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  • View in gallery

    Distribution of precipitation in Pakistan during 1986–2011: (a) the seasonal rainfall cycle for 12 months (mm month−1) and (b) the averaged JA rainfall (mm) and (c) its standard deviation (mm).

  • View in gallery

    Composite patterns of the 500-hPa geopotential height anomalies (m) for (a) the wet years, (b) the dry years, and the 850-hPa circulation anomalies (m s−1) for (c) the wet years and (d) the dry years in Pakistan. Anomalies are relative to the mean climatology in JA during 1986–2011. The letter A indicates anticyclone circulation, and C indicates cyclone circulation.

  • View in gallery

    The spatial patterns and time coefficients of the three leading modes of the EOF analysis of the JA precipitation over Pakistan during the period 1986–2011: (a) EOF1 mode, (b) PC1, (c) EOF2 mode, (d) PC2, (e) EOF3 mode, and (f) PC3.

  • View in gallery

    TCCs between precipitation series over Pakistan and prewinter predictors: (a) U850, (b) U200, (c) V850, and (d) SLP. Each predictor is calculated as the averaged value of grid points from boxes.

  • View in gallery

    TCC between NCEP–NCAR reanalysis and CGCM outputs in JA for 1986–2011: (a) H500, (b) U850, (c) U200, (d) V850, (e) V200, (f) T850, and (g) SLP.

  • View in gallery

    TCC between precipitation series over Pakistan and CGCM predictors: (a) H500, (b) V850, (c) T850, and (d) SLP.

  • View in gallery

    The observed precipitation for Pakistan and forecast by cross validation for (a) NCEP-LR and NCEP-OSR and (b) CGCM-LR and CGCM-OSR. Here, OBS indicates precipitation observations, and CGCM represents raw CGCM output.

  • View in gallery

    The observed precipitation for Pakistan and real forecast tests for (a) NCEP-LR and NCEP-OSR and (b) CGCM-LR and CGCM-OSR. Here, OBS indicates precipitation observations.

  • View in gallery

    NS index and PC2 of the EOF analysis of the JA precipitation over Pakistan from 1986 to 2011.

  • View in gallery

    TCC between NS index and prewinter predictors: (a) U850, (b) U200, (c) V850, and (d) SLP. Each predictor is calculated as the averaged values of grid points from boxes.

  • View in gallery

    NS index and forecast by cross validation for NCEP-LR, NCEP-OSR, and CGCM. Here, OBS indicates an NS index observation and CGCM stands for raw CGCM output.

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A Comparison of Statistical Approaches for Seasonal Precipitation Prediction in Pakistan

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  • 1 National Climate Center, China Meteorological Administration, Beijing, China
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Abstract

The present study focuses on two statistical approaches for improving seasonal precipitation prediction skills for Pakistan. Precipitation over Pakistan is concentrated in July–August (JA), when droughts and floods occur recurrently and cause disasters. Empirical orthogonal function (EOF) analysis is used to assess spatial patterns of precipitation, and two precipitation patterns are identified: a consistent pattern and a north–south dipole pattern. Two statistical approaches, the statistical regression method using prewinter predictors and statistical downscaling, are employed to perform rainfall predictions for JA in Pakistan. Linear regression (LR) and optimal subset regression (OSR) are used for each approach, and the regression forecast methods are compared with the raw model outputs. Historical data for large-scale variables from the NCEP–NCAR reanalysis and version 1.0 of the coupled atmosphere–ocean general circulation model from the Beijing Climate Center (CGCM1.0/BCC) outputs in 1986–2011 are used as predictors for the statistical prewinter method and statistical downscaling, respectively. In the majority of the years, the statistical prewinter method and statistical downscaling are able to correct the erroneous signs of the raw dynamical model output for the consistent pattern. The statistical prewinter method is found to provide more skillful predictions than the statistical downscaling on the prediction of the dipolelike pattern. The best prediction skills for the consistent pattern and dipolelike pattern are provided by NCEP-OSR and NCEP-LR, which have significant correlations of 0.39 and 0.40, respectively. For all the forecast methods in this study, prewinter prediction and downscaled prediction show considerable improvements when compared with model output. These statistical methods provide valuable approaches for studying local climates.

Corresponding author address: Ting Ding, National Climate Center, China Meteorological Administration, No. 46, Zhongguancun South Street, Haidian District, Beijing 100081, China. E-mail: dingting@cma.gov.cn

Abstract

The present study focuses on two statistical approaches for improving seasonal precipitation prediction skills for Pakistan. Precipitation over Pakistan is concentrated in July–August (JA), when droughts and floods occur recurrently and cause disasters. Empirical orthogonal function (EOF) analysis is used to assess spatial patterns of precipitation, and two precipitation patterns are identified: a consistent pattern and a north–south dipole pattern. Two statistical approaches, the statistical regression method using prewinter predictors and statistical downscaling, are employed to perform rainfall predictions for JA in Pakistan. Linear regression (LR) and optimal subset regression (OSR) are used for each approach, and the regression forecast methods are compared with the raw model outputs. Historical data for large-scale variables from the NCEP–NCAR reanalysis and version 1.0 of the coupled atmosphere–ocean general circulation model from the Beijing Climate Center (CGCM1.0/BCC) outputs in 1986–2011 are used as predictors for the statistical prewinter method and statistical downscaling, respectively. In the majority of the years, the statistical prewinter method and statistical downscaling are able to correct the erroneous signs of the raw dynamical model output for the consistent pattern. The statistical prewinter method is found to provide more skillful predictions than the statistical downscaling on the prediction of the dipolelike pattern. The best prediction skills for the consistent pattern and dipolelike pattern are provided by NCEP-OSR and NCEP-LR, which have significant correlations of 0.39 and 0.40, respectively. For all the forecast methods in this study, prewinter prediction and downscaled prediction show considerable improvements when compared with model output. These statistical methods provide valuable approaches for studying local climates.

Corresponding author address: Ting Ding, National Climate Center, China Meteorological Administration, No. 46, Zhongguancun South Street, Haidian District, Beijing 100081, China. E-mail: dingting@cma.gov.cn

1. Introduction

Precipitation is one of the most important variables for many climate prediction services and applications. There are two main approaches available to make precipitation forecasts. The first approach is a statistical method that involves developing statistical relationships based on observed historical data. The obvious advantage of statistical methods is that they involve low computing costs (Zorita and von Storch 1999). Another approach commonly used involves numerical models. Various models that represent the physics and dynamics of the climate system are also important for making predictions on different time scales. These models are able to simulate the large-scale atmospheric variables in a generally realistic manner (von Storch et al. 1993).

Although general circulation models (GCMs) can reasonably represent the large-scale aspects of climate, generally, they do not provide enough prediction information for the local climate. Because of their coarse resolution of several hundreds of kilometers, they may have limited practicality for small-scale local areas (Juneng et al. 2010). In addition, in general, there is little confidence in GCMs for simulating regional-scale climate variability. Different approaches are used to overcome the inadequacies of GCMs in simulating local climate conditions, and they are mainly divided into two categories (Chu et al. 2008). One approach is dynamical downscaling, involving a nested regional climate model. The approach requires enough computer power to improve resolution and is costly (Easterling 1999), and a considerable amount of storage space is required for archiving model outputs (Chu et al. 2008). Another approach used to improve poor predictions of local climate is statistical downscaling. Statistical downscaling aims at specifying the local field (the predictand, e.g., precipitation) from a large-scale field (the predictor), which is accurately predicted by the dynamical model (Feddersen and Andersen 2005). In recent years, many statistical methods have been used in statistical downscaling predictions, such as multiple linear regression (MLR), optimal subset regression (OSR), partial least squares regression, singular value decomposition, canonical correlation analysis, classification and regression trees, and neural networks (von Storch et al. 1993; Zorita and von Storch 1999; Landman and Tennant 2000; Widmann et al. 2003; Kostopoulou et al. 2007; Ke et al. 2009; Wei and Huang 2010; Fan et al. 2012). Statistical downscaling usually focuses on the relationships between large- and small-scale variables according to empirically derived, statistical formulations. This approach can be performed more inexpensively and quickly on a personal computer rather than using dynamical downscaling, which requires a workstation or supercomputer. Compared with dynamic downscaling, statistical downscaling is easily adjusted to new areas (Wetterhall et al. 2005).

The monsoon rainfall anomaly exerts a significant impact on agriculture, human health, and society (Hussain et al. 2010; Webster et al. 2011). Located in South Asia along the Arabian Sea in the south, Pakistan is at the western edge of the South Asian monsoon system and is greatly influenced by monsoons during the summer. During July 2010, monsoonal deluges occurred over Pakistan, and the flooding is being described as the worst flash flood in the living memory of the entire region. The catastrophic flood resulted in close to 2000 deaths, exceeded $40 billion (U.S. dollars) in damage, and caused an agricultural crisis that may last for years (Webster et al. 2011). If precipitation forecasts in Pakistan had been available, the high risk of flood could have been foreseen, and the damage could have been reduced. On time scales of 1–2 weeks, Webster et al. (2011) has found that by using a multiyear analysis Pakistan rainfall is highly predictable out to 6–8 days, including rainfall in the summer of 2010. Next, a critical question to answer is whether rainfall in Pakistan is predictable on a seasonal time scale and how it should be predicted. Statistical downscaling by the coupled atmosphere–ocean general circulation model (CGCM) was applied for seasonal precipitation prediction over Islamabad, Pakistan, by Karori and Zhang (2008). They used 500-hPa geopotential height (H500), 850-hPa air temperature (T850), and the sea level pressure (SLP) as predictors for summer precipitation prediction using the Coupled Pattern Projection Model and multiple linear regression. The training period was 1983–2002, and the correlation coefficient between the predicted precipitation and the observation was calculated for 1983–2006. The 24 years (1983–2006) contain the relationship between the observation and the predicted precipitation in the training period from 1983 to 2002. The temporal correlation coefficient (TCC) developed by Karori and Zhang (2008) hardly represented the accuracy of real predictions because the period for the real forecast tests should be left out. The predictor selected over the South Pacific Ocean provided better prediction skills than CGCM outputs, but the predictor did not have anything to do with the precipitation, as the authors noted. Thus, the characteristics of the precipitation in Pakistan and the associated atmospheric circulation should be analyzed first, before downscaling. In the study by Karori and Zhang (2008), the prediction model was applied for one city (Islamabad, the capital city of Pakistan), but prediction of the consistent precipitation pattern and the varying precipitation pattern should be studied. Moreover, due to the inevitable errors of the CGCM, other prediction methods without the CGCM (e.g., pure statistical methods) should be investigated and compared with statistical downscaling for the local precipitation.

The experimental forecast in Pakistan is calculated in the same manner for each station in Pakistan as that in Islamabad by Karori and Zhang (2008), but that seasonal prediction is not in the form of digits. Experimental season forecasts by the Pakistan Meteorological Department (PMD) began in 2009, which is a short period of time for operational forecasting and statistical validation. The comparison between the operational forecasts and the observation is not quantitative. No specific technique to validate the seasonal forecast is applied in the operational forecast by PMD. As a regional climate center in Asia authorized by the World Meteorological Organization (WMO), the Beijing Climate Center (BCC) is devoted to delivering climate prediction products to other countries in Asia. A climate prediction platform is to be established so that it can help to provide operational predictions and validation to other Asian countries such as Pakistan. The prediction information provided by CGCM raw model outputs is very limited. Thus, the present work aims to develop seasonal precipitation prediction methods in Pakistan and to compare the predictive skills of statistical regression with prewinter predictors and statistical downscaling. The validation will also be provided to estimate how accurately the predictive approaches will perform in practice.

The paper is organized as follows. Section 2 describes the data and methods used, and section 3 discusses the climatology and rainfall variations over Pakistan. The results of precipitation prediction and validation for all of Pakistan as a whole and for a dipole pattern are illustrated in sections 4 and 5, respectively. Finally, a discussion and the conclusions are presented in section 6.

2. Data and method

In the present study, monthly outputs of version 1.0 of the BCC CGCM during July–August (JA) of 1986–2011 are provided for downscaling. The CGCM1.0 is used for operational climate prediction at the BCC with the hindcast period 1983–2002 (Li et al. 2005). The CGCM outputs can be obtained from the BCC each month. The model exhibits poor summer precipitation prediction in China, but relatively good prediction of large-scale variables (Ke et al. 2011). Statistical downscaling forecast models by CGCM1.0/BCC are constructed and perform relatively well over China and for different regions within the country (Ke et al. 2011; Gu et al. 2012). The operational forecast is generated by the CGCM1.0/BCC, which consists of T63L16 as the atmospheric general circulation model (AGCM) and L30T63 as the ocean general circulation model (OGCM) coupled with each other in a daily flux correction scheme. Forecasts are started from observed conditions on the last 8 days of the previous month and run forward over a range of 6 months. There are 48 members for the ensemble forecast with six oceanic initial conditions provided by the Global Ocean Data Assimilation System (GODAS) and eight atmospheric initial conditions from the assimilation of the National Meteorological Center of the China Meteorological Administration at 0000 UTC for the last 8 days of the previous month. The variables selected as potential predictor candidates include H500, the 850-hPa wind velocity fields (U850 and V850), the 200-hPa wind velocity fields (U200 and V200), T850, and SLP. These variables at such specific levels are commonly used for statistical downscaling (Kang et al. 2007, 2009; Zhu et al. 2008; Chu et al. 2008; Juneng et al. 2010). Additionally, height at the middle level (500 hPa), temperature at 850 hPa, and winds at the low level (850 or 700 hPa) and the upper level (200 hPa) are the primary variables used to investigate the circulation anomalies over southwest Asia, as used by Ullah and Gao (2012) and Hong et al. (2011). The bias correction of precipitation simulated by CGCM is completed before the precipitation outputs are used. The raw model output has been rescaled by the ratio of the standard deviation of the observed precipitation to that from simulations.

The observed monthly precipitation data used in this study are from the Global Precipitation Climatology Centre (GPCC) monthly precipitation (monitoring) product (Rudolf and Schneider 2005; Rudolf et al. 2010). Based on quality-controlled data from 7000 to 8000 stations, the GPCC monitoring precipitation product is calculated for the period from January 1986 to December 2011. The gridded data are near–real time, updated within 2 months after the observation month. The gridded monthly precipitation datasets are available in spatial resolutions of 1.0° latitude × 1.0° longitude for the global land surface. There are 84 grid points in Pakistan. The data cover a period beginning in 1986; however, precipitation datasets can be updated regularly in time and have a higher resolution than the 2.5° × 2.5° grid system. The spatial resolution of 2.5° × 2.5° is coarse for Pakistan precipitation prediction, especially for precipitation pattern prediction, because the 2.5° × 2.5° grid system has only 11 grid points located over Pakistan. The other observed atmospheric variables are constructed from National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) Reanalysis 2 (Kistler et al. 2001). These observations are used to evaluate the model prediction skills of circulation variables and develop the forecast method for precipitation prediction. The datasets use the 2.5° grid. The atmospheric fields for 0°–60°N and 0°–180°E from NCEP–NCAR Reanalysis 2 are analyzed. Considering the probable physical relation between the predictor and the predictand, the area of the predictors is chosen near the forecast field, not over the globe. Additionally, H500, U850, V850, U200, V200, T850, and SLP are taken as predictors to make predictions.

Two sets of variables are employed separately as predictors: NCEP–NCAR reanalysis data in prewinter as predictors in the early period and large-scale variables by CGCM outputs as predictors during the same period. For the former approach, prewinter large-scale variables that have a high correlation with rainfall over Pakistan are selected to develop the regression model. According to the latter method, the large-scale circulation simulated by a GCM is associated with the local variables observed simultaneously. Predictors in each set are calculated as the averaged large-scale variables on grids with significant correlation in boxes.

Empirical orthogonal function (EOF) analysis is a method of studying spatial patterns of variability and temporal variation (Preisendorfer 1988; Jackson 1991; von Storch and Navarra 1995). In section 3, EOF is performed to identify different precipitation patterns in Pakistan. Two statistical regression techniques are used for the application. The first approach used to develop the relationship between precipitation and predictors is linear regression (LR), including unary linear regression and multiple linear regression. Another regression method is the OSR method (Furnival 1971; Furnival and Wilson 1974). This technique extracts an optimal combination between predictors and precipitation. Hindcasting with the regression model occurs for 1986–2005, and the real forecast test is done for 2006–11. Additionally, the raw CGCM outputs of precipitation are compared with the regression methods mentioned above as the baseline.

The regression procedure is tested within a leave-one-out cross-validation framework (Michaelsen 1987). One year is removed as a forecast year, leaving the other years as the training period for developing the statistical relation. In this way, the downscaling forecast is performed in turn for all the years.

The TCC and the rate of the same sign of anomaly (RSSA) are used to justify the prediction accuracy in the study. RSSA is the rate of the number of years in which the predicted anomalies are the same in sign as the observation for the entire studied period (Lang 2011). A higher RSSA indicates higher prediction skill. The perfect forecasts will correctly predict the observation anomalies with the same sign for all years with an RSSA of 100%. Forecasts with little or no skill will yield an RSSA of approximately 50%. The TCC is a measure of the linear relationship between the prediction and the observation, while the RSSA provides a summary prediction performance on the anomaly. A t test is performed to test the significance of the TCC between two series (Huang 2004).

3. Precipitation in Pakistan and the associated atmospheric circulations

Pakistan is at the western edge of the pluvial region of the monsoon (Webster et al. 2011). This section documents the basic features of precipitation in Pakistan and atmospheric circulation characteristics in flood or drought years. Summer rainfall in Pakistan is monsoonal. The monsoon period in Pakistan is from June to September, and the other months are part of the dry season. More than 50% of the annual precipitation occurs in the monsoon period, especially in JA (Suleman et al. 1995). To identify the rainy season in Pakistan, the seasonal rainfall cycle for 12 months averaged over Pakistan during 1986–2011 is shown in Fig. 1a. The maximum rainfall occurs in July, with an average of 59.7 mm, whereas the second maximum rainfall is observed in August, with an average of 55.0 mm. The rainfall in other months is not more than 30 mm, which is half of the maximum rainfall in July. A small amount of rainfall occurs from October to January (less than 20 mm), and the minimum rainfall in November is 5.7 mm. Over Pakistan, precipitation is concentrated in the JA season, which accounts for approximately 40% of the annual total. The seasonal features motivate us to focus on precipitation for JA.

Fig. 1.
Fig. 1.

Distribution of precipitation in Pakistan during 1986–2011: (a) the seasonal rainfall cycle for 12 months (mm month−1) and (b) the averaged JA rainfall (mm) and (c) its standard deviation (mm).

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

The precipitation distribution in Pakistan is uneven. The distribution of the JA mean precipitation from 1986 to 2011 is shown in Fig. 1b. In JA, a large amount of precipitation is confined in the north and southeast parts of Pakistan and concentrated in northeast Pakistan, reaching up to 300 mm for 2 months. This is consistent with earlier findings that large rainfall events of approximately 6–8 mm day−1 occurred in northern Pakistan in May–August (Webster et al. 2011). Over the southern part of Pakistan, less than 100 mm of precipitation is recorded in JA, and less than 50 mm is recorded in the southwest part of the country. A large standard deviation of precipitation is also found in the north and southeast parts of Pakistan (Fig. 1c), and this reveals a larger interannual variation in the northern part of Pakistan than in the south.

Interannual variations of precipitation are closely related with atmospheric circulation anomalies. In Figs. 2a and 2b, the composite patterns of 500-hPa geopotential height anomalies for the wet years and the dry years are shown. The anomalies are calculated against the mean climatology for JA 1986–2011. The wet (dry) years are selected with precipitation larger (smaller) than the mean climatology for more than σ (standard deviation) over Pakistan during JA. The average rainfall is 114.8 mm, and σ is 46.2 mm. The wet years are 1988, 1992, 1994, 1995, 2003, 2006, and 2010, whereas the dry years are 1987, 1991, 1999, and 2002. Opposite distributions of the 500-hPa geopotential height anomalies are obvious between the two mean cases. In wet years, positive height anomalies are observed in Pakistan and Afghanistan, while negative height anomalies occur in the Arabian Sea and the middle latitudes north of 40°N. The precipitation tends to be below normal when negative height anomalies are found in the north of Pakistan and when positive height anomalies are found from north of Africa to the Indian Ocean and in Mongolia. This distribution suggests that negative anomalies over the Arabian Sea, which may be as a result of the enhancement of the trough in lower latitudes, are favorable for above-normal precipitation over Pakistan. The correlation patterns between precipitation in Pakistan and the 500-hPa height anomalies also show similar results.

Fig. 2.
Fig. 2.

Composite patterns of the 500-hPa geopotential height anomalies (m) for (a) the wet years, (b) the dry years, and the 850-hPa circulation anomalies (m s−1) for (c) the wet years and (d) the dry years in Pakistan. Anomalies are relative to the mean climatology in JA during 1986–2011. The letter A indicates anticyclone circulation, and C indicates cyclone circulation.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

Correspondingly, the anomalous circulation patterns in the lower troposphere are different in wet and dry years. The critical roles of moisture transport affecting monsoon activity in two contrasting summers during a relatively wet year (1994) and a relatively dry year (2002) were compared by Ullah and Gao (2012). They determined that the moisture transport over the Arabian Sea was the major source of rainfall in Pakistan and neighboring regions during summer. As Figs. 2c and 2d show, there are anticyclone circulation anomalies over Afghanistan and cyclone circulation anomalies over the Arabian Sea at 850 hPa in wet years, while anticyclone circulation anomalies occur over the Arabian Sea in dry years. The monsoon plays a key role in the rainy season for Pakistan. In Fig. 2c, there are two streams of anomalous water vapor transportation in wet years. The anomalous southeasterlies from the Bay of Bengal and anomalous southwesterlies from west of the Arabian Sea merge in the north of India and become anomalous easterlies over Pakistan. The anomalous easterly winds are indicative of the strengthening of the South Asian monsoon. More water vapor is brought to the north of India and Pakistan, resulting in above-normal precipitation in this region. In July 2010, the anomaly precipitation over Pakistan was enormous by virtue of the westward flow of Bay of Bengal air into the region (Houze et al. 2011). In dry years, anomalous westerly winds from the Bay of Bengal with less water vapor are observed over Pakistan, causing below-normal precipitation in the region. The anomalous winds from the Bay of Bengal change directions in wet and dry years.

Before analyzing the precipitation prediction over Pakistan, the spatial organization of the precipitation field is discussed. Figure 3 shows spatial patterns and time coefficients of the three leading modes of the EOF analysis of the JA precipitation over Pakistan for a period of 26 yr from 1986 to 2011. It is found that the first leading mode, which has the same sign over Pakistan, accounts for 49.2% of the total variance. This implies that nearly half of the total climate variability depends significantly on the regional-scale signals contained in the leading mode. The variation for the principal component (PC) of the first leading mode is large before 1995 and relatively small after 1996. However, in 2010, the time coefficient of the first leading mode is the largest in 26 yr, indicating a flood summer in this year. The second mode can explain 15.5% of the total variance and shows a north–south dipole structure. The time coefficient of the second leading mode is large in 1994 and 2003, in which above-normal precipitation was found in the south and below-normal precipitation was found in the north. The third pattern accounts for 11.3% of the total variance and shows a tripole pattern. If one year (e.g., 2011) is left out in the EOF calculation, the three leading modes and variances do not change much.

Fig. 3.
Fig. 3.

The spatial patterns and time coefficients of the three leading modes of the EOF analysis of the JA precipitation over Pakistan during the period 1986–2011: (a) EOF1 mode, (b) PC1, (c) EOF2 mode, (d) PC2, (e) EOF3 mode, and (f) PC3.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

From the EOF analysis, it can be found that the precipitation in different parts of Pakistan shows quite different interannual variations with each other. Consequently, precipitation prediction for the consistent pattern over Pakistan is not enough. The prediction of other precipitation patterns is also required, such as opposite signs in the north and south. Moreover, one needs to search for different predictors for different rainfall patterns. In this study, the consistent pattern and the north–south dipolelike pattern of precipitation are predicted separately, and different predictors are used for those two patterns to make sure the predictors are the ones with the best prediction skill for a given pattern.

4. Prediction skills for the consistent pattern

The predictand of the consistent pattern is calculated as the average rainfall of 84 grid points over Pakistan. Predictors and their corresponding domains can be selected based on a correlation analysis (Chen et al. 2012). Correlations between precipitation series over Pakistan and prewinter predictors are shown in Fig. 4. The prewinter predictors are averaged over December–February. For a sample size of 20 yr (1986–2005), a correlation coefficient between 0.44 and 0.56 has a significance level between 0.05 and 0.01 as determined by the t test. Seven predictors are selected from U850, U200, V850, and SLP, as the numbers show in Fig. 4, whereas no significant correlation relationship is found between the precipitation series and other variables. Each predictor is calculated as the averaged values of grid points that have a significant correlation (at the 0.05 level) with the precipitation series in each box and is defined as
e1
where is the predictor at time , is the number of grid points that are significantly correlated with the predictand in a box, and is the large-scale variable at time in the ith grid point significantly correlated with the predictand. Not all the grid points in each box are averaged as predictors. The predictors are normalized to eliminate the effect of the different sizes of black boxes.
Fig. 4.
Fig. 4.

TCCs between precipitation series over Pakistan and prewinter predictors: (a) U850, (b) U200, (c) V850, and (d) SLP. Each predictor is calculated as the averaged value of grid points from boxes.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

There are a number of options for predictors. Different variables and regions are tested to produce robust results as predictors. The TCC between the observed precipitation and each prewinter predictor for 1986–2011 is shown on the second line in Table 1. There are three selection steps needed to establish a forecast regression model. 1) To have more predictors, a TCC up to 0.38 (significant at the 0.1 level for 1986–2005) is set as the criteria of selection. Predictors 1, 2, 5, 6, and 7 have a significant correlation with the precipitation series, while predictors 3 and 4 are removed. 2) To avoid accidental correlation, the correlation relationship should be stable within a certain range, not only in a few grid points. The predictor calculated by less than four grid points in a box is removed (e.g., predictor 6). 3) In the LR method, the independence of predictors should be checked to avoid similar or overlapping predictors. Table 2 shows the TCC between each pair of prewinter predictors for 1986–2011. To determine the independent predictors, t tests are performed. The TCC between each pair of predictors is significant at the 0.05 level as determined by the t test, which indicates that each pair of predictors is dependent. Thus, each predictor is used to build a regression model separately in the LR method. However, in the OSR method, four predictors (1, 2, 5, and 7) are put into the model, and the most suitable variables are used for describing the large-scale conditions.

Table 1.

The TCC between the observed precipitation and each prewinter predictor and between the observed precipitation and the downscaling methods for 1986–2011.

Table 1.

Table 2.

The TCC between each pair of prewinter predictors for the observed precipitation for 1986–2011.

Table 2.

Statistical downscaling is based on the premise that large-scale atmospheric circulation patterns can be well simulated by dynamical models. The CGCM1.0/BCC simulated fields are validated before they are analyzed to establish a forecasting relationship. In general, the prediction of circulation fields shows a higher level of skill than precipitation. It is widely accepted that GCMs are able to reasonably simulate the large-scale atmospheric variables, such as H500 and SLP (von Storch et al. 1993; Kang et al. 2007). For most climate model systems that participate in the Climate Prediction and its Application to Society (CliPAS) project, the 200-hPa streamfunction shows very good correlation skills almost everywhere between 40°S and 60°N, except in the equatorial region, and H500 shows high prediction skills confined to the global tropics with a north–south seasonal migration (Wang et al. 2009). Figure 5 shows the spatial patterns of TCC between NCEP–NCAR reanalysis and CGCM outputs in JA for 1986–2011 in the region 0°–60°N, 0°–180°E. Consistent with many other GCM models, the TCC score of H500 by CGCM1.0/BCC over most regions at low latitudes is significant at the 0.1 level (above 0.38). The prediction skills for other variables by CGCM1.0/BCC are not as good as H500 in the tropics. However, these variables are capable of simulating large-scale circulation in some areas. In the region of the Arabian Sea, U200, V850, and T850 show good prediction skills. Over East Africa, U850 and T850 have high prediction skills, with the TCC above 0.38. In the northwest Pacific and Southeast Asia V200, T850, and SLP are the variables with high prediction skills. Over Pakistan and surrounding areas, the TCCs of H500 and V850 in the south of Pakistan are significant at the 0.1 level, whereas those of U200 and V850 are significant in the north of Pakistan.

Fig. 5.
Fig. 5.

TCC between NCEP–NCAR reanalysis and CGCM outputs in JA for 1986–2011: (a) H500, (b) U850, (c) U200, (d) V850, (e) V200, (f) T850, and (g) SLP.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

CGCM output downscaling approaches with a pure statistical model are compared with prewinter predictors. There are different choices for predictors in the CGCMs. The selection of appropriate predictors, or characteristics from the large-scale atmospheric circulation, is one of the most important steps in a downscaling process. Two main conditions should be satisfied first; that is, the data should be 1) reliably simulated by CGCMs and 2) strongly correlated with the observed precipitation. For the first step, the grids of large-scale CGCM outputs significantly correlated with reanalysis data on corresponding grid points (at the 0.1 level) are marked as the well-simulated grids. To obtain more grids, 0.1 is set as the significance level for the first step. Then, the well-simulated grids that are significantly related with the precipitation series are selected as grids satisfying the two conditions. A stricter significance level of 0.05 is set as the criteria for selecting grid points in the second step to obtain a more robust regression model than that used in the first step. The TCCs between the precipitation and variables on the grids satisfying the two conditions are given in Fig. 6. Similar to the prewinter predictors from the NCEP–NCAR reanalysis, seven variables from CGCM outputs from H500, V850, T850, and SLP are selected as potential predictors, whereas no grids from U850, U200, and V200 satisfy the two conditions. At the southwest of the Bay of Bengal along the equator V850 changes directions in wet years and dry years, as shown in Figs. 2c and 2d. Although the TCC of 0.3 in this region does not reach the 0.05 significance level in Fig. 6b, V850 in box 4 is selected as a potential CGCM predictor due to its clear physical mechanism and importance to Pakistan's precipitation cycle. Table 1 gives the TCC between the observed precipitation and each CGCM predictor for 1986–2011. Predictors 1, 3, and 5 are highly related with the precipitation series and are significant at the 0.05 level. The predictors are calculated as the average values of more than four grid points. The TCCs between each two predictors are calculated in Table 3, and dependency is found between each pair of CGCM predictors. Thus, different predictors are used to build an LR model separately, in a similar manner to that used for the prewinter predictors.

Fig. 6.
Fig. 6.

TCC between precipitation series over Pakistan and CGCM predictors: (a) H500, (b) V850, (c) T850, and (d) SLP.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

Table 3.

The TCC between each pair of predictors determined by downscaling methods for the observed precipitation for 1986–2011. All TCCs are significant at the 0.01 level by the t test.

Table 3.

To produce robust results, a period of model hindcasts and corresponding observations is required. With the limitation of observed high-resolution data, the 26-yr period of 1986–2011 is chosen. Anomalies are departures from the mean climatology during JA 1986–2011. Hindcasts from statistical methods by NCEP prewinter variables and downscaling by CGCM outputs are available for 1986–2011 for the LR and OSR methods, respectively. The downscaling is carried out by leave-one-out cross-validation. Tables 4 and 5 give the TCC and RSSA between the observed precipitation and hindcasts determined by prewinter predictors, downscaling methods, and CGCM outputs for 1986–2011. For the 26 yr, NCEP-LR methods using predictors 2 and 7 and NCEP-OSR can yield reliable results, with a TCC above 0.33. NCEP-OSR has the best prediction skill. CGCM-LR methods using predictors 3 and 5 can also predict the precipitation series with a TCC above 0.33. For most years, CGCM downscaling predictors and most NCEP prewinter predictors can estimate the sign of precipitation correctly, with an RSSA above 60%. These methods perform much better than raw CGCM output, which only has an RSSA of 54% and a TCC of 0.03 with little prediction skill. The RSSA of all the CGCM predictors is 69%, higher than that of prewinter statistical methods. It can be seen that prediction skills are improved considerably through prewinter statistical methods and downscaling methods. Among the methods using different predictors, the TCCs between the observation and NCEP-LR and NCER-OSR are close to those between the observation and CGCM-LR. From Tables 4 and 5, it is found that the most accurate prediction method for the Pakistan precipitation series is NCEP-OSR, with the correlation between the observation and the forecast equal to 0.39. This suggests that large-scale variables in prewinter are useful in predicting local rainfall by means of the statistical strategy, and CGCM downscaling is found to provide more accurate predictions than the raw dynamical model output.

Table 4.

The TCC and RSSA between the observed precipitation and hindcasts for prewinter predictors for 1986–2011.

Table 4.
Table 5.

TCC and RSSA between the observed precipitation and hindcasts of predictors by downscaling methods and CGCM outputs for 1986–2011.

Table 5.

The optimum results by Karori and Zhang (2008) were that the TCC for 1983–2006 between the observed precipitation and the predicted precipitation over Islamabad by SLP, H500, and T850 were 0.41, 0.53, and 0.38, respectively. The TCC for 1983–2006 between the observed precipitation and the predicted precipitation from MLR with three predictors (SLP, H500, and T850) was 0.65. However, the training period was 1983–2002, and the forecast verification period was 2003–06. The TCC by Karori and Zhang (2008) was calculated for 1983–2006, and the 24 yr (1983–2006) contains the relationship between the observation and the predicted precipitation in the training period from 1983 to 2002. Moreover, no significant test was applied to check the independence between the three predictors for MLR. Thus, the TCC by Karori and Zhang (2008) hardly represents the accuracy of the real prediction. In the present work, the TCC is calculated within a leave-one-out cross-validation framework, and dependent predictors in the regression model are removed. This procedure estimates how accurately a predictive model will perform in practice. Although the TCC by Karori and Zhang (2008) is higher than the results in the present work, the former is less reliable in practice.

The observed precipitation and hindcasts by different predictors are shown in Fig. 7. For NCEP-LR, predictor 7 has the best prediction by TCC, while CGCM predictor 3 has the highest TCC for CGCM-LR. In Figs. 7a and 7b, respectively, prewinter predictor 7 and CGCM predictor 3 are selected to build LR models. The regression equation for prewinter predictor 7 is
e2
and for CGCM predictor 3 it is
e3
where Y(t) is the predictand and X(t) is the predictor. Predictors 1, 2, 5, and 7 by NCEP and predictors 1, 3, and 5 by CGCM downscaling are used in OSR to build a most suitable regression model. Compared with the observation, NCEP-LR, NCEP-OSR, CGCM-LR, and CGCM-OSR predict the same sign of anomalies in 18, 17, 19, and 19 yr, respectively. As shown in Fig. 7, forecasts by prewinter predictors and CGCM predictors perform better than the model outputs over most years. In the heavy rainfall year of 2010, CGCM-LR, CGCM-OSR, and raw CGCM output forecasts have an opposite sign with the observed above-normal precipitation in 2010. In addition, the operational forecast cannot predict the above-normal precipitation in JA in 2010 as well (Pakistan Meteorological Department 2012). NCEP-LR and NCEP-OSR forecasts can predict the same sign with the observed predictand successfully in this year, in spite of the underestimation of the extreme precipitation anomaly. In the prewinter of 2010 (from December 2009 to February 2010), the abnormal H500 in box 7 of Fig. 6d is below −2 gpm, which indicates above-normal precipitation in the incoming JA. However, the degree of the abnormality is difficult to predict for 2010. The usual circulation patterns responsible for the floods were of a type that does not normally occur in this region, and the rainstorms exhibited a great departure from their usual behavior during the South Asian monsoon season (Houze et al. 2011). The active period of monsoon embedded in the La Niña phase resulted in the deluges (Webster et al. 2011), and this is not easy to capture with prewinter predictors or the CGCM outputs.
Fig. 7.
Fig. 7.

The observed precipitation for Pakistan and forecast by cross validation for (a) NCEP-LR and NCEP-OSR and (b) CGCM-LR and CGCM-OSR. Here, OBS indicates precipitation observations, and CGCM represents raw CGCM output.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

Figures 8a and 8b show the observed precipitation for Pakistan and the real forecast tests by NCEP prewinter predictors and CGCM downscaling methods. The models are trained during the first 20 yr (1986–2005), and forecasts are subsequently made for the next 6 yr. The anomalies are calculated against the mean climatology for 1986–2005. NCEP-LR, NCEP-OSR, CGCM-LR, and CGCM-OSR predict the same sign of rainfall anomalies as the observations in 4, 3, 4, and 4 yr, respectively. The forecasts predict the above-normal precipitation in 2010, and the NCEP prewinter predictors predict a closer anomaly than the CGCM predictors; however, none of these methods can predict the extreme anomaly this year.

Fig. 8.
Fig. 8.

The observed precipitation for Pakistan and real forecast tests for (a) NCEP-LR and NCEP-OSR and (b) CGCM-LR and CGCM-OSR. Here, OBS indicates precipitation observations.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

5. Prediction skills for the dipole pattern

In this section, the north–south (NS) index is first defined to present the rainfall distribution pattern, and then prediction validation of the NS index will be given. As Fig. 3c shows, the second-leading mode has a dipole structure. Figure 9 shows the NS index and time coefficients of the second mode of the EOF analysis for JA precipitation over Pakistan from 1986 to 2011. The NS index is defined by the normalized precipitation difference between north and south (north − south):
e4
where is the normalized series for the average precipitation over north Pakistan and is the normalized series for the average precipitation over south Pakistan. The north and south are divided by the zero line in Fig. 3c. The normalized series is calculated for each dataset as the actual value minus the mean of the series divided by the standard deviation of the series. A positive NS index denotes more rainfall anomalies in the north than in the south, while a negative NS index indicates less rainfall anomalies in the north than in the south. For comparison, the sign of the NS index and PC2 are reversed for most years. The correlation coefficient between the NS index and PC2 is −0.88, and it is significant at the 0.001 level. This indicates that the NS index can rationally describe the dipole pattern of rainfall over Pakistan. PC2 is the time coefficient of the second mode of the EOF analysis, which is a mathematical decomposition of a dataset in terms of orthogonal basis functions. PC2 may not represent the actual precipitation pattern in some years. In JA 1992, PC2 is −3.0. However, the NS index in that year is approximately zero, which means a consistent precipitation pattern. Thus, the NS index is used as the predictand.
Fig. 9.
Fig. 9.

NS index and PC2 of the EOF analysis of the JA precipitation over Pakistan from 1986 to 2011.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

Similarly to Fig. 4, correlations between the NS index series over Pakistan and prewinter predictors are shown in Fig. 10. Eight potential predictors are selected from U850, U200, V850, and SLP. The TCC between the NS index and eight potential predictors is given in Table 6. Predictors 2, 4, 6, and 8 are found to have significant correlation with the NS index. However, two pairs of predictors—2 and 6, and 2 and 8—are significantly correlated at the 0.01 level, whereas predictors 6 and 8 are independent, with a TCC of 0.02 (Table 7). Predictors 6 and 8 in Fig. 10 are chosen as NCEP multiple LR predictors. The TCCs between the observed NS index and the CGCM large-scale outputs are also calculated. However, no potential predictor by CGCM outputs is found because the number of grid points with significant TCCs in one box is smaller than four.

Fig. 10.
Fig. 10.

TCC between NS index and prewinter predictors: (a) U850, (b) U200, (c) V850, and (d) SLP. Each predictor is calculated as the averaged values of grid points from boxes.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

Table 6.

TCC between the NS index and each prewinter predictor for 1986–2011.

Table 6.
Table 7.

TCC between each pair of prewinter predictors for the NS index for 1986–2011.

Table 7.

Table 8 gives the TCC and RSSA between the NS index and hindcasts determined by different prewinter predictors and CGCM outputs for 1986–2011. The best prediction skill among these predictors with the highest significant TCC of 0.40 (at the 0.05 level) and the highest RSSA of 69% are found for predictor 6. NCEP multiple LR by predictors 6 and 8 and NCEP-OSR also have prediction skill with a TCC significant at the 0.1 level. For prewinter predictors of the NS index, the TCC is 0.4 for predictor 6, 0.21 for predictor 8, and 0.36 for predictors 6 and 8. The prediction accuracy does change with predictors added, but the results of the two predictors 6 and 8 do not show improvement over one predictor (6). No significant correlation exists between the observed NS index and the NS index forecast by CGCM raw outputs, and TCC is approximately zero, which indicates poor prediction skill for CGCM outputs. CGCM downscaling is not considered due to the poor correlation between the NS index and the CGCM large-scale outputs.

Table 8.

TCC and RSSA between the NS index and hindcasts for prewinter predictors for 1986–2011.

Table 8.

Figure 11 shows the NS index and forecast determined by cross validation for NCEP-LR and NCEP-OSR. Predictor 6 gives the best prediction skill for the NS index, as Table 8 shows. NCEP-LR is calculated by predictor 6, and the regression equation is
e5
where is the predictand and is the predictor. The hindcast results of Fig. 11 are computed relative to 1986–2011 climatology. Prewinter predictors by NCEP-LR and NCEP-OSR successfully predict the sign of the NS index in 19 and 17 yr, respectively, but none of these methods can predict the 2010 pattern well.
Fig. 11.
Fig. 11.

NS index and forecast by cross validation for NCEP-LR, NCEP-OSR, and CGCM. Here, OBS indicates an NS index observation and CGCM stands for raw CGCM output.

Citation: Weather and Forecasting 28, 5; 10.1175/WAF-D-12-00112.1

6. Discussion and conclusions

Based on monthly gridded precipitation data, CGCM outputs, and NCEP–NCAR reanalysis data for the period 1986–2011, relatively simple statistical methods are applied for the purposes of precipitation prediction in Pakistan. First, the geographical patterns, temporal variation of precipitation in Pakistan, and the associated atmospheric circulations have been investigated. Precipitation in Pakistan is greatly influenced by the South Asian monsoon during the summer. In wet years, positive height anomalies occur at 500 hPa in South Asia (including Pakistan and Afghanistan), and anticyclone circulation anomalies over Afghanistan and cyclone circulation anomalies in the Arabian Sea at 850 hPa are observed. Above-normal precipitation over Pakistan is closely related with two streams of anomalous water vapor transportation from the Bay of Bengal and west of the Arabian Sea. Based on an EOF analysis, the first leading mode shows a consistent pattern, while the second mode exhibits a north–south dipole distribution.

NCEP–NCAR reanalysis data in prewinter significantly correlated with precipitation series are employed as predictors in the early period. In addition, statistical downscaling is developed to derive information on local or regional scales from the global-scale outputs generated by CGCM1.0/BCC. The predictions from the raw CGCM outputs are also carried out for comparison. It is found that both statistical methods by prewinter predictors and statistical downscaling techniques by CGCM outputs significantly improve the prediction accuracy for the precipitation anomalies. For the consistent precipitation pattern over Pakistan, NCEP prewinter predictors and CGCM downscaling predictors can forecast the sign of precipitation correctly in most years, and the correlations between observation and hindcasts by NCEP prewinter predictors and CGCM downscaling predictors are up to 0.39 and 0.36, which are significant improvements compared with the 0.03 determined by raw CGCM outputs for 1986–2011. For the NS index, good prediction skill for NCEP prewinter predictors is found with the highest TCC of 0.40, while raw model outputs perform poorly with correlation coefficients of approximately zero. The raw CGCM exhibits poor accuracy in simulating the precipitation series and NS index, while NCEP prewinter predictors demonstrate good prediction skill for both of them. Neither CGCM nor statistical downscaling yielded a good degree of performance for the NS index over Pakistan. The inconsistent precipitation is more difficult to predict than the consistent pattern for CGCM outputs.

Generally, the best prediction skills for NCEP prewinter predictors are close to those made by CGCM downscaling predictors in precipitation prediction over Pakistan. However, the NCEP prewinter predictors provide skillful prediction for the inconsistent pattern, while CGCM downscaling has little prediction accuracy for the inconsistent pattern. The NS index (inconsistent pattern) is the difference between the north and the south and is defined using a smaller scale than the precipitation series (consistent pattern) averaged over all of Pakistan. Perhaps it is difficult for statistical downscaling by CGCM outputs to be applied for small scales (e.g., NS index). Alternatively, this may have arisen because of a misrepresentation of the CGCM outputs by the statistical model. LR and OSR are used to develop the forecast model. The TCC of the NCEP-OSR of the consistent pattern is higher than other LRs for predictors, but for the NS index, LR by one best predictor is better than OSR. Although LR is a relatively simple method in general, it performs better than OSR for prewinter statistical methods and statistical downscaling. OSR does not always provide the best prediction skill. For some predictands, OSR does not show much improvement in prediction skills over LR, and this may be due to the small number of predictors for OSR.

The performances of the seasonal precipitation prediction approaches in Pakistan are compared in this paper. Each approach belongs to one of the broad families of existing techniques: a method based on prewinter large-scale variables, as representative of pure statistical methods, and a method based on CGCM outputs, as representative of statistical downscaling methods. For the former approach, the links between prewinter local large-scale circulation and precipitation anomalies in July–August have not been investigated thoroughly. Further studies of the mechanism are needed to explain the relationships between the prewinter local large-scale circulation and precipitation through local circulation in summer. The latter approach improves prediction accuracy by correcting the erroneous signs of the precipitation anomalies in coarse-resolution predictions of the CGCM to a certain extent. On the one hand, the success of downscaling forecasting is based on the quality of the predictions of the large-scale atmospheric variables provided by CGCMs. Predictions based on downscaling are sensitive to model errors in the predictor field. The large-scale variables from other CGCM outputs will be taken as the potential predictors and compared with the present results, and other better model outputs are expected to achieve better prediction skill. On the other hand, some complex and nonlinear downscaling methods will be applied for further improvements in precipitation prediction in our future work.

Acknowledgments

This research was supported by the National Basic Research Program of China (973 Program; Grant 2012CB955902), the Young Scientists Fund of the National Natural Science Foundation of China (Grants 41005051, 41205039, and 41105070), the China Meteorological Administration Research and Development Special Fund for Public Welfare (Meteorology; Grant GYHY201306024), and the National Key Technologies Research and Development Program of China (Grant 2009BAC51B05). The authors acknowledge the support of the Innovation Team of Climate Prediction of the CMA National Climate Center. The authors thank the three anonymous reviewers and the editor for their helpful comments and suggestions.

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