have been examined only in a few studies (Nanditha et al 2023).In addition, the predictive skill of the existing meteorological forecast systems is yet to be examined for the 2022 Pakistan flood.Nanditha et al (2023) explained that multiday extreme precipitation on wet antecedent soil moisture conditions was the primary driver of Pakistan flood 2022.However, in our analysis, we used only precipitation as an indicator to predict flood, which has also been done in previous studies (Webster et al 2011, Ushiyama et al 2014).Considering the significant devastation and loss of life caused by the 2022 flood in Pakistan, it is crucial to examine the effectiveness of forecast models.Therefore, we evaluated the performance of four forecast models (UKMO, KMA, ECMWF, and GEFS) in predicting the extreme rainfall that resulted in the August 2022 flood in Pakistan.We used forecast products from TIGGE (Bougeault et al 2010), which have been developed as part of THORPEX.THORPEX is a World Weather Research Programme to accelerate the improvements in the accuracy of 1 day to 2-week high-impact weather forecasts (Shapiro and Thorpe 2004, Richardson et al 2005, Parsons et al 2017).TIGGE includes predictions of 13 NWP models, and forecasts from those are made available by ECMWF and CMA (Amini et al 2021).These multimodel ensemble prediction systems (EPS) make it easier to explore the uncertainties in NWP due to perturbations in the model's physics and parameterization methods (Keller et al 2011).Moreover, the availability of operational NWP data products offers new chances to advance the scientific understanding of predicting specific weather systems.We obtained forecast data from NWPs under TIGGE via the ECMWF archive (https://apps.ecmwf.int/datasets/data/tigge).We used four operational ensemble prediction systems: ECMWF, KMA, UKMO, and GEFS (table 1).The perturbed predictions in the forecast models are formed by altering the initial conditions in the control forecast using the data-assimilation process (Ye et al 2016).
GEFS forecast system has a spatial resolution of T1534 (∼12.5 km) implemented for a daily operational forecast that has been operational since 1 June 2018.GEFS forecast is based on the global atmospheric model GFS as a global spectral (semi-Lagrangian grid) model (GSM) version 14.0.2adopted from NCEP along with its 4D ensemble-variational (4D-Ens-Var) analysis system (Kleist and Ide 2012, 2015, Buehner et al 2013).The GEFS v14.0.2 provides daily 10 day forecasts for 21 ensemble members (1 control and 20 perturbed), initialized at 00:00 UTC.Thus, the prediction system is like the NCEP-GEFS (Zhou et al 2016(Zhou et al , 2017) ) system except for the resolution of perturbed members, which are run at the same resolution of T1534 as the control member (Mukhopadhyay et al 2021).
The ECMWF high-resolution forecast system comprises 50 members and is run twice daily on 91 vertical levels (extending up to 1 Pa) at a resolution of TC0639 (18 km) and has a lead time of 15 d.UKMO forecasts 18 ensemble members (1 control and 17 perturbed) at a 7.25 day lead time.KMA provides 10.5 d lead forecasts from 25 ensemble members.We analyzed the ensemble forecasts from all the models initialized at 00:00 UTC from 1 August 2022 to 31 August 2022.We regridded the forecasts from all the selected models to 0.1 • spatial resolution using bilinear interpolation to make it consistent with the observed gridded precipitation product (GPM).We choose a lead time of six days, the common lead time across all the models, excluding the forecast of the zeroth day.For example, suppose a model is initialized on August 1 (at 00:0 UTC) and has a 7 day lead.In that case, it includes a zeroth day forecast for the same day as the initialization date and forecasts six days ahead until 7 August.More details of ensemble prediction models are provided in table 1.
The Pakistan 2022 flood surpassed the previous floods in terms of spatial coverage, damage, loss of life, and displacement of communities.To gain further insights into its magnitude, we compared the frequency of days exceeding the extreme threshold for each year.We defined extreme events as days exceeding 10 mm of 2 day accumulated rainfall over Pakistan (Webster et al 2011).To determine how severe the flood was in 2022, we also looked at a 20 mm threshold over a specific flood-affected region of Pakistan.The selected threshold is considerably smaller than the maximum daily rainfall observations at individual stations because of the greater averaging area.
To demonstrate the spatial variability of rainfall forecasts from each model (ECMWF, KMA, UKMO, and GEFS), we used the ensemble mean of two-day accumulated rainfall from all the members of the individual forecast models.Different models offer various lead times and ensemble members.Our assessment is based on the two-day accumulated extreme rainfall during (17-18 August 2022) from each forecast model at 1 day, 3 day, and 5 day lead times.We use a categorical skill score to evaluate the models' predictability performance, i.e., hit rate (HR).The hit rate is calculated as the ratio of all hits (i.e., forecasts exceeding the climatology threshold plus one standard deviation) to the total of hits and misses (Swets 1986).The hit rate ranges from 0 to 1, with a higher value indicating the better performance of a model.The hit rate provides an overview of the models correctly capturing extreme rainfall across the study region.Instead of estimating the hit rate based on a single day, we evaluated the hit rate for 16 August-25 August (days with continuous high rainfall during August 2022) and finally took an average of all the values of hit rate to estimate the overall model's performance during that period.In order to assess the performance of the forecast models and compare them with actual observations, we computed the normalized root mean square error (NRMSE) and normalized mean absolute error (NMAE) for each model.We calculated both metrics at 1 day (1 d), 3 day (3 d), and 5 day (5 d) lead forecasts covering the period from 1 to 31 August 2022.Both metrics range from 0 to 1, where a value of 0 signifies a perfect prediction, and a value of 1 represents a prediction as bad as simply predicting the mean of the target variable at all times.
To evaluate whether a forecast model can provide helpful information for different rainfall pulses during August at different lead times, we analyzed the probability of each member predicting rainfall exceeding the threshold as in Webster et al (2011).The exceedance threshold is the observed rainfall climatology plus one standard deviation (SD) for all four selected models.For instance, if a model has 51 ensemble members and 28 out of the total members successfully capture the threshold (i.e.rainfall climatology plus one standard deviation), the probability of crossing the threshold will be 28 * 100/51 = 54.9% for that model.
We also compared the model's overall performance.To do so, we compared area averaged observed 2 day accumulated rainfall for the selected region against forecast models at different leads (1-6 d).We examined the deviation among all ensemble members in predicting two days of accumulated rainfall at different lead scales for each forecast model to understand the robustness of their predictions.We calculated the standard deviation using 2 day accumulated rainfall from 17 to 18 August from all forecast model members to examine uncertainty in each ensemble member with lead time and model.A smaller standard deviation (uncertainty) indicates higher confidence in the prediction.

Extreme rainfall and the August 2022 flood in Pakistan
The incessant heavy rainfall in August 2022 across the southern provinces of Pakistan (Balochistan and Sindh) caused disastrous floods and massive loss of lives and property (Otto et al 2022, PMD 2022b).The rainfall departure of the August 2022 event from its climatology in Pakistan's southern areas exceeded 500%, making it the wettest month since 1961 (PMD 2022a).We analyzed the climatology of the GPM rainfall dataset from 2003 to 2021 for August month (figure 1(a)).Climatologically, the mean rainfall rate in the flood-affected region was approximately 5 mm d −1 .However, in August 2022 (figure 1(b)), total rainfall exceeded 16 mm d −1 in southern Pakistan.The extreme rain that caused floods occurred during the 16-25 August, mainly centered in the southern provinces of Pakistan (figure 1(c)).The highest 2 day accumulated rainfall in the region occurred on 17-18 August 2022.Rainfall in the flood-affected region exceeded 80 mm (against the climatological mean of <10 mm) during 17-18 August 2022.Additionally, the second-highest 2 day accumulated rainfall occurred on 23-24 August 2022.Rainfall in the flood-affected region considerably exceeded the climatological mean for the entire month of August.
We estimated the frequency of extreme events in the flood-affected area (exceeding 10 mm and 20 mm two-day accumulated rainfall) from 2003 to 2022 to examine how anomalous the rain was in 2022 (figures 1(d) and (e)).2022 stands out with the highest extreme rainfall events for both (10 and 20 mm) thresholds.While the climatological two-day accumulated rainfall is less than 10 mm, on the 17 and 18 of August 2022, the single-day rainfall exceeded 40 mm, indicating the severity of the event (figure S1).

Was the 2022 extreme rainfall predictable?
Even though there have been several recent studies, it still needs to be determined if the extreme rainfall that caused floods in Pakistan in 2022 was predictable.The predictability of a rainfall event refers to the extent to which it can be forecasted or anticipated in advance.Moreover, predictability represents the measure of the likelihood or possibility of accurately predicting or anticipating the occurrence of that particular event.To answer this, we compared the two-day cumulative rainfall forecast at 1-5 d lead during the 17-18 August 2022 (which shows the highest accumulated 2 d rainfall in August) against the observed rainfall from GPM (figure 2).At a one-day lead, all the four forecast models demonstrated a similar spatial pattern in the coverage of the accumulated rainfall over a two-day period, which closely resembled the observed rainfall that occurred on 17-18 August 2022.As the lead time increases, there is a clear trend of decreasing forecast skill in terms of how closely the predicted spatial patterns resemble the observed pattern of extreme rainfall.The UKMO model showed a similar spatial pattern as the observed rainfall among the four models up to 5 day lead time.Similarly, the ECMWF model also captured the spatial extent of extreme rainfall.On the other hand, the GEFS and KMA models only captured the rainfall extent at a 1 day lead time, while underestimating the region experiencing extreme rainfall.Our findings are consistent with Saedi et al (2020), who demonstrated the accuracy of TIGGE models for rainfall prediction in Iran at a 24 hour lead time.Further, to quantify the models' forecast skill and for better readability and interpretation of the results, we estimated the hit rate for each model at 1 day, 3 day, and 5 day lead for each grid (figure 3(A)).At 1 day lead, all four models (ECMWF, KMA, UKMO, and GEFS) displayed satisfactory forecast skill (hit rate >0.5) for two-day accumulated rainfall on 17-18 August 2022 over Pakistan (figure 3(A)).At 1 day and 3 day lead, we notice that the hit rate is higher (greater than 0.6) for both the UKMO and ECMWF models, while it is slightly lower for the GEFS and KMA models.The UKMO and ECMWF provide extreme rainfall forecasts with higher hit rates (i.e.greater than 0.5) up to a 5 day lead.
We find that NRMSE (figure 3  model predictions and the actual observations.For all the forecast models, NRMSE and NMAE values are below 0.5, indicating generally satisfactory forecast skills.However, UKMO and ECMWF stand out with even lower values, indicating their predictions are more accurate compared to the other two models (GEFS and KMA).
Along with the spatial variability captured by the models, we evaluated the forecast skill for extreme rainfall at different lead times (figure 4).We calculated the probability (see methods for details) of two-day accumulated rainfall exceeding the threshold (climatological mean plus one standard deviation) for each model during 11-28 August 2022 (figure 4).All the model forecasts can predict the extreme rainfall exceedance threshold up to six days in advance with a probability of occurrence greater than 70% for the 17-18 August peak rainfall.We also observe that all the models exhibit good skill for the second extreme rainfall event (23-24 August 2022) at 1 and 2 d lead (figure 4).We further analyzed the change in probability by increasing the rainfall threshold to two and three standard deviations (figures S2 and S3).We find that forecast skill of the ensemble members was reduced in capturing the extreme rainfall for the increased thresholds.The 17-18 August 2022, extreme rainfall that caused the flood was predictable at the three standard deviations threshold from its climatological mean, as all the models exhibited a probability higher than 50% at all leads (1-6 d).However, the models predicted none of the remaining extreme rainfall events that occurred in August 2022 (figures S2 and S3).While we did not bias-correct rainfall forecast against observations, the models were able to provide an early warning of extreme rainfall that caused a massive Next, we compared the performance of forecast models with area-averaged (selected region in figure 1(a)) two-day accumulated rainfall with the observed (GPM) rainfall (figure 5).All the models underestimated the extreme rainfall even at a 1 day lead except UKMO, which overestimated extreme rainfall till the 3 day lead.Different forecast models involve different parameterization schemes, which can contribute to differences in precipitation forecasts (Amini et al 2021).GEFS underestimated the predicted rainfall, with moderate skill up to a 2 day lead.We also investigated the deviation among ensemble members of each forecast model in predicting two days of accumulated rainfall at various leads (figure 5).We observe that all the models exhibit less deviation among members at a shorter lead than a longer lead indicating that uncertainty increases with the lead time (Yang et al 2021, Xiang et al 2022).UKMO showed the highest uncertainty regarding standard deviation among all its ensemble members.Our results demonstrate that UKMO and ECMWF produce forecasts closer to the observations for longer lead times (up to 6 d), which are consistent to the study by Zarei et al (2022) who reported that ECMWF and UKMO outperformed the other forecast models in Iran.
We assessed the probabilistic skill of state-of-the-art global weather forecasting systems over the Pakistan region for the August 2022 flood.Climatologically, precipitation frequency was remarkably high in August 2022 compared to previous years.The 2 day accumulated rainfall on 17-18 August was anomalously high compared to the previous years.We examined the performance of each model using various metrics at different lead times.Our findings show that UKMO and ECMWF models demonstrate a strong performance, particularly up to five days in advance, with a hit rate greater than 0.5 and NRMSE and NMAE values less than or equal to 0.5.In contrast, GEFS and KMA provide moderate forecast skills for extreme rainfall.Sridevi et al (2022) reported that GEFS does not capture rainfall adequately for large rainfall events because of the spatial shift of the rainfall pattern, which can be improved by including a better analysis scheme and model physics.Due to unavailability of the hindcast from the models, we could not estimate additional skill scores, which can be used for the evaluation of the forecast skills of the models.In addition, ensemble members from UKMO and ECMWF models can be used to examine if the probabilistic ensemble forecast can be enhanced further.In addition, developing an ensemble multi-model flood forecast system could leverage the strengths of both models, improving overall forecast skill that can assist preparedness for potential floods (Krishnamurti et al 2000, Yun et al 2003).
Our results show the significance of employing ensemble prediction systems for flood forecasting in Pakistan, which is critical for early warning and preparedness.Several countries (The United States, Australia, and numerous European nations) benefit from ensemble forecasts in their operational flood forecasting systems (Emerton et al 2016).The effectiveness of ensemble forecasting was demonstrated during the Pakistan 2010 flood, where the GloFAS system, which provides ensemble hydrological forecasts, showed a 100% probability of exceeding the severe alert level, as reported by Alfieri et al (2013).Vegad and Mishra (2022) highlighted the advantage of using probabilistic forecasts over deterministic ones for flood prediction.They reported that probabilistic forecasting could provide more reliable and accurate information, essential for effective flood management.Thus, incorporating the ensemble forecasting technique into Pakistan's current operational flood forecasting, which already includes several other NWPs (Shreshtha et al 2019), can help improve the country's existing early warning system.
The flood early warning system faces a few challenges; one is the inadequate lead time of meteorological forecasts, making it difficult to provide timely (more than 2 d as mentioned in Fakhruddin et al (2015)) and accurate warnings (with hit rate >0.5) to people in flood-prone areas.However, ensemble hydrological forecasts are required to demarcate flood hazard zones for flood forecasting and management.Sometimes, good meteorological forecasts may only sometimes translate into reliable hydrological forecasts (Roulin andVennitsem 2015, Valdez et al 2022).Increasing ensemble members (Zsoter et al 2020) and lead time (Vegad and Mishra 2022) can help improve the flood forecasting system.In some cases, despite having adequate lead time, flood forecasts may only reach some individuals at risk due to ineffective early warning communication and dissemination strategies (Ramos et al 2010, Pagano et al 2014).Moreover, it is difficult to understand and communicate the probabilistic nature of forecasts to users and the general public (Mohr et al 2023).Therefore, for a flood warning to be effective, it must reach the right stakeholders at the right time and format.A flood warning must be tailored to the interests, needs, and values of the local communities to elicit a response.An effective flood early warning system could help reduce damage, economic inequality, and vulnerability among a more significant portion of the population.

Conclusions
Based on our findings, the following conclusions can be made: (1) The analysis of the flood event in Pakistan during August 2022 indicates that precipitation rates were exceptionally above average from a climatological perspective.Specifically, the rainfall in the flood-affected region exceeded 80 mm, which is significantly higher than the climatological mean (less than 20 mm), during the period of 17-18 August 2022.This emphasizes the exceptional nature of the precipitation during that time, contributing to the severity and impact of the flood event.
(2) Though the Pakistan 2022 flood was highly anomalous, it was predictable up to 6 d in advance with a probability greater than 60% using TIGGE NWP models.
(3) The forecasting models UKMO and ECMWF show promising results up to 5 d in advance, while the KMA and GEFS models tend to underestimate rainfall extent after a 1 day lead time.However, all models could capture extreme precipitation during 17-18 August, exceeding three standard deviations from the climatology at a 6 day lead time, demonstrating the reliability of the forecasting models in predicting extreme precipitation events.(4) Among all the models, ECMWF and UKMO exhibited the highest hit rate (>0.5) and the lowest NRMSE (<0.3) and NMAE (<0.25) values at all leads, indicating their strong predictive capabilities.(5) Developing a flood early warning system is challenging.However, a lack of understanding of the probabilistic nature of forecasts and a communication gap between stakeholders can also result in ineffective flood mitigation measures.
(B)) and NMAE (figure 3(C)) are consistent with the hit rate, demonstrating that ECMWF and UKMO models achieve lower NRMSE and NMAE scores at each lead time compared to GEFS and KMA.Lower NRMSE and NMAE values indicate a stronger agreement between the

Figure 3 .
Figure 3.Comparison of model performance using different metrics: (A) hit rate, (B) NRMSE, and (C) NMAE for predicting precipitation averaged over the study region.The predictions are provided by four models: (a) ECMWF, (b) GEFS, (c) KMA, and (d) UKMO at 1-day, 3-day, and 5-day lead times.The hit rate ranges from zero to one, with higher values indicating better model performance.NRMSE and NMAE also range from 0 to 1, where lower values indicate lower prediction errors compared to the observations, reflecting good model performance.

Figure 4 .
Figure 4. Forecast lead time diagram of the probability that members of the models (a) ECMWF, (b) KMA, (c) UKMO, and (d) GEFS forecast for the red region (figure 1(a)) exceeds the observed GPM August climatology (2003-2021) plus one standard deviation.The blue line represents the observed two-day accumulated GPM rainfall (mm d −1 ) averaged for the same region from 11 to 28 August 2022 (units on the right axis).The colorbar shows the probability of exceeding August climatology (2003-2021) plus one standard deviation from 0% to 100% at a different lead time (1-10 d) shown on the left axis.

Figure 5 .
Figure 5.Comparison of observed vs. forecast precipitation averaged over study region for four models (a) ECMWF, (b) KMA, (c) UKMO, and (d) GEFS for 1-6 d lead time.The blue bar represents the observed (GPM) two-day accumulated rainfall during 18 August 2022, averaged over the study region.The orange bar represents the ensemble mean of all the forecast members of selected models.The error bar represents the one standard deviation among all the ensemble members of models.

Table 1 .
List of the meteorological forecast centers used in the study.

. Data and methods 2.1. Datasets We
(Tan et al 2019)Level 3 Zipser 2015)ulti-satellite Retrievals for Global Precipitation Mission (GPM) 3IMERGHHL v06-Late Run (https://disc.gsfc.nasa.gov)commonlyknownas the multi-satellite precipitation estimate with climatological gauge calibration.The Integrated Multi-satellite Retrievals for GPM (IMERG) combines intercalibrated observations from satellites in the GPM constellation and has been available since June 2000 in three runs: early, late, and final(Tan et al 2019).Gridded precipitation is available at 0.1 • spatial resolution from 2003 to August 2022(Hou et al 2014, Liu andZipser 2015).The (Mukhopadhyay et al 2019)bines four observations from multiple passive microwave satellites in the GPM constellation using the IMERG algorithm.GPM accurately captures the spatial-temporal variability in precipitation in tropical regions and is widely used for the analysis of extreme precipitation (Murali Krishna et al 2017, Pradhan et al 2022) and has been compared with observed datasets over Pakistan and captures seasonality in precipitation fairly well(Arshad et al 2021).GPM rainfall was used as a reference to compare TIGGE(Deoras et al 2021)and GEFS precipitation forecast products(Mukhopadhyay et al 2019).